Finite Group Databasebeta

← #27193547

Subgroups — #27193547

Order 13184.

216 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 97 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#20267844C211yesmaximal, characteristic
2C2×C4⋊(C103⋊C8)C211yesmaximal, characteristic
3Q8⋊(C103⋊C8)C214yesmaximal, complemented
4#533×C103C211yesmaximal, characteristic
5C22×C103⋊C8—21no—
6C4⋊(C103⋊C8)—21no—
7C4⋊(C103⋊C8)—21no—
8C4⋊(C103⋊C8)C2212yes—
9C22⋊(C103⋊C8)—21no—
10C4×C103⋊C8C2212yes—
11C4⋊Q8×C103C411yescharacteristic
12C4⋊Q8×C103C411yescharacteristic
13#125×C103—21no—
14C22⋊Q8×C103—21no—
15C22⋊Q8×C103C412yes—
16C4×Q8×C103—21no—
17C4×Q8×C103C2212yes—
18#117×C103—21no—
19C2×C42×C103C2211yescharacteristic
20C2×C103⋊C8—22no—
21C2×C103⋊C8—22no—
22C2×C103⋊C8—42no—
23C2×Q8×C103—21no—
24C2×Q8×C103C2×C412yes—
25C22×C4×C103C2×C411yescharacteristic
26C22×C4×C103D411yescharacteristic
27C22×C4×C103D411yescharacteristic
28C4⋊C4×C103—21no—
29C4⋊C4×C103—21no—
30C4⋊C4×C103—21no—
31C4⋊C4×C103—22no—
32C4⋊C4×C103—22no—
33C4⋊C4×C103C2×C412yes—
34C22⋊C4×C103—22no—
35C42×C103—22no—
36C42×C103C2×C411yescharacteristic
37C42×C103D411yescharacteristic
38C42×C103D411yescharacteristic
39C42×C103C2311yescharacteristic
40C23×C103C22⋊C411yescharacteristic
41Q8×C103—24no—
42Q8×C103—42no—
43C2×C4×C103—22no—
44C2×C4×C103—22no—
45C2×C4×C103—22no—
46C2×C4×C103—41no—
47C2×C4×C103C22⋊C411yescharacteristic
48C2×C4×C103C22⋊C411yescharacteristic
49C2×C4×C103C22⋊C411yescharacteristic
50C2×C4×C103SD1612yes—
51C2×C4×C103Q1612yes—
52C2×C4×C103C22×C411yescharacteristic
53C2×C4×C103C2×D411yescharacteristic
54C2×C4×C103C2×D411yescharacteristic
55C103⋊C8—42no—
56C103⋊C8—42no—
57C22×C103—21no—
58C22×C103—21no—
59C22×C103#10312yes—
60C22×C103C2×C22⋊C411yescharacteristic
61C4×C103—21no—
62C4×C103—21no—
63C4×C103—21no—
64C4×C103—42no—
65C4×C103—42no—
66C4×C103#10312yes—
67C4×C103#13112yes—
68C4×C103C2×SD1611yescharacteristic
69C4×C103C2×Q1611yescharacteristic
70C2×C103—22no—
71C2×C103#40811yescharacteristic
72C2×C103C2×#10311yescharacteristic
73C2×C103#42111yescharacteristic
74#1481—1031nomaximal, Sylow
75C103#148111yescharacteristic, complemented, Sylow
76#533D10311yescharacteristic
77#431—1031no—
78C2×C4⋊C8—1031no—
79Q8⋊C8—1034no—
80C22×C8—2061no—
81C4⋊Q8Dic10311yescharacteristic
82C4⋊Q8Dic10311yescharacteristic
83#125—21no—
84C22⋊Q8—21no—
85C22⋊Q8Dic10312yes—
86C4×Q8—21no—
87C4×Q8C2×D10312yes—
88#117—21no—
89C2×C42C2×D10311yescharacteristic
90C4⋊C8—1032no—
91C4⋊C8—2061no—
92C4⋊C8—2061no—
93C22⋊C8—2061no—
94C4×C8—1032no—
95C2×Q8—21no—
96C2×Q8C2×Dic10312yes—
97C22×C4C2×Dic10311yescharacteristic
98C22×C4C22⋊D10311yescharacteristic
99C22×C4C22⋊D10311yescharacteristic
100C2×C8—4122no—
101C2×C8—2062no—
102C2×C8—2062no—
103C4⋊C4—21no—
104C4⋊C4—21no—
105C4⋊C4—21no—
106C4⋊C4—22no—
107C4⋊C4—22no—
108C4⋊C4C2×Dic10312yes—
109C22⋊C4—22no—
110C42—22no—
111C42C2×Dic10311yescharacteristic
112C42C22⋊D10311yescharacteristic
113C42C22⋊D10311yescharacteristic
114C42C22×D10311yescharacteristic
115C23C22⋊Dic10311yescharacteristic
116Q8—24no—
117Q8—42no—
118C2×C4—22no—
119C2×C4—22no—
120C2×C4—22no—
121C2×C4—41no—
122C2×C4C22⋊Dic10311yescharacteristic
123C2×C4C22⋊Dic10311yescharacteristic
124C2×C4C22⋊Dic10311yescharacteristic
125C2×C4#1311009212yes—
126C2×C4#1311009512yes—
127C2×C4C22×Dic10311yescharacteristic
128C2×C4C2×C22⋊D10311yescharacteristic
129C2×C4C2×C22⋊D10311yescharacteristic
130C8—4122no—
131C8—4122no—
132C22—21no—
133C22—21no—
134C22#1569294512yes—
135C22C2×C22⋊Dic10311yescharacteristic
136C4—21no—
137C4—21no—
138C4—21no—
139C4—42no—
140C4—42no—
141C4#1569294512yes—
142C4#1569302812yes—
143C4C2×#1311009211yescharacteristic
144C4C2×#1311009511yescharacteristic
145C2—22no—
146C2#2026775811yescharacteristic
147C2C2×#1569294511yescharacteristic
148C2#2026780811yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D103
commutatorC2×C4×C103C22×C4
FrattiniC42C22×D103
Fitting#533×C103C2
socleC22×C103C2×C22⋊C4
prime radicalC23×C103C22⋊C4
cosocleC42×C103C23
hypercenter#533D103
hypocenterC103#1481
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
3. Q8⋊(C103⋊C8)C2semidirect
75. C103#1481semidirect

Maximal subgroups

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

subgroupindex
#202678442
C2×C4⋊(C103⋊C8)2
Q8⋊(C103⋊C8)2
#533×C1032
#1481103