Finite Group Databasebeta

← #27194152

Subgroups — #27194152

Order 13184.

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

normal subgroups only

This group has 210 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#20268119C212yesmaximal
2#20267721C211yesmaximal, characteristic
3#20267528C212yesmaximal
4#20267517C211yesmaximal, characteristic
5#544×C103C211yesmaximal, characteristic
6C2×C4⋊Dic103C2211yescharacteristic
7C2×Dic103⋊C4—21no—
8#15692952—22no—
9#15692945—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
19C22×Dic103—21no—
20C22×Dic103—21no—
21C2×C103⋊C8—22no—
22C4⋊Dic103—22no—
23Dic103⋊C4—42no—
24C2×Q8×C103—21no—
25C2×Q8×C103D412yes—
26C22×C4×C103D411yescharacteristic
27C22×C4×C103D411yescharacteristic
28C22×C4×C103C2311yescharacteristic
29C4⋊C4×C103—21no—
30C4⋊C4×C103—21no—
31C4⋊C4×C103—21no—
32C4⋊C4×C103—22no—
33C4⋊C4×C103—22no—
34C4⋊C4×C103—22no—
35C4⋊C4×C103D412yes—
36C22⋊C4×C103—22no—
37C42×C103—22no—
38C23×C103C2×D411yescharacteristic
39Q8×C103—42no—
40Q8×C103—81no—
41C2×C4×C103—21no—
42C2×C4×C103—21no—
43C2×C4×C103—22no—
44C2×C4×C103—22no—
45C2×C4×C103—21no—
46C2×C4×C103—41no—
47C2×C4×C103—41no—
48C2×C4×C103SD1612yes—
49C2×C4×C103C2×D412yes—
50C2×Dic103—22no—
51C2×Dic103—41no—
52C2×Dic103—41no—
53C2×Dic103—41no—
54C2×Dic103—41no—
55C2×Dic103—41no—
56C103⋊C8—42no—
57C22×C103—21no—
58C22×C103—21no—
59C22×C103#12011yescharacteristic
60C22×C103C2×SD1611yescharacteristic
61C22×C103#13711yescharacteristic
62C4×C103—22no—
63C4×C103—22no—
64C4×C103—42no—
65C4×C103—41no—
66C4×C103—42no—
67Dic103—42no—
68Dic103—81no—
69C2×C103—21no—
70C2×C103—21no—
71C2×C103#44811yescharacteristic
72C2×C103#45611yescharacteristic
73C2×C103#45811yescharacteristic
74#1611—1031nomaximal, Sylow
75C103#161111yescharacteristic, complemented, Sylow
76#544D10311yescharacteristic
77#483—1032no—
78#398—1031no—
79#328—1032no—
80#324—1031no—
81C4⋊Q8—22no—
82#125—22no—
83C22⋊Q8—21no—
84C22⋊Q8C2×D10312yes—
85#117—21no—
86C2×C4⋊C4—1031no—
87C2×C4⋊C4—2061no—
88C2×C4⋊C4C2×D10311yescharacteristic
89#106—2062no—
90#103—2062no—
91C22⋊C8—1032no—
92#95—1031no—
93#95—2061no—
94C2×Q8—21no—
95C2×Q8C22⋊D10312yes—
96C22×C4—2061no—
97C22×C4—2061no—
98C22×C4C22⋊D10311yescharacteristic
99C22×C4C22⋊D10311yescharacteristic
100C22×C4C22×D10311yescharacteristic
101C2×C8—2062no—
102C4⋊C4—21no—
103C4⋊C4—21no—
104C4⋊C4—21no—
105C4⋊C4—22no—
106C4⋊C4—22no—
107C4⋊C4—22no—
108C4⋊C4—4122no—
109C4⋊C4—2062no—
110C4⋊C4C22⋊D10312yes—
111C22⋊C4—22no—
112C42—22no—
113C23C2×C22⋊D10311yescharacteristic
114Q8—42no—
115Q8—81no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—22no—
119C2×C4—22no—
120C2×C4—21no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—4121no—
124C2×C4—4121no—
125C2×C4—4121no—
126C2×C4—4121no—
127C2×C4—4121no—
128C2×C4—2062no—
129C2×C4#1311009212yes—
130C2×C4C2×C22⋊D10312yes—
131C8—4122no—
132C22—21no—
133C22—21no—
134C22#1569299011yescharacteristic
135C22C2×#1311009211yescharacteristic
136C22#1569305211yescharacteristic
137C4—22no—
138C4—22no—
139C4—42no—
140C4—41no—
141C4—42no—
142C4—8241no—
143C4—4122no—
144C2—21no—
145C2—21no—
146C2#2026793011yescharacteristic
147C2#2026797411yescharacteristic
148C2#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#1611
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
75. C103#1611semidirect

Maximal subgroups

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

subgroupindex
#202681192
#202677212
#202675282
#202675172
#544×C1032
#1611103