Finite Group Databasebeta

← #3861×Dic13⋊C3 #37524668

Subgroups — #3861×Dic13⋊C3 #37524668

Order 22932.

360 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 94 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×C13⋊C3×#3861C211yesmaximal, characteristic
2Dic13×#3861C311yesmaximal, characteristic, complemented
3#21439550C311yesmaximal, characteristic, complemented
4#21439549C311yesmaximal, characteristic, complemented
5C72×Dic13⋊C3C311yesmaximal, characteristic, complemented
6C13⋊C3×#3861C411yescharacteristic, complemented, Hall
7C2×#14274262C2×C311yescharacteristic
8C2×#14274263C2×C311yescharacteristic
9C2×C13×#3861C2×C311yescharacteristic
10C2×C72×C13⋊C3C2×C311yescharacteristic
11ΓL(1,𝔽8)×Dic13⋊C3—77nomaximal
12ΓL(1,𝔽8)×Dic13⋊C3—71nomaximal
13C72×Dic13C3211yescharacteristic, complemented, Hall
14#14274263C3×C411yescharacteristic, complemented
15#14274262C3×C411yescharacteristic, complemented
16C13×#3861C3×C411yescharacteristic, complemented
17C72×C13⋊C3C3×C411yescharacteristic, complemented
18C3×C4×#3861—131nomaximal, Hall
19C2×ΓL(1,𝔽8)×C13⋊C3—77no—
20C2×ΓL(1,𝔽8)×C13⋊C3—71no—
21C2×C72×C13C2×C3211yescharacteristic
22#11763958—71no—
23#11763958—77no—
24#11763957—71no—
25#11763957—77no—
26ΓL(1,𝔽8)×Dic13—77no—
27ΓL(1,𝔽8)×Dic13—71no—
28C7×Dic13⋊C3ΓL(1,𝔽8)11yescharacteristic, complemented
29C7×Dic13⋊C3ΓL(1,𝔽8)17yescomplemented
30C2×C3×#3861—131no—
31ΓL(1,𝔽8)×C13⋊C3—77no—
32ΓL(1,𝔽8)×C13⋊C3—71no—
33C72×C13C32×C411yescharacteristic, complemented, Hall
34C3×C4×C72—131no—
35C4×#3861—131no—
36C4×#3861—131no—
37C4×#3861—131no—
38C2×#63271—71no—
39C2×#63271—77no—
40C2×#63270—71no—
41C2×#63270—77no—
42C2×C13×ΓL(1,𝔽8)—77no—
43C2×C13×ΓL(1,𝔽8)—71no—
44C2×C7×C13⋊C3C2×ΓL(1,𝔽8)11yescharacteristic
45C2×C7×C13⋊C3C2×ΓL(1,𝔽8)17yes—
46C3×Dic13⋊C3—491noHall
47C3×#3861—131noHall
48C7×Dic13C3×ΓL(1,𝔽8)11yescharacteristic, complemented
49C7×Dic13C3×ΓL(1,𝔽8)17yescomplemented
50C2×C3×C72—131no—
51C2×#3861—131no—
52C2×#3861—131no—
53C2×#3861D13⋊C311yescharacteristic
54#63271—71no—
55#63271—77no—
56#63270—71no—
57#63270—77no—
58C7×C13⋊C3C4×ΓL(1,𝔽8)11yescharacteristic, complemented
59C7×C13⋊C3C4×ΓL(1,𝔽8)17yescomplemented
60C13×ΓL(1,𝔽8)—77no—
61C13×ΓL(1,𝔽8)—71no—
62C3×C4×ΓL(1,𝔽8)—917no—
63C3×C4×ΓL(1,𝔽8)—911no—
64C2×C3×C13⋊C3—491no—
65C4×C72—131noHall
66C2×C7×C13C2×C3×ΓL(1,𝔽8)11yescharacteristic
67C2×C7×C13C2×C3×ΓL(1,𝔽8)17yes—
68C3×Dic13—491no—
69Dic13⋊C3—491no—
70Dic13⋊C3—491no—
71Dic13⋊C3#386111yescharacteristic, direct product factor
72C3×C72—131no—
73#3861—131no—
74#3861—131no—
75#3861Dic13⋊C311yescharacteristic, direct product factor
76C2×C3×ΓL(1,𝔽8)—917no—
77C2×C3×ΓL(1,𝔽8)—911no—
78C3×C13⋊C3—491noHall
79C2×C72C3×D13⋊C311yescharacteristic
80C7×C13C3×C4×ΓL(1,𝔽8)11yescharacteristic, complemented
81C7×C13C3×C4×ΓL(1,𝔽8)17yescomplemented
82C3×C4×C7—131no—
83C3×C4×C7—137no—
84C4×ΓL(1,𝔽8)—2737no—
85C4×ΓL(1,𝔽8)—911no—
86C4×ΓL(1,𝔽8)—911no—
87C4×ΓL(1,𝔽8)—911no—
88C4×ΓL(1,𝔽8)—917no—
89C4×ΓL(1,𝔽8)—917no—
90C2×C3×C13—491no—
91C2×C13⋊C3—491no—
92C2×C13⋊C3—491no—
93C2×C13⋊C3C2×#386111yescharacteristic
94C3×ΓL(1,𝔽8)—917no—
95C3×ΓL(1,𝔽8)—911no—
96Dic13C3×#386111yescharacteristic, complemented, Hall
97C72C3×Dic13⋊C311yescharacteristic, complemented, Sylow
98C2×C3×C7—131no—
99C2×C3×C7—137no—
100C2×ΓL(1,𝔽8)—77no—
101C2×ΓL(1,𝔽8)—71no—
102C2×ΓL(1,𝔽8)—911no—
103C2×ΓL(1,𝔽8)—917no—
104C2×ΓL(1,𝔽8)—911no—
105C2×ΓL(1,𝔽8)—917no—
106C3×C13—491no—
107C13⋊C3—491no—
108C13⋊C3—491no—
109C13⋊C3C4×#386111yescharacteristic, complemented
110C32×C4—6371noHall
111C4×C7—131no—
112C4×C7—397no—
113C2×C13C2×C3×#386111yescharacteristic
114C3×C7—131no—
115C3×C7—137no—
116ΓL(1,𝔽8)—77no—
117ΓL(1,𝔽8)—71no—
118ΓL(1,𝔽8)—911no—
119ΓL(1,𝔽8)—917no—
120ΓL(1,𝔽8)—911no—
121ΓL(1,𝔽8)—917no—
122C2×C32—6371no—
123C2×C7ΓL(1,𝔽8)×D13⋊C311yescharacteristic
124C2×C7ΓL(1,𝔽8)×D13⋊C317yes—
125C13C3×C4×#386111yescharacteristic, complemented, Sylow
126C3×C4—131no—
127C3×C4—19111no—
128C3×C4—6371no—
129C3×C4—6371no—
130C32—6371noSylow
131C7ΓL(1,𝔽8)×Dic13⋊C311yescharacteristic, complemented
132C7ΓL(1,𝔽8)×Dic13⋊C317yescomplemented
133C2×C3—131no—
134C2×C3—491no—
135C2×C3—6371no—
136C2×C3—6371no—
137C4—391noSylow
138C3—131no—
139C3—491no—
140C3—6371no—
141C3—6371no—
142C2D13⋊C3×#386111yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2D13⋊C3×#3861
commutator, hypocenterC72×C13C32×C4
Fitting, socle, cosocleC2×C72×C13C2×C32
prime radicalC2×C13⋊C3×#3861C2
LCSG ▷ C72×C13
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. Dic13×#3861C3semidirect
3. #21439550C3semidirect
4. #21439549C3semidirect
5. C72×Dic13⋊C3C3semidirect
6. C13⋊C3×#3861C4semidirect
13. C72×Dic13C32semidirect
14. #14274263C3×C4semidirect
15. #14274262C3×C4semidirect
16. C13×#3861C3×C4semidirect
17. C72×C13⋊C3C3×C4semidirect
28. C7×Dic13⋊C3ΓL(1,𝔽8)semidirect
29. C7×Dic13⋊C3ΓL(1,𝔽8)semidirect
33. C72×C13C32×C4semidirect
48. C7×Dic13C3×ΓL(1,𝔽8)semidirect
49. C7×Dic13C3×ΓL(1,𝔽8)semidirect
58. C7×C13⋊C3C4×ΓL(1,𝔽8)semidirect
59. C7×C13⋊C3C4×ΓL(1,𝔽8)semidirect
71. Dic13⋊C3#3861direct (N × H)
75. #3861Dic13⋊C3direct (N × H)
80. C7×C13C3×C4×ΓL(1,𝔽8)semidirect
81. C7×C13C3×C4×ΓL(1,𝔽8)semidirect
96. Dic13C3×#3861semidirect
97. C72C3×Dic13⋊C3semidirect
109. C13⋊C3C4×#3861semidirect
125. C13C3×C4×#3861semidirect
131. C7ΓL(1,𝔽8)×Dic13⋊C3semidirect
132. C7ΓL(1,𝔽8)×Dic13⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×C13⋊C3×#38612
Dic13×#38613
#214395503
#214395493
C72×Dic13⋊C33
ΓL(1,𝔽8)×Dic13⋊C37
C3×C4×#386113