Finite Group Databasebeta

← #13076661

Subgroups — #13076661

Order 1408.

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

normal subgroups only

This group has 580 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×#124C211yesmaximal, characteristic, complemented
2C2×#66928C211yesmaximal, characteristic, complemented
3#10622844C212yesmaximal, complemented
4#10622836C212yesmaximal, complemented
5#10622574C214yesmaximal, complemented
6#10622573C212yesmaximal, complemented
7#10622560C212yesmaximal, complemented
8#10622549C211yesmaximal, characteristic, complemented
9C22×Q8×C11C2211yescharacteristic
10C22×D4×C11C2211yescharacteristic
11C22×C22⋊D11C2214yes—
12C22×D44C2211yescharacteristic
13C22×Dic22C2211yescharacteristic
14C11×#124—24no—
15C2×C11×C22⋊C4C2212yes—
16C2×C11×C22⋊C4C2212yes—
17C2×C42×C11C2211yescharacteristic
18C2×C22⋊Dic11C2214yes—
19C2×(C2×D11)⋊C4C2212yes—
20C2×(C2×D11)⋊C4C2212yes—
21C2×(C2×D11)⋊C4C2214yes—
22C2×C4⋊Dic11C2212yes—
23#66928—24no—
24C11⋊#95C2212yes—
25C11⋊#95C2212yes—
26C11⋊#95C2214yes—
27C24×C11C2312yes—
28C23×D11C2312yes—
29C2×Q8×C11—22no—
30C2×Q8×C11—42no—
31C2×D4×C11—22no—
32C2×D4×C11—42no—
33C22×C4×C11C2312yes—
34C22×C4×C11C2311yescharacteristic
35C22×C4×C11C2311yescharacteristic
36C22×C4×C11C2311yescharacteristic
37C2×C22⋊D11—44no—
38C2×C22⋊D11—44no—
39C2×C22⋊D11—44no—
40C22×Dic11C2314yes—
41C22×Dic11C2312yes—
42C2×D44—22no—
43C2×D44—42no—
44C2×Dic22—22no—
45C2×Dic22—42no—
46C11×C22⋊C4—24no—
47C11×C22⋊C4—24no—
48C42×C11D414yescomplemented
49C22⋊Dic11—44no—
50(C2×D11)⋊C4—24no—
51(C2×D11)⋊C4—24no—
52(C2×D11)⋊C4—44no—
53C4⋊Dic11—42no—
54#2819—111nomaximal, Sylow
55C23×C11—22no—
56C23×C11—24no—
57C23×C11—22no—
58C23×C11—24no—
59C23×C11—22no—
60C23×C11C2411yescharacteristic
61C22×D11—22no—
62C22×D11—24no—
63C22×D11—24no—
64C22×D11—22no—
65C22×D11—22no—
66Q8×C11—44no—
67D4×C11—44no—
68C2×C4×C11—21no—
69C2×C4×C11—22no—
70C2×C4×C11—22no—
71C2×C4×C11—21no—
72C2×C4×C11—22no—
73C2×C4×C11—24no—
74C2×C4×C11C2×D412yes—
75C2×C4×C11C2×D412yes—
76C2×C4×C11C2×D412yes—
77C22⋊D11—416no—
78C2×Dic11—22no—
79C2×Dic11—24no—
80C2×Dic11—24no—
81C2×Dic11—24no—
82C2×Dic11—24no—
83D44—44no—
84Dic22—44no—
85C2×#124—111no—
86C2×#124D1111yescharacteristic, complemented
87#394—114no—
88#393—112no—
89#393—112no—
90#392—112no—
91#392—112no—
92#382—111no—
93C22×C11—42no—
94C22×C11—42no—
95C22×C11—42no—
96C22×C11—44no—
97C22×C11—44no—
98C22×C11C22×D411yescharacteristic
99C22×C11H(5,𝔽2)12yes—
100C22×C11H(5,𝔽2)12yes—
101C22×C11H(5,𝔽2)11yescharacteristic
102C22×C112−1+411yescharacteristic
103C2×D11—42no—
104C2×D11—42no—
105C2×D11—42no—
106C2×D11—44no—
107C2×D11—44no—
108C4×C11—22no—
109C4×C11—22no—
110C4×C11—22no—
111C4×C11—42no—
112Dic11—42no—
113Dic11—44no—
114C22×Q8—111no—
115C22×Q8C2×D1111yescharacteristic
116C22×D4—114no—
117C22×D4—111no—
118C22×D4C2×D1111yescharacteristic
119#124—24no—
120#124—224no—
121C2×C4⋊C4—112no—
122C2×C22⋊C4—112no—
123C2×C22⋊C4—112no—
124C2×C22⋊C4—114no—
125C2×C22⋊C4—114no—
126C2×C22⋊C4C2×D1112yes—
127C2×C22⋊C4C2×D1112yes—
128C2×C42C2×D1111yescharacteristic
129#95—112no—
130#95—112no—
131#95—114no—
132C2×C11—82no—
133C2×C11#53511yescharacteristic
134C2×C11#53511yescharacteristic
135C2×C11#53711yescharacteristic
136C2×C11H(3,𝔽4)12yes—
137C2×C11#56212yes—
138D11—82no—
139C24—112no—
140C24C22×D1112yes—
141C2×Q8—22no—
142C2×Q8—42no—
143C2×Q8—222no—
144C2×Q8—442no—
145C2×D4—22no—
146C2×D4—42no—
147C2×D4—222no—
148C2×D4—442no—
149C2×D4—444no—
150C2×D4—444no—
151C2×D4—444no—
152C22×C4—114no—
153C22×C4—112no—
154C22×C4C22×D1112yes—
155C22×C4C22×D1111yescharacteristic
156C22×C4C22×D1111yescharacteristic
157C22×C4C22×D1111yescharacteristic
158C4⋊C4—442no—
159C22⋊C4—24no—
160C22⋊C4—24no—
161C22⋊C4—224no—
162C22⋊C4—224no—
163C22⋊C4—444no—
164C22⋊C4—444no—
165C42C22⋊D1114yescomplemented
166C11#281911yescharacteristic, complemented, Sylow
167C23—24no—
168C23—24no—
169C23—22no—
170C23—22no—
171C23—22no—
172C23—224no—
173C23—224no—
174C23—222no—
175C23—222no—
176C23—222no—
177C23C23×D1111yescharacteristic
178Q8—44no—
179Q8—444no—
180D4—44no—
181D4—444no—
182D4—4416no—
183C2×C4—22no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—24no—
188C2×C4—22no—
189C2×C4—224no—
190C2×C4—224no—
191C2×C4—224no—
192C2×C4—224no—
193C2×C4—222no—
194C2×C4C2×C22⋊D1112yes—
195C2×C4C2×C22⋊D1112yes—
196C2×C4C2×C22⋊D1112yes—
197C22—42no—
198C22—42no—
199C22—42no—
200C22—44no—
201C22—44no—
202C22—442no—
203C22—442no—
204C22—442no—
205C22—444no—
206C22—444no—
207C22#6703712yes—
208C22#6704212yes—
209C22#6704211yescharacteristic
210C22#6704311yescharacteristic
211C22C22×C22⋊D1111yescharacteristic
212C4—22no—
213C4—22no—
214C4—22no—
215C4—42no—
216C4—442no—
217C4—444no—
218C2—82no—
219C2—882no—
220C2#1062321412yes—
221C2#1062321512yes—
222C2#1062333611yescharacteristic
223C2#1062336111yescharacteristic
224C2#1062336411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#124C2
hypercenterC2×#124D11
hypocenterC11#2819
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×C11×#124C2semidirect
2. C2×#66928C2semidirect
3. #10622844C2semidirect
4. #10622836C2semidirect
5. #10622574C2semidirect
6. #10622573C2semidirect
7. #10622560C2semidirect
8. #10622549C2semidirect
48. C42×C11D4semidirect
86. C2×#124D11semidirect
165. C42C22⋊D11semidirect
166. C11#2819semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1242
C2×#669282
#106228442
#106228362
#106225742
#106225732
#106225602
#106225492
#281911