Finite Group Databasebeta

← #28293284

Subgroups — #28293284

Order 13568.

10986 conjugacy classes of subgroups.

The subgroup lattice has 1626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811459C211yesmaximal, characteristic, complemented
2C2×2−1+4×D53C211yesmaximal, characteristic, complemented
3#20288506C212yesmaximal, complemented
4#20288501C216yesmaximal, complemented
5#20288499C212yesmaximal, complemented
6#20288494C216yesmaximal, complemented
7#20288396C211yesmaximal, characteristic, complemented
8#20288395C211yesmaximal, characteristic, complemented
9#20288393C213yesmaximal, complemented
10#20288391C213yesmaximal, complemented
11#20288390C213yesmaximal, complemented
12#20288388C211yesmaximal, characteristic, complemented
13#20288387C213yesmaximal, complemented
14#20288365C212yesmaximal, complemented
15#20288361C212yesmaximal, complemented
16#20288354C216yesmaximal, complemented
17#20288352C216yesmaximal, complemented
18#20288045C213yesmaximal, complemented
19#20288043C213yesmaximal, complemented
20C2×#16811196C213yesmaximal, complemented
21#536×D53C213yesmaximal, complemented
22#20287915C211yesmaximal, characteristic, complemented
23C53×#3489C211yesmaximal, characteristic, complemented
24#16811459—216no—
25C2×#13133265C2211yescharacteristic
26C2×#13133265C2213yescomplemented
27C2×#13133265C2212yescomplemented
28C2×#13133265C2211yescharacteristic, complemented
29C2×#13133264C2211yescharacteristic
30C2×#13133264C2213yescomplemented
31C2×#13133264C2211yescharacteristic, complemented
32C2×#13133264C2213yescomplemented
33C2×#13133264C2216yescomplemented
342−1+4×D53—216no—
35C2×#13133263C2213yes—
36C2×#13133263C2211yescharacteristic, complemented
37C2×#13133262C2213yes—
38C2×#13133262C2213yescomplemented
39C22×#11719945C2213yes—
40C22×#11719945C2213yescomplemented
41C2×#41×D53C2213yes—
42C2×#41×D53C2211yescharacteristic
43C2×#41×D53C2213yescomplemented
44C2×#41×D53C2216yescomplemented
45C2×#41×D53C2211yescharacteristic, complemented
46C2×#41×D53C2213yescomplemented
47C22×Q8×D53C2213yescomplemented
48C22×Q8×D53C2212yescomplemented
49Q8×D212C2212yescomplemented
50D4×Dic106C2216yescomplemented
51#16811288C2216yescomplemented
52Q8×C22⋊D53C2212yescomplemented
53Q8×C22⋊D53C2212yescomplemented
54#16811286C2216yescomplemented
55#16811286C2216yescomplemented
56#16811285C2212yescomplemented
57#16811284C2212yescomplemented
58#16811283C2216yescomplemented
59#16811282C2216yescomplemented
60#16811281C2216yescomplemented
61#16811280C2212yescomplemented
62#16811279C2216yescomplemented
63#16811278C2216yescomplemented
64#16811277C2216yescomplemented
65#16811276C2216yescomplemented
66#16811275C2216yescomplemented
67#16811275C2216yescomplemented
68#16811274C22112yescomplemented
69#16811273C22112yescomplemented
70#16811272C2216yescomplemented
71#16811272C2216yescomplemented
72#16811271C22112yescomplemented
73#16811271C22112yescomplemented
74#16811270C2216yescomplemented
75#16811269C2216yescomplemented
76#16811268C2216yescomplemented
77#16811267C2216yescomplemented
78#16811266C2216yescomplemented
79#16811265C22112yescomplemented
80#16811264C2216yescomplemented
81#16811263C22112yescomplemented
82#16811262C22112yescomplemented
83#16811261C2216yescomplemented
84#16811260C22112yescomplemented
85#16811204C2213yescomplemented
86#16811203C2213yescomplemented
87#16811203C2213yescomplemented
88#16811202C2213yescomplemented
89#16811202C2213yescomplemented
90#16811201C2213yescomplemented
91#16811201C2213yescomplemented
92#16811199C2213yescomplemented
93#16811198C2216yescomplemented
94#16811197C2213yescomplemented
95#16811196C2213yescomplemented
96#16811196C2216yescomplemented
97#16811196C2213yescomplemented
98#16811196C2216yescomplemented
99#16811196C2216yescomplemented
100#16811196C2216yescomplemented
101#16811196C2216yescomplemented
102#16811196C2216yescomplemented
103#16811196C2216yescomplemented
104#16811196C2216yescomplemented
105#16811195C22112yescomplemented
106#16811195C2216yescomplemented
107#16811194C2213yescomplemented
108#16811193C2216yescomplemented
109#16811189C2213yescomplemented
110#16811189C2216yescomplemented
111#16811189C2211yescharacteristic, complemented
112#16811188C2216yescomplemented
113#16811184C2216yescomplemented
114#16811183C2216yescomplemented
115#16811181C22112yescomplemented
116#16811170C2216yescomplemented
117#16811170C2216yescomplemented
118#16811168C22112yescomplemented
119C2×#13133216C2216yescomplemented
120C4⋊Q8×D53C2216yescomplemented
121C2×#13133203C2216yescomplemented
122#124×D53C2216yescomplemented
123#16811136C2216yescomplemented
124#16811136C2216yescomplemented
125#16811135C2213yescomplemented
126#16811134C2213yescomplemented
127#16811133C2216yescomplemented
128#16811133C2216yescomplemented
129#16811132C2216yescomplemented
130#16811132C2216yescomplemented
131#16811130C2213yescomplemented
132C2×#13133202C2216yescomplemented
133C2×#13133199C2216yescomplemented
134#123×D53C22112yescomplemented
135C2×#13133197C2213yescomplemented
136C2×#13133196C2213yescomplemented
137C2×#13133193C2213yescomplemented
138C22⋊Q8×D53C2216yescomplemented
139C22⋊Q8×D53C2216yescomplemented
140#16811106C2211yescharacteristic, complemented
141#16811104C2213yescomplemented
142#16811103C2213yescomplemented
143#16811099C2212yescomplemented
144#16811095C2216yescomplemented
145C4×#11719949C2212yescomplemented
146C4×#11719947C2216yescomplemented
147C2×#13133175C2213yescomplemented
148#117×D53C2213yescomplemented
149C2×2−1+4×C53C2211yescharacteristic, complemented
150C22×#41×C53C2211yescharacteristic, complemented
151D4×Q8×C53C2212yescomplemented
152C53×#548C2212yescomplemented
153C53×#547C2216yescomplemented
154C53×#546C2216yescomplemented
155C53×#537C2213yescomplemented
156C53×#536C2213yescomplemented
157C53×#525C2213yescomplemented
158C2×C22⋊Q8×C53C2213yescomplemented
159C53×#520C2211yescharacteristic, complemented
160#13133265—216no—
161#13133265—28no—
162#13133265—28no—
163#13133265—224no—
164#13133264—28no—
165#13133264—28no—
166#13133264—248no—
167#13133264—224no—
168#13133264—224no—
169#13133263—28no—
170#13133263—224no—
171#13133262—224no—
172#13133262—224no—
173C2×#11719949C2316yes—
174C2×#11719949C2313yes—
175C2×#11719949C2311yescharacteristic
176C2×#11719949C2313yes—
177C2×#11719949C2313yes—
178C2×#11719949C2311yescharacteristic
179C2×#11719945—224no—
180C2×#11719945—224no—
181C2×#11719945C23112yes—
182C2×#11719945C2316yes—
183C2×#11719945C2316yes—
184C2×#11719945C2313yes—
185C2×#11719945C2313yes—
186C2×#11719945C2313yes—
187C2×#11719945C2313yes—
188C2×#11719945C2313yes—
189C2×#11719945C2316yes—
190C2×#11719945C2313yes—
191C2×#11719945C2313yes—
192C2×#11719945C2313yes—
193C2×#11719945C2311yescharacteristic
194C2×#11719945C2313yes—
195C2×#11719945C2313yes—
196C2×#11719945C2313yes—
197C2×#11719945C2313yes—
198C2×#11719947C2316yes—
199C2×#11719947C2316yes—
200C2×#11719947C23112yes—
201C2×#11719947C2313yes—
202C2×#11719947C2313yes—
203C2×#11719947C2313yes—
204C2×#11719947C2313yes—
205C2×#11719947C2316yes—
206C2×#11719947C2316yes—
207C2×#11719947C2313yes—
208#41×D53—28no—
209#41×D53—248no—
210#41×D53—224no—
211#41×D53—224no—
212#41×D53—224no—
213#41×D53D4116yescomplemented
214C22×Dic106C2316yes—
215C22×Dic106C2313yes—
216C22×Dic106C2313yes—
217C22×Dic106C2316yes—
218C22×Dic106C2313yes—
219C2×Q8×D53—216no—
220C2×Q8×D53—224no—
221C2×Q8×D53C2312yes—
222C2×Q8×D53C2316yes—
223C2×Q8×D53C2313yes—
224C2×Q8×D53C2311yescharacteristic
225C2×Q8×D53C2316yes—
226C2×Q8×D53C2316yes—
227C2×Q8×D53C2313yes—
228C2×Q8×D53C2316yes—
229C2×Q8×D53C2313yes—
230C2×Q8×D53C2311yescharacteristic
231C22×D212C2313yes—
232C22×D212C2313yes—
233C22×C22⋊D53C2313yes—
234C22×C22⋊D53C2313yes—
235C22×C22⋊D53C2316yes—
236C2×D4×D53C2316yes—
237C2×D4×D53C2313yes—
238C2×D4×D53C2313yes—
239C2×D4×D53C2316yes—
240C2×D4×D53C2313yes—
241C2×D4×D53C2316yes—
242C2×D4×D53C2311yescharacteristic
243C2×D4×D53C2313yes—
244C22×C4×D53C2316yes—
245C22×C4×D53C2313yes—
246C22×C4×D53C2316yes—
247C22×C4×D53C2316yes—
248C22×C4×D53C2313yes—
249#13133217C2316yes—
250#13133216C23112yes—
251#13133216C23112yes—
252#13133216C2316yes—
253#13133216C23112yes—
254#13133216C2316yes—
255#13133215C2316yes—
256#13133215C2316yes—
257#13133213C2316yes—
258#13133213C2312yes—
259#13133206C2316yes—
260#13133205C2316yes—
261#13133204C2316yes—
262#13133203C23112yes—
263#13133203C23112yes—
264#13133203C2316yes—
265#13133203C23112yes—
266#13133203C2316yes—
267#13133203C2316yes—
268#13133203C2312yes—
269#13133202C23112yes—
270#13133202C23112yes—
271#13133202C23112yes—
272#13133202C2316yes—
273#13133202C23112yes—
274#13133202C2316yes—
275#13133201C23112yes—
276#13133201C2316yes—
277#13133200C2316yes—
278#13133200C23112yes—
279#13133199C23112yes—
280#13133199C23112yes—
281#13133199C23112yes—
282#13133199C2316yes—
283#13133199C23112yes—
284#13133199C2316yes—
285#13133198C23112yes—
286#13133198C2316yes—
287#13133197C2316yes—
288#13133197C2316yes—
289#13133197C2316yes—
290#13133197C2313yes—
291#13133197C2316yes—
292#13133197C2313yes—
293#13133196C2316yes—
294#13133196C2316yes—
295#13133196C2316yes—
296#13133196C2313yes—
297#13133196C2316yes—
298#13133196C2313yes—
299#13133195C23112yes—
300#13133195C2316yes—
301#13133195C2316yes—
302#13133195C23112yes—
303#13133194C2316yes—
304#13133194C23112yes—
305#13133194C2316yes—
306#13133194C23112yes—
307#13133193C2316yes—
308#13133193C2316yes—
309#13133193C2316yes—
310#13133193C2313yes—
311#13133193C2316yes—
312#13133193C2313yes—
313#13133192C2316yes—
314#13133192C2316yes—
315#13133192C2316yes—
316#13133192C2311yescharacteristic
317#13133192C2313yes—
318#13133191C23112yes—
319#13133191C2316yes—
320#13133191C2311yescharacteristic
321#13133191C2313yes—
322#13133190C2316yes—
323#13133190C2316yes—
324#13133190C2316yes—
325#13133190C2316yes—
326#13133190C2316yes—
327#13133190C2316yes—
328#13133189C23112yes—
329#13133189C23112yes—
330#13133189C2316yes—
331#13133189C2316yes—
332#13133188C2316yes—
333#13133188C2316yes—
334#13133188C2316yes—
335#13133188C2311yescharacteristic
336#13133188C2313yes—
337#13133187C23112yes—
338#13133187C2316yes—
339#13133187C2312yes—
340#13133187C2316yes—
341#13133186C2316yes—
342#13133185C23112yes—
343#13133185C2316yes—
344#13133185C2312yes—
345#13133185C2316yes—
346Q8×Dic53C2312yes—
347C4×Dic106C2316yes—
348#13133182C2316yes—
349C4×D212C2316yes—
350C4×D212C2316yes—
351C4×D212C2316yes—
352D4×Dic53C2316yes—
353D4×Dic53C23112yes—
354#13133179C2316yes—
355#13133179C23112yes—
356C4×C22⋊D53C2316yes—
357C4×C22⋊D53C2316yes—
358C4×C22⋊D53C2316yes—
359C4×C22⋊D53C23112yes—
360C4×C22⋊D53C2316yes—
361#13133177C23112yes—
362#13133177C23112yes—
363#13133177C23112yes—
364#13133176C2313yes—
365#13133175C2311yescharacteristic
366#13133175C2313yes—
367#13133175C2316yes—
368#13133175C2316yes—
369#13133175C2316yes—
370#13133174C2316yes—
371#13133173C2316yes—
372C2×C4⋊Dic53C2316yes—
373C2×C4⋊Dic53C2313yes—
374C2×#11719919C2316yes—
375C2×#11719919C2316yes—
376C4⋊C4×D53C23112yes—
377C4⋊C4×D53C23112yes—
378C4⋊C4×D53C2313yes—
379C4⋊C4×D53C2313yes—
380C2×C22⋊Dic53C2316yes—
381C2×#11719921C2316yes—
382C2×#11719921C2316yes—
383C2×#11719921C2316yes—
384C22⋊C4×D53C23112yes—
385C22⋊C4×D53C23112yes—
386C22⋊C4×D53C2316yes—
387C2×C4×Dic53C2316yes—
388C42×D53C2316yes—
3892−1+4×C53—28no—
390C2×#41×C53—28no—
391C2×#41×C53C2313yes—
392C2×#41×C53C2316yes—
393C2×#41×C53C2311yescharacteristic
394C2×#41×C53C2313yes—
395C2×#41×C53C2313yes—
396C2×#41×C53C2311yescharacteristic
397C22×Q8×C53C2312yes—
398C22×Q8×C53C2311yescharacteristic
399C22×Q8×C53C2313yes—
400C22×D4×C53C2313yes—
401C23×C4×C53C2313yes—
402C4⋊Q8×C53C2316yes—
403#124×C53C2316yes—
404#123×C53C23112yes—
405#123×C53C2316yes—
406C22⋊Q8×C53C2316yes—
407C22⋊Q8×C53C2316yes—
408C22⋊Q8×C53C2316yes—
409C22⋊Q8×C53C2313yes—
410C22⋊Q8×C53C2316yes—
411C22⋊Q8×C53C2313yes—
412#121×C53C2316yes—
413#121×C53C23112yes—
414#121×C53C2311yescharacteristic
415#121×C53C2313yes—
416#120×C53C2316yes—
417C4×Q8×C53C2312yes—
418C4×D4×C53C2316yes—
419C4×D4×C53C2316yes—
420C4×D4×C53C2316yes—
421#117×C53C2313yes—
422C2×C4⋊C4×C53C2316yes—
423C2×C4⋊C4×C53C2313yes—
424C2×C22⋊C4×C53C2316yes—
425C24×C53C2413yes—
426C23×D53C2416yes—
427C23×D53C2413yes—
428C23×D53C2412yes—
429C23×D53C2413yes—
430#41×C53—24no—
431#41×C53—212no—
432#41×C53—224no—
433#41×C53—212no—
434#41×C53—212no—
435#41×C53C2×D418yes—
436C2×Q8×C53—24no—
437C2×Q8×C53—28no—
438C2×Q8×C53—212no—
439C2×Q8×C53C2413yes—
440C2×Q8×C53C2416yes—
441C2×Q8×C53C2413yes—
442C2×Q8×C53C2411yescharacteristic
443C2×D4×C53—212no—
444C2×D4×C53C2416yes—
445C2×D4×C53C2411yescharacteristic
446C2×D4×C53C2416yes—
447C2×D4×C53C2413yes—
448C2×D4×C53C2412yes—
449C2×D4×C53C2416yes—
450C2×D4×C53C2413yes—
451C22×C4×C53—212no—
452C22×C4×C53C2416yes—
453C22×C4×C53C2413yes—
454C22×C4×C53C2416yes—
455C22×C4×C53C2413yes—
456C22×C4×C53C2413yes—
457C22×C4×C53C2411yescharacteristic
458C22×C4×C53C2413yes—
459C22×C4×C53C2416yes—
460C22×C4×C53C2413yes—
461C2×C22⋊D53—212no—
462C2×C22⋊D53—224no—
463C2×C22⋊D53—212no—
464C2×C22⋊D53C2416yes—
465C2×C22⋊D53C2413yes—
466C2×C22⋊D53C2411yescharacteristic
467C2×C22⋊D53C2416yes—
468C2×C22⋊D53C2413yes—
469C2×C22⋊D53C2413yes—
470C2×C22⋊D53C2413yes—
471C2×C22⋊D53C2413yes—
472C2×C22⋊D53C2416yes—
473C2×C22⋊D53C2413yes—
474C2×C22⋊D53C2411yescharacteristic
475C2×C22⋊D53C2412yes—
476C2×C22⋊D53C2416yes—
477C2×C22⋊D53C2416yes—
478C2×C22⋊D53C2412yes—
479C2×C22⋊D53C2412yes—
480C2×C22⋊D53C2416yes—
481C22×Dic53C2416yes—
482C22×Dic53C2413yes—
483C22×Dic53C2416yes—
484C22×Dic53C2416yes—
485C22×Dic53C2416yes—
486C22×Dic53C2413yes—
487#11719949—24no—
488#11719949—212no—
489#11719949—224no—
490#11719949—212no—
491#11719949—212no—
492#11719949C2×D418yes—
493Q8×D53—28no—
494Q8×D53—24no—
495Q8×D53—224no—
496Q8×D53—212no—
497Q8×D53—224no—
498Q8×D53—224no—
499Q8×D53—212no—
500Q8×D53—224no—
501Q8×D53—212no—
502Q8×D53C2×D418yes—
503#11719947—212no—
504#11719947—224no—
505#11719947—224no—
506#11719947—248no—
507#11719947—224no—
508#11719947—224no—
509#11719947—212no—
510#11719947—212no—
511#11719947—212no—
512#11719947C2×D4124yes—
513D4×D53—224no—
514D4×D53—224no—
515D4×D53—212no—
516D4×D53—224no—
517D4×D53—212no—
518D4×D53—24no—
519D4×D53—212no—
520D4×D53C2×D4124yes—
521#11719945—212no—
522#11719945—212no—
523#11719945—248no—
524#11719945—224no—
525#11719945—224no—
526#11719945—212no—
527#11719945—212no—
528#11719945—212no—
529#11719945—224no—
530#11719945—212no—
531#11719945—24no—
532#11719945—212no—
533#11719945—212no—
534#11719945—212no—
535#11719945—212no—
536#11719945—212no—
537#11719945C2×D4124yes—
538C2×D212—212no—
539C2×D212—212no—
540C2×D212C2416yes—
541C2×D212C2413yes—
542C2×D212C2411yescharacteristic
543C2×D212C2413yes—
544C2×D212C2413yes—
545C2×D212C2411yescharacteristic
546C2×D212C2413yes—
547C2×D212C2416yes—
548C2×D212C2412yes—
549C2×D212C2413yes—
550C2×C4×D53—224no—
551C2×C4×D53—212no—
552C2×C4×D53—224no—
553C2×C4×D53—224no—
554C2×C4×D53C2×D4124yes—
555C2×C4×D53C24112yes—
556C2×C4×D53C2416yes—
557C2×C4×D53C2416yes—
558C2×C4×D53C2416yes—
559C2×C4×D53C2416yes—
560C2×C4×D53C2413yes—
561C2×C4×D53C2413yes—
562C2×C4×D53C2411yescharacteristic
563C2×C4×D53C2413yes—
564C2×C4×D53C2416yes—
565C2×C4×D53C2416yes—
566C2×C4×D53C2416yes—
567C2×C4×D53C2413yes—
568C2×C4×D53C2413yes—
569C2×C4×D53C2413yes—
570C2×C4×D53C2411yescharacteristic
571C2×Dic106—212no—
572C2×Dic106—224no—
573C2×Dic106—212no—
574C2×Dic106—224no—
575C2×Dic106—212no—
576C2×Dic106C24112yes—
577C2×Dic106C2413yes—
578C2×Dic106C2413yes—
579C2×Dic106C2413yes—
580C2×Dic106C2416yes—
581C2×Dic106C2413yes—
582C2×Dic106C2416yes—
583C2×Dic106C2413yes—
584C2×Dic106C2411yescharacteristic
585C2×Dic106C2413yes—
586C4⋊C4×C53C2413yes—
587C4⋊C4×C53C2416yes—
588C4⋊C4×C53C2416yes—
589C4⋊C4×C53C24112yes—
590C4⋊C4×C53C2411yescharacteristic
591C4⋊C4×C53C2416yes—
592C22⋊C4×C53C2416yes—
593C22⋊C4×C53C24112yes—
594C22⋊C4×C53C2416yes—
595C22⋊C4×C53C2412yes—
596C22⋊C4×C53C2416yes—
597C22⋊C4×C53C2416yes—
598C42×C53C2416yes—
599C22⋊Dic53C2416yes—
600C22⋊Dic53C24112yes—
601C22⋊Dic53C2416yes—
602C22⋊Dic53C2416yes—
603C22⋊Dic53C2412yes—
604C22⋊Dic53C2416yes—
605#11719921C2412yes—
606#11719921C2416yes—
607#11719921C2416yes—
608#11719921C2416yes—
609#11719921C24112yes—
610#11719921C24112yes—
611#11719921C2416yes—
612#11719921C2416yes—
613#11719921C24112yes—
614#11719921C2416yes—
615#11719921C2412yes—
616#11719921C2416yes—
617#11719921C2412yes—
618C4⋊Dic53C2411yescharacteristic
619C4⋊Dic53C2416yes—
620C4⋊Dic53C2413yes—
621C4⋊Dic53C24112yes—
622C4⋊Dic53C2416yes—
623C4⋊Dic53C2416yes—
624#11719919C2416yes—
625#11719919C2416yes—
626#11719919C24112yes—
627#11719919C24112yes—
628#11719919C2416yes—
629#11719919C2416yes—
630#11719919C2416yes—
631#11719919C2416yes—
632C4×Dic53C2412yes—
633C4×Dic53C2416yes—
634C4×Dic53C2416yes—
635C4×Dic53C24112yes—
636C23×C53—26no—
637C23×C53—43no—
638C23×C53—43no—
639C23×C53C2512yes—
640C23×C53C2513yes—
641C23×C53C2511yescharacteristic
642C23×C53C2513yes—
643C22×D53—26no—
644C22×D53—24no—
645C22×D53—212no—
646C22×D53—43no—
647C22×D53—43no—
648C22×D53—42no—
649C22×D53—42no—
650C22×D53—46no—
651C22×D53—46no—
652C22×D53—43no—
653C22×D53—43no—
654C22×D53C22×D4112yes—
655C22×D53C2512yes—
656C22×D53C2513yes—
657C22×D53C2511yescharacteristic
658C22×D53C2513yes—
659C22×D53C2511yescharacteristic
660Q8×C53—212no—
661Q8×C53—26no—
662Q8×C53—26no—
663Q8×C53C22×D414yes—
664D4×C53—212no—
665D4×C53—212no—
666D4×C53—26no—
667D4×C53—22no—
668D4×C53—42no—
669D4×C53—46no—
670D4×C53C22×D4112yes—
671C2×C4×C53—212no—
672C2×C4×C53—26no—
673C2×C4×C53—212no—
674C2×C4×C53—26no—
675C2×C4×C53—26no—
676C2×C4×C53—22no—
677C2×C4×C53—26no—
678C2×C4×C53—46no—
679C2×C4×C53C22×D4112yes—
680C2×C4×C53C2511yescharacteristic
681C2×C4×C53C2516yes—
682C2×C4×C53C2513yes—
683C2×C4×C53C2512yes—
684C2×C4×C53C2516yes—
685C2×C4×C53C2513yes—
686C2×C4×C53C2511yescharacteristic
687C22⋊D53—212no—
688C22⋊D53—212no—
689C22⋊D53—22no—
690C22⋊D53—26no—
691C22⋊D53—212no—
692C22⋊D53—26no—
693C22⋊D53—26no—
694C22⋊D53—22no—
695C22⋊D53—26no—
696C22⋊D53—24no—
697C22⋊D53—26no—
698C22⋊D53—26no—
699C22⋊D53—42no—
700C22⋊D53—42no—
701C22⋊D53—46no—
702C22⋊D53—46no—
703C22⋊D53C22×D4124yes—
704C2×Dic53—212no—
705C2×Dic53—26no—
706C2×Dic53—212no—
707C2×Dic53—212no—
708C2×Dic53—46no—
709C2×Dic53C22×D4112yes—
710C2×Dic53C2516yes—
711C2×Dic53C2511yescharacteristic
712C2×Dic53C2513yes—
713C2×Dic53C2512yes—
714C2×Dic53C2516yes—
715C2×Dic53C2511yescharacteristic
716C2×Dic53C2513yes—
717D212—22no—
718D212—26no—
719D212—26no—
720D212—26no—
721D212—212no—
722D212—26no—
723D212—22no—
724D212—42no—
725D212—46no—
726D212C22×D4112yes—
727C4×D53—212no—
728C4×D53—212no—
729C4×D53—224no—
730C4×D53—22no—
731C4×D53—26no—
732C4×D53—26no—
733C4×D53—26no—
734C4×D53—212no—
735C4×D53—212no—
736C4×D53—212no—
737C4×D53—46no—
738C4×D53—46no—
739C4×D53C22×D4112yes—
740C4×D53C22×D4112yes—
741C4×D53C22×D414yes—
742C4×D53C22×D4112yes—
743Dic106—212no—
744Dic106—26no—
745Dic106—26no—
746Dic106—22no—
747Dic106—26no—
748Dic106—212no—
749Dic106—224no—
750Dic106—26no—
751Dic106—26no—
752Dic106C22×D4112yes—
753#62859—531nomaximal, Sylow
754C22×C53—23no—
755C22×C53—23no—
756C22×C53—22no—
757C22×C53—23no—
758C22×C53—21no—
759C22×C53—22no—
760C22×C53—23no—
761C22×C53—21no—
762C22×C53—22no—
763C22×C53—23no—
764C22×C53—21no—
765C22×C53—86no—
766C22×C53C23×D416yes—
767C22×C53C2611yescharacteristic
768C2×D53—23no—
769C2×D53—23no—
770C2×D53—21no—
771C2×D53—21no—
772C2×D53—22no—
773C2×D53—21no—
774C2×D53—23no—
775C2×D53—22no—
776C2×D53—21no—
777C2×D53—23no—
778C2×D53—22no—
779C2×D53—23no—
780C2×D53—21no—
781C2×D53—412no—
782C2×D53—48no—
783C2×D53—812no—
784C2×D53—86no—
785C2×D53C23×D412yes—
786C2×D53C23×D416yes—
787C4×C53—21no—
788C4×C53—26no—
789C4×C53—23no—
790C4×C53—22no—
791C4×C53—26no—
792C4×C53C23×D416yes—
793C4×C53C23×D412yes—
794Dic53—26no—
795Dic53—23no—
796Dic53—21no—
797Dic53—22no—
798Dic53—26no—
799Dic53C23×D412yes—
800Dic53C23×D416yes—
801C2×#585—531no—
802C22×2−1+4—531no—
803#3500—532no—
804#3500—536no—
805#3499—532no—
806#3499—536no—
807#3489—531no—
808#3489—531no—
809#3489—533no—
810#3489—533no—
811#3489—533no—
812#3489—533no—
813#3489—531no—
814#3489D5311yescharacteristic, complemented
815#3486—532no—
816#3486—532no—
817#3485—536no—
818#3485—536no—
819#3449—533no—
820#3449—533no—
821C2×#536—533no—
822C2×#536—533no—
823#3428—531no—
824C2×C53—26no—
825C2×C53—42no—
826C2×C53—43no—
827C2×C53—41no—
828C2×C53C24×D411yescharacteristic
829C2×C532−1+611yescharacteristic
830C2×C532−1+611yescharacteristic
831D53—22no—
832D53—26no—
833D53—42no—
834D53—43no—
835D53—41no—
836#585—10616no—
837C2×2−1+4—533no—
838C2×2−1+4—531no—
839C2×2−1+4—536no—
840C2×2−1+4—531no—
841C2×2−1+4—533no—
842C2×2−1+4—533no—
843C2×2−1+4—532no—
844C2×2−1+4—531no—
845C2×2−1+4—531no—
846C2×2−1+4—10616no—
847C2×2−1+4C2×D5311yescharacteristic, complemented
848C2×H(5,𝔽2)—533no—
849C2×H(5,𝔽2)—531no—
850C2×H(5,𝔽2)—533no—
851C2×H(5,𝔽2)—533no—
852C22×#41—531no—
853C22×#41—533no—
854C22×#41—536no—
855C22×#41—533no—
856C22×#41—533no—
857C22×#41—531no—
858C22×#41—533no—
859C22×#41—533no—
860C22×#41C2×D5311yescharacteristic, complemented
861C23×Q8—533no—
862C23×Q8—532no—
863D4×Q8—532no—
864D4×Q8—532no—
865D4×Q8—536no—
866D4×Q8—536no—
867D4×Q8—536no—
868D4×Q8—532no—
869D4×Q8—536no—
870D4×Q8C2×D5312yescomplemented
871#548—532no—
872#548—532no—
873#548—536no—
874#548—536no—
875#548—536no—
876#548—532no—
877#548—536no—
878#548C2×D5312yescomplemented
879#547—536no—
880#547—536no—
881#547—536no—
882#547—5312no—
883#547—5312no—
884#547—536no—
885#547—536no—
886#547—5312no—
887#547—536no—
888#547—536no—
889#547—5312no—
890#547C2×D5316yescomplemented
891#546—536no—
892#546—536no—
893#546—536no—
894#546—5312no—
895#546—536no—
896#546—536no—
897#546—5312no—
898#546—5312no—
899#546—536no—
900#546—536no—
901#546—5312no—
902#546C2×D5316yescomplemented
903#537—533no—
904#537—533no—
905#537—533no—
906#537—533no—
907#537—533no—
908#537—533no—
909#537—533no—
910#537C2×D5313yescomplemented
911#536—533no—
912#536—533no—
913#536—536no—
914#536—536no—
915#536—5312no—
916#536—536no—
917#536—533no—
918#536—536no—
919#536—533no—
920#536—536no—
921#536—536no—
922#536—536no—
923#536—536no—
924#536—536no—
925#536—536no—
926#536—536no—
927#536—533no—
928#536C2×D5313yescomplemented
929#535—533no—
930#535—531no—
931#535—536no—
932#535—536no—
933#534—536no—
934#534—5312no—
935#534—536no—
936#532—5312no—
937#532—536no—
938#532—536no—
939C2×C4⋊Q8—536no—
940C2×C4⋊Q8—536no—
941C2×#124—536no—
942C2×#124—536no—
943#525—533no—
944#525—533no—
945#525—536no—
946#525—536no—
947#525—536no—
948#525—536no—
949#525—536no—
950#525—536no—
951#525—533no—
952#525C2×D5313yescomplemented
953C2×#123—5312no—
954C2×#123—536no—
955C2×#123—536no—
956C2×C22⋊Q8—533no—
957C2×C22⋊Q8—533no—
958C2×C22⋊Q8—536no—
959C2×C22⋊Q8—536no—
960C2×C22⋊Q8—533no—
961C2×C22⋊Q8C2×D5313yescomplemented
962#520—531no—
963#520—533no—
964#520—533no—
965#520C2×D5311yescharacteristic, complemented
966#519—532no—
967#518—536no—
968C4×#41—532no—
969C4×#41—536no—
970C2×#117—533no—
971C2×#117—533no—
972C53#6285911yescharacteristic, complemented, Sylow
9732−1+4—28no—
9742−1+4—1068no—
9752−1+4—10616no—
9762−1+4—10624no—
9772−1+4—1068no—
9782−1+4—1068no—
9792−1+4—10648no—
9802−1+4—10624no—
9812−1+4—10624no—
9822−1+4—1068no—
983H(5,𝔽2)—10624no—
984H(5,𝔽2)—10624no—
985H(5,𝔽2)—10624no—
986H(5,𝔽2)—1068no—
987C2×#41—28no—
988C2×#41—5316no—
989C2×#41—531no—
990C2×#41—533no—
991C2×#41—533no—
992C2×#41—536no—
993C2×#41—533no—
994C2×#41—531no—
995C2×#41—533no—
996C2×#41—533no—
997C2×#41—533no—
998C2×#41—536no—
999C2×#41—536no—
1000C2×#41—536no—
1001C2×#41—5312no—
1002C2×#41—533no—
1003C2×#41—536no—
1004C2×#41—533no—
1005C2×#41—533no—
1006C2×#41—533no—
1007C2×#41—533no—
1008C2×#41—533no—
1009C2×#41—536no—
1010C2×#41—533no—
1011C2×#41—533no—
1012C2×#41—533no—
1013C2×#41—531no—
1014C2×#41—533no—
1015C2×#41—533no—
1016C2×#41—533no—
1017C2×#41—536no—
1018C2×#41—5312no—
1019C2×#41—533no—
1020C2×#41—536no—
1021C2×#41—533no—
1022C2×#41—10624no—
1023C2×#41—10624no—
1024C2×#41—10624no—
1025C2×#41—10624no—
1026C2×#41—10648no—
1027C2×#41—10624no—
1028C2×#41—1068no—
1029C2×#41C22×D5313yes—
1030C2×#41C22×D5313yes—
1031C2×#41C22×D5316yes—
1032C2×#41C22×D5313yes—
1033C2×#41C22×D5311yescharacteristic
1034C2×#41C22×D5311yescharacteristic
1035C22×Q8—531no—
1036C22×Q8—536no—
1037C22×Q8—536no—
1038C22×Q8—533no—
1039C22×Q8—533no—
1040C22×Q8—536no—
1041C22×Q8—536no—
1042C22×Q8—532no—
1043C22×Q8—533no—
1044C22×Q8—531no—
1045C22×Q8—533no—
1046C22×Q8—536no—
1047C22×Q8—533no—
1048C22×Q8—536no—
1049C22×Q8—533no—
1050C22×Q8—10624no—
1051C22×Q8—10616no—
1052C22×Q8C22×D5313yes—
1053C22×Q8C22×D5312yes—
1054C22×Q8C22×D5311yescharacteristic
1055C22×D4—533no—
1056C22×D4—533no—
1057C22×D4—533no—
1058C22×D4—536no—
1059C22×D4—536no—
1060C22×D4—533no—
1061C22×D4—536no—
1062C22×D4—531no—
1063C22×D4—536no—
1064C22×D4—533no—
1065C22×D4—533no—
1066C22×D4—533no—
1067C22×D4—533no—
1068C22×D4C22×D5313yes—
1069C23×C4—533no—
1070C23×C4—536no—
1071C23×C4—533no—
1072C23×C4—536no—
1073C23×C4—536no—
1074C23×C4C22×D5313yes—
1075C4⋊Q8—536no—
1076C4⋊Q8—536no—
1077C4⋊Q8—536no—
1078C4⋊Q8—5312no—
1079C4⋊Q8—536no—
1080C4⋊Q8—5312no—
1081C4⋊Q8—5312no—
1082C4⋊Q8—536no—
1083C4⋊Q8C22×D5316yes—
1084#127—536no—
1085#127—532no—
1086#124—536no—
1087#124—536no—
1088#124—536no—
1089#124—5312no—
1090#124—536no—
1091#124—5312no—
1092#124—5312no—
1093#124—536no—
1094#124—532no—
1095#124—536no—
1096#124C22×D5316yes—
1097#123—5312no—
1098#123—536no—
1099#123—5312no—
1100#123—536no—
1101#123—536no—
1102#123—5312no—
1103#123—536no—
1104#123—5312no—
1105#123—5312no—
1106#123—5312no—
1107#123—536no—
1108#123—5312no—
1109#123—536no—
1110#123—5312no—
1111#123—5312no—
1112#123—5312no—
1113#123—5312no—
1114#123—536no—
1115#123C22×D53112yes—
1116#123C22×D5316yes—
1117C22⋊Q8—533no—
1118C22⋊Q8—536no—
1119C22⋊Q8—533no—
1120C22⋊Q8—536no—
1121C22⋊Q8—536no—
1122C22⋊Q8—536no—
1123C22⋊Q8—536no—
1124C22⋊Q8—533no—
1125C22⋊Q8—533no—
1126C22⋊Q8—536no—
1127C22⋊Q8—536no—
1128C22⋊Q8—536no—
1129C22⋊Q8—533no—
1130C22⋊Q8—536no—
1131C22⋊Q8—533no—
1132C22⋊Q8—5312no—
1133C22⋊Q8—5312no—
1134C22⋊Q8—536no—
1135C22⋊Q8—536no—
1136C22⋊Q8—536no—
1137C22⋊Q8—536no—
1138C22⋊Q8—536no—
1139C22⋊Q8—5312no—
1140C22⋊Q8—5312no—
1141C22⋊Q8—536no—
1142C22⋊Q8—536no—
1143C22⋊Q8C22×D5313yes—
1144C22⋊Q8C22×D5316yes—
1145C22⋊Q8C22×D5313yes—
1146C22⋊Q8C22×D5316yes—
1147C22⋊Q8C22×D5316yes—
1148C22⋊Q8C22×D5316yes—
1149#121—531no—
1150#121—533no—
1151#121—536no—
1152#121—536no—
1153#121—536no—
1154#121—536no—
1155#121—536no—
1156#121—5312no—
1157#121—5312no—
1158#121—533no—
1159#121—531no—
1160#121—536no—
1161#121—5312no—
1162#121—531no—
1163#121—533no—
1164#121—536no—
1165#121—536no—
1166#121—536no—
1167#121—536no—
1168#121—536no—
1169#121—536no—
1170#121—536no—
1171#121—536no—
1172#121—536no—
1173#121C22×D5313yes—
1174#121C22×D5316yes—
1175#121C22×D5311yescharacteristic
1176#121C22×D53112yes—
1177#120—536no—
1178#120—536no—
1179#120—532no—
1180#120—5312no—
1181#120—536no—
1182#120—536no—
1183#120—532no—
1184#120—536no—
1185#120—5312no—
1186#120C22×D5316yes—
1187C4×Q8—532no—
1188C4×Q8—536no—
1189C4×Q8—536no—
1190C4×Q8C22×D5312yes—
1191C4×D4—536no—
1192C4×D4—5312no—
1193C4×D4—5312no—
1194C4×D4—536no—
1195C4×D4—536no—
1196C4×D4—536no—
1197C4×D4—536no—
1198C4×D4—536no—
1199C4×D4—5312no—
1200C4×D4—5312no—
1201C4×D4—5312no—
1202C4×D4—5312no—
1203C4×D4—536no—
1204C4×D4—536no—
1205C4×D4—536no—
1206C4×D4C22×D5316yes—
1207C4×D4C22×D5316yes—
1208C4×D4C22×D5316yes—
1209#117—533no—
1210#117—531no—
1211#117—533no—
1212#117—536no—
1213#117—536no—
1214#117—536no—
1215#117—536no—
1216#117—536no—
1217#117C22×D5313yes—
1218C2×C4⋊C4—533no—
1219C2×C4⋊C4—536no—
1220C2×C4⋊C4—536no—
1221C2×C4⋊C4—536no—
1222C2×C4⋊C4—533no—
1223C2×C4⋊C4—533no—
1224C2×C4⋊C4—5312no—
1225C2×C4⋊C4—5312no—
1226C2×C4⋊C4C22×D5313yes—
1227C2×C4⋊C4C22×D5316yes—
1228C2×C22⋊C4—536no—
1229C2×C22⋊C4—536no—
1230C2×C22⋊C4—536no—
1231C2×C22⋊C4—536no—
1232C2×C22⋊C4—536no—
1233C2×C22⋊C4—5312no—
1234C2×C22⋊C4—5312no—
1235C2×C22⋊C4C22×D5316yes—
1236C2×C42—536no—
1237C2×C42—536no—
1238C24—533no—
1239C24—536no—
1240C24—533no—
1241C24—532no—
1242C24C23×D5313yes—
1243#41—24no—
1244#41—212no—
1245#41—224no—
1246#41—212no—
1247#41—212no—
1248#41—538no—
1249#41—5324no—
1250#41—5324no—
1251#41—1064no—
1252#41—10612no—
1253#41—10612no—
1254#41—10612no—
1255#41—10612no—
1256#41—10612no—
1257#41—10612no—
1258#41—10612no—
1259#41—10624no—
1260#41—10624no—
1261#41—10612no—
1262#41—10648no—
1263#41—10624no—
1264#41—10612no—
1265#41—10624no—
1266#41—10612no—
1267#41—10624no—
1268#41—10612no—
1269#41—10612no—
1270#41—10612no—
1271#41—10624no—
1272#41—10648no—
1273#41—10612no—
1274#41—10612no—
1275#41—10624no—
1276#41—1064no—
1277#41—10612no—
1278#41—10624no—
1279#41—10612no—
1280#41—10612no—
1281#41D4×D5318yes—
1282C2×Q8—28no—
1283C2×Q8—24no—
1284C2×Q8—212no—
1285C2×Q8—538no—
1286C2×Q8—533no—
1287C2×Q8—533no—
1288C2×Q8—5312no—
1289C2×Q8—536no—
1290C2×Q8—533no—
1291C2×Q8—533no—
1292C2×Q8—533no—
1293C2×Q8—536no—
1294C2×Q8—533no—
1295C2×Q8—531no—
1296C2×Q8—10624no—
1297C2×Q8—10612no—
1298C2×Q8—10624no—
1299C2×Q8—10612no—
1300C2×Q8—10612no—
1301C2×Q8—10624no—
1302C2×Q8—10624no—
1303C2×Q8—10624no—
1304C2×Q8—10612no—
1305C2×Q8—10624no—
1306C2×Q8—10612no—
1307C2×Q8—1068no—
1308C2×Q8—1064no—
1309C2×Q8—10612no—
1310C2×Q8C23×D5313yes—
1311C2×Q8C23×D5316yes—
1312C2×Q8C23×D5313yes—
1313C2×Q8C23×D5311yescharacteristic
1314C2×D4—212no—
1315C2×D4—536no—
1316C2×D4—5324no—
1317C2×D4—536no—
1318C2×D4—536no—
1319C2×D4—533no—
1320C2×D4—531no—
1321C2×D4—533no—
1322C2×D4—533no—
1323C2×D4—536no—
1324C2×D4—533no—
1325C2×D4—533no—
1326C2×D4—533no—
1327C2×D4—531no—
1328C2×D4—532no—
1329C2×D4—536no—
1330C2×D4—532no—
1331C2×D4—536no—
1332C2×D4—532no—
1333C2×D4—533no—
1334C2×D4—536no—
1335C2×D4—533no—
1336C2×D4—531no—
1337C2×D4—531no—
1338C2×D4—533no—
1339C2×D4—533no—
1340C2×D4—533no—
1341C2×D4—536no—
1342C2×D4—532no—
1343C2×D4—10612no—
1344C2×D4—10612no—
1345C2×D4—1064no—
1346C2×D4—10612no—
1347C2×D4—10612no—
1348C2×D4—10624no—
1349C2×D4—10612no—
1350C2×D4—10624no—
1351C2×D4—10624no—
1352C2×D4—10624no—
1353C2×D4—10612no—
1354C2×D4—10612no—
1355C2×D4C23×D5316yes—
1356C2×D4C23×D5311yescharacteristic
1357C2×D4C23×D5316yes—
1358C2×D4C23×D5313yes—
1359C2×D4C23×D5316yes—
1360C2×D4C23×D5312yes—
1361C2×D4C23×D5313yes—
1362C22×C4—212no—
1363C22×C4—533no—
1364C22×C4—5324no—
1365C22×C4—533no—
1366C22×C4—533no—
1367C22×C4—531no—
1368C22×C4—533no—
1369C22×C4—536no—
1370C22×C4—533no—
1371C22×C4—536no—
1372C22×C4—536no—
1373C22×C4—536no—
1374C22×C4—5312no—
1375C22×C4—536no—
1376C22×C4—536no—
1377C22×C4—536no—
1378C22×C4—536no—
1379C22×C4—533no—
1380C22×C4—533no—
1381C22×C4—531no—
1382C22×C4—533no—
1383C22×C4—536no—
1384C22×C4—536no—
1385C22×C4—536no—
1386C22×C4—10624no—
1387C22×C4—10624no—
1388C22×C4—10624no—
1389C22×C4—10612no—
1390C22×C4C23×D5316yes—
1391C22×C4C23×D5313yes—
1392C22×C4C23×D5316yes—
1393C22×C4C23×D5313yes—
1394C22×C4C23×D5313yes—
1395C22×C4C23×D5313yes—
1396C22×C4C23×D5311yescharacteristic
1397C22×C4C23×D5316yes—
1398C22×C4C23×D5313yes—
1399C4⋊C4—533no—
1400C4⋊C4—531no—
1401C4⋊C4—5312no—
1402C4⋊C4—536no—
1403C4⋊C4—536no—
1404C4⋊C4—536no—
1405C4⋊C4—5312no—
1406C4⋊C4—536no—
1407C4⋊C4—536no—
1408C4⋊C4—5312no—
1409C4⋊C4—536no—
1410C4⋊C4—536no—
1411C4⋊C4—536no—
1412C4⋊C4—536no—
1413C4⋊C4C23×D5311yescharacteristic
1414C4⋊C4C23×D5316yes—
1415C4⋊C4C23×D5313yes—
1416C4⋊C4C23×D53112yes—
1417C4⋊C4C23×D5316yes—
1418C4⋊C4C23×D5316yes—
1419C22⋊C4—5312no—
1420C22⋊C4—536no—
1421C22⋊C4—536no—
1422C22⋊C4—536no—
1423C22⋊C4—536no—
1424C22⋊C4—532no—
1425C22⋊C4—536no—
1426C22⋊C4—532no—
1427C22⋊C4—536no—
1428C22⋊C4—5312no—
1429C22⋊C4—536no—
1430C22⋊C4—536no—
1431C22⋊C4—5312no—
1432C22⋊C4—536no—
1433C22⋊C4—5312no—
1434C22⋊C4—536no—
1435C22⋊C4—532no—
1436C22⋊C4—536no—
1437C22⋊C4—532no—
1438C22⋊C4C23×D5316yes—
1439C22⋊C4C23×D53112yes—
1440C22⋊C4C23×D5316yes—
1441C22⋊C4C23×D5316yes—
1442C22⋊C4C23×D5316yes—
1443C22⋊C4C23×D5312yes—
1444C42—536no—
1445C42—532no—
1446C42—5312no—
1447C42—536no—
1448C42C23×D5316yes—
1449C23—26no—
1450C23—43no—
1451C23—43no—
1452C23—531no—
1453C23—533no—
1454C23—5312no—
1455C23—533no—
1456C23—531no—
1457C23—532no—
1458C23—10612no—
1459C23—1064no—
1460C23—1066no—
1461C23—2123no—
1462C23—2123no—
1463C23—2126no—
1464C23—2126no—
1465C23—2123no—
1466C23—2123no—
1467C23—2122no—
1468C23—2122no—
1469C23C24×D5313yes—
1470C23C24×D5311yescharacteristic
1471C23C24×D5312yes—
1472C23C24×D5313yes—
1473Q8—26no—
1474Q8—212no—
1475Q8—26no—
1476Q8—5312no—
1477Q8—10612no—
1478Q8—10624no—
1479Q8—1062no—
1480Q8—1066no—
1481Q8—1066no—
1482Q8—1066no—
1483Q8—1066no—
1484Q8—10612no—
1485Q8—1066no—
1486Q8C2×D4×D5314yes—
1487D4—212no—
1488D4—212no—
1489D4—26no—
1490D4—22no—
1491D4—42no—
1492D4—46no—
1493D4—5324no—
1494D4—5312no—
1495D4—1062no—
1496D4—1066no—
1497D4—1066no—
1498D4—1066no—
1499D4—10612no—
1500D4—1062no—
1501D4—1066no—
1502D4—1066no—
1503D4—1066no—
1504D4—1064no—
1505D4—1062no—
1506D4—1066no—
1507D4—1066no—
1508D4—1066no—
1509D4—10612no—
1510D4—10612no—
1511D4—10612no—
1512D4—1066no—
1513D4—1062no—
1514D4—2122no—
1515D4—2126no—
1516D4—2126no—
1517D4—2126no—
1518D4—2122no—
1519D4—2122no—
1520D4C2×D4×D53112yes—
1521C2×C4—26no—
1522C2×C4—212no—
1523C2×C4—22no—
1524C2×C4—26no—
1525C2×C4—26no—
1526C2×C4—26no—
1527C2×C4—212no—
1528C2×C4—46no—
1529C2×C4—5312no—
1530C2×C4—531no—
1531C2×C4—533no—
1532C2×C4—534no—
1533C2×C4—5312no—
1534C2×C4—5312no—
1535C2×C4—5312no—
1536C2×C4—536no—
1537C2×C4—532no—
1538C2×C4—536no—
1539C2×C4—531no—
1540C2×C4—533no—
1541C2×C4—10612no—
1542C2×C4—10612no—
1543C2×C4—10612no—
1544C2×C4—10612no—
1545C2×C4—10624no—
1546C2×C4—10612no—
1547C2×C4—10612no—
1548C2×C4—1066no—
1549C2×C4—10612no—
1550C2×C4—1066no—
1551C2×C4—1062no—
1552C2×C4—1066no—
1553C2×C4—1066no—
1554C2×C4—10612no—
1555C2×C4—2126no—
1556C2×C4—2126no—
1557C2×C4—2126no—
1558C2×C4C2×D4×D53112yes—
1559C2×C4C24×D5316yes—
1560C2×C4C24×D5312yes—
1561C2×C4C24×D5316yes—
1562C2×C4C24×D5313yes—
1563C2×C4C24×D5311yescharacteristic
1564C2×C4C24×D5313yes—
1565C2×C4C24×D5311yescharacteristic
1566C22—23no—
1567C22—23no—
1568C22—21no—
1569C22—22no—
1570C22—23no—
1571C22—21no—
1572C22—22no—
1573C22—23no—
1574C22—22no—
1575C22—23no—
1576C22—21no—
1577C22—86no—
1578C22—532no—
1579C22—536no—
1580C22—1063no—
1581C22—1061no—
1582C22—1063no—
1583C22—1061no—
1584C22—1062no—
1585C22—1063no—
1586C22—1061no—
1587C22—1062no—
1588C22—1061no—
1589C22—1063no—
1590C22—1062no—
1591C22—1063no—
1592C22—1061no—
1593C22—4246no—
1594C22—42412no—
1595C22—21212no—
1596C22—2128no—
1597C22C22×D4×D5316yes—
1598C22C25×D5311yescharacteristic
1599C4—21no—
1600C4—23no—
1601C4—26no—
1602C4—22no—
1603C4—26no—
1604C4—532no—
1605C4—536no—
1606C4—1063no—
1607C4—1061no—
1608C4—1066no—
1609C4—1066no—
1610C4—1062no—
1611C4C22×D4×D5312yes—
1612C4C22×D4×D5316yes—
1613C2—26no—
1614C2—41no—
1615C2—43no—
1616C2—42no—
1617C2—1066no—
1618C2—1062no—
1619C2—2121no—
1620C2—2123no—
1621C2—2122no—
1622C2C23×D4×D5311yescharacteristic
1623C2#2028952711yescharacteristic
1624C2#2028952811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3489C2
hypercenter#3489D53
hypocenterC53#62859
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3489

Complements

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

NH ≅ G/Ntype
1. C2×#16811459C2semidirect
2. C2×2−1+4×D53C2semidirect
3. #20288506C2semidirect
4. #20288501C2semidirect
5. #20288499C2semidirect
6. #20288494C2semidirect
7. #20288396C2semidirect
8. #20288395C2semidirect
9. #20288393C2semidirect
10. #20288391C2semidirect
11. #20288390C2semidirect
12. #20288388C2semidirect
13. #20288387C2semidirect
14. #20288365C2semidirect
15. #20288361C2semidirect
16. #20288354C2semidirect
17. #20288352C2semidirect
18. #20288045C2semidirect
19. #20288043C2semidirect
20. C2×#16811196C2semidirect
21. #536×D53C2semidirect
22. #20287915C2semidirect
23. C53×#3489C2semidirect
26. C2×#13133265C22semidirect
27. C2×#13133265C22semidirect
28. C2×#13133265C22semidirect
30. C2×#13133264C22semidirect
31. C2×#13133264C22semidirect
32. C2×#13133264C22semidirect
33. C2×#13133264C22semidirect
36. C2×#13133263C22semidirect
38. C2×#13133262C22semidirect
40. C22×#11719945C22semidirect
43. C2×#41×D53C22semidirect
44. C2×#41×D53C22semidirect
45. C2×#41×D53C22semidirect
46. C2×#41×D53C22semidirect
47. C22×Q8×D53C22semidirect
48. C22×Q8×D53C22semidirect
49. Q8×D212C22semidirect
50. D4×Dic106C22semidirect
51. #16811288C22semidirect
52. Q8×C22⋊D53C22semidirect
53. Q8×C22⋊D53C22semidirect
54. #16811286C22semidirect
55. #16811286C22semidirect
56. #16811285C22semidirect
57. #16811284C22semidirect
58. #16811283C22semidirect
59. #16811282C22semidirect
60. #16811281C22semidirect
61. #16811280C22semidirect
62. #16811279C22semidirect
63. #16811278C22semidirect
64. #16811277C22semidirect
65. #16811276C22semidirect
66. #16811275C22semidirect
67. #16811275C22semidirect
68. #16811274C22semidirect
69. #16811273C22semidirect
70. #16811272C22semidirect
71. #16811272C22semidirect
72. #16811271C22semidirect
73. #16811271C22semidirect
74. #16811270C22semidirect
75. #16811269C22semidirect
76. #16811268C22semidirect
77. #16811267C22semidirect
78. #16811266C22semidirect
79. #16811265C22semidirect
80. #16811264C22semidirect
81. #16811263C22semidirect
82. #16811262C22semidirect
83. #16811261C22semidirect
84. #16811260C22semidirect
85. #16811204C22semidirect
86. #16811203C22semidirect
87. #16811203C22semidirect
88. #16811202C22semidirect
89. #16811202C22semidirect
90. #16811201C22semidirect
91. #16811201C22semidirect
92. #16811199C22semidirect
93. #16811198C22semidirect
94. #16811197C22semidirect
95. #16811196C22semidirect
96. #16811196C22semidirect
97. #16811196C22semidirect
98. #16811196C22semidirect
99. #16811196C22semidirect
100. #16811196C22semidirect
101. #16811196C22semidirect
102. #16811196C22semidirect
103. #16811196C22semidirect
104. #16811196C22semidirect
105. #16811195C22semidirect
106. #16811195C22semidirect
107. #16811194C22semidirect
108. #16811193C22semidirect
109. #16811189C22semidirect
110. #16811189C22semidirect
111. #16811189C22semidirect
112. #16811188C22semidirect
113. #16811184C22semidirect
114. #16811183C22semidirect
115. #16811181C22semidirect
116. #16811170C22semidirect
117. #16811170C22semidirect
118. #16811168C22semidirect
119. C2×#13133216C22semidirect
120. C4⋊Q8×D53C22semidirect
121. C2×#13133203C22semidirect
122. #124×D53C22semidirect
123. #16811136C22semidirect
124. #16811136C22semidirect
125. #16811135C22semidirect
126. #16811134C22semidirect
127. #16811133C22semidirect
128. #16811133C22semidirect
129. #16811132C22semidirect
130. #16811132C22semidirect
131. #16811130C22semidirect
132. C2×#13133202C22semidirect
133. C2×#13133199C22semidirect
134. #123×D53C22semidirect
135. C2×#13133197C22semidirect
136. C2×#13133196C22semidirect
137. C2×#13133193C22semidirect
138. C22⋊Q8×D53C22semidirect
139. C22⋊Q8×D53C22semidirect
140. #16811106C22semidirect
141. #16811104C22semidirect
142. #16811103C22semidirect
143. #16811099C22semidirect
144. #16811095C22semidirect
145. C4×#11719949C22semidirect
146. C4×#11719947C22semidirect
147. C2×#13133175C22semidirect
148. #117×D53C22semidirect
149. C2×2−1+4×C53C22semidirect
150. C22×#41×C53C22semidirect
151. D4×Q8×C53C22semidirect
152. C53×#548C22semidirect
153. C53×#547C22semidirect
154. C53×#546C22semidirect
155. C53×#537C22semidirect
156. C53×#536C22semidirect
157. C53×#525C22semidirect
158. C2×C22⋊Q8×C53C22semidirect
159. C53×#520C22semidirect
213. #41×D53D4semidirect
814. #3489D53semidirect
847. C2×2−1+4C2×D53semidirect
860. C22×#41C2×D53semidirect
870. D4×Q8C2×D53semidirect
878. #548C2×D53semidirect
890. #547C2×D53semidirect
902. #546C2×D53semidirect
910. #537C2×D53semidirect
928. #536C2×D53semidirect
952. #525C2×D53semidirect
961. C2×C22⋊Q8C2×D53semidirect
965. #520C2×D53semidirect
972. C53#62859semidirect

Maximal subgroups

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

subgroupindex
C2×#168114592
C2×2−1+4×D532
#202885062
#202885012
#202884992
#202884942
#202883962
#202883952
#202883932
#202883912
#202883902
#202883882
#202883872
#202883652
#202883612
#202883542
#202883522
#202880452
#202880432
C2×#168111962
#536×D532
#202879152
C53×#34892
#6285953