Finite Group Databasebeta

← #15781468

Subgroups — #15781468

Order 3328.

316 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 115 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#13123768C211yesmaximal, characteristic
2#13116602C211yesmaximal, characteristic
3#13112923C212yesmaximal
4#13112917C212yesmaximal
5C13×#2110C211yesmaximal, characteristic
6#11719222C411yescharacteristic
7C2×C13×M32C2212yes—
8C13×#405C2211yescharacteristic
9#11718780C411yescharacteristic
10#11718779C411yescharacteristic
11#11718762C2211yescharacteristic
12C2×C8×Dic13C2211yescharacteristic
13C2×#88052C2212yes—
14#11718660C411yescharacteristic
15#11718362—22no—
16C8×Dic26—22no—
17C13×#347—22no—
18#11718055—22no—
19C2×C13×M16C2×C411yescharacteristic
20C22×C8×C13C2311yescharacteristic
21C13×#117C2×C411yescharacteristic
22#88180C2×C411yescharacteristic
23C2×C4×Dic13C2×C411yescharacteristic
24C2×#6099C2×C411yescharacteristic
25C22×#1055C2×C411yescharacteristic
26#88144—21no—
27#88142—21no—
28#88132—22no—
29C4×Dic26—22no—
30C13×M32—22no—
31C13×M32Q814yescomplemented
32C2×C13×C16—22no—
33C13×#97D412yes—
34C4×C8×C13D412yes—
35#88055—21no—
36#88054—22no—
37#88054—22no—
38C8×Dic13—21no—
39C8×Dic13—21no—
40C8×Dic13—21no—
41#88052—22no—
42#88052—22no—
43C2×#6090—22no—
44C4⋊#1055—22no—
45#13270—131nomaximal, Sylow
46C22×C4×C13C22×C411yescharacteristic
47C22×Dic13—21no—
48C2×Dic26—22no—
49C13×M16—22no—
50C2×C8×C13C22⋊C412yes—
51C2×C8×C13C2×D411yescharacteristic
52C2×C8×C13C2×D411yescharacteristic
53C2×C8×C13C2×Q812yes—
54C2×C8×C13#4112yes—
55C13×C4⋊C4—21no—
56C13×C22⋊C4—21no—
57C42×C13C22⋊C412yes—
58C22⋊Dic13M1612yes—
59C4⋊Dic13—22no—
60C4⋊Dic13—21no—
61#6101—22no—
62#6101—22no—
63C4×Dic13—21no—
64C4×Dic13—21no—
65C4×Dic13M1611yescharacteristic
66C4×Dic13M1611yescharacteristic
67#6099—22no—
68C2×#1055—21no—
69C2×#1055—21no—
70C2×#1055—22no—
71C13×C16—24no—
72#6090—42no—
73#2960—131no—
74#2153—131no—
75#2110D1311yescharacteristic
76#1378—132no—
77#1376—132no—
78C23×C13C2×M1611yescharacteristic
79C2×C4×C13—22no—
80C2×C4×C13C2×C22⋊C411yescharacteristic
81C2×C4×C13C4×Q812yes—
82C2×C4×C13C2×M1611yescharacteristic
83C2×C4×C13#13112yes—
84C2×Dic13—21no—
85C2×Dic13—21no—
86C2×Dic13—22no—
87C2×Dic13—42no—
88Dic26—44no—
89C8×C13—22no—
90C8×C13C22⋊Q812yes—
91C8×C13#12411yescharacteristic
92C8×C13C4⋊Q811yescharacteristic
93#1055—41no—
94#1055—41no—
95#533—131no—
96C2×M32—132no—
97C2×M32C2×D1312yes—
98#446—262no—
99C8×Q8—262no—
100#424—131no—
101#424—131no—
102#423—131no—
103#405—131no—
104#405C2×D1311yescharacteristic
105C2×C4×C8—131no—
106#364—262no—
107#347—22no—
108C22×C13—41no—
109C22×C13#40711yescharacteristic
110C22×C13#44612yes—
111C4×C13—42no—
112C4×C13#39111yescharacteristic
113C4×C13#40811yescharacteristic
114C4×C13#44612yes—
115Dic13—22no—
116Dic13—42no—
117Dic13—41no—
118C2×M16—131no—
119C2×M16C4×D1311yescharacteristic
120C22×C8—131no—
121C22×C8C22×D1311yescharacteristic
122C4⋊Q8—261no—
123#125—261no—
124C22⋊Q8—262no—
125C4×Q8—262no—
126#117—131no—
127#117C4×D1311yescharacteristic
128C2×C42—131no—
129M32—22no—
130M32—262no—
131M32—262no—
132M32Dic2614yescomplemented
133C2×C16—22no—
134C2×C16—262no—
135C4⋊C8—262no—
136C4⋊C8—262no—
137C4⋊C8—262no—
138#97—261no—
139#97C22⋊D1312yes—
140C4×C8—261no—
141C4×C8—261no—
142C4×C8—261no—
143C4×C8D5212yes—
144C2×C13—21no—
145C2×C13—22no—
146C2×C13#198511yescharacteristic
147C2×Q8—262no—
148C22×C4—261no—
149C22×C4C2×C4×D1311yescharacteristic
150M16—22no—
151M16—262no—
152C2×C8—262no—
153C2×C8—261no—
154C2×C8—261no—
155C2×C8#610312yes—
156C2×C8C2×Dic2612yes—
157C2×C8C2×D5211yescharacteristic
158C2×C8#612712yes—
159C2×C8C2×C22⋊D1311yescharacteristic
160C4⋊C4—21no—
161C4⋊C4—262no—
162C4⋊C4—262no—
163C4⋊C4—262no—
164C4⋊C4—261no—
165C22⋊C4—21no—
166C22⋊C4—132no—
167C42—131no—
168C42—131no—
169C42—261no—
170C42—261no—
171C42#610312yes—
172C16—24no—
173C16—522no—
174C13#1327011yescharacteristic, complemented, Sylow
175C23M16×D1311yescharacteristic
176Q8—524no—
177C2×C4—22no—
178C2×C4—261no—
179C2×C4—261no—
180C2×C4—262no—
181C2×C4—522no—
182C2×C4C4×Dic2612yes—
183C2×C4M16×D1311yescharacteristic
184C2×C4#8816112yes—
185C2×C4C2×#610311yescharacteristic
186C8—22no—
187C8—521no—
188C8—521no—
189C8#8812311yescharacteristic
190C8#8812911yescharacteristic
191C8#8817812yes—
192C22—41no—
193C22#1171836212yes—
194C22#1171878711yescharacteristic
195C4—42no—
196C4—262no—
197C4—521no—
198C4—522no—
199C4#1171836212yes—
200C4#1171859011yescharacteristic
201C4#1171879011yescharacteristic
202C2—21no—
203C2—22no—
204C2#1311577611yescharacteristic
subgroupG/H
centerC8#88129
commutatorC22×C4×C13C22×C4
FrattiniC22×C8C22×D13
FittingC13×#2110C2
socleC2×C13#1985
prime radicalC23×C13C2×M16
cosocleC22×C8×C13C23
hypercenter#2110D13
hypocenterC13#13270
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C8 ◁ C22×C8 ◁ #2110

Complements

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

NH ≅ G/Ntype
31. C13×M32Q8semidirect
132. M32Dic26semidirect
174. C13#13270semidirect

Maximal subgroups

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

subgroupindex
#131237682
#131166022
#131129232
#131129172
C13×#21102
#1327013