Finite Group Databasebeta

← #11783756

Subgroups — #11783756

Order 1152.

838 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 838 conjugacy classes of subgroups — too many to draw. Only its 94 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
1C2×#64090C211yesmaximal, characteristic
2C2×#63786C212yesmaximal
3C4×C22⋊#157C212yesmaximal, complemented
4#10590206C212yesmaximal, complemented
5C22×#638C2211yescharacteristic
6C23×C3⋊Dic3C411yescharacteristic, complemented
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×C22⋊#157C2214yes—
9C2×C4×#157—22no—
10C2×C32×C22⋊C4C411yescharacteristic, complemented
11C2×#3752C2211yescharacteristic
12C2×#3750C411yescharacteristic, complemented
13C2×C4×C3⋊Dic3C411yescharacteristic, complemented
14#64090—22no—
15#64090—22no—
16#63786C418yescomplemented
17#63781—22no—
18C2×#67⋊C4—62no—
19C24×C32C2×C411yescharacteristic
20C23×C3⋊D3C2311yescharacteristic
21C22×#157—24no—
22C22×C32×C4C2×C411yescharacteristic
23C22×C32×C4C2×C411yescharacteristic
24C2×#638—22no—
25C2×#638—22no—
26C2×#638C2×C414yes—
27C22×C3⋊Dic3—21no—
28C22×C3⋊Dic3—21no—
29C22×C3⋊Dic3—42no—
30C22×C3⋊Dic3C2×C411yescharacteristic
31C22×C3⋊Dic3C2×C411yescharacteristic
32C22×C3⋊Dic3C2×C411yescharacteristic
33C2×C4×C3⋊D3—42no—
34C2×C4×C3⋊D3D412yes—
35C2×C4×C3⋊D3D412yes—
36C22⋊#157—24no—
37C22⋊#157C2×C418yescomplemented
38C4×#157—44no—
39C32×C22⋊C4—22no—
40#3752—22no—
41#3750—22no—
42C4×C3⋊Dic3—21no—
43C4×C3⋊Dic3—21no—
44C4×#99—91nomaximal, Sylow
45C22×#67—62no—
46C23×Dic3—62no—
47C22×C4×D3—62no—
48C2×C3×C22⋊C4—22no—
49C2×(C2×D3)⋊C4—62no—
50C2×Dic3⋊C4—62no—
51C2×C4×Dic3—62no—
52#67⋊C4—68no—
53#67⋊C4—68no—
54C23×C32—21no—
55C23×C32—21no—
56C23×C32—41no—
57C23×C32—41no—
58C23×C32C4212yescomplemented
59C23×C32C22×C411yescharacteristic
60C22×C3⋊D3—41no—
61C22×C3⋊D3—41no—
62C22×C3⋊D3C22×C412yes—
63C22×C3⋊D3C2×D412yes—
64C22×C3⋊D3#4112yes—
65C2×#157—28no—
66C2×#157—44no—
67C2×#157—44no—
68C2×C32×C4—21no—
69C2×C32×C4—41no—
70C2×C32×C4—41no—
71C2×C32×C4C22⋊C412yes—
72#638—28no—
73C2×C3⋊Dic3—21no—
74C2×C3⋊Dic3—21no—
75C2×C3⋊Dic3—22no—
76C2×C3⋊Dic3—21no—
77C2×C3⋊Dic3—42no—
78C2×C3⋊Dic3—42no—
79C2×C3⋊Dic3—41no—
80C2×C3⋊Dic3C4212yescomplemented
81C2×C3⋊Dic3C22⋊C411yescharacteristic
82C2×C3⋊Dic3C22⋊C411yescharacteristic
83C4×C3⋊D3—24no—
84C4×C3⋊D3—42no—
85C2×C4×D4—91no—
86C2×#99—92no—
87C4×C22⋊C4—92no—
88#342—92no—
89C24×C3—22no—
90C23×D3—62no—
91C22×C3×C4—22no—
92C22×C3×C4—22no—
93C2×#67—68no—
94C2×#67—68no—
95C2×#67—68no—
96C22×Dic3—62no—
97C22×Dic3—62no—
98C22×Dic3—62no—
99C22×Dic3—64no—
100C22×Dic3—64no—
101C22×Dic3—128no—
102C2×C4×D3—64no—
103C2×C4×D3—64no—
104C2×C4×D3—128no—
105C3×C22⋊C4—28no—
106(C2×D3)⋊C4—68no—
107Dic3⋊C4—68no—
108C4×Dic3—64no—
109C4×Dic3—64no—
110C22×C32—21no—
111C22×C32—21no—
112C22×C32—22no—
113C22×C32—42no—
114C22×C32—42no—
115C22×C32—41no—
116C22×C32—41no—
117C22×C32C2×C4211yescharacteristic
118C22×C32C2×C22⋊C411yescharacteristic
119C22×C32#11711yescharacteristic
120C2×C3⋊D3—22no—
121C2×C3⋊D3—22no—
122C2×C3⋊D3—42no—
123C2×C3⋊D3—42no—
124C2×C3⋊D3C4×D414yes—
125#157—48no—
126C32×C4—22no—
127C32×C4—41no—
128C3⋊Dic3—22no—
129C3⋊Dic3—21no—
130C3⋊Dic3—41no—
131C3⋊Dic3#9912yescomplemented
132C22×D4—91no—
133C23×C4—91no—
134C23×C4—91no—
135C4×D4—182no—
136C4×D4—182no—
137C2×C4⋊C4—91no—
138C2×C22⋊C4—94no—
139C2×C22⋊C4—91no—
140C2×C22⋊C4#15711yescharacteristic, complemented
141C2×C42—91no—
142C2×C42—182no—
143#99—98no—
144#95—182no—
145C23×C3—24no—
146C23×C3—24no—
147C23×C3—22no—
148C23×C3—24no—
149C23×C3—44no—
150C23×C3—44no—
151C22×D3—64no—
152C22×D3—64no—
153C22×D3—64no—
154C22×D3—124no—
155C22×D3—124no—
156C2×C3×C4—24no—
157C2×C3×C4—24no—
158C2×C3×C4—44no—
159C2×C3×C4—44no—
160#67—632no—
161C2×Dic3—64no—
162C2×Dic3—62no—
163C2×Dic3—62no—
164C2×Dic3—64no—
165C2×Dic3—68no—
166C2×Dic3—64no—
167C2×Dic3—64no—
168C2×Dic3—128no—
169C2×Dic3—128no—
170C2×Dic3—124no—
171C4×D3—128no—
172C4×D3—128no—
173C2×C32—21no—
174C2×C32—21no—
175C2×C32—42no—
176C2×C32C4×C22⋊C411yescharacteristic
177C2×C32C2×#9911yescharacteristic
178C2×C32#41011yescharacteristic
179C3⋊D3—24no—
180C24—91no—
181C24C2×#15711yescharacteristic
182C2×D4—94no—
183C2×D4—182no—
184C2×D4—182no—
185C22×C4—91no—
186C22×C4—91no—
187C22×C4—92no—
188C22×C4—92no—
189C22×C4—91no—
190C22×C4—181no—
191C22×C4—181no—
192C22×C4—184no—
193C22×C4—362no—
194C22×C4—362no—
195C22×C4C2×#15711yescharacteristic
196C22×C4C2×#15711yescharacteristic
197C4⋊C4—182no—
198C22⋊C4—22no—
199C22⋊C4—98no—
200C22⋊C4—182no—
201C22⋊C4—184no—
202C42—181no—
203C42—181no—
204C42—364no—
205C22×C3—24no—
206C22×C3—24no—
207C22×C3—28no—
208C22×C3—22no—
209C22×C3—22no—
210C22×C3—22no—
211C22×C3—44no—
212C22×C3—48no—
213C22×C3—48no—
214C22×C3—44no—
215C2×D3—68no—
216C2×D3—124no—
217C2×D3—124no—
218C2×D3—128no—
219C2×D3—128no—
220C3×C4—44no—
221C3×C4—44no—
222Dic3—64no—
223Dic3—64no—
224Dic3—68no—
225Dic3—124no—
226C32C4×#9911yescharacteristic, complemented, Sylow
227C23—21no—
228C23—21no—
229C23—41no—
230C23—41no—
231C23—92no—
232C23—92no—
233C23—92no—
234C23—361no—
235C23—361no—
236C23C4×#15712yescomplemented
237C23C22×#15711yescharacteristic
238D4—188no—
239C2×C4—21no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—91no—
243C2×C4—92no—
244C2×C4—91no—
245C2×C4—184no—
246C2×C4—182no—
247C2×C4—181no—
248C2×C4—181no—
249C2×C4—188no—
250C2×C4—181no—
251C2×C4—362no—
252C2×C4—362no—
253C2×C4—362no—
254C2×C4—364no—
255C2×C4—364no—
256C2×C4—361no—
257C2×C4C22⋊#15712yes—
258C2×C3—24no—
259C2×C3—24no—
260C2×C3—22no—
261C2×C3—22no—
262C2×C3—22no—
263C2×C3—48no—
264D3—128no—
265C22—21no—
266C22—21no—
267C22—22no—
268C22—42no—
269C22—42no—
270C22—41no—
271C22—41no—
272C22—94no—
273C22—182no—
274C22—182no—
275C22—362no—
276C22—362no—
277C22C2×C4×#15711yescharacteristic
278C22#6428611yescharacteristic
279C22C2×C22⋊#15711yescharacteristic
280C4—22no—
281C4—41no—
282C4—92no—
283C4—182no—
284C4—181no—
285C4—368no—
286C4—361no—
287C3—22no—
288C2—21no—
289C2—21no—
290C2—42no—
291C2—184no—
292C2C4×C22⋊#15711yescharacteristic
293C2#1059381711yescharacteristic
294C2#1059381811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC22×C32C2×C42
FrattiniC23C22×#157
FittingC2×C32×C22⋊C4C4
socleC22×C32C2×C22⋊C4
prime radicalC22×#638C22
cosocleC23×C3⋊D3C23
hypercenterC2×C22⋊C4#157
hypocenterC32C4×#99
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C4×C22⋊#157C2semidirect
4. #10590206C2semidirect
6. C23×C3⋊Dic3C4semidirect
10. C2×C32×C22⋊C4C4semidirect
12. C2×#3750C4semidirect
13. C2×C4×C3⋊Dic3C4semidirect
16. #63786C4semidirect
37. C22⋊#157C2×C4semidirect
58. C23×C32C42semidirect
80. C2×C3⋊Dic3C42semidirect
131. C3⋊Dic3#99semidirect
140. C2×C22⋊C4#157semidirect
226. C32C4×#99semidirect
236. C23C4×#157semidirect

Maximal subgroups

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

subgroupindex
C2×#640902
C2×#637862
C4×C22⋊#1572
#105902062
C4×#999