Finite Group Databasebeta

← #11872945

Subgroups — #11872945

Order 1152.

876 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596005C211yesmaximal, characteristic, complemented
2C3×#5523C211yesmaximal, characteristic, complemented
3C3×#5000C211yesmaximal, characteristic, complemented
4#10591173C211yesmaximal, characteristic, complemented
5#10591163C211yesmaximal, characteristic
6#10591135C211yesmaximal, characteristic, complemented
7#10591133C211yesmaximal, characteristic, complemented
8C4×#3719C211yesmaximal, characteristic, complemented
9#10590368C211yesmaximal, characteristic, complemented
10#10590366C211yesmaximal, characteristic, complemented
11#10590362C211yesmaximal, characteristic, complemented
12#10590360C211yesmaximal, characteristic, complemented
13C4×#3714C211yesmaximal, characteristic, complemented
14#10590283C211yesmaximal, characteristic, complemented
15#10590272C211yesmaximal, characteristic, complemented
16#82569—31nomaximal
17#79388—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C32×#117C2211yescharacteristic
20#64139C2211yescharacteristic
21#64133C2211yescharacteristic
22#64107—21no—
23#64105—21no—
24#64094—21no—
25#64092—21no—
26#64084C2211yescharacteristic
27C4×C4⋊(C3⋊D3)C2211yescharacteristic
28#64078C2211yescharacteristic
29C4×#634C2211yescharacteristic
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C3×#892—21no—
32C3×D3×C4⋊C4—21no—
33C3×#67⋊C4—21no—
34C3×#67⋊C4—21no—
35C3×C4×D12C2211yescharacteristic
36C3×C4×D12C2211yescharacteristic
37C3×C4×Dic6C2211yescharacteristic
38C3×C4×Dic6C2211yescharacteristic
39C2×#3719C2211yescharacteristic
40C2×#3717C2211yescharacteristic
41C2×#3716C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C3×#830C2211yescharacteristic
44C3×#830C2211yescharacteristic
45C3×C4⋊(C3⋊C8)C2211yescharacteristic
46C3×C4⋊(C3⋊C8)C2211yescharacteristic
47C3×#803C2211yescharacteristic
48C3×C4×C3⋊C8C2211yescharacteristic
49#63575C2211yescharacteristic
50#63575C2211yescharacteristic
51#63575C2211yescharacteristic
52#63575C2211yescharacteristic
53#63567C2211yescharacteristic
54#63567C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic
61C3×#520—31no—
62#5534—31no—
63#5534—31no—
64#5534—61no—
65#5523D311yescharacteristic, complemented
66C3×#433—31no—
67#5239—31no—
68#5238—31no—
69C4×#216—31no—
70#5028—31no—
71#5026—31no—
72#5021—31no—
73#5018—31no—
74#5016—31no—
75C4×#213—31no—
76#5007—31no—
77#5000D311yescharacteristic, complemented
78#4970—31no—
79#4967—31no—
80#4850—31no—
81#4846—31no—
82#4845—31no—
83#4844—31no—
84#4736—31no—
85#4734—31no—
86#4733—31no—
87#4722—31no—
88#4710—31no—
89#4710—31no—
90C4×Dic12—31no—
91C4×D24—31no—
92C22×C32×C4C2311yescharacteristic
93C2×#638—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×#634—21no—
97C2×#634C2311yescharacteristic
98C2×C3×#67—21no—
99C22×C3×Dic3—21no—
100C3×#235—22no—
101C3×#235—22no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×Dic6C2311yescharacteristic
107C32×C4⋊C4D411yescharacteristic
108C32×C4⋊C4D411yescharacteristic
109C32×C22⋊C4D411yescharacteristic
110C32×C22⋊C4D411yescharacteristic
111C32×C42C2311yescharacteristic
112C32×C42C2311yescharacteristic
113#3757—21no—
114#3752—21no—
115#3752—21no—
116#3752—21no—
117#3752—21no—
118C4⋊(C3⋊Dic3)—21no—
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121#3750—21no—
122#3750—21no—
123C4×C3⋊Dic3—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3—21no—
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137#3719—22no—
138#3717—22no—
139#3716—22no—
140#3714—22no—
141#3124—91noSylow
142C2×C3×#41—31no—
143C2×#235C2×D311yescharacteristic
144C3×C4×Q8—31no—
145C3×C4×Q8—31no—
146C3×C4×D4—31no—
147C3×C4×D4—31no—
148C3×C4×D4—61no—
149C3×C4×D4—61no—
150C3×#117—21no—
151C3×#117—61no—
152C3×#117C2×D311yescharacteristic
153C3×#117C2×D311yescharacteristic
154C2×C3×C4⋊C4—31no—
155C2×C3×C4⋊C4—61no—
156C2×#216—31no—
157C2×#215—31no—
158C2×#214—31no—
159C2×#213—31no—
160#930—31no—
161#930—31no—
162#930—61no—
163C2×C4⋊Dic3C2×D311yescharacteristic
164#924—31no—
165#924—31no—
166#924—61no—
167C2×Dic12—31no—
168C2×D24—31no—
169C2×#204—31no—
170C2×#204—31no—
171#898—62no—
172#898—61no—
173#898—61no—
174#896—62no—
175#896—61no—
176#896—61no—
177#892—21no—
178D3×C4⋊C4—21no—
179#885—62no—
180#885—61no—
181#885—61no—
182#883—62no—
183#883—61no—
184#883—61no—
185#67⋊C4—21no—
186#67⋊C4—21no—
187#875—31no—
188#875—31no—
189#875—61no—
190C4×D12—31no—
191C4×D12—31no—
192C4×D12—61no—
193C4×D12C2×D311yescharacteristic
194C4×D12C2×D311yescharacteristic
195#869—31no—
196#869—31no—
197#869—61no—
198C4×Dic6—31no—
199C4×Dic6—31no—
200C4×Dic6—61no—
201C4×Dic6C2×D311yescharacteristic
202C4×Dic6C2×D311yescharacteristic
203C3×C4⋊C8—31no—
204C3×C4⋊C8—31no—
205C3×C22⋊C8—31no—
206C3×C22⋊C8—31no—
207C3×#97—31no—
208C3×C4×C8—31no—
209#835—31no—
210#835—31no—
211#832—31no—
212#832—31no—
213#830C2×D311yescharacteristic
214#830C2×D311yescharacteristic
215#821—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#818—31no—
220#818—31no—
221#818—31no—
222#818—31no—
223#816—31no—
224#816—31no—
225#816—31no—
226#816—31no—
227#810—31no—
228#810—31no—
229#809—31no—
230#809—31no—
231#807—31no—
232#807—31no—
233#807—31no—
234#807—31no—
235C4⋊(C3⋊C8)C2×D311yescharacteristic
236C4⋊(C3⋊C8)C2×D311yescharacteristic
237#803C2×D311yescharacteristic
238C4×C3⋊C8C2×D311yescharacteristic
239C23×C32C2×D411yescharacteristic
240C22×C3⋊D3—21no—
241C22×C3×D3—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250#638—81no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)—21no—
256C4×C3⋊D3—81no—
257#634—21no—
258#634—21no—
259#634—81no—
260C3×#67—24no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—81no—
265C3×D12—21no—
266C3×D12#4112yes—
267C3×C4×D3—24no—
268C3×C4×D3—81no—
269C3×C4×D3—81no—
270C3×Dic6—21no—
271C3×Dic6#4112yes—
272C3×C3⋊C8—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#542—91no—
277#520—31no—
278#484—91no—
279#480—91no—
280#477—91no—
281#474—91no—
282#464—91no—
283#463—91no—
284#452—91no—
285#449—91no—
286#440—91no—
287#440—91no—
288C4×Q16—91no—
289C4×D8—91no—
290#433—31no—
291C3×#41—62no—
292C3×#41—62no—
293C2×C3×Q8—31no—
294C2×C3×D4—31no—
295C2×C3×D4—61no—
296C22×C3×C4—21no—
297C22×C3×C4—61no—
298C22×C3×C4—61no—
299C22×C3×C4—61no—
300C22×C3×C4—61no—
301C22×C3×C4C22×D311yescharacteristic
302C22×C3×C4C22×D311yescharacteristic
303C2×#67—21no—
304C2×#67—62no—
305C2×#67—61no—
306C2×#67—61no—
307C22×Dic3—21no—
308#235—22no—
309#235—22no—
310C2×D12—31no—
311C2×D12—31no—
312C2×D12—61no—
313C2×D12C22×D311yescharacteristic
314C2×C4×D3—21no—
315C2×C4×D3—21no—
316C2×C4×D3—21no—
317C2×C4×D3—62no—
318C2×C4×D3—61no—
319C2×C4×D3—61no—
320C2×Dic6—31no—
321C2×Dic6—31no—
322C2×Dic6—61no—
323C2×Dic6—62no—
324C2×Dic6—61no—
325C2×Dic6—61no—
326C2×Dic6C22×D311yescharacteristic
327C2×C3×C8—31no—
328C2×C3×C8—31no—
329C2×C3×C8—31no—
330C2×C3×C8—31no—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4D1211yescharacteristic
339C3×C4⋊C4D1211yescharacteristic
340C3×C4⋊C4#6711yescharacteristic
341C3×C4⋊C4#6711yescharacteristic
342C3×C22⋊C4—21no—
343C3×C22⋊C4—21no—
344C3×C22⋊C4—61no—
345C3×C22⋊C4—61no—
346C3×C22⋊C4D1211yescharacteristic
347C3×C22⋊C4D1211yescharacteristic
348C3×C22⋊C4#6711yescharacteristic
349C3×C22⋊C4#6711yescharacteristic
350C3×C42—21no—
351C3×C42—21no—
352C3×C42—61no—
353C3×C42—61no—
354C3×C42C22×D311yescharacteristic
355C3×C42C22×D311yescharacteristic
356C3×C42C22×D311yescharacteristic
357C3×C42C22×D311yescharacteristic
358#217—62no—
359#217—61no—
360#217—61no—
361#216—62no—
362#215—62no—
363#214—62no—
364#213—62no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—21no—
367(C2×D3)⋊C4—62no—
368(C2×D3)⋊C4—62no—
369(C2×D3)⋊C4—62no—
370(C2×D3)⋊C4—62no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379C4⋊Dic3—21no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—31no—
383C4⋊Dic3—31no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—62no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3C22×D311yescharacteristic
390C4⋊Dic3C22×D311yescharacteristic
391Dic3⋊C4—21no—
392Dic3⋊C4—21no—
393Dic3⋊C4—62no—
394Dic3⋊C4—62no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399C4×Dic3—21no—
400C4×Dic3—21no—
401C4×Dic3—62no—
402C4×Dic3—61no—
403C4×Dic3—61no—
404C2×C3⋊C8C22×D311yescharacteristic
405C2×C3⋊C8C22×D311yescharacteristic
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408Dic12—62no—
409D24—62no—
410#204—62no—
411#204—62no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32C22×D411yescharacteristic
416C2×C3⋊D3—41no—
417C2×C3⋊D3—41no—
418C2×C3⋊D3—41no—
419C2×C3×D3—22no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C32×C4—21no—
423C32×C4—21no—
424C32×C4—21no—
425C32×C4—21no—
426C32×C4—21no—
427C32×C4C2×#4111yescharacteristic
428C32×C4C2×#4111yescharacteristic
429C3⋊Dic3—41no—
430C3⋊Dic3—41no—
431C3⋊Dic3—41no—
432C3×Dic3—22no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C2×#41—31no—
436C2×Q16—91no—
437C2×SD16—91no—
438C2×SD16—91no—
439C2×D8—91no—
440C4⋊Q8—91no—
441#126—181no—
442#124—91no—
443#124—181no—
444#123—181no—
445C22⋊Q8—91no—
446C22⋊Q8—181no—
447#121—91no—
448C4×Q8—31no—
449C4×Q8—31no—
450C4×Q8—91no—
451C4×D4—31no—
452C4×D4—31no—
453C4×D4—61no—
454C4×D4—61no—
455C4×D4—91no—
456#117—61no—
457#117D3211yescharacteristic
458C2×C4⋊C4—31no—
459C2×C4⋊C4—61no—
460#107—91no—
461#107—91no—
462#107—91no—
463#107—91no—
464C4⋊C8—31no—
465C4⋊C8—31no—
466#103—91no—
467#103—91no—
468#103—91no—
469#103—91no—
470#102—91no—
471#102—91no—
472#102—91no—
473#102—91no—
474C22⋊C8—31no—
475C22⋊C8—31no—
476#97—31no—
477C4×C8—31no—
478C23×C3—21no—
479C23×C3—61no—
480C23×C3C2×D1211yescharacteristic
481C23×C3C2×#6711yescharacteristic
482C22×D3—21no—
483C22×D3—62no—
484C22×D3—61no—
485C22×D3—61no—
486C3×Q8—32no—
487C3×Q8—61no—
488C3×D4—32no—
489C3×D4—64no—
490C3×D4—61no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—64no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—241no—
508C2×C3×C4—241no—
509C2×C3×C4—241no—
510C2×C3×C4C2×D1211yescharacteristic
511C2×C3×C4C2×D1211yescharacteristic
512C2×C3×C4C2×D1211yescharacteristic
513C2×C3×C4C2×D1211yescharacteristic
514C2×C3×C4C2×D1211yescharacteristic
515C2×C3×C4C2×#6711yescharacteristic
516C2×C3×C4C2×#6711yescharacteristic
517C2×C3×C4C2×#6711yescharacteristic
518C2×C3×C4C2×#6711yescharacteristic
519C2×C3×C4C2×#6711yescharacteristic
520C2×C3×C4C23×D311yescharacteristic
521C2×C3×C4C23×D311yescharacteristic
522#67—24no—
523#67—241no—
524#67—241no—
525#67—242no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—62no—
530C2×Dic3—62no—
531C2×Dic3—62no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—81no—
539D12—21no—
540D12—61no—
541D12—61no—
542D12—61no—
543D12—61no—
544D12—121no—
545D12—121no—
546D12#23512yes—
547C4×D3—24no—
548C4×D3—81no—
549C4×D3—81no—
550C4×D3—241no—
551C4×D3—241no—
552C4×D3—242no—
553Dic6—21no—
554Dic6—61no—
555Dic6—61no—
556Dic6—61no—
557Dic6—61no—
558Dic6—121no—
559Dic6—121no—
560Dic6—241no—
561Dic6—241no—
562Dic6—242no—
563Dic6#23512yes—
564C3×C8—61no—
565C3×C8—61no—
566C3×C8—61no—
567C3×C8—61no—
568C3⋊C8—21no—
569C3⋊C8—21no—
570C3⋊C8—21no—
571C3⋊C8—21no—
572C2×C32—41no—
573C2×C32#52511yescharacteristic
574C2×C32#57611yescharacteristic
575C2×C32#57811yescharacteristic
576C3⋊D3—81no—
577C3×D3—42no—
578#41—62no—
579#41—62no—
580C2×Q8—31no—
581C2×Q8—91no—
582C2×Q8—181no—
583C2×D4—31no—
584C2×D4—61no—
585C2×D4—91no—
586C2×D4—181no—
587C22×C4—61no—
588C22×C4—61no—
589C22×C4—61no—
590C22×C4—61no—
591C22×C4—181no—
592C22×C4C2×D3211yescharacteristic
593Q16—182no—
594SD16—182no—
595SD16—182no—
596D8—182no—
597C2×C8—31no—
598C2×C8—31no—
599C2×C8—31no—
600C2×C8—31no—
601C4⋊C4—31no—
602C4⋊C4—31no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4—61no—
606C4⋊C4—91no—
607C4⋊C4—91no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4—181no—
611C4⋊C4#62611yescharacteristic
612C4⋊C4#62611yescharacteristic
613C22⋊C4—61no—
614C22⋊C4—61no—
615C22⋊C4—181no—
616C22⋊C4—181no—
617C22⋊C4—181no—
618C22⋊C4—181no—
619C22⋊C4—181no—
620C22⋊C4#62611yescharacteristic
621C22⋊C4#62611yescharacteristic
622C42—61no—
623C42—61no—
624C42—181no—
625C42C2×D3211yescharacteristic
626C42C2×D3211yescharacteristic
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—41no—
637C22×C3—62no—
638C22×C3—121no—
639C22×C3—121no—
640C22×C3C22×D1211yescharacteristic
641C22×C3C22×#6711yescharacteristic
642C2×D3—22no—
643C2×D3—41no—
644C2×D3—41no—
645C2×D3—122no—
646C2×D3—122no—
647C2×D3—122no—
648C2×D3—121no—
649C2×D3—121no—
650C2×D3—121no—
651C2×D3—121no—
652C2×D3—121no—
653C2×D3—121no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—41no—
671C3×C4—62no—
672C3×C4—121no—
673C3×C4—121no—
674C3×C4C2×#23511yescharacteristic
675C3×C4C2×#23511yescharacteristic
676C3×C4D3×#4111yescharacteristic
677C3×C4D3×#4111yescharacteristic
678Dic3—22no—
679Dic3—41no—
680Dic3—41no—
681Dic3—122no—
682Dic3—122no—
683Dic3—122no—
684Dic3—121no—
685Dic3—121no—
686Dic3—121no—
687Dic3—121no—
688Dic3—121no—
689Dic3—121no—
690C32#312411yescharacteristic, complemented, Sylow
691C23—61no—
692C23—181no—
693C23C2×#62611yescharacteristic
694Q8—32no—
695Q8—61no—
696Q8—181no—
697Q8—181no—
698Q8—721no—
699D4—32no—
700D4—64no—
701D4—61no—
702D4—181no—
703D4—181no—
704D4—721no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—64no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—181no—
712C2×C4—181no—
713C2×C4—181no—
714C2×C4—241no—
715C2×C4—241no—
716C2×C4—241no—
717C2×C4—721no—
718C2×C4C2×#62611yescharacteristic
719C2×C4C2×#62611yescharacteristic
720C2×C4C2×#62611yescharacteristic
721C2×C4C2×#62611yescharacteristic
722C2×C4C2×#62611yescharacteristic
723C2×C4C22×D3211yescharacteristic
724C8—61no—
725C8—61no—
726C8—61no—
727C8—61no—
728C2×C3—21no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—41no—
732C2×C3—41no—
733C2×C3—81no—
734C2×C3—122no—
735C2×C3#552411yescharacteristic
736C2×C3#575211yescharacteristic
737C2×C3#575311yescharacteristic
738C2×C3#579111yescharacteristic
739C2×C3#583511yescharacteristic
740C2×C3#583811yescharacteristic
741D3—42no—
742D3—242no—
743D3—241no—
744D3—241no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—62no—
749C22—121no—
750C22—121no—
751C22—361no—
752C22—361no—
753C22—361no—
754C22C22×#62611yescharacteristic
755C4—21no—
756C4—21no—
757C4—21no—
758C4—21no—
759C4—21no—
760C4—62no—
761C4—121no—
762C4—121no—
763C4—361no—
764C4—361no—
765C4—361no—
766C4D3×#23511yescharacteristic
767C4D3×#23511yescharacteristic
768C3—21no—
769C3#7938811yescharacteristic, complemented
770C3#8256911yescharacteristic, complemented
771C2—41no—
772C2—122no—
773C2—721no—
774C2#1059502311yescharacteristic
775C2#1059544911yescharacteristic
776C2#1059545011yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radical#10591163C2
hypercenter#117D32
hypocenterC32#3124
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10596005C2semidirect
2. C3×#5523C2semidirect
3. C3×#5000C2semidirect
4. #10591173C2semidirect
6. #10591135C2semidirect
7. #10591133C2semidirect
8. C4×#3719C2semidirect
9. #10590368C2semidirect
10. #10590366C2semidirect
11. #10590362C2semidirect
12. #10590360C2semidirect
13. C4×#3714C2semidirect
14. #10590283C2semidirect
15. #10590272C2semidirect
65. #5523D3semidirect
77. #5000D3semidirect
690. C32#3124semidirect
769. C3#79388semidirect
770. C3#82569semidirect

Maximal subgroups

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

subgroupindex
#105960052
C3×#55232
C3×#50002
#105911732
#105911632
#105911352
#105911332
C4×#37192
#105903682
#105903662
#105903622
#105903602
C4×#37142
#105902832
#105902722
#825693
#793883