Finite Group Databasebeta

← #11878420

Subgroups — #11878420

Order 1152.

811 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5628C211yesmaximal, characteristic
2#10594884C211yesmaximal, characteristic
3#10592751C211yesmaximal, characteristic, complemented
4C3×#5051C211yesmaximal, characteristic, complemented
5#10591653C211yesmaximal, characteristic, complemented
6#10591595C211yesmaximal, characteristic, complemented
7#10591594C211yesmaximal, characteristic, complemented
8#10591558C211yesmaximal, characteristic, complemented
9#10591189C211yesmaximal, characteristic, complemented
10#10591187C211yesmaximal, characteristic, complemented
11#10591070C211yesmaximal, characteristic
12#10590604C211yesmaximal, characteristic, complemented
13#10590519C211yesmaximal, characteristic, complemented
14#10590448C211yesmaximal, characteristic, complemented
15#10590429C211yesmaximal, characteristic, complemented
16#83413—31nomaximal
17#80767—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21C32×C22⋊Q8C2211yescharacteristic
22C2×#3756C2211yescharacteristic
23#64133C2211yescharacteristic
24C2×#3748C2211yescharacteristic
25C3×#946C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic
27C3×#924C2211yescharacteristic
28C3×#924C2211yescharacteristic
29C22×C3×C3⋊C8C2211yescharacteristic
30C3×#897C2211yescharacteristic
31C3×#894—21no—
32C3×#892C2211yescharacteristic
33C3×#888—21no—
34C3×#885—21no—
35C3×#883—21no—
36#63969—21no—
37#63959—21no—
38#63884—21no—
39#63857C2211yescharacteristic
40#63856C2211yescharacteristic
41#63841C2211yescharacteristic
42#63839—21no—
43C2×#3719C2211yescharacteristic
44C2×#3718C2211yescharacteristic
45#63662C2211yescharacteristic
46#63637C2211yescharacteristic
47#63635C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#810C2211yescharacteristic
50C3×#807C2211yescharacteristic
51#63575C2211yescharacteristic
52#63574C2211yescharacteristic
53#63567C2211yescharacteristic
54#63566C2211yescharacteristic
55#63565C2211yescharacteristic
56#63565C2211yescharacteristic
57(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
58(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#536—31no—
62#5825—31no—
63#5628—31no—
64#5628D311yescharacteristic
65C3×#467—31no—
66#5234—31no—
67#5228—31no—
68#5228—31no—
69#5186—31no—
70#5186—31no—
71#5116—31no—
72#5110—31no—
73#5052—31no—
74#5052—31no—
75#5052—31no—
76#5052—31no—
77#5052—61no—
78#5051—31no—
79#5051D311yescharacteristic, complemented
80#5050—31no—
81#5050—31no—
82#5045—31no—
83#5045—31no—
84#4996—31no—
85#4996—31no—
86#4888—31no—
87#4888—31no—
88#4814—31no—
89#4814—31no—
90#4809—31no—
91#4809—31no—
92C2×C32×Q8C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C3×#67D411yescharacteristic
96C2×C3×#67D411yescharacteristic
97C3×D3×Q8—41no—
98C3×D3×Q8—41no—
99C3×#235—41no—
100C3×#235—41no—
101C2×C3×D12D411yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6—21no—
106C2×C3×Dic6D411yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×#627—21no—
110C2×D3×Dic3—21no—
111D3×Dic6—41no—
112D3×Dic6—41no—
113C32×C4⋊C4—21no—
114C32×C4⋊C4C2311yescharacteristic
115C32×C22⋊C4—21no—
116#3757—21no—
117#3756—41no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119#3750—21no—
120#3748—41no—
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C3×#217—21no—
124C3×#217—21no—
125C3×#216—41no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×C4×Dic3—21no—
136C2×C3×C3⋊C8—41no—
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139#3724—21no—
140Dic3⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144Dic32—21no—
145#3719—41no—
146#3718—41no—
147#3202—91noSylow
148C2×C3×#41—31no—
149C22×C3×Q8—31no—
150C2×D3×Q8—31no—
151C2×D3×Q8C2×D311yescharacteristic
152C2×#235C2×D311yescharacteristic
153C22×Dic6—31no—
154C2×C3×Q16—31no—
155C22×C3×C8—31no—
156C3×C4⋊Q8—61no—
157C3×#124—61no—
158C3×#123—61no—
159C3×#123—61no—
160C3×C22⋊Q8—21no—
161C3×C22⋊Q8—31no—
162C3×C22⋊Q8—31no—
163C3×C22⋊Q8—31no—
164C3×C22⋊Q8—31no—
165C3×C22⋊Q8C2×D311yescharacteristic
166C3×C22⋊Q8C2×D311yescharacteristic
167C3×#117—31no—
168#946—31no—
169#946C2×D311yescharacteristic
170#944—61no—
171C2×#216—31no—
172C2×#216—31no—
173C2×#216—31no—
174C2×#216—31no—
175C2×#216—31no—
176C2×#216—61no—
177C2×#216C2×D311yescharacteristic
178#936—61no—
179#935—61no—
180#935—61no—
181#926—31no—
182#924—31no—
183#924—31no—
184#924—31no—
185#924—31no—
186#924—61no—
187#924C2×D311yescharacteristic
188#924C2×D311yescharacteristic
189C2×#208—31no—
190C2×#208—31no—
191C2×#208—61no—
192C22×C3⋊C8C2×D311yescharacteristic
193C2×Dic12—31no—
194#897—31no—
195#897C2×D311yescharacteristic
196#894—21no—
197#894—61no—
198#892—31no—
199#892C2×D311yescharacteristic
200#888—21no—
201#888—61no—
202#885—21no—
203#885—61no—
204#883—21no—
205#883—61no—
206C3×#107—31no—
207C3×#103—31no—
208C3×#103—31no—
209#835—31no—
210#835—31no—
211#835—31no—
212#835—31no—
213#835—31no—
214#835—61no—
215#835C2×D311yescharacteristic
216#830—31no—
217#830—31no—
218#830—31no—
219#830—31no—
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8—31no—
223(C2×D3)⋊C8—31no—
224#818—31no—
225#816—31no—
226#816—31no—
227#810—31no—
228#810—31no—
229#810—31no—
230#810—31no—
231#810—31no—
232#810—61no—
233#810C2×D311yescharacteristic
234#808—31no—
235#808—31no—
236#808—31no—
237#808—31no—
238#808—61no—
239#807—31no—
240#807C2×D311yescharacteristic
241C23×C32C2×D411yescharacteristic
242C22×C3×D3C2×D411yescharacteristic
243C22×C3×D3C2×D411yescharacteristic
244C32×Q8—21no—
245C32×Q8—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254#634—21no—
255#634—21no—
256C3×#67—41no—
257C3×#67—41no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×D12—41no—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—42no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274C3×Dic6—41no—
275C3×Dic6—42no—
276#627—42no—
277D3×Dic3—42no—
278C3⋊(C3⋊C8)—21no—
279C3⋊(C3⋊C8)—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#536—31no—
283#536—91no—
284#485—91no—
285#485—91no—
286#485—91no—
287#485—91no—
288#470—91no—
289#470—91no—
290#467—31no—
291#467—91no—
292#451—91no—
293#451—91no—
294#451—91no—
295#451—91no—
296#408—91no—
297C3×#41—121no—
298C3×#41—121no—
299C2×C3×Q8—21no—
300C2×C3×Q8—31no—
301C2×C3×Q8—31no—
302C2×C3×Q8—31no—
303C2×C3×Q8—61no—
304C2×C3×Q8—121no—
305C2×C3×Q8—121no—
306C2×C3×Q8C22×D311yescharacteristic
307C2×C3×Q8C22×D311yescharacteristic
308C2×C3×D4—31no—
309C2×C3×D4—31no—
310C2×C3×D4—31no—
311C22×C3×C4—21no—
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—61no—
315C22×C3×C4C22×D311yescharacteristic
316C22×C3×C4C22×D311yescharacteristic
317C2×#67#6711yescharacteristic
318C2×#67#6711yescharacteristic
319C22×Dic3—61no—
320D3×Q8—41no—
321D3×Q8—41no—
322D3×Q8—121no—
323D3×Q8—121no—
324#235—41no—
325#235—41no—
326C2×D12#6711yescharacteristic
327C2×C4×D3—21no—
328C2×C4×D3—61no—
329C2×C4×D3C22×D311yescharacteristic
330C2×C4×D3C22×D311yescharacteristic
331C2×Dic6—21no—
332C2×Dic6—31no—
333C2×Dic6—31no—
334C2×Dic6—61no—
335C2×Dic6—61no—
336C2×Dic6—61no—
337C2×Dic6—121no—
338C2×Dic6—121no—
339C2×Dic6#6711yescharacteristic
340C2×Dic6C22×D311yescharacteristic
341C2×Dic6C22×D311yescharacteristic
342C3×Q16—121no—
343C2×C3×C8—31no—
344C2×C3×C8—31no—
345C2×C3×C8—121no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—41no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C22⋊C4—21no—
359C3×C22⋊C4—21no—
360C3×C22⋊C4—41no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C22⋊C4—61no—
365C3×C22⋊C4—61no—
366C3×C42—61no—
367#217—21no—
368#217—21no—
369#217—61no—
370#217—61no—
371#217—61no—
372#217—61no—
373#217—61no—
374#217—121no—
375#216—41no—
376#216—121no—
377#216—121no—
378#216—121no—
379#216—121no—
380#216—121no—
381#216—122no—
382(C2×D3)⋊C4—21no—
383(C2×D3)⋊C4—21no—
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388C4⋊Dic3—21no—
389C4⋊Dic3—31no—
390C4⋊Dic3—31no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3C22×D311yescharacteristic
394C4⋊Dic3C22×D311yescharacteristic
395Dic3⋊C4—21no—
396Dic3⋊C4—21no—
397Dic3⋊C4—21no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—121no—
404C4×Dic3—21no—
405C4×Dic3—61no—
406C4×Dic3—61no—
407#208—121no—
408#208—121no—
409#208—122no—
410C2×C3⋊C8—31no—
411C2×C3⋊C8—31no—
412C2×C3⋊C8—31no—
413C2×C3⋊C8—31no—
414C2×C3⋊C8—41no—
415C2×C3⋊C8—61no—
416C2×C3⋊C8—61no—
417C2×C3⋊C8C22×D311yescharacteristic
418C2×C3⋊C8C22×D311yescharacteristic
419Dic12—121no—
420C22×C32—21no—
421C22×C32—21no—
422C22×C32—21no—
423C22×C32C22×D411yescharacteristic
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—21no—
429C2×C3×D3—21no—
430C32×C4—21no—
431C32×C4—41no—
432C32×C4—41no—
433C32×C4H(5,𝔽2)11yescharacteristic
434C32×C4H(5,𝔽2)11yescharacteristic
435C3⋊Dic3—41no—
436C3⋊Dic3—41no—
437C3×Dic3—21no—
438C3×Dic3—21no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C3×Dic3—41no—
443C2×#41—31no—
444C22×Q8—31no—
445C22×Q8—91no—
446C2×Q16—31no—
447C2×Q16—91no—
448C2×Q16—91no—
449C2×Q16—91no—
450C2×M16—91no—
451C22×C8—31no—
452C4⋊Q8—61no—
453C4⋊Q8—181no—
454#124—61no—
455#124—181no—
456#123—61no—
457#123—61no—
458#123—181no—
459#123—181no—
460C22⋊Q8—31no—
461C22⋊Q8—31no—
462C22⋊Q8—31no—
463C22⋊Q8—31no—
464C22⋊Q8—91no—
465C22⋊Q8—91no—
466C22⋊Q8—91no—
467C22⋊Q8D3211yescharacteristic
468#117—31no—
469#117—91no—
470#107—31no—
471#107—91no—
472#106—91no—
473#106—91no—
474#103—31no—
475#103—31no—
476#103—91no—
477#103—91no—
478#103—91no—
479#103—91no—
480#103—91no—
481#103—91no—
482C22⋊C8—91no—
483C22⋊C8—91no—
484C22⋊C8—91no—
485C22⋊C8—91no—
486C23×C3—21no—
487C23×C3—31no—
488C23×C3—31no—
489C23×C3D3×D411yescharacteristic
490C23×C3C2×#6711yescharacteristic
491C22×D3C2×#6711yescharacteristic
492C22×D3C2×#6711yescharacteristic
493C3×Q8—21no—
494C3×Q8—21no—
495C3×Q8—21no—
496C3×Q8—21no—
497C3×Q8—41no—
498C3×Q8—41no—
499C3×Q8—61no—
500C3×Q8—61no—
501C3×Q8—61no—
502C3×Q8—61no—
503C3×Q8—121no—
504C3×Q8—122no—
505C3×D4—121no—
506C3×D4—121no—
507C3×D4—121no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—31no—
519C2×C3×C4—31no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—122no—
533C2×C3×C4D3×D411yescharacteristic
534C2×C3×C4C2×#6711yescharacteristic
535C2×C3×C4C23×D311yescharacteristic
536C2×C3×C4C23×D311yescharacteristic
537#67—41no—
538#67—41no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—121no—
548C2×Dic3—121no—
549C2×Dic3—122no—
550C2×Dic3C2×#6711yescharacteristic
551C2×Dic3C2×#6711yescharacteristic
552D12—41no—
553C4×D3—21no—
554C4×D3—21no—
555C4×D3—21no—
556C4×D3—21no—
557C4×D3—42no—
558C4×D3—122no—
559Dic6—21no—
560Dic6—21no—
561Dic6—21no—
562Dic6—21no—
563Dic6—41no—
564Dic6—42no—
565Dic6—61no—
566Dic6—61no—
567Dic6—61no—
568Dic6—61no—
569Dic6—121no—
570Dic6—121no—
571Dic6—122no—
572Dic6—122no—
573C3×C8—61no—
574C3×C8—61no—
575C3⋊C8—21no—
576C3⋊C8—21no—
577C3⋊C8—62no—
578C3⋊C8—61no—
579C3⋊C8—61no—
580C3⋊C8—61no—
581C3⋊C8—61no—
582C3⋊C8—121no—
583C2×C32—41no—
584C2×C32#53411yescharacteristic
585C2×C32#57811yescharacteristic
586C2×C32#57811yescharacteristic
587C3×D3—41no—
588C3×D3—41no—
589#41—121no—
590#41—121no—
591C2×Q8—31no—
592C2×Q8—31no—
593C2×Q8—31no—
594C2×Q8—61no—
595C2×Q8—91no—
596C2×Q8—121no—
597C2×Q8—121no—
598C2×Q8—181no—
599C2×Q8—361no—
600C2×Q8—361no—
601C2×Q8C2×D3211yescharacteristic
602C2×D4—31no—
603C2×D4—31no—
604C2×D4—31no—
605C22×C4—31no—
606C22×C4—31no—
607C22×C4—61no—
608C22×C4—181no—
609C22×C4C2×D3211yescharacteristic
610Q16—121no—
611Q16—361no—
612Q16—361no—
613Q16—361no—
614M16—361no—
615C2×C8—31no—
616C2×C8—31no—
617C2×C8—91no—
618C2×C8—91no—
619C2×C8—121no—
620C4⋊C4—21no—
621C4⋊C4—31no—
622C4⋊C4—31no—
623C4⋊C4—61no—
624C4⋊C4—61no—
625C4⋊C4—61no—
626C4⋊C4—61no—
627C4⋊C4—91no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4—181no—
631C4⋊C4C2×D3211yescharacteristic
632C22⋊C4—21no—
633C22⋊C4—61no—
634C22⋊C4—61no—
635C22⋊C4—61no—
636C22⋊C4—61no—
637C22⋊C4—61no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C22⋊C4—181no—
642C42—61no—
643C42—181no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—61no—
655C22×C3—61no—
656C22×C3—61no—
657C22×C3—61no—
658C22×C3—61no—
659C22×C3—61no—
660C22×C3C2×D3×D411yescharacteristic
661C22×C3C22×#6711yescharacteristic
662C2×D3—21no—
663C2×D3—21no—
664C2×D3—21no—
665C2×D3—21no—
666C2×D3—21no—
667C2×D3—21no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—61no—
678C3×C4—61no—
679C3×C4—81no—
680C3×C4—81no—
681C3×C4—121no—
682C3×C4—121no—
683C3×C4—121no—
684C3×C4—121no—
685C3×C4#100411yescharacteristic
686C3×C4#100411yescharacteristic
687C3×C4#100411yescharacteristic
688C3×C4#100911yescharacteristic
689Dic3—21no—
690Dic3—21no—
691Dic3—41no—
692Dic3—41no—
693Dic3—41no—
694Dic3—41no—
695Dic3—121no—
696Dic3—121no—
697Dic3—121no—
698Dic3—121no—
699Dic3—241no—
700Dic3—241no—
701C32#320211yescharacteristic, complemented, Sylow
702C23—31no—
703C23—31no—
704C23D3×#6711yescharacteristic
705Q8—21no—
706Q8—21no—
707Q8—61no—
708Q8—61no—
709Q8—61no—
710Q8—61no—
711Q8—121no—
712Q8—122no—
713Q8—181no—
714Q8—181no—
715Q8—362no—
716D4—121no—
717D4—121no—
718D4—121no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—31no—
724C2×C4—31no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—122no—
734C2×C4—181no—
735C2×C4—181no—
736C2×C4—362no—
737C2×C4D3×#6711yescharacteristic
738C2×C4C22×D3211yescharacteristic
739C8—61no—
740C8—61no—
741C8—181no—
742C8—181no—
743C2×C3—21no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—41no—
747C2×C3—41no—
748C2×C3—81no—
749C2×C3—121no—
750C2×C3—121no—
751C2×C3#560511yescharacteristic
752C2×C3#576611yescharacteristic
753C2×C3#577111yescharacteristic
754C2×C3#580411yescharacteristic
755C2×C3#583811yescharacteristic
756C2×C3#583811yescharacteristic
757D3—41no—
758D3—41no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—61no—
763C22—61no—
764C22—61no—
765C22—61no—
766C22—61no—
767C22—61no—
768C22C2×D3×#6711yescharacteristic
769C4—21no—
770C4—41no—
771C4—41no—
772C4—61no—
773C4—61no—
774C4—121no—
775C4—121no—
776C4—121no—
777C4—121no—
778C4—361no—
779C4—361no—
780C4#6431311yescharacteristic
781C4#6431411yescharacteristic
782C3—21no—
783C3#8076711yescharacteristic, complemented
784C3#8341311yescharacteristic, complemented
785C2—41no—
786C2—121no—
787C2—121no—
788C2#1059530211yescharacteristic
789C2#1059532711yescharacteristic
790C2#1059546711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×#235C22
hypercenterC22⋊Q8D32
hypocenterC32#3202
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #10592751C2semidirect
4. C3×#5051C2semidirect
5. #10591653C2semidirect
6. #10591595C2semidirect
7. #10591594C2semidirect
8. #10591558C2semidirect
9. #10591189C2semidirect
10. #10591187C2semidirect
12. #10590604C2semidirect
13. #10590519C2semidirect
14. #10590448C2semidirect
15. #10590429C2semidirect
79. #5051D3semidirect
701. C32#3202semidirect
783. C3#80767semidirect
784. C3#83413semidirect

Maximal subgroups

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

subgroupindex
C3×#56282
#105948842
#105927512
C3×#50512
#105916532
#105915952
#105915942
#105915582
#105911892
#105911872
#105910702
#105906042
#105905192
#105904482
#105904292
#834133
#807673