Finite Group Databasebeta

← #13079403

Subgroups — #13079403

Order 1408.

424 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 113 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#10623137C212yesmaximal, complemented
2C11×#466C211yesmaximal, characteristic, complemented
3#10622771C212yesmaximal, complemented
4#10622729C211yesmaximal, characteristic, complemented
5C2×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
6#10622654C212yesmaximal, complemented
7#10622501C212yesmaximal, complemented
8#10622397C212yesmaximal, complemented
9#10622396C212yesmaximal, complemented
10C2×#4341C2212yes—
11C22×C4×D11C2211yescharacteristic
12C2×C11×D8C2211yescharacteristic, complemented
13C22×C8×C11C2211yescharacteristic
14C11×#121C2212yes—
15#66991C2212yes—
16#66990—22no—
17D4×Dic11—22no—
18C2×#4324C2212yescomplemented
19#66977C2212yes—
20C22×C11⋊C8C2211yescharacteristic
21C2×Dic44C2211yescharacteristic, complemented
22#66950C2212yes—
23#66945C2212yes—
24#66936—22no—
25(C22⋊D11)⋊C4—22no—
26C11×#107C2211yescharacteristic, complemented
27C11×#102C2212yescomplemented
28#66896C2212yescomplemented
29(C2×D11)⋊C8C2212yes—
30(C2×D11)⋊C8C2212yes—
31#66882C2211yescharacteristic, complemented
32#66880C2212yescomplemented
33#66874C2212yescomplemented
34#66872C2212yescomplemented
35C23×D11D411yescharacteristic
36C2×D4×C11—22no—
37C2×D4×C11C2312yes—
38C22×C4×C11C2311yescharacteristic
39C2×C22⋊D11—22no—
40C2×C22⋊D11—22no—
41C22×Dic11—22no—
42C22×Dic11D411yescharacteristic
43#4341—42no—
44#4341—42no—
45C2×C4×D11—41no—
46C2×C4×D11—41no—
47C2×C4×D11D412yes—
48C2×C4×D11C2312yes—
49C2×Dic22C2312yes—
50C11×D8—41no—
51C2×C8×C11—41no—
52C2×C8×C11C2311yescharacteristic
53C2×C8×C11C2311yescharacteristic
54C11×C4⋊C4C2312yes—
55C11×C22⋊C4—22no—
56C22⋊Dic11—22no—
57C22⋊Dic11—22no—
58#4324—42no—
59(C2×D11)⋊C4—22no—
60(C2×D11)⋊C4—22no—
61C4⋊Dic11—22no—
62C4⋊Dic11C2312yes—
63Dic11⋊C4—22no—
64C4×Dic11—22no—
65C2×C11⋊C8—41no—
66C2×C11⋊C8C2312yes—
67Dic44—41no—
68#3191—111nomaximal, Sylow
69C23×C11—22no—
70C23×C11C2×D411yescharacteristic
71C22×D11—22no—
72C22×D11—41no—
73C22×D11—41no—
74C22×D11C2×D412yes—
75D4×C11—22no—
76D4×C11—22no—
77D4×C11—44no—
78C2×C4×C11—21no—
79C2×C4×C11—21no—
80C2×C4×C11—22no—
81C2×C4×C11C2×D411yescharacteristic
82C2×C4×C11C2411yescharacteristic
83C22⋊D11—44no—
84C22⋊D11—44no—
85C2×Dic11—22no—
86C2×Dic11—22no—
87C2×Dic11—41no—
88C2×Dic11—44no—
89C2×Dic11C2×D412yes—
90C4×D11—22no—
91C4×D11—22no—
92C4×D11—42no—
93Dic22—22no—
94Dic22—22no—
95C8×C11—21no—
96C8×C11—21no—
97C11⋊C8—22no—
98#525—112no—
99#485—112no—
100#482—112no—
101#467—111no—
102#466D1111yescharacteristic, complemented
103#465—112no—
104#452—112no—
105#449—112no—
106C2×C22⋊C8—111no—
107C22×C11—21no—
108C22×C11—21no—
109C22×C11—42no—
110C22×C11—42no—
111C22×C11—42no—
112C22×C11#13512yes—
113C22×C11C22×D411yescharacteristic
114C2×D11—22no—
115C2×D11—22no—
116C2×D11—22no—
117C2×D11—44no—
118C4×C11—21no—
119C4×C11—42no—
120C4×C11H(5,𝔽2)11yescharacteristic
121C4×C11H(5,𝔽2)11yescharacteristic
122Dic11—22no—
123Dic11—42no—
124Dic11—42no—
125C2×#41—112no—
126C23×C4—111no—
127C2×Q16—111no—
128C2×SD16—112no—
129C2×D8C2×D1111yescharacteristic, complemented
130C22×C8—111no—
131C22×C8C2×D1111yescharacteristic
132#123—222no—
133C22⋊Q8—112no—
134C22⋊Q8—112no—
135#121—112no—
136#121C2×D1112yes—
137#120—222no—
138C4×D4—222no—
139C4×D4—222no—
140#117—112no—
141#107—111no—
142#107C2×D1111yescharacteristic, complemented
143#106—112no—
144#103—112no—
145#103—112no—
146#102—112no—
147#102C2×D1112yescomplemented
148C22⋊C8—112no—
149C22⋊C8—112no—
150C2×C11—22no—
151C2×C11—82no—
152C2×C11#53411yescharacteristic
153C2×C11C2×#13511yescharacteristic
154C2×C11#57511yescharacteristic
155D11—42no—
156C24—111no—
157#41—442no—
158#41—442no—
159C2×Q8—112no—
160C2×D4—22no—
161C2×D4—222no—
162C2×D4—222no—
163C2×D4C22×D1112yes—
164C22×C4—111no—
165C22×C4—112no—
166C22×C4—112no—
167C22×C4—222no—
168C22×C4—441no—
169C22×C4—441no—
170C22×C4C22×D1111yescharacteristic
171Q16—441no—
172SD16—442no—
173D8—41no—
174C2×C8—41no—
175C2×C8—112no—
176C2×C8—441no—
177C2×C8C22×D1111yescharacteristic
178C2×C8C22×D1111yescharacteristic
179C4⋊C4—112no—
180C4⋊C4—222no—
181C4⋊C4—222no—
182C4⋊C4C22×D1112yes—
183C22⋊C4—22no—
184C22⋊C4—222no—
185C22⋊C4—222no—
186C22⋊C4—222no—
187C22⋊C4—222no—
188C42—222no—
189C11#319111yescharacteristic, complemented, Sylow
190C23—22no—
191C23—112no—
192C23—222no—
193C23—441no—
194C23—441no—
195C23D4×D1111yescharacteristic
196Q8—222no—
197Q8—222no—
198D4—22no—
199D4—22no—
200D4—44no—
201D4—444no—
202D4—444no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—112no—
207C2×C4—222no—
208C2×C4—222no—
209C2×C4—222no—
210C2×C4—222no—
211C2×C4—442no—
212C2×C4—441no—
213C2×C4—444no—
214C2×C4D4×D1111yescharacteristic
215C2×C4C23×D1111yescharacteristic
216C8—21no—
217C8—21no—
218C8—222no—
219C22—21no—
220C22—21no—
221C22—42no—
222C22—42no—
223C22—42no—
224C22—222no—
225C22—222no—
226C22—222no—
227C22—444no—
228C22#6696512yes—
229C22C2×D4×D1111yescharacteristic
230C4—21no—
231C4—42no—
232C4—222no—
233C4—442no—
234C4—442no—
235C4#6703711yescharacteristic
236C4#6704211yescharacteristic
237C2—22no—
238C2—82no—
239C2—442no—
240C2#1062313611yescharacteristic
241C2C2×#6696511yescharacteristic
242C2#1062329911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#466C2
socleC22×C11C22×D4
hypercenter#466D11
hypocenterC11#3191
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #10623137C2semidirect
2. C11×#466C2semidirect
3. #10622771C2semidirect
4. #10622729C2semidirect
5. C2×(C2×D11)⋊C8C2semidirect
6. #10622654C2semidirect
7. #10622501C2semidirect
8. #10622397C2semidirect
9. #10622396C2semidirect
12. C2×C11×D8C22semidirect
18. C2×#4324C22semidirect
21. C2×Dic44C22semidirect
26. C11×#107C22semidirect
27. C11×#102C22semidirect
28. #66896C22semidirect
31. #66882C22semidirect
32. #66880C22semidirect
33. #66874C22semidirect
34. #66872C22semidirect
102. #466D11semidirect
129. C2×D8C2×D11semidirect
142. #107C2×D11semidirect
147. #102C2×D11semidirect
189. C11#3191semidirect

Maximal subgroups

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

subgroupindex
#106231372
C11×#4662
#106227712
#106227292
C2×(C2×D11)⋊C82
#106226542
#106225012
#106223972
#106223962
#319111