Finite Group Databasebeta

← #11870619

Subgroups — #11870619

Order 1152.

947 conjugacy classes of subgroups.

The subgroup lattice has 783 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3828C211yesmaximal, characteristic, complemented
2C3×#5479C211yesmaximal, characteristic, complemented
3C3×#4925C211yesmaximal, characteristic, complemented
4#10591184C211yesmaximal, characteristic, complemented
5#10591182C211yesmaximal, characteristic
6#10591127C211yesmaximal, characteristic, complemented
7#10591093C211yesmaximal, characteristic, complemented
8C4×#3719C211yesmaximal, characteristic, complemented
9#10590378C211yesmaximal, characteristic, complemented
10C4×#3717C211yesmaximal, characteristic, complemented
11C4×#3716C211yesmaximal, characteristic, complemented
12#10590356C211yesmaximal, characteristic, complemented
13C4×#3714C211yesmaximal, characteristic, complemented
14#10590308C211yesmaximal, characteristic, complemented
15#10590292C211yesmaximal, characteristic, complemented
16#83140—31nomaximal
17#79299—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×C32×C42C2211yescharacteristic
20C4×#638—21no—
21C4×#638—21no—
22#64135C2211yescharacteristic
23C4×C4⋊(C3⋊D3)C2211yescharacteristic
24C4×C4⋊(C3⋊D3)C2211yescharacteristic
25#64081—21no—
26C42×C3⋊D3—21no—
27C4×#634C2211yescharacteristic
28C4×#634C2211yescharacteristic
29C3×#930C2211yescharacteristic
30C3×#929—21no—
31C3×C4×#67—21no—
32C3×#924C2211yescharacteristic
33C3×#876—21no—
34C3×#875C2211yescharacteristic
35C3×C4×D12C2211yescharacteristic
36C3×#872—21no—
37C3×#870C2211yescharacteristic
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×#529—31no—
62#5479D311yescharacteristic, complemented
63C4×#235—31no—
64C4×#235—31no—
65C4×#235—61no—
66C3×#431—31no—
67#5066—31no—
68#5063—31no—
69#5057—31no—
70#5054—31no—
71#5047—31no—
72#5045—31no—
73#5037—31no—
74#5035—31no—
75C4×#216—31no—
76C4×#215—31no—
77C4×#214—31no—
78C4×#213—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—
96#3828—22no—
97#3828—22no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4×C3⋊D3—21no—
100C2×C4×C3⋊D3—21no—
101C2×C4×C3⋊D3—21no—
102C2×#634C2311yescharacteristic
103C2×C3×#67—21no—
104C2×C3×D12C2311yescharacteristic
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—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117#3750—21no—
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3—21no—
120C4×C3⋊Dic3—21no—
121C3×#217—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—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×Dic3⋊C4—21no—
131C3×Dic3⋊C4—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×#235—31no—
143C2×#235—31no—
144C2×#235—61no—
145C3×#126—61no—
146C3×#125—31no—
147C3×#124—31no—
148C3×#123—61no—
149C3×C22⋊Q8—31no—
150C3×#121—31no—
151C3×C4×Q8—31no—
152C3×C4×D4—31no—
153C3×C4×D4—61no—
154C3×#117—61no—
155C2×C3×C42—21no—
156C2×C3×C42C2×D311yescharacteristic
157C2×C3×C42C2×D311yescharacteristic
158C2×#216—31no—
159C2×#215—31no—
160C2×#214—31no—
161C2×#213—31no—
162#930C2×D311yescharacteristic
163#929—21no—
164C4×#67—21no—
165C4×#67—62no—
166C4×#67—62no—
167C4×#67—61no—
168C4×#67—61no—
169C4×#67—61no—
170C4×#67—61no—
171#926—31no—
172#926—31no—
173#926—61no—
174#924C2×D311yescharacteristic
175C2×Dic12—31no—
176C2×D24—31no—
177C2×#204—31no—
178C2×#204—31no—
179#876—21no—
180#875C2×D311yescharacteristic
181C4×D12—31no—
182C4×D12—31no—
183C4×D12—31no—
184C4×D12—31no—
185C4×D12—61no—
186C4×D12—61no—
187C4×D12C2×D311yescharacteristic
188#872—21no—
189#872—62no—
190#872—61no—
191#872—61no—
192C42×D3—62no—
193C42×D3—61no—
194C42×D3—61no—
195#870C2×D311yescharacteristic
196C4×Dic6—31no—
197C4×Dic6—31no—
198C4×Dic6—31no—
199C4×Dic6—31no—
200C4×Dic6—61no—
201C4×Dic6—61no—
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—21no—
243C2×C32×C4—21no—
244C2×C32×C4—22no—
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—24no—
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—21no—
256C4⋊(C3⋊D3)—21no—
257C4⋊(C3⋊D3)#4112yes—
258C4×C3⋊D3—24no—
259C4×C3⋊D3—42no—
260C4×C3⋊D3—42no—
261#634—21no—
262#634#4112yes—
263C3×#67—42no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C3×D12—21no—
268C3×D12—21no—
269C3×C4×D3—42no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272C3×C3⋊C8—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#529—31no—
277C4×#41—91no—
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—
291C2×C3×Q8—31no—
292C2×C3×D4—31no—
293C2×C3×D4—61no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—61no—
298C22×C3×C4D1211yescharacteristic
299C22×C3×C4D1211yescharacteristic
300C22×C3×C4#6711yescharacteristic
301C22×C3×C4#6711yescharacteristic
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C2×#67—21no—
305C2×#67—62no—
306C2×#67—61no—
307C2×#67—61no—
308#235—62no—
309#235—62no—
310#235—62no—
311#235—62no—
312#235—64no—
313#235—64no—
314C2×D12—31no—
315C2×D12—31no—
316C2×D12—61no—
317C2×D12C22×D311yescharacteristic
318C2×C4×D3—21no—
319C2×C4×D3—62no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×C4×D3—62no—
323C2×C4×D3—62no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×Dic6—31no—
329C2×Dic6—31no—
330C2×Dic6—61no—
331C2×Dic6C22×D311yescharacteristic
332C2×C3×C8—31no—
333C2×C3×C8—31no—
334C2×C3×C8—31no—
335C2×C3×C8—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C22⋊C4—61no—
343C3×C22⋊C4—61no—
344C3×C22⋊C4—61no—
345C3×C22⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C42—21no—
348C3×C42—21no—
349C3×C42—21no—
350C3×C42—21no—
351C3×C42—61no—
352C3×C42D1211yescharacteristic
353C3×C42D1211yescharacteristic
354C3×C42#6711yescharacteristic
355C3×C42#6711yescharacteristic
356C3×C42C22×D311yescharacteristic
357C3×C42C22×D311yescharacteristic
358C3×C42C22×D311yescharacteristic
359C3×C42C22×D311yescharacteristic
360#217—21no—
361#217—62no—
362#217—61no—
363#217—61no—
364#216—62no—
365#215—62no—
366#214—62no—
367#213—62no—
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—62no—
373(C2×D3)⋊C4—62no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3C22×D311yescharacteristic
385C4⋊Dic3C22×D311yescharacteristic
386Dic3⋊C4—21no—
387Dic3⋊C4—21no—
388Dic3⋊C4—21no—
389Dic3⋊C4—21no—
390Dic3⋊C4—62no—
391Dic3⋊C4—62no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396C4×Dic3—21no—
397C4×Dic3—62no—
398C4×Dic3—62no—
399C4×Dic3—62no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3—61no—
405C4×Dic3—61no—
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410Dic12—62no—
411D24—62no—
412#204—62no—
413#204—62no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32C22×D411yescharacteristic
418C2×C3⋊D3—22no—
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C32×C4—21no—
425C32×C4—21no—
426C32×C4—21no—
427C32×C4—21no—
428C32×C4#13512yes—
429C32×C4C2×#4111yescharacteristic
430C32×C4C2×#4111yescharacteristic
431C3⋊Dic3—22no—
432C3⋊Dic3—41no—
433C3⋊Dic3—41no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C2×#41—91no—
438C2×Q16—91no—
439C2×SD16—91no—
440C2×SD16—91no—
441C2×D8—91no—
442#126—61no—
443#125—31no—
444#124—31no—
445#123—61no—
446C22⋊Q8—31no—
447#121—31no—
448C4×Q8—31no—
449C4×Q8—91no—
450C4×Q8—91no—
451C4×D4—31no—
452C4×D4—61no—
453C4×D4—91no—
454C4×D4—91no—
455C4×D4—181no—
456C4×D4—181no—
457#117—61no—
458#117—91no—
459#117—181no—
460C2×C42—181no—
461C2×C42D3211yescharacteristic
462#107—91no—
463#107—91no—
464#106—91no—
465#106—91no—
466C4⋊C8—31no—
467C4⋊C8—31no—
468#103—91no—
469#103—91no—
470#103—91no—
471#103—91no—
472#102—91no—
473#102—91no—
474#102—91no—
475#102—91no—
476C22⋊C8—31no—
477C22⋊C8—31no—
478C4×C8—31no—
479C4×C8—31no—
480C23×C3—21no—
481C23×C3—61no—
482C23×C3C2×D1211yescharacteristic
483C23×C3C2×#6711yescharacteristic
484C22×D3—21no—
485C22×D3—62no—
486C22×D3—61no—
487C22×D3—61no—
488C3×Q8—61no—
489C3×Q8—61no—
490C3×D4—61no—
491C3×D4—61no—
492C3×D4—122no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—22no—
496C2×C3×C4—22no—
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—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—42no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—42no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
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—42no—
528#67—68no—
529#67—64no—
530#67—64no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—62no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—62no—
538C2×Dic3—62no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543D12—21no—
544D12—21no—
545D12—32no—
546D12—32no—
547D12—62no—
548D12—62no—
549D12—61no—
550D12—61no—
551C4×D3—42no—
552C4×D3—68no—
553C4×D3—64no—
554C4×D3—64no—
555C4×D3—124no—
556C4×D3—122no—
557C4×D3—122no—
558C4×D3—124no—
559C4×D3—122no—
560C4×D3—122no—
561Dic6—21no—
562Dic6—21no—
563Dic6—32no—
564Dic6—32no—
565Dic6—62no—
566Dic6—62no—
567Dic6—61no—
568Dic6—61no—
569C3×C8—61no—
570C3×C8—61no—
571C3×C8—61no—
572C3×C8—61no—
573C3⋊C8—21no—
574C3⋊C8—21no—
575C3⋊C8—21no—
576C3⋊C8—21no—
577C2×C32—41no—
578C2×C32#52511yescharacteristic
579C2×C32C2×#13511yescharacteristic
580C2×C32#57511yescharacteristic
581C3⋊D3—42no—
582C3×D3—81no—
583#41—182no—
584#41—182no—
585C2×Q8—31no—
586C2×Q8—91no—
587C2×D4—31no—
588C2×D4—61no—
589C2×D4—91no—
590C2×D4—181no—
591C22×C4—61no—
592C22×C4—181no—
593C22×C4—181no—
594C22×C4—181no—
595C22×C4#62611yescharacteristic
596C22×C4#62611yescharacteristic
597C22×C4C2×D3211yescharacteristic
598Q16—182no—
599SD16—182no—
600SD16—182no—
601D8—182no—
602C2×C8—31no—
603C2×C8—31no—
604C2×C8—31no—
605C2×C8—31no—
606C4⋊C4—31no—
607C4⋊C4—31no—
608C4⋊C4—61no—
609C4⋊C4—61no—
610C4⋊C4—61no—
611C4⋊C4—61no—
612C4⋊C4—91no—
613C4⋊C4—91no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C22⋊C4—61no—
617C22⋊C4—61no—
618C22⋊C4—61no—
619C22⋊C4—61no—
620C22⋊C4—61no—
621C22⋊C4—181no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C42—61no—
625C42—181no—
626C42—181no—
627C42—181no—
628C42#62611yescharacteristic
629C42#62611yescharacteristic
630C42C2×D3211yescharacteristic
631C42C2×D3211yescharacteristic
632C22×C3—22no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—121no—
643C22×C3—121no—
644C22×C3—121no—
645C22×C3C22×D1211yescharacteristic
646C22×C3C22×#6711yescharacteristic
647C2×D3—41no—
648C2×D3—41no—
649C2×D3—41no—
650C2×D3—64no—
651C2×D3—62no—
652C2×D3—62no—
653C2×D3—122no—
654C2×D3—122no—
655C2×D3—121no—
656C2×D3—121no—
657C2×D3—121no—
658C2×D3—121no—
659C3×C4—22no—
660C3×C4—22no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—22no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—121no—
675C3×C4—121no—
676C3×C4—121no—
677C3×C4#90412yes—
678C3×C4#95012yes—
679C3×C4D3×#4111yescharacteristic
680C3×C4D3×#4111yescharacteristic
681C3×C4D3×#4111yescharacteristic
682C3×C4D3×#4111yescharacteristic
683Dic3—41no—
684Dic3—41no—
685Dic3—41no—
686Dic3—64no—
687Dic3—62no—
688Dic3—62no—
689Dic3—122no—
690Dic3—122no—
691Dic3—121no—
692Dic3—121no—
693Dic3—121no—
694Dic3—121no—
695C32#310211yescharacteristic, complemented, Sylow
696C23—61no—
697C23—181no—
698C23C2×#62611yescharacteristic
699Q8—61no—
700Q8—61no—
701Q8—92no—
702Q8—181no—
703D4—61no—
704D4—61no—
705D4—92no—
706D4—122no—
707D4—184no—
708D4—181no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—41no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—122no—
717C2×C4—184no—
718C2×C4—181no—
719C2×C4—181no—
720C2×C4—181no—
721C2×C4—362no—
722C2×C4—362no—
723C2×C4C2×#62611yescharacteristic
724C2×C4C2×#62611yescharacteristic
725C2×C4C2×#62611yescharacteristic
726C2×C4C2×#62611yescharacteristic
727C2×C4C2×#62611yescharacteristic
728C2×C4C22×D3211yescharacteristic
729C8—61no—
730C8—61no—
731C8—61no—
732C8—61no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—42no—
737C2×C3—41no—
738C2×C3—41no—
739C2×C3—241no—
740C2×C3#552411yescharacteristic
741C2×C3C2×#90411yescharacteristic
742C2×C3#574811yescharacteristic
743C2×C3C2×#95011yescharacteristic
744C2×C3#582211yescharacteristic
745C2×C3#582811yescharacteristic
746D3—81no—
747D3—124no—
748D3—122no—
749D3—122no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—121no—
754C22—121no—
755C22—121no—
756C22—182no—
757C22—361no—
758C22—361no—
759C22C22×#62611yescharacteristic
760C4—21no—
761C4—21no—
762C4—21no—
763C4—21no—
764C4—121no—
765C4—121no—
766C4—121no—
767C4—182no—
768C4—361no—
769C4—361no—
770C4#6382912yes—
771C4#6430611yescharacteristic
772C4#6430611yescharacteristic
773C3—21no—
774C3#7929911yescharacteristic, complemented
775C3#8314011yescharacteristic, complemented
776C2—41no—
777C2—241no—
778C2—362no—
779C2C2×#6382911yescharacteristic
780C2#1059479511yescharacteristic
781C2#1059503411yescharacteristic
subgroupG/H
centerC2×C4C2×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC22×C32C22×D4
prime radical#10591182C2
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. C4×#3828C2semidirect
2. C3×#5479C2semidirect
3. C3×#4925C2semidirect
4. #10591184C2semidirect
6. #10591127C2semidirect
7. #10591093C2semidirect
8. C4×#3719C2semidirect
9. #10590378C2semidirect
10. C4×#3717C2semidirect
11. C4×#3716C2semidirect
12. #10590356C2semidirect
13. C4×#3714C2semidirect
14. #10590308C2semidirect
15. #10590292C2semidirect
62. #5479D3semidirect
79. #4925D3semidirect
695. C32#3102semidirect
774. C3#79299semidirect
775. C3#83140semidirect

Maximal subgroups

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

subgroupindex
C4×#38282
C3×#54792
C3×#49252
#105911842
#105911822
#105911272
#105910932
C4×#37192
#105903782
C4×#37172
C4×#37162
#105903562
C4×#37142
#105903082
#105902922
#831403
#792993