Finite Group Databasebeta

← #28293047

Subgroups — #28293047

Order 13568.

6428 conjugacy classes of subgroups.

The subgroup lattice has 1688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289323C214yesmaximal, complemented
2#20289322C214yesmaximal, complemented
3#20289207C212yesmaximal, complemented
4#20289206C212yesmaximal, complemented
5#20289202C214yesmaximal, complemented
6#20289191C212yesmaximal, complemented
7#20289127C212yesmaximal, complemented
8#20288962C214yesmaximal, complemented
9#20288810C214yesmaximal, complemented
10#20288809C214yesmaximal, complemented
11#20288600C212yesmaximal, complemented
12#20288595C212yesmaximal, complemented
13#20288593C214yesmaximal, complemented
14#20288577C211yesmaximal, characteristic, complemented
15#20288572C212yesmaximal, complemented
16#20288529C212yesmaximal, complemented
17#20288528C212yesmaximal, complemented
18#20288525C211yesmaximal, characteristic, complemented
19#20288520C211yesmaximal, characteristic, complemented
20#20288519C212yesmaximal, complemented
21#20288468C212yesmaximal, complemented
22#20288464C212yesmaximal, complemented
23#20288455C214yesmaximal, complemented
24#20288010C211yesmaximal, characteristic
25C2×#16811177C211yesmaximal, characteristic, complemented
26#533×D53C211yesmaximal, characteristic, complemented
27C53×#3507C211yesmaximal, characteristic, complemented
28C53⋊#564C2218yescomplemented
29#16811376C2218yescomplemented
30#16811375C2218yes—
31#16811374C2218yes—
32#16811359C2212yescomplemented
33Q8×Dic106C2212yescomplemented
34Q8×Dic106C2212yescomplemented
35Q8×Dic106C2214yescomplemented
36Q8×Dic106C2212yescomplemented
37#16811353C2212yescomplemented
38#16811352C2214yescomplemented
39#16811352C2212yescomplemented
40#16811352C2212yescomplemented
41#16811351C2214yescomplemented
42#16811351C2212yescomplemented
43#16811351C2214yescomplemented
44#16811350C2214yescomplemented
45#16811350C2218yescomplemented
46#16811350C2214yescomplemented
47#16811350C2214yescomplemented
48#16811349C2214yescomplemented
49#16811349C2214yescomplemented
50#16811349C2214yescomplemented
51#16811348C2212yescomplemented
52#16811348C2214yescomplemented
53#16811348C2212yescomplemented
54#16811348C2214yescomplemented
55#16811344C2214yes—
56#16811343C2214yescomplemented
57#16811343C2212yescomplemented
58#16811342C2214yescomplemented
59#16811342C2214yescomplemented
60#16811342C2214yescomplemented
61#16811342C2214yescomplemented
62#16811342C2214yescomplemented
63#16811341C2214yes—
64#16811340C2218yes—
65#16811332C2218yes—
66#16811332C2214yescomplemented
67#16811331C2214yes—
68#16811330C2212yescomplemented
69#16811328C2214yes—
70#16811315C2214yes—
71#16811313C2218yes—
72#16811313C2214yescomplemented
73#16811312C2218yes—
74#16811312C2214yes—
75#16811310C2218yes—
76#16811310C2218yes—
77#16811310C2218yes—
78#16811310C2218yescomplemented
79#16811309C2218yes—
80#16811309C2218yes—
81#16811308C2214yes—
82#16811307C2214yes—
83#16811306C2218yes—
84#16811302C2218yes—
85#16811296C2218yes—
86D4×Dic106C2218yes—
87D4×Dic106C2214yescomplemented
88D4×Dic106C2214yescomplemented
89#16811286C2218yes—
90#16811254C2212yes—
91#16811254C2214yes—
92#16811254C2214yescomplemented
93#16811253C2214yes—
94#16811253C2218yes—
95#16811252C2214yes—
96#16811252C2218yescomplemented
97#16811251C2212yes—
98#16811251C2214yescomplemented
99#16811242C2214yes—
100#16811242C2214yes—
101#16811238C2214yes—
102#16811238C2214yes—
103#16811236C2214yes—
104#16811235C2218yescomplemented
105#16811234C2214yes—
106#16811233C2218yescomplemented
107#16811233C2214yescomplemented
108#16811233C2214yescomplemented
109#16811232C2218yes—
110#16811231C2214yes—
111#16811231C2214yes—
112#16811230C2218yescomplemented
113#16811230C2218yescomplemented
114#16811230C2218yescomplemented
115#16811230C2218yescomplemented
116#16811218C2214yes—
117#16811216C2218yes—
118#16811195C2218yes—
119#16811194C2212yes—
120#16811193C2214yes—
121#16811180C2211yescharacteristic
122#16811180C2211yescharacteristic
123#16811180C2214yes—
124#16811179C2212yes—
125#16811178C2211yescharacteristic
126#16811178C2211yescharacteristic
127#16811178C2211yescharacteristic
128#16811178C2214yes—
129#16811178C2211yescharacteristic
130#16811177C2212yes—
131#16811177C2212yes—
132#16811177C2212yes—
133#16811177C2212yes—
134#16811177C2212yes—
135#16811177C2212yes—
136#16811177C2212yes—
137#16811177C2212yes—
138#16811177C2212yes—
139#16811177C2212yes—
140#16811177C2214yes—
141#16811176C2212yes—
142#16811176C2214yescomplemented
143#16811175C2212yes—
144#16811175C2212yes—
145#16811175C2214yes—
146#16811175C2214yescomplemented
147#16811175C2214yescomplemented
148#16811171C2211yescharacteristic
149#16811171C2211yescharacteristic
150C2×#13133216C2211yescharacteristic
151C2×#13133216C2214yescomplemented
152C2×#13133215C2211yescharacteristic
153C4⋊Q8×D53C2211yescharacteristic
154C4⋊Q8×D53C2211yescharacteristic
155#16811155C2212yes—
156#16811155C2212yes—
157#16811155C2214yes—
158#16811154C2212yes—
159#16811154C2212yes—
160#16811154C2214yes—
161#16811152C2212yes—
162#16811152C2212yes—
163#16811152C2214yes—
164C2×#13133207C2212yes—
165#125×D53C2212yes—
166#16811133C2212yes—
167#16811133C2212yes—
168#16811130C2212yes—
169C2×#13133197C2211yescharacteristic
170C2×#13133195C2212yes—
171C2×#13133193C2211yescharacteristic
172C22⋊Q8×D53C2212yes—
173C22⋊Q8×D53C2212yes—
174#16811106C2212yes—
175#16811102C2214yes—
176#16811101C2212yes—
177#16811100C2212yes—
178#16811100C2218yescomplemented
179#16811099C2214yes—
180#41×Dic53C2212yes—
181C4×#11719947C2212yes—
182C4×#11719947C2212yes—
183C2×C4×Dic106C2211yescharacteristic
184C2×C4×Dic106C2212yes—
185C4×Q8×D53C2212yes—
186C4×Q8×D53C2212yes—
187C2×#13133174C2212yes—
188#117×D53C2212yes—
189C2×C42×D53C2211yescharacteristic
190C53×#559C2212yescomplemented
191C53×#557C2212yescomplemented
192C53×#556C2214yescomplemented
193C53×#556C2212yescomplemented
194C53×#554C2212yescomplemented
195C53×#552C2214yescomplemented
196C53×#539C2214yes—
197C53×#536C2212yes—
198C53×#533C2211yescharacteristic
199C53×#532C2211yescharacteristic
200C53×#529C2214yes—
201C53×#520C2212yes—
202C2×C4×Q8×C53C2211yescharacteristic
203C2×#11719947C2312yes—
204C2×#11719947C2312yes—
205C22×Dic106C2311yescharacteristic
206C22×Dic106C2318yes—
207C22×Dic106C2312yes—
208C2×Q8×D53C2312yes—
209C2×Q8×D53C2312yes—
210C22×C4×D53C2311yescharacteristic
211C22×C4×D53C2311yescharacteristic
212C22×C4×D53C2311yescharacteristic
213#13133217C2318yes—
214#13133217C2314yes—
215#13133217C2314yes—
216#13133217C2311yescharacteristic
217#13133217C2311yescharacteristic
218#13133217C2314yes—
219#13133217C2311yescharacteristic
220#13133217C2311yescharacteristic
221#13133216C2318yes—
222#13133216C2318yes—
223#13133216C2318yes—
224#13133216C2312yes—
225#13133216C2312yes—
226#13133216C2314yes—
227#13133216C2314yes—
228#13133216C2314yes—
229#13133216C2314yes—
230#13133216C2318yes—
231#13133216C2312yes—
232#13133216C2318yes—
233#13133216C2318yes—
234#13133216C2312yes—
235#13133216C2312yes—
236#13133216C2312yes—
237#13133216C2312yes—
238#13133216C2312yes—
239#13133215C2318yes—
240#13133215C2312yes—
241#13133215C2312yes—
242#13133215C2312yes—
243#13133215C2314yes—
244#13133215C2314yes—
245#13133215C2312yes—
246#13133215C2312yes—
247#13133215C2312yes—
248#13133212C2318yes—
249#13133212C2318yes—
250#13133212C2318yes—
251#13133211C2318yes—
252#13133210C2318yes—
253#13133210C2318yes—
254#13133210C2318yes—
255#13133210C2318yes—
256#13133210C2318yes—
257#13133210C2318yes—
258#13133210C2318yes—
259#13133210C2318yes—
260#13133210C2318yes—
261#13133210C2318yes—
262#13133210C2314yes—
263#13133210C2314yes—
264#13133209C2318yes—
265#13133209C2318yes—
266#13133209C2318yes—
267#13133209C2312yes—
268#13133209C2314yes—
269#13133209C2312yes—
270#13133208C2314yes—
271#13133208C2314yes—
272#13133208C2318yes—
273#13133208C2318yes—
274#13133208C2318yes—
275#13133208C2318yes—
276#13133208C2318yes—
277#13133208C2318yes—
278#13133208C2314yes—
279#13133208C2314yes—
280#13133208C2312yes—
281#13133208C2312yes—
282#13133208C2312yes—
283#13133208C2312yes—
284#13133207C2318yes—
285#13133207C2318yes—
286#13133207C2318yes—
287#13133207C2318yes—
288#13133207C2318yes—
289#13133207C2318yes—
290#13133207C2318yes—
291#13133207C2318yes—
292#13133207C2318yes—
293#13133207C2314yes—
294#13133207C2318yes—
295#13133207C2318yes—
296#13133207C2318yes—
297#13133207C2314yes—
298#13133207C2314yes—
299#13133207C2314yes—
300#13133207C2314yes—
301#13133207C2314yes—
302#13133204C2314yes—
303#13133204C2312yes—
304#13133204C2314yes—
305#13133204C2312yes—
306#13133203C2318yes—
307#13133203C2318yes—
308#13133201C2318yes—
309#13133200C2318yes—
310#13133199C2318yes—
311#13133199C2318yes—
312#13133199C2314yes—
313#13133199C2314yes—
314#13133198C2318yes—
315#13133198C2314yes—
316#13133198C2318yes—
317#13133197C2318yes—
318#13133197C2312yes—
319#13133197C2312yes—
320#13133197C2312yes—
321#13133197C2312yes—
322#13133197C2312yes—
323#13133197C2312yes—
324#13133197C2312yes—
325#13133197C2312yes—
326#13133196C2318yes—
327#13133196C2318yes—
328#13133196C2318yes—
329#13133196C2318yes—
330#13133196C2314yes—
331#13133196C2314yes—
332#13133196C2312yes—
333#13133196C2312yes—
334#13133196C2312yes—
335#13133196C2312yes—
336#13133195C2314yes—
337#13133195C2318yes—
338#13133195C2314yes—
339#13133195C2314yes—
340#13133195C2314yes—
341#13133195C2314yes—
342#13133195C2314yes—
343#13133194C2318yes—
344#13133194C2318yes—
345#13133194C2314yes—
346#13133194C2318yes—
347#13133194C2318yes—
348#13133194C2318yes—
349#13133194C2318yes—
350#13133194C2318yes—
351#13133194C2318yes—
352#13133194C2314yes—
353#13133194C2318yes—
354#13133193C2312yes—
355#13133193C2312yes—
356#13133193C2312yes—
357#13133193C2312yes—
358#13133193C2312yes—
359#13133193C2312yes—
360#13133193C2312yes—
361#13133193C2312yes—
362#13133188C2312yes—
363#13133188C2312yes—
364#13133188C2312yes—
365#13133188C2312yes—
366#13133185C2314yes—
367Q8×Dic53C2314yes—
368Q8×Dic53C2314yes—
369Q8×Dic53C2312yes—
370Q8×Dic53C2312yes—
371Q8×Dic53C2314yes—
372Q8×Dic53C2314yes—
373Q8×Dic53C2314yes—
374Q8×Dic53C2314yes—
375Q8×Dic53C2312yes—
376Q8×Dic53C2312yes—
377C4×Dic106C2318yes—
378C4×Dic106C2314yes—
379C4×Dic106C2314yes—
380C4×Dic106C2318yes—
381C4×Dic106C2318yes—
382C4×Dic106C2318yes—
383C4×Dic106C2312yes—
384C4×Dic106C2312yes—
385C4×Dic106C2314yes—
386C4×Dic106C2312yes—
387C4×Dic106C2312yes—
388C4×Dic106C2312yes—
389C4×Dic106C2314yes—
390C4×Dic106C2314yes—
391C4×Dic106C2314yes—
392C4×Dic106C2314yes—
393C4×Dic106C2314yes—
394C4×Dic106C2312yes—
395C4×Dic106C2314yes—
396C4×Dic106C2314yes—
397C4×Dic106C2312yes—
398C4×Dic106C2312yes—
399#13133182C2318yes—
400#13133182C2314yes—
401#13133182C2318yes—
402#13133182C2318yes—
403#13133182C2314yes—
404#13133182C2318yes—
405#13133182C2314yes—
406#13133182C2312yes—
407#13133182C2314yes—
408#13133182C2312yes—
409#13133182C2314yes—
410#13133182C2314yes—
411#13133182C2312yes—
412#13133182C2312yes—
413D4×Dic53C2314yes—
414D4×Dic53C2318yes—
415D4×Dic53C2312yes—
416D4×Dic53C2312yes—
417D4×Dic53C2314yes—
418D4×Dic53C2314yes—
419D4×Dic53C2314yes—
420D4×Dic53C2312yes—
421D4×Dic53C2312yes—
422C4×C22⋊D53C2318yes—
423C4×C22⋊D53C2314yes—
424C4×C22⋊D53C2314yes—
425#13133177C2314yes—
426#13133177C2318yes—
427#13133177C2314yes—
428#13133176C2318yes—
429#13133176C2314yes—
430#13133176C2318yes—
431#13133176C2312yes—
432#13133176C2312yes—
433#13133176C2314yes—
434#13133175C2318yes—
435#13133175C2312yes—
436#13133175C2312yes—
437#13133175C2312yes—
438#13133175C2312yes—
439#13133174C2318yes—
440#13133174C2314yes—
441#13133174C2314yes—
442#13133174C2314yes—
443#13133174C2314yes—
444#13133174C2314yes—
445#13133173C2318yes—
446#13133173C2318yes—
447#13133173C2318yes—
448#13133173C2314yes—
449#13133173C2318yes—
450#13133173C2318yes—
451#13133173C2314yes—
452#13133173C2314yes—
453C2×C4⋊Dic53C2312yes—
454C2×C4⋊Dic53C2314yes—
455C2×C4⋊Dic53C2311yescharacteristic
456C2×#11719919C2318yes—
457C2×#11719919C2312yes—
458C2×#11719919C2312yes—
459C2×#11719919C2312yes—
460C2×#11719919C2312yes—
461C2×#11719919C2312yes—
462C4⋊C4×D53C2312yes—
463C4⋊C4×D53C2312yes—
464C4⋊C4×D53C2314yes—
465C4⋊C4×D53C2312yes—
466C4⋊C4×D53C2312yes—
467C4⋊C4×D53C2314yes—
468C2×#11719921C2312yes—
469C2×#11719921C2312yes—
470C22⋊C4×D53C2314yes—
471C2×C4×Dic53C2311yescharacteristic
472C2×C4×Dic53C2311yescharacteristic
473C2×C4×Dic53C2311yescharacteristic
474C2×C4×Dic53C2312yes—
475C2×C4×Dic53C2314yes—
476C42×D53C2311yescharacteristic
477C42×D53C2311yescharacteristic
478C42×D53C2311yescharacteristic
479C42×D53C2311yescharacteristic
480C42×D53C2311yescharacteristic
481C42×D53C2311yescharacteristic
482C42×D53C2311yescharacteristic
483C42×D53C2311yescharacteristic
484C42×D53C2314yes—
485C2×#41×C53C2312yes—
486C22×Q8×C53C2311yescharacteristic
487C4⋊Q8×C53C2311yescharacteristic
488C4⋊Q8×C53C2311yescharacteristic
489C4⋊Q8×C53C2311yescharacteristic
490C4⋊Q8×C53C2314yes—
491#127×C53C2311yescharacteristic
492#126×C53C2318yes—
493#126×C53C2318yes—
494#125×C53C2314yes—
495#125×C53C2312yes—
496#125×C53C2318yes—
497#124×C53C2314yes—
498#124×C53C2312yes—
499#124×C53C2314yes—
500#123×C53C2318yes—
501#123×C53C2318yes—
502C22⋊Q8×C53C2318yes—
503C22⋊Q8×C53C2314yes—
504C22⋊Q8×C53C2312yes—
505C22⋊Q8×C53C2312yes—
506C22⋊Q8×C53C2314yes—
507#121×C53C2312yes—
508#121×C53C2312yes—
509C4×Q8×C53C2312yes—
510C4×Q8×C53C2312yes—
511C4×Q8×C53C2312yes—
512C4×Q8×C53C2312yes—
513C4×Q8×C53C2314yes—
514C4×Q8×C53C2314yes—
515C4×Q8×C53C2312yes—
516C4×Q8×C53C2312yes—
517C4×D4×C53C2318yes—
518C4×D4×C53C2314yes—
519C4×D4×C53C2314yes—
520C4×D4×C53C2312yes—
521C4×D4×C53C2312yes—
522#117×C53C2312yes—
523#117×C53C2314yes—
524#117×C53C2318yes—
525C2×C4⋊C4×C53C2311yescharacteristic
526C2×C4⋊C4×C53C2312yes—
527C2×C4⋊C4×C53C2314yes—
528C2×C42×C53C2312yes—
529C2×C42×C53C2311yescharacteristic
530C23×D53C2411yescharacteristic
531#41×C53—28no—
532C2×Q8×C53—24no—
533C2×Q8×C53C2412yes—
534C2×Q8×C53C2412yes—
535C2×Q8×C53C2412yes—
536C2×Q8×C53C2412yes—
537C2×Q8×C53C2412yes—
538C2×D4×C53C2412yes—
539C2×D4×C53C2414yes—
540C2×D4×C53C2412yes—
541C2×D4×C53C2412yes—
542C22×C4×C53C2411yescharacteristic
543C22×C4×C53C2412yes—
544C22×C4×C53C2414yes—
545C22×C4×C53C2412yes—
546C22×C4×C53C2411yescharacteristic
547C22×C4×C53C2418yes—
548C22×C4×C53C2411yescharacteristic
549C2×C22⋊D53C2414yes—
550C2×C22⋊D53C2414yes—
551C22×Dic53C2411yescharacteristic
552C22×Dic53C2411yescharacteristic
553C22×Dic53C2411yescharacteristic
554C22×Dic53C2412yes—
555C22×Dic53C2414yes—
556C22×Dic53C2414yes—
557C22×Dic53C2412yes—
558C22×Dic53C2418yes—
559Q8×D53—28no—
560Q8×D53—44no—
561#11719947—28no—
562#11719947—44no—
563C2×C4×D53—24no—
564C2×C4×D53—24no—
565C2×C4×D53—42no—
566C2×C4×D53C2411yescharacteristic
567C2×C4×D53C2411yescharacteristic
568C2×C4×D53C2411yescharacteristic
569C2×C4×D53C2411yescharacteristic
570C2×C4×D53C2411yescharacteristic
571C2×C4×D53C2411yescharacteristic
572C2×C4×D53C2411yescharacteristic
573C2×C4×D53C2411yescharacteristic
574C2×C4×D53C2411yescharacteristic
575C2×C4×D53C2414yes—
576C2×C4×D53C2411yescharacteristic
577C2×C4×D53C2411yescharacteristic
578C2×C4×D53C2414yes—
579C2×C4×D53C2411yescharacteristic
580C2×Dic106—24no—
581C2×Dic106—44no—
582C2×Dic106—416no—
583C2×Dic106C2412yes—
584C2×Dic106C2414yes—
585C2×Dic106C2412yes—
586C2×Dic106C2412yes—
587C2×Dic106C2414yes—
588C2×Dic106C2412yes—
589C2×Dic106C2414yes—
590C2×Dic106C2418yes—
591C2×Dic106C2412yes—
592C2×Dic106C2412yes—
593C2×Dic106C2414yes—
594C2×Dic106C2418yes—
595C4⋊C4×C53C2412yes—
596C4⋊C4×C53C2412yes—
597C4⋊C4×C53C2412yes—
598C4⋊C4×C53C2418yes—
599C4⋊C4×C53C2414yes—
600C4⋊C4×C53C2414yes—
601C4⋊C4×C53C2412yes—
602C4⋊C4×C53C2414yes—
603C4⋊C4×C53C2418yes—
604C4⋊C4×C53C2412yes—
605C4⋊C4×C53C2412yes—
606C4⋊C4×C53C2412yes—
607C4⋊C4×C53C2414yes—
608C4⋊C4×C53C2418yes—
609C4⋊C4×C53C2412yes—
610C22⋊C4×C53C2414yes—
611C22⋊C4×C53C2414yes—
612C22⋊C4×C53C2418yes—
613C22⋊C4×C53C2418yes—
614C22⋊C4×C53C2414yes—
615C22⋊C4×C53C2418yes—
616C42×C53C2414yes—
617C42×C53C2411yescharacteristic
618C42×C53C2411yescharacteristic
619C42×C53C2414yes—
620C42×C53C2411yescharacteristic
621C42×C53C2411yescharacteristic
622C42×C53C2418yes—
623C42×C53C2414yes—
624C22⋊Dic53C2414yes—
625C22⋊Dic53C2414yes—
626C22⋊Dic53C2414yes—
627C22⋊Dic53C2418yes—
628C22⋊Dic53C2414yes—
629C22⋊Dic53C2418yes—
630C22⋊Dic53C2414yes—
631C22⋊Dic53C2414yes—
632C22⋊Dic53C2418yes—
633#11719921C2414yes—
634#11719921C2414yes—
635#11719921C2414yes—
636#11719921C2414yes—
637#11719921C2414yes—
638#11719921C2414yes—
639#11719921C2414yes—
640#11719921C2414yes—
641C4⋊Dic53C2412yes—
642C4⋊Dic53C2412yes—
643C4⋊Dic53C2412yes—
644C4⋊Dic53C2412yes—
645C4⋊Dic53C2414yes—
646C4⋊Dic53C2414yes—
647C4⋊Dic53C2412yes—
648C4⋊Dic53C2414yes—
649C4⋊Dic53C2412yes—
650C4⋊Dic53C2418yes—
651C4⋊Dic53C2414yes—
652C4⋊Dic53C2412yes—
653C4⋊Dic53C2412yes—
654C4⋊Dic53C2418yes—
655C4⋊Dic53C2412yes—
656C4⋊Dic53C2412yes—
657C4⋊Dic53C2414yes—
658C4⋊Dic53C2414yes—
659C4⋊Dic53C2418yes—
660C4⋊Dic53C2418yes—
661C4⋊Dic53C2418yes—
662#11719919C2414yes—
663#11719919C2414yes—
664#11719919C2414yes—
665#11719919C2414yes—
666#11719919C2414yes—
667#11719919C2414yes—
668#11719919C2414yes—
669#11719919C2414yes—
670#11719919C2414yes—
671#11719919C2414yes—
672#11719919C2414yes—
673#11719919C2414yes—
674#11719919C2414yes—
675#11719919C2414yes—
676#11719919C2418yes—
677#11719919C2418yes—
678#11719919C2414yes—
679#11719919C2414yes—
680#11719919C2414yes—
681#11719919C2414yes—
682#11719919C2414yes—
683#11719919C2414yes—
684#11719919C2414yes—
685#11719919C2414yes—
686#11719919C2418yes—
687#11719919C2418yes—
688#11719919C2418yes—
689#11719919C2418yes—
690#11719919C2418yes—
691#11719919C2418yes—
692C4×Dic53C2411yescharacteristic
693C4×Dic53C2411yescharacteristic
694C4×Dic53C2411yescharacteristic
695C4×Dic53C2411yescharacteristic
696C4×Dic53C2411yescharacteristic
697C4×Dic53C2411yescharacteristic
698C4×Dic53C2411yescharacteristic
699C4×Dic53C2411yescharacteristic
700C4×Dic53C2411yescharacteristic
701C4×Dic53C2411yescharacteristic
702C4×Dic53C2411yescharacteristic
703C4×Dic53C2411yescharacteristic
704C4×Dic53C2414yes—
705C4×Dic53C2414yes—
706C4×Dic53C2414yes—
707C4×Dic53C2414yes—
708C4×Dic53C2414yes—
709C4×Dic53C2414yes—
710C4×Dic53C2414yes—
711C4×Dic53C2414yes—
712C4×Dic53C2418yes—
713C4×Dic53C2418yes—
714C4×Dic53C2418yes—
715C4×Dic53C2418yes—
716C4×Dic53C2418yes—
717C23×C53C2514yes—
718C23×C53C2511yescharacteristic
719C22×D53—22no—
720C22×D53—22no—
721C22×D53—41no—
722C22×D53C2511yescharacteristic
723C22×D53C2511yescharacteristic
724Q8×C53—24no—
725Q8×C53—24no—
726Q8×C53—24no—
727Q8×C53—24no—
728Q8×C53—42no—
729D4×C53—28no—
730D4×C53—24no—
731D4×C53—24no—
732D4×C53—42no—
733C2×C4×C53—24no—
734C2×C4×C53—22no—
735C2×C4×C53—28no—
736C2×C4×C53—42no—
737C2×C4×C53—48no—
738C2×C4×C53—41no—
739C2×C4×C532−1+414yes—
740C2×C4×C53C2514yes—
741C2×C4×C53C2514yes—
742C2×C4×C53C2511yescharacteristic
743C2×C4×C53C2511yescharacteristic
744C2×C4×C53C2514yes—
745C2×C4×C53C2511yescharacteristic
746C2×C4×C53C2514yes—
747C2×C4×C53C2514yes—
748C2×C4×C53C2511yescharacteristic
749C2×C4×C53C2511yescharacteristic
750C2×C4×C53C2511yescharacteristic
751C22⋊D53—28no—
752C22⋊D53—44no—
753C2×Dic53—24no—
754C2×Dic53—22no—
755C2×Dic53—22no—
756C2×Dic53—28no—
757C2×Dic53—22no—
758C2×Dic53—28no—
759C2×Dic53—48no—
760C2×Dic53—42no—
761C2×Dic53C2514yes—
762C2×Dic53C2511yescharacteristic
763C2×Dic53C2514yes—
764C2×Dic53C2514yes—
765C2×Dic53C2514yes—
766C2×Dic53C2514yes—
767C2×Dic53C2514yes—
768C2×Dic53C2511yescharacteristic
769C2×Dic53C2511yescharacteristic
770C2×Dic53C2511yescharacteristic
771C2×Dic53C2511yescharacteristic
772C2×Dic53C2511yescharacteristic
773C4×D53—22no—
774C4×D53—28no—
775C4×D53—22no—
776C4×D53—22no—
777C4×D53—22no—
778C4×D53—22no—
779C4×D53—22no—
780C4×D53—22no—
781C4×D53—22no—
782C4×D53—22no—
783C4×D53—41no—
784C4×D53—41no—
785C4×D53—44no—
786C4×D532−1+414yes—
787Dic106—24no—
788Dic106—24no—
789Dic106—24no—
790Dic106—24no—
791Dic106—28no—
792Dic106—28no—
793Dic106—28no—
794Dic106—48no—
795Dic106—48no—
796Dic106—44no—
797Dic106—42no—
798Dic106—42no—
799#62837—531nomaximal, Sylow
800C22×C53—21no—
801C22×C53—21no—
802C22×C53—24no—
803C22×C53—24no—
804C22×C53—24no—
805C22×C53C2×2−1+412yes—
806C22×C53C2611yescharacteristic
807C2×D53—21no—
808C2×D53—21no—
809C2×D53—21no—
810C2×D53—21no—
811C2×D53—21no—
812C2×D53—44no—
813C2×D53C2×2−1+412yes—
814C4×C53—24no—
815C4×C53—21no—
816C4×C53—24no—
817C4×C53—24no—
818C4×C53—24no—
819C4×C53—24no—
820C4×C53—21no—
821C4×C53—21no—
822C4×C53C2×2−1+412yes—
823C4×C53C2×2−1+412yes—
824C4×C53C2×2−1+412yes—
825Dic53—24no—
826Dic53—24no—
827Dic53—24no—
828Dic53—21no—
829Dic53—21no—
830Dic53—21no—
831Dic53—24no—
832Dic53—24no—
833Dic53—24no—
834Dic53—21no—
835Dic53C2×2−1+412yes—
836Dic53#58512yes—
837#3563—534no—
838#3563—534no—
839#3556—532no—
840#3555—532no—
841#3555—534no—
842#3555—532no—
843#3550—532no—
844#3538—534no—
845#3523—534no—
846#3523—534no—
847#3509—532no—
848#3509—534no—
849#3509—532no—
850#3507—532no—
851#3507—531no—
852#3507D5311yescharacteristic, complemented
853#3503—532no—
854#3503—532no—
855#3502—532no—
856#3502—531no—
857#3502—531no—
858#3495—532no—
859#3495—534no—
860#3495—532no—
861#3444—531no—
862C2×#533—531no—
863C2×#533—531no—
864C2×C53—22no—
865C2×C53—44no—
866C2×C53C22×2−1+411yescharacteristic
867C2×C53C22×2−1+411yescharacteristic
868C2×C53C2×#58511yescharacteristic
869D53—22no—
870D53—41no—
871#564—538no—
872#563—538no—
873#563—538no—
874#563—538no—
875#559—532no—
876#559C2×D5312yescomplemented
877Q82—532no—
878Q82—532no—
879Q82—532no—
880Q82—534no—
881Q82—532no—
882#557—532no—
883#557—534no—
884#557—532no—
885#557—534no—
886#557—538no—
887#557—534no—
888#557—534no—
889#557—534no—
890#557—534no—
891#557—534no—
892#557—534no—
893#557—532no—
894#557—534no—
895#557—534no—
896#557—532no—
897#557—532no—
898#557—534no—
899#557C2×D5312yescomplemented
900#556—538no—
901#556—534no—
902#556—534no—
903#556—534no—
904#556—534no—
905#556—534no—
906#556—534no—
907#556—532no—
908#556—534no—
909#556—534no—
910#556C2×D5312yescomplemented
911#556C2×D5314yescomplemented
912#554—534no—
913#554—532no—
914#554—538no—
915#554—534no—
916#554—534no—
917#554C2×D5312yescomplemented
918#552—538no—
919#552—538no—
920#552—538no—
921#552—538no—
922#552—538no—
923#552—538no—
924#552—534no—
925#552—534no—
926#552—538no—
927#552—534no—
928#552—538no—
929#552—534no—
930#552—538no—
931#552—534no—
932#552C2×D5314yescomplemented
933#551—538no—
934#551—538no—
935D4×Q8—538no—
936D4×Q8—538no—
937D4×Q8—534no—
938D4×Q8—534no—
939#544—534no—
940#544—538no—
941#544—534no—
942#544—538no—
943#544—532no—
944#544—534no—
945#544—532no—
946#544—534no—
947#544—534no—
948#542—534no—
949#542—534no—
950#542—534no—
951#542—534no—
952#541—534no—
953#541—538no—
954#541—538no—
955#541—538no—
956#541—538no—
957#541—534no—
958#541—538no—
959#541—534no—
960#541—534no—
961#541—538no—
962#541—534no—
963#541—534no—
964#541—538no—
965#539—538no—
966#539—534no—
967#539C2×D5314yes—
968#536—532no—
969#536—534no—
970#536—538no—
971#536C2×D5312yes—
972#533—531no—
973#533—531no—
974#533—531no—
975#533—531no—
976#533—534no—
977#533—532no—
978#533—532no—
979#533—532no—
980#533—534no—
981#533—534no—
982#533—534no—
983#533—532no—
984#533—532no—
985#533—532no—
986#533—532no—
987#533—532no—
988#533—532no—
989#533—532no—
990#533—532no—
991#533—532no—
992#533—532no—
993#533—534no—
994#533—532no—
995#533—534no—
996#533—531no—
997#533—531no—
998#533—534no—
999#533C2×D5311yescharacteristic
1000#532—531no—
1001#532—531no—
1002#532C2×D5311yescharacteristic
1003C2×C4⋊Q8—531no—
1004C2×C4⋊Q8—531no—
1005C2×C4⋊Q8—531no—
1006C2×C4⋊Q8—531no—
1007C2×C4⋊Q8—534no—
1008#529—532no—
1009#529—532no—
1010#529—534no—
1011#529—532no—
1012#529—532no—
1013#529—534no—
1014#529—532no—
1015#529—532no—
1016#529—534no—
1017#529C2×D5314yes—
1018C2×#125—532no—
1019C2×#125—532no—
1020#525—532no—
1021#525—532no—
1022#525—532no—
1023C2×C22⋊Q8—531no—
1024C2×C22⋊Q8—532no—
1025C2×C22⋊Q8—532no—
1026C2×C22⋊Q8—532no—
1027C2×C22⋊Q8—531no—
1028#520—532no—
1029#520—534no—
1030#520C2×D5312yes—
1031#519—532no—
1032#519—534no—
1033#519—532no—
1034#519—538no—
1035C4×#41—532no—
1036C4×#41—532no—
1037C4×#41—532no—
1038C2×C4×Q8—532no—
1039C2×C4×Q8—532no—
1040C2×C4×Q8—531no—
1041C2×C4×Q8—532no—
1042C2×C4×Q8C2×D5311yescharacteristic
1043C2×#117—532no—
1044C2×#117—532no—
1045C22×C42—531no—
1046C53#6283711yescharacteristic, complemented, Sylow
1047C2×#41—532no—
1048C2×#41—532no—
1049C2×#41C22×D5312yes—
1050C22×Q8—532no—
1051C22×Q8—532no—
1052C22×Q8—531no—
1053C22×Q8—532no—
1054C22×Q8—538no—
1055C22×Q8C22×D5311yescharacteristic
1056C23×C4—531no—
1057C23×C4—531no—
1058C23×C4—531no—
1059C4⋊Q8—532no—
1060C4⋊Q8—532no—
1061C4⋊Q8—532no—
1062C4⋊Q8—532no—
1063C4⋊Q8—532no—
1064C4⋊Q8—532no—
1065C4⋊Q8—534no—
1066C4⋊Q8—534no—
1067C4⋊Q8—538no—
1068C4⋊Q8—532no—
1069C4⋊Q8—532no—
1070C4⋊Q8—532no—
1071C4⋊Q8—532no—
1072C4⋊Q8—532no—
1073C4⋊Q8—532no—
1074C4⋊Q8—532no—
1075C4⋊Q8—532no—
1076C4⋊Q8—538no—
1077C4⋊Q8—538no—
1078C4⋊Q8—534no—
1079C4⋊Q8—534no—
1080C4⋊Q8—534no—
1081C4⋊Q8—534no—
1082C4⋊Q8—538no—
1083C4⋊Q8—538no—
1084C4⋊Q8—538no—
1085C4⋊Q8—538no—
1086C4⋊Q8—531no—
1087C4⋊Q8—531no—
1088C4⋊Q8—531no—
1089C4⋊Q8—531no—
1090C4⋊Q8—534no—
1091C4⋊Q8—534no—
1092C4⋊Q8—534no—
1093C4⋊Q8—538no—
1094C4⋊Q8C22×D5311yescharacteristic
1095C4⋊Q8C22×D5311yescharacteristic
1096C4⋊Q8C22×D5311yescharacteristic
1097C4⋊Q8C22×D5314yes—
1098#127C22×D5311yescharacteristic
1099#126—538no—
1100#126—538no—
1101#126—538no—
1102#126—534no—
1103#126—534no—
1104#126—538no—
1105#126—538no—
1106#126—538no—
1107#126—538no—
1108#126—538no—
1109#126—538no—
1110#126—538no—
1111#126—538no—
1112#126—538no—
1113#126—538no—
1114#126—538no—
1115#126C22×D5318yes—
1116#126C22×D5318yes—
1117#125—534no—
1118#125—534no—
1119#125—534no—
1120#125—532no—
1121#125—532no—
1122#125—534no—
1123#125—534no—
1124#125—534no—
1125#125—532no—
1126#125—532no—
1127#125—534no—
1128#125—534no—
1129#125—538no—
1130#125—538no—
1131#125—538no—
1132#125—538no—
1133#125—538no—
1134#125—534no—
1135#125—534no—
1136#125—538no—
1137#125—538no—
1138#125—538no—
1139#125—538no—
1140#125—538no—
1141#125—538no—
1142#125—538no—
1143#125—538no—
1144#125—538no—
1145#125—538no—
1146#125—538no—
1147#125—538no—
1148#125—538no—
1149#125—532no—
1150#125—532no—
1151#125—534no—
1152#125—538no—
1153#125—538no—
1154#125—538no—
1155#125C22×D5312yes—
1156#125C22×D5314yes—
1157#125C22×D5318yes—
1158#124—532no—
1159#124—532no—
1160#124—534no—
1161#124—534no—
1162#124—538no—
1163#124—538no—
1164#124C22×D5312yes—
1165#124C22×D5314yes—
1166#124C22×D5314yes—
1167#123—534no—
1168#123—538no—
1169#123—538no—
1170#123—538no—
1171#123—534no—
1172#123—534no—
1173#123—538no—
1174#123—538no—
1175#123—538no—
1176#123C22×D5318yes—
1177#123C22×D5318yes—
1178C22⋊Q8—532no—
1179C22⋊Q8—532no—
1180C22⋊Q8—532no—
1181C22⋊Q8—532no—
1182C22⋊Q8—532no—
1183C22⋊Q8—532no—
1184C22⋊Q8—532no—
1185C22⋊Q8—532no—
1186C22⋊Q8—532no—
1187C22⋊Q8—532no—
1188C22⋊Q8—532no—
1189C22⋊Q8—532no—
1190C22⋊Q8—534no—
1191C22⋊Q8—534no—
1192C22⋊Q8—538no—
1193C22⋊Q8—538no—
1194C22⋊Q8—538no—
1195C22⋊Q8—538no—
1196C22⋊Q8—532no—
1197C22⋊Q8—534no—
1198C22⋊Q8—534no—
1199C22⋊Q8—534no—
1200C22⋊Q8—532no—
1201C22⋊Q8—532no—
1202C22⋊Q8—534no—
1203C22⋊Q8—532no—
1204C22⋊Q8—534no—
1205C22⋊Q8—532no—
1206C22⋊Q8—534no—
1207C22⋊Q8—532no—
1208C22⋊Q8—532no—
1209C22⋊Q8—532no—
1210C22⋊Q8—538no—
1211C22⋊Q8—538no—
1212C22⋊Q8—534no—
1213C22⋊Q8—534no—
1214C22⋊Q8—538no—
1215C22⋊Q8—538no—
1216C22⋊Q8—538no—
1217C22⋊Q8—538no—
1218C22⋊Q8—538no—
1219C22⋊Q8—538no—
1220C22⋊Q8—538no—
1221C22⋊Q8—538no—
1222C22⋊Q8—538no—
1223C22⋊Q8C22×D5312yes—
1224C22⋊Q8C22×D5312yes—
1225C22⋊Q8C22×D5314yes—
1226C22⋊Q8C22×D5314yes—
1227C22⋊Q8C22×D5318yes—
1228#121—532no—
1229#121—532no—
1230#121—532no—
1231#121—532no—
1232#121C22×D5312yes—
1233#121C22×D5312yes—
1234#120—534no—
1235C4×Q8—532no—
1236C4×Q8—532no—
1237C4×Q8—532no—
1238C4×Q8—532no—
1239C4×Q8—534no—
1240C4×Q8—534no—
1241C4×Q8—534no—
1242C4×Q8—534no—
1243C4×Q8—534no—
1244C4×Q8—534no—
1245C4×Q8—534no—
1246C4×Q8—532no—
1247C4×Q8—534no—
1248C4×Q8—532no—
1249C4×Q8—532no—
1250C4×Q8—532no—
1251C4×Q8—534no—
1252C4×Q8—538no—
1253C4×Q8—534no—
1254C4×Q8—538no—
1255C4×Q8—538no—
1256C4×Q8—538no—
1257C4×Q8—534no—
1258C4×Q8—534no—
1259C4×Q8—534no—
1260C4×Q8—534no—
1261C4×Q8—534no—
1262C4×Q8—534no—
1263C4×Q8—532no—
1264C4×Q8—534no—
1265C4×Q8—532no—
1266C4×Q8—534no—
1267C4×Q8—532no—
1268C4×Q8—532no—
1269C4×Q8—532no—
1270C4×Q8—532no—
1271C4×Q8—532no—
1272C4×Q8—532no—
1273C4×Q8—534no—
1274C4×Q8—538no—
1275C4×Q8—538no—
1276C4×Q8—538no—
1277C4×Q8—538no—
1278C4×Q8—534no—
1279C4×Q8—534no—
1280C4×Q8—534no—
1281C4×Q8C22×D5312yes—
1282C4×Q8C22×D5312yes—
1283C4×Q8C22×D5312yes—
1284C4×Q8C22×D5312yes—
1285C4×Q8C22×D5312yes—
1286C4×Q8C22×D5312yes—
1287C4×Q8C22×D5314yes—
1288C4×Q8C22×D5314yes—
1289C4×D4—534no—
1290C4×D4—534no—
1291C4×D4—532no—
1292C4×D4—532no—
1293C4×D4—532no—
1294C4×D4—532no—
1295C4×D4—538no—
1296C4×D4—534no—
1297C4×D4—534no—
1298C4×D4—534no—
1299C4×D4—534no—
1300C4×D4—538no—
1301C4×D4—534no—
1302C4×D4—534no—
1303C4×D4—538no—
1304C4×D4C22×D5312yes—
1305C4×D4C22×D5312yes—
1306C4×D4C22×D5314yes—
1307C4×D4C22×D5314yes—
1308C4×D4C22×D5318yes—
1309#117—532no—
1310#117—532no—
1311#117—534no—
1312#117—538no—
1313#117—538no—
1314#117—534no—
1315#117—532no—
1316#117—532no—
1317#117—532no—
1318#117—532no—
1319#117—538no—
1320#117—534no—
1321#117—534no—
1322#117—534no—
1323#117—538no—
1324#117—538no—
1325#117—538no—
1326#117—538no—
1327#117—538no—
1328#117—534no—
1329#117—534no—
1330#117—534no—
1331#117—534no—
1332#117—534no—
1333#117—538no—
1334#117C22×D5312yes—
1335#117C22×D5318yes—
1336#117C22×D5314yes—
1337C2×C4⋊C4—532no—
1338C2×C4⋊C4—532no—
1339C2×C4⋊C4—531no—
1340C2×C4⋊C4—532no—
1341C2×C4⋊C4—532no—
1342C2×C4⋊C4—532no—
1343C2×C4⋊C4—532no—
1344C2×C4⋊C4—538no—
1345C2×C4⋊C4—534no—
1346C2×C4⋊C4—532no—
1347C2×C4⋊C4—532no—
1348C2×C4⋊C4—532no—
1349C2×C4⋊C4—534no—
1350C2×C4⋊C4—534no—
1351C2×C4⋊C4—532no—
1352C2×C4⋊C4C22×D5311yescharacteristic
1353C2×C4⋊C4C22×D5312yes—
1354C2×C4⋊C4C22×D5314yes—
1355C2×C22⋊C4—532no—
1356C2×C22⋊C4—532no—
1357C2×C22⋊C4—534no—
1358C2×C42—532no—
1359C2×C42—531no—
1360C2×C42—534no—
1361C2×C42—531no—
1362C2×C42—531no—
1363C2×C42—534no—
1364C2×C42—531no—
1365C2×C42—531no—
1366C2×C42—531no—
1367C2×C42—531no—
1368C2×C42—531no—
1369C2×C42—531no—
1370C2×C42—531no—
1371C2×C42—531no—
1372C2×C42C22×D5312yes—
1373C2×C42C22×D5311yescharacteristic
1374C24—531no—
1375#41—28no—
1376#41—1068no—
1377#41—2124no—
1378C2×Q8—24no—
1379C2×Q8—534no—
1380C2×Q8—532no—
1381C2×Q8—532no—
1382C2×Q8—532no—
1383C2×Q8—532no—
1384C2×Q8—534no—
1385C2×Q8—534no—
1386C2×Q8—532no—
1387C2×Q8—534no—
1388C2×Q8—538no—
1389C2×Q8—538no—
1390C2×Q8—532no—
1391C2×Q8—1068no—
1392C2×Q8—1064no—
1393C2×Q8—2124no—
1394C2×Q8—21216no—
1395C2×Q8—2124no—
1396C2×Q8C23×D5312yes—
1397C2×Q8C23×D5312yes—
1398C2×Q8C23×D5312yes—
1399C2×Q8C23×D5312yes—
1400C2×Q8C23×D5312yes—
1401C2×D4—534no—
1402C2×D4—534no—
1403C2×D4C23×D5314yes—
1404C2×D4C23×D5312yes—
1405C2×D4C23×D5312yes—
1406C2×D4C23×D5312yes—
1407C22×C4—531no—
1408C22×C4—531no—
1409C22×C4—531no—
1410C22×C4—531no—
1411C22×C4—532no—
1412C22×C4—534no—
1413C22×C4—534no—
1414C22×C4—532no—
1415C22×C4—538no—
1416C22×C4—531no—
1417C22×C4—531no—
1418C22×C4—531no—
1419C22×C4—531no—
1420C22×C4—531no—
1421C22×C4—531no—
1422C22×C4—531no—
1423C22×C4—531no—
1424C22×C4—531no—
1425C22×C4—534no—
1426C22×C4—531no—
1427C22×C4—531no—
1428C22×C4—534no—
1429C22×C4—1064no—
1430C22×C4—1064no—
1431C22×C4—2122no—
1432C22×C4C23×D5311yescharacteristic
1433C22×C4C23×D5314yes—
1434C22×C4C23×D5312yes—
1435C22×C4C23×D5311yescharacteristic
1436C22×C4C23×D5312yes—
1437C22×C4C23×D5318yes—
1438C22×C4C23×D5311yescharacteristic
1439C4⋊C4—534no—
1440C4⋊C4—534no—
1441C4⋊C4—532no—
1442C4⋊C4—532no—
1443C4⋊C4—534no—
1444C4⋊C4—532no—
1445C4⋊C4—534no—
1446C4⋊C4—534no—
1447C4⋊C4—534no—
1448C4⋊C4—534no—
1449C4⋊C4—534no—
1450C4⋊C4—534no—
1451C4⋊C4—534no—
1452C4⋊C4—534no—
1453C4⋊C4—534no—
1454C4⋊C4—532no—
1455C4⋊C4—532no—
1456C4⋊C4—538no—
1457C4⋊C4—538no—
1458C4⋊C4—538no—
1459C4⋊C4—534no—
1460C4⋊C4—534no—
1461C4⋊C4—534no—
1462C4⋊C4—534no—
1463C4⋊C4—534no—
1464C4⋊C4—534no—
1465C4⋊C4—534no—
1466C4⋊C4—534no—
1467C4⋊C4—534no—
1468C4⋊C4—534no—
1469C4⋊C4—532no—
1470C4⋊C4—532no—
1471C4⋊C4—532no—
1472C4⋊C4—532no—
1473C4⋊C4—534no—
1474C4⋊C4—534no—
1475C4⋊C4—532no—
1476C4⋊C4—534no—
1477C4⋊C4—534no—
1478C4⋊C4—534no—
1479C4⋊C4—534no—
1480C4⋊C4—538no—
1481C4⋊C4—538no—
1482C4⋊C4—538no—
1483C4⋊C4—538no—
1484C4⋊C4—538no—
1485C4⋊C4—538no—
1486C4⋊C4—538no—
1487C4⋊C4—538no—
1488C4⋊C4—538no—
1489C4⋊C4—538no—
1490C4⋊C4C23×D5312yes—
1491C4⋊C4C23×D5312yes—
1492C4⋊C4C23×D5314yes—
1493C4⋊C4C23×D5312yes—
1494C4⋊C4C23×D5314yes—
1495C4⋊C4C23×D5312yes—
1496C4⋊C4C23×D5312yes—
1497C4⋊C4C23×D5312yes—
1498C4⋊C4C23×D5318yes—
1499C4⋊C4C23×D5314yes—
1500C4⋊C4C23×D5314yes—
1501C4⋊C4C23×D5312yes—
1502C4⋊C4C23×D5312yes—
1503C4⋊C4C23×D5318yes—
1504C4⋊C4C23×D5318yes—
1505C22⋊C4—534no—
1506C22⋊C4—534no—
1507C22⋊C4—534no—
1508C22⋊C4—538no—
1509C22⋊C4—534no—
1510C22⋊C4—534no—
1511C22⋊C4—534no—
1512C22⋊C4—538no—
1513C22⋊C4—538no—
1514C22⋊C4—534no—
1515C22⋊C4—534no—
1516C22⋊C4—534no—
1517C22⋊C4—534no—
1518C22⋊C4—534no—
1519C22⋊C4—534no—
1520C22⋊C4—534no—
1521C22⋊C4—534no—
1522C22⋊C4C23×D5314yes—
1523C22⋊C4C23×D5314yes—
1524C22⋊C4C23×D5318yes—
1525C22⋊C4C23×D5314yes—
1526C22⋊C4C23×D5318yes—
1527C22⋊C4C23×D5318yes—
1528C42—531no—
1529C42—531no—
1530C42—531no—
1531C42—531no—
1532C42—531no—
1533C42—531no—
1534C42—531no—
1535C42—531no—
1536C42—531no—
1537C42—531no—
1538C42—531no—
1539C42—531no—
1540C42—534no—
1541C42—534no—
1542C42—534no—
1543C42—534no—
1544C42—534no—
1545C42—534no—
1546C42—534no—
1547C42—534no—
1548C42—538no—
1549C42—538no—
1550C42—538no—
1551C42—538no—
1552C42—538no—
1553C42C23×D5311yescharacteristic
1554C42C23×D5311yescharacteristic
1555C42C23×D5311yescharacteristic
1556C42C23×D5311yescharacteristic
1557C42C23×D5314yes—
1558C42C23×D5314yes—
1559C42C23×D5314yes—
1560C42C23×D5318yes—
1561C23—531no—
1562C23—531no—
1563C23—1062no—
1564C23—1062no—
1565C23—2121no—
1566C23C24×D5314yes—
1567C23C24×D5311yescharacteristic
1568Q8—24no—
1569Q8—24no—
1570Q8—24no—
1571Q8—24no—
1572Q8—42no—
1573Q8—1068no—
1574Q8—1068no—
1575Q8—1068no—
1576Q8—1064no—
1577Q8—1064no—
1578Q8—1064no—
1579Q8—1064no—
1580Q8—2124no—
1581Q8—2128no—
1582Q8—2128no—
1583Q8—2122no—
1584Q8—2122no—
1585D4—28no—
1586D4—24no—
1587D4—24no—
1588D4—42no—
1589D4—1068no—
1590D4—2124no—
1591C2×C4—24no—
1592C2×C4—22no—
1593C2×C4—28no—
1594C2×C4—41no—
1595C2×C4—42no—
1596C2×C4—48no—
1597C2×C4—531no—
1598C2×C4—531no—
1599C2×C4—534no—
1600C2×C4—531no—
1601C2×C4—534no—
1602C2×C4—534no—
1603C2×C4—534no—
1604C2×C4—534no—
1605C2×C4—531no—
1606C2×C4—531no—
1607C2×C4—531no—
1608C2×C4—534no—
1609C2×C4—534no—
1610C2×C4—1062no—
1611C2×C4—1062no—
1612C2×C4—1062no—
1613C2×C4—1062no—
1614C2×C4—1068no—
1615C2×C4—1062no—
1616C2×C4—1062no—
1617C2×C4—1068no—
1618C2×C4—1068no—
1619C2×C4—1062no—
1620C2×C4—1064no—
1621C2×C4—1062no—
1622C2×C4—1062no—
1623C2×C4—1062no—
1624C2×C4—1062no—
1625C2×C4—1062no—
1626C2×C4—2121no—
1627C2×C4—2121no—
1628C2×C4—2124no—
1629C2×C4—2122no—
1630C2×C4—2128no—
1631C2×C4#1313326414yes—
1632C2×C4C24×D5311yescharacteristic
1633C2×C4C24×D5314yes—
1634C2×C4C24×D5314yes—
1635C2×C4C24×D5314yes—
1636C2×C4C24×D5314yes—
1637C2×C4C24×D5311yescharacteristic
1638C2×C4C24×D5311yescharacteristic
1639C2×C4C24×D5314yes—
1640C2×C4C24×D5311yescharacteristic
1641C2×C4C24×D5311yescharacteristic
1642C2×C4C24×D5311yescharacteristic
1643C22—21no—
1644C22—21no—
1645C22—24no—
1646C22—24no—
1647C22—24no—
1648C22—532no—
1649C22—1061no—
1650C22—1061no—
1651C22—1061no—
1652C22—1061no—
1653C22—1061no—
1654C22—2124no—
1655C22C2×#1313326412yes—
1656C22C25×D5311yescharacteristic
1657C4—21no—
1658C4—24no—
1659C4—24no—
1660C4—24no—
1661C4—24no—
1662C4—24no—
1663C4—21no—
1664C4—21no—
1665C4—532no—
1666C4—532no—
1667C4—1061no—
1668C4—1064no—
1669C4—1064no—
1670C4—1061no—
1671C4—1061no—
1672C4—1064no—
1673C4—1061no—
1674C4—1064no—
1675C4—1064no—
1676C4—1064no—
1677C42−1+4×D5312yes—
1678C4C2×#1313326412yes—
1679C4C2×#1313326412yes—
1680C2—22no—
1681C2—44no—
1682C2—1062no—
1683C2—2121no—
1684C2C2×2−1+4×D5311yescharacteristic
1685C2C22×#1313326411yescharacteristic
1686C2#585×D5311yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3507C2
prime radical#20288010C2
hypercenter#3507D53
hypocenterC53#62837
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3507

Complements

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

NH ≅ G/Ntype
1. #20289323C2semidirect
2. #20289322C2semidirect
3. #20289207C2semidirect
4. #20289206C2semidirect
5. #20289202C2semidirect
6. #20289191C2semidirect
7. #20289127C2semidirect
8. #20288962C2semidirect
9. #20288810C2semidirect
10. #20288809C2semidirect
11. #20288600C2semidirect
12. #20288595C2semidirect
13. #20288593C2semidirect
14. #20288577C2semidirect
15. #20288572C2semidirect
16. #20288529C2semidirect
17. #20288528C2semidirect
18. #20288525C2semidirect
19. #20288520C2semidirect
20. #20288519C2semidirect
21. #20288468C2semidirect
22. #20288464C2semidirect
23. #20288455C2semidirect
25. C2×#16811177C2semidirect
26. #533×D53C2semidirect
27. C53×#3507C2semidirect
28. C53⋊#564C22semidirect
29. #16811376C22semidirect
32. #16811359C22semidirect
33. Q8×Dic106C22semidirect
34. Q8×Dic106C22semidirect
35. Q8×Dic106C22semidirect
36. Q8×Dic106C22semidirect
37. #16811353C22semidirect
38. #16811352C22semidirect
39. #16811352C22semidirect
40. #16811352C22semidirect
41. #16811351C22semidirect
42. #16811351C22semidirect
43. #16811351C22semidirect
44. #16811350C22semidirect
45. #16811350C22semidirect
46. #16811350C22semidirect
47. #16811350C22semidirect
48. #16811349C22semidirect
49. #16811349C22semidirect
50. #16811349C22semidirect
51. #16811348C22semidirect
52. #16811348C22semidirect
53. #16811348C22semidirect
54. #16811348C22semidirect
56. #16811343C22semidirect
57. #16811343C22semidirect
58. #16811342C22semidirect
59. #16811342C22semidirect
60. #16811342C22semidirect
61. #16811342C22semidirect
62. #16811342C22semidirect
66. #16811332C22semidirect
68. #16811330C22semidirect
72. #16811313C22semidirect
78. #16811310C22semidirect
87. D4×Dic106C22semidirect
88. D4×Dic106C22semidirect
92. #16811254C22semidirect
96. #16811252C22semidirect
98. #16811251C22semidirect
104. #16811235C22semidirect
106. #16811233C22semidirect
107. #16811233C22semidirect
108. #16811233C22semidirect
112. #16811230C22semidirect
113. #16811230C22semidirect
114. #16811230C22semidirect
115. #16811230C22semidirect
142. #16811176C22semidirect
146. #16811175C22semidirect
147. #16811175C22semidirect
151. C2×#13133216C22semidirect
178. #16811100C22semidirect
190. C53×#559C22semidirect
191. C53×#557C22semidirect
192. C53×#556C22semidirect
193. C53×#556C22semidirect
194. C53×#554C22semidirect
195. C53×#552C22semidirect
852. #3507D53semidirect
876. #559C2×D53semidirect
899. #557C2×D53semidirect
910. #556C2×D53semidirect
911. #556C2×D53semidirect
917. #554C2×D53semidirect
932. #552C2×D53semidirect
1046. C53#62837semidirect

Maximal subgroups

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

subgroupindex
#202893232
#202893222
#202892072
#202892062
#202892022
#202891912
#202891272
#202889622
#202888102
#202888092
#202886002
#202885952
#202885932
#202885772
#202885722
#202885292
#202885282
#202885252
#202885202
#202885192
#202884682
#202884642
#202884552
#202880102
C2×#168111772
#533×D532
C53×#35072
#6283753