Finite Group Databasebeta

← #15672372

Subgroups — #15672372

Order 2944.

238 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 51 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#13093046C211yesmaximal, characteristic
2#13092575C211yesmaximal, characteristic
3#13092572C211yesmaximal, characteristic
4#13092338C211yesmaximal, characteristic
5#13092153C211yesmaximal, characteristic
6#13092142C211yesmaximal, characteristic
7C23×#328C211yesmaximal, characteristic
8C22×Dic46C2211yescharacteristic
9C23×C22⋊Q8C2211yescharacteristic
10#10625115—21no—
11C2×#67275—21no—
12C2×C4⋊Dic23—21no—
13#10625095C2211yescharacteristic
14C2×Dic23⋊C4C2211yescharacteristic
15C2×Dic92—21no—
16#10625060—21no—
17#10625060—21no—
18#10625059—21no—
19#10625049—21no—
20#10625048—21no—
21C23×C22⋊C8C2211yescharacteristic
22C23×#95C2211yescharacteristic
23C23⋊#95—21no—
24C22⋊(C23⋊C8)C2211yescharacteristic
25#10624998—21no—
26#10624992—21no—
27C2×Q8×C23D411yescharacteristic
28C22×C4×C23—21no—
29C22×C4×C23C2311yescharacteristic
30C22×Dic23—21no—
31C22×Dic23D411yescharacteristic
32C22×Dic23D411yescharacteristic
33C2×Dic46—21no—
34C2×Dic46—21no—
35C2×Dic46—21no—
36C2×Dic46—42no—
37C2×Dic46D411yescharacteristic
38C2×C8×C23—21no—
39C4⋊C4×C23—21no—
40C4⋊C4×C23D411yescharacteristic
41C22⋊C4×C23—21no—
42C22⋊Dic23—21no—
43#67275—42no—
44C4⋊Dic23—21no—
45C4⋊Dic23—42no—
46C4⋊Dic23D411yescharacteristic
47Dic23⋊C4—21no—
48Dic23⋊C4—21no—
49Dic23⋊C4—21no—
50Dic23⋊C4—21no—
51Dic23⋊C4—21no—
52Dic23⋊C4—21no—
53Dic23⋊C4—21no—
54C4×Dic23—21no—
55C4×Dic23—21no—
56C2×C23⋊C8—21no—
57Dic92—42no—
58C23×C23C2×D411yescharacteristic
59Q8×C23—41no—
60C2×C4×C23—22no—
61C2×C4×C23—21no—
62C2×C4×C23—21no—
63C2×C4×C23—41no—
64C2×C4×C23—41no—
65C2×C4×C23—41no—
66C2×C4×C23C2×D411yescharacteristic
67C2×C4×C23C2×D411yescharacteristic
68C2×Dic23—21no—
69C2×Dic23—21no—
70C2×Dic23—22no—
71C2×Dic23—21no—
72C2×Dic23—21no—
73C2×Dic23—21no—
74C2×Dic23—41no—
75C2×Dic23—41no—
76C2×Dic23—41no—
77C2×Dic23Q1612yescomplemented
78Dic46—22no—
79Dic46—22no—
80Dic46—41no—
81Dic46—41no—
82Dic46—41no—
83Dic46—81no—
84C8×C23—41no—
85C23⋊C8—41no—
86#1605—231nomaximal, Sylow
87C22×C23—21no—
88C22×C23—21no—
89C22×C23#12011yescharacteristic
90C22×C23C2×Q1611yescharacteristic
91C22×C23#13711yescharacteristic
92C4×C23—21no—
93C4×C23—21no—
94C4×C23—42no—
95C4×C23—41no—
96C4×C23—41no—
97Dic23—22no—
98Dic23—41no—
99Dic23—42no—
100Dic23—41no—
101Dic23—41no—
102#544—231no—
103#451—231no—
104#451—231no—
105#395—231no—
106#328—231no—
107#328D2311yescharacteristic
108#324—231no—
109C2×C23—21no—
110C2×C23—21no—
111C2×C23#45111yescharacteristic
112C2×C23#45611yescharacteristic
113C2×C23B(4,𝔽2)11yescharacteristic
114C22×Q8—231no—
115C2×Q16—461no—
116C2×Q16—461no—
117C4⋊Q8—461no—
118C4⋊Q8—461no—
119#125—461no—
120#125—461no—
121C22⋊Q8—231no—
122C22⋊Q8—461no—
123C22⋊Q8C2×D2311yescharacteristic
124#117—461no—
125C2×C4⋊C4—231no—
126C2×C4⋊C4—461no—
127#103—461no—
128#103—461no—
129C22⋊C8—231no—
130C22⋊C8C2×D2311yescharacteristic
131#95—461no—
132#95C2×D2311yescharacteristic
133C23#160511yescharacteristic, complemented, Sylow
134C2×Q8—231no—
135C2×Q8—461no—
136C2×Q8—461no—
137C2×Q8—461no—
138C2×Q8—922no—
139C2×Q8D9211yescharacteristic
140C22×C4—21no—
141C22×C4—231no—
142C22×C4—231no—
143C22×C4—461no—
144C22×C4C22×D2311yescharacteristic
145Q16—922no—
146Q16—922no—
147C2×C8—21no—
148C2×C8—461no—
149C4⋊C4—21no—
150C4⋊C4—231no—
151C4⋊C4—461no—
152C4⋊C4—461no—
153C4⋊C4—461no—
154C4⋊C4—461no—
155C4⋊C4—461no—
156C4⋊C4—461no—
157C4⋊C4—461no—
158C4⋊C4—461no—
159C4⋊C4—922no—
160C4⋊C4D9211yescharacteristic
161C22⋊C4—21no—
162C22⋊C4—461no—
163C42—461no—
164C42—461no—
165C23D4×D2311yescharacteristic
166Q8—41no—
167Q8—462no—
168Q8—462no—
169Q8—921no—
170Q8—921no—
171Q8—921no—
172Q8—1841no—
173C2×C4—22no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—232no—
180C2×C4—461no—
181C2×C4—461no—
182C2×C4—462no—
183C2×C4—461no—
184C2×C4—461no—
185C2×C4—461no—
186C2×C4—921no—
187C2×C4—921no—
188C2×C4—921no—
189C2×C4C2×D9211yescharacteristic
190C2×C4D4×D2311yescharacteristic
191C8—41no—
192C8—921no—
193C22—21no—
194C22—21no—
195C22#1062505311yescharacteristic
196C22#1062508611yescharacteristic
197C22Q16×D2311yescharacteristic
198C4—21no—
199C4—21no—
200C4—42no—
201C4—41no—
202C4—41no—
203C4—462no—
204C4—921no—
205C4—922no—
206C4—921no—
207C4—921no—
208C2—21no—
209C2—21no—
210C2#1309257411yescharacteristic
211C2#1309260111yescharacteristic
212C2#1309260511yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#328C2
socleC22×C23#120
prime radicalC23×C23C2×D4
hypercenter#328D23
hypocenterC23#1605
LCSG ▷ C22×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
77. C2×Dic23Q16semidirect
133. C23#1605semidirect

Maximal subgroups

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

subgroupindex
#130930462
#130925752
#130925722
#130923382
#130921532
#130921422
C23×#3282
#160523