Finite Group Databasebeta

← #15674358

Subgroups — #15674358

Order 2944.

300 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 141 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×#10625040C211yesmaximal, characteristic
2#13092287C211yesmaximal, characteristic
3#13092180C214yesmaximal
4C2×C4×C8×C23C211yesmaximal, characteristic
5C22×Dic46—21no—
6C22×C8×C23C2212yes—
7C2×C42×C23C2211yescharacteristic
8C2×C4⋊Dic23—21no—
9C2×C4⋊Dic23—21no—
10C2×C4⋊Dic23—21no—
11C2×C4⋊Dic23C2212yes—
12C2×C4⋊Dic23C2212yes—
13#10625040—22no—
14#10625040C414yescomplemented
15C4×C8×C23—22no—
16C22×C4×C23D411yescharacteristic
17C22×C4×C23D411yescharacteristic
18C22×C4×C23C2311yescharacteristic
19C22×Dic23—22no—
20C22×Dic23—22no—
21C2×Dic46—24no—
22C2×Dic46—42no—
23C2×Dic46—42no—
24C2×C8×C23—22no—
25C2×C8×C23—22no—
26C2×C8×C23Q814yescomplemented
27C42×C23C2×C412yes—
28C42×C23D412yes—
29C4⋊Dic23—24no—
30C4⋊Dic23—22no—
31C4⋊Dic23—24no—
32C4⋊Dic23—42no—
33C4⋊Dic23—42no—
34C4⋊Dic23C2×C414yes—
35C23×C23C2×D411yescharacteristic
36C2×C4×C23C22⋊C412yes—
37C2×C4×C23C22⋊C412yes—
38C2×C4×C23D812yes—
39C2×C4×C23SD1612yes—
40C2×C4×C23SD1612yes—
41C2×C4×C23Q1612yes—
42C2×C4×C23C22×C411yescharacteristic
43C2×C4×C23C2×D411yescharacteristic
44C2×C4×C23C2×Q812yes—
45C2×C4×C23#4112yes—
46C2×Dic23—24no—
47C2×Dic23—42no—
48C2×Dic23—42no—
49C2×Dic23—42no—
50C2×Dic23—42no—
51C2×Dic23—42no—
52Dic46—48no—
53C8×C23—24no—
54#1990—231nomaximal, Sylow
55C22×C23C2×C22⋊C411yescharacteristic
56C22×C23#12411yescharacteristic
57C22×C23C4⋊Q811yescharacteristic
58C22×C23C2×D811yescharacteristic
59C22×C23C2×SD1611yescharacteristic
60C22×C23C2×SD1611yescharacteristic
61C22×C23C2×Q1611yescharacteristic
62C4×C23#10214yes—
63C4×C23#10314yes—
64C4×C23C4×Q812yes—
65C4×C23C22⋊Q812yes—
66Dic23—44no—
67Dic23—82no—
68C2×C4⋊Q8—231no—
69C2×C4×C8D2311yescharacteristic
70#384—231no—
71#340—234no—
72C2×C23#39111yescharacteristic
73C2×C23C2×#10211yescharacteristic
74C2×C23C2×#10311yescharacteristic
75C2×C23#48611yescharacteristic
76C2×C23#48711yescharacteristic
77C2×C23#49811yescharacteristic
78C2×C23#50011yescharacteristic
79C22×Q8—461no—
80C22×C8C2×D2312yes—
81C4⋊Q8—234no—
82C4⋊Q8—462no—
83C2×C4⋊C4—232no—
84C2×C4⋊C4—232no—
85C2×C4⋊C4—461no—
86C2×C4⋊C4—461no—
87C2×C4⋊C4—461no—
88C2×C42C2×D2311yescharacteristic
89C4×C8—22no—
90C23#199011yescharacteristic, complemented, Sylow
91C2×Q8—464no—
92C2×Q8—922no—
93C2×Q8—922no—
94C22×C4—462no—
95C22×C4—462no—
96C22×C4D9211yescharacteristic
97C22×C4D9211yescharacteristic
98C22×C4C22×D2311yescharacteristic
99C2×C8—22no—
100C2×C8—22no—
101C2×C8Dic4614yescomplemented
102C4⋊C4—234no—
103C4⋊C4—464no—
104C4⋊C4—462no—
105C4⋊C4—464no—
106C4⋊C4—922no—
107C4⋊C4—922no—
108C42C4×D2312yes—
109C42C22⋊D2312yes—
110C23C2×D9211yescharacteristic
111Q8—928no—
112C2×C4—464no—
113C2×C4—922no—
114C2×C4—922no—
115C2×C4—922no—
116C2×C4—922no—
117C2×C4—922no—
118C2×C4#6726312yes—
119C2×C4#6726312yes—
120C2×C4D18412yes—
121C2×C4Dic9212yes—
122C2×C4(C2×D23)⋊C412yes—
123C2×C4(C2×D23)⋊C412yes—
124C2×C4C2×Dic4612yes—
125C2×C4C2×C4×D2311yescharacteristic
126C2×C4#6728812yes—
127C2×C4C2×C22⋊D2311yescharacteristic
128C8—24no—
129C22#1062504011yescharacteristic
130C22#1062504611yescharacteristic
131C22C2×#6726311yescharacteristic
132C22C2×#6726311yescharacteristic
133C22C2×D18411yescharacteristic
134C22C2×Dic9211yescharacteristic
135C22C2×(C2×D23)⋊C411yescharacteristic
136C4—924no—
137C4—1842no—
138C4#1062499814yes—
139C4#1062500314yes—
140C4C4×Dic4612yes—
141C4#1062509512yes—
142C2#1309232311yescharacteristic
143C2C2×#1062500311yescharacteristic
144C2C2×#1062499811yescharacteristic
145C2#1309276411yescharacteristic
146C2#1309276811yescharacteristic
147C2#1309281511yescharacteristic
148C2#1309282211yescharacteristic
subgroupG/H
centerC23C2×D92
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC2×C4×C8×C23C2
socle, prime radicalC23×C23C2×D4
cosocleC22×C4×C23C23
hypercenterC2×C4×C8D23
hypocenterC23#1990
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
14. #10625040C4semidirect
26. C2×C8×C23Q8semidirect
90. C23#1990semidirect
101. C2×C8Dic46semidirect

Maximal subgroups

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

subgroupindex
C2×#106250402
#130922872
#130921802
C2×C4×C8×C232
#199023