Finite Group Databasebeta

← #11909912

Subgroups — #11909912

Order 1152.

2084 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596041C211yesmaximal, characteristic, complemented
2C3×Q8×D12C211yesmaximal, characteristic, complemented
3C3×C4×D3×Q8C211yesmaximal, characteristic, complemented
4Q8×#625C212yesmaximal, complemented
5#10595347C212yesmaximal, complemented
6#10594551C216yesmaximal, complemented
7#10594345C216yesmaximal, complemented
8#10593974C213yesmaximal
9#10593879C213yesmaximal, complemented
10#10593864C213yesmaximal, complemented
11#10593859C213yesmaximal, complemented
12#86753—31nomaximal
13#85804—31nomaximal
14C2×C3×D3×Q8C2212yes—
15C2×C3×D3×Q8C2211yescharacteristic
16C32×C4×Q8C2211yescharacteristic
17Q8×C3⋊Dic3C2212yes—
18#64099C2216yes—
19#64078C2213yes—
20C4×#634C2213yes—
21C3×Q8×Dic3C2211yescharacteristic
22C3×#897C2216yes—
23C3×D3×C4⋊C4C2213yes—
24C3×#887C2213yes—
25C3×C4×D12C2213yes—
26C3×C42×D3C2213yes—
27C3×#869C2213yes—
28C3×C4×Dic6C2213yes—
29#63908C2211yescharacteristic
30#63905C2216yes—
31C4×#625C2216yes—
32#63873C2216yes—
33#63869C2216yes—
34#63869C2213yes—
35#63861C22112yes—
36#63860C2213yes—
37#63859C2216yes—
38#63857C2213yes—
39#63856C2216yes—
40#63856C2216yes—
41#63855C2216yes—
42#63847C22112yes—
43#63844C2216yes—
44#63843C2216yes—
45Dic3×Dic6C2216yes—
46#63841C2216yes—
47#63841C2216yes—
48C3×D4×Q8—31no—
49C2×C3×C4×Q8—31no—
50Q8×#67—32no—
51Q8×#67—32no—
52#5812—32no—
53#5728—33no—
54#5721—33no—
55#5639—36no—
56#5625—36no—
57#5584—33no—
58#5583—36no—
59Q8×D12D311yescharacteristic, complemented
60#5572—32no—
61C4×D3×Q8D311yescharacteristic, complemented
62#5570—31no—
63#5570—31no—
64#5570—61no—
65#5567—33no—
66#5557—33no—
67#5542—33no—
68#5513—36no—
69#5479—33no—
70#5470—33no—
71C2×C32×Q8C2311yescharacteristic
72C2×#634C2313yes—
73C3×D3×Q8—24no—
74C3×D3×Q8—28no—
75C2×C3×D12C2311yescharacteristic
76C2×C3×C4×D3C2313yes—
77C2×C3×C4×D3C2313yes—
78C2×C3×C4×D3C2316yes—
79C2×C3×C4×D3C2311yescharacteristic
80C2×C3×Dic6C2313yes—
81C2×C3×Dic6C2316yes—
82C2×#625C2312yes—
83C32×C4⋊C4C2313yes—
84C32×C42C2313yes—
85C4⋊(C3⋊Dic3)C2311yescharacteristic
86C4⋊(C3⋊Dic3)C2316yes—
87C4⋊(C3⋊Dic3)C2316yes—
88#3750C2316yes—
89C4×C3⋊Dic3C2316yes—
90C3×(C2×D3)⋊C4C2316yes—
91C3×C4⋊Dic3C2313yes—
92C3×C4⋊Dic3C2316yes—
93C3×C4⋊Dic3C2313yes—
94C3×Dic3⋊C4C2316yes—
95C3×C4×Dic3C2313yes—
96C3×C4×Dic3C2313yes—
97C3×C4×Dic3C2313yes—
98#3724C23112yes—
99#3724C2316yes—
100Dic3⋊Dic3C2316yes—
101Dic3⋊Dic3C2316yes—
102(C2×D3)⋊Dic3C2316yes—
103(C2×D3)⋊Dic3C2316yes—
104(C2×D3)⋊Dic3C2312yes—
105(C2×D3)⋊Dic3C2316yes—
106Dic32C23112yes—
107#3523—91noSylow
108C22×C3×Q8—32no—
109C22×C3×Q8—31no—
110C2×D3×Q8C2×D311yescharacteristic
111C2×D3×Q8C2×D312yes—
112C3×C4⋊Q8—33no—
113C3×C22⋊Q8—36no—
114C3×C4×Q8—21no—
115C3×C4×Q8—31no—
116C3×C4×Q8—33no—
117C3×C4×Q8—33no—
118C3×C4×Q8C2×D311yescharacteristic
119C3×C4×Q8C2×D311yescharacteristic
120C3×C4×D4—33no—
121C2×C3×C4⋊C4—33no—
122C2×C3×C42—33no—
123#946—36no—
124#946—36no—
125Q8×Dic3—32no—
126Q8×Dic3—32no—
127Q8×Dic3—36no—
128Q8×Dic3—36no—
129Q8×Dic3—62no—
130Q8×Dic3C2×D311yescharacteristic
131#944—36no—
132#944—36no—
133#938—31no—
134#936—33no—
135#930—31no—
136#929—36no—
137C4×#67—36no—
138C4×#67—36no—
139#926—36no—
140#926—36no—
141#926—36no—
142#924—36no—
143#924—36no—
144#924—33no—
145#898—312no—
146#897—33no—
147#897C2×D316yes—
148#892—36no—
149#892—36no—
150D3×C4⋊C4C2×D313yes—
151#890—36no—
152#890—36no—
153#890—33no—
154#890—36no—
155#890—66no—
156#889—312no—
157#889—312no—
158#887—36no—
159#887—36no—
160#887C2×D313yes—
161#883—36no—
162#879—312no—
163#879—36no—
164#876—36no—
165#875—33no—
166C4×D12C2×D313yes—
167#872—36no—
168C42×D3C2×D313yes—
169#870—36no—
170#870—33no—
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—63no—
180C4×Dic6C2×D313yes—
181C22×C3×D3C2412yes—
182C22×C3×D3C2411yescharacteristic
183C32×Q8#4114yes—
184C2×C32×C4C2413yes—
185C2×C32×C4C2413yes—
186C2×C32×C4C2411yescharacteristic
187C2×C3⋊Dic3C2416yes—
188C2×C3⋊Dic3C2412yes—
189#634—26no—
190C2×C3×Dic3C2413yes—
191C2×C3×Dic3C2416yes—
192C2×C3×Dic3C2411yescharacteristic
193C2×C3×Dic3C2413yes—
194C3×D12—22no—
195C3×C4×D3—26no—
196C3×C4×D3—26no—
197C3×C4×D3—212no—
198C3×C4×D3—22no—
199C3×Dic6—26no—
200C3×Dic6—212no—
201#625—24no—
202#557—93no—
203#557—91no—
204#556—93no—
205#552—96no—
206D4×Q8—31no—
207D4×Q8—92no—
208#541—96no—
209#533—93no—
210#529—93no—
211#519—92no—
212C2×C4×Q8—31no—
213C2×C3×Q8—21no—
214C2×C3×Q8—33no—
215C2×C3×Q8—36no—
216C2×C3×Q8—68no—
217C2×C3×Q8—64no—
218C2×C3×Q8C22×D311yescharacteristic
219C2×C3×Q8C22×D311yescharacteristic
220C2×C3×D4—31no—
221C22×C3×C4—31no—
222C22×C3×C4—33no—
223C22×C3×C4—36no—
224C22×C3×C4—33no—
225C2×#67—32no—
226C2×#67—32no—
227D3×Q8—24no—
228D3×Q8—28no—
229C2×D12C22×D311yescharacteristic
230C2×C4×D3C22×D311yescharacteristic
231C2×C4×D3C22×D313yes—
232C2×C4×D3C22×D313yes—
233C2×C4×D3C22×D316yes—
234C2×Dic6—33no—
235C2×Dic6—33no—
236C2×Dic6—63no—
237C2×Dic6C22×D316yes—
238C2×Dic6C22×D313yes—
239C3×C4⋊C4—23no—
240C3×C4⋊C4—33no—
241C3×C4⋊C4—33no—
242C3×C4⋊C4—36no—
243C3×C4⋊C4—36no—
244C3×C4⋊C4C22×D313yes—
245C3×C4⋊C4C22×D313yes—
246C3×C22⋊C4—36no—
247C3×C42—23no—
248C3×C42—33no—
249C3×C42—33no—
250C3×C42—33no—
251C3×C42C22×D313yes—
252C3×C42C22×D313yes—
253#217—36no—
254#217—32no—
255#217—36no—
256#217—36no—
257(C2×D3)⋊C4—32no—
258(C2×D3)⋊C4—36no—
259(C2×D3)⋊C4—36no—
260(C2×D3)⋊C4—36no—
261(C2×D3)⋊C4C22×D316yes—
262C4⋊Dic3—31no—
263C4⋊Dic3—31no—
264C4⋊Dic3—36no—
265C4⋊Dic3—36no—
266C4⋊Dic3—36no—
267C4⋊Dic3—36no—
268C4⋊Dic3—36no—
269C4⋊Dic3—36no—
270C4⋊Dic3—61no—
271C4⋊Dic3—66no—
272C4⋊Dic3—66no—
273C4⋊Dic3C22×D313yes—
274C4⋊Dic3C22×D313yes—
275C4⋊Dic3C22×D316yes—
276Dic3⋊C4—36no—
277Dic3⋊C4—36no—
278Dic3⋊C4—36no—
279Dic3⋊C4—312no—
280Dic3⋊C4—36no—
281Dic3⋊C4—36no—
282Dic3⋊C4—312no—
283Dic3⋊C4—36no—
284Dic3⋊C4—66no—
285Dic3⋊C4C22×D316yes—
286C4×Dic3—36no—
287C4×Dic3—36no—
288C4×Dic3—312no—
289C4×Dic3—312no—
290C4×Dic3—66no—
291C4×Dic3C22×D313yes—
292C4×Dic3C22×D313yes—
293C4×Dic3C22×D313yes—
294C22×C32C2511yescharacteristic
295C2×C3×D3—21no—
296C2×C3×D3—21no—
297C2×C3×D3—22no—
298C2×C3×D3—22no—
299C2×C3×D3—22no—
300C2×C3×D32−1+412yes—
301C32×C4—23no—
302C32×C4C2×#4116yes—
303C32×C42−1+412yes—
304C3⋊Dic3—22no—
305C3⋊Dic3—26no—
306C3×Dic3—23no—
307C3×Dic3—26no—
308C3×Dic3—21no—
309C3×Dic3—23no—
310C22×Q8—31no—
311C22×Q8—32no—
312C4⋊Q8—33no—
313C4⋊Q8—96no—
314C4⋊Q8—93no—
315#126—96no—
316#126—912no—
317#125—93no—
318#125—96no—
319#125—912no—
320#125—96no—
321#124—93no—
322#123—96no—
323C22⋊Q8—36no—
324C22⋊Q8—93no—
325C22⋊Q8—96no—
326C22⋊Q8—96no—
327#121—91no—
328C4×Q8—31no—
329C4×Q8—33no—
330C4×Q8—33no—
331C4×Q8—96no—
332C4×Q8—96no—
333C4×Q8—96no—
334C4×Q8—92no—
335C4×Q8—93no—
336C4×Q8D3211yescharacteristic
337C4×D4—33no—
338C4×D4—96no—
339#117—96no—
340#117—96no—
341#117—96no—
342C2×C4⋊C4—33no—
343C2×C42—33no—
344C23×C3—31no—
345C23×C3—32no—
346C22×D3C23×D312yes—
347C22×D3C23×D311yescharacteristic
348C3×Q8—24no—
349C3×Q8—612no—
350C3×Q8—66no—
351C3×Q8#23514yes—
352C3×Q8#23714yes—
353C3×D4—62no—
354C2×C3×C4—23no—
355C2×C3×C4—21no—
356C2×C3×C4—23no—
357C2×C3×C4—33no—
358C2×C3×C4—36no—
359C2×C3×C4—31no—
360C2×C3×C4—33no—
361C2×C3×C4—66no—
362C2×C3×C4—612no—
363C2×C3×C4—66no—
364C2×C3×C4—62no—
365C2×C3×C4C23×D313yes—
366C2×C3×C4C23×D313yes—
367C2×C3×C4C23×D313yes—
368C2×C3×C4C23×D313yes—
369C2×C3×C4C23×D311yescharacteristic
370C2×C3×C4C23×D311yescharacteristic
371#67—64no—
372#67—64no—
373C2×Dic3—32no—
374C2×Dic3—32no—
375C2×Dic3—36no—
376C2×Dic3—36no—
377C2×Dic3—62no—
378C2×Dic3—66no—
379C2×Dic3C23×D313yes—
380C2×Dic3C23×D316yes—
381C2×Dic3C23×D311yescharacteristic
382C2×Dic3C23×D313yes—
383D12—22no—
384C4×D3—26no—
385C4×D3—26no—
386C4×D3—212no—
387C4×D3—22no—
388Dic6—26no—
389Dic6—212no—
390Dic6—66no—
391Dic6—66no—
392Dic6—126no—
393C2×C32C22×#4111yescharacteristic
394C2×C32C2×2−1+411yescharacteristic
395C2×C32C2×2−1+411yescharacteristic
396C3×D3—22no—
397C3×D3—42no—
398C2×Q8—33no—
399C2×Q8—36no—
400C2×Q8—64no—
401C2×Q8—68no—
402C2×Q8—93no—
403C2×Q8C2×D3211yescharacteristic
404C2×D4—31no—
405C2×D4—92no—
406C22×C4—31no—
407C22×C4—33no—
408C22×C4—33no—
409C22×C4—36no—
410C4⋊C4—33no—
411C4⋊C4—36no—
412C4⋊C4—36no—
413C4⋊C4—33no—
414C4⋊C4—96no—
415C4⋊C4—96no—
416C4⋊C4—96no—
417C4⋊C4—912no—
418C4⋊C4—96no—
419C4⋊C4—96no—
420C4⋊C4—91no—
421C4⋊C4—96no—
422C4⋊C4C2×D3213yes—
423C22⋊C4—36no—
424C22⋊C4—92no—
425C22⋊C4—96no—
426C22⋊C4—96no—
427C22⋊C4—96no—
428C42—33no—
429C42—33no—
430C42—33no—
431C42—912no—
432C42—96no—
433C42C2×D3213yes—
434C22×C3—21no—
435C22×C3—32no—
436C22×C3—61no—
437C22×C3—61no—
438C22×C3—62no—
439C22×C3—62no—
440C22×C3—62no—
441C22×C3C24×D311yescharacteristic
442C22×C3C24×D311yescharacteristic
443C2×D3—21no—
444C2×D3—21no—
445C2×D3—22no—
446C2×D3—22no—
447C2×D3—22no—
448C2×D3#101012yes—
449C3×C4—23no—
450C3×C4—23no—
451C3×C4—26no—
452C3×C4—22no—
453C3×C4—43no—
454C3×C4—66no—
455C3×C4—63no—
456C3×C4—61no—
457C3×C4—63no—
458C3×C4C2×#23516yes—
459C3×C4C2×#23716yes—
460C3×C4#100712yes—
461C3×C4#100712yes—
462Dic3—23no—
463Dic3—26no—
464Dic3—21no—
465Dic3—23no—
466Dic3—66no—
467Dic3—66no—
468Dic3—62no—
469Dic3—62no—
470Dic3—126no—
471Dic3—122no—
472C32#352311yescharacteristic, complemented, Sylow
473C23—31no—
474C23—32no—
475Q8—66no—
476Q8—612no—
477Q8—186no—
478Q8#379514yes—
479D4—62no—
480D4—184no—
481C2×C4—31no—
482C2×C4—33no—
483C2×C4—33no—
484C2×C4—36no—
485C2×C4—66no—
486C2×C4—66no—
487C2×C4—612no—
488C2×C4—62no—
489C2×C4—96no—
490C2×C4—92no—
491C2×C4C22×D3213yes—
492C2×C4C22×D3213yes—
493C2×C4C22×D3211yescharacteristic
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—62no—
498C2×C3—122no—
499C2×C3C22×#23511yescharacteristic
500C2×C3C22×#23711yescharacteristic
501C2×C3C2×#100711yescharacteristic
502C2×C3C2×#100711yescharacteristic
503C2×C3C2×#101011yescharacteristic
504C2×C3D3×2−1+411yescharacteristic
505D3—22no—
506D3—42no—
507C22—32no—
508C22—61no—
509C22—61no—
510C22—62no—
511C22—62no—
512C22—62no—
513C22C23×D3211yescharacteristic
514C4—23no—
515C4—63no—
516C4—66no—
517C4—61no—
518C4—63no—
519C4—186no—
520C4—182no—
521C4C2×#379516yes—
522C4#6431612yes—
523C3—21no—
524C3#8580411yescharacteristic, complemented
525C3#8675311yescharacteristic, complemented
526C2—62no—
527C2—122no—
528C2C22×#379511yescharacteristic
529C2C2×#6431611yescharacteristic
530C2D3×#101011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
prime radical#63908C22
hypercenterC4×Q8D32
hypocenterC32#3523
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #10596041C2semidirect
2. C3×Q8×D12C2semidirect
3. C3×C4×D3×Q8C2semidirect
4. Q8×#625C2semidirect
5. #10595347C2semidirect
6. #10594551C2semidirect
7. #10594345C2semidirect
9. #10593879C2semidirect
10. #10593864C2semidirect
11. #10593859C2semidirect
59. Q8×D12D3semidirect
61. C4×D3×Q8D3semidirect
472. C32#3523semidirect
524. C3#85804semidirect
525. C3#86753semidirect

Maximal subgroups

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

subgroupindex
#105960412
C3×Q8×D122
C3×C4×D3×Q82
Q8×#6252
#105953472
#105945512
#105943452
#105939742
#105938792
#105938642
#105938592
#867533
#858043