Finite Group Databasebeta

← #27193486

Subgroups — #27193486

Order 13184.

236 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 69 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×#15692986C211yesmaximal, characteristic
2#20267845C212yesmaximal
3#20267517C211yesmaximal, characteristic
4#20267516C212yesmaximal
5#324×C103C211yesmaximal, characteristic
6C22×Dic206C411yescharacteristic
7#15692986—22no—
8#15692986—22no—
9C2×Dic103⋊C4C411yescharacteristic
10C2×Dic103⋊C4C2211yescharacteristic
11C2×C4×Dic103C411yescharacteristic
12C2×C4×Dic103C411yescharacteristic
13C2×C4×Dic103C2211yescharacteristic
14Dic103⋊C8—22no—
15C22⋊(C103⋊C8)C2212yes—
16#15692931—22no—
17C2×C4⋊C4×C103C2211yescharacteristic
18C22⋊C8×C103C2212yes—
19C2×Dic206—22no—
20C2×Dic206—22no—
21C2×Dic206—22no—
22C22×Dic103C2×C411yescharacteristic
23C22×Dic103C2×C411yescharacteristic
24C22×Dic103C2×C411yescharacteristic
25C22×Dic103C2×C411yescharacteristic
26C2×C103⋊C8—22no—
27Dic103⋊C4—22no—
28Dic103⋊C4—22no—
29C4×Dic103—21no—
30C4×Dic103—21no—
31C4×Dic103—21no—
32C4×Dic103—21no—
33C4×Dic103D412yes—
34C4×Dic103D412yes—
35C22×C4×C103C2×C411yescharacteristic
36C22×C4×C103C2×C411yescharacteristic
37C22×C4×C103C2311yescharacteristic
38C2×C8×C103—22no—
39C4⋊C4×C103—22no—
40C23×C103C22×C411yescharacteristic
41C2×C4×C103—21no—
42C2×C4×C103—21no—
43C2×C4×C103—21no—
44C2×C4×C103—41no—
45C2×C4×C103—41no—
46C2×C4×C103M1612yes—
47C2×C4×C103C2×D412yes—
48C2×Dic103—21no—
49C2×Dic103—21no—
50C2×Dic103—21no—
51C2×Dic103—21no—
52C2×Dic103—22no—
53C2×Dic103—21no—
54C2×Dic103—41no—
55C2×Dic103C22⋊C411yescharacteristic
56C2×Dic103C22⋊C412yes—
57C2×Dic103C22⋊C411yescharacteristic
58C2×Dic103M1612yes—
59Dic206—28no—
60C8×C103—42no—
61C103⋊C8—42no—
62C22×C103—21no—
63C22×C103—21no—
64C22×C103C2×C22⋊C411yescharacteristic
65C22×C103C2×M1611yescharacteristic
66C22×C103C2×M1611yescharacteristic
67C4×C103—22no—
68C4×C103—22no—
69C4×C103—41no—
70Dic103—22no—
71Dic103—22no—
72Dic103—21no—
73Dic103—41no—
74Dic103#10112yes—
75C2×C103—21no—
76C2×C103—21no—
77C2×C103#40711yescharacteristic
78C2×C103#41011yescharacteristic
79C2×C103C2×#10111yescharacteristic
80#1467—1031nomaximal, Sylow
81C103#146711yescharacteristic, complemented, Sylow
82C2×C4×Q8—1031no—
83#432—1032no—
84#324—1031no—
85#324—1032no—
86#324D10311yescharacteristic
87C22×Q8—1031no—
88C4×Q8—2062no—
89C4×Q8—2062no—
90C2×C4⋊C4—1031no—
91C2×C4⋊C4—1031no—
92C2×C4⋊C4C2×D10311yescharacteristic
93C2×C42—1031no—
94C2×C42—1031no—
95C2×C42—1031no—
96C4⋊C8—2062no—
97C22⋊C8—1032no—
98C22⋊C8C2×D10312yes—
99#97—2062no—
100C2×Q8—2062no—
101C2×Q8—2062no—
102C2×Q8—2062no—
103C22×C4—1031no—
104C22×C4—1031no—
105C22×C4—1031no—
106C22×C4—1031no—
107C22×C4C4×D10311yescharacteristic
108C22×C4C4×D10311yescharacteristic
109C22×C4C22×D10311yescharacteristic
110C2×C8—22no—
111C2×C8—2062no—
112C4⋊C4—22no—
113C4⋊C4—2062no—
114C4⋊C4—2062no—
115C42—1032no—
116C42—1032no—
117C42—2061no—
118C42—2061no—
119C42—2061no—
120C42—2061no—
121C23C2×C4×D10311yescharacteristic
122Q8—2068no—
123C2×C4—21no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—41no—
127C2×C4—41no—
128C2×C4—1031no—
129C2×C4—1031no—
130C2×C4—1032no—
131C2×C4—1032no—
132C2×C4—4121no—
133C2×C4—2062no—
134C2×C4—2061no—
135C2×C4—2061no—
136C2×C4—2061no—
137C2×C4—2061no—
138C2×C4—2061no—
139C2×C4#1311008812yes—
140C2×C4D4×D10312yes—
141C8—42no—
142C8—4122no—
143C22—21no—
144C22—21no—
145C22C22⋊C4×D10311yescharacteristic
146C22M16×D10311yescharacteristic
147C22C2×#1311008811yescharacteristic
148C4—22no—
149C4—22no—
150C4—41no—
151C4—1032no—
152C4—4121no—
153C4—2062no—
154C4—2062no—
155C4—2061no—
156C2—21no—
157C2—21no—
158C2#2026775311yescharacteristic
159C2#2026776311yescharacteristic
160C2#101×D10311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D103
commutator, prime radicalC23×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#324×C103C2
socleC22×C103C2×C22⋊C4
cosocleC22×C4×C103C23
hypercenter#324D103
hypocenterC103#1467
LCSG ▷ C23×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
81. C103#1467semidirect

Maximal subgroups

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

subgroupindex
C2×#156929862
#202678452
#202675172
#202675162
#324×C1032
#1467103