Finite Group Databasebeta

← #15671665

Subgroups — #15671665

Order 2944.

520 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 197 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×C23⋊#95C211yesmaximal, characteristic
2C2×C23⋊#95C214yesmaximal
3C2×C23⋊#95C211yesmaximal, characteristic
4C22×C4⋊C4×C23C211yesmaximal, characteristic
5C23×C4×C23C2212yes—
6C23×C4×C23C2211yescharacteristic
7C23×Dic23C2212yes—
8C23×Dic23C2212yes—
9C2×C4⋊C4×C23—22no—
10C2×C4⋊C4×C23—22no—
11C2×C4⋊C4×C23C414yescomplemented
12C23⋊#95—22no—
13C23⋊#95—22no—
14C23⋊#95—28no—
15C24×C23C2311yescharacteristic
16C22×C4×C23—24no—
17C22×C4×C23—22no—
18C22×C4×C23—22no—
19C22×C4×C23—24no—
20C22×C4×C23—24no—
21C22×C4×C23C2×C414yes—
22C22×C4×C23C2×C412yes—
23C22×C4×C23D412yes—
24C22×C4×C23D412yes—
25C22×Dic23—24no—
26C22×Dic23—22no—
27C22×Dic23—22no—
28C22×Dic23—24no—
29C22×Dic23—24no—
30C22×Dic23—22no—
31C22×Dic23—22no—
32C22×Dic23—24no—
33C22×Dic23D414yes—
34C22×Dic23Q814yes—
35C4⋊C4×C23—28no—
36C23×C23C22×C411yescharacteristic
37C23×C23C2×D412yes—
38C23×C23C2×D411yescharacteristic
39C23×C23C2×D411yescharacteristic
40C23×C23C2×Q812yes—
41C23×C23#4114yes—
42C23×C23#4112yes—
43C23×C23#4112yes—
44C2×C4×C23—24no—
45C2×C4×C23—24no—
46C2×C4×C23—24no—
47C2×C4×C23—24no—
48C2×C4×C23—28no—
49C2×C4×C23—44no—
50C2×C4×C23—42no—
51C2×C4×C23—42no—
52C2×C4×C23C22⋊C414yes—
53C2×Dic23—24no—
54C2×Dic23—28no—
55C2×Dic23—24no—
56C2×Dic23—28no—
57C2×Dic23—44no—
58C2×Dic23—42no—
59C2×Dic23—42no—
60C2×Dic23—42no—
61C2×Dic23—44no—
62C2×Dic23—42no—
63#1445—231nomaximal, Sylow
64C22×C23C2×C22⋊C411yescharacteristic
65C22×C23#11712yes—
66C22×C23C4×D412yes—
67C22×C23C4×Q812yes—
68C22×C23#12112yes—
69C22×C23C22⋊Q814yes—
70C22×C23C22⋊Q812yes—
71C22×C23#12314yes—
72C22×C23#12312yes—
73C22×C23#12312yes—
74C22×C23#12411yescharacteristic
75C22×C23#12411yescharacteristic
76C22×C23#12514yes—
77C22×C23#12614yes—
78C22×C23#12711yescharacteristic
79C22×C23C4⋊Q811yescharacteristic
80C4×C23—24no—
81C4×C23—44no—
82Dic23—44no—
83Dic23—44no—
84C22×C4⋊C4D2311yescharacteristic
85C2×#95—234no—
86C2×#95—231no—
87C2×#95—231no—
88C2×C23#38111yescharacteristic
89C2×C23#38714yes—
90C2×C23#39011yescharacteristic
91C2×C23#39111yescharacteristic
92C2×C23#39712yes—
93C2×C23#39812yes—
94C2×C23#39912yes—
95C2×C23#40012yes—
96C23×C4—232no—
97C23×C4—232no—
98C23×C4C2×D2312yes—
99C23×C4C2×D2311yescharacteristic
100C2×C4⋊C4—22no—
101C2×C4⋊C4—22no—
102C2×C4⋊C4Dic2314yescomplemented
103#95—468no—
104#95—462no—
105#95—462no—
106C23#144511yescharacteristic, complemented, Sylow
107C24C22×D2311yescharacteristic
108C22×C4—24no—
109C22×C4—24no—
110C22×C4—24no—
111C22×C4—22no—
112C22×C4—22no—
113C22×C4—234no—
114C22×C4—234no—
115C22×C4—464no—
116C22×C4—464no—
117C22×C4—464no—
118C22×C4—462no—
119C22×C4—464no—
120C22×C4—462no—
121C22×C4—462no—
122C22×C4—462no—
123C22×C4C2×Dic2314yes—
124C22×C4C2×Dic2312yes—
125C22×C4C22⋊D2312yes—
126C22×C4C22⋊D2312yes—
127C4⋊C4—28no—
128C23#6728814yes—
129C23D4×D2312yes—
130C23#6729012yes—
131C23Q8×D2312yes—
132C23#6729212yes—
133C23C22×Dic2311yescharacteristic
134C23C2×C22⋊D2311yescharacteristic
135C23C2×C22⋊D2311yescharacteristic
136C2×C4—24no—
137C2×C4—24no—
138C2×C4—24no—
139C2×C4—28no—
140C2×C4—24no—
141C2×C4—42no—
142C2×C4—44no—
143C2×C4—42no—
144C2×C4—468no—
145C2×C4—468no—
146C2×C4—464no—
147C2×C4—464no—
148C2×C4—924no—
149C2×C4—924no—
150C2×C4—922no—
151C2×C4—922no—
152C2×C4—922no—
153C2×C4—922no—
154C2×C4C22⋊Dic2314yes—
155C22#1062506014yes—
156C22#1062506514yes—
157C22#1062506714yes—
158C22#1062506914yes—
159C22#1062509712yes—
160C22#1062510012yes—
161C22#1062510012yes—
162C22D4×Dic2312yes—
163C22#1062510711yescharacteristic
164C22#1062510912yes—
165C22#1062511111yescharacteristic
166C22#1062511511yescharacteristic
167C22Q8×Dic2312yes—
168C22#1062511712yes—
169C22#1062511811yescharacteristic
170C22C2×C22⋊Dic2311yescharacteristic
171C4—24no—
172C4—44no—
173C4—924no—
174C4—924no—
175C2#1309228011yescharacteristic
176C2#1309230314yes—
177C2#1309232011yescharacteristic
178C2#1309232411yescharacteristic
179C2#1309234312yes—
180C2#1309234812yes—
181C2#1309235212yes—
182C2#1309235512yes—
subgroupG/H
center, FrattiniC24C22×D23
commutatorC23×C23C22×C4
FittingC22×C4⋊C4×C23C2
socle, prime radical, cosocleC24×C23C23
hypercenterC22×C4⋊C4D23
hypocenterC23#1445
LCSG ▷ C23×C23 ▷ C23
UCSC1 ◁ C24 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
11. C2×C4⋊C4×C23C4semidirect
102. C2×C4⋊C4Dic23semidirect
106. C23#1445semidirect

Maximal subgroups

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

subgroupindex
C2×C23⋊#952
C22×C4⋊C4×C232
#144523