Finite Group Databasebeta

← #11909788

Subgroups — #11909788

Order 1152.

2364 conjugacy classes of subgroups.

The subgroup lattice has 555 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596048C211yesmaximal, characteristic, complemented
2C3×C4×D3×Q8C211yesmaximal, characteristic, complemented
3C3×Q8×Dic6C211yesmaximal, characteristic, complemented
4#10595353C212yesmaximal, complemented
5#10595342C212yesmaximal, complemented
6#10594517C216yesmaximal, complemented
7#10594352C216yesmaximal, complemented
8#10593970C213yesmaximal, complemented
9#10593963C213yesmaximal, complemented
10#10593958C213yesmaximal, complemented
11#10593870C213yesmaximal, complemented
12#87043—31nomaximal
13#85821—31nomaximal
14C2×#3832C2212yes—
15C2×C3×D3×Q8C2211yescharacteristic
16C2×#3799C2216yes—
17C32×C4×Q8C2211yescharacteristic
18#64104C2216yes—
19#64083C2213yes—
20C4×C4⋊(C3⋊D3)C2213yes—
21C3×Q8×Dic3C2212yes—
22C3×Q8×Dic3C2211yescharacteristic
23C3×D3×C4⋊C4C2213yes—
24C3×#888C2216yes—
25C3×#887C2213yes—
26C3×C42×D3C2213yes—
27C3×#869C2213yes—
28C3×C4×Dic6C2213yes—
29C3×C4×Dic6C2213yes—
30#63909C2216yes—
31#63909C2213yes—
32C4×#626C2216yes—
33#63900C2216yes—
34#63897C22112yes—
35#63894C2216yes—
36#63894C2216yes—
37#63894C2216yes—
38#63888C22112yes—
39#63874C2216yes—
40#63871C2216yes—
41#63869C2213yes—
42#63868C2216yes—
43#63864C2216yes—
44#63864C2216yes—
45#63864C2213yes—
46#63856C2211yescharacteristic
47#63850C2216yes—
48C3×Q82—31no—
49C2×C3×C4×Q8—31no—
50#5817—32no—
51#5733—36no—
52#5730—33no—
53#5726—36no—
54#5725—33no—
55#5585—33no—
56#5585—33no—
57#5582—36no—
58#5580—33no—
59#5579—33no—
60#5577—31no—
61#5577—31no—
62#5577—61no—
63#5576—32no—
64#5574—32no—
65#5574—32no—
66C4×D3×Q8D311yescharacteristic, complemented
67Q8×Dic6D311yescharacteristic, complemented
68#5507—36no—
69#5479—33no—
70#5477—33no—
71C2×C32×Q8C2311yescharacteristic
72#3832—28no—
73C2×C4⋊(C3⋊D3)C2313yes—
74C2×C4⋊(C3⋊D3)C2316yes—
75C2×C4⋊(C3⋊D3)C2316yes—
76C2×C4×C3⋊D3C2316yes—
77C3×D3×Q8—24no—
78C2×C3×C4×D3C2313yes—
79C2×C3×C4×D3C2313yes—
80C2×C3×C4×D3C2311yescharacteristic
81C2×C3×Dic6C2313yes—
82C2×C3×Dic6C2311yescharacteristic
83C2×C3×Dic6C2316yes—
84C2×#626C2316yes—
85C2×#624C23112yes—
86#3799—412no—
87C32×C4⋊C4C2313yes—
88C32×C42C2313yes—
89#3752C2316yes—
90C4⋊(C3⋊Dic3)C2311yescharacteristic
91C3×C4⋊Dic3C2316yes—
92C3×C4⋊Dic3C2313yes—
93C3×C4⋊Dic3C2313yes—
94C3×Dic3⋊C4C2316yes—
95C3×Dic3⋊C4C2316yes—
96C3×C4×Dic3C2313yes—
97C3×C4×Dic3C2313yes—
98C3×C4×Dic3C2316yes—
99C3×C4×Dic3C2313yes—
100#3724C2316yes—
101#3724C2312yes—
102Dic3⋊Dic3C2316yes—
103#3722C2316yes—
104#3722C2316yes—
105#3722C2316yes—
106#3722C23112yes—
107(C2×D3)⋊Dic3C2312yes—
108#3522—91noSylow
109C22×C3×Q8—31no—
110C2×#239—32no—
111C2×#239—32no—
112C2×#239—36no—
113C2×#239—62no—
114C2×D3×Q8C2×D311yescharacteristic
115C2×#235—36no—
116C3×C4⋊Q8—36no—
117C3×C4⋊Q8—33no—
118C3×C4×Q8—21no—
119C3×C4×Q8—32no—
120C3×C4×Q8—31no—
121C3×C4×Q8—33no—
122C3×C4×Q8—33no—
123C3×C4×Q8—33no—
124C3×C4×Q8C2×D311yescharacteristic
125C3×C4×Q8C2×D311yescharacteristic
126C2×C3×C4⋊C4—33no—
127C2×C3×C42—33no—
128#947—36no—
129#947—36no—
130#947—33no—
131#946—31no—
132#946—36no—
133#946—312no—
134Q8×Dic3C2×D312yes—
135Q8×Dic3C2×D311yescharacteristic
136#930—33no—
137#930—36no—
138#929—36no—
139C4×#67—36no—
140#924—31no—
141#898—36no—
142#897—36no—
143#896—312no—
144#895—33no—
145#895—36no—
146#895—36no—
147#895—36no—
148#895—66no—
149#894—36no—
150#894—312no—
151#894—312no—
152#893—36no—
153#893—36no—
154#893—36no—
155D3×C4⋊C4—36no—
156D3×C4⋊C4—36no—
157D3×C4⋊C4C2×D313yes—
158#890—33no—
159#888C2×D316yes—
160#887C2×D313yes—
161#876—36no—
162#875—36no—
163#875—36no—
164#875—33no—
165#874—33no—
166#874—33no—
167#874—63no—
168C4×D12—36no—
169C4×D12—33no—
170C4×D12—33no—
171C4×D12—36no—
172C4×D12—36no—
173C4×D12—36no—
174C4×D12—63no—
175#872—36no—
176#872—36no—
177C42×D3C2×D313yes—
178#870—33no—
179#869C2×D313yes—
180C4×Dic6C2×D313yes—
181C4×Dic6C2×D313yes—
182C22×C3⋊D3C2416yes—
183C22×C3×D3C2411yescharacteristic
184C32×Q8#4114yescomplemented
185C2×C32×C4C2413yes—
186C2×C32×C4C2413yes—
187C2×C32×C4C2411yescharacteristic
188C2×C3⋊Dic3C2412yes—
189C4⋊(C3⋊D3)—212no—
190C4⋊(C3⋊D3)—26no—
191C4⋊(C3⋊D3)—46no—
192C4×C3⋊D3—212no—
193C2×C3×Dic3C2412yes—
194C2×C3×Dic3C2413yes—
195C2×C3×Dic3C2411yescharacteristic
196C2×C3×Dic3C2416yes—
197C2×C3×Dic3C2413yes—
198C3×C4×D3—26no—
199C3×C4×D3—26no—
200C3×C4×D3—22no—
201C3×Dic6—26no—
202C3×Dic6—22no—
203C3×Dic6—46no—
204#626—212no—
205#624—412no—
206#559—93no—
207Q82—31no—
208#554—93no—
209#550—91no—
210#548—92no—
211#547—96no—
212#542—96no—
213#532—93no—
214#529—93no—
215#520—92no—
216C2×C4×Q8—31no—
217C2×C3×Q8—21no—
218C2×C3×Q8—33no—
219C2×C3×Q8—31no—
220C2×C3×Q8—36no—
221C2×C3×Q8—64no—
222C2×C3×Q8C22×D311yescharacteristic
223C2×C3×Q8C22×D311yescharacteristic
224C22×C3×C4—31no—
225C22×C3×C4—33no—
226C22×C3×C4—33no—
227C2×#67—36no—
228#239—68no—
229#239—68no—
230#239—128no—
231#239—1212no—
232D3×Q8—24no—
233#235—1212no—
234C2×D12—36no—
235C2×D12—33no—
236C2×D12—33no—
237C2×D12—36no—
238C2×D12—36no—
239C2×D12—36no—
240C2×D12—36no—
241C2×D12—63no—
242C2×D12—66no—
243C2×D12—66no—
244C2×C4×D3—36no—
245C2×C4×D3—36no—
246C2×C4×D3—312no—
247C2×C4×D3—312no—
248C2×C4×D3—66no—
249C2×C4×D3C22×D311yescharacteristic
250C2×C4×D3C22×D313yes—
251C2×C4×D3C22×D313yes—
252C2×Dic6C22×D311yescharacteristic
253C2×Dic6C22×D313yes—
254C2×Dic6C22×D316yes—
255C3×C4⋊C4—23no—
256C3×C4⋊C4—33no—
257C3×C4⋊C4—33no—
258C3×C4⋊C4—36no—
259C3×C4⋊C4—36no—
260C3×C4⋊C4—36no—
261C3×C4⋊C4C22×D313yes—
262C3×C4⋊C4C22×D313yes—
263C3×C42—23no—
264C3×C42—33no—
265C3×C42—33no—
266C3×C42—36no—
267C3×C42—33no—
268C3×C42C22×D313yes—
269C3×C42C22×D313yes—
270#217—32no—
271(C2×D3)⋊C4—32no—
272(C2×D3)⋊C4—36no—
273(C2×D3)⋊C4—36no—
274(C2×D3)⋊C4—36no—
275(C2×D3)⋊C4—36no—
276(C2×D3)⋊C4—36no—
277(C2×D3)⋊C4—36no—
278(C2×D3)⋊C4—36no—
279(C2×D3)⋊C4—312no—
280(C2×D3)⋊C4—36no—
281(C2×D3)⋊C4—312no—
282(C2×D3)⋊C4—66no—
283C4⋊Dic3—31no—
284C4⋊Dic3—31no—
285C4⋊Dic3—36no—
286C4⋊Dic3—61no—
287C4⋊Dic3C22×D313yes—
288C4⋊Dic3C22×D313yes—
289C4⋊Dic3C22×D316yes—
290Dic3⋊C4—36no—
291Dic3⋊C4—36no—
292Dic3⋊C4—32no—
293Dic3⋊C4—32no—
294Dic3⋊C4—36no—
295Dic3⋊C4C22×D316yes—
296Dic3⋊C4C22×D316yes—
297C4×Dic3C22×D313yes—
298C4×Dic3C22×D316yes—
299C4×Dic3C22×D313yes—
300C4×Dic3C22×D313yes—
301C22×C32C2511yescharacteristic
302C2×C3⋊D3—26no—
303C2×C3⋊D3—26no—
304C2×C3⋊D3—26no—
305C2×C3×D3—21no—
306C2×C3×D3—21no—
307C2×C3×D3H(5,𝔽2)12yes—
308C32×C4—23no—
309C32×C4C2×#4116yes—
310C32×C42−1+412yes—
311C3⋊Dic3—22no—
312C3×Dic3—23no—
313C3×Dic3—23no—
314C3×Dic3—26no—
315C3×Dic3—22no—
316C3×Dic3—21no—
317C2×#41—96no—
318C2×#41—92no—
319C22×Q8—31no—
320C4⋊Q8—36no—
321C4⋊Q8—33no—
322#127—93no—
323#126—96no—
324#125—93no—
325#124—93no—
326#124—96no—
327#124—96no—
328#123—912no—
329#123—96no—
330C22⋊Q8—912no—
331C22⋊Q8—96no—
332C22⋊Q8—91no—
333#121—93no—
334#121—96no—
335#121—96no—
336C4×Q8—31no—
337C4×Q8—32no—
338C4×Q8—33no—
339C4×Q8—33no—
340C4×Q8—33no—
341C4×Q8D3211yescharacteristic
342C4×D4—96no—
343C4×D4—96no—
344C4×D4—96no—
345C4×D4—96no—
346C4×D4—93no—
347#117—96no—
348C2×C4⋊C4—33no—
349C2×C4⋊C4—96no—
350C2×C42—33no—
351C23×C3—31no—
352C22×D3—36no—
353C22×D3—36no—
354C22×D3—66no—
355C22×D3C23×D311yescharacteristic
356C3×Q8—24no—
357C3×Q8—66no—
358C3×Q8—62no—
359C3×Q8—126no—
360C3×Q8#23514yescomplemented
361C3×Q8#23914yescomplemented
362C2×C3×C4—21no—
363C2×C3×C4—23no—
364C2×C3×C4—23no—
365C2×C3×C4—31no—
366C2×C3×C4—33no—
367C2×C3×C4—33no—
368C2×C3×C4—36no—
369C2×C3×C4—32no—
370C2×C3×C4—66no—
371C2×C3×C4—66no—
372C2×C3×C4—62no—
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—32no—
381C2×Dic3—32no—
382C2×Dic3—62no—
383C2×Dic3C23×D311yescharacteristic
384C2×Dic3C23×D312yes—
385C2×Dic3C23×D313yes—
386C2×Dic3C23×D313yes—
387C2×Dic3C23×D316yes—
388D12—612no—
389D12—612no—
390D12—612no—
391D12—66no—
392D12—66no—
393D12—126no—
394D12—1212no—
395D12—126no—
396D12—126no—
397D12—246no—
398C4×D3—26no—
399C4×D3—26no—
400C4×D3—22no—
401C4×D3—612no—
402C4×D3—612no—
403C4×D3—1212no—
404C4×D3—1212no—
405C4×D3—1212no—
406Dic6—26no—
407Dic6—22no—
408Dic6—46no—
409C2×C32C22×#4111yescharacteristic
410C2×C32C2×H(5,𝔽2)11yescharacteristic
411C2×C32C2×2−1+411yescharacteristic
412C3⋊D3—46no—
413C3×D3—22no—
414#41—188no—
415#41—3612no—
416C2×Q8—31no—
417C2×Q8—33no—
418C2×Q8—36no—
419C2×Q8—64no—
420C2×Q8C2×D3211yescharacteristic
421C2×D4—96no—
422C2×D4—93no—
423C2×D4—96no—
424C2×D4—96no—
425C22×C4—31no—
426C22×C4—33no—
427C22×C4—33no—
428C22×C4—912no—
429C22×C4—96no—
430C4⋊C4—33no—
431C4⋊C4—36no—
432C4⋊C4—36no—
433C4⋊C4—33no—
434C4⋊C4—36no—
435C4⋊C4—96no—
436C4⋊C4—92no—
437C4⋊C4—96no—
438C4⋊C4—91no—
439C4⋊C4C2×D3213yes—
440C22⋊C4—96no—
441C22⋊C4—96no—
442C22⋊C4—912no—
443C22⋊C4—96no—
444C22⋊C4—92no—
445C22⋊C4—96no—
446C42—33no—
447C42—33no—
448C42—33no—
449C42—36no—
450C42C2×D3213yes—
451C22×C3—21no—
452C22×C3—32no—
453C22×C3—61no—
454C22×C3—61no—
455C22×C3C24×D311yescharacteristic
456C22×C3C24×D311yescharacteristic
457C2×D3—21no—
458C2×D3—21no—
459C2×D3—66no—
460C2×D3—66no—
461C2×D3—66no—
462C2×D3—66no—
463C2×D3—66no—
464C2×D3—66no—
465C2×D3—126no—
466C2×D3—126no—
467C2×D3—126no—
468C2×D3#100912yes—
469C3×C4—23no—
470C3×C4—23no—
471C3×C4—26no—
472C3×C4—22no—
473C3×C4—43no—
474C3×C4—63no—
475C3×C4—61no—
476C3×C4—62no—
477C3×C4—66no—
478C3×C4—63no—
479C3×C4C2×#23516yes—
480C3×C4C2×#23916yes—
481C3×C4#100712yes—
482C3×C4#100712yes—
483Dic3—23no—
484Dic3—22no—
485Dic3—21no—
486Dic3—23no—
487Dic3—26no—
488Dic3—62no—
489Dic3—62no—
490Dic3—122no—
491C32#352211yescharacteristic, complemented, Sylow
492C23—31no—
493C23—96no—
494Q8—66no—
495Q8—62no—
496Q8—126no—
497Q8#379914yescomplemented
498D4—1812no—
499D4—1812no—
500D4—186no—
501D4—366no—
502C2×C4—31no—
503C2×C4—32no—
504C2×C4—33no—
505C2×C4—33no—
506C2×C4—36no—
507C2×C4—66no—
508C2×C4—66no—
509C2×C4—62no—
510C2×C4—92no—
511C2×C4—1812no—
512C2×C4—3612no—
513C2×C4C22×D3213yes—
514C2×C4C22×D3213yes—
515C2×C4C22×D3211yescharacteristic
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—62no—
520C2×C3C22×#23511yescharacteristic
521C2×C3C22×#23911yescharacteristic
522C2×C3C2×#100711yescharacteristic
523C2×C3C2×#100711yescharacteristic
524C2×C3C2×#100911yescharacteristic
525C2×C3D3×H(5,𝔽2)11yescharacteristic
526D3—22no—
527D3—126no—
528D3—126no—
529D3—246no—
530C22—32no—
531C22—61no—
532C22—61no—
533C22—186no—
534C22—186no—
535C22—186no—
536C22C23×D3211yescharacteristic
537C4—23no—
538C4—63no—
539C4—61no—
540C4—62no—
541C4—63no—
542C4—66no—
543C4—182no—
544C4C2×#379916yes—
545C4#6431612yes—
546C3—21no—
547C3#8582111yescharacteristic, complemented
548C3#8704311yescharacteristic, complemented
549C2—62no—
550C2—366no—
551C2C22×#379911yescharacteristic
552C2C2×#6431611yescharacteristic
553C2D3×#100911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
hypercenterC4×Q8D32
hypocenterC32#3522
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #10596048C2semidirect
2. C3×C4×D3×Q8C2semidirect
3. C3×Q8×Dic6C2semidirect
4. #10595353C2semidirect
5. #10595342C2semidirect
6. #10594517C2semidirect
7. #10594352C2semidirect
8. #10593970C2semidirect
9. #10593963C2semidirect
10. #10593958C2semidirect
11. #10593870C2semidirect
66. C4×D3×Q8D3semidirect
67. Q8×Dic6D3semidirect
184. C32×Q8#41semidirect
360. C3×Q8#235semidirect
361. C3×Q8#239semidirect
491. C32#3522semidirect
497. Q8#3799semidirect
547. C3#85821semidirect
548. C3#87043semidirect

Maximal subgroups

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

subgroupindex
#105960482
C3×C4×D3×Q82
C3×Q8×Dic62
#105953532
#105953422
#105945172
#105943522
#105939702
#105939632
#105939582
#105938702
#870433
#858213