Finite Group Databasebeta

← #13078715

Subgroups — #13078715

Order 1408.

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

normal subgroups only

This group has 444 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×C4×D4×C11C211yesmaximal, characteristic
2#10623001C211yesmaximal, characteristic, complemented
3#10622831C212yesmaximal
4#10622632C212yesmaximal, complemented
5#10622631C214yesmaximal, complemented
6#10622620C212yesmaximal, complemented
7#10622583C212yesmaximal, complemented
8#10622539C211yesmaximal, characteristic, complemented
9C22×D4×C11C2211yescharacteristic
10C23×C4×C11—21no—
11C4×D4×C11—21no—
12C4×D4×C11—21no—
13C4×D4×C11C2212yes—
14C4×D4×C11C2212yes—
15C2×C11×C4⋊C4C2211yescharacteristic
16C2×C11×C22⋊C4—21no—
17C2×C42×C11C2211yescharacteristic
18C2×#4324C2214yes—
19#66979—21no—
20#66977—21no—
21#66977C2212yes—
22#66923—21no—
23#66922C2211yescharacteristic, complemented
24#66922C2211yescharacteristic, complemented
25C4×Dic22—21no—
26C4×Dic22C2212yescomplemented
27#66896C2214yes—
28C22⋊(C11⋊C8)C2212yes—
29#66874C2214yescomplemented
30#66871C2214yescomplemented
31C4⋊(C11⋊C8)C2212yescomplemented
32#66867C2212yescomplemented
33C24×C11—21no—
34C2×D4×C11—24no—
35C2×D4×C11—21no—
36C2×D4×C11C2312yes—
37C22×C4×C11—21no—
38C22×C4×C11—22no—
39C22×C4×C11—22no—
40C22×C4×C11—44no—
41C22×C4×C11D411yescharacteristic
42C22×C4×C11D411yescharacteristic
43C22×C4×C11C2311yescharacteristic
44C2×Dic22—21no—
45C2×Dic22C2312yes—
46C11×C4⋊C4—21no—
47C11×C4⋊C4C2312yes—
48C11×C22⋊C4—22no—
49C11×C22⋊C4—22no—
50C42×C11D411yescharacteristic
51C42×C11D411yescharacteristic
52C42×C11C2311yescharacteristic
53C42×C11C2311yescharacteristic
54C22⋊Dic11—22no—
55#4324—28no—
56C4⋊Dic11—21no—
57C4⋊Dic11—21no—
58C4⋊Dic11—21no—
59C4⋊Dic11C2312yes—
60Dic11⋊C4—22no—
61Dic11⋊C4—22no—
62C4×Dic11—22no—
63C2×C11⋊C8C2314yes—
64#3110—111nomaximal, Sylow
65C23×C11—24no—
66C23×C11—22no—
67C23×C11—42no—
68C23×C11—42no—
69C23×C11C2×D411yescharacteristic
70D4×C11—24no—
71D4×C11—22no—
72D4×C11#4114yes—
73C2×C4×C11—22no—
74C2×C4×C11—22no—
75C2×C4×C11—22no—
76C2×C4×C11—22no—
77C2×C4×C11—44no—
78C2×C4×C11—42no—
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
86C2×Dic11—22no—
87C2×Dic11—22no—
88Dic22—24no—
89Dic22—42no—
90C11⋊C8—24no—
91#533—111no—
92C2×C4×D4D1111yescharacteristic
93#484—112no—
94#474—112no—
95#461—112no—
96#450—112no—
97#440—114no—
98#432—111no—
99C22×C11—21no—
100C22×C11—21no—
101C22×C11—24no—
102C22×C11—48no—
103C22×C11—42no—
104C22×C11—42no—
105C22×C11#13712yes—
106C22×C11C22×D411yescharacteristic
107C4×C11—21no—
108C4×C11—21no—
109C4×C11—21no—
110C4×C11—21no—
111C4×C11—42no—
112C4×C11AGL(1,ℤ/8)12yes—
113C4×C11C2×#4112yes—
114Dic11—42no—
115Dic11—42no—
116C22×D4C2×D1111yescharacteristic
117C23×C4—21no—
118C2×SD16—114no—
119C4⋊Q8—111no—
120C4⋊Q8—111no—
121#125—221no—
122C22⋊Q8—112no—
123C22⋊Q8—221no—
124C4×Q8—112no—
125C4×Q8—221no—
126C4×D4—21no—
127C4×D4—21no—
128C4×D4C2×D1112yes—
129C4×D4C2×D1112yes—
130#117—221no—
131C2×C4⋊C4C2×D1111yescharacteristic
132C2×C22⋊C4—21no—
133C2×C42C2×D1111yescharacteristic
134#107—114no—
135C4⋊C8—112no—
136#103—114no—
137#102—114no—
138C22⋊C8—112no—
139#97—112no—
140C2×C11—22no—
141C2×C11—44no—
142C2×C11#52511yescharacteristic
143C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
144C2×C11C2×#13711yescharacteristic
145C24—21no—
146C2×Q8—112no—
147C2×Q8—221no—
148C2×D4—24no—
149C2×D4—21no—
150C2×D4C22×D1112yes—
151C22×C4—21no—
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—44no—
155C22×C4C22⋊D1111yescharacteristic
156C22×C4C22⋊D1111yescharacteristic
157C22×C4C22×D1111yescharacteristic
158SD16—228no—
159C2×C8—114no—
160C4⋊C4—21no—
161C4⋊C4—112no—
162C4⋊C4—221no—
163C4⋊C4—221no—
164C4⋊C4—222no—
165C4⋊C4—222no—
166C4⋊C4—221no—
167C4⋊C4C22×D1112yes—
168C22⋊C4—22no—
169C22⋊C4—22no—
170C22⋊C4—222no—
171C42—222no—
172C42C22⋊D1111yescharacteristic
173C42C22⋊D1111yescharacteristic
174C42C22×D1111yescharacteristic
175C42C22×D1111yescharacteristic
176C11#311011yescharacteristic, complemented, Sylow
177C23—24no—
178C23—22no—
179C23—42no—
180C23—42no—
181C23C2×C22⋊D1111yescharacteristic
182Q8—224no—
183Q8—442no—
184D4—24no—
185D4—22no—
186D4#433914yes—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—44no—
192C2×C4—42no—
193C2×C4—44no—
194C2×C4—222no—
195C2×C4—222no—
196C2×C4C2×C22⋊D1111yescharacteristic
197C2×C4C2×C22⋊D1111yescharacteristic
198C2×C4C2×C22⋊D1111yescharacteristic
199C2×C4C2×C22⋊D1111yescharacteristic
200C2×C4C2×C22⋊D1111yescharacteristic
201C2×C4C23×D1111yescharacteristic
202C8—224no—
203C22—21no—
204C22—21no—
205C22—24no—
206C22—48no—
207C22—42no—
208C22—42no—
209C22#6700412yes—
210C22C22×C22⋊D1111yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—21no—
215C4—42no—
216C4—442no—
217C4—442no—
218C4#6698512yes—
219C4C2×#433912yes—
220C2—22no—
221C2—44no—
222C2#1062332211yescharacteristic
223C2C2×#6698511yescharacteristic
224C2C2×#6700411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C4×D4×C11C2
socleC22×C11C22×D4
prime radicalC22×D4×C11C22
hypercenterC2×C4×D4D11
hypocenterC11#3110
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. #10623001C2semidirect
4. #10622632C2semidirect
5. #10622631C2semidirect
6. #10622620C2semidirect
7. #10622583C2semidirect
8. #10622539C2semidirect
23. #66922C22semidirect
24. #66922C22semidirect
26. C4×Dic22C22semidirect
29. #66874C22semidirect
30. #66871C22semidirect
31. C4⋊(C11⋊C8)C22semidirect
32. #66867C22semidirect
176. C11#3110semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×C112
#106230012
#106228312
#106226322
#106226312
#106226202
#106225832
#106225392
#311011