Finite Group Databasebeta

← #11870729

Subgroups — #11870729

Order 1152.

935 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#624C211yesmaximal, characteristic, complemented
2#10594518C211yesmaximal, characteristic
3#10592505C211yesmaximal, characteristic, complemented
4C3×#4791C211yesmaximal, characteristic, complemented
5C3×#4788C211yesmaximal, characteristic, complemented
6#10591617C211yesmaximal, characteristic, complemented
7#10591592C211yesmaximal, characteristic, complemented
8#10591536C211yesmaximal, characteristic, complemented
9#10590879C211yesmaximal, characteristic, complemented
10#10590758C211yesmaximal, characteristic, complemented
11#10590649C211yesmaximal, characteristic, complemented
12#10590643C211yesmaximal, characteristic, complemented
13#10590487C211yesmaximal, characteristic, complemented
14#10590479C211yesmaximal, characteristic, complemented
15#10590445C211yesmaximal, characteristic, complemented
16#80996—31nomaximal
17#79653—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×#3799—21no—
20C2×#3755C2211yescharacteristic
21C2×#3744C2211yescharacteristic
22#64104C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic
25C2×C3×#215C2211yescharacteristic
26C3×#893C2211yescharacteristic
27C3×#888C2211yescharacteristic
28#63916C2211yescharacteristic
29#63911C2211yescharacteristic
30#63910—21no—
31#63907—21no—
32#63904—21no—
33#63900—21no—
34#63900C2211yescharacteristic
35#63894C2211yescharacteristic
36C4×#624—21no—
37C4×#624C2211yescharacteristic
38#63844—21no—
39#63844—21no—
40#63844C2211yescharacteristic
41#63844C2211yescharacteristic
42C2×#3716C2211yescharacteristic
43C32×#103C2211yescharacteristic
44#63647C2211yescharacteristic
45#63637C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#821C2211yescharacteristic
48C3×#817C2211yescharacteristic
49C3×Dic3⋊C8C2211yescharacteristic
50C3×C8×Dic3C2211yescharacteristic
51C3×#808C2211yescharacteristic
52C3×#808C2211yescharacteristic
53#63574C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63567C2211yescharacteristic
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic
58#63562C2211yescharacteristic
59#63557C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5725—31no—
62C4×D3×Q8—31no—
63C4×D3×Q8—31no—
64#5548—31no—
65C3×#475—31no—
66C3×C4×SD16—31no—
67#5170—31no—
68#5163—31no—
69#5094—31no—
70#5027—31no—
71C4×#215—31no—
72C4×#214—31no—
73#4863—31no—
74#4863—31no—
75#4863—31no—
76#4854—31no—
77#4852—31no—
78#4852—31no—
79#4848—31no—
80#4833—31no—
81#4806—31no—
82#4806—31no—
83#4806—31no—
84#4806—61no—
85#4791D311yescharacteristic, complemented
86#4788—31no—
87#4788D311yescharacteristic, complemented
88#4777—31no—
89#4762—31no—
90C4×#204—31no—
91#4685—31no—
92C2×C32×Q8C2311yescharacteristic
93Q8×C3⋊D3—22no—
94Q8×C3⋊D3—22no—
95C2×C4⋊(C3⋊D3)—21no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4×C3⋊D3—21no—
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×#634—21no—
100C2×#634C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×Dic6—21no—
104C2×#626—21no—
105C2×#626—21no—
106C2×#626—21no—
107C2×#624—21no—
108C2×#624—21no—
109C2×#624D411yescharacteristic
110C2×#624D411yescharacteristic
111#3799—44no—
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114#3755—22no—
115#3752—21no—
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117#3744—22no—
118C3×#215—22no—
119C3×(C2×D3)⋊C4—21no—
120C3×C4⋊Dic3—21no—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×C4×Dic3—21no—
127C3×C4×Dic3—21no—
128C3×C4×Dic3C2311yescharacteristic
129C3×C4×Dic3C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132#3724—21no—
133#3724—21no—
134#3724—21no—
135#3722—21no—
136(C2×D3)⋊Dic3—21no—
137Dic32—21no—
138Dic32—21no—
139Dic32D411yescharacteristic
140Dic32D411yescharacteristic
141#3716—22no—
142#3103—91noSylow
143C2×#239—61no—
144C2×D3×Q8—31no—
145C2×D3×Q8—31no—
146C2×D3×Q8—61no—
147C2×#235—61no—
148C2×C3×SD16—31no—
149C3×C4⋊Q8—31no—
150C3×C4×Q8—31no—
151C3×C4×Q8—31no—
152C3×C4×D4—31no—
153#947—61no—
154Q8×Dic3C2×D311yescharacteristic
155Q8×Dic3C2×D311yescharacteristic
156C2×#215—31no—
157C2×#215—31no—
158C2×#215—61no—
159C2×#215C2×D311yescharacteristic
160#940—31no—
161#938—31no—
162C2×#214—31no—
163C4×#67—61no—
164C2×#204—31no—
165C2×#204—31no—
166C2×#204—31no—
167C2×#204—61no—
168#895—31no—
169#895—31no—
170#895—31no—
171#895—61no—
172#895—61no—
173#893—31no—
174#893—61no—
175#893C2×D311yescharacteristic
176D3×C4⋊C4—31no—
177D3×C4⋊C4—31no—
178D3×C4⋊C4—61no—
179D3×C4⋊C4—61no—
180#888C2×D311yescharacteristic
181#887—31no—
182#887—31no—
183#887—61no—
184#887—61no—
185#885—61no—
186#884—61no—
187#874—31no—
188C4×D12—31no—
189C42×D3—31no—
190C42×D3—31no—
191C42×D3—61no—
192C42×D3—61no—
193C4×Dic6—31no—
194C4×Dic6—31no—
195C4×Dic6—61no—
196C4×Dic6—61no—
197C3×#106—31no—
198C3×#106—31no—
199C3×#106—31no—
200C3×C4⋊C8—31no—
201C3×#103—21no—
202C3×#103—31no—
203C3×#103C2×D311yescharacteristic
204C3×#103C2×D311yescharacteristic
205C3×#102—31no—
206C3×C4×C8—31no—
207#835C2×D311yescharacteristic
208#832—31no—
209#821—31no—
210#821—31no—
211#821C2×D311yescharacteristic
212(C2×D3)⋊C8—31no—
213(C2×D3)⋊C8—31no—
214(C2×D3)⋊C8—31no—
215(C2×D3)⋊C8—31no—
216(C2×D3)⋊C8—61no—
217#817C2×D311yescharacteristic
218#816—31no—
219Dic3⋊C8—31no—
220Dic3⋊C8C2×D311yescharacteristic
221C8×Dic3—31no—
222C8×Dic3C2×D311yescharacteristic
223#810—31no—
224#810—31no—
225#810—31no—
226#810—61no—
227#809—31no—
228#809—31no—
229#809—31no—
230#808—31no—
231#808—31no—
232#808C2×D311yescharacteristic
233#808C2×D311yescharacteristic
234C4⋊(C3⋊C8)—31no—
235C4×C3⋊C8—31no—
236C22×C3⋊D3—21no—
237C22×C3⋊D3C2×D411yescharacteristic
238C22×C3×D3—21no—
239C32×Q8—21no—
240C32×Q8#4112yescomplemented
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4C2411yescharacteristic
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3C2×D411yescharacteristic
246C4⋊(C3⋊D3)—21no—
247C4⋊(C3⋊D3)—21no—
248C4⋊(C3⋊D3)—42no—
249C4×C3⋊D3—24no—
250C4×C3⋊D3—21no—
251C4×C3⋊D3—21no—
252#634—24no—
253#634—21no—
254#634#4112yescomplemented
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—21no—
263C3×D12—21no—
264C3×C4×D3—42no—
265C3×Dic6—42no—
266#626—42no—
267#626—42no—
268#626—42no—
269#624—41no—
270#624—42no—
271#624—42no—
272#624SD1614yescomplemented
273C32×C8—21no—
274C3⋊(C3⋊C8)—21no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277#532—91no—
278C2×C4×Q8—91no—
279#481—91no—
280#481—91no—
281#475—31no—
282#475—91no—
283#460—91no—
284#460—91no—
285#448—91no—
286#448—91no—
287C4×SD16—31no—
288C4×SD16—91no—
289C4×SD16—91no—
290C4×SD16—91no—
291#431—91no—
292C2×C3×Q8—21no—
293C2×C3×Q8—61no—
294C2×C3×Q8C22×D311yescharacteristic
295C2×C3×Q8C22×D311yescharacteristic
296C2×C3×D4—31no—
297C22×C3×C4—61no—
298C2×#67—61no—
299C2×#67—61no—
300C2×#67—61no—
301#239—124no—
302D3×Q8—62no—
303D3×Q8—62no—
304D3×Q8—62no—
305D3×Q8—62no—
306D3×Q8—122no—
307D3×Q8—122no—
308#235—124no—
309C2×D12—31no—
310C2×D12—31no—
311C2×D12—61no—
312C2×D12—61no—
313C2×D12—61no—
314C2×D12—61no—
315C2×D12—61no—
316C2×D12—61no—
317C2×D12—121no—
318C2×D12C22×D311yescharacteristic
319C2×C4×D3—21no—
320C2×C4×D3—31no—
321C2×C4×D3—31no—
322C2×C4×D3—31no—
323C2×C4×D3—31no—
324C2×C4×D3—31no—
325C2×C4×D3—31no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—121no—
334C2×Dic6—21no—
335C2×Dic6—31no—
336C2×Dic6—31no—
337C2×Dic6—61no—
338C2×Dic6—61no—
339C2×Dic6—61no—
340C2×Dic6—121no—
341C3×SD16—62no—
342C2×C3×C8—21no—
343C2×C3×C8—31no—
344C2×C3×C8—31no—
345C2×C3×C8C22×D311yescharacteristic
346C2×C3×C8C22×D311yescharacteristic
347C3×C4⋊C4—21no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C22⋊C4—61no—
357C3×C42—31no—
358C3×C42—31no—
359C3×C42—61no—
360C3×C42—61no—
361#217—61no—
362#215—22no—
363#215—62no—
364#215—62no—
365#215—122no—
366#214—62no—
367(C2×D3)⋊C4—21no—
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—121no—
374C4⋊Dic3—21no—
375C4⋊Dic3—21no—
376C4⋊Dic3C22×D311yescharacteristic
377C4⋊Dic3C22×D311yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
379Dic3⋊C4—21no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386C4×Dic3—21no—
387C4×Dic3—21no—
388C4×Dic3—31no—
389C4×Dic3—31no—
390C4×Dic3—31no—
391C4×Dic3—31no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3C22×D311yescharacteristic
397C4×Dic3C22×D311yescharacteristic
398C2×C3⋊C8—31no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—61no—
401C2×C3⋊C8C22×D311yescharacteristic
402C2×C3⋊C8C22×D311yescharacteristic
403#204—62no—
404#204—62no—
405#204—62no—
406#204—122no—
407C22×C32C22×D411yescharacteristic
408C2×C3⋊D3—21no—
409C2×C3⋊D3—21no—
410C2×C3⋊D3—41no—
411C2×C3⋊D3—41no—
412C2×C3⋊D3—41no—
413C2×C3⋊D3C2×SD1612yes—
414C2×C3×D3—41no—
415C2×C3×D3—41no—
416C2×C3×D3—41no—
417C32×C4—22no—
418C32×C4—41no—
419C32×C4C2×#4111yescharacteristic
420C32×C4C2×#4111yescharacteristic
421C3⋊Dic3—21no—
422C3⋊Dic3—22no—
423C3×Dic3—21no—
424C3×Dic3—21no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3C2×SD1612yes—
429C3×Dic3C2×SD1612yes—
430C2×#41—181no—
431C22×Q8—91no—
432C2×SD16—31no—
433C2×SD16—91no—
434C2×SD16—91no—
435C2×SD16—91no—
436C4⋊Q8—31no—
437#127—91no—
438#124—181no—
439#121—91no—
440#121—91no—
441#121—181no—
442C4×Q8—31no—
443C4×Q8—31no—
444C4×Q8—91no—
445C4×Q8—91no—
446C4×Q8—181no—
447C4×Q8—181no—
448C4×D4—31no—
449C4×D4—91no—
450C4×D4—181no—
451C2×C4⋊C4—91no—
452C2×C4⋊C4—181no—
453C2×C42—91no—
454C2×C42—181no—
455#106—31no—
456#106—31no—
457#106—31no—
458#106—91no—
459C4⋊C8—31no—
460C4⋊C8—91no—
461#103—31no—
462#103—91no—
463#103—91no—
464#103D3211yescharacteristic
465#102—31no—
466#102—91no—
467#102—91no—
468#102—91no—
469C22⋊C8—91no—
470C22⋊C8—91no—
471C4×C8—31no—
472C4×C8—91no—
473C23×C3—61no—
474C22×D3—21no—
475C22×D3—31no—
476C22×D3—31no—
477C22×D3—61no—
478C22×D3—61no—
479C22×D3—61no—
480C22×D3—121no—
481C3×Q8—21no—
482C3×Q8—21no—
483C3×Q8—22no—
484C3×Q8—41no—
485C3×Q8—122no—
486C3×Q8#23512yescomplemented
487C3×Q8#23912yescomplemented
488C3×D4—61no—
489C3×D4—61no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—31no—
496C2×C3×C4—31no—
497C2×C3×C4—31no—
498C2×C3×C4—31no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—122no—
505C2×C3×C4C23×D311yescharacteristic
506C2×C3×C4C23×D311yescharacteristic
507#67—122no—
508#67—122no—
509#67—122no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—31no—
514C2×Dic3—31no—
515C2×Dic3—61no—
516C2×Dic3—61no—
517C2×Dic3—61no—
518C2×Dic3—121no—
519C2×Dic3D3×D411yescharacteristic
520C2×Dic3D3×D411yescharacteristic
521C2×Dic3D3×D411yescharacteristic
522C2×Dic3D3×D411yescharacteristic
523D12—21no—
524D12—21no—
525D12—61no—
526D12—61no—
527D12—61no—
528D12—61no—
529D12—121no—
530D12—121no—
531D12—122no—
532D12—122no—
533D12—122no—
534D12—122no—
535D12—122no—
536D12—242no—
537C4×D3—34no—
538C4×D3—34no—
539C4×D3—42no—
540C4×D3—64no—
541C4×D3—64no—
542C4×D3—61no—
543C4×D3—61no—
544C4×D3—61no—
545C4×D3—61no—
546C4×D3—121no—
547C4×D3—121no—
548C4×D3—124no—
549C4×D3—121no—
550C4×D3—121no—
551C4×D3—122no—
552C4×D3—122no—
553C4×D3—122no—
554C4×D3—122no—
555Dic6—32no—
556Dic6—32no—
557Dic6—42no—
558Dic6—62no—
559Dic6—64no—
560Dic6—64no—
561Dic6—61no—
562Dic6—61no—
563Dic6—121no—
564Dic6—124no—
565C3×C8—21no—
566C3×C8—21no—
567C3×C8—41no—
568C3×C8—61no—
569C3×C8—61no—
570C3⋊C8—21no—
571C3⋊C8—21no—
572C3⋊C8—61no—
573C3⋊C8—61no—
574C3⋊C8—121no—
575C2×C32#52511yescharacteristic
576C2×C32C22×SD1611yescharacteristic
577C2×C32#57511yescharacteristic
578C3⋊D3—22no—
579C3⋊D3—81no—
580C3×D3—81no—
581#41—364no—
582C2×Q8—61no—
583C2×Q8—91no—
584C2×Q8—181no—
585C2×Q8—182no—
586C2×Q8—182no—
587C2×Q8C2×D3211yescharacteristic
588C2×D4—31no—
589C2×D4—91no—
590C2×D4—181no—
591C2×D4—181no—
592C2×D4—181no—
593C2×D4—181no—
594C22×C4—61no—
595C22×C4—91no—
596C22×C4—91no—
597C22×C4—91no—
598C22×C4—181no—
599C22×C4—181no—
600C22×C4—181no—
601SD16—62no—
602SD16—182no—
603SD16—182no—
604SD16—182no—
605C2×C8—31no—
606C2×C8—31no—
607C2×C8—91no—
608C2×C8C2×D3211yescharacteristic
609C4⋊C4—31no—
610C4⋊C4—31no—
611C4⋊C4—31no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4—61no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C4⋊C4—181no—
618C4⋊C4C2×D3211yescharacteristic
619C22⋊C4—61no—
620C22⋊C4—181no—
621C22⋊C4—181no—
622C22⋊C4—181no—
623C42—31no—
624C42—31no—
625C42—61no—
626C42—61no—
627C42—91no—
628C42—91no—
629C42—181no—
630C42—181no—
631C22×C3—21no—
632C22×C3—121no—
633C22×C3—121no—
634C22×C3—121no—
635C22×C3C2×D3×D411yescharacteristic
636C22×C3C2×D3×D411yescharacteristic
637C2×D3—32no—
638C2×D3—32no—
639C2×D3—41no—
640C2×D3—41no—
641C2×D3—41no—
642C2×D3—62no—
643C2×D3—61no—
644C2×D3—61no—
645C2×D3—61no—
646C2×D3—61no—
647C2×D3—121no—
648C2×D3—121no—
649C2×D3—121no—
650C2×D3—121no—
651C2×D3—121no—
652C2×D3—121no—
653C2×D3—121no—
654C2×D3—121no—
655C2×D3—241no—
656C2×D3—241no—
657C2×D3—241no—
658C3×C4—22no—
659C3×C4—22no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—32no—
663C3×C4—32no—
664C3×C4—42no—
665C3×C4—41no—
666C3×C4—41no—
667C3×C4—61no—
668C3×C4—61no—
669C3×C4—81no—
670C3×C4—121no—
671C3×C4—121no—
672C3×C4—121no—
673C3×C4C2×#23511yescharacteristic
674C3×C4C2×#23911yescharacteristic
675C3×C4D3×#4111yescharacteristic
676C3×C4D3×#4111yescharacteristic
677Dic3—21no—
678Dic3—21no—
679Dic3—41no—
680Dic3—41no—
681Dic3—41no—
682Dic3—62no—
683Dic3—61no—
684Dic3—62no—
685Dic3—61no—
686Dic3—122no—
687Dic3—121no—
688Dic3D3×SD1612yes—
689Dic3D3×SD1612yes—
690C32#310311yescharacteristic, complemented, Sylow
691C23—61no—
692C23—91no—
693C23—181no—
694Q8—21no—
695Q8—92no—
696Q8—122no—
697Q8—184no—
698Q8—181no—
699Q8#379912yescomplemented
700D4—61no—
701D4—61no—
702D4—181no—
703D4—181no—
704D4—362no—
705D4—362no—
706D4—362no—
707D4—362no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—31no—
711C2×C4—31no—
712C2×C4—31no—
713C2×C4—31no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—94no—
718C2×C4—91no—
719C2×C4—122no—
720C2×C4—184no—
721C2×C4—181no—
722C2×C4—181no—
723C2×C4—181no—
724C2×C4—362no—
725C2×C4—361no—
726C2×C4—362no—
727C2×C4C22×D3211yescharacteristic
728C8—21no—
729C8—61no—
730C8—61no—
731C8—181no—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—241no—
736C2×C3#554711yescharacteristic
737C2×C3#562711yescharacteristic
738C2×C3C2×D3×SD1611yescharacteristic
739C2×C3C2×D3×SD1611yescharacteristic
740C2×C3#576811yescharacteristic
741C2×C3#577711yescharacteristic
742D3—62no—
743D3—62no—
744D3—81no—
745D3—122no—
746D3—241no—
747D3—241no—
748D3—481no—
749C22—92no—
750C22—121no—
751C22—121no—
752C22—121no—
753C22—181no—
754C22—181no—
755C22—361no—
756C22—361no—
757C22—361no—
758C22D32×D411yescharacteristic
759C4—22no—
760C4—32no—
761C4—32no—
762C4—41no—
763C4—61no—
764C4—61no—
765C4—121no—
766C4—121no—
767C4—121no—
768C4—181no—
769C4—182no—
770C4C2×#379911yescharacteristic
771C4#6431211yescharacteristic
772C3—21no—
773C3#7965311yescharacteristic, complemented
774C3#8099611yescharacteristic, complemented
775C2—182no—
776C2—241no—
777C2—721no—
778C2#1059406611yescharacteristic
779C2D32×SD1611yescharacteristic
780C2#1059476311yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#10594518C2
hypercenter#103D32
hypocenterC32#3103
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. Q8×#624C2semidirect
3. #10592505C2semidirect
4. C3×#4791C2semidirect
5. C3×#4788C2semidirect
6. #10591617C2semidirect
7. #10591592C2semidirect
8. #10591536C2semidirect
9. #10590879C2semidirect
10. #10590758C2semidirect
11. #10590649C2semidirect
12. #10590643C2semidirect
13. #10590487C2semidirect
14. #10590479C2semidirect
15. #10590445C2semidirect
85. #4791D3semidirect
87. #4788D3semidirect
240. C32×Q8#41semidirect
254. #634#41semidirect
272. #624SD16semidirect
486. C3×Q8#235semidirect
487. C3×Q8#239semidirect
690. C32#3103semidirect
699. Q8#3799semidirect
773. C3#79653semidirect
774. C3#80996semidirect

Maximal subgroups

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

subgroupindex
Q8×#6242
#105945182
#105925052
C3×#47912
C3×#47882
#105916172
#105915922
#105915362
#105908792
#105907582
#105906492
#105906432
#105904872
#105904792
#105904452
#809963
#796533