Finite Group Databasebeta

← #13074720

Subgroups — #13074720

Order 1408.

804 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 804 conjugacy classes of subgroups — too many to draw. Only its 165 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×C11×#121C211yesmaximal, characteristic, complemented
2C2×#66992C214yesmaximal, complemented
3C2×#66983C211yesmaximal, characteristic, complemented
4#10622836C212yesmaximal, complemented
5C2×C11⋊#95C211yesmaximal, characteristic, complemented
6#10622605C212yesmaximal, complemented
7#10622573C212yesmaximal, complemented
8#10622562C212yesmaximal, complemented
9C22×D4×C11C2212yes—
10C22×D4×C11C2211yescharacteristic
11C23×C4×C11C2211yescharacteristic
12C22×C22⋊D11C2212yes—
13C22×C22⋊D11C2214yes—
14C23×Dic11C2212yes—
15C22×D44C2211yescharacteristic
16C11×#121—24no—
17C2×C11×C4⋊C4C2211yescharacteristic
18C2×C11×C22⋊C4C2212yes—
19C2×C22⋊Dic11C2214yes—
20#66992—216no—
21#66983—24no—
22C2×(C2×D11)⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2214yes—
24C2×C4⋊Dic11C2211yescharacteristic
25C2×Dic11⋊C4C2214yes—
26C11⋊#95C2212yes—
27C11⋊#95C2212yes—
28C24×C11C2312yes—
29C24×C11C2311yescharacteristic
30C23×D11C2312yes—
31C2×D4×C11—28no—
32C2×D4×C11—24no—
33C2×D4×C11—22no—
34C2×D4×C11—42no—
35C22×C4×C11—42no—
36C22×C4×C11D414yescomplemented
37C22×C4×C11C2312yes—
38C22×C4×C11C2311yescharacteristic
39C22×C4×C11C2311yescharacteristic
40C2×C22⋊D11—28no—
41C2×C22⋊D11—24no—
42C2×C22⋊D11—28no—
43C2×C22⋊D11—44no—
44C2×C22⋊D11—44no—
45C22×Dic11—42no—
46C22×Dic11—42no—
47C22×Dic11D418yescomplemented
48C22×Dic11C2312yes—
49C22×Dic11C2314yes—
50C2×D44—22no—
51C2×D44—42no—
52C11×C4⋊C4—22no—
53C11×C22⋊C4—24no—
54C22⋊Dic11—28no—
55(C2×D11)⋊C4—28no—
56(C2×D11)⋊C4—24no—
57C4⋊Dic11—22no—
58Dic11⋊C4—28no—
59#2656—111nomaximal, Sylow
60C23×C11—21no—
61C23×C11—22no—
62C23×C11—21no—
63C23×C11—24no—
64C23×C11—22no—
65C23×C11—22no—
66C23×C11—24no—
67C23×C11—22no—
68C23×C11C2×D414yes—
69C23×C11C2×D412yes—
70C23×C11C2411yescharacteristic
71C22×D11—22no—
72C22×D11—24no—
73C22×D11—24no—
74C22×D11—22no—
75C22×D11—22no—
76D4×C11—44no—
77D4×C11—48no—
78C2×C4×C11—22no—
79C2×C4×C11—22no—
80C2×C4×C11—24no—
81C2×C4×C11—22no—
82C2×C4×C11—44no—
83C2×C4×C11C2×D412yes—
84C2×C4×C11C2×D412yes—
85C22⋊D11—416no—
86C22⋊D11—48no—
87C2×Dic11—24no—
88C2×Dic11—24no—
89C2×Dic11—24no—
90C2×Dic11—22no—
91C2×Dic11—48no—
92C2×Dic11C2×D418yes—
93D44—44no—
94C2×#121—114no—
95C2×#121—111no—
96C2×#121D1111yescharacteristic, complemented
97#399—112no—
98#399—112no—
99#392—112no—
100#392—112no—
101C2×#95—111no—
102C22×C11—22no—
103C22×C11—24no—
104C22×C11—22no—
105C22×C11—24no—
106C22×C11—42no—
107C22×C11—42no—
108C22×C11—44no—
109C22×C11—42no—
110C22×C11—44no—
111C22×C11#12714yes—
112C22×C11C22×D412yes—
113C22×C11C22×D411yescharacteristic
114C22×C11H(5,𝔽2)12yes—
115C22×C11H(5,𝔽2)11yescharacteristic
116C22×C112−1+411yescharacteristic
117C2×D11—42no—
118C2×D11—42no—
119C2×D11—44no—
120C2×D11—42no—
121C2×D11—44no—
122C4×C11—22no—
123C4×C11—22no—
124C4×C11—42no—
125Dic11—28no—
126Dic11—42no—
127C22×D4—112no—
128C22×D4—114no—
129C22×D4—111no—
130C22×D4C2×D1112yes—
131C22×D4C2×D1111yescharacteristic
132C23×C4—112no—
133C23×C4C2×D1111yescharacteristic
134#121—24no—
135#121—2216no—
136#121—224no—
137C2×C4⋊C4—114no—
138C2×C4⋊C4—111no—
139C2×C4⋊C4C2×D1111yescharacteristic
140C2×C22⋊C4—114no—
141C2×C22⋊C4—114no—
142C2×C22⋊C4—112no—
143C2×C22⋊C4C2×D1112yes—
144#95—112no—
145#95—112no—
146C2×C11—24no—
147C2×C11—82no—
148C2×C11C2×#12711yescharacteristic
149C2×C11#53411yescharacteristic
150C2×C11#53412yes—
151C2×C11#53711yescharacteristic
152C2×C11#53712yes—
153D11—82no—
154C24—112no—
155C24C22×D1112yes—
156C24C22×D1111yescharacteristic
157C2×D4—28no—
158C2×D4—24no—
159C2×D4—22no—
160C2×D4—42no—
161C2×D4—228no—
162C2×D4—228no—
163C2×D4—224no—
164C2×D4—222no—
165C2×D4—442no—
166C2×D4—444no—
167C2×D4—444no—
168C22×C4—42no—
169C22×C4—114no—
170C22×C4—118no—
171C22×C4—112no—
172C22×C4—442no—
173C22×C4—442no—
174C22×C4C22⋊D1114yescomplemented
175C22×C4C22×D1112yes—
176C22×C4C22×D1111yescharacteristic
177C22×C4C22×D1111yescharacteristic
178C4⋊C4—22no—
179C4⋊C4—228no—
180C4⋊C4—222no—
181C22⋊C4—24no—
182C22⋊C4—228no—
183C22⋊C4—228no—
184C22⋊C4—224no—
185C11#265611yescharacteristic, complemented, Sylow
186C23—22no—
187C23—21no—
188C23—21no—
189C23—24no—
190C23—24no—
191C23—22no—
192C23—22no—
193C23—22no—
194C23—224no—
195C23—224no—
196C23—222no—
197C23—222no—
198C23—222no—
199C23D4×D1114yes—
200C23C2×C22⋊D1112yes—
201C23C23×D1111yescharacteristic
202D4—44no—
203D4—48no—
204D4—444no—
205D4—4416no—
206D4—448no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—24no—
210C2×C4—22no—
211C2×C4—44no—
212C2×C4—118no—
213C2×C4—224no—
214C2×C4—224no—
215C2×C4—224no—
216C2×C4—222no—
217C2×C4—448no—
218C2×C4C2×C22⋊D1112yes—
219C2×C4C2×C22⋊D1112yes—
220C22—22no—
221C22—22no—
222C22—24no—
223C22—24no—
224C22—42no—
225C22—42no—
226C22—42no—
227C22—44no—
228C22—44no—
229C22—442no—
230C22—442no—
231C22—442no—
232C22—444no—
233C22—444no—
234C22#6699314yes—
235C22C2×D4×D1112yes—
236C22#6703712yes—
237C22#6704211yescharacteristic
238C22#6704311yescharacteristic
239C22C22×C22⋊D1111yescharacteristic
240C4—22no—
241C4—22no—
242C4—42no—
243C4—228no—
244C4—442no—
245C2—24no—
246C2—82no—
247C2—882no—
248C2#1062312812yes—
249C2#1062313612yes—
250C2C2×#6699311yescharacteristic
251C2#1062333511yescharacteristic
252C2#1062336411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#121C2
hypercenterC2×#121D11
hypocenterC11#2656
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×C11×#121C2semidirect
2. C2×#66992C2semidirect
3. C2×#66983C2semidirect
4. #10622836C2semidirect
5. C2×C11⋊#95C2semidirect
6. #10622605C2semidirect
7. #10622573C2semidirect
8. #10622562C2semidirect
36. C22×C4×C11D4semidirect
47. C22×Dic11D4semidirect
96. C2×#121D11semidirect
174. C22×C4C22⋊D11semidirect
185. C11#2656semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1212
C2×#669922
C2×#669832
#106228362
C2×C11⋊#952
#106226052
#106225732
#106225622
#265611