Finite Group Databasebeta

← #27194188

Subgroups — #27194188

Order 13184.

202 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 53 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#20268422C211yesmaximal, characteristic
2#20268127C212yesmaximal
3#20267730C211yesmaximal, characteristic
4#20267529C212yesmaximal
5#324×C103C211yesmaximal, characteristic
6#15693020—22no—
7#15693012—22no—
8#15693000—21no—
9#15693000C2212yes—
10#15692980—21no—
11C2×C4⋊Dic103C2211yescharacteristic
12#15692955—22no—
13#15692946—22no—
14C103⋊#95—21no—
15C103⋊#95—21no—
16C103⋊#95C2211yescharacteristic
17C2×C4⋊C4×C103C2211yescharacteristic
18C22⋊C8×C103C2212yes—
19C2×Dic206—21no—
20C2×Dic206D412yes—
21C22×Dic103—21no—
22C22×Dic103—21no—
23C4⋊Dic103—21no—
24C4⋊Dic103—21no—
25C4⋊Dic103—21no—
26C4⋊Dic103—22no—
27C4⋊Dic103D412yes—
28Dic103⋊C4—22no—
29Dic103⋊C4—22no—
30C22⋊Dic103—22no—
31C4×Dic103—22no—
32C22×C4×C103D411yescharacteristic
33C22×C4×C103D411yescharacteristic
34C22×C4×C103C2311yescharacteristic
35C2×C8×C103—22no—
36C4⋊C4×C103—22no—
37C23×C103C2×D411yescharacteristic
38C2×C4×C103—21no—
39C2×C4×C103—21no—
40C2×C4×C103—21no—
41C2×C4×C103—41no—
42C2×C4×C103—41no—
43C2×C4×C103Q1612yes—
44C2×C4×C103C2×D412yes—
45C2×Dic103—22no—
46C2×Dic103—22no—
47C2×Dic103—41no—
48C2×Dic103—41no—
49C2×Dic103—42no—
50C2×Dic103—41no—
51C2×Dic103—41no—
52Dic206—42no—
53Dic206—81no—
54C8×C103—42no—
55C22×C103—21no—
56C22×C103—21no—
57C22×C103#12011yescharacteristic
58C22×C103C2×Q1611yescharacteristic
59C22×C103#13711yescharacteristic
60C4×C103—22no—
61C4×C103—22no—
62C4×C103—41no—
63Dic103—42no—
64Dic103—42no—
65Dic103—81no—
66Dic103—81no—
67C2×C103—21no—
68C2×C103—21no—
69C2×C103#45111yescharacteristic
70C2×C103#45411yescharacteristic
71C2×C103#45811yescharacteristic
72#1617—1031nomaximal, Sylow
73C103#161711yescharacteristic, complemented, Sylow
74#544—1031no—
75#484—1032no—
76#400—1031no—
77#328—1032no—
78#324D10311yescharacteristic
79C4⋊Q8—2062no—
80#125—2062no—
81C22⋊Q8—1032no—
82C22⋊Q8—2061no—
83#117—2061no—
84C2×C4⋊C4—1031no—
85C2×C4⋊C4C2×D10311yescharacteristic
86#107—2062no—
87#103—2062no—
88C22⋊C8C2×D10312yes—
89#95—1031no—
90#95—2061no—
91#95—2061no—
92C2×Q8—1032no—
93C2×Q8—2061no—
94C22×C4—2061no—
95C22×C4—2061no—
96C22×C4D41211yescharacteristic
97C22×C4D41211yescharacteristic
98C22×C4C22×D10311yescharacteristic
99C2×C8—22no—
100C4⋊C4—22no—
101C4⋊C4—1032no—
102C4⋊C4—2062no—
103C4⋊C4—2061no—
104C4⋊C4—2061no—
105C4⋊C4—2061no—
106C4⋊C4—2062no—
107C4⋊C4—2062no—
108C22⋊C4—2062no—
109C42—2062no—
110C23C2×D41211yescharacteristic
111Q8—8241no—
112Q8—4122no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—4121no—
119C2×C4—4121no—
120C2×C4—4122no—
121C2×C4—4121no—
122C2×C4—4121no—
123C2×C4—2062no—
124C2×C4—2062no—
125C2×C4Dic41212yes—
126C2×C4D4×D10312yes—
127C8—42no—
128C22—21no—
129C22—21no—
130C22#1569299111yescharacteristic
131C22C2×Dic41211yescharacteristic
132C22#1569305411yescharacteristic
133C4—22no—
134C4—22no—
135C4—41no—
136C4—8241no—
137C4—8241no—
138C4—4122no—
139C4—4122no—
140C2—21no—
141C2—21no—
142C2#2026794911yescharacteristic
143C2#2026796611yescharacteristic
144C2#2026798211yescharacteristic
subgroupG/H
centerC22#15692991
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
Fitting#324×C103C2
socleC22×C103#120
prime radicalC23×C103C2×D4
hypercenter#324D103
hypocenterC103#1617
LCSG ▷ C22×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
73. C103#1617semidirect

Maximal subgroups

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

subgroupindex
#202684222
#202681272
#202677302
#202675292
#324×C1032
#1617103