Finite Group Databasebeta

← #15671725

Subgroups — #15671725

Order 2944.

312 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 71 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×C4⋊C4×D23C211yesmaximal, characteristic
2#13092379C212yesmaximal
3#13092143C211yesmaximal, characteristic, complemented
4#13092142C212yesmaximal, complemented
5C23×#324C211yesmaximal, characteristic, complemented
6C22×C4×D23C411yescharacteristic
7C22×C4×D23C411yescharacteristic
8C22×C4×D23C2211yescharacteristic
9C2×C4⋊C4×C23C2211yescharacteristic
10C2×C4⋊Dic23C411yescharacteristic
11C2×Dic23⋊C4C411yescharacteristic
12C2×Dic23⋊C4C2211yescharacteristic
13C2×#67262—22no—
14C4⋊C4×D23—22no—
15C4⋊C4×D23—22no—
16C23×C22⋊C8C2212yes—
17C22⋊(C23⋊C8)C2212yes—
18(C2×D23)⋊C8—22no—
19C23×D23C2×C411yescharacteristic
20C22×C4×C23C2×C411yescharacteristic
21C22×C4×C23C2×C411yescharacteristic
22C22×C4×C23C2311yescharacteristic
23C22×Dic23C2×C411yescharacteristic
24C22×Dic23C2×C411yescharacteristic
25C22×Dic23C2×C411yescharacteristic
26C2×C4×D23—21no—
27C2×C4×D23—21no—
28C2×C4×D23—22no—
29C2×C4×D23—22no—
30C2×C4×D23—21no—
31C2×C4×D23—21no—
32C2×C4×D23—42no—
33C2×C4×D23—42no—
34C2×C4×D23D412yes—
35C2×C4×D23D412yes—
36C2×C8×C23—22no—
37C4⋊C4×C23—22no—
38C4⋊Dic23—22no—
39Dic23⋊C4—22no—
40Dic23⋊C4—22no—
41C2×C23⋊C8—22no—
42#67262—44no—
43C23×C23C22×C411yescharacteristic
44C22×D23—21no—
45C22×D23—21no—
46C22×D23—22no—
47C22×D23—22no—
48C22×D23C22⋊C411yescharacteristic
49C22×D23C22⋊C411yescharacteristic
50C2×C4×C23—21no—
51C2×C4×C23—21no—
52C2×C4×C23—21no—
53C2×C4×C23—41no—
54C2×C4×C23—41no—
55C2×C4×C23M1612yescomplemented
56C2×C4×C23C2×D412yes—
57C2×Dic23—21no—
58C2×Dic23—21no—
59C2×Dic23—21no—
60C2×Dic23—41no—
61C2×Dic23—41no—
62C2×Dic23C22⋊C412yes—
63C2×Dic23M1612yescomplemented
64C4×D23—24no—
65C4×D23—24no—
66C4×D23—24no—
67C4×D23—42no—
68C4×D23—42no—
69C4×D23—42no—
70C8×C23—42no—
71C23⋊C8—42no—
72#1463—231nomaximal, Sylow
73C22×C23—21no—
74C22×C23—21no—
75C22×C23C2×C22⋊C411yescharacteristic
76C22×C23C2×M1611yescharacteristic
77C22×C23C2×M1611yescharacteristic
78C2×D23—24no—
79C2×D23—24no—
80C2×D23—21no—
81C2×D23—21no—
82C2×D23—21no—
83C2×D23—21no—
84C2×D23#9912yes—
85C2×D23#10112yes—
86C4×C23—22no—
87C4×C23—22no—
88C4×C23—41no—
89Dic23—22no—
90Dic23—22no—
91Dic23—41no—
92C22×C4⋊C4—231no—
93#407—232no—
94#324—231no—
95#324—232no—
96#324D2311yescharacteristic, complemented
97C2×C23—21no—
98C2×C23—21no—
99C2×C23#40711yescharacteristic
100C2×C23C2×#9911yescharacteristic
101C2×C23C2×#10111yescharacteristic
102D23—22no—
103D23—22no—
104C23×C4—231no—
105C23×C4—231no—
106C23×C4—231no—
107C2×M16—462no—
108C2×C4⋊C4—231no—
109C2×C4⋊C4—231no—
110C2×C4⋊C4—231no—
111C2×C4⋊C4—462no—
112C2×C4⋊C4—462no—
113C2×C4⋊C4C2×D2311yescharacteristic
114C22⋊C8—232no—
115C22⋊C8—462no—
116C22⋊C8C2×D2312yes—
117C23#146311yescharacteristic, complemented, Sylow
118C24—231no—
119C22×C4—231no—
120C22×C4—231no—
121C22×C4—232no—
122C22×C4—232no—
123C22×C4—231no—
124C22×C4—462no—
125C22×C4—461no—
126C22×C4—461no—
127C22×C4—461no—
128C22×C4—461no—
129C22×C4—462no—
130C22×C4—922no—
131C22×C4—922no—
132C22×C4C4×D2311yescharacteristic
133C22×C4C4×D2311yescharacteristic
134C22×C4C22×D2311yescharacteristic
135M16—924no—
136C2×C8—22no—
137C2×C8—462no—
138C4⋊C4—22no—
139C4⋊C4—462no—
140C4⋊C4—462no—
141C4⋊C4—462no—
142C23—231no—
143C23—231no—
144C23—462no—
145C23—462no—
146C23—461no—
147C23—461no—
148C23C2×C4×D2311yescharacteristic
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—232no—
155C2×C4—232no—
156C2×C4—464no—
157C2×C4—464no—
158C2×C4—464no—
159C2×C4—461no—
160C2×C4—461no—
161C2×C4—461no—
162C2×C4—922no—
163C2×C4—922no—
164C2×C4—922no—
165C2×C4—921no—
166C2×C4—921no—
167C2×C4#6726212yescomplemented
168C2×C4D4×D2312yes—
169C8—42no—
170C8—922no—
171C22—21no—
172C22—21no—
173C22—232no—
174C22—232no—
175C22—464no—
176C22—464no—
177C22—461no—
178C22—461no—
179C22—461no—
180C22—461no—
181C22C22⋊C4×D2311yescharacteristic
182C22C2×#6726211yescharacteristic
183C22M16×D2311yescharacteristic
184C4—22no—
185C4—22no—
186C4—41no—
187C4—462no—
188C4—462no—
189C4—921no—
190C2—21no—
191C2—21no—
192C2—462no—
193C2—462no—
194C2#1309237911yescharacteristic
195C2#99×D2311yescharacteristic
196C2#101×D2311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D23
commutatorC23×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#324C2
socleC22×C23C2×C22⋊C4
prime radicalC23×D23C2×C4
cosocleC22×C4×C23C23
hypercenter#324D23
hypocenterC23#1463
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
3. #13092143C2semidirect
4. #13092142C2semidirect
5. C23×#324C2semidirect
55. C2×C4×C23M16semidirect
63. C2×Dic23M16semidirect
96. #324D23semidirect
117. C23#1463semidirect
167. C2×C4#67262semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D232
#130923792
#130921432
#130921422
C23×#3242
#146323