Finite Group Databasebeta

← #11773207

Subgroups — #11773207

Order 1152.

1154 conjugacy classes of subgroups; only the 206 normal subgroups are shown.

normal subgroups only

This group has 1154 conjugacy classes of subgroups — too many to draw. Only its 206 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
1C22×C4⋊#157C212yesmaximal
2C2×C42×C3⋊D3C211yesmaximal, characteristic
3C2×#63781C214yesmaximal
4C23×#157C2214yes—
5C22×C4×C3⋊D3C2212yes—
6C22×C4×C3⋊D3C2211yescharacteristic
7C2×C4⋊#157—24no—
8C2×C4⋊#157—24no—
9C2×C4⋊#157C418yescomplemented
10C2×C32×C42C411yescharacteristic, complemented
11C2×C4×C3⋊Dic3C411yescharacteristic, complemented
12C2×C4×C3⋊Dic3C412yescomplemented
13C42×C3⋊D3—24no—
14#63781—28no—
15C2×C42×D3—62no—
16C23×C3⋊D3C2311yescharacteristic
17C22×#157—24no—
18C22×#157—24no—
19C22×#157—28no—
20C22×#157—28no—
21C22×#157C2×C418yes—
22C22×C32×C4C2×C412yes—
23C22×C32×C4C2×C411yescharacteristic
24C22×C3⋊Dic3C2×C412yes—
25C22×C3⋊Dic3C2×C411yescharacteristic
26C2×C4×C3⋊D3—24no—
27C2×C4×C3⋊D3—24no—
28C2×C4×C3⋊D3C2×C414yes—
29C2×C4×C3⋊D3D414yes—
30C2×C4×C3⋊D3D412yes—
31C2×C4×C3⋊D3D414yes—
32C2×C4×C3⋊D3Q814yes—
33C2×C4×C3⋊D3Q812yes—
34C4⋊#157—216no—
35C32×C42—22no—
36C4×C3⋊Dic3—22no—
37C4×C3⋊Dic3—24no—
38C4⋊#95—91nomaximal, Sylow
39C22×C4×D3—62no—
40C22×C4×D3—64no—
41C2×C3×C42—22no—
42C2×C4×Dic3—64no—
43C2×C4×Dic3—62no—
44C42×D3—616no—
45C23×C32C22×C411yescharacteristic
46C22×C3⋊D3C22×C412yes—
47C22×C3⋊D3C2×D411yescharacteristic
48C22×C3⋊D3C2×D412yes—
49C22×C3⋊D3C2×D412yes—
50C22×C3⋊D3C2×Q811yescharacteristic
51C22×C3⋊D3C2×Q812yes—
52C22×C3⋊D3#4114yes—
53C2×#157—28no—
54C2×#157—216no—
55C2×#157—48no—
56C2×#157—44no—
57C2×#157—44no—
58C2×C32×C4—22no—
59C2×C32×C4—22no—
60C2×C32×C4C4212yes—
61C2×C32×C4C22⋊C412yes—
62C2×C32×C4C4⋊C412yes—
63C2×C32×C4C4⋊C414yescomplemented
64C2×C3⋊Dic3—22no—
65C2×C3⋊Dic3—22no—
66C2×C3⋊Dic3C4212yes—
67C2×C3⋊Dic3C22⋊C412yes—
68C2×C3⋊Dic3C4⋊C412yes—
69C2×C3⋊Dic3C4⋊C414yescomplemented
70C4×C3⋊D3—28no—
71C4×C3⋊D3—28no—
72C4×C3⋊D3C22⋊C418yes—
73C4×C3⋊D3C4⋊C418yes—
74C22×C4⋊C4—92no—
75C22×C42—91no—
76C2×#95—94no—
77C23×D3—62no—
78C22×C3×C4—24no—
79C22×C3×C4—22no—
80C22×Dic3—62no—
81C22×Dic3—64no—
82C2×C4×D3—68no—
83C2×C4×D3—68no—
84C2×C4×D3—64no—
85C2×C4×D3—68no—
86C2×C4×D3—64no—
87C2×C4×D3—68no—
88C2×C4×D3—616no—
89C2×C4×D3—616no—
90C3×C42—28no—
91C4×Dic3—616no—
92C4×Dic3—68no—
93C22×C32C2×C4211yescharacteristic
94C22×C32C2×C22⋊C411yescharacteristic
95C22×C32C2×C4⋊C411yescharacteristic
96C22×C32C2×C4⋊C412yes—
97C22×C32#11712yes—
98C2×C3⋊D3C2×C22⋊C412yes—
99C2×C3⋊D3C2×C4⋊C412yes—
100C2×C3⋊D3C4×D414yes—
101C2×C3⋊D3C4×Q814yes—
102C2×C3⋊D3#12114yes—
103C2×C3⋊D3C22⋊Q814yes—
104C2×C3⋊D3#12412yes—
105C2×C3⋊D3#12512yes—
106C2×C3⋊D3#12711yescharacteristic
107C2×C3⋊D3C4⋊Q812yes—
108C2×C3⋊D3C4⋊Q811yescharacteristic
109#157—48no—
110C32×C4—24no—
111C32×C4#9514yescomplemented
112C3⋊Dic3—24no—
113C3⋊Dic3#9514yescomplemented
114C23×C4—91no—
115C23×C4—92no—
116C23×C4—94no—
117C2×C4⋊C4—98no—
118C2×C4⋊C4—184no—
119C2×C4⋊C4—184no—
120C2×C42—92no—
121C2×C42—91no—
122C2×C42—184no—
123C2×C42#15711yescharacteristic, complemented
124#95—188no—
125C23×C3—22no—
126C22×D3—64no—
127C22×D3—64no—
128C22×D3—62no—
129C22×D3—64no—
130C22×D3—62no—
131C22×D3—64no—
132C22×D3—68no—
133C2×C3×C4—28no—
134C2×C3×C4—28no—
135C2×C3×C4—24no—
136C2×C3×C4—24no—
137C2×C3×C4—28no—
138C2×C3×C4—24no—
139C2×Dic3—64no—
140C2×Dic3—64no—
141C2×Dic3—64no—
142C2×Dic3—68no—
143C2×Dic3—68no—
144C2×Dic3—68no—
145C4×D3—616no—
146C4×D3—616no—
147C4×D3—632no—
148C4×D3—632no—
149C2×C32C2×#9511yescharacteristic
150C2×C32C4×C4⋊C412yes—
151C2×C32#38012yes—
152C2×C32#38211yescharacteristic
153C2×C32#38411yescharacteristic
154C3⋊D3#38914yes—
155C3⋊D3#39012yes—
156C3⋊D3#39112yes—
157C24—91no—
158C22×C4—91no—
159C22×C4—94no—
160C22×C4—92no—
161C22×C4—92no—
162C22×C4—94no—
163C22×C4—92no—
164C22×C4—94no—
165C22×C4—94no—
166C22×C4—98no—
167C22×C4—184no—
168C22×C4—184no—
169C22×C4—188no—
170C22×C4—184no—
171C22×C4—184no—
172C22×C4—188no—
173C22×C4C2×#15712yes—
174C22×C4C2×#15711yescharacteristic
175C4⋊C4—1816no—
176C42—22no—
177C42—184no—
178C42—182no—
179C22×C3—22no—
180C22×C3—22no—
181C22×C3—24no—
182C22×C3—24no—
183C22×C3—22no—
184C2×D3—64no—
185C2×D3—64no—
186C2×D3—68no—
187C2×D3—68no—
188C2×D3—68no—
189C2×D3—68no—
190C2×D3—64no—
191C2×D3—64no—
192C2×D3—62no—
193C2×D3—64no—
194C2×D3—62no—
195C3×C4—216no—
196C3×C4—28no—
197Dic3—68no—
198Dic3—616no—
199C32C4⋊#9511yescharacteristic, complemented, Sylow
200C23—92no—
201C23—91no—
202C23—92no—
203C23—91no—
204C23—92no—
205C23—94no—
206C23—92no—
207C23C22×#15711yescharacteristic
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—92no—
211C2×C4—92no—
212C2×C4—92no—
213C2×C4—98no—
214C2×C4—98no—
215C2×C4—94no—
216C2×C4—188no—
217C2×C4—188no—
218C2×C4—182no—
219C2×C4—182no—
220C2×C4—188no—
221C2×C4—1816no—
222C2×C4—368no—
223C2×C4—364no—
224C2×C4—364no—
225C2×C4C4×#15712yes—
226C2×C4C4⋊#15712yes—
227C2×C4C4⋊#15714yescomplemented
228C2×C4C22⋊#15712yes—
229C2×C3—22no—
230C2×C3—24no—
231C2×C3—24no—
232C2×C3—22no—
233C2×C3—22no—
234D3—68no—
235D3—64no—
236D3—64no—
237C22—92no—
238C22—92no—
239C22—94no—
240C22—94no—
241C22—94no—
242C22—94no—
243C22—91no—
244C22—91no—
245C22—92no—
246C22—92no—
247C22—92no—
248C22C2×C4×#15711yescharacteristic
249C22C2×C4⋊#15711yescharacteristic
250C22C2×C4⋊#15712yes—
251C22#6428612yes—
252C22C2×C22⋊#15711yescharacteristic
253C4—24no—
254C4—94no—
255C4—184no—
256C4—368no—
257C4#6378114yescomplemented
258C3—22no—
259C2—92no—
260C2—92no—
261C2—94no—
262C2C4×C4⋊#15712yes—
263C2#1059373511yescharacteristic
264C2#1059373611yescharacteristic
265C2C2×#6378111yescharacteristic
266C2#1059381212yes—
subgroupG/H
center, FrattiniC23C22×#157
commutatorC22×C32C2×C42
FittingC2×C32×C42C4
socleC23×C32C22×C4
prime radical, cosocleC23×C3⋊D3C23
hypercenterC2×C42#157
hypocenterC32C4⋊#95
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
9. C2×C4⋊#157C4semidirect
10. C2×C32×C42C4semidirect
11. C2×C4×C3⋊Dic3C4semidirect
12. C2×C4×C3⋊Dic3C4semidirect
63. C2×C32×C4C4⋊C4semidirect
69. C2×C3⋊Dic3C4⋊C4semidirect
111. C32×C4#95semidirect
113. C3⋊Dic3#95semidirect
123. C2×C42#157semidirect
199. C32C4⋊#95semidirect
227. C2×C4C4⋊#157semidirect
257. C4#63781semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊#1572
C2×C42×C3⋊D32
C2×#637812
C4⋊#959