Finite Group Databasebeta

← C2×#11719077 #13131511

Subgroups — C2×#11719077 #13131511

Order 1664.

412 conjugacy classes of subgroups; only the 170 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 170 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×#88146C211yesmaximal, characteristic
2C2×#88112C211yesmaximal, characteristic, complemented
3C2×#88111C211yesmaximal, characteristic
4C2×#88111C211yesmaximal, characteristic
5C2×#88110C211yesmaximal, characteristic, complemented
6C2×C4⋊#1057C211yesmaximal, characteristic, complemented
7C2×C4×#1057C211yesmaximal, characteristic, complemented
8#11719077C218yesmaximal, direct product factor
9C22×C4×D13C2211yescharacteristic
10C22×#1057C2211yescharacteristic
11C22×#1057C2211yescharacteristic
12C22×#1057C2211yescharacteristic
13C22×#1057C2211yescharacteristic
14C2×C13×C4⋊C4C411yescharacteristic
15C2×#6103C411yescharacteristic
16C2×#6103C411yescharacteristic
17C2×C4⋊Dic13C411yescharacteristic
18C2×C4×Dic13C2211yescharacteristic
19C2×C4×Dic13C2211yescharacteristic
20#88146C414yes—
21#88146C2214yes—
22#88112C2214yescomplemented
23#88111C2214yes—
24#88111C2214yes—
25#88110C2214yescomplemented
26C4⋊#1057C2214yescomplemented
27C4×#1057C2214yescomplemented
28C23×D13C2×C411yescharacteristic
29C22×C4×C13C2×C411yescharacteristic
30C22×C4×C13C2×C411yescharacteristic
31C22×C4×C13C2×C411yescharacteristic
32C22×Dic13C2×C411yescharacteristic
33C22×Dic13C2×C411yescharacteristic
34C22×Dic13C2311yescharacteristic
35C2×C4×D13—22no—
36C2×C4×D13—22no—
37C2×C4×D13C2×C412yes—
38C2×C4×D13C2312yes—
39C2×#1057—22no—
40C2×#1057—22no—
41C2×#1057—22no—
42C2×#1057—22no—
43C2×#1057C2312yes—
44C2×#1057C2312yes—
45C2×#1057C2312yes—
46C2×#1057C2312yes—
47C13×C4⋊C4C2×C414yes—
48#6103C2×C414yes—
49#6103C2×C414yes—
50C4⋊Dic13C2×C414yes—
51C4×Dic13C2×C412yes—
52C4×Dic13C2×C412yes—
53C4×Dic13C2312yes—
54C4×Dic13C2312yes—
55C2×#433—131nomaximal, Sylow
56C23×C13C22×C411yescharacteristic
57C22×D13—22no—
58C22×D13—22no—
59C22×D13—22no—
60C22×D13C22×C412yes—
61C2×C4×C13—22no—
62C2×C4×C13—22no—
63C2×C4×C13—22no—
64C2×C4×C13C22×C412yes—
65C2×C4×C13C22×C412yes—
66C2×C4×C13C22×C412yes—
67C2×Dic13—22no—
68C2×Dic13—22no—
69C2×Dic13C22×C412yes—
70C2×Dic13C22×C412yes—
71C2×Dic13C22×C411yescharacteristic
72C2×Dic13#4112yes—
73C2×Dic13#4112yes—
74C2×Dic13C2411yescharacteristic
75C4×D13—24no—
76C4×D13—22no—
77C4×D13—22no—
78#1057—22no—
79#1057—22no—
80#1057—22no—
81#1057—22no—
82C2×#117—131no—
83#433—138no—
84C2×C4⋊C8—131no—
85C2×C4⋊C8—131no—
86C2×C22⋊C8—131no—
87C2×C22⋊C8—131no—
88C2×#97—131no—
89C2×C4×C8—131no—
90C22×C13#11712yes—
91C22×C13#13112yes—
92C22×C13#13112yes—
93C22×C13C23×C411yescharacteristic
94C2×D13—22no—
95C2×D13—22no—
96C2×D13—22no—
97C2×D13—44no—
98C4×C13—22no—
99C4×C13—22no—
100C4×C13—22no—
101Dic13—22no—
102Dic13—22no—
103Dic13#11712yes—
104Dic13C2×#4111yescharacteristic
105Dic13C2×#4111yescharacteristic
106C23×C4—131no—
107C22×C8—131no—
108C22×C8—131no—
109C22×C8—131no—
110C22×C8—131no—
111#117—134no—
112#117—134no—
113C2×C4⋊C4—131no—
114C2×C4⋊C4#26111yescharacteristic
115C2×C22⋊C4—131no—
116C2×C22⋊C4—131no—
117C2×C42—131no—
118C2×C42—131no—
119C4⋊C8—134no—
120C4⋊C8—134no—
121C22⋊C8—134no—
122C22⋊C8—134no—
123#97—134no—
124C4×C8—134no—
125C2×C13#43314yescomplemented
126C2×C13C2×#11711yescharacteristic
127C2×C13C2×#13111yescharacteristic
128C2×C13C2×#13111yescharacteristic
129D13—42no—
130C24—131no—
131C22×C4—131no—
132C22×C4—131no—
133C22×C4—131no—
134C22×C4—132no—
135C22×C4—132no—
136C22×C4—262no—
137C22×C4—262no—
138C22×C4C2×#26111yescharacteristic
139C22×C4C2×#26111yescharacteristic
140C22×C4C2×#26111yescharacteristic
141C2×C8—132no—
142C2×C8—132no—
143C2×C8—132no—
144C2×C8—132no—
145C2×C8—262no—
146C2×C8—262no—
147C2×C8—262no—
148C2×C8—262no—
149C4⋊C4—134no—
150C4⋊C4C2×#26114yes—
151C22⋊C4—134no—
152C22⋊C4—134no—
153C42—132no—
154C42—132no—
155C42—132no—
156C42—132no—
157C13C2×#43311yescharacteristic, complemented, Sylow
158C23—132no—
159C23—262no—
160C23—262no—
161C23—262no—
162C23C22×#26111yescharacteristic
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—132no—
167C2×C4—132no—
168C2×C4—131no—
169C2×C4—131no—
170C2×C4—132no—
171C2×C4—132no—
172C2×C4—264no—
173C2×C4—262no—
174C2×C4—262no—
175C2×C4—262no—
176C2×C4—262no—
177C2×C4C22×#26112yes—
178C2×C4C22×#26112yes—
179C2×C4C22×#26112yes—
180C8—262no—
181C8—262no—
182C8—262no—
183C8—262no—
184C22—262no—
185C22—262no—
186C22—262no—
187C22—524no—
188C22#8823712yes—
189C22#8823812yes—
190C22#8824012yes—
191C22C23×#26111yescharacteristic
192C4—22no—
193C4—22no—
194C4—22no—
195C4—132no—
196C4—131no—
197C4—131no—
198C4—262no—
199C4—262no—
200C2—522no—
201C2#1171907714yesdirect product factor
202C2C2×#8823711yescharacteristic
203C2C2×#8823811yescharacteristic
204C2C2×#8824011yescharacteristic
subgroupG/H
centerC23C22×#261
commutatorC22×C13C23×C4
FrattiniC22C23×#261
FittingC2×C13×C4⋊C4C4
socleC23×C13C22×C4
prime radicalC23×D13C2×C4
cosocleC2×Dic13C24
hypercenterC2×C4⋊C4#261
hypocenterC13C2×#433
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#88112C2semidirect
5. C2×#88110C2semidirect
6. C2×C4⋊#1057C2semidirect
7. C2×C4×#1057C2semidirect
8. #11719077C2direct (N × H)
22. #88112C22semidirect
25. #88110C22semidirect
26. C4⋊#1057C22semidirect
27. C4×#1057C22semidirect
125. C2×C13#433semidirect
157. C13C2×#433semidirect
201. C2#11719077direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#881462
C2×#881122
C2×#881112
C2×#881102
C2×C4⋊#10572
C2×C4×#10572
#117190772
C2×#43313