Finite Group Databasebeta

← #11887078

Subgroups — #11887078

Order 1152.

1386 conjugacy classes of subgroups.

The subgroup lattice has 411 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#554C211yesmaximal, characteristic, complemented
2D4×C4⋊(C3⋊D3)C211yesmaximal, characteristic
3#10592787C211yesmaximal, characteristic, complemented
4#10592783C211yesmaximal, characteristic, complemented
5#10592747C212yesmaximal, complemented
6#10592745C212yesmaximal, complemented
7#10592726C211yesmaximal, characteristic, complemented
8C4×#3755C211yesmaximal, characteristic, complemented
9D4×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
10#10592667C212yesmaximal, complemented
11C2×#63636C212yesmaximal, complemented
12#83634—34nomaximal
13C2×D4×C3⋊D3—21no—
14C22×C4⋊(C3⋊D3)C2212yes—
15C32×C4⋊Q8C2211yescharacteristic, complemented
16C32×#125—21no—
17C32×C22⋊Q8—22no—
18C32×C22⋊Q8C2212yescomplemented
19C32×C4×Q8C2211yescharacteristic, complemented
20C32×C4×D4—21no—
21C32×C4×D4C2211yescharacteristic
22C2×C32×C4⋊C4C2212yescomplemented
23C2×#3755C2211yescharacteristic
24C2×#3755C2212yescomplemented
25#64139C2212yes—
26C22×C3⋊(C3⋊C8)C2212yescomplemented
27#64104—21no—
28#64091—22no—
29#64083C2211yescharacteristic
30C4×C4⋊(C3⋊D3)C2211yescharacteristic
31#63662C2211yescharacteristic, complemented
32#63657C2212yescomplemented
33#63636C2212yes—
34#63636C2211yescharacteristic
35#63636C2212yescomplemented
36#63636C2212yescomplemented
37#63636C2212yescomplemented
38#63635C2212yescomplemented
39#63635C2211yescharacteristic, complemented
40C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
41C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
42C3×#554D314yescomplemented
43D4×D12—34no—
44#5088—34no—
45#5084—34no—
46#5048—38no—
47#5046—38no—
48#5027—34no—
49C4×#215—34no—
50D4×C3⋊C8—34no—
51#4968—38no—
52C2×#809—38no—
53C23×C3⋊D3—22no—
54C2×C32×Q8—21no—
55C2×C32×Q8C2311yescharacteristic
56C2×C32×D4D411yescharacteristic
57C22×C32×C4—22no—
58C22×C32×C4C2312yes—
59C2×#638—22no—
60D4×C3⋊D3—44no—
61C2×C4⋊(C3⋊D3)—24no—
62C2×C4⋊(C3⋊D3)—21no—
63C2×C4⋊(C3⋊D3)—22no—
64C2×C4⋊(C3⋊D3)—21no—
65C2×C4⋊(C3⋊D3)—42no—
66C2×C4⋊(C3⋊D3)C2312yes—
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C32×C4⋊C4—22no—
70C32×C4⋊C4—21no—
71C32×C4⋊C4—21no—
72C32×C4⋊C4—22no—
73C32×C4⋊C4D411yescharacteristic
74C32×C4⋊C4C2311yescharacteristic
75C32×C4⋊C4C2312yes—
76C32×C22⋊C4—22no—
77C32×C22⋊C4D412yes—
78C32×C42—21no—
79C32×C42C2311yescharacteristic
80#3755—22no—
81#3755—42no—
82#3752—21no—
83#3752—22no—
84C4⋊(C3⋊Dic3)C2311yescharacteristic
85C2×C3⋊(C3⋊C8)—42no—
86C2×C3⋊(C3⋊C8)C2311yescharacteristic
87C2×C3⋊(C3⋊C8)C2312yes—
88C2×C3⋊(C3⋊C8)C2311yescharacteristic
89#3295—91noSylow
90C2×D3×D4—64no—
91C22×D12—38no—
92C3×C4⋊Q8C2×D314yescomplemented
93C3×#125—24no—
94C3×C22⋊Q8—28no—
95C3×C22⋊Q8C2×D318yescomplemented
96C3×C4×Q8C2×D314yescomplemented
97C3×C4×D4—24no—
98C3×C4×D4C2×D314yes—
99C2×C3×C4⋊C4C2×D318yescomplemented
100C2×#215—34no—
101C2×#215—38no—
102#930—38no—
103C22×C3⋊C8—38no—
104#895—64no—
105#882—68no—
106#874—34no—
107C4×D12—34no—
108#835—34no—
109#830—38no—
110#809—34no—
111#809—38no—
112#809—38no—
113#809—38no—
114#809—38no—
115#808—34no—
116#808—38no—
117C4⋊(C3⋊C8)—34no—
118C4×C3⋊C8—34no—
119C23×C32C2×D412yes—
120C22×C3⋊D3—21no—
121C22×C3⋊D3—22no—
122C22×C3⋊D3—44no—
123C22×C3⋊D3—44no—
124C22×C3⋊D3—82no—
125C32×Q8—21no—
126C32×Q8—21no—
127C32×Q8—81no—
128C32×D4SD1614yescomplemented
129C2×C32×C4—22no—
130C2×C32×C4—22no—
131C2×C32×C4—21no—
132C2×C32×C4—21no—
133C2×C32×C4—22no—
134C2×C32×C4—82no—
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D412yes—
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2411yescharacteristic
139#638—44no—
140C2×C3⋊Dic3—21no—
141C4⋊(C3⋊D3)—22no—
142C4⋊(C3⋊D3)—21no—
143C4⋊(C3⋊D3)—22no—
144C4⋊(C3⋊D3)—44no—
145C4⋊(C3⋊D3)—42no—
146C4⋊(C3⋊D3)—81no—
147C4⋊(C3⋊D3)#4112yes—
148C4×C3⋊D3—42no—
149C3⋊(C3⋊C8)—21no—
150C3⋊(C3⋊C8)—21no—
151C3⋊(C3⋊C8)—22no—
152#554C3⋊D311yescharacteristic, complemented
153D42—91no—
154#486—91no—
155#481—92no—
156#476—91no—
157#465—92no—
158#460—91no—
159#450—92no—
160C4×SD16—91no—
161C8×D4—91no—
162C2×#102—92no—
163C23×D3—68no—
164C2×C3×Q8—24no—
165C2×C3×Q8C22×D314yes—
166C2×C3×D4#6714yes—
167C22×C3×C4—28no—
168C22×C3×C4C22×D318yes—
169C2×#67—68no—
170D3×D4—1216no—
171C2×D12—34no—
172C2×D12—38no—
173C2×D12—616no—
174C2×D12—64no—
175C2×D12—68no—
176C2×D12—64no—
177C2×D12—128no—
178C2×C4×D3—64no—
179C3×C4⋊C4—28no—
180C3×C4⋊C4—24no—
181C3×C4⋊C4—24no—
182C3×C4⋊C4—28no—
183C3×C4⋊C4#6714yes—
184C3×C4⋊C4C22×D314yes—
185C3×C4⋊C4C22×D318yes—
186C3×C22⋊C4—28no—
187C3×C22⋊C4#6718yes—
188C3×C42—24no—
189C3×C42C22×D314yes—
190#215—68no—
191#215—128no—
192(C2×D3)⋊C4—64no—
193(C2×D3)⋊C4—68no—
194C4⋊Dic3—34no—
195C2×C3⋊C8—34no—
196C2×C3⋊C8—34no—
197C2×C3⋊C8—38no—
198C2×C3⋊C8—128no—
199C22×C32—22no—
200C22×C32—22no—
201C22×C32C2×SD1614yes—
202C22×C32C22×D411yescharacteristic
203C2×C3⋊D3—22no—
204C2×C3⋊D3—41no—
205C2×C3⋊D3—41no—
206C2×C3⋊D3—42no—
207C2×C3⋊D3—42no—
208C2×C3⋊D3—42no—
209C2×C3⋊D3—88no—
210C32×C4—22no—
211C32×C4—21no—
212C32×C4—41no—
213C32×C4—41no—
214C32×C4—42no—
215C32×C4C2×SD1612yes—
216C32×C4C2×#4111yescharacteristic
217C32×C4H(5,𝔽2)11yescharacteristic
218C3⋊Dic3—41no—
219C22×D4—92no—
220C22×D4—181no—
221C2×SD16—91no—
222C2×SD16—92no—
223C22×C8—92no—
224C4⋊Q8C2×C3⋊D311yescharacteristic, complemented
225#127—91no—
226#125—21no—
227C22⋊Q8—22no—
228C22⋊Q8C2×C3⋊D312yescomplemented
229#121—92no—
230#121—181no—
231#120—182no—
232C4×Q8C2×C3⋊D311yescharacteristic, complemented
233C4×D4—21no—
234C4×D4—91no—
235C4×D4C2×C3⋊D311yescharacteristic
236C2×C4⋊C4C2×C3⋊D312yescomplemented
237#106—91no—
238#106—92no—
239C4⋊C8—91no—
240#103—91no—
241#102—91no—
242#102—92no—
243#102—92no—
244#102—92no—
245#102—92no—
246C22⋊C8—92no—
247C4×C8—91no—
248C23×C3C2×#6718yes—
249C22×D3—64no—
250C22×D3—68no—
251C22×D3—1216no—
252C22×D3—1216no—
253C22×D3—248no—
254C3×Q8—24no—
255C3×Q8—24no—
256C3×Q8—84no—
257C3×D4#215116yescomplemented
258C2×C3×C4—28no—
259C2×C3×C4—28no—
260C2×C3×C4—24no—
261C2×C3×C4—24no—
262C2×C3×C4—28no—
263C2×C3×C4—88no—
264C2×C3×C4C2×#6714yes—
265C2×C3×C4C2×#6718yes—
266C2×C3×C4C2×#6714yes—
267C2×C3×C4C23×D314yes—
268#67—1216no—
269C2×Dic3—64no—
270D12—38no—
271D12—68no—
272D12—64no—
273D12—68no—
274D12—1216no—
275D12—128no—
276D12—244no—
277C4×D3—128no—
278C3⋊C8—64no—
279C3⋊C8—64no—
280C3⋊C8—68no—
281C2×C32—24no—
282C2×C32#54611yescharacteristic
283C2×C32C22×SD1611yescharacteristic
284C2×C32#57611yescharacteristic
285C3⋊D3—42no—
286C3⋊D3—82no—
287C24—182no—
288C2×Q8—21no—
289C2×Q8C22×C3⋊D311yescharacteristic
290C2×D4—91no—
291C2×D4—92no—
292C2×D4—184no—
293C2×D4—182no—
294C2×D4—182no—
295C2×D4—181no—
296C2×D4—181no—
297C2×D4—362no—
298C2×D4—364no—
299C2×D4#63811yescharacteristic
300C22×C4—22no—
301C22×C4—181no—
302C22×C4C22×C3⋊D312yes—
303SD16—182no—
304SD16—362no—
305C2×C8—91no—
306C2×C8—91no—
307C2×C8—92no—
308C2×C8—362no—
309C4⋊C4—22no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—22no—
313C4⋊C4—91no—
314C4⋊C4#63811yescharacteristic
315C4⋊C4C22×C3⋊D311yescharacteristic
316C4⋊C4C22×C3⋊D312yes—
317C22⋊C4—22no—
318C22⋊C4—181no—
319C22⋊C4—182no—
320C22⋊C4#63812yes—
321C42—21no—
322C42C22×C3⋊D311yescharacteristic
323C22×C3—28no—
324C22×C3—28no—
325C22×C3C2×#215116yes—
326C22×C3C22×#6714yes—
327C2×D3—68no—
328C2×D3—124no—
329C2×D3—124no—
330C2×D3—128no—
331C2×D3—128no—
332C2×D3—128no—
333C2×D3—2432no—
334C3×C4—28no—
335C3×C4—24no—
336C3×C4—44no—
337C3×C4—44no—
338C3×C4—48no—
339C3×C4C2×#21518yes—
340C3×C4D3×#4114yes—
341C3×C4#100914yes—
342Dic3—124no—
343C32#329511yescharacteristic, complemented, Sylow
344C23—181no—
345C23—182no—
346C23—364no—
347C23—364no—
348C23—722no—
349C23C2×#63812yes—
350Q8—21no—
351Q8—21no—
352Q8—81no—
353D4—92no—
354D4—182no—
355D4—181no—
356D4—182no—
357D4—364no—
358D4—364no—
359D4—362no—
360D4—721no—
361D4#375514yescomplemented
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—22no—
367C2×C4—82no—
368C2×C4—181no—
369C2×C4—362no—
370C2×C4C2×#63811yescharacteristic
371C2×C4C2×#63812yes—
372C2×C4C2×#63811yescharacteristic
373C2×C4C23×C3⋊D311yescharacteristic
374C8—181no—
375C8—181no—
376C8—182no—
377C2×C3—216no—
378C2×C3C22×#21514yes—
379C2×C3#582914yes—
380C2×C3#583514yes—
381D3—128no—
382D3—248no—
383C22—22no—
384C22—22no—
385C22—182no—
386C22—361no—
387C22—361no—
388C22—362no—
389C22—362no—
390C22—362no—
391C22—728no—
392C22C2×#375514yes—
393C22C22×#63811yescharacteristic
394C4—22no—
395C4—21no—
396C4—41no—
397C4—41no—
398C4—42no—
399C4—361no—
400C4C2×#375512yes—
401C4#41×C3⋊D311yescharacteristic
402C4#6436611yescharacteristic
403C3#8363414yescomplemented
404C2—24no—
405C2—362no—
406C2—722no—
407C2C22×#375511yescharacteristic
408C2#1059630011yescharacteristic
409C2#1059630611yescharacteristic
subgroupG/H
centerC22C22×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#554C2
socleC22×C32C22×D4
prime radicalD4×C4⋊(C3⋊D3)C2
hypercenter#554C3⋊D3
hypocenterC32#3295
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4 ◁ #554

Complements

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

NH ≅ G/Ntype
1. C32×#554C2semidirect
3. #10592787C2semidirect
4. #10592783C2semidirect
5. #10592747C2semidirect
6. #10592745C2semidirect
7. #10592726C2semidirect
8. C4×#3755C2semidirect
9. D4×C3⋊(C3⋊C8)C2semidirect
10. #10592667C2semidirect
11. C2×#63636C2semidirect
15. C32×C4⋊Q8C22semidirect
18. C32×C22⋊Q8C22semidirect
19. C32×C4×Q8C22semidirect
22. C2×C32×C4⋊C4C22semidirect
24. C2×#3755C22semidirect
26. C22×C3⋊(C3⋊C8)C22semidirect
31. #63662C22semidirect
32. #63657C22semidirect
35. #63636C22semidirect
36. #63636C22semidirect
37. #63636C22semidirect
38. #63635C22semidirect
39. #63635C22semidirect
40. C4⋊(C3⋊(C3⋊C8))C22semidirect
41. C4×C3⋊(C3⋊C8)C22semidirect
42. C3×#554D3semidirect
92. C3×C4⋊Q8C2×D3semidirect
95. C3×C22⋊Q8C2×D3semidirect
96. C3×C4×Q8C2×D3semidirect
99. C2×C3×C4⋊C4C2×D3semidirect
128. C32×D4SD16semidirect
152. #554C3⋊D3semidirect
224. C4⋊Q8C2×C3⋊D3semidirect
228. C22⋊Q8C2×C3⋊D3semidirect
232. C4×Q8C2×C3⋊D3semidirect
236. C2×C4⋊C4C2×C3⋊D3semidirect
257. C3×D4#215semidirect
343. C32#3295semidirect
361. D4#3755semidirect
403. C3#83634semidirect

Maximal subgroups

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

subgroupindex
C32×#5542
D4×C4⋊(C3⋊D3)2
#105927872
#105927832
#105927472
#105927452
#105927262
C4×#37552
D4×C3⋊(C3⋊C8)2
#105926672
C2×#636362
#836343