Finite Group Databasebeta

← #28292967

Subgroups — #28292967

Order 13568.

6528 conjugacy classes of subgroups.

The subgroup lattice has 1718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289360C214yesmaximal, complemented
2#20289333C214yesmaximal, complemented
3#20289217C214yesmaximal, complemented
4#20289197C212yesmaximal, complemented
5#20289180C212yesmaximal, complemented
6#20289152C212yesmaximal, complemented
7#20289055C212yesmaximal, complemented
8#20288918C214yesmaximal, complemented
9#20288803C212yesmaximal, complemented
10#20288792C212yesmaximal, complemented
11#20288752C214yesmaximal, complemented
12#20288732C212yesmaximal, complemented
13#20288693C214yesmaximal, complemented
14#20288693C212yesmaximal, complemented
15#20288611C212yesmaximal, complemented
16#20288577C211yesmaximal, characteristic, complemented
17#20288571C214yesmaximal, complemented
18#20288564C211yesmaximal, characteristic, complemented
19#20288541C212yesmaximal, complemented
20#20288520C211yesmaximal, characteristic, complemented
21#20288516C211yesmaximal, characteristic, complemented
22#20288469C212yesmaximal, complemented
23#20288455C214yesmaximal, complemented
24#20288452C212yesmaximal, complemented
25C2×#16811180C211yesmaximal, characteristic, complemented
26C2×#16811157C211yesmaximal, characteristic, complemented
27C53×#3444C211yesmaximal, characteristic, complemented
28#16811375C2218yescomplemented
29#16811375C2218yescomplemented
30#16811374C2218yescomplemented
31#16811368C2218yescomplemented
32#16811359C2212yescomplemented
33#16811356C2214yescomplemented
34#16811356C2214yescomplemented
35#16811355C2214yescomplemented
36Q8×Dic106C2212yescomplemented
37#16811353C2212yescomplemented
38#16811351C2214yescomplemented
39#16811351C2212yescomplemented
40#16811350C2214yescomplemented
41#16811349C2214yescomplemented
42#16811349C2214yescomplemented
43#16811348C2212yescomplemented
44#16811348C2212yescomplemented
45#16811347C2212yescomplemented
46#16811345C2214yescomplemented
47#16811345C2214yescomplemented
48#16811343C2212yescomplemented
49#16811343C2214yescomplemented
50#16811342C2214yescomplemented
51#16811341C2218yescomplemented
52#16811341C2214yescomplemented
53#16811340C2218yescomplemented
54#16811338C2214yes—
55#16811338C2212yescomplemented
56#16811334C2212yescomplemented
57#16811333C2212yescomplemented
58#16811333C2214yescomplemented
59#16811332C2218yes—
60#16811332C2218yes—
61#16811332C2214yescomplemented
62#16811332C2214yescomplemented
63#16811330C2212yescomplemented
64#16811330C2214yescomplemented
65#16811329C2214yescomplemented
66#16811319C2214yes—
67#16811319C2214yes—
68#16811319C2214yescomplemented
69#16811315C2214yescomplemented
70#16811313C2214yescomplemented
71#16811313C2214yescomplemented
72#16811313C2214yescomplemented
73#16811312C2214yescomplemented
74#16811312C2218yescomplemented
75#16811310C2218yes—
76#16811309C2218yescomplemented
77#16811306C2218yescomplemented
78#16811306C2218yescomplemented
79#16811306C2218yescomplemented
80#16811304C2218yes—
81#16811302C2218yes—
82#16811302C2218yes—
83#16811296C2218yes—
84#16811293C2212yescomplemented
85Q8×D212C2212yescomplemented
86#16811288C2212yescomplemented
87#16811286C2214yescomplemented
88#16811280C2214yescomplemented
89#16811279C2214yescomplemented
90#16811277C2214yes—
91#16811277C2212yescomplemented
92#16811273C2214yescomplemented
93#16811272C2218yescomplemented
94#16811272C2214yescomplemented
95#16811260C2218yes—
96#16811253C2214yescomplemented
97#16811252C2214yes—
98#16811251C2212yes—
99#16811251C2212yes—
100#16811251C2214yescomplemented
101#16811251C2214yescomplemented
102#16811248C2214yes—
103#16811246C2214yes—
104#16811244C2214yescomplemented
105#16811244C2214yescomplemented
106#16811242C2214yescomplemented
107#16811241C2218yescomplemented
108#16811240C2214yescomplemented
109#16811238C2214yescomplemented
110#16811238C2218yescomplemented
111#16811237C2218yescomplemented
112#16811236C2214yescomplemented
113#16811233C2214yescomplemented
114#16811232C2218yescomplemented
115#16811231C2214yescomplemented
116#16811231C2218yescomplemented
117#16811226C2214yes—
118#16811218C2214yes—
119#16811217C2218yescomplemented
120#16811216C2218yescomplemented
121#16811215C2218yescomplemented
122#16811215C2218yescomplemented
123#16811215C2218yescomplemented
124#16811210C2214yes—
125#16811195C2218yescomplemented
126#16811194C2212yes—
127#16811193C2214yescomplemented
128#16811187C2212yes—
129#16811180C2211yescharacteristic
130#16811180C2211yescharacteristic
131#16811180C2212yes—
132#16811180C2212yes—
133#16811180C2212yes—
134#16811180C2212yescomplemented
135#16811180C2212yescomplemented
136#16811180C2211yescharacteristic, complemented
137#16811180C2212yescomplemented
138#16811180C2211yescharacteristic, complemented
139#16811180C2214yescomplemented
140#16811175C2214yes—
141#16811175C2214yescomplemented
142#16811168C2214yes—
143C2×#13133217C2211yescharacteristic, complemented
144C2×#13133217C2211yescharacteristic, complemented
145#16811159C2214yes—
146#16811157C2212yes—
147#16811157C2212yes—
148#16811157C2212yes—
149#16811157C2212yes—
150#16811157C2212yes—
151#16811157C2212yes—
152#16811157C2212yes—
153#16811157C2212yes—
154#16811157C2214yescomplemented
155#16811157C2214yescomplemented
156#16811154C2214yes—
157#16811154C2214yescomplemented
158C2×#13133211C2212yes—
159C2×#13133209C2211yescharacteristic
160C2×#13133209C2212yescomplemented
161C2×#13133209C2214yescomplemented
162C2×#13133205C2211yescharacteristic
163#16811133C2214yes—
164C2×#13133200C2212yes—
165C2×#13133196C2212yes—
166C2×#13133196C2212yes—
167C2×#13133196C2211yescharacteristic
168C22⋊Q8×D53C2214yes—
169C2×#13133191C2211yescharacteristic
170#16811106C2212yes—
171#16811106C2212yes—
172#16811102C2214yescomplemented
173#16811102C2218yescomplemented
174#16811100C2212yes—
175#16811099C2214yescomplemented
176#16811097C2212yes—
177C2×C4×Dic106C2211yescharacteristic
178C2×C4×Dic106C2212yescomplemented
179C2×C4×Dic106C2212yescomplemented
180C2×C4×D212C2211yescharacteristic
181C2×C4×C22⋊D53C2212yes—
182C2×#13133176C2212yes—
183C2×#13133174C2212yes—
184C53×#533C2211yescharacteristic
185C53×#533C2211yescharacteristic, complemented
186C53×#533C2211yescharacteristic, complemented
187C53×#532C2211yescharacteristic
188C53×#532C2211yescharacteristic, complemented
189C53×#532C2211yescharacteristic, complemented
190C53×#529C2212yes—
191C53×#529C2212yes—
192C53×#529C2212yescomplemented
193C53×#529C2212yescomplemented
194C53×#529C2212yescomplemented
195C53×#529C2212yescomplemented
196C53×#525C2212yes—
197C53×#525C2212yes—
198C53×#525C2212yes—
199C4×#41×C53C2212yes—
200C4×#41×C53C2212yescomplemented
201C4×#41×C53C2212yescomplemented
202C22×C42×C53C2211yescharacteristic
203C2×#11719947C2318yes—
204C2×#11719947C2314yes—
205C22×Dic106C2311yescharacteristic
206C22×Dic106C2312yes—
207C22×Dic106C2312yes—
208C2×Q8×D53C2314yes—
209C22×D212C2311yescharacteristic
210C22×C22⋊D53C2312yes—
211C22×C4×D53C2312yes—
212#13133217C2314yes—
213#13133217C2311yescharacteristic
214#13133217C2311yescharacteristic
215#13133217C2314yes—
216#13133217C2311yescharacteristic
217#13133217C2311yescharacteristic
218#13133217C2312yes—
219#13133217C2312yes—
220#13133217C2312yes—
221#13133217C2312yes—
222#13133217C2312yes—
223#13133217C2312yes—
224#13133216C2314yes—
225#13133216C2318yes—
226#13133216C2314yes—
227#13133216C2318yes—
228#13133216C2314yes—
229#13133216C2318yes—
230#13133215C2314yes—
231#13133215C2318yes—
232#13133215C2314yes—
233#13133213C2314yes—
234#13133212C2318yes—
235#13133212C2318yes—
236#13133212C2318yes—
237#13133212C2318yes—
238#13133212C2318yes—
239#13133211C2318yes—
240#13133211C2318yes—
241#13133211C2314yes—
242#13133211C2314yes—
243#13133211C2314yes—
244#13133211C2314yes—
245#13133210C2318yes—
246#13133210C2318yes—
247#13133210C2318yes—
248#13133210C2318yes—
249#13133210C2318yes—
250#13133210C2318yes—
251#13133209C2314yes—
252#13133209C2318yes—
253#13133209C2318yes—
254#13133209C2312yes—
255#13133209C2314yes—
256#13133209C2314yes—
257#13133209C2312yes—
258#13133209C2312yes—
259#13133209C2312yes—
260#13133209C2312yes—
261#13133209C2312yes—
262#13133209C2312yes—
263#13133209C2312yes—
264#13133209C2314yes—
265#13133208C2318yes—
266#13133208C2318yes—
267#13133208C2314yes—
268#13133208C2318yes—
269#13133208C2314yes—
270#13133208C2314yes—
271#13133207C2318yes—
272#13133207C2318yes—
273#13133207C2318yes—
274#13133207C2318yes—
275#13133207C2318yes—
276#13133207C2318yes—
277#13133206C2314yes—
278#13133205C2312yes—
279#13133205C2312yes—
280#13133205C2312yes—
281#13133205C2312yes—
282#13133204C2314yes—
283#13133204C2318yes—
284#13133204C2314yes—
285#13133203C2318yes—
286#13133203C2318yes—
287#13133203C2318yes—
288#13133203C2318yes—
289#13133203C2318yes—
290#13133201C2318yes—
291#13133201C2318yes—
292#13133201C2318yes—
293#13133200C2314yes—
294#13133200C2318yes—
295#13133200C2318yes—
296#13133200C2314yes—
297#13133200C2314yes—
298#13133200C2314yes—
299#13133199C2318yes—
300#13133199C2318yes—
301#13133199C2318yes—
302#13133199C2318yes—
303#13133199C2318yes—
304#13133198C2318yes—
305#13133198C2318yes—
306#13133198C2318yes—
307#13133198C2318yes—
308#13133197C2318yes—
309#13133197C2314yes—
310#13133197C2314yes—
311#13133197C2318yes—
312#13133196C2312yes—
313#13133196C2318yes—
314#13133196C2312yes—
315#13133196C2318yes—
316#13133196C2314yes—
317#13133196C2314yes—
318#13133196C2314yes—
319#13133196C2312yes—
320#13133196C2312yes—
321#13133196C2314yes—
322#13133196C2314yes—
323#13133196C2312yes—
324#13133196C2312yes—
325#13133196C2312yes—
326#13133196C2312yes—
327#13133196C2312yes—
328#13133196C2312yes—
329#13133196C2312yes—
330#13133196C2314yes—
331#13133196C2312yes—
332#13133195C2318yes—
333#13133195C2318yes—
334#13133195C2318yes—
335#13133195C2318yes—
336#13133195C2318yes—
337#13133194C2318yes—
338#13133194C2318yes—
339#13133194C2318yes—
340#13133194C2318yes—
341#13133194C2318yes—
342#13133194C2318yes—
343#13133194C2318yes—
344#13133194C2318yes—
345#13133194C2318yes—
346#13133193C2314yes—
347#13133193C2318yes—
348#13133191C2312yes—
349#13133191C2314yes—
350#13133191C2314yes—
351#13133191C2312yes—
352#13133191C2312yes—
353#13133191C2312yes—
354#13133189C2318yes—
355#13133189C2318yes—
356#13133189C2318yes—
357#13133188C2314yes—
358#13133188C2318yes—
359#13133185C2318yes—
360Q8×Dic53C2314yes—
361Q8×Dic53C2314yes—
362Q8×Dic53C2314yes—
363C4×Dic106C2312yes—
364C4×Dic106C2312yes—
365C4×Dic106C2312yes—
366C4×Dic106C2318yes—
367C4×Dic106C2314yes—
368C4×Dic106C2312yes—
369C4×Dic106C2314yes—
370C4×Dic106C2314yes—
371C4×Dic106C2312yes—
372C4×Dic106C2312yes—
373C4×Dic106C2318yes—
374C4×Dic106C2314yes—
375C4×Dic106C2314yes—
376C4×Dic106C2312yes—
377C4×Dic106C2312yes—
378C4×Dic106C2312yes—
379C4×Dic106C2312yes—
380C4×Dic106C2312yes—
381C4×Dic106C2312yes—
382C4×Dic106C2314yes—
383#13133182C2314yes—
384#13133182C2314yes—
385#13133182C2318yes—
386#13133182C2318yes—
387#13133182C2314yes—
388#13133182C2314yes—
389C4×D212C2314yes—
390C4×D212C2312yes—
391C4×D212C2312yes—
392C4×D212C2314yes—
393C4×D212C2312yes—
394C4×D212C2312yes—
395D4×Dic53C2314yes—
396D4×Dic53C2318yes—
397D4×Dic53C2314yes—
398D4×Dic53C2318yes—
399D4×Dic53C2318yes—
400D4×Dic53C2314yes—
401#13133179C2314yes—
402#13133179C2314yes—
403C4×C22⋊D53C2314yes—
404C4×C22⋊D53C2318yes—
405C4×C22⋊D53C2314yes—
406C4×C22⋊D53C2318yes—
407C4×C22⋊D53C2314yes—
408C4×C22⋊D53C2314yes—
409#13133177C2318yes—
410#13133177C2318yes—
411#13133177C2318yes—
412#13133176C2314yes—
413#13133176C2312yes—
414#13133176C2314yes—
415#13133176C2314yes—
416#13133176C2312yes—
417#13133176C2312yes—
418#13133176C2312yes—
419#13133176C2314yes—
420#13133175C2318yes—
421#13133175C2314yes—
422#13133174C2318yes—
423#13133174C2318yes—
424#13133174C2314yes—
425#13133174C2314yes—
426#13133174C2314yes—
427#13133174C2314yes—
428#13133173C2318yes—
429#13133173C2318yes—
430#13133173C2318yes—
431#13133173C2318yes—
432C2×C4⋊Dic53C2312yes—
433C2×C4⋊Dic53C2312yes—
434C2×C4⋊Dic53C2314yes—
435C2×C4⋊Dic53C2314yes—
436C2×C4⋊Dic53C2312yes—
437C2×C4⋊Dic53C2311yescharacteristic
438C2×C4⋊Dic53C2311yescharacteristic
439C2×C4⋊Dic53C2312yes—
440C2×#11719919C2314yes—
441C2×#11719919C2318yes—
442C2×#11719919C2318yes—
443C2×#11719919C2312yes—
444C2×#11719919C2312yes—
445C2×#11719919C2312yes—
446C2×#11719919C2312yes—
447C2×#11719919C2314yes—
448C4⋊C4×D53C2314yes—
449C4⋊C4×D53C2318yes—
450C2×C22⋊Dic53C2312yes—
451C2×C22⋊Dic53C2314yes—
452C2×#11719921C2312yes—
453C2×#11719921C2312yes—
454C2×#11719921C2312yes—
455C2×#11719921C2312yes—
456C22⋊C4×D53C2318yes—
457C2×C4×Dic53C2312yes—
458C2×C4×Dic53C2314yes—
459C2×#41×C53C2312yes—
460C2×#41×C53C2312yes—
461C2×#41×C53C2312yes—
462C23×C4×C53C2311yescharacteristic
463C23×C4×C53C2311yescharacteristic
464C23×C4×C53C2311yescharacteristic
465C4⋊Q8×C53C2311yescharacteristic
466C4⋊Q8×C53C2311yescharacteristic
467C4⋊Q8×C53C2311yescharacteristic
468#127×C53C2311yescharacteristic
469#126×C53C2314yes—
470#126×C53C2314yes—
471#125×C53C2312yes—
472#125×C53C2312yes—
473#125×C53C2312yes—
474#124×C53C2312yes—
475#124×C53C2312yes—
476#124×C53C2312yes—
477#123×C53C2314yes—
478#123×C53C2314yes—
479#123×C53C2314yes—
480C22⋊Q8×C53C2312yes—
481C22⋊Q8×C53C2312yes—
482C22⋊Q8×C53C2312yes—
483C22⋊Q8×C53C2312yes—
484C22⋊Q8×C53C2312yes—
485C22⋊Q8×C53C2312yes—
486#121×C53C2312yes—
487#121×C53C2312yes—
488#121×C53C2312yes—
489#121×C53C2312yes—
490#121×C53C2312yes—
491#121×C53C2312yes—
492#120×C53C2314yes—
493C4×Q8×C53C2312yes—
494C4×Q8×C53C2312yes—
495C4×Q8×C53C2312yes—
496C4×Q8×C53C2312yes—
497C4×Q8×C53C2312yes—
498C4×Q8×C53C2312yes—
499C4×D4×C53C2314yes—
500C4×D4×C53C2312yes—
501C4×D4×C53C2314yes—
502C4×D4×C53C2314yes—
503C4×D4×C53C2312yes—
504C4×D4×C53C2312yes—
505C4×D4×C53C2314yes—
506C4×D4×C53C2314yes—
507C4×D4×C53C2314yes—
508C4×D4×C53C2312yes—
509C4×D4×C53C2312yes—
510C4×D4×C53C2312yes—
511#117×C53C2312yes—
512#117×C53C2314yes—
513#117×C53C2312yes—
514#117×C53C2312yes—
515#117×C53C2314yes—
516#117×C53C2314yes—
517C2×C42×C53C2311yescharacteristic
518C2×C42×C53C2311yescharacteristic
519C2×C42×C53C2311yescharacteristic
520C2×C42×C53C2311yescharacteristic
521C2×C42×C53C2311yescharacteristic
522C2×C42×C53C2311yescharacteristic
523C2×C42×C53C2311yescharacteristic
524C2×C42×C53C2311yescharacteristic
525C2×C42×C53C2311yescharacteristic
526C2×C42×C53C2311yescharacteristic
527C2×C42×C53C2311yescharacteristic
528C2×C42×C53C2311yescharacteristic
529C2×C42×C53C2314yes—
530C24×C53C2411yescharacteristic
531C23×D53C2412yes—
532#41×C53—28no—
533#41×C53—44no—
534#41×C53—44no—
535C2×Q8×C53C2412yes—
536C2×Q8×C53C2412yes—
537C2×Q8×C53C2412yes—
538C2×D4×C53C2414yes—
539C2×D4×C53C2414yes—
540C2×D4×C53C2412yes—
541C2×D4×C53C2412yes—
542C2×D4×C53C2414yes—
543C2×D4×C53C2412yes—
544C22×C4×C53—24no—
545C22×C4×C53—42no—
546C22×C4×C53—42no—
547C22×C4×C53C2411yescharacteristic
548C22×C4×C53C2411yescharacteristic
549C22×C4×C53C2411yescharacteristic
550C22×C4×C53C2411yescharacteristic
551C22×C4×C53C2411yescharacteristic
552C22×C4×C53C2411yescharacteristic
553C22×C4×C53C2411yescharacteristic
554C22×C4×C53C2411yescharacteristic
555C22×C4×C53C2411yescharacteristic
556C22×C4×C53C2411yescharacteristic
557C22×C4×C53C2414yes—
558C22×C4×C53C2411yescharacteristic
559C22×C4×C53C2411yescharacteristic
560C22×C4×C53C2411yescharacteristic
561C22×C4×C53C2411yescharacteristic
562C22×C4×C53C2411yescharacteristic
563C22×C4×C53C2411yescharacteristic
564C22×C4×C53C2411yescharacteristic
565C22×C4×C53C2414yes—
566C22×C4×C53C2414yes—
567C22×C4×C53C2411yescharacteristic
568C2×C22⋊D53—44no—
569C2×C22⋊D53C2414yes—
570C2×C22⋊D53C2418yes—
571C2×C22⋊D53C2418yes—
572C2×C22⋊D53C2414yes—
573C22×Dic53C2412yes—
574C22×Dic53C2414yes—
575C22×Dic53C2412yes—
576C22×Dic53C2414yes—
577C22×Dic53C2412yes—
578C22×Dic53C2418yes—
579C22×Dic53C2418yes—
580Q8×D53—48no—
581#11719947—48no—
582#11719947—416no—
583C2×D212—24no—
584C2×D212C2412yes—
585C2×D212C2412yes—
586C2×C4×D53—44no—
587C2×C4×D53C2414yes—
588C2×C4×D53C2418yes—
589C2×C4×D53C2418yes—
590C2×C4×D53C2414yes—
591C2×Dic106—24no—
592C2×Dic106—44no—
593C2×Dic106—44no—
594C2×Dic106C2412yes—
595C2×Dic106C2412yes—
596C2×Dic106C2412yes—
597C2×Dic106C2412yes—
598C2×Dic106C2418yes—
599C2×Dic106C2418yes—
600C2×Dic106C2412yes—
601C2×Dic106C2414yes—
602C2×Dic106C2414yes—
603C2×Dic106C2412yes—
604C4⋊C4×C53C2412yes—
605C4⋊C4×C53C2412yes—
606C4⋊C4×C53C2412yes—
607C4⋊C4×C53C2412yes—
608C4⋊C4×C53C2412yes—
609C4⋊C4×C53C2412yes—
610C4⋊C4×C53C2414yes—
611C4⋊C4×C53C2414yes—
612C4⋊C4×C53C2414yes—
613C4⋊C4×C53C2414yes—
614C4⋊C4×C53C2414yes—
615C4⋊C4×C53C2414yes—
616C22⋊C4×C53C2414yes—
617C22⋊C4×C53C2414yes—
618C22⋊C4×C53C2414yes—
619C22⋊C4×C53C2414yes—
620C22⋊C4×C53C2414yes—
621C22⋊C4×C53C2414yes—
622C22⋊C4×C53C2414yes—
623C22⋊C4×C53C2414yes—
624C22⋊C4×C53C2414yes—
625C42×C53C2411yescharacteristic
626C42×C53C2411yescharacteristic
627C42×C53C2411yescharacteristic
628C42×C53C2411yescharacteristic
629C42×C53C2411yescharacteristic
630C42×C53C2411yescharacteristic
631C42×C53C2411yescharacteristic
632C42×C53C2411yescharacteristic
633C42×C53C2411yescharacteristic
634C42×C53C2411yescharacteristic
635C42×C53C2411yescharacteristic
636C42×C53C2411yescharacteristic
637C42×C53C2411yescharacteristic
638C42×C53C2411yescharacteristic
639C42×C53C2411yescharacteristic
640C42×C53C2411yescharacteristic
641C42×C53C2414yes—
642C42×C53C2414yes—
643C42×C53C2414yes—
644C22⋊Dic53C2414yes—
645C22⋊Dic53C2414yes—
646C22⋊Dic53C2414yes—
647C22⋊Dic53C2414yes—
648C22⋊Dic53C2414yes—
649C22⋊Dic53C2414yes—
650C22⋊Dic53C2418yes—
651C22⋊Dic53C2418yes—
652C22⋊Dic53C2418yes—
653C22⋊Dic53C2418yes—
654#11719921C2418yes—
655#11719921C2418yes—
656#11719921C2414yes—
657#11719921C2414yes—
658#11719921C2414yes—
659#11719921C2414yes—
660#11719921C2414yes—
661#11719921C2414yes—
662#11719921C2414yes—
663#11719921C2414yes—
664#11719921C2418yes—
665#11719921C2418yes—
666C4⋊Dic53C2412yes—
667C4⋊Dic53C2418yes—
668C4⋊Dic53C2412yes—
669C4⋊Dic53C2412yes—
670C4⋊Dic53C2412yes—
671C4⋊Dic53C2412yes—
672C4⋊Dic53C2412yes—
673C4⋊Dic53C2412yes—
674C4⋊Dic53C2412yes—
675C4⋊Dic53C2414yes—
676C4⋊Dic53C2414yes—
677C4⋊Dic53C2412yes—
678C4⋊Dic53C2412yes—
679C4⋊Dic53C2418yes—
680C4⋊Dic53C2418yes—
681C4⋊Dic53C2414yes—
682C4⋊Dic53C2414yes—
683C4⋊Dic53C2412yes—
684C4⋊Dic53C2412yes—
685C4⋊Dic53C2418yes—
686#11719919C2414yes—
687#11719919C2418yes—
688#11719919C2418yes—
689#11719919C2414yes—
690#11719919C2414yes—
691#11719919C2414yes—
692#11719919C2414yes—
693#11719919C2414yes—
694#11719919C2414yes—
695#11719919C2414yes—
696#11719919C2414yes—
697#11719919C2414yes—
698#11719919C2418yes—
699#11719919C2418yes—
700#11719919C2414yes—
701#11719919C2414yes—
702#11719919C2414yes—
703#11719919C2414yes—
704#11719919C2414yes—
705#11719919C2414yes—
706#11719919C2418yes—
707#11719919C2418yes—
708#11719919C2418yes—
709#11719919C2418yes—
710C4×Dic53C2414yes—
711C4×Dic53C2414yes—
712C4×Dic53C2414yes—
713C4×Dic53C2414yes—
714C4×Dic53C2414yes—
715C4×Dic53C2414yes—
716C4×Dic53C2418yes—
717C4×Dic53C2418yes—
718C4×Dic53C2418yes—
719C4×Dic53C2418yes—
720C23×C53—22no—
721C23×C53—22no—
722C23×C53—41no—
723C23×C53C2514yes—
724C23×C53C2511yescharacteristic
725C23×C53C2511yescharacteristic
726C23×C53C2511yescharacteristic
727C22×D53—24no—
728C22×D53—42no—
729C22×D53—42no—
730C22×D53C2514yes—
731Q8×C53—24no—
732Q8×C53—24no—
733Q8×C53—42no—
734D4×C53—28no—
735D4×C53—28no—
736D4×C53—24no—
737D4×C53—24no—
738D4×C53—44no—
739D4×C53—42no—
740C2×C4×C53—22no—
741C2×C4×C53—22no—
742C2×C4×C53—22no—
743C2×C4×C53—22no—
744C2×C4×C53—22no—
745C2×C4×C53—22no—
746C2×C4×C53—22no—
747C2×C4×C53—28no—
748C2×C4×C53—22no—
749C2×C4×C53—22no—
750C2×C4×C53—22no—
751C2×C4×C53—41no—
752C2×C4×C53—41no—
753C2×C4×C53—41no—
754C2×C4×C53—41no—
755C2×C4×C53—41no—
756C2×C4×C53—41no—
757C2×C4×C53—41no—
758C2×C4×C53—44no—
759C2×C4×C53—44no—
760C2×C4×C532−1+414yes—
761C2×C4×C53C2511yescharacteristic
762C2×C4×C53C2511yescharacteristic
763C2×C4×C53C2511yescharacteristic
764C2×C4×C53C2514yes—
765C2×C4×C53C2514yes—
766C2×C4×C53C2511yescharacteristic
767C2×C4×C53C2511yescharacteristic
768C2×C4×C53C2511yescharacteristic
769C2×C4×C53C2511yescharacteristic
770C2×C4×C53C2511yescharacteristic
771C2×C4×C53C2511yescharacteristic
772C2×C4×C53C2514yes—
773C2×C4×C53C2511yescharacteristic
774C2×C4×C53C2511yescharacteristic
775C2×C4×C53C2511yescharacteristic
776C22⋊D53—28no—
777C22⋊D53—48no—
778C22⋊D53—48no—
779C22⋊D53—44no—
780C2×Dic53—24no—
781C2×Dic53—28no—
782C2×Dic53—44no—
783C2×Dic53—42no—
784C2×Dic53—48no—
785C2×Dic53—48no—
786C2×Dic53—42no—
787C2×Dic53C2514yes—
788C2×Dic53C2514yes—
789C2×Dic53C2514yes—
790C2×Dic53C2514yes—
791C2×Dic53C2514yes—
792C2×Dic53C2514yes—
793C2×Dic53C2514yes—
794D212—24no—
795D212—24no—
796C4×D53—28no—
797C4×D53—44no—
798C4×D53—48no—
799C4×D53—48no—
800Dic106—24no—
801Dic106—24no—
802Dic106—24no—
803Dic106—24no—
804Dic106—44no—
805Dic106—42no—
806Dic106—44no—
807Dic106—42no—
808Dic106—48no—
809Dic106—48no—
810#62831—531nomaximal, Sylow
811C22×C53—21no—
812C22×C53—21no—
813C22×C53—21no—
814C22×C53—21no—
815C22×C53—21no—
816C22×C53—24no—
817C22×C53—24no—
818C22×C53—24no—
819C22×C53—21no—
820C22×C53—21no—
821C22×C53—44no—
822C22×C53C2×2−1+412yes—
823C22×C53#58512yes—
824C22×C53C2611yescharacteristic
825C2×D53—24no—
826C2×D53—24no—
827C2×D53—24no—
828C2×D53—84no—
829C4×C53—21no—
830C4×C53—21no—
831C4×C53—24no—
832C4×C53—21no—
833C4×C53—21no—
834C4×C53—21no—
835C4×C53—24no—
836C4×C53—24no—
837C4×C53—21no—
838C4×C53—21no—
839C4×C53—21no—
840C4×C53—21no—
841C4×C53C2×2−1+412yes—
842C4×C53C2×2−1+412yes—
843C4×C53#58512yes—
844Dic53—24no—
845Dic53—24no—
846Dic53—24no—
847Dic53—24no—
848Dic53—24no—
849Dic53—24no—
850Dic53—24no—
851#3565—534no—
852#3564—534no—
853#3557—534no—
854#3555—532no—
855#3554—532no—
856#3552—532no—
857#3544—532no—
858#3535—534no—
859#3523—532no—
860#3522—532no—
861#3520—534no—
862#3518—532no—
863#3515—534no—
864#3515—532no—
865#3510—532no—
866#3507—531no—
867#3507—534no—
868#3506—531no—
869#3504—532no—
870#3502—531no—
871#3501—531no—
872#3495—534no—
873#3495—532no—
874#3494—532no—
875#3444D5311yescharacteristic, complemented
876C2×#533—531no—
877C2×#529—531no—
878C2×C53—22no—
879C2×C53—22no—
880C2×C53—44no—
881C2×C53—41no—
882C2×C53C22×2−1+411yescharacteristic
883C2×C53C2×#58511yescharacteristic
884C2×C53C2×#58511yescharacteristic
885D53—44no—
886#563—538no—
887#563—538no—
888#563—538no—
889#562—538no—
890#559—532no—
891#559—534no—
892#559—534no—
893#559—534no—
894Q82—532no—
895Q82—532no—
896#557—532no—
897#557—532no—
898#557—534no—
899#557—534no—
900#557—534no—
901#557—532no—
902#557—534no—
903#556—532no—
904#556—538no—
905#556—534no—
906#556—534no—
907#556—534no—
908#556—534no—
909#556—532no—
910#556—538no—
911#556—534no—
912#555—534no—
913#555—532no—
914#554—532no—
915#554—534no—
916#554—532no—
917#554—534no—
918#554—534no—
919#554—532no—
920#554—538no—
921#554—538no—
922#554—534no—
923#554—534no—
924#553—534no—
925#553—534no—
926#553—534no—
927#552—538no—
928#552—538no—
929#552—534no—
930#552—534no—
931#552—534no—
932#552—534no—
933#552—538no—
934#552—538no—
935#552—538no—
936#552—538no—
937#552—534no—
938#551—538no—
939#551—538no—
940#551—538no—
941#551—538no—
942#550—532no—
943D4×Q8—532no—
944D4×Q8—534no—
945D4×Q8—532no—
946#548—534no—
947#548—534no—
948#547—534no—
949#547—538no—
950#547—534no—
951#547—534no—
952#547—532no—
953#546—538no—
954#544—534no—
955#544—534no—
956#544—532no—
957#544—532no—
958#544—534no—
959#544—534no—
960#543—534no—
961#542—534no—
962#542—538no—
963#542—538no—
964#542—534no—
965#542—534no—
966#542—534no—
967#542—538no—
968#542—534no—
969#542—534no—
970#541—534no—
971#541—538no—
972#541—534no—
973#541—534no—
974#541—538no—
975#540—534no—
976#539—538no—
977#539—538no—
978#539—534no—
979#539—538no—
980#539—538no—
981#539—538no—
982#538—534no—
983#536—532no—
984#536—534no—
985#536—538no—
986#535—532no—
987#533—534no—
988#533—534no—
989#533—532no—
990#533—531no—
991#533—531no—
992#533—532no—
993#533—532no—
994#533—531no—
995#533—531no—
996#533—532no—
997#533—532no—
998#533—532no—
999#533—534no—
1000#533C2×D5311yescharacteristic
1001#533C2×D5311yescharacteristic, complemented
1002#533C2×D5311yescharacteristic, complemented
1003#532—534no—
1004#532C2×D5311yescharacteristic
1005#532C2×D5311yescharacteristic, complemented
1006#532C2×D5311yescharacteristic, complemented
1007C2×C4⋊Q8—531no—
1008C2×C4⋊Q8—531no—
1009#529—534no—
1010#529—534no—
1011#529—534no—
1012#529—532no—
1013#529—532no—
1014#529—532no—
1015#529—532no—
1016#529—532no—
1017#529—532no—
1018#529—532no—
1019#529—532no—
1020#529—534no—
1021#529—534no—
1022#529C2×D5312yes—
1023#529C2×D5312yes—
1024#529C2×D5312yescomplemented
1025#529C2×D5312yescomplemented
1026#529C2×D5312yescomplemented
1027#529C2×D5312yescomplemented
1028C2×#126—532no—
1029C2×#125—531no—
1030C2×#125—532no—
1031C2×#125—534no—
1032C2×#124—531no—
1033#525—534no—
1034#525C2×D5312yes—
1035#525C2×D5312yes—
1036#525C2×D5312yes—
1037C2×#123—532no—
1038C2×C22⋊Q8—531no—
1039C2×C22⋊Q8—532no—
1040C2×C22⋊Q8—532no—
1041C2×C22⋊Q8—534no—
1042C2×#121—531no—
1043#520—532no—
1044#520—532no—
1045#520—534no—
1046#520—538no—
1047#519—534no—
1048#519—532no—
1049#518—532no—
1050C4×#41C2×D5312yes—
1051C4×#41C2×D5312yescomplemented
1052C4×#41C2×D5312yescomplemented
1053C2×C4×Q8—531no—
1054C2×C4×Q8—532no—
1055C2×C4×Q8—532no—
1056C2×C4×D4—532no—
1057C2×C4×D4—531no—
1058C2×#117—532no—
1059C2×#117—532no—
1060C22×C42C2×D5311yescharacteristic
1061C53#6283111yescharacteristic, complemented, Sylow
1062C2×#41—534no—
1063C2×#41—538no—
1064C2×#41C22×D5312yes—
1065C2×#41C22×D5312yes—
1066C2×#41C22×D5312yes—
1067C22×Q8—534no—
1068C22×Q8—531no—
1069C22×Q8—532no—
1070C22×Q8—532no—
1071C22×D4—532no—
1072C22×D4—531no—
1073C23×C4—532no—
1074C23×C4C22×D5311yescharacteristic
1075C23×C4C22×D5311yescharacteristic
1076C23×C4C22×D5311yescharacteristic
1077C4⋊Q8—534no—
1078C4⋊Q8—534no—
1079C4⋊Q8—538no—
1080C4⋊Q8—534no—
1081C4⋊Q8—534no—
1082C4⋊Q8—534no—
1083C4⋊Q8—538no—
1084C4⋊Q8—538no—
1085C4⋊Q8—538no—
1086C4⋊Q8—532no—
1087C4⋊Q8—532no—
1088C4⋊Q8—532no—
1089C4⋊Q8—532no—
1090C4⋊Q8—531no—
1091C4⋊Q8—531no—
1092C4⋊Q8—531no—
1093C4⋊Q8—531no—
1094C4⋊Q8—532no—
1095C4⋊Q8—532no—
1096C4⋊Q8—534no—
1097C4⋊Q8—534no—
1098C4⋊Q8C22×D5311yescharacteristic
1099C4⋊Q8C22×D5311yescharacteristic
1100C4⋊Q8C22×D5311yescharacteristic
1101#127—534no—
1102#127C22×D5311yescharacteristic
1103#126—538no—
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—534no—
1115#126—534no—
1116#126—534no—
1117#126—534no—
1118#126—538no—
1119#126—538no—
1120#126C22×D5314yes—
1121#126C22×D5314yes—
1122#125—534no—
1123#125—534no—
1124#125—534no—
1125#125—538no—
1126#125—538no—
1127#125—538no—
1128#125—538no—
1129#125—538no—
1130#125—538no—
1131#125—538no—
1132#125—538no—
1133#125—538no—
1134#125—532no—
1135#125—532no—
1136#125—532no—
1137#125—532no—
1138#125—532no—
1139#125—532no—
1140#125—534no—
1141#125—534no—
1142#125—532no—
1143#125—532no—
1144#125—538no—
1145#125—538no—
1146#125—534no—
1147#125—534no—
1148#125C22×D5312yes—
1149#125C22×D5312yes—
1150#125C22×D5312yes—
1151#124—534no—
1152#124—534no—
1153#124—534no—
1154#124—538no—
1155#124—538no—
1156#124—538no—
1157#124—538no—
1158#124—538no—
1159#124—538no—
1160#124—532no—
1161#124—532no—
1162#124—532no—
1163#124—532no—
1164#124C22×D5312yes—
1165#124C22×D5312yes—
1166#124C22×D5312yes—
1167#123—538no—
1168#123—538no—
1169#123—538no—
1170#123—538no—
1171#123—534no—
1172#123—534no—
1173#123—534no—
1174#123—534no—
1175#123—538no—
1176#123—538no—
1177#123—538no—
1178#123—538no—
1179#123—538no—
1180#123—538no—
1181#123—538no—
1182#123—538no—
1183#123—538no—
1184#123—538no—
1185#123C22×D5314yes—
1186#123C22×D5314yes—
1187#123C22×D5314yes—
1188C22⋊Q8—534no—
1189C22⋊Q8—538no—
1190C22⋊Q8—532no—
1191C22⋊Q8—532no—
1192C22⋊Q8—532no—
1193C22⋊Q8—532no—
1194C22⋊Q8—532no—
1195C22⋊Q8—532no—
1196C22⋊Q8—532no—
1197C22⋊Q8—532no—
1198C22⋊Q8—534no—
1199C22⋊Q8—532no—
1200C22⋊Q8—532no—
1201C22⋊Q8—532no—
1202C22⋊Q8—532no—
1203C22⋊Q8—534no—
1204C22⋊Q8—534no—
1205C22⋊Q8—534no—
1206C22⋊Q8—534no—
1207C22⋊Q8—534no—
1208C22⋊Q8—538no—
1209C22⋊Q8—538no—
1210C22⋊Q8—538no—
1211C22⋊Q8—534no—
1212C22⋊Q8—534no—
1213C22⋊Q8—538no—
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⋊Q8—538no—
1224C22⋊Q8—538no—
1225C22⋊Q8—538no—
1226C22⋊Q8—538no—
1227C22⋊Q8—538no—
1228C22⋊Q8C22×D5312yes—
1229C22⋊Q8C22×D5312yes—
1230C22⋊Q8C22×D5312yes—
1231C22⋊Q8C22×D5312yes—
1232C22⋊Q8C22×D5312yes—
1233C22⋊Q8C22×D5312yes—
1234#121—534no—
1235#121—538no—
1236#121—538no—
1237#121—538no—
1238#121—538no—
1239#121—532no—
1240#121—532no—
1241#121—532no—
1242#121—532no—
1243#121—534no—
1244#121—534no—
1245#121C22×D5312yes—
1246#121C22×D5312yes—
1247#121C22×D5312yes—
1248#121C22×D5312yes—
1249#121C22×D5312yes—
1250#121C22×D5312yes—
1251#120—538no—
1252#120C22×D5314yes—
1253C4×Q8—534no—
1254C4×Q8—534no—
1255C4×Q8—534no—
1256C4×Q8—534no—
1257C4×Q8—534no—
1258C4×Q8—538no—
1259C4×Q8—534no—
1260C4×Q8—534no—
1261C4×Q8—538no—
1262C4×Q8—532no—
1263C4×Q8—532no—
1264C4×Q8—532no—
1265C4×Q8—532no—
1266C4×Q8—532no—
1267C4×Q8—532no—
1268C4×Q8—534no—
1269C4×Q8—532no—
1270C4×Q8—532no—
1271C4×Q8—532no—
1272C4×Q8—534no—
1273C4×Q8—532no—
1274C4×Q8—534no—
1275C4×Q8—534no—
1276C4×Q8—532no—
1277C4×Q8—532no—
1278C4×Q8—534no—
1279C4×Q8—534no—
1280C4×Q8—538no—
1281C4×Q8—538no—
1282C4×Q8C22×D5312yes—
1283C4×Q8C22×D5312yes—
1284C4×Q8C22×D5312yes—
1285C4×Q8C22×D5312yes—
1286C4×Q8C22×D5312yes—
1287C4×Q8C22×D5312yes—
1288C4×D4—538no—
1289C4×D4—538no—
1290C4×D4—538no—
1291C4×D4—534no—
1292C4×D4—534no—
1293C4×D4—534no—
1294C4×D4—534no—
1295C4×D4—534no—
1296C4×D4—534no—
1297C4×D4—534no—
1298C4×D4—538no—
1299C4×D4—538no—
1300C4×D4—534no—
1301C4×D4—534no—
1302C4×D4—538no—
1303C4×D4—538no—
1304C4×D4—538no—
1305C4×D4—532no—
1306C4×D4—532no—
1307C4×D4—532no—
1308C4×D4—532no—
1309C4×D4—534no—
1310C4×D4—534no—
1311C4×D4C22×D5314yes—
1312C4×D4C22×D5314yes—
1313C4×D4C22×D5312yes—
1314C4×D4C22×D5312yes—
1315C4×D4C22×D5314yes—
1316C4×D4C22×D5312yes—
1317C4×D4C22×D5314yes—
1318C4×D4C22×D5314yes—
1319C4×D4C22×D5314yes—
1320C4×D4C22×D5312yes—
1321C4×D4C22×D5312yes—
1322C4×D4C22×D5312yes—
1323#117—532no—
1324#117—532no—
1325#117—534no—
1326#117—534no—
1327#117—532no—
1328#117—532no—
1329#117—534no—
1330#117—534no—
1331#117—534no—
1332#117—538no—
1333#117—538no—
1334#117—538no—
1335#117—538no—
1336#117—538no—
1337#117—534no—
1338#117—534no—
1339#117—534no—
1340#117—534no—
1341#117—538no—
1342#117—538no—
1343#117C22×D5312yes—
1344#117C22×D5314yes—
1345#117C22×D5312yes—
1346#117C22×D5312yes—
1347#117C22×D5314yes—
1348#117C22×D5314yes—
1349C2×C4⋊C4—532no—
1350C2×C4⋊C4—532no—
1351C2×C4⋊C4—532no—
1352C2×C4⋊C4—532no—
1353C2×C4⋊C4—531no—
1354C2×C4⋊C4—532no—
1355C2×C4⋊C4—531no—
1356C2×C4⋊C4—534no—
1357C2×C4⋊C4—534no—
1358C2×C4⋊C4—532no—
1359C2×C4⋊C4—532no—
1360C2×C4⋊C4—532no—
1361C2×C4⋊C4—538no—
1362C2×C4⋊C4—538no—
1363C2×C4⋊C4—534no—
1364C2×C4⋊C4—534no—
1365C2×C4⋊C4—538no—
1366C2×C4⋊C4—534no—
1367C2×C22⋊C4—534no—
1368C2×C22⋊C4—532no—
1369C2×C22⋊C4—532no—
1370C2×C22⋊C4—532no—
1371C2×C22⋊C4—532no—
1372C2×C22⋊C4—532no—
1373C2×C22⋊C4—538no—
1374C2×C42—532no—
1375C2×C42—534no—
1376C2×C42C22×D5311yescharacteristic
1377C2×C42C22×D5311yescharacteristic
1378C2×C42C22×D5311yescharacteristic
1379C2×C42C22×D5311yescharacteristic
1380C2×C42C22×D5311yescharacteristic
1381C2×C42C22×D5314yes—
1382C2×C42C22×D5311yescharacteristic
1383C2×C42C22×D5311yescharacteristic
1384C2×C42C22×D5311yescharacteristic
1385C2×C42C22×D5311yescharacteristic
1386C2×C42C22×D5311yescharacteristic
1387C2×C42C22×D5311yescharacteristic
1388C2×C42C22×D5311yescharacteristic
1389C24—532no—
1390C24C23×D5311yescharacteristic
1391#41—28no—
1392#41—44no—
1393#41—44no—
1394#41—21216no—
1395#41—2128no—
1396C2×Q8—532no—
1397C2×Q8—532no—
1398C2×Q8—532no—
1399C2×Q8—532no—
1400C2×Q8—532no—
1401C2×Q8—538no—
1402C2×Q8—534no—
1403C2×Q8—534no—
1404C2×Q8—538no—
1405C2×Q8—532no—
1406C2×Q8—1064no—
1407C2×Q8—2124no—
1408C2×Q8—2124no—
1409C2×Q8—2128no—
1410C2×Q8C23×D5312yes—
1411C2×Q8C23×D5312yes—
1412C2×Q8C23×D5312yes—
1413C2×D4—534no—
1414C2×D4—538no—
1415C2×D4—538no—
1416C2×D4—534no—
1417C2×D4—532no—
1418C2×D4—532no—
1419C2×D4—1064no—
1420C2×D4—2124no—
1421C2×D4C23×D5314yes—
1422C2×D4C23×D5312yes—
1423C2×D4C23×D5314yes—
1424C2×D4C23×D5312yes—
1425C2×D4C23×D5314yes—
1426C2×D4C23×D5312yes—
1427C22×C4—24no—
1428C22×C4—42no—
1429C22×C4—42no—
1430C22×C4—532no—
1431C22×C4—534no—
1432C22×C4—534no—
1433C22×C4—532no—
1434C22×C4—532no—
1435C22×C4—538no—
1436C22×C4—538no—
1437C22×C4—534no—
1438C22×C4—538no—
1439C22×C4—538no—
1440C22×C4—534no—
1441C22×C4—2124no—
1442C22×C4C23×D5311yescharacteristic
1443C22×C4C23×D5311yescharacteristic
1444C22×C4C23×D5311yescharacteristic
1445C22×C4C23×D5311yescharacteristic
1446C22×C4C23×D5311yescharacteristic
1447C22×C4C23×D5311yescharacteristic
1448C22×C4C23×D5311yescharacteristic
1449C22×C4C23×D5311yescharacteristic
1450C22×C4C23×D5311yescharacteristic
1451C22×C4C23×D5311yescharacteristic
1452C22×C4C23×D5314yes—
1453C22×C4C23×D5311yescharacteristic
1454C22×C4C23×D5311yescharacteristic
1455C22×C4C23×D5311yescharacteristic
1456C22×C4C23×D5311yescharacteristic
1457C22×C4C23×D5311yescharacteristic
1458C22×C4C23×D5311yescharacteristic
1459C22×C4C23×D5311yescharacteristic
1460C22×C4C23×D5314yes—
1461C22×C4C23×D5314yes—
1462C22×C4C23×D5311yescharacteristic
1463C4⋊C4—532no—
1464C4⋊C4—532no—
1465C4⋊C4—532no—
1466C4⋊C4—532no—
1467C4⋊C4—534no—
1468C4⋊C4—534no—
1469C4⋊C4—534no—
1470C4⋊C4—532no—
1471C4⋊C4—534no—
1472C4⋊C4—534no—
1473C4⋊C4—538no—
1474C4⋊C4—538no—
1475C4⋊C4—532no—
1476C4⋊C4—532no—
1477C4⋊C4—534no—
1478C4⋊C4—532no—
1479C4⋊C4—534no—
1480C4⋊C4—534no—
1481C4⋊C4—534no—
1482C4⋊C4—534no—
1483C4⋊C4—534no—
1484C4⋊C4—532no—
1485C4⋊C4—532no—
1486C4⋊C4—534no—
1487C4⋊C4—534no—
1488C4⋊C4—534no—
1489C4⋊C4—538no—
1490C4⋊C4—538no—
1491C4⋊C4—538no—
1492C4⋊C4—538no—
1493C4⋊C4—538no—
1494C4⋊C4—534no—
1495C4⋊C4—534no—
1496C4⋊C4—532no—
1497C4⋊C4—534no—
1498C4⋊C4—534no—
1499C4⋊C4—532no—
1500C4⋊C4—534no—
1501C4⋊C4—534no—
1502C4⋊C4—538no—
1503C4⋊C4—538no—
1504C4⋊C4—538no—
1505C4⋊C4—538no—
1506C4⋊C4—538no—
1507C4⋊C4C23×D5312yes—
1508C4⋊C4C23×D5314yes—
1509C4⋊C4C23×D5312yes—
1510C4⋊C4C23×D5314yes—
1511C4⋊C4C23×D5312yes—
1512C4⋊C4C23×D5312yes—
1513C4⋊C4C23×D5312yes—
1514C4⋊C4C23×D5312yes—
1515C4⋊C4C23×D5314yes—
1516C4⋊C4C23×D5314yes—
1517C4⋊C4C23×D5314yes—
1518C4⋊C4C23×D5314yes—
1519C22⋊C4—534no—
1520C22⋊C4—534no—
1521C22⋊C4—534no—
1522C22⋊C4—534no—
1523C22⋊C4—534no—
1524C22⋊C4—534no—
1525C22⋊C4—538no—
1526C22⋊C4—538no—
1527C22⋊C4—538no—
1528C22⋊C4—538no—
1529C22⋊C4—534no—
1530C22⋊C4—534no—
1531C22⋊C4—534no—
1532C22⋊C4—534no—
1533C22⋊C4—534no—
1534C22⋊C4—534no—
1535C22⋊C4—538no—
1536C22⋊C4—538no—
1537C22⋊C4—534no—
1538C22⋊C4—534no—
1539C22⋊C4—538no—
1540C22⋊C4—538no—
1541C22⋊C4C23×D5314yes—
1542C22⋊C4C23×D5314yes—
1543C22⋊C4C23×D5314yes—
1544C22⋊C4C23×D5314yes—
1545C22⋊C4C23×D5314yes—
1546C22⋊C4C23×D5314yes—
1547C22⋊C4C23×D5314yes—
1548C22⋊C4C23×D5314yes—
1549C22⋊C4C23×D5314yes—
1550C42—534no—
1551C42—534no—
1552C42—534no—
1553C42—534no—
1554C42—534no—
1555C42—534no—
1556C42—538no—
1557C42—538no—
1558C42—538no—
1559C42—538no—
1560C42C23×D5311yescharacteristic
1561C42C23×D5311yescharacteristic
1562C42C23×D5311yescharacteristic
1563C42C23×D5311yescharacteristic
1564C42C23×D5311yescharacteristic
1565C42C23×D5311yescharacteristic
1566C42C23×D5311yescharacteristic
1567C42C23×D5311yescharacteristic
1568C42C23×D5311yescharacteristic
1569C42C23×D5311yescharacteristic
1570C42C23×D5311yescharacteristic
1571C42C23×D5311yescharacteristic
1572C42C23×D5311yescharacteristic
1573C42C23×D5311yescharacteristic
1574C42C23×D5311yescharacteristic
1575C42C23×D5311yescharacteristic
1576C42C23×D5314yes—
1577C42C23×D5314yes—
1578C42C23×D5314yes—
1579C23—22no—
1580C23—22no—
1581C23—41no—
1582C23—534no—
1583C23—1064no—
1584C23—2122no—
1585C23—2122no—
1586C23C24×D5311yescharacteristic
1587C23C24×D5314yes—
1588C23C24×D5311yescharacteristic
1589C23C24×D5311yescharacteristic
1590Q8—24no—
1591Q8—24no—
1592Q8—42no—
1593Q8—1064no—
1594Q8—1064no—
1595Q8—1064no—
1596Q8—1064no—
1597Q8—2122no—
1598Q8—2124no—
1599Q8—2122no—
1600Q8—2124no—
1601Q8—2128no—
1602Q8—2128no—
1603D4—28no—
1604D4—28no—
1605D4—24no—
1606D4—24no—
1607D4—42no—
1608D4—44no—
1609D4—1068no—
1610D4—1064no—
1611D4—1064no—
1612D4—2124no—
1613D4—2128no—
1614D4—2128no—
1615C2×C4—22no—
1616C2×C4—22no—
1617C2×C4—22no—
1618C2×C4—22no—
1619C2×C4—22no—
1620C2×C4—22no—
1621C2×C4—22no—
1622C2×C4—28no—
1623C2×C4—22no—
1624C2×C4—22no—
1625C2×C4—22no—
1626C2×C4—41no—
1627C2×C4—41no—
1628C2×C4—41no—
1629C2×C4—41no—
1630C2×C4—41no—
1631C2×C4—41no—
1632C2×C4—41no—
1633C2×C4—44no—
1634C2×C4—44no—
1635C2×C4—534no—
1636C2×C4—534no—
1637C2×C4—534no—
1638C2×C4—534no—
1639C2×C4—534no—
1640C2×C4—534no—
1641C2×C4—534no—
1642C2×C4—1064no—
1643C2×C4—1068no—
1644C2×C4—1068no—
1645C2×C4—2124no—
1646C2×C4—2128no—
1647C2×C4—2128no—
1648C2×C4—2122no—
1649C2×C4—2122no—
1650C2×C4—2124no—
1651C2×C4—2128no—
1652C2×C4—2128no—
1653C2×C4#1313326414yes—
1654C2×C4C24×D5311yescharacteristic
1655C2×C4C24×D5311yescharacteristic
1656C2×C4C24×D5314yes—
1657C2×C4C24×D5314yes—
1658C2×C4C24×D5314yes—
1659C2×C4C24×D5311yescharacteristic
1660C2×C4C24×D5311yescharacteristic
1661C2×C4C24×D5311yescharacteristic
1662C2×C4C24×D5311yescharacteristic
1663C2×C4C24×D5311yescharacteristic
1664C2×C4C24×D5311yescharacteristic
1665C2×C4C24×D5311yescharacteristic
1666C2×C4C24×D5311yescharacteristic
1667C2×C4C24×D5311yescharacteristic
1668C2×C4C24×D5311yescharacteristic
1669C22—21no—
1670C22—21no—
1671C22—21no—
1672C22—21no—
1673C22—21no—
1674C22—24no—
1675C22—21no—
1676C22—21no—
1677C22—24no—
1678C22—24no—
1679C22—44no—
1680C22—1064no—
1681C22—1064no—
1682C22—1064no—
1683C22—4244no—
1684C22C2×#1313326412yes—
1685C22#1681145912yes—
1686C22C25×D5311yescharacteristic
1687C4—21no—
1688C4—21no—
1689C4—24no—
1690C4—21no—
1691C4—21no—
1692C4—21no—
1693C4—21no—
1694C4—21no—
1695C4—21no—
1696C4—21no—
1697C4—24no—
1698C4—24no—
1699C4—1064no—
1700C4—1064no—
1701C4—1064no—
1702C4—1064no—
1703C4—1064no—
1704C4—1064no—
1705C4—1064no—
1706C4C2×#1313326412yes—
1707C4C2×#1313326412yes—
1708C4#1681145912yes—
1709C2—22no—
1710C2—22no—
1711C2—41no—
1712C2—44no—
1713C2—2124no—
1714C2C22×#1313326411yescharacteristic
1715C2C2×#1681145911yescharacteristic
1716C2C2×#1681145911yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3444C2
hypercenter#3444D53
hypocenterC53#62831
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. #20289360C2semidirect
2. #20289333C2semidirect
3. #20289217C2semidirect
4. #20289197C2semidirect
5. #20289180C2semidirect
6. #20289152C2semidirect
7. #20289055C2semidirect
8. #20288918C2semidirect
9. #20288803C2semidirect
10. #20288792C2semidirect
11. #20288752C2semidirect
12. #20288732C2semidirect
13. #20288693C2semidirect
14. #20288693C2semidirect
15. #20288611C2semidirect
16. #20288577C2semidirect
17. #20288571C2semidirect
18. #20288564C2semidirect
19. #20288541C2semidirect
20. #20288520C2semidirect
21. #20288516C2semidirect
22. #20288469C2semidirect
23. #20288455C2semidirect
24. #20288452C2semidirect
25. C2×#16811180C2semidirect
26. C2×#16811157C2semidirect
27. C53×#3444C2semidirect
28. #16811375C22semidirect
29. #16811375C22semidirect
30. #16811374C22semidirect
31. #16811368C22semidirect
32. #16811359C22semidirect
33. #16811356C22semidirect
34. #16811356C22semidirect
35. #16811355C22semidirect
36. Q8×Dic106C22semidirect
37. #16811353C22semidirect
38. #16811351C22semidirect
39. #16811351C22semidirect
40. #16811350C22semidirect
41. #16811349C22semidirect
42. #16811349C22semidirect
43. #16811348C22semidirect
44. #16811348C22semidirect
45. #16811347C22semidirect
46. #16811345C22semidirect
47. #16811345C22semidirect
48. #16811343C22semidirect
49. #16811343C22semidirect
50. #16811342C22semidirect
51. #16811341C22semidirect
52. #16811341C22semidirect
53. #16811340C22semidirect
55. #16811338C22semidirect
56. #16811334C22semidirect
57. #16811333C22semidirect
58. #16811333C22semidirect
61. #16811332C22semidirect
62. #16811332C22semidirect
63. #16811330C22semidirect
64. #16811330C22semidirect
65. #16811329C22semidirect
68. #16811319C22semidirect
69. #16811315C22semidirect
70. #16811313C22semidirect
71. #16811313C22semidirect
72. #16811313C22semidirect
73. #16811312C22semidirect
74. #16811312C22semidirect
76. #16811309C22semidirect
77. #16811306C22semidirect
78. #16811306C22semidirect
79. #16811306C22semidirect
84. #16811293C22semidirect
85. Q8×D212C22semidirect
86. #16811288C22semidirect
87. #16811286C22semidirect
88. #16811280C22semidirect
89. #16811279C22semidirect
91. #16811277C22semidirect
92. #16811273C22semidirect
93. #16811272C22semidirect
94. #16811272C22semidirect
96. #16811253C22semidirect
100. #16811251C22semidirect
101. #16811251C22semidirect
104. #16811244C22semidirect
105. #16811244C22semidirect
106. #16811242C22semidirect
107. #16811241C22semidirect
108. #16811240C22semidirect
109. #16811238C22semidirect
110. #16811238C22semidirect
111. #16811237C22semidirect
112. #16811236C22semidirect
113. #16811233C22semidirect
114. #16811232C22semidirect
115. #16811231C22semidirect
116. #16811231C22semidirect
119. #16811217C22semidirect
120. #16811216C22semidirect
121. #16811215C22semidirect
122. #16811215C22semidirect
123. #16811215C22semidirect
125. #16811195C22semidirect
127. #16811193C22semidirect
134. #16811180C22semidirect
135. #16811180C22semidirect
136. #16811180C22semidirect
137. #16811180C22semidirect
138. #16811180C22semidirect
139. #16811180C22semidirect
141. #16811175C22semidirect
143. C2×#13133217C22semidirect
144. C2×#13133217C22semidirect
154. #16811157C22semidirect
155. #16811157C22semidirect
157. #16811154C22semidirect
160. C2×#13133209C22semidirect
161. C2×#13133209C22semidirect
172. #16811102C22semidirect
173. #16811102C22semidirect
175. #16811099C22semidirect
178. C2×C4×Dic106C22semidirect
179. C2×C4×Dic106C22semidirect
185. C53×#533C22semidirect
186. C53×#533C22semidirect
188. C53×#532C22semidirect
189. C53×#532C22semidirect
192. C53×#529C22semidirect
193. C53×#529C22semidirect
194. C53×#529C22semidirect
195. C53×#529C22semidirect
200. C4×#41×C53C22semidirect
201. C4×#41×C53C22semidirect
875. #3444D53semidirect
1001. #533C2×D53semidirect
1002. #533C2×D53semidirect
1005. #532C2×D53semidirect
1006. #532C2×D53semidirect
1024. #529C2×D53semidirect
1025. #529C2×D53semidirect
1026. #529C2×D53semidirect
1027. #529C2×D53semidirect
1051. C4×#41C2×D53semidirect
1052. C4×#41C2×D53semidirect
1061. C53#62831semidirect

Maximal subgroups

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

subgroupindex
#202893602
#202893332
#202892172
#202891972
#202891802
#202891522
#202890552
#202889182
#202888032
#202887922
#202887522
#202887322
#202886932
#202886112
#202885772
#202885712
#202885642
#202885412
#202885202
#202885162
#202884692
#202884552
#202884522
C2×#168111802
C2×#168111572
C53×#34442
#6283153