Finite Group Databasebeta

← #15672437

Subgroups — #15672437

Order 2944.

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

normal subgroups only

This group has 202 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#13092752C211yesmaximal, characteristic
3#13092355C211yesmaximal, characteristic
4#13092155C211yesmaximal, characteristic
5#13092154C211yesmaximal, characteristic
6#13092142C211yesmaximal, characteristic
7C23×#484C211yesmaximal, characteristic
8C23×C22⋊Q8C2211yescharacteristic
9C2×C4⋊C4×C23C2211yescharacteristic
10#10625115—21no—
11#10625095C2211yescharacteristic
12C2×Dic23⋊C4C2211yescharacteristic
13#10625060—21no—
14#10625060—21no—
15#10625059—21no—
16#10625049—21no—
17#10625048—21no—
18C23×#107—21no—
19C23×#103—21no—
20C23×C22⋊C8C2211yescharacteristic
21C23⋊#95—21no—
22C23⋊#95—21no—
23C23⋊#95C2211yescharacteristic
24C22⋊(C23⋊C8)C2211yescharacteristic
25#10624992—21no—
26#10624989—21no—
27C2×Q8×C23D411yescharacteristic
28C22×C4×C23—21no—
29C22×C4×C23C2311yescharacteristic
30C22×Dic23—21no—
31C22×Dic23D411yescharacteristic
32C22×Dic23D411yescharacteristic
33C2×Dic46—21no—
34C2×Dic46D411yescharacteristic
35C2×C8×C23—21no—
36C4⋊C4×C23—21no—
37C4⋊C4×C23—21no—
38C4⋊C4×C23—21no—
39C4⋊C4×C23D411yescharacteristic
40C22⋊C4×C23—21no—
41C22⋊Dic23—21no—
42C4⋊Dic23—21no—
43C4⋊Dic23D411yescharacteristic
44Dic23⋊C4—21no—
45Dic23⋊C4—21no—
46Dic23⋊C4—21no—
47Dic23⋊C4—21no—
48Dic23⋊C4—21no—
49Dic23⋊C4—21no—
50Dic23⋊C4—21no—
51C4×Dic23—21no—
52C4×Dic23—21no—
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—42no—
60C2×C4×C23—41no—
61C2×C4×C23C2×D411yescharacteristic
62C2×C4×C23C2×D411yescharacteristic
63C2×Dic23—21no—
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×Dic23Q1612yes—
73Dic46—41no—
74Dic46—81no—
75C8×C23—41no—
76C23⋊C8—41no—
77#1617—231nomaximal, Sylow
78C22×C23—21no—
79C22×C23—21no—
80C22×C23#12011yescharacteristic
81C22×C23C2×Q1611yescharacteristic
82C22×C23#13711yescharacteristic
83C4×C23—21no—
84C4×C23—21no—
85C4×C23—41no—
86C4×C23—41no—
87C4×C23—81no—
88Dic23—22no—
89Dic23—41no—
90Dic23—41no—
91Dic23—41no—
92Dic23—81no—
93#544—231no—
94#484—231no—
95#484D2311yescharacteristic
96#400—231no—
97#328—231no—
98#328—231no—
99#324—231no—
100C2×C23—21no—
101C2×C23—21no—
102C2×C23#45111yescharacteristic
103C2×C23#45411yescharacteristic
104C2×C23#45811yescharacteristic
105C4⋊Q8—461no—
106C4⋊Q8—461no—
107#125—461no—
108#125—461no—
109C22⋊Q8—231no—
110C22⋊Q8—461no—
111C22⋊Q8C2×D2311yescharacteristic
112#117—461no—
113C2×C4⋊C4—231no—
114C2×C4⋊C4C2×D2311yescharacteristic
115#107—21no—
116#107—461no—
117#103—21no—
118#103—461no—
119C22⋊C8—231no—
120C22⋊C8C2×D2311yescharacteristic
121#95—231no—
122#95—461no—
123#95—461no—
124C23#161711yescharacteristic, complemented, Sylow
125C2×Q8—231no—
126C2×Q8—461no—
127C2×Q8C22⋊D2311yescharacteristic
128C22×C4—21no—
129C22×C4—231no—
130C22×C4—231no—
131C22×C4—461no—
132C22×C4C22×D2311yescharacteristic
133C2×C8—21no—
134C2×C8—461no—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—231no—
139C4⋊C4—461no—
140C4⋊C4—461no—
141C4⋊C4—461no—
142C4⋊C4—461no—
143C4⋊C4—461no—
144C4⋊C4—461no—
145C4⋊C4—461no—
146C4⋊C4—461no—
147C4⋊C4C22⋊D2311yescharacteristic
148C22⋊C4—21no—
149C22⋊C4—461no—
150C42—461no—
151C42—461no—
152C23D4×D2311yescharacteristic
153Q8—41no—
154Q8—921no—
155Q8—1841no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—42no—
160C2×C4—41no—
161C2×C4—232no—
162C2×C4—461no—
163C2×C4—461no—
164C2×C4—461no—
165C2×C4—461no—
166C2×C4—461no—
167C2×C4—921no—
168C2×C4—921no—
169C2×C4—921no—
170C2×C4—921no—
171C2×C4D4×D2311yescharacteristic
172C2×C4C2×C22⋊D2311yescharacteristic
173C8—41no—
174C8—921no—
175C22—21no—
176C22—21no—
177C22Q16×D2311yescharacteristic
178C22#1062508911yescharacteristic
179C22#1062510811yescharacteristic
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—81no—
185C4—462no—
186C4—921no—
187C4—921no—
188C4—921no—
189C4—1841no—
190C2—21no—
191C2—21no—
192C2#1309257111yescharacteristic
193C2#1309258811yescharacteristic
194C2#1309260611yescharacteristic
subgroupG/H
centerC22#10625108
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#484C2
socleC22×C23#120
prime radicalC23×C23C2×D4
hypercenter#484D23
hypocenterC23#1617
LCSG ▷ C22×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
124. C23#1617semidirect

Maximal subgroups

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

subgroupindex
#130930462
#130927522
#130923552
#130921552
#130921542
#130921422
C23×#4842
#161723