Finite Group Databasebeta

← #27194186

Subgroups — #27194186

Order 13184.

202 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 57 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#20268124C212yesmaximal
2#20267730C211yesmaximal, characteristic
3#20267528C212yesmaximal
4#20267517C211yesmaximal, characteristic
5#544×C103C211yesmaximal, characteristic
6C2×C4⋊Dic103C2211yescharacteristic
7#15692954—22no—
8#15692945—22no—
9C22⋊(C103⋊C8)C2212yes—
10C103⋊#95—21no—
11C103⋊#95—21no—
12C103⋊#95C2211yescharacteristic
13C4⋊Q8×C103—22no—
14#125×C103—22no—
15C22⋊Q8×C103—21no—
16C22⋊Q8×C103C2212yes—
17#117×C103—21no—
18C2×C4⋊C4×C103C2211yescharacteristic
19C22×Dic103—21no—
20C22×Dic103—21no—
21C2×C103⋊C8—22no—
22C4⋊Dic103—22no—
23C2×Q8×C103—21no—
24C2×Q8×C103D412yes—
25C22×C4×C103D411yescharacteristic
26C22×C4×C103D411yescharacteristic
27C22×C4×C103C2311yescharacteristic
28C4⋊C4×C103—21no—
29C4⋊C4×C103—21no—
30C4⋊C4×C103—21no—
31C4⋊C4×C103—22no—
32C4⋊C4×C103—22no—
33C4⋊C4×C103—22no—
34C4⋊C4×C103D412yes—
35C22⋊C4×C103—22no—
36C42×C103—22no—
37C23×C103C2×D411yescharacteristic
38Q8×C103—42no—
39Q8×C103—81no—
40C2×C4×C103—21no—
41C2×C4×C103—21no—
42C2×C4×C103—22no—
43C2×C4×C103—22no—
44C2×C4×C103—21no—
45C2×C4×C103—41no—
46C2×C4×C103—41no—
47C2×C4×C103Q1612yes—
48C2×C4×C103C2×D412yes—
49C2×Dic103—41no—
50C2×Dic103—41no—
51C2×Dic103—42no—
52C2×Dic103—41no—
53C2×Dic103—41no—
54C103⋊C8—42no—
55C22×C103—21no—
56C22×C103—21no—
57C22×C103#12011yescharacteristic
58C22×C103C2×Q1611yescharacteristic
59C22×C103#13711yescharacteristic
60C4×C103—22no—
61C4×C103—22no—
62C4×C103—42no—
63C4×C103—41no—
64C4×C103—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#544D10311yescharacteristic
75#484—1032no—
76#400—1031no—
77#328—1032no—
78#324—1031no—
79C4⋊Q8—22no—
80#125—22no—
81C22⋊Q8—21no—
82C22⋊Q8C2×D10312yes—
83#117—21no—
84C2×C4⋊C4—1031no—
85C2×C4⋊C4C2×D10311yescharacteristic
86#107—2062no—
87#103—2062no—
88C22⋊C8—1032no—
89#95—1031no—
90#95—2061no—
91#95—2061no—
92C2×Q8—21no—
93C2×Q8C22⋊D10312yes—
94C22×C4—2061no—
95C22×C4—2061no—
96C22×C4C22⋊D10311yescharacteristic
97C22×C4C22⋊D10311yescharacteristic
98C22×C4C22×D10311yescharacteristic
99C2×C8—2062no—
100C4⋊C4—21no—
101C4⋊C4—21no—
102C4⋊C4—21no—
103C4⋊C4—22no—
104C4⋊C4—22no—
105C4⋊C4—22no—
106C4⋊C4—2062no—
107C4⋊C4C22⋊D10312yes—
108C22⋊C4—22no—
109C42—22no—
110C23C2×C22⋊D10311yescharacteristic
111Q8—42no—
112Q8—81no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—22no—
116C2×C4—22no—
117C2×C4—21no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—4121no—
121C2×C4—4121no—
122C2×C4—4122no—
123C2×C4—4121no—
124C2×C4—4121no—
125C2×C4#1311009512yes—
126C2×C4C2×C22⋊D10312yes—
127C8—4122no—
128C22—21no—
129C22—21no—
130C22#1569299011yescharacteristic
131C22C2×#1311009511yescharacteristic
132C22#1569305211yescharacteristic
133C4—22no—
134C4—22no—
135C4—42no—
136C4—41no—
137C4—42no—
138C4—8241no—
139C4—8241no—
140C2—21no—
141C2—21no—
142C2#2026794711yescharacteristic
143C2#2026796411yescharacteristic
144C2#2026798111yescharacteristic
subgroupG/H
centerC22#15692990
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
Fitting#544×C103C2
socleC22×C103#120
prime radicalC23×C103C2×D4
hypercenter#544D103
hypocenterC103#1617
LCSG ▷ C22×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

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
#202681242
#202677302
#202675282
#202675172
#544×C1032
#1617103