Finite Group Databasebeta

← C2×#13066787 #14674118

Subgroups — C2×#13066787 #14674118

Order 2816.

390 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 83 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×#10622183C212yesmaximal
2#13066787C214yesmaximal, direct product factor
3C2×C11×#490C211yesmaximal, characteristic
4C2×C11×#127C2211yescharacteristic
5C2×C11×#125C411yescharacteristic, complemented
6C11×#490—22no—
7C11×#490C412yescomplemented
8C11×#490C2212yes—
9C2×C11×#102—22no—
10C2×C11×#97C411yescharacteristic, complemented
11C2×#66898—22no—
12#10622183—22no—
13#10622183C2214yes—
14C22×D4×C11—41no—
15C22×D4×C11D412yes—
16C22×C8×C11—21no—
17C11×#127—41no—
18C11×#127C2×C411yescharacteristic
19C11×#127D412yes—
20C11×#127C2311yescharacteristic
21C11×#125—21no—
22C11×#125—41no—
23C11×#125C2×C412yescomplemented
24C2×C11×C4⋊C4—21no—
25C2×C11×C4⋊C4—41no—
26C2×C42×C11C2×C411yescharacteristic
27C2×C22⋊Dic11—42no—
28C11×#102—24no—
29C11×#102—24no—
30C11×#97—21no—
31C11×#97C2×C412yescomplemented
32#66898—24no—
33#66898—42no—
34C2×#1412—111nomaximal, Sylow
35C24×C11—22no—
36C2×D4×C11—22no—
37C2×D4×C11—42no—
38C2×D4×C11—42no—
39C2×D4×C11—41no—
40C2×D4×C11—42no—
41C2×D4×C11—41no—
42C2×D4×C11—84no—
43C2×D4×C11C22⋊C412yes—
44C2×D4×C11C2×D412yes—
45C22×C4×C11—21no—
46C22×C4×C11—41no—
47C22×C4×C11C22⋊C411yescharacteristic
48C22×Dic11—82no—
49C2×C8×C11—22no—
50C2×C8×C11—41no—
51C2×C8×C11—41no—
52C11×C4⋊C4—22no—
53C11×C4⋊C4—42no—
54C11×C4⋊C4—42no—
55C11×C4⋊C4—41no—
56C42×C11—21no—
57C42×C11C22⋊C411yescharacteristic
58C42×C11C22×C411yescharacteristic
59C22⋊Dic11—44no—
60C22⋊Dic11—82no—
61C2×#490D1111yescharacteristic
62C2×#353—112no—
63#1412—114no—
64C23×C11—22no—
65C23×C11—22no—
66C23×C11—42no—
67C23×C11—42no—
68C23×C11—84no—
69C23×C11#9911yescharacteristic
70D4×C11—42no—
71D4×C11—42no—
72D4×C11—82no—
73D4×C11—82no—
74D4×C11—84no—
75D4×C11—82no—
76C2×C4×C11—21no—
77C2×C4×C11—21no—
78C2×C4×C11—21no—
79C2×C4×C11—21no—
80C2×C4×C11—42no—
81C2×C4×C11—42no—
82C2×C4×C11—82no—
83C2×C4×C11#9911yescharacteristic
84C2×C4×C11C2×C22⋊C411yescharacteristic
85C2×Dic11—84no—
86C2×Dic11—164no—
87C8×C11—42no—
88C2×#127C2×D1111yescharacteristic
89C2×#125Dic1111yescharacteristic, complemented
90#490—22no—
91#490Dic1112yescomplemented
92#490C2×D1112yes—
93C2×#102—22no—
94C2×#99—222no—
95C2×#97Dic1111yescharacteristic, complemented
96#353—114no—
97#353—222no—
98C22×C11—22no—
99C22×C11—42no—
100C22×C11—42no—
101C22×C11—82no—
102C22×C11—82no—
103C22×C11—84no—
104C22×C11—162no—
105C22×C11#35411yescharacteristic
106C22×C11#35411yescharacteristic
107C22×C11C2×#9911yescharacteristic
108C4×C11—21no—
109C4×C11—21no—
110C4×C11—41no—
111C4×C11—41no—
112C4×C11—82no—
113Dic11—164no—
114C22×D4—41no—
115C22×D4C22⋊D1112yes—
116C22×C8—21no—
117#127—41no—
118#127C2×Dic1111yescharacteristic
119#127C22⋊D1112yes—
120#127C22×D1111yescharacteristic
121#125—21no—
122#125—41no—
123#125C2×Dic1112yescomplemented
124C2×C4⋊C4—21no—
125C2×C4⋊C4—41no—
126C2×C22⋊C4—442no—
127C2×C42C2×Dic1111yescharacteristic
128#102—24no—
129#102—24no—
130#99—224no—
131#99—442no—
132#97—21no—
133#97C2×Dic1112yescomplemented
134C2×C11—21no—
135C2×C11—21no—
136C2×C11—82no—
137C2×C11—82no—
138C2×C11#141212yescomplemented
139C2×C11C2×#35411yescharacteristic
140C24—22no—
141C2×D4—22no—
142C2×D4—42no—
143C2×D4—42no—
144C2×D4—41no—
145C2×D4—41no—
146C2×D4—42no—
147C2×D4—84no—
148C2×D4C22⋊Dic1112yes—
149C2×D4C2×C22⋊D1112yes—
150C22×C4—21no—
151C22×C4—41no—
152C22×C4—882no—
153C22×C4C22⋊Dic1111yescharacteristic
154C2×C8—22no—
155C2×C8—41no—
156C2×C8—41no—
157C4⋊C4—22no—
158C4⋊C4—42no—
159C4⋊C4—42no—
160C4⋊C4—41no—
161C22⋊C4—444no—
162C22⋊C4—882no—
163C42—21no—
164C42C22⋊Dic1111yescharacteristic
165C42C22×Dic1111yescharacteristic
166C11C2×#141211yescharacteristic, complemented, Sylow
167C23—22no—
168C23—22no—
169C23—42no—
170C23—42no—
171C23—84no—
172C23#6689811yescharacteristic
173D4—42no—
174D4—42no—
175D4—82no—
176D4—82no—
177D4—82no—
178D4—84no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—82no—
186C2×C4—884no—
187C2×C4—1764no—
188C2×C4#6689811yescharacteristic
189C2×C4C2×C22⋊Dic1111yescharacteristic
190C8—42no—
191C22—22no—
192C22—42no—
193C22—42no—
194C22—82no—
195C22—82no—
196C22—84no—
197C22—162no—
198C22#1062217911yescharacteristic
199C22#1062217911yescharacteristic
200C22C2×#6689811yescharacteristic
201C4—21no—
202C4—21no—
203C4—41no—
204C4—41no—
205C4—82no—
206C4—1764no—
207C2—21no—
208C2—21no—
209C2—82no—
210C2—82no—
211C2#1306678712yesdirect product factor
212C2C2×#1062217911yescharacteristic
subgroupG/H
centerC22#10622179
commutatorC42×C11C22×C4
Frattini#127C22×D11
FittingC2×C11×#490C2
socleC22×C11#354
prime radicalC2×C11×#127C22
cosocleC11×#127C23
hypercenterC2×#490D11
hypocenterC11C2×#1412
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×#127 ◁ C2×#490

Complements

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

NH ≅ G/Ntype
2. #13066787C2direct (N × H)
5. C2×C11×#125C4semidirect
7. C11×#490C4semidirect
10. C2×C11×#97C4semidirect
23. C11×#125C2×C4semidirect
31. C11×#97C2×C4semidirect
89. C2×#125Dic11semidirect
91. #490Dic11semidirect
95. C2×#97Dic11semidirect
123. #125C2×Dic11semidirect
133. #97C2×Dic11semidirect
138. C2×C11#1412semidirect
166. C11C2×#1412semidirect
211. C2#13066787direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106221832
#130667872
C2×C11×#4902
C2×#141211