Finite Group Databasebeta

← #13130634

Subgroups — #13130634

Order 1664.

272 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 104 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×#88100C211yesmaximal, characteristic
2C2×C8×#261C211yesmaximal, characteristic
3C4×C4⋊#261C211yesmaximal, characteristic
4D13⋊(C4⋊C8)C211yesmaximal, characteristic
5D13×#97C211yesmaximal, characteristic
6(C2×#261)⋊C8C211yesmaximal, characteristic
7(C2×#261)⋊C8C211yesmaximal, characteristic
8C2×C4⋊#261C412yes—
9C2×C4×#261C2211yescharacteristic
10C2×C4×#261C2211yescharacteristic
11C2×D13⋊C8C2211yescharacteristic
12C2×D13⋊C8C2211yescharacteristic
13C2×C8×D13C2211yescharacteristic
14C2×C8×D13C2211yescharacteristic
15C42×D13C2211yescharacteristic
16(C2×#261)⋊C4C412yes—
17#88112C412yescomplemented
18C4⋊#1057C412yescomplemented
19#88100—22no—
20C8×#261—22no—
21C13×#97C411yescharacteristic, complemented
22#88055C411yescharacteristic, complemented
23#88055C411yescharacteristic, complemented
24#88043C411yescharacteristic, complemented
25C22×#261C2×C412yes—
26C22×#261C2×C412yes—
27C2×C4×D13C2×C411yescharacteristic
28C2×C4×D13C2×C411yescharacteristic
29C2×C4×D13C2311yescharacteristic
30C2×#1057C2×C412yes—
31C2×#1057C2×C412yes—
32C4⋊#261—24no—
33C4×#261—21no—
34C4×#261—21no—
35C4×#261—21no—
36C4×#261—21no—
37D13⋊C8—21no—
38D13⋊C8—21no—
39D13⋊C8—21no—
40D13⋊C8—21no—
41C2×C8×C13C2×C411yescharacteristic
42C2×C8×C13C2×C411yescharacteristic
43C42×C13C2×C411yescharacteristic
44C4×Dic13C2×C411yescharacteristic
45C4×Dic13C2×C411yescharacteristic
46C4×Dic13C2×C411yescharacteristic
47C2×#1055C2×C411yescharacteristic
48C2×#1055C2×C411yescharacteristic
49C8×D13—21no—
50C8×D13—21no—
51C8×D13D412yes—
52C8×D13Q812yes—
53#1771—131nomaximal, Sylow
54C22×D13C22×C411yescharacteristic
55C2×#261—22no—
56C2×#261—22no—
57C2×#261—22no—
58C2×#261—22no—
59C2×#261—22no—
60C2×#261M1614yes—
61C2×C4×C13C4211yescharacteristic
62C2×C4×C13C4211yescharacteristic
63C2×C4×C13C22×C411yescharacteristic
64C2×Dic13C4211yescharacteristic
65C2×Dic13C4211yescharacteristic
66C2×Dic13C22×C411yescharacteristic
67C4×D13—22no—
68C4×D13—22no—
69C4×D13C2×D411yescharacteristic
70C4×D13C2×Q811yescharacteristic
71C4×D13#4111yescharacteristic
72C4×D13#4111yescharacteristic
73#1057—22no—
74#1057—22no—
75C8×C13—21no—
76C8×C13C4⋊C412yescomplemented
77#1055—21no—
78#1055C4⋊C412yescomplemented
79C2×C4⋊C8—131no—
80C2×#97—131no—
81C2×#97—131no—
82C2×C4×C8—131no—
83C4×C4⋊C4—131no—
84#336—131no—
85#336—131no—
86C22×C13C2×C4211yescharacteristic
87C2×D13C4×D411yescharacteristic
88C2×D13C4×Q811yescharacteristic
89C2×D13C2×M1612yes—
90C2×D13#13112yes—
91#261—24no—
92#261—42no—
93C4×C13—21no—
94C4×C13—21no—
95C4×C13C2×C4⋊C411yescharacteristic
96C4×C13#11711yescharacteristic
97Dic13—21no—
98Dic13—21no—
99Dic13C4×D411yescharacteristic
100Dic13C4×Q811yescharacteristic
101C22×C8—131no—
102C22×C8—131no—
103C22×C8—131no—
104C22×C8—131no—
105C2×C4⋊C4—132no—
106C2×C42—131no—
107C2×C42—131no—
108C2×C42—131no—
109C4⋊C8—132no—
110C4⋊C8—132no—
111#97—131no—
112#97—131no—
113#97—131no—
114#97—262no—
115#97#26111yescharacteristic, complemented
116C4×C8—262no—
117#95—132no—
118C2×C13C4×C4⋊C411yescharacteristic
119C2×C13C4×M1611yescharacteristic
120C2×C13#40511yescharacteristic
121D13#43512yes—
122D13#44612yes—
123C22×C4—131no—
124C22×C4—132no—
125C22×C4—131no—
126C22×C4—131no—
127C22×C4—132no—
128C2×C8—131no—
129C2×C8—132no—
130C2×C8—132no—
131C2×C8—132no—
132C2×C8—132no—
133C2×C8—131no—
134C2×C8—261no—
135C2×C8—261no—
136C2×C8—261no—
137C2×C8—261no—
138C2×C8—261no—
139C2×C8—261no—
140C2×C8C2×#26111yescharacteristic
141C2×C8C2×#26111yescharacteristic
142C4⋊C4—264no—
143C42—131no—
144C42—131no—
145C42—131no—
146C42—261no—
147C42—261no—
148C42—261no—
149C42—261no—
150C42C2×#26111yescharacteristic
151C13#177111yescharacteristic, complemented, Sylow
152C23—131no—
153C2×C4—131no—
154C2×C4—131no—
155C2×C4—131no—
156C2×C4—131no—
157C2×C4—131no—
158C2×C4—134no—
159C2×C4—131no—
160C2×C4—131no—
161C2×C4—262no—
162C2×C4—262no—
163C2×C4—262no—
164C2×C4—262no—
165C2×C4—262no—
166C2×C4—262no—
167C2×C4—262no—
168C2×C4C4×#26111yescharacteristic
169C2×C4C4×#26111yescharacteristic
170C2×C4C22×#26111yescharacteristic
171C8—21no—
172C8—132no—
173C8—262no—
174C8—262no—
175C8—261no—
176C8C4⋊#26112yescomplemented
177C22—131no—
178C22—131no—
179C22—132no—
180C22—132no—
181C22C2×C4×#26111yescharacteristic
182C4—21no—
183C4—21no—
184C4—131no—
185C4—131no—
186C4—264no—
187C4—261no—
188C4—261no—
189C4—522no—
190C4C2×C4⋊#26111yescharacteristic
191C4#8823711yescharacteristic
192C2—132no—
193C2—132no—
194C2C4×C4⋊#26111yescharacteristic
195C2M16×#26111yescharacteristic
196C2#1171909911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×#261
commutator, socleC22×C13C2×C42
FittingC13×#97C4
prime radicalC22×D13C22×C4
cosocleC2×C4×D13C23
hypercenter#97#261
hypocenterC13#1771
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #97

Complements

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

NH ≅ G/Ntype
17. #88112C4semidirect
18. C4⋊#1057C4semidirect
21. C13×#97C4semidirect
22. #88055C4semidirect
23. #88055C4semidirect
24. #88043C4semidirect
76. C8×C13C4⋊C4semidirect
78. #1055C4⋊C4semidirect
115. #97#261semidirect
151. C13#1771semidirect
176. C8C4⋊#261semidirect

Maximal subgroups

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

subgroupindex
C2×#881002
C2×C8×#2612
C4×C4⋊#2612
D13⋊(C4⋊C8)2
D13×#972
(C2×#261)⋊C82
#177113