Finite Group Databasebeta

← #13131025

Subgroups — #13131025

Order 1664.

324 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 74 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×#88200C211yesmaximal, characteristic
2#11719136C211yesmaximal, characteristic
3C4×C22⋊#261C211yesmaximal, characteristic
4#11718289C214yesmaximal
5C22×Q8×C13C411yescharacteristic, complemented
6C22×C4×D13C2211yescharacteristic
7C2×C22⋊#261C2212yes—
8C2×C22⋊#261C2212yes—
9C2×C4⋊#261—21no—
10C2×C4×#261—21no—
11#88200—21no—
12#88200—21no—
13#88200—21no—
14#88200—21no—
15C2×#6103C2212yes—
16C2×C4⋊Dic13C411yescharacteristic, complemented
17C2×#6101C412yescomplemented
18(C2×#261)⋊C4—21no—
19(C2×#261)⋊C4—21no—
20C23×D13C2311yescharacteristic
21C22×#261—22no—
22C22×#261—22no—
23C2×Q8×C13—21no—
24C2×Q8×C13—21no—
25C2×Q8×C13—42no—
26C22×C4×C13C2×C412yes—
27C22×C4×C13C2×C411yescharacteristic
28C22×Dic13C2×C412yes—
29C22×Dic13C2×C411yescharacteristic
30C2×C4×D13—42no—
31C2×C4×D13D411yescharacteristic
32C2×C4×D13D411yescharacteristic
33C2×C4×D13D411yescharacteristic
34C2×C4×D13D411yescharacteristic
35C22⋊#261—22no—
36C22⋊#261—24no—
37C22⋊#261Q814yescomplemented
38C4⋊#261—42no—
39C4×#261—42no—
40#6103—22no—
41#6103—22no—
42C4⋊Dic13—21no—
43C4⋊Dic13—21no—
44#6101—22no—
45#6101—22no—
46#1996—131nomaximal, Sylow
47C23×C13C22×C411yescharacteristic
48C22×D13—41no—
49C22×D13—41no—
50C22×D13C2×D411yescharacteristic
51C22×D13C2×D411yescharacteristic
52C22×D13C2×Q812yes—
53C22×D13#4112yes—
54C2×#261—24no—
55C2×#261—42no—
56C2×#261—42no—
57C2×#261—42no—
58C2×#261—42no—
59C2×#261—42no—
60Q8×C13—42no—
61Q8×C13—42no—
62C2×C4×C13—22no—
63C2×C4×C13—22no—
64C2×C4×C13—42no—
65C2×C4×C13C22⋊C411yescharacteristic
66C2×C4×C13C22⋊C411yescharacteristic
67C2×Dic13—22no—
68C2×Dic13—41no—
69C2×Dic13—42no—
70C2×Dic13C22⋊C411yescharacteristic
71C2×Dic13C22⋊C411yescharacteristic
72C4×D13—22no—
73C4×D13—22no—
74C4×D13—41no—
75C4×D13—41no—
76C2×C22⋊Q8—131no—
77#380—131no—
78C4×C22⋊C4—131no—
79#342—134no—
80C22×C13—21no—
81C22×C13—21no—
82C22×C13C2×C22⋊C411yescharacteristic
83C22×C13C4×Q812yes—
84C2×D13—21no—
85C2×D13—21no—
86C2×D13—21no—
87C2×D13—21no—
88C2×D13—42no—
89C2×D13—42no—
90C2×D13C22⋊Q812yes—
91C2×D13#12411yescharacteristic
92C2×D13C4⋊Q811yescharacteristic
93#261—44no—
94#261—82no—
95C4×C13—21no—
96C4×C13—42no—
97C4×C13#9912yes—
98Dic13—21no—
99Dic13—21no—
100Dic13—42no—
101C22×Q8#26111yescharacteristic, complemented
102C23×C4—131no—
103C22⋊Q8—261no—
104C22⋊Q8—261no—
105C22⋊Q8—261no—
106C22⋊Q8—261no—
107C2×C4⋊C4—132no—
108C2×C4⋊C4—131no—
109C2×C4⋊C4—261no—
110C2×C22⋊C4—132no—
111C2×C22⋊C4—132no—
112C2×C22⋊C4—132no—
113C2×C42—261no—
114#95—261no—
115#95—261no—
116C2×C13—22no—
117C2×C13#39111yescharacteristic
118C2×C13C2×#9911yescharacteristic
119C2×C13#41011yescharacteristic
120D13—22no—
121D13—21no—
122D13—21no—
123C24—131no—
124C2×Q8—21no—
125C2×Q8—21no—
126C2×Q8—42no—
127C22×C4—131no—
128C22×C4—131no—
129C22×C4—131no—
130C22×C4—131no—
131C22×C4—131no—
132C22×C4—132no—
133C22×C4—262no—
134C22×C4—262no—
135C22×C4—522no—
136C22×C4C2×#26112yes—
137C22×C4C2×#26111yescharacteristic
138C4⋊C4—262no—
139C4⋊C4—262no—
140C4⋊C4—261no—
141C4⋊C4—261no—
142C4⋊C4—522no—
143C22⋊C4—134no—
144C22⋊C4—262no—
145C22⋊C4—262no—
146C22⋊C4—262no—
147C22⋊C4—264no—
148C42—522no—
149C13#199611yescharacteristic, complemented, Sylow
150C23—131no—
151C23—131no—
152C23—132no—
153C23—132no—
154C23—521no—
155C23—521no—
156C23C22×#26111yescharacteristic
157Q8—42no—
158Q8—42no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—42no—
162C2×C4—131no—
163C2×C4—131no—
164C2×C4—262no—
165C2×C4—262no—
166C2×C4—264no—
167C2×C4—262no—
168C2×C4—521no—
169C2×C4—521no—
170C2×C4—521no—
171C2×C4—522no—
172C2×C4—522no—
173C2×C4—522no—
174C2×C4—522no—
175C2×C4—522no—
176C2×C4—522no—
177C2×C4C22⋊#26111yescharacteristic
178C2×C4C22⋊#26111yescharacteristic
179C22—21no—
180C22—21no—
181C22—132no—
182C22—131no—
183C22—131no—
184C22—261no—
185C22—261no—
186C22—261no—
187C22—261no—
188C22—522no—
189C22—522no—
190C22Q8×#26112yes—
191C22C2×C22⋊#26111yescharacteristic
192C4—21no—
193C4—42no—
194C4—261no—
195C4—261no—
196C4—524no—
197C4—522no—
198C4—1042no—
199C4#8811912yes—
200C2—22no—
201C2—262no—
202C2—261no—
203C2—261no—
204C2#1171915611yescharacteristic
205C2(C2×#261)⋊Q811yescharacteristic
206C2C2×#8811911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC23×C13C22×C4
FrattiniC23C22×#261
FittingC22×Q8×C13C4
socleC22×C13C2×C22⋊C4
prime radical, cosocleC23×D13C23
hypercenterC22×Q8#261
hypocenterC13#1996
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
5. C22×Q8×C13C4semidirect
16. C2×C4⋊Dic13C4semidirect
17. C2×#6101C4semidirect
37. C22⋊#261Q8semidirect
101. C22×Q8#261semidirect
149. C13#1996semidirect

Maximal subgroups

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

subgroupindex
C2×#882002
#117191362
C4×C22⋊#2612
#117182892
#199613