Finite Group Databasebeta

← #15674559

Subgroups — #15674559

Order 2944.

246 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 67 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#13093048C211yesmaximal, characteristic
2#13092427C212yesmaximal
3#13092322C211yesmaximal, characteristic
4#13092178C212yesmaximal
5C23×#343C211yesmaximal, characteristic
6C22×Dic46C2211yescharacteristic
7C2×M16×C23C2212yes—
8C2×C4⋊C4×C23C2211yescharacteristic
9#10625097C2212yes—
10#10625095—22no—
11C2×C4×Dic23C2211yescharacteristic
12#10625061—22no—
13#10625059—22no—
14C23⋊#95—22no—
15#10624998—22no—
16#10624998—22no—
17C22×C4×C23D412yes—
18C22×C4×C23C2311yescharacteristic
19C22×Dic23—21no—
20C22×Dic23—21no—
21C2×Dic46—22no—
22C2×Dic46—22no—
23C2×Dic46—21no—
24C2×Dic46—22no—
25C2×Dic46Q812yescomplemented
26M16×C23—22no—
27M16×C23—22no—
28C2×C8×C23—22no—
29C4⋊C4×C23—22no—
30C22⋊Dic23—22no—
31C4⋊Dic23—22no—
32C4⋊Dic23D412yes—
33C4⋊Dic23D412yes—
34Dic23⋊C4—24no—
35C4×Dic23—22no—
36C4×Dic23—22no—
37C23×C23C2×D411yescharacteristic
38C2×C4×C23—22no—
39C2×C4×C23—42no—
40C2×C4×C23C2×D412yes—
41C2×C4×C23C2×Q811yescharacteristic
42C2×C4×C23#4112yes—
43C2×C4×C23#4111yescharacteristic
44C2×Dic23—22no—
45C2×Dic23—22no—
46C2×Dic23—22no—
47C2×Dic23—22no—
48C2×Dic23—41no—
49C2×Dic23—41no—
50C2×Dic23—41no—
51C2×Dic23—41no—
52Dic46—24no—
53Dic46—42no—
54Dic46—82no—
55C8×C23—42no—
56#2028—231nomaximal, Sylow
57C22×C23—21no—
58C22×C23—21no—
59C22×C23#12011yescharacteristic
60C22×C23C22⋊Q811yescharacteristic
61C22×C23#12411yescharacteristic
62C4×C23—42no—
63C4×C23C22⋊Q812yes—
64C4×C23#12412yes—
65Dic23—42no—
66Dic23—42no—
67Dic23—42no—
68Dic23—42no—
69#544—231no—
70#419—232no—
71#391—231no—
72#343D2311yescharacteristic
73#339—232no—
74C2×C23—21no—
75C2×C23—21no—
76C2×C23#39311yescharacteristic
77C2×C23#45511yescharacteristic
78C2×C23#45611yescharacteristic
79C22×Q8—231no—
80C2×M16C2×D2312yes—
81C4⋊Q8—462no—
82#125—462no—
83C22⋊Q8—462no—
84#117—232no—
85C2×C4⋊C4C2×D2311yescharacteristic
86C2×C42—231no—
87#103—462no—
88#103—462no—
89#95—462no—
90C23#202811yescharacteristic, complemented, Sylow
91C2×Q8—232no—
92C2×Q8—462no—
93C2×Q8—461no—
94C2×Q8—462no—
95C2×Q8—462no—
96C22×C4—461no—
97C22×C4—461no—
98C22×C4D9212yes—
99C22×C4C22×D2311yescharacteristic
100M16—22no—
101M16—22no—
102C2×C8—22no—
103C4⋊C4—22no—
104C4⋊C4—232no—
105C4⋊C4—232no—
106C4⋊C4—462no—
107C4⋊C4—464no—
108C22⋊C4—462no—
109C42—462no—
110C42—462no—
111C23C2×D9211yescharacteristic
112Q8—464no—
113Q8—922no—
114Q8—1842no—
115C2×C4—22no—
116C2×C4—42no—
117C2×C4—462no—
118C2×C4—462no—
119C2×C4—462no—
120C2×C4—462no—
121C2×C4—921no—
122C2×C4—921no—
123C2×C4—921no—
124C2×C4—921no—
125C2×C4#6728812yes—
126C2×C4D4×D2312yes—
127C2×C4#6729011yescharacteristic
128C2×C4Q8×D2311yescharacteristic
129C8—42no—
130C22—21no—
131C22—21no—
132C22#1062504611yescharacteristic
133C22#1062505311yescharacteristic
134C22#1062506811yescharacteristic
135C4—42no—
136C4—922no—
137C4—922no—
138C4—922no—
139C4—922no—
140C4#1062505612yes—
141C4#1062506712yes—
142C2—21no—
143C2—21no—
144C2#1309233011yescharacteristic
145C2#1309259711yescharacteristic
146C2#1309260211yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#343C2
socleC22×C23#120
prime radicalC23×C23C2×D4
hypercenter#343D23
hypocenterC23#2028
LCSG ▷ C22×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
25. C2×Dic46Q8semidirect
90. C23#2028semidirect

Maximal subgroups

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

subgroupindex
#130930482
#130924272
#130923222
#130921782
C23×#3432
#202823