Finite Group Databasebeta

← #11887575

Subgroups — #11887575

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
1#10594526C211yesmaximal, characteristic, complemented
2#10594370C211yesmaximal, characteristic
3#10592553C211yesmaximal, characteristic, complemented
4C3×#4864C211yesmaximal, characteristic, complemented
5C3×#4862C211yesmaximal, characteristic, complemented
6#10590822C211yesmaximal, characteristic, complemented
7#10590748C211yesmaximal, characteristic, complemented
8#10590717C211yesmaximal, characteristic, complemented
9D3×#816C211yesmaximal, characteristic, complemented
10#10590603C211yesmaximal, characteristic, complemented
11D3×#810C211yesmaximal, characteristic, complemented
12#10590567C211yesmaximal, characteristic, complemented
13#10590501C211yesmaximal, characteristic, complemented
14#10590460C211yesmaximal, characteristic, complemented
15#10590439C211yesmaximal, characteristic, complemented
16#81450—31nomaximal
17#80689—31nomaximal
18C2×#3795—21no—
19C2×D3×Dic6C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21#64097C2211yescharacteristic
22#64096C2211yescharacteristic
23C2×C3×#204C2211yescharacteristic
24C2×C3×D3×C8C2211yescharacteristic
25C3×#897C2211yescharacteristic
26C3×#897C2211yescharacteristic
27C3×#895C2211yescharacteristic
28C3×D3×C4⋊C4C2211yescharacteristic
29#63919—21no—
30#63908C2211yescharacteristic
31#63905—21no—
32#63902—21no—
33C4×#625C2211yescharacteristic
34#63899—21no—
35#63899—21no—
36#63898C2211yescharacteristic
37#63896—21no—
38D3×C4⋊Dic3C2211yescharacteristic
39#63884—21no—
40#63873C2211yescharacteristic
41C2×#3716C2211yescharacteristic
42C2×#3715C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44C32×#106C2211yescharacteristic
45#63643C2211yescharacteristic
46#63641C2211yescharacteristic
47#63637C2211yescharacteristic
48#63635C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#809C2211yescharacteristic
54C3×#808C2211yescharacteristic
55#63567C2211yescharacteristic
56#63566C2211yescharacteristic
57#63566C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63553C2211yescharacteristic
61#5632—31no—
62#5632—31no—
63#5611—31no—
64#5507—31no—
65C3×#483—31no—
66C3×#465—31no—
67#5170—31no—
68#5162—31no—
69C8×#67—31no—
70C2×#816—31no—
71#5048—31no—
72#5043—31no—
73#5040—31no—
74C2×#810—31no—
75#4864D311yescharacteristic, complemented
76#4862—31no—
77#4862D311yescharacteristic, complemented
78#4854—31no—
79#4854—31no—
80#4854—61no—
81#4852—31no—
82#4818—31no—
83#4806—31no—
84D3×#103—31no—
85D3×#103—31no—
86#4792—31no—
87#4792—31no—
88#4778—31no—
89#4758—31no—
90#4738—31no—
91#67⋊C8—31no—
92C2×#634—21no—
93C2×#634C2311yescharacteristic
94C2×C3×D12—21no—
95C2×C3×D12C2311yescharacteristic
96C2×C3×C4×D3—21no—
97C2×C3×C4×D3C2311yescharacteristic
98C2×C3×C4×D3C2311yescharacteristic
99C2×C3×Dic6C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C2×#627—21no—
102C2×#627—21no—
103C2×#625—21no—
104C2×#625D411yescharacteristic
105C2×D3×Dic3—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109#3795—44no—
110D3×Dic6—22no—
111D3×Dic6—22no—
112D3×Dic6—41no—
113D3×Dic6—41no—
114C2×C32×C8C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C32×C4⋊C4C2311yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118#3750—21no—
119#3750—21no—
120C4×C3⋊Dic3—21no—
121C4×C3⋊Dic3C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C3×#204—41no—
133C3×D3×C8—41no—
134#3724—21no—
135#3724—21no—
136#3724D411yescharacteristic
137Dic3⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3D411yescharacteristic
141(C2×D3)⋊Dic3D411yescharacteristic
142#3716—22no—
143#3715—41no—
144D3×C3⋊C8—41no—
145#3298—91noSylow
146C2×D3×Q8—31no—
147C2×D3×Q8—31no—
148C2×#237—61no—
149C2×#235—61no—
150C22×Dic6—31no—
151C22×Dic6—31no—
152C2×C3×SD16—31no—
153C22×C3×C8—31no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—31no—
156C3×#121—31no—
157C2×C3×C4⋊C4—31no—
158#944—31no—
159#944—31no—
160C2×#215—31no—
161#938—31no—
162#935—61no—
163D4×Dic3—31no—
164C2×#214—31no—
165C2×#214—31no—
166#930—31no—
167#929—61no—
168C4×#67—31no—
169C4×#67—31no—
170C2×C4⋊Dic3—31no—
171C22×C3⋊C8—31no—
172C2×#204—31no—
173C2×#204C2×D311yescharacteristic
174C2×D3×C8—31no—
175C2×D3×C8C2×D311yescharacteristic
176#897C2×D311yescharacteristic
177#897C2×D311yescharacteristic
178#896—61no—
179#896—61no—
180#896—61no—
181#895C2×D311yescharacteristic
182#894—61no—
183#893—31no—
184D3×C4⋊C4—31no—
185D3×C4⋊C4C2×D311yescharacteristic
186#888—31no—
187#888—31no—
188#888—61no—
189#888—61no—
190#888—61no—
191#887—31no—
192#887—31no—
193#887—61no—
194#883—61no—
195#67⋊C4—61no—
196#67⋊C4—61no—
197#878—61no—
198#878—61no—
199#878—61no—
200C3×#106—21no—
201C3×#106—31no—
202C3×#106C2×D311yescharacteristic
203C3×#106C2×D311yescharacteristic
204C3×#103—31no—
205C3×#103—31no—
206C3×#103—31no—
207C3×#102—31no—
208C3×C22⋊C8—31no—
209#835—31no—
210#835—31no—
211#835—31no—
212#830—31no—
213(C2×D3)⋊C8—31no—
214(C2×D3)⋊C8C2×D311yescharacteristic
215#816—31no—
216#816—31no—
217#816—31no—
218#816—31no—
219#816—31no—
220#816—61no—
221#816C2×D311yescharacteristic
222Dic3⋊C8—31no—
223Dic3⋊C8—31no—
224Dic3⋊C8—61no—
225C8×Dic3—31no—
226C8×Dic3—31no—
227#810—31no—
228#810—31no—
229#810—31no—
230#810—31no—
231#810—61no—
232#810C2×D311yescharacteristic
233#810C2×D311yescharacteristic
234#809C2×D311yescharacteristic
235#808—31no—
236#808—31no—
237#808—61no—
238#808C2×D311yescharacteristic
239C22×C3×D3—21no—
240C22×C3×D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2411yescharacteristic
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3C2×D411yescharacteristic
248C2×C3⋊Dic3C2×D411yescharacteristic
249#634—21no—
250#634—42no—
251#634#4112yescomplemented
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×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269#627—42no—
270#627—42no—
271#625—42no—
272#625SD1614yescomplemented
273D3×Dic3—42no—
274D3×Dic3—42no—
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—31no—
285#483—91no—
286#475—91no—
287#465—31no—
288#465—91no—
289#461—91no—
290#448—91no—
291#448—91no—
292C4×SD16—91no—
293C8×D4—91no—
294C2×#103—91no—
295C2×#103—91no—
296C2×C3×Q8—31no—
297C2×C3×Q8—31no—
298C2×C3×D4—31no—
299C2×C3×D4—61no—
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—61no—
303C2×#67—31no—
304C2×#67—31no—
305C2×#67—61no—
306C2×#67—61no—
307C22×Dic3—61no—
308C22×Dic3—61no—
309C22×Dic3—61no—
310C22×Dic3—61no—
311D3×Q8—62no—
312D3×Q8—62no—
313D3×Q8—121no—
314D3×Q8—121no—
315#237—124no—
316#235—124no—
317C2×D12—21no—
318C2×D12C22×D311yescharacteristic
319C2×C4×D3—21no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3C22×D311yescharacteristic
325C2×C4×D3C22×D311yescharacteristic
326C2×Dic6—31no—
327C2×Dic6—31no—
328C2×Dic6—61no—
329C2×Dic6—62no—
330C2×Dic6—62no—
331C2×Dic6—61no—
332C2×Dic6—61no—
333C2×Dic6—61no—
334C2×Dic6—61no—
335C2×Dic6—61no—
336C2×Dic6—61no—
337C2×Dic6—121no—
338C2×Dic6—121no—
339C2×Dic6—121no—
340C2×Dic6C22×D311yescharacteristic
341C2×Dic6C22×D311yescharacteristic
342C3×SD16—121no—
343C2×C3×C8—21no—
344C2×C3×C8—31no—
345C2×C3×C8—31no—
346C2×C3×C8—121no—
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C22×D311yescharacteristic
349C3×C4⋊C4—21no—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C4⋊C4C22×D311yescharacteristic
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362#217—31no—
363#217—31no—
364#217—61no—
365#217—61no—
366#215—121no—
367#214—62no—
368#214—121no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—31no—
373(C2×D3)⋊C4—31no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376C4⋊Dic3—21no—
377C4⋊Dic3—21no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
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—121no—
396Dic3⋊C4—121no—
397C4×Dic3—31no—
398C4×Dic3—31no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—121no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8—121no—
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409#204—41no—
410#204—62no—
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—41no—
424C32×C4—41no—
425C32×C4C2×#4111yescharacteristic
426C32×C4H(5,𝔽2)11yescharacteristic
427C3⋊Dic3—22no—
428C3⋊Dic3—21no—
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—91no—
438C22×Q8—91no—
439C2×SD16—31no—
440C2×SD16—91no—
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—31no—
450C22⋊Q8—31no—
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—31no—
463#106—91no—
464#106D3211yescharacteristic
465C4⋊C8—91no—
466#103—31no—
467#103—31no—
468#103—31no—
469#103—91no—
470#103—91no—
471#103—91no—
472#103—91no—
473#103—91no—
474#103—91no—
475#102—31no—
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—61no—
486C3×Q8—61no—
487C3×Q8—61no—
488C3×Q8—61no—
489C3×D4—61no—
490C3×D4—61no—
491C3×D4—122no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
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—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—122no—
509C2×C3×C4C23×D311yescharacteristic
510C2×C3×C4C23×D311yescharacteristic
511#67—34no—
512#67—34no—
513#67—122no—
514#67—122no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—31no—
519C2×Dic3—31no—
520C2×Dic3—31no—
521C2×Dic3—31no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—121no—
529C2×Dic3—121no—
530C2×Dic3—122no—
531C2×Dic3—122no—
532C2×Dic3—122no—
533C2×Dic3—122no—
534C2×Dic3D3×D411yescharacteristic
535C2×Dic3D3×D411yescharacteristic
536D12—21no—
537D12—21no—
538D12—42no—
539C4×D3—21no—
540C4×D3—21no—
541C4×D3—21no—
542C4×D3—21no—
543C4×D3—42no—
544C4×D3—122no—
545C4×D3—122no—
546C4×D3—122no—
547C4×D3—122no—
548Dic6—21no—
549Dic6—21no—
550Dic6—21no—
551Dic6—21no—
552Dic6—32no—
553Dic6—32no—
554Dic6—62no—
555Dic6—61no—
556Dic6—61no—
557Dic6—121no—
558Dic6—122no—
559Dic6—122no—
560Dic6—122no—
561Dic6—122no—
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—91no—
585C2×Q8—181no—
586C2×Q8—181no—
587C2×Q8—181no—
588C2×Q8—182no—
589C2×Q8—182no—
590C2×Q8—361no—
591C2×Q8—361no—
592C2×D4—31no—
593C2×D4—61no—
594C2×D4—91no—
595C2×D4—181no—
596C22×C4—31no—
597C22×C4—31no—
598C22×C4—61no—
599C22×C4—181no—
600C22×C4—181no—
601C22×C4—181no—
602C22×C4—181no—
603SD16—121no—
604SD16—182no—
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—61no—
615C4⋊C4—61no—
616C4⋊C4—91no—
617C4⋊C4—91no—
618C4⋊C4—181no—
619C4⋊C4—181no—
620C4⋊C4—181no—
621C4⋊C4—181no—
622C4⋊C4—181no—
623C4⋊C4C2×D3211yescharacteristic
624C4⋊C4C2×D3211yescharacteristic
625C22⋊C4—61no—
626C22⋊C4—61no—
627C22⋊C4—61no—
628C22⋊C4—91no—
629C22⋊C4—91no—
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—21no—
656C3×C4—21no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—61no—
662C3×C4—61no—
663C3×C4—81no—
664C3×C4—81no—
665C3×C4—121no—
666C3×C4—121no—
667C3×C4—121no—
668C3×C4#100411yescharacteristic
669C3×C4D3×#4111yescharacteristic
670C3×C4D3×#4111yescharacteristic
671C3×C4#100911yescharacteristic
672Dic3—21no—
673Dic3—21no—
674Dic3—32no—
675Dic3—32no—
676Dic3—41no—
677Dic3—41no—
678Dic3—41no—
679Dic3—62no—
680Dic3—62no—
681Dic3—61no—
682Dic3—61no—
683Dic3—62no—
684Dic3—122no—
685Dic3—121no—
686Dic3—121no—
687Dic3—121no—
688Dic3—241no—
689C32#329811yescharacteristic, complemented, Sylow
690C23—31no—
691C23—31no—
692C23—61no—
693Q8—61no—
694Q8—61no—
695Q8—61no—
696Q8—61no—
697Q8—92no—
698Q8—181no—
699Q8—362no—
700Q8—362no—
701Q8—362no—
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—181no—
722C2×C4—181no—
723C2×C4—362no—
724C2×C4—362no—
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#561011yescharacteristic
739C2×C3#565411yescharacteristic
740C2×C3C2×D3×SD1611yescharacteristic
741C2×C3C2×D3×SD1611yescharacteristic
742C2×C3#577111yescharacteristic
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—41no—
758C4—41no—
759C4—61no—
760C4—61no—
761C4—92no—
762C4—121no—
763C4—121no—
764C4—121no—
765C4—182no—
766C4—181no—
767C4—361no—
768C4#6430711yescharacteristic
769C4#6431911yescharacteristic
770C3—21no—
771C3#8068911yescharacteristic, complemented
772C3#8145011yescharacteristic, complemented
773C2—62no—
774C2—62no—
775C2—241no—
776C2#1059461711yescharacteristic
777C2D32×SD1611yescharacteristic
778C2#1059475611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radical#10594370C2
hypercenter#106D32
hypocenterC32#3298
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
1. #10594526C2semidirect
3. #10592553C2semidirect
4. C3×#4864C2semidirect
5. C3×#4862C2semidirect
6. #10590822C2semidirect
7. #10590748C2semidirect
8. #10590717C2semidirect
9. D3×#816C2semidirect
10. #10590603C2semidirect
11. D3×#810C2semidirect
12. #10590567C2semidirect
13. #10590501C2semidirect
14. #10590460C2semidirect
15. #10590439C2semidirect
75. #4864D3semidirect
77. #4862D3semidirect
251. #634#41semidirect
272. #625SD16semidirect
689. C32#3298semidirect
771. C3#80689semidirect
772. C3#81450semidirect

Maximal subgroups

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

subgroupindex
#105945262
#105943702
#105925532
C3×#48642
C3×#48622
#105908222
#105907482
#105907172
D3×#8162
#105906032
D3×#8102
#105905672
#105905012
#105904602
#105904392
#814503
#806893