Finite Group Databasebeta

← #11909791

Subgroups — #11909791

Order 1152.

2364 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596189C211yesmaximal, characteristic, complemented
2C3×#5716C211yesmaximal, characteristic, complemented
3C3×#5713C211yesmaximal, characteristic, complemented
4#10595274C212yesmaximal, complemented
5#10595219C212yesmaximal, complemented
6#10595211C214yesmaximal, complemented
7#10595210C212yesmaximal, complemented
8#10595173C212yesmaximal, complemented
9#10595161C212yesmaximal, complemented
10#10595149C214yesmaximal, complemented
11#10595136C212yesmaximal, complemented
12#10595131C212yesmaximal, complemented
13#10595121C212yesmaximal, complemented
14#10593958C211yesmaximal, characteristic, complemented
15C4×D3×Dic6C211yesmaximal, characteristic, complemented
16#10593870C211yesmaximal, characteristic, complemented
17#10593856C211yesmaximal, characteristic, complemented
18#87055—31nomaximal
19#86229—31nomaximal
20C2×#3830C2212yes—
21C2×C3×#237C2212yes—
22C2×#3804C2214yes—
23C2×D3×Dic6C2211yescharacteristic
24C32×#127C2211yescharacteristic
25#64149C2212yes—
26#64148C2214yes—
27#64147C2212yes—
28D4×C3⋊Dic3C2212yes—
29C4×C4⋊(C3⋊D3)C2211yescharacteristic
30C4×#634C2211yescharacteristic
31C3×#938C2212yes—
32C3×#938C2212yes—
33C3×#936C2212yes—
34C3×#936C2212yes—
35C3×#936C2212yes—
36C3×#935C2214yes—
37C3×D4×Dic3C2212yes—
38C3×D4×Dic3C2212yes—
39C3×D4×Dic3C2212yes—
40C3×D4×Dic3C2212yes—
41C3×C42×D3C2211yescharacteristic
42C3×#869C2211yescharacteristic
43C3×C4×Dic6C2211yescharacteristic
44C3×C4×Dic6C2211yescharacteristic
45#63982C2214yes—
46#63975C2214yes—
47#67⋊Dic3C2214yes—
48#63971C2214yes—
49#63969C2214yes—
50C2×#3724C2214yes—
51#63966C2214yes—
52#63964C2214yes—
53#63964C2214yes—
54#63957C2214yes—
55#63956C2214yes—
56#63953C2214yes—
57#63953C2214yes—
58#63952C2214yes—
59#63952C2214yes—
60#63919C2212yes—
61#63918C2212yes—
62C4×#627C2212yes—
63#63909C2211yescharacteristic
64C4×#626C2212yes—
65#63900C2212yes—
66#63894C2212yes—
67D3×C4⋊Dic3C2211yescharacteristic
68#63888C2214yes—
69D3×Dic3⋊C4C2212yes—
70C4×D3×Dic3C2212yes—
71#63874C2212yes—
72#63871C2212yes—
73#63869C2211yescharacteristic
74#63869C2212yes—
75#63868C2212yes—
76#63864C2211yescharacteristic
77#63856C2211yescharacteristic
78#63850C2212yes—
79#63844C2212yes—
80#63844C2211yescharacteristic
81#63843C2212yes—
82Dic3×Dic6C2211yescharacteristic
83#63839C2214yes—
84#63837C2212yes—
85C3×#559—31no—
86C3×#532—31no—
87#5824—34no—
88#5730—31no—
89#5722—31no—
90#5718—31no—
91#5718—31no—
92#5718—61no—
93#5716D311yescharacteristic, complemented
94#5713D311yescharacteristic, complemented
95#5682—32no—
96#5681—32no—
97#5680—32no—
98#5677—32no—
99#5669—34no—
100#5662—34no—
101#5655—34no—
102#5611—32no—
103#5600—32no—
104#5598—32no—
105#5596—32no—
106#5580—31no—
107#5579—31no—
108C4×D3×Q8—31no—
109Q8×Dic6—31no—
110#5561—32no—
111#5559—32no—
112#5551—32no—
113#5548—32no—
114#5546—32no—
115#5546—32no—
116#5539—32no—
117#5539—32no—
118#5479—31no—
119C2×C4×Dic6—31no—
120C2×C32×D4C2312yes—
121C2×C32×D4C2312yes—
122C2×C32×D4C2312yes—
123C2×#638C2314yes—
124C2×#638C2314yes—
125C22×C3⋊Dic3C2314yes—
126#3830—28no—
127C2×C4⋊(C3⋊D3)C2311yescharacteristic
128C2×C4×C3⋊D3C2312yes—
129C2×#634C2311yescharacteristic
130C2×C3×#67C2314yes—
131C22×C3×Dic3C2314yes—
132C22×C3×Dic3C2314yes—
133C3×#237—44no—
134C2×C3×C4×D3C2311yescharacteristic
135C2×C3×C4×D3C2311yescharacteristic
136C2×C3×C4×D3C2311yescharacteristic
137C2×C3×Dic6C2311yescharacteristic
138C2×C3×Dic6C2311yescharacteristic
139C2×C3×Dic6C2312yes—
140C2×#627C2312yes—
141C2×#627C2314yes—
142C2×#626C2312yes—
143C2×#624C2314yes—
144#3804—48no—
145C2×D3×Dic3C2312yes—
146C2×D3×Dic3C2312yes—
147D3×Dic6—24no—
148C32×C42C2311yescharacteristic
149#3757C2314yes—
150#3752C2312yes—
151C4⋊(C3⋊Dic3)C2311yescharacteristic
152C4⋊(C3⋊Dic3)C2311yescharacteristic
153#3750C2312yes—
154C4×C3⋊Dic3C2312yes—
155C3×#217C2314yes—
156C3×#217C2314yes—
157C3×#217C2314yes—
158C3×#217C2314yes—
159C3×#217C2314yes—
160C3×C4⋊Dic3C2311yescharacteristic
161C3×C4⋊Dic3C2311yescharacteristic
162C3×C4⋊Dic3C2312yes—
163C3×C4⋊Dic3C2312yes—
164C3×Dic3⋊C4C2312yes—
165C3×Dic3⋊C4C2312yes—
166C3×C4×Dic3C2311yescharacteristic
167C3×C4×Dic3C2311yescharacteristic
168C3×C4×Dic3C2312yes—
169C3×C4×Dic3C2312yes—
170C3×C4×Dic3C2311yescharacteristic
171#3724C2314yes—
172#3724C2312yes—
173#3724C2312yes—
174#3724C2312yes—
175#3724C2314yes—
176Dic3⋊Dic3C2312yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2312yes—
179Dic3⋊Dic3C2312yes—
180Dic3⋊Dic3C2314yes—
181#3722C2312yes—
182#3722C2312yes—
183#3722C2312yes—
184#3722C2314yes—
185(C2×D3)⋊Dic3C2312yes—
186Dic32C2312yes—
187Dic32C2312yes—
188Dic32C2314yes—
189#3522—91noSylow
190C2×C3×#41—32no—
191C2×D3×Q8—31no—
192C2×#237—32no—
193C2×#237—32no—
194C2×#237—34no—
195C2×#237—62no—
196C2×#237C2×D312yes—
197C2×#235—34no—
198C22×Dic6—31no—
199C3×C4⋊Q8—31no—
200C3×#127—21no—
201C3×#127C2×D311yescharacteristic
202C3×#127C2×D311yescharacteristic
203C3×#124—32no—
204C3×#124—32no—
205C3×#124—32no—
206C3×#123—34no—
207C3×#121—32no—
208C3×#121—32no—
209C3×C4×Q8—31no—
210C3×C4×Q8—31no—
211C3×C4×D4—32no—
212C3×C4×D4—32no—
213C3×C4×D4—32no—
214C3×C4×D4—32no—
215C2×C3×C42—31no—
216#947—31no—
217#946—31no—
218#946—32no—
219#946—34no—
220Q8×Dic3—32no—
221Q8×Dic3—31no—
222#944—34no—
223#940—32no—
224#940—32no—
225#940—62no—
226#939—34no—
227#939—34no—
228#939—34no—
229#939—64no—
230#938—32no—
231#938—32no—
232#938—62no—
233#938C2×D312yes—
234#938C2×D312yes—
235#936C2×D312yes—
236#936C2×D312yes—
237#936C2×D312yes—
238#935—34no—
239#935C2×D314yes—
240D4×Dic3—32no—
241D4×Dic3—32no—
242D4×Dic3—34no—
243D4×Dic3—62no—
244D4×Dic3C2×D312yes—
245D4×Dic3C2×D312yes—
246D4×Dic3C2×D312yes—
247D4×Dic3C2×D312yes—
248#930—31no—
249#929—34no—
250#929—32no—
251C4×#67—34no—
252C4×#67—34no—
253C4×#67—32no—
254C2×C4⋊Dic3—31no—
255#924—31no—
256#924—34no—
257#924—34no—
258C2×Dic3⋊C4—34no—
259C2×Dic3⋊C4—34no—
260C2×Dic3⋊C4—32no—
261C2×C4×Dic3—32no—
262#898—32no—
263#897—32no—
264#896—34no—
265#895—31no—
266#894—32no—
267#893—32no—
268D3×C4⋊C4—32no—
269D3×C4⋊C4—31no—
270D3×C4⋊C4—32no—
271D3×C4⋊C4—32no—
272#890—32no—
273#890—31no—
274#888—34no—
275#888—32no—
276#888—32no—
277#888—32no—
278#887—32no—
279#887—32no—
280#887—32no—
281#887—31no—
282#886—34no—
283#885—34no—
284#885—34no—
285#885—34no—
286#885—34no—
287#884—34no—
288#883—34no—
289#883—34no—
290#883—34no—
291#67⋊C4—34no—
292#67⋊C4—34no—
293#67⋊C4—34no—
294#879—34no—
295#879—34no—
296#878—34no—
297#878—34no—
298#878—34no—
299#878—34no—
300#877—34no—
301#877—34no—
302#876—32no—
303#875—31no—
304C4×D12—32no—
305C4×D12—31no—
306C4×D12—31no—
307C4×D12—32no—
308C4×D12—61no—
309#872—32no—
310#872—32no—
311C42×D3—32no—
312C42×D3C2×D311yescharacteristic
313#870—32no—
314#870—31no—
315#869—32no—
316#869C2×D311yescharacteristic
317C4×Dic6—31no—
318C4×Dic6—31no—
319C4×Dic6—31no—
320C4×Dic6—32no—
321C4×Dic6—31no—
322C4×Dic6—32no—
323C4×Dic6—32no—
324C4×Dic6—32no—
325C4×Dic6—61no—
326C4×Dic6C2×D311yescharacteristic
327C4×Dic6C2×D311yescharacteristic
328C23×C32C2414yes—
329C22×C3⋊D3C2412yes—
330C22×C3×D3C2411yescharacteristic
331C32×D4—24no—
332C32×D4—24no—
333C32×D4—42no—
334C2×C32×C4C2411yescharacteristic
335C2×C32×C4C2411yescharacteristic
336C2×C32×C4C2411yescharacteristic
337#638—28no—
338#638—44no—
339C2×C3⋊Dic3—28no—
340C2×C3⋊Dic3C2412yes—
341C2×C3⋊Dic3C2412yes—
342C2×C3⋊Dic3C2412yes—
343C4⋊(C3⋊D3)—22no—
344C4×C3⋊D3—24no—
345#634#4114yescomplemented
346C3×#67—28no—
347C2×C3×Dic3—44no—
348C2×C3×Dic3—44no—
349C2×C3×Dic3C2411yescharacteristic
350C2×C3×Dic3C2412yes—
351C2×C3×Dic3C2412yes—
352C2×C3×Dic3C2414yes—
353C2×C3×Dic3C2412yes—
354C2×C3×Dic3C2411yescharacteristic
355C2×C3×Dic3C2411yescharacteristic
356C2×C3×Dic3C2412yes—
357C3×C4×D3—22no—
358C3×C4×D3—22no—
359C3×C4×D3—22no—
360C3×Dic6—22no—
361C3×Dic6—22no—
362C3×Dic6—42no—
363#627—24no—
364#627—44no—
365#626—24no—
366#624—44no—
367D3×Dic3—24no—
368D3×Dic3—24no—
369#559—31no—
370#559—92no—
371Q82—91no—
372#554—92no—
373#554—91no—
374#550—91no—
375#548—92no—
376#547—92no—
377#547—94no—
378#542—92no—
379#542—94no—
380#532—31no—
381#532—92no—
382#529—91no—
383#529—92no—
384#520—92no—
385C2×C4×Q8—91no—
386C3×#41—124no—
387C2×C3×Q8—31no—
388C2×C3×Q8—31no—
389C2×C3×Q8—32no—
390C2×C3×D4—22no—
391C2×C3×D4—22no—
392C2×C3×D4—22no—
393C2×C3×D4—34no—
394C2×C3×D4C22×D312yes—
395C2×C3×D4C22×D312yes—
396C2×C3×D4C22×D312yes—
397C2×C3×D4C22×D312yes—
398C2×C3×D4C22×D312yes—
399C2×C3×D4C22×D312yes—
400C22×C3×C4—34no—
401C22×C3×C4—34no—
402C22×C3×C4—31no—
403C22×C3×C4—31no—
404C22×C3×C4—31no—
405C2×#67—34no—
406C2×#67—34no—
407C2×#67—34no—
408C2×#67—34no—
409C2×#67—32no—
410C2×#67—64no—
411C2×#67—64no—
412C2×#67C22×D314yes—
413C22×Dic3—34no—
414C22×Dic3—34no—
415C22×Dic3—32no—
416C22×Dic3—32no—
417C22×Dic3—64no—
418C22×Dic3C22×D314yes—
419C22×Dic3C22×D314yes—
420D3×Q8—64no—
421#237—44no—
422#237—68no—
423#237—68no—
424#237—128no—
425#237—128no—
426#235—128no—
427C2×D12—32no—
428C2×D12—31no—
429C2×D12—31no—
430C2×D12—61no—
431C2×C4×D3—32no—
432C2×C4×D3—32no—
433C2×C4×D3—32no—
434C2×C4×D3—32no—
435C2×C4×D3—34no—
436C2×C4×D3—34no—
437C2×C4×D3—62no—
438C2×C4×D3C22×D311yescharacteristic
439C2×C4×D3C22×D311yescharacteristic
440C2×C4×D3C22×D311yescharacteristic
441C2×Dic6—31no—
442C2×Dic6—31no—
443C2×Dic6—32no—
444C2×Dic6—32no—
445C2×Dic6—34no—
446C2×Dic6—34no—
447C2×Dic6—61no—
448C2×Dic6—64no—
449C2×Dic6C22×D311yescharacteristic
450C2×Dic6C22×D311yescharacteristic
451C2×Dic6C22×D312yes—
452C3×C4⋊C4—32no—
453C3×C4⋊C4—32no—
454C3×C4⋊C4—31no—
455C3×C4⋊C4—32no—
456C3×C4⋊C4—31no—
457C3×C4⋊C4—32no—
458C3×C22⋊C4—34no—
459C3×C22⋊C4—34no—
460C3×C22⋊C4—34no—
461C3×C22⋊C4—34no—
462C3×C22⋊C4—34no—
463C3×C42—21no—
464C3×C42—31no—
465C3×C42—31no—
466C3×C42—31no—
467C3×C42—32no—
468C3×C42—32no—
469C3×C42C22×D311yescharacteristic
470C3×C42C22×D311yescharacteristic
471#217—34no—
472#217—34no—
473#217—32no—
474#217—64no—
475#217C22×D314yes—
476#217C22×D314yes—
477#217C22×D314yes—
478#217C22×D314yes—
479#217C22×D314yes—
480(C2×D3)⋊C4—32no—
481(C2×D3)⋊C4—32no—
482(C2×D3)⋊C4—32no—
483(C2×D3)⋊C4—32no—
484(C2×D3)⋊C4—32no—
485(C2×D3)⋊C4—32no—
486(C2×D3)⋊C4—32no—
487(C2×D3)⋊C4—32no—
488(C2×D3)⋊C4—34no—
489(C2×D3)⋊C4—32no—
490(C2×D3)⋊C4—34no—
491(C2×D3)⋊C4—62no—
492C4⋊Dic3—31no—
493C4⋊Dic3—31no—
494C4⋊Dic3—31no—
495C4⋊Dic3—31no—
496C4⋊Dic3—32no—
497C4⋊Dic3—32no—
498C4⋊Dic3—34no—
499C4⋊Dic3—32no—
500C4⋊Dic3—34no—
501C4⋊Dic3—61no—
502C4⋊Dic3—61no—
503C4⋊Dic3C22×D311yescharacteristic
504C4⋊Dic3C22×D312yes—
505C4⋊Dic3C22×D311yescharacteristic
506C4⋊Dic3C22×D312yes—
507Dic3⋊C4—32no—
508Dic3⋊C4—32no—
509Dic3⋊C4—32no—
510Dic3⋊C4—32no—
511Dic3⋊C4—34no—
512Dic3⋊C4—32no—
513Dic3⋊C4—32no—
514Dic3⋊C4—32no—
515Dic3⋊C4—32no—
516Dic3⋊C4—34no—
517Dic3⋊C4—34no—
518Dic3⋊C4—32no—
519Dic3⋊C4—32no—
520Dic3⋊C4—32no—
521Dic3⋊C4—34no—
522Dic3⋊C4—34no—
523Dic3⋊C4—34no—
524Dic3⋊C4—62no—
525Dic3⋊C4C22×D312yes—
526Dic3⋊C4C22×D312yes—
527C4×Dic3—32no—
528C4×Dic3—32no—
529C4×Dic3—32no—
530C4×Dic3—32no—
531C4×Dic3—34no—
532C4×Dic3—32no—
533C4×Dic3—32no—
534C4×Dic3—34no—
535C4×Dic3—62no—
536C4×Dic3C22×D311yescharacteristic
537C4×Dic3C22×D312yes—
538C4×Dic3C22×D312yes—
539C4×Dic3C22×D311yescharacteristic
540C4×Dic3C22×D311yescharacteristic
541C22×C32—24no—
542C22×C32—24no—
543C22×C32—24no—
544C22×C32C2511yescharacteristic
545C2×C3⋊D3—22no—
546C2×C3⋊D3—22no—
547C2×C3⋊D3—22no—
548C2×C3×D3—21no—
549C2×C3×D3—21no—
550C2×C3×D3H(5,𝔽2)12yes—
551C32×C4—21no—
552C32×C4C2×#4112yes—
553C32×C42−1+412yes—
554C3⋊Dic3—22no—
555C3⋊Dic3—22no—
556C3⋊Dic3C2×#4114yes—
557C3×Dic3—22no—
558C3×Dic3—21no—
559C3×Dic3—22no—
560C3×Dic3—24no—
561C3×Dic3—22no—
562C3×Dic3—21no—
563C3×Dic3—22no—
564C3×Dic3—21no—
565C2×#41—32no—
566C2×#41—94no—
567C2×#41—92no—
568C22×Q8—91no—
569C4⋊Q8—31no—
570C4⋊Q8—92no—
571C4⋊Q8—92no—
572C4⋊Q8—94no—
573#127—92no—
574#127D3211yescharacteristic
575#126—92no—
576#126—94no—
577#125—91no—
578#125—92no—
579#124—32no—
580#124—32no—
581#124—32no—
582#124—91no—
583#124—94no—
584#124—94no—
585#123—34no—
586#123—94no—
587#123—94no—
588#123—94no—
589#123—92no—
590C22⋊Q8—94no—
591C22⋊Q8—94no—
592C22⋊Q8—94no—
593C22⋊Q8—94no—
594C22⋊Q8—92no—
595C22⋊Q8—91no—
596#121—32no—
597#121—32no—
598#121—94no—
599#121—91no—
600#121—92no—
601#121—94no—
602C4×Q8—31no—
603C4×Q8—31no—
604C4×Q8—92no—
605C4×Q8—91no—
606C4×Q8—92no—
607C4×Q8—92no—
608C4×Q8—91no—
609C4×Q8—92no—
610C4×Q8—91no—
611C4×D4—32no—
612C4×D4—32no—
613C4×D4—32no—
614C4×D4—32no—
615C4×D4—92no—
616C4×D4—92no—
617C4×D4—94no—
618C4×D4—94no—
619C4×D4—94no—
620C4×D4—92no—
621C4×D4—91no—
622#117—92no—
623#117—94no—
624C2×C4⋊C4—92no—
625C2×C4⋊C4—92no—
626C2×C4⋊C4—91no—
627C2×C4⋊C4—94no—
628C2×C42—31no—
629C2×C42—92no—
630C23×C3—24no—
631C23×C3—31no—
632C23×C3C23×D314yes—
633C23×C3C23×D314yes—
634C22×D3—32no—
635C22×D3—32no—
636C22×D3—62no—
637C22×D3C23×D311yescharacteristic
638C3×Q8—62no—
639C3×Q8—62no—
640C3×Q8—122no—
641C3×D4—24no—
642C3×D4—24no—
643C3×D4—24no—
644C3×D4—24no—
645C3×D4—44no—
646C3×D4—44no—
647C3×D4—42no—
648C3×D4—42no—
649C3×D4—68no—
650C3×D4—82no—
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—31no—
655C2×C3×C4—32no—
656C2×C3×C4—32no—
657C2×C3×C4—34no—
658C2×C3×C4—32no—
659C2×C3×C4—31no—
660C2×C3×C4—32no—
661C2×C3×C4—31no—
662C2×C3×C4—62no—
663C2×C3×C4—62no—
664C2×C3×C4—62no—
665C2×C3×C4—124no—
666C2×C3×C4—124no—
667C2×C3×C4C23×D311yescharacteristic
668C2×C3×C4C23×D311yescharacteristic
669C2×C3×C4C23×D311yescharacteristic
670C2×C3×C4C23×D311yescharacteristic
671C2×C3×C4C23×D311yescharacteristic
672C2×C3×C4C23×D311yescharacteristic
673#67—28no—
674#67—64no—
675#67—68no—
676#67—68no—
677#67—128no—
678#67—124no—
679#67—124no—
680#67—244no—
681C2×Dic3—32no—
682C2×Dic3—32no—
683C2×Dic3—32no—
684C2×Dic3—32no—
685C2×Dic3—32no—
686C2×Dic3—32no—
687C2×Dic3—44no—
688C2×Dic3—44no—
689C2×Dic3—62no—
690C2×Dic3—62no—
691C2×Dic3—62no—
692C2×Dic3—64no—
693C2×Dic3—64no—
694C2×Dic3—68no—
695C2×Dic3—68no—
696C2×Dic3—128no—
697C2×Dic3C23×D311yescharacteristic
698C2×Dic3C23×D312yes—
699C2×Dic3C23×D312yes—
700C2×Dic3C23×D312yes—
701C2×Dic3C23×D314yes—
702C2×Dic3C23×D311yescharacteristic
703C2×Dic3C23×D311yescharacteristic
704C2×Dic3C23×D312yes—
705D12—64no—
706D12—62no—
707D12—62no—
708D12—122no—
709C4×D3—22no—
710C4×D3—22no—
711C4×D3—22no—
712C4×D3—64no—
713C4×D3—64no—
714C4×D3—64no—
715C4×D3—64no—
716C4×D3—124no—
717C4×D3—124no—
718C4×D3—124no—
719Dic6—22no—
720Dic6—22no—
721Dic6—34no—
722Dic6—34no—
723Dic6—42no—
724Dic6—64no—
725Dic6—64no—
726Dic6—64no—
727Dic6—124no—
728Dic6—124no—
729C2×C32—44no—
730C2×C32C22×#4111yescharacteristic
731C2×C32C2×H(5,𝔽2)11yescharacteristic
732C2×C32C2×2−1+411yescharacteristic
733C3⋊D3—42no—
734C3×D3—22no—
735#41—124no—
736#41—188no—
737#41—368no—
738C2×Q8—31no—
739C2×Q8—31no—
740C2×Q8—32no—
741C2×Q8—92no—
742C2×Q8—94no—
743C2×Q8—91no—
744C2×Q8—184no—
745C2×D4—34no—
746C2×D4—92no—
747C2×D4—94no—
748C2×D4—94no—
749C2×D4—91no—
750C2×D4C2×D3212yes—
751C2×D4C2×D3212yes—
752C2×D4C2×D3212yes—
753C22×C4—34no—
754C22×C4—34no—
755C22×C4—31no—
756C22×C4—31no—
757C22×C4—31no—
758C22×C4—94no—
759C22×C4—92no—
760C22×C4—92no—
761C22×C4—94no—
762C22×C4—92no—
763C4⋊C4—31no—
764C4⋊C4—32no—
765C4⋊C4—32no—
766C4⋊C4—31no—
767C4⋊C4—32no—
768C4⋊C4—32no—
769C4⋊C4—92no—
770C4⋊C4—92no—
771C4⋊C4—94no—
772C4⋊C4—94no—
773C4⋊C4—92no—
774C4⋊C4—92no—
775C4⋊C4—92no—
776C4⋊C4—92no—
777C4⋊C4—94no—
778C4⋊C4—94no—
779C4⋊C4—92no—
780C4⋊C4—91no—
781C4⋊C4—91no—
782C22⋊C4—34no—
783C22⋊C4—34no—
784C22⋊C4—34no—
785C22⋊C4—34no—
786C22⋊C4—34no—
787C22⋊C4—92no—
788C22⋊C4—92no—
789C22⋊C4—94no—
790C22⋊C4—92no—
791C22⋊C4—92no—
792C22⋊C4—94no—
793C22⋊C4—92no—
794C42—31no—
795C42—31no—
796C42—31no—
797C42—32no—
798C42—32no—
799C42—92no—
800C42—92no—
801C42—94no—
802C42—92no—
803C42C2×D3211yescharacteristic
804C22×C3—24no—
805C22×C3—24no—
806C22×C3—24no—
807C22×C3—24no—
808C22×C3—24no—
809C22×C3—24no—
810C22×C3—21no—
811C22×C3—32no—
812C22×C3—44no—
813C22×C3—44no—
814C22×C3—44no—
815C22×C3—61no—
816C22×C3—61no—
817C22×C3C24×D311yescharacteristic
818C22×C3C24×D311yescharacteristic
819C2×D3—21no—
820C2×D3—21no—
821C2×D3—62no—
822C2×D3—62no—
823C2×D3—62no—
824C2×D3—62no—
825C2×D3—62no—
826C2×D3—62no—
827C2×D3—122no—
828C2×D3—122no—
829C2×D3—122no—
830C2×D3#100412yes—
831C3×C4—21no—
832C3×C4—21no—
833C3×C4—22no—
834C3×C4—22no—
835C3×C4—41no—
836C3×C4—62no—
837C3×C4—62no—
838C3×C4—61no—
839C3×C4—62no—
840C3×C4—61no—
841C3×C4—62no—
842C3×C4—64no—
843C3×C4—61no—
844C3×C4D3×#4112yes—
845C3×C4D3×#4112yes—
846C3×C4#101012yes—
847C3×C4#101012yes—
848Dic3—24no—
849Dic3—21no—
850Dic3—22no—
851Dic3—21no—
852Dic3—22no—
853Dic3—21no—
854Dic3—22no—
855Dic3—22no—
856Dic3—34no—
857Dic3—34no—
858Dic3—64no—
859Dic3—62no—
860Dic3—62no—
861Dic3—62no—
862Dic3—62no—
863Dic3—122no—
864Dic3—122no—
865C32#352211yescharacteristic, complemented, Sylow
866C23—31no—
867C23—92no—
868C23C22×D3214yes—
869Q8—62no—
870Q8—62no—
871Q8—94no—
872Q8—122no—
873Q8—184no—
874Q8—364no—
875D4—24no—
876D4—24no—
877D4—42no—
878D4—68no—
879D4—184no—
880D4—188no—
881D4—182no—
882D4—364no—
883C2×C4—31no—
884C2×C4—31no—
885C2×C4—31no—
886C2×C4—32no—
887C2×C4—32no—
888C2×C4—32no—
889C2×C4—32no—
890C2×C4—34no—
891C2×C4—62no—
892C2×C4—62no—
893C2×C4—62no—
894C2×C4—92no—
895C2×C4—92no—
896C2×C4—92no—
897C2×C4—124no—
898C2×C4—124no—
899C2×C4—184no—
900C2×C4—184no—
901C2×C4—188no—
902C2×C4—184no—
903C2×C4—364no—
904C2×C4C22×D3211yescharacteristic
905C2×C4C22×D3211yescharacteristic
906C2×C4C22×D3211yescharacteristic
907C2×C3—21no—
908C2×C3—21no—
909C2×C3—21no—
910C2×C3—44no—
911C2×C3—44no—
912C2×C3—62no—
913C2×C3—84no—
914C2×C3C2×#100411yescharacteristic
915C2×C3C2×D3×#4111yescharacteristic
916C2×C3C2×D3×#4111yescharacteristic
917C2×C3C2×#101011yescharacteristic
918C2×C3C2×#101011yescharacteristic
919C2×C3D3×H(5,𝔽2)11yescharacteristic
920D3—22no—
921D3—122no—
922D3—122no—
923D3—242no—
924C22—24no—
925C22—24no—
926C22—24no—
927C22—32no—
928C22—61no—
929C22—61no—
930C22—182no—
931C22—182no—
932C22—182no—
933C22C23×D3211yescharacteristic
934C4—21no—
935C4—61no—
936C4—62no—
937C4—61no—
938C4—62no—
939C4—61no—
940C4—62no—
941C4—62no—
942C4—64no—
943C4—94no—
944C4—182no—
945C4—182no—
946C4#6430912yes—
947C4#6431212yes—
948C3—21no—
949C3#8622911yescharacteristic, complemented
950C3#8705511yescharacteristic, complemented
951C2—44no—
952C2—62no—
953C2—362no—
954C2C2×#6430911yescharacteristic
955C2C2×#6431211yescharacteristic
956C2D3×#100411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#127C22
hypercenter#127D32
hypocenterC32#3522
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #10596189C2semidirect
2. C3×#5716C2semidirect
3. C3×#5713C2semidirect
4. #10595274C2semidirect
5. #10595219C2semidirect
6. #10595211C2semidirect
7. #10595210C2semidirect
8. #10595173C2semidirect
9. #10595161C2semidirect
10. #10595149C2semidirect
11. #10595136C2semidirect
12. #10595131C2semidirect
13. #10595121C2semidirect
14. #10593958C2semidirect
15. C4×D3×Dic6C2semidirect
16. #10593870C2semidirect
17. #10593856C2semidirect
93. #5716D3semidirect
94. #5713D3semidirect
345. #634#41semidirect
865. C32#3522semidirect
949. C3#86229semidirect
950. C3#87055semidirect

Maximal subgroups

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

subgroupindex
#105961892
C3×#57162
C3×#57132
#105952742
#105952192
#105952112
#105952102
#105951732
#105951612
#105951492
#105951362
#105951312
#105951212
#105939582
C4×D3×Dic62
#105938702
#105938562
#870553
#862293