Finite Group Databasebeta

← #27195867

Subgroups — #27195867

Order 13184.

248 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 113 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
1C2×C4⋊(C103⋊C8)C211yesmaximal, characteristic
2C2×Dic103⋊C8C212yesmaximal
3C4×C4⋊Dic103C211yesmaximal, characteristic
4#20267545C212yesmaximal
5C2×#97×C103C211yesmaximal, characteristic
6C22×C103⋊C8C2212yes—
7C2×C4⋊Dic103C412yes—
8C2×C4×Dic103C2212yes—
9C4⋊(C103⋊C8)—22no—
10Dic103⋊C8—24no—
11C103⋊#95C411yescharacteristic
12C103⋊#95C411yescharacteristic
13C22×C8×C103C2211yescharacteristic
14C22×C8×C103C2211yescharacteristic
15C2×C42×C103C2211yescharacteristic
16#97×C103—22no—
17C22×Dic103C2×C412yes—
18C22×Dic103C2×C412yes—
19C2×C103⋊C8—22no—
20C2×C103⋊C8—22no—
21C2×C103⋊C8—22no—
22C4⋊Dic103—24no—
23C4×Dic103—22no—
24C4×Dic103—22no—
25C22×C4×C103C2×C411yescharacteristic
26C22×C4×C103C2×C411yescharacteristic
27C22×C4×C103C2311yescharacteristic
28C2×C8×C103—21no—
29C2×C8×C103—21no—
30C2×C8×C103—21no—
31C2×C8×C103—21no—
32C2×C8×C103D412yes—
33C2×C8×C103Q812yes—
34C42×C103D412yes—
35C42×C103Q812yes—
36C23×C103C22×C411yescharacteristic
37C2×C4×C103—22no—
38C2×C4×C103—22no—
39C2×C4×C103C4⋊C412yes—
40C2×C4×C103C4⋊C412yes—
41C2×C4×C103C2×D411yescharacteristic
42C2×C4×C103C2×D411yescharacteristic
43C2×C4×C103C2×Q811yescharacteristic
44C2×C4×C103C2×Q811yescharacteristic
45C2×C4×C103#4111yescharacteristic
46C2×C4×C103#4111yescharacteristic
47C2×Dic103—22no—
48C2×Dic103—22no—
49C2×Dic103—22no—
50C2×Dic103—22no—
51C2×Dic103—22no—
52C2×Dic103M1614yes—
53C8×C103—22no—
54C8×C103—22no—
55C103⋊C8—42no—
56C22×C103C2×C4⋊C411yescharacteristic
57C22×C103C4×D411yescharacteristic
58C22×C103C4×Q811yescharacteristic
59C22×C103C2×M1612yes—
60C22×C103#13112yes—
61C4×C103—22no—
62C4×C103—22no—
63C4×C103#12111yescharacteristic
64C4×C103C22⋊Q811yescharacteristic
65C4×C103#12511yescharacteristic
66C4×C103C4⋊Q811yescharacteristic
67Dic103—24no—
68Dic103—42no—
69C2×C103#38911yescharacteristic
70C2×C103#42311yescharacteristic
71C2×C103#42411yescharacteristic
72C2×C103#43512yes—
73C2×C103#44612yes—
74#1940—1031nomaximal, Sylow
75C103#194011yescharacteristic, complemented, Sylow
76C2×C4⋊C8—1032no—
77C2×C4⋊C8—1031no—
78C2×#97D10311yescharacteristic
79C4×C4⋊C4—1031no—
80#336—1032no—
81C22×C8—1032no—
82C22×C8C2×D10311yescharacteristic
83C22×C8C2×D10311yescharacteristic
84C2×C4⋊C4—1032no—
85C2×C42—1032no—
86C2×C42C2×D10311yescharacteristic
87C4⋊C8—2064no—
88C4⋊C8—2062no—
89#97—22no—
90#95—1031no—
91#95—1031no—
92C22×C4—1032no—
93C22×C4—1032no—
94C22×C4C4×D10311yescharacteristic
95C22×C4C4×D10311yescharacteristic
96C22×C4C22×D10311yescharacteristic
97C2×C8—21no—
98C2×C8—21no—
99C2×C8—21no—
100C2×C8—21no—
101C2×C8—2062no—
102C2×C8—2062no—
103C2×C8—2062no—
104C2×C8Dic20612yes—
105C2×C8D41212yes—
106C4⋊C4—2064no—
107C42—2062no—
108C42—2062no—
109C42Dic20612yes—
110C42C22⋊D10312yes—
111C23C2×C4×D10311yescharacteristic
112C2×C4—22no—
113C2×C4—22no—
114C2×C4—1034no—
115C2×C4—2062no—
116C2×C4—2062no—
117C2×C4—2062no—
118C2×C4—2062no—
119C2×C4—2062no—
120C2×C4Dic103⋊C412yes—
121C2×C4Dic103⋊C412yes—
122C2×C4C2×C22⋊D10311yescharacteristic
123C2×C4C2×D41211yescharacteristic
124C2×C4C2×Dic20611yescharacteristic
125C2×C4C2×Dic20611yescharacteristic
126C2×C4#1311010511yescharacteristic
127C2×C4#1311010511yescharacteristic
128C8—22no—
129C8—22no—
130C8—4122no—
131C22C2×Dic103⋊C411yescharacteristic
132C22C4×D41211yescharacteristic
133C22C4×Dic20611yescharacteristic
134C22M16×D10312yes—
135C22#1569302912yes—
136C4—22no—
137C4—22no—
138C4—4122no—
139C4—2064no—
140C4#1569299511yescharacteristic
141C4#1569300011yescharacteristic
142C4#1569301311yescharacteristic
143C4#1569302111yescharacteristic
144C2#2026768911yescharacteristic
145C2#2026781411yescharacteristic
146C2#2026781911yescharacteristic
147C2#2026786412yes—
148C2#2026791912yes—
subgroupG/H
center, FrattiniC22×C4C22×D103
commutator, socle, prime radicalC23×C103C22×C4
FittingC2×#97×C103C2
cosocleC22×C4×C103C23
hypercenterC2×#97D103
hypocenterC103#1940
LCSG ▷ C23×C103 ▷ C103
UCSC1 ◁ C22×C4 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
75. C103#1940semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊(C103⋊C8)2
C2×Dic103⋊C82
C4×C4⋊Dic1032
#202675452
C2×#97×C1032
#1940103