Finite Group Databasebeta

← #11870631

Subgroups — #11870631

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×#3832C211yesmaximal, characteristic, complemented
2#10593875C211yesmaximal, characteristic, complemented
3C3×C4×#216C211yesmaximal, characteristic, complemented
4C3×C4×#215C211yesmaximal, characteristic, complemented
5#10591615C211yesmaximal, characteristic, complemented
6#10591612C211yesmaximal, characteristic, complemented
7#10591602C211yesmaximal, characteristic, complemented
8#10591593C211yesmaximal, characteristic
9#10590540C211yesmaximal, characteristic, complemented
10#10590527C211yesmaximal, characteristic, complemented
11#10590512C211yesmaximal, characteristic, complemented
12#10590435C211yesmaximal, characteristic, complemented
13C4×#3717C211yesmaximal, characteristic, complemented
14C4×#3714C211yesmaximal, characteristic, complemented
15#10590297C211yesmaximal, characteristic, complemented
16#79746—31nomaximal
17#79694—31nomaximal
18C2×#3832C2211yescharacteristic
19C32×C4×Q8C2211yescharacteristic
20Q8×C3⋊Dic3C2211yescharacteristic
21#64102—21no—
22#64102C2211yescharacteristic
23#64101—21no—
24#64101C2211yescharacteristic
25C4×C4⋊(C3⋊D3)—21no—
26C4×C4⋊(C3⋊D3)C2211yescharacteristic
27C42×C3⋊D3—21no—
28C42×C3⋊D3C2211yescharacteristic
29C2×C3×#216C2211yescharacteristic
30C2×C3×#215C2211yescharacteristic
31C3×C4×D12C2211yescharacteristic
32C3×C4×Dic6C2211yescharacteristic
33#63916C2211yescharacteristic
34C4×#626—21no—
35#63872C2211yescharacteristic
36#63871C2211yescharacteristic
37#63863C2211yescharacteristic
38#63862—21no—
39#63855—21no—
40#63853—21no—
41C2×#3717C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C3×#835C2211yescharacteristic
44C3×#835C2211yescharacteristic
45C3×#810C2211yescharacteristic
46C3×#809C2211yescharacteristic
47C3×#808C2211yescharacteristic
48C3×#807C2211yescharacteristic
49C3×C4×C3⋊C8C2211yescharacteristic
50C3×C4×C3⋊C8C2211yescharacteristic
51#63575C2211yescharacteristic
52#63573C2211yescharacteristic
53#63572C2211yescharacteristic
54#63572C2211yescharacteristic
55#63566C2211yescharacteristic
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic
58#63563C2211yescharacteristic
59#63557C2211yescharacteristic
60#63557C2211yescharacteristic
61#5580—31no—
62C4×#239—31no—
63C4×#239—31no—
64C4×#239—61no—
65#5557—31no—
66C3×C4×Q16—31no—
67C3×C4×SD16—31no—
68#5187—31no—
69#5185—31no—
70#5172—31no—
71#5166—31no—
72C4×#216D311yescharacteristic, complemented
73C4×#215—31no—
74C4×#215D311yescharacteristic, complemented
75C4×#213—31no—
76#4891—31no—
77#4885—31no—
78#4871—31no—
79#4868—31no—
80#4819—31no—
81#4814—31no—
82#4810—31no—
83#4808—31no—
84#4799—31no—
85#4796—31no—
86#4787—31no—
87#4779—31no—
88C4×D24—31no—
89C4×#204—31no—
90#4685—31no—
91#4685—31no—
92C2×C32×Q8C2311yescharacteristic
93#3832—22no—
94#3832—22no—
95C2×C4⋊(C3⋊D3)—21no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4×C3⋊D3—21no—
98C2×C4×C3⋊D3—21no—
99C2×C4×C3⋊D3—21no—
100C2×C4×C3⋊D3D411yescharacteristic
101C2×C4×C3⋊D3D411yescharacteristic
102C2×C4×C3⋊D3C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×Dic6C2311yescharacteristic
106C2×#626—21no—
107C32×C4⋊C4—21no—
108C32×C4⋊C4C2311yescharacteristic
109C32×C42—21no—
110C32×C42C2311yescharacteristic
111#3752—21no—
112#3752—21no—
113#3752—21no—
114C4⋊(C3⋊Dic3)—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4×C3⋊Dic3—21no—
117C4×C3⋊Dic3—21no—
118C4×C3⋊Dic3D411yescharacteristic
119C4×C3⋊Dic3D411yescharacteristic
120C4×C3⋊Dic3C2311yescharacteristic
121C3×#216—22no—
122C3×#215—22no—
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×C4×Dic3—21no—
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135#3722—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139#3717—22no—
140#3714—22no—
141#3102—91noSylow
142C2×#239—31no—
143C2×#239—31no—
144C2×#239—61no—
145C2×C3×Q16—31no—
146C2×C3×SD16—31no—
147C3×C4×Q8—21no—
148C3×C4×Q8—31no—
149C3×C4×Q8C2×D311yescharacteristic
150C3×C4×Q8C2×D311yescharacteristic
151C3×C4×D4—31no—
152#947—31no—
153#946—31no—
154Q8×Dic3—31no—
155Q8×Dic3—31no—
156Q8×Dic3—61no—
157C2×#216C2×D311yescharacteristic
158C2×#215—31no—
159C2×#215C2×D311yescharacteristic
160#938—31no—
161#936—31no—
162C2×#213—31no—
163C4×#67—61no—
164#926—61no—
165C2×D24—31no—
166C2×#204—31no—
167#898—61no—
168#897—31no—
169#895—31no—
170#894—61no—
171#893—31no—
172#893—31no—
173#893—61no—
174#893—61no—
175#893—61no—
176#893—62no—
177#892—31no—
178#892—31no—
179#892—61no—
180#892—61no—
181#892—61no—
182#892—62no—
183#890—31no—
184#890—31no—
185#883—61no—
186#879—61no—
187C4×D12—31no—
188C4×D12—31no—
189C4×D12—61no—
190C4×D12—61no—
191C4×D12—61no—
192C4×D12—62no—
193C4×D12—61no—
194C4×D12C2×D311yescharacteristic
195#872—61no—
196C42×D3—31no—
197C42×D3—31no—
198C42×D3—61no—
199C42×D3—61no—
200C42×D3—61no—
201C42×D3—62no—
202C4×Dic6C2×D311yescharacteristic
203C3×#107—31no—
204C3×#106—31no—
205C3×#103—31no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#102—31no—
209C3×C4×C8—31no—
210C3×C4×C8—31no—
211#835—31no—
212#835C2×D311yescharacteristic
213#835C2×D311yescharacteristic
214#832—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—31no—
222#818—31no—
223#817—31no—
224#816—31no—
225Dic3⋊C8—31no—
226Dic3⋊C8—31no—
227Dic3⋊C8—31no—
228Dic3⋊C8—31no—
229#810C2×D311yescharacteristic
230#809—31no—
231#809—31no—
232#809C2×D311yescharacteristic
233#808—31no—
234#808C2×D311yescharacteristic
235#807—31no—
236#807C2×D311yescharacteristic
237C4×C3⋊C8C2×D311yescharacteristic
238C4×C3⋊C8C2×D311yescharacteristic
239C22×C3⋊D3—21no—
240C22×C3⋊D3C2×D411yescharacteristic
241C22×C3×D3—21no—
242C32×Q8—21no—
243C32×Q8#4112yes—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3C2×D411yescharacteristic
251C2×C3⋊Dic3C2×D411yescharacteristic
252C2×C3⋊Dic3C2×D411yescharacteristic
253C4⋊(C3⋊D3)—24no—
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)#4112yes—
256C4×C3⋊D3—24no—
257C4×C3⋊D3—21no—
258C4×C3⋊D3—21no—
259C4×C3⋊D3—22no—
260C4×C3⋊D3—41no—
261C4×C3⋊D3—42no—
262C4×C3⋊D3—42no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C3×D12—21no—
267C3×D12—21no—
268C3×C4×D3—42no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271#626—42no—
272C3×C3⋊C8—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#529—91no—
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—31no—
287C4×SD16—31no—
288C4×SD16—91no—
289C4×D8—91no—
290#431—91no—
291C2×C3×Q8—21no—
292C2×C3×Q8—31no—
293C2×C3×Q8C22×D311yescharacteristic
294C2×C3×Q8C22×D311yescharacteristic
295C2×C3×D4—31no—
296C22×C3×C4—61no—
297C2×#67—61no—
298#239—62no—
299#239—62no—
300#239—64no—
301#239—64no—
302#239—62no—
303#239—62no—
304C2×D12—31no—
305C2×D12—31no—
306C2×D12—61no—
307C2×D12—61no—
308C2×D12—61no—
309C2×D12—62no—
310C2×D12—61no—
311C2×D12C22×D311yescharacteristic
312C2×C4×D3—21no—
313C2×C4×D3—31no—
314C2×C4×D3—31no—
315C2×C4×D3—31no—
316C2×C4×D3—31no—
317C2×C4×D3—31no—
318C2×C4×D3—31no—
319C2×C4×D3—61no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—62no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—62no—
328C2×C4×D3—62no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×Dic6C22×D311yescharacteristic
332C3×Q16—62no—
333C3×SD16—62no—
334C2×C3×C8—31no—
335C2×C3×C8—31no—
336C2×C3×C8—31no—
337C2×C3×C8—31no—
338C3×C4⋊C4—22no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C22⋊C4—61no—
348C3×C42—22no—
349C3×C42—21no—
350C3×C42—21no—
351C3×C42—21no—
352C3×C42—61no—
353C3×C42C22×D311yescharacteristic
354C3×C42C22×D311yescharacteristic
355#217—61no—
356#217—61no—
357#217—61no—
358#216—22no—
359#215—22no—
360#215—62no—
361#213—62no—
362(C2×D3)⋊C4—21no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—62no—
373(C2×D3)⋊C4—62no—
374(C2×D3)⋊C4—62no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—62no—
386C4⋊Dic3C22×D311yescharacteristic
387C4⋊Dic3C22×D311yescharacteristic
388Dic3⋊C4—21no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392C4×Dic3—21no—
393C4×Dic3—31no—
394C4×Dic3—31no—
395C4×Dic3—31no—
396C4×Dic3—31no—
397C4×Dic3—31no—
398C4×Dic3—31no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3—61no—
405C4×Dic3—61no—
406C4×Dic3—62no—
407C4×Dic3—62no—
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411C2×C3⋊C8C22×D311yescharacteristic
412D24—62no—
413#204—62no—
414C22×C32C22×D411yescharacteristic
415C2×C3⋊D3—21no—
416C2×C3⋊D3—22no—
417C2×C3⋊D3—21no—
418C2×C3⋊D3—21no—
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C32×C4—22no—
425C32×C4—21no—
426C32×C4—41no—
427C32×C4#13512yes—
428C32×C4C2×#4111yescharacteristic
429C32×C4C2×#4111yescharacteristic
430C3⋊Dic3—21no—
431C3⋊Dic3—21no—
432C3⋊Dic3—21no—
433C3⋊Dic3—41no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C2×#41—91no—
438C2×Q16—31no—
439C2×SD16—31no—
440C2×SD16—91no—
441C2×D8—91no—
442#126—181no—
443#125—91no—
444#124—91no—
445#123—181no—
446C22⋊Q8—91no—
447#121—91no—
448C4×Q8—31no—
449C4×Q8—91no—
450C4×Q8D3211yescharacteristic
451C4×D4—31no—
452C4×D4—91no—
453C4×D4—91no—
454C4×D4—181no—
455C4×D4—181no—
456C4×D4—181no—
457#117—91no—
458#117—181no—
459#117—181no—
460C2×C42—91no—
461C2×C42—181no—
462#107—31no—
463#107—91no—
464#106—31no—
465#106—91no—
466C4⋊C8—91no—
467C4⋊C8—91no—
468#103—31no—
469#103—31no—
470#103—31no—
471#103—91no—
472#102—31no—
473#102—91no—
474#102—91no—
475#102—91no—
476C22⋊C8—91no—
477C22⋊C8—91no—
478C4×C8—31no—
479C4×C8—31no—
480C23×C3—61no—
481C22×D3—21no—
482C22×D3—31no—
483C22×D3—31no—
484C22×D3—61no—
485C22×D3—62no—
486C22×D3—61no—
487C22×D3—61no—
488C3×Q8—22no—
489C3×Q8—21no—
490C3×Q8—21no—
491C3×Q8—22no—
492C3×Q8—61no—
493C3×Q8—61no—
494C3×Q8#23512yes—
495C3×Q8#23512yes—
496C3×D4—61no—
497C3×D4—61no—
498C2×C3×C4—22no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—22no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—122no—
511C2×C3×C4D3×D411yescharacteristic
512C2×C3×C4D3×D411yescharacteristic
513C2×C3×C4D3×D411yescharacteristic
514C2×C3×C4D3×D411yescharacteristic
515C2×C3×C4C23×D311yescharacteristic
516C2×C3×C4C23×D311yescharacteristic
517#67—122no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—31no—
522C2×Dic3—31no—
523C2×Dic3—31no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—62no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533D12—21no—
534D12—21no—
535D12—32no—
536D12—32no—
537D12—62no—
538D12—68no—
539D12—64no—
540D12—64no—
541D12—62no—
542D12—61no—
543D12—61no—
544D12—122no—
545C4×D3—42no—
546C4×D3—68no—
547C4×D3—64no—
548C4×D3—64no—
549C4×D3—62no—
550C4×D3—62no—
551C4×D3—62no—
552C4×D3—62no—
553C4×D3—61no—
554C4×D3—61no—
555C4×D3—61no—
556C4×D3—61no—
557C4×D3—122no—
558C4×D3—121no—
559C4×D3—121no—
560C4×D3—122no—
561C4×D3—124no—
562C4×D3—122no—
563C4×D3—122no—
564C4×D3—124no—
565C4×D3—122no—
566C4×D3—122no—
567Dic6—21no—
568Dic6—21no—
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#52511yescharacteristic
578C2×C32C2×#13511yescharacteristic
579C2×C32#57511yescharacteristic
580C3⋊D3—41no—
581C3⋊D3—42no—
582C3×D3—81no—
583#41—182no—
584#41—182no—
585C2×Q8—31no—
586C2×Q8C2×D3211yescharacteristic
587C2×D4—31no—
588C2×D4—91no—
589C2×D4—181no—
590C2×D4—181no—
591C22×C4—61no—
592C22×C4—91no—
593C22×C4—91no—
594C22×C4—91no—
595C22×C4—181no—
596C22×C4—181no—
597C22×C4—181no—
598Q16—62no—
599SD16—62no—
600SD16—182no—
601D8—182no—
602C2×C8—31no—
603C2×C8—31no—
604C2×C8—31no—
605C2×C8—31no—
606C4⋊C4—21no—
607C4⋊C4—31no—
608C4⋊C4—31no—
609C4⋊C4—61no—
610C4⋊C4—91no—
611C4⋊C4—181no—
612C4⋊C4—181no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C4⋊C4C2×D3211yescharacteristic
616C22⋊C4—61no—
617C22⋊C4—181no—
618C22⋊C4—181no—
619C22⋊C4—181no—
620C22⋊C4—181no—
621C22⋊C4—181no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C42—21no—
625C42—61no—
626C42—91no—
627C42—91no—
628C42—91no—
629C42—181no—
630C42—181no—
631C42C2×D3211yescharacteristic
632C22×C3—21no—
633C22×C3—121no—
634C22×C3—121no—
635C22×C3—121no—
636C22×C3C2×D3×D411yescharacteristic
637C22×C3C2×D3×D411yescharacteristic
638C2×D3—41no—
639C2×D3—41no—
640C2×D3—41no—
641C2×D3—64no—
642C2×D3—62no—
643C2×D3—61no—
644C2×D3—61no—
645C2×D3—61no—
646C2×D3—61no—
647C2×D3—62no—
648C2×D3—62no—
649C2×D3—61no—
650C2×D3—61no—
651C2×D3—121no—
652C2×D3—121no—
653C2×D3—122no—
654C2×D3—122no—
655C2×D3—121no—
656C2×D3—121no—
657C2×D3—121no—
658C2×D3—121no—
659C3×C4—24no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—22no—
663C3×C4—22no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—22no—
667C3×C4—41no—
668C3×C4—42no—
669C3×C4—41no—
670C3×C4—41no—
671C3×C4—121no—
672C3×C4—121no—
673C3×C4—121no—
674C3×C4#91612yes—
675C3×C4#91912yes—
676C3×C4C2×#23511yescharacteristic
677C3×C4C2×#23511yescharacteristic
678C3×C4D3×#4111yescharacteristic
679C3×C4D3×#4111yescharacteristic
680Dic3—41no—
681Dic3—41no—
682Dic3—41no—
683Dic3—62no—
684Dic3—62no—
685Dic3—61no—
686Dic3—61no—
687Dic3—61no—
688Dic3—61no—
689Dic3—61no—
690Dic3—61no—
691Dic3—121no—
692Dic3—122no—
693Dic3—121no—
694Dic3—121no—
695C32#310211yescharacteristic, complemented, Sylow
696C23—61no—
697C23—91no—
698C23—181no—
699Q8—21no—
700Q8—61no—
701Q8—61no—
702Q8#379812yes—
703D4—61no—
704D4—61no—
705D4—92no—
706D4—184no—
707D4—181no—
708D4—362no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—91no—
715C2×C4—91no—
716C2×C4—91no—
717C2×C4—122no—
718C2×C4—184no—
719C2×C4—181no—
720C2×C4—181no—
721C2×C4—182no—
722C2×C4—181no—
723C2×C4—361no—
724C2×C4—362no—
725C2×C4—362no—
726C2×C4#381111yescharacteristic
727C2×C4#381111yescharacteristic
728C2×C4C22×D3211yescharacteristic
729C8—61no—
730C8—61no—
731C8—61no—
732C8—61no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—241no—
737C2×C3#554711yescharacteristic
738C2×C3#554711yescharacteristic
739C2×C3C2×#91611yescharacteristic
740C2×C3C2×#91911yescharacteristic
741C2×C3#576811yescharacteristic
742C2×C3#576811yescharacteristic
743D3—81no—
744D3—122no—
745D3—124no—
746D3—121no—
747D3—122no—
748D3—121no—
749D3—122no—
750C22—121no—
751C22—121no—
752C22—121no—
753C22—181no—
754C22—181no—
755C22—182no—
756C22—181no—
757C22—361no—
758C22—361no—
759C22C2×#381111yescharacteristic
760C4—21no—
761C4—22no—
762C4—41no—
763C4—121no—
764C4—121no—
765C4—121no—
766C4—181no—
767C4—181no—
768C4—181no—
769C4—361no—
770C4#6395012yes—
771C4C2×#379811yescharacteristic
772C4#6430611yescharacteristic
773C3—21no—
774C3#7969411yescharacteristic, complemented
775C3#7974611yescharacteristic, complemented
776C2—241no—
777C2—361no—
778C2—362no—
779C2#1059501611yescharacteristic
780C2C2×#6395011yescharacteristic
781C2#1059546011yescharacteristic
subgroupG/H
centerC2×C4#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#10591593C2
hypercenterC4×Q8D32
hypocenterC32#3102
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C4×#3832C2semidirect
2. #10593875C2semidirect
3. C3×C4×#216C2semidirect
4. C3×C4×#215C2semidirect
5. #10591615C2semidirect
6. #10591612C2semidirect
7. #10591602C2semidirect
9. #10590540C2semidirect
10. #10590527C2semidirect
11. #10590512C2semidirect
12. #10590435C2semidirect
13. C4×#3717C2semidirect
14. C4×#3714C2semidirect
15. #10590297C2semidirect
72. C4×#216D3semidirect
74. C4×#215D3semidirect
695. C32#3102semidirect
774. C3#79694semidirect
775. C3#79746semidirect

Maximal subgroups

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

subgroupindex
C4×#38322
#105938752
C3×C4×#2162
C3×C4×#2152
#105916152
#105916122
#105916022
#105915932
#105905402
#105905272
#105905122
#105904352
C4×#37172
C4×#37142
#105902972
#797463
#796943