Finite Group Databasebeta

← #11870618

Subgroups — #11870618

Order 1152.

909 conjugacy classes of subgroups.

The subgroup lattice has 779 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595950C211yesmaximal, characteristic, complemented
2C3×C4×#235C211yesmaximal, characteristic, complemented
3C3×#4925C211yesmaximal, characteristic, complemented
4#10591173C211yesmaximal, characteristic, complemented
5#10591163C211yesmaximal, characteristic
6#10591136C211yesmaximal, characteristic, complemented
7#10591134C211yesmaximal, characteristic, complemented
8C4×#3719C211yesmaximal, characteristic, complemented
9#10590368C211yesmaximal, characteristic, complemented
10#10590366C211yesmaximal, characteristic, complemented
11C4×#3717C211yesmaximal, characteristic, complemented
12C4×#3716C211yesmaximal, characteristic, complemented
13C4×#3714C211yesmaximal, characteristic, complemented
14#10590302C211yesmaximal, characteristic, complemented
15#10590271C211yesmaximal, characteristic, complemented
16#82528—31nomaximal
17#79299—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C2×C32×C42C2211yescharacteristic
20#64139C2211yescharacteristic
21#64138—21no—
22C4×#638—21no—
23#64133C2211yescharacteristic
24#64085—21no—
25#64084C2211yescharacteristic
26C4×C4⋊(C3⋊D3)C2211yescharacteristic
27#64081—21no—
28#64079C2211yescharacteristic
29C4×#634C2211yescharacteristic
30C3×C4×#67—21no—
31C3×C4×#67—21no—
32C3×#926C2211yescharacteristic
33C3×C4×D12C2211yescharacteristic
34C3×C4×D12C2211yescharacteristic
35C3×#872—21no—
36C3×C42×D3—21no—
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×C4×C3⋊C8C2211yescharacteristic
48C3×C4×C3⋊C8C2211yescharacteristic
49#63575C2211yescharacteristic
50#63575C2211yescharacteristic
51#63573C2211yescharacteristic
52#63573C2211yescharacteristic
53#63567C2211yescharacteristic
54#63567C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic
61C3×C4×#41—31no—
62#5479—31no—
63#5479—31no—
64#5479—61no—
65C4×#235D311yescharacteristic, complemented
66C3×#431—31no—
67#5239—31no—
68#5238—31no—
69C4×#216—31no—
70#5028—31no—
71C4×#215—31no—
72#5022—31no—
73C4×#214—31no—
74#5016—31no—
75C4×#213—31no—
76#5009—31no—
77#5003—31no—
78#4996—31no—
79#4925D311yescharacteristic, complemented
80#4847—31no—
81#4845—31no—
82#4844—31no—
83#4829—31no—
84#4737—31no—
85#4734—31no—
86#4733—31no—
87#4723—31no—
88C4×Dic12—31no—
89C4×D24—31no—
90C4×#204—31no—
91C4×#204—31no—
92C22×C32×C4D411yescharacteristic
93C22×C32×C4D411yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×#638—21no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4×C3⋊D3—21no—
98C2×#634C2311yescharacteristic
99C2×C3×#67—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×C42D411yescharacteristic
108C32×C42D411yescharacteristic
109C32×C42C2311yescharacteristic
110C32×C42C2311yescharacteristic
111#3757—21no—
112#3752—21no—
113#3752—21no—
114#3752—21no—
115#3752—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118#3750—21no—
119#3750—21no—
120#3750—21no—
121#3750—21no—
122C4×C3⋊Dic3—21no—
123C3×#217—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×C4×Dic3—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#3102—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—31no—
151C3×#117—61no—
152C2×C3×C42—21no—
153C2×C3×C42—61no—
154C2×C3×C42C2×D311yescharacteristic
155C2×C3×C42C2×D311yescharacteristic
156C2×#216—31no—
157C2×#215—31no—
158C2×#214—31no—
159C2×#213—31no—
160#930—31no—
161#930—31no—
162#930—61no—
163#929—62no—
164#929—61no—
165#929—61no—
166C4×#67—21no—
167C4×#67—21no—
168C4×#67—62no—
169C4×#67—61no—
170C4×#67—61no—
171#926C2×D311yescharacteristic
172#924—31no—
173#924—31no—
174#924—61no—
175C2×Dic12—31no—
176C2×D24—31no—
177C2×#204—31no—
178C2×#204—31no—
179#876—62no—
180#876—61no—
181#876—61no—
182#875—31no—
183#875—31no—
184#875—61no—
185C4×D12—31no—
186C4×D12—31no—
187C4×D12—61no—
188C4×D12C2×D311yescharacteristic
189C4×D12C2×D311yescharacteristic
190#872—21no—
191#872—62no—
192#872—61no—
193#872—61no—
194C42×D3—21no—
195#870—31no—
196#870—31no—
197#870—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×C4×C8—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#817—31no—
222#817—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#808—31no—
232#808—31no—
233#807—31no—
234#807—31no—
235C4⋊(C3⋊C8)C2×D311yescharacteristic
236C4⋊(C3⋊C8)C2×D311yescharacteristic
237C4×C3⋊C8C2×D311yescharacteristic
238C4×C3⋊C8C2×D311yescharacteristic
239C23×C32C2×D411yescharacteristic
240C22×C3⋊D3—21no—
241C22×C3×D3—21no—
242C2×C32×C4—22no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—41no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252#638—42no—
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—21no—
256C4⋊(C3⋊D3)—21no—
257C4⋊(C3⋊D3)—21no—
258C4×C3⋊D3—42no—
259#634—21no—
260#634—21no—
261C3×#67—24no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C3×D12—21no—
266C3×D12#4112yes—
267C3×C4×D3—24no—
268C3×C4×D3—42no—
269C3×C4×D3—42no—
270C3×Dic6—21no—
271C3×Dic6#4112yes—
272C3×C3⋊C8—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#529—91no—
277C4×#41—31no—
278#485—91no—
279#482—91no—
280#479—91no—
281#478—91no—
282#464—91no—
283#463—91no—
284#452—91no—
285#449—91no—
286C4×Q16—91no—
287C4×SD16—91no—
288C4×SD16—91no—
289C4×D8—91no—
290#431—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—21no—
298C22×C3×C4—21no—
299C22×C3×C4—61no—
300C22×C3×C4—61no—
301C22×C3×C4—61no—
302C22×C3×C4D1211yescharacteristic
303C22×C3×C4D1211yescharacteristic
304C22×C3×C4#6711yescharacteristic
305C22×C3×C4#6711yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C22×D311yescharacteristic
308C2×#67—21no—
309C2×#67—62no—
310C2×#67—61no—
311C2×#67—61no—
312#235—22no—
313#235—22no—
314C2×D12—31no—
315C2×D12—31no—
316C2×D12—61no—
317C2×D12C22×D311yescharacteristic
318C2×C4×D3—21no—
319C2×C4×D3—21no—
320C2×C4×D3—21no—
321C2×C4×D3—62no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×Dic6—31no—
325C2×Dic6—31no—
326C2×Dic6—61no—
327C2×Dic6C22×D311yescharacteristic
328C2×C3×C8—31no—
329C2×C3×C8—31no—
330C2×C3×C8—31no—
331C2×C3×C8—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—61no—
335C3×C4⋊C4—61no—
336C3×C22⋊C4—61no—
337C3×C22⋊C4—61no—
338C3×C22⋊C4—61no—
339C3×C42—21no—
340C3×C42—21no—
341C3×C42—21no—
342C3×C42—21no—
343C3×C42—61no—
344C3×C42—61no—
345C3×C42—61no—
346C3×C42D1211yescharacteristic
347C3×C42D1211yescharacteristic
348C3×C42#6711yescharacteristic
349C3×C42#6711yescharacteristic
350C3×C42C22×D311yescharacteristic
351C3×C42C22×D311yescharacteristic
352C3×C42C22×D311yescharacteristic
353C3×C42C22×D311yescharacteristic
354#217—21no—
355#217—62no—
356#217—61no—
357#217—61no—
358#216—62no—
359#215—62no—
360#214—62no—
361#213—62no—
362(C2×D3)⋊C4—21no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—62no—
365(C2×D3)⋊C4—62no—
366(C2×D3)⋊C4—62no—
367(C2×D3)⋊C4—62no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
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—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3C22×D311yescharacteristic
383C4⋊Dic3C22×D311yescharacteristic
384Dic3⋊C4—21no—
385Dic3⋊C4—21no—
386Dic3⋊C4—62no—
387Dic3⋊C4—62no—
388Dic3⋊C4—62no—
389Dic3⋊C4—62no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398C4×Dic3—21no—
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#13512yes—
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—
440#126—181no—
441#125—91no—
442#124—91no—
443#123—181no—
444C22⋊Q8—91no—
445#121—91no—
446C4×Q8—31no—
447C4×Q8—31no—
448C4×Q8—91no—
449C4×D4—31no—
450C4×D4—31no—
451C4×D4—61no—
452C4×D4—61no—
453C4×D4—91no—
454C4×D4—181no—
455#117—31no—
456#117—61no—
457#117—181no—
458C2×C42—61no—
459C2×C42D3211yescharacteristic
460#107—91no—
461#107—91no—
462#106—91no—
463#106—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—
476C4×C8—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—22no—
492C2×C3×C4—22no—
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—21no—
502C2×C3×C4—21no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—42no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—42no—
509C2×C3×C4—64no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—122no—
514C2×C3×C4—122no—
515C2×C3×C4C2×D1211yescharacteristic
516C2×C3×C4C2×D1211yescharacteristic
517C2×C3×C4C2×D1211yescharacteristic
518C2×C3×C4C2×D1211yescharacteristic
519C2×C3×C4C2×D1211yescharacteristic
520C2×C3×C4C2×#6711yescharacteristic
521C2×C3×C4C2×#6711yescharacteristic
522C2×C3×C4C2×#6711yescharacteristic
523C2×C3×C4C2×#6711yescharacteristic
524C2×C3×C4C2×#6711yescharacteristic
525C2×C3×C4C23×D311yescharacteristic
526C2×C3×C4C23×D311yescharacteristic
527#67—24no—
528#67—124no—
529#67—122no—
530#67—122no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—62no—
535C2×Dic3—62no—
536C2×Dic3—62no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543D12—21no—
544D12—61no—
545D12—61no—
546D12—61no—
547D12—61no—
548D12—121no—
549D12—121no—
550D12#23512yes—
551C4×D3—24no—
552C4×D3—42no—
553C4×D3—42no—
554C4×D3—124no—
555C4×D3—122no—
556C4×D3—122no—
557Dic6—21no—
558Dic6—61no—
559Dic6—61no—
560Dic6—61no—
561Dic6—61no—
562Dic6—121no—
563Dic6—121no—
564Dic6#23512yes—
565C3×C8—61no—
566C3×C8—61no—
567C3×C8—61no—
568C3×C8—61no—
569C3⋊C8—21no—
570C3⋊C8—21no—
571C3⋊C8—21no—
572C3⋊C8—21no—
573C2×C32—41no—
574C2×C32#52511yescharacteristic
575C2×C32C2×#13511yescharacteristic
576C2×C32#57511yescharacteristic
577C3⋊D3—81no—
578C3×D3—42no—
579#41—62no—
580#41—62no—
581C2×Q8—31no—
582C2×Q8—91no—
583C2×D4—31no—
584C2×D4—61no—
585C2×D4—91no—
586C2×D4—181no—
587C22×C4—61no—
588C22×C4—61no—
589C22×C4—61no—
590C22×C4—181no—
591C22×C4#62611yescharacteristic
592C22×C4#62611yescharacteristic
593C22×C4C2×D3211yescharacteristic
594Q16—182no—
595SD16—182no—
596SD16—182no—
597D8—182no—
598C2×C8—31no—
599C2×C8—31no—
600C2×C8—31no—
601C2×C8—31no—
602C4⋊C4—31no—
603C4⋊C4—31no—
604C4⋊C4—61no—
605C4⋊C4—61no—
606C4⋊C4—91no—
607C4⋊C4—91no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4—181no—
611C4⋊C4—181no—
612C22⋊C4—61no—
613C22⋊C4—61no—
614C22⋊C4—61no—
615C22⋊C4—181no—
616C22⋊C4—181no—
617C22⋊C4—181no—
618C22⋊C4—181no—
619C22⋊C4—181no—
620C42—61no—
621C42—61no—
622C42—61no—
623C42—181no—
624C42#62611yescharacteristic
625C42#62611yescharacteristic
626C42C2×D3211yescharacteristic
627C42C2×D3211yescharacteristic
628C22×C3—22no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—62no—
639C22×C3—121no—
640C22×C3—121no—
641C22×C3C22×D1211yescharacteristic
642C22×C3C22×#6711yescharacteristic
643C2×D3—22no—
644C2×D3—41no—
645C2×D3—41no—
646C2×D3—122no—
647C2×D3—122no—
648C2×D3—122no—
649C2×D3—121no—
650C2×D3—121no—
651C2×D3—121no—
652C2×D3—121no—
653C2×D3—121no—
654C2×D3—121no—
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—22no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—62no—
671C3×C4—121no—
672C3×C4—121no—
673C3×C4#90412yes—
674C3×C4#95012yes—
675C3×C4C2×#23511yescharacteristic
676C3×C4C2×#23511yescharacteristic
677C3×C4D3×#4111yescharacteristic
678C3×C4D3×#4111yescharacteristic
679Dic3—22no—
680Dic3—41no—
681Dic3—41no—
682Dic3—122no—
683Dic3—122no—
684Dic3—122no—
685Dic3—121no—
686Dic3—121no—
687Dic3—121no—
688Dic3—121no—
689Dic3—121no—
690Dic3—121no—
691C32#310211yescharacteristic, complemented, Sylow
692C23—61no—
693C23—181no—
694C23C2×#62611yescharacteristic
695Q8—32no—
696Q8—61no—
697Q8—181no—
698Q8—181no—
699D4—32no—
700D4—64no—
701D4—61no—
702D4—181no—
703D4—181no—
704D4—362no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—41no—
709C2×C4—64no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—122no—
714C2×C4—122no—
715C2×C4—181no—
716C2×C4—181no—
717C2×C4—181no—
718C2×C4—362no—
719C2×C4C2×#62611yescharacteristic
720C2×C4C2×#62611yescharacteristic
721C2×C4C2×#62611yescharacteristic
722C2×C4C2×#62611yescharacteristic
723C2×C4C2×#62611yescharacteristic
724C2×C4C22×D3211yescharacteristic
725C8—61no—
726C8—61no—
727C8—61no—
728C8—61no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—42no—
733C2×C3—41no—
734C2×C3—41no—
735C2×C3—122no—
736C2×C3#552411yescharacteristic
737C2×C3C2×#90411yescharacteristic
738C2×C3#574811yescharacteristic
739C2×C3#579111yescharacteristic
740C2×C3C2×#95011yescharacteristic
741C2×C3#582211yescharacteristic
742D3—42no—
743D3—242no—
744D3—241no—
745D3—241no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—62no—
750C22—121no—
751C22—121no—
752C22—361no—
753C22—361no—
754C22—361no—
755C22C22×#62611yescharacteristic
756C4—21no—
757C4—21no—
758C4—21no—
759C4—21no—
760C4—62no—
761C4—121no—
762C4—121no—
763C4—361no—
764C4—361no—
765C4—361no—
766C4#6382912yes—
767C4D3×#23511yescharacteristic
768C4D3×#23511yescharacteristic
769C3—21no—
770C3#7929911yescharacteristic, complemented
771C3#8252811yescharacteristic, complemented
772C2—41no—
773C2—122no—
774C2—721no—
775C2C2×#6382911yescharacteristic
776C2#1059479511yescharacteristic
777C2#1059502311yescharacteristic
subgroupG/H
centerC2×C4C2×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC22×C32C22×D4
prime radical#10591163C2
hypercenterC2×C42D32
hypocenterC32#3102
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. #10595950C2semidirect
2. C3×C4×#235C2semidirect
3. C3×#4925C2semidirect
4. #10591173C2semidirect
6. #10591136C2semidirect
7. #10591134C2semidirect
8. C4×#3719C2semidirect
9. #10590368C2semidirect
10. #10590366C2semidirect
11. C4×#3717C2semidirect
12. C4×#3716C2semidirect
13. C4×#3714C2semidirect
14. #10590302C2semidirect
15. #10590271C2semidirect
65. C4×#235D3semidirect
79. #4925D3semidirect
691. C32#3102semidirect
770. C3#79299semidirect
771. C3#82528semidirect

Maximal subgroups

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

subgroupindex
#105959502
C3×C4×#2352
C3×#49252
#105911732
#105911632
#105911362
#105911342
C4×#37192
#105903682
#105903662
C4×#37172
C4×#37162
C4×#37142
#105903022
#105902712
#825283
#792993