Finite Group Databasebeta

← #11783906

Subgroups — #11783906

Order 1152.

630 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C4×#3832C211yesmaximal, characteristic
2C2×#63785C212yesmaximal
3#10593733C211yesmaximal, characteristic, complemented
4C4×#3788C211yesmaximal, characteristic, complemented
5#10590164C212yesmaximal, complemented
6C2×#3832C2211yescharacteristic
7C2×C4×#157C2212yes—
8C2×#3788C2212yes—
9C32×C4×Q8C411yescharacteristic, complemented
10Q8×C3⋊Dic3C411yescharacteristic, complemented
11#64102—21no—
12#64102C411yescharacteristic, complemented
13#64101—21no—
14#64101C2211yescharacteristic
15C4×C4⋊(C3⋊D3)—21no—
16C4×C4⋊(C3⋊D3)C411yescharacteristic, complemented
17C42×C3⋊D3—21no—
18C42×C3⋊D3C2211yescharacteristic
19#63785C418yescomplemented
20#63781—21no—
21#63781—21no—
22#63777—21no—
23C4×#622—21no—
24C4×#239—62no—
25C22×#157—22no—
26C2×C32×Q8C2×C411yescharacteristic
27#3832—22no—
28#3832C2×C414yes—
29C2×C4⋊(C3⋊D3)—21no—
30C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
31C2×C4×C3⋊D3—21no—
32C2×C4×C3⋊D3—21no—
33C2×C4×C3⋊D3—21no—
34C2×C4×C3⋊D3D411yescharacteristic
35C2×C4×C3⋊D3D411yescharacteristic
36C2×C4×C3⋊D3C2311yescharacteristic
37C2×#622—22no—
38C4×#157—22no—
39C4×#157C2×C414yescomplemented
40#3788—22no—
41#3788C2×C414yescomplemented
42C32×C4⋊C4—21no—
43C32×C4⋊C4C2×C411yescharacteristic
44C32×C42—21no—
45C32×C42C2×C411yescharacteristic
46#3752—21no—
47#3752—21no—
48#3752—21no—
49C4⋊(C3⋊Dic3)—21no—
50C4⋊(C3⋊Dic3)C2×C411yescharacteristic
51C4×C3⋊Dic3—21no—
52C4×C3⋊Dic3—21no—
53C4×C3⋊Dic3C2×C411yescharacteristic
54C4×C3⋊Dic3D411yescharacteristic
55C4×C3⋊Dic3D411yescharacteristic
56#1759—91nomaximal, Sylow
57C2×#239—62no—
58C3×C4×Q8—22no—
59Q8×Dic3—62no—
60#893—62no—
61#893—64no—
62#892—62no—
63#892—64no—
64C4×D12—62no—
65C4×D12—64no—
66C42×D3—62no—
67C42×D3—64no—
68C22×C3⋊D3—21no—
69C22×C3⋊D3C2×D411yescharacteristic
70C2×#157—24no—
71C2×#157—42no—
72C2×#157—42no—
73C32×Q8—21no—
74C32×Q8C4212yes—
75C2×C32×C4—21no—
76C2×C32×C4—21no—
77C2×C32×C4C22⋊C411yescharacteristic
78C2×C32×C4C22⋊C411yescharacteristic
79C2×C32×C4C22×C411yescharacteristic
80C2×C3⋊Dic3—21no—
81C2×C3⋊Dic3C22⋊C411yescharacteristic
82C2×C3⋊Dic3C22⋊C411yescharacteristic
83C2×C3⋊Dic3C2×D411yescharacteristic
84C4⋊(C3⋊D3)—24no—
85C4⋊(C3⋊D3)—21no—
86C4⋊(C3⋊D3)C4212yes—
87C4×C3⋊D3—24no—
88C4×C3⋊D3—41no—
89C4×C3⋊D3—41no—
90C4×C3⋊D3—42no—
91C4×C3⋊D3—42no—
92C4×C3⋊D3C22×C412yes—
93C4×C3⋊D3#4112yes—
94#622—24no—
95C4×#41—91no—
96C2×#104—92no—
97C4×M16—91no—
98#376—91no—
99#339—92no—
100C2×C3×Q8—22no—
101#239—68no—
102#239—68no—
103C2×D12—62no—
104C2×D12—64no—
105C2×C4×D3—62no—
106C2×C4×D3—62no—
107C2×C4×D3—62no—
108C2×C4×D3—64no—
109C2×C4×D3—64no—
110C2×C4×D3—64no—
111C3×C4⋊C4—24no—
112C3×C4⋊C4—22no—
113C3×C42—24no—
114C3×C42—22no—
115(C2×D3)⋊C4—64no—
116(C2×D3)⋊C4—64no—
117(C2×D3)⋊C4—64no—
118C4⋊Dic3—62no—
119C4⋊Dic3—64no—
120C4×Dic3—62no—
121C4×Dic3—62no—
122C4×Dic3—62no—
123C4×Dic3—64no—
124C4×Dic3—64no—
125C22×C32C2×C22⋊C411yescharacteristic
126C2×C3⋊D3—22no—
127C2×C3⋊D3—21no—
128C2×C3⋊D3—21no—
129C2×C3⋊D3—41no—
130C2×C3⋊D3—41no—
131C2×C3⋊D3C4×D412yes—
132#157—44no—
133C32×C4—22no—
134C32×C4—21no—
135C32×C4—21no—
136C32×C4—41no—
137C32×C4C2×C4211yescharacteristic
138C32×C4#11711yescharacteristic
139C3⋊Dic3—21no—
140C3⋊Dic3—21no—
141C3⋊Dic3—41no—
142C3⋊Dic3C4×D412yes—
143C2×#41—91no—
144C2×M16—92no—
145C4×Q8—91no—
146C4×Q8#15711yescharacteristic, complemented
147C4×D4—91no—
148C4×D4—91no—
149C4×D4—181no—
150C4×D4—181no—
151#117—91no—
152#117—181no—
153C2×C42—91no—
154C2×C42—92no—
155C2×C42—181no—
156#104—98no—
157#97—181no—
158C4×C8—181no—
159#95—181no—
160#95—181no—
161C22×D3—62no—
162C22×D3—64no—
163C3×Q8—24no—
164C3×Q8—24no—
165C2×C3×C4—24no—
166C2×C3×C4—24no—
167C2×C3×C4—22no—
168C2×C3×C4—22no—
169C2×C3×C4—22no—
170C2×Dic3—62no—
171C2×Dic3—62no—
172C2×Dic3—62no—
173C2×Dic3—64no—
174D12—64no—
175D12—616no—
176D12—64no—
177C4×D3—64no—
178C4×D3—64no—
179C4×D3—616no—
180C4×D3—124no—
181C4×D3—128no—
182C4×D3—124no—
183C4×D3—128no—
184C2×C32C4×C22⋊C411yescharacteristic
185C2×C32#42111yescharacteristic
186C2×C32#42111yescharacteristic
187C3⋊D3—22no—
188C3⋊D3—42no—
189#41—94no—
190#41—182no—
191C2×Q8C2×#15711yescharacteristic
192C2×D4—91no—
193C2×D4—181no—
194C22×C4—91no—
195C22×C4—91no—
196C22×C4—91no—
197C22×C4—181no—
198C22×C4—181no—
199C22×C4—182no—
200C22×C4—181no—
201M16—94no—
202M16—182no—
203C2×C8—182no—
204C4⋊C4—21no—
205C4⋊C4—91no—
206C4⋊C4—181no—
207C4⋊C4C2×#15711yescharacteristic
208C22⋊C4—181no—
209C22⋊C4—181no—
210C22⋊C4—181no—
211C42—21no—
212C42—91no—
213C42—91no—
214C42—91no—
215C42—94no—
216C42—181no—
217C42—181no—
218C42—182no—
219C42C2×#15711yescharacteristic
220C22×C3—22no—
221C2×D3—64no—
222C2×D3—68no—
223C2×D3—122no—
224C2×D3—122no—
225C2×D3—124no—
226C2×D3—124no—
227C3×C4—28no—
228C3×C4—24no—
229C3×C4—22no—
230C3×C4—22no—
231C3×C4—42no—
232C3×C4—44no—
233Dic3—64no—
234Dic3—64no—
235Dic3—122no—
236Dic3—124no—
237C32#175911yescharacteristic, complemented, Sylow
238C23—91no—
239C23—181no—
240Q8—21no—
241Q8C4×#15712yes—
242D4—92no—
243D4—184no—
244D4—181no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—91no—
248C2×C4—92no—
249C2×C4—92no—
250C2×C4—91no—
251C2×C4—91no—
252C2×C4—184no—
253C2×C4—184no—
254C2×C4—181no—
255C2×C4—361no—
256C2×C4—361no—
257C2×C4—362no—
258C2×C4—362no—
259C2×C4—362no—
260C2×C4—362no—
261C2×C4C22⋊#15711yescharacteristic
262C2×C4C22⋊#15711yescharacteristic
263C2×C4C22×#15711yescharacteristic
264C8—184no—
265C2×C3—22no—
266C2×C3—22no—
267C2×C3—22no—
268D3—124no—
269D3—128no—
270C22—92no—
271C22—181no—
272C22—181no—
273C22—182no—
274C22—361no—
275C22—361no—
276C22C2×C22⋊#15711yescharacteristic
277C4—22no—
278C4—21no—
279C4—21no—
280C4—41no—
281C4—92no—
282C4—181no—
283C4—181no—
284C4—364no—
285C4—361no—
286C4C2×C4×#15711yescharacteristic
287C4#6428611yescharacteristic
288C3—22no—
289C2—182no—
290C2—362no—
291C2C4×C22⋊#15711yescharacteristic
292C2#1059383111yescharacteristic
293C2#1059384211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC32×C4C2×C42
FrattiniC2×C4C22×#157
FittingC32×C4×Q8C4
socleC22×C32C2×C22⋊C4
prime radicalC2×#3832C22
cosocleC2×C4×C3⋊D3C23
hypercenterC4×Q8#157
hypocenterC32#1759
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
3. #10593733C2semidirect
4. C4×#3788C2semidirect
5. #10590164C2semidirect
9. C32×C4×Q8C4semidirect
10. Q8×C3⋊Dic3C4semidirect
12. #64102C4semidirect
16. C4×C4⋊(C3⋊D3)C4semidirect
19. #63785C4semidirect
39. C4×#157C2×C4semidirect
41. #3788C2×C4semidirect
146. C4×Q8#157semidirect
237. C32#1759semidirect

Maximal subgroups

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

subgroupindex
C4×#38322
C2×#637852
#105937332
C4×#37882
#105901642
#17599