Finite Group Databasebeta

← #11888028

Subgroups — #11888028

Order 1152.

848 conjugacy classes of subgroups.

The subgroup lattice has 777 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5641C211yesmaximal, characteristic, complemented
2#10594834C211yesmaximal, characteristic
3#10592746C211yesmaximal, characteristic, complemented
4C3×#5051C211yesmaximal, characteristic, complemented
5#10591657C211yesmaximal, characteristic, complemented
6#10591625C211yesmaximal, characteristic, complemented
7#10591596C211yesmaximal, characteristic, complemented
8#10591536C211yesmaximal, characteristic, complemented
9C3⋊C8×#67C211yesmaximal, characteristic, complemented
10#10591105C211yesmaximal, characteristic, complemented
11#10591102C211yesmaximal, characteristic, complemented
12#10590610C211yesmaximal, characteristic, complemented
13#10590560C211yesmaximal, characteristic, complemented
14#10590464C211yesmaximal, characteristic, complemented
15#10590429C211yesmaximal, characteristic, complemented
16#83664—31nomaximal
17#80776—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C32×C22⋊Q8C2211yescharacteristic
21C2×#3756C2211yescharacteristic
22C2×#3755C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic
25C2×C3×#216C2211yescharacteristic
26C3×C4×#67C2211yescharacteristic
27C3×#926C2211yescharacteristic
28C3×#924C2211yescharacteristic
29C22×C3×C3⋊C8C2211yescharacteristic
30C3×#898—21no—
31C3×#892C2211yescharacteristic
32C3×#888C2211yescharacteristic
33C3×#887—21no—
34C3×#885—21no—
35C3×#879—21no—
36#63975—21no—
37#63958—21no—
38#63894C2211yescharacteristic
39#63883—21no—
40#63866C2211yescharacteristic
41#63857C2211yescharacteristic
42#63853—21no—
43C2×D3×C3⋊C8C2211yescharacteristic
44#63657C2211yescharacteristic
45#63637C2211yescharacteristic
46#63636C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#810C2211yescharacteristic
49C3×#807C2211yescharacteristic
50#63576C2211yescharacteristic
51#63574C2211yescharacteristic
52Dic3⋊(C3⋊C8)C2211yescharacteristic
53#63567C2211yescharacteristic
54#63567C2211yescharacteristic
55#63565C2211yescharacteristic
56#63565C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#556—31no—
62#5641D311yescharacteristic, complemented
63#5631—31no—
64#5551—31no—
65C3×#467—31no—
66#5187—31no—
67#5182—31no—
68#5113—31no—
69C8×#67—31no—
70#5093—31no—
71#5087—31no—
72#5051—31no—
73#5051D311yescharacteristic, complemented
74#5047—31no—
75#5047—31no—
76#5047—31no—
77#5047—61no—
78#5045—31no—
79#5031—31no—
80C4×#215—31no—
81D4×C3⋊C8—31no—
82#5002—31no—
83#5002—31no—
84#4996—31no—
85#4996—31no—
86#4890—31no—
87#4888—31no—
88#4813—31no—
89#4804—31no—
90#4792—31no—
91#4788—31no—
92C2×C32×Q8C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C2×#638—21no—
95#3828—22no—
96#3828—41no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×#634C2311yescharacteristic
100C2×C3×#67D411yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6—21no—
103C2×C3×Dic6C2311yescharacteristic
104C2×#626—21no—
105C2×#624—21no—
106C2×#624—21no—
107#3799—22no—
108#3799—41no—
109C32×C4⋊C4—21no—
110C32×C4⋊C4C2311yescharacteristic
111C32×C22⋊C4—21no—
112#3756—41no—
113#3755—22no—
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C3×#217—21no—
117C3×#217—21no—
118C3×#217D411yescharacteristic
119C3×#216—41no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4D411yescharacteristic
131C3×C4×Dic3—21no—
132C3×C4×Dic3—21no—
133C3×C4×Dic3—21no—
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8—41no—
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140Dic3⋊Dic3—21no—
141#3722—21no—
142(C2×D3)⋊Dic3—21no—
143D3×C3⋊C8—41no—
144#3302—91noSylow
145C2×#239—31no—
146C2×#235—31no—
147C2×#235—31no—
148C2×#235—31no—
149C2×#235—61no—
150C2×C3×Q16—31no—
151C22×C3×C8—31no—
152C3×C4⋊Q8—31no—
153C3×#126—61no—
154C3×#126—61no—
155C3×#124—61no—
156C3×C22⋊Q8—21no—
157C3×C22⋊Q8—31no—
158C3×C22⋊Q8—31no—
159C3×C22⋊Q8C2×D311yescharacteristic
160C3×C22⋊Q8C2×D311yescharacteristic
161C3×C4×Q8—31no—
162C3×C4×Q8—61no—
163C3×C4×D4—31no—
164C3×#117—31no—
165C3×#117—31no—
166#946C2×D311yescharacteristic
167Q8×Dic3C2×D311yescharacteristic
168#944—31no—
169C2×#216—31no—
170C2×#216—31no—
171C2×#216—61no—
172C2×#216C2×D311yescharacteristic
173C2×#215—31no—
174C2×#215—31no—
175C2×#215—61no—
176#938—61no—
177C4×#67C2×D311yescharacteristic
178#926C2×D311yescharacteristic
179#924—31no—
180#924C2×D311yescharacteristic
181C22×C3⋊C8—31no—
182C22×C3⋊C8C2×D311yescharacteristic
183C2×D3×C8—31no—
184#898—21no—
185#897—31no—
186#894—61no—
187#893—31no—
188#892C2×D311yescharacteristic
189D3×C4⋊C4—61no—
190D3×C4⋊C4—61no—
191#888C2×D311yescharacteristic
192#887—21no—
193#885—21no—
194#884—61no—
195#883—61no—
196#883—61no—
197#883—61no—
198#879—21no—
199C4×D12—31no—
200#869—31no—
201C3×#107—31no—
202C3×#103—31no—
203C3×#103—31no—
204#835—31no—
205#835—31no—
206#835C2×D311yescharacteristic
207#830—31no—
208#830—31no—
209#830—31no—
210#830—61no—
211#821—31no—
212#821—31no—
213(C2×D3)⋊C8—31no—
214#816—31no—
215#816—31no—
216Dic3⋊C8—31no—
217C8×Dic3—31no—
218#810—31no—
219#810—31no—
220#810—31no—
221#810—31no—
222#810—31no—
223#810—31no—
224#810—61no—
225#810C2×D311yescharacteristic
226#809—31no—
227#809—31no—
228#809—31no—
229#809—31no—
230#809—61no—
231#808—31no—
232#808—31no—
233#807—31no—
234#807—31no—
235#807C2×D311yescharacteristic
236C4⋊(C3⋊C8)—31no—
237C4×C3⋊C8—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3⋊D3—21no—
240C22×C3×D3C2×D411yescharacteristic
241C32×Q8—21no—
242C32×Q8—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249#638—42no—
250C2×C3⋊Dic3—21no—
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)#4112yes—
253C4×C3⋊D3—42no—
254#634—21no—
255#634—21no—
256C3×#67—22no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—42no—
269#626—42no—
270#624—42no—
271#624—42no—
272C3⋊(C3⋊C8)—21no—
273C3⋊(C3⋊C8)—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#556—31no—
277#547—91no—
278#487—91no—
279#485—91no—
280#485—91no—
281#474—91no—
282#467—31no—
283#467—91no—
284#462—91no—
285#452—91no—
286#452—91no—
287C4×SD16—91no—
288C8×D4—91no—
289#416—91no—
290#416—91no—
291C2×C3×Q8—21no—
292C2×C3×Q8—31no—
293C2×C3×Q8—61no—
294C2×C3×Q8C22×D311yescharacteristic
295C2×C3×Q8C22×D311yescharacteristic
296C2×C3×D4—31no—
297C22×C3×C4—21no—
298C22×C3×C4—31no—
299C22×C3×C4C22×D311yescharacteristic
300C22×C3×C4C22×D311yescharacteristic
301C2×#67—61no—
302C2×#67—61no—
303C2×#67—61no—
304C2×#67—121no—
305C2×#67#6711yescharacteristic
306#239—62no—
307#239—121no—
308#235—62no—
309#235—62no—
310#235—62no—
311#235—122no—
312#235—121no—
313#235—121no—
314#235—121no—
315#235—122no—
316C2×D12—31no—
317C2×D12—31no—
318C2×D12—61no—
319C2×D12—61no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—121no—
327C2×C4×D3C22×D311yescharacteristic
328C2×Dic6—21no—
329C2×Dic6—31no—
330C2×Dic6—31no—
331C2×Dic6—61no—
332C2×Dic6C22×D311yescharacteristic
333C3×Q16—121no—
334C2×C3×C8—31no—
335C2×C3×C8—31no—
336C2×C3×C8—121no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—41no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C4⋊C4C22×D311yescharacteristic
351C3×C22⋊C4—21no—
352C3×C22⋊C4—21no—
353C3×C22⋊C4—31no—
354C3×C22⋊C4—31no—
355C3×C22⋊C4—41no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C42—31no—
361C3×C42—61no—
362C3×C42—61no—
363C3×C42—61no—
364#217—21no—
365#217—21no—
366#217—61no—
367#217#6711yescharacteristic
368#216—41no—
369#216—121no—
370#216—121no—
371#216—122no—
372#215—62no—
373#215—62no—
374#215—122no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4#6711yescharacteristic
381C4⋊Dic3—21no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3C22×D311yescharacteristic
386C4⋊Dic3C22×D311yescharacteristic
387C4⋊Dic3C22×D311yescharacteristic
388Dic3⋊C4—21no—
389Dic3⋊C4—21no—
390Dic3⋊C4—21no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4#6711yescharacteristic
395C4×Dic3—21no—
396C4×Dic3—21no—
397C4×Dic3—21no—
398C4×Dic3C22×D311yescharacteristic
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—41no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8—121no—
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409D3×C8—121no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32C22×D411yescharacteristic
414C2×C3⋊D3—22no—
415C2×C3⋊D3—41no—
416C2×C3⋊D3—41no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C32×C4—21no—
421C32×C4—41no—
422C32×C4—41no—
423C32×C4C2×#4111yescharacteristic
424C32×C4H(5,𝔽2)11yescharacteristic
425C3⋊Dic3—41no—
426C3×Dic3—21no—
427C3×Dic3—21no—
428C3×Dic3—41no—
429C3×Dic3—41no—
430C3×Dic3—41no—
431C3×Dic3—41no—
432C3×Dic3#13512yes—
433C2×#41—91no—
434C2×#41—91no—
435C2×Q16—31no—
436C2×Q16—91no—
437C2×SD16—91no—
438C22×C8—31no—
439C22×C8—91no—
440C4⋊Q8—31no—
441C4⋊Q8—91no—
442#126—61no—
443#126—61no—
444#124—61no—
445#123—181no—
446#123—181no—
447C22⋊Q8—31no—
448C22⋊Q8—31no—
449C22⋊Q8—91no—
450C22⋊Q8D3211yescharacteristic
451#121—181no—
452C4×Q8—31no—
453C4×Q8—61no—
454C4×D4—31no—
455C4×D4—91no—
456#117—31no—
457#117—31no—
458C2×C4⋊C4—181no—
459#107—31no—
460#107—91no—
461#106—91no—
462C4⋊C8—91no—
463#103—31no—
464#103—31no—
465#103—91no—
466#103—91no—
467#103—91no—
468#103—91no—
469#103—91no—
470#102—91no—
471#102—91no—
472#102—91no—
473C22⋊C8—91no—
474C22⋊C8—91no—
475C4×C8—91no—
476C23×C3—21no—
477C23×C3—31no—
478C23×C3D3×D411yescharacteristic
479C23×C3C2×#6711yescharacteristic
480C22×D3—61no—
481C22×D3—61no—
482C22×D3—121no—
483C22×D3C2×#6711yescharacteristic
484C3×Q8—21no—
485C3×Q8—21no—
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—41no—
489C3×Q8—41no—
490C3×Q8—61no—
491C3×Q8—61no—
492C3×Q8—122no—
493C3×D4—62no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
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—31no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4D3×D411yescharacteristic
518C2×C3×C4C2×#6711yescharacteristic
519C2×C3×C4C23×D311yescharacteristic
520C2×C3×C4C23×D311yescharacteristic
521#67—22no—
522#67—122no—
523#67—122no—
524#67—122no—
525#67—124no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—121no—
533C2×Dic3C2×#6711yescharacteristic
534C2×Dic3C2×#6711yescharacteristic
535C2×Dic3C2×#6711yescharacteristic
536D12—32no—
537D12—32no—
538D12—62no—
539D12—61no—
540D12—61no—
541D12—121no—
542D12—122no—
543C4×D3—21no—
544C4×D3—21no—
545C4×D3—122no—
546C4×D3—122no—
547C4×D3—122no—
548C4×D3—122no—
549C4×D3—122no—
550C4×D3—124no—
551C4×D3—122no—
552Dic6—21no—
553Dic6—21no—
554Dic6—42no—
555Dic6—62no—
556Dic6—61no—
557Dic6—61no—
558Dic6—61no—
559Dic6—61no—
560Dic6—121no—
561C3×C8—61no—
562C3×C8—61no—
563C3⋊C8—21no—
564C3⋊C8—21no—
565C3⋊C8—61no—
566C3⋊C8—61no—
567C3⋊C8—61no—
568C3⋊C8—61no—
569C3⋊C8—121no—
570C3⋊C8—121no—
571C2×C32—41no—
572C2×C32#54611yescharacteristic
573C2×C32C2×#13511yescharacteristic
574C2×C32#57811yescharacteristic
575C3⋊D3—42no—
576C3×D3—41no—
577#41—182no—
578#41—182no—
579#41—361no—
580#41—361no—
581C2×Q8—31no—
582C2×Q8—61no—
583C2×Q8—91no—
584C2×Q8C2×D3211yescharacteristic
585C2×D4—31no—
586C2×D4—91no—
587C2×D4—181no—
588C2×D4—181no—
589C22×C4—31no—
590C22×C4—181no—
591C22×C4—181no—
592C22×C4—181no—
593C22×C4C2×D3211yescharacteristic
594Q16—121no—
595Q16—361no—
596SD16—182no—
597C2×C8—31no—
598C2×C8—31no—
599C2×C8—91no—
600C2×C8—91no—
601C2×C8—121no—
602C2×C8—361no—
603C4⋊C4—21no—
604C4⋊C4—31no—
605C4⋊C4—31no—
606C4⋊C4—31no—
607C4⋊C4—31no—
608C4⋊C4—61no—
609C4⋊C4—61no—
610C4⋊C4—61no—
611C4⋊C4—61no—
612C4⋊C4—181no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C4⋊C4C2×D3211yescharacteristic
616C22⋊C4—21no—
617C22⋊C4—31no—
618C22⋊C4—31no—
619C22⋊C4—61no—
620C22⋊C4—61no—
621C22⋊C4—61no—
622C22⋊C4—61no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C42—31no—
626C42—61no—
627C42—61no—
628C42—61no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—61no—
640C22×C3—61no—
641C22×C3—61no—
642C22×C3C2×D3×D411yescharacteristic
643C22×C3C22×#6711yescharacteristic
644C2×D3—21no—
645C2×D3—21no—
646C2×D3—21no—
647C2×D3—62no—
648C2×D3—62no—
649C2×D3—122no—
650C2×D3—121no—
651C2×D3—121no—
652C2×D3—121no—
653C2×D3—121no—
654C2×D3—241no—
655C2×D3—241no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—32no—
661C3×C4—41no—
662C3×C4—41no—
663C3×C4—41no—
664C3×C4—41no—
665C3×C4—41no—
666C3×C4—61no—
667C3×C4—61no—
668C3×C4—81no—
669C3×C4—81no—
670C3×C4—121no—
671C3×C4—121no—
672C3×C4—121no—
673C3×C4—121no—
674C3×C4#100411yescharacteristic
675C3×C4D3×#4111yescharacteristic
676C3×C4D3×#4111yescharacteristic
677C3×C4#100911yescharacteristic
678Dic3—21no—
679Dic3—21no—
680Dic3—41no—
681Dic3—41no—
682Dic3—41no—
683Dic3—41no—
684Dic3—122no—
685Dic3—121no—
686Dic3—121no—
687Dic3#95012yes—
688C32#330211yescharacteristic, complemented, Sylow
689C23—31no—
690C23—181no—
691C23D3×#6711yescharacteristic
692Q8—21no—
693Q8—21no—
694Q8—61no—
695Q8—61no—
696Q8—122no—
697Q8—181no—
698Q8—181no—
699D4—62no—
700D4—92no—
701D4—181no—
702D4—362no—
703D4—362no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—31no—
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—181no—
718C2×C4—362no—
719C2×C4—362no—
720C2×C4—362no—
721C2×C4D3×#6711yescharacteristic
722C2×C4C22×D3211yescharacteristic
723C8—61no—
724C8—61no—
725C8—181no—
726C8—181no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—21no—
730C2×C3—41no—
731C2×C3—41no—
732C2×C3—81no—
733C2×C3—121no—
734C2×C3#561011yescharacteristic
735C2×C3#576611yescharacteristic
736C2×C3D3×#13511yescharacteristic
737C2×C3C2×#95011yescharacteristic
738C2×C3#582911yescharacteristic
739C2×C3#583811yescharacteristic
740D3—41no—
741D3—122no—
742D3—122no—
743D3—242no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—61no—
748C22—61no—
749C22—61no—
750C22—182no—
751C22—361no—
752C22—361no—
753C22C2×D3×#6711yescharacteristic
754C4—21no—
755C4—32no—
756C4—41no—
757C4—41no—
758C4—61no—
759C4—61no—
760C4—121no—
761C4—121no—
762C4—121no—
763C4—121no—
764C4—361no—
765C4#6431211yescharacteristic
766C4#6431411yescharacteristic
767C3—21no—
768C3#8077611yescharacteristic, complemented
769C3#8366411yescharacteristic, complemented
770C2—41no—
771C2—121no—
772C2—362no—
773C2#1059530511yescharacteristic
774C2#1059532711yescharacteristic
775C2D3×#95011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radical#10594834C2
hypercenterC22⋊Q8D32
hypocenterC32#3302
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5641C2semidirect
3. #10592746C2semidirect
4. C3×#5051C2semidirect
5. #10591657C2semidirect
6. #10591625C2semidirect
7. #10591596C2semidirect
8. #10591536C2semidirect
9. C3⋊C8×#67C2semidirect
10. #10591105C2semidirect
11. #10591102C2semidirect
12. #10590610C2semidirect
13. #10590560C2semidirect
14. #10590464C2semidirect
15. #10590429C2semidirect
62. #5641D3semidirect
73. #5051D3semidirect
688. C32#3302semidirect
768. C3#80776semidirect
769. C3#83664semidirect

Maximal subgroups

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

subgroupindex
C3×#56412
#105948342
#105927462
C3×#50512
#105916572
#105916252
#105915962
#105915362
C3⋊C8×#672
#105911052
#105911022
#105906102
#105905602
#105904642
#105904292
#836643
#807763