Finite Group Databasebeta

← #15671764

Subgroups — #15671764

Order 2944.

214 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 69 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×#10625047C211yesmaximal, characteristic
2#13092474C211yesmaximal, characteristic, complemented
3#13092142C212yesmaximal, complemented
4#13092140C212yesmaximal
5C23×#431C211yesmaximal, characteristic, complemented
6C2×C42×C23C2211yescharacteristic
7C2×(C2×D23)⋊C4C411yescharacteristic
8C2×(C2×D23)⋊C4C411yescharacteristic
9C2×(C2×D23)⋊C4C2211yescharacteristic
10C2×Dic23⋊C4C411yescharacteristic
11C2×Dic23⋊C4C411yescharacteristic
12C2×Dic23⋊C4C2211yescharacteristic
13#10625047—21no—
14#10625047—21no—
15#10625047—21no—
16#10625047—21no—
17C23×C4⋊C8—21no—
18C23×C22⋊C8C2212yes—
19C4×C8×C23—21no—
20C22⋊(C23⋊C8)C2212yes—
21C4⋊(C23⋊C8)—21no—
22#10624985—21no—
23C23×D23C2×C411yescharacteristic
24C22×C4×C23C2×C411yescharacteristic
25C22×C4×C23C2×C411yescharacteristic
26C22×C4×C23C2311yescharacteristic
27C22×Dic23C2×C411yescharacteristic
28C22×Dic23C2×C411yescharacteristic
29C22×Dic23C2×C411yescharacteristic
30C2×C8×C23—22no—
31C42×C23D411yescharacteristic
32C42×C23D411yescharacteristic
33C42×C23D411yescharacteristic
34C42×C23D411yescharacteristic
35(C2×D23)⋊C4—21no—
36(C2×D23)⋊C4—21no—
37(C2×D23)⋊C4—21no—
38(C2×D23)⋊C4—21no—
39(C2×D23)⋊C4—21no—
40(C2×D23)⋊C4—21no—
41Dic23⋊C4—21no—
42Dic23⋊C4—21no—
43Dic23⋊C4—21no—
44Dic23⋊C4—21no—
45Dic23⋊C4—21no—
46Dic23⋊C4—21no—
47C2×C23⋊C8—22no—
48C23×C23C22×C411yescharacteristic
49C22×D23—21no—
50C22×D23—22no—
51C22×D23—41no—
52C22×D23—41no—
53C2×C4×C23—22no—
54C2×C4×C23—41no—
55C2×C4×C23—41no—
56C2×C4×C23C22⋊C411yescharacteristic
57C2×C4×C23C22⋊C411yescharacteristic
58C2×C4×C23C22⋊C411yescharacteristic
59C2×C4×C23C22⋊C411yescharacteristic
60C2×C4×C23C2×D411yescharacteristic
61C2×C4×C23C2×D411yescharacteristic
62C2×Dic23—21no—
63C2×Dic23—21no—
64C2×Dic23—21no—
65C2×Dic23—22no—
66C2×Dic23—41no—
67C2×Dic23—41no—
68C8×C23—42no—
69C23⋊C8—42no—
70#1473—231nomaximal, Sylow
71C22×C23—21no—
72C22×C23—21no—
73C22×C23C2×C22⋊C411yescharacteristic
74C22×C23#13112yes—
75C2×D23—41no—
76C2×D23—41no—
77C2×D23—41no—
78C2×D23—82no—
79C4×C23—21no—
80C4×C23—21no—
81C4×C23—21no—
82C4×C23—21no—
83C4×C23—21no—
84C4×C23—21no—
85Dic23—41no—
86Dic23—41no—
87Dic23—41no—
88C2×#126—231no—
89#432—231no—
90#431D2311yescharacteristic, complemented
91#324—232no—
92#323—232no—
93C2×C23—22no—
94C2×C23#40811yescharacteristic
95C2×C23#41011yescharacteristic
96C2×C23#41311yescharacteristic
97D23—81no—
98#126—461no—
99#126—461no—
100#126—461no—
101#126—461no—
102C2×C4⋊C4—231no—
103C2×C4⋊C4—231no—
104C2×C4⋊C4—231no—
105C2×C22⋊C4—231no—
106C2×C22⋊C4—231no—
107C2×C22⋊C4—231no—
108C2×C42C2×D2311yescharacteristic
109C4⋊C8—21no—
110C4⋊C8—461no—
111C22⋊C8—232no—
112C22⋊C8C2×D2312yes—
113#97—461no—
114C4×C8—21no—
115C23#147311yescharacteristic, complemented, Sylow
116C24—231no—
117C22×C4—231no—
118C22×C4—231no—
119C22×C4—231no—
120C22×C4C4×D2311yescharacteristic
121C22×C4C4×D2311yescharacteristic
122C22×C4C22×D2311yescharacteristic
123C2×C8—22no—
124C2×C8—462no—
125C4⋊C4—461no—
126C4⋊C4—461no—
127C4⋊C4—461no—
128C4⋊C4—461no—
129C4⋊C4—461no—
130C4⋊C4—461no—
131C22⋊C4—461no—
132C22⋊C4—461no—
133C22⋊C4—461no—
134C22⋊C4—461no—
135C22⋊C4—461no—
136C22⋊C4—461no—
137C42D9211yescharacteristic
138C42D9211yescharacteristic
139C42C22⋊D2311yescharacteristic
140C42C22⋊D2311yescharacteristic
141C23—461no—
142C23—462no—
143C23—921no—
144C23—921no—
145C23C2×C4×D2311yescharacteristic
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—462no—
150C2×C4—461no—
151C2×C4—461no—
152C2×C4—461no—
153C2×C4—921no—
154C2×C4—921no—
155C2×C4(C2×D23)⋊C411yescharacteristic
156C2×C4(C2×D23)⋊C411yescharacteristic
157C2×C4(C2×D23)⋊C411yescharacteristic
158C2×C4(C2×D23)⋊C411yescharacteristic
159C2×C4C2×D9211yescharacteristic
160C2×C4C2×C22⋊D2311yescharacteristic
161C8—42no—
162C8—922no—
163C22—21no—
164C22—21no—
165C22—921no—
166C22—921no—
167C22—921no—
168C22—1842no—
169C22#1062507212yes—
170C22C2×(C2×D23)⋊C411yescharacteristic
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—21no—
177C4—921no—
178C4—921no—
179C4—921no—
180C2—22no—
181C2—1841no—
182C2#1309238311yescharacteristic
183C2#1309239011yescharacteristic
184C2#1309239911yescharacteristic
subgroupG/H
centerC22C2×(C2×D23)⋊C4
commutatorC23×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#431C2
socleC22×C23C2×C22⋊C4
prime radicalC23×D23C2×C4
cosocleC22×C4×C23C23
hypercenter#431D23
hypocenterC23#1473
LCSG ▷ C23×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #13092474C2semidirect
3. #13092142C2semidirect
5. C23×#431C2semidirect
90. #431D23semidirect
115. C23#1473semidirect

Maximal subgroups

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

subgroupindex
C2×#106250472
#130924742
#130921422
#130921402
C23×#4312
#147323