Finite Group Databasebeta

← #15671959

Subgroups — #15671959

Order 2944.

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

normal subgroups only

This group has 220 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
1#13092969C211yesmaximal, characteristic
2#13092467C211yesmaximal, characteristic
3#13092281C211yesmaximal, 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×Dic23⋊C4—21no—
13C2×C4×Dic23C2211yescharacteristic
14#10625060—21no—
15#10625059C411yescharacteristic, complemented
16#10625058—21no—
17#10625058C411yescharacteristic, complemented
18#10625049—21no—
19#10625048—21no—
20C23×C22⋊C8C2211yescharacteristic
21C23×#95C2211yescharacteristic
22C23⋊#95—21no—
23C23⋊#95C2211yescharacteristic
24C22⋊(C23⋊C8)C2211yescharacteristic
25Dic23⋊C8—21no—
26C8×Dic23—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—
47Dic23⋊C4—42no—
48C4×Dic23—21no—
49C4×Dic23—21no—
50C4×Dic23C2×C411yescharacteristic
51C4×Dic23C2×C411yescharacteristic
52C4×Dic23D411yescharacteristic
53C4×Dic23D411yescharacteristic
54C2×C23⋊C8—21no—
55C23×C23C2×D411yescharacteristic
56Q8×C23—41no—
57C2×C4×C23—21no—
58C2×C4×C23—21no—
59C2×C4×C23—41no—
60C2×C4×C23—41no—
61C2×C4×C23—41no—
62C2×C4×C23—41no—
63C2×C4×C23C22×C411yescharacteristic
64C2×C4×C23C2×D411yescharacteristic
65C2×Dic23—21no—
66C2×Dic23—21no—
67C2×Dic23—41no—
68C2×Dic23—41no—
69C2×Dic23—41no—
70C2×Dic23—41no—
71C2×Dic23C22⋊C411yescharacteristic
72C2×Dic23C22⋊C411yescharacteristic
73C2×Dic23C22⋊C411yescharacteristic
74C2×Dic23C22⋊C411yescharacteristic
75C2×Dic23SD1612yes—
76C2×Dic23Q1612yes—
77Dic46—42no—
78Dic46—41no—
79C8×C23—41no—
80C23⋊C8—41no—
81#1518—231nomaximal, Sylow
82C22×C23—21no—
83C22×C23—21no—
84C22×C23C2×C22⋊C411yescharacteristic
85C22×C23C2×SD1611yescharacteristic
86C22×C23C2×Q1611yescharacteristic
87C4×C23—21no—
88C4×C23—21no—
89C4×C23—41no—
90C4×C23—41no—
91C4×C23—81no—
92Dic23—21no—
93Dic23—21no—
94Dic23—41no—
95Dic23—41no—
96Dic23—81no—
97Dic23#10312yes—
98Dic23#10312yes—
99#533—231no—
100#431—231no—
101#382—231no—
102#328—231no—
103#328—231no—
104#328—231no—
105#328D2311yescharacteristic
106C2×C23—21no—
107C2×C23—21no—
108C2×C23#41011yescharacteristic
109C2×C23C2×#10311yescharacteristic
110C2×C23#42111yescharacteristic
111C4⋊Q8—231no—
112C4⋊Q8—231no—
113#125—461no—
114C22⋊Q8—231no—
115C22⋊Q8—461no—
116C22⋊Q8C2×D2311yescharacteristic
117C4×Q8—231no—
118C4×Q8—231no—
119C4×Q8—461no—
120#117—461no—
121C2×C4⋊C4—461no—
122C2×C42—231no—
123C4⋊C8—461no—
124C22⋊C8—231no—
125C22⋊C8C2×D2311yescharacteristic
126C4×C8—461no—
127#95—231no—
128#95—461no—
129#95C2×D2311yescharacteristic
130C23#151811yescharacteristic, complemented, Sylow
131C2×Q8—231no—
132C2×Q8—461no—
133C2×Q8C4×D2311yescharacteristic
134C22×C4—21no—
135C22×C4—231no—
136C22×C4—231no—
137C22×C4—461no—
138C22×C4C22×D2311yescharacteristic
139C2×C8—21no—
140C2×C8—461no—
141C4⋊C4—21no—
142C4⋊C4—231no—
143C4⋊C4—461no—
144C4⋊C4—461no—
145C4⋊C4—461no—
146C4⋊C4—461no—
147C4⋊C4—461no—
148C4⋊C4—461no—
149C4⋊C4—922no—
150C4⋊C4C4×D2311yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—461no—
153C42—231no—
154C42—231no—
155C42—231no—
156C42—231no—
157C42—461no—
158C42—461no—
159C23D4×D2311yescharacteristic
160Q8—41no—
161Q8—921no—
162Q8—922no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—231no—
170C2×C4—231no—
171C2×C4—232no—
172C2×C4—232no—
173C2×C4—231no—
174C2×C4—231no—
175C2×C4—461no—
176C2×C4—461no—
177C2×C4—921no—
178C2×C4—921no—
179C2×C4—921no—
180C2×C4—921no—
181C2×C4C2×C4×D2311yescharacteristic
182C2×C4D4×D2311yescharacteristic
183C8—41no—
184C8—921no—
185C22—21no—
186C22—21no—
187C22C22⋊C4×D2311yescharacteristic
188C22SD16×D2311yescharacteristic
189C22Q16×D2311yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—81no—
195C4—232no—
196C4—232no—
197C4—461no—
198C4—461no—
199C4—921no—
200C4—921no—
201C4—1841no—
202C2—21no—
203C2—21no—
204C2#1309238911yescharacteristic
205C2#103×D2311yescharacteristic
206C2#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#1518
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
15. #10625059C4semidirect
17. #10625058C4semidirect
130. C23#1518semidirect

Maximal subgroups

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

subgroupindex
#130929692
#130924672
#130922812
#130921552
#130921542
#130921532
C23×#3282
#151823