Finite Group Databasebeta

← #27194118

Subgroups — #27194118

Order 13184.

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

normal subgroups only

This group has 238 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#20267946C212yesmaximal
2#20267711C211yesmaximal, characteristic
3#20267528C212yesmaximal
4#20267517C211yesmaximal, characteristic
5#544×C103C211yesmaximal, characteristic
6C22×Dic206C2211yescharacteristic
7C2×#13110095—22no—
8C2×Dic103⋊C4—21no—
9#15692944—22no—
10C22⋊(C103⋊C8)C2212yes—
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
19C2×Dic206—22no—
20C2×Dic206—42no—
21C22×Dic103—21no—
22C22×Dic103—21no—
23#13110095—44no—
24C2×C103⋊C8—22no—
25Dic103⋊C4—42no—
26C2×Q8×C103—21no—
27C2×Q8×C103D412yes—
28C22×C4×C103D411yescharacteristic
29C22×C4×C103D411yescharacteristic
30C22×C4×C103C2311yescharacteristic
31C4⋊C4×C103—21no—
32C4⋊C4×C103—21no—
33C4⋊C4×C103—21no—
34C4⋊C4×C103—22no—
35C4⋊C4×C103—22no—
36C4⋊C4×C103—22no—
37C4⋊C4×C103D412yes—
38C22⋊C4×C103—22no—
39C42×C103—22no—
40C23×C103C2×D411yescharacteristic
41Q8×C103—42no—
42Q8×C103—81no—
43C2×C4×C103—21no—
44C2×C4×C103—21no—
45C2×C4×C103—22no—
46C2×C4×C103—22no—
47C2×C4×C103—21no—
48C2×C4×C103—41no—
49C2×C4×C103—41no—
50C2×C4×C103Q1612yescomplemented
51C2×C4×C103C2×D412yes—
52C2×Dic103—22no—
53C2×Dic103—22no—
54C2×Dic103—41no—
55C2×Dic103—41no—
56C2×Dic103—41no—
57C2×Dic103—41no—
58Dic206—24no—
59Dic206—42no—
60C103⋊C8—42no—
61C22×C103—21no—
62C22×C103—21no—
63C22×C103#12011yescharacteristic
64C22×C103C2×Q1611yescharacteristic
65C22×C103#13711yescharacteristic
66C4×C103—22no—
67C4×C103—22no—
68C4×C103—42no—
69C4×C103—41no—
70C4×C103—42no—
71Dic103—42no—
72Dic103—42no—
73C2×C103—21no—
74C2×C103—21no—
75C2×C103#45111yescharacteristic
76C2×C103#45611yescharacteristic
77C2×C103B(4,𝔽2)11yescharacteristic
78#1605—1031nomaximal, Sylow
79C103#160511yescharacteristic, complemented, Sylow
80#544D10311yescharacteristic
81#451—1032no—
82#395—1031no—
83#328—1032no—
84#324—1031no—
85C22×Q8—1031no—
86C2×Q16—2062no—
87C4⋊Q8—22no—
88#125—22no—
89C22⋊Q8—21no—
90C22⋊Q8C2×D10312yes—
91#117—21no—
92C2×C4⋊C4—2061no—
93C2×C4⋊C4C2×D10311yescharacteristic
94#103—2062no—
95C22⋊C8—1032no—
96#95—1031no—
97#95—2061no—
98C2×Q8—21no—
99C2×Q8—4122no—
100C2×Q8—2062no—
101C2×Q8C22⋊D10312yes—
102C22×C4—2061no—
103C22×C4—2061no—
104C22×C4C22⋊D10311yescharacteristic
105C22×C4C22⋊D10311yescharacteristic
106C22×C4C22×D10311yescharacteristic
107Q16—4124no—
108C2×C8—2062no—
109C4⋊C4—21no—
110C4⋊C4—21no—
111C4⋊C4—21no—
112C4⋊C4—22no—
113C4⋊C4—22no—
114C4⋊C4—22no—
115C4⋊C4—4122no—
116C4⋊C4C22⋊D10312yes—
117C22⋊C4—22no—
118C42—22no—
119C23C2×C22⋊D10311yescharacteristic
120Q8—42no—
121Q8—81no—
122Q8—4122no—
123Q8—2064no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—22no—
127C2×C4—22no—
128C2×C4—21no—
129C2×C4—41no—
130C2×C4—41no—
131C2×C4—4121no—
132C2×C4—4121no—
133C2×C4—4121no—
134C2×C4—4121no—
135C2×C4—2062no—
136C2×C4—2062no—
137C2×C4#1311009512yescomplemented
138C2×C4C2×C22⋊D10312yes—
139C8—4122no—
140C22—21no—
141C22—21no—
142C22#1569299011yescharacteristic
143C22C2×#1311009511yescharacteristic
144C22#1569305211yescharacteristic
145C4—22no—
146C4—22no—
147C4—42no—
148C4—41no—
149C4—42no—
150C4—4122no—
151C4—4122no—
152C2—21no—
153C2—21no—
154C2#2026794711yescharacteristic
155C2#2026797411yescharacteristic
156C2#2026797811yescharacteristic
subgroupG/H
centerC22#15692990
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
Fitting#544×C103C2
socleC22×C103#120
prime radicalC23×C103C2×D4
hypercenter#544D103
hypocenterC103#1605
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
50. C2×C4×C103Q16semidirect
79. C103#1605semidirect
137. C2×C4#13110095semidirect

Maximal subgroups

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

subgroupindex
#202679462
#202677112
#202675282
#202675172
#544×C1032
#1605103