Finite Group Databasebeta

← #11860679

Subgroups — #11860679

Order 1152.

866 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 866 conjugacy classes of subgroups — too many to draw. Only its 160 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596642C212yesmaximal, complemented
2C2×D8×C3⋊D3C211yesmaximal, characteristic
3#10593814C212yesmaximal, complemented
4#10593778C214yesmaximal, complemented
5D8×#157C214yesmaximal, complemented
6#10593768C211yesmaximal, characteristic, complemented
7#10593765C211yesmaximal, characteristic, complemented
8C2×D4×C3⋊D3C2212yes—
9C2×C22⋊#157—24no—
10D4×#157—24no—
11D4×#157C2218yescomplemented
12#64286C2212yes—
13#64286C2211yescharacteristic
14#64283C2211yescharacteristic
15C2×C32×D8C411yescharacteristic, complemented
16C2×#3753C412yescomplemented
17D8×C3⋊D3C412yescomplemented
18D8×C3⋊D3C412yescomplemented
19D8×C3⋊D3C2212yes—
20D8×C3⋊D3C2212yes—
21C2×#3745C411yescharacteristic, complemented
22C2×C8×C3⋊D3C2211yescharacteristic
23#63782C2218yescomplemented
24#63769C2212yescomplemented
25#63768C2212yescomplemented
26#63767C2212yescomplemented
27C8×#157C2212yescomplemented
28C2×D3×D8—62no—
29C23×C3⋊D3—22no—
30C22×#157—28no—
31C2×C32×D4C2×C412yescomplemented
32C2×#638—22no—
33D4×C3⋊D3—22no—
34D4×C3⋊D3—22no—
35D4×C3⋊D3C2×C414yescomplemented
36D4×C3⋊D3C2314yes—
37C2×C4⋊(C3⋊D3)C2×C412yescomplemented
38C2×C4×C3⋊D3C2311yescharacteristic
39C22⋊#157—22no—
40C22⋊#157—28no—
41C22⋊#157D412yes—
42#3792—21no—
43C4⋊#157D412yes—
44C4⋊#157C2314yes—
45C4×#157—22no—
46C4×#157C2312yes—
47#3788—21no—
48#3787C2312yes—
49C32×D8C2×C412yescomplemented
50C32×D8C2×C412yescomplemented
51C2×C32×C8C2×C411yescharacteristic, complemented
52#3753C2×C414yescomplemented
53#3753C2×C414yescomplemented
54C2×C3⋊(C3⋊C8)C2×C411yescharacteristic, complemented
55#3745C2×C412yescomplemented
56#3745C2×C412yescomplemented
57C8×C3⋊D3C2×C411yescharacteristic, complemented
58C8×C3⋊D3C2×C411yescharacteristic, complemented
59C8×C3⋊D3C2311yescharacteristic
60C8×C3⋊D3C2311yescharacteristic
61#2948—91nomaximal, Sylow
62C2×D3×D4—64no—
63C2×C3×D8—22no—
64C2×#213—64no—
65D3×D8—64no—
66D3×D8—64no—
67D3×D8—64no—
68D3×D8—64no—
69C2×D24—62no—
70C2×D3×C8—62no—
71C23×C32—22no—
72C22×C3⋊D3—22no—
73C22×C3⋊D3—24no—
74C22×C3⋊D3—24no—
75C22×C3⋊D3—84no—
76C22×C3⋊D3C2×D411yescharacteristic
77C2×#157—24no—
78C2×#157—88no—
79C2×#157C2×D414yes—
80C32×D4—22no—
81C32×D4C22×C414yes—
82C2×C32×C4C22×C411yescharacteristic
83#638—24no—
84#638—24no—
85C2×C3⋊Dic3#4111yescharacteristic
86C4⋊(C3⋊D3)—22no—
87C4⋊(C3⋊D3)C22×C414yes—
88C4×C3⋊D3C22×C411yescharacteristic
89C4×C3⋊D3C2×D411yescharacteristic
90C4×C3⋊D3#4111yescharacteristic
91C4×C3⋊D3C2411yescharacteristic
92#622—22no—
93C32×C8C22×C411yescharacteristic
94C32×C8C22×C411yescharacteristic
95C3⋊(C3⋊C8)C22×C411yescharacteristic
96C3⋊(C3⋊C8)C22×C411yescharacteristic
97C22×D8—91no—
98#518—92no—
99#442—94no—
100C4×D8—94no—
101#427—91no—
102#418—92no—
103#405—91no—
104C23×D3—124no—
105C2×C3×D4—24no—
106C2×#67—124no—
107D3×D4—68no—
108D3×D4—68no—
109D3×D4—124no—
110D3×D4—124no—
111C2×D12—64no—
112C2×C4×D3—62no—
113C3×D8—24no—
114C3×D8—24no—
115C2×C3×C8—22no—
116#213—68no—
117#213—68no—
118C2×C3⋊C8—62no—
119D24—64no—
120D24—64no—
121D3×C8—62no—
122D3×C8—62no—
123D3×C8—62no—
124D3×C8—62no—
125C22×C32—24no—
126C22×C32—82no—
127C22×C32C4×D411yescharacteristic
128C2×C3⋊D3—22no—
129C2×C3⋊D3—24no—
130C2×C3⋊D3—48no—
131C2×C3⋊D3—84no—
132C2×C3⋊D3—82no—
133C2×C3⋊D3C4×D411yescharacteristic
134C2×C3⋊D3C22×D411yescharacteristic
135#157—24no—
136#157—44no—
137C32×C4C4×D411yescharacteristic
138C32×C4C23×C411yescharacteristic
139C3⋊Dic3C4×D411yescharacteristic
140C3⋊Dic3C2×#4111yescharacteristic
141C22×D4—92no—
142C2×D8—92no—
143C2×D8—92no—
144C2×D8—92no—
145C2×D8—92no—
146C2×D8—92no—
147C2×D8—91no—
148C2×D8#15711yescharacteristic, complemented
149C2×M16—91no—
150C22×C8—91no—
151C4×D4—98no—
152C4×D4—184no—
153#117—91no—
154#117—92no—
155C2×C22⋊C4—184no—
156#107—92no—
157#106—92no—
158#102—98no—
159#97—92no—
160C4×C8—92no—
161C23×C3—44no—
162C22×D3—62no—
163C22×D3—128no—
164C22×D3—128no—
165C22×D3—124no—
166C22×D3—2416no—
167C3×D4—28no—
168C3×D4—44no—
169C2×C3×C4—22no—
170#67—128no—
171#67—128no—
172C2×Dic3—62no—
173D12—68no—
174D12—124no—
175C4×D3—62no—
176C4×D3—62no—
177C4×D3—62no—
178C4×D3—62no—
179C3×C8—22no—
180C3×C8—22no—
181C3⋊C8—62no—
182C3⋊C8—62no—
183C2×C32—21no—
184C2×C32—44no—
185C2×C32C2×C4×D411yescharacteristic
186C3⋊D3—21no—
187C3⋊D3—44no—
188C3⋊D3#57612yes—
189C24—182no—
190C2×D4—94no—
191C2×D4—94no—
192C2×D4—92no—
193C2×D4—182no—
194C2×D4—182no—
195C2×D4—182no—
196C2×D4C2×#15712yescomplemented
197C22×C4—91no—
198C22×C4—188no—
199D8—94no—
200D8—94no—
201D8—92no—
202D8—92no—
203D8C2×#15712yescomplemented
204D8C2×#15712yescomplemented
205M16—181no—
206M16—181no—
207C2×C8—91no—
208C2×C8—91no—
209C2×C8—91no—
210C2×C8—91no—
211C2×C8—91no—
212C2×C8—92no—
213C2×C8C2×#15711yescharacteristic, complemented
214C4⋊C4—92no—
215C4⋊C4—94no—
216C22⋊C4—92no—
217C22⋊C4—188no—
218C22⋊C4—182no—
219C42—92no—
220C42—182no—
221C22×C3—22no—
222C22×C3—48no—
223C22×C3—88no—
224C2×D3—62no—
225C2×D3—62no—
226C2×D3—68no—
227C2×D3—128no—
228C2×D3—2416no—
229C2×D3—2416no—
230C2×D3—248no—
231C3×C4—22no—
232C3×C4—22no—
233Dic3—62no—
234Dic3—62no—
235C32#294811yescharacteristic, complemented, Sylow
236C23—22no—
237C23—91no—
238C23—184no—
239C23—184no—
240C23—182no—
241C23—724no—
242D4—22no—
243D4—94no—
244D4—184no—
245D4—184no—
246D4—182no—
247D4C22×#15714yes—
248C2×C4—91no—
249C2×C4—91no—
250C2×C4—91no—
251C2×C4—91no—
252C2×C4—91no—
253C2×C4—94no—
254C2×C4—184no—
255C2×C4—728no—
256C2×C4C22×#15711yescharacteristic
257C8—91no—
258C8—91no—
259C8—182no—
260C8C22×#15711yescharacteristic
261C8C22×#15711yescharacteristic
262C2×C3—24no—
263C2×C3—22no—
264C2×C3—88no—
265D3—64no—
266D3—64no—
267D3—248no—
268C22—24no—
269C22—82no—
270C22—91no—
271C22—91no—
272C22—182no—
273C22—184no—
274C22—368no—
275C22—722no—
276C22—724no—
277C22D4×#15711yescharacteristic
278C4—91no—
279C4—91no—
280C4—184no—
281C4—364no—
282C4D4×#15711yescharacteristic
283C4C23×#15711yescharacteristic
284C3—22no—
285C2—21no—
286C2—44no—
287C2—92no—
288C2—181no—
289C2—364no—
290C2C2×D4×#15711yescharacteristic
subgroupG/H
centerC2C2×D4×#157
commutatorC32×C4C23×C4
FrattiniC4C23×#157
FittingC2×C32×D8C4
socleC2×C32C2×C4×D4
prime radicalC2×D8×C3⋊D3C2
cosocleC4×C3⋊D3C24
hypercenterC2×D8#157
hypocenterC32#2948
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #10596642C2semidirect
3. #10593814C2semidirect
4. #10593778C2semidirect
5. D8×#157C2semidirect
6. #10593768C2semidirect
7. #10593765C2semidirect
11. D4×#157C22semidirect
15. C2×C32×D8C4semidirect
16. C2×#3753C4semidirect
17. D8×C3⋊D3C4semidirect
18. D8×C3⋊D3C4semidirect
21. C2×#3745C4semidirect
23. #63782C22semidirect
24. #63769C22semidirect
25. #63768C22semidirect
26. #63767C22semidirect
27. C8×#157C22semidirect
31. C2×C32×D4C2×C4semidirect
35. D4×C3⋊D3C2×C4semidirect
37. C2×C4⋊(C3⋊D3)C2×C4semidirect
49. C32×D8C2×C4semidirect
50. C32×D8C2×C4semidirect
51. C2×C32×C8C2×C4semidirect
52. #3753C2×C4semidirect
53. #3753C2×C4semidirect
54. C2×C3⋊(C3⋊C8)C2×C4semidirect
55. #3745C2×C4semidirect
56. #3745C2×C4semidirect
57. C8×C3⋊D3C2×C4semidirect
58. C8×C3⋊D3C2×C4semidirect
148. C2×D8#157semidirect
196. C2×D4C2×#157semidirect
203. D8C2×#157semidirect
204. D8C2×#157semidirect
213. C2×C8C2×#157semidirect
235. C32#2948semidirect

Maximal subgroups

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

subgroupindex
#105966422
C2×D8×C3⋊D32
#105938142
#105937782
D8×#1572
#105937682
#105937652
#29489