Finite Group Databasebeta

← #11904211

Subgroups — #11904211

Order 1152.

2343 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3832C211yesmaximal, characteristic, complemented
2C3×Q8×D12C211yesmaximal, characteristic, complemented
3C3×#5570C211yesmaximal, characteristic, complemented
4D3×Q8×Dic3C212yesmaximal, complemented
5#10595342C212yesmaximal, complemented
6#10594457C216yesmaximal, complemented
7#10594453C216yesmaximal, complemented
8#10593896C213yesmaximal, complemented
9C4×#3796C213yesmaximal, complemented
10#10593866C213yesmaximal, complemented
11#10593865C213yesmaximal, complemented
12#87017—31nomaximal
13#86744—31nomaximal
14C2×#3832C2211yescharacteristic
15C2×C3×D3×Q8C2212yes—
16C2×#3796C2213yes—
17C32×C4×Q8C2211yescharacteristic
18Q8×C3⋊Dic3C2211yescharacteristic
19#64102C2213yes—
20#64101C2213yes—
21C4×C4⋊(C3⋊D3)C2213yes—
22C42×C3⋊D3C2213yes—
23C3×Q8×Dic3C2212yes—
24C3×#897C2216yes—
25C3×#890C2216yes—
26C3×C4×D12C2213yes—
27C3×#869C2213yes—
28C3×#869C2213yes—
29C3×C4×Dic6C2213yes—
30#63909C2216yes—
31C4×#626C2216yes—
32#63898C2211yescharacteristic
33#63890C22112yes—
34D3×C4⋊Dic3C2216yes—
35#63881C2216yes—
36#63878C2216yes—
37C4×D3×Dic3C2216yes—
38#63872C2216yes—
39#63871C2216yes—
40#63871C2216yes—
41#63864C2216yes—
42#63849C2213yes—
43#63849C2216yes—
44#63848C22112yes—
45#63843C2216yes—
46#63843C2213yes—
47Dic3×Dic6C2216yes—
48C3×#557—31no—
49C3×D4×Q8—31no—
50#5817—32no—
51C2×Q8×Dic3—32no—
52#5732—33no—
53#5728—33no—
54#5728—33no—
55#5726—33no—
56#5694—36no—
57#5691—36no—
58#5642—36no—
59#5624—36no—
60#5584—33no—
61#5576—32no—
62Q8×D12D311yescharacteristic, complemented
63C4×#239—31no—
64C4×#239—31no—
65C4×#239—33no—
66C4×#239—61no—
67C4×D3×Q8—32no—
68#5570D311yescharacteristic, complemented
69#5555—33no—
70C4×#237—33no—
71C2×C32×Q8C2311yescharacteristic
72#3832—24no—
73C2×C4⋊(C3⋊D3)C2313yes—
74C2×C4×C3⋊D3C2313yes—
75C2×C4×C3⋊D3C2313yes—
76C2×C4×C3⋊D3C2313yes—
77C3×D3×Q8—28no—
78C2×C3×D12C2311yescharacteristic
79C2×C3×C4×D3C2316yes—
80C2×C3×Dic6C2316yes—
81C2×C3×Dic6C2313yes—
82C2×#626C2316yes—
83C2×D3×Dic3C2316yes—
84C2×D3×Dic3C2312yes—
85#3796—212no—
86C32×C4⋊C4C2313yes—
87C32×C42C2313yes—
88#3752C2316yes—
89C4⋊(C3⋊Dic3)C2313yes—
90C4×C3⋊Dic3C2311yescharacteristic
91C4×C3⋊Dic3C2313yes—
92C4×C3⋊Dic3C2313yes—
93C3×(C2×D3)⋊C4C2316yes—
94C3×C4⋊Dic3C2316yes—
95C3×C4⋊Dic3C2316yes—
96C3×C4⋊Dic3C2316yes—
97C3×C4⋊Dic3C2313yes—
98C3×C4⋊Dic3C2311yescharacteristic
99C3×Dic3⋊C4C2316yes—
100C3×C4×Dic3C2316yes—
101Dic3⋊Dic3C23112yes—
102Dic3⋊Dic3C2316yes—
103#3722C2316yes—
104#3722C23112yes—
105(C2×D3)⋊Dic3C2312yes—
106Dic32C2316yes—
107Dic32C2316yes—
108#3482—91noSylow
109C22×C3×Q8—32no—
110C2×#239—31no—
111C2×#239—31no—
112C2×#239—33no—
113C2×#239—61no—
114C2×D3×Q8C2×D312yes—
115C2×#237—33no—
116C3×C4⋊Q8—33no—
117C3×C4⋊Q8—33no—
118C3×#125—36no—
119C3×C22⋊Q8—36no—
120C3×C4×Q8—21no—
121C3×C4×Q8—32no—
122C3×C4×Q8—33no—
123C3×C4×Q8C2×D311yescharacteristic
124C3×C4×Q8C2×D311yescharacteristic
125C3×C4×D4—33no—
126#947—36no—
127#946—36no—
128#946—36no—
129Q8×Dic3—31no—
130Q8×Dic3—31no—
131Q8×Dic3—33no—
132Q8×Dic3—36no—
133Q8×Dic3—36no—
134Q8×Dic3—61no—
135Q8×Dic3C2×D312yes—
136D4×Dic3—31no—
137#930—36no—
138C4×#67—36no—
139C2×C4⋊Dic3—36no—
140C2×C4×Dic3—36no—
141#898—312no—
142#898—312no—
143#897—36no—
144#897—36no—
145#897C2×D316yes—
146#895—36no—
147#894—312no—
148#893—31no—
149#893—33no—
150#893—33no—
151#893—36no—
152#893—63no—
153#892—33no—
154#892—33no—
155#892—36no—
156#892—36no—
157#892—36no—
158#892—33no—
159#892—33no—
160#892—63no—
161D3×C4⋊C4—36no—
162#890—36no—
163#890—36no—
164#890C2×D316yes—
165#887—36no—
166#887—33no—
167#886—312no—
168#67⋊C4—36no—
169#877—36no—
170#875—36no—
171C4×D12—36no—
172C4×D12—33no—
173C4×D12—33no—
174C4×D12—63no—
175C4×D12C2×D313yes—
176C42×D3—36no—
177C42×D3—33no—
178C42×D3—33no—
179C42×D3—63no—
180#869C2×D313yes—
181#869C2×D313yes—
182C4×Dic6—36no—
183C4×Dic6C2×D313yes—
184C22×C3⋊D3C2413yes—
185C22×C3×D3C2412yes—
186C32×Q8#4114yescomplemented
187C2×C32×C4C2413yes—
188C2×C32×C4C2413yes—
189C2×C32×C4C2411yescharacteristic
190C2×C3⋊Dic3C2413yes—
191C2×C3⋊Dic3C2411yescharacteristic
192C2×C3⋊Dic3C2411yescharacteristic
193C4⋊(C3⋊D3)—26no—
194C4×C3⋊D3—26no—
195C4×C3⋊D3—26no—
196C4×C3⋊D3—26no—
197C2×C3×Dic3C2412yes—
198C2×C3×Dic3C2416yes—
199C2×C3×Dic3C2416yes—
200C3×D12#4114yescomplemented
201C3×C4×D3—212no—
202C3×Dic6—26no—
203C3×Dic6—212no—
204#626—212no—
205D3×Dic3—212no—
206D3×Dic3—24no—
207#557—31no—
208#556—93no—
209#552—96no—
210D4×Q8—31no—
211#548—92no—
212#547—93no—
213#533—93no—
214#529—96no—
215C4×#41—93no—
216C4×#41—91no—
217C2×C4×Q8—92no—
218C2×C3×Q8—21no—
219C2×C3×Q8—36no—
220C2×C3×Q8—33no—
221C2×C3×Q8—68no—
222C2×C3×Q8C22×D311yescharacteristic
223C2×C3×Q8C22×D311yescharacteristic
224C2×C3×D4—31no—
225C22×C3×C4—36no—
226C2×#67—36no—
227C22×Dic3—36no—
228C22×Dic3—32no—
229#239—68no—
230#239—64no—
231#239—64no—
232#239—612no—
233D3×Q8—28no—
234#237—612no—
235C2×D12—36no—
236C2×D12—33no—
237C2×D12—33no—
238C2×D12—63no—
239C2×D12C22×D311yescharacteristic
240C2×C4×D3—32no—
241C2×C4×D3—36no—
242C2×C4×D3—33no—
243C2×C4×D3—33no—
244C2×C4×D3—33no—
245C2×C4×D3—33no—
246C2×C4×D3—33no—
247C2×C4×D3—33no—
248C2×C4×D3—63no—
249C2×C4×D3—63no—
250C2×C4×D3—63no—
251C2×C4×D3C22×D316yes—
252C2×Dic6C22×D316yes—
253C2×Dic6C22×D313yes—
254C3×C4⋊C4—23no—
255C3×C4⋊C4—36no—
256C3×C4⋊C4—33no—
257C3×C4⋊C4—36no—
258C3×C4⋊C4—36no—
259C3×C4⋊C4—31no—
260C3×C4⋊C4—36no—
261C3×C4⋊C4C22×D313yes—
262C3×C4⋊C4C22×D313yes—
263C3×C22⋊C4—36no—
264C3×C42—23no—
265C3×C42—36no—
266C3×C42C22×D313yes—
267C3×C42C22×D313yes—
268#217—32no—
269(C2×D3)⋊C4—32no—
270(C2×D3)⋊C4—36no—
271(C2×D3)⋊C4—36no—
272(C2×D3)⋊C4—36no—
273(C2×D3)⋊C4—312no—
274(C2×D3)⋊C4—36no—
275(C2×D3)⋊C4—312no—
276(C2×D3)⋊C4—66no—
277(C2×D3)⋊C4C22×D316yes—
278C4⋊Dic3—33no—
279C4⋊Dic3—33no—
280C4⋊Dic3—36no—
281C4⋊Dic3—312no—
282C4⋊Dic3—63no—
283C4⋊Dic3C22×D311yescharacteristic
284C4⋊Dic3C22×D313yes—
285C4⋊Dic3C22×D316yes—
286C4⋊Dic3C22×D316yes—
287C4⋊Dic3C22×D316yes—
288Dic3⋊C4—312no—
289Dic3⋊C4—36no—
290Dic3⋊C4C22×D316yes—
291C4×Dic3—31no—
292C4×Dic3—33no—
293C4×Dic3—31no—
294C4×Dic3—33no—
295C4×Dic3—33no—
296C4×Dic3—33no—
297C4×Dic3—36no—
298C4×Dic3—36no—
299C4×Dic3—36no—
300C4×Dic3—36no—
301C4×Dic3—61no—
302C4×Dic3—63no—
303C4×Dic3—63no—
304C4×Dic3C22×D316yes—
305C22×C32C2511yescharacteristic
306C2×C3⋊D3—23no—
307C2×C3⋊D3—23no—
308C2×C3⋊D3—23no—
309C2×C3×D3—22no—
310C2×C3×D3—22no—
311C2×C3×D3C2×#4114yes—
312C32×C4—23no—
313C32×C4C2×#4116yes—
314C32×C4C2×#4112yes—
315C3⋊Dic3—21no—
316C3⋊Dic3—23no—
317C3⋊Dic32−1+412yes—
318C3×Dic3—26no—
319C3×Dic3—26no—
320C3×Dic3—22no—
321C2×#41—93no—
322C2×#41—91no—
323C22×Q8—32no—
324C4⋊Q8—33no—
325C4⋊Q8—33no—
326#126—912no—
327#125—36no—
328#125—96no—
329#124—96no—
330#123—912no—
331C22⋊Q8—36no—
332C22⋊Q8—96no—
333C22⋊Q8—96no—
334#121—96no—
335C4×Q8—32no—
336C4×Q8—33no—
337C4×Q8—96no—
338C4×Q8—96no—
339C4×Q8—93no—
340C4×Q8—91no—
341C4×Q8D3211yescharacteristic
342C4×D4—33no—
343C4×D4—96no—
344C4×D4—96no—
345C4×D4—91no—
346C4×D4—93no—
347C4×D4—93no—
348#117—96no—
349#117—93no—
350#117—96no—
351#117—93no—
352C2×C4⋊C4—96no—
353C2×C42—96no—
354C2×C42—93no—
355C23×C3—32no—
356C22×D3—33no—
357C22×D3—33no—
358C22×D3—63no—
359C22×D3C23×D312yes—
360C3×Q8—24no—
361C3×Q8—66no—
362C3×Q8—612no—
363C3×Q8#23714yescomplemented
364C3×Q8#23914yescomplemented
365C3×D4—34no—
366C2×C3×C4—23no—
367C2×C3×C4—21no—
368C2×C3×C4—23no—
369C2×C3×C4—32no—
370C2×C3×C4—36no—
371C2×C3×C4—36no—
372C2×C3×C4—612no—
373C2×C3×C4C23×D313yes—
374C2×C3×C4C23×D313yes—
375C2×C3×C4C23×D313yes—
376C2×C3×C4C23×D313yes—
377C2×C3×C4C23×D311yescharacteristic
378C2×C3×C4C23×D311yescharacteristic
379#67—612no—
380C2×Dic3—31no—
381C2×Dic3—31no—
382C2×Dic3—31no—
383C2×Dic3—33no—
384C2×Dic3—31no—
385C2×Dic3—33no—
386C2×Dic3—61no—
387C2×Dic3—61no—
388C2×Dic3—63no—
389C2×Dic3—64no—
390C2×Dic3—612no—
391C2×Dic3C23×D312yes—
392C2×Dic3C23×D316yes—
393C2×Dic3C23×D316yes—
394D12—612no—
395D12—612no—
396D12—66no—
397D12—66no—
398D12#23914yescomplemented
399C4×D3—212no—
400C4×D3—66no—
401C4×D3—66no—
402C4×D3—64no—
403C4×D3—612no—
404C4×D3—612no—
405C4×D3—66no—
406C4×D3—66no—
407C4×D3—66no—
408C4×D3—66no—
409C4×D3—126no—
410C4×D3—126no—
411Dic6—212no—
412Dic6—26no—
413C2×C32C22×#4111yescharacteristic
414C2×C32C22×#4111yescharacteristic
415C2×C32C2×2−1+411yescharacteristic
416C3⋊D3—43no—
417C3×D3—24no—
418#41—1812no—
419#41—184no—
420C2×Q8—33no—
421C2×Q8—36no—
422C2×Q8—68no—
423C2×Q8C2×D3211yescharacteristic
424C2×D4—31no—
425C2×D4—96no—
426C2×D4—93no—
427C22×C4—36no—
428C22×C4—92no—
429C22×C4—96no—
430C22×C4—93no—
431C22×C4—93no—
432C22×C4—93no—
433C4⋊C4—36no—
434C4⋊C4—31no—
435C4⋊C4—33no—
436C4⋊C4—36no—
437C4⋊C4—36no—
438C4⋊C4—36no—
439C4⋊C4—912no—
440C4⋊C4—96no—
441C4⋊C4—93no—
442C4⋊C4C2×D3213yes—
443C22⋊C4—36no—
444C22⋊C4—96no—
445C22⋊C4—912no—
446C22⋊C4—92no—
447C22⋊C4—96no—
448C42—36no—
449C42—96no—
450C42—96no—
451C42—93no—
452C42—91no—
453C42—93no—
454C42C2×D3213yes—
455C22×C3—21no—
456C22×C3—34no—
457C22×C3—62no—
458C22×C3—62no—
459C22×C3C24×D311yescharacteristic
460C22×C3C24×D311yescharacteristic
461C2×D3—22no—
462C2×D3—22no—
463C2×D3—66no—
464C2×D3—63no—
465C2×D3—63no—
466C2×D3—63no—
467C2×D3—63no—
468C2×D3—63no—
469C2×D3—63no—
470C2×D3—123no—
471C2×D3—123no—
472C2×D3C2×#23914yes—
473C3×C4—23no—
474C3×C4—23no—
475C3×C4—26no—
476C3×C4—22no—
477C3×C4—43no—
478C3×C4—66no—
479C3×C4—66no—
480C3×C4—62no—
481C3×C4C2×#23716yes—
482C3×C4C2×#23916yes—
483C3×C4C2×#23912yes—
484C3×C4D3×#4112yes—
485Dic3—26no—
486Dic3—26no—
487Dic3—22no—
488Dic3—32no—
489Dic3—32no—
490Dic3—62no—
491Dic3—62no—
492Dic3—61no—
493Dic3—61no—
494Dic3—63no—
495Dic3—63no—
496Dic3—123no—
497C32#348211yescharacteristic, complemented, Sylow
498C23—32no—
499C23—93no—
500Q8—612no—
501Q8—66no—
502Q8#379614yescomplemented
503D4—34no—
504D4—1812no—
505D4—186no—
506C2×C4—32no—
507C2×C4—36no—
508C2×C4—36no—
509C2×C4—612no—
510C2×C4—91no—
511C2×C4—91no—
512C2×C4—93no—
513C2×C4—186no—
514C2×C4—184no—
515C2×C4—1812no—
516C2×C4—186no—
517C2×C4—186no—
518C2×C4C22×D3213yes—
519C2×C4C22×D3213yes—
520C2×C4C22×D3211yescharacteristic
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—64no—
525C2×C3C22×#23711yescharacteristic
526C2×C3C22×#23911yescharacteristic
527C2×C3C22×#23911yescharacteristic
528C2×C3C2×D3×#4111yescharacteristic
529C2×C3D3×2−1+411yescharacteristic
530C2×C3D3×2−1+411yescharacteristic
531D3—24no—
532D3—126no—
533D3—123no—
534D3—123no—
535C22—34no—
536C22—62no—
537C22—62no—
538C22—183no—
539C22—183no—
540C22—183no—
541C22C23×D3211yescharacteristic
542C4—23no—
543C4—66no—
544C4—66no—
545C4—62no—
546C4—92no—
547C4—181no—
548C4—183no—
549C4C2×#379616yes—
550C4D3×#23912yes—
551C3—21no—
552C3#8674411yescharacteristic, complemented
553C3#8701711yescharacteristic, complemented
554C2—64no—
555C2—363no—
556C2C22×#379611yescharacteristic
557C2C2×D3×#23911yescharacteristic
558C2#1059669411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
hypercenterC4×Q8D32
hypocenterC32#3482
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C4×#3832C2semidirect
2. C3×Q8×D12C2semidirect
3. C3×#5570C2semidirect
4. D3×Q8×Dic3C2semidirect
5. #10595342C2semidirect
6. #10594457C2semidirect
7. #10594453C2semidirect
8. #10593896C2semidirect
9. C4×#3796C2semidirect
10. #10593866C2semidirect
11. #10593865C2semidirect
62. Q8×D12D3semidirect
68. #5570D3semidirect
186. C32×Q8#41semidirect
200. C3×D12#41semidirect
363. C3×Q8#237semidirect
364. C3×Q8#239semidirect
398. D12#239semidirect
497. C32#3482semidirect
502. Q8#3796semidirect
552. C3#86744semidirect
553. C3#87017semidirect

Maximal subgroups

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

subgroupindex
C4×#38322
C3×Q8×D122
C3×#55702
D3×Q8×Dic32
#105953422
#105944572
#105944532
#105938962
C4×#37962
#105938662
#105938652
#870173
#867443