Finite Group Databasebeta

← #13069788

Subgroups — #13069788

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#10623001C211yesmaximal, characteristic, complemented
2C2×C11×#104C211yesmaximal, characteristic
3#10622853C211yesmaximal, characteristic
4#10622849C211yesmaximal, characteristic
5#10622197C211yesmaximal, characteristic, complemented
6#10622195C211yesmaximal, characteristic, complemented
7#10622161C211yesmaximal, characteristic, complemented
8C2×C11×#41C2211yescharacteristic
9C2×C11×M16C2211yescharacteristic
10C2×C42×C11C2211yescharacteristic
11#66979C2211yescharacteristic
12#66979C2211yescharacteristic
13#66979C2211yescharacteristic
14#66977—22no—
15C2×#4318C2211yescharacteristic
16#66923—21no—
17#66922—21no—
18C4×Dic22—22no—
19C11×#104—21no—
20C11×#104—21no—
21#66901—22no—
22#66898—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×C11—21no—
32C22×C4×C11C2311yescharacteristic
33C2×Dic22—22no—
34C11×M16—21no—
35C11×M16—21no—
36C2×C8×C11—21no—
37C42×C11—21no—
38C42×C11D411yescharacteristic
39C42×C11D411yescharacteristic
40C22⋊Dic11—21no—
41C22⋊Dic11—21no—
42C22⋊Dic11D412yes—
43C4⋊Dic11—22no—
44C4⋊Dic11—21no—
45C4⋊Dic11—21no—
46C4⋊Dic11—21no—
47Dic11⋊C4—24no—
48C4×Dic11—21no—
49C4×Dic11—21no—
50C4×Dic11D412yes—
51#4318—21no—
52#4318—21no—
53C2×C11⋊C8—21no—
54#2031—111nomaximal, Sylow
55C23×C11—21no—
56C23×C11C2×D411yescharacteristic
57Q8×C11—21no—
58Q8×C11—21no—
59D4×C11—21no—
60D4×C11—21no—
61D4×C11—41no—
62D4×C11—41no—
63C2×C4×C11—21no—
64C2×C4×C11—21no—
65C2×C4×C11—21no—
66C2×C4×C11—42no—
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—22no—
76C2×Dic11—22no—
77C2×Dic11—41no—
78Dic22—44no—
79C8×C11—41no—
80C11⋊C8—41no—
81#533—111no—
82#421—111no—
83C2×#104D1111yescharacteristic
84#410—111no—
85#344—111no—
86#339—111no—
87H(3,ℤ/4)—111no—
88C22×C11—41no—
89C22×C11—41no—
90C22×C11—81no—
91C22×C11#12011yescharacteristic
92C22×C11C22⋊Q811yescharacteristic
93C22×C11#12411yescharacteristic
94C4×C11—22no—
95C4×C11—41no—
96C4×C11—41no—
97C4×C11C22⋊Q811yescharacteristic
98C4×C11C22⋊Q811yescharacteristic
99C4×C11#12411yescharacteristic
100C4×C11#12411yescharacteristic
101Dic11—42no—
102Dic11—42no—
103Dic11—81no—
104C2×#41C2×D1111yescharacteristic
105C2×M16—111no—
106C2×M16C2×D1111yescharacteristic
107C4⋊Q8—221no—
108#125—221no—
109C22⋊Q8—222no—
110C4×Q8—222no—
111#117—111no—
112#117—111no—
113#117—111no—
114C2×C42C2×D1111yescharacteristic
115#104—21no—
116#104—21no—
117#104—222no—
118#99—222no—
119C2×C11—21no—
120C2×C11—21no—
121C2×C11—21no—
122C2×C11—81no—
123C2×C11#39311yescharacteristic
124#41—21no—
125#41—21no—
126#41—21no—
127#41—21no—
128C2×Q8—222no—
129C2×Q8Dic2211yescharacteristic, complemented
130C2×D4—21no—
131C2×D4Dic2211yescharacteristic, complemented
132C22×C4—21no—
133C22×C4—21no—
134C22×C4C22×D1111yescharacteristic
135M16—21no—
136M16—21no—
137M16—221no—
138M16—221no—
139C2×C8—21no—
140C2×C8—221no—
141C4⋊C4—224no—
142C4⋊C4—222no—
143C4⋊C4—221no—
144C4⋊C4—221no—
145C4⋊C4—221no—
146C22⋊C4—112no—
147C22⋊C4—221no—
148C22⋊C4—221no—
149C42—21no—
150C42—112no—
151C42—221no—
152C42—221no—
153C42C22⋊D1111yescharacteristic
154C42C22⋊D1111yescharacteristic
155C11#203111yescharacteristic, complemented, Sylow
156C23—21no—
157C23D4×D1111yescharacteristic
158Q8—21no—
159Q8—21no—
160Q8—444no—
161D4—21no—
162D4—21no—
163D4—41no—
164D4—41no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—42no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—222no—
172C2×C4—222no—
173C2×C4—441no—
174C2×C4C2×Dic2211yescharacteristic
175C2×C4#433911yescharacteristic
176C2×C4D4×D1111yescharacteristic
177C2×C4#434111yescharacteristic
178C2×C4#434111yescharacteristic
179C2×C4C2×C22⋊D1111yescharacteristic
180C8—41no—
181C8—441no—
182C22—41no—
183C22—41no—
184C22—81no—
185C22#6693111yescharacteristic
186C22#6693811yescharacteristic
187C22#6699011yescharacteristic
188C4—22no—
189C4—41no—
190C4—41no—
191C4—442no—
192C4—442no—
193C4—881no—
194C4#6693111yescharacteristic
195C4#6693811yescharacteristic
196C4#6697711yescharacteristic
197C4#6698911yescharacteristic
198C2—21no—
199C2—21no—
200C2—21no—
201C2—81no—
202C2#1062256011yescharacteristic
subgroupG/H
centerC4#66938
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC2×C11×#104C2
socleC2×C11#393
prime radicalC2×C11×#41C22
hypercenterC2×#104D11
hypocenterC11#2031
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
1. #10623001C2semidirect
5. #10622197C2semidirect
6. #10622195C2semidirect
7. #10622161C2semidirect
27. C2×Q8×C11Q8semidirect
29. C2×D4×C11Q8semidirect
129. C2×Q8Dic22semidirect
131. C2×D4Dic22semidirect
155. C11#2031semidirect

Maximal subgroups

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

subgroupindex
#106230012
C2×C11×#1042
#106228532
#106228492
#106221972
#106221952
#106221612
#203111