Finite Group Databasebeta

← C2×#11718237 #13131086

Subgroups — C2×#11718237 #13131086

Order 1664.

278 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 58 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×#88140C211yesmaximal, characteristic
2C2×#88121C211yesmaximal, characteristic
3C2×#88119C211yesmaximal, characteristic
4#11718237C214yesmaximal, direct product factor
5C22×C22⋊D13C2211yescharacteristic
6C23×Dic13C411yescharacteristic, complemented
7C2×C22⋊#261—21no—
8C2×#6122—21no—
9C2×C13×C22⋊C4C411yescharacteristic, complemented
10C2×#6103—21no—
11C2×C4⋊Dic13—21no—
12#88140—21no—
13#88140—21no—
14#88140C412yescomplemented
15#88140C2212yes—
16#88121—21no—
17#88121C2212yes—
18#88119—21no—
19#88119C2212yes—
20C24×C13C2×C411yescharacteristic
21C23×D13D411yescharacteristic
22C22×#261—41no—
23C22×C4×C13—21no—
24C2×C22⋊D13—41no—
25C2×C22⋊D13—41no—
26C2×C22⋊D13C2×C411yescharacteristic
27C2×C22⋊D13D411yescharacteristic
28C2×C22⋊D13D411yescharacteristic
29C2×C22⋊D13C2311yescharacteristic
30C22×Dic13—21no—
31C22×Dic13—21no—
32C22×Dic13—41no—
33C22×Dic13—41no—
34C22×Dic13C2×C412yescomplemented
35C22×Dic13D411yescharacteristic
36C22⋊#261—22no—
37C22⋊#261—41no—
38#6122—22no—
39#6122—41no—
40C2×#1057—41no—
41C13×C22⋊C4—21no—
42C13×C22⋊C4C2×C412yescomplemented
43#6103—22no—
44#6103—22no—
45C4⋊Dic13—22no—
46C4⋊Dic13—22no—
47C2×#352—131nomaximal, Sylow
48C23×C13—21no—
49C23×C13—21no—
50C23×C13—42no—
51C23×C13C22⋊C411yescharacteristic
52C23×C13C22⋊C411yescharacteristic
53C23×C13C22×C411yescharacteristic
54C22×D13—21no—
55C22×D13—21no—
56C22×D13—42no—
57C22×D13C22⋊C411yescharacteristic
58C22×D13C2×D411yescharacteristic
59C2×#261—42no—
60C2×#261—82no—
61C2×C4×C13—22no—
62C2×C4×C13—42no—
63C22⋊D13—41no—
64C22⋊D13—41no—
65C22⋊D13—41no—
66C22⋊D13—41no—
67C2×Dic13—21no—
68C2×Dic13—21no—
69C2×Dic13—22no—
70C2×Dic13—42no—
71C2×Dic13—41no—
72C2×Dic13—41no—
73C2×Dic13—42no—
74C2×Dic13C22⋊C411yescharacteristic
75C2×Dic13C2×D411yescharacteristic
76#1057—42no—
77C2×#123—131no—
78C2×#100—131no—
79C2×#99—131no—
80#352—134no—
81C22×C13—22no—
82C22×C13—21no—
83C22×C13—21no—
84C22×C13—41no—
85C22×C13—41no—
86C22×C13—42no—
87C22×C13—42no—
88C22×C13#9911yescharacteristic
89C22×C13#9911yescharacteristic
90C22×C13C2×C22⋊C411yescharacteristic
91C2×D13—21no—
92C2×D13—21no—
93C2×D13—42no—
94C2×D13—41no—
95C2×D13—41no—
96C2×D13—81no—
97#261—82no—
98C4×C13—42no—
99Dic13—21no—
100Dic13—21no—
101Dic13—42no—
102C22×D4—131no—
103C23×C4—131no—
104C2×M16—261no—
105#123—132no—
106#123—132no—
107#123—261no—
108#123—261no—
109C2×C4⋊C4—261no—
110C2×C22⋊C4—261no—
111C2×C22⋊C4—261no—
112C2×C22⋊C4#26111yescharacteristic, complemented
113#100—132no—
114#100—261no—
115#99—132no—
116#99—261no—
117C2×C13—21no—
118C2×C13—21no—
119C2×C13—41no—
120C2×C13—41no—
121C2×C13#35212yescomplemented
122C2×C13C2×#9911yescharacteristic
123D13—41no—
124D13—41no—
125C24—131no—
126C24C2×#26111yescharacteristic
127C2×D4—131no—
128C2×D4—131no—
129C2×D4—131no—
130C2×D4—131no—
131C2×D4—521no—
132C2×D4—521no—
133C22×C4—21no—
134C22×C4—131no—
135C22×C4—132no—
136C22×C4—261no—
137C22×C4—261no—
138C22×C4—521no—
139C22×C4—521no—
140C22×C4—521no—
141M16—262no—
142M16—521no—
143C2×C8—521no—
144C4⋊C4—262no—
145C4⋊C4—262no—
146C22⋊C4—21no—
147C22⋊C4—262no—
148C22⋊C4—262no—
149C22⋊C4—262no—
150C22⋊C4—521no—
151C22⋊C4C2×#26112yescomplemented
152C13C2×#35211yescharacteristic, complemented, Sylow
153C23—21no—
154C23—21no—
155C23—42no—
156C23—131no—
157C23—131no—
158C23—261no—
159C23—261no—
160C23—522no—
161C23C22⋊#26111yescharacteristic
162C23C22⋊#26111yescharacteristic
163C23C22×#26111yescharacteristic
164D4—521no—
165D4—521no—
166D4—521no—
167D4—521no—
168C2×C4—22no—
169C2×C4—42no—
170C2×C4—131no—
171C2×C4—131no—
172C2×C4—261no—
173C2×C4—261no—
174C2×C4—262no—
175C2×C4—522no—
176C2×C4—521no—
177C2×C4—521no—
178C2×C4—522no—
179C2×C4—522no—
180C2×C4—1042no—
181C8—522no—
182C22—22no—
183C22—21no—
184C22—21no—
185C22—41no—
186C22—41no—
187C22—42no—
188C22—42no—
189C22—261no—
190C22—261no—
191C22—521no—
192C22—521no—
193C22—522no—
194C22—1041no—
195C22#8810711yescharacteristic
196C22#8810711yescharacteristic
197C22C2×C22⋊#26111yescharacteristic
198C4—42no—
199C4—261no—
200C4—261no—
201C4—522no—
202C4—1042no—
203C2—21no—
204C2—21no—
205C2—41no—
206C2—41no—
207C2—521no—
208C2—521no—
209C2#1171823712yesdirect product factor
210C2C2×#8810711yescharacteristic
subgroupG/H
centerC22#88107
commutatorC23×C13C22×C4
FrattiniC23C22×#261
FittingC2×C13×C22⋊C4C4
socleC22×C13#99
prime radicalC22×C22⋊D13C22
cosocleC2×C22⋊D13C23
hypercenterC2×C22⋊C4#261
hypocenterC13C2×#352
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. #11718237C2direct (N × H)
6. C23×Dic13C4semidirect
9. C2×C13×C22⋊C4C4semidirect
14. #88140C4semidirect
34. C22×Dic13C2×C4semidirect
42. C13×C22⋊C4C2×C4semidirect
112. C2×C22⋊C4#261semidirect
121. C2×C13#352semidirect
151. C22⋊C4C2×#261semidirect
152. C13C2×#352semidirect
209. C2#11718237direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#881402
C2×#881212
C2×#881192
#117182372
C2×#35213