Finite Group Databasebeta

← #11889303

Subgroups — #11889303

Order 1152.

860 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×#5676C211yesmaximal, characteristic
2#10593863C211yesmaximal, characteristic, complemented
3#10592753C211yesmaximal, characteristic, complemented
4C3×#5055C211yesmaximal, characteristic, complemented
5#10591599C211yesmaximal, characteristic, complemented
6#10591598C211yesmaximal, characteristic, complemented
7#10591558C211yesmaximal, characteristic, complemented
8#10591556C211yesmaximal, characteristic, complemented
9#10591460C211yesmaximal, characteristic, complemented
10#10591459C211yesmaximal, characteristic, complemented
11#10591423C211yesmaximal, characteristic, complemented
12#10591421C211yesmaximal, characteristic, complemented
13#10590360C211yesmaximal, characteristic, complemented
14#10590326C211yesmaximal, characteristic, complemented
15#10590266C211yesmaximal, characteristic, complemented
16#83497—31nomaximal
17#81698—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C32×#124C2211yescharacteristic
21C2×#3756C2211yescharacteristic, complemented
22C2×#3754C2211yescharacteristic
23C4×#634C2211yescharacteristic, complemented
24C3×#946C2211yescharacteristic
25C3×#938C2211yescharacteristic
26C3×#884—21no—
27C3×#883—21no—
28C3×#882—21no—
29C3×D3×C22⋊C4—21no—
30C3×C4×D12C2211yescharacteristic
31C3×C4×D12C2211yescharacteristic
32C3×#869C2211yescharacteristic, complemented
33#63863—21no—
34#63858—21no—
35#63858—21no—
36#63857C2211yescharacteristic
37#63857C2211yescharacteristic, complemented
38#63843—21no—
39#63841C2211yescharacteristic
40#63841C2211yescharacteristic, complemented
41C2×#3716C2211yescharacteristic
42C2×#3711C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63662C2211yescharacteristic, complemented
45#63659C2211yescharacteristic
46C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×#835C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic
50C3×#832C2211yescharacteristic
51C3×#803C2211yescharacteristic, complemented
52#63575C2211yescharacteristic, complemented
53#63574C2211yescharacteristic, complemented
54#63574C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63563C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61C3×#546—31no—
62#5732—31no—
63#5676D311yescharacteristic
64#5542—31no—
65C3×#489—31no—
66#5239—31no—
67#5233—31no—
68#5218—31no—
69#5215—31no—
70#5084—31no—
71#5055D311yescharacteristic, complemented
72#5054—31no—
73#5054—31no—
74#5054—61no—
75#5052—31no—
76#5045—31no—
77#5041—31no—
78#5035—31no—
79#5018—31no—
80#5011—31no—
81#5008—31no—
82#4816—31no—
83#4814—31no—
84#4808—31no—
85#4804—31no—
86#4784—31no—
87#4778—31no—
88#4776—31no—
89#4770—31no—
90#4710—31no—
91#4706—31no—
92C23×C3×D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C3×#239—22no—
99C3×#239—41no—
100C3×D3×D4—22no—
101C3×D3×D4—41no—
102C2×C3×D12—21no—
103C2×C3×D12D411yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6—21no—
110C32×C22⋊C4—21no—
111C32×C22⋊C4—21no—
112C32×C42C2311yescharacteristic
113#3756—41no—
114#3754—41no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117C4×C3⋊Dic3—21no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×#217—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×(C2×D3)⋊C4D411yescharacteristic
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3D411yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139Dic32—21no—
140Dic32—21no—
141#3716—22no—
142#3711—41no—
143D3×C3⋊C8—41no—
144#3311—91noSylow
145C2×C3×#41—31no—
146C22×C3×D4—31no—
147C2×#239C2×D311yescharacteristic
148C2×D3×D4C2×D311yescharacteristic
149C3×C4⋊Q8—31no—
150C3×#124—21no—
151C3×#124C2×D311yescharacteristic
152C3×#124C2×D311yescharacteristic
153C3×#123—61no—
154C3×C22⋊Q8—31no—
155C3×#121—31no—
156C3×#121—61no—
157C3×#120—61no—
158C3×C4×D4—31no—
159C3×C4×D4—31no—
160C2×C3×C22⋊C4—61no—
161#947—61no—
162#946C2×D311yescharacteristic
163Q8×Dic3—61no—
164C2×#216—31no—
165C2×#216—31no—
166C2×#216—61no—
167#938C2×D311yescharacteristic
168#936—61no—
169C2×#214—31no—
170C2×#214—31no—
171C2×#214—31no—
172C2×#214—61no—
173#926—31no—
174#926—31no—
175#924—31no—
176#924—31no—
177C2×#208—31no—
178C22×C3⋊C8—31no—
179C2×#204—31no—
180C2×ΓL(1,𝔽25)—31no—
181C2×D3×C8—31no—
182#898—61no—
183#898—61no—
184#897—31no—
185#897—31no—
186#892—31no—
187#892—31no—
188#887—61no—
189#884—21no—
190#883—21no—
191#882—21no—
192D3×C22⋊C4—21no—
193#879—61no—
194#879—61no—
195C4×D12C2×D311yescharacteristic
196C4×D12C2×D311yescharacteristic
197#869C2×D311yescharacteristic, complemented
198C4×Dic6—31no—
199C4×Dic6—31no—
200C4×Dic6—61no—
201C3×#103—31no—
202C3×#103—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#97—31no—
206#835—31no—
207#835—31no—
208#835—61no—
209#835C2×D311yescharacteristic, complemented
210#835C2×D311yescharacteristic, complemented
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#832—31no—
216#832—61no—
217#832C2×D311yescharacteristic
218#832C2×D311yescharacteristic
219#830—31no—
220#830—31no—
221#821—31no—
222(C2×D3)⋊C8—31no—
223(C2×D3)⋊C8—31no—
224#818—31no—
225#816—31no—
226#810—31no—
227#809—31no—
228#809—31no—
229#808—31no—
230#808—31no—
231#808—31no—
232#808—31no—
233#807—31no—
234C4⋊(C3⋊C8)—31no—
235C4⋊(C3⋊C8)—31no—
236C4⋊(C3⋊C8)—61no—
237#803C2×D311yescharacteristic, complemented
238C23×C32—21no—
239C22×C3×D3—21no—
240C22×C3×D3—42no—
241C22×C3×D3—42no—
242C22×C3×D3—81no—
243C22×C3×D3C2×D411yescharacteristic
244C22×C3×D3C2×D411yescharacteristic
245C32×Q8—21no—
246C32×Q8—21no—
247C32×D4—21no—
248C32×D4—21no—
249C2×C32×C4—21no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2411yescharacteristic
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255#634—21no—
256#634—21no—
257C3×#67—42no—
258C3×#67—81no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×D12—21no—
265C3×D12—41no—
266C3×D12—42no—
267C3×D12#4112yes—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×C4×D3—21no—
272C3×C4×D3—42no—
273C3×C4×D3—81no—
274C3×Dic6—42no—
275C3⋊(C3⋊C8)—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#556—91no—
280#546—31no—
281#489—31no—
282#485—91no—
283#482—91no—
284#476—91no—
285#470—91no—
286#465—91no—
287#464—91no—
288#452—91no—
289#450—91no—
290#440—91no—
291#435—91no—
292#418—91no—
293#416—91no—
294C24×C3—61no—
295C23×D3—21no—
296C3×#41—62no—
297C3×#41—121no—
298C2×C3×Q8—21no—
299C2×C3×Q8—61no—
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×D4—21no—
303C2×C3×D4—31no—
304C2×C3×D4—31no—
305C2×C3×D4—61no—
306C2×C3×D4—61no—
307C2×C3×D4—62no—
308C2×C3×D4—61no—
309C2×C3×D4—121no—
310C2×C3×D4C22×D311yescharacteristic
311C2×C3×D4C22×D311yescharacteristic
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
316C2×#67—21no—
317C2×#67—21no—
318#239—22no—
319#239—41no—
320D3×D4—22no—
321D3×D4—41no—
322C2×D12—21no—
323C2×D12#6711yescharacteristic
324C2×D12C22×D311yescharacteristic
325C2×C4×D3—21no—
326C2×C4×D3—21no—
327C2×C4×D3C22×D311yescharacteristic
328C2×C4×D3C22×D311yescharacteristic
329C2×Dic6—21no—
330C2×Dic6—31no—
331C2×Dic6—31no—
332C2×Dic6—61no—
333C2×C3×C8—31no—
334C2×C3×C8—31no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C22⋊C4—21no—
342C3×C22⋊C4—21no—
343C3×C22⋊C4—21no—
344C3×C22⋊C4—21no—
345C3×C22⋊C4—31no—
346C3×C22⋊C4—31no—
347C3×C22⋊C4—41no—
348C3×C22⋊C4—41no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C42—21no—
353C3×C42C22×D311yescharacteristic
354C3×C42C22×D311yescharacteristic
355#217—21no—
356#217—61no—
357#217—61no—
358#217—61no—
359#217—61no—
360#216—121no—
361#216—121no—
362#216—122no—
363#214—62no—
364#214—121no—
365#214—121no—
366#214—122no—
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4#6711yescharacteristic
374(C2×D3)⋊C4#6711yescharacteristic
375C4⋊Dic3—21no—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3#6711yescharacteristic
382C4⋊Dic3C22×D311yescharacteristic
383C4⋊Dic3C22×D311yescharacteristic
384C4⋊Dic3C22×D311yescharacteristic
385Dic3⋊C4—21no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—121no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—121no—
398#208—121no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—61no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8—121no—
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408#204—62no—
409ΓL(1,𝔽25)—121no—
410D3×C8—121no—
411C22×C32—41no—
412C22×C32—41no—
413C22×C32—41no—
414C22×C32C22×D411yescharacteristic
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—22no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—84no—
425C32×C4—21no—
426C32×C4—21no—
427C32×C4—41no—
428C32×C4C2×#4111yescharacteristic
429C32×C4H(5,𝔽2)11yescharacteristic
430C3⋊Dic3—41no—
431C3⋊Dic3—41no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C2×#41—31no—
438C22×D4—31no—
439C2×Q16—91no—
440C2×SD16—91no—
441C2×SD16—91no—
442C2×M16—91no—
443C22×C8—91no—
444C4⋊Q8—31no—
445#126—181no—
446#126—181no—
447#124—181no—
448#124D3211yescharacteristic
449#123—61no—
450C22⋊Q8—31no—
451C22⋊Q8—91no—
452C22⋊Q8—91no—
453#121—31no—
454#121—61no—
455#120—61no—
456C4×Q8—91no—
457C4×Q8—181no—
458C4×D4—31no—
459C4×D4—31no—
460#117—91no—
461#117—91no—
462C2×C22⋊C4—61no—
463#107—91no—
464#106—91no—
465#106—91no—
466C4⋊C8—91no—
467#103—31no—
468#103—31no—
469#103—91no—
470#103—91no—
471#102—31no—
472#102—31no—
473#102—91no—
474#102—91no—
475#102—91no—
476#102—91no—
477C22⋊C8—91no—
478C22⋊C8—91no—
479#97—31no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—31no—
483C23×C3—31no—
484C23×C3—41no—
485C23×C3—61no—
486C23×C3—122no—
487C23×C3—122no—
488C23×C3—241no—
489C22×D3—21no—
490C22×D3—42no—
491C22×D3—42no—
492C22×D3—81no—
493C22×D3C2×#6711yescharacteristic
494C22×D3C2×#6711yescharacteristic
495C3×Q8—21no—
496C3×Q8—21no—
497C3×Q8—21no—
498C3×Q8—21no—
499C3×Q8—41no—
500C3×Q8—41no—
501C3×Q8—122no—
502C3×D4—21no—
503C3×D4—21no—
504C3×D4—21no—
505C3×D4—21no—
506C3×D4—32no—
507C3×D4—41no—
508C3×D4—41no—
509C3×D4—61no—
510C3×D4—121no—
511C3×D4—122no—
512C3×D4—122no—
513C3×D4—241no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—41no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—122no—
530C2×C3×C4—241no—
531C2×C3×C4D3×D411yescharacteristic
532C2×C3×C4D3×D411yescharacteristic
533C2×C3×C4C2×#6711yescharacteristic
534C2×C3×C4C2×#6711yescharacteristic
535C2×C3×C4C23×D311yescharacteristic
536C2×C3×C4C23×D311yescharacteristic
537#67—42no—
538#67—81no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—121no—
547C2×Dic3—121no—
548C2×Dic3C2×#6711yescharacteristic
549C2×Dic3C2×#6711yescharacteristic
550D12—21no—
551D12—41no—
552D12—42no—
553D12#23712yes—
554C4×D3—21no—
555C4×D3—21no—
556C4×D3—21no—
557C4×D3—21no—
558C4×D3—42no—
559C4×D3—81no—
560Dic6—42no—
561Dic6—62no—
562Dic6—61no—
563Dic6—61no—
564Dic6—61no—
565Dic6—61no—
566Dic6—121no—
567C3×C8—61no—
568C3×C8—61no—
569C3⋊C8—21no—
570C3⋊C8—21no—
571C3⋊C8—61no—
572C3⋊C8—61no—
573C3⋊C8—61no—
574C3⋊C8—61no—
575C3⋊C8—121no—
576C3⋊C8—121no—
577C2×C32—81no—
578C2×C32#54611yescharacteristic
579C2×C32#57511yescharacteristic
580C2×C32#57711yescharacteristic
581C3×D3—41no—
582C3×D3—41no—
583C3×D3—42no—
584C24—61no—
585#41—62no—
586#41—121no—
587C2×Q8—61no—
588C2×Q8—91no—
589C2×Q8C2×D3211yescharacteristic
590C2×D4—31no—
591C2×D4—31no—
592C2×D4—61no—
593C2×D4—61no—
594C2×D4—62no—
595C2×D4—61no—
596C2×D4—121no—
597C2×D4C2×D3211yescharacteristic
598C22×C4—31no—
599C22×C4—31no—
600C22×C4—61no—
601C22×C4—61no—
602Q16—361no—
603SD16—182no—
604SD16—361no—
605M16—361no—
606C2×C8—31no—
607C2×C8—31no—
608C2×C8—91no—
609C2×C8—91no—
610C2×C8—361no—
611C4⋊C4—31no—
612C4⋊C4—31no—
613C4⋊C4—31no—
614C4⋊C4—31no—
615C4⋊C4—61no—
616C4⋊C4—61no—
617C4⋊C4—91no—
618C4⋊C4—181no—
619C4⋊C4—181no—
620C4⋊C4—181no—
621C22⋊C4—21no—
622C22⋊C4—21no—
623C22⋊C4—31no—
624C22⋊C4—31no—
625C22⋊C4—61no—
626C22⋊C4—61no—
627C22⋊C4—61no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C42—181no—
633C42—181no—
634C42—181no—
635C42C2×D3211yescharacteristic
636C22×C3—21no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—61no—
644C22×C3—61no—
645C22×C3—62no—
646C22×C3—61no—
647C22×C3—61no—
648C22×C3—61no—
649C22×C3—61no—
650C22×C3—81no—
651C22×C3—81no—
652C22×C3—81no—
653C22×C3—121no—
654C22×C3—121no—
655C22×C3—244no—
656C22×C3C2×D3×D411yescharacteristic
657C22×C3C22×#6711yescharacteristic
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—22no—
661C2×D3—21no—
662C2×D3—21no—
663C2×D3—21no—
664C2×D3—21no—
665C2×D3—41no—
666C2×D3—41no—
667C2×D3—84no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—41no—
678C3×C4—61no—
679C3×C4—61no—
680C3×C4—81no—
681C3×C4—121no—
682C3×C4—121no—
683C3×C4—121no—
684C3×C4C2×#23711yescharacteristic
685C3×C4#100411yescharacteristic
686C3×C4D3×#4111yescharacteristic
687C3×C4#100911yescharacteristic
688Dic3—21no—
689Dic3—21no—
690Dic3—41no—
691Dic3—41no—
692Dic3—41no—
693Dic3—122no—
694Dic3—121no—
695Dic3—121no—
696Dic3—121no—
697Dic3—121no—
698Dic3—241no—
699C32#331111yescharacteristic, complemented, Sylow
700C23—21no—
701C23—31no—
702C23—31no—
703C23—61no—
704C23—122no—
705C23—122no—
706C23—241no—
707Q8—21no—
708Q8—21no—
709Q8—122no—
710Q8—181no—
711Q8—181no—
712D4—21no—
713D4—21no—
714D4—32no—
715D4—61no—
716D4—121no—
717D4—122no—
718D4—122no—
719D4—241no—
720C2×C4—21no—
721C2×C4—31no—
722C2×C4—31no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—122no—
731C2×C4—181no—
732C2×C4—181no—
733C2×C4—241no—
734C2×C4D3×#6711yescharacteristic
735C2×C4D3×#6711yescharacteristic
736C2×C4C22×D3211yescharacteristic
737C8—61no—
738C8—61no—
739C8—181no—
740C8—181no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—21no—
744C2×C3—81no—
745C2×C3—81no—
746C2×C3—121no—
747C2×C3—121no—
748C2×C3—122no—
749C2×C3—161no—
750C2×C3#567611yescharacteristic
751C2×C3#577311yescharacteristic
752C2×C3#577811yescharacteristic
753C2×C3#580611yescharacteristic
754C2×C3#582211yescharacteristic
755C2×C3#583611yescharacteristic
756D3—41no—
757D3—41no—
758D3—42no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—61no—
763C22—61no—
764C22—61no—
765C22—61no—
766C22—61no—
767C22—61no—
768C22—62no—
769C22—121no—
770C22—121no—
771C22—244no—
772C22C2×D3×#6711yescharacteristic
773C4—21no—
774C4—21no—
775C4—41no—
776C4—61no—
777C4—61no—
778C4—121no—
779C4—121no—
780C4—121no—
781C4—361no—
782C4—361no—
783C4D3×#23711yescharacteristic
784C4#6431411yescharacteristic
785C3—21no—
786C3#8169811yescharacteristic, complemented
787C3#8349711yescharacteristic, complemented
788C2—81no—
789C2—121no—
790C2—121no—
791C2—122no—
792C2#1059522911yescharacteristic
793C2#1059546411yescharacteristic
794C2#1059546911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#124C22
socleC22×C32C22×D4
prime radicalC3×#5676C2
hypercenter#124D32
hypocenterC32#3311
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #10593863C2semidirect
3. #10592753C2semidirect
4. C3×#5055C2semidirect
5. #10591599C2semidirect
6. #10591598C2semidirect
7. #10591558C2semidirect
8. #10591556C2semidirect
9. #10591460C2semidirect
10. #10591459C2semidirect
11. #10591423C2semidirect
12. #10591421C2semidirect
13. #10590360C2semidirect
14. #10590326C2semidirect
15. #10590266C2semidirect
21. C2×#3756C22semidirect
23. C4×#634C22semidirect
32. C3×#869C22semidirect
37. #63857C22semidirect
40. #63841C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. #63662C22semidirect
46. C4⋊(C3⋊(C3⋊C8))C22semidirect
47. C3×#835C22semidirect
48. C3×#835C22semidirect
51. C3×#803C22semidirect
52. #63575C22semidirect
53. #63574C22semidirect
54. #63574C22semidirect
55. #63567C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
71. #5055D3semidirect
197. #869C2×D3semidirect
209. #835C2×D3semidirect
210. #835C2×D3semidirect
237. #803C2×D3semidirect
699. C32#3311semidirect
786. C3#81698semidirect
787. C3#83497semidirect

Maximal subgroups

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

subgroupindex
C3×#56762
#105938632
#105927532
C3×#50552
#105915992
#105915982
#105915582
#105915562
#105914602
#105914592
#105914232
#105914212
#105903602
#105903262
#105902662
#834973
#816983