Finite Group Databasebeta

← #13069790

Subgroups — #13069790

Order 1408.

244 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 65 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#10623048C211yesmaximal, characteristic, complemented
2C11×#410C211yesmaximal, characteristic
3#10622849C211yesmaximal, characteristic
4C2×#66901C211yesmaximal, characteristic
5#10622171C211yesmaximal, characteristic, complemented
6#10622170C211yesmaximal, characteristic, complemented
7#10622169C211yesmaximal, characteristic, complemented
8C2×C11×#41C2211yescharacteristic
9C11×#117C2211yescharacteristic
10C11×#117C2211yescharacteristic
11#66979C2211yescharacteristic
12C2×C4×Dic11C2211yescharacteristic
13C2×#4318C2211yescharacteristic
14C2×#4318C2211yescharacteristic
15#66943—21no—
16#66941—21no—
17#66931—22no—
18C4×Dic22—22no—
19C11×#99—22no—
20#66901—21no—
21#66901—21no—
22#66901—22no—
23C11×#41—21no—
24C11×#41—21no—
25C11×#41—21no—
26C11×#41—21no—
27C2×Q8×C11Q811yescharacteristic, complemented
28C2×D4×C11—21no—
29C2×D4×C11Q811yescharacteristic, complemented
30C22×C4×C11—21no—
31C22×C4×C11C2311yescharacteristic
32C22×Dic11—21no—
33C2×Dic22—22no—
34C11×C4⋊C4—21no—
35C11×C4⋊C4—21no—
36C11×C22⋊C4—21no—
37C11×C22⋊C4D412yes—
38C42×C11—21no—
39C42×C11—21no—
40C22⋊Dic11—21no—
41C4⋊Dic11—22no—
42C4⋊Dic11—21no—
43Dic11⋊C4—22no—
44Dic11⋊C4—22no—
45C4×Dic11—21no—
46C4×Dic11D412yes—
47C4×Dic11D411yescharacteristic
48C4×Dic11D411yescharacteristic
49#4318—21no—
50#4318—21no—
51#4318—21no—
52#4318—21no—
53C2×C11⋊C8—21no—
54C2×C11⋊C8—21no—
55#2031—111nomaximal, Sylow
56C23×C11—21no—
57C23×C11C2×D411yescharacteristic
58Q8×C11—21no—
59Q8×C11—21no—
60D4×C11—21no—
61D4×C11—21no—
62D4×C11—41no—
63D4×C11—41no—
64C2×C4×C11—22no—
65C2×C4×C11—21no—
66C2×C4×C11—41no—
67C2×C4×C11—41no—
68C2×C4×C11—41no—
69C2×C4×C11C2×D411yescharacteristic
70C2×C4×C11C2×D411yescharacteristic
71C2×C4×C11C2×Q811yescharacteristic
72C2×C4×C11#4111yescharacteristic
73C2×C4×C11#4111yescharacteristic
74C2×C4×C11#4111yescharacteristic
75C2×Dic11—21no—
76C2×Dic11—21no—
77C2×Dic11—22no—
78C2×Dic11—42no—
79Dic22—44no—
80C11⋊C8—41no—
81C11⋊C8—41no—
82#533—111no—
83#421—111no—
84C2×#104—111no—
85#410D1111yescharacteristic
86#344—111no—
87#339—111no—
88H(3,ℤ/4)—111no—
89C22×C11—41no—
90C22×C11—41no—
91C22×C11—81no—
92C22×C11#12011yescharacteristic
93C22×C11C22⋊Q811yescharacteristic
94C22×C11#12411yescharacteristic
95C4×C11—42no—
96C4×C11—41no—
97C4×C11—81no—
98C4×C11C22⋊Q811yescharacteristic
99C4×C11C22⋊Q811yescharacteristic
100C4×C11#12411yescharacteristic
101C4×C11#12411yescharacteristic
102Dic11—22no—
103Dic11—42no—
104Dic11—41no—
105C2×#41C2×D1111yescharacteristic
106C2×M16—111no—
107C2×M16—111no—
108C4⋊Q8—221no—
109#125—221no—
110C22⋊Q8—222no—
111C4×Q8—222no—
112#117—111no—
113#117C2×D1111yescharacteristic
114#117C2×D1111yescharacteristic
115C2×C42—111no—
116#104—221no—
117#104—221no—
118#104—222no—
119#99—22no—
120C2×C11—21no—
121C2×C11—21no—
122C2×C11—21no—
123C2×C11—81no—
124C2×C11#39311yescharacteristic
125#41—21no—
126#41—21no—
127#41—21no—
128#41—21no—
129C2×Q8—222no—
130C2×Q8Dic2211yescharacteristic, complemented
131C2×D4—21no—
132C2×D4Dic2211yescharacteristic, complemented
133C22×C4—21no—
134C22×C4—221no—
135C22×C4C22×D1111yescharacteristic
136M16—221no—
137M16—221no—
138M16—221no—
139M16—221no—
140C2×C8—221no—
141C2×C8—221no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—222no—
145C4⋊C4—222no—
146C4⋊C4—222no—
147C4⋊C4—221no—
148C22⋊C4—21no—
149C22⋊C4—221no—
150C22⋊C4C22⋊D1112yes—
151C42—21no—
152C42—21no—
153C42—111no—
154C42—111no—
155C42—112no—
156C42—221no—
157C11#203111yescharacteristic, complemented, Sylow
158C23—21no—
159C23C2×C22⋊D1111yescharacteristic
160Q8—21no—
161Q8—21no—
162Q8—444no—
163D4—21no—
164D4—21no—
165D4—41no—
166D4—41no—
167C2×C4—21no—
168C2×C4—22no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—221no—
173C2×C4—221no—
174C2×C4—222no—
175C2×C4—442no—
176C2×C4C2×Dic2211yescharacteristic
177C2×C4#433911yescharacteristic
178C2×C4D4×D1111yescharacteristic
179C2×C4D4×D1111yescharacteristic
180C2×C4#434111yescharacteristic
181C2×C4#434111yescharacteristic
182C8—441no—
183C8—441no—
184C22—41no—
185C22—41no—
186C22—81no—
187C22#6697711yescharacteristic
188C22#6698911yescharacteristic
189C22#6699011yescharacteristic
190C4—42no—
191C4—41no—
192C4—81no—
193C4—222no—
194C4—441no—
195C4—442no—
196C4#6693111yescharacteristic
197C4#6693111yescharacteristic
198C4#6693811yescharacteristic
199C4#6693811yescharacteristic
200C2—21no—
201C2—21no—
202C2—21no—
203C2—81no—
204C2#1062256011yescharacteristic
subgroupG/H
centerC4#66938
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#410C2
socleC2×C11#393
prime radicalC2×C11×#41C22
hypercenter#410D11
hypocenterC11#2031
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
1. #10623048C2semidirect
5. #10622171C2semidirect
6. #10622170C2semidirect
7. #10622169C2semidirect
27. C2×Q8×C11Q8semidirect
29. C2×D4×C11Q8semidirect
130. C2×Q8Dic22semidirect
132. C2×D4Dic22semidirect
157. C11#2031semidirect

Maximal subgroups

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

subgroupindex
#106230482
C11×#4102
#106228492
C2×#669012
#106221712
#106221702
#106221692
#203111