Finite Group Databasebeta

← #11902599

Subgroups — #11902599

Order 1152.

3389 conjugacy classes of subgroups.

The subgroup lattice has 569 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64319C211yesmaximal, characteristic, complemented
2C2×D32×Q8C211yesmaximal, characteristic, complemented
3C4×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
4C3×#5576C212yesmaximal, complemented
5#10595409C212yesmaximal, complemented
6#10594631C213yesmaximal, complemented
7#10594612C213yesmaximal, complemented
8#10594525C216yesmaximal, complemented
9#10594009C213yesmaximal, complemented
10C4×#3802C213yesmaximal, complemented
11#10593905C216yesmaximal, complemented
12D3×#548—32nomaximal
13C2×Q8×C3⋊D3C2211yescharacteristic
14C2×C3×#239C2212yescomplemented
15C2×C3×D3×Q8C2212yescomplemented
16#64319—28no—
17D32×Q8—28no—
18C2×#3802C2213yes—
19C2×#3802C2213yes—
20C2×C4×D32C2213yes—
21C2×C4×D32C2213yes—
22C2×#3797C2213yes—
23C2×#3795C2216yescomplemented
24C2×D3×Dic6C2216yescomplemented
25C32×C4×Q8C2211yescharacteristic, complemented
26Q8×C3⋊Dic3C2211yescharacteristic, complemented
27C4⋊C4×C3⋊D3C2213yes—
28#64096C2213yescomplemented
29C42×C3⋊D3C2213yes—
30C4×#634C2213yescomplemented
31C3×#897C2216yescomplemented
32C3×#895C2216yescomplemented
33C3×#875C2216yescomplemented
34C3×C4×D12C2216yescomplemented
35#63921C2216yes—
36#63921C2211yescharacteristic
37#63921C2213yes—
38#63915C2216yescomplemented
39#63915C2216yescomplemented
40#63908C2216yescomplemented
41#63902C2216yescomplemented
42C4×#625C2216yescomplemented
43#63900C2213yes—
44#63899C22112yescomplemented
45#63898C2216yescomplemented
46#63885C22112yescomplemented
47#63863C2216yescomplemented
48#63856C2216yescomplemented
49C2×D3×#41—32no—
50C22×D3×Q8—32no—
51C3×#548—32no—
52#5831—32no—
53#5817—32no—
54#5677—36no—
55D3×#124—36no—
56#5633—36no—
57D3×C22⋊Q8—36no—
58D3×#121—36no—
59#5598—36no—
60#5576D312yescomplemented
61C4×D3×Q8—32no—
62C4×D3×Q8—61no—
63#5552—36no—
64C4×D3×D4—36no—
65C22×D32C2313yes—
66C22×D32C2311yescharacteristic
67C2×C32×Q8C2311yescharacteristic
68Q8×C3⋊D3D418yescomplemented
69C2×C4×C3⋊D3C2313yes—
70C2×C4×C3⋊D3C2311yescharacteristic
71C2×C4×C3⋊D3C2313yes—
72C2×#634C2313yes—
73C3×#239—28no—
74C3×D3×Q8—28no—
75C2×C3×D12C2316yes—
76C2×C3×D12C2316yes—
77C2×C3×C4×D3C2316yes—
78C2×C3×C4×D3C2316yes—
79C2×C3×Dic6C2316yes—
80C2×#627C2316yes—
81C2×#625C2316yes—
82C2×#625C2316yes—
83C2×#624C2313yes—
84C2×#624C2311yescharacteristic
85C2×D3×Dic3C2316yes—
86C2×D3×Dic3C2316yes—
87#3802—212no—
88#3802—212no—
89C4×D32—212no—
90C4×D32—212no—
91#3797—212no—
92#3795—224no—
93D3×Dic6—224no—
94C32×C4⋊C4C2313yes—
95C32×C42C2313yes—
96C4⋊(C3⋊Dic3)C2313yes—
97#3750C2316yes—
98C4×C3⋊Dic3C2313yes—
99C4×C3⋊Dic3C2313yes—
100C4×C3⋊Dic3C2313yes—
101C3×(C2×D3)⋊C4C23112yes—
102C3×(C2×D3)⋊C4C2312yes—
103C3×(C2×D3)⋊C4C2316yes—
104C3×C4⋊Dic3C2316yes—
105#3724C2316yes—
106(C2×D3)⋊Dic3C23112yes—
107(C2×D3)⋊Dic3C2316yes—
108(C2×D3)⋊Dic3C2312yes—
109C2×#548—91noSylow
110C2×C3×#41—32no—
111C22×C3×Q8—32no—
112D3×#41—616no—
113C2×#239C2×D312yescomplemented
114C2×D3×Q8—32no—
115C2×D3×Q8—36no—
116C2×D3×Q8—36no—
117C2×D3×Q8—61no—
118C2×D3×Q8—616no—
119C2×D3×Q8C2×D312yescomplemented
120C2×#237—36no—
121C2×D3×D4—36no—
122C2×D3×D4—36no—
123C2×#235—36no—
124C22×C4×D3—36no—
125C22×C4×D3—36no—
126C22×Dic6—36no—
127C3×#124—36no—
128C3×C22⋊Q8—36no—
129C3×#121—36no—
130C3×C4×Q8—21no—
131C3×C4×Q8C2×D312yescomplemented
132C3×C4×D4—36no—
133#947—36no—
134#946—36no—
135Q8×Dic3—32no—
136Q8×Dic3—61no—
137#939—312no—
138#938—36no—
139#936—36no—
140D4×Dic3—36no—
141#930—36no—
142C4×#67—36no—
143C4×#67—36no—
144#924—36no—
145#897C2×D316yescomplemented
146#896—312no—
147#895C2×D316yescomplemented
148#893—36no—
149D3×C4⋊C4—36no—
150D3×C4⋊C4—36no—
151D3×C4⋊C4—63no—
152#887—36no—
153#887—63no—
154#885—312no—
155#885—312no—
156#884—312no—
157#67⋊C4—36no—
158#67⋊C4—36no—
159D3×C22⋊C4—36no—
160D3×C22⋊C4—312no—
161D3×C22⋊C4—32no—
162#878—312no—
163#875C2×D316yescomplemented
164C4×D12C2×D316yescomplemented
165C42×D3—36no—
166C42×D3—63no—
167C4×Dic6—36no—
168C4×Dic6—63no—
169C22×C3⋊D3C2411yescharacteristic
170C22×C3×D3C2416yes—
171C22×C3×D3C2412yes—
172C2×D32—22no—
173C2×D32—22no—
174C2×D32—26no—
175C2×D32—26no—
176C2×D32—26no—
177C2×D32#4114yescomplemented
178C32×Q8C2×D414yescomplemented
179C2×C32×C4C2413yes—
180C2×C32×C4C2411yescharacteristic
181C2×C32×C4C2413yes—
182C2×C3⋊Dic3C2411yescharacteristic
183C2×C3⋊Dic3C2413yes—
184C2×C3⋊Dic3C2413yes—
185C4×C3⋊D3—22no—
186C4×C3⋊D3—26no—
187C4×C3⋊D3C2×D4112yes—
188#634C2×D4112yescomplemented
189C2×C3×Dic3C2416yes—
190C2×C3×Dic3C2412yes—
191C3×D12—212no—
192C3×D12—212no—
193C3×C4×D3—212no—
194C3×C4×D3—212no—
195C3×Dic6—212no—
196#627—212no—
197#625—212no—
198#625—212no—
199#624—26no—
200#624—22no—
201D3×Dic3—212no—
202D3×Dic3—212no—
203C22×#41—91no—
204C23×Q8—91no—
205#548—32no—
206#548—96no—
207#548—96no—
208#548—92no—
209C2×#124—93no—
210C2×C22⋊Q8—93no—
211C2×#121—93no—
212C2×C4×Q8—91no—
213C2×C4×D4—93no—
214C23×D3—32no—
215C23×D3—36no—
216C3×#41—68no—
217C2×C3×Q8—21no—
218C2×C3×Q8—36no—
219C2×C3×Q8—68no—
220C2×C3×Q8C22×D312yes—
221C2×C3×D4—36no—
222C2×C3×D4—36no—
223C22×C3×C4—36no—
224C22×C3×C4—36no—
225C2×#67—36no—
226C2×#67—36no—
227C2×#67—312no—
228C22×Dic3—36no—
229C22×Dic3—36no—
230#239—28no—
231D3×Q8—28no—
232D3×Q8—316no—
233D3×Q8—68no—
234D3×Q8—624no—
235D3×Q8—624no—
236#237—624no—
237D3×D4—624no—
238D3×D4—624no—
239#235—624no—
240C2×D12C22×D316yes—
241C2×D12C22×D316yes—
242C2×C4×D3—36no—
243C2×C4×D3—36no—
244C2×C4×D3—36no—
245C2×C4×D3—32no—
246C2×C4×D3—36no—
247C2×C4×D3—36no—
248C2×C4×D3—32no—
249C2×C4×D3—61no—
250C2×C4×D3—63no—
251C2×C4×D3—63no—
252C2×C4×D3—624no—
253C2×C4×D3—624no—
254C2×C4×D3C22×D316yes—
255C2×C4×D3C22×D316yes—
256C2×Dic6—36no—
257C2×Dic6—312no—
258C2×Dic6—63no—
259C2×Dic6—624no—
260C2×Dic6C22×D316yes—
261C3×C4⋊C4—23no—
262C3×C4⋊C4—36no—
263C3×C4⋊C4C22×D316yes—
264C3×C22⋊C4—312no—
265C3×C22⋊C4—32no—
266C3×C22⋊C4—36no—
267C3×C42—23no—
268C3×C42C22×D316yes—
269#217—312no—
270#217—36no—
271#217—32no—
272(C2×D3)⋊C4—312no—
273(C2×D3)⋊C4—36no—
274(C2×D3)⋊C4—32no—
275(C2×D3)⋊C4C22×D312yes—
276(C2×D3)⋊C4C22×D316yes—
277(C2×D3)⋊C4C22×D3112yes—
278C4⋊Dic3—36no—
279C4⋊Dic3—63no—
280C4⋊Dic3C22×D316yes—
281Dic3⋊C4—312no—
282Dic3⋊C4—36no—
283Dic3⋊C4—36no—
284Dic3⋊C4—66no—
285C4×Dic3—36no—
286C4×Dic3—36no—
287C4×Dic3—36no—
288C4×Dic3—63no—
289C4×Dic3—63no—
290C4×Dic3—63no—
291C22×C32C2511yescharacteristic
292C2×C3⋊D3C22×D412yes—
293C2×C3⋊D3C2×#4112yes—
294C2×C3⋊D32−1+412yes—
295C2×C3×D3—22no—
296C2×C3×D3—22no—
297C2×C3×D3—26no—
298C2×C3×D3—26no—
299C2×C3×D3—26no—
300C2×C3×D3C2×#4114yescomplemented
301D32—28no—
302D32—412no—
303C32×C4—21no—
304C32×C4—23no—
305C32×C4C22×D416yes—
306C3⋊Dic3—21no—
307C3⋊Dic3—23no—
308C3⋊Dic3C22×D416yes—
309C3×Dic3—22no—
310C3×Dic3—26no—
311C2×#41—32no—
312C2×#41—96no—
313C2×#41—188no—
314C22×Q8—32no—
315C22×Q8—96no—
316C22×Q8—93no—
317C22×Q8—91no—
318C22×Q8—188no—
319C22×D4—93no—
320C22×D4—93no—
321C23×C4—93no—
322C23×C4—93no—
323#124—36no—
324#124—96no—
325#124—96no—
326#124—96no—
327C22⋊Q8—36no—
328C22⋊Q8—912no—
329C22⋊Q8—96no—
330#121—36no—
331#121—912no—
332#121—96no—
333C4×Q8—91no—
334C4×Q8—93no—
335C4×Q8—93no—
336C4×Q8D3211yescharacteristic, complemented
337C4×D4—36no—
338C4×D4—96no—
339C4×D4—96no—
340C4×D4—96no—
341C2×C4⋊C4—93no—
342C2×C4⋊C4—93no—
343C2×C22⋊C4—91no—
344C2×C22⋊C4—93no—
345C2×C22⋊C4—96no—
346C2×C42—93no—
347C23×C3—32no—
348C23×C3—36no—
349C22×D3—32no—
350C22×D3—38no—
351C22×D3—61no—
352C22×D3—64no—
353C22×D3—64no—
354C22×D3—612no—
355C22×D3—612no—
356C22×D3—612no—
357C22×D3C23×D316yes—
358C22×D3C23×D312yes—
359C3×Q8—24no—
360C3×Q8—612no—
361C3×Q8D3×D418yescomplemented
362C3×D4—612no—
363C3×D4—612no—
364C2×C3×C4—21no—
365C2×C3×C4—23no—
366C2×C3×C4—23no—
367C2×C3×C4—32no—
368C2×C3×C4—36no—
369C2×C3×C4—612no—
370C2×C3×C4—612no—
371C2×C3×C4C23×D312yes—
372C2×C3×C4C23×D316yes—
373C2×C3×C4C23×D316yes—
374#67—624no—
375#67—612no—
376#67—612no—
377C2×Dic3—36no—
378C2×Dic3—32no—
379C2×Dic3—36no—
380C2×Dic3—61no—
381C2×Dic3—63no—
382C2×Dic3—63no—
383C2×Dic3—612no—
384C2×Dic3—612no—
385C2×Dic3C23×D312yes—
386C2×Dic3C23×D316yes—
387D12—212no—
388D12—212no—
389C4×D3—212no—
390C4×D3—212no—
391C4×D3—324no—
392C4×D3—612no—
393C4×D3—64no—
394C4×D3—612no—
395C4×D3—612no—
396C4×D3—612no—
397C4×D3—64no—
398C4×D3—612no—
399C4×D3—64no—
400C4×D3—126no—
401Dic6—212no—
402Dic6—324no—
403Dic6—612no—
404Dic6—624no—
405C2×C32C23×D411yescharacteristic
406C2×C32C22×#4111yescharacteristic
407C2×C32C2×2−1+411yescharacteristic
408C3⋊D3#54814yescomplemented
409C3×D3—24no—
410C3×D3—46no—
411C24—91no—
412C24—93no—
413#41—68no—
414#41—1824no—
415C2×Q8—36no—
416C2×Q8—68no—
417C2×Q8—96no—
418C2×Q8—98no—
419C2×Q8—93no—
420C2×Q8—1824no—
421C2×Q8—1812no—
422C2×Q8C2×D3211yescharacteristic
423C2×D4—36no—
424C2×D4—36no—
425C2×D4—96no—
426C2×D4—96no—
427C2×D4—1812no—
428C2×D4—1812no—
429C22×C4—36no—
430C22×C4—36no—
431C22×C4—93no—
432C22×C4—91no—
433C22×C4—96no—
434C22×C4—96no—
435C22×C4—93no—
436C22×C4—91no—
437C22×C4—93no—
438C22×C4—1812no—
439C22×C4—1812no—
440C4⋊C4—36no—
441C4⋊C4—96no—
442C4⋊C4—96no—
443C4⋊C4—93no—
444C4⋊C4C2×D3213yes—
445C22⋊C4—32no—
446C22⋊C4—36no—
447C22⋊C4—312no—
448C22⋊C4—92no—
449C22⋊C4—96no—
450C22⋊C4—912no—
451C42—93no—
452C42—93no—
453C42—93no—
454C42C2×D3213yes—
455C22×C3—21no—
456C22×C3—34no—
457C22×C3—62no—
458C22×C3—62no—
459C22×C3—66no—
460C22×C3—66no—
461C22×C3—66no—
462C22×C3C24×D312yes—
463C2×D3—22no—
464C2×D3—22no—
465C2×D3—26no—
466C2×D3—26no—
467C2×D3—26no—
468C2×D3—34no—
469C2×D3—34no—
470C2×D3—34no—
471C2×D3—62no—
472C2×D3—62no—
473C2×D3—62no—
474C2×D3—616no—
475C2×D3—1224no—
476C2×D3D3×#4114yescomplemented
477C3×C4—22no—
478C3×C4—26no—
479C3×C4—22no—
480C3×C4—26no—
481C3×C4—43no—
482C3×C4—66no—
483C3×C4—62no—
484C3×C4C2×D3×D4112yes—
485Dic3—26no—
486Dic3—22no—
487Dic3—312no—
488Dic3—66no—
489Dic3—62no—
490Dic3—66no—
491Dic3—62no—
492Dic3—123no—
493C32C2×#54811yescharacteristic, complemented, Sylow
494C23—32no—
495C23—36no—
496C23—94no—
497C23—91no—
498C23—182no—
499C23—182no—
500C23—186no—
501C23—186no—
502C23—186no—
503Q8—612no—
504Q8—912no—
505Q8—1812no—
506Q8#380214yescomplemented
507D4—612no—
508D4—612no—
509D4—1812no—
510D4—1812no—
511C2×C4—36no—
512C2×C4—32no—
513C2×C4—612no—
514C2×C4—612no—
515C2×C4—93no—
516C2×C4—912no—
517C2×C4—91no—
518C2×C4—93no—
519C2×C4—186no—
520C2×C4—182no—
521C2×C4—182no—
522C2×C4—186no—
523C2×C4—1812no—
524C2×C4—1812no—
525C2×C4C22×D3211yescharacteristic
526C2×C4C22×D3213yes—
527C2×C4C22×D3213yes—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—64no—
532C2×C3—126no—
533C2×C3C22×D3×D412yes—
534C2×C3C2×D3×#4112yes—
535C2×C3D3×2−1+412yes—
536D3—24no—
537D3—38no—
538D3—46no—
539D3—64no—
540C22—34no—
541C22—62no—
542C22—62no—
543C22—66no—
544C22—66no—
545C22—66no—
546C22—92no—
547C22—92no—
548C22—92no—
549C22—188no—
550C22—3612no—
551C22C23×D3211yescharacteristic
552C4—21no—
553C4—23no—
554C4—62no—
555C4—66no—
556C4—96no—
557C4—181no—
558C4—183no—
559C4C2×#380216yes—
560C3—21no—
561C3D3×#54812yescomplemented
562C2—64no—
563C2—94no—
564C2—126no—
565C2C22×#380211yescharacteristic
566C2#1059668711yescharacteristic
567C2D32×#4111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
hypercenterC4×Q8D32
hypocenterC32C2×#548
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#64319C2semidirect
2. C2×D32×Q8C2semidirect
3. C4×Q8×C3⋊D3C2semidirect
4. C3×#5576C2semidirect
5. #10595409C2semidirect
6. #10594631C2semidirect
7. #10594612C2semidirect
8. #10594525C2semidirect
9. #10594009C2semidirect
10. C4×#3802C2semidirect
11. #10593905C2semidirect
14. C2×C3×#239C22semidirect
15. C2×C3×D3×Q8C22semidirect
23. C2×#3795C22semidirect
24. C2×D3×Dic6C22semidirect
25. C32×C4×Q8C22semidirect
26. Q8×C3⋊Dic3C22semidirect
28. #64096C22semidirect
30. C4×#634C22semidirect
31. C3×#897C22semidirect
32. C3×#895C22semidirect
33. C3×#875C22semidirect
34. C3×C4×D12C22semidirect
38. #63915C22semidirect
39. #63915C22semidirect
40. #63908C22semidirect
41. #63902C22semidirect
42. C4×#625C22semidirect
44. #63899C22semidirect
45. #63898C22semidirect
46. #63885C22semidirect
47. #63863C22semidirect
48. #63856C22semidirect
60. #5576D3semidirect
68. Q8×C3⋊D3D4semidirect
113. C2×#239C2×D3semidirect
119. C2×D3×Q8C2×D3semidirect
131. C3×C4×Q8C2×D3semidirect
145. #897C2×D3semidirect
147. #895C2×D3semidirect
163. #875C2×D3semidirect
164. C4×D12C2×D3semidirect
177. C2×D32#41semidirect
178. C32×Q8C2×D4semidirect
188. #634C2×D4semidirect
300. C2×C3×D3C2×#41semidirect
336. C4×Q8D32semidirect
361. C3×Q8D3×D4semidirect
408. C3⋊D3#548semidirect
476. C2×D3D3×#41semidirect
493. C32C2×#548semidirect
506. Q8#3802semidirect
561. C3D3×#548semidirect

Maximal subgroups

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

subgroupindex
C2×#643192
C2×D32×Q82
C4×Q8×C3⋊D32
C3×#55762
#105954092
#105946312
#105946122
#105945252
#105940092
C4×#38022
#105939052
D3×#5483