Finite Group Databasebeta

← #13080008

Subgroups — #13080008

Order 1408.

342 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 115 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×#462C211yesmaximal, characteristic, complemented
4#10622802C212yesmaximal
5#10622795C212yesmaximal, complemented
6#10622703C211yesmaximal, characteristic, complemented
7#10622633C211yesmaximal, characteristic, complemented
8#10622464C211yesmaximal, characteristic, complemented
9#10622450C211yesmaximal, characteristic
10#10622429C212yesmaximal
11#10622404C212yesmaximal, complemented
12C2×C11×Q16C2212yes—
13C11×C4⋊Q8C2211yescharacteristic
14C4×Q8×C11C2211yescharacteristic
15#66999C2212yes—
16#66999C2211yescharacteristic
17Q8×Dic11C2212yes—
18#66997C2211yescharacteristic
19C2×#4326C2212yes—
20C2×#4313C2212yes—
21#66950—21no—
22#66950C2211yescharacteristic
23#66949—21no—
24#66945—21no—
25#66943—21no—
26#66942—21no—
27#66941C2211yescharacteristic
28#66940—21no—
29#66925—21no—
30C42×D11C2211yescharacteristic
31#66922C2211yescharacteristic
32C4×Dic22—21no—
33C4×Dic22C2211yescharacteristic
34C11×C4⋊C8C2211yescharacteristic
35C11×#103C2212yes—
36#66899C2212yes—
37#66899C2212yes—
38#66881C2212yes—
39#66880C2212yes—
40Dic11⋊C8C2212yes—
41#66872C2212yes—
42C4⋊(C11⋊C8)C2211yescharacteristic
43C2×Q8×C11C2311yescharacteristic
44C2×Q8×C11C2312yes—
45C2×C4×D11D411yescharacteristic
46C2×C4×D11D411yescharacteristic
47C2×C4×D11C2311yescharacteristic
48C2×Dic22—21no—
49C2×Dic22—21no—
50C2×Dic22C2311yescharacteristic
51C11×Q16—42no—
52C2×C8×C11C2312yes—
53C11×C4⋊C4—21no—
54C11×C4⋊C4—21no—
55C11×C4⋊C4—21no—
56C11×C4⋊C4C2311yescharacteristic
57C42×C11—21no—
58C42×C11C2311yescharacteristic
59#4326—42no—
60(C2×D11)⋊C4—21no—
61(C2×D11)⋊C4—21no—
62(C2×D11)⋊C4—22no—
63C4⋊Dic11—21no—
64C4⋊Dic11—22no—
65C4⋊Dic11—21no—
66C4⋊Dic11C2312yes—
67C4⋊Dic11C2311yescharacteristic
68Dic11⋊C4—21no—
69Dic11⋊C4—21no—
70Dic11⋊C4—21no—
71Dic11⋊C4—21no—
72Dic11⋊C4—22no—
73Dic11⋊C4—21no—
74C4×Dic11—22no—
75C4×Dic11—21no—
76C4×Dic11D411yescharacteristic
77C4×Dic11D411yescharacteristic
78C4×Dic11C2311yescharacteristic
79C2×C11⋊C8C2312yes—
80#4313—42no—
81#3255—111nomaximal, Sylow
82C22×D11C2×D411yescharacteristic
83Q8×C11—22no—
84Q8×C11—21no—
85Q8×C11—21no—
86Q8×C11—22no—
87C2×C4×C11—22no—
88C2×C4×C11—21no—
89C2×C4×C11—21no—
90C2×C4×C11C2×D411yescharacteristic
91C2×C4×C11C2×D411yescharacteristic
92C2×C4×C11C2411yescharacteristic
93C2×Dic11—21no—
94C2×Dic11—21no—
95C2×Dic11—22no—
96C2×Dic11C2×D411yescharacteristic
97C2×Dic11C2×D411yescharacteristic
98C2×Dic11C2×D411yescharacteristic
99C4×D11—22no—
100C4×D11—21no—
101C4×D11—21no—
102C4×D11—22no—
103Dic22—21no—
104Dic22—21no—
105Dic22—42no—
106Dic22—42no—
107C8×C11—22no—
108C11⋊C8—22no—
109#533—111no—
110#533—111no—
111#475—111no—
112#475—111no—
113#475—112no—
114#470—112no—
115#470—112no—
116#462—112no—
117#462—111no—
118#462D1111yescharacteristic, complemented
119#423—111no—
120C22×C11C22×D411yescharacteristic
121C2×D11—21no—
122C2×D11—21no—
123C2×D11—21no—
124C4×C11—21no—
125C4×C11—42no—
126C4×C11—41no—
127C4×C11—41no—
128C4×C11#13712yes—
129C4×C11H(5,𝔽2)11yescharacteristic
130C4×C112−1+411yescharacteristic
131Dic11—21no—
132Dic11—21no—
133Dic11—41no—
134Dic11—42no—
135Dic11—41no—
136Dic11#13712yes—
137C2×Q16—112no—
138C2×Q16C2×D1112yes—
139C2×M16—112no—
140C4⋊Q8—111no—
141C4⋊Q8—111no—
142C4⋊Q8—111no—
143C4⋊Q8C2×D1111yescharacteristic
144#125—221no—
145#125—221no—
146C22⋊Q8—111no—
147C22⋊Q8—112no—
148C22⋊Q8—111no—
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#106—112no—
160#106—112no—
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×C11C2×#13711yescharacteristic
170C2×C11C2×#13711yescharacteristic
171D11—41no—
172C2×Q8—111no—
173C2×Q8—221no—
174C2×Q8—221no—
175C2×Q8C22×D1111yescharacteristic
176C2×Q8C22×D1112yes—
177C22×C4—111no—
178C22×C4—111no—
179C22×C4—111no—
180Q16—42no—
181Q16—442no—
182M16—442no—
183C2×C8—112no—
184C2×C8C22×D1112yes—
185C4⋊C4—21no—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—111no—
189C4⋊C4—112no—
190C4⋊C4—221no—
191C4⋊C4—221no—
192C4⋊C4—222no—
193C4⋊C4—221no—
194C4⋊C4—222no—
195C4⋊C4—221no—
196C4⋊C4—221no—
197C4⋊C4—221no—
198C4⋊C4—221no—
199C4⋊C4C22×D1111yescharacteristic
200C22⋊C4—221no—
201C22⋊C4—221no—
202C22⋊C4—222no—
203C42—21no—
204C42—111no—
205C42—111no—
206C42—111no—
207C42—222no—
208C42—221no—
209C42C22×D1111yescharacteristic
210C11#325511yescharacteristic, complemented, Sylow
211C23—111no—
212Q8—21no—
213Q8—22no—
214Q8—21no—
215Q8—22no—
216Q8—221no—
217Q8—221no—
218Q8—442no—
219Q8—442no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—111no—
224C2×C4—111no—
225C2×C4—111no—
226C2×C4—222no—
227C2×C4—222no—
228C2×C4—221no—
229C2×C4—221no—
230C2×C4—222no—
231C2×C4—221no—
232C2×C4—221no—
233C2×C4D4×D1111yescharacteristic
234C2×C4D4×D1111yescharacteristic
235C2×C4C23×D1111yescharacteristic
236C8—22no—
237C8—222no—
238C22—221no—
239C22—221no—
240C22—221no—
241C22C2×D4×D1111yescharacteristic
242C4—21no—
243C4—41no—
244C4—41no—
245C4—42no—
246C4—112no—
247C4—221no—
248C4—221no—
249C4—442no—
250C4—441no—
251C4—441no—
252C4#6697112yes—
253C4#6703711yescharacteristic
254C4#6704311yescharacteristic
255C2—441no—
256C2#1062313911yescharacteristic
257C2C2×#6697111yescharacteristic
258C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#462C2
socleC22×C11C22×D4
prime radicalC22×D11C2×D4
hypercenter#462D11
hypocenterC11#3255
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
3. C11×#462C2semidirect
5. #10622795C2semidirect
6. #10622703C2semidirect
7. #10622633C2semidirect
8. #10622464C2semidirect
11. #10622404C2semidirect
118. #462D11semidirect
210. C11#3255semidirect

Maximal subgroups

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

subgroupindex
#106232592
#106231092
C11×#4622
#106228022
#106227952
#106227032
#106226332
#106224642
#106224502
#106224292
#106224042
#325511