Finite Group Databasebeta

← #11906298

Subgroups — #11906298

Order 1152.

2061 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595987C211yesmaximal, characteristic
2C3×#5519C211yesmaximal, characteristic
3C3×#5517C211yesmaximal, characteristic
4#10595051C211yesmaximal, characteristic
5#10595049C211yesmaximal, characteristic
6#10594828C211yesmaximal, characteristic
7C2×#63844C211yesmaximal, characteristic
8#10594324C212yesmaximal, complemented
9#10594318C212yesmaximal, complemented
10#10594318C212yesmaximal, complemented
11#10594313C212yesmaximal, complemented
12#10594033C214yesmaximal
13#10594030C214yesmaximal
14#10593864C212yesmaximal, complemented
15#10593856C212yesmaximal, complemented
16#10593852C212yesmaximal, complemented
17#10593852C212yesmaximal, complemented
18#86585—31nomaximal
19#86258—31nomaximal
20C22×#634C2211yescharacteristic
21C32×#117C2211yescharacteristic
22#64135C2211yescharacteristic
23#64096C2212yes—
24#64096C2212yes—
25#64086C2214yes—
26C4×#634C2212yes—
27C4×#634C2212yes—
28C3×#926C2211yescharacteristic
29C3×#926C2211yescharacteristic
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C3×#890C2211yescharacteristic
33C3×#890C2212yes—
34C3×#890C2211yescharacteristic
35C3×#888C2211yescharacteristic
36C3×#888C2212yes—
37C3×#888C2211yescharacteristic
38C3×#878C2212yes—
39C3×#878C2212yes—
40C3×#878C2214yes—
41C3×#870C2212yes—
42C3×#869C2212yes—
43C3×C4×Dic6C2212yes—
44C3×C4×Dic6C2212yes—
45C2×#3724C2212yes—
46#63964C2212yes—
47#63964C2212yes—
48#63964C2214yes—
49#63957C2214yes—
50C2×Dic32C2212yes—
51#63919C2212yes—
52#63919C2214yes—
53#63918C2211yescharacteristic
54#63918C2212yes—
55#63918C2211yescharacteristic
56C4×#627C2212yes—
57C4×#627C2212yes—
58#63873C2214yes—
59#63872C2212yes—
60#63870C2214yes—
61#63870C2214yes—
62#63869C2211yescharacteristic
63#63869C2212yes—
64#63869C2211yescharacteristic
65#63847C2214yes—
66#63847C2214yes—
67#63847C2214yes—
68#63847C2214yes—
69#63844C2212yes—
70#63844C2212yes—
71#63844C2212yes—
72#63844C2212yes—
73#63844C2212yes—
74#63844C2212yes—
75#63844C2212yes—
76#63844C2212yes—
77#63843C2214yes—
78#63843C2214yes—
79#63839C2214yes—
80#63839C2214yes—
81#63839C2214yes—
82#63839C2214yes—
83#63838C2214yes—
84#63838C2214yes—
85C3×#544—31no—
86C3×#533—31no—
87#5722—32no—
88#5722—32no—
89#5722—32no—
90#5721—32no—
91#5721—32no—
92#5721—32no—
93#5685—32no—
94#5685—32no—
95#5685—32no—
96#5685—32no—
97#5685—32no—
98#5685—32no—
99#5623—34no—
100#5623—34no—
101#5622—34no—
102#5622—34no—
103#5567—32no—
104#5567—32no—
105#5567—32no—
106Q8×Dic6—32no—
107#5519—31no—
108#5519D311yescharacteristic
109#5517—31no—
110#5517D311yescharacteristic
111#5516—31no—
112#5516—31no—
113#5516—31no—
114#5516—31no—
115#5516—61no—
116#5500—31no—
117C2×#887—31no—
118#5470—31no—
119C2×C4×Dic6—31no—
120C22×C32×C4C2311yescharacteristic
121C22×C3⋊Dic3C2312yes—
122C2×#634Q818yescomplemented
123C2×#634C2312yes—
124C2×#634C2312yes—
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2312yes—
128C2×C3×Dic6C2312yes—
129C2×C3×Dic6C2314yes—
130C2×C3×Dic6C2312yes—
131C2×#627C2312yes—
132C2×#627C2314yes—
133C2×#627C2312yes—
134C32×C4⋊C4C2311yescharacteristic
135C32×C4⋊C4C2311yescharacteristic
136C32×C22⋊C4C2312yes—
137C32×C42C2312yes—
138#3757C2312yes—
139C4⋊(C3⋊Dic3)C2311yescharacteristic
140C4⋊(C3⋊Dic3)C2311yescharacteristic
141#3750C2314yes—
142#3750C2314yes—
143C4×C3⋊Dic3C2314yes—
144C4×C3⋊Dic3C2314yes—
145C4×C3⋊Dic3C2312yes—
146C3×#217C2312yes—
147C3×#217C2312yes—
148C3×C4⋊Dic3C2312yes—
149C3×C4⋊Dic3C2314yes—
150C3×C4⋊Dic3C2312yes—
151C3×C4⋊Dic3C2312yes—
152C3×C4⋊Dic3C2311yescharacteristic
153C3×C4⋊Dic3C2311yescharacteristic
154C3×C4⋊Dic3C2312yes—
155C3×C4⋊Dic3C2311yescharacteristic
156C3×C4⋊Dic3C2311yescharacteristic
157C3×Dic3⋊C4C2312yes—
158C3×Dic3⋊C4C2314yes—
159C3×Dic3⋊C4C2312yes—
160C3×Dic3⋊C4C2312yes—
161C3×Dic3⋊C4C2314yes—
162C3×Dic3⋊C4C2312yes—
163C3×C4×Dic3C2311yescharacteristic
164C3×C4×Dic3C2312yes—
165C3×C4×Dic3C2311yescharacteristic
166C3×C4×Dic3C2311yescharacteristic
167C3×C4×Dic3C2311yescharacteristic
168C3×C4×Dic3C2312yes—
169#3724C2312yes—
170#3724C2314yes—
171#3724C2314yes—
172#3724C2314yes—
173#3724C2314yes—
174#3724C2314yes—
175#3724C2312yes—
176Dic3⋊Dic3C2312yes—
177Dic3⋊Dic3C2312yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2312yes—
181Dic3⋊Dic3C2312yes—
182Dic32C2314yes—
183Dic32C2314yes—
184Dic32C2314yes—
185Dic32C2314yes—
186#3502—91noSylow
187C22×Dic6—31no—
188C22×Dic6—31no—
189C22×Dic6—61no—
190C3×C4⋊Q8—31no—
191C3×C4⋊Q8—32no—
192C3×C4⋊Q8—31no—
193C3×C4⋊Q8—32no—
194C3×#125—31no—
195C3×#125—31no—
196C3×#125—32no—
197C3×#125—32no—
198C3×C22⋊Q8—32no—
199C3×C22⋊Q8—32no—
200C3×C22⋊Q8—34no—
201C3×C4×Q8—32no—
202C3×C4×Q8—32no—
203C3×#117—21no—
204C3×#117—31no—
205C3×#117—31no—
206C3×#117C2×D311yescharacteristic
207C3×#117C2×D311yescharacteristic
208C2×C3×C4⋊C4—31no—
209C2×C3×C42—31no—
210Q8×Dic3—34no—
211Q8×Dic3—34no—
212#944—34no—
213#944—34no—
214#944—34no—
215#944—34no—
216#944—34no—
217#944—34no—
218#926—31no—
219#926—31no—
220#926—61no—
221#926C2×D311yescharacteristic
222#926C2×D311yescharacteristic
223C2×C4⋊Dic3C2×D311yescharacteristic
224#924—32no—
225#924—32no—
226#924—34no—
227C2×Dic3⋊C4—32no—
228C2×Dic3⋊C4—32no—
229C2×C4×Dic3—32no—
230C2×C4×Dic3—32no—
231C2×C4×Dic3C2×D311yescharacteristic
232#890—32no—
233#890—32no—
234#890—31no—
235#890—32no—
236#890—31no—
237#890C2×D311yescharacteristic
238#890C2×D312yes—
239#890C2×D311yescharacteristic
240#889—34no—
241#889—34no—
242#889—34no—
243#889—34no—
244#889—34no—
245#889—34no—
246#889—34no—
247#889—34no—
248#889—34no—
249#889—34no—
250#889—34no—
251#889—34no—
252#888—34no—
253#888—34no—
254#888—34no—
255#888—34no—
256#888—32no—
257#888—32no—
258#888—34no—
259#888—34no—
260#888—31no—
261#888—32no—
262#888—31no—
263#888C2×D311yescharacteristic
264#888C2×D312yes—
265#888C2×D311yescharacteristic
266#887—34no—
267#887—34no—
268#887—32no—
269#887—32no—
270#887—32no—
271#887—32no—
272#887—34no—
273#887—34no—
274#887—34no—
275#887—34no—
276#887—32no—
277#887—32no—
278#887—32no—
279#887—32no—
280#887—32no—
281#887—32no—
282#887—32no—
283#887—32no—
284#887—62no—
285#887—62no—
286#878—32no—
287#878—32no—
288#878—34no—
289#878C2×D312yes—
290#878C2×D312yes—
291#878C2×D314yes—
292#877—34no—
293#877—34no—
294#877—34no—
295#877—34no—
296#877—64no—
297#870—31no—
298#870—31no—
299#870—32no—
300#870C2×D312yes—
301#869—31no—
302#869—31no—
303#869—32no—
304#869C2×D312yes—
305C4×Dic6—32no—
306C4×Dic6—32no—
307C4×Dic6—32no—
308C4×Dic6—32no—
309C4×Dic6—32no—
310C4×Dic6—32no—
311C4×Dic6—32no—
312C4×Dic6—32no—
313C4×Dic6—32no—
314C4×Dic6—32no—
315C4×Dic6—32no—
316C4×Dic6—32no—
317C4×Dic6—32no—
318C4×Dic6—32no—
319C4×Dic6—32no—
320C4×Dic6—32no—
321C4×Dic6—62no—
322C4×Dic6—62no—
323C4×Dic6C2×D312yes—
324C4×Dic6C2×D312yes—
325C23×C32C2411yescharacteristic
326C2×C32×C4C2×Q814yes—
327C2×C32×C4C2412yes—
328C2×C32×C4C2412yes—
329C2×C32×C4C2411yescharacteristic
330C2×C32×C4C2411yescharacteristic
331C2×C3⋊Dic3C2×Q818yes—
332C2×C3⋊Dic3C2412yes—
333C2×C3⋊Dic3C2412yes—
334C2×C3⋊Dic3C2414yes—
335#634C2×Q818yes—
336#634C2×Q818yes—
337C2×C3×Dic3—22no—
338C2×C3×Dic3—41no—
339C2×C3×Dic3—42no—
340C2×C3×Dic3C2411yescharacteristic
341C2×C3×Dic3C2412yes—
342C2×C3×Dic3C2412yes—
343C2×C3×Dic3C2412yes—
344C2×C3×Dic3C2414yes—
345C2×C3×Dic3C2412yes—
346C2×C3×Dic3C2411yescharacteristic
347C2×C3×Dic3C2411yescharacteristic
348C2×C3×Dic3C2411yescharacteristic
349C3×Dic6—24no—
350C3×Dic6—42no—
351C3×Dic6—44no—
352#627—24no—
353#627—44no—
354#627—42no—
355Q82—92no—
356Q82—92no—
357#557—92no—
358#557—92no—
359#557—92no—
360#557—92no—
361#557—92no—
362#557—92no—
363#544—31no—
364#544—91no—
365#544—94no—
366#533—31no—
367#533—91no—
368#533—94no—
369#519—91no—
370#519—91no—
371C2×C4×Q8—91no—
372C2×C3×Q8—32no—
373C2×C3×Q8—32no—
374C2×C3×Q8—34no—
375C22×C3×C4—21no—
376C22×C3×C4—31no—
377C22×C3×C4—32no—
378C22×C3×C4—31no—
379C22×C3×C4C22×D311yescharacteristic
380C22×C3×C4C22×D311yescharacteristic
381C22×Dic3—32no—
382C22×Dic3—32no—
383C22×Dic3—62no—
384C22×Dic3C22×D311yescharacteristic
385C22×Dic3C22×D312yes—
386C22×Dic3C22×D311yescharacteristic
387C2×Dic6—38no—
388C2×Dic6—38no—
389C2×Dic6—32no—
390C2×Dic6—32no—
391C2×Dic6—32no—
392C2×Dic6—32no—
393C2×Dic6—32no—
394C2×Dic6—32no—
395C2×Dic6—32no—
396C2×Dic6—32no—
397C2×Dic6—34no—
398C2×Dic6—34no—
399C2×Dic6—62no—
400C2×Dic6—62no—
401C2×Dic6—68no—
402C2×Dic6C22×D312yes—
403C2×Dic6C22×D312yes—
404C2×Dic6C22×D314yes—
405C3×C4⋊C4—21no—
406C3×C4⋊C4—21no—
407C3×C4⋊C4—32no—
408C3×C4⋊C4—31no—
409C3×C4⋊C4—32no—
410C3×C4⋊C4—32no—
411C3×C4⋊C4—31no—
412C3×C4⋊C4—31no—
413C3×C4⋊C4—32no—
414C3×C4⋊C4—32no—
415C3×C4⋊C4—31no—
416C3×C4⋊C4—34no—
417C3×C4⋊C4—34no—
418C3×C4⋊C4—34no—
419C3×C4⋊C4—32no—
420C3×C4⋊C4—32no—
421C3×C4⋊C4—32no—
422C3×C4⋊C4C22×D311yescharacteristic
423C3×C4⋊C4C22×D311yescharacteristic
424C3×C4⋊C4C22×D311yescharacteristic
425C3×C4⋊C4C22×D311yescharacteristic
426C3×C22⋊C4—22no—
427C3×C22⋊C4—32no—
428C3×C22⋊C4—32no—
429C3×C22⋊C4C22×D312yes—
430C3×C22⋊C4C22×D312yes—
431C3×C42—22no—
432C3×C42—31no—
433C3×C42—31no—
434C3×C42—32no—
435C3×C42—31no—
436C3×C42—32no—
437C3×C42—31no—
438C3×C42C22×D312yes—
439C3×C42C22×D312yes—
440#217—32no—
441#217—32no—
442#217—62no—
443#217C22×D312yes—
444#217C22×D312yes—
445C4⋊Dic3—31no—
446C4⋊Dic3—31no—
447C4⋊Dic3—31no—
448C4⋊Dic3—31no—
449C4⋊Dic3—32no—
450C4⋊Dic3—32no—
451C4⋊Dic3—32no—
452C4⋊Dic3—32no—
453C4⋊Dic3—34no—
454C4⋊Dic3—34no—
455C4⋊Dic3—61no—
456C4⋊Dic3—61no—
457C4⋊Dic3C22×D311yescharacteristic
458C4⋊Dic3C22×D312yes—
459C4⋊Dic3C22×D311yescharacteristic
460C4⋊Dic3C22×D311yescharacteristic
461C4⋊Dic3C22×D312yes—
462C4⋊Dic3C22×D311yescharacteristic
463C4⋊Dic3C22×D312yes—
464C4⋊Dic3C22×D312yes—
465C4⋊Dic3C22×D314yes—
466Dic3⋊C4—34no—
467Dic3⋊C4—34no—
468Dic3⋊C4—34no—
469Dic3⋊C4—34no—
470Dic3⋊C4—34no—
471Dic3⋊C4—34no—
472Dic3⋊C4—32no—
473Dic3⋊C4—32no—
474Dic3⋊C4—32no—
475Dic3⋊C4—32no—
476Dic3⋊C4—34no—
477Dic3⋊C4—34no—
478Dic3⋊C4—34no—
479Dic3⋊C4—34no—
480Dic3⋊C4—32no—
481Dic3⋊C4—32no—
482Dic3⋊C4—32no—
483Dic3⋊C4—32no—
484Dic3⋊C4—34no—
485Dic3⋊C4—34no—
486Dic3⋊C4—34no—
487Dic3⋊C4—34no—
488Dic3⋊C4—34no—
489Dic3⋊C4—34no—
490Dic3⋊C4—64no—
491Dic3⋊C4—64no—
492Dic3⋊C4C22×D312yes—
493Dic3⋊C4C22×D312yes—
494Dic3⋊C4C22×D312yes—
495Dic3⋊C4C22×D312yes—
496Dic3⋊C4C22×D314yes—
497Dic3⋊C4C22×D314yes—
498C4×Dic3—32no—
499C4×Dic3—32no—
500C4×Dic3—34no—
501C4×Dic3—34no—
502C4×Dic3—34no—
503C4×Dic3—34no—
504C4×Dic3—34no—
505C4×Dic3—34no—
506C4×Dic3—34no—
507C4×Dic3—34no—
508C4×Dic3—34no—
509C4×Dic3—34no—
510C4×Dic3—34no—
511C4×Dic3—34no—
512C4×Dic3—64no—
513C4×Dic3—64no—
514C4×Dic3—62no—
515C4×Dic3C22×D311yescharacteristic
516C4×Dic3C22×D312yes—
517C4×Dic3C22×D311yescharacteristic
518C4×Dic3C22×D311yescharacteristic
519C4×Dic3C22×D312yes—
520C4×Dic3C22×D311yescharacteristic
521C22×C32—21no—
522C22×C32—21no—
523C22×C32C22×Q812yes—
524C22×C32C2511yescharacteristic
525C32×C4—22no—
526C32×C4—22no—
527C32×C4C22×Q812yes—
528C32×C4C22×Q812yes—
529C3⋊Dic3—22no—
530C3⋊Dic3—22no—
531C3⋊Dic3C22×Q818yes—
532C3×Dic3—22no—
533C3×Dic3—22no—
534C3×Dic3—21no—
535C3×Dic3—22no—
536C3×Dic3—21no—
537C3×Dic3—22no—
538C3×Dic3—24no—
539C3×Dic3—21no—
540C3×Dic32−1+412yes—
541C22×Q8—91no—
542C4⋊Q8—31no—
543C4⋊Q8—31no—
544C4⋊Q8—32no—
545C4⋊Q8—32no—
546C4⋊Q8—91no—
547C4⋊Q8—91no—
548C4⋊Q8—92no—
549C4⋊Q8—92no—
550C4⋊Q8—94no—
551C4⋊Q8—94no—
552C4⋊Q8—94no—
553C4⋊Q8—94no—
554C4⋊Q8—94no—
555C4⋊Q8—94no—
556#125—31no—
557#125—31no—
558#125—32no—
559#125—32no—
560#125—91no—
561#125—91no—
562#125—92no—
563#125—94no—
564#125—94no—
565#125—94no—
566#125—94no—
567#125—94no—
568#125—94no—
569#125—92no—
570C22⋊Q8—32no—
571C22⋊Q8—32no—
572C22⋊Q8—34no—
573C22⋊Q8—92no—
574C22⋊Q8—92no—
575C22⋊Q8—94no—
576C4×Q8—32no—
577C4×Q8—32no—
578C4×Q8—92no—
579C4×Q8—92no—
580C4×Q8—92no—
581C4×Q8—92no—
582C4×Q8—92no—
583C4×Q8—92no—
584C4×Q8—92no—
585C4×Q8—92no—
586C4×Q8—92no—
587C4×Q8—92no—
588C4×Q8—94no—
589C4×Q8—94no—
590C4×Q8—94no—
591C4×Q8—94no—
592C4×Q8—92no—
593C4×Q8—92no—
594C4×Q8—92no—
595C4×Q8—92no—
596#117—31no—
597#117—31no—
598#117—94no—
599#117—91no—
600#117—94no—
601#117D3211yescharacteristic
602C2×C4⋊C4—31no—
603C2×C4⋊C4—92no—
604C2×C42—31no—
605C2×C42—92no—
606C23×C3—21no—
607C23×C3C23×D311yescharacteristic
608C23×C3C23×D311yescharacteristic
609C3×Q8—64no—
610C3×Q8—124no—
611C3×Q8—122no—
612C2×C3×C4—21no—
613C2×C3×C4—21no—
614C2×C3×C4—22no—
615C2×C3×C4—22no—
616C2×C3×C4—24no—
617C2×C3×C4—31no—
618C2×C3×C4—31no—
619C2×C3×C4—32no—
620C2×C3×C4—32no—
621C2×C3×C4—32no—
622C2×C3×C4—34no—
623C2×C3×C4—32no—
624C2×C3×C4—31no—
625C2×C3×C4—31no—
626C2×C3×C4—62no—
627C2×C3×C4—122no—
628C2×C3×C4—121no—
629C2×C3×C4D3×Q814yes—
630C2×C3×C4D3×Q814yes—
631C2×C3×C4C23×D312yes—
632C2×C3×C4C23×D312yes—
633C2×C3×C4C23×D312yes—
634C2×C3×C4C23×D312yes—
635C2×C3×C4C23×D311yescharacteristic
636C2×C3×C4C23×D311yescharacteristic
637C2×C3×C4C23×D311yescharacteristic
638C2×C3×C4C23×D311yescharacteristic
639C2×Dic3—22no—
640C2×Dic3—38no—
641C2×Dic3—38no—
642C2×Dic3—34no—
643C2×Dic3—34no—
644C2×Dic3—32no—
645C2×Dic3—32no—
646C2×Dic3—32no—
647C2×Dic3—32no—
648C2×Dic3—41no—
649C2×Dic3—42no—
650C2×Dic3—68no—
651C2×Dic3—64no—
652C2×Dic3—62no—
653C2×Dic3—62no—
654C2×Dic3C23×D311yescharacteristic
655C2×Dic3C23×D312yes—
656C2×Dic3C23×D312yes—
657C2×Dic3C23×D312yes—
658C2×Dic3C23×D312yes—
659C2×Dic3C23×D314yes—
660C2×Dic3C23×D311yescharacteristic
661C2×Dic3C23×D311yescharacteristic
662C2×Dic3C23×D311yescharacteristic
663Dic6—24no—
664Dic6—38no—
665Dic6—38no—
666Dic6—38no—
667Dic6—38no—
668Dic6—42no—
669Dic6—44no—
670Dic6—68no—
671Dic6—68no—
672Dic6—64no—
673Dic6—64no—
674Dic6—124no—
675Dic6—122no—
676Dic6—122no—
677Dic6—124no—
678C2×C32—22no—
679C2×C32C23×Q811yescharacteristic
680C2×C32C2×2−1+411yescharacteristic
681C2×C32#58511yescharacteristic
682C2×Q8—32no—
683C2×Q8—32no—
684C2×Q8—34no—
685C2×Q8—92no—
686C2×Q8—92no—
687C2×Q8—94no—
688C2×Q8—92no—
689C2×Q8—92no—
690C2×Q8—98no—
691C22×C4—31no—
692C22×C4—31no—
693C22×C4—32no—
694C22×C4—92no—
695C22×C4C2×D3211yescharacteristic
696C4⋊C4—32no—
697C4⋊C4—32no—
698C4⋊C4—31no—
699C4⋊C4—31no—
700C4⋊C4—31no—
701C4⋊C4—31no—
702C4⋊C4—32no—
703C4⋊C4—32no—
704C4⋊C4—32no—
705C4⋊C4—32no—
706C4⋊C4—32no—
707C4⋊C4—32no—
708C4⋊C4—34no—
709C4⋊C4—34no—
710C4⋊C4—34no—
711C4⋊C4—94no—
712C4⋊C4—94no—
713C4⋊C4—94no—
714C4⋊C4—94no—
715C4⋊C4—92no—
716C4⋊C4—92no—
717C4⋊C4—92no—
718C4⋊C4—92no—
719C4⋊C4—94no—
720C4⋊C4—92no—
721C4⋊C4—94no—
722C4⋊C4—92no—
723C4⋊C4—94no—
724C4⋊C4—94no—
725C4⋊C4—91no—
726C4⋊C4—94no—
727C4⋊C4—91no—
728C4⋊C4C2×D3211yescharacteristic
729C4⋊C4C2×D3211yescharacteristic
730C22⋊C4—32no—
731C22⋊C4—32no—
732C22⋊C4—92no—
733C22⋊C4C2×D3212yes—
734C42—31no—
735C42—31no—
736C42—31no—
737C42—31no—
738C42—32no—
739C42—32no—
740C42—94no—
741C42—94no—
742C42—94no—
743C42—94no—
744C42—94no—
745C42—94no—
746C42—92no—
747C42C2×D3212yes—
748C22×C3—21no—
749C22×C3—21no—
750C22×C3—21no—
751C22×C3—21no—
752C22×C3—22no—
753C22×C3—21no—
754C22×C3—41no—
755C22×C3—41no—
756C22×C3C2×D3×Q812yes—
757C22×C3C2×D3×Q812yes—
758C22×C3C24×D311yescharacteristic
759C22×C3C24×D311yescharacteristic
760C3×C4—22no—
761C3×C4—22no—
762C3×C4—22no—
763C3×C4—22no—
764C3×C4—22no—
765C3×C4—22no—
766C3×C4—32no—
767C3×C4—42no—
768C3×C4—42no—
769C3×C4—62no—
770C3×C4—64no—
771C3×C4—62no—
772C3×C4—61no—
773C3×C4—62no—
774C3×C4—61no—
775C3×C4—61no—
776C3×C4—62no—
777C3×C4C2×D3×Q812yes—
778C3×C4C2×D3×Q812yes—
779C3×C4C2×D3×Q812yes—
780C3×C4C2×D3×Q812yes—
781Dic3—22no—
782Dic3—21no—
783Dic3—21no—
784Dic3—22no—
785Dic3—21no—
786Dic3—22no—
787Dic3—24no—
788Dic3—22no—
789Dic3—38no—
790Dic3—38no—
791Dic3—68no—
792Dic3—62no—
793Dic3—62no—
794Dic3—62no—
795Dic3—62no—
796Dic3—122no—
797Dic3—122no—
798Dic3#101012yes—
799C32#350211yescharacteristic, complemented, Sylow
800C23C22×D3211yescharacteristic
801Q8—64no—
802Q8—98no—
803Q8—98no—
804Q8—122no—
805Q8—124no—
806Q8—184no—
807Q8—364no—
808Q8—362no—
809C2×C4—31no—
810C2×C4—31no—
811C2×C4—31no—
812C2×C4—31no—
813C2×C4—32no—
814C2×C4—32no—
815C2×C4—32no—
816C2×C4—32no—
817C2×C4—34no—
818C2×C4—62no—
819C2×C4—98no—
820C2×C4—94no—
821C2×C4—92no—
822C2×C4—92no—
823C2×C4—121no—
824C2×C4—122no—
825C2×C4#379714yes—
826C2×C4C22×D3212yes—
827C2×C4C22×D3212yes—
828C2×C4C22×D3211yescharacteristic
829C2×C4C22×D3211yescharacteristic
830C2×C3—22no—
831C2×C3—22no—
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—21no—
835C2×C3—42no—
836C2×C3C22×D3×Q811yescharacteristic
837C2×C3C22×D3×Q811yescharacteristic
838C2×C3C2×#101011yescharacteristic
839C2×C3#596411yescharacteristic
840C2×C3#596611yescharacteristic
841C2×C3D3×2−1+411yescharacteristic
842C22—21no—
843C22—21no—
844C22C2×#379712yes—
845C22C23×D3211yescharacteristic
846C4—22no—
847C4—22no—
848C4—32no—
849C4—61no—
850C4—62no—
851C4—62no—
852C4—61no—
853C4—64no—
854C4—61no—
855C4—62no—
856C4—62no—
857C4—98no—
858C4—182no—
859C4—182no—
860C4C2×#379712yes—
861C4C2×#379712yes—
862C3—21no—
863C3#8625811yescharacteristic, complemented
864C3#8658511yescharacteristic, complemented
865C2—22no—
866C2C22×#379711yescharacteristic
867C2D3×#101011yescharacteristic
868C2#1059669611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#117C22
prime radicalC23×C32C24
hypercenter#117D32
hypocenterC32#3502
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
8. #10594324C2semidirect
9. #10594318C2semidirect
10. #10594318C2semidirect
11. #10594313C2semidirect
14. #10593864C2semidirect
15. #10593856C2semidirect
16. #10593852C2semidirect
17. #10593852C2semidirect
122. C2×#634Q8semidirect
799. C32#3502semidirect
863. C3#86258semidirect
864. C3#86585semidirect

Maximal subgroups

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

subgroupindex
#105959872
C3×#55192
C3×#55172
#105950512
#105950492
#105948282
C2×#638442
#105943242
#105943182
#105943132
#105940332
#105940302
#105938642
#105938562
#105938522
#865853
#862583