Finite Group Databasebeta

← #15673512

Subgroups — #15673512

Order 2944.

260 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 117 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×Dic23⋊C8C212yesmaximal
2C42×Dic23C211yesmaximal, characteristic
3#13092172C211yesmaximal, characteristic
4#13092171C212yesmaximal
5C23×#336C211yesmaximal, characteristic
6C22×C8×C23C2212yes—
7C2×C42×C23C2211yescharacteristic
8C2×C4×Dic23C411yescharacteristic
9C2×C4×Dic23C411yescharacteristic
10C2×C4×Dic23C411yescharacteristic
11C2×C4×Dic23C411yescharacteristic
12C2×C4×Dic23C2211yescharacteristic
13C2×C4×Dic23C2211yescharacteristic
14C22×C23⋊C8C2212yes—
15Dic23⋊C8—24no—
16C22×C4×C23C2×C411yescharacteristic
17C22×C4×C23C2×C411yescharacteristic
18C22×C4×C23C2311yescharacteristic
19C22×Dic23C2×C411yescharacteristic
20C22×Dic23C2×C411yescharacteristic
21C22×Dic23C2×C411yescharacteristic
22C22×Dic23C2×C411yescharacteristic
23C2×C8×C23—22no—
24C2×C8×C23—22no—
25C2×C8×C23—22no—
26C42×C23—22no—
27C4×Dic23—22no—
28C4×Dic23—22no—
29C4×Dic23—22no—
30C4×Dic23—22no—
31C4×Dic23C814yescomplemented
32C4×Dic23D412yes—
33C4×Dic23Q812yes—
34C2×C23⋊C8—22no—
35C2×C23⋊C8—22no—
36C2×C23⋊C8—22no—
37C23×C23C22×C411yescharacteristic
38C2×C4×C23—21no—
39C2×C4×C23—21no—
40C2×C4×C23—21no—
41C2×C4×C23—21no—
42C2×C4×C23C2×C812yes—
43C2×C4×C23M1612yes—
44C2×C4×C23C2×D411yescharacteristic
45C2×C4×C23C2×Q811yescharacteristic
46C2×C4×C23#4112yes—
47C2×C4×C23#4112yes—
48C2×Dic23—21no—
49C2×Dic23—21no—
50C2×Dic23—21no—
51C2×Dic23—21no—
52C2×Dic23—21no—
53C2×Dic23—21no—
54C2×Dic23C4⋊C412yes—
55C2×Dic23C4⋊C412yes—
56C2×Dic23C2×C812yes—
57C2×Dic23C2×C812yes—
58C2×Dic23M1612yes—
59C2×Dic23M1612yes—
60C8×C23—42no—
61C23⋊C8—42no—
62#1831—231nomaximal, Sylow
63C22×C23C2×C4⋊C411yescharacteristic
64C22×C23#11711yescharacteristic
65C22×C23#11711yescharacteristic
66C22×C23C22×C811yescharacteristic
67C22×C23C2×M1611yescharacteristic
68C22×C23C2×M1611yescharacteristic
69C22×C23C2×M1611yescharacteristic
70C4×C23—22no—
71C4×C23—22no—
72C4×C23#12412yes—
73C4×C23#12512yes—
74Dic23—22no—
75Dic23—22no—
76Dic23—22no—
77Dic23C4⋊C814yes—
78C2×C4⋊C8—232no—
79C43—231no—
80#336—232no—
81#336—231no—
82#336D2311yescharacteristic
83C2×C23#38211yescharacteristic
84C2×C23C2×C4⋊C811yescharacteristic
85C2×C23#42311yescharacteristic
86C2×C23#43111yescharacteristic
87C2×C23#43111yescharacteristic
88C2×C23#43211yescharacteristic
89C2×C23#43211yescharacteristic
90C22×C8—232no—
91C22×C8C2×D2312yes—
92C2×C42—231no—
93C2×C42—231no—
94C2×C42—231no—
95C2×C42—231no—
96C2×C42—231no—
97C2×C42—231no—
98C2×C42C2×D2311yescharacteristic
99C4⋊C8—464no—
100C23#183111yescharacteristic, complemented, Sylow
101C22×C4—231no—
102C22×C4—231no—
103C22×C4—231no—
104C22×C4—231no—
105C22×C4C4×D2311yescharacteristic
106C22×C4C4×D2311yescharacteristic
107C22×C4C22×D2311yescharacteristic
108C2×C8—22no—
109C2×C8—22no—
110C2×C8—22no—
111C2×C8—462no—
112C2×C8—462no—
113C2×C8—462no—
114C42—22no—
115C42—234no—
116C42—232no—
117C42—232no—
118C42—462no—
119C42—462no—
120C42—462no—
121C42—462no—
122C23C2×C4×D2311yescharacteristic
123C2×C4—21no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—21no—
127C2×C4—232no—
128C2×C4—232no—
129C2×C4—232no—
130C2×C4—232no—
131C2×C4—232no—
132C2×C4—232no—
133C2×C4—461no—
134C2×C4—461no—
135C2×C4—461no—
136C2×C4—461no—
137C2×C4—461no—
138C2×C4—461no—
139C2×C4C8×D2312yes—
140C2×C4#6726212yes—
141C2×C4#6728812yes—
142C2×C4D4×D2311yescharacteristic
143C2×C4#6729012yes—
144C2×C4Q8×D2311yescharacteristic
145C8—42no—
146C8—922no—
147C22#1062504311yescharacteristic
148C22#1062504811yescharacteristic
149C22C4⋊C4×D2311yescharacteristic
150C22C2×C8×D2311yescharacteristic
151C22C2×#6726211yescharacteristic
152C22M16×D2311yescharacteristic
153C22M16×D2311yescharacteristic
154C4—22no—
155C4—22no—
156C4—234no—
157C4—462no—
158C4—462no—
159C4—462no—
160C4#1062505612yes—
161C4#1062506012yes—
162C2#1309228111yescharacteristic
163C2C4⋊C8×D2311yescharacteristic
164C2#1309243911yescharacteristic
165C2#1309246711yescharacteristic
166C2#1309246811yescharacteristic
167C2#1309247111yescharacteristic
168C2#1309247211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C22×D23
commutatorC22×C23C22×C8
FittingC23×#336C2
socle, prime radicalC23×C23C22×C4
cosocleC22×C4×C23C23
hypercenter#336D23
hypocenterC23#1831
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C22×C4 ◁ #336

Complements

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

NH ≅ G/Ntype
31. C4×Dic23C8semidirect
100. C23#1831semidirect

Maximal subgroups

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

subgroupindex
C2×Dic23⋊C82
C42×Dic232
#130921722
#130921712
C23×#3362
#183123