Finite Group Databasebeta

← #13079960

Subgroups — #13079960

Order 1408.

348 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 121 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
1#10623259C211yesmaximal, characteristic
2#10623109C211yesmaximal, characteristic
3C11×#477C211yesmaximal, characteristic, complemented
4#10622704C211yesmaximal, characteristic, complemented
5#10622644C211yesmaximal, characteristic, complemented
6#10622500C212yesmaximal
7#10622488C212yesmaximal, complemented
8#10622462C211yesmaximal, characteristic, complemented
9D11×C4⋊C8C211yesmaximal, characteristic
10#10622426C212yesmaximal
11#10622406C212yesmaximal, complemented
12C11×C4⋊Q8C2211yescharacteristic
13C4×Q8×C11C2211yescharacteristic
14#66999—21no—
15#66999C2211yescharacteristic
16Q8×Dic11—21no—
17#66997C2211yescharacteristic
18C2×#4326C2212yes—
19C2×Dic44C2212yes—
20C2×C8×D11C2212yes—
21#66950C2212yes—
22#66950C2211yescharacteristic
23#66949—21no—
24#66945—21no—
25#66943—21no—
26#66942—21no—
27#66941C2211yescharacteristic
28#66940C2212yes—
29#66925—21no—
30C42×D11C2211yescharacteristic
31#66922C2211yescharacteristic
32C4×Dic22—21no—
33C4×Dic22C2211yescharacteristic
34C11×#107C2212yes—
35C11×C4⋊C8C2211yescharacteristic
36C11×#103C2212yes—
37#66880C2212yes—
38Dic11⋊C8C2212yes—
39#66874C2212yes—
40#66874C2212yes—
41#66871C2212yes—
42C4⋊(C11⋊C8)C2211yescharacteristic
43C2×Q8×C11—21no—
44C2×Q8×C11C2311yescharacteristic
45C2×C4×D11D411yescharacteristic
46C2×C4×D11D411yescharacteristic
47C2×C4×D11C2311yescharacteristic
48C2×Dic22—21no—
49C2×Dic22C2311yescharacteristic
50C2×Dic22C2312yes—
51C2×C8×C11C2312yes—
52C11×C4⋊C4—21no—
53C11×C4⋊C4—21no—
54C11×C4⋊C4C2312yes—
55C11×C4⋊C4C2311yescharacteristic
56C42×C11—21no—
57C42×C11C2311yescharacteristic
58#4326—42no—
59(C2×D11)⋊C4—21no—
60(C2×D11)⋊C4—21no—
61(C2×D11)⋊C4—22no—
62C4⋊Dic11—21no—
63C4⋊Dic11—22no—
64C4⋊Dic11—21no—
65C4⋊Dic11—21no—
66C4⋊Dic11C2311yescharacteristic
67Dic11⋊C4—21no—
68Dic11⋊C4—21no—
69Dic11⋊C4—21no—
70Dic11⋊C4—21no—
71Dic11⋊C4—22no—
72Dic11⋊C4—21no—
73C4×Dic11—22no—
74C4×Dic11—21no—
75C4×Dic11D411yescharacteristic
76C4×Dic11D411yescharacteristic
77C4×Dic11C2311yescharacteristic
78C2×C11⋊C8C2312yes—
79Dic44—42no—
80C8×D11—42no—
81#3249—111nomaximal, Sylow
82C22×D11C2×D411yescharacteristic
83Q8×C11—21no—
84Q8×C11—21no—
85Q8×C11—42no—
86C2×C4×C11—22no—
87C2×C4×C11—21no—
88C2×C4×C11—21no—
89C2×C4×C11C2×D411yescharacteristic
90C2×C4×C11C2×D411yescharacteristic
91C2×C4×C11C2411yescharacteristic
92C2×Dic11—21no—
93C2×Dic11—21no—
94C2×Dic11—22no—
95C2×Dic11C2×D411yescharacteristic
96C2×Dic11C2×D411yescharacteristic
97C2×Dic11C2×D411yescharacteristic
98C4×D11—21no—
99C4×D11—21no—
100C4×D11—41no—
101C4×D11Q1614yescomplemented
102Dic22—21no—
103Dic22—22no—
104Dic22—21no—
105Dic22—22no—
106Dic22—42no—
107C8×C11—22no—
108C11⋊C8—22no—
109#533—111no—
110#533—111no—
111#477—111no—
112#477—112no—
113#477D1111yescharacteristic, complemented
114#467—112no—
115#467—112no—
116#462—111no—
117#462—111no—
118#462—112no—
119C2×C4⋊C8—111no—
120C22×C11C22×D411yescharacteristic
121C2×D11—21no—
122C2×D11—21no—
123C2×D11C2×Q1612yes—
124C4×C11—21no—
125C4×C11—41no—
126C4×C11—42no—
127C4×C11—41no—
128C4×C11C2×Q1612yes—
129C4×C11H(5,𝔽2)11yescharacteristic
130C4×C112−1+411yescharacteristic
131Dic11—21no—
132Dic11—21no—
133Dic11—41no—
134Dic11—42no—
135Dic11—41no—
136Dic11C2×Q1612yes—
137C2×Q16—112no—
138C2×Q16—112no—
139C22×C8—112no—
140C4⋊Q8—111no—
141C4⋊Q8—111no—
142C4⋊Q8—111no—
143C4⋊Q8C2×D1111yescharacteristic
144#125—221no—
145#125—221no—
146C22⋊Q8—111no—
147C22⋊Q8—111no—
148C22⋊Q8—112no—
149C22⋊Q8—221no—
150C22⋊Q8—221no—
151C4×Q8—112no—
152C4×Q8—111no—
153C4×Q8—221no—
154C4×Q8—221no—
155C4×Q8C2×D1111yescharacteristic
156#117—221no—
157#117—221no—
158C2×C42—111no—
159#107—112no—
160#107C2×D1112yes—
161C4⋊C8—112no—
162C4⋊C8—111no—
163C4⋊C8C2×D1111yescharacteristic
164#103—112no—
165#103—112no—
166#103—112no—
167#103C2×D1112yes—
168C2×C11#53711yescharacteristic
169C2×C11C22×Q1611yescharacteristic
170C2×C11#57511yescharacteristic
171D11—22no—
172C2×Q8—21no—
173C2×Q8—112no—
174C2×Q8—111no—
175C2×Q8—221no—
176C2×Q8C22×D1111yescharacteristic
177C22×C4—111no—
178C22×C4—111no—
179C22×C4—111no—
180Q16—442no—
181Q16—442no—
182C2×C8—112no—
183C2×C8—442no—
184C2×C8C22×D1112yes—
185C4⋊C4—21no—
186C4⋊C4—21no—
187C4⋊C4—111no—
188C4⋊C4—221no—
189C4⋊C4—221no—
190C4⋊C4—222no—
191C4⋊C4—221no—
192C4⋊C4—221no—
193C4⋊C4—222no—
194C4⋊C4—221no—
195C4⋊C4—221no—
196C4⋊C4—221no—
197C4⋊C4—221no—
198C4⋊C4C22×D1111yescharacteristic
199C4⋊C4C22×D1112yes—
200C22⋊C4—221no—
201C22⋊C4—221no—
202C22⋊C4—222no—
203C42—21no—
204C42—111no—
205C42—111no—
206C42—111no—
207C42—222no—
208C42—221no—
209C42C22×D1111yescharacteristic
210C11#324911yescharacteristic, complemented, Sylow
211C23—111no—
212Q8—21no—
213Q8—21no—
214Q8—42no—
215Q8—222no—
216Q8—221no—
217Q8—221no—
218Q8—222no—
219Q8—442no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—111no—
224C2×C4—114no—
225C2×C4—111no—
226C2×C4—111no—
227C2×C4—221no—
228C2×C4—221no—
229C2×C4—221no—
230C2×C4—222no—
231C2×C4—221no—
232C2×C4—441no—
233C2×C4D4×D1111yescharacteristic
234C2×C4D4×D1111yescharacteristic
235C2×C4C23×D1111yescharacteristic
236C8—22no—
237C8—222no—
238C22—112no—
239C22—221no—
240C22—221no—
241C22C2×D4×D1111yescharacteristic
242C4—21no—
243C4—42no—
244C4—41no—
245C4—41no—
246C4—112no—
247C4—221no—
248C4—221no—
249C4—441no—
250C4—442no—
251C4—441no—
252C4Q16×D1112yes—
253C4#6704011yescharacteristic
254C4#6704211yescharacteristic
255C2—222no—
256C2#1062316011yescharacteristic
257C2C2×Q16×D1111yescharacteristic
258C2#1062330411yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#477C2
socleC22×C11C22×D4
prime radicalC22×D11C2×D4
hypercenter#477D11
hypocenterC11#3249
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
3. C11×#477C2semidirect
4. #10622704C2semidirect
5. #10622644C2semidirect
7. #10622488C2semidirect
8. #10622462C2semidirect
11. #10622406C2semidirect
101. C4×D11Q16semidirect
113. #477D11semidirect
210. C11#3249semidirect

Maximal subgroups

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

subgroupindex
#106232592
#106231092
C11×#4772
#106227042
#106226442
#106225002
#106224882
#106224622
D11×C4⋊C82
#106224262
#106224062
#324911