Finite Group Databasebeta

← #13069776

Subgroups — #13069776

Order 1408.

246 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 67 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#10623050C211yesmaximal, characteristic
2#10622733C211yesmaximal, characteristic
3#10622617C211yesmaximal, characteristic
4#10622542C211yesmaximal, characteristic
5C11×#339C211yesmaximal, characteristic
6#10622192C211yesmaximal, characteristic
7#10622161C211yesmaximal, characteristic
8C22×Dic22C2211yescharacteristic
9C2×C11×M16C2211yescharacteristic
10C11×#117C2211yescharacteristic
11C2×C42×C11C2211yescharacteristic
12#66979C2211yescharacteristic
13C2×C4⋊Dic11C2211yescharacteristic
14C2×#4318C2211yescharacteristic
15#66943—21no—
16#66941—21no—
17#66931—22no—
18#66923—21no—
19#66922—21no—
20C11⋊#95—22no—
21#66880—21no—
22#66880—21no—
23#66874—21no—
24#66874—21no—
25C22×C4×C11—21no—
26C22×C4×C11C2311yescharacteristic
27C22×Dic11—21no—
28C22×Dic11D412yes—
29C2×Dic22—22no—
30C2×Dic22—21no—
31C2×Dic22—21no—
32C2×Dic22—21no—
33C2×Dic22—21no—
34C2×Dic22—21no—
35C2×Dic22Q812yescomplemented
36C11×M16—21no—
37C11×M16—21no—
38C2×C8×C11—21no—
39C11×C4⋊C4D411yescharacteristic
40C11×C4⋊C4D411yescharacteristic
41C11×C22⋊C4—21no—
42C42×C11—21no—
43C42×C11—21no—
44C42×C11—21no—
45C22⋊Dic11—21no—
46C4⋊Dic11—22no—
47C4⋊Dic11—21no—
48C4⋊Dic11—21no—
49C4⋊Dic11D411yescharacteristic
50C4⋊Dic11D411yescharacteristic
51Dic11⋊C4—22no—
52Dic11⋊C4—22no—
53C4×Dic11—21no—
54#4318—21no—
55#4318—21no—
56C2×C11⋊C8—21no—
57#2028—111nomaximal, Sylow
58C23×C11C2×D411yescharacteristic
59C2×C4×C11—22no—
60C2×C4×C11—21no—
61C2×C4×C11—21no—
62C2×C4×C11—41no—
63C2×C4×C11—41no—
64C2×C4×C11C2×D411yescharacteristic
65C2×C4×C11C2×D411yescharacteristic
66C2×C4×C11C2×Q811yescharacteristic
67C2×C4×C11#4111yescharacteristic
68C2×C4×C11#4111yescharacteristic
69C2×C4×C11#4111yescharacteristic
70C2×Dic11—21no—
71C2×Dic11—21no—
72C2×Dic11—22no—
73C2×Dic11—22no—
74C2×Dic11—41no—
75C2×Dic11—41no—
76C2×Dic11—42no—
77Dic22—22no—
78Dic22—22no—
79Dic22—41no—
80Dic22—41no—
81Dic22—82no—
82C8×C11—41no—
83C11⋊C8—41no—
84#544—111no—
85#419—111no—
86#419—111no—
87#391—111no—
88#343—111no—
89#339—111no—
90#339D1111yescharacteristic
91C22×C11—21no—
92C22×C11—21no—
93C22×C11#12011yescharacteristic
94C22×C11C22⋊Q811yescharacteristic
95C22×C11#12411yescharacteristic
96C4×C11—42no—
97C4×C11—41no—
98C4×C11—41no—
99C4×C11C22⋊Q811yescharacteristic
100C4×C11C22⋊Q811yescharacteristic
101C4×C11#12411yescharacteristic
102C4×C11#12411yescharacteristic
103Dic11—42no—
104Dic11—41no—
105Dic11—42no—
106Dic11—41no—
107C22×Q8—111no—
108C2×M16—111no—
109C2×M16C2×D1111yescharacteristic
110C4⋊Q8—221no—
111C4⋊Q8—221no—
112#125—221no—
113#125—221no—
114C22⋊Q8—222no—
115#117—111no—
116#117C2×D1111yescharacteristic
117C2×C4⋊C4—111no—
118C2×C42C2×D1111yescharacteristic
119#103—221no—
120#103—221no—
121#103—221no—
122#103—221no—
123#95—222no—
124C2×C11—21no—
125C2×C11—21no—
126C2×C11#39311yescharacteristic
127C2×C11#45511yescharacteristic
128C2×C11#45611yescharacteristic
129C2×Q8—112no—
130C2×Q8—222no—
131C2×Q8—221no—
132C2×Q8—221no—
133C2×Q8—221no—
134C2×Q8—221no—
135C2×Q8—221no—
136C22×C4—21no—
137C22×C4—112no—
138C22×C4—221no—
139C22×C4C22×D1111yescharacteristic
140M16—21no—
141M16—21no—
142M16—221no—
143M16—221no—
144C2×C8—21no—
145C2×C8—221no—
146C4⋊C4—111no—
147C4⋊C4—111no—
148C4⋊C4—222no—
149C4⋊C4—222no—
150C4⋊C4—222no—
151C4⋊C4—221no—
152C4⋊C4—221no—
153C4⋊C4D4411yescharacteristic
154C4⋊C4D4411yescharacteristic
155C22⋊C4—21no—
156C22⋊C4—221no—
157C42—21no—
158C42—21no—
159C42—21no—
160C42—221no—
161C11#202811yescharacteristic, complemented, Sylow
162C23D4×D1111yescharacteristic
163Q8—222no—
164Q8—222no—
165Q8—441no—
166Q8—441no—
167Q8—882no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—221no—
174C2×C4—221no—
175C2×C4—222no—
176C2×C4—222no—
177C2×C4—441no—
178C2×C4—441no—
179C2×C4—442no—
180C2×C4C2×D4411yescharacteristic
181C2×C4#433911yescharacteristic
182C2×C4#433911yescharacteristic
183C2×C4D4×D1111yescharacteristic
184C2×C4#434111yescharacteristic
185C2×C4Q8×D1111yescharacteristic
186C8—41no—
187C8—441no—
188C22—21no—
189C22—21no—
190C22#6693511yescharacteristic
191C22#6693811yescharacteristic
192C22#6694911yescharacteristic
193C4—42no—
194C4—41no—
195C4—41no—
196C4—442no—
197C4—442no—
198C4—441no—
199C4—441no—
200C4#6692811yescharacteristic
201C4#6693811yescharacteristic
202C4#6694911yescharacteristic
203C4#6695011yescharacteristic
204C2—21no—
205C2—21no—
206C2#1062228611yescharacteristic
207C2#1062243811yescharacteristic
208C2#1062243911yescharacteristic
subgroupG/H
centerC22#66935
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#339C2
socleC22×C11#120
prime radicalC23×C11C2×D4
hypercenter#339D11
hypocenterC11#2028
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
35. C2×Dic22Q8semidirect
161. C11#2028semidirect

Maximal subgroups

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

subgroupindex
#106230502
#106227332
#106226172
#106225422
C11×#3392
#106221922
#106221612
#202811