Finite Group Databasebeta

← #13079643

Subgroups — #13079643

Order 1408.

386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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×C4⋊Q8C211yesmaximal, characteristic, complemented
2#10623010C211yesmaximal, characteristic
3#10622841C212yesmaximal, complemented
4#10622840C212yesmaximal
5#10622703C212yesmaximal, complemented
6#10622699C212yesmaximal, complemented
7#10622696C212yesmaximal, complemented
8#10622695C212yesmaximal, complemented
9#10622539C211yesmaximal, characteristic, complemented
10C22×Q8×C11C2212yes—
11C11×C4⋊Q8—21no—
12C11×C4⋊Q8—21no—
13C11×C4⋊Q8C2212yes—
14C11×C4⋊Q8C2212yes—
15C2×C11×C4⋊C4—21no—
16C2×C11×C4⋊C4—21no—
17C2×C42×C11C2211yescharacteristic
18C2×#4326C2214yes—
19C2×#4325C2214yes—
20#66983C2211yescharacteristic
21#66982—21no—
22C4×C22⋊D11—21no—
23#66977C2211yescharacteristic
24#66929—21no—
25#66928C2211yescharacteristic
26C4×D44C2211yescharacteristic
27#66925—21no—
28#66923C2211yescharacteristic
29C4×Dic22C2211yescharacteristic
30#66899C2214yes—
31#66899C2214yes—
32C22⋊(C11⋊C8)C2212yes—
33C4⋊(C11⋊C8)C2212yes—
34#66867C2212yes—
35C2×Q8×C11—22no—
36C2×Q8×C11—44no—
37C2×Q8×C11C2314yes—
38C22×C4×C11—22no—
39C22×C4×C11D411yescharacteristic
40C22×C4×C11D411yescharacteristic
41C22×C4×C11C2311yescharacteristic
42C2×C22⋊D11—21no—
43C2×D44C2311yescharacteristic
44C2×C4×D11—21no—
45C2×Dic22C2311yescharacteristic
46C11×C4⋊C4—22no—
47C11×C4⋊C4—22no—
48C11×C4⋊C4—22no—
49C11×C4⋊C4—22no—
50C42×C11D411yescharacteristic
51C42×C11D411yescharacteristic
52C42×C11C2311yescharacteristic
53C42×C11C2311yescharacteristic
54C22⋊Dic11—21no—
55#4326—44no—
56#4325—44no—
57(C2×D11)⋊C4—21no—
58(C2×D11)⋊C4—21no—
59(C2×D11)⋊C4—21no—
60(C2×D11)⋊C4—21no—
61C4⋊Dic11C2311yescharacteristic
62C4⋊Dic11C2311yescharacteristic
63Dic11⋊C4—21no—
64Dic11⋊C4—21no—
65Dic11⋊C4—21no—
66Dic11⋊C4—21no—
67C4×Dic11—21no—
68C2×C11⋊C8C2314yes—
69#3218—111nomaximal, Sylow
70C23×C11C2×D411yescharacteristic
71C22×D11—21no—
72Q8×C11—24no—
73Q8×C11—24no—
74Q8×C11—44no—
75C2×C4×C11—22no—
76C2×C4×C11—22no—
77C2×C4×C11—22no—
78C2×C4×C11—24no—
79C2×C4×C11—44no—
80C2×C4×C11C2×D411yescharacteristic
81C2×C4×C11C2×D411yescharacteristic
82C2×C4×C11C2×D411yescharacteristic
83C2×C4×C11C2×D411yescharacteristic
84C2×C4×C11C2×D411yescharacteristic
85C2×C4×C11C2411yescharacteristic
86C22⋊D11—42no—
87C2×Dic11—21no—
88C2×Dic11—21no—
89C2×Dic11—21no—
90D44—22no—
91C4×D11—42no—
92Dic22—22no—
93C11⋊C8—24no—
94C2×C4⋊Q8D1111yescharacteristic, complemented
95#529—111no—
96#497—112no—
97#491—112no—
98#462—112no—
99#461—112no—
100#451—112no—
101#448—112no—
102#432—111no—
103C22×C11—21no—
104C22×C11—21no—
105C22×C11#13712yes—
106C22×C11C22×D411yescharacteristic
107C2×D11—41no—
108C2×D11—41no—
109C2×D11—41no—
110C4×C11—21no—
111C4×C11—21no—
112C4×C11—21no—
113C4×C11—21no—
114C4×C11—44no—
115C4×C11#13712yes—
116C4×C11H(5,𝔽2)12yes—
117Dic11—41no—
118Dic11—41no—
119Dic11—41no—
120C22×Q8C2×D1112yes—
121C2×Q16—114no—
122C2×SD16—114no—
123C4⋊Q8—21no—
124C4⋊Q8—21no—
125C4⋊Q8C2×D1112yes—
126C4⋊Q8C2×D1112yes—
127#126—221no—
128#125—111no—
129#124—111no—
130#123—221no—
131C22⋊Q8—111no—
132#121—111no—
133C4×Q8—111no—
134C4×D4—111no—
135C4×D4—221no—
136#117—221no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—21no—
139C2×C42C2×D1111yescharacteristic
140C4⋊C8—112no—
141#103—114no—
142#103—114no—
143C22⋊C8—112no—
144#97—112no—
145C2×C11—22no—
146C2×C11#53511yescharacteristic
147C2×C11C2×#13711yescharacteristic
148C2×C11C2×#13711yescharacteristic
149D11—81no—
150C2×Q8—22no—
151C2×Q8—44no—
152C2×Q8—111no—
153C2×Q8C22×D1114yes—
154C2×D4—111no—
155C2×D4—221no—
156C22×C4—22no—
157C22×C4—221no—
158C22×C4C22⋊D1111yescharacteristic
159C22×C4C22⋊D1111yescharacteristic
160C22×C4C22×D1111yescharacteristic
161Q16—444no—
162SD16—444no—
163C2×C8—114no—
164C4⋊C4—22no—
165C4⋊C4—22no—
166C4⋊C4—22no—
167C4⋊C4—22no—
168C4⋊C4—111no—
169C4⋊C4—111no—
170C4⋊C4—221no—
171C4⋊C4—221no—
172C4⋊C4—221no—
173C4⋊C4—221no—
174C22⋊C4—221no—
175C22⋊C4—221no—
176C22⋊C4—221no—
177C22⋊C4—221no—
178C22⋊C4—221no—
179C42—221no—
180C42C22⋊D1111yescharacteristic
181C42C22⋊D1111yescharacteristic
182C42C22×D1111yescharacteristic
183C42C22×D1111yescharacteristic
184C11#321811yescharacteristic, complemented, Sylow
185C23—221no—
186C23C2×C22⋊D1111yescharacteristic
187Q8—24no—
188Q8—24no—
189Q8—44no—
190Q8—222no—
191D4—222no—
192D4—442no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—24no—
197C2×C4—44no—
198C2×C4—221no—
199C2×C4—221no—
200C2×C4—221no—
201C2×C4—442no—
202C2×C4C2×C22⋊D1111yescharacteristic
203C2×C4C2×C22⋊D1111yescharacteristic
204C2×C4C2×C22⋊D1111yescharacteristic
205C2×C4C2×C22⋊D1111yescharacteristic
206C2×C4C2×C22⋊D1111yescharacteristic
207C2×C4C23×D1111yescharacteristic
208C8—224no—
209C22—21no—
210C22—21no—
211C22—441no—
212C22—441no—
213C22—441no—
214C22#6699512yes—
215C22C22×C22⋊D1111yescharacteristic
216C4—21no—
217C4—21no—
218C4—21no—
219C4—21no—
220C4—44no—
221C4—441no—
222C4—441no—
223C4—441no—
224C4#6699512yes—
225C4#6703712yes—
226C2—22no—
227C2—881no—
228C2#1062333611yescharacteristic
229C2C2×#6699511yescharacteristic
230C2C2×#6699511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C11×C4⋊Q8C2
socleC22×C11C22×D4
prime radical#66983C22
hypercenterC2×C4⋊Q8D11
hypocenterC11#3218
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C11×C4⋊Q8C2semidirect
3. #10622841C2semidirect
5. #10622703C2semidirect
6. #10622699C2semidirect
7. #10622696C2semidirect
8. #10622695C2semidirect
9. #10622539C2semidirect
94. C2×C4⋊Q8D11semidirect
184. C11#3218semidirect

Maximal subgroups

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

subgroupindex
C2×C11×C4⋊Q82
#106230102
#106228412
#106228402
#106227032
#106226992
#106226962
#106226952
#106225392
#321811