Finite Group Databasebeta

← #15671946

Subgroups — #15671946

Order 2944.

208 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 61 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
1#13092969C211yesmaximal, characteristic
2#13092471C211yesmaximal, characteristic
3#13092284C211yesmaximal, characteristic
4#13092155C211yesmaximal, characteristic
5#13092154C211yesmaximal, characteristic
6#13092153C211yesmaximal, characteristic
7C23×#328C211yesmaximal, characteristic
8C23×C22⋊Q8C2211yescharacteristic
9Q8×Dic23C411yescharacteristic, complemented
10#10625115C411yescharacteristic, complemented
11#10625095C2211yescharacteristic
12C2×C4×Dic23C2211yescharacteristic
13#10625060—21no—
14#10625059C411yescharacteristic, complemented
15#10625058—21no—
16#10625058C411yescharacteristic, complemented
17#10625049—21no—
18#10625048—21no—
19C23×C22⋊C8C2211yescharacteristic
20C23×#95C2211yescharacteristic
21C23⋊#95—21no—
22C23⋊#95—21no—
23C23⋊#95C2211yescharacteristic
24C22⋊(C23⋊C8)C2211yescharacteristic
25#10624997—21no—
26Dic23⋊C8—21no—
27C2×Q8×C23C2×C411yescharacteristic
28C22×C4×C23—21no—
29C22×C4×C23C2311yescharacteristic
30C22×Dic23—21no—
31C22×Dic23D411yescharacteristic
32C22×Dic23D411yescharacteristic
33C2×Dic46—21no—
34C2×Dic46C2×C411yescharacteristic
35C2×C8×C23—21no—
36C4⋊C4×C23—21no—
37C4⋊C4×C23C2×C411yescharacteristic
38C22⋊C4×C23—21no—
39C22⋊Dic23—21no—
40C4⋊Dic23—21no—
41C4⋊Dic23C2×C411yescharacteristic
42Dic23⋊C4—21no—
43Dic23⋊C4—21no—
44Dic23⋊C4—21no—
45Dic23⋊C4—21no—
46Dic23⋊C4—21no—
47C4×Dic23—21no—
48C4×Dic23—21no—
49C4×Dic23C2×C411yescharacteristic
50C4×Dic23C2×C411yescharacteristic
51C4×Dic23D411yescharacteristic
52C4×Dic23D411yescharacteristic
53C2×C23⋊C8—21no—
54C23×C23C2×D411yescharacteristic
55Q8×C23—41no—
56C2×C4×C23—21no—
57C2×C4×C23—21no—
58C2×C4×C23—41no—
59C2×C4×C23—41no—
60C2×C4×C23—41no—
61C2×C4×C23—41no—
62C2×C4×C23C22×C411yescharacteristic
63C2×C4×C23C2×D411yescharacteristic
64C2×Dic23—21no—
65C2×Dic23—21no—
66C2×Dic23—21no—
67C2×Dic23—21no—
68C2×Dic23—41no—
69C2×Dic23—41no—
70C2×Dic23—41no—
71C2×Dic23—41no—
72C2×Dic23C22⋊C411yescharacteristic
73C2×Dic23C22⋊C411yescharacteristic
74C2×Dic23C22⋊C411yescharacteristic
75C2×Dic23C22⋊C411yescharacteristic
76Dic46—42no—
77Dic46—41no—
78C8×C23—41no—
79C23⋊C8—41no—
80#1515—231nomaximal, Sylow
81C22×C23—21no—
82C22×C23—21no—
83C22×C23C2×C22⋊C411yescharacteristic
84C22×C23#13711yescharacteristic
85C22×C23#13711yescharacteristic
86C4×C23—21no—
87C4×C23—21no—
88C4×C23—41no—
89C4×C23—41no—
90C4×C23—81no—
91Dic23—21no—
92Dic23—21no—
93Dic23—21no—
94Dic23—21no—
95Dic23—41no—
96Dic23—41no—
97Dic23—81no—
98#533—231no—
99#432—231no—
100#383—231no—
101#328—231no—
102#328—231no—
103#328—231no—
104#328D2311yescharacteristic
105C2×C23—21no—
106C2×C23—21no—
107C2×C23#41011yescharacteristic
108C2×C23#41911yescharacteristic
109C2×C23#42111yescharacteristic
110C4⋊Q8—231no—
111C4⋊Q8—231no—
112#125—461no—
113C22⋊Q8—231no—
114C22⋊Q8—461no—
115C22⋊Q8C2×D2311yescharacteristic
116C4×Q8—231no—
117C4×Q8—231no—
118C4×Q8—461no—
119#117—461no—
120C2×C42—231no—
121C4⋊C8—461no—
122C22⋊C8—231no—
123C22⋊C8C2×D2311yescharacteristic
124#97—461no—
125#95—231no—
126#95—461no—
127#95—461no—
128#95C2×D2311yescharacteristic
129C23#151511yescharacteristic, complemented, Sylow
130C2×Q8—231no—
131C2×Q8—461no—
132C2×Q8C4×D2311yescharacteristic
133C22×C4—21no—
134C22×C4—231no—
135C22×C4—231no—
136C22×C4—461no—
137C22×C4C22×D2311yescharacteristic
138C2×C8—21no—
139C2×C8—461no—
140C4⋊C4—21no—
141C4⋊C4—231no—
142C4⋊C4—461no—
143C4⋊C4—461no—
144C4⋊C4—461no—
145C4⋊C4—461no—
146C4⋊C4—461no—
147C4⋊C4—461no—
148C4⋊C4C4×D2311yescharacteristic
149C22⋊C4—21no—
150C22⋊C4—461no—
151C42—231no—
152C42—231no—
153C42—231no—
154C42—231no—
155C42—461no—
156C42—461no—
157C23D4×D2311yescharacteristic
158Q8—41no—
159Q8—921no—
160Q8—922no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—231no—
168C2×C4—231no—
169C2×C4—231no—
170C2×C4—231no—
171C2×C4—461no—
172C2×C4—461no—
173C2×C4—461no—
174C2×C4—461no—
175C2×C4—921no—
176C2×C4—921no—
177C2×C4—921no—
178C2×C4—921no—
179C2×C4C2×C4×D2311yescharacteristic
180C2×C4D4×D2311yescharacteristic
181C8—41no—
182C8—921no—
183C22—21no—
184C22—21no—
185C22C22⋊C4×D2311yescharacteristic
186C22#1062508611yescharacteristic
187C22#1062508911yescharacteristic
188C4—21no—
189C4—21no—
190C4—41no—
191C4—41no—
192C4—81no—
193C4—461no—
194C4—461no—
195C4—461no—
196C4—461no—
197C4—921no—
198C4—921no—
199C4—1841no—
200C2—21no—
201C2—21no—
202C2#1309238911yescharacteristic
203C2#1309242411yescharacteristic
204C2#1309243211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D23
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#328C2
socleC22×C23C2×C22⋊C4
prime radicalC23×C23C2×D4
cosocleC22×C4×C23C23
hypercenter#328D23
hypocenterC23#1515
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
9. Q8×Dic23C4semidirect
10. #10625115C4semidirect
14. #10625059C4semidirect
16. #10625058C4semidirect
129. C23#1515semidirect

Maximal subgroups

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

subgroupindex
#130929692
#130924712
#130922842
#130921552
#130921542
#130921532
C23×#3282
#151523