Finite Group Databasebeta

← #15671734

Subgroups — #15671734

Order 2944.

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

normal subgroups only

This group has 316 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×#10625064C211yesmaximal, characteristic
2#13092379C212yesmaximal, complemented
3#13092143C211yesmaximal, characteristic, complemented
4#13092140C212yesmaximal, complemented
5C23×#324C211yesmaximal, characteristic, complemented
6C22×D92C411yescharacteristic
7C22×C4×D23C411yescharacteristic
8C22×C4×D23C2211yescharacteristic
9C2×C4⋊C4×C23C2211yescharacteristic
10C2×(C2×D23)⋊C4C411yescharacteristic
11C2×(C2×D23)⋊C4C2211yescharacteristic
12C2×C4×Dic23C411yescharacteristic
13C2×#67262—22no—
14#10625064—22no—
15#10625064—22no—
16C23×C22⋊C8C2212yes—
17C22⋊(C23⋊C8)C2212yes—
18(C2×D23)⋊C8—22no—
19C23×D23C2×C411yescharacteristic
20C23×D23C2×C411yescharacteristic
21C22×C4×C23C2×C411yescharacteristic
22C22×C4×C23C2×C411yescharacteristic
23C22×C4×C23C2311yescharacteristic
24C22×Dic23C2×C411yescharacteristic
25C22×Dic23C2×C411yescharacteristic
26C2×D92—22no—
27C2×D92—22no—
28C2×D92—22no—
29C2×C4×D23—21no—
30C2×C4×D23—21no—
31C2×C4×D23—42no—
32C2×C4×D23—42no—
33C2×C4×D23D412yes—
34C2×C4×D23D412yes—
35C2×C8×C23—22no—
36C4⋊C4×C23—22no—
37(C2×D23)⋊C4—22no—
38(C2×D23)⋊C4—22no—
39C4×Dic23—21no—
40C4×Dic23—21no—
41C2×C23⋊C8—22no—
42#67262—44no—
43C23×C23C22×C411yescharacteristic
44C22×D23—21no—
45C22×D23—21no—
46C22×D23—21no—
47C22×D23—21no—
48C22×D23—41no—
49C22×D23—41no—
50C22×D23—41no—
51C22×D23—41no—
52C22×D23C22⋊C412yes—
53C22×D23M1612yescomplemented
54C2×C4×C23—21no—
55C2×C4×C23—21no—
56C2×C4×C23—21no—
57C2×C4×C23—41no—
58C2×C4×C23—41no—
59C2×C4×C23M1612yescomplemented
60C2×C4×C23C2×D412yes—
61C2×Dic23—22no—
62C2×Dic23—21no—
63C2×Dic23—41no—
64C2×Dic23C22⋊C411yescharacteristic
65C2×Dic23C22⋊C411yescharacteristic
66D92—28no—
67C4×D23—24no—
68C4×D23—42no—
69C4×D23—42no—
70C4×D23—42no—
71C8×C23—42no—
72C23⋊C8—42no—
73#1465—231nomaximal, Sylow
74C22×C23—21no—
75C22×C23—21no—
76C22×C23C2×C22⋊C411yescharacteristic
77C22×C23C2×M1611yescharacteristic
78C22×C23C2×M1611yescharacteristic
79C2×D23—22no—
80C2×D23—22no—
81C2×D23—22no—
82C2×D23—22no—
83C2×D23—42no—
84C2×D23—42no—
85C2×D23—42no—
86C2×D23—41no—
87C2×D23—41no—
88C2×D23—42no—
89C4×C23—22no—
90C4×C23—22no—
91C4×C23—41no—
92Dic23—21no—
93Dic23—41no—
94Dic23#9912yes—
95C2×C4×D4—231no—
96#407—232no—
97#324—231no—
98#324D2311yescharacteristic, complemented
99#323—232no—
100C2×C23—21no—
101C2×C23—21no—
102C2×C23#40711yescharacteristic
103C2×C23C2×#9911yescharacteristic
104C2×C23#41311yescharacteristic
105D23—42no—
106D23—42no—
107C22×D4—231no—
108C23×C4—231no—
109C23×C4—231no—
110C2×M16—462no—
111C4×D4—462no—
112C4×D4—462no—
113C2×C4⋊C4C2×D2311yescharacteristic
114C2×C22⋊C4—231no—
115C2×C22⋊C4—231no—
116C2×C42—231no—
117C22⋊C8—232no—
118C22⋊C8—462no—
119C22⋊C8C2×D2312yes—
120C23#146511yescharacteristic, complemented, Sylow
121C24—231no—
122C24—231no—
123C2×D4—462no—
124C2×D4—462no—
125C2×D4—462no—
126C22×C4—231no—
127C22×C4—232no—
128C22×C4—232no—
129C22×C4—231no—
130C22×C4—461no—
131C22×C4—461no—
132C22×C4—922no—
133C22×C4—922no—
134C22×C4C4×D2311yescharacteristic
135C22×C4C4×D2311yescharacteristic
136C22×C4C22×D2311yescharacteristic
137M16—924no—
138C2×C8—22no—
139C2×C8—462no—
140C4⋊C4—22no—
141C22⋊C4—462no—
142C22⋊C4—462no—
143C42—461no—
144C42—461no—
145C23—232no—
146C23—232no—
147C23—461no—
148C23—461no—
149C23—461no—
150C23—461no—
151C23—921no—
152C23—921no—
153C23—921no—
154C23—921no—
155C23C2×C4×D2311yescharacteristic
156D4—468no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—231no—
163C2×C4—231no—
164C2×C4—464no—
165C2×C4—462no—
166C2×C4—461no—
167C2×C4—922no—
168C2×C4—922no—
169C2×C4—922no—
170C2×C4—921no—
171C2×C4#6726212yescomplemented
172C2×C4D4×D2312yes—
173C8—42no—
174C8—922no—
175C22—21no—
176C22—21no—
177C22—462no—
178C22—462no—
179C22—462no—
180C22—462no—
181C22—922no—
182C22—922no—
183C22—922no—
184C22—922no—
185C22—921no—
186C22—921no—
187C22C22⋊C4×D2311yescharacteristic
188C22C2×#6726211yescharacteristic
189C22M16×D2311yescharacteristic
190C4—22no—
191C4—22no—
192C4—41no—
193C4—232no—
194C4—461no—
195C4—921no—
196C2—21no—
197C2—21no—
198C2—922no—
199C2—922no—
200C2#1309237911yescharacteristic
201C2#99×D2311yescharacteristic
202C2#1309240011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D23
commutatorC23×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#324C2
socleC22×C23C2×C22⋊C4
prime radicalC22×D92C4
cosocleC22×C4×C23C23
hypercenter#324D23
hypocenterC23#1465
LCSG ▷ C23×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #13092379C2semidirect
3. #13092143C2semidirect
4. #13092140C2semidirect
5. C23×#324C2semidirect
53. C22×D23M16semidirect
59. C2×C4×C23M16semidirect
98. #324D23semidirect
120. C23#1465semidirect
171. C2×C4#67262semidirect

Maximal subgroups

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

subgroupindex
C2×#106250642
#130923792
#130921432
#130921402
C23×#3242
#146523