Finite Group Databasebeta

← #28292319

Subgroups — #28292319

Order 13568.

7094 conjugacy classes of subgroups.

The subgroup lattice has 2028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288807C213yesmaximal, complemented
2#20288805C211yesmaximal, characteristic, complemented
3#20288796C213yesmaximal, complemented
4#20288794C211yesmaximal, characteristic, complemented
5#20288708C211yesmaximal, characteristic, complemented
6#20288704C213yesmaximal, complemented
7#20288698C213yesmaximal, complemented
8#20288576C213yesmaximal, complemented
9#20288574C213yesmaximal, complemented
10#20288522C211yesmaximal, characteristic, complemented
11#20288483C211yesmaximal, characteristic, complemented
12#20288423C213yesmaximal, complemented
13#20288419C213yesmaximal, complemented
14#20288365C211yesmaximal, characteristic, complemented
15#20288361C211yesmaximal, characteristic, complemented
16#20288335C211yesmaximal, characteristic, complemented
17#20288334C213yesmaximal, complemented
18#20288331C211yesmaximal, characteristic, complemented
19#20288329C213yesmaximal, complemented
20#20288309C213yesmaximal, complemented
21#20288305C211yesmaximal, characteristic, complemented
22#20288294C213yesmaximal, complemented
23Q8×#11719947C211yesmaximal, characteristic, complemented
24#20288147C213yesmaximal, complemented
25#20288141C213yesmaximal, complemented
26#20288009C213yesmaximal, complemented
27#20288009C213yesmaximal, complemented
28#20287926C211yesmaximal, characteristic, complemented
29#20287924C211yesmaximal, characteristic, complemented
30C2×C4×Q8×D53C211yesmaximal, characteristic, complemented
31C53×#3516C211yesmaximal, characteristic, complemented
32C2×#13133265C2211yescharacteristic
33C2×#13133264C2211yescharacteristic
34C22×Q8×D53C2211yescharacteristic
35#16811357C2216yescomplemented
36#16811356C2213yescomplemented
37#16811355C2213yescomplemented
38Q8×Dic106C2211yescharacteristic, complemented
39#16811353C2213yescomplemented
40#16811351C2213yescomplemented
41#16811351C2213yescomplemented
42#16811350C2213yescomplemented
43#16811350C2213yescomplemented
44#16811350C2216yescomplemented
45#16811349C2211yescharacteristic, complemented
46#16811349C2211yescharacteristic, complemented
47#16811348C2213yescomplemented
48#16811346C2213yescomplemented
49#16811345C2213yescomplemented
50#16811344C2213yescomplemented
51#16811342C2213yescomplemented
52#16811341C2213yescomplemented
53#16811341C2216yescomplemented
54#16811340C2216yescomplemented
55#16811340C2216yescomplemented
56#16811332C2216yes—
57#16811331C2213yes—
58#16811331C2213yescomplemented
59#16811330C2213yes—
60#16811328C2213yes—
61#16811328C2213yescomplemented
62#16811327C2216yes—
63#16811327C2216yescomplemented
64#16811325C2213yes—
65#16811322C2216yes—
66#16811321C2213yes—
67#16811319C2213yes—
68#16811316C2216yes—
69#16811314C2213yes—
70#16811314C2213yescomplemented
71#16811313C2213yescomplemented
72#16811312C2213yes—
73#16811311C2213yes—
74#16811311C2213yescomplemented
75#16811309C2216yes—
76#16811309C2216yescomplemented
77#16811307C2213yes—
78#16811306C2216yescomplemented
79#16811305C2216yes—
80#16811292C2211yescharacteristic, complemented
81#16811291C2213yescomplemented
82Q8×D212C2211yescharacteristic
83D4×Dic106C2213yes—
84#16811288C2213yes—
85Q8×C22⋊D53C2211yescharacteristic
86Q8×C22⋊D53C2211yescharacteristic
87Q8×C22⋊D53C2211yescharacteristic, complemented
88#16811286C2213yes—
89#16811286C2213yes—
90#16811286C2213yescomplemented
91#16811285C2211yescharacteristic
92#16811285C2211yescharacteristic, complemented
93#16811284C2211yescharacteristic
94#16811283C2213yes—
95#16811282C2213yes—
96#16811282C2213yescomplemented
97#16811281C2213yes—
98#16811281C2213yescomplemented
99#16811280C2211yescharacteristic
100#16811279C2213yes—
101#16811278C2213yes—
102#16811276C2213yes—
103#16811275C2216yes—
104#16811274C2213yes—
105#16811273C2213yes—
106#16811271C2216yes—
107#16811253C2213yes—
108#16811250C2213yes—
109#16811245C2213yescomplemented
110#16811244C2213yescomplemented
111#16811239C2216yescomplemented
112#16811238C2213yescomplemented
113#16811237C2216yescomplemented
114#16811235C2213yescomplemented
115#16811232C2216yescomplemented
116#16811231C2213yescomplemented
117#16811231C2213yescomplemented
118#16811230C2216yescomplemented
119#16811221C2216yes—
120#16811219C2216yes—
121#16811216C2216yes—
122#16811214C2216yes—
123#16811203C2213yes—
124#16811202C2213yes—
125#16811198C2213yes—
126#16811196C2213yes—
127#16811196C2213yes—
128#16811193C2213yes—
129#16811179C2213yes—
130#16811179C2213yes—
131#16811179C2216yescomplemented
132#16811178C2213yescomplemented
133#16811178C2213yescomplemented
134#16811177C2213yes—
135#16811177C2213yes—
136#16811175C2213yes—
137#16811175C2213yes—
138#16811175C2213yescomplemented
139#16811175C2213yescomplemented
140#16811175C2216yescomplemented
141#16811172C2213yes—
142#16811172C2213yes—
143#16811170C2213yes—
144#16811170C2213yes—
145#16811168C2213yes—
146#16811168C2213yes—
147#16811159C2213yescomplemented
148#16811158C2213yes—
149#16811158C2213yes—
150#16811158C2213yescomplemented
151#16811157C2213yes—
152#16811157C2213yes—
153#16811156C2216yes—
154#16811156C2213yes—
155#16811156C2213yes—
156#16811156C2213yes—
157#16811156C2213yes—
158#16811156C2216yes—
159#16811156C2216yescomplemented
160#16811154C2213yescomplemented
161#16811152C2213yes—
162#16811152C2213yes—
163#16811152C2213yescomplemented
164#16811151C2213yes—
165#16811151C2213yes—
166#16811151C2216yes—
167#16811150C2213yes—
168#16811150C2216yes—
169#16811150C2213yes—
170#16811150C2216yescomplemented
171#16811136C2213yes—
172#16811136C2213yes—
173#16811133C2213yes—
174#16811133C2213yes—
175#16811132C2213yes—
176#16811132C2213yes—
177#16811132C2216yes—
178#16811131C2211yescharacteristic
179#16811131C2213yes—
180#16811105C2213yes—
181#16811105C2211yescharacteristic, complemented
182#16811104C2213yes—
183#16811103C2213yes—
184#16811103C2213yescomplemented
185#16811102C2213yes—
186#16811102C2213yescomplemented
187#16811100C2213yescomplemented
188#16811099C2211yescharacteristic
189#16811099C2211yescharacteristic
190#16811099C2211yescharacteristic, complemented
191#16811099C2213yescomplemented
192#41×Dic53C2211yescharacteristic, complemented
193C4×#11719949C2213yes—
194C4×#11719949C2213yes—
195C4×#11719949C2211yescharacteristic, complemented
196#16811091C2216yes—
197#16811091C2213yes—
198#16811091C2213yes—
199#16811091C2213yescomplemented
200C4×#11719947C2213yes—
201C4×#11719947C2213yes—
202C4×#11719947C2216yes—
203C4×#11719947C2213yes—
204C4×#11719947C2213yes—
205C4×#11719947C2213yescomplemented
206C2×Q8×Dic53C2211yescharacteristic
207C2×Q8×Dic53C2211yescharacteristic, complemented
208C2×C4×Dic106C2213yes—
209C2×#13133182C2213yes—
210C2×#13133182C2213yescomplemented
211C4×Q8×D53C2211yescharacteristic
212C4×Q8×D53C2211yescharacteristic
213C4×Q8×D53C2213yes—
214C4×Q8×D53C2213yes—
215C4×Q8×D53C2213yes—
216C4×Q8×D53C2211yescharacteristic
217C4×Q8×D53C2213yes—
218C4×Q8×D53C2211yescharacteristic
219C4×Q8×D53C2211yescharacteristic, complemented
220C4×Q8×D53C2213yescomplemented
221C2×C4⋊C4×D53C2213yes—
222C2×C42×D53C2213yes—
223C53×#557C2211yescharacteristic, complemented
224C53×#556C2213yescomplemented
225C53×#554C2213yes—
226C53×#553C2213yes—
227C53×#552C2213yescomplemented
228D4×Q8×C53C2211yescharacteristic
229C53×#548C2211yescharacteristic
230C53×#548C2211yescharacteristic, complemented
231C53×#542C2213yescomplemented
232C53×#541C2213yescomplemented
233C53×#529C2213yes—
234C53×#529C2213yes—
235C53×#520C2211yescharacteristic, complemented
236C53×#519C2211yescharacteristic, complemented
237C2×C4×Q8×C53C2211yescharacteristic
238#13133265—28no—
239#13133264—28no—
240C2×#11719949C2311yescharacteristic
241C2×#11719949C2313yes—
242C2×#11719949C2313yes—
243C2×#11719945C2313yes—
244C2×#11719945C2313yes—
245C2×#11719945C2313yes—
246C2×#11719945C2316yes—
247C2×#11719947C2313yes—
248C2×#11719947C2311yescharacteristic
249C2×#11719947C2313yes—
250C2×#11719947C2313yes—
251C2×#11719947C2313yes—
252C22×Dic106C2313yes—
253C22×Dic106C2313yes—
254C2×Q8×D53—28no—
255C2×Q8×D53C2311yescharacteristic
256C2×Q8×D53C2313yes—
257C2×Q8×D53C2313yes—
258C2×Q8×D53C2311yescharacteristic
259C2×Q8×D53C2313yes—
260C2×Q8×D53C2311yescharacteristic
261C22×C4×D53C2311yescharacteristic
262C22×C4×D53C2313yes—
263C22×C4×D53C2313yes—
264#13133217C2313yes—
265#13133217C2313yes—
266#13133216C2316yes—
267#13133216C2313yes—
268#13133216C2313yes—
269#13133216C2316yes—
270#13133216C2316yes—
271#13133216C2313yes—
272#13133216C2313yes—
273#13133216C2313yes—
274#13133216C2313yes—
275#13133215C2316yes—
276#13133215C2313yes—
277#13133215C2313yes—
278#13133215C2313yes—
279#13133215C2313yes—
280#13133213C2313yes—
281#13133213C2313yes—
282#13133212C2316yes—
283#13133212C2316yes—
284#13133212C2316yes—
285#13133212C2316yes—
286#13133212C2313yes—
287#13133212C2313yes—
288#13133211C2313yes—
289#13133211C2316yes—
290#13133211C2313yes—
291#13133211C2316yes—
292#13133210C2316yes—
293#13133210C2316yes—
294#13133210C2316yes—
295#13133210C2316yes—
296#13133210C2313yes—
297#13133210C2313yes—
298#13133209C2316yes—
299#13133209C2313yes—
300#13133209C2313yes—
301#13133209C2313yes—
302#13133208C2313yes—
303#13133208C2316yes—
304#13133208C2316yes—
305#13133208C2313yes—
306#13133207C2316yes—
307#13133207C2316yes—
308#13133207C2313yes—
309#13133207C2316yes—
310#13133207C2316yes—
311#13133207C2316yes—
312#13133207C2313yes—
313#13133207C2316yes—
314#13133207C2313yes—
315#13133207C2316yes—
316#13133207C2313yes—
317#13133207C2316yes—
318#13133206C2313yes—
319#13133205C2313yes—
320#13133205C2313yes—
321#13133205C2313yes—
322#13133204C2313yes—
323#13133203C2316yes—
324#13133203C2313yes—
325#13133203C2316yes—
326#13133203C2313yes—
327#13133203C2313yes—
328#13133203C2316yes—
329#13133203C2313yes—
330#13133203C2316yes—
331#13133202C2316yes—
332#13133202C2313yes—
333#13133202C2313yes—
334#13133202C2316yes—
335#13133202C2316yes—
336#13133202C2313yes—
337#13133202C2313yes—
338#13133202C2316yes—
339#13133201C2316yes—
340#13133200C2316yes—
341#13133200C2311yescharacteristic
342#13133200C2313yes—
343#13133199C2313yes—
344#13133199C2316yes—
345#13133199C2316yes—
346#13133199C2313yes—
347#13133199C2316yes—
348#13133199C2313yes—
349#13133199C2313yes—
350#13133199C2316yes—
351#13133198C2316yes—
352#13133197C2316yes—
353#13133197C2313yes—
354#13133197C2313yes—
355#13133197C2313yes—
356#13133197C2313yes—
357#13133197C2313yes—
358#13133196C2316yes—
359#13133196C2313yes—
360#13133196C2313yes—
361#13133196C2313yes—
362#13133196C2313yes—
363#13133196C2313yes—
364#13133195C2316yes—
365#13133195C2316yes—
366#13133195C2316yes—
367#13133195C2316yes—
368#13133195C2316yes—
369#13133195C2313yes—
370#13133195C2313yes—
371#13133195C2311yescharacteristic
372#13133195C2313yes—
373#13133195C2313yes—
374#13133195C2311yescharacteristic
375#13133195C2316yes—
376#13133194C2316yes—
377#13133194C2316yes—
378#13133194C2316yes—
379#13133194C2316yes—
380#13133194C2316yes—
381#13133194C2313yes—
382#13133194C2313yes—
383#13133194C2316yes—
384#13133193C2316yes—
385#13133193C2313yes—
386#13133193C2313yes—
387#13133193C2313yes—
388#13133193C2313yes—
389#13133193C2313yes—
390#13133192C2313yes—
391#13133192C2313yes—
392#13133192C2313yes—
393#13133191C2313yes—
394#13133191C2313yes—
395#13133191C2313yes—
396#13133190C2313yes—
397#13133190C2313yes—
398#13133190C2316yes—
399#13133190C2311yescharacteristic
400#13133190C2313yes—
401#13133190C2313yes—
402#13133190C2311yescharacteristic
403#13133190C2316yes—
404#13133189C2316yes—
405#13133189C2313yes—
406#13133189C2313yes—
407#13133189C2316yes—
408#13133188C2313yes—
409#13133188C2313yes—
410#13133188C2313yes—
411#13133187C2311yescharacteristic
412#13133187C2313yes—
413#13133185C2311yescharacteristic
414#13133185C2313yes—
415Q8×Dic53C2311yescharacteristic
416Q8×Dic53C2311yescharacteristic
417Q8×Dic53C2311yescharacteristic
418Q8×Dic53C2313yes—
419Q8×Dic53C2313yes—
420Q8×Dic53C2311yescharacteristic
421Q8×Dic53C2313yes—
422Q8×Dic53C2313yes—
423Q8×Dic53C2313yes—
424C4×Dic106C2313yes—
425C4×Dic106C2313yes—
426C4×Dic106C2313yes—
427C4×Dic106C2316yes—
428C4×Dic106C2316yes—
429C4×Dic106C2313yes—
430C4×Dic106C2313yes—
431C4×Dic106C2316yes—
432C4×Dic106C2313yes—
433C4×Dic106C2316yes—
434C4×Dic106C2313yes—
435C4×Dic106C2313yes—
436C4×Dic106C2313yes—
437C4×Dic106C2313yes—
438C4×Dic106C2313yes—
439#13133182C2313yes—
440#13133182C2313yes—
441#13133182C2313yes—
442#13133182C2316yes—
443#13133182C2313yes—
444#13133182C2316yes—
445#13133182C2313yes—
446#13133182C2313yes—
447#13133182C2316yes—
448#13133182C2313yes—
449#13133182C2316yes—
450#13133182C2313yes—
451#13133182C2313yes—
452#13133182C2313yes—
453#13133182C2313yes—
454#13133182C2313yes—
455#13133182C2316yes—
456#13133182C2313yes—
457#13133182C2313yes—
458#13133182C2313yes—
459#13133182C2316yes—
460C4×D212C2313yes—
461C4×D212C2313yes—
462C4×D212C2313yes—
463C4×D212C2313yes—
464C4×D212C2316yes—
465C4×D212C2313yes—
466D4×Dic53C2313yes—
467D4×Dic53C2316yes—
468D4×Dic53C2313yes—
469D4×Dic53C2313yes—
470D4×Dic53C2313yes—
471D4×Dic53C2313yes—
472#13133179C2313yes—
473#13133179C2316yes—
474#13133179C2311yescharacteristic
475#13133179C2313yes—
476#13133179C2313yes—
477#13133179C2313yes—
478#13133179C2313yes—
479#13133179C2313yes—
480#13133179C2311yescharacteristic
481#13133179C2313yes—
482C4×C22⋊D53C2313yes—
483C4×C22⋊D53C2313yes—
484C4×C22⋊D53C2316yes—
485C4×C22⋊D53C2313yes—
486C4×C22⋊D53C2313yes—
487C4×C22⋊D53C2313yes—
488C4×C22⋊D53C2313yes—
489C4×C22⋊D53C2316yes—
490C4×C22⋊D53C2316yes—
491C4×C22⋊D53C2316yes—
492#13133177C2316yes—
493#13133177C2316yes—
494#13133177C2316yes—
495#13133177C2316yes—
496#13133177C2316yes—
497#13133177C2313yes—
498#13133177C2313yes—
499#13133177C2313yes—
500#13133177C2313yes—
501#13133177C2311yescharacteristic
502#13133177C2313yes—
503#13133177C2313yes—
504#13133177C2313yes—
505#13133177C2311yescharacteristic
506#13133177C2313yes—
507#13133177C2313yes—
508#13133177C2313yes—
509#13133177C2313yes—
510#13133177C2313yes—
511#13133177C2316yes—
512#13133176C2313yes—
513#13133175C2313yes—
514#13133175C2313yes—
515#13133175C2313yes—
516#13133175C2313yes—
517#13133175C2313yes—
518#13133175C2313yes—
519#13133175C2313yes—
520#13133175C2316yes—
521#13133175C2313yes—
522#13133175C2313yes—
523#13133175C2313yes—
524#13133175C2316yes—
525#13133174C2316yes—
526#13133174C2316yes—
527#13133174C2316yes—
528#13133174C2313yes—
529#13133174C2313yes—
530#13133174C2313yes—
531#13133174C2313yes—
532#13133173C2313yes—
533#13133173C2316yes—
534#13133173C2313yes—
535#13133173C2311yescharacteristic
536#13133173C2313yes—
537#13133173C2316yes—
538#13133173C2313yes—
539#13133173C2313yes—
540#13133173C2316yes—
541C2×C4⋊Dic53C2313yes—
542C2×C4⋊Dic53C2313yes—
543C2×#11719919C2316yes—
544C2×#11719919C2316yes—
545C4⋊C4×D53C2316yes—
546C4⋊C4×D53C2313yes—
547C4⋊C4×D53C2313yes—
548C4⋊C4×D53C2316yes—
549C4⋊C4×D53C2313yes—
550C4⋊C4×D53C2313yes—
551C4⋊C4×D53C2313yes—
552C4⋊C4×D53C2313yes—
553C4⋊C4×D53C2316yes—
554C2×C4×Dic53C2313yes—
555C2×C4×Dic53C2313yes—
556C2×C4×Dic53C2313yes—
557C2×C4×Dic53C2316yes—
558C2×C4×Dic53C2313yes—
559C2×C4×Dic53C2313yes—
560C42×D53C2313yes—
561C42×D53C2313yes—
562C42×D53C2313yes—
563C42×D53C2313yes—
564C42×D53C2313yes—
565C42×D53C2313yes—
566C42×D53C2313yes—
567C42×D53C2313yes—
568C42×D53C2313yes—
569C42×D53C2316yes—
570C42×D53C2313yes—
571C2×#41×C53C2311yescharacteristic
572C22×Q8×C53C2311yescharacteristic
573C22×Q8×C53C2311yescharacteristic
574C4⋊Q8×C53C2313yes—
575C4⋊Q8×C53C2313yes—
576#126×C53C2313yes—
577#126×C53C2316yes—
578#126×C53C2313yes—
579#126×C53C2316yes—
580#125×C53C2316yes—
581#125×C53C2313yes—
582#125×C53C2313yes—
583#125×C53C2313yes—
584#124×C53C2313yes—
585#124×C53C2313yes—
586#124×C53C2313yes—
587#123×C53C2316yes—
588#123×C53C2311yescharacteristic
589#123×C53C2313yes—
590C22⋊Q8×C53C2316yes—
591C22⋊Q8×C53C2313yes—
592C22⋊Q8×C53C2313yes—
593C22⋊Q8×C53C2313yes—
594C22⋊Q8×C53C2313yes—
595C22⋊Q8×C53C2313yes—
596#121×C53C2313yes—
597#121×C53C2313yes—
598#121×C53C2313yes—
599C4×Q8×C53C2311yescharacteristic
600C4×Q8×C53C2311yescharacteristic
601C4×Q8×C53C2311yescharacteristic
602C4×Q8×C53C2311yescharacteristic
603C4×Q8×C53C2313yes—
604C4×Q8×C53C2313yes—
605C4×Q8×C53C2313yes—
606C4×Q8×C53C2313yes—
607C4×Q8×C53C2313yes—
608C4×D4×C53C2313yes—
609C4×D4×C53C2313yes—
610C4×D4×C53C2313yes—
611C4×D4×C53C2313yes—
612C4×D4×C53C2313yes—
613C4×D4×C53C2316yes—
614#117×C53C2313yes—
615#117×C53C2313yes—
616#117×C53C2313yes—
617#117×C53C2316yes—
618C2×C4⋊C4×C53C2313yes—
619C2×C4⋊C4×C53C2313yes—
620C2×C42×C53C2313yes—
621C23×D53C2411yescharacteristic
622#41×C53—24no—
623C2×Q8×C53—24no—
624C2×Q8×C53—24no—
625C2×Q8×C53C2413yes—
626C2×Q8×C53C2413yes—
627C2×Q8×C53C2413yes—
628C2×Q8×C53C2411yescharacteristic
629C2×D4×C53C2411yescharacteristic
630C2×D4×C53C2413yes—
631C2×D4×C53C2413yes—
632C2×D4×C53C2413yes—
633C22×C4×C53C2411yescharacteristic
634C22×C4×C53C2413yes—
635C22×C4×C53C2413yes—
636C22×C4×C53C2413yes—
637C22×C4×C53C2413yes—
638C22×C4×C53C2416yes—
639C2×C22⋊D53C2411yescharacteristic
640C2×C22⋊D53C2413yes—
641C2×C22⋊D53C2413yes—
642C2×C22⋊D53C2411yescharacteristic
643C2×C22⋊D53C2413yes—
644C2×C22⋊D53C2411yescharacteristic
645C2×C22⋊D53C2413yes—
646C2×C22⋊D53C2413yes—
647C2×C22⋊D53C2413yes—
648C2×C22⋊D53C2411yescharacteristic
649C2×C22⋊D53C2416yes—
650C22×Dic53C2413yes—
651C22×Dic53C2411yescharacteristic
652C22×Dic53C2413yes—
653C22×Dic53C2416yes—
654C22×Dic53C2413yes—
655C22×Dic53C2413yes—
656C22×Dic53C2413yes—
657C22×Dic53C2411yescharacteristic
658#11719949—24no—
659#11719949—212no—
660#11719949—46no—
661Q8×D53—24no—
662Q8×D53—24no—
663Q8×D53—212no—
664Q8×D53—212no—
665Q8×D53—212no—
666Q8×D53#4118yescomplemented
667#11719947—24no—
668#11719947—212no—
669#11719947—212no—
670#11719947—212no—
671#11719947—46no—
672#11719945—212no—
673#11719945—212no—
674#11719945—212no—
675#11719945—412no—
676C2×D212C2411yescharacteristic
677C2×D212C2413yes—
678C2×D212C2413yes—
679C2×D212C2413yes—
680C2×D212C2411yescharacteristic
681C2×D212C2413yes—
682C2×C4×D53—24no—
683C2×C4×D53—212no—
684C2×C4×D53—46no—
685C2×C4×D53C2411yescharacteristic
686C2×C4×D53C2411yescharacteristic
687C2×C4×D53C2411yescharacteristic
688C2×C4×D53C2411yescharacteristic
689C2×C4×D53C2411yescharacteristic
690C2×C4×D53C2413yes—
691C2×C4×D53C2413yes—
692C2×C4×D53C2413yes—
693C2×C4×D53C2413yes—
694C2×C4×D53C2413yes—
695C2×C4×D53C2413yes—
696C2×C4×D53C2416yes—
697C2×C4×D53C2413yes—
698C2×C4×D53C2413yes—
699C2×C4×D53C2413yes—
700C2×C4×D53C2413yes—
701C2×C4×D53C2416yes—
702C2×C4×D53C2413yes—
703C2×C4×D53C2413yes—
704C2×C4×D53C2413yes—
705C2×Dic106—212no—
706C2×Dic106—212no—
707C2×Dic106C2413yes—
708C2×Dic106C2411yescharacteristic
709C2×Dic106C2413yes—
710C2×Dic106C2413yes—
711C2×Dic106C2416yes—
712C2×Dic106C2413yes—
713C2×Dic106C2413yes—
714C2×Dic106C2416yes—
715C2×Dic106C2413yes—
716C2×Dic106C2413yes—
717C4⋊C4×C53C2413yes—
718C4⋊C4×C53C2413yes—
719C4⋊C4×C53C2413yes—
720C4⋊C4×C53C2413yes—
721C4⋊C4×C53C2416yes—
722C4⋊C4×C53C2411yescharacteristic
723C4⋊C4×C53C2413yes—
724C4⋊C4×C53C2413yes—
725C4⋊C4×C53C2413yes—
726C4⋊C4×C53C2413yes—
727C4⋊C4×C53C2416yes—
728C4⋊C4×C53C2413yes—
729C4⋊C4×C53C2413yes—
730C4⋊C4×C53C2416yes—
731C4⋊C4×C53C2413yes—
732C4⋊C4×C53C2411yescharacteristic
733C4⋊C4×C53C2413yes—
734C22⋊C4×C53C2413yes—
735C22⋊C4×C53C2411yescharacteristic
736C22⋊C4×C53C2413yes—
737C22⋊C4×C53C2413yes—
738C22⋊C4×C53C2413yes—
739C22⋊C4×C53C2416yes—
740C22⋊C4×C53C2411yescharacteristic
741C22⋊C4×C53C2413yes—
742C22⋊C4×C53C2411yescharacteristic
743C22⋊C4×C53C2416yes—
744C22⋊C4×C53C2413yes—
745C22⋊C4×C53C2413yes—
746C42×C53C2413yes—
747C42×C53C2413yes—
748C42×C53C2413yes—
749C42×C53C2413yes—
750C42×C53C2416yes—
751C42×C53C2413yes—
752C42×C53C2413yes—
753C22⋊Dic53C2416yes—
754C22⋊Dic53C2411yescharacteristic
755C22⋊Dic53C2413yes—
756C22⋊Dic53C2413yes—
757C22⋊Dic53C2413yes—
758C22⋊Dic53C2416yes—
759C22⋊Dic53C2413yes—
760C22⋊Dic53C2413yes—
761#11719921C2411yescharacteristic
762#11719921C2411yescharacteristic
763#11719921C2411yescharacteristic
764#11719921C2413yes—
765#11719921C2413yes—
766#11719921C2413yes—
767#11719921C2413yes—
768#11719921C2413yes—
769#11719921C2413yes—
770#11719921C2413yes—
771#11719921C2416yes—
772#11719921C2413yes—
773#11719921C2416yes—
774#11719921C2411yescharacteristic
775#11719921C2411yescharacteristic
776#11719921C2411yescharacteristic
777#11719921C2416yes—
778#11719921C2413yes—
779#11719921C2413yes—
780#11719921C2413yes—
781#11719921C2413yes—
782#11719921C2416yes—
783#11719921C2413yes—
784#11719921C2413yes—
785C4⋊Dic53C2413yes—
786C4⋊Dic53C2413yes—
787C4⋊Dic53C2416yes—
788C4⋊Dic53C2413yes—
789C4⋊Dic53C2416yes—
790C4⋊Dic53C2413yes—
791C4⋊Dic53C2413yes—
792C4⋊Dic53C2416yes—
793C4⋊Dic53C2413yes—
794C4⋊Dic53C2413yes—
795C4⋊Dic53C2413yes—
796C4⋊Dic53C2413yes—
797C4⋊Dic53C2413yes—
798#11719919C2416yes—
799#11719919C2416yes—
800#11719919C2416yes—
801#11719919C2416yes—
802#11719919C2413yes—
803#11719919C2413yes—
804#11719919C2416yes—
805#11719919C2413yes—
806#11719919C2413yes—
807#11719919C2411yescharacteristic
808#11719919C2413yes—
809#11719919C2413yes—
810#11719919C2413yes—
811#11719919C2411yescharacteristic
812#11719919C2413yes—
813#11719919C2413yes—
814#11719919C2416yes—
815#11719919C2413yes—
816#11719919C2413yes—
817#11719919C2411yescharacteristic
818#11719919C2413yes—
819#11719919C2413yes—
820#11719919C2413yes—
821#11719919C2413yes—
822#11719919C2416yes—
823#11719919C2413yes—
824#11719919C2411yescharacteristic
825#11719919C2416yes—
826#11719919C2416yes—
827#11719919C2416yes—
828C4×Dic53C2413yes—
829C4×Dic53C2413yes—
830C4×Dic53C2411yescharacteristic
831C4×Dic53C2413yes—
832C4×Dic53C2413yes—
833C4×Dic53C2413yes—
834C4×Dic53C2413yes—
835C4×Dic53C2413yes—
836C4×Dic53C2413yes—
837C4×Dic53C2413yes—
838C4×Dic53C2413yes—
839C4×Dic53C2413yes—
840C4×Dic53C2413yes—
841C4×Dic53C2413yes—
842C4×Dic53C2413yes—
843C4×Dic53C2413yes—
844C4×Dic53C2413yes—
845C4×Dic53C2416yes—
846C4×Dic53C2411yescharacteristic
847C4×Dic53C2413yes—
848C4×Dic53C2416yes—
849C4×Dic53C2413yes—
850C4×Dic53C2416yes—
851C4×Dic53C2413yes—
852C4×Dic53C2413yes—
853C23×C53C2513yes—
854C23×C53C2511yescharacteristic
855C23×C53C2511yescharacteristic
856C22×D53—22no—
857C22×D53—22no—
858C22×D53—22no—
859C22×D53C2513yes—
860C22×D53C2511yescharacteristic
861C22×D53C2511yescharacteristic
862C22×D53C2511yescharacteristic
863Q8×C53—26no—
864Q8×C53—26no—
865Q8×C53—43no—
866Q8×C53C2×#4114yes—
867D4×C53—22no—
868D4×C53—26no—
869D4×C53—26no—
870D4×C53—43no—
871C2×C4×C53—22no—
872C2×C4×C53—26no—
873C2×C4×C53—26no—
874C2×C4×C53—26no—
875C2×C4×C53—43no—
876C2×C4×C53—46no—
877C2×C4×C53C2511yescharacteristic
878C2×C4×C53C2513yes—
879C2×C4×C53C2513yes—
880C2×C4×C53C2513yes—
881C2×C4×C53C2513yes—
882C2×C4×C53C2511yescharacteristic
883C2×C4×C53C2513yes—
884C2×C4×C53C2513yes—
885C2×C4×C53C2511yescharacteristic
886C2×C4×C53C2511yescharacteristic
887C2×C4×C53C2511yescharacteristic
888C2×C4×C53C2513yes—
889C22⋊D53—26no—
890C22⋊D53—22no—
891C22⋊D53—22no—
892C22⋊D53—26no—
893C22⋊D53—26no—
894C22⋊D53—22no—
895C22⋊D53—26no—
896C22⋊D53—26no—
897C22⋊D53—26no—
898C22⋊D53—22no—
899C22⋊D53—46no—
900C2×Dic53—26no—
901C2×Dic53—212no—
902C2×Dic53—26no—
903C2×Dic53—22no—
904C2×Dic53—43no—
905C2×Dic53—43no—
906C2×Dic53—43no—
907C2×Dic532−1+414yescomplemented
908C2×Dic53C2513yes—
909C2×Dic53C2511yescharacteristic
910C2×Dic53C2513yes—
911C2×Dic53C2513yes—
912C2×Dic53C2511yescharacteristic
913C2×Dic53C2513yes—
914C2×Dic53C2511yescharacteristic
915C2×Dic53C2513yes—
916C2×Dic53C2513yes—
917C2×Dic53C2513yes—
918C2×Dic53C2511yescharacteristic
919C2×Dic53C2511yescharacteristic
920D212—22no—
921D212—26no—
922D212—26no—
923D212—22no—
924D212—26no—
925D212—43no—
926C4×D53—26no—
927C4×D53—26no—
928C4×D53—26no—
929C4×D53—26no—
930C4×D53—26no—
931C4×D53—26no—
932C4×D53—26no—
933C4×D53—212no—
934C4×D53—22no—
935C4×D53—22no—
936C4×D53—22no—
937C4×D53—22no—
938C4×D53—22no—
939C4×D53—26no—
940C4×D53—43no—
941C4×D53—43no—
942C4×D53—46no—
943C4×D53—43no—
944C4×D53—43no—
945C4×D53C2×#41112yes—
946Dic106—26no—
947Dic106—26no—
948Dic106—26no—
949Dic106—212no—
950Dic106—26no—
951Dic106—22no—
952Dic106—26no—
953Dic106—46no—
954Dic106—43no—
955Dic106C2×#41112yes—
956#62788—531nomaximal, Sylow
957C22×C53—21no—
958C22×C53—21no—
959C22×C53—23no—
960C22×C53—21no—
961C22×C53—23no—
962C22×C53—21no—
963C22×C53—21no—
964C22×C53—23no—
965C22×C53C2×2−1+412yes—
966C22×C53C2611yescharacteristic
967C2×D53—28no—
968C2×D53—21no—
969C2×D53—21no—
970C2×D53—21no—
971C2×D53—21no—
972C2×D53—23no—
973C2×D53—21no—
974C2×D53—23no—
975C2×D53—21no—
976C2×D53—21no—
977C2×D53—23no—
978C2×D53C22×#4112yes—
979C2×D53#58512yes—
980C4×C53—21no—
981C4×C53—23no—
982C4×C53—23no—
983C4×C53—21no—
984C4×C53—23no—
985C4×C53—21no—
986C4×C53—21no—
987C4×C53—23no—
988C4×C53—23no—
989C4×C53—23no—
990C4×C53—21no—
991C4×C53C22×#4116yes—
992Dic53—23no—
993Dic53—21no—
994Dic53—23no—
995Dic53—21no—
996Dic53—23no—
997Dic53—23no—
998Dic53—21no—
999Dic53—23no—
1000Dic53—23no—
1001Dic53C22×#4116yes—
1002Dic53C2×2−1+412yes—
1003Dic53C2×2−1+412yes—
1004#3523—533no—
1005#3523—531no—
1006#3522—533no—
1007#3522—531no—
1008#3516—533no—
1009#3516—533no—
1010#3516—531no—
1011#3516D5311yescharacteristic, complemented
1012#3507—533no—
1013#3507—533no—
1014#3502—531no—
1015#3497—531no—
1016#3492—533no—
1017#3492—533no—
1018#3486—531no—
1019#3486—531no—
1020#3482—531no—
1021#3482—533no—
1022#3482—533no—
1023#3482—531no—
1024#3480—533no—
1025#3480—531no—
1026Q8×#41—533no—
1027Q8×#41—531no—
1028#3461—533no—
1029#3461—533no—
1030#3444—533no—
1031#3444—533no—
1032C4×2−1+4—531no—
1033C4×2−1+4—531no—
1034C22×C4×Q8—531no—
1035C2×C53—22no—
1036C2×C53—43no—
1037C2×C53—41no—
1038C2×C53C23×#4111yescharacteristic
1039C2×C53C22×2−1+411yescharacteristic
1040C2×C53C2×#58511yescharacteristic
1041D53—22no—
1042D53—22no—
1043D53—43no—
1044D53—41no—
1045C2×2−1+4—531no—
1046C2×2−1+4—531no—
1047C23×Q8—531no—
1048#559—533no—
1049#559—536no—
1050#559—533no—
1051Q82—533no—
1052Q82—531no—
1053#557—533no—
1054#557—536no—
1055#557—533no—
1056#557—533no—
1057#557—531no—
1058#557—531no—
1059#557—533no—
1060#557—533no—
1061#557C2×D5311yescharacteristic, complemented
1062#556—536no—
1063#556—536no—
1064#556—533no—
1065#556—533no—
1066#556—533no—
1067#556—533no—
1068#556—533no—
1069#556—536no—
1070#556C2×D5313yescomplemented
1071#554—536no—
1072#554—536no—
1073#554—533no—
1074#554—533no—
1075#554—533no—
1076#554—536no—
1077#554—533no—
1078#554—533no—
1079#554C2×D5313yes—
1080#553—536no—
1081#553—533no—
1082#553—533no—
1083#553—536no—
1084#553—533no—
1085#553C2×D5313yes—
1086#552—536no—
1087#552—536no—
1088#552—536no—
1089#552—533no—
1090#552—533no—
1091#552—533no—
1092#552—533no—
1093#552—533no—
1094#552—533no—
1095#552—536no—
1096#552—533no—
1097#552C2×D5313yescomplemented
1098#550—531no—
1099#550—533no—
1100D4×Q8—531no—
1101D4×Q8—531no—
1102D4×Q8—531no—
1103D4×Q8—533no—
1104D4×Q8—533no—
1105D4×Q8—533no—
1106D4×Q8—533no—
1107D4×Q8—531no—
1108D4×Q8—533no—
1109D4×Q8C2×D5311yescharacteristic
1110#548—531no—
1111#548—531no—
1112#548—533no—
1113#548—533no—
1114#548—533no—
1115#548—533no—
1116#548—531no—
1117#548—531no—
1118#548—533no—
1119#548—533no—
1120#548C2×D5311yescharacteristic
1121#548C2×D5311yescharacteristic, complemented
1122#547—533no—
1123#547—536no—
1124#547—536no—
1125#547—533no—
1126#547—533no—
1127#547—533no—
1128#544—533no—
1129#544—533no—
1130#542—536no—
1131#542—536no—
1132#542—533no—
1133#542—533no—
1134#542—533no—
1135#542C2×D5313yescomplemented
1136#541—536no—
1137#541—536no—
1138#541—533no—
1139#541—533no—
1140#541—533no—
1141#541C2×D5313yescomplemented
1142#539—536no—
1143#539—536no—
1144#539—536no—
1145#539—536no—
1146#537—533no—
1147#537—533no—
1148#536—533no—
1149#536—533no—
1150#536—533no—
1151#536—533no—
1152#533—533no—
1153#533—533no—
1154#533—533no—
1155#533—533no—
1156#533—536no—
1157#533—533no—
1158#533—533no—
1159#533—533no—
1160#533—533no—
1161#533—536no—
1162#533—533no—
1163#533—533no—
1164#532—533no—
1165#532—533no—
1166#532—533no—
1167#532—533no—
1168#532—533no—
1169#532—533no—
1170#529—536no—
1171#529—533no—
1172#529—533no—
1173#529—533no—
1174#529—533no—
1175#529—536no—
1176#529—536no—
1177#529—533no—
1178#529—533no—
1179#529—533no—
1180#529—533no—
1181#529—533no—
1182#529—533no—
1183#529—536no—
1184#529—533no—
1185#529—533no—
1186#529—536no—
1187#529—533no—
1188#529—533no—
1189#529—536no—
1190#529—533no—
1191#529—533no—
1192#529—533no—
1193#529—533no—
1194#529C2×D5313yes—
1195#529C2×D5313yes—
1196#525—531no—
1197#525—533no—
1198#525—533no—
1199#525—533no—
1200#525—533no—
1201#525—533no—
1202#525—533no—
1203#525—533no—
1204#525—536no—
1205#520—533no—
1206#520—531no—
1207#520—533no—
1208#520—533no—
1209#520—533no—
1210#520—533no—
1211#520—533no—
1212#520C2×D5311yescharacteristic, complemented
1213#519—531no—
1214#519—531no—
1215#519—533no—
1216#519—531no—
1217#519—533no—
1218#519C2×D5311yescharacteristic, complemented
1219C4×#41—531no—
1220C4×#41—533no—
1221C4×#41—533no—
1222C4×#41—531no—
1223C4×#41—533no—
1224C4×#41—536no—
1225C4×#41—533no—
1226C4×#41—533no—
1227C4×#41—533no—
1228C4×#41—533no—
1229C4×#41—533no—
1230C4×#41—533no—
1231C4×#41—536no—
1232C4×#41—533no—
1233C2×C4×Q8—531no—
1234C2×C4×Q8—531no—
1235C2×C4×Q8—531no—
1236C2×C4×Q8—533no—
1237C2×C4×Q8—531no—
1238C2×C4×Q8—533no—
1239C2×C4×Q8—531no—
1240C2×C4×Q8—533no—
1241C2×C4×Q8—531no—
1242C2×C4×Q8—533no—
1243C2×C4×Q8—531no—
1244C2×C4×Q8—533no—
1245C2×C4×Q8—533no—
1246C2×C4×Q8—533no—
1247C2×C4×Q8—533no—
1248C2×C4×Q8C2×D5311yescharacteristic
1249C22×C4⋊C4—533no—
1250C22×C42—533no—
1251C53#6278811yescharacteristic, complemented, Sylow
12522−1+4—1068no—
12532−1+4—1068no—
1254C2×#41—533no—
1255C2×#41—531no—
1256C2×#41—533no—
1257C2×#41—533no—
1258C2×#41—531no—
1259C2×#41—533no—
1260C2×#41—533no—
1261C2×#41—533no—
1262C2×#41—533no—
1263C2×#41—533no—
1264C2×#41—533no—
1265C2×#41—536no—
1266C2×#41C22×D5311yescharacteristic
1267C22×Q8—531no—
1268C22×Q8—533no—
1269C22×Q8—533no—
1270C22×Q8—531no—
1271C22×Q8—533no—
1272C22×Q8—531no—
1273C22×Q8—533no—
1274C22×Q8—533no—
1275C22×Q8—1068no—
1276C22×Q8C22×D5311yescharacteristic
1277C22×Q8C22×D5311yescharacteristic
1278C23×C4—533no—
1279C23×C4—531no—
1280C23×C4—533no—
1281C4⋊Q8—533no—
1282C4⋊Q8—533no—
1283C4⋊Q8—533no—
1284C4⋊Q8—533no—
1285C4⋊Q8—536no—
1286C4⋊Q8—533no—
1287C4⋊Q8—533no—
1288C4⋊Q8—533no—
1289C4⋊Q8—533no—
1290C4⋊Q8—536no—
1291C4⋊Q8—536no—
1292C4⋊Q8—536no—
1293C4⋊Q8—533no—
1294C4⋊Q8—533no—
1295C4⋊Q8—533no—
1296C4⋊Q8—533no—
1297C4⋊Q8C22×D5313yes—
1298C4⋊Q8C22×D5313yes—
1299#127—533no—
1300#127—533no—
1301#126—533no—
1302#126—533no—
1303#126—536no—
1304#126—536no—
1305#126—536no—
1306#126—536no—
1307#126—533no—
1308#126—533no—
1309#126—536no—
1310#126—536no—
1311#126—536no—
1312#126—536no—
1313#126—536no—
1314#126—533no—
1315#126—533no—
1316#126—536no—
1317#126C22×D5316yes—
1318#126C22×D5313yes—
1319#126C22×D5313yes—
1320#126C22×D5316yes—
1321#125—536no—
1322#125—533no—
1323#125—533no—
1324#125—536no—
1325#125—533no—
1326#125—533no—
1327#125—536no—
1328#125—536no—
1329#125—533no—
1330#125—533no—
1331#125—536no—
1332#125—536no—
1333#125—536no—
1334#125—536no—
1335#125—536no—
1336#125—536no—
1337#125—533no—
1338#125—533no—
1339#125—533no—
1340#125—536no—
1341#125C22×D5313yes—
1342#125C22×D5313yes—
1343#125C22×D5313yes—
1344#125C22×D5316yes—
1345#124—533no—
1346#124—533no—
1347#124—536no—
1348#124—533no—
1349#124—533no—
1350#124—536no—
1351#124—533no—
1352#124—533no—
1353#124—536no—
1354#124—536no—
1355#124—533no—
1356#124—533no—
1357#124—533no—
1358#124C22×D5313yes—
1359#124C22×D5313yes—
1360#124C22×D5313yes—
1361#123—536no—
1362#123—533no—
1363#123—531no—
1364#123—536no—
1365#123—533no—
1366#123—533no—
1367#123—536no—
1368#123—536no—
1369#123—533no—
1370#123—533no—
1371#123—536no—
1372#123—536no—
1373#123—536no—
1374#123—533no—
1375#123—533no—
1376#123—536no—
1377#123—533no—
1378#123—533no—
1379#123—536no—
1380#123—536no—
1381#123—536no—
1382#123C22×D5311yescharacteristic
1383#123C22×D5313yes—
1384#123C22×D5316yes—
1385C22⋊Q8—533no—
1386C22⋊Q8—533no—
1387C22⋊Q8—533no—
1388C22⋊Q8—533no—
1389C22⋊Q8—533no—
1390C22⋊Q8—536no—
1391C22⋊Q8—533no—
1392C22⋊Q8—533no—
1393C22⋊Q8—533no—
1394C22⋊Q8—533no—
1395C22⋊Q8—533no—
1396C22⋊Q8—536no—
1397C22⋊Q8—531no—
1398C22⋊Q8—533no—
1399C22⋊Q8—533no—
1400C22⋊Q8—531no—
1401C22⋊Q8—536no—
1402C22⋊Q8—533no—
1403C22⋊Q8—533no—
1404C22⋊Q8—533no—
1405C22⋊Q8—533no—
1406C22⋊Q8—536no—
1407C22⋊Q8—533no—
1408C22⋊Q8—536no—
1409C22⋊Q8—533no—
1410C22⋊Q8—536no—
1411C22⋊Q8—533no—
1412C22⋊Q8—536no—
1413C22⋊Q8—536no—
1414C22⋊Q8—536no—
1415C22⋊Q8—533no—
1416C22⋊Q8—533no—
1417C22⋊Q8—536no—
1418C22⋊Q8—536no—
1419C22⋊Q8—536no—
1420C22⋊Q8—536no—
1421C22⋊Q8—536no—
1422C22⋊Q8—536no—
1423C22⋊Q8C22×D5313yes—
1424C22⋊Q8C22×D5313yes—
1425C22⋊Q8C22×D5313yes—
1426C22⋊Q8C22×D5313yes—
1427C22⋊Q8C22×D5313yes—
1428C22⋊Q8C22×D5316yes—
1429#121—533no—
1430#121—533no—
1431#121—533no—
1432#121—533no—
1433#121—536no—
1434#121—533no—
1435#121—536no—
1436#121—533no—
1437#121—533no—
1438#121—533no—
1439#121—533no—
1440#121—533no—
1441#121—533no—
1442#121—531no—
1443#121—533no—
1444#121—533no—
1445#121—531no—
1446#121—536no—
1447#121—533no—
1448#121—533no—
1449#121—536no—
1450#121C22×D5313yes—
1451#121C22×D5313yes—
1452#121C22×D5313yes—
1453#120—533no—
1454#120—531no—
1455#120—533no—
1456#120—531no—
1457C4×Q8—531no—
1458C4×Q8—533no—
1459C4×Q8—531no—
1460C4×Q8—533no—
1461C4×Q8—533no—
1462C4×Q8—531no—
1463C4×Q8—533no—
1464C4×Q8—531no—
1465C4×Q8—533no—
1466C4×Q8—533no—
1467C4×Q8—536no—
1468C4×Q8—533no—
1469C4×Q8—533no—
1470C4×Q8—536no—
1471C4×Q8—533no—
1472C4×Q8—533no—
1473C4×Q8—533no—
1474C4×Q8—533no—
1475C4×Q8—533no—
1476C4×Q8—536no—
1477C4×Q8—533no—
1478C4×Q8—533no—
1479C4×Q8—533no—
1480C4×Q8—533no—
1481C4×Q8—536no—
1482C4×Q8—533no—
1483C4×Q8—533no—
1484C4×Q8—533no—
1485C4×Q8—536no—
1486C4×Q8—536no—
1487C4×Q8—533no—
1488C4×Q8—536no—
1489C4×Q8—533no—
1490C4×Q8—533no—
1491C4×Q8—533no—
1492C4×Q8—536no—
1493C4×Q8—533no—
1494C4×Q8—533no—
1495C4×Q8—536no—
1496C4×Q8—533no—
1497C4×Q8—533no—
1498C4×Q8—536no—
1499C4×Q8—533no—
1500C4×Q8—533no—
1501C4×Q8—533no—
1502C4×Q8C22×D5311yescharacteristic
1503C4×Q8C22×D5313yes—
1504C4×Q8C22×D5311yescharacteristic
1505C4×Q8C22×D5313yes—
1506C4×Q8C22×D5311yescharacteristic
1507C4×Q8C22×D5313yes—
1508C4×Q8C22×D5313yes—
1509C4×Q8C22×D5311yescharacteristic
1510C4×Q8C22×D5313yes—
1511C4×D4—533no—
1512C4×D4—533no—
1513C4×D4—536no—
1514C4×D4—533no—
1515C4×D4—533no—
1516C4×D4—533no—
1517C4×D4—536no—
1518C4×D4—536no—
1519C4×D4—533no—
1520C4×D4—533no—
1521C4×D4—533no—
1522C4×D4—533no—
1523C4×D4—536no—
1524C4×D4—533no—
1525C4×D4—533no—
1526C4×D4—536no—
1527C4×D4—531no—
1528C4×D4—533no—
1529C4×D4—533no—
1530C4×D4—531no—
1531C4×D4—533no—
1532C4×D4—533no—
1533C4×D4—533no—
1534C4×D4—533no—
1535C4×D4—536no—
1536C4×D4—533no—
1537C4×D4—531no—
1538C4×D4—533no—
1539C4×D4—533no—
1540C4×D4—531no—
1541C4×D4—533no—
1542C4×D4—533no—
1543C4×D4—533no—
1544C4×D4—533no—
1545C4×D4—533no—
1546C4×D4—533no—
1547C4×D4—536no—
1548C4×D4—536no—
1549C4×D4—536no—
1550C4×D4—533no—
1551C4×D4—533no—
1552C4×D4—536no—
1553C4×D4—536no—
1554C4×D4—536no—
1555C4×D4—533no—
1556C4×D4—533no—
1557C4×D4—536no—
1558C4×D4—533no—
1559C4×D4—533no—
1560C4×D4—533no—
1561C4×D4—533no—
1562C4×D4—533no—
1563C4×D4C22×D5313yes—
1564C4×D4C22×D5313yes—
1565C4×D4C22×D5313yes—
1566C4×D4C22×D5313yes—
1567C4×D4C22×D5316yes—
1568C4×D4C22×D5313yes—
1569#117—533no—
1570#117—533no—
1571#117—533no—
1572#117—536no—
1573#117—533no—
1574#117—533no—
1575#117—533no—
1576#117—533no—
1577#117—536no—
1578#117—533no—
1579#117—533no—
1580#117—533no—
1581#117—533no—
1582#117—531no—
1583#117—533no—
1584#117—536no—
1585#117—536no—
1586#117—533no—
1587#117—533no—
1588#117—536no—
1589#117—533no—
1590#117—533no—
1591#117—533no—
1592#117—533no—
1593#117—533no—
1594#117—533no—
1595#117—536no—
1596#117—536no—
1597#117—536no—
1598#117C22×D5313yes—
1599#117C22×D5313yes—
1600#117C22×D5313yes—
1601#117C22×D5316yes—
1602C2×C4⋊C4—536no—
1603C2×C4⋊C4—533no—
1604C2×C4⋊C4—536no—
1605C2×C4⋊C4—533no—
1606C2×C4⋊C4—533no—
1607C2×C4⋊C4—533no—
1608C2×C4⋊C4—536no—
1609C2×C4⋊C4—536no—
1610C2×C4⋊C4—533no—
1611C2×C4⋊C4—533no—
1612C2×C4⋊C4—536no—
1613C2×C4⋊C4—533no—
1614C2×C4⋊C4—533no—
1615C2×C4⋊C4C22×D5313yes—
1616C2×C4⋊C4C22×D5313yes—
1617C2×C42—533no—
1618C2×C42—533no—
1619C2×C42—533no—
1620C2×C42—536no—
1621C2×C42—533no—
1622C2×C42—533no—
1623C2×C42—533no—
1624C2×C42—533no—
1625C2×C42—533no—
1626C2×C42—533no—
1627C2×C42—533no—
1628C2×C42—533no—
1629C2×C42—533no—
1630C2×C42—533no—
1631C2×C42—533no—
1632C2×C42—533no—
1633C2×C42—536no—
1634C2×C42C22×D5313yes—
1635C24—531no—
1636#41—24no—
1637#41—10612no—
1638#41—10612no—
1639#41—10612no—
1640#41—10612no—
1641#41—1064no—
1642#41—10612no—
1643#41—10612no—
1644#41—10612no—
1645#41—1064no—
1646#41—21212no—
1647#41—2126no—
1648#41—2126no—
1649C2×Q8—24no—
1650C2×Q8—24no—
1651C2×Q8—538no—
1652C2×Q8—533no—
1653C2×Q8—531no—
1654C2×Q8—533no—
1655C2×Q8—536no—
1656C2×Q8—533no—
1657C2×Q8—533no—
1658C2×Q8—533no—
1659C2×Q8—533no—
1660C2×Q8—533no—
1661C2×Q8—536no—
1662C2×Q8—10612no—
1663C2×Q8—10612no—
1664C2×Q8—10612no—
1665C2×Q8—10612no—
1666C2×Q8—10612no—
1667C2×Q8—1064no—
1668C2×Q8—1064no—
1669C2×Q8C23×D5313yes—
1670C2×Q8C23×D5313yes—
1671C2×Q8C23×D5313yes—
1672C2×Q8C23×D5311yescharacteristic
1673C2×D4—531no—
1674C2×D4—533no—
1675C2×D4—531no—
1676C2×D4—533no—
1677C2×D4—531no—
1678C2×D4—533no—
1679C2×D4—533no—
1680C2×D4—531no—
1681C2×D4—533no—
1682C2×D4—533no—
1683C2×D4—536no—
1684C2×D4—531no—
1685C2×D4—533no—
1686C2×D4—533no—
1687C2×D4—531no—
1688C2×D4—533no—
1689C2×D4—533no—
1690C2×D4C23×D5313yes—
1691C2×D4C23×D5311yescharacteristic
1692C2×D4C23×D5313yes—
1693C2×D4C23×D5313yes—
1694C22×C4—531no—
1695C22×C4—533no—
1696C22×C4—533no—
1697C22×C4—531no—
1698C22×C4—533no—
1699C22×C4—536no—
1700C22×C4—533no—
1701C22×C4—533no—
1702C22×C4—533no—
1703C22×C4—531no—
1704C22×C4—531no—
1705C22×C4—531no—
1706C22×C4—531no—
1707C22×C4—533no—
1708C22×C4—531no—
1709C22×C4—533no—
1710C22×C4—533no—
1711C22×C4—533no—
1712C22×C4—533no—
1713C22×C4—533no—
1714C22×C4—536no—
1715C22×C4—533no—
1716C22×C4—533no—
1717C22×C4—533no—
1718C22×C4—533no—
1719C22×C4—533no—
1720C22×C4—533no—
1721C22×C4—536no—
1722C22×C4—1064no—
1723C22×C4—10612no—
1724C22×C4—2126no—
1725C22×C4C23×D5311yescharacteristic
1726C22×C4C23×D5313yes—
1727C22×C4C23×D5313yes—
1728C22×C4C23×D5313yes—
1729C22×C4C23×D5313yes—
1730C22×C4C23×D5316yes—
1731C4⋊C4—536no—
1732C4⋊C4—533no—
1733C4⋊C4—536no—
1734C4⋊C4—533no—
1735C4⋊C4—536no—
1736C4⋊C4—536no—
1737C4⋊C4—536no—
1738C4⋊C4—533no—
1739C4⋊C4—533no—
1740C4⋊C4—533no—
1741C4⋊C4—536no—
1742C4⋊C4—533no—
1743C4⋊C4—533no—
1744C4⋊C4—536no—
1745C4⋊C4—533no—
1746C4⋊C4—533no—
1747C4⋊C4—533no—
1748C4⋊C4—533no—
1749C4⋊C4—531no—
1750C4⋊C4—533no—
1751C4⋊C4—531no—
1752C4⋊C4—531no—
1753C4⋊C4—533no—
1754C4⋊C4—533no—
1755C4⋊C4—531no—
1756C4⋊C4—536no—
1757C4⋊C4—533no—
1758C4⋊C4—536no—
1759C4⋊C4—533no—
1760C4⋊C4—533no—
1761C4⋊C4—533no—
1762C4⋊C4—536no—
1763C4⋊C4—533no—
1764C4⋊C4—533no—
1765C4⋊C4—536no—
1766C4⋊C4—533no—
1767C4⋊C4—533no—
1768C4⋊C4—536no—
1769C4⋊C4—536no—
1770C4⋊C4—533no—
1771C4⋊C4—533no—
1772C4⋊C4—533no—
1773C4⋊C4—533no—
1774C4⋊C4C23×D5313yes—
1775C4⋊C4C23×D5313yes—
1776C4⋊C4C23×D5316yes—
1777C4⋊C4C23×D5313yes—
1778C4⋊C4C23×D5313yes—
1779C4⋊C4C23×D5313yes—
1780C4⋊C4C23×D5311yescharacteristic
1781C4⋊C4C23×D5313yes—
1782C4⋊C4C23×D5313yes—
1783C4⋊C4C23×D5313yes—
1784C4⋊C4C23×D5313yes—
1785C4⋊C4C23×D5313yes—
1786C4⋊C4C23×D5313yes—
1787C4⋊C4C23×D5313yes—
1788C4⋊C4C23×D5316yes—
1789C4⋊C4C23×D5311yescharacteristic
1790C4⋊C4C23×D5316yes—
1791C22⋊C4—536no—
1792C22⋊C4—533no—
1793C22⋊C4—531no—
1794C22⋊C4—533no—
1795C22⋊C4—533no—
1796C22⋊C4—536no—
1797C22⋊C4—533no—
1798C22⋊C4—533no—
1799C22⋊C4—531no—
1800C22⋊C4—533no—
1801C22⋊C4—533no—
1802C22⋊C4—531no—
1803C22⋊C4—533no—
1804C22⋊C4—531no—
1805C22⋊C4—533no—
1806C22⋊C4—531no—
1807C22⋊C4—536no—
1808C22⋊C4—533no—
1809C22⋊C4—533no—
1810C22⋊C4—533no—
1811C22⋊C4—531no—
1812C22⋊C4—533no—
1813C22⋊C4—531no—
1814C22⋊C4—536no—
1815C22⋊C4—533no—
1816C22⋊C4—533no—
1817C22⋊C4—536no—
1818C22⋊C4—533no—
1819C22⋊C4—533no—
1820C22⋊C4—536no—
1821C22⋊C4—533no—
1822C22⋊C4—533no—
1823C22⋊C4C23×D5311yescharacteristic
1824C22⋊C4C23×D5313yes—
1825C22⋊C4C23×D5313yes—
1826C22⋊C4C23×D5313yes—
1827C22⋊C4C23×D5311yescharacteristic
1828C22⋊C4C23×D5313yes—
1829C22⋊C4C23×D5316yes—
1830C22⋊C4C23×D5313yes—
1831C22⋊C4C23×D5313yes—
1832C22⋊C4C23×D5311yescharacteristic
1833C22⋊C4C23×D5313yes—
1834C22⋊C4C23×D5316yes—
1835C42—533no—
1836C42—533no—
1837C42—533no—
1838C42—531no—
1839C42—533no—
1840C42—533no—
1841C42—531no—
1842C42—533no—
1843C42—533no—
1844C42—533no—
1845C42—533no—
1846C42—533no—
1847C42—533no—
1848C42—533no—
1849C42—533no—
1850C42—533no—
1851C42—533no—
1852C42—533no—
1853C42—533no—
1854C42—533no—
1855C42—536no—
1856C42—536no—
1857C42—536no—
1858C42—533no—
1859C42—533no—
1860C42C23×D5313yes—
1861C42C23×D5313yes—
1862C42C23×D5313yes—
1863C42C23×D5313yes—
1864C42C23×D5316yes—
1865C42C23×D5313yes—
1866C42C23×D5313yes—
1867C23—531no—
1868C23—531no—
1869C23—531no—
1870C23—533no—
1871C23—1062no—
1872C23—1062no—
1873C23—1062no—
1874C23C24×D5311yescharacteristic
1875C23C24×D5313yes—
1876C23C24×D5311yescharacteristic
1877Q8—26no—
1878Q8—26no—
1879Q8—43no—
1880Q8—5312no—
1881Q8—10612no—
1882Q8—1066no—
1883Q8—1066no—
1884Q8—1062no—
1885Q8—1066no—
1886Q8—1066no—
1887Q8—1066no—
1888Q8—2126no—
1889Q8—2123no—
1890Q8#41×D5314yes—
1891D4—26no—
1892D4—22no—
1893D4—26no—
1894D4—43no—
1895D4—1062no—
1896D4—1066no—
1897D4—1066no—
1898D4—1062no—
1899D4—1062no—
1900D4—1066no—
1901D4—1066no—
1902D4—1066no—
1903D4—1062no—
1904D4—1066no—
1905D4—1066no—
1906D4—1062no—
1907D4—1062no—
1908D4—1066no—
1909D4—1066no—
1910D4—2123no—
1911D4—2126no—
1912C2×C4—22no—
1913C2×C4—26no—
1914C2×C4—26no—
1915C2×C4—26no—
1916C2×C4—43no—
1917C2×C4—46no—
1918C2×C4—534no—
1919C2×C4—531no—
1920C2×C4—531no—
1921C2×C4—533no—
1922C2×C4—5312no—
1923C2×C4—533no—
1924C2×C4—533no—
1925C2×C4—531no—
1926C2×C4—533no—
1927C2×C4—531no—
1928C2×C4—533no—
1929C2×C4—533no—
1930C2×C4—531no—
1931C2×C4—533no—
1932C2×C4—1062no—
1933C2×C4—1062no—
1934C2×C4—1062no—
1935C2×C4—1062no—
1936C2×C4—1066no—
1937C2×C4—10612no—
1938C2×C4—1066no—
1939C2×C4—1062no—
1940C2×C4—1066no—
1941C2×C4—1066no—
1942C2×C4—1066no—
1943C2×C4—1066no—
1944C2×C4—10612no—
1945C2×C4—1066no—
1946C2×C4—1062no—
1947C2×C4—1066no—
1948C2×C4—1066no—
1949C2×C4—1066no—
1950C2×C4—2123no—
1951C2×C4—2123no—
1952C2×C4—2126no—
1953C2×C4—2123no—
1954C2×C4—2123no—
1955C2×C4—2123no—
1956C2×C4—2123no—
1957C2×C4—2123no—
1958C2×C4C24×D5311yescharacteristic
1959C2×C4C24×D5311yescharacteristic
1960C2×C4C24×D5313yes—
1961C2×C4C24×D5311yescharacteristic
1962C2×C4C24×D5311yescharacteristic
1963C2×C4C24×D5313yes—
1964C2×C4C24×D5313yes—
1965C2×C4C24×D5313yes—
1966C2×C4C24×D5313yes—
1967C2×C4C24×D5313yes—
1968C2×C4C24×D5311yescharacteristic
1969C2×C4C24×D5313yes—
1970C22—21no—
1971C22—21no—
1972C22—21no—
1973C22—23no—
1974C22—21no—
1975C22—23no—
1976C22—23no—
1977C22—21no—
1978C22—532no—
1979C22—532no—
1980C22—1068no—
1981C22—1061no—
1982C22—1061no—
1983C22—1061no—
1984C22—1061no—
1985C22—1063no—
1986C22—1061no—
1987C22—1061no—
1988C22—1063no—
1989C22—1061no—
1990C22—1063no—
1991C222−1+4×D5312yes—
1992C22C25×D5311yescharacteristic
1993C4—21no—
1994C4—23no—
1995C4—23no—
1996C4—21no—
1997C4—21no—
1998C4—21no—
1999C4—23no—
2000C4—23no—
2001C4—23no—
2002C4—23no—
2003C4—21no—
2004C4—536no—
2005C4—532no—
2006C4—532no—
2007C4—1063no—
2008C4—1061no—
2009C4—1063no—
2010C4—1063no—
2011C4—1061no—
2012C4—1063no—
2013C4—1063no—
2014C4—1063no—
2015C4—1061no—
2016C4C2×#41×D5316yes—
2017C2—22no—
2018C2—41no—
2019C2—43no—
2020C2—1062no—
2021C2—1062no—
2022C2—2123no—
2023C2—2121no—
2024C2C22×#41×D5311yescharacteristic
2025C2C2×2−1+4×D5311yescharacteristic
2026C2#585×D5311yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3516C2
hypercenter#3516D53
hypocenterC53#62788
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3516

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #20288807C2semidirect
2. #20288805C2semidirect
3. #20288796C2semidirect
4. #20288794C2semidirect
5. #20288708C2semidirect
6. #20288704C2semidirect
7. #20288698C2semidirect
8. #20288576C2semidirect
9. #20288574C2semidirect
10. #20288522C2semidirect
11. #20288483C2semidirect
12. #20288423C2semidirect
13. #20288419C2semidirect
14. #20288365C2semidirect
15. #20288361C2semidirect
16. #20288335C2semidirect
17. #20288334C2semidirect
18. #20288331C2semidirect
19. #20288329C2semidirect
20. #20288309C2semidirect
21. #20288305C2semidirect
22. #20288294C2semidirect
23. Q8×#11719947C2semidirect
24. #20288147C2semidirect
25. #20288141C2semidirect
26. #20288009C2semidirect
27. #20288009C2semidirect
28. #20287926C2semidirect
29. #20287924C2semidirect
30. C2×C4×Q8×D53C2semidirect
31. C53×#3516C2semidirect
35. #16811357C22semidirect
36. #16811356C22semidirect
37. #16811355C22semidirect
38. Q8×Dic106C22semidirect
39. #16811353C22semidirect
40. #16811351C22semidirect
41. #16811351C22semidirect
42. #16811350C22semidirect
43. #16811350C22semidirect
44. #16811350C22semidirect
45. #16811349C22semidirect
46. #16811349C22semidirect
47. #16811348C22semidirect
48. #16811346C22semidirect
49. #16811345C22semidirect
50. #16811344C22semidirect
51. #16811342C22semidirect
52. #16811341C22semidirect
53. #16811341C22semidirect
54. #16811340C22semidirect
55. #16811340C22semidirect
58. #16811331C22semidirect
61. #16811328C22semidirect
63. #16811327C22semidirect
70. #16811314C22semidirect
71. #16811313C22semidirect
74. #16811311C22semidirect
76. #16811309C22semidirect
78. #16811306C22semidirect
80. #16811292C22semidirect
81. #16811291C22semidirect
87. Q8×C22⋊D53C22semidirect
90. #16811286C22semidirect
92. #16811285C22semidirect
96. #16811282C22semidirect
98. #16811281C22semidirect
109. #16811245C22semidirect
110. #16811244C22semidirect
111. #16811239C22semidirect
112. #16811238C22semidirect
113. #16811237C22semidirect
114. #16811235C22semidirect
115. #16811232C22semidirect
116. #16811231C22semidirect
117. #16811231C22semidirect
118. #16811230C22semidirect
131. #16811179C22semidirect
132. #16811178C22semidirect
133. #16811178C22semidirect
138. #16811175C22semidirect
139. #16811175C22semidirect
140. #16811175C22semidirect
147. #16811159C22semidirect
150. #16811158C22semidirect
159. #16811156C22semidirect
160. #16811154C22semidirect
163. #16811152C22semidirect
170. #16811150C22semidirect
181. #16811105C22semidirect
184. #16811103C22semidirect
186. #16811102C22semidirect
187. #16811100C22semidirect
190. #16811099C22semidirect
191. #16811099C22semidirect
192. #41×Dic53C22semidirect
195. C4×#11719949C22semidirect
199. #16811091C22semidirect
205. C4×#11719947C22semidirect
207. C2×Q8×Dic53C22semidirect
210. C2×#13133182C22semidirect
219. C4×Q8×D53C22semidirect
220. C4×Q8×D53C22semidirect
223. C53×#557C22semidirect
224. C53×#556C22semidirect
227. C53×#552C22semidirect
230. C53×#548C22semidirect
231. C53×#542C22semidirect
232. C53×#541C22semidirect
235. C53×#520C22semidirect
236. C53×#519C22semidirect
666. Q8×D53#41semidirect
907. C2×Dic532−1+4semidirect
1011. #3516D53semidirect
1061. #557C2×D53semidirect
1070. #556C2×D53semidirect
1097. #552C2×D53semidirect
1121. #548C2×D53semidirect
1135. #542C2×D53semidirect
1141. #541C2×D53semidirect
1212. #520C2×D53semidirect
1218. #519C2×D53semidirect
1251. C53#62788semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202888072
#202888052
#202887962
#202887942
#202887082
#202887042
#202886982
#202885762
#202885742
#202885222
#202884832
#202884232
#202884192
#202883652
#202883612
#202883352
#202883342
#202883312
#202883292
#202883092
#202883052
#202882942
Q8×#117199472
#202881472
#202881412
#202880092
#202879262
#202879242
C2×C4×Q8×D532
C53×#35162
#6278853