Finite Group Databasebeta

← #27192966

Subgroups — #27192966

Order 13184.

158 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 61 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#20267689C211yesmaximal, characteristic
2#20267546C211yesmaximal, characteristic
3#336×C103C211yesmaximal, characteristic
4C22×C103⋊C8—21no—
5C2×C4⋊Dic103C411yescharacteristic
6C2×C4⋊Dic103C411yescharacteristic
7C2×Dic103⋊C4—21no—
8C103⋊#95—21no—
9C22×C8×C103—21no—
10C2×C42×C103C2211yescharacteristic
11C22×Dic103—21no—
12C22×Dic103—21no—
13C2×C103⋊C8—22no—
14C2×C103⋊C8—41no—
15C2×C103⋊C8—41no—
16C4⋊Dic103—21no—
17C4⋊Dic103—41no—
18C4⋊Dic103C812yescomplemented
19Dic103⋊C4—41no—
20Dic103⋊C4—41no—
21C22×C4×C103C2×C411yescharacteristic
22C22×C4×C103D411yescharacteristic
23C22×C4×C103D411yescharacteristic
24C2×C8×C103—22no—
25C2×C8×C103—41no—
26C2×C8×C103—41no—
27C42×C103—41no—
28C23×C103C22⋊C411yescharacteristic
29C2×C4×C103—21no—
30C2×C4×C103—21no—
31C2×C4×C103—21no—
32C2×C4×C103—21no—
33C2×C4×C103—21no—
34C2×C4×C103—21no—
35C2×C4×C103C2×C811yescharacteristic
36C2×C4×C103M1611yescharacteristic
37C2×C4×C103D811yescharacteristic
38C2×C4×C103SD1611yescharacteristic
39C2×C4×C103SD1611yescharacteristic
40C2×C4×C103Q1611yescharacteristic
41C2×Dic103—22no—
42C2×Dic103—41no—
43C2×Dic103—41no—
44C2×Dic103—41no—
45C2×Dic103—41no—
46C2×Dic103—41no—
47C8×C103—42no—
48C103⋊C8—42no—
49C22×C103C22⋊C811yescharacteristic
50C22×C103#9911yescharacteristic
51C22×C103#10111yescharacteristic
52C22×C103#10211yescharacteristic
53C22×C103#10311yescharacteristic
54C22×C103#10411yescharacteristic
55C22×C103#10411yescharacteristic
56C4×C103—21no—
57C4×C103—21no—
58C4×C103—21no—
59C4×C103—21no—
60C4×C103—21no—
61C4×C103—21no—
62Dic103—42no—
63Dic103—81no—
64C2×C103#32411yescharacteristic
65C2×C103D4⋊C811yescharacteristic
66C2×C103Q8⋊C811yescharacteristic
67C2×C103#32711yescharacteristic
68C2×C103#32811yescharacteristic
69C2×C103#33011yescharacteristic
70C2×C103#33211yescharacteristic
71#1271—1031nomaximal, Sylow
72C103#127111yescharacteristic, complemented, Sylow
73#389—1031no—
74#336—1031no—
75#336D10311yescharacteristic
76C22×C8—21no—
77C22×C8—2061no—
78C2×C4⋊C4—1031no—
79C2×C4⋊C4—1031no—
80C2×C4⋊C4—2061no—
81C2×C42C2×D10311yescharacteristic
82#95—2061no—
83C22×C4—2061no—
84C22×C4—2061no—
85C22×C4C4×D10311yescharacteristic
86C22×C4D41211yescharacteristic
87C22×C4C22⋊D10311yescharacteristic
88C2×C8—22no—
89C2×C8—41no—
90C2×C8—41no—
91C2×C8—4121no—
92C2×C8—4121no—
93C2×C8—2062no—
94C4⋊C4—1032no—
95C4⋊C4—4121no—
96C4⋊C4—4121no—
97C4⋊C4—4121no—
98C4⋊C4—2061no—
99C42—41no—
100C23(C2×D103)⋊C411yescharacteristic
101C2×C4—21no—
102C2×C4—21no—
103C2×C4—21no—
104C2×C4—21no—
105C2×C4—21no—
106C2×C4—21no—
107C2×C4—4121no—
108C2×C4—4121no—
109C2×C4—4121no—
110C2×C4—4121no—
111C2×C4—4121no—
112C2×C4—2062no—
113C2×C4C8×D10311yescharacteristic
114C2×C4#1311008811yescharacteristic
115C2×C4D82411yescharacteristic
116C2×C4#1311009311yescharacteristic
117C2×C4#1311009411yescharacteristic
118C2×C4#1311009511yescharacteristic
119C8—42no—
120C8—4122no—
121C22(C2×D103)⋊C811yescharacteristic
122C22#1569293511yescharacteristic
123C22#1569293911yescharacteristic
124C22#1569294311yescharacteristic
125C22#1569294411yescharacteristic
126C22#1569294711yescharacteristic
127C22#1569294911yescharacteristic
128C4—21no—
129C4—21no—
130C4—21no—
131C4—21no—
132C4—21no—
133C4—21no—
134C4—8241no—
135C4—4122no—
136C2#2026751611yescharacteristic
137C2#2026752011yescharacteristic
138C2#2026752111yescharacteristic
139C2#2026752611yescharacteristic
140C2#2026752711yescharacteristic
141C2#2026753211yescharacteristic
142C2#2026753611yescharacteristic
subgroupG/H
centerC23(C2×D103)⋊C4
commutatorC2×C4×C103C2×C8
FrattiniC2×C42C2×D103
Fitting#336×C103C2
socle, prime radicalC23×C103C22⋊C4
cosocleC2×C42×C103C22
hypercenter#336D103
hypocenterC103#1271
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ C2×C42 ◁ #336

Complements

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

NH ≅ G/Ntype
18. C4⋊Dic103C8semidirect
72. C103#1271semidirect

Maximal subgroups

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

subgroupindex
#202676892
#202675462
#336×C1032
#1271103