Finite Group Databasebeta

← #15671759

Subgroups — #15671759

Order 2944.

270 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 65 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×#10625067C211yesmaximal, characteristic
2#13092379C211yesmaximal, characteristic
3C22⋊C8×D23C211yesmaximal, characteristic
4#13092143C211yesmaximal, characteristic, complemented
5#13092142C211yesmaximal, characteristic, complemented
6#13092142C211yesmaximal, characteristic, complemented
7C23×#324C211yesmaximal, characteristic, complemented
8C22×C4×D23C2211yescharacteristic
9C22×Dic46C411yescharacteristic
10C2×C4⋊C4×C23C2211yescharacteristic
11C2×(C2×D23)⋊C4C411yescharacteristic
12C2×(C2×D23)⋊C4C411yescharacteristic
13C2×Dic23⋊C4C411yescharacteristic
14C2×Dic23⋊C4C2211yescharacteristic
15C2×#67262—21no—
16C2×C8×D23—21no—
17#10625067—21no—
18#10625067—21no—
19#10625067—21no—
20#10625067—21no—
21C23×C22⋊C8C2211yescharacteristic
22C23×C22⋊C8C2211yescharacteristic
23C22⋊(C23⋊C8)C2211yescharacteristic
24C22⋊(C23⋊C8)C2211yescharacteristic
25(C2×D23)⋊C8—21no—
26(C2×D23)⋊C8—21no—
27C23×D23C2×C411yescharacteristic
28C22×C4×C23C2×C411yescharacteristic
29C22×C4×C23C2×C411yescharacteristic
30C22×C4×C23C2311yescharacteristic
31C22×Dic23C2×C411yescharacteristic
32C22×Dic23C2×C411yescharacteristic
33C22×Dic23C2×C411yescharacteristic
34C2×C4×D23—42no—
35C2×C4×D23D411yescharacteristic
36C2×C4×D23D411yescharacteristic
37C2×C4×D23D411yescharacteristic
38C2×C4×D23D411yescharacteristic
39C2×Dic46—21no—
40C2×Dic46—21no—
41C2×Dic46—42no—
42C2×C8×C23—21no—
43C2×C8×C23—21no—
44C4⋊C4×C23—21no—
45C4⋊C4×C23—21no—
46(C2×D23)⋊C4—21no—
47(C2×D23)⋊C4—21no—
48(C2×D23)⋊C4—21no—
49(C2×D23)⋊C4—21no—
50Dic23⋊C4—21no—
51Dic23⋊C4—21no—
52Dic23⋊C4—21no—
53Dic23⋊C4—21no—
54C2×C23⋊C8—21no—
55C2×C23⋊C8—21no—
56#67262—42no—
57C8×D23—42no—
58C23×C23C22×C411yescharacteristic
59C22×D23—21no—
60C22×D23—21no—
61C22×D23—22no—
62C22×D23—41no—
63C22×D23C22⋊C411yescharacteristic
64C22×D23C22⋊C411yescharacteristic
65C2×C4×C23—21no—
66C2×C4×C23—21no—
67C2×C4×C23—21no—
68C2×C4×C23—21no—
69C2×C4×C23—41no—
70C2×C4×C23—41no—
71C2×C4×C23C2×D411yescharacteristic
72C2×C4×C23C2×D411yescharacteristic
73C2×Dic23—22no—
74C2×Dic23—21no—
75C2×Dic23—21no—
76C2×Dic23—21no—
77C2×Dic23—21no—
78C2×Dic23—41no—
79C2×Dic23C22⋊C411yescharacteristic
80C2×Dic23C22⋊C411yescharacteristic
81C4×D23—22no—
82C4×D23—22no—
83C4×D23—41no—
84C4×D23—41no—
85Dic46—42no—
86Dic46—42no—
87C8×C23—41no—
88C8×C23—41no—
89C23⋊C8—41no—
90C23⋊C8—41no—
91#1472—231nomaximal, Sylow
92C22×C23—21no—
93C22×C23—21no—
94C22×C23C2×C22⋊C411yescharacteristic
95C22×C23#13111yescharacteristic
96C22×C23#13111yescharacteristic
97C2×D23—21no—
98C2×D23—21no—
99C2×D23—21no—
100C2×D23—21no—
101C2×D23—21no—
102C2×D23—42no—
103C2×D23—42no—
104C2×D23#10112yes—
105C4×C23—21no—
106C4×C23—21no—
107C4×C23—41no—
108C4×C23—41no—
109Dic23—21no—
110Dic23—41no—
111Dic23—41no—
112Dic23#9912yes—
113C2×C22⋊Q8—231no—
114#407—231no—
115C2×C22⋊C8—231no—
116#324—231no—
117#324—231no—
118#324—231no—
119#324D2311yescharacteristic, complemented
120C2×C23—21no—
121C2×C23—21no—
122C2×C23#40811yescharacteristic
123C2×C23C2×#9911yescharacteristic
124C2×C23C2×#10111yescharacteristic
125D23—22no—
126D23—41no—
127C22×Q8—231no—
128C23×C4—231no—
129C2×M16—461no—
130C22×C8—461no—
131C22⋊Q8—461no—
132C22⋊Q8—461no—
133C22⋊Q8—461no—
134C22⋊Q8—461no—
135C2×C4⋊C4—231no—
136C2×C4⋊C4—231no—
137C2×C4⋊C4C2×D2311yescharacteristic
138C2×C22⋊C4—231no—
139C2×C22⋊C4—231no—
140C22⋊C8—231no—
141C22⋊C8—231no—
142C22⋊C8—461no—
143C22⋊C8—461no—
144C22⋊C8C2×D2311yescharacteristic
145C22⋊C8C2×D2311yescharacteristic
146C23#147211yescharacteristic, complemented, Sylow
147C24—231no—
148C2×Q8—461no—
149C2×Q8—461no—
150C2×Q8—922no—
151C22×C4—231no—
152C22×C4—231no—
153C22×C4—231no—
154C22×C4—231no—
155C22×C4—231no—
156C22×C4—231no—
157C22×C4—231no—
158C22×C4—922no—
159C22×C4C4×D2311yescharacteristic
160C22×C4C4×D2311yescharacteristic
161C22×C4C22×D2311yescharacteristic
162M16—922no—
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—461no—
166C2×C8—461no—
167C2×C8—922no—
168C4⋊C4—21no—
169C4⋊C4—21no—
170C4⋊C4—461no—
171C4⋊C4—461no—
172C4⋊C4—461no—
173C4⋊C4—461no—
174C22⋊C4—461no—
175C22⋊C4—461no—
176C22⋊C4—461no—
177C22⋊C4—461no—
178C23—231no—
179C23—231no—
180C23—462no—
181C23—461no—
182C23—461no—
183C23—921no—
184C23C2×C4×D2311yescharacteristic
185Q8—922no—
186Q8—922no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—231no—
194C2×C4—231no—
195C2×C4—462no—
196C2×C4—462no—
197C2×C4—462no—
198C2×C4—461no—
199C2×C4—461no—
200C2×C4—461no—
201C2×C4—461no—
202C2×C4—921no—
203C2×C4—921no—
204C2×C4—921no—
205C2×C4D4×D2311yescharacteristic
206C2×C4D4×D2311yescharacteristic
207C8—41no—
208C8—41no—
209C8—921no—
210C8—921no—
211C22—21no—
212C22—21no—
213C22—232no—
214C22—461no—
215C22—461no—
216C22—461no—
217C22—461no—
218C22—461no—
219C22—922no—
220C22—922no—
221C22C22⋊C4×D2311yescharacteristic
222C22#1062507211yescharacteristic
223C22#1062507811yescharacteristic
224C4—21no—
225C4—21no—
226C4—41no—
227C4—41no—
228C4—232no—
229C4—461no—
230C4—921no—
231C4—921no—
232C2—21no—
233C2—21no—
234C2—462no—
235C2—921no—
236C2#1309238211yescharacteristic
237C2#99×D2311yescharacteristic
238C2#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#1472
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
4. #13092143C2semidirect
5. #13092142C2semidirect
6. #13092142C2semidirect
7. C23×#324C2semidirect
119. #324D23semidirect
146. C23#1472semidirect

Maximal subgroups

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

subgroupindex
C2×#106250672
#130923792
C22⋊C8×D232
#130921432
#130921422
C23×#3242
#147223