Finite Group Databasebeta

← Q8×#3795 #11903765

Subgroups — Q8×#3795 #11903765

Order 1152.

2242 conjugacy classes of subgroups.

The subgroup lattice has 549 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#634C211yesmaximal, characteristic, complemented
2C3×Q8×D12C211yesmaximal, characteristic, complemented
3C3×C4×D3×Q8C211yesmaximal, characteristic, complemented
4Q8×#625C212yesmaximal, complemented
5D3×Q8×Dic3C212yesmaximal, complemented
6#10594532C216yesmaximal, complemented
7#10594385C216yesmaximal, complemented
8#10593960C213yesmaximal, complemented
9C4×#3795C213yesmaximal
10#10593864C213yesmaximal, complemented
11#10593859C213yesmaximal, complemented
12Q8×#237—31nomaximal
13Q8×#235—31nomaximal
14C2×C3×D3×Q8C2212yes—
15C2×C3×D3×Q8C2211yescharacteristic
16C2×#3795C2211yescharacteristic
17C32×C4×Q8C2211yescharacteristic
18Q8×C3⋊Dic3C2212yes—
19#64097C2216yes—
20#64078C2213yes—
21C4×#634C2213yes—
22C3×Q8×Dic3C2211yescharacteristic
23C3×#897C2216yes—
24C3×D3×C4⋊C4C2213yes—
25C3×#887C2213yes—
26C3×C4×D12C2213yes—
27C3×C42×D3C2213yes—
28C3×#869C2213yes—
29C3×C4×Dic6C2213yes—
30C4×#625C2216yes—
31#63896C22112yes—
32Dic3×D12C2213yes—
33D3×C4⋊Dic3C2216yes—
34#63879C2216yes—
35#63877C2216yes—
36C4×D3×Dic3C2216yes—
37#63873C2216yes—
38#63869C2216yes—
39#63857C2216yes—
40#63856C2216yes—
41#63856C2216yes—
42#63847C22112yes—
43#63844C2216yes—
44#63844C2213yes—
45#63843C2216yes—
46Dic3×Dic6C2216yes—
47#63841C2213yes—
48C3×D4×Q8—31no—
49C2×C3×C4×Q8—31no—
50Q8×#67—32no—
51Q8×#67—32no—
52C2×Q8×Dic3—32no—
53#5728—33no—
54#5721—33no—
55#5635—36no—
56#5622—36no—
57#5579—33no—
58#5578—36no—
59Q8×D12D311yescharacteristic, complemented
60C4×D3×Q8—32no—
61C4×D3×Q8D311yescharacteristic, complemented
62#5567—33no—
63Q8×Dic6—31no—
64Q8×Dic6—31no—
65Q8×Dic6—61no—
66#5543—33no—
67C4×#237—33no—
68#5511—36no—
69C4×#235—33no—
70#5470—33no—
71C2×C32×Q8C2311yescharacteristic
72C2×#634C2316yes—
73C2×#634C2311yescharacteristic
74C3×D3×Q8—24no—
75C3×D3×Q8—28no—
76C2×C3×D12C2311yescharacteristic
77C2×C3×C4×D3C2313yes—
78C2×C3×C4×D3C2316yes—
79C2×C3×C4×D3C2313yes—
80C2×C3×C4×D3C2311yescharacteristic
81C2×C3×Dic6C2313yes—
82C2×C3×Dic6C2316yes—
83C2×#625C2312yes—
84C2×D3×Dic3C2316yes—
85C2×D3×Dic3C2312yes—
86#3795Q818yesdirect product factor
87C32×C4⋊C4C2313yes—
88C32×C42C2313yes—
89C4⋊(C3⋊Dic3)C2313yes—
90C4⋊(C3⋊Dic3)C2316yes—
91#3750C2316yes—
92C4×C3⋊Dic3C2316yes—
93C3×(C2×D3)⋊C4C2316yes—
94C3×C4⋊Dic3C2313yes—
95C3×C4⋊Dic3C2316yes—
96C3×C4⋊Dic3C2313yes—
97C3×Dic3⋊C4C2316yes—
98C3×C4×Dic3C2313yes—
99C3×C4×Dic3C2313yes—
100C3×C4×Dic3C2313yes—
101#3724C2316yes—
102#3724C23112yes—
103Dic3⋊Dic3C23112yes—
104(C2×D3)⋊Dic3C2316yes—
105(C2×D3)⋊Dic3C2316yes—
106Dic32C2316yes—
107Dic32C2316yes—
108Q8×#41—91noSylow
109C22×C3×Q8—32no—
110C22×C3×Q8—31no—
111C2×D3×Q8C2×D311yescharacteristic
112C2×D3×Q8C2×D312yes—
113C2×#237—31no—
114C2×#235—31no—
115C3×C4⋊Q8—33no—
116C3×C22⋊Q8—36no—
117C3×C4×Q8—21no—
118C3×C4×Q8—31no—
119C3×C4×Q8—33no—
120C3×C4×Q8—33no—
121C3×C4×Q8C2×D311yescharacteristic
122C3×C4×Q8C2×D311yescharacteristic
123C3×C4×D4—33no—
124C2×C3×C4⋊C4—33no—
125C2×C3×C42—33no—
126#946—36no—
127#946—36no—
128Q8×Dic3—32no—
129Q8×Dic3—32no—
130Q8×Dic3—36no—
131Q8×Dic3—36no—
132Q8×Dic3—62no—
133Q8×Dic3C2×D311yescharacteristic
134#944—36no—
135#944—36no—
136D4×Dic3—33no—
137C4×#67—36no—
138C4×#67—36no—
139C4×#67—36no—
140#926—33no—
141C2×C4⋊Dic3—36no—
142#924—36no—
143#924—36no—
144#924—36no—
145C2×C4×Dic3—36no—
146#897—36no—
147#897C2×D316yes—
148#896—312no—
149#892—33no—
150D3×C4⋊C4—36no—
151D3×C4⋊C4C2×D313yes—
152#890—36no—
153#889—312no—
154#889—312no—
155#888—36no—
156#888—36no—
157#888—66no—
158#887—36no—
159#887—33no—
160#887—36no—
161#887C2×D313yes—
162#67⋊C4—36no—
163#878—312no—
164#877—36no—
165C4×D12—33no—
166C4×D12C2×D313yes—
167#872—36no—
168C42×D3—36no—
169C42×D3C2×D313yes—
170#870—36no—
171#869—33no—
172#869—33no—
173#869—63no—
174#869C2×D313yes—
175C4×Dic6—36no—
176C4×Dic6—33no—
177C4×Dic6—33no—
178C4×Dic6—36no—
179C4×Dic6—33no—
180C4×Dic6—63no—
181C4×Dic6C2×D313yes—
182C22×C3×D3C2411yescharacteristic
183C22×C3×D3C2412yes—
184C32×Q8#4114yescomplemented
185C2×C32×C4C2413yes—
186C2×C32×C4C2411yescharacteristic
187C2×C32×C4C2413yes—
188C2×C3⋊Dic3C2416yes—
189C2×C3⋊Dic3C2412yes—
190#634—46no—
191#634C2×Q814yescomplemented
192C2×C3×Dic3C2416yes—
193C2×C3×Dic3C2413yes—
194C2×C3×Dic3C2413yes—
195C2×C3×Dic3C2411yescharacteristic
196C3×D12C2×Q814yescomplemented
197C3×C4×D3—26no—
198C3×C4×D3—212no—
199C3×C4×D3—43no—
200C3×C4×D3C2×Q814yescomplemented
201C3×Dic6—26no—
202C3×Dic6—212no—
203#625C2×Q818yescomplemented
204D3×Dic3—46no—
205D3×Dic3C2×Q818yescomplemented
206Q82—91no—
207#557—93no—
208#554—96no—
209#554—93no—
210D4×Q8—31no—
211D4×Q8—92no—
212#533—93no—
213#533—96no—
214C4×#41—93no—
215C2×C4×Q8—31no—
216C2×C4×Q8—92no—
217C2×C3×Q8—21no—
218C2×C3×Q8—33no—
219C2×C3×Q8—36no—
220C2×C3×Q8—68no—
221C2×C3×Q8—64no—
222C2×C3×Q8C22×D311yescharacteristic
223C2×C3×Q8C22×D311yescharacteristic
224C2×C3×D4—31no—
225C22×C3×C4—31no—
226C22×C3×C4—36no—
227C22×C3×C4—33no—
228C22×C3×C4—33no—
229C2×#67—32no—
230C2×#67—32no—
231C22×Dic3—32no—
232C22×Dic3—36no—
233D3×Q8—24no—
234D3×Q8—28no—
235#237—38no—
236#235—38no—
237C2×D12C22×D311yescharacteristic
238C2×C4×D3—32no—
239C2×C4×D3—36no—
240C2×C4×D3C22×D316yes—
241C2×C4×D3C22×D313yes—
242C2×C4×D3C22×D313yes—
243C2×C4×D3C22×D311yescharacteristic
244C2×Dic6—31no—
245C2×Dic6—31no—
246C2×Dic6—36no—
247C2×Dic6—36no—
248C2×Dic6—61no—
249C2×Dic6—66no—
250C2×Dic6C22×D316yes—
251C2×Dic6C22×D313yes—
252C3×C4⋊C4—23no—
253C3×C4⋊C4—33no—
254C3×C4⋊C4—36no—
255C3×C4⋊C4—33no—
256C3×C4⋊C4—36no—
257C3×C4⋊C4C22×D313yes—
258C3×C4⋊C4C22×D313yes—
259C3×C22⋊C4—36no—
260C3×C42—23no—
261C3×C42—33no—
262C3×C42—33no—
263C3×C42—33no—
264C3×C42C22×D313yes—
265C3×C42C22×D313yes—
266#217—36no—
267#217—36no—
268(C2×D3)⋊C4—36no—
269(C2×D3)⋊C4—36no—
270(C2×D3)⋊C4C22×D316yes—
271C4⋊Dic3—33no—
272C4⋊Dic3—33no—
273C4⋊Dic3—36no—
274C4⋊Dic3—36no—
275C4⋊Dic3—312no—
276C4⋊Dic3—63no—
277C4⋊Dic3—66no—
278C4⋊Dic3C22×D313yes—
279C4⋊Dic3C22×D316yes—
280C4⋊Dic3C22×D313yes—
281Dic3⋊C4—36no—
282Dic3⋊C4—36no—
283Dic3⋊C4—312no—
284Dic3⋊C4—312no—
285Dic3⋊C4—36no—
286Dic3⋊C4—36no—
287Dic3⋊C4—312no—
288Dic3⋊C4—66no—
289Dic3⋊C4C22×D316yes—
290C4×Dic3—36no—
291C4×Dic3—36no—
292C4×Dic3—36no—
293C4×Dic3—36no—
294C4×Dic3—36no—
295C4×Dic3—36no—
296C4×Dic3—66no—
297C4×Dic3C22×D313yes—
298C4×Dic3C22×D313yes—
299C4×Dic3C22×D313yes—
300C22×C32C2511yescharacteristic
301C2×C3×D3—21no—
302C2×C3×D3—22no—
303C2×C3×D3—22no—
304C2×C3×D3—21no—
305C2×C3×D3C22×Q814yes—
306C2×C3×D3C22×Q812yes—
307C32×C4—23no—
308C32×C4C22×Q812yes—
309C32×C4C2×#4116yes—
310C3⋊Dic3—26no—
311C3⋊Dic3C22×Q814yes—
312C3×Dic3—23no—
313C3×Dic3—26no—
314C3×Dic3—23no—
315C3×Dic3C22×Q812yes—
316C2×#41—91no—
317C22×Q8—31no—
318C22×Q8—32no—
319C4⋊Q8—33no—
320C4⋊Q8—96no—
321C4⋊Q8—96no—
322C4⋊Q8—93no—
323#125—96no—
324#125—912no—
325C22⋊Q8—36no—
326C22⋊Q8—912no—
327C22⋊Q8—96no—
328C22⋊Q8—96no—
329C22⋊Q8—96no—
330C4×Q8—31no—
331C4×Q8—33no—
332C4×Q8—33no—
333C4×Q8—93no—
334C4×Q8—96no—
335C4×Q8—96no—
336C4×Q8—96no—
337C4×Q8—92no—
338C4×Q8—93no—
339C4×Q8D3211yescharacteristic
340C4×D4—33no—
341C4×D4—93no—
342C4×D4—96no—
343C4×D4—96no—
344#117—96no—
345#117—93no—
346C2×C4⋊C4—33no—
347C2×C4⋊C4—96no—
348C2×C42—33no—
349C2×C42—96no—
350C23×C3—31no—
351C23×C3—32no—
352C22×D3C23×D311yescharacteristic
353C22×D3C23×D312yes—
354C3×Q8—24no—
355C3×Q8—612no—
356C3×Q8—66no—
357C3×Q8#23514yescomplemented
358C3×Q8#23714yescomplemented
359C3×D4—34no—
360C2×C3×C4—23no—
361C2×C3×C4—21no—
362C2×C3×C4—23no—
363C2×C3×C4—31no—
364C2×C3×C4—34no—
365C2×C3×C4—33no—
366C2×C3×C4—36no—
367C2×C3×C4—33no—
368C2×C3×C4—612no—
369C2×C3×C4—66no—
370C2×C3×C4—123no—
371C2×C3×C4C23×D313yes—
372C2×C3×C4C23×D313yes—
373C2×C3×C4C23×D313yes—
374C2×C3×C4C23×D313yes—
375C2×C3×C4C23×D311yescharacteristic
376C2×C3×C4C23×D311yescharacteristic
377#67—38no—
378#67—38no—
379C2×Dic3—32no—
380C2×Dic3—32no—
381C2×Dic3—38no—
382C2×Dic3—36no—
383C2×Dic3—36no—
384C2×Dic3—62no—
385C2×Dic3—66no—
386C2×Dic3—126no—
387C2×Dic3C23×D313yes—
388C2×Dic3C23×D316yes—
389C2×Dic3C23×D313yes—
390C2×Dic3C23×D311yescharacteristic
391D12D3×Q814yescomplemented
392C4×D3—26no—
393C4×D3—212no—
394C4×D3—38no—
395C4×D3—43no—
396C4×D3—126no—
397C4×D3D3×Q814yescomplemented
398Dic6—26no—
399Dic6—212no—
400Dic6—34no—
401Dic6—34no—
402Dic6—64no—
403Dic6—126no—
404Dic6—126no—
405Dic6—246no—
406C2×C32C23×Q811yescharacteristic
407C2×C32C22×#4111yescharacteristic
408C2×C32#58511yescharacteristic
409C3×D3—22no—
410C3×D3—24no—
411#41—98no—
412C2×Q8—33no—
413C2×Q8—36no—
414C2×Q8—64no—
415C2×Q8—68no—
416C2×Q8—91no—
417C2×Q8—96no—
418C2×Q8C2×D3211yescharacteristic
419C2×D4—31no—
420C2×D4—92no—
421C22×C4—31no—
422C22×C4—33no—
423C22×C4—36no—
424C22×C4—33no—
425C22×C4—92no—
426C22×C4—96no—
427C4⋊C4—33no—
428C4⋊C4—36no—
429C4⋊C4—33no—
430C4⋊C4—36no—
431C4⋊C4—912no—
432C4⋊C4—96no—
433C4⋊C4—912no—
434C4⋊C4—96no—
435C4⋊C4—96no—
436C4⋊C4—93no—
437C4⋊C4C2×D3213yes—
438C22⋊C4—36no—
439C22⋊C4—96no—
440C22⋊C4—96no—
441C42—33no—
442C42—33no—
443C42—33no—
444C42—96no—
445C42—96no—
446C42—96no—
447C42C2×D3213yes—
448C22×C3—21no—
449C22×C3—34no—
450C22×C3—32no—
451C22×C3—62no—
452C22×C3—61no—
453C22×C3—62no—
454C22×C3—61no—
455C22×C3C24×D311yescharacteristic
456C22×C3C24×D311yescharacteristic
457C2×D3—21no—
458C2×D3—22no—
459C2×D3—21no—
460C2×D3—22no—
461C2×D3C2×D3×Q814yes—
462C2×D3C2×D3×Q812yes—
463C3×C4—23no—
464C3×C4—23no—
465C3×C4—26no—
466C3×C4—22no—
467C3×C4—32no—
468C3×C4—43no—
469C3×C4—66no—
470C3×C4—63no—
471C3×C4—63no—
472C3×C4C2×#23516yes—
473C3×C4C2×#23716yes—
474C3×C4C2×D3×Q812yes—
475C3×C4C2×D3×Q812yes—
476Dic3—23no—
477Dic3—26no—
478Dic3—23no—
479Dic3—34no—
480Dic3—34no—
481Dic3—64no—
482Dic3—66no—
483Dic3—66no—
484Dic3—126no—
485Dic3C2×D3×Q812yes—
486C32Q8×#4111yescharacteristic, complemented, Sylow
487C23—32no—
488C23—31no—
489Q8—66no—
490Q8—612no—
491Q8—94no—
492Q8—366no—
493Q8#379514yesdirect product factor
494D4—34no—
495D4—98no—
496C2×C4—31no—
497C2×C4—34no—
498C2×C4—33no—
499C2×C4—33no—
500C2×C4—36no—
501C2×C4—66no—
502C2×C4—612no—
503C2×C4—98no—
504C2×C4—92no—
505C2×C4—96no—
506C2×C4—123no—
507C2×C4—366no—
508C2×C4C22×D3213yes—
509C2×C4C22×D3213yes—
510C2×C4C22×D3211yescharacteristic
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—64no—
515C2×C3—62no—
516C2×C3C22×#23511yescharacteristic
517C2×C3C22×#23711yescharacteristic
518C2×C3C22×D3×Q811yescharacteristic
519C2×C3C22×D3×Q811yescharacteristic
520C2×C3#596411yescharacteristic
521C2×C3#596811yescharacteristic
522D3—22no—
523D3—24no—
524C22—32no—
525C22—34no—
526C22—62no—
527C22—61no—
528C22—61no—
529C22—62no—
530C22C23×D3211yescharacteristic
531C4—23no—
532C4—32no—
533C4—63no—
534C4—66no—
535C4—63no—
536C4—94no—
537C4—186no—
538C4C2×#379516yes—
539C4D32×Q812yes—
540C3—21no—
541C3Q8×#23511yescharacteristic, complemented
542C3Q8×#23711yescharacteristic, complemented
543C2—62no—
544C2—64no—
545C2C22×#379511yescharacteristic
546C2C2×D32×Q811yescharacteristic
547C2#1059669711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
prime radicalC2×#3795C22
hypercenterC4×Q8D32
hypocenterC32Q8×#41
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. Q8×#634C2semidirect
2. C3×Q8×D12C2semidirect
3. C3×C4×D3×Q8C2semidirect
4. Q8×#625C2semidirect
5. D3×Q8×Dic3C2semidirect
6. #10594532C2semidirect
7. #10594385C2semidirect
8. #10593960C2semidirect
10. #10593864C2semidirect
11. #10593859C2semidirect
59. Q8×D12D3semidirect
61. C4×D3×Q8D3semidirect
86. #3795Q8direct (N × H)
184. C32×Q8#41semidirect
191. #634C2×Q8semidirect
196. C3×D12C2×Q8semidirect
200. C3×C4×D3C2×Q8semidirect
203. #625C2×Q8semidirect
205. D3×Dic3C2×Q8semidirect
357. C3×Q8#235semidirect
358. C3×Q8#237semidirect
391. D12D3×Q8semidirect
397. C4×D3D3×Q8semidirect
486. C32Q8×#41semidirect
493. Q8#3795direct (N × H)
541. C3Q8×#235semidirect
542. C3Q8×#237semidirect

Maximal subgroups

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

subgroupindex
Q8×#6342
C3×Q8×D122
C3×C4×D3×Q82
Q8×#6252
D3×Q8×Dic32
#105945322
#105943852
#105939602
C4×#37952
#105938642
#105938592
Q8×#2373
Q8×#2353