Finite Group Databasebeta

← #28293023

Subgroups — #28293023

Order 13568.

7254 conjugacy classes of subgroups.

The subgroup lattice has 1724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289308C214yesmaximal, complemented
2#20289297C214yesmaximal, complemented
3#20289181C214yesmaximal, complemented
4#20289082C214yesmaximal, complemented
5#20289026C218yesmaximal, complemented
6#20288720C214yesmaximal, complemented
7#20288673C214yesmaximal, complemented
8#20288647C218yesmaximal, complemented
9#20288625C214yesmaximal, complemented
10#20288614C211yesmaximal, characteristic, complemented
11#20288606C211yesmaximal, characteristic, complemented
12#20288600C211yesmaximal, characteristic, complemented
13#20288586C211yesmaximal, characteristic, complemented
14#20288583C214yesmaximal, complemented
15#20288504C211yesmaximal, characteristic, complemented
16#20288503C211yesmaximal, characteristic, complemented
17#20288497C211yesmaximal, characteristic, complemented
18#20288489C211yesmaximal, characteristic, complemented
19#20288373C211yesmaximal, characteristic, complemented
20#20288369C211yesmaximal, characteristic, complemented
21#20288357C211yesmaximal, characteristic, complemented
22#20288007C211yesmaximal, characteristic, complemented
23#20288007C211yesmaximal, characteristic, complemented
24C2×#16811169C211yesmaximal, characteristic, complemented
25C53×#3485C211yesmaximal, characteristic, complemented
26C2×#13133265C2211yescharacteristic, complemented
27C2×#13133264C2211yescharacteristic, complemented
28C2×#13133263C2211yescharacteristic
29C22×#11719945C2211yescharacteristic, complemented
30#16811370C2218yescomplemented
31#16811368C2218yescomplemented
32#16811362C2218yescomplemented
33#16811361C2218yescomplemented
34#16811357C2218yescomplemented
35#16811356C2214yescomplemented
36#16811356C2214yescomplemented
37#16811355C2214yescomplemented
38#16811348C2214yescomplemented
39#16811347C2214yescomplemented
40#16811343C2214yescomplemented
41#16811342C2214yescomplemented
42#16811337C2218yescomplemented
43#16811328C2218yescomplemented
44#16811321C2218yescomplemented
45#16811318C2218yescomplemented
46#16811318C2218yescomplemented
47#16811318C2218yescomplemented
48#16811310C2218yescomplemented
49#16811301C2218yescomplemented
50#16811299C2218yescomplemented
51#16811299C2218yescomplemented
52#16811296C2218yescomplemented
53#16811294C2214yescomplemented
54#16811294C2214yescomplemented
55#16811292C2214yescomplemented
56#16811292C2214yescomplemented
57#16811292C2214yescomplemented
58#16811291C2218yescomplemented
59#16811291C2214yescomplemented
60#16811286C2214yescomplemented
61#16811283C2214yescomplemented
62#16811283C2214yescomplemented
63#16811282C2214yescomplemented
64#16811280C2214yescomplemented
65#16811280C2214yescomplemented
66#16811280C2214yescomplemented
67#16811278C2214yescomplemented
68#16811275C2214yescomplemented
69#16811275C2214yescomplemented
70#16811271C2218yescomplemented
71#16811270C2214yescomplemented
72#16811269C2214yescomplemented
73#16811267C2218yescomplemented
74#16811267C2214yescomplemented
75#16811265C2218yescomplemented
76#16811264C2214yescomplemented
77#16811263C2218yescomplemented
78#16811263C2218yescomplemented
79#16811260C2218yescomplemented
80D4×C22⋊D53C2218yes—
81D4×C22⋊D53C2214yescomplemented
82#16811246C2214yescomplemented
83#16811241C2218yescomplemented
84#16811241C2218yescomplemented
85#16811238C2214yescomplemented
86#16811233C2214yescomplemented
87#16811226C2218yescomplemented
88#16811225C2218yescomplemented
89#16811225C2218yescomplemented
90#16811224C2214yescomplemented
91#16811223C2218yescomplemented
92#16811220C2218yescomplemented
93#16811216C2218yescomplemented
94#16811211C2218yescomplemented
95#16811209C2218yescomplemented
96#16811208C2218yescomplemented
97#16811205C2218yescomplemented
98#16811202C2218yescomplemented
99#16811199C2211yescharacteristic, complemented
100#16811198C2212yescomplemented
101#16811198C2212yescomplemented
102#16811194C2211yescharacteristic
103#16811194C2212yescomplemented
104#16811193C2212yescomplemented
105#16811192C2211yescharacteristic, complemented
106#16811191C2212yescomplemented
107#16811190C2211yescharacteristic
108#16811190C2214yescomplemented
109#16811190C2212yescomplemented
110#16811190C2212yescomplemented
111#16811190C2211yescharacteristic, complemented
112#16811188C2214yescomplemented
113#16811188C2218yescomplemented
114#16811187C2211yescharacteristic
115#16811187C2212yescomplemented
116#16811183C2214yescomplemented
117#16811176C2211yescharacteristic, complemented
118#16811176C2211yescharacteristic, complemented
119#16811175C2212yescomplemented
120#16811175C2212yescomplemented
121#16811175C2214yescomplemented
122#16811174C2212yescomplemented
123#16811172C2212yescomplemented
124#16811170C2214yescomplemented
125#16811169C2211yescharacteristic
126#16811169C2211yescharacteristic
127#16811169C2214yescomplemented
128#16811169C2214yescomplemented
129#16811169C2214yescomplemented
130#16811169C2212yescomplemented
131#16811169C2214yescomplemented
132#16811169C2212yescomplemented
133#16811168C2212yescomplemented
134#16811168C2212yescomplemented
135C2×#13133215C2211yescharacteristic, complemented
136C4⋊Q8×D53C2212yescomplemented
137C2×#13133213C2211yescharacteristic
138C2×#13133213C2212yescomplemented
139#16811159C2212yescomplemented
140#16811159C2212yescomplemented
141#16811159C2214yescomplemented
142#16811155C2214yescomplemented
143#16811154C2212yescomplemented
144#16811154C2212yescomplemented
145#16811153C2214yescomplemented
146#16811153C2214yescomplemented
147#16811150C2214yescomplemented
148#16811150C2214yescomplemented
149C2×#13133206C2211yescharacteristic, complemented
150C2×#13133204C2211yescharacteristic, complemented
151C2×#13133204C2212yescomplemented
152#124×D53C2212yescomplemented
153#16811134C2211yescharacteristic, complemented
154#16811134C2211yescharacteristic, complemented
155#16811134C2214yescomplemented
156#16811131C2214yescomplemented
157#16811129C2214yescomplemented
158#16811129C2214yescomplemented
159#123×D53C2214yescomplemented
160C2×#13133189C2214yescomplemented
161#16811104C2218yescomplemented
162#16811101C2211yescharacteristic, complemented
163#16811100C2211yescharacteristic, complemented
164#16811097C2211yescharacteristic, complemented
165#16811096C2218yescomplemented
166#41×Dic53C2211yescharacteristic
167#41×Dic53C2211yescharacteristic, complemented
168#16811091C2211yescharacteristic, complemented
169#16811091C2211yescharacteristic, complemented
170C4×#11719947C2214yescomplemented
171C4×#11719947C2214yescomplemented
172C2×C4×C22⋊D53C2214yescomplemented
173C22×C4×Dic53C2211yescharacteristic, complemented
174C2×H(5,𝔽2)×C53C2211yescharacteristic
175C22×#41×C53C2211yescharacteristic, complemented
176C53×#547C2214yescomplemented
177C53×#547C2214yescomplemented
178C53×#546C2214yescomplemented
179C53×#546C2214yescomplemented
180C53×#536C2211yescharacteristic
181C53×#536C2211yescharacteristic, complemented
182C53×#534C2214yescomplemented
183C53×#525C2211yescharacteristic
184C53×#525C2211yescharacteristic, complemented
185C2×#123×C53C2214yescomplemented
186C53×#518C2211yescharacteristic, complemented
187#13133265—44no—
188#13133264—44no—
189#13133263—44no—
190C2×#11719949C2312yes—
191C2×#11719949C2312yes—
192C2×#11719949C2312yes—
193C2×#11719945—44no—
194C2×#11719945C2311yescharacteristic
195C2×#11719945C2311yescharacteristic
196C2×#11719945C2314yes—
197C2×#11719945C2314yes—
198C2×#11719945C2314yes—
199C2×#11719945C2312yes—
200C2×#11719945C2312yes—
201C2×#11719945C2318yes—
202C2×#11719947C2314yes—
203C2×#11719947C2312yes—
204C2×#11719947C2314yes—
205C2×#11719947C2314yes—
206C22×Dic106C2311yescharacteristic
207C22×Dic106C2312yes—
208C2×Q8×D53C2312yes—
209C2×Q8×D53C2312yes—
210C2×Q8×D53C2312yes—
211C22×D212C2311yescharacteristic
212C22×D212C2312yes—
213C22×C22⋊D53C2314yes—
214C22×C22⋊D53C2318yes—
215C22×C22⋊D53C2312yes—
216C2×D4×D53C2314yes—
217C2×D4×D53C2312yes—
218C23×Dic53C2312yes—
219C22×C4×D53C2312yes—
220#13133217C2312yes—
221#13133216C2318yes—
222#13133216C2312yes—
223#13133216C2312yes—
224#13133215C2312yes—
225#13133215C2314yes—
226#13133215C2311yescharacteristic
227#13133215C2312yes—
228#13133215C2312yes—
229#13133215C2311yescharacteristic
230#13133214C2312yes—
231#13133213C2318yes—
232#13133213C2312yes—
233#13133213C2318yes—
234#13133213C2318yes—
235#13133213C2312yes—
236#13133213C2312yes—
237#13133213C2314yes—
238#13133213C2312yes—
239#13133213C2312yes—
240#13133213C2311yescharacteristic
241#13133213C2311yescharacteristic
242#13133212C2318yes—
243#13133212C2318yes—
244#13133212C2314yes—
245#13133212C2314yes—
246#13133210C2314yes—
247#13133210C2318yes—
248#13133210C2318yes—
249#13133210C2318yes—
250#13133210C2318yes—
251#13133210C2314yes—
252#13133208C2318yes—
253#13133208C2312yes—
254#13133208C2312yes—
255#13133207C2318yes—
256#13133207C2318yes—
257#13133207C2314yes—
258#13133207C2314yes—
259#13133206C2314yes—
260#13133206C2312yes—
261#13133206C2312yes—
262#13133206C2312yes—
263#13133206C2311yescharacteristic
264#13133206C2311yescharacteristic
265#13133205C2312yes—
266#13133205C2312yes—
267#13133204C2318yes—
268#13133204C2314yes—
269#13133204C2312yes—
270#13133204C2318yes—
271#13133204C2312yes—
272#13133204C2312yes—
273#13133204C2311yescharacteristic
274#13133204C2312yes—
275#13133204C2312yes—
276#13133204C2311yescharacteristic
277#13133203C2318yes—
278#13133203C2318yes—
279#13133203C2318yes—
280#13133203C2318yes—
281#13133203C2318yes—
282#13133203C2314yes—
283#13133203C2314yes—
284#13133202C2318yes—
285#13133202C2318yes—
286#13133202C2318yes—
287#13133201C2314yes—
288#13133201C2318yes—
289#13133201C2314yes—
290#13133201C2314yes—
291#13133200C2318yes—
292#13133200C2318yes—
293#13133200C2312yes—
294#13133200C2312yes—
295#13133199C2318yes—
296#13133199C2318yes—
297#13133199C2318yes—
298#13133199C2318yes—
299#13133199C2318yes—
300#13133199C2318yes—
301#13133198C2314yes—
302#13133198C2318yes—
303#13133198C2314yes—
304#13133198C2314yes—
305#13133197C2314yes—
306#13133197C2318yes—
307#13133196C2314yes—
308#13133196C2318yes—
309#13133196C2312yes—
310#13133196C2312yes—
311#13133196C2318yes—
312#13133196C2318yes—
313#13133195C2318yes—
314#13133195C2318yes—
315#13133195C2318yes—
316#13133194C2318yes—
317#13133194C2314yes—
318#13133194C2314yes—
319#13133194C2318yes—
320#13133194C2314yes—
321#13133194C2314yes—
322#13133192C2318yes—
323#13133192C2314yes—
324#13133191C2312yes—
325#13133191C2314yes—
326#13133191C2312yes—
327#13133191C2318yes—
328#13133191C2318yes—
329#13133191C2318yes—
330#13133190C2318yes—
331#13133190C2318yes—
332#13133190C2318yes—
333#13133190C2318yes—
334#13133190C2318yes—
335#13133190C2318yes—
336#13133190C2318yes—
337#13133189C2314yes—
338#13133189C2318yes—
339#13133189C2314yes—
340#13133189C2318yes—
341#13133189C2318yes—
342#13133189C2318yes—
343#13133189C2314yes—
344#13133189C2318yes—
345#13133189C2318yes—
346#13133189C2318yes—
347#13133189C2314yes—
348#13133188C2314yes—
349#13133188C2318yes—
350#13133188C2318yes—
351#13133188C2314yes—
352#13133188C2318yes—
353#13133188C2318yes—
354#13133188C2318yes—
355#13133187C2318yes—
356#13133187C2314yes—
357#13133186C2318yes—
358#13133186C2314yes—
359#13133186C2314yes—
360#13133186C2318yes—
361#13133186C2312yes—
362#13133186C2312yes—
363#13133185C2318yes—
364#13133185C2314yes—
365#13133185C2318yes—
366Q8×Dic53C2312yes—
367Q8×Dic53C2314yes—
368Q8×Dic53C2314yes—
369Q8×Dic53C2312yes—
370C4×Dic106C2314yes—
371C4×Dic106C2314yes—
372C4×Dic106C2314yes—
373#13133182C2312yes—
374#13133182C2314yes—
375#13133182C2312yes—
376#13133182C2318yes—
377#13133182C2314yes—
378#13133182C2314yes—
379C4×D212C2314yes—
380D4×Dic53C2314yes—
381D4×Dic53C2312yes—
382D4×Dic53C2314yes—
383D4×Dic53C2314yes—
384D4×Dic53C2312yes—
385D4×Dic53C2314yes—
386#13133179C2312yes—
387#13133179C2318yes—
388#13133179C2314yes—
389#13133179C2312yes—
390#13133179C2318yes—
391C4×C22⋊D53C2314yes—
392C4×C22⋊D53C2318yes—
393C4×C22⋊D53C2314yes—
394C4×C22⋊D53C2314yes—
395C4×C22⋊D53C2314yes—
396C4×C22⋊D53C2318yes—
397C4×C22⋊D53C2318yes—
398C4×C22⋊D53C2318yes—
399C4×C22⋊D53C2318yes—
400C4×C22⋊D53C2318yes—
401C4×C22⋊D53C2318yes—
402C4×C22⋊D53C2318yes—
403C4×C22⋊D53C2318yes—
404C4×C22⋊D53C2318yes—
405#13133177C2314yes—
406#13133177C2314yes—
407#13133177C2318yes—
408#13133177C2318yes—
409#13133177C2314yes—
410#13133177C2318yes—
411#13133177C2314yes—
412#13133177C2314yes—
413#13133177C2314yes—
414#13133176C2314yes—
415#13133176C2318yes—
416#13133176C2311yescharacteristic
417#13133176C2312yes—
418#13133176C2311yescharacteristic
419#13133176C2312yes—
420#13133175C2318yes—
421#13133175C2314yes—
422#13133175C2314yes—
423#13133174C2312yes—
424#13133174C2312yes—
425#13133173C2314yes—
426#13133173C2314yes—
427#13133173C2318yes—
428#13133173C2314yes—
429#13133173C2314yes—
430#13133173C2314yes—
431C2×#11719919C2314yes—
432C4⋊C4×D53C2318yes—
433C4⋊C4×D53C2318yes—
434C2×C22⋊Dic53C2314yes—
435C2×C22⋊Dic53C2318yes—
436C2×#11719921C2314yes—
437C22⋊C4×D53C2318yes—
438C22⋊C4×D53C2318yes—
439C22⋊C4×D53C2314yes—
440C2×C4×Dic53C2312yes—
441C2×C4×Dic53C2312yes—
442C2×C4×Dic53C2312yes—
443C2×C4×Dic53C2311yescharacteristic
444C2×C4×Dic53C2311yescharacteristic
445C2×C4×Dic53C2312yes—
446C2×C4×Dic53C2312yes—
447C2×C4×Dic53C2312yes—
448C2×C4×Dic53C2312yes—
449C42×D53C2312yes—
450C42×D53C2312yes—
451H(5,𝔽2)×C53—44no—
452C2×#41×C53—44no—
453C2×#41×C53C2311yescharacteristic
454C2×#41×C53C2311yescharacteristic
455C2×#41×C53C2312yes—
456C2×#41×C53C2314yes—
457C2×#41×C53C2314yes—
458C2×#41×C53C2312yes—
459C22×Q8×C53C2311yescharacteristic
460C22×D4×C53C2311yescharacteristic
461C22×D4×C53C2314yes—
462C22×D4×C53C2312yes—
463C22×D4×C53C2312yes—
464C22×D4×C53C2312yes—
465C23×C4×C53C2311yescharacteristic
466C23×C4×C53C2312yes—
467C4⋊Q8×C53C2312yes—
468C4⋊Q8×C53C2312yes—
469#124×C53C2312yes—
470#124×C53C2312yes—
471#123×C53C2314yes—
472#123×C53C2314yes—
473#123×C53C2318yes—
474#123×C53C2312yes—
475#123×C53C2312yes—
476#123×C53C2318yes—
477#123×C53C2318yes—
478C22⋊Q8×C53C2314yes—
479C22⋊Q8×C53C2312yes—
480C22⋊Q8×C53C2314yes—
481C22⋊Q8×C53C2312yes—
482#121×C53C2312yes—
483#121×C53C2312yes—
484#121×C53C2318yes—
485#121×C53C2318yes—
486#120×C53C2312yes—
487#120×C53C2312yes—
488#120×C53C2318yes—
489C4×D4×C53C2314yes—
490C4×D4×C53C2314yes—
491C4×D4×C53C2314yes—
492C4×D4×C53C2314yes—
493#117×C53C2311yescharacteristic
494#117×C53C2311yescharacteristic
495C2×C4⋊C4×C53C2318yes—
496C2×C22⋊C4×C53C2314yes—
497C2×C22⋊C4×C53C2318yes—
498C24×C53C2412yes—
499C24×C53C2411yescharacteristic
500C24×C53C2414yes—
501C23×D53C2412yes—
502C23×D53C2414yes—
503#41×C53—24no—
504#41×C53—24no—
505#41×C53—48no—
506#41×C53—48no—
507#41×C53—44no—
508#41×C53—44no—
509C2×Q8×C53—24no—
510C2×Q8×C53C2412yes—
511C2×Q8×C53C2412yes—
512C2×Q8×C53C2411yescharacteristic
513C2×Q8×C53C2411yescharacteristic
514C2×D4×C53—24no—
515C2×D4×C53—44no—
516C2×D4×C53—44no—
517C2×D4×C53—44no—
518C2×D4×C53—48no—
519C2×D4×C53C2412yes—
520C2×D4×C53C2412yes—
521C2×D4×C53C2412yes—
522C2×D4×C53C2412yes—
523C2×D4×C53C2411yescharacteristic
524C2×D4×C53C2411yescharacteristic
525C2×D4×C53C2414yes—
526C2×D4×C53C2414yes—
527C2×D4×C53C2418yes—
528C2×D4×C53C2414yes—
529C2×D4×C53C2414yes—
530C22×C4×C53—24no—
531C22×C4×C53—44no—
532C22×C4×C53C2412yes—
533C22×C4×C53C2412yes—
534C22×C4×C53C2412yes—
535C22×C4×C53C2412yes—
536C22×C4×C53C2411yescharacteristic
537C22×C4×C53C2412yes—
538C22×C4×C53C2418yes—
539C22×C4×C53C2418yes—
540C22×C4×C53C2414yes—
541C22×C4×C53C2411yescharacteristic
542C2×C22⋊D53—416no—
543C2×C22⋊D53—48no—
544C2×C22⋊D53—44no—
545C2×C22⋊D53C2414yes—
546C2×C22⋊D53C2412yes—
547C2×C22⋊D53C2412yes—
548C2×C22⋊D53C2418yes—
549C2×C22⋊D53C2418yes—
550C2×C22⋊D53C2414yes—
551C2×C22⋊D53C2414yes—
552C2×C22⋊D53C2414yes—
553C2×C22⋊D53C2418yes—
554C2×C22⋊D53C2418yes—
555C2×C22⋊D53C2418yes—
556C2×C22⋊D53C2418yes—
557C2×C22⋊D53C2414yes—
558C2×C22⋊D53C2414yes—
559C22×Dic53—44no—
560C22×Dic53C2412yes—
561C22×Dic53C2412yes—
562C22×Dic53C2412yes—
563C22×Dic53C2414yes—
564C22×Dic53C2412yes—
565C22×Dic53C2412yes—
566C22×Dic53C2412yes—
567C22×Dic53C2412yes—
568C22×Dic53C2414yes—
569C22×Dic53C2414yes—
570#11719949—44no—
571#11719949—44no—
572#11719949—44no—
573Q8×D53—44no—
574Q8×D53—44no—
575Q8×D53—44no—
576#11719947—44no—
577#11719947—48no—
578#11719947—48no—
579#11719947—48no—
580D4×D53—44no—
581D4×D53—48no—
582#11719945—24no—
583#11719945—24no—
584#11719945—416no—
585#11719945—48no—
586#11719945—48no—
587#11719945—44no—
588#11719945—44no—
589#11719945—48no—
590C2×D212—24no—
591C2×D212—44no—
592C2×D212C2411yescharacteristic
593C2×D212C2412yes—
594C2×D212C2411yescharacteristic
595C2×D212C2412yes—
596C2×D212C2418yes—
597C2×D212C2414yes—
598C2×D212C2414yes—
599C2×C4×D53—44no—
600C2×C4×D53C2414yes—
601C2×C4×D53C2412yes—
602C2×C4×D53C2412yes—
603C2×C4×D53C2414yes—
604C2×C4×D53C2418yes—
605C2×C4×D53C2414yes—
606C2×C4×D53C2418yes—
607C2×C4×D53C2414yes—
608C2×C4×D53C2414yes—
609C2×C4×D53C2414yes—
610C2×Dic106—24no—
611C2×Dic106—44no—
612C2×Dic106C2414yes—
613C2×Dic106C2411yescharacteristic
614C2×Dic106C2411yescharacteristic
615C2×Dic106C2412yes—
616C2×Dic106C2412yes—
617C2×Dic106C2414yes—
618C2×Dic106C2414yes—
619C2×Dic106C2414yes—
620C4⋊C4×C53C2414yes—
621C4⋊C4×C53C2414yes—
622C4⋊C4×C53C2418yes—
623C4⋊C4×C53C2418yes—
624C4⋊C4×C53C2412yes—
625C4⋊C4×C53C2412yes—
626C22⋊C4×C53C2412yes—
627C22⋊C4×C53C2412yes—
628C22⋊C4×C53C2414yes—
629C22⋊C4×C53C2414yes—
630C22⋊C4×C53C2418yes—
631C22⋊C4×C53C2418yes—
632C22⋊C4×C53C2418yes—
633C22⋊C4×C53C2414yes—
634C22⋊C4×C53C2414yes—
635C42×C53C2412yes—
636C42×C53C2412yes—
637C22⋊Dic53C2414yes—
638C22⋊Dic53C2412yes—
639C22⋊Dic53C2418yes—
640C22⋊Dic53C2418yes—
641C22⋊Dic53C2418yes—
642C22⋊Dic53C2418yes—
643C22⋊Dic53C2412yes—
644C22⋊Dic53C2414yes—
645C22⋊Dic53C2414yes—
646C22⋊Dic53C2414yes—
647C22⋊Dic53C2418yes—
648C22⋊Dic53C2414yes—
649C22⋊Dic53C2414yes—
650#11719921C2414yes—
651#11719921C2418yes—
652#11719921C2418yes—
653#11719921C2418yes—
654#11719921C2418yes—
655#11719921C2418yes—
656#11719921C2414yes—
657#11719921C2414yes—
658#11719921C2414yes—
659#11719921C2414yes—
660#11719921C2414yes—
661#11719921C2418yes—
662C4⋊Dic53C2418yes—
663C4⋊Dic53C2414yes—
664C4⋊Dic53C2414yes—
665C4⋊Dic53C2412yes—
666C4⋊Dic53C2412yes—
667C4⋊Dic53C2414yes—
668C4⋊Dic53C2414yes—
669C4⋊Dic53C2418yes—
670#11719919C2414yes—
671#11719919C2414yes—
672#11719919C2418yes—
673#11719919C2418yes—
674#11719919C2418yes—
675#11719919C2414yes—
676#11719919C2414yes—
677#11719919C2414yes—
678#11719919C2414yes—
679#11719919C2414yes—
680#11719919C2414yes—
681#11719919C2418yes—
682#11719919C2414yes—
683#11719919C2414yes—
684C4×Dic53C2411yescharacteristic
685C4×Dic53C2411yescharacteristic
686C4×Dic53C2414yes—
687C4×Dic53C2414yes—
688C4×Dic53C2412yes—
689C4×Dic53C2412yes—
690C4×Dic53C2411yescharacteristic
691C4×Dic53C2411yescharacteristic
692C4×Dic53C2412yes—
693C4×Dic53C2412yes—
694C4×Dic53C2412yes—
695C4×Dic53C2412yes—
696C4×Dic53C2414yes—
697C4×Dic53C2414yes—
698C4×Dic53C2412yes—
699C4×Dic53C2412yes—
700C4×Dic53C2418yes—
701C4×Dic53C2418yes—
702C23×C53—22no—
703C23×C53—24no—
704C23×C53—42no—
705C23×C53—44no—
706C23×C53—48no—
707C23×C53—44no—
708C23×C53C2512yes—
709C23×C53C2512yes—
710C23×C53C2512yes—
711C23×C53C2514yes—
712C23×C53C2511yescharacteristic
713C22×D53—24no—
714C22×D53—44no—
715C22×D53—44no—
716C22×D53—48no—
717C22×D53C2512yes—
718C22×D53C2512yes—
719C22×D53C2514yes—
720Q8×C53—22no—
721Q8×C53—24no—
722Q8×C53—24no—
723Q8×C53—22no—
724D4×C53—24no—
725D4×C53—24no—
726D4×C53—22no—
727D4×C53—22no—
728D4×C53—24no—
729D4×C53—24no—
730D4×C53—44no—
731D4×C53—44no—
732D4×C53—44no—
733D4×C53—44no—
734D4×C53—48no—
735C2×C4×C53—22no—
736C2×C4×C53—24no—
737C2×C4×C53—24no—
738C2×C4×C53—24no—
739C2×C4×C53—24no—
740C2×C4×C53—24no—
741C2×C4×C53—48no—
742C2×C4×C53—48no—
743C2×C4×C53—44no—
744C2×C4×C53H(5,𝔽2)14yes—
745C2×C4×C53C2512yes—
746C2×C4×C53C2514yes—
747C2×C4×C53C2514yes—
748C2×C4×C53C2514yes—
749C2×C4×C53C2512yes—
750C2×C4×C53C2512yes—
751C2×C4×C53C2511yescharacteristic
752C2×C4×C53C2511yescharacteristic
753C22⋊D53—24no—
754C22⋊D53—24no—
755C22⋊D53—216no—
756C22⋊D53—28no—
757C22⋊D53—48no—
758C22⋊D53—44no—
759C22⋊D53—44no—
760C22⋊D53—48no—
761C22⋊D53—44no—
762C22⋊D53—44no—
763C22⋊D53—44no—
764C22⋊D53—48no—
765C22⋊D53—48no—
766C22⋊D53—48no—
767C2×Dic53—24no—
768C2×Dic53—24no—
769C2×Dic53—24no—
770C2×Dic53—28no—
771C2×Dic53—24no—
772C2×Dic53—44no—
773C2×Dic53—44no—
774C2×Dic53—42no—
775C2×Dic53—42no—
776C2×Dic53—42no—
777C2×Dic53C2512yes—
778C2×Dic53C2512yes—
779C2×Dic53C2514yes—
780C2×Dic53C2512yes—
781C2×Dic53C2514yes—
782C2×Dic53C2514yes—
783C2×Dic53C2512yes—
784C2×Dic53C2512yes—
785C2×Dic53C2512yes—
786D212—24no—
787D212—24no—
788D212—22no—
789D212—22no—
790D212—44no—
791D212—48no—
792D212—44no—
793C4×D53—24no—
794C4×D53—24no—
795C4×D53—28no—
796C4×D53—48no—
797C4×D53—48no—
798C4×D53—44no—
799C4×D53—44no—
800C4×D53—44no—
801C4×D53—44no—
802C4×D53—44no—
803Dic106—24no—
804Dic106—24no—
805Dic106—22no—
806Dic106—22no—
807Dic106—28no—
808Dic106—44no—
809Dic106—44no—
810Dic106—44no—
811#62836—531nomaximal, Sylow
812C22×C53—22no—
813C22×C53—22no—
814C22×C53—22no—
815C22×C53—22no—
816C22×C53—24no—
817C22×C53—22no—
818C22×C53—22no—
819C22×C53—24no—
820C22×C53—24no—
821C22×C53—28no—
822C22×C53—44no—
823C22×C53—84no—
824C22×C53—164no—
825C22×C53C2×H(5,𝔽2)12yes—
826C22×C53C2611yescharacteristic
827C2×D53—22no—
828C2×D53—22no—
829C2×D53—24no—
830C2×D53—24no—
831C2×D53—28no—
832C2×D53—24no—
833C2×D53—84no—
834C2×D53—164no—
835C4×C53—22no—
836C4×C53—24no—
837C4×C53—22no—
838C4×C53—22no—
839C4×C53—24no—
840C4×C53—24no—
841C4×C53C2×H(5,𝔽2)12yes—
842C4×C53C2×H(5,𝔽2)12yes—
843Dic53—24no—
844Dic53—22no—
845Dic53—22no—
846Dic53—24no—
847Dic53—22no—
848Dic53—24no—
849Dic53—22no—
850Dic53—22no—
851Dic53#58514yes—
852#3562—534no—
853#3562—534no—
854#3554—534no—
855#3546—534no—
856#3542—538no—
857#3517—534no—
858#3514—534no—
859#3513—538no—
860#3511—534no—
861#3510—531no—
862#3510—531no—
863#3509—531no—
864#3508—534no—
865#3508—531no—
866#3500—531no—
867#3500—531no—
868#3499—531no—
869#3498—531no—
870#3487—531no—
871#3487—531no—
872#3485—531no—
873#3485D5311yescharacteristic, complemented
874#3444—531no—
875#3444—531no—
876C2×#532—531no—
877C2×C53—22no—
878C2×C53—42no—
879C2×C53—42no—
880C2×C53—44no—
881C2×C53—42no—
882C2×C53C22×H(5,𝔽2)11yescharacteristic
883C2×C53C2×#58512yes—
884D53—42no—
885D53—44no—
886D53—42no—
887C2×2−1+4—531no—
888C2×2−1+4—531no—
889C2×H(5,𝔽2)—531no—
890C2×H(5,𝔽2)C2×D5311yescharacteristic
891C22×#41—531no—
892C22×#41C2×D5311yescharacteristic, complemented
893#562—538no—
894#562—538no—
895#560—538no—
896#560—538no—
897#559—534no—
898#559—538no—
899#559—534no—
900#559—534no—
901#557—534no—
902#556—534no—
903#556—534no—
904#556—534no—
905#555—538no—
906#554—538no—
907#553—538no—
908#553—538no—
909#553—538no—
910#553—538no—
911#552—538no—
912#551—538no—
913#551—538no—
914#551—538no—
915#551—538no—
916#550—534no—
917#550—534no—
918#550—534no—
919#550—534no—
920#550—538no—
921#550—534no—
922#550—534no—
923D4×Q8—534no—
924#548—534no—
925#548—534no—
926#548—534no—
927#548—534no—
928#548—534no—
929#548—534no—
930#547—538no—
931#547—534no—
932#547—534no—
933#547—534no—
934#547C2×D5314yescomplemented
935#547C2×D5314yescomplemented
936#546—534no—
937#546—538no—
938#546—538no—
939#546—534no—
940#546—534no—
941#546—538no—
942#546—534no—
943#546—538no—
944#546—538no—
945#546C2×D5314yescomplemented
946#546C2×D5314yescomplemented
947D42—538no—
948D42—534no—
949#542—538no—
950#542—538no—
951#542—534no—
952#542—534no—
953#541—534no—
954#540—538no—
955#540—538no—
956#540—538no—
957#540—538no—
958#540—534no—
959#539—538no—
960#539—538no—
961#538—538no—
962#538—538no—
963#538—538no—
964#538—538no—
965#537—538no—
966#536—531no—
967#536—532no—
968#536—532no—
969#536—532no—
970#536—532no—
971#536—531no—
972#536C2×D5311yescharacteristic
973#536C2×D5311yescharacteristic, complemented
974#535—531no—
975#535—532no—
976#535—531no—
977#535—531no—
978#535—534no—
979#535—532no—
980#535—532no—
981#535—532no—
982#535—534no—
983#535—538no—
984#535—531no—
985#534—534no—
986#534C2×D5314yescomplemented
987#533—532no—
988#533—532no—
989#533—534no—
990#533—531no—
991#533—531no—
992#532—534no—
993#532—534no—
994#532—534no—
995#532—534no—
996#532—531no—
997#532—531no—
998#532—532no—
999#532—532no—
1000#532—532no—
1001#532—532no—
1002#532—532no—
1003#532—532no—
1004#532—534no—
1005C2×C4⋊Q8—531no—
1006C2×C4⋊Q8—532no—
1007C2×#127—531no—
1008C2×#127—532no—
1009#529—534no—
1010#529—534no—
1011#529—532no—
1012#529—532no—
1013#529—534no—
1014#529—532no—
1015#529—532no—
1016#529—534no—
1017#529—534no—
1018#529—534no—
1019C2×#124—531no—
1020C2×#124—531no—
1021C2×#124—532no—
1022C2×#124—532no—
1023#525—531no—
1024#525—531no—
1025#525—534no—
1026#525—534no—
1027#525—534no—
1028#525—534no—
1029#525C2×D5311yescharacteristic
1030#525C2×D5311yescharacteristic, complemented
1031C2×#123—534no—
1032C2×#123C2×D5314yescomplemented
1033C2×#121—534no—
1034#520—538no—
1035#519—531no—
1036#519—531no—
1037#518—531no—
1038#518—538no—
1039#518C2×D5311yescharacteristic, complemented
1040C4×#41—531no—
1041C4×#41—531no—
1042C4×#41—534no—
1043C4×#41—534no—
1044C4×#41—531no—
1045C4×#41—531no—
1046C2×C4×D4—534no—
1047C22×C42—531no—
1048C53#6283611yescharacteristic, complemented, Sylow
10492−1+4—2124no—
10502−1+4—2124no—
1051H(5,𝔽2)—44no—
1052H(5,𝔽2)—2124no—
1053C2×#41—44no—
1054C2×#41—532no—
1055C2×#41—532no—
1056C2×#41—532no—
1057C2×#41—534no—
1058C2×#41—534no—
1059C2×#41—534no—
1060C2×#41—532no—
1061C2×#41—531no—
1062C2×#41—531no—
1063C2×#41—538no—
1064C2×#41—534no—
1065C2×#41—534no—
1066C2×#41—534no—
1067C2×#41—532no—
1068C2×#41—532no—
1069C2×#41—2124no—
1070C2×#41C22×D5311yescharacteristic
1071C2×#41C22×D5311yescharacteristic
1072C2×#41C22×D5314yes—
1073C2×#41C22×D5314yes—
1074C2×#41C22×D5312yes—
1075C2×#41C22×D5312yes—
1076C22×Q8—532no—
1077C22×Q8—532no—
1078C22×Q8—532no—
1079C22×Q8—531no—
1080C22×Q8—532no—
1081C22×Q8C22×D5311yescharacteristic
1082C22×D4—534no—
1083C22×D4—538no—
1084C22×D4—532no—
1085C22×D4—534no—
1086C22×D4—532no—
1087C22×D4—531no—
1088C22×D4—532no—
1089C22×D4C22×D5311yescharacteristic
1090C22×D4C22×D5312yes—
1091C22×D4C22×D5314yes—
1092C22×D4C22×D5312yes—
1093C22×D4C22×D5312yes—
1094C23×C4—532no—
1095C23×C4—532no—
1096C23×C4C22×D5311yescharacteristic
1097C23×C4C22×D5312yes—
1098C4⋊Q8—531no—
1099C4⋊Q8—532no—
1100C4⋊Q8—532no—
1101C4⋊Q8—534no—
1102C4⋊Q8—531no—
1103C4⋊Q8—532no—
1104C4⋊Q8—538no—
1105C4⋊Q8—532no—
1106C4⋊Q8—532no—
1107C4⋊Q8—532no—
1108C4⋊Q8C22×D5312yes—
1109C4⋊Q8C22×D5312yes—
1110#127—531no—
1111#127—532no—
1112#127—532no—
1113#127—534no—
1114#127—532no—
1115#127—532no—
1116#127—538no—
1117#127—531no—
1118#127—532no—
1119#127—538no—
1120#127—538no—
1121#127—532no—
1122#126—534no—
1123#126—534no—
1124#126—538no—
1125#126—538no—
1126#126—534no—
1127#126—534no—
1128#126—538no—
1129#126—538no—
1130#126—538no—
1131#126—538no—
1132#125—532no—
1133#125—534no—
1134#125—532no—
1135#125—534no—
1136#125—538no—
1137#125—538no—
1138#125—538no—
1139#124—532no—
1140#124—532no—
1141#124—534no—
1142#124—531no—
1143#124—531no—
1144#124—532no—
1145#124—531no—
1146#124—532no—
1147#124—532no—
1148#124—534no—
1149#124—532no—
1150#124—532no—
1151#124—538no—
1152#124—531no—
1153#124—532no—
1154#124—538no—
1155#124—538no—
1156#124—534no—
1157#124—534no—
1158#124—538no—
1159#124—538no—
1160#124—538no—
1161#124—538no—
1162#124—532no—
1163#124—532no—
1164#124C22×D5312yes—
1165#124C22×D5312yes—
1166#123—534no—
1167#123—534no—
1168#123—534no—
1169#123—538no—
1170#123—532no—
1171#123—532no—
1172#123—538no—
1173#123—538no—
1174#123—538no—
1175#123—538no—
1176#123—538no—
1177#123—534no—
1178#123—538no—
1179#123—534no—
1180#123—534no—
1181#123—538no—
1182#123—538no—
1183#123—538no—
1184#123—538no—
1185#123—538no—
1186#123—538no—
1187#123C22×D5312yes—
1188#123C22×D5312yes—
1189#123C22×D5314yes—
1190#123C22×D5314yes—
1191#123C22×D5318yes—
1192#123C22×D5318yes—
1193#123C22×D5318yes—
1194C22⋊Q8—532no—
1195C22⋊Q8—532no—
1196C22⋊Q8—538no—
1197C22⋊Q8—534no—
1198C22⋊Q8—538no—
1199C22⋊Q8—538no—
1200C22⋊Q8—538no—
1201C22⋊Q8—534no—
1202C22⋊Q8—538no—
1203C22⋊Q8—538no—
1204C22⋊Q8—538no—
1205C22⋊Q8—534no—
1206C22⋊Q8—534no—
1207C22⋊Q8—534no—
1208C22⋊Q8—534no—
1209C22⋊Q8—538no—
1210C22⋊Q8—538no—
1211C22⋊Q8C22×D5312yes—
1212C22⋊Q8C22×D5312yes—
1213C22⋊Q8C22×D5314yes—
1214C22⋊Q8C22×D5314yes—
1215#121—538no—
1216#121—538no—
1217#121—538no—
1218#121—538no—
1219#121—534no—
1220#121—534no—
1221#121—534no—
1222#121—534no—
1223#121—534no—
1224#121—534no—
1225#121—538no—
1226#121—538no—
1227#121—538no—
1228#121—538no—
1229#121—538no—
1230#121—538no—
1231#121—538no—
1232#121—538no—
1233#121—532no—
1234#121—532no—
1235#121—538no—
1236#121—534no—
1237#121—538no—
1238#121—538no—
1239#121—534no—
1240#121—538no—
1241#121—538no—
1242#121—538no—
1243#121—538no—
1244#121—538no—
1245#121—538no—
1246#121—538no—
1247#121—538no—
1248#121C22×D5312yes—
1249#121C22×D5312yes—
1250#121C22×D5318yes—
1251#121C22×D5318yes—
1252#120—532no—
1253#120—532no—
1254#120—534no—
1255#120—534no—
1256#120—538no—
1257#120—538no—
1258#120—534no—
1259#120—538no—
1260#120—538no—
1261#120—534no—
1262#120—538no—
1263#120C22×D5312yes—
1264#120C22×D5312yes—
1265#120C22×D5318yes—
1266C4×Q8—532no—
1267C4×Q8—532no—
1268C4×Q8—534no—
1269C4×Q8—534no—
1270C4×Q8—534no—
1271C4×Q8—532no—
1272C4×Q8—532no—
1273C4×Q8—534no—
1274C4×Q8—534no—
1275C4×Q8—538no—
1276C4×Q8—534no—
1277C4×Q8—534no—
1278C4×Q8—534no—
1279C4×D4—534no—
1280C4×D4—534no—
1281C4×D4—534no—
1282C4×D4—534no—
1283C4×D4—532no—
1284C4×D4—532no—
1285C4×D4—538no—
1286C4×D4—538no—
1287C4×D4—538no—
1288C4×D4—538no—
1289C4×D4—534no—
1290C4×D4—534no—
1291C4×D4—534no—
1292C4×D4—534no—
1293C4×D4—538no—
1294C4×D4—538no—
1295C4×D4—538no—
1296C4×D4—538no—
1297C4×D4—538no—
1298C4×D4—538no—
1299C4×D4—532no—
1300C4×D4—532no—
1301C4×D4—534no—
1302C4×D4—538no—
1303C4×D4—538no—
1304C4×D4—534no—
1305C4×D4—534no—
1306C4×D4—534no—
1307C4×D4—534no—
1308C4×D4—534no—
1309C4×D4—534no—
1310C4×D4—538no—
1311C4×D4—538no—
1312C4×D4—538no—
1313C4×D4—534no—
1314C4×D4C22×D5314yes—
1315C4×D4C22×D5314yes—
1316C4×D4C22×D5314yes—
1317C4×D4C22×D5314yes—
1318#117—531no—
1319#117—531no—
1320#117—532no—
1321#117—532no—
1322#117—534no—
1323#117—538no—
1324#117—534no—
1325#117—534no—
1326#117—538no—
1327#117—534no—
1328#117—534no—
1329#117—534no—
1330#117—534no—
1331#117—538no—
1332#117—534no—
1333#117—532no—
1334#117—532no—
1335#117C22×D5311yescharacteristic
1336#117C22×D5311yescharacteristic
1337C2×C4⋊C4—534no—
1338C2×C4⋊C4—538no—
1339C2×C4⋊C4—538no—
1340C2×C4⋊C4C22×D5318yes—
1341C2×C22⋊C4—534no—
1342C2×C22⋊C4—538no—
1343C2×C22⋊C4—534no—
1344C2×C22⋊C4—534no—
1345C2×C22⋊C4—538no—
1346C2×C22⋊C4—538no—
1347C2×C22⋊C4C22×D5318yes—
1348C2×C22⋊C4C22×D5314yes—
1349C2×C42—532no—
1350C2×C42—532no—
1351C2×C42—532no—
1352C2×C42—531no—
1353C2×C42—532no—
1354C2×C42—531no—
1355C2×C42—532no—
1356C2×C42—532no—
1357C2×C42—532no—
1358C2×C42—532no—
1359C2×C42—532no—
1360C24—532no—
1361C24—534no—
1362C24C23×D5312yes—
1363C24C23×D5311yescharacteristic
1364C24C23×D5314yes—
1365#41—24no—
1366#41—24no—
1367#41—48no—
1368#41—48no—
1369#41—44no—
1370#41—44no—
1371#41—1064no—
1372#41—1064no—
1373#41—2128no—
1374#41—2128no—
1375#41—2128no—
1376#41—2124no—
1377#41—2124no—
1378#41—21216no—
1379#41—2128no—
1380#41—2128no—
1381#41—2124no—
1382#41—2128no—
1383#41—2124no—
1384#41—2124no—
1385#41—2124no—
1386C2×Q8—24no—
1387C2×Q8—534no—
1388C2×Q8—531no—
1389C2×Q8—532no—
1390C2×Q8—532no—
1391C2×Q8—531no—
1392C2×Q8—534no—
1393C2×Q8—534no—
1394C2×Q8—534no—
1395C2×Q8—1064no—
1396C2×Q8—2124no—
1397C2×Q8—2124no—
1398C2×Q8—2124no—
1399C2×Q8—2124no—
1400C2×Q8C23×D5311yescharacteristic
1401C2×Q8C23×D5312yes—
1402C2×Q8C23×D5312yes—
1403C2×Q8C23×D5311yescharacteristic
1404C2×D4—24no—
1405C2×D4—44no—
1406C2×D4—44no—
1407C2×D4—44no—
1408C2×D4—48no—
1409C2×D4—538no—
1410C2×D4—534no—
1411C2×D4—532no—
1412C2×D4—532no—
1413C2×D4—534no—
1414C2×D4—534no—
1415C2×D4—538no—
1416C2×D4—538no—
1417C2×D4—538no—
1418C2×D4—538no—
1419C2×D4—534no—
1420C2×D4—534no—
1421C2×D4—534no—
1422C2×D4—538no—
1423C2×D4—532no—
1424C2×D4—532no—
1425C2×D4—531no—
1426C2×D4—531no—
1427C2×D4—538no—
1428C2×D4—534no—
1429C2×D4—534no—
1430C2×D4—1064no—
1431C2×D4—2124no—
1432C2×D4—2124no—
1433C2×D4—2128no—
1434C2×D4—21216no—
1435C2×D4—2124no—
1436C2×D4—2128no—
1437C2×D4C23×D5312yes—
1438C2×D4C23×D5312yes—
1439C2×D4C23×D5311yescharacteristic
1440C2×D4C23×D5311yescharacteristic
1441C2×D4C23×D5312yes—
1442C2×D4C23×D5312yes—
1443C2×D4C23×D5314yes—
1444C2×D4C23×D5314yes—
1445C2×D4C23×D5314yes—
1446C2×D4C23×D5318yes—
1447C2×D4C23×D5314yes—
1448C22×C4—24no—
1449C22×C4—44no—
1450C22×C4—532no—
1451C22×C4—532no—
1452C22×C4—532no—
1453C22×C4—534no—
1454C22×C4—532no—
1455C22×C4—532no—
1456C22×C4—532no—
1457C22×C4—532no—
1458C22×C4—534no—
1459C22×C4—534no—
1460C22×C4—534no—
1461C22×C4—532no—
1462C22×C4—532no—
1463C22×C4—534no—
1464C22×C4—538no—
1465C22×C4—534no—
1466C22×C4—538no—
1467C22×C4—534no—
1468C22×C4—534no—
1469C22×C4—534no—
1470C22×C4—2124no—
1471C22×C4—2124no—
1472C22×C4C23×D5312yes—
1473C22×C4C23×D5312yes—
1474C22×C4C23×D5311yescharacteristic
1475C22×C4C23×D5312yes—
1476C22×C4C23×D5312yes—
1477C22×C4C23×D5312yes—
1478C22×C4C23×D5318yes—
1479C22×C4C23×D5318yes—
1480C22×C4C23×D5314yes—
1481C22×C4C23×D5311yescharacteristic
1482C4⋊C4—534no—
1483C4⋊C4—538no—
1484C4⋊C4—534no—
1485C4⋊C4—538no—
1486C4⋊C4—538no—
1487C4⋊C4—538no—
1488C4⋊C4—534no—
1489C4⋊C4—534no—
1490C4⋊C4—534no—
1491C4⋊C4—534no—
1492C4⋊C4—532no—
1493C4⋊C4—532no—
1494C4⋊C4—534no—
1495C4⋊C4—534no—
1496C4⋊C4—534no—
1497C4⋊C4—534no—
1498C4⋊C4—534no—
1499C4⋊C4—534no—
1500C4⋊C4—534no—
1501C4⋊C4—534no—
1502C4⋊C4—538no—
1503C4⋊C4—538no—
1504C4⋊C4C23×D5314yes—
1505C4⋊C4C23×D5318yes—
1506C4⋊C4C23×D5314yes—
1507C4⋊C4C23×D5318yes—
1508C4⋊C4C23×D5312yes—
1509C4⋊C4C23×D5312yes—
1510C22⋊C4—534no—
1511C22⋊C4—532no—
1512C22⋊C4—538no—
1513C22⋊C4—538no—
1514C22⋊C4—538no—
1515C22⋊C4—538no—
1516C22⋊C4—532no—
1517C22⋊C4—534no—
1518C22⋊C4—538no—
1519C22⋊C4—534no—
1520C22⋊C4—534no—
1521C22⋊C4—534no—
1522C22⋊C4—534no—
1523C22⋊C4—534no—
1524C22⋊C4—538no—
1525C22⋊C4—538no—
1526C22⋊C4—538no—
1527C22⋊C4—538no—
1528C22⋊C4—538no—
1529C22⋊C4—534no—
1530C22⋊C4—534no—
1531C22⋊C4—538no—
1532C22⋊C4—534no—
1533C22⋊C4—534no—
1534C22⋊C4—534no—
1535C22⋊C4C23×D5314yes—
1536C22⋊C4C23×D5312yes—
1537C22⋊C4C23×D5318yes—
1538C22⋊C4C23×D5312yes—
1539C22⋊C4C23×D5314yes—
1540C22⋊C4C23×D5318yes—
1541C22⋊C4C23×D5318yes—
1542C22⋊C4C23×D5314yes—
1543C22⋊C4C23×D5314yes—
1544C42—531no—
1545C42—531no—
1546C42—532no—
1547C42—532no—
1548C42—531no—
1549C42—531no—
1550C42—532no—
1551C42—532no—
1552C42—532no—
1553C42—532no—
1554C42—534no—
1555C42—534no—
1556C42—534no—
1557C42—532no—
1558C42—534no—
1559C42—532no—
1560C42—538no—
1561C42—538no—
1562C42C23×D5312yes—
1563C42C23×D5312yes—
1564C23—22no—
1565C23—24no—
1566C23—42no—
1567C23—44no—
1568C23—44no—
1569C23—48no—
1570C23—532no—
1571C23—534no—
1572C23—532no—
1573C23—1064no—
1574C23—2124no—
1575C23—2128no—
1576C23—2124no—
1577C23C24×D5312yes—
1578C23C24×D5314yes—
1579C23C24×D5312yes—
1580C23C24×D5312yes—
1581C23C24×D5311yescharacteristic
1582Q8—24no—
1583Q8—24no—
1584Q8—22no—
1585Q8—22no—
1586Q8—1068no—
1587Q8—1064no—
1588Q8—1064no—
1589Q8—1062no—
1590Q8—1062no—
1591Q8—2124no—
1592Q8—2124no—
1593Q8—2124no—
1594D4—24no—
1595D4—24no—
1596D4—24no—
1597D4—24no—
1598D4—22no—
1599D4—22no—
1600D4—44no—
1601D4—44no—
1602D4—48no—
1603D4—44no—
1604D4—44no—
1605D4—10616no—
1606D4—1068no—
1607D4—1064no—
1608D4—1064no—
1609D4—1064no—
1610D4—1064no—
1611D4—1062no—
1612D4—1062no—
1613D4—2124no—
1614D4—2128no—
1615D4—2124no—
1616D4—2128no—
1617D4—2128no—
1618D4—2128no—
1619D4—2124no—
1620D4—2128no—
1621D4—2124no—
1622D4—2124no—
1623D4—2128no—
1624D4—2124no—
1625D4—2124no—
1626C2×C4—22no—
1627C2×C4—24no—
1628C2×C4—24no—
1629C2×C4—24no—
1630C2×C4—24no—
1631C2×C4—24no—
1632C2×C4—48no—
1633C2×C4—44no—
1634C2×C4—48no—
1635C2×C4—532no—
1636C2×C4—532no—
1637C2×C4—534no—
1638C2×C4—532no—
1639C2×C4—534no—
1640C2×C4—532no—
1641C2×C4—532no—
1642C2×C4—532no—
1643C2×C4—534no—
1644C2×C4—1068no—
1645C2×C4—1064no—
1646C2×C4—1064no—
1647C2×C4—1064no—
1648C2×C4—1068no—
1649C2×C4—1064no—
1650C2×C4—1064no—
1651C2×C4—1064no—
1652C2×C4—2128no—
1653C2×C4—2124no—
1654C2×C4—2124no—
1655C2×C4—2124no—
1656C2×C4—2124no—
1657C2×C4—2128no—
1658C2×C4—2124no—
1659C2×C4—2122no—
1660C2×C4—2122no—
1661C2×C4—2122no—
1662C2×C4—2124no—
1663C2×C4—2124no—
1664C2×C4#1313326214yes—
1665C2×C4C24×D5312yes—
1666C2×C4C24×D5314yes—
1667C2×C4C24×D5312yes—
1668C2×C4C24×D5314yes—
1669C2×C4C24×D5312yes—
1670C2×C4C24×D5314yes—
1671C2×C4C24×D5311yescharacteristic
1672C2×C4C24×D5311yescharacteristic
1673C22—22no—
1674C22—22no—
1675C22—22no—
1676C22—22no—
1677C22—24no—
1678C22—28no—
1679C22—22no—
1680C22—22no—
1681C22—24no—
1682C22—24no—
1683C22—44no—
1684C22—84no—
1685C22—164no—
1686C22—8484no—
1687C22—1062no—
1688C22—1062no—
1689C22—1064no—
1690C22—1064no—
1691C22—1064no—
1692C22—1068no—
1693C22—4244no—
1694C22C2×#1313326212yes—
1695C22C25×D5311yescharacteristic
1696C4—22no—
1697C4—22no—
1698C4—22no—
1699C4—24no—
1700C4—24no—
1701C4—24no—
1702C4—534no—
1703C4—1062no—
1704C4—1062no—
1705C4—1064no—
1706C4—1062no—
1707C4—1062no—
1708C4—1062no—
1709C4—1064no—
1710C4—1064no—
1711C4C2×#1313326212yes—
1712C4C2×#1313326212yes—
1713C2—22no—
1714C2—42no—
1715C2—44no—
1716C2—42no—
1717C2—42no—
1718C2—2122no—
1719C2—2124no—
1720C2—2122no—
1721C2C22×#1313326211yescharacteristic
1722C2#585×D5312yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3485C2
hypercenter#3485D53
hypocenterC53#62836
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3485

Complements

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

NH ≅ G/Ntype
1. #20289308C2semidirect
2. #20289297C2semidirect
3. #20289181C2semidirect
4. #20289082C2semidirect
5. #20289026C2semidirect
6. #20288720C2semidirect
7. #20288673C2semidirect
8. #20288647C2semidirect
9. #20288625C2semidirect
10. #20288614C2semidirect
11. #20288606C2semidirect
12. #20288600C2semidirect
13. #20288586C2semidirect
14. #20288583C2semidirect
15. #20288504C2semidirect
16. #20288503C2semidirect
17. #20288497C2semidirect
18. #20288489C2semidirect
19. #20288373C2semidirect
20. #20288369C2semidirect
21. #20288357C2semidirect
22. #20288007C2semidirect
23. #20288007C2semidirect
24. C2×#16811169C2semidirect
25. C53×#3485C2semidirect
26. C2×#13133265C22semidirect
27. C2×#13133264C22semidirect
29. C22×#11719945C22semidirect
30. #16811370C22semidirect
31. #16811368C22semidirect
32. #16811362C22semidirect
33. #16811361C22semidirect
34. #16811357C22semidirect
35. #16811356C22semidirect
36. #16811356C22semidirect
37. #16811355C22semidirect
38. #16811348C22semidirect
39. #16811347C22semidirect
40. #16811343C22semidirect
41. #16811342C22semidirect
42. #16811337C22semidirect
43. #16811328C22semidirect
44. #16811321C22semidirect
45. #16811318C22semidirect
46. #16811318C22semidirect
47. #16811318C22semidirect
48. #16811310C22semidirect
49. #16811301C22semidirect
50. #16811299C22semidirect
51. #16811299C22semidirect
52. #16811296C22semidirect
53. #16811294C22semidirect
54. #16811294C22semidirect
55. #16811292C22semidirect
56. #16811292C22semidirect
57. #16811292C22semidirect
58. #16811291C22semidirect
59. #16811291C22semidirect
60. #16811286C22semidirect
61. #16811283C22semidirect
62. #16811283C22semidirect
63. #16811282C22semidirect
64. #16811280C22semidirect
65. #16811280C22semidirect
66. #16811280C22semidirect
67. #16811278C22semidirect
68. #16811275C22semidirect
69. #16811275C22semidirect
70. #16811271C22semidirect
71. #16811270C22semidirect
72. #16811269C22semidirect
73. #16811267C22semidirect
74. #16811267C22semidirect
75. #16811265C22semidirect
76. #16811264C22semidirect
77. #16811263C22semidirect
78. #16811263C22semidirect
79. #16811260C22semidirect
81. D4×C22⋊D53C22semidirect
82. #16811246C22semidirect
83. #16811241C22semidirect
84. #16811241C22semidirect
85. #16811238C22semidirect
86. #16811233C22semidirect
87. #16811226C22semidirect
88. #16811225C22semidirect
89. #16811225C22semidirect
90. #16811224C22semidirect
91. #16811223C22semidirect
92. #16811220C22semidirect
93. #16811216C22semidirect
94. #16811211C22semidirect
95. #16811209C22semidirect
96. #16811208C22semidirect
97. #16811205C22semidirect
98. #16811202C22semidirect
99. #16811199C22semidirect
100. #16811198C22semidirect
101. #16811198C22semidirect
103. #16811194C22semidirect
104. #16811193C22semidirect
105. #16811192C22semidirect
106. #16811191C22semidirect
108. #16811190C22semidirect
109. #16811190C22semidirect
110. #16811190C22semidirect
111. #16811190C22semidirect
112. #16811188C22semidirect
113. #16811188C22semidirect
115. #16811187C22semidirect
116. #16811183C22semidirect
117. #16811176C22semidirect
118. #16811176C22semidirect
119. #16811175C22semidirect
120. #16811175C22semidirect
121. #16811175C22semidirect
122. #16811174C22semidirect
123. #16811172C22semidirect
124. #16811170C22semidirect
127. #16811169C22semidirect
128. #16811169C22semidirect
129. #16811169C22semidirect
130. #16811169C22semidirect
131. #16811169C22semidirect
132. #16811169C22semidirect
133. #16811168C22semidirect
134. #16811168C22semidirect
135. C2×#13133215C22semidirect
136. C4⋊Q8×D53C22semidirect
138. C2×#13133213C22semidirect
139. #16811159C22semidirect
140. #16811159C22semidirect
141. #16811159C22semidirect
142. #16811155C22semidirect
143. #16811154C22semidirect
144. #16811154C22semidirect
145. #16811153C22semidirect
146. #16811153C22semidirect
147. #16811150C22semidirect
148. #16811150C22semidirect
149. C2×#13133206C22semidirect
150. C2×#13133204C22semidirect
151. C2×#13133204C22semidirect
152. #124×D53C22semidirect
153. #16811134C22semidirect
154. #16811134C22semidirect
155. #16811134C22semidirect
156. #16811131C22semidirect
157. #16811129C22semidirect
158. #16811129C22semidirect
159. #123×D53C22semidirect
160. C2×#13133189C22semidirect
161. #16811104C22semidirect
162. #16811101C22semidirect
163. #16811100C22semidirect
164. #16811097C22semidirect
165. #16811096C22semidirect
167. #41×Dic53C22semidirect
168. #16811091C22semidirect
169. #16811091C22semidirect
170. C4×#11719947C22semidirect
171. C4×#11719947C22semidirect
172. C2×C4×C22⋊D53C22semidirect
173. C22×C4×Dic53C22semidirect
175. C22×#41×C53C22semidirect
176. C53×#547C22semidirect
177. C53×#547C22semidirect
178. C53×#546C22semidirect
179. C53×#546C22semidirect
181. C53×#536C22semidirect
182. C53×#534C22semidirect
184. C53×#525C22semidirect
185. C2×#123×C53C22semidirect
186. C53×#518C22semidirect
873. #3485D53semidirect
892. C22×#41C2×D53semidirect
934. #547C2×D53semidirect
935. #547C2×D53semidirect
945. #546C2×D53semidirect
946. #546C2×D53semidirect
973. #536C2×D53semidirect
986. #534C2×D53semidirect
1030. #525C2×D53semidirect
1032. C2×#123C2×D53semidirect
1039. #518C2×D53semidirect
1048. C53#62836semidirect

Maximal subgroups

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

subgroupindex
#202893082
#202892972
#202891812
#202890822
#202890262
#202887202
#202886732
#202886472
#202886252
#202886142
#202886062
#202886002
#202885862
#202885832
#202885042
#202885032
#202884972
#202884892
#202883732
#202883692
#202883572
#202880072
C2×#168111692
C53×#34852
#6283653