Finite Group Databasebeta

← #13076638

Subgroups — #13076638

Order 1408.

644 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 133 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×#66983C211yesmaximal, characteristic, complemented
3#10622836C214yesmaximal, complemented
4#10622836C212yesmaximal, complemented
5#10622824C211yesmaximal, characteristic, complemented
6#10622606C212yesmaximal, complemented
7#10622573C212yesmaximal, complemented
8#10622566C212yesmaximal, complemented
9C22×D4×C11C2212yes—
10C22×D4×C11C2211yescharacteristic
11C23×C4×C11C2211yescharacteristic
12C22×C22⋊D11C2212yes—
13C22×C22⋊D11C2214yes—
14C22×D44C2211yescharacteristic
15C11×#121—24no—
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×C11×C22⋊C4C2212yes—
18C2×C22⋊Dic11C2214yes—
19C2×C22⋊Dic11C2212yes—
20#66983—24no—
21C2×(C2×D11)⋊C4C2212yes—
22C2×(C2×D11)⋊C4C2214yes—
23C2×C4⋊Dic11C2211yescharacteristic
24C11⋊#95C2212yes—
25C11⋊#95C2214yes—
26C11⋊#95C2212yes—
27C24×C11C2312yes—
28C24×C11C2311yescharacteristic
29C23×D11C2312yes—
30C2×D4×C11—24no—
31C2×D4×C11—22no—
32C2×D4×C11—42no—
33C2×D4×C11—44no—
34C22×C4×C11—42no—
35C22×C4×C11D414yescomplemented
36C22×C4×C11C2312yes—
37C22×C4×C11C2311yescharacteristic
38C22×C4×C11C2311yescharacteristic
39C2×C22⋊D11—24no—
40C2×C22⋊D11—44no—
41C2×C22⋊D11—44no—
42C2×C22⋊D11—44no—
43C2×C22⋊D11—44no—
44C22×Dic11C2314yes—
45C22×Dic11C2312yes—
46C2×D44—22no—
47C2×D44—42no—
48C11×C4⋊C4—22no—
49C11×C22⋊C4—24no—
50C22⋊Dic11—42no—
51C22⋊Dic11—44no—
52(C2×D11)⋊C4—24no—
53(C2×D11)⋊C4—44no—
54C4⋊Dic11—22no—
55#2815—111nomaximal, Sylow
56C23×C11—22no—
57C23×C11—22no—
58C23×C11—22no—
59C23×C11—22no—
60C23×C11—22no—
61C23×C11—22no—
62C23×C11—24no—
63C23×C11—24no—
64C23×C11C2×D412yes—
65C23×C11C2411yescharacteristic
66C22×D11—22no—
67C22×D11—22no—
68C22×D11—24no—
69C22×D11—22no—
70C22×D11—24no—
71D4×C11—44no—
72D4×C11—48no—
73C2×C4×C11—22no—
74C2×C4×C11—22no—
75C2×C4×C11—22no—
76C2×C4×C11—24no—
77C2×C4×C11—44no—
78C2×C4×C11C2×D412yes—
79C2×C4×C11C2×D412yes—
80C22⋊D11—48no—
81C22⋊D11—416no—
82C2×Dic11—22no—
83C2×Dic11—24no—
84C2×Dic11—24no—
85C2×Dic11—24no—
86C2×Dic11—24no—
87D44—44no—
88C2×#121—111no—
89C2×#121D1111yescharacteristic, complemented
90#397—112no—
91#397—112no—
92#392—112no—
93#392—114no—
94#392—112no—
95#381—111no—
96C22×C11—22no—
97C22×C11—22no—
98C22×C11—22no—
99C22×C11—44no—
100C22×C11—42no—
101C22×C11—42no—
102C22×C11—42no—
103C22×C11—44no—
104C22×C11—44no—
105C22×C11C22×D411yescharacteristic
106C22×C11H(5,𝔽2)12yes—
107C22×C11H(5,𝔽2)12yes—
108C22×C11H(5,𝔽2)12yes—
109C2×D11—42no—
110C2×D11—42no—
111C2×D11—42no—
112C2×D11—44no—
113C2×D11—44no—
114C4×C11—22no—
115C4×C11—22no—
116C4×C11—42no—
117Dic11—42no—
118Dic11—44no—
119C22×D4—112no—
120C22×D4—114no—
121C22×D4—111no—
122C22×D4C2×D1112yes—
123C22×D4C2×D1111yescharacteristic
124C23×C4C2×D1111yescharacteristic
125#121—24no—
126#121—224no—
127C2×C4⋊C4—111no—
128C2×C4⋊C4C2×D1111yescharacteristic
129C2×C22⋊C4—112no—
130C2×C22⋊C4—112no—
131C2×C22⋊C4—114no—
132C2×C22⋊C4—114no—
133C2×C22⋊C4C2×D1112yes—
134#95—112no—
135#95—112no—
136#95—114no—
137C2×C11—42no—
138C2×C11—82no—
139C2×C11#53411yescharacteristic
140C2×C11#53511yescharacteristic
141C2×C11#53511yescharacteristic
142C2×C11#56014yes—
143D11—82no—
144C24—112no—
145C24C22×D1112yes—
146C24C22×D1111yescharacteristic
147C2×D4—24no—
148C2×D4—22no—
149C2×D4—42no—
150C2×D4—44no—
151C2×D4—224no—
152C2×D4—222no—
153C2×D4—442no—
154C2×D4—444no—
155C2×D4—444no—
156C2×D4—444no—
157C2×D4—444no—
158C22×C4—42no—
159C22×C4—114no—
160C22×C4—112no—
161C22×C4C22⋊D1114yescomplemented
162C22×C4C22×D1112yes—
163C22×C4C22×D1111yescharacteristic
164C22×C4C22×D1111yescharacteristic
165C4⋊C4—22no—
166C4⋊C4—222no—
167C22⋊C4—24no—
168C22⋊C4—224no—
169C22⋊C4—444no—
170C22⋊C4—442no—
171C22⋊C4—444no—
172C11#281511yescharacteristic, complemented, Sylow
173C23—22no—
174C23—22no—
175C23—22no—
176C23—24no—
177C23—24no—
178C23—22no—
179C23—22no—
180C23—22no—
181C23—222no—
182C23—224no—
183C23—222no—
184C23—224no—
185C23—222no—
186C23C2×C22⋊D1112yes—
187C23C23×D1111yescharacteristic
188D4—44no—
189D4—48no—
190D4—444no—
191D4—448no—
192D4—4416no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—24no—
196C2×C4—22no—
197C2×C4—44no—
198C2×C4—224no—
199C2×C4—224no—
200C2×C4—224no—
201C2×C4—224no—
202C2×C4—222no—
203C2×C4C2×C22⋊D1112yes—
204C2×C4C2×C22⋊D1112yes—
205C22—22no—
206C22—22no—
207C22—22no—
208C22—44no—
209C22—42no—
210C22—42no—
211C22—42no—
212C22—44no—
213C22—44no—
214C22—442no—
215C22—442no—
216C22—442no—
217C22—444no—
218C22—444no—
219C22#6703712yes—
220C22#6703712yes—
221C22#6704212yes—
222C22C22×C22⋊D1111yescharacteristic
223C4—22no—
224C4—22no—
225C4—42no—
226C4—442no—
227C4—444no—
228C2—42no—
229C2—82no—
230C2—882no—
231C2#1062315114yes—
232C2#1062333511yescharacteristic
233C2#1062333611yescharacteristic
234C2#1062336111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#121C2
hypercenterC2×#121D11
hypocenterC11#2815
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×#66983C2semidirect
3. #10622836C2semidirect
4. #10622836C2semidirect
5. #10622824C2semidirect
6. #10622606C2semidirect
7. #10622573C2semidirect
8. #10622566C2semidirect
35. C22×C4×C11D4semidirect
89. C2×#121D11semidirect
161. C22×C4C22⋊D11semidirect
172. C11#2815semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1212
C2×#669832
#106228362
#106228242
#106226062
#106225732
#106225662
#281511