Finite Group Databasebeta

← #11887229

Subgroups — #11887229

Order 1152.

869 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5529C211yesmaximal, characteristic, complemented
2#10595067C211yesmaximal, characteristic
3#10592702C211yesmaximal, characteristic, complemented
4C3×#5002C211yesmaximal, characteristic, complemented
5#10591177C211yesmaximal, characteristic, complemented
6#10591170C211yesmaximal, characteristic, complemented
7C3⋊C8×#67C211yesmaximal, characteristic, complemented
8#10590596C211yesmaximal, characteristic, complemented
9D3×#809C211yesmaximal, characteristic, complemented
10#10590537C211yesmaximal, characteristic, complemented
11#10590536C211yesmaximal, characteristic, complemented
12#10590518C211yesmaximal, characteristic, complemented
13#10590516C211yesmaximal, characteristic, complemented
14#10590467C211yesmaximal, characteristic, complemented
15#10590453C211yesmaximal, characteristic, complemented
16#83598—31nomaximal
17#78845—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C32×#117C2211yescharacteristic, complemented
21#64139C2211yescharacteristic
22C3×C4×#67C2211yescharacteristic
23C3×#924C2211yescharacteristic, complemented
24C22×C3×C3⋊C8C2211yescharacteristic, 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#63971—21no—
35D3×(C2×D3)⋊C4—21no—
36Dic3×D12C2211yescharacteristic
37#63864C2211yescharacteristic
38#63856C2211yescharacteristic
39#63850—21no—
40C2×#3718C2211yescharacteristic, complemented
41C2×#3717C2211yescharacteristic
42C2×#3715C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63657C2211yescharacteristic, complemented
45#63636C2211yescharacteristic
46#63636C2211yescharacteristic
47#63635C2211yescharacteristic, complemented
48#63634C2211yescharacteristic, complemented
49C3×#810C2211yescharacteristic, complemented
50C3×#810C2211yescharacteristic, complemented
51C3×#809C2211yescharacteristic
52C3×#809C2211yescharacteristic
53#63573C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63565C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#552—31no—
62#5829—31no—
63#5550—31no—
64#5529D311yescharacteristic, complemented
65C3×#416—31no—
66#5239—31no—
67#5114—31no—
68C8×#67—31no—
69#5068—31no—
70#5066—31no—
71#5051—31no—
72#5048—31no—
73#5047—31no—
74#5046—31no—
75#5028—31no—
76C4×#215—31no—
77D4×C3⋊C8—31no—
78#5003—31no—
79#5003—31no—
80#5003—61no—
81#5002D311yescharacteristic, complemented
82#4971—31no—
83C2×#809—31no—
84#4813—31no—
85#4805—31no—
86#4800—31no—
87#4798—31no—
88#4776—31no—
89D3×#102—31no—
90#4763—31no—
91#4758—31no—
92C22×D32—21no—
93C22×C32×C4C2311yescharacteristic
94C2×#638—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67D411yescharacteristic
98C3×#235—22no—
99C3×#235—41no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×#626—21no—
107C2×D3×Dic3—21no—
108D3×D12—22no—
109D3×D12—41no—
110C32×C4⋊C4C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112C32×C22⋊C4—21no—
113C32×C42—21no—
114#3752—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#217—21no—
119C3×#217D411yescharacteristic
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4D411yescharacteristic
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4D411yescharacteristic
130C3×C4×Dic3—21no—
131C3×C4×Dic3C2311yescharacteristic
132C2×C3×C3⋊C8—41no—
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3724—21no—
136#3722—21no—
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140#3718—41no—
141#3717—41no—
142#3715—22no—
143D3×C3⋊C8—41no—
144#3296—91noSylow
145C2×C3×#41—31no—
146C2×D3×D4—31no—
147C2×#235C2×D311yescharacteristic
148C22×D12—31no—
149C22×C3×C8—31no—
150C3×#126—61no—
151C3×#125—31no—
152C3×#125—61no—
153C3×#123—61no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—31no—
156C3×C4×Q8—31no—
157C3×C4×D4—31no—
158C3×#117—21no—
159C3×#117—61no—
160C3×#117C2×D311yescharacteristic, complemented
161C3×#117C2×D311yescharacteristic, complemented
162C2×C3×C4⋊C4—31no—
163#947—31no—
164#946—31no—
165C2×#216—31no—
166C2×#216—31no—
167C2×#215—31no—
168C2×#215—31no—
169#939—61no—
170#937—61no—
171#937—61no—
172D4×Dic3—31no—
173C2×#214—31no—
174#930—31no—
175#930—31no—
176#930—61no—
177#929—61no—
178C4×#67C2×D311yescharacteristic
179C2×(C2×D3)⋊C4—61no—
180#924—31no—
181#924C2×D311yescharacteristic, complemented
182C22×C3⋊C8—31no—
183C22×C3⋊C8C2×D311yescharacteristic, complemented
184C2×#204—31no—
185C2×D3×C8—31no—
186#897C2×D311yescharacteristic
187#894—61no—
188D3×C4⋊C4C2×D311yescharacteristic
189#890C2×D311yescharacteristic, complemented
190#887C2×D311yescharacteristic, complemented
191#884—61no—
192#883—21no—
193D3×C22⋊C4—61no—
194#879—21no—
195#875—31no—
196C4×D12—31no—
197#872—21no—
198#870—21no—
199C3×#103—31no—
200C3×#103—31no—
201C3×#102—31no—
202C3×#102—31no—
203#835—31no—
204#835—31no—
205#832—31no—
206#830—31no—
207#830—31no—
208#830—31no—
209#830—61no—
210#821—31no—
211(C2×D3)⋊C8—31no—
212#817—31no—
213#816—31no—
214Dic3⋊C8—31no—
215C8×Dic3—31no—
216#810—31no—
217#810C2×D311yescharacteristic, complemented
218#810C2×D311yescharacteristic, complemented
219#809—31no—
220#809—31no—
221#809—31no—
222#809—31no—
223#809—31no—
224#809—31no—
225#809—61no—
226#809—61no—
227#809C2×D311yescharacteristic
228#809C2×D311yescharacteristic
229#808—31no—
230#808—31no—
231#808—31no—
232#808—61no—
233#807—31no—
234#807—31no—
235#807—61no—
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—81no—
252C2×C3⋊Dic3—21no—
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)—21no—
255C3×#67—22no—
256C3×#67—42no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×D12—21no—
264C3×D12#4112yes—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—42no—
268C3×C4×D3—42no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272C3×Dic6—21no—
273#626—42no—
274D3×Dic3—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—91no—
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—31no—
293C2×#102—91no—
294C23×D3—61no—
295C23×D3—61no—
296C3×#41—62no—
297C3×#41—121no—
298C2×C3×Q8—31no—
299C2×C3×Q8—31no—
300C2×C3×D4—31no—
301C2×C3×D4—31no—
302C2×C3×D4—61no—
303C22×C3×C4—21no—
304C22×C3×C4—31no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C22×D311yescharacteristic
309C2×#67—21no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—121no—
314C2×#67#6711yescharacteristic
315C22×Dic3—61no—
316D3×D4—62no—
317D3×D4—121no—
318#235—22no—
319#235—41no—
320C2×D12—31no—
321C2×D12—31no—
322C2×D12—61no—
323C2×D12—62no—
324C2×D12—61no—
325C2×D12—121no—
326C2×D12C22×D311yescharacteristic
327C2×C4×D3—21no—
328C2×C4×D3—21no—
329C2×C4×D3—61no—
330C2×C4×D3C22×D311yescharacteristic
331C2×Dic6C22×D311yescharacteristic
332C2×Dic6C22×D311yescharacteristic
333C2×C3×C8—31no—
334C2×C3×C8—31no—
335C2×C3×C8—121no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C22⋊C4—21no—
351C3×C22⋊C4—21no—
352C3×C22⋊C4—31no—
353C3×C22⋊C4—31no—
354C3×C22⋊C4—41no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C42—21no—
358C3×C42—21no—
359C3×C42—31no—
360C3×C42—41no—
361C3×C42—61no—
362#217—21no—
363#217—61no—
364#217—61no—
365#217#6711yescharacteristic
366#216—121no—
367#216—121no—
368#215—62no—
369#215—121no—
370#214—62no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—121no—
381(C2×D3)⋊C4#6711yescharacteristic
382C4⋊Dic3—21no—
383C4⋊Dic3—21no—
384C4⋊Dic3—31no—
385C4⋊Dic3—31no—
386C4⋊Dic3—61no—
387C4⋊Dic3C22×D311yescharacteristic
388Dic3⋊C4—21no—
389Dic3⋊C4—21no—
390Dic3⋊C4—21no—
391Dic3⋊C4—21no—
392Dic3⋊C4—61no—
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—41no—
402C2×C3⋊C8—61no—
403C2×C3⋊C8—61no—
404C2×C3⋊C8—121no—
405C2×C3⋊C8C22×D311yescharacteristic
406C2×C3⋊C8C22×D311yescharacteristic
407#204—121no—
408D3×C8—121no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32C22×D411yescharacteristic
413C2×C3⋊D3—41no—
414C2×C3⋊D3—41no—
415C2×C3⋊D3—41no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—22no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3#13512yes—
422D32—84no—
423C32×C4—21no—
424C32×C4—41no—
425C32×C4—41no—
426C32×C4C2×#4111yescharacteristic
427C32×C4H(5,𝔽2)11yescharacteristic
428C3⋊Dic3—41no—
429C3×Dic3—21no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C2×#41—31no—
436C22×D4—91no—
437C2×Q16—91no—
438C2×SD16—91no—
439C2×SD16—91no—
440C22×C8—31no—
441C22×C8—91no—
442#126—61no—
443#125—31no—
444#125—61no—
445#124—91no—
446#123—61no—
447#123—181no—
448C22⋊Q8—31no—
449C22⋊Q8—31no—
450C22⋊Q8—91no—
451#121—91no—
452#121—181no—
453#120—181no—
454C4×Q8—31no—
455C4×D4—31no—
456C4×D4—91no—
457#117—61no—
458#117D3211yescharacteristic, complemented
459C2×C4⋊C4—31no—
460C2×C22⋊C4—181no—
461#107—91no—
462#106—91no—
463#106—91no—
464C4⋊C8—91no—
465#103—31no—
466#103—31no—
467#103—91no—
468#103—91no—
469#102—31no—
470#102—31no—
471#102—91no—
472#102—91no—
473#102—91no—
474#102—91no—
475C22⋊C8—91no—
476C22⋊C8—91no—
477C4×C8—91no—
478C23×C3—21no—
479C23×C3—31no—
480C23×C3—61no—
481C23×C3D3×D411yescharacteristic
482C23×C3C2×#6711yescharacteristic
483C22×D3—21no—
484C22×D3—61no—
485C22×D3—61no—
486C22×D3—121no—
487C22×D3—122no—
488C22×D3—122no—
489C22×D3—122no—
490C22×D3—122no—
491C22×D3—241no—
492C22×D3—241no—
493C22×D3C2×#6711yescharacteristic
494C3×Q8—61no—
495C3×Q8—61no—
496C3×Q8—61no—
497C3×Q8—61no—
498C3×D4—32no—
499C3×D4—62no—
500C3×D4—61no—
501C3×D4—122no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
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—31no—
513C2×C3×C4—31no—
514C2×C3×C4—31no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—122no—
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—42no—
532#67—122no—
533#67—241no—
534#67—241no—
535#67—242no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—121no—
542C2×Dic3—241no—
543C2×Dic3C2×#6711yescharacteristic
544C2×Dic3C2×#6711yescharacteristic
545C2×Dic3C2×#6711yescharacteristic
546D12—21no—
547D12—61no—
548D12—61no—
549D12—61no—
550D12—61no—
551D12—121no—
552D12—121no—
553D12—122no—
554D12#23512yes—
555C4×D3—21no—
556C4×D3—21no—
557C4×D3—42no—
558C4×D3—42no—
559C4×D3—241no—
560Dic6—21no—
561Dic6—21no—
562Dic6—21no—
563Dic6—21no—
564C3×C8—61no—
565C3×C8—61no—
566C3⋊C8—21no—
567C3⋊C8—21no—
568C3⋊C8—61no—
569C3⋊C8—61no—
570C3⋊C8—61no—
571C3⋊C8—61no—
572C3⋊C8—121no—
573C3⋊C8—121no—
574C2×C32—41no—
575C2×C32#54611yescharacteristic
576C2×C32C2×#13511yescharacteristic
577C2×C32#57711yescharacteristic
578C3⋊D3—81no—
579C3×D3—22no—
580C3×D3—42no—
581C24—181no—
582#41—62no—
583#41—121no—
584C2×Q8—31no—
585C2×Q8—31no—
586C2×D4—31no—
587C2×D4—31no—
588C2×D4—61no—
589C2×D4—91no—
590C2×D4—181no—
591C2×D4—182no—
592C2×D4—181no—
593C2×D4—361no—
594C22×C4—31no—
595C22×C4—61no—
596C22×C4—61no—
597C22×C4—181no—
598C22×C4C2×D3211yescharacteristic
599Q16—361no—
600SD16—182no—
601SD16—361no—
602C2×C8—31no—
603C2×C8—31no—
604C2×C8—91no—
605C2×C8—91no—
606C2×C8—121no—
607C2×C8—361no—
608C4⋊C4—31no—
609C4⋊C4—31no—
610C4⋊C4—61no—
611C4⋊C4—61no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4—61no—
615C4⋊C4—61no—
616C4⋊C4—91no—
617C4⋊C4—181no—
618C4⋊C4C2×D3211yescharacteristic
619C4⋊C4C2×D3211yescharacteristic
620C22⋊C4—21no—
621C22⋊C4—31no—
622C22⋊C4—31no—
623C22⋊C4—61no—
624C22⋊C4—61no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C42—21no—
631C42—31no—
632C42—61no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—32no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—62no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3C2×D3×D411yescharacteristic
650C22×C3C22×#6711yescharacteristic
651C2×D3—21no—
652C2×D3—21no—
653C2×D3—22no—
654C2×D3—41no—
655C2×D3—41no—
656C2×D3—121no—
657C2×D3—121no—
658C2×D3—121no—
659C2×D3—121no—
660C2×D3—121no—
661C2×D3—121no—
662C2×D3—241no—
663C2×D3—241no—
664C2×D3—241no—
665C2×D3—244no—
666C2×D3—244no—
667C2×D3#95012yes—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—61no—
678C3×C4—61no—
679C3×C4—61no—
680C3×C4—81no—
681C3×C4—81no—
682C3×C4—121no—
683C3×C4—121no—
684C3×C4—121no—
685C3×C4C2×#23511yescharacteristic
686C3×C4#100411yescharacteristic
687C3×C4D3×#4111yescharacteristic
688C3×C4#100911yescharacteristic
689Dic3—21no—
690Dic3—21no—
691Dic3—21no—
692Dic3—41no—
693Dic3—41no—
694Dic3—41no—
695Dic3—121no—
696Dic3—121no—
697Dic3—241no—
698C32#329611yescharacteristic, complemented, Sylow
699C23—31no—
700C23—61no—
701C23—181no—
702C23—362no—
703C23—362no—
704C23—721no—
705C23D3×#6711yescharacteristic
706Q8—61no—
707Q8—61no—
708Q8—61no—
709Q8—61no—
710D4—32no—
711D4—62no—
712D4—61no—
713D4—122no—
714D4—181no—
715D4—181no—
716D4—362no—
717D4—721no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—31no—
723C2×C4—31no—
724C2×C4—31no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—122no—
731C2×C4—122no—
732C2×C4—181no—
733C2×C4—721no—
734C2×C4D3×#6711yescharacteristic
735C2×C4C22×D3211yescharacteristic
736C8—61no—
737C8—61no—
738C8—181no—
739C8—181no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—41no—
744C2×C3—41no—
745C2×C3—62no—
746C2×C3—81no—
747C2×C3—122no—
748C2×C3#549011yescharacteristic
749C2×C3D3×#13511yescharacteristic
750C2×C3#577011yescharacteristic
751C2×C3C2×#95011yescharacteristic
752C2×C3#582911yescharacteristic
753C2×C3#583711yescharacteristic
754D3—22no—
755D3—42no—
756D3—241no—
757D3—241no—
758D3—481no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—32no—
763C22—61no—
764C22—61no—
765C22—62no—
766C22—121no—
767C22—121no—
768C22—361no—
769C22—361no—
770C22—361no—
771C22—724no—
772C22C2×D3×#6711yescharacteristic
773C4—21no—
774C4—41no—
775C4—41no—
776C4—61no—
777C4—61no—
778C4—61no—
779C4—121no—
780C4—121no—
781C4—121no—
782C4—361no—
783C4D3×#23511yescharacteristic
784C4#6430711yescharacteristic
785C3—21no—
786C3#7884511yescharacteristic, complemented
787C3#8359811yescharacteristic, complemented
788C2—41no—
789C2—62no—
790C2—122no—
791C2—721no—
792C2#1059506511yescharacteristic
793C2D3×#95011yescharacteristic
794C2#1059545711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radical#10595067C2
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. #10592702C2semidirect
4. C3×#5002C2semidirect
5. #10591177C2semidirect
6. #10591170C2semidirect
7. C3⋊C8×#67C2semidirect
8. #10590596C2semidirect
9. D3×#809C2semidirect
10. #10590537C2semidirect
11. #10590536C2semidirect
12. #10590518C2semidirect
13. #10590516C2semidirect
14. #10590467C2semidirect
15. #10590453C2semidirect
20. C32×#117C22semidirect
23. C3×#924C22semidirect
24. C22×C3×C3⋊C8C22semidirect
27. C3×#890C22semidirect
28. C3×#887C22semidirect
40. C2×#3718C22semidirect
44. #63657C22semidirect
47. #63635C22semidirect
48. #63634C22semidirect
49. C3×#810C22semidirect
50. C3×#810C22semidirect
53. #63573C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63566C22semidirect
56. #63565C22semidirect
60. Dic3×C3⋊C8C22semidirect
64. #5529D3semidirect
81. #5002D3semidirect
160. C3×#117C2×D3semidirect
161. C3×#117C2×D3semidirect
181. #924C2×D3semidirect
183. C22×C3⋊C8C2×D3semidirect
189. #890C2×D3semidirect
190. #887C2×D3semidirect
217. #810C2×D3semidirect
218. #810C2×D3semidirect
458. #117D32semidirect
698. C32#3296semidirect
786. C3#78845semidirect
787. C3#83598semidirect

Maximal subgroups

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

subgroupindex
C3×#55292
#105950672
#105927022
C3×#50022
#105911772
#105911702
C3⋊C8×#672
#105905962
D3×#8092
#105905372
#105905362
#105905182
#105905162
#105904672
#105904532
#835983
#788453