Finite Group Databasebeta

← C2×#13066649 #14664944

Subgroups — C2×#13066649 #14664944

Order 2816.

366 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 99 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×#10622104C212yesmaximal, complemented
2#13066649C214yesmaximal, direct product factor
3C2×C11×#490C211yesmaximal, characteristic
4C2×C11×#127C411yescharacteristic
5C2×C11×#125C411yescharacteristic
6C11×#490—22no—
7C11×#490C412yes—
8C11×#490C2212yes—
9C2×C11×#102—22no—
10C2×C11×#97C2211yescharacteristic
11C2×#66876—22no—
12#10622104—22no—
13#10622104C2214yescomplemented
14C22×D4×C11—21no—
15C22×D4×C11—41no—
16C22×C8×C11D412yes—
17C11×#127—21no—
18C11×#127—41no—
19C11×#127C2×C412yes—
20C11×#125—21no—
21C11×#125—41no—
22C11×#125C2×C412yes—
23C2×C11×C4⋊C4—21no—
24C2×C11×C4⋊C4—41no—
25C2×C42×C11C2×C411yescharacteristic
26C11×#102—24no—
27C11×#102—24no—
28C11×#97C2×C411yescharacteristic
29C11×#97D412yes—
30C11×#97C2311yescharacteristic
31#66876—24no—
32#66876—24no—
33C2×C11⋊C16—24no—
34C2×#1355—111nomaximal, Sylow
35C24×C11—41no—
36C2×D4×C11—22no—
37C2×D4×C11—42no—
38C2×D4×C11—42no—
39C2×D4×C11—41no—
40C2×D4×C11—42no—
41C2×D4×C11—42no—
42C2×D4×C11—84no—
43C22×C4×C11—21no—
44C22×C4×C11—41no—
45C22×C4×C11C22⋊C411yescharacteristic
46C2×C8×C11—22no—
47C2×C8×C11—22no—
48C2×C8×C11C22⋊C412yes—
49C2×C8×C11C2×D412yes—
50C11×C4⋊C4—22no—
51C11×C4⋊C4—42no—
52C11×C4⋊C4—42no—
53C11×C4⋊C4—41no—
54C42×C11—21no—
55C42×C11C22⋊C411yescharacteristic
56C42×C11C22×C411yescharacteristic
57C11⋊C16—28no—
58C2×#490D1111yescharacteristic
59C2×#347—112no—
60#1355—114no—
61C23×C11—42no—
62C23×C11—84no—
63C23×C11—81no—
64C23×C11—81no—
65C23×C11#10011yescharacteristic
66D4×C11—44no—
67D4×C11—84no—
68D4×C11—84no—
69D4×C11—82no—
70C2×C4×C11—21no—
71C2×C4×C11—21no—
72C2×C4×C11—42no—
73C2×C4×C11—42no—
74C2×C4×C11—82no—
75C2×C4×C11#10011yescharacteristic
76C2×C4×C11#10412yes—
77C2×C4×C11#10412yes—
78C2×C4×C11C2×C22⋊C411yescharacteristic
79C8×C11—22no—
80C8×C11—22no—
81C2×#127Dic1111yescharacteristic
82C2×#125Dic1111yescharacteristic
83C2×M32—222no—
84#490—22no—
85#490Dic1112yes—
86#490C2×D1112yes—
87C2×#102—22no—
88C2×#97C2×D1111yescharacteristic
89#347—114no—
90#347—222no—
91C22×C11—22no—
92C22×C11—84no—
93C22×C11—82no—
94C22×C11—162no—
95C22×C11—162no—
96C22×C11#32911yescharacteristic
97C22×C11#32911yescharacteristic
98C22×C11C2×#10011yescharacteristic
99C4×C11—41no—
100C4×C11—41no—
101C4×C11—82no—
102C4×C11#32912yes—
103C4×C11C2×#10412yes—
104C22×D4—21no—
105C22×D4—41no—
106C22×C8C22⋊D1112yes—
107#127—21no—
108#127—41no—
109#127C2×Dic1112yes—
110#125—21no—
111#125—41no—
112#125C2×Dic1112yes—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—41no—
115C2×C42C2×Dic1111yescharacteristic
116M32—224no—
117M32—224no—
118C2×C16—224no—
119#102—24no—
120#102—24no—
121#97C2×Dic1111yescharacteristic
122#97C22⋊D1112yes—
123#97C22×D1111yescharacteristic
124C2×C11—21no—
125C2×C11—21no—
126C2×C11—162no—
127C2×C11#135512yescomplemented
128C2×C11C2×#32911yescharacteristic
129C24—41no—
130C2×D4—22no—
131C2×D4—42no—
132C2×D4—42no—
133C2×D4—41no—
134C2×D4—42no—
135C2×D4—42no—
136C2×D4—84no—
137C22×C4—21no—
138C22×C4—41no—
139C22×C4C22⋊Dic1111yescharacteristic
140C2×C8—22no—
141C2×C8—22no—
142C2×C8C22⋊Dic1112yes—
143C2×C8C2×C22⋊D1112yes—
144C4⋊C4—22no—
145C4⋊C4—42no—
146C4⋊C4—42no—
147C4⋊C4—41no—
148C42—21no—
149C42C22⋊Dic1111yescharacteristic
150C42C22×Dic1111yescharacteristic
151C16—228no—
152C11C2×#135511yescharacteristic, complemented, Sylow
153C23—42no—
154C23—84no—
155C23—81no—
156C23—81no—
157C23#6689711yescharacteristic
158D4—44no—
159D4—84no—
160D4—84no—
161D4—82no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—82no—
167C2×C4#6689711yescharacteristic
168C2×C4#6690112yes—
169C2×C4#6690112yes—
170C2×C4C2×C22⋊Dic1111yescharacteristic
171C8—22no—
172C8—22no—
173C22—22no—
174C22—84no—
175C22—82no—
176C22—162no—
177C22—162no—
178C22#1062217811yescharacteristic
179C22#1062217811yescharacteristic
180C22C2×#6689711yescharacteristic
181C4—41no—
182C4—41no—
183C4—82no—
184C4#1062217812yes—
185C4C2×#6690112yes—
186C2—21no—
187C2—21no—
188C2—162no—
189C2#1306664912yesdirect product factor
190C2C2×#1062217811yescharacteristic
subgroupG/H
centerC22#10622178
commutatorC42×C11C22×C4
Frattini#97C22×D11
FittingC2×C11×#490C2
socleC22×C11#329
prime radicalC2×C11×#127C4
cosocleC11×#97C23
hypercenterC2×#490D11
hypocenterC11C2×#1355
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#97 ◁ C2×#490

Complements

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

NH ≅ G/Ntype
1. C2×#10622104C2semidirect
2. #13066649C2direct (N × H)
13. #10622104C22semidirect
127. C2×C11#1355semidirect
152. C11C2×#1355semidirect
189. C2#13066649direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106221042
#130666492
C2×C11×#4902
C2×#135511