Finite Group Databasebeta

← #11904212

Subgroups — #11904212

Order 1152.

2288 conjugacy classes of subgroups.

The subgroup lattice has 544 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×#239C211yesmaximal, characteristic, complemented
4#10595409C212yesmaximal, complemented
5D3×Q8×Dic3C212yesmaximal, complemented
6#10594456C216yesmaximal, complemented
7#10594444C216yesmaximal, complemented
8#10593895C213yesmaximal, complemented
9C4×#3795C213yesmaximal, complemented
10#10593863C213yesmaximal, complemented
11#10593859C213yesmaximal, complemented
12#86744—31nomaximal
13#85844—31nomaximal
14C2×C3×#239C2211yescharacteristic
15C2×C3×D3×Q8C2212yes—
16C2×#3795C2213yes—
17C32×C4×Q8C2211yescharacteristic
18Q8×C3⋊Dic3C2212yes—
19#64099C2216yes—
20#64078C2213yes—
21C4×#634C2213yes—
22C3×Q8×Dic3C2211yescharacteristic
23C3×#897C2216yes—
24C3×#893C2213yes—
25C3×#892C2213yes—
26C3×C4×D12C2213yes—
27C3×C4×D12C2213yes—
28C3×C42×D3C2213yes—
29C3×#869C2213yes—
30#63908C2216yes—
31C4×#625C2216yes—
32Dic3×D12C2211yescharacteristic
33#63891C22112yes—
34D3×C4⋊Dic3C2216yes—
35#63879C2216yes—
36#63877C2216yes—
37C4×D3×Dic3C2216yes—
38#63869C2216yes—
39#63863C2216yes—
40#63858C22112yes—
41#63857C2216yes—
42#63856C2216yes—
43#63844C2213yes—
44#63843C2216yes—
45Dic3×Dic6C2216yes—
46#63841C2216yes—
47#63841C2213yes—
48C3×D4×Q8—31no—
49C3×C4×#41—31no—
50#5831—32no—
51#5817—32no—
52C2×Q8×Dic3—32no—
53#5732—33no—
54#5728—33no—
55#5642—36no—
56#5624—36no—
57Q8×D12D311yescharacteristic, complemented
58C4×#239D311yescharacteristic, complemented
59C4×D3×Q8—32no—
60#5570—31no—
61#5570—31no—
62#5570—61no—
63#5557—36no—
64#5555—33no—
65#5551—33no—
66#5542—33no—
67C4×#237—33no—
68#5529—36no—
69C4×#235—33no—
70#5470—33no—
71C2×C32×Q8C2311yescharacteristic
72C2×#634C2313yes—
73C3×#239—24no—
74C3×D3×Q8—28no—
75C2×C3×D12C2313yes—
76C2×C3×D12C2311yescharacteristic
77C2×C3×C4×D3C2313yes—
78C2×C3×C4×D3C2313yes—
79C2×C3×C4×D3C2316yes—
80C2×C3×C4×D3C2313yes—
81C2×C3×Dic6C2316yes—
82C2×#625C2316yes—
83C2×D3×Dic3C2316yes—
84C2×D3×Dic3C2312yes—
85#3795—212no—
86C32×C4⋊C4C2313yes—
87C32×C42C2313yes—
88C4⋊(C3⋊Dic3)C2311yescharacteristic
89C4⋊(C3⋊Dic3)C2316yes—
90C4⋊(C3⋊Dic3)C2316yes—
91#3750C2316yes—
92C4×C3⋊Dic3C2316yes—
93C3×(C2×D3)⋊C4C2316yes—
94C3×(C2×D3)⋊C4C2316yes—
95C3×C4⋊Dic3C2313yes—
96C3×C4⋊Dic3C2316yes—
97C3×C4⋊Dic3C2313yes—
98C3×C4×Dic3C2313yes—
99C3×C4×Dic3C2313yes—
100C3×C4×Dic3C2311yescharacteristic
101#3724C2316yes—
102Dic3⋊Dic3C23112yes—
103(C2×D3)⋊Dic3C23112yes—
104(C2×D3)⋊Dic3C2316yes—
105(C2×D3)⋊Dic3C2312yes—
106Dic32C2316yes—
107Dic32C2316yes—
108#3482—91noSylow
109C2×C3×#41—31no—
110C22×C3×Q8—32no—
111C2×#239C2×D311yescharacteristic
112C2×D3×Q8C2×D312yes—
113C2×#237—33no—
114C2×#235—33no—
115C3×C4⋊Q8—33no—
116C3×C22⋊Q8—36no—
117C3×C4×Q8—21no—
118C3×C4×Q8—31no—
119C3×C4×Q8C2×D311yescharacteristic
120C3×C4×Q8C2×D311yescharacteristic
121C3×C4×D4—33no—
122C3×C4×D4—33no—
123C3×C4×D4—33no—
124C3×#117—33no—
125C2×C3×C42—33no—
126#947—36no—
127#946—36no—
128Q8×Dic3—32no—
129Q8×Dic3—32no—
130Q8×Dic3—36no—
131Q8×Dic3—36no—
132Q8×Dic3—62no—
133Q8×Dic3C2×D311yescharacteristic
134#938—36no—
135#936—36no—
136D4×Dic3—31no—
137#930—36no—
138C4×#67—36no—
139C4×#67—36no—
140C4×#67—36no—
141#926—36no—
142#926—33no—
143C2×C4⋊Dic3—36no—
144#924—36no—
145#924—36no—
146C2×C4×Dic3—36no—
147#898—312no—
148#897—36no—
149#897C2×D316yes—
150#893C2×D313yes—
151#892—36no—
152#892—33no—
153#892C2×D313yes—
154D3×C4⋊C4—36no—
155#890—36no—
156#890—36no—
157#890—36no—
158#890—66no—
159#887—36no—
160#887—33no—
161#886—312no—
162#883—312no—
163#67⋊C4—36no—
164#879—312no—
165#877—36no—
166C4×D12—31no—
167C4×D12C2×D313yes—
168C4×D12C2×D313yes—
169#872—36no—
170C42×D3—36no—
171C42×D3C2×D313yes—
172#870—36no—
173#869—33no—
174#869—33no—
175#869—63no—
176#869C2×D313yes—
177C4×Dic6—36no—
178C4×Dic6—33no—
179C4×Dic6—33no—
180C4×Dic6—33no—
181C4×Dic6—63no—
182C22×C3×D3C2413yes—
183C22×C3×D3C2412yes—
184C32×Q8#4114yescomplemented
185C2×C32×C4C2413yes—
186C2×C32×C4C2411yescharacteristic
187C2×C32×C4C2413yes—
188C2×C3⋊Dic3C2412yes—
189C2×C3⋊Dic3C2416yes—
190#634—26no—
191C2×C3×Dic3C2416yes—
192C2×C3×Dic3C2413yes—
193C2×C3×Dic3C2411yescharacteristic
194C2×C3×Dic3C2411yescharacteristic
195C3×D12—26no—
196C3×D12#4114yescomplemented
197C3×C4×D3—26no—
198C3×C4×D3—212no—
199C3×C4×D3—26no—
200C3×C4×D3—26no—
201C3×Dic6—212no—
202#625—212no—
203D3×Dic3—212no—
204D3×Dic3—24no—
205#557—91no—
206#556—93no—
207#552—96no—
208D4×Q8—31no—
209#548—92no—
210#547—93no—
211#533—93no—
212#529—96no—
213C4×#41—31no—
214C4×#41—93no—
215C2×C4×Q8—92no—
216C3×#41—64no—
217C2×C3×Q8—21no—
218C2×C3×Q8—36no—
219C2×C3×Q8—68no—
220C2×C3×Q8C22×D311yescharacteristic
221C2×C3×Q8C22×D311yescharacteristic
222C2×C3×D4—31no—
223C2×C3×D4—33no—
224C22×C3×C4—36no—
225C22×C3×C4—33no—
226C22×C3×C4—33no—
227C22×C3×C4—33no—
228C2×#67—36no—
229C2×#67—36no—
230C22×Dic3—36no—
231C22×Dic3—32no—
232#239—24no—
233D3×Q8—28no—
234#237—612no—
235#235—612no—
236C2×D12C22×D313yes—
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×D313yes—
244C2×Dic6—33no—
245C2×Dic6—33no—
246C2×Dic6—63no—
247C2×Dic6C22×D316yes—
248C3×C4⋊C4—23no—
249C3×C4⋊C4—33no—
250C3×C4⋊C4—33no—
251C3×C4⋊C4—36no—
252C3×C4⋊C4C22×D313yes—
253C3×C4⋊C4C22×D313yes—
254C3×C22⋊C4—36no—
255C3×C22⋊C4—36no—
256C3×C42—23no—
257C3×C42—31no—
258C3×C42—33no—
259C3×C42—33no—
260C3×C42C22×D313yes—
261C3×C42C22×D313yes—
262#217—32no—
263#217—36no—
264#217—312no—
265(C2×D3)⋊C4—32no—
266(C2×D3)⋊C4—36no—
267(C2×D3)⋊C4—312no—
268(C2×D3)⋊C4C22×D316yes—
269(C2×D3)⋊C4C22×D316yes—
270C4⋊Dic3—31no—
271C4⋊Dic3—31no—
272C4⋊Dic3—36no—
273C4⋊Dic3—36no—
274C4⋊Dic3—36no—
275C4⋊Dic3—36no—
276C4⋊Dic3—312no—
277C4⋊Dic3—61no—
278C4⋊Dic3—66no—
279C4⋊Dic3—66no—
280C4⋊Dic3C22×D313yes—
281C4⋊Dic3C22×D316yes—
282C4⋊Dic3C22×D313yes—
283Dic3⋊C4—36no—
284Dic3⋊C4—36no—
285Dic3⋊C4—36no—
286Dic3⋊C4—312no—
287Dic3⋊C4—36no—
288Dic3⋊C4—66no—
289C4×Dic3—36no—
290C4×Dic3—36no—
291C4×Dic3—36no—
292C4×Dic3—36no—
293C4×Dic3—36no—
294C4×Dic3—36no—
295C4×Dic3—66no—
296C4×Dic3C22×D311yescharacteristic
297C4×Dic3C22×D313yes—
298C4×Dic3C22×D313yes—
299C22×C32C2511yescharacteristic
300C2×C3×D3—22no—
301C2×C3×D3—22no—
302C2×C3×D3—23no—
303C2×C3×D3—23no—
304C2×C3×D3—23no—
305C2×C3×D3C2×#4114yes—
306C32×C4—23no—
307C32×C4C2×#4116yes—
308C32×C4C2×#4112yes—
309C3⋊Dic3—26no—
310C3⋊Dic3—22no—
311C3×Dic3—23no—
312C3×Dic3—26no—
313C3×Dic3—21no—
314C3×Dic32−1+412yes—
315C2×#41—31no—
316C2×#41—93no—
317C22×Q8—32no—
318C4⋊Q8—33no—
319C4⋊Q8—93no—
320#126—912no—
321#125—96no—
322#125—96no—
323#124—96no—
324#123—912no—
325C22⋊Q8—36no—
326C22⋊Q8—96no—
327C22⋊Q8—96no—
328#121—96no—
329C4×Q8—31no—
330C4×Q8—93no—
331C4×Q8—96no—
332C4×Q8—96no—
333C4×Q8—92no—
334C4×Q8—93no—
335C4×Q8D3211yescharacteristic
336C4×D4—33no—
337C4×D4—33no—
338C4×D4—33no—
339C4×D4—91no—
340C4×D4—96no—
341C4×D4—96no—
342#117—33no—
343#117—96no—
344#117—93no—
345#117—96no—
346C2×C4⋊C4—96no—
347C2×C42—33no—
348C2×C42—96no—
349C23×C3—32no—
350C23×C3—33no—
351C22×D3C23×D313yes—
352C22×D3C23×D312yes—
353C3×Q8—24no—
354C3×Q8—612no—
355C3×Q8#23514yescomplemented
356C3×Q8#23714yescomplemented
357C3×D4—34no—
358C3×D4—66no—
359C2×C3×C4—23no—
360C2×C3×C4—21no—
361C2×C3×C4—23no—
362C2×C3×C4—31no—
363C2×C3×C4—33no—
364C2×C3×C4—36no—
365C2×C3×C4—31no—
366C2×C3×C4—66no—
367C2×C3×C4—612no—
368C2×C3×C4—66no—
369C2×C3×C4—66no—
370C2×C3×C4C23×D313yes—
371C2×C3×C4C23×D313yes—
372C2×C3×C4C23×D313yes—
373C2×C3×C4C23×D313yes—
374C2×C3×C4C23×D311yescharacteristic
375C2×C3×C4C23×D311yescharacteristic
376#67—612no—
377#67—612no—
378C2×Dic3—32no—
379C2×Dic3—32no—
380C2×Dic3—36no—
381C2×Dic3—36no—
382C2×Dic3—62no—
383C2×Dic3—66no—
384C2×Dic3—612no—
385C2×Dic3—64no—
386C2×Dic3C23×D313yes—
387C2×Dic3C23×D316yes—
388C2×Dic3C23×D311yescharacteristic
389C2×Dic3C23×D311yescharacteristic
390D12—26no—
391D12#23914yescomplemented
392C4×D3—26no—
393C4×D3—212no—
394C4×D3—26no—
395C4×D3—26no—
396C4×D3—64no—
397C4×D3—612no—
398Dic6—212no—
399Dic6—66no—
400Dic6—66no—
401Dic6—126no—
402C2×C32C22×#4111yescharacteristic
403C2×C32C22×#4111yescharacteristic
404C2×C32C2×2−1+411yescharacteristic
405C3×D3—24no—
406C3×D3—43no—
407#41—64no—
408#41—1812no—
409C2×Q8—36no—
410C2×Q8—68no—
411C2×Q8—93no—
412C2×Q8C2×D3211yescharacteristic
413C2×D4—31no—
414C2×D4—33no—
415C2×D4—96no—
416C22×C4—33no—
417C22×C4—33no—
418C22×C4—33no—
419C22×C4—36no—
420C22×C4—92no—
421C22×C4—96no—
422C4⋊C4—33no—
423C4⋊C4—33no—
424C4⋊C4—36no—
425C4⋊C4—912no—
426C4⋊C4—96no—
427C4⋊C4—96no—
428C4⋊C4—91no—
429C4⋊C4—96no—
430C4⋊C4—96no—
431C4⋊C4C2×D3213yes—
432C22⋊C4—36no—
433C22⋊C4—36no—
434C22⋊C4—92no—
435C22⋊C4—96no—
436C22⋊C4—912no—
437C42—31no—
438C42—33no—
439C42—33no—
440C42—96no—
441C42—96no—
442C42—96no—
443C42C2×D3213yes—
444C22×C3—21no—
445C22×C3—34no—
446C22×C3—62no—
447C22×C3—62no—
448C22×C3—63no—
449C22×C3—63no—
450C22×C3—63no—
451C22×C3C24×D311yescharacteristic
452C22×C3C24×D311yescharacteristic
453C2×D3—22no—
454C2×D3—22no—
455C2×D3—23no—
456C2×D3—23no—
457C2×D3—23no—
458C2×D3C2×#23914yes—
459C3×C4—23no—
460C3×C4—23no—
461C3×C4—26no—
462C3×C4—22no—
463C3×C4—32no—
464C3×C4—43no—
465C3×C4—66no—
466C3×C4—61no—
467C3×C4—63no—
468C3×C4C2×#23516yes—
469C3×C4C2×#23716yes—
470C3×C4C2×#23912yes—
471C3×C4D3×#4112yes—
472Dic3—21no—
473Dic3—26no—
474Dic3—23no—
475Dic3—66no—
476Dic3—66no—
477Dic3—62no—
478Dic3—62no—
479Dic3—126no—
480Dic3—122no—
481Dic3#101012yes—
482C32#348211yescharacteristic, complemented, Sylow
483C23—32no—
484C23—33no—
485Q8—612no—
486Q8—186no—
487Q8#379514yescomplemented
488D4—34no—
489D4—66no—
490D4—1812no—
491C2×C4—31no—
492C2×C4—31no—
493C2×C4—33no—
494C2×C4—36no—
495C2×C4—66no—
496C2×C4—612no—
497C2×C4—66no—
498C2×C4—66no—
499C2×C4—92no—
500C2×C4—96no—
501C2×C4—184no—
502C2×C4—1812no—
503C2×C4C22×D3213yes—
504C2×C4C22×D3213yes—
505C2×C4C22×D3211yescharacteristic
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—64no—
510C2×C3—123no—
511C2×C3C22×#23511yescharacteristic
512C2×C3C22×#23711yescharacteristic
513C2×C3C22×#23911yescharacteristic
514C2×C3C2×D3×#4111yescharacteristic
515C2×C3C2×#101011yescharacteristic
516C2×C3D3×2−1+411yescharacteristic
517D3—24no—
518D3—43no—
519C22—34no—
520C22—62no—
521C22—62no—
522C22—63no—
523C22—63no—
524C22—63no—
525C22C23×D3211yescharacteristic
526C4—23no—
527C4—32no—
528C4—61no—
529C4—66no—
530C4—63no—
531C4—186no—
532C4—182no—
533C4C2×#379516yes—
534C4D3×#23912yes—
535C3—21no—
536C3#8584411yescharacteristic, complemented
537C3#8674411yescharacteristic, complemented
538C2—64no—
539C2—123no—
540C2C22×#379511yescharacteristic
541C2C2×D3×#23911yescharacteristic
542C2D3×#101011yescharacteristic
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. #10596041C2semidirect
2. C3×Q8×D12C2semidirect
3. C3×C4×#239C2semidirect
4. #10595409C2semidirect
5. D3×Q8×Dic3C2semidirect
6. #10594456C2semidirect
7. #10594444C2semidirect
8. #10593895C2semidirect
9. C4×#3795C2semidirect
10. #10593863C2semidirect
11. #10593859C2semidirect
57. Q8×D12D3semidirect
58. C4×#239D3semidirect
184. C32×Q8#41semidirect
196. C3×D12#41semidirect
355. C3×Q8#235semidirect
356. C3×Q8#237semidirect
391. D12#239semidirect
482. C32#3482semidirect
487. Q8#3795semidirect
536. C3#85844semidirect
537. C3#86744semidirect

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×#2392
#105954092
D3×Q8×Dic32
#105944562
#105944442
#105938952
C4×#37952
#105938632
#105938592
#867443
#858443