Finite Group Databasebeta

← #15671712

Subgroups — #15671712

Order 2944.

332 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 81 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×(C22⋊D23)⋊C4C211yesmaximal, characteristic
2C22⋊C8×D23C212yesmaximal, complemented
3#13092142C212yesmaximal, complemented
4#13092141C211yesmaximal, characteristic, complemented
5C23×#323C211yesmaximal, characteristic, complemented
6C22×C22⋊D23C411yescharacteristic
7C23×Dic23C411yescharacteristic
8C22×C4×D23C2211yescharacteristic
9C2×C22⋊C4×C23C2211yescharacteristic
10C2×(C2×D23)⋊C4C411yescharacteristic
11C2×Dic23⋊C4C2211yescharacteristic
12C2×C4×Dic23C411yescharacteristic
13C2×C8×D23—22no—
14(C22⋊D23)⋊C4—22no—
15(C22⋊D23)⋊C4—22no—
16C23×C22⋊C8C2212yes—
17C22⋊(C23⋊C8)C2212yes—
18(C2×D23)⋊C8—22no—
19C24×C23C2×C411yescharacteristic
20C23×D23C2×C411yescharacteristic
21C22×C4×C23C2×C411yescharacteristic
22C22×C4×C23C2311yescharacteristic
23C2×C22⋊D23—22no—
24C2×C22⋊D23—22no—
25C2×C22⋊D23C814yescomplemented
26C22×Dic23—21no—
27C22×Dic23—21no—
28C22×Dic23—42no—
29C22×Dic23C2×C411yescharacteristic
30C22×Dic23C2×C411yescharacteristic
31C22×Dic23C2×C411yescharacteristic
32C2×C4×D23—42no—
33C2×C4×D23D412yes—
34C2×C4×D23D412yes—
35C2×C8×C23—22no—
36C22⋊C4×C23—22no—
37(C2×D23)⋊C4—22no—
38Dic23⋊C4—22no—
39C4×Dic23—21no—
40C4×Dic23—21no—
41C2×C23⋊C8—22no—
42C8×D23—44no—
43C23×C23—21no—
44C23×C23—21no—
45C23×C23—41no—
46C23×C23—41no—
47C23×C23C2×C812yescomplemented
48C23×C23C22×C411yescharacteristic
49C22×D23—41no—
50C22×D23—41no—
51C22×D23C22⋊C412yes—
52C22×D23C2×C812yes—
53C22×D23M1612yes—
54C2×C4×C23—21no—
55C2×C4×C23—41no—
56C2×C4×C23—41no—
57C2×C4×C23C2×D412yes—
58C22⋊D23—28no—
59C2×Dic23—21no—
60C2×Dic23—21no—
61C2×Dic23—22no—
62C2×Dic23—21no—
63C2×Dic23—42no—
64C2×Dic23—42no—
65C2×Dic23—41no—
66C2×Dic23C22⋊C411yescharacteristic
67C2×Dic23C22⋊C411yescharacteristic
68C2×Dic23C2×C812yescomplemented
69C4×D23—24no—
70C4×D23—42no—
71C8×C23—42no—
72C23⋊C8—42no—
73#1459—231nomaximal, Sylow
74C22×C23—21no—
75C22×C23—21no—
76C22×C23—22no—
77C22×C23—42no—
78C22×C23—42no—
79C22×C23—41no—
80C22×C23—41no—
81C22×C23C2×C22⋊C411yescharacteristic
82C22×C23C22×C811yescharacteristic
83C22×C23C2×M1611yescharacteristic
84C2×D23—22no—
85C2×D23—22no—
86C2×D23—42no—
87C2×D23—42no—
88C2×D23C22⋊C814yes—
89C4×C23—22no—
90C4×C23—41no—
91Dic23—22no—
92Dic23—21no—
93Dic23—41no—
94Dic23#9912yes—
95C2×C4×D4—231no—
96C2×C22⋊C8—232no—
97#324—232no—
98#323—231no—
99#323D2311yescharacteristic, complemented
100C2×C23—21no—
101C2×C23—21no—
102C2×C23—42no—
103C2×C23C2×C22⋊C811yescharacteristic
104C2×C23C2×#9911yescharacteristic
105C2×C23#41311yescharacteristic
106D23—24no—
107C22×D4—231no—
108C23×C4—231no—
109C23×C4—231no—
110C22×C8—462no—
111C4×D4—462no—
112C4×D4—462no—
113C2×C4⋊C4—231no—
114C2×C22⋊C4—231no—
115C2×C22⋊C4C2×D2311yescharacteristic
116C2×C42—231no—
117C22⋊C8—232no—
118C22⋊C8—462no—
119C22⋊C8C2×D2312yes—
120C23#145911yescharacteristic, complemented, Sylow
121C24—231no—
122C24C4×D2311yescharacteristic
123C2×D4—234no—
124C2×D4—462no—
125C2×D4—462no—
126C22×C4—231no—
127C22×C4—231no—
128C22×C4—232no—
129C22×C4—232no—
130C22×C4—231no—
131C22×C4—461no—
132C22×C4—461no—
133C22×C4—922no—
134C22×C4—922no—
135C22×C4C4×D2311yescharacteristic
136C22×C4C22×D2311yescharacteristic
137C2×C8—22no—
138C2×C8—462no—
139C2×C8—924no—
140C4⋊C4—462no—
141C22⋊C4—22no—
142C22⋊C4—462no—
143C42—461no—
144C42—461no—
145C23—21no—
146C23—21no—
147C23—41no—
148C23—41no—
149C23—232no—
150C23—232no—
151C23—232no—
152C23—921no—
153C23—921no—
154C23C8×D2312yescomplemented
155C23C2×C4×D2311yescharacteristic
156D4—468no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—231no—
161C2×C4—231no—
162C2×C4—232no—
163C2×C4—464no—
164C2×C4—462no—
165C2×C4—461no—
166C2×C4—461no—
167C2×C4—461no—
168C2×C4—922no—
169C2×C4—922no—
170C2×C4—922no—
171C2×C4—921no—
172C2×C4D4×D2312yes—
173C8—42no—
174C8—922no—
175C22—21no—
176C22—21no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—234no—
183C22—462no—
184C22—462no—
185C22—922no—
186C22—922no—
187C22C22⋊C4×D2311yescharacteristic
188C22C2×C8×D2311yescharacteristic
189C22M16×D2311yescharacteristic
190C4—22no—
191C4—41no—
192C4—232no—
193C4—462no—
194C4—461no—
195C4—921no—
196C2—21no—
197C2—21no—
198C2—42no—
199C2—464no—
200C2C22⋊C8×D2311yescharacteristic
201C2#99×D2311yescharacteristic
202C2#1309239811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D23
commutatorC22×C23C22×C8
FrattiniC22×C4C22×D23
FittingC23×#323C2
socleC22×C23C2×C22⋊C4
prime radicalC22×C22⋊D23C4
cosocleC22×C4×C23C23
hypercenter#323D23
hypocenterC23#1459
LCSG ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. C22⋊C8×D23C2semidirect
3. #13092142C2semidirect
4. #13092141C2semidirect
5. C23×#323C2semidirect
25. C2×C22⋊D23C8semidirect
47. C23×C23C2×C8semidirect
68. C2×Dic23C2×C8semidirect
99. #323D23semidirect
120. C23#1459semidirect
154. C23C8×D23semidirect

Maximal subgroups

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

subgroupindex
C2×(C22⋊D23)⋊C42
C22⋊C8×D232
#130921422
#130921412
C23×#3232
#145923