Finite Group Databasebeta

← #11887227

Subgroups — #11887227

Order 1152.

895 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5529C211yesmaximal, characteristic, complemented
2#10595078C211yesmaximal, characteristic
3#10592701C211yesmaximal, characteristic, complemented
4C3×#5003C211yesmaximal, characteristic, complemented
5#10591184C211yesmaximal, characteristic, complemented
6#10591179C211yesmaximal, characteristic, complemented
7#67⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8#10590596C211yesmaximal, characteristic, complemented
9D3×#809C211yesmaximal, characteristic, complemented
10#10590579C211yesmaximal, characteristic, complemented
11#10590533C211yesmaximal, characteristic, complemented
12#10590532C211yesmaximal, characteristic, complemented
13#10590468C211yesmaximal, characteristic, complemented
14#10590458C211yesmaximal, characteristic, complemented
15#10590426C211yesmaximal, characteristic, complemented
16#83598—31nomaximal
17#81381—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C32×#117C2211yescharacteristic, complemented
21C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
22C3×#930C2211yescharacteristic
23C3×C4×#67C2211yescharacteristic
24C3×#924C2211yescharacteristic, complemented
25C3×#897C2211yescharacteristic
26C3×D3×C4⋊C4C2211yescharacteristic
27C3×#890C2211yescharacteristic, complemented
28C3×#887C2211yescharacteristic, complemented
29C3×#883—21no—
30C3×#879—21no—
31C3×#872—21no—
32C3×#870—21no—
33#63983—21no—
34#63958—21no—
35#63921—21no—
36#63894C2211yescharacteristic
37#63860C2211yescharacteristic
38#63857C2211yescharacteristic
39#63853—21no—
40C2×#3719C2211yescharacteristic, complemented
41C2×#3717C2211yescharacteristic
42C2×#3715C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63637C2211yescharacteristic, complemented
45#63637C2211yescharacteristic, complemented
46#63636C2211yescharacteristic
47#63636C2211yescharacteristic
48C3×#830C2211yescharacteristic, complemented
49C3×#809C2211yescharacteristic
50C3×#809C2211yescharacteristic
51C3×#808C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53#63574C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63565C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#552—31no—
62#5612—31no—
63#5550—31no—
64#5529D311yescharacteristic, complemented
65C3×#482—31no—
66#5068—31no—
67#5066—31no—
68#5051—31no—
69#5048—31no—
70#5047—31no—
71#5046—31no—
72#5041—31no—
73#5028—31no—
74C4×#215—31no—
75D4×C3⋊C8—31no—
76#5003D311yescharacteristic, complemented
77#5002—31no—
78#5002—31no—
79#5002—61no—
80#4971—31no—
81C2×#809—31no—
82#4891—31no—
83#4887—31no—
84#4862—31no—
85#4852—31no—
86#4776—31no—
87D3×#102—31no—
88#4768—31no—
89#4767—31no—
90#4733—31no—
91#67⋊C8—31no—
92C22×D32—21no—
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×#67—21no—
101C2×C3×#67D411yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×#626—21no—
107C2×#624—21no—
108D3×D12—22no—
109D3×D12—41no—
110C32×C4⋊C4C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112C32×C22⋊C4—21no—
113C32×C42—21no—
114C2×C3⋊(C3⋊C8)—41no—
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C3×#217—21no—
118C3×#217D411yescharacteristic
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4D411yescharacteristic
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4D411yescharacteristic
131C3×C4×Dic3—21no—
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135Dic3⋊Dic3—21no—
136#3722—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140#3719—41no—
141#3717—22no—
142#3715—41no—
143D3×C3⋊C8—41no—
144#3296—91noSylow
145C2×D3×D4—31no—
146C2×#235—31no—
147C2×#235—31no—
148C2×#235—61no—
149C22×D12—31no—
150C3×#126—61no—
151C3×#125—31no—
152C3×#125—61no—
153C3×#123—61no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—31no—
156C3×#121—31no—
157C3×C4×Q8—31no—
158C3×C4×D4—31no—
159C3×#117—21no—
160C3×#117—61no—
161C3×#117C2×D311yescharacteristic, complemented
162C3×#117C2×D311yescharacteristic, complemented
163C2×C3×C4⋊C4—31no—
164C2×#216—31no—
165C2×#215—31no—
166C2×#215—31no—
167#938—61no—
168#937—61no—
169#937—61no—
170#936—31no—
171C2×#214—31no—
172#930C2×D311yescharacteristic
173C4×#67C2×D311yescharacteristic
174#924—31no—
175#924C2×D311yescharacteristic, complemented
176C22×C3⋊C8—31no—
177C22×C3⋊C8—31no—
178C22×C3⋊C8—31no—
179C22×C3⋊C8—61no—
180C2×Dic12—31no—
181C2×#204—31no—
182C2×D3×C8—31no—
183#897—31no—
184#897C2×D311yescharacteristic
185#894—61no—
186#893—31no—
187D3×C4⋊C4C2×D311yescharacteristic
188#890C2×D311yescharacteristic, complemented
189#887C2×D311yescharacteristic, complemented
190#884—61no—
191#883—21no—
192#883—61no—
193D3×C22⋊C4—61no—
194D3×C22⋊C4—61no—
195#879—21no—
196#875—31no—
197C4×D12—31no—
198#872—21no—
199#870—21no—
200C3×#107—31no—
201C3×#106—31no—
202C3×#102—31no—
203C3×#102—31no—
204C3×C22⋊C8—31no—
205#835—31no—
206#832—31no—
207#830—31no—
208#830C2×D311yescharacteristic, complemented
209#821—31no—
210(C2×D3)⋊C8—31no—
211#816—31no—
212Dic3⋊C8—31no—
213C8×Dic3—31no—
214#810—31no—
215#810—31no—
216#810—31no—
217#810—31no—
218#810—31no—
219#810—31no—
220#810—61no—
221#810—61no—
222#809—31no—
223#809—31no—
224#809—31no—
225#809—31no—
226#809—31no—
227#809—31no—
228#809—61no—
229#809—61no—
230#809C2×D311yescharacteristic
231#809C2×D311yescharacteristic
232#808—31no—
233#808—31no—
234#808C2×D311yescharacteristic, complemented
235#807C2×D311yescharacteristic, complemented
236C4⋊(C3⋊C8)—31no—
237C4×C3⋊C8—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3⋊D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C2×D32—42no—
243C2×D32—42no—
244C2×D32—81no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2411yescharacteristic
251#638—42no—
252C2×C3⋊Dic3—21no—
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)#4112yes—
255C4×C3⋊D3—42no—
256#634—21no—
257#634—21no—
258C3×#67—22no—
259C3×#67—81no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×D12—21no—
267C3×D12—21no—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—42no—
271C3×Dic6—21no—
272C3×Dic6—21no—
273#626—42no—
274#624—81no—
275C3⋊(C3⋊C8)—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#552—31no—
280#546—91no—
281#488—91no—
282#483—91no—
283#482—31no—
284#478—91no—
285#467—91no—
286#465—91no—
287#464—91no—
288#452—91no—
289#450—91no—
290C4×SD16—91no—
291C8×D4—91no—
292#416—91no—
293C2×#102—91no—
294C23×D3—61no—
295C23×D3—61no—
296C2×C3×Q8—31no—
297C2×C3×D4—31no—
298C2×C3×D4—31no—
299C2×C3×D4—61no—
300C22×C3×C4—21no—
301C22×C3×C4—31no—
302C22×C3×C4—61no—
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C22×D311yescharacteristic
305C2×#67—21no—
306C2×#67—61no—
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—121no—
310C2×#67#6711yescharacteristic
311D3×D4—62no—
312D3×D4—121no—
313#235—62no—
314#235—62no—
315#235—64no—
316#235—121no—
317#235—121no—
318#235—122no—
319C2×D12—31no—
320C2×D12—31no—
321C2×D12—61no—
322C2×D12—62no—
323C2×D12—61no—
324C2×D12—121no—
325C2×D12C22×D311yescharacteristic
326C2×C4×D3—21no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—121no—
332C2×C4×D3C22×D311yescharacteristic
333C2×Dic6—31no—
334C2×Dic6—31no—
335C2×Dic6—61no—
336C2×Dic6C22×D311yescharacteristic
337C2×C3×C8—31no—
338C2×C3×C8—31no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4C22×D311yescharacteristic
351C3×C4⋊C4C22×D311yescharacteristic
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C22⋊C4—21no—
355C3×C22⋊C4—21no—
356C3×C22⋊C4—31no—
357C3×C22⋊C4—31no—
358C3×C22⋊C4—41no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C42—21no—
363C3×C42—21no—
364C3×C42—31no—
365C3×C42—41no—
366C3×C42—61no—
367#217—21no—
368#217—61no—
369#217—61no—
370#217—61no—
371#217#6711yescharacteristic
372#216—121no—
373#215—62no—
374#215—121no—
375#214—121no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4#6711yescharacteristic
384C4⋊Dic3—21no—
385C4⋊Dic3—21no—
386C4⋊Dic3—61no—
387C4⋊Dic3C22×D311yescharacteristic
388C4⋊Dic3C22×D311yescharacteristic
389Dic3⋊C4—21no—
390Dic3⋊C4—21no—
391Dic3⋊C4—21no—
392Dic3⋊C4—21no—
393Dic3⋊C4—61no—
394Dic3⋊C4#6711yescharacteristic
395C4×Dic3—21no—
396C4×Dic3C22×D311yescharacteristic
397C2×C3⋊C8—31no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—61no—
402C2×C3⋊C8—61no—
403C2×C3⋊C8—121no—
404C2×C3⋊C8—121no—
405C2×C3⋊C8—121no—
406C2×C3⋊C8—122no—
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409Dic12—121no—
410#204—62no—
411D3×C8—121no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32C22×D411yescharacteristic
416C2×C3⋊D3—22no—
417C2×C3⋊D3—41no—
418C2×C3⋊D3—41no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3#13512yes—
425D32—84no—
426C32×C4—21no—
427C32×C4—41no—
428C32×C4—41no—
429C32×C4C2×#4111yescharacteristic
430C32×C4H(5,𝔽2)11yescharacteristic
431C3⋊Dic3—41no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C2×#41—91no—
439C22×D4—91no—
440C2×Q16—91no—
441C2×SD16—91no—
442C2×SD16—91no—
443C22×C8—91no—
444C22×C8—91no—
445#126—61no—
446#125—31no—
447#125—61no—
448#124—91no—
449#123—61no—
450#123—181no—
451C22⋊Q8—31no—
452C22⋊Q8—31no—
453C22⋊Q8—91no—
454#121—31no—
455#121—181no—
456#120—181no—
457C4×Q8—31no—
458C4×D4—31no—
459C4×D4—91no—
460#117—61no—
461#117D3211yescharacteristic, complemented
462C2×C4⋊C4—31no—
463C2×C22⋊C4—181no—
464#107—31no—
465#106—31no—
466#106—91no—
467C4⋊C8—91no—
468#103—91no—
469#103—91no—
470#103—91no—
471#103—91no—
472#102—31no—
473#102—31no—
474#102—91no—
475#102—91no—
476#102—91no—
477#102—91no—
478C22⋊C8—31no—
479C22⋊C8—91no—
480C4×C8—91no—
481C23×C3—21no—
482C23×C3—31no—
483C23×C3—61no—
484C23×C3D3×D411yescharacteristic
485C23×C3C2×#6711yescharacteristic
486C22×D3—21no—
487C22×D3—61no—
488C22×D3—61no—
489C22×D3—121no—
490C22×D3—122no—
491C22×D3—122no—
492C22×D3—122no—
493C22×D3—122no—
494C22×D3—241no—
495C22×D3—241no—
496C22×D3C2×#6711yescharacteristic
497C3×Q8—61no—
498C3×Q8—61no—
499C3×D4—62no—
500C3×D4—61no—
501C3×D4—61no—
502C3×D4—241no—
503C2×C3×C4—22no—
504C2×C3×C4—22no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—31no—
516C2×C3×C4—31no—
517C2×C3×C4—31no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—122no—
526C2×C3×C4D3×D411yescharacteristic
527C2×C3×C4C2×#6711yescharacteristic
528C2×C3×C4C23×D311yescharacteristic
529C2×C3×C4C23×D311yescharacteristic
530#67—22no—
531#67—81no—
532#67—122no—
533#67—122no—
534#67—122no—
535#67—124no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—121no—
542C2×Dic3C2×#6711yescharacteristic
543C2×Dic3C2×#6711yescharacteristic
544C2×Dic3C2×#6711yescharacteristic
545D12—21no—
546D12—21no—
547D12—32no—
548D12—32no—
549D12—62no—
550D12—61no—
551D12—61no—
552D12—121no—
553D12—122no—
554C4×D3—21no—
555C4×D3—21no—
556C4×D3—42no—
557C4×D3—122no—
558C4×D3—122no—
559C4×D3—124no—
560C4×D3—241no—
561C4×D3—241no—
562Dic6—21no—
563Dic6—21no—
564Dic6—62no—
565Dic6—61no—
566Dic6—61no—
567Dic6—61no—
568Dic6—61no—
569Dic6—121no—
570C3×C8—61no—
571C3×C8—61no—
572C3⋊C8—21no—
573C3⋊C8—21no—
574C3⋊C8—61no—
575C3⋊C8—61no—
576C3⋊C8—61no—
577C3⋊C8—61no—
578C3⋊C8—121no—
579C3⋊C8—121no—
580C2×C32—41no—
581C2×C32#54611yescharacteristic
582C2×C32C2×#13511yescharacteristic
583C2×C32#57711yescharacteristic
584C3⋊D3—42no—
585C3×D3—22no—
586C3×D3—81no—
587C24—181no—
588#41—182no—
589#41—361no—
590C2×Q8—31no—
591C2×Q8—91no—
592C2×D4—31no—
593C2×D4—31no—
594C2×D4—61no—
595C2×D4—91no—
596C2×D4—181no—
597C2×D4—182no—
598C2×D4—181no—
599C2×D4—361no—
600C22×C4—31no—
601C22×C4—61no—
602C22×C4—181no—
603C22×C4—181no—
604C22×C4C2×D3211yescharacteristic
605Q16—361no—
606SD16—182no—
607SD16—361no—
608C2×C8—31no—
609C2×C8—31no—
610C2×C8—91no—
611C2×C8—91no—
612C2×C8—361no—
613C2×C8—361no—
614C4⋊C4—31no—
615C4⋊C4—31no—
616C4⋊C4—31no—
617C4⋊C4—61no—
618C4⋊C4—61no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4—61no—
622C4⋊C4—61no—
623C4⋊C4—181no—
624C4⋊C4C2×D3211yescharacteristic
625C4⋊C4C2×D3211yescharacteristic
626C22⋊C4—21no—
627C22⋊C4—31no—
628C22⋊C4—31no—
629C22⋊C4—61no—
630C22⋊C4—61no—
631C22⋊C4—61no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C42—21no—
637C42—31no—
638C42—61no—
639C22×C3—22no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—32no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—61no—
651C22×C3—61no—
652C22×C3—121no—
653C22×C3—121no—
654C22×C3—121no—
655C22×C3C2×D3×D411yescharacteristic
656C22×C3C22×#6711yescharacteristic
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—41no—
660C2×D3—41no—
661C2×D3—41no—
662C2×D3—62no—
663C2×D3—62no—
664C2×D3—122no—
665C2×D3—121no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—121no—
669C2×D3—241no—
670C2×D3—241no—
671C2×D3—244no—
672C2×D3—244no—
673C2×D3#95012yes—
674C3×C4—22no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—41no—
680C3×C4—41no—
681C3×C4—41no—
682C3×C4—41no—
683C3×C4—61no—
684C3×C4—61no—
685C3×C4—61no—
686C3×C4—81no—
687C3×C4—81no—
688C3×C4—121no—
689C3×C4—121no—
690C3×C4—121no—
691C3×C4D3×#4111yescharacteristic
692C3×C4D3×#4111yescharacteristic
693C3×C4#100911yescharacteristic
694C3×C4#100911yescharacteristic
695Dic3—21no—
696Dic3—21no—
697Dic3—21no—
698Dic3—41no—
699Dic3—41no—
700Dic3—41no—
701Dic3—122no—
702Dic3—121no—
703Dic3—121no—
704C32#329611yescharacteristic, complemented, Sylow
705C23—31no—
706C23—61no—
707C23—181no—
708C23—362no—
709C23—362no—
710C23—721no—
711C23D3×#6711yescharacteristic
712Q8—61no—
713Q8—61no—
714Q8—181no—
715Q8—181no—
716D4—62no—
717D4—61no—
718D4—61no—
719D4—92no—
720D4—181no—
721D4—241no—
722D4—362no—
723D4—362no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—31no—
729C2×C4—31no—
730C2×C4—31no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—122no—
737C2×C4—181no—
738C2×C4—362no—
739C2×C4—721no—
740C2×C4D3×#6711yescharacteristic
741C2×C4C22×D3211yescharacteristic
742C8—61no—
743C8—61no—
744C8—181no—
745C8—181no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—42no—
750C2×C3—41no—
751C2×C3—41no—
752C2×C3—62no—
753C2×C3—241no—
754C2×C3#565411yescharacteristic
755C2×C3D3×#13511yescharacteristic
756C2×C3#577511yescharacteristic
757C2×C3C2×#95011yescharacteristic
758C2×C3#582911yescharacteristic
759C2×C3#583711yescharacteristic
760D3—22no—
761D3—81no—
762D3—122no—
763D3—122no—
764D3—242no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—32no—
769C22—61no—
770C22—61no—
771C22—121no—
772C22—121no—
773C22—121no—
774C22—182no—
775C22—361no—
776C22—361no—
777C22—724no—
778C22C2×D3×#6711yescharacteristic
779C4—21no—
780C4—41no—
781C4—41no—
782C4—61no—
783C4—61no—
784C4—61no—
785C4—121no—
786C4—121no—
787C4—121no—
788C4—361no—
789C4#6430611yescharacteristic
790C4#6430811yescharacteristic
791C3—21no—
792C3#8138111yescharacteristic, complemented
793C3#8359811yescharacteristic, complemented
794C2—41no—
795C2—62no—
796C2—241no—
797C2—362no—
798C2#1059506811yescharacteristic
799C2D3×#95011yescharacteristic
800C2#1059545511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radical#10595078C2
hypercenter#117D32
hypocenterC32#3296
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C3×#5529C2semidirect
3. #10592701C2semidirect
4. C3×#5003C2semidirect
5. #10591184C2semidirect
6. #10591179C2semidirect
7. #67⋊(C3⋊C8)C2semidirect
8. #10590596C2semidirect
9. D3×#809C2semidirect
10. #10590579C2semidirect
11. #10590533C2semidirect
12. #10590532C2semidirect
13. #10590468C2semidirect
14. #10590458C2semidirect
15. #10590426C2semidirect
20. C32×#117C22semidirect
21. C22×C3⋊(C3⋊C8)C22semidirect
24. C3×#924C22semidirect
27. C3×#890C22semidirect
28. C3×#887C22semidirect
40. C2×#3719C22semidirect
44. #63637C22semidirect
45. #63637C22semidirect
48. C3×#830C22semidirect
51. C3×#808C22semidirect
52. C3×#807C22semidirect
53. #63574C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63567C22semidirect
56. #63565C22semidirect
60. Dic3×C3⋊C8C22semidirect
64. #5529D3semidirect
76. #5003D3semidirect
161. C3×#117C2×D3semidirect
162. C3×#117C2×D3semidirect
175. #924C2×D3semidirect
188. #890C2×D3semidirect
189. #887C2×D3semidirect
208. #830C2×D3semidirect
234. #808C2×D3semidirect
235. #807C2×D3semidirect
461. #117D32semidirect
704. C32#3296semidirect
792. C3#81381semidirect
793. C3#83598semidirect

Maximal subgroups

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

subgroupindex
C3×#55292
#105950782
#105927012
C3×#50032
#105911842
#105911792
#67⋊(C3⋊C8)2
#105905962
D3×#8092
#105905792
#105905332
#105905322
#105904682
#105904582
#105904262
#835983
#813813