Finite Group Databasebeta

← #11887531

Subgroups — #11887531

Order 1152.

888 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#625C211yesmaximal, characteristic, complemented
2#10594370C211yesmaximal, characteristic
3#10592490C211yesmaximal, characteristic, complemented
4C3×#4806C211yesmaximal, characteristic, complemented
5C3×D3×#103C211yesmaximal, characteristic, complemented
6#10591583C211yesmaximal, characteristic, complemented
7#10591571C211yesmaximal, characteristic, complemented
8D3×#835C211yesmaximal, characteristic, complemented
9#10590829C211yesmaximal, characteristic, complemented
10#10590748C211yesmaximal, characteristic, complemented
11#10590717C211yesmaximal, characteristic, complemented
12#10590675C211yesmaximal, characteristic, complemented
13#10590567C211yesmaximal, characteristic, complemented
14#10590516C211yesmaximal, characteristic, complemented
15#10590514C211yesmaximal, characteristic, complemented
16#80049—31nomaximal
17#78805—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×#3795—21no—
21Q8×C3⋊Dic3C2211yescharacteristic
22#64097C2211yescharacteristic
23C2×C3×#215C2211yescharacteristic
24C2×C3×#204C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic
26C3×#895C2211yescharacteristic
27C3×D3×C4⋊C4C2211yescharacteristic
28#63908C2211yescharacteristic
29#63905—21no—
30C4×#625—21no—
31C4×#625C2211yescharacteristic
32#63898C2211yescharacteristic
33#63896—21no—
34D3×C4⋊Dic3C2211yescharacteristic
35#63884—21no—
36#63873—21no—
37#63873C2211yescharacteristic
38#63856—21no—
39#63856—21no—
40#63856C2211yescharacteristic
41#63856C2211yescharacteristic
42C2×#3715C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44C32×#103C2211yescharacteristic
45#63662C2211yescharacteristic
46#63644C2211yescharacteristic
47#63641C2211yescharacteristic
48#63635C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#810C2211yescharacteristic
54#63573C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63563C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63553C2211yescharacteristic
61Q8×#67—31no—
62Q8×#67—31no—
63#5611—31no—
64#5507—31no—
65C3×#448—31no—
66C2×C3×#103—31no—
67#5227—31no—
68C2×#835—31no—
69#5171—31no—
70#5170—31no—
71#5162—31no—
72Dic3×SD16—31no—
73#5114—31no—
74C8×#67—31no—
75#5041—31no—
76#4971—31no—
77#4818—31no—
78#4807—31no—
79#4806D311yescharacteristic, complemented
80#4805—31no—
81#4805—31no—
82D3×#103—31no—
83D3×#103D311yescharacteristic, complemented
84#4792—31no—
85#4792—31no—
86#4791—31no—
87#4791—31no—
88#4791—61no—
89#4788—31no—
90#67⋊C8—31no—
91#4721—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×#634—21no—
94C3×D3×Q8—22no—
95C3×D3×Q8—22no—
96C3×D3×Q8—41no—
97C3×D3×Q8—41no—
98C2×C3×D12—21no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6—21no—
106C2×C3×Dic6—21no—
107C2×C3×Dic6C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×#625—21no—
110C2×#625D411yescharacteristic
111C2×D3×Dic3—21no—
112C2×D3×Dic3—21no—
113#3795—44no—
114C2×C32×C8C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C4⋊(C3⋊Dic3)—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119#3750—21no—
120C4×C3⋊Dic3—21no—
121C4×C3⋊Dic3C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C3×#215—22no—
124C3×(C2×D3)⋊C4—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×#204—41no—
130C3×D3×C8—41no—
131#3724—21no—
132#3724—21no—
133#3724—21no—
134#3724—21no—
135#3724D411yescharacteristic
136Dic3⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3D411yescharacteristic
142(C2×D3)⋊Dic3D411yescharacteristic
143#3715—41no—
144D3×C3⋊C8—41no—
145#3298—91noSylow
146C22×C3×Q8—31no—
147C22×C3×Q8—31no—
148C2×D3×Q8C2×D311yescharacteristic
149C2×D3×Q8C2×D311yescharacteristic
150C2×#237—61no—
151C2×#235—61no—
152C2×C3×SD16—31no—
153C2×C3×SD16—31no—
154C22×C3×C8—31no—
155C3×#121—31no—
156C2×C3×C4⋊C4—31no—
157#946—31no—
158#946—31no—
159#946—61no—
160#946—61no—
161Q8×Dic3—31no—
162Q8×Dic3—31no—
163Q8×Dic3—61no—
164#944—31no—
165#944—31no—
166#944—61no—
167#944—61no—
168C2×#215—31no—
169C2×#215C2×D311yescharacteristic
170#938—31no—
171#935—61no—
172D4×Dic3—31no—
173C2×#214—31no—
174#930—31no—
175#929—61no—
176C4×#67—31no—
177C4×#67—31no—
178C4×#67—61no—
179C4×#67—61no—
180C2×C4⋊Dic3—31no—
181#924—31no—
182#924—31no—
183#924—61no—
184#924—61no—
185C22×C3⋊C8—31no—
186C2×#204C2×D311yescharacteristic
187C2×D3×C8—31no—
188C2×D3×C8C2×D311yescharacteristic
189#896—61no—
190#895C2×D311yescharacteristic
191#894—61no—
192#893—31no—
193D3×C4⋊C4—31no—
194D3×C4⋊C4C2×D311yescharacteristic
195#888—31no—
196#888—31no—
197#888—61no—
198#883—61no—
199#878—61no—
200C3×#103—21no—
201C3×#103—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#103C2×D311yescharacteristic
206C3×#103C2×D311yescharacteristic
207C3×C22⋊C8—31no—
208#835—31no—
209#835—31no—
210#835—31no—
211#835—31no—
212#835—31no—
213#835—61no—
214#835C2×D311yescharacteristic
215#832—31no—
216#830—31no—
217#821—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8C2×D311yescharacteristic
220#817—31no—
221#817—31no—
222#817—31no—
223#817—61no—
224#816—31no—
225#816—31no—
226#816C2×D311yescharacteristic
227Dic3⋊C8—31no—
228Dic3⋊C8—31no—
229Dic3⋊C8—61no—
230C8×Dic3—31no—
231C8×Dic3—31no—
232#810—31no—
233#810C2×D311yescharacteristic
234#810C2×D311yescharacteristic
235#808—31no—
236#808—31no—
237#808—31no—
238#808—61no—
239C22×C3×D3—21no—
240C22×C3×D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C32×Q8—21no—
243C32×Q8#4112yescomplemented
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2411yescharacteristic
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3C2×D411yescharacteristic
250C2×C3⋊Dic3C2×D411yescharacteristic
251#634—42no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C3×D12—21no—
258C3×D12—21no—
259C3×D12—42no—
260C3×C4×D3—21no—
261C3×C4×D3—21no—
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×C4×D3—42no—
265C3×C4×D3—42no—
266C3×C4×D3—42no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6—42no—
272C3×Dic6—42no—
273#625—42no—
274#625SD1614yescomplemented
275D3×Dic3—42no—
276D3×Dic3—42no—
277C32×C8—21no—
278C3⋊(C3⋊C8)—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281D4×Q8—91no—
282#547—91no—
283#487—91no—
284#483—91no—
285#483—91no—
286#475—91no—
287#465—91no—
288#465—91no—
289#461—91no—
290#448—31no—
291#448—91no—
292C4×SD16—91no—
293C8×D4—91no—
294C2×#103—31no—
295C2×#103—91no—
296C2×C3×Q8—21no—
297C2×C3×Q8—31no—
298C2×C3×Q8—31no—
299C2×C3×Q8—61no—
300C2×C3×Q8—61no—
301C2×C3×Q8—62no—
302C2×C3×Q8—62no—
303C2×C3×Q8—121no—
304C2×C3×Q8—121no—
305C2×C3×Q8C22×D311yescharacteristic
306C2×C3×Q8C22×D311yescharacteristic
307C2×C3×D4—31no—
308C2×C3×D4—61no—
309C22×C3×C4—31no—
310C22×C3×C4—31no—
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C2×#67—31no—
315C2×#67—31no—
316C2×#67—61no—
317C2×#67—61no—
318C22×Dic3—61no—
319C22×Dic3—61no—
320D3×Q8—22no—
321D3×Q8—22no—
322D3×Q8—41no—
323D3×Q8—41no—
324#237—124no—
325#235—124no—
326C2×D12—21no—
327C2×D12C22×D311yescharacteristic
328C2×C4×D3—21no—
329C2×C4×D3—21no—
330C2×C4×D3—21no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3C22×D311yescharacteristic
334C2×C4×D3C22×D311yescharacteristic
335C2×Dic6—21no—
336C2×Dic6—21no—
337C2×Dic6—61no—
338C2×Dic6—61no—
339C2×Dic6—121no—
340C2×Dic6C22×D311yescharacteristic
341C2×Dic6C22×D311yescharacteristic
342C3×SD16—62no—
343C3×SD16—121no—
344C2×C3×C8—21no—
345C2×C3×C8—31no—
346C2×C3×C8—31no—
347C2×C3×C8—121no—
348C2×C3×C8C22×D311yescharacteristic
349C2×C3×C8C22×D311yescharacteristic
350C3×C4⋊C4—21no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C22⋊C4—61no—
356#217—31no—
357#217—31no—
358#217—61no—
359#217—61no—
360#217—61no—
361#217—61no—
362#215—22no—
363#215—121no—
364#214—121no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—31no—
367(C2×D3)⋊C4—31no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372C4⋊Dic3—31no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—121no—
382C4⋊Dic3C22×D311yescharacteristic
383Dic3⋊C4—21no—
384Dic3⋊C4—31no—
385Dic3⋊C4—31no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—121no—
398C4×Dic3—31no—
399C4×Dic3—31no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—121no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8—121no—
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410#204—41no—
411D3×C8—41no—
412D3×C8—121no—
413C22×C32C22×D411yescharacteristic
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—41no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3C2×SD1612yes—
422C2×C3×D3C2×SD1612yes—
423C32×C4—22no—
424C32×C4—41no—
425C32×C4C2×#4111yescharacteristic
426C32×C4H(5,𝔽2)11yescharacteristic
427C3⋊Dic3—21no—
428C3⋊Dic3—41no—
429C3⋊Dic3—41no—
430C3⋊Dic3C2×SD1612yes—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C2×#41—181no—
437C22×Q8—31no—
438C22×Q8—31no—
439C2×SD16—31no—
440C2×SD16—31no—
441C2×SD16—91no—
442C22×C8—31no—
443C22×C8—91no—
444C4⋊Q8—91no—
445C4⋊Q8—91no—
446C4⋊Q8—181no—
447#123—181no—
448#123—181no—
449C22⋊Q8—91no—
450C22⋊Q8—91no—
451C22⋊Q8—181no—
452C22⋊Q8—181no—
453C22⋊Q8—181no—
454#121—31no—
455#121—91no—
456C4×Q8—91no—
457C4×D4—91no—
458C4×D4—91no—
459C4×D4—181no—
460C2×C4⋊C4—31no—
461C2×C4⋊C4—91no—
462#106—91no—
463#106—91no—
464#106—91no—
465C4⋊C8—91no—
466#103—31no—
467#103—31no—
468#103—31no—
469#103—31no—
470#103—91no—
471#103—91no—
472#103—91no—
473#103—91no—
474#103D3211yescharacteristic
475#102—91no—
476C22⋊C8—31no—
477C22⋊C8—91no—
478C4×C8—91no—
479C23×C3—31no—
480C23×C3—31no—
481C23×C3—61no—
482C22×D3—21no—
483C22×D3D3×D411yescharacteristic
484C22×D3D3×D411yescharacteristic
485C3×Q8—21no—
486C3×Q8—21no—
487C3×Q8—22no—
488C3×Q8—41no—
489C3×Q8—61no—
490C3×Q8—61no—
491C3×Q8—61no—
492C3×Q8—61no—
493C3×Q8—122no—
494C3×Q8—122no—
495C3×Q8#23512yescomplemented
496C3×Q8#23712yescomplemented
497C3×D4—61no—
498C3×D4—61no—
499C3×D4—122no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—122no—
517C2×C3×C4—122no—
518C2×C3×C4—122no—
519C2×C3×C4C23×D311yescharacteristic
520C2×C3×C4C23×D311yescharacteristic
521#67—34no—
522#67—34no—
523#67—122no—
524#67—122no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—31no—
529C2×Dic3—31no—
530C2×Dic3—31no—
531C2×Dic3—31no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—121no—
539C2×Dic3—121no—
540C2×Dic3—122no—
541C2×Dic3—122no—
542C2×Dic3D3×D411yescharacteristic
543C2×Dic3D3×D411yescharacteristic
544D12—21no—
545D12—21no—
546D12—42no—
547C4×D3—21no—
548C4×D3—21no—
549C4×D3—21no—
550C4×D3—21no—
551C4×D3—42no—
552C4×D3—42no—
553C4×D3—42no—
554C4×D3—122no—
555C4×D3—122no—
556Dic6—21no—
557Dic6—21no—
558Dic6—21no—
559Dic6—21no—
560Dic6—42no—
561Dic6—42no—
562Dic6—122no—
563Dic6—122no—
564Dic6—242no—
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#54611yescharacteristic
576C2×C32C22×SD1611yescharacteristic
577C2×C32#57811yescharacteristic
578C3×D3—22no—
579C3×D3—22no—
580C3×D3—81no—
581#41—364no—
582C2×Q8—31no—
583C2×Q8—31no—
584C2×Q8—61no—
585C2×Q8—61no—
586C2×Q8—62no—
587C2×Q8—62no—
588C2×Q8—121no—
589C2×Q8—121no—
590C2×Q8—181no—
591C2×Q8C2×D3211yescharacteristic
592C2×D4—31no—
593C2×D4—61no—
594C2×D4—91no—
595C2×D4—181no—
596C22×C4—31no—
597C22×C4—31no—
598C22×C4—61no—
599C22×C4—61no—
600C22×C4—61no—
601C22×C4—181no—
602C22×C4—181no—
603SD16—62no—
604SD16—121no—
605SD16—361no—
606C2×C8—31no—
607C2×C8—31no—
608C2×C8—91no—
609C2×C8—121no—
610C2×C8—361no—
611C2×C8C2×D3211yescharacteristic
612C4⋊C4—31no—
613C4⋊C4—61no—
614C4⋊C4—91no—
615C4⋊C4—91no—
616C4⋊C4—91no—
617C4⋊C4—181no—
618C4⋊C4—181no—
619C4⋊C4—181no—
620C4⋊C4—181no—
621C4⋊C4—181no—
622C4⋊C4—181no—
623C4⋊C4—181no—
624C4⋊C4C2×D3211yescharacteristic
625C22⋊C4—61no—
626C22⋊C4—91no—
627C22⋊C4—91no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C42—91no—
633C42—181no—
634C22×C3—21no—
635C22×C3—32no—
636C22×C3—32no—
637C22×C3—61no—
638C22×C3—61no—
639C22×C3—61no—
640C22×C3—61no—
641C22×C3—121no—
642C22×C3—121no—
643C22×C3—121no—
644C22×C3C2×D3×D411yescharacteristic
645C22×C3C2×D3×D411yescharacteristic
646C2×D3—21no—
647C2×D3—21no—
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—41no—
651C2×D3—41no—
652C2×D3—41no—
653C2×D3D3×SD1612yes—
654C2×D3D3×SD1612yes—
655C3×C4—22no—
656C3×C4—22no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—42no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—61no—
663C3×C4—61no—
664C3×C4—81no—
665C3×C4—121no—
666C3×C4—121no—
667C3×C4—121no—
668C3×C4C2×#23511yescharacteristic
669C3×C4C2×#23711yescharacteristic
670C3×C4#100411yescharacteristic
671C3×C4#100411yescharacteristic
672Dic3—21no—
673Dic3—21no—
674Dic3—32no—
675Dic3—32no—
676Dic3—41no—
677Dic3—41no—
678Dic3—41no—
679Dic3—62no—
680Dic3—61no—
681Dic3—61no—
682Dic3—121no—
683Dic3—121no—
684Dic3—121no—
685Dic3—121no—
686Dic3—121no—
687Dic3—241no—
688Dic3—241no—
689C32#329811yescharacteristic, complemented, Sylow
690C23—31no—
691C23—31no—
692C23—61no—
693Q8—21no—
694Q8—61no—
695Q8—61no—
696Q8—61no—
697Q8—61no—
698Q8—122no—
699Q8—122no—
700Q8—362no—
701Q8#379512yescomplemented
702D4—61no—
703D4—61no—
704D4—94no—
705D4—122no—
706D4—362no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—31no—
710C2×C4—31no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—91no—
719C2×C4—91no—
720C2×C4—122no—
721C2×C4—122no—
722C2×C4—122no—
723C2×C4—181no—
724C2×C4—181no—
725C2×C4—362no—
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—62no—
736C2×C3—62no—
737C2×C3—241no—
738C2×C3#549011yescharacteristic
739C2×C3#559111yescharacteristic
740C2×C3C2×D3×SD1611yescharacteristic
741C2×C3C2×D3×SD1611yescharacteristic
742C2×C3#576611yescharacteristic
743C2×C3#577911yescharacteristic
744D3—22no—
745D3—22no—
746D3—81no—
747C22—32no—
748C22—32no—
749C22—61no—
750C22—61no—
751C22—61no—
752C22—61no—
753C22—121no—
754C22—121no—
755C22—121no—
756C22D32×D411yescharacteristic
757C4—22no—
758C4—41no—
759C4—61no—
760C4—61no—
761C4—92no—
762C4—121no—
763C4—121no—
764C4—121no—
765C4—181no—
766C4—361no—
767C4—361no—
768C4C2×#379511yescharacteristic
769C4#6431311yescharacteristic
770C3—21no—
771C3#7880511yescharacteristic, complemented
772C3#8004911yescharacteristic, complemented
773C2—62no—
774C2—62no—
775C2—241no—
776C2#1059418411yescharacteristic
777C2D32×SD1611yescharacteristic
778C2#1059476611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#10594370C2
hypercenter#103D32
hypocenterC32#3298
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×#625C2semidirect
3. #10592490C2semidirect
4. C3×#4806C2semidirect
5. C3×D3×#103C2semidirect
6. #10591583C2semidirect
7. #10591571C2semidirect
8. D3×#835C2semidirect
9. #10590829C2semidirect
10. #10590748C2semidirect
11. #10590717C2semidirect
12. #10590675C2semidirect
13. #10590567C2semidirect
14. #10590516C2semidirect
15. #10590514C2semidirect
79. #4806D3semidirect
83. D3×#103D3semidirect
243. C32×Q8#41semidirect
274. #625SD16semidirect
495. C3×Q8#235semidirect
496. C3×Q8#237semidirect
689. C32#3298semidirect
701. Q8#3795semidirect
771. C3#78805semidirect
772. C3#80049semidirect

Maximal subgroups

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

subgroupindex
Q8×#6252
#105943702
#105924902
C3×#48062
C3×D3×#1032
#105915832
#105915712
D3×#8352
#105908292
#105907482
#105907172
#105906752
#105905672
#105905162
#105905142
#800493
#788053