Finite Group Databasebeta

← #13074444

Subgroups — #13074444

Order 1408.

488 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 143 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×#66945C211yesmaximal, characteristic
2C2×#66941C211yesmaximal, characteristic, complemented
3C11×#400C211yesmaximal, characteristic, complemented
4#10622605C211yesmaximal, characteristic
5#10622599C211yesmaximal, characteristic, complemented
6#10622290C211yesmaximal, characteristic
7#10622286C212yesmaximal
8#10622280C212yesmaximal
9#10622269C212yesmaximal, complemented
10#10622263C211yesmaximal, characteristic, complemented
11#10622260C212yesmaximal, complemented
12C22×C4×D11C2211yescharacteristic
13C22×Dic22C2212yes—
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C11×C4⋊C4C2211yescharacteristic
16C2×(C2×D11)⋊C4C2211yescharacteristic
17C2×(C2×D11)⋊C4C2211yescharacteristic
18C2×(C2×D11)⋊C4C2212yes—
19C2×(C2×D11)⋊C4C2212yes—
20C2×C4⋊Dic11C2211yescharacteristic
21C2×C4⋊Dic11C2211yescharacteristic
22C2×C4⋊Dic11C2212yes—
23C2×Dic11⋊C4C2212yes—
24C2×Dic11⋊C4C2212yes—
25C2×Dic11⋊C4C2212yes—
26C2×C4×Dic11C2211yescharacteristic
27C2×C4×Dic11C2211yescharacteristic
28#66945—24no—
29#66941—24no—
30C11×#95C2212yes—
31C11×#95C2211yescharacteristic
32C11×#95C2212yes—
33C11⋊#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2211yescharacteristic
36C11⋊#95C2212yes—
37C23×D11C2311yescharacteristic
38C22×C4×C11C2311yescharacteristic
39C22×C4×C11C2312yes—
40C22×C4×C11C2312yes—
41C22×C4×C11C2311yescharacteristic
42C22×C4×C11C2311yescharacteristic
43C22×Dic11C2312yes—
44C22×Dic11C2312yes—
45C22×Dic11C2311yescharacteristic
46C22×Dic11C2311yescharacteristic
47C22×Dic11C2311yescharacteristic
48C2×C4×D11—22no—
49C2×C4×D11—22no—
50C2×C4×D11Q814yescomplemented
51C2×Dic22—24no—
52C2×Dic22—42no—
53C2×Dic22—42no—
54C11×C4⋊C4—22no—
55C11×C4⋊C4—22no—
56(C2×D11)⋊C4—22no—
57(C2×D11)⋊C4—22no—
58(C2×D11)⋊C4—42no—
59(C2×D11)⋊C4—42no—
60C4⋊Dic11—22no—
61C4⋊Dic11—22no—
62C4⋊Dic11—42no—
63Dic11⋊C4—24no—
64Dic11⋊C4—24no—
65Dic11⋊C4—42no—
66C4×Dic11—22no—
67C4×Dic11D414yes—
68#2628—111nomaximal, Sylow
69C23×C11C2411yescharacteristic
70C22×D11—21no—
71C22×D11—21no—
72C22×D11—22no—
73C22×D11—22no—
74C22×D11C2×Q812yes—
75C2×C4×C11—21no—
76C2×C4×C11—21no—
77C2×C4×C11—22no—
78C2×C4×C11—21no—
79C2×C4×C11—22no—
80C2×C4×C11—22no—
81C2×C4×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11C2×D412yes—
87C2×C4×C11C2×Q812yes—
88C2×Dic11—22no—
89C2×Dic11—21no—
90C2×Dic11—22no—
91C2×Dic11—22no—
92C2×Dic11—22no—
93C2×Dic11—22no—
94C2×Dic11—22no—
95C2×Dic11—22no—
96C2×Dic11—22no—
97C2×Dic11C2×D412yes—
98C2×Dic11C2×D412yes—
99C2×Dic11C2×Q812yes—
100C2×Dic11#4112yes—
101C4×D11—28no—
102Dic22—48no—
103C2×C4⋊Q8—111no—
104C2×#117—111no—
105#400—111no—
106#400D1111yescharacteristic, complemented
107#399—111no—
108#399—111no—
109#395—112no—
110#393—112no—
111#389—112no—
112#382—111no—
113#380—112no—
114C22×C11C22×D411yescharacteristic
115C22×C11C22×Q811yescharacteristic
116C22×C11C2×#4111yescharacteristic
117C22×C11H(5,𝔽2)12yes—
118C22×C112−1+412yes—
119C2×D11—22no—
120C2×D11—24no—
121C2×D11—41no—
122C2×D11—41no—
123C2×D11—42no—
124C4×C11—22no—
125C4×C11—22no—
126C4×C11—42no—
127C4×C11—41no—
128C4×C11—42no—
129Dic11—22no—
130Dic11—42no—
131Dic11—41no—
132Dic11—42no—
133Dic11C22⋊Q814yes—
134C22×Q8—112no—
135C23×C4—111no—
136C4⋊Q8—224no—
137#117—224no—
138C2×C4⋊C4—111no—
139C2×C4⋊C4—112no—
140C2×C4⋊C4—111no—
141C2×C4⋊C4—112no—
142C2×C4⋊C4—112no—
143C2×C4⋊C4—112no—
144C2×C4⋊C4C2×D1111yescharacteristic
145C2×C4⋊C4C2×D1111yescharacteristic
146C2×C22⋊C4—111no—
147C2×C22⋊C4—111no—
148C2×C22⋊C4—112no—
149C2×C22⋊C4—112no—
150C2×C42—111no—
151C2×C42—111no—
152#95—112no—
153#95—112no—
154#95—111no—
155#95—112no—
156#95C2×D1112yes—
157#95C2×D1111yescharacteristic
158#95C2×D1112yes—
159C2×C11C2×C22⋊Q811yescharacteristic
160C2×C11#53511yescharacteristic
161C2×C11#53611yescharacteristic
162C2×C11#54212yes—
163C2×C11#54412yes—
164D11—42no—
165C24—111no—
166C2×Q8—224no—
167C2×Q8—442no—
168C2×Q8—442no—
169C22×C4—111no—
170C22×C4—111no—
171C22×C4—114no—
172C22×C4—112no—
173C22×C4—112no—
174C22×C4—111no—
175C22×C4—222no—
176C22×C4—222no—
177C22×C4C22×D1111yescharacteristic
178C22×C4C22×D1112yes—
179C22×C4C22×D1112yes—
180C22×C4C22×D1111yescharacteristic
181C22×C4C22×D1111yescharacteristic
182C4⋊C4—22no—
183C4⋊C4—22no—
184C4⋊C4—222no—
185C4⋊C4—224no—
186C4⋊C4—224no—
187C4⋊C4—222no—
188C4⋊C4—442no—
189C4⋊C4—442no—
190C22⋊C4—222no—
191C22⋊C4—222no—
192C22⋊C4—442no—
193C22⋊C4—442no—
194C42—114no—
195C42—222no—
196C11#262811yescharacteristic, complemented, Sylow
197C23—112no—
198C23—221no—
199C23—221no—
200C23—222no—
201C23—222no—
202C23C23×D1111yescharacteristic
203Q8—448no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—112no—
216C2×C4—112no—
217C2×C4—112no—
218C2×C4—112no—
219C2×C4—228no—
220C2×C4—222no—
221C2×C4—221no—
222C2×C4—222no—
223C2×C4—222no—
224C2×C4—222no—
225C2×C4—222no—
226C2×C4—222no—
227C2×C4—222no—
228C2×C4—222no—
229C2×C4D4×D1112yes—
230C2×C4Q8×D1112yes—
231C22—222no—
232C22—224no—
233C22—442no—
234C22—441no—
235C22—441no—
236C22C2×D4×D1111yescharacteristic
237C22C2×Q8×D1111yescharacteristic
238C22#41×D1111yescharacteristic
239C22#6704212yes—
240C22#6704312yes—
241C4—22no—
242C4—22no—
243C4—42no—
244C4—41no—
245C4—42no—
246C4—114no—
247C4—222no—
248C4—442no—
249C4—442no—
250C4—441no—
251C2—442no—
252C2D11×C22⋊Q811yescharacteristic
253C2#1062317911yescharacteristic
254C2#1062320511yescharacteristic
255C2#1062322012yes—
256C2#1062324112yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#400C2
prime radicalC23×D11C23
hypercenter#400D11
hypocenterC11#2628
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
2. C2×#66941C2semidirect
3. C11×#400C2semidirect
5. #10622599C2semidirect
9. #10622269C2semidirect
10. #10622263C2semidirect
11. #10622260C2semidirect
50. C2×C4×D11Q8semidirect
106. #400D11semidirect
196. C11#2628semidirect

Maximal subgroups

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

subgroupindex
C2×#669452
C2×#669412
C11×#4002
#106226052
#106225992
#106222902
#106222862
#106222802
#106222692
#106222632
#106222602
#262811