Finite Group Databasebeta

← #11884273

Subgroups — #11884273

Order 1152.

1076 conjugacy classes of subgroups.

The subgroup lattice has 897 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5631C211yesmaximal, characteristic, complemented
2C2×#63939C211yesmaximal, characteristic, complemented
3#10595078C211yesmaximal, characteristic, complemented
4C2×#63829C211yesmaximal, characteristic, complemented
5#10592746C211yesmaximal, characteristic, complemented
6C3×#5048C211yesmaximal, characteristic, complemented
7#10591605C211yesmaximal, characteristic, complemented
8#10591599C211yesmaximal, characteristic, complemented
9#10591565C211yesmaximal, characteristic, complemented
10#10591161C211yesmaximal, characteristic, complemented
11#10591155C211yesmaximal, characteristic, complemented
12#10590596C211yesmaximal, characteristic, complemented
13#10590589C211yesmaximal, characteristic, complemented
14#10590587C211yesmaximal, characteristic, complemented
15#10590530C211yesmaximal, characteristic, complemented
16#83522—31nomaximal
17#80675—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic, complemented
21C2×D3×D12C2211yescharacteristic
22C32×C22⋊Q8C2211yescharacteristic, complemented
23C2×#3756C2211yescharacteristic, complemented
24C2×#3755C2211yescharacteristic
25C3×#944C2211yescharacteristic, complemented
26C2×C3×#215C2211yescharacteristic
27C3×#930C2211yescharacteristic
28C3×C4×#67C2211yescharacteristic
29C22×C3×C3⋊C8C2211yescharacteristic, complemented
30C3×#897C2211yescharacteristic
31C3×#894—21no—
32C3×#893C2211yescharacteristic, complemented
33C3×D3×C4⋊C4—21no—
34C3×#884—21no—
35C3×#883—21no—
36#63983—21no—
37#63958—21no—
38#63939—24no—
39#63921—21no—
40#63894C2211yescharacteristic
41#63860C2211yescharacteristic
42#63857C2211yescharacteristic
43#63853—21no—
44C2×#3719C2211yescharacteristic, complemented
45C2×#3717C2211yescharacteristic
46#63829—24no—
47C2×#3716C2211yescharacteristic, complemented
48C2×#3715C2211yescharacteristic
49C2×#3714C2211yescharacteristic
50C2×#3713C2211yescharacteristic
51C2×#3711C2211yescharacteristic
52#63657C2211yescharacteristic, complemented
53#63637C2211yescharacteristic, complemented
54#63636C2211yescharacteristic
55C3×#835C2211yescharacteristic, complemented
56C3×#809C2211yescharacteristic
57C3×#808C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62#63554C2211yescharacteristic, complemented
63C3×#547—31no—
64C2×#950—31no—
65C2×#949—31no—
66C2×#914—31no—
67C2×#904—31no—
68#5631D311yescharacteristic, complemented
69#5612—31no—
70#5550—31no—
71C3×#465—31no—
72#5239—31no—
73#5238—31no—
74#5167—31no—
75#5111—31no—
76#5086—31no—
77#5083—31no—
78#5052—31no—
79#5048D311yescharacteristic, complemented
80#5047—31no—
81#5047—31no—
82#5047—61no—
83#5046—31no—
84#5037—31no—
85#5016—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—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C2×#638—21no—
98#3828—22no—
99#3828—41no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4×C3⋊D3—21no—
102C2×#634C2311yescharacteristic
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×#67D411yescharacteristic
106C3×#239—22no—
107C3×#239—41no—
108C3×#235—22no—
109C3×#235—41no—
110C2×C3×D12—21no—
111C2×C3×D12C2311yescharacteristic
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3—21no—
116C2×C3×C4×D3C2311yescharacteristic
117C2×C3×Dic6C2311yescharacteristic
118C2×#626—21no—
119C2×#624—21no—
120D3×D12—22no—
121D3×D12—41no—
122C32×C4⋊C4—21no—
123C32×C4⋊C4C2311yescharacteristic
124C32×C22⋊C4—21no—
125#3756—41no—
126#3755—22no—
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129C3×#217D411yescharacteristic
130C3×#215—22no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4D411yescharacteristic
135C3×C4⋊Dic3—21no—
136C3×C4⋊Dic3C2311yescharacteristic
137C3×Dic3⋊C4—21no—
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—
145#3722—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149#3719—22no—
150#3717—22no—
151#3716—22no—
152#3715—41no—
153#3714D414yescomplemented
154#3713—22no—
155#3711—22no—
156#3267—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×#239C2×D311yescharacteristic
160C2×D3×D4—31no—
161C2×#235—31no—
162C2×#235—31no—
163C2×#235—61no—
164C2×#235C2×D311yescharacteristic, complemented
165C22×D12—31no—
166C2×C3×SD16—31no—
167C22×C3×C8—31no—
168C3×C4⋊Q8—31no—
169C3×#123—61no—
170C3×#123—61no—
171C3×C22⋊Q8—21no—
172C3×C22⋊Q8—31no—
173C3×C22⋊Q8C2×D311yescharacteristic, complemented
174C3×C22⋊Q8C2×D311yescharacteristic, complemented
175C3×#121—31no—
176C3×#121—61no—
177C3×C4×D4—31no—
178C3×C4×D4—31no—
179C2×C3×C4⋊C4—61no—
180#950—64no—
181#949—64no—
182#944C2×D311yescharacteristic, complemented
183C2×#216—31no—
184C2×#216—31no—
185C2×#216—31no—
186C2×#216—61no—
187C2×#215—31no—
188C2×#215—31no—
189C2×#215—31no—
190C2×#215—31no—
191C2×#215—61no—
192C2×#215C2×D311yescharacteristic
193#938—61no—
194#937—61no—
195#937—61no—
196#936—31no—
197C2×#214—31no—
198C2×#214—31no—
199C2×#213—31no—
200C2×#213—31no—
201C2×#213—31no—
202#930C2×D311yescharacteristic
203C4×#67C2×D311yescharacteristic
204#924—31no—
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—21no—
217#894—61no—
218#893—31no—
219#893C2×D311yescharacteristic, complemented
220D3×C4⋊C4—21no—
221#884—21no—
222#884—61no—
223#883—21no—
224#883—61no—
225D3×C22⋊C4—61no—
226D3×C22⋊C4—61no—
227#875—31no—
228C4×D12—31no—
229C3×#106—31no—
230C3×#103—31no—
231C3×#102—31no—
232#835—31no—
233#835C2×D311yescharacteristic, complemented
234#832—31no—
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#809—31no—
247#809—31no—
248#809—31no—
249#809—61no—
250#809C2×D311yescharacteristic
251#808C2×D311yescharacteristic, complemented
252C4⋊(C3⋊C8)—31no—
253#803—31no—
254C23×C32C2×D411yescharacteristic
255C22×C3⋊D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3C2×D411yescharacteristic
259C2×D32—42no—
260C2×D32—42no—
261C2×D32—81no—
262C32×Q8—21no—
263C32×Q8—21no—
264C2×C32×C4—21no—
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—81no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3C2×D411yescharacteristic
283C2×C3×Dic3C2×D411yescharacteristic
284C2×C3×Dic3C2×D411yescharacteristic
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—42no—
289C3×D12C2×D412yes—
290C3×C4×D3—21no—
291C3×C4×D3—21no—
292C3×C4×D3—42no—
293C3×C4×D3—42no—
294C3×C4×D3—42no—
295C3×Dic6—21no—
296C3×Dic6—21no—
297#626—42no—
298#624—81no—
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—31no—
306#546—91no—
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—
318C23×D3—61no—
319C23×D3—61no—
320C3×#41—62no—
321C3×#41—62no—
322C3×#41—121no—
323C3×#41—121no—
324C2×C3×Q8—21no—
325C2×C3×Q8—31no—
326C2×C3×Q8C22×D311yescharacteristic
327C2×C3×Q8C22×D311yescharacteristic
328C2×C3×D4—31no—
329C2×C3×D4—31no—
330C2×C3×D4—31no—
331C2×C3×D4—61no—
332C2×C3×D4—61no—
333C2×C3×D4—61no—
334C22×C3×C4—21no—
335C22×C3×C4—31no—
336C22×C3×C4—61no—
337C22×C3×C4—61no—
338C22×C3×C4—61no—
339C22×C3×C4C22×D311yescharacteristic
340C22×C3×C4C22×D311yescharacteristic
341C2×#67—21no—
342C2×#67—21no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—121no—
347C2×#67#6711yescharacteristic
348#239—22no—
349#239—41no—
350D3×D4—62no—
351D3×D4—121no—
352#235—22no—
353#235—41no—
354#235—62no—
355#235—62no—
356#235—122no—
357#235—121no—
358#235—121no—
359#235—122no—
360C2×D12—21no—
361C2×D12—31no—
362C2×D12—31no—
363C2×D12—61no—
364C2×D12—62no—
365C2×D12—61no—
366C2×D12—121no—
367C2×D12C22×D311yescharacteristic
368C2×D12C22×D311yescharacteristic
369C2×C4×D3—21no—
370C2×C4×D3—21no—
371C2×C4×D3—21no—
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
382C3×SD16—62no—
383C2×C3×C8—31no—
384C2×C3×C8—31no—
385C2×C3×C8—62no—
386C3×C4⋊C4—21no—
387C3×C4⋊C4—21no—
388C3×C4⋊C4—21no—
389C3×C4⋊C4—31no—
390C3×C4⋊C4—31no—
391C3×C4⋊C4—41no—
392C3×C4⋊C4—61no—
393C3×C4⋊C4—61no—
394C3×C4⋊C4—61no—
395C3×C4⋊C4C22×D311yescharacteristic
396C3×C4⋊C4C22×D311yescharacteristic
397C3×C22⋊C4—21no—
398C3×C22⋊C4—21no—
399C3×C22⋊C4—31no—
400C3×C22⋊C4—31no—
401C3×C22⋊C4—41no—
402C3×C22⋊C4—61no—
403C3×C22⋊C4—61no—
404C3×C22⋊C4—61no—
405C3×C42—31no—
406#217—61no—
407#217—61no—
408#217—61no—
409#217#6711yescharacteristic
410#216—62no—
411#216—121no—
412#216—121no—
413#216—122no—
414#215—22no—
415#215—62no—
416#215—62no—
417#215—62no—
418#215—122no—
419#215—121no—
420#214—62no—
421#214—121no—
422#213—34no—
423#213—62no—
424#213—62no—
425(C2×D3)⋊C4—21no—
426(C2×D3)⋊C4—21no—
427(C2×D3)⋊C4—21no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4#6711yescharacteristic
434C4⋊Dic3—21no—
435C4⋊Dic3—61no—
436C4⋊Dic3C22×D311yescharacteristic
437Dic3⋊C4—21no—
438Dic3⋊C4—21no—
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×C32C22×D411yescharacteristic
461C2×C3⋊D3—22no—
462C2×C3⋊D3—41no—
463C2×C3⋊D3—41no—
464C2×C3×D3—21no—
465C2×C3×D3—22no—
466C2×C3×D3—21no—
467C2×C3×D3—21no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473D32—84no—
474C32×C4—21no—
475C32×C4—41no—
476C32×C4—41no—
477C32×C4C22×D411yescharacteristic
478C32×C4H(5,𝔽2)11yescharacteristic
479C3⋊Dic3—41no—
480C3×Dic3—21no—
481C3×Dic3—21no—
482C3×Dic3—21no—
483C3×Dic3—41no—
484C3×Dic3—41no—
485C2×#41—31no—
486C2×#41—31no—
487C2×#41—91no—
488C22×D4—91no—
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—31no—
503#124—91no—
504#123—61no—
505#123—61no—
506#123—181no—
507C22⋊Q8—31no—
508C22⋊Q8—91no—
509C22⋊Q8D3211yescharacteristic, complemented
510#121—31no—
511#121—61no—
512#121—181no—
513#120—181no—
514C4×D4—31no—
515C4×D4—31no—
516C4×D4—91no—
517C2×C4⋊C4—61no—
518C2×C22⋊C4—181no—
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—31no—
532C23×C3—61no—
533C23×C3—61no—
534C23×C3D3×D411yescharacteristic
535C23×C3C2×#6711yescharacteristic
536C22×D3—21no—
537C22×D3—21no—
538C22×D3—61no—
539C22×D3—61no—
540C22×D3—121no—
541C22×D3—122no—
542C22×D3—122no—
543C22×D3—122no—
544C22×D3—122no—
545C22×D3—241no—
546C22×D3—241no—
547C22×D3C2×#6711yescharacteristic
548C3×Q8—21no—
549C3×Q8—21no—
550C3×Q8—21no—
551C3×Q8—21no—
552C3×Q8—41no—
553C3×Q8—41no—
554C3×Q8—61no—
555C3×Q8—61no—
556C3×D4—32no—
557C3×D4—61no—
558C3×D4—61no—
559C3×D4—61no—
560C3×D4—122no—
561C3×D4—121no—
562C3×D4—122no—
563C3×D4—241no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
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—31no—
575C2×C3×C4—31no—
576C2×C3×C4—31no—
577C2×C3×C4—41no—
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—122no—
586C2×C3×C4—122no—
587C2×C3×C4—122no—
588C2×C3×C4D3×D411yescharacteristic
589C2×C3×C4C2×#6711yescharacteristic
590C2×C3×C4C23×D311yescharacteristic
591C2×C3×C4C23×D311yescharacteristic
592#67—41no—
593#67—42no—
594#67—81no—
595#67—122no—
596#67—122no—
597#67—122no—
598#67—124no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—61no—
602C2×Dic3—61no—
603C2×Dic3—121no—
604C2×Dic3C2×#6711yescharacteristic
605C2×Dic3C2×#6711yescharacteristic
606C2×Dic3C2×#6711yescharacteristic
607D12—21no—
608D12—21no—
609D12—21no—
610D12—32no—
611D12—32no—
612D12—42no—
613D12—62no—
614D12—61no—
615D12—61no—
616D12—121no—
617D12—122no—
618D12D3×D412yes—
619C4×D3—21no—
620C4×D3—21no—
621C4×D3—42no—
622C4×D3—42no—
623C4×D3—42no—
624C4×D3—122no—
625C4×D3—122no—
626C4×D3—124no—
627C4×D3—241no—
628C4×D3—241no—
629Dic6—21no—
630Dic6—21no—
631Dic6—62no—
632Dic6—61no—
633Dic6—61no—
634Dic6—61no—
635Dic6—61no—
636Dic6—121no—
637C3×C8—32no—
638C3×C8—61no—
639C3⋊C8—21no—
640C3⋊C8—61no—
641C3⋊C8—61no—
642C3⋊C8—61no—
643C3⋊C8—61no—
644C3⋊C8—121no—
645C3⋊C8—121no—
646C3⋊C8D3×D412yes—
647C2×C32—41no—
648C2×C32D4211yescharacteristic
649C2×C32#57511yescharacteristic
650C2×C32#57711yescharacteristic
651C3⋊D3—42no—
652C3×D3—41no—
653C3×D3—42no—
654C3×D3—81no—
655C24—181no—
656#41—62no—
657#41—62no—
658#41—121no—
659#41—121no—
660#41—182no—
661#41—361no—
662C2×Q8—31no—
663C2×Q8—91no—
664C2×Q8C2×D3211yescharacteristic
665C2×D4—31no—
666C2×D4—31no—
667C2×D4—31no—
668C2×D4—61no—
669C2×D4—61no—
670C2×D4—61no—
671C2×D4—91no—
672C2×D4—181no—
673C2×D4—182no—
674C2×D4—181no—
675C2×D4—361no—
676C22×C4—31no—
677C22×C4—61no—
678C22×C4—61no—
679C22×C4—61no—
680C22×C4—181no—
681C22×C4—181no—
682C22×C4C2×D3211yescharacteristic
683Q16—182no—
684Q16—361no—
685SD16—62no—
686SD16—182no—
687SD16—182no—
688SD16—182no—
689SD16—361no—
690D8—94no—
691D8—182no—
692M16—182no—
693C2×C8—31no—
694C2×C8—31no—
695C2×C8—62no—
696C2×C8—91no—
697C2×C8—91no—
698C4⋊C4—21no—
699C4⋊C4—31no—
700C4⋊C4—31no—
701C4⋊C4—61no—
702C4⋊C4—61no—
703C4⋊C4—61no—
704C4⋊C4—181no—
705C4⋊C4C2×D3211yescharacteristic
706C22⋊C4—21no—
707C22⋊C4—31no—
708C22⋊C4—31no—
709C22⋊C4—61no—
710C22⋊C4—61no—
711C22⋊C4—61no—
712C22⋊C4—181no—
713C22⋊C4—181no—
714C22⋊C4—181no—
715C22⋊C4—181no—
716C42—31no—
717C22×C3—21no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—21no—
722C22×C3—21no—
723C22×C3—21no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—61no—
728C22×C3—61no—
729C22×C3—61no—
730C22×C3—62no—
731C22×C3—121no—
732C22×C3—121no—
733C22×C3—121no—
734C22×C3—121no—
735C22×C3—121no—
736C22×C3C2×D3×D411yescharacteristic
737C22×C3C22×#6711yescharacteristic
738C2×D3—21no—
739C2×D3—22no—
740C2×D3—21no—
741C2×D3—21no—
742C2×D3—41no—
743C2×D3—41no—
744C2×D3—41no—
745C2×D3—41no—
746C2×D3—41no—
747C2×D3—62no—
748C2×D3—62no—
749C2×D3—122no—
750C2×D3—121no—
751C2×D3—121no—
752C2×D3—121no—
753C2×D3—121no—
754C2×D3—241no—
755C2×D3—241no—
756C2×D3—244no—
757C2×D3—244no—
758C3×C4—21no—
759C3×C4—21no—
760C3×C4—21no—
761C3×C4—21no—
762C3×C4—41no—
763C3×C4—41no—
764C3×C4—41no—
765C3×C4—41no—
766C3×C4—41no—
767C3×C4—61no—
768C3×C4—61no—
769C3×C4—61no—
770C3×C4—81no—
771C3×C4—81no—
772C3×C4—121no—
773C3×C4—121no—
774C3×C4C2×D3×D411yescharacteristic
775C3×C4C2×D3×D411yescharacteristic
776C3×C4#100411yescharacteristic
777C3×C4#100911yescharacteristic
778Dic3—21no—
779Dic3—21no—
780Dic3—21no—
781Dic3—41no—
782Dic3—41no—
783Dic3—122no—
784Dic3—121no—
785Dic3—121no—
786C32#326711yescharacteristic, complemented, Sylow
787C23—31no—
788C23—61no—
789C23—61no—
790C23—181no—
791C23—362no—
792C23—362no—
793C23—721no—
794C23D3×#6711yescharacteristic
795Q8—21no—
796Q8—21no—
797Q8—61no—
798Q8—61no—
799Q8—181no—
800Q8—181no—
801D4—32no—
802D4—61no—
803D4—61no—
804D4—61no—
805D4—92no—
806D4—122no—
807D4—121no—
808D4—122no—
809D4—181no—
810D4—241no—
811D4—362no—
812D4—362no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—31no—
818C2×C4—31no—
819C2×C4—31no—
820C2×C4—61no—
821C2×C4—61no—
822C2×C4—61no—
823C2×C4—61no—
824C2×C4—122no—
825C2×C4—122no—
826C2×C4—122no—
827C2×C4—181no—
828C2×C4—362no—
829C2×C4—721no—
830C2×C4D3×#6711yescharacteristic
831C2×C4C22×D3211yescharacteristic
832C8—32no—
833C8—61no—
834C8—181no—
835C8—181no—
836C2×C3—21no—
837C2×C3—21no—
838C2×C3—21no—
839C2×C3—41no—
840C2×C3—41no—
841C2×C3—81no—
842C2×C3—121no—
843C2×C3—122no—
844C2×C3—241no—
845C2×C3#560911yescharacteristic
846C2×C3#576211yescharacteristic
847C2×C3#576811yescharacteristic
848C2×C3D4×#6711yescharacteristic
849C2×C3#582211yescharacteristic
850C2×C3#583711yescharacteristic
851D3—41no—
852D3—42no—
853D3—81no—
854D3—122no—
855D3—122no—
856D3—242no—
857C22—21no—
858C22—21no—
859C22—21no—
860C22—61no—
861C22—61no—
862C22—62no—
863C22—61no—
864C22—121no—
865C22—121no—
866C22—121no—
867C22—121no—
868C22—121no—
869C22—182no—
870C22—361no—
871C22—361no—
872C22—724no—
873C22C2×D3×#6711yescharacteristic
874C4—21no—
875C4—41no—
876C4—41no—
877C4—61no—
878C4—61no—
879C4—61no—
880C4—121no—
881C4—121no—
882C4—361no—
883C4D32×D411yescharacteristic
884C4#6431411yescharacteristic
885C3—21no—
886C3#8067511yescharacteristic, complemented
887C3#8352211yescharacteristic, complemented
888C2—41no—
889C2—121no—
890C2—122no—
891C2—241no—
892C2—362no—
893C2#1059529111yescharacteristic
894C2#1059531811yescharacteristic
895C2#1059545311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
hypercenterC22⋊Q8D32
hypocenterC32#3267
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5631C2semidirect
2. C2×#63939C2semidirect
3. #10595078C2semidirect
4. C2×#63829C2semidirect
5. #10592746C2semidirect
6. C3×#5048C2semidirect
7. #10591605C2semidirect
8. #10591599C2semidirect
9. #10591565C2semidirect
10. #10591161C2semidirect
11. #10591155C2semidirect
12. #10590596C2semidirect
13. #10590589C2semidirect
14. #10590587C2semidirect
15. #10590530C2semidirect
20. C2×C3×#235C22semidirect
22. C32×C22⋊Q8C22semidirect
23. C2×#3756C22semidirect
25. C3×#944C22semidirect
29. C22×C3×C3⋊C8C22semidirect
32. C3×#893C22semidirect
44. C2×#3719C22semidirect
47. C2×#3716C22semidirect
52. #63657C22semidirect
53. #63637C22semidirect
55. C3×#835C22semidirect
57. C3×#808C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63565C22semidirect
60. #63562C22semidirect
62. #63554C22semidirect
68. #5631D3semidirect
79. #5048D3semidirect
153. #3714D4semidirect
164. C2×#235C2×D3semidirect
173. C3×C22⋊Q8C2×D3semidirect
174. C3×C22⋊Q8C2×D3semidirect
182. #944C2×D3semidirect
206. C22×C3⋊C8C2×D3semidirect
219. #893C2×D3semidirect
233. #835C2×D3semidirect
251. #808C2×D3semidirect
509. C22⋊Q8D32semidirect
786. C32#3267semidirect
886. C3#80675semidirect
887. C3#83522semidirect

Maximal subgroups

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

subgroupindex
C3×#56312
C2×#639392
#105950782
C2×#638292
#105927462
C3×#50482
#105916052
#105915992
#105915652
#105911612
#105911552
#105905962
#105905892
#105905872
#105905302
#835223
#806753