Finite Group Databasebeta

← #11910767

Subgroups — #11910767

Order 1152.

2293 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595964C211yesmaximal, characteristic, complemented
2C3×#5495C212yesmaximal, complemented
3C2×#63975C211yesmaximal, characteristic, complemented
4#10595502C211yesmaximal, characteristic, complemented
5#10595500C212yesmaximal, complemented
6#10595027C212yesmaximal, complemented
7#10594978C212yesmaximal, complemented
8#10594946C212yesmaximal, complemented
9#10594814C212yesmaximal, complemented
10#10594244C211yesmaximal, characteristic, complemented
11#10594243C212yesmaximal, complemented
12#10594165C211yesmaximal, characteristic, complemented
13#10594162C212yesmaximal, complemented
14#10594142C211yesmaximal, characteristic, complemented
15#10594128C212yesmaximal, complemented
16#10594079C212yesmaximal, complemented
17#10594077C212yesmaximal, complemented
18#10594045C212yesmaximal, complemented
19#10594036C211yesmaximal, characteristic, complemented
20#86819—32nomaximal
21C22×#638C2211yescharacteristic
22C22×#638C2211yescharacteristic
23C22×#624C2211yescharacteristic, complemented
24C2×#3805C2211yescharacteristic, complemented
25C2×#3804C2212yes—
26C2×C32×C22⋊C4C2211yescharacteristic
27#64139C2212yes—
28#64139C2212yes—
29#64095C2212yes—
30#64095C2211yescharacteristic
31#64095C2211yescharacteristic
32#64091C2212yes—
33#64091C2211yescharacteristic
34#64091C2211yescharacteristic
35C3×#953C2212yes—
36C2×C3×#217C2212yes—
37C3×#929C2212yescomplemented
38C3×C4×#67C2212yescomplemented
39C3×#926C2212yescomplemented
40C3×#924C2212yescomplemented
41C3×#886C2212yescomplemented
42C3×#885C2212yescomplemented
43C3×#883C2212yescomplemented
44C3×#67⋊C4C2212yescomplemented
45C3×#879C2212yescomplemented
46C3×#879C2212yescomplemented
47C3×#878C2212yescomplemented
48C3×#877C2212yescomplemented
49#63982C2212yescomplemented
50#63981C2212yescomplemented
51#63981C2212yescomplemented
52#63979C2211yescharacteristic
53#63979C2211yescharacteristic, complemented
54#63978C2212yes—
55#63975C2212yes—
56#63975C2211yescharacteristic
57#63975C2211yescharacteristic
58#63975C2211yescharacteristic, complemented
59#63975C2212yescomplemented
60#63975C2211yescharacteristic, complemented
61#63975C2212yescomplemented
62#63974C2212yescomplemented
63#67⋊Dic3C2212yescomplemented
64#63971C2212yes—
65#63971C2212yescomplemented
66#63971C2212yescomplemented
67#63966C2212yes—
68C2×Dic3⋊Dic3C2212yescomplemented
69C2×#3722C2211yescharacteristic, complemented
70#63958C2212yescomplemented
71#63957C2211yescharacteristic, complemented
72#63953C2211yescharacteristic
73#63953C2212yescomplemented
74#63953C2211yescharacteristic, complemented
75#63952C2212yes—
76#63918C2212yescomplemented
77#63910C2212yescomplemented
78#63910C2212yescomplemented
79#63910C2212yescomplemented
80#63909C2212yescomplemented
81#63907C2212yescomplemented
82#63906C2212yescomplemented
83#63897C2212yescomplemented
84#63895C2212yescomplemented
85#63895C2212yescomplemented
86#63895C2212yescomplemented
87#63894C2212yescomplemented
88#63894C2212yescomplemented
89#63893C2212yescomplemented
90#63891C2212yescomplemented
91#63890C2212yescomplemented
92D3×C4⋊Dic3C2212yescomplemented
93#63888C2212yescomplemented
94#63880C2212yescomplemented
95#63880C2212yescomplemented
96#63880C2212yescomplemented
97#63869C2212yescomplemented
98#63868C2212yescomplemented
99#63868C2212yescomplemented
100#63864C2212yescomplemented
101#63850C2212yescomplemented
102#63848C2212yescomplemented
103#63848C2212yescomplemented
104#63845C2212yescomplemented
105#63845C2212yescomplemented
106Dic3×Dic6C2212yescomplemented
107#63836C2212yescomplemented
108C3×#551—32no—
109#5712—32no—
110#5707—32no—
111#5705—32no—
112#5704—32no—
113#5681—32no—
114#5678—32no—
115#5667—32no—
116#5666—32no—
117#5665—32no—
118#5663—32no—
119#5656—32no—
120#5655—32no—
121#5647—32no—
122#5644—32no—
123#5643—32no—
124#5642—32no—
125#5592—32no—
126#5591—32no—
127#5565—32no—
128#5562—32no—
129#5560—32no—
130#5555—32no—
131#5534—32no—
132#5531—32no—
133#5530—32no—
134#5524—32no—
135#5495D312yescomplemented
136#5493—32no—
137#5493—61no—
138#5490—32no—
139C2×#883—32no—
140C24×C32C2311yescharacteristic
141C23×C3⋊D3C2311yescharacteristic
142C23×C3⋊D3C2311yescharacteristic
143C22×C32×C4C2312yes—
144C2×#638—42no—
145C2×#638—42no—
146C2×#638C2312yes—
147C2×#638C2311yescharacteristic
148C2×#638C2311yescharacteristic
149C2×#638C2312yes—
150C2×#638C2311yescharacteristic
151C2×#638C2311yescharacteristic
152C22×C3⋊Dic3C2311yescharacteristic
153C22×C3⋊Dic3C2311yescharacteristic
154C2×C4⋊(C3⋊D3)C2312yes—
155C2×C4⋊(C3⋊D3)C2312yes—
156C2×C3×#67C2312yes—
157C2×C3×#67C2312yes—
158C2×C3×#67C2312yes—
159C22×C3×Dic3C2312yes—
160C22×C3×Dic3C2312yes—
161C2×C3×C4×D3C2312yes—
162C2×C3×Dic6C2312yes—
163C2×#627C2312yes—
164C2×#627C2311yescharacteristic
165C2×#626C2312yes—
166C2×#626C2312yes—
167C2×#626C2312yes—
168C2×#626C2312yes—
169C2×#625C2311yescharacteristic
170C2×#624—42no—
171C2×#624C2312yes—
172C2×#624C2311yescharacteristic
173C2×#624C2312yes—
174C2×#624C2311yescharacteristic
175C2×#624C2312yes—
176#3805—42no—
177#3804—44no—
178C2×D3×Dic3C2312yes—
179C2×D3×Dic3C2312yes—
180C32×C22⋊C4C2312yes—
181C32×C22⋊C4C2311yescharacteristic
182C32×C22⋊C4C2311yescharacteristic
183#3752C2312yes—
184#3752C2312yes—
185#3752C2312yes—
186#3752C2312yes—
187C4⋊(C3⋊Dic3)C2312yes—
188C4⋊(C3⋊Dic3)C2312yes—
189C3×#217C2312yes—
190C3×#217C2312yes—
191C3×#217C2312yes—
192C3×#217C2312yes—
193C3×#217C2312yes—
194C3×#217C2312yes—
195C3×#217C2312yes—
196C3×(C2×D3)⋊C4C2312yes—
197C3×(C2×D3)⋊C4C2312yes—
198C3×(C2×D3)⋊C4C2312yes—
199C3×C4⋊Dic3C2312yes—
200C3×C4⋊Dic3C2312yes—
201C3×C4⋊Dic3C2312yes—
202C3×Dic3⋊C4C2312yes—
203C3×Dic3⋊C4C2312yes—
204C3×Dic3⋊C4C2312yes—
205C3×Dic3⋊C4C2312yes—
206C3×Dic3⋊C4C2312yes—
207C3×C4×Dic3C2312yes—
208C3×C4×Dic3C2312yes—
209C3×C4×Dic3C2312yes—
210#3724C2312yes—
211#3724C2312yes—
212Dic3⋊Dic3C2312yes—
213Dic3⋊Dic3C2312yes—
214Dic3⋊Dic3C2312yes—
215Dic3⋊Dic3C2312yes—
216Dic3⋊Dic3C2312yes—
217Dic3⋊Dic3C2312yes—
218Dic3⋊Dic3C2312yes—
219#3722C2312yes—
220#3722C2312yes—
221#3722C2312yes—
222#3722C2312yes—
223#3722C2312yes—
224#3722C2312yes—
225#3722C2311yescharacteristic
226#3722C2312yes—
227#3722C2311yescharacteristic
228(C2×D3)⋊Dic3C2312yes—
229Dic32C2311yescharacteristic
230Dic32C2311yescharacteristic
231Dic32C2312yes—
232#3533—91noSylow
233C22×#67—32no—
234C22×#67—32no—
235C22×#67—61no—
236C22×#67—61no—
237C2×#237—32no—
238C2×#237—32no—
239C2×#235—32no—
240C22×C4×D3—32no—
241C3×#126—32no—
242C3×#126—32no—
243C3×#124—32no—
244C3×#123—32no—
245C3×#123—32no—
246C3×#123—32no—
247C3×C22⋊Q8—32no—
248C3×C22⋊Q8—32no—
249C3×#120—32no—
250C3×C4×D4—32no—
251C3×C4×D4—32no—
252C3×#117—32no—
253C3×#117—32no—
254C2×C3×C22⋊C4—21no—
255C2×C3×C22⋊C4—32no—
256C2×C3×C22⋊C4C2×D312yes—
257#953C2×D312yes—
258C2×#217C2×D312yes—
259#947—32no—
260#947—32no—
261#946—32no—
262Q8×Dic3—32no—
263#940—32no—
264#940—32no—
265#939—32no—
266#939—32no—
267#939—32no—
268#939—32no—
269#938—32no—
270#937—32no—
271#937—32no—
272D4×Dic3—32no—
273#930—32no—
274#930—32no—
275#930—32no—
276#930—32no—
277#930—32no—
278#930—32no—
279#930—32no—
280#930—62no—
281#930—62no—
282#929—32no—
283#929—32no—
284#929C2×D312yescomplemented
285C4×#67—32no—
286C4×#67C2×D312yescomplemented
287C2×(C2×D3)⋊C4—32no—
288#926C2×D312yescomplemented
289C2×C4⋊Dic3—32no—
290C2×C4⋊Dic3—32no—
291#924C2×D312yescomplemented
292C2×Dic3⋊C4—32no—
293#898—32no—
294#898—32no—
295#898—32no—
296#898—32no—
297#898—32no—
298#898—32no—
299#897—32no—
300#897—32no—
301#897—32no—
302#897—32no—
303#896—32no—
304#896—32no—
305#896—32no—
306#896—32no—
307#895—32no—
308#895—32no—
309#895—32no—
310#895—32no—
311#894—32no—
312#894—32no—
313#894—32no—
314#894—32no—
315#893—32no—
316#893—32no—
317#892—32no—
318D3×C4⋊C4—32no—
319#890—32no—
320#890—32no—
321#890—32no—
322#889—32no—
323#889—32no—
324#888—32no—
325#886—32no—
326#886—32no—
327#886—32no—
328#886—32no—
329#886—32no—
330#886—32no—
331#886—32no—
332#886—61no—
333#886—62no—
334#886—61no—
335#886C2×D312yescomplemented
336#885—32no—
337#885—32no—
338#885—32no—
339#885—32no—
340#885—32no—
341#885C2×D312yescomplemented
342#884—32no—
343#884—32no—
344#884—32no—
345#884—32no—
346#884—32no—
347#884—32no—
348#884—32no—
349#884—32no—
350#883—32no—
351#883—32no—
352#883—32no—
353#883—32no—
354#883—32no—
355#883—32no—
356#883—32no—
357#883—32no—
358#883—32no—
359#883—32no—
360#883—32no—
361#883C2×D312yescomplemented
362#882—32no—
363#882—32no—
364#882—32no—
365#882—32no—
366#882—32no—
367#882—32no—
368#882—62no—
369#882—61no—
370#882—61no—
371#67⋊C4—32no—
372#67⋊C4—32no—
373#67⋊C4—32no—
374#67⋊C4—32no—
375#67⋊C4—32no—
376#67⋊C4C2×D312yescomplemented
377D3×C22⋊C4—32no—
378D3×C22⋊C4—32no—
379#879C2×D312yescomplemented
380#879C2×D312yescomplemented
381#878—32no—
382#878—32no—
383#878—32no—
384#878C2×D312yescomplemented
385#877—32no—
386#877C2×D312yescomplemented
387#876—32no—
388#876—32no—
389#875—32no—
390C4×D12—32no—
391C4×D12—32no—
392C4×D12—32no—
393C4×D12—32no—
394C4×D12—32no—
395#872—32no—
396#870—32no—
397#869—32no—
398C4×Dic6—32no—
399C23×C32—22no—
400C23×C32—42no—
401C23×C32C2411yescharacteristic
402C23×C32C2411yescharacteristic
403C23×C32C2411yescharacteristic
404C22×C3⋊D3—22no—
405C22×C3⋊D3—41no—
406C22×C3⋊D3—42no—
407C22×C3⋊D3—42no—
408C22×C3⋊D3C2411yescharacteristic
409C22×C3⋊D3C2411yescharacteristic
410C22×C3⋊D3C2412yes—
411C22×C3×D3C2412yes—
412C2×C32×C4—42no—
413C2×C32×C4C2412yes—
414C2×C32×C4C2412yes—
415#638—24no—
416#638—41no—
417#638—41no—
418#638—42no—
419#638—41no—
420#638—41no—
421C2×C3⋊Dic3—22no—
422C2×C3⋊Dic3—41no—
423C2×C3⋊Dic3C2411yescharacteristic
424C2×C3⋊Dic3C2412yes—
425C2×C3⋊Dic3C2411yescharacteristic
426C4⋊(C3⋊D3)—42no—
427C4⋊(C3⋊D3)—42no—
428C3×#67—24no—
429C3×#67—42no—
430C3×#67—42no—
431C2×C3×Dic3—24no—
432C2×C3×Dic3—42no—
433C2×C3×Dic3C2412yes—
434C2×C3×Dic3C2412yes—
435C2×C3×Dic3C2412yes—
436C2×C3×Dic3C2412yes—
437C2×C3×Dic3C2412yes—
438C2×C3×Dic3C2412yes—
439C2×C3×Dic3C2412yes—
440C3×C4×D3—42no—
441C3×Dic6—42no—
442#627—42no—
443#627—41no—
444#626—42no—
445#626—42no—
446#626—42no—
447#626—42no—
448#625—41no—
449#624—42no—
450#624—41no—
451#624—42no—
452#624—41no—
453#624—42no—
454D3×Dic3—42no—
455D3×Dic3—42no—
456#563—91no—
457#562—92no—
458#560—91no—
459#559—91no—
460#553—92no—
461#552—92no—
462#551—32no—
463#551—91no—
464#547—92no—
465#546—92no—
466#542—92no—
467#540—92no—
468#539—92no—
469#538—92no—
470#538—92no—
471#535—91no—
472#534—91no—
473#525—92no—
474C2×#123—91no—
475C24×C3—21no—
476C24×C3C22×D312yes—
477C23×D3—32no—
478C23×D3—32no—
479C23×D3—61no—
480C23×D3—61no—
481C2×C3×Q8—32no—
482C2×C3×D4—32no—
483C2×C3×D4—32no—
484C2×C3×D4—32no—
485C22×C3×C4—22no—
486C22×C3×C4—32no—
487C22×C3×C4—32no—
488C22×C3×C4—32no—
489C22×C3×C4C22×D312yes—
490C22×C3×C4C22×D312yes—
491C2×#67—32no—
492C2×#67—32no—
493C2×#67—32no—
494C2×#67—32no—
495C2×#67—32no—
496C2×#67—32no—
497C2×#67—32no—
498C2×#67—32no—
499C2×#67—32no—
500C2×#67—32no—
501C2×#67—32no—
502C2×#67—32no—
503C2×#67—32no—
504C2×#67—62no—
505C2×#67—61no—
506C2×#67—61no—
507C2×#67—61no—
508C2×#67—62no—
509C2×#67—61no—
510C2×#67—124no—
511C2×#67—124no—
512C2×#67—124no—
513C2×#67—124no—
514C2×#67C22×D312yes—
515C2×#67C22×D312yes—
516C2×#67C22×D312yes—
517C22×Dic3—32no—
518C22×Dic3—32no—
519C22×Dic3—32no—
520C22×Dic3—32no—
521C22×Dic3—61no—
522C22×Dic3—61no—
523C22×Dic3C22×D312yes—
524C22×Dic3C22×D312yes—
525#237—124no—
526#237—124no—
527#235—124no—
528C2×D12—32no—
529C2×D12—32no—
530C2×D12—32no—
531C2×D12—32no—
532C2×D12—32no—
533C2×D12—32no—
534C2×D12—32no—
535C2×D12—32no—
536C2×D12—62no—
537C2×D12—62no—
538C2×C4×D3—32no—
539C2×C4×D3—32no—
540C2×C4×D3—32no—
541C2×C4×D3—32no—
542C2×C4×D3—32no—
543C2×C4×D3—32no—
544C2×C4×D3—32no—
545C2×C4×D3—32no—
546C2×C4×D3—32no—
547C2×C4×D3—32no—
548C2×C4×D3—124no—
549C2×C4×D3C22×D312yes—
550C2×Dic6—32no—
551C2×Dic6—32no—
552C2×Dic6—32no—
553C2×Dic6C22×D312yes—
554C3×C4⋊C4—32no—
555C3×C4⋊C4—32no—
556C3×C4⋊C4—32no—
557C3×C4⋊C4—32no—
558C3×C4⋊C4—32no—
559C3×C4⋊C4—32no—
560C3×C4⋊C4—32no—
561C3×C4⋊C4—32no—
562C3×C22⋊C4—22no—
563C3×C22⋊C4—21no—
564C3×C22⋊C4—21no—
565C3×C22⋊C4—32no—
566C3×C22⋊C4—32no—
567C3×C22⋊C4—32no—
568C3×C22⋊C4—32no—
569C3×C22⋊C4—32no—
570C3×C22⋊C4—32no—
571C3×C22⋊C4—32no—
572C3×C22⋊C4—32no—
573C3×C22⋊C4—32no—
574C3×C22⋊C4—32no—
575C3×C22⋊C4C22×D312yes—
576C3×C22⋊C4C22×D312yes—
577C3×C22⋊C4C22×D312yes—
578C3×C22⋊C4C22×D312yes—
579C3×C42—32no—
580C3×C42—32no—
581C3×C42—32no—
582#217—32no—
583#217C22×D312yes—
584#217C22×D312yes—
585#217C22×D312yes—
586#217C22×D312yes—
587#217C22×D312yes—
588#217C22×D312yes—
589#217C22×D312yes—
590(C2×D3)⋊C4—32no—
591(C2×D3)⋊C4—32no—
592(C2×D3)⋊C4—32no—
593(C2×D3)⋊C4—32no—
594(C2×D3)⋊C4—32no—
595(C2×D3)⋊C4—32no—
596(C2×D3)⋊C4—32no—
597(C2×D3)⋊C4—32no—
598(C2×D3)⋊C4—32no—
599(C2×D3)⋊C4—32no—
600(C2×D3)⋊C4—32no—
601(C2×D3)⋊C4—32no—
602(C2×D3)⋊C4—32no—
603(C2×D3)⋊C4—32no—
604(C2×D3)⋊C4—32no—
605(C2×D3)⋊C4—32no—
606(C2×D3)⋊C4—32no—
607(C2×D3)⋊C4—32no—
608(C2×D3)⋊C4—32no—
609(C2×D3)⋊C4—32no—
610(C2×D3)⋊C4—32no—
611(C2×D3)⋊C4—32no—
612(C2×D3)⋊C4—32no—
613(C2×D3)⋊C4—32no—
614(C2×D3)⋊C4—32no—
615(C2×D3)⋊C4—62no—
616(C2×D3)⋊C4—62no—
617(C2×D3)⋊C4—62no—
618(C2×D3)⋊C4—62no—
619(C2×D3)⋊C4C22×D312yes—
620(C2×D3)⋊C4C22×D312yes—
621(C2×D3)⋊C4C22×D312yes—
622C4⋊Dic3—32no—
623C4⋊Dic3—32no—
624C4⋊Dic3—32no—
625C4⋊Dic3—32no—
626C4⋊Dic3—32no—
627C4⋊Dic3—32no—
628C4⋊Dic3—32no—
629C4⋊Dic3—32no—
630C4⋊Dic3—32no—
631C4⋊Dic3—32no—
632C4⋊Dic3—32no—
633C4⋊Dic3—62no—
634C4⋊Dic3—62no—
635C4⋊Dic3C22×D312yes—
636C4⋊Dic3C22×D312yes—
637C4⋊Dic3C22×D312yes—
638Dic3⋊C4—32no—
639Dic3⋊C4—32no—
640Dic3⋊C4—32no—
641Dic3⋊C4—32no—
642Dic3⋊C4—32no—
643Dic3⋊C4—32no—
644Dic3⋊C4—32no—
645Dic3⋊C4—32no—
646Dic3⋊C4—32no—
647Dic3⋊C4—32no—
648Dic3⋊C4—32no—
649Dic3⋊C4C22×D312yes—
650Dic3⋊C4C22×D312yes—
651Dic3⋊C4C22×D312yes—
652Dic3⋊C4C22×D312yes—
653Dic3⋊C4C22×D312yes—
654C4×Dic3—32no—
655C4×Dic3—32no—
656C4×Dic3—32no—
657C4×Dic3—32no—
658C4×Dic3C22×D312yes—
659C4×Dic3C22×D312yes—
660C4×Dic3C22×D312yes—
661C22×C32—21no—
662C22×C32—21no—
663C22×C32—22no—
664C22×C32—22no—
665C22×C32—22no—
666C22×C32—82no—
667C22×C32H(5,𝔽2)12yes—
668C22×C32C2511yescharacteristic
669C2×C3⋊D3—21no—
670C2×C3⋊D3—21no—
671C2×C3⋊D3—22no—
672C2×C3⋊D3—22no—
673C2×C3⋊D3—22no—
674C2×C3⋊D3—22no—
675C2×C3⋊D3—22no—
676C2×C3⋊D3—44no—
677C2×C3⋊D3—82no—
678C2×C3×D3—22no—
679C2×C3×D3—22no—
680C2×C3×D3—22no—
681C32×C4—22no—
682C32×C4—22no—
683C3⋊Dic3—21no—
684C3⋊Dic3—22no—
685C3⋊Dic3—21no—
686C3×Dic3—22no—
687C3×Dic3—22no—
688C3×Dic3—22no—
689C3×Dic3—22no—
690C3×Dic3—22no—
691C3×Dic3—22no—
692C3×Dic3—22no—
693C2×#41—92no—
694C2×#41—91no—
695C22×D4—91no—
696C22×D4—91no—
697C23×C4—91no—
698C4⋊Q8—92no—
699#127—91no—
700#127—91no—
701#126—32no—
702#126—32no—
703#126—92no—
704#126—92no—
705#126—92no—
706#126—92no—
707#125—92no—
708#125—92no—
709#125—92no—
710#124—32no—
711#124—92no—
712#124—91no—
713#124—91no—
714#124—92no—
715#124—92no—
716#123—32no—
717#123—32no—
718#123—32no—
719#123—92no—
720#123—92no—
721#123—91no—
722#123—91no—
723#123—91no—
724#123—91no—
725#123—92no—
726#123—92no—
727#123—92no—
728#123—92no—
729#123—92no—
730#123—92no—
731#123—91no—
732#123—92no—
733#123—91no—
734C22⋊Q8—32no—
735C22⋊Q8—32no—
736C22⋊Q8—92no—
737C22⋊Q8—92no—
738C22⋊Q8—92no—
739C22⋊Q8—92no—
740C22⋊Q8—92no—
741C22⋊Q8—92no—
742#121—92no—
743#121—92no—
744#121—92no—
745#121—92no—
746#121—92no—
747#121—92no—
748#121—92no—
749#121—92no—
750#121—92no—
751#121—92no—
752#121—92no—
753#121—92no—
754#120—32no—
755#120—92no—
756#120—92no—
757#120—92no—
758#120—91no—
759#120—91no—
760C4×Q8—92no—
761C4×D4—32no—
762C4×D4—32no—
763C4×D4—92no—
764C4×D4—92no—
765C4×D4—92no—
766C4×D4—92no—
767C4×D4—92no—
768C4×D4—92no—
769C4×D4—92no—
770#117—32no—
771#117—32no—
772#117—92no—
773#117—91no—
774C2×C4⋊C4—92no—
775C2×C4⋊C4—92no—
776C2×C22⋊C4—32no—
777C2×C22⋊C4—92no—
778C2×C22⋊C4—91no—
779C2×C22⋊C4D3211yescharacteristic
780C23×C3—24no—
781C23×C3—24no—
782C23×C3—21no—
783C23×C3—21no—
784C23×C3—21no—
785C23×C3—32no—
786C23×C3—42no—
787C23×C3—42no—
788C23×C3—82no—
789C23×C3C23×D312yes—
790C23×C3C23×D312yes—
791C23×C3C23×D312yes—
792C22×D3—32no—
793C22×D3—32no—
794C22×D3—32no—
795C22×D3—32no—
796C22×D3—61no—
797C22×D3—61no—
798C22×D3—62no—
799C22×D3—64no—
800C22×D3—122no—
801C22×D3—122no—
802C22×D3—122no—
803C22×D3—122no—
804C22×D3—122no—
805C22×D3—122no—
806C22×D3—122no—
807C22×D3—242no—
808C22×D3—242no—
809C22×D3C23×D312yes—
810C3×Q8—122no—
811C3×D4—64no—
812C3×D4—122no—
813C3×D4—122no—
814C2×C3×C4—22no—
815C2×C3×C4—22no—
816C2×C3×C4—32no—
817C2×C3×C4—32no—
818C2×C3×C4—32no—
819C2×C3×C4—32no—
820C2×C3×C4—32no—
821C2×C3×C4—32no—
822C2×C3×C4—32no—
823C2×C3×C4—42no—
824C2×C3×C4—42no—
825C2×C3×C4—64no—
826C2×C3×C4—82no—
827C2×C3×C4—122no—
828C2×C3×C4—122no—
829C2×C3×C4C23×D312yes—
830C2×C3×C4C23×D312yes—
831C2×C3×C4C23×D312yes—
832C2×C3×C4C23×D312yes—
833#67—24no—
834#67—42no—
835#67—42no—
836#67—64no—
837#67—64no—
838#67—124no—
839#67—122no—
840#67—122no—
841#67—122no—
842#67—122no—
843#67—122no—
844#67—122no—
845#67—122no—
846#67—122no—
847#67—122no—
848#67—122no—
849#67—122no—
850#67—122no—
851#67—122no—
852#67—122no—
853#67—122no—
854#67—124no—
855C2×Dic3—24no—
856C2×Dic3—32no—
857C2×Dic3—32no—
858C2×Dic3—32no—
859C2×Dic3—32no—
860C2×Dic3—42no—
861C2×Dic3—61no—
862C2×Dic3—62no—
863C2×Dic3—61no—
864C2×Dic3—64no—
865C2×Dic3—122no—
866C2×Dic3—122no—
867C2×Dic3—122no—
868C2×Dic3—122no—
869C2×Dic3—122no—
870C2×Dic3C23×D312yes—
871C2×Dic3C23×D312yes—
872C2×Dic3C23×D312yes—
873C2×Dic3C23×D312yes—
874C2×Dic3C23×D312yes—
875C2×Dic3C23×D312yes—
876C2×Dic3C23×D312yes—
877D12—122no—
878D12—122no—
879D12—122no—
880D12—122no—
881D12—122no—
882D12—122no—
883D12—122no—
884D12—122no—
885D12—242no—
886D12—242no—
887C4×D3—42no—
888C4×D3—122no—
889C4×D3—122no—
890C4×D3—122no—
891C4×D3—122no—
892C4×D3—122no—
893C4×D3—122no—
894C4×D3—122no—
895C4×D3—122no—
896C4×D3—122no—
897C4×D3—122no—
898Dic6—42no—
899Dic6—122no—
900Dic6—122no—
901Dic6—122no—
902C2×C32—22no—
903C2×C32—41no—
904C2×C32—41no—
905C2×C32C2×H(5,𝔽2)11yescharacteristic
906C2×C32#58512yes—
907C3⋊D3—41no—
908C3⋊D3—41no—
909C3⋊D3—42no—
910C3×D3—42no—
911C24—91no—
912C24—91no—
913C24C2×D3211yescharacteristic
914#41—364no—
915#41—362no—
916C2×Q8—32no—
917C2×Q8—92no—
918C2×Q8—91no—
919C2×D4—32no—
920C2×D4—32no—
921C2×D4—32no—
922C2×D4—92no—
923C2×D4—92no—
924C2×D4—92no—
925C2×D4—92no—
926C2×D4—92no—
927C2×D4—91no—
928C2×D4—91no—
929C2×D4—91no—
930C2×D4—91no—
931C2×D4—92no—
932C2×D4—91no—
933C2×D4—92no—
934C2×D4—92no—
935C2×D4—362no—
936C2×D4—362no—
937C22×C4—32no—
938C22×C4—32no—
939C22×C4—32no—
940C22×C4—92no—
941C22×C4—92no—
942C22×C4—91no—
943C22×C4—92no—
944C22×C4—91no—
945C22×C4—92no—
946C22×C4—92no—
947C22×C4—91no—
948C22×C4—91no—
949C22×C4—362no—
950C22×C4C2×D3212yes—
951C4⋊C4—32no—
952C4⋊C4—32no—
953C4⋊C4—32no—
954C4⋊C4—32no—
955C4⋊C4—32no—
956C4⋊C4—32no—
957C4⋊C4—32no—
958C4⋊C4—32no—
959C4⋊C4—92no—
960C4⋊C4—92no—
961C4⋊C4—92no—
962C4⋊C4—92no—
963C4⋊C4—92no—
964C4⋊C4—92no—
965C4⋊C4—92no—
966C4⋊C4—92no—
967C4⋊C4—92no—
968C4⋊C4—92no—
969C4⋊C4—92no—
970C22⋊C4—32no—
971C22⋊C4—32no—
972C22⋊C4—32no—
973C22⋊C4—32no—
974C22⋊C4—32no—
975C22⋊C4—32no—
976C22⋊C4—32no—
977C22⋊C4—32no—
978C22⋊C4—32no—
979C22⋊C4—32no—
980C22⋊C4—92no—
981C22⋊C4—91no—
982C22⋊C4—92no—
983C22⋊C4—92no—
984C22⋊C4—91no—
985C22⋊C4—92no—
986C22⋊C4—92no—
987C22⋊C4—92no—
988C22⋊C4—92no—
989C22⋊C4—92no—
990C22⋊C4—92no—
991C22⋊C4—92no—
992C22⋊C4—92no—
993C22⋊C4—92no—
994C22⋊C4C2×D3212yes—
995C22⋊C4C2×D3211yescharacteristic
996C22⋊C4C2×D3211yescharacteristic
997C42—32no—
998C42—32no—
999C42—32no—
1000C42—91no—
1001C42—91no—
1002C42—92no—
1003C22×C3—22no—
1004C22×C3—22no—
1005C22×C3—22no—
1006C22×C3—22no—
1007C22×C3—22no—
1008C22×C3—22no—
1009C22×C3—22no—
1010C22×C3—22no—
1011C22×C3—22no—
1012C22×C3—22no—
1013C22×C3—22no—
1014C22×C3—21no—
1015C22×C3—42no—
1016C22×C3—42no—
1017C22×C3—42no—
1018C22×C3—62no—
1019C22×C3—62no—
1020C22×C3—62no—
1021C22×C3—84no—
1022C22×C3—84no—
1023C22×C3#100914yes—
1024C22×C3C24×D312yes—
1025C2×D3—22no—
1026C2×D3—22no—
1027C2×D3—22no—
1028C2×D3—62no—
1029C2×D3—62no—
1030C2×D3—62no—
1031C2×D3—62no—
1032C2×D3—62no—
1033C2×D3—62no—
1034C2×D3—62no—
1035C2×D3—62no—
1036C2×D3—62no—
1037C2×D3—62no—
1038C2×D3—62no—
1039C2×D3—62no—
1040C2×D3—122no—
1041C2×D3—122no—
1042C2×D3—122no—
1043C2×D3—122no—
1044C2×D3—121no—
1045C2×D3—121no—
1046C2×D3—122no—
1047C2×D3—128no—
1048C2×D3—244no—
1049C2×D3—244no—
1050C2×D3—244no—
1051C3×C4—22no—
1052C3×C4—22no—
1053C3×C4—22no—
1054C3×C4—22no—
1055C3×C4—42no—
1056C3×C4—42no—
1057C3×C4—62no—
1058C3×C4—62no—
1059C3×C4—62no—
1060C3×C4—62no—
1061C3×C4—62no—
1062C3×C4—62no—
1063C3×C4—62no—
1064Dic3—22no—
1065Dic3—22no—
1066Dic3—22no—
1067Dic3—22no—
1068Dic3—22no—
1069Dic3—22no—
1070Dic3—22no—
1071Dic3—62no—
1072Dic3—62no—
1073Dic3—62no—
1074Dic3—62no—
1075Dic3—121no—
1076Dic3—121no—
1077Dic3—122no—
1078C32#353311yescharacteristic, complemented, Sylow
1079C23—22no—
1080C23—32no—
1081C23—42no—
1082C23—91no—
1083C23—91no—
1084C23—92no—
1085C23—182no—
1086C23—362no—
1087C23—361no—
1088C23—362no—
1089C23C22×D3211yescharacteristic
1090C23C22×D3211yescharacteristic
1091C23C22×D3211yescharacteristic
1092Q8—122no—
1093Q8—362no—
1094Q8—361no—
1095D4—64no—
1096D4—122no—
1097D4—122no—
1098D4—184no—
1099D4—362no—
1100D4—362no—
1101D4—362no—
1102D4—362no—
1103D4—362no—
1104D4—362no—
1105D4—361no—
1106D4—361no—
1107D4—361no—
1108D4—361no—
1109D4—362no—
1110D4—361no—
1111C2×C4—32no—
1112C2×C4—32no—
1113C2×C4—32no—
1114C2×C4—32no—
1115C2×C4—32no—
1116C2×C4—32no—
1117C2×C4—32no—
1118C2×C4—42no—
1119C2×C4—64no—
1120C2×C4—91no—
1121C2×C4—92no—
1122C2×C4—91no—
1123C2×C4—122no—
1124C2×C4—122no—
1125C2×C4—182no—
1126C2×C4—361no—
1127C2×C4—362no—
1128C2×C4—361no—
1129C2×C4—362no—
1130C2×C4—362no—
1131C2×C4—362no—
1132C2×C4—362no—
1133C2×C4—361no—
1134C2×C4C22×D3212yes—
1135C2×C4C22×D3212yes—
1136C2×C3—24no—
1137C2×C3—21no—
1138C2×C3—22no—
1139C2×C3—42no—
1140C2×C3—42no—
1141C2×C3—42no—
1142C2×C3—42no—
1143C2×C3—42no—
1144C2×C3—122no—
1145C2×C3C2×#100912yes—
1146C2×C3#596412yes—
1147C2×C3#596612yes—
1148D3—42no—
1149D3—122no—
1150D3—122no—
1151D3—122no—
1152D3—122no—
1153D3—241no—
1154D3—241no—
1155D3—242no—
1156C22—22no—
1157C22—21no—
1158C22—21no—
1159C22—22no—
1160C22—22no—
1161C22—62no—
1162C22—62no—
1163C22—62no—
1164C22—82no—
1165C22—181no—
1166C22—181no—
1167C22—182no—
1168C22—182no—
1169C22—182no—
1170C22—182no—
1171C22—182no—
1172C22—364no—
1173C22—722no—
1174C22#6430812yes—
1175C22C23×D3211yescharacteristic
1176C4—22no—
1177C4—22no—
1178C4—62no—
1179C4—62no—
1180C4—62no—
1181C4—62no—
1182C4—62no—
1183C4—62no—
1184C4—62no—
1185C4—181no—
1186C4—181no—
1187C4—182no—
1188C3—21no—
1189C3#8681912yescomplemented
1190C2—22no—
1191C2—41no—
1192C2—41no—
1193C2—122no—
1194C2—361no—
1195C2—361no—
1196C2—362no—
1197C2C2×#6430811yescharacteristic
1198C2#1059667812yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C22⋊C4C22
hypercenterC2×C22⋊C4D32
hypocenterC32#3533
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #10595964C2semidirect
2. C3×#5495C2semidirect
3. C2×#63975C2semidirect
4. #10595502C2semidirect
5. #10595500C2semidirect
6. #10595027C2semidirect
7. #10594978C2semidirect
8. #10594946C2semidirect
9. #10594814C2semidirect
10. #10594244C2semidirect
11. #10594243C2semidirect
12. #10594165C2semidirect
13. #10594162C2semidirect
14. #10594142C2semidirect
15. #10594128C2semidirect
16. #10594079C2semidirect
17. #10594077C2semidirect
18. #10594045C2semidirect
19. #10594036C2semidirect
23. C22×#624C22semidirect
24. C2×#3805C22semidirect
37. C3×#929C22semidirect
38. C3×C4×#67C22semidirect
39. C3×#926C22semidirect
40. C3×#924C22semidirect
41. C3×#886C22semidirect
42. C3×#885C22semidirect
43. C3×#883C22semidirect
44. C3×#67⋊C4C22semidirect
45. C3×#879C22semidirect
46. C3×#879C22semidirect
47. C3×#878C22semidirect
48. C3×#877C22semidirect
49. #63982C22semidirect
50. #63981C22semidirect
51. #63981C22semidirect
53. #63979C22semidirect
58. #63975C22semidirect
59. #63975C22semidirect
60. #63975C22semidirect
61. #63975C22semidirect
62. #63974C22semidirect
63. #67⋊Dic3C22semidirect
65. #63971C22semidirect
66. #63971C22semidirect
68. C2×Dic3⋊Dic3C22semidirect
69. C2×#3722C22semidirect
70. #63958C22semidirect
71. #63957C22semidirect
73. #63953C22semidirect
74. #63953C22semidirect
76. #63918C22semidirect
77. #63910C22semidirect
78. #63910C22semidirect
79. #63910C22semidirect
80. #63909C22semidirect
81. #63907C22semidirect
82. #63906C22semidirect
83. #63897C22semidirect
84. #63895C22semidirect
85. #63895C22semidirect
86. #63895C22semidirect
87. #63894C22semidirect
88. #63894C22semidirect
89. #63893C22semidirect
90. #63891C22semidirect
91. #63890C22semidirect
92. D3×C4⋊Dic3C22semidirect
93. #63888C22semidirect
94. #63880C22semidirect
95. #63880C22semidirect
96. #63880C22semidirect
97. #63869C22semidirect
98. #63868C22semidirect
99. #63868C22semidirect
100. #63864C22semidirect
101. #63850C22semidirect
102. #63848C22semidirect
103. #63848C22semidirect
104. #63845C22semidirect
105. #63845C22semidirect
106. Dic3×Dic6C22semidirect
107. #63836C22semidirect
135. #5495D3semidirect
284. #929C2×D3semidirect
286. C4×#67C2×D3semidirect
288. #926C2×D3semidirect
291. #924C2×D3semidirect
335. #886C2×D3semidirect
341. #885C2×D3semidirect
361. #883C2×D3semidirect
376. #67⋊C4C2×D3semidirect
379. #879C2×D3semidirect
380. #879C2×D3semidirect
384. #878C2×D3semidirect
386. #877C2×D3semidirect
1078. C32#3533semidirect
1189. C3#86819semidirect

Maximal subgroups

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

subgroupindex
#105959642
C3×#54952
C2×#639752
#105955022
#105955002
#105950272
#105949782
#105949462
#105948142
#105942442
#105942432
#105941652
#105941622
#105941422
#105941282
#105940792
#105940772
#105940452
#105940362
#868193