Finite Group Databasebeta

← #11889259

Subgroups — #11889259

Order 1152.

857 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×#5612C211yesmaximal, characteristic
2#10594841C211yesmaximal, characteristic, complemented
3#10592734C211yesmaximal, characteristic, complemented
4C3×#5041C211yesmaximal, characteristic, complemented
5#10591488C211yesmaximal, characteristic, complemented
6#10591458C211yesmaximal, characteristic, complemented
7#10591442C211yesmaximal, characteristic, complemented
8#10591421C211yesmaximal, characteristic, complemented
9#10591170C211yesmaximal, characteristic, complemented
10#10591155C211yesmaximal, characteristic, complemented
11#10591084C211yesmaximal, characteristic, complemented
12#10590558C211yesmaximal, characteristic, complemented
13#10590520C211yesmaximal, characteristic, complemented
14#10590478C211yesmaximal, characteristic, complemented
15#10590447C211yesmaximal, characteristic, complemented
16#83497—31nomaximal
17#80686—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C32×#121C2211yescharacteristic
21#64135C2211yescharacteristic, complemented
22C3×#938—21no—
23C3×#937—21no—
24C3×#936C2211yescharacteristic
25C2×C3×#214C2211yescharacteristic
26C3×C4×#67C2211yescharacteristic
27C3×#924C2211yescharacteristic, complemented
28C22×C3×C3⋊C8C2211yescharacteristic, complemented
29C3×#897C2211yescharacteristic
30C3×#893C2211yescharacteristic
31C3×#883—21no—
32C3×D3×C22⋊C4—21no—
33#63959—21no—
34#63956—21no—
35#63918C2211yescharacteristic, complemented
36#63862—21no—
37#63856C2211yescharacteristic
38Dic3×Dic6C2211yescharacteristic, complemented
39#63841C2211yescharacteristic
40#63838—21no—
41C2×#3718C2211yescharacteristic, complemented
42C2×#3715C2211yescharacteristic
43C2×#3711C2211yescharacteristic
44#63659C2211yescharacteristic
45#63659C2211yescharacteristic
46#63657C2211yescharacteristic, complemented
47#63635C2211yescharacteristic, complemented
48#63634C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic
50C3×#810C2211yescharacteristic, complemented
51C3×#808C2211yescharacteristic, complemented
52Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
53#63566C2211yescharacteristic, complemented
54#63566C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63563C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63554C2211yescharacteristic, complemented
61C3×#546—31no—
62#5641—31no—
63#5612D311yescharacteristic
64#5542—31no—
65C3×#465—31no—
66#5239—31no—
67#5233—31no—
68#5218—31no—
69#5215—31no—
70#5169—31no—
71#5166—31no—
72#5113—31no—
73#5111—31no—
74#5055—31no—
75#5054—31no—
76#5052—31no—
77#5047—31no—
78#5045—31no—
79#5041D311yescharacteristic, complemented
80#5035—31no—
81#5035—31no—
82#5035—61no—
83#5018—31no—
84#5011—31no—
85#5008—31no—
86#4870—31no—
87#4868—31no—
88#4817—31no—
89#4816—31no—
90#4770—31no—
91#4765—31no—
92C23×C3×D3—21no—
93C2×C32×D4—21no—
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C2×C3×#67D411yescharacteristic
99C3×D3×D4—22no—
100C3×D3×D4—41no—
101C3×#235—22no—
102C3×#235—41no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×#627—21no—
110C32×C4⋊C4C2311yescharacteristic
111C32×C22⋊C4—21no—
112#3757—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4×C3⋊Dic3—21no—
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#217—21no—
119C3×#217—21no—
120C3×#217—21no—
121C3×#217D411yescharacteristic
122C3×#214—41no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4D411yescharacteristic
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8—41no—
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134#3724—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139Dic32—21no—
140Dic32—21no—
141#3718—41no—
142#3715—22no—
143#3711—41no—
144#3311—91noSylow
145C2×C3×#41—31no—
146C22×C3×D4—31no—
147C2×D3×D4C2×D311yescharacteristic
148C2×#235C2×D311yescharacteristic
149C2×C3×SD16—31no—
150C22×C3×C8—31no—
151C3×#124—31no—
152C3×#123—61no—
153C3×C22⋊Q8—31no—
154C3×C22⋊Q8—31no—
155C3×#121—21no—
156C3×#121—61no—
157C3×#121C2×D311yescharacteristic
158C3×#121C2×D311yescharacteristic
159C3×#120—61no—
160C3×C4×D4—31no—
161C3×C4×D4—31no—
162C2×C3×C22⋊C4—61no—
163#946—31no—
164Q8×Dic3—31no—
165C2×#216—31no—
166C2×#216—31no—
167C2×#215—31no—
168#938—21no—
169#937—21no—
170#936—61no—
171#936C2×D311yescharacteristic
172C2×#214—31no—
173C2×#214C2×D311yescharacteristic
174C4×#67C2×D311yescharacteristic
175#926—31no—
176#926—31no—
177#926—31no—
178#926—61no—
179#924—31no—
180#924C2×D311yescharacteristic, complemented
181C2×#208—31no—
182C22×C3⋊C8C2×D311yescharacteristic, complemented
183C2×ΓL(1,𝔽25)—31no—
184#898—61no—
185#897C2×D311yescharacteristic
186#893C2×D311yescharacteristic
187#892—31no—
188#888—31no—
189#887—61no—
190#887—61no—
191#885—61no—
192#883—21no—
193D3×C22⋊C4—21no—
194#879—61no—
195#879—61no—
196#879—61no—
197#869—31no—
198C4×Dic6—31no—
199C3×#106—31no—
200C3×#103—31no—
201C3×#102—31no—
202#835—31no—
203#835—31no—
204#835—31no—
205#832—31no—
206#832—31no—
207#832—31no—
208#832—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832—61no—
213#832—61no—
214#832C2×D311yescharacteristic
215#830—31no—
216#830—31no—
217#830—31no—
218#830—61no—
219#821—31no—
220#821—31no—
221(C2×D3)⋊C8—31no—
222#816—31no—
223#816—31no—
224#815—31no—
225Dic3⋊C8—31no—
226#810—31no—
227#810C2×D311yescharacteristic, complemented
228#809—31no—
229#808—31no—
230#808—31no—
231#808—61no—
232#808C2×D311yescharacteristic, complemented
233#807—31no—
234#807—31no—
235#807—61no—
236C4⋊(C3⋊C8)—31no—
237#803—31no—
238C23×C32—21no—
239C23×C32C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3—42no—
242C22×C3×D3—42no—
243C22×C3×D3—81no—
244C22×C3×D3C2×D411yescharacteristic
245C32×D4—21no—
246C32×D4—21no—
247C32×D4—81no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2411yescharacteristic
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255C3×#67—41no—
256C3×#67—42no—
257C3×#67—42no—
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×D12—21no—
265C3×D12#4112yes—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—42no—
269C3×C4×D3—81no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274#627—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—91no—
282#485—91no—
283#482—91no—
284#476—91no—
285#470—91no—
286#465—31no—
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—31no—
299C2×C3×Q8—31no—
300C2×C3×D4—21no—
301C2×C3×D4—21no—
302C2×C3×D4—21no—
303C2×C3×D4—31no—
304C2×C3×D4—31no—
305C2×C3×D4—41no—
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—21no—
313C22×C3×C4—31no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
316C22×C3×C4C22×D311yescharacteristic
317C22×C3×C4C22×D311yescharacteristic
318C2×#67—21no—
319C2×#67—21no—
320C2×#67#6711yescharacteristic
321D3×D4—22no—
322D3×D4—41no—
323#235—22no—
324#235—41no—
325C2×D12C22×D311yescharacteristic
326C2×C4×D3—21no—
327C2×C4×D3—21no—
328C2×C4×D3C22×D311yescharacteristic
329C2×Dic6—61no—
330C2×Dic6—61no—
331C2×Dic6C22×D311yescharacteristic
332C2×Dic6C22×D311yescharacteristic
333C3×SD16—121no—
334C2×C3×C8—31no—
335C2×C3×C8—31no—
336C2×C3×C8—121no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C4⋊C4C22×D311yescharacteristic
344C3×C22⋊C4—21no—
345C3×C22⋊C4—21no—
346C3×C22⋊C4—31no—
347C3×C22⋊C4—31no—
348C3×C22⋊C4—41no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C42—31no—
355#217—21no—
356#217—21no—
357#217—21no—
358#217—61no—
359#217—61no—
360#217—61no—
361#217—61no—
362#217—121no—
363#217#6711yescharacteristic
364#216—121no—
365#216—121no—
366#215—62no—
367#214—41no—
368#214—62no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4#6711yescharacteristic
374C4⋊Dic3—21no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3C22×D311yescharacteristic
384Dic3⋊C4—21no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4#6711yescharacteristic
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—121no—
397C4×Dic3C22×D311yescharacteristic
398#208—121no—
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⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408ΓL(1,𝔽25)—121no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—41no—
413C22×C32—41no—
414C22×C32—41no—
415C22×C32C22×D411yescharacteristic
416C2×C3×D3—21no—
417C2×C3×D3—22no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—84no—
423C32×C4—21no—
424C32×C4—41no—
425C32×C4C2×#4111yescharacteristic
426C32×C4H(5,𝔽2)11yescharacteristic
427C3⋊Dic3—41no—
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—31no—
437C2×Q16—91no—
438C2×SD16—31no—
439C2×SD16—91no—
440C2×M16—91no—
441C22×C8—31no—
442C4⋊Q8—91no—
443#126—181no—
444#126—181no—
445#124—31no—
446#124—181no—
447#123—61no—
448C22⋊Q8—31no—
449C22⋊Q8—31no—
450C22⋊Q8—91no—
451#121—61no—
452#121D3211yescharacteristic
453#120—61no—
454C4×Q8—91no—
455C4×Q8—181no—
456C4×D4—31no—
457C4×D4—31no—
458#117—91no—
459#117—91no—
460C2×C22⋊C4—61no—
461#107—91no—
462#106—31no—
463#106—91no—
464C4⋊C8—91no—
465#103—31no—
466#103—91no—
467#103—91no—
468#103—91no—
469#102—31no—
470#102—91no—
471#102—91no—
472#102—91no—
473#102—91no—
474#102—91no—
475C22⋊C8—91no—
476C22⋊C8—91no—
477#97—91no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—21no—
481C23×C3—31no—
482C23×C3—41no—
483C23×C3—61no—
484C23×C3—122no—
485C23×C3—122no—
486C23×C3—241no—
487C23×C3D3×D411yescharacteristic
488C23×C3C2×#6711yescharacteristic
489C22×D3—21no—
490C22×D3—42no—
491C22×D3—42no—
492C22×D3—81no—
493C22×D3C2×#6711yescharacteristic
494C3×Q8—61no—
495C3×Q8—61no—
496C3×Q8—61no—
497C3×Q8—61no—
498C3×D4—21no—
499C3×D4—21no—
500C3×D4—21no—
501C3×D4—21no—
502C3×D4—32no—
503C3×D4—41no—
504C3×D4—41no—
505C3×D4—61no—
506C3×D4—81no—
507C3×D4—81no—
508C3×D4—82no—
509C3×D4—121no—
510C3×D4—122no—
511C3×D4—122no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—31no—
521C2×C3×C4—31no—
522C2×C3×C4—31no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—122no—
532C2×C3×C4—241no—
533C2×C3×C4D3×D411yescharacteristic
534C2×C3×C4C2×#6711yescharacteristic
535C2×C3×C4C23×D311yescharacteristic
536C2×C3×C4C23×D311yescharacteristic
537#67—41no—
538#67—42no—
539#67—42no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—121no—
548C2×Dic3—121no—
549C2×Dic3C2×#6711yescharacteristic
550C2×Dic3C2×#6711yescharacteristic
551C2×Dic3C2×#6711yescharacteristic
552D12—21no—
553D12#23712yes—
554C4×D3—21no—
555C4×D3—21no—
556C4×D3—42no—
557C4×D3—81no—
558Dic6—21no—
559Dic6—21no—
560Dic6—21no—
561Dic6—21no—
562Dic6—122no—
563Dic6—122no—
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—81no—
576C2×C32#54611yescharacteristic
577C2×C32#57511yescharacteristic
578C2×C32#57711yescharacteristic
579C3×D3—41no—
580C3×D3—42no—
581C24—61no—
582#41—62no—
583#41—121no—
584C2×Q8—31no—
585C2×Q8—31no—
586C2×Q8—181no—
587C2×D4—21no—
588C2×D4—31no—
589C2×D4—31no—
590C2×D4—61no—
591C2×D4—62no—
592C2×D4—61no—
593C2×D4—121no—
594C2×D4C2×D3211yescharacteristic
595C22×C4—31no—
596C22×C4—61no—
597C22×C4—61no—
598C22×C4C2×D3211yescharacteristic
599Q16—361no—
600SD16—121no—
601SD16—182no—
602M16—361no—
603C2×C8—31no—
604C2×C8—31no—
605C2×C8—91no—
606C2×C8—91no—
607C2×C8—121no—
608C4⋊C4—31no—
609C4⋊C4—31no—
610C4⋊C4—61no—
611C4⋊C4—61no—
612C4⋊C4—91no—
613C4⋊C4—91no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C4⋊C4C2×D3211yescharacteristic
618C22⋊C4—21no—
619C22⋊C4—31no—
620C22⋊C4—31no—
621C22⋊C4—61no—
622C22⋊C4—61no—
623C22⋊C4—61no—
624C22⋊C4—61no—
625C22⋊C4—61no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C42—31no—
630C42—181no—
631C42—181no—
632C42—181no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—61no—
650C22×C3—61no—
651C22×C3—61no—
652C22×C3—62no—
653C22×C3—81no—
654C22×C3—81no—
655C22×C3—81no—
656C22×C3—121no—
657C22×C3—121no—
658C22×C3—244no—
659C22×C3C2×D3×D411yescharacteristic
660C22×C3C22×#6711yescharacteristic
661C2×D3—21no—
662C2×D3—22no—
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—41no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—61no—
676C3×C4—61no—
677C3×C4—61no—
678C3×C4—81no—
679C3×C4—121no—
680C3×C4—121no—
681C3×C4—121no—
682C3×C4C2×#23711yescharacteristic
683C3×C4#100411yescharacteristic
684C3×C4#100411yescharacteristic
685C3×C4D3×#4111yescharacteristic
686Dic3—21no—
687Dic3—21no—
688Dic3—21no—
689Dic3—41no—
690Dic3—41no—
691Dic3—41no—
692Dic3—121no—
693Dic3—121no—
694Dic3—121no—
695Dic3—121no—
696Dic3—241no—
697Dic3—241no—
698C32#331111yescharacteristic, complemented, Sylow
699C23—21no—
700C23—31no—
701C23—61no—
702C23—122no—
703C23—122no—
704C23—241no—
705C23D3×#6711yescharacteristic
706Q8—61no—
707Q8—61no—
708Q8—61no—
709Q8—61no—
710Q8—362no—
711D4—21no—
712D4—21no—
713D4—32no—
714D4—61no—
715D4—81no—
716D4—121no—
717D4—122no—
718D4—122no—
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—181no—
732C2×C4—181no—
733C2×C4—241no—
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—81no—
746C2×C3—81no—
747C2×C3—81no—
748C2×C3—121no—
749C2×C3—122no—
750C2×C3—161no—
751C2×C3#561011yescharacteristic
752C2×C3#576211yescharacteristic
753C2×C3#576811yescharacteristic
754C2×C3#580611yescharacteristic
755C2×C3#582211yescharacteristic
756C2×C3#583611yescharacteristic
757D3—41no—
758D3—42no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—61no—
766C22—61no—
767C22—62no—
768C22—61no—
769C22—121no—
770C22—121no—
771C22—244no—
772C22C2×D3×#6711yescharacteristic
773C4—21no—
774C4—41no—
775C4—61no—
776C4—61no—
777C4—61no—
778C4—121no—
779C4—121no—
780C4—121no—
781C4—361no—
782C4—361no—
783C4D3×#23711yescharacteristic
784C4#6431311yescharacteristic
785C3—21no—
786C3#8068611yescharacteristic, complemented
787C3#8349711yescharacteristic, complemented
788C2—41no—
789C2—81no—
790C2—121no—
791C2—122no—
792C2#1059510511yescharacteristic
793C2#1059515011yescharacteristic
794C2#1059545311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
prime radicalC3×#5612C2
hypercenter#121D32
hypocenterC32#3311
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. #10594841C2semidirect
3. #10592734C2semidirect
4. C3×#5041C2semidirect
5. #10591488C2semidirect
6. #10591458C2semidirect
7. #10591442C2semidirect
8. #10591421C2semidirect
9. #10591170C2semidirect
10. #10591155C2semidirect
11. #10591084C2semidirect
12. #10590558C2semidirect
13. #10590520C2semidirect
14. #10590478C2semidirect
15. #10590447C2semidirect
21. #64135C22semidirect
27. C3×#924C22semidirect
28. C22×C3×C3⋊C8C22semidirect
35. #63918C22semidirect
38. Dic3×Dic6C22semidirect
41. C2×#3718C22semidirect
46. #63657C22semidirect
47. #63635C22semidirect
48. #63634C22semidirect
50. C3×#810C22semidirect
51. C3×#808C22semidirect
52. Dic3⋊(C3⋊C8)C22semidirect
53. #63566C22semidirect
54. #63566C22semidirect
55. #63565C22semidirect
60. #63554C22semidirect
79. #5041D3semidirect
180. #924C2×D3semidirect
182. C22×C3⋊C8C2×D3semidirect
227. #810C2×D3semidirect
232. #808C2×D3semidirect
698. C32#3311semidirect
786. C3#80686semidirect
787. C3#83497semidirect

Maximal subgroups

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

subgroupindex
C3×#56122
#105948412
#105927342
C3×#50412
#105914882
#105914582
#105914422
#105914212
#105911702
#105911552
#105910842
#105905582
#105905202
#105904782
#105904472
#834973
#806863