Finite Group Databasebeta

← #15772259

Subgroups — #15772259

Order 3328.

330 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 131 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
1#13116639C212yesmaximal
2#13112776C214yesmaximal
3C2×C8×Q8×C13C211yesmaximal, characteristic
4C2×C4×Q8×C13C411yescharacteristic
5C8×Q8×C13—22no—
6C8×Q8×C13—22no—
7C2×C13×C4⋊C8C411yescharacteristic
8C2×C13×C4⋊C8C2212yes—
9C2×C4×C8×C13C412yes—
10C2×C4×C8×C13C2211yescharacteristic
11C22⋊#6090C2214yes—
12C4⋊#6090—22no—
13#11718053—22no—
14C22×Q8×C13C811yescharacteristic
15C22×C8×C13C2×C411yescharacteristic
16C22×C8×C13C2×C412yes—
17C22×C8×C13C2311yescharacteristic
18C4×Q8×C13—22no—
19C4×Q8×C13—22no—
20C2×C13×C4⋊C4C811yescharacteristic
21C2×C13×C4⋊C4C812yes—
22C2×C42×C13C2×C412yes—
23C2×C42×C13C2×C411yescharacteristic
24C13×C4⋊C8—24no—
25C13×C4⋊C8—22no—
26C4×C8×C13—22no—
27C4×C8×C13—22no—
28C4×C8×C13D412yes—
29C4×C8×C13D412yes—
30C2×#6090—24no—
31#11494—131nomaximal, Sylow
32C2×Q8×C13—22no—
33C2×Q8×C13—24no—
34C22×C4×C13C2×C811yescharacteristic
35C22×C4×C13C2×C812yes—
36C22×C4×C13C2×C812yes—
37C22×C4×C13C2×C811yescharacteristic
38C22×C4×C13C22×C411yescharacteristic
39C2×C8×C13—22no—
40C2×C8×C13—22no—
41C2×C8×C13—41no—
42C2×C8×C13—42no—
43C2×C8×C13C22⋊C411yescharacteristic
44C2×C8×C13C22⋊C411yescharacteristic
45C2×C8×C13C2×D412yes—
46C13×C4⋊C4—24no—
47C13×C4⋊C4—22no—
48C42×C13—22no—
49C42×C13—22no—
50C42×C13C22⋊C412yes—
51C42×C13M1612yes—
52#6090—44no—
53C2×C8×Q8D1311yescharacteristic
54#2163—132no—
55#1322—134no—
56C23×C13C22×C811yescharacteristic
57Q8×C13—28no—
58C2×C4×C13—22no—
59C2×C4×C13—22no—
60C2×C4×C13—22no—
61C2×C4×C13—21no—
62C2×C4×C13—21no—
63C2×C4×C13—22no—
64C2×C4×C13—41no—
65C2×C4×C13—42no—
66C2×C4×C13C22⋊C812yes—
67C2×C4×C13C22⋊C812yes—
68C2×C4×C13M3214yes—
69C2×C4×C13C2×C22⋊C411yescharacteristic
70C2×C4×C13C2×M1611yescharacteristic
71C8×C13—22no—
72C8×C13—21no—
73C8×C13—42no—
74C8×C13#10112yes—
75C2×C4×Q8Dic1311yescharacteristic
76C8×Q8—22no—
77C8×Q8—22no—
78C2×C4⋊C8Dic1311yescharacteristic
79C2×C4⋊C8C2×D1312yes—
80C2×C4×C8Dic1312yes—
81C2×C4×C8C2×D1311yescharacteristic
82C4⋊C16—262no—
83C22⋊C16—134no—
84#346—262no—
85C22×C13—21no—
86C22×C13—21no—
87C22×C13C2×C22⋊C811yescharacteristic
88C22×C13C2×M3212yes—
89C4×C13—22no—
90C4×C13—24no—
91C4×C13—22no—
92C4×C13—21no—
93C4×C13—42no—
94C4×C13#41011yescharacteristic
95C4×C13C2×#10111yescharacteristic
96C22×Q8#105511yescharacteristic
97C22×C8C2×Dic1311yescharacteristic
98C22×C8C2×Dic1312yes—
99C22×C8C22×D1311yescharacteristic
100C4×Q8—22no—
101C4×Q8—22no—
102C2×C4⋊C4#105511yescharacteristic
103C2×C4⋊C4#105512yes—
104C2×C42C2×Dic1312yes—
105C2×C42C2×Dic1311yescharacteristic
106C2×C16—264no—
107C4⋊C8—24no—
108C4⋊C8—22no—
109C4×C8—22no—
110C4×C8—22no—
111C4×C8C22⋊D1312yes—
112C4×C8C22⋊D1312yes—
113C2×C13—22no—
114C2×C13#146111yescharacteristic
115C2×C13#211211yescharacteristic
116C2×C13#211511yescharacteristic
117C2×Q8—22no—
118C2×Q8—24no—
119C22×C4C2×#105511yescharacteristic
120C22×C4C2×#105512yes—
121C22×C4C2×#105512yes—
122C22×C4C2×#105511yescharacteristic
123C22×C4C22×Dic1311yescharacteristic
124C2×C8—22no—
125C2×C8—22no—
126C2×C8—41no—
127C2×C8—42no—
128C2×C8C22⋊Dic1311yescharacteristic
129C2×C8C22⋊Dic1311yescharacteristic
130C2×C8C2×C22⋊D1312yes—
131C4⋊C4—24no—
132C4⋊C4—22no—
133C42—22no—
134C42—22no—
135C42#609912yes—
136C42C22⋊Dic1312yes—
137C16—524no—
138C13#1149411yescharacteristic, complemented, Sylow
139C23C22×#105511yescharacteristic
140Q8—28no—
141C2×C4—22no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—42no—
149C2×C4#8805214yes—
150C2×C4C22⋊#105512yes—
151C2×C4C22⋊#105512yes—
152C2×C4C2×#609911yescharacteristic
153C2×C4C2×C22⋊Dic1311yescharacteristic
154C8—21no—
155C8—22no—
156C8—42no—
157C8#8807612yes—
158C22—21no—
159C22—21no—
160C22C2×#8805212yes—
161C22C2×C22⋊#105511yescharacteristic
162C4—22no—
163C4—24no—
164C4—22no—
165C4—21no—
166C4—42no—
167C4C2×#8807611yescharacteristic
168C4#1171890111yescharacteristic
169C2—22no—
170C2#1311316011yescharacteristic
171C2#1311644711yescharacteristic
172C2#1311645711yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊Dic13
commutator, prime radicalC23×C13C22×C8
FrattiniC22×C8C22×D13
FittingC2×C8×Q8×C13C2
socleC22×C13C2×C22⋊C8
cosocleC22×C8×C13C23
hypercenterC2×C8×Q8D13
hypocenterC13#11494
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C4×C8 ◁ C2×C8×Q8

Complements

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

NH ≅ G/Ntype
138. C13#11494semidirect

Maximal subgroups

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

subgroupindex
#131166392
#131127762
C2×C8×Q8×C132
#1149413