Finite Group Databasebeta

← #11884274

Subgroups — #11884274

Order 1152.

1062 conjugacy classes of subgroups.

The subgroup lattice has 892 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#10595067C211yesmaximal, characteristic, complemented
4C2×#63822C211yesmaximal, characteristic, complemented
5#10592747C211yesmaximal, characteristic, complemented
6C3×#5047C211yesmaximal, characteristic, complemented
7#10591608C211yesmaximal, characteristic, complemented
8#10591597C211yesmaximal, characteristic, complemented
9#10591564C211yesmaximal, characteristic, complemented
10#10591163C211yesmaximal, characteristic, complemented
11#10591158C211yesmaximal, characteristic, complemented
12#10590596C211yesmaximal, characteristic, complemented
13#10590534C211yesmaximal, characteristic, complemented
14#10590520C211yesmaximal, characteristic, complemented
15#10590455C211yesmaximal, characteristic, complemented
16#83522—31nomaximal
17#80264—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic, complemented
21C2×D3×D12C2211yescharacteristic
22C32×C22⋊Q8C2211yescharacteristic, complemented
23C2×#3755C2211yescharacteristic
24#64139C2211yescharacteristic
25C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
26C3×#944C2211yescharacteristic, complemented
27C2×C3×#216C2211yescharacteristic, complemented
28C2×C3×#215C2211yescharacteristic
29C3×C4×#67C2211yescharacteristic
30C3×#897C2211yescharacteristic
31C3×#894—21no—
32C3×#893C2211yescharacteristic, complemented
33C3×D3×C4⋊C4—21no—
34C3×#884—21no—
35C3×#883—21no—
36#63983—21no—
37#63971—21no—
38#63939—24no—
39D3×(C2×D3)⋊C4—21no—
40Dic3×D12C2211yescharacteristic
41#63864C2211yescharacteristic
42#63856C2211yescharacteristic
43#63850—21no—
44C2×#3718C2211yescharacteristic, complemented
45C2×#3717C2211yescharacteristic
46C2×#3715C2211yescharacteristic
47C2×#3715C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic
49#63822—24no—
50C2×#3713C2211yescharacteristic
51C2×#3711C2211yescharacteristic
52#63662C2211yescharacteristic, complemented
53#63636C2211yescharacteristic
54#63635C2211yescharacteristic, complemented
55C3×#830C2211yescharacteristic, complemented
56C3×#810C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62#63554C2211yescharacteristic, complemented
63C3×#547—31no—
64#5829—31no—
65C2×#950—31no—
66C2×#950—31no—
67C2×#949—31no—
68C2×#914—31no—
69#5631D311yescharacteristic, complemented
70#5550—31no—
71C3×#452—31no—
72#5239—31no—
73#5238—31no—
74#5190—31no—
75#5187—31no—
76#5162—31no—
77#5086—31no—
78#5083—31no—
79#5052—31no—
80#5048—31no—
81#5048—31no—
82#5048—61no—
83#5047D311yescharacteristic, complemented
84#5046—31no—
85#5016—31no—
86#5014—31no—
87#5011—31no—
88#4819—31no—
89#4816—31no—
90#4785—31no—
91#4776—31no—
92#4734—31no—
93#4730—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C2×#638—21no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C2×C3×#67D411yescharacteristic
102C3×#239—22no—
103C3×#239—41no—
104C3×#235—22no—
105C3×#235—22no—
106C3×#235—41no—
107C3×#235—41no—
108C2×C3×D12—21no—
109C2×C3×D12C2311yescharacteristic
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117C2×C3×Dic6C2311yescharacteristic
118C2×#626—21no—
119C2×D3×Dic3—21no—
120D3×D12—22no—
121D3×D12—41no—
122C32×C4⋊C4—21no—
123C32×C4⋊C4C2311yescharacteristic
124C32×C22⋊C4—21no—
125#3755—22no—
126#3752—21no—
127C4⋊(C3⋊Dic3)C2311yescharacteristic
128C2×C3⋊(C3⋊C8)—22no—
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C3×#217D411yescharacteristic
132C3×#216—41no—
133C3×#215—22no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4D411yescharacteristic
137C3×C4⋊Dic3—21no—
138C3×Dic3⋊C4—21no—
139C3×Dic3⋊C4—21no—
140C3×Dic3⋊C4D411yescharacteristic
141C3×C4×Dic3C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144#3724—21no—
145#3722—21no—
146#3722—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149#3718—22no—
150#3717—41no—
151#3715—22no—
152#3715—22no—
153#3714—22no—
154#3713D414yescomplemented
155#3711—22no—
156#3267—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×C3×#41—31no—
160C2×#239C2×D311yescharacteristic
161C2×D3×D4—31no—
162C2×#235C2×D311yescharacteristic
163C2×#235C2×D311yescharacteristic, complemented
164C22×D12—31no—
165C2×C3×Q16—31no—
166C2×C3×SD16—31no—
167C3×C4⋊Q8—31no—
168C3×#123—61no—
169C3×#123—61no—
170C3×C22⋊Q8—21no—
171C3×C22⋊Q8—31no—
172C3×C22⋊Q8C2×D311yescharacteristic, complemented
173C3×C22⋊Q8C2×D311yescharacteristic, complemented
174C3×#121—61no—
175C3×C4×D4—31no—
176C3×C4×D4—31no—
177C2×C3×C4⋊C4—61no—
178#950—64no—
179#950—64no—
180#949—64no—
181#947—31no—
182#946—31no—
183#944C2×D311yescharacteristic, complemented
184C2×#216—31no—
185C2×#216—31no—
186C2×#216C2×D311yescharacteristic, complemented
187C2×#215—31no—
188C2×#215—31no—
189C2×#215—31no—
190C2×#215—31no—
191C2×#215—31no—
192C2×#215—61no—
193C2×#215C2×D311yescharacteristic
194#939—61no—
195#937—61no—
196#937—61no—
197D4×Dic3—31no—
198C2×#214—31no—
199C2×#214—31no—
200C2×#213—31no—
201C2×#213—31no—
202C2×#213—31no—
203#930—31no—
204#930—31no—
205#930—61no—
206#929—61no—
207C4×#67C2×D311yescharacteristic
208C2×(C2×D3)⋊C4—61no—
209#924—31no—
210C2×#208—31no—
211C22×C3⋊C8—31no—
212C22×C3⋊C8—31no—
213C22×C3⋊C8—61no—
214#914—64no—
215C2×D24—31no—
216C2×#204—31no—
217C2×ΓL(1,𝔽25)—31no—
218#897C2×D311yescharacteristic
219#894—21no—
220#894—61no—
221#893C2×D311yescharacteristic, complemented
222D3×C4⋊C4—21no—
223#884—21no—
224#884—61no—
225#883—21no—
226D3×C22⋊C4—61no—
227#875—31no—
228C4×D12—31no—
229C3×#103—31no—
230C3×#102—31no—
231C3×C22⋊C8—31no—
232#835—31no—
233#835—31no—
234#835—31no—
235#835—61no—
236#832—31no—
237#830—31no—
238#830C2×D311yescharacteristic, complemented
239#821—31no—
240(C2×D3)⋊C8—31no—
241#816—31no—
242#815—31no—
243Dic3⋊C8—31no—
244#810C2×D311yescharacteristic, complemented
245#809—31no—
246#809—31no—
247#809—61no—
248#809C2×D311yescharacteristic
249#808—31no—
250#808—31no—
251#808—61no—
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—81no—
271C2×C3⋊Dic3—21no—
272C4⋊(C3⋊D3)—21no—
273C4⋊(C3⋊D3)—21no—
274C3×#67—41no—
275C3×#67—42no—
276C3×#67—42no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3C2×D411yescharacteristic
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—42no—
285C3×D12C2×D412yes—
286C3×D12C2×D412yes—
287C3×C4×D3—21no—
288C3×C4×D3—21no—
289C3×C4×D3—42no—
290C3×C4×D3—42no—
291C3×C4×D3—42no—
292C3×C4×D3—42no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295C3×Dic6—21no—
296C3×Dic6—21no—
297#626—42no—
298D3×Dic3—81no—
299C3⋊(C3⋊C8)—21no—
300C3⋊(C3⋊C8)C2×D412yes—
301C3×C3⋊C8—21no—
302C3×C3⋊C8—21no—
303C2×AGL(1,ℤ/8)—91no—
304C2×#135—91no—
305#547—31no—
306#546—91no—
307#497—91no—
308#470—91no—
309#465—91no—
310#463—91no—
311#461—91no—
312#452—31no—
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—62no—
323C3×#41—121no—
324C3×#41—121no—
325C3×#41—121no—
326C2×C3×Q8—21no—
327C2×C3×Q8—31no—
328C2×C3×Q8—31no—
329C2×C3×Q8C22×D311yescharacteristic
330C2×C3×Q8C22×D311yescharacteristic
331C2×C3×D4—31no—
332C2×C3×D4—31no—
333C2×C3×D4—31no—
334C2×C3×D4—61no—
335C2×C3×D4—61no—
336C2×C3×D4—61no—
337C22×C3×C4—21no—
338C22×C3×C4—31no—
339C22×C3×C4—61no—
340C22×C3×C4—61no—
341C22×C3×C4—61no—
342C22×C3×C4—61no—
343C22×C3×C4C22×D311yescharacteristic
344C22×C3×C4C22×D311yescharacteristic
345C2×#67—21no—
346C2×#67—21no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—61no—
350C2×#67—121no—
351C2×#67#6711yescharacteristic
352C22×Dic3—61no—
353#239—22no—
354#239—41no—
355D3×D4—62no—
356D3×D4—121no—
357#235—22no—
358#235—22no—
359#235—41no—
360#235—41no—
361C2×D12—21no—
362C2×D12—31no—
363C2×D12—31no—
364C2×D12—61no—
365C2×D12—62no—
366C2×D12—61no—
367C2×D12—121no—
368C2×D12C22×D311yescharacteristic
369C2×D12C22×D311yescharacteristic
370C2×C4×D3—21no—
371C2×C4×D3—21no—
372C2×C4×D3—21no—
373C2×C4×D3—21no—
374C2×C4×D3—61no—
375C2×C4×D3C22×D311yescharacteristic
376C2×Dic6C22×D311yescharacteristic
377C2×Dic6C22×D311yescharacteristic
378C3×Q16—121no—
379C3×SD16—62no—
380C2×C3×C8—31no—
381C2×C3×C8—31no—
382C3×C4⋊C4—21no—
383C3×C4⋊C4—21no—
384C3×C4⋊C4—21no—
385C3×C4⋊C4—31no—
386C3×C4⋊C4—41no—
387C3×C4⋊C4—61no—
388C3×C4⋊C4—61no—
389C3×C4⋊C4—61no—
390C3×C4⋊C4C22×D311yescharacteristic
391C3×C4⋊C4C22×D311yescharacteristic
392C3×C22⋊C4—21no—
393C3×C22⋊C4—21no—
394C3×C22⋊C4—31no—
395C3×C22⋊C4—31no—
396C3×C22⋊C4—41no—
397C3×C22⋊C4—61no—
398C3×C22⋊C4—61no—
399C3×C42—31no—
400#217—61no—
401#217—61no—
402#217#6711yescharacteristic
403#216—41no—
404#216—62no—
405#216—62no—
406#215—22no—
407#215—62no—
408#215—62no—
409#215—62no—
410#215—62no—
411#215—122no—
412#215—121no—
413#214—62no—
414#214—62no—
415#213—34no—
416#213—34no—
417#213—62no—
418(C2×D3)⋊C4—21no—
419(C2×D3)⋊C4—21no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—61no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—121no—
429(C2×D3)⋊C4#6711yescharacteristic
430C4⋊Dic3—21no—
431C4⋊Dic3—31no—
432C4⋊Dic3—31no—
433C4⋊Dic3—61no—
434Dic3⋊C4—21no—
435Dic3⋊C4—21no—
436Dic3⋊C4—61no—
437Dic3⋊C4—61no—
438Dic3⋊C4#6711yescharacteristic
439C4×Dic3C22×D311yescharacteristic
440#208—62no—
441C2×C3⋊C8—31no—
442C2×C3⋊C8—31no—
443C2×C3⋊C8—31no—
444C2×C3⋊C8—31no—
445C2×C3⋊C8—61no—
446C2×C3⋊C8—61no—
447C2×C3⋊C8—62no—
448C2×C3⋊C8—62no—
449C2×C3⋊C8—122no—
450C2×C3⋊C8C22×D311yescharacteristic
451C2×C3⋊C8C22×D311yescharacteristic
452D24—62no—
453#204—121no—
454ΓL(1,𝔽25)—62no—
455C22×C32—21no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32C22×D411yescharacteristic
459C2×C3⋊D3—41no—
460C2×C3⋊D3—41no—
461C2×C3⋊D3—41no—
462C2×C3×D3—22no—
463C2×C3×D3—21no—
464C2×C3×D3—22no—
465C2×C3×D3—21no—
466C2×C3×D3—21no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471D32—84no—
472C32×C4—21no—
473C32×C4—41no—
474C32×C4—41no—
475C32×C4C22×D411yescharacteristic
476C32×C4H(5,𝔽2)11yescharacteristic
477C3⋊Dic3—41no—
478C3×Dic3—21no—
479C3×Dic3—21no—
480C3×Dic3—21no—
481C3×Dic3—41no—
482C3×Dic3—41no—
483C2×#41—31no—
484C2×#41—31no—
485C2×#41—31no—
486C22×D4—91no—
487AGL(1,ℤ/8)—184no—
488#135—184no—
489C2×Q16—31no—
490C2×Q16—91no—
491C2×SD16—31no—
492C2×SD16—91no—
493C2×SD16—91no—
494C2×SD16—91no—
495C2×SD16—91no—
496C2×D8—91no—
497C2×D8—91no—
498C2×M16—91no—
499C22×C8—91no—
500C4⋊Q8—31no—
501#124—91no—
502#123—61no—
503#123—61no—
504#123—181no—
505C22⋊Q8—31no—
506C22⋊Q8—91no—
507C22⋊Q8D3211yescharacteristic, complemented
508#121—61no—
509#121—91no—
510#121—181no—
511#120—181no—
512C4×D4—31no—
513C4×D4—31no—
514C4×D4—91no—
515C2×C4⋊C4—61no—
516C2×C22⋊C4—181no—
517#106—91no—
518C4⋊C8—91no—
519#103—31no—
520#103—91no—
521#103—91no—
522#102—31no—
523#102—91no—
524#102—91no—
525C22⋊C8—31no—
526C22⋊C8—91no—
527#97—91no—
528C23×C3—21no—
529C23×C3—31no—
530C23×C3—61no—
531C23×C3—61no—
532C23×C3D3×D411yescharacteristic
533C23×C3C2×#6711yescharacteristic
534C22×D3—21no—
535C22×D3—21no—
536C22×D3—61no—
537C22×D3—61no—
538C22×D3—121no—
539C22×D3—122no—
540C22×D3—122no—
541C22×D3—122no—
542C22×D3—122no—
543C22×D3—241no—
544C22×D3—241no—
545C22×D3C2×#6711yescharacteristic
546C3×Q8—21no—
547C3×Q8—21no—
548C3×Q8—21no—
549C3×Q8—21no—
550C3×Q8—41no—
551C3×Q8—41no—
552C3×Q8—61no—
553C3×Q8—61no—
554C3×Q8—61no—
555C3×Q8—61no—
556C3×D4—32no—
557C3×D4—32no—
558C3×D4—61no—
559C3×D4—61no—
560C3×D4—122no—
561C3×D4—121no—
562C3×D4—122no—
563C3×D4—122no—
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×C4—122no—
589C2×C3×C4D3×D411yescharacteristic
590C2×C3×C4C2×#6711yescharacteristic
591C2×C3×C4C23×D311yescharacteristic
592C2×C3×C4C23×D311yescharacteristic
593#67—41no—
594#67—42no—
595#67—42no—
596#67—122no—
597#67—241no—
598#67—241no—
599#67—242no—
600C2×Dic3—21no—
601C2×Dic3—21no—
602C2×Dic3—61no—
603C2×Dic3—61no—
604C2×Dic3—121no—
605C2×Dic3—241no—
606C2×Dic3C2×#6711yescharacteristic
607C2×Dic3C2×#6711yescharacteristic
608C2×Dic3C2×#6711yescharacteristic
609D12—21no—
610D12—21no—
611D12—42no—
612D12—61no—
613D12—61no—
614D12—61no—
615D12—61no—
616D12—121no—
617D12—121no—
618D12—122no—
619D12D3×D412yes—
620D12D3×D412yes—
621C4×D3—21no—
622C4×D3—21no—
623C4×D3—42no—
624C4×D3—42no—
625C4×D3—42no—
626C4×D3—42no—
627C4×D3—241no—
628Dic6—21no—
629Dic6—21no—
630Dic6—21no—
631Dic6—21no—
632C3×C8—61no—
633C3×C8—61no—
634C3⋊C8—21no—
635C3⋊C8—21no—
636C3⋊C8—32no—
637C3⋊C8—32no—
638C3⋊C8—62no—
639C3⋊C8—61no—
640C3⋊C8—61no—
641C3⋊C8—121no—
642C2×C32—41no—
643C2×C32D4211yescharacteristic
644C2×C32#57511yescharacteristic
645C2×C32#57711yescharacteristic
646C3⋊D3—81no—
647C3×D3—41no—
648C3×D3—42no—
649C3×D3—42no—
650C24—181no—
651#41—62no—
652#41—62no—
653#41—62no—
654#41—121no—
655#41—121no—
656#41—121no—
657C2×Q8—31no—
658C2×Q8—31no—
659C2×Q8C2×D3211yescharacteristic
660C2×D4—31no—
661C2×D4—31no—
662C2×D4—31no—
663C2×D4—61no—
664C2×D4—61no—
665C2×D4—61no—
666C2×D4—91no—
667C2×D4—181no—
668C2×D4—182no—
669C2×D4—181no—
670C2×D4—361no—
671C22×C4—31no—
672C22×C4—61no—
673C22×C4—61no—
674C22×C4—61no—
675C22×C4—61no—
676C22×C4—181no—
677C22×C4C2×D3211yescharacteristic
678Q16—121no—
679Q16—182no—
680SD16—62no—
681SD16—182no—
682SD16—182no—
683SD16—182no—
684SD16—361no—
685D8—94no—
686D8—182no—
687M16—182no—
688C2×C8—31no—
689C2×C8—31no—
690C2×C8—91no—
691C2×C8—91no—
692C2×C8—182no—
693C4⋊C4—21no—
694C4⋊C4—31no—
695C4⋊C4—61no—
696C4⋊C4—61no—
697C4⋊C4—61no—
698C4⋊C4—91no—
699C4⋊C4—181no—
700C4⋊C4C2×D3211yescharacteristic
701C22⋊C4—21no—
702C22⋊C4—31no—
703C22⋊C4—31no—
704C22⋊C4—61no—
705C22⋊C4—61no—
706C22⋊C4—181no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C22⋊C4—181no—
710C22⋊C4—181no—
711C42—31no—
712C22×C3—22no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—21no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—41no—
721C22×C3—41no—
722C22×C3—61no—
723C22×C3—61no—
724C22×C3—62no—
725C22×C3—61no—
726C22×C3—62no—
727C22×C3—121no—
728C22×C3—121no—
729C22×C3—121no—
730C22×C3—121no—
731C22×C3C2×D3×D411yescharacteristic
732C22×C3C22×#6711yescharacteristic
733C2×D3—21no—
734C2×D3—22no—
735C2×D3—21no—
736C2×D3—21no—
737C2×D3—22no—
738C2×D3—41no—
739C2×D3—41no—
740C2×D3—41no—
741C2×D3—41no—
742C2×D3—121no—
743C2×D3—121no—
744C2×D3—121no—
745C2×D3—121no—
746C2×D3—121no—
747C2×D3—121no—
748C2×D3—241no—
749C2×D3—241no—
750C2×D3—241no—
751C2×D3—244no—
752C2×D3—244no—
753C3×C4—21no—
754C3×C4—21no—
755C3×C4—21no—
756C3×C4—21no—
757C3×C4—41no—
758C3×C4—41no—
759C3×C4—41no—
760C3×C4—41no—
761C3×C4—41no—
762C3×C4—61no—
763C3×C4—61no—
764C3×C4—61no—
765C3×C4—81no—
766C3×C4—81no—
767C3×C4—121no—
768C3×C4—121no—
769C3×C4C2×D3×D411yescharacteristic
770C3×C4C2×D3×D411yescharacteristic
771C3×C4#100411yescharacteristic
772C3×C4#100411yescharacteristic
773Dic3—21no—
774Dic3—21no—
775Dic3—21no—
776Dic3—41no—
777Dic3—41no—
778Dic3—121no—
779Dic3—121no—
780Dic3—241no—
781C32#326711yescharacteristic, complemented, Sylow
782C23—31no—
783C23—61no—
784C23—61no—
785C23—181no—
786C23—362no—
787C23—362no—
788C23—721no—
789C23D3×#6711yescharacteristic
790Q8—21no—
791Q8—21no—
792Q8—61no—
793Q8—61no—
794Q8—61no—
795Q8—61no—
796D4—32no—
797D4—32no—
798D4—61no—
799D4—61no—
800D4—122no—
801D4—121no—
802D4—122no—
803D4—122no—
804D4—181no—
805D4—181no—
806D4—362no—
807D4—721no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—31no—
813C2×C4—31no—
814C2×C4—31no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—61no—
818C2×C4—61no—
819C2×C4—122no—
820C2×C4—122no—
821C2×C4—122no—
822C2×C4—122no—
823C2×C4—181no—
824C2×C4—721no—
825C2×C4D3×#6711yescharacteristic
826C2×C4C22×D3211yescharacteristic
827C8—61no—
828C8—61no—
829C8—92no—
830C8—181no—
831C2×C3—21no—
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—42no—
835C2×C3—41no—
836C2×C3—41no—
837C2×C3—122no—
838C2×C3—121no—
839C2×C3—122no—
840C2×C3#559011yescharacteristic
841C2×C3#576811yescharacteristic
842C2×C3#577811yescharacteristic
843C2×C3D4×#6711yescharacteristic
844C2×C3#582211yescharacteristic
845C2×C3#583711yescharacteristic
846D3—41no—
847D3—42no—
848D3—42no—
849D3—241no—
850D3—241no—
851D3—481no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—61no—
856C22—61no—
857C22—62no—
858C22—62no—
859C22—61no—
860C22—121no—
861C22—121no—
862C22—121no—
863C22—121no—
864C22—361no—
865C22—361no—
866C22—361no—
867C22—724no—
868C22C2×D3×#6711yescharacteristic
869C4—21no—
870C4—41no—
871C4—41no—
872C4—61no—
873C4—61no—
874C4—61no—
875C4—121no—
876C4—121no—
877C4—361no—
878C4D32×D411yescharacteristic
879C4#6431311yescharacteristic
880C3—21no—
881C3#8026411yescharacteristic, complemented
882C3#8352211yescharacteristic, complemented
883C2—41no—
884C2—121no—
885C2—122no—
886C2—122no—
887C2—721no—
888C2#1059528711yescharacteristic
889C2#1059531911yescharacteristic
890C2#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. #10595067C2semidirect
4. C2×#63822C2semidirect
5. #10592747C2semidirect
6. C3×#5047C2semidirect
7. #10591608C2semidirect
8. #10591597C2semidirect
9. #10591564C2semidirect
10. #10591163C2semidirect
11. #10591158C2semidirect
12. #10590596C2semidirect
13. #10590534C2semidirect
14. #10590520C2semidirect
15. #10590455C2semidirect
20. C2×C3×#235C22semidirect
22. C32×C22⋊Q8C22semidirect
25. C22×C3⋊(C3⋊C8)C22semidirect
26. C3×#944C22semidirect
27. C2×C3×#216C22semidirect
32. C3×#893C22semidirect
44. C2×#3718C22semidirect
47. C2×#3715C22semidirect
52. #63662C22semidirect
54. #63635C22semidirect
55. C3×#830C22semidirect
56. C3×#810C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63566C22semidirect
60. #63563C22semidirect
62. #63554C22semidirect
69. #5631D3semidirect
83. #5047D3semidirect
154. #3713D4semidirect
163. C2×#235C2×D3semidirect
172. C3×C22⋊Q8C2×D3semidirect
173. C3×C22⋊Q8C2×D3semidirect
183. #944C2×D3semidirect
186. C2×#216C2×D3semidirect
221. #893C2×D3semidirect
238. #830C2×D3semidirect
244. #810C2×D3semidirect
507. C22⋊Q8D32semidirect
781. C32#3267semidirect
881. C3#80264semidirect
882. 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
#105950672
C2×#638222
#105927472
C3×#50472
#105916082
#105915972
#105915642
#105911632
#105911582
#105905962
#105905342
#105905202
#105904552
#835223
#802643