Finite Group Databasebeta

← #11884257

Subgroups — #11884257

Order 1152.

1081 conjugacy classes of subgroups.

The subgroup lattice has 901 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5612C211yesmaximal, characteristic, complemented
2C2×#63934C211yesmaximal, characteristic, complemented
3#10594834C211yesmaximal, characteristic, complemented
4C2×#63829C211yesmaximal, characteristic, complemented
5#10592736C211yesmaximal, characteristic, complemented
6C3×#5041C211yesmaximal, characteristic, complemented
7#10591491C211yesmaximal, characteristic, complemented
8#10591459C211yesmaximal, characteristic, complemented
9#10591432C211yesmaximal, characteristic, complemented
10#10591170C211yesmaximal, characteristic, complemented
11#10591155C211yesmaximal, characteristic, complemented
12#10590616C211yesmaximal, characteristic, complemented
13#10590589C211yesmaximal, characteristic, complemented
14#10590587C211yesmaximal, characteristic, complemented
15#10590559C211yesmaximal, characteristic, complemented
16#83503—31nomaximal
17#80675—31nomaximal
18C2×#3828C2211yescharacteristic, complemented
19C2×C3×D3×D4C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C2×#3799C2211yescharacteristic
22C32×#121C2211yescharacteristic
23C2×#3754C2211yescharacteristic
24C2×#3753C2211yescharacteristic
25C3×#938—21no—
26C3×#937—21no—
27C3×#936C2211yescharacteristic
28C2×C3×#214C2211yescharacteristic
29C3×C4×#67C2211yescharacteristic
30C3×#924C2211yescharacteristic, complemented
31C22×C3×C3⋊C8C2211yescharacteristic, complemented
32C3×#897C2211yescharacteristic
33C3×#893C2211yescharacteristic
34C3×#883—21no—
35C3×D3×C22⋊C4—21no—
36#63975—21no—
37#63958—21no—
38#63934—24no—
39#63894C2211yescharacteristic, complemented
40#63883—21no—
41#63866C2211yescharacteristic, complemented
42#63857C2211yescharacteristic
43#63853—21no—
44C2×#3719C2211yescharacteristic, complemented
45C2×#3718C2211yescharacteristic, complemented
46C2×#3717C2211yescharacteristic, complemented
47#63829—24no—
48C2×#3716C2211yescharacteristic
49C2×#3715C2211yescharacteristic
50C2×#3714C2211yescharacteristic
51C2×#3711C2211yescharacteristic
52#63657C2211yescharacteristic, complemented
53#63637C2211yescharacteristic, complemented
54#63636C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic
56C3×#810C2211yescharacteristic, complemented
57C3×#808C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63562C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62#63554C2211yescharacteristic, complemented
63C3×#546—31no—
64C2×#950—31no—
65C2×#932—31no—
66C2×#914—31no—
67C2×#904—31no—
68#5631—31no—
69#5612D311yescharacteristic, complemented
70#5551—31no—
71C3×#465—31no—
72#5239—31no—
73#5218—31no—
74#5167—31no—
75#5111—31no—
76#5060—31no—
77#5057—31no—
78#5052—31no—
79#5047—31no—
80#5047—31no—
81#5041D311yescharacteristic, complemented
82#5037—31no—
83#5037—31no—
84#5037—61no—
85#5019—31no—
86#5014—31no—
87#5011—31no—
88#4869—31no—
89#4867—31no—
90#4818—31no—
91#4808—31no—
92#4787—31no—
93#4776—31no—
94C23×C3×D3—21no—
95C2×C32×D4—21no—
96C2×C32×D4C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C2×#638—21no—
99#3828—22no—
100#3828—41no—
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×C4×C3⋊D3—21no—
103C2×#634C2311yescharacteristic
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C2×C3×#67D411yescharacteristic
107C3×D3×D4—22no—
108C3×D3×D4—41no—
109C3×#235—22no—
110C3×#235—41no—
111C2×C3×D12C2311yescharacteristic
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×Dic6C2311yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117C2×#626—21no—
118C2×#624—21no—
119C2×#624—21no—
120#3799—22no—
121#3799—41no—
122C32×C4⋊C4C2311yescharacteristic
123C32×C22⋊C4—21no—
124#3754—41no—
125#3753—22no—
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C3×#217—21no—
129C3×#217—21no—
130C3×#217—21no—
131C3×#217D411yescharacteristic
132C3×#214—22no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4D411yescharacteristic
136C3×C4⋊Dic3—21no—
137C3×C4⋊Dic3C2311yescharacteristic
138C3×Dic3⋊C4—21no—
139C3×Dic3⋊C4D411yescharacteristic
140C3×C4×Dic3C2311yescharacteristic
141C2×C3×C3⋊C8—22no—
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144Dic3⋊Dic3—21no—
145Dic3⋊Dic3—21no—
146Dic3⋊Dic3—21no—
147#3722—21no—
148(C2×D3)⋊Dic3—21no—
149#3719—22no—
150#3718—41no—
151#3717—22no—
152#3716—22no—
153#3715—22no—
154#3714D414yescomplemented
155#3711—22no—
156#3267—91noSylow
157C2×C3×#41—31no—
158C22×C3×D4—31no—
159C2×#239—31no—
160C2×D3×D4C2×D311yescharacteristic
161C2×#235—31no—
162C2×#235—31no—
163C2×#235—31no—
164C2×#235—61no—
165C2×#235C2×D311yescharacteristic
166C2×C3×SD16—31no—
167C22×C3×C8—31no—
168C3×#124—31no—
169C3×#123—61no—
170C3×C22⋊Q8—31no—
171C3×C22⋊Q8—31no—
172C3×#121—21no—
173C3×#121—61no—
174C3×#121C2×D311yescharacteristic
175C3×#121C2×D311yescharacteristic
176C3×#120—61no—
177C3×C4×D4—31no—
178C3×C4×D4—31no—
179C2×C3×C22⋊C4—61no—
180#950—64no—
181#944—31no—
182C2×#216—31no—
183C2×#216—31no—
184C2×#216—31no—
185C2×#215—31no—
186C2×#215—31no—
187#938—21no—
188#938—61no—
189#937—21no—
190#936C2×D311yescharacteristic
191C2×#214—31no—
192C2×#214—31no—
193C2×#214—31no—
194C2×#214—31no—
195C2×#214—61no—
196C2×#214C2×D311yescharacteristic
197#932—64no—
198C2×#213—31no—
199C2×#213—31no—
200C2×#213—31no—
201C2×#213—61no—
202C4×#67C2×D311yescharacteristic
203#924—31no—
204#924C2×D311yescharacteristic, complemented
205C2×#208—31no—
206C22×C3⋊C8C2×D311yescharacteristic, complemented
207#914—64no—
208C2×Dic12—31no—
209#904—64no—
210C2×D24—31no—
211C2×#204—31no—
212C2×#204—31no—
213C2×ΓL(1,𝔽25)—31no—
214#897—31no—
215#897C2×D311yescharacteristic
216#894—61no—
217#893—31no—
218#893C2×D311yescharacteristic
219D3×C4⋊C4—61no—
220D3×C4⋊C4—61no—
221#884—61no—
222#883—21no—
223#883—61no—
224#883—61no—
225#883—61no—
226D3×C22⋊C4—21no—
227C4×D12—31no—
228#869—31no—
229C3×#106—31no—
230C3×#103—31no—
231C3×#102—31no—
232#835—31no—
233#832—31no—
234#832C2×D311yescharacteristic
235#830—31no—
236#830—31no—
237#830—31no—
238#830—61no—
239(C2×D3)⋊C8—31no—
240#815—31no—
241Dic3⋊C8—31no—
242#810—31no—
243#810—31no—
244#810—31no—
245#810—61no—
246#810C2×D311yescharacteristic, complemented
247#809—31no—
248#809—31no—
249#809—31no—
250#809—61no—
251#808C2×D311yescharacteristic, complemented
252C4⋊(C3⋊C8)—31no—
253#803—31no—
254C23×C32—21no—
255C23×C32C2×D411yescharacteristic
256C22×C3⋊D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—42no—
259C22×C3×D3—42no—
260C22×C3×D3—81no—
261C22×C3×D3C2×D411yescharacteristic
262C32×D4—21no—
263C32×D4—21no—
264C32×D4—81no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4C2×D411yescharacteristic
269C2×C32×C4C2411yescharacteristic
270#638—42no—
271C2×C3⋊Dic3—21no—
272C4⋊(C3⋊D3)—21no—
273C4⋊(C3⋊D3)C2×D412yes—
274C4×C3⋊D3—42no—
275#634—21no—
276#634—21no—
277C3×#67—41no—
278C3×#67—42no—
279C3×#67—42no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3C2×D411yescharacteristic
284C2×C3×Dic3C2×D411yescharacteristic
285C2×C3×Dic3C2×D411yescharacteristic
286C3×D12—21no—
287C3×D12C2×D412yes—
288C3×C4×D3—21no—
289C3×C4×D3—21no—
290C3×C4×D3—42no—
291C3×C4×D3—81no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295C3×Dic6—21no—
296#626—42no—
297#624—42no—
298#624—42no—
299C3⋊(C3⋊C8)—21no—
300C3⋊(C3⋊C8)—21no—
301C3×C3⋊C8—21no—
302C3×C3⋊C8C2×D412yes—
303C2×AGL(1,ℤ/8)—91no—
304C2×#135—91no—
305#547—91no—
306#546—31no—
307#497—91no—
308#470—91no—
309#465—31no—
310#463—91no—
311#461—91no—
312#452—91no—
313#452—91no—
314#450—91no—
315#449—91no—
316#442—91no—
317#435—91no—
318C24×C3—61no—
319C23×D3—21no—
320C3×#41—62no—
321C3×#41—121no—
322C2×C3×Q8—31no—
323C2×C3×Q8—31no—
324C2×C3×D4—21no—
325C2×C3×D4—21no—
326C2×C3×D4—21no—
327C2×C3×D4—31no—
328C2×C3×D4—31no—
329C2×C3×D4—41no—
330C2×C3×D4—61no—
331C2×C3×D4—62no—
332C2×C3×D4—61no—
333C2×C3×D4—121no—
334C2×C3×D4C22×D311yescharacteristic
335C2×C3×D4C22×D311yescharacteristic
336C22×C3×C4—21no—
337C22×C3×C4—31no—
338C22×C3×C4—61no—
339C22×C3×C4—61no—
340C22×C3×C4C22×D311yescharacteristic
341C22×C3×C4C22×D311yescharacteristic
342C2×#67—21no—
343C2×#67—21no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—121no—
348C2×#67#6711yescharacteristic
349#239—62no—
350#239—121no—
351D3×D4—22no—
352D3×D4—41no—
353#235—22no—
354#235—41no—
355#235—62no—
356#235—62no—
357#235—62no—
358#235—122no—
359#235—121no—
360#235—121no—
361#235—121no—
362#235—122no—
363C2×D12—31no—
364C2×D12—31no—
365C2×D12—61no—
366C2×D12—61no—
367C2×D12C22×D311yescharacteristic
368C2×C4×D3—21no—
369C2×C4×D3—21no—
370C2×C4×D3—61no—
371C2×C4×D3—61no—
372C2×C4×D3—61no—
373C2×C4×D3—61no—
374C2×C4×D3—61no—
375C2×C4×D3—61no—
376C2×C4×D3—121no—
377C2×C4×D3C22×D311yescharacteristic
378C2×Dic6—31no—
379C2×Dic6—31no—
380C2×Dic6—61no—
381C2×Dic6C22×D311yescharacteristic
382C2×Dic6C22×D311yescharacteristic
383C3×SD16—62no—
384C2×C3×C8—31no—
385C2×C3×C8—31no—
386C2×C3×C8—62no—
387C3×C4⋊C4—21no—
388C3×C4⋊C4—31no—
389C3×C4⋊C4—31no—
390C3×C4⋊C4—61no—
391C3×C4⋊C4—61no—
392C3×C4⋊C4C22×D311yescharacteristic
393C3×C4⋊C4C22×D311yescharacteristic
394C3×C22⋊C4—21no—
395C3×C22⋊C4—21no—
396C3×C22⋊C4—31no—
397C3×C22⋊C4—31no—
398C3×C22⋊C4—41no—
399C3×C22⋊C4—61no—
400C3×C22⋊C4—61no—
401C3×C22⋊C4—61no—
402C3×C22⋊C4—61no—
403C3×C22⋊C4—61no—
404C3×C42—31no—
405#217—21no—
406#217—21no—
407#217—21no—
408#217—61no—
409#217#6711yescharacteristic
410#216—62no—
411#216—121no—
412#216—121no—
413#215—62no—
414#215—62no—
415#214—22no—
416#214—62no—
417#214—62no—
418#214—121no—
419#214—121no—
420#214—122no—
421#213—34no—
422#213—62no—
423#213—62no—
424#213—122no—
425(C2×D3)⋊C4—21no—
426(C2×D3)⋊C4—21no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4#6711yescharacteristic
431C4⋊Dic3—21no—
432C4⋊Dic3—61no—
433C4⋊Dic3—61no—
434C4⋊Dic3—61no—
435C4⋊Dic3C22×D311yescharacteristic
436Dic3⋊C4—21no—
437Dic3⋊C4—61no—
438Dic3⋊C4—61no—
439Dic3⋊C4—61no—
440Dic3⋊C4#6711yescharacteristic
441C4×Dic3C22×D311yescharacteristic
442#208—62no—
443C2×C3⋊C8—22no—
444C2×C3⋊C8—31no—
445C2×C3⋊C8—31no—
446C2×C3⋊C8—31no—
447C2×C3⋊C8—31no—
448C2×C3⋊C8—61no—
449C2×C3⋊C8—61no—
450C2×C3⋊C8C22×D311yescharacteristic
451C2×C3⋊C8C22×D311yescharacteristic
452Dic12—62no—
453D24—34no—
454#204—62no—
455#204—62no—
456ΓL(1,𝔽25)—62no—
457C22×C32—21no—
458C22×C32—21no—
459C22×C32—21no—
460C22×C32—41no—
461C22×C32—41no—
462C22×C32—41no—
463C22×C32C22×D411yescharacteristic
464C2×C3⋊D3—22no—
465C2×C3⋊D3—41no—
466C2×C3⋊D3—41no—
467C2×C3×D3—21no—
468C2×C3×D3—22no—
469C2×C3×D3—21no—
470C2×C3×D3—21no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—84no—
474C32×C4—21no—
475C32×C4—41no—
476C32×C4C22×D411yescharacteristic
477C32×C4H(5,𝔽2)11yescharacteristic
478C3⋊Dic3—41no—
479C3×Dic3—21no—
480C3×Dic3—21no—
481C3×Dic3—21no—
482C3×Dic3—41no—
483C3×Dic3—41no—
484C3×Dic3—41no—
485C2×#41—31no—
486C2×#41—91no—
487C2×#41—91no—
488C22×D4—31no—
489AGL(1,ℤ/8)—184no—
490#135—184no—
491C2×Q16—91no—
492C2×Q16—91no—
493C2×SD16—31no—
494C2×SD16—91no—
495C2×SD16—91no—
496C2×SD16—91no—
497C2×SD16—91no—
498C2×D8—91no—
499C2×D8—91no—
500C2×M16—91no—
501C22×C8—31no—
502C4⋊Q8—91no—
503#124—31no—
504#123—61no—
505#123—181no—
506#123—181no—
507C22⋊Q8—31no—
508C22⋊Q8—31no—
509C22⋊Q8—91no—
510#121—61no—
511#121—181no—
512#121D3211yescharacteristic
513#120—61no—
514C4×D4—31no—
515C4×D4—31no—
516C4×D4—91no—
517C2×C4⋊C4—181no—
518C2×C22⋊C4—61no—
519#106—31no—
520C4⋊C8—91no—
521#103—31no—
522#103—91no—
523#103—91no—
524#102—31no—
525#102—91no—
526#102—91no—
527C22⋊C8—91no—
528C22⋊C8—91no—
529#97—91no—
530C23×C3—21no—
531C23×C3—21no—
532C23×C3—21no—
533C23×C3—31no—
534C23×C3—41no—
535C23×C3—61no—
536C23×C3—122no—
537C23×C3—122no—
538C23×C3—241no—
539C23×C3D3×D411yescharacteristic
540C23×C3C2×#6711yescharacteristic
541C22×D3—21no—
542C22×D3—42no—
543C22×D3—42no—
544C22×D3—61no—
545C22×D3—61no—
546C22×D3—81no—
547C22×D3—121no—
548C22×D3C2×#6711yescharacteristic
549C3×Q8—61no—
550C3×Q8—61no—
551C3×Q8—61no—
552C3×Q8—61no—
553C3×D4—21no—
554C3×D4—21no—
555C3×D4—21no—
556C3×D4—21no—
557C3×D4—32no—
558C3×D4—41no—
559C3×D4—41no—
560C3×D4—61no—
561C3×D4—81no—
562C3×D4—81no—
563C3×D4—82no—
564C3×D4—121no—
565C3×D4—122no—
566C3×D4—122no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—31no—
576C2×C3×C4—31no—
577C2×C3×C4—31no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—122no—
587C2×C3×C4—241no—
588C2×C3×C4D3×D411yescharacteristic
589C2×C3×C4C2×#6711yescharacteristic
590C2×C3×C4C23×D311yescharacteristic
591C2×C3×C4C23×D311yescharacteristic
592#67—41no—
593#67—42no—
594#67—42no—
595#67—122no—
596#67—122no—
597#67—122no—
598#67—124no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—21no—
602C2×Dic3—61no—
603C2×Dic3—61no—
604C2×Dic3—121no—
605C2×Dic3C2×#6711yescharacteristic
606C2×Dic3C2×#6711yescharacteristic
607C2×Dic3C2×#6711yescharacteristic
608D12—21no—
609D12—32no—
610D12—32no—
611D12—62no—
612D12—61no—
613D12—61no—
614D12—121no—
615D12—122no—
616D12D3×D412yes—
617C4×D3—21no—
618C4×D3—21no—
619C4×D3—42no—
620C4×D3—81no—
621C4×D3—122no—
622C4×D3—122no—
623C4×D3—122no—
624C4×D3—122no—
625C4×D3—122no—
626C4×D3—122no—
627C4×D3—124no—
628Dic6—21no—
629Dic6—21no—
630Dic6—21no—
631Dic6—21no—
632Dic6—62no—
633Dic6—61no—
634Dic6—61no—
635Dic6—61no—
636Dic6—61no—
637Dic6—121no—
638C3×C8—32no—
639C3×C8—61no—
640C3⋊C8—21no—
641C3⋊C8—61no—
642C3⋊C8—61no—
643C3⋊C8—61no—
644C3⋊C8—61no—
645C3⋊C8—121no—
646C3⋊C8—121no—
647C3⋊C8D3×D412yes—
648C2×C32—41no—
649C2×C32—81no—
650C2×C32D4211yescharacteristic
651C2×C32#57511yescharacteristic
652C2×C32#57711yescharacteristic
653C3⋊D3—42no—
654C3×D3—41no—
655C3×D3—42no—
656C24—61no—
657#41—62no—
658#41—121no—
659#41—182no—
660#41—182no—
661#41—361no—
662#41—361no—
663C2×Q8—31no—
664C2×Q8—31no—
665C2×Q8—91no—
666C2×D4—21no—
667C2×D4—31no—
668C2×D4—31no—
669C2×D4—61no—
670C2×D4—62no—
671C2×D4—61no—
672C2×D4—91no—
673C2×D4—121no—
674C2×D4—181no—
675C2×D4—181no—
676C2×D4C2×D3211yescharacteristic
677C22×C4—31no—
678C22×C4—61no—
679C22×C4—61no—
680C22×C4—181no—
681C22×C4—181no—
682C22×C4—181no—
683C22×C4C2×D3211yescharacteristic
684Q16—182no—
685Q16—361no—
686SD16—62no—
687SD16—182no—
688SD16—182no—
689SD16—182no—
690SD16—361no—
691D8—94no—
692D8—182no—
693M16—182no—
694C2×C8—31no—
695C2×C8—31no—
696C2×C8—62no—
697C2×C8—91no—
698C2×C8—91no—
699C4⋊C4—31no—
700C4⋊C4—31no—
701C4⋊C4—61no—
702C4⋊C4—61no—
703C4⋊C4—181no—
704C4⋊C4—181no—
705C4⋊C4—181no—
706C4⋊C4C2×D3211yescharacteristic
707C22⋊C4—21no—
708C22⋊C4—31no—
709C22⋊C4—31no—
710C22⋊C4—61no—
711C22⋊C4—61no—
712C22⋊C4—61no—
713C22⋊C4—61no—
714C22⋊C4—61no—
715C22⋊C4—181no—
716C22⋊C4—181no—
717C42—31no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—21no—
722C22×C3—21no—
723C22×C3—21no—
724C22×C3—21no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—61no—
735C22×C3—61no—
736C22×C3—61no—
737C22×C3—62no—
738C22×C3—81no—
739C22×C3—81no—
740C22×C3—81no—
741C22×C3—121no—
742C22×C3—121no—
743C22×C3—244no—
744C22×C3C2×D3×D411yescharacteristic
745C22×C3C22×#6711yescharacteristic
746C2×D3—21no—
747C2×D3—22no—
748C2×D3—21no—
749C2×D3—21no—
750C2×D3—41no—
751C2×D3—41no—
752C2×D3—62no—
753C2×D3—62no—
754C2×D3—84no—
755C2×D3—122no—
756C2×D3—121no—
757C2×D3—121no—
758C2×D3—121no—
759C2×D3—121no—
760C2×D3—241no—
761C2×D3—241no—
762C3×C4—21no—
763C3×C4—21no—
764C3×C4—21no—
765C3×C4—21no—
766C3×C4—41no—
767C3×C4—41no—
768C3×C4—41no—
769C3×C4—61no—
770C3×C4—61no—
771C3×C4—61no—
772C3×C4—81no—
773C3×C4—121no—
774C3×C4—121no—
775C3×C4—121no—
776C3×C4C2×D3×D411yescharacteristic
777C3×C4C2×D3×D411yescharacteristic
778C3×C4#100411yescharacteristic
779C3×C4#100911yescharacteristic
780Dic3—21no—
781Dic3—21no—
782Dic3—21no—
783Dic3—41no—
784Dic3—41no—
785Dic3—41no—
786Dic3—122no—
787Dic3—121no—
788Dic3—121no—
789C32#326711yescharacteristic, complemented, Sylow
790C23—21no—
791C23—31no—
792C23—61no—
793C23—122no—
794C23—122no—
795C23—181no—
796C23—241no—
797C23D3×#6711yescharacteristic
798Q8—61no—
799Q8—61no—
800Q8—61no—
801Q8—61no—
802Q8—181no—
803Q8—181no—
804D4—21no—
805D4—21no—
806D4—32no—
807D4—61no—
808D4—81no—
809D4—92no—
810D4—121no—
811D4—122no—
812D4—122no—
813D4—181no—
814D4—362no—
815D4—362no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—31no—
820C2×C4—31no—
821C2×C4—31no—
822C2×C4—61no—
823C2×C4—61no—
824C2×C4—61no—
825C2×C4—61no—
826C2×C4—61no—
827C2×C4—122no—
828C2×C4—181no—
829C2×C4—241no—
830C2×C4—362no—
831C2×C4—362no—
832C2×C4—362no—
833C2×C4D3×#6711yescharacteristic
834C2×C4C22×D3211yescharacteristic
835C8—32no—
836C8—61no—
837C8—181no—
838C8—181no—
839C2×C3—21no—
840C2×C3—21no—
841C2×C3—21no—
842C2×C3—41no—
843C2×C3—41no—
844C2×C3—81no—
845C2×C3—81no—
846C2×C3—81no—
847C2×C3—121no—
848C2×C3—122no—
849C2×C3—161no—
850C2×C3#560911yescharacteristic
851C2×C3#576211yescharacteristic
852C2×C3#576811yescharacteristic
853C2×C3D4×#6711yescharacteristic
854C2×C3#582211yescharacteristic
855C2×C3#583611yescharacteristic
856D3—41no—
857D3—42no—
858D3—122no—
859D3—122no—
860D3—242no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—61no—
868C22—61no—
869C22—61no—
870C22—62no—
871C22—121no—
872C22—121no—
873C22—182no—
874C22—244no—
875C22—361no—
876C22—361no—
877C22C2×D3×#6711yescharacteristic
878C4—21no—
879C4—41no—
880C4—61no—
881C4—61no—
882C4—61no—
883C4—121no—
884C4—121no—
885C4—121no—
886C4—361no—
887C4D32×D411yescharacteristic
888C4#6431411yescharacteristic
889C3—21no—
890C3#8067511yescharacteristic, complemented
891C3#8350311yescharacteristic, complemented
892C2—41no—
893C2—81no—
894C2—121no—
895C2—122no—
896C2—362no—
897C2#1059510511yescharacteristic
898C2#1059529111yescharacteristic
899C2#1059545311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3267
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
1. C3×#5612C2semidirect
2. C2×#63934C2semidirect
3. #10594834C2semidirect
4. C2×#63829C2semidirect
5. #10592736C2semidirect
6. C3×#5041C2semidirect
7. #10591491C2semidirect
8. #10591459C2semidirect
9. #10591432C2semidirect
10. #10591170C2semidirect
11. #10591155C2semidirect
12. #10590616C2semidirect
13. #10590589C2semidirect
14. #10590587C2semidirect
15. #10590559C2semidirect
18. C2×#3828C22semidirect
30. C3×#924C22semidirect
31. C22×C3×C3⋊C8C22semidirect
39. #63894C22semidirect
41. #63866C22semidirect
44. C2×#3719C22semidirect
45. C2×#3718C22semidirect
46. C2×#3717C22semidirect
52. #63657C22semidirect
53. #63637C22semidirect
54. #63636C22semidirect
56. C3×#810C22semidirect
57. C3×#808C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63565C22semidirect
62. #63554C22semidirect
69. #5612D3semidirect
81. #5041D3semidirect
154. #3714D4semidirect
204. #924C2×D3semidirect
206. C22×C3⋊C8C2×D3semidirect
246. #810C2×D3semidirect
251. #808C2×D3semidirect
789. C32#3267semidirect
890. C3#80675semidirect
891. C3#83503semidirect

Maximal subgroups

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

subgroupindex
C3×#56122
C2×#639342
#105948342
C2×#638292
#105927362
C3×#50412
#105914912
#105914592
#105914322
#105911702
#105911552
#105906162
#105905892
#105905872
#105905592
#835033
#806753