Finite Group Databasebeta

← C2×#13113007 #15783264

Subgroups — C2×#13113007 #15783264

Order 3328.

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×#11718137C212yesmaximal
2#13113007C214yesmaximal, direct product factor
3C2×C13×#490C211yesmaximal, characteristic
4C2×C13×#127C2211yescharacteristic
5C2×C13×#125C411yescharacteristic, complemented
6C13×#490—22no—
7C13×#490C412yescomplemented
8C13×#490C2212yes—
9C2×C13×#102—22no—
10C2×C13×#97C411yescharacteristic, complemented
11C2×#88074—22no—
12#11718137—22no—
13#11718137C2214yes—
14C22×D4×C13—41no—
15C22×D4×C13D412yes—
16C22×C8×C13—21no—
17C13×#127—41no—
18C13×#127C2×C411yescharacteristic
19C13×#127D412yes—
20C13×#127C2311yescharacteristic
21C13×#125—21no—
22C13×#125—41no—
23C13×#125C2×C412yescomplemented
24C2×C13×C4⋊C4—21no—
25C2×C13×C4⋊C4—41no—
26C2×C42×C13C2×C411yescharacteristic
27C2×C22⋊Dic13—42no—
28C13×#102—24no—
29C13×#102—24no—
30C13×#97—21no—
31C13×#97C2×C412yescomplemented
32#88074—24no—
33#88074—42no—
34C2×#1412—131nomaximal, Sylow
35C24×C13—22no—
36C2×D4×C13—22no—
37C2×D4×C13—42no—
38C2×D4×C13—42no—
39C2×D4×C13—41no—
40C2×D4×C13—42no—
41C2×D4×C13—41no—
42C2×D4×C13—84no—
43C2×D4×C13C22⋊C412yes—
44C2×D4×C13C2×D412yes—
45C22×C4×C13—21no—
46C22×C4×C13—41no—
47C22×C4×C13C22⋊C411yescharacteristic
48C22×Dic13—82no—
49C2×C8×C13—22no—
50C2×C8×C13—41no—
51C2×C8×C13—41no—
52C13×C4⋊C4—22no—
53C13×C4⋊C4—42no—
54C13×C4⋊C4—42no—
55C13×C4⋊C4—41no—
56C42×C13—21no—
57C42×C13C22⋊C411yescharacteristic
58C42×C13C22×C411yescharacteristic
59C22⋊Dic13—44no—
60C22⋊Dic13—82no—
61C2×#490D1311yescharacteristic
62C2×#353—132no—
63#1412—134no—
64C23×C13—22no—
65C23×C13—22no—
66C23×C13—42no—
67C23×C13—42no—
68C23×C13—84no—
69C23×C13#9911yescharacteristic
70D4×C13—42no—
71D4×C13—42no—
72D4×C13—82no—
73D4×C13—82no—
74D4×C13—84no—
75D4×C13—82no—
76C2×C4×C13—21no—
77C2×C4×C13—21no—
78C2×C4×C13—21no—
79C2×C4×C13—21no—
80C2×C4×C13—42no—
81C2×C4×C13—42no—
82C2×C4×C13—82no—
83C2×C4×C13#9911yescharacteristic
84C2×C4×C13C2×C22⋊C411yescharacteristic
85C2×Dic13—84no—
86C2×Dic13—164no—
87C8×C13—42no—
88C2×#127C2×D1311yescharacteristic
89C2×#125Dic1311yescharacteristic, complemented
90#490—22no—
91#490Dic1312yescomplemented
92#490C2×D1312yes—
93C2×#102—22no—
94C2×#99—262no—
95C2×#97Dic1311yescharacteristic, complemented
96#353—134no—
97#353—262no—
98C22×C13—22no—
99C22×C13—42no—
100C22×C13—42no—
101C22×C13—82no—
102C22×C13—82no—
103C22×C13—84no—
104C22×C13—162no—
105C22×C13#35411yescharacteristic
106C22×C13#35411yescharacteristic
107C22×C13C2×#9911yescharacteristic
108C4×C13—21no—
109C4×C13—21no—
110C4×C13—41no—
111C4×C13—41no—
112C4×C13—82no—
113Dic13—164no—
114C22×D4—41no—
115C22×D4C22⋊D1312yes—
116C22×C8—21no—
117#127—41no—
118#127C2×Dic1311yescharacteristic
119#127C22⋊D1312yes—
120#127C22×D1311yescharacteristic
121#125—21no—
122#125—41no—
123#125C2×Dic1312yescomplemented
124C2×C4⋊C4—21no—
125C2×C4⋊C4—41no—
126C2×C22⋊C4—522no—
127C2×C42C2×Dic1311yescharacteristic
128#102—24no—
129#102—24no—
130#99—264no—
131#99—522no—
132#97—21no—
133#97C2×Dic1312yescomplemented
134C2×C13—21no—
135C2×C13—21no—
136C2×C13—82no—
137C2×C13—82no—
138C2×C13#141212yescomplemented
139C2×C13C2×#35411yescharacteristic
140C24—22no—
141C2×D4—22no—
142C2×D4—42no—
143C2×D4—42no—
144C2×D4—41no—
145C2×D4—42no—
146C2×D4—41no—
147C2×D4—84no—
148C2×D4C22⋊Dic1312yes—
149C2×D4C2×C22⋊D1312yes—
150C22×C4—21no—
151C22×C4—41no—
152C22×C4—1042no—
153C22×C4C22⋊Dic1311yescharacteristic
154C2×C8—22no—
155C2×C8—41no—
156C2×C8—41no—
157C4⋊C4—22no—
158C4⋊C4—42no—
159C4⋊C4—42no—
160C4⋊C4—41no—
161C22⋊C4—524no—
162C22⋊C4—1042no—
163C42—21no—
164C42C22⋊Dic1311yescharacteristic
165C42C22×Dic1311yescharacteristic
166C13C2×#141211yescharacteristic, complemented, Sylow
167C23—22no—
168C23—22no—
169C23—42no—
170C23—42no—
171C23—84no—
172C23#8807411yescharacteristic
173D4—42no—
174D4—42no—
175D4—82no—
176D4—82no—
177D4—84no—
178D4—82no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—82no—
186C2×C4—1044no—
187C2×C4—2084no—
188C2×C4#8807411yescharacteristic
189C2×C4C2×C22⋊Dic1311yescharacteristic
190C8—42no—
191C22—22no—
192C22—42no—
193C22—42no—
194C22—82no—
195C22—82no—
196C22—84no—
197C22—162no—
198C22#1171813311yescharacteristic
199C22#1171813311yescharacteristic
200C22C2×#8807411yescharacteristic
201C4—21no—
202C4—21no—
203C4—41no—
204C4—41no—
205C4—82no—
206C4—2084no—
207C2—21no—
208C2—21no—
209C2—82no—
210C2—82no—
211C2#1311300712yesdirect product factor
212C2C2×#1171813311yescharacteristic
subgroupG/H
centerC22#11718133
commutatorC42×C13C22×C4
Frattini#127C22×D13
FittingC2×C13×#490C2
socleC22×C13#354
prime radicalC2×C13×#127C22
cosocleC13×#127C23
hypercenterC2×#490D13
hypocenterC13C2×#1412
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×#127 ◁ C2×#490

Complements

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

NH ≅ G/Ntype
2. #13113007C2direct (N × H)
5. C2×C13×#125C4semidirect
7. C13×#490C4semidirect
10. C2×C13×#97C4semidirect
23. C13×#125C2×C4semidirect
31. C13×#97C2×C4semidirect
89. C2×#125Dic13semidirect
91. #490Dic13semidirect
95. C2×#97Dic13semidirect
123. #125C2×Dic13semidirect
133. #97C2×Dic13semidirect
138. C2×C13#1412semidirect
166. C13C2×#1412semidirect
211. C2#13113007direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117181372
#131130072
C2×C13×#4902
C2×#141213