Finite Group Databasebeta

← #15672428

Subgroups — #15672428

Order 2944.

208 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 53 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#13092750C211yesmaximal, characteristic, complemented
2#13092733C211yesmaximal, characteristic
3#13092356C211yesmaximal, characteristic, complemented
4#13092154C211yesmaximal, characteristic, complemented
5#13092151C211yesmaximal, characteristic
6#13092143C211yesmaximal, characteristic, complemented
7C23×#539C211yesmaximal, characteristic
8C23×#126—21no—
9C23×#125—21no—
10C23×#123—21no—
11C23×#123—21no—
12C23×C22⋊Q8—21no—
13C23×C22⋊Q8C2211yescharacteristic
14C23×#121C2211yescharacteristic
15C4×D4×C23—21no—
16C2×C4⋊C4×C23C2211yescharacteristic
17C2×C4⋊Dic23C2211yescharacteristic
18#10625017—21no—
19#10625014—21no—
20C23⋊#95—21no—
21C23⋊#95—21no—
22C23⋊#95C2211yescharacteristic
23C22⋊(C23⋊C8)C2211yescharacteristic
24C22⋊(C23⋊C8)C2211yescharacteristic
25#10624990—21no—
26#10624989—21no—
27C2×Q8×C23D411yescharacteristic
28C2×D4×C23—21no—
29C2×D4×C23D411yescharacteristic
30C22×C4×C23—21no—
31C22×C4×C23D411yescharacteristic
32C22×C4×C23D411yescharacteristic
33C22×C4×C23C2311yescharacteristic
34C22×Dic23—21no—
35C22×Dic23—21no—
36C4⋊C4×C23—21no—
37C4⋊C4×C23—21no—
38C4⋊C4×C23—21no—
39C4⋊C4×C23—21no—
40C4⋊C4×C23—21no—
41C4⋊C4×C23—21no—
42C4⋊C4×C23D411yescharacteristic
43C4⋊C4×C23D411yescharacteristic
44C22⋊C4×C23—21no—
45C22⋊C4×C23—21no—
46C22⋊C4×C23—21no—
47C22⋊C4×C23—21no—
48C22⋊C4×C23—21no—
49C42×C23—21no—
50C4⋊Dic23—21no—
51C4⋊Dic23—21no—
52C2×C23⋊C8—21no—
53C2×C23⋊C8—21no—
54C23×C23—21no—
55C23×C23C2×D411yescharacteristic
56Q8×C23—41no—
57D4×C23—41no—
58D4×C23—41no—
59D4×C23—41no—
60C2×C4×C23—21no—
61C2×C4×C23—21no—
62C2×C4×C23—21no—
63C2×C4×C23—21no—
64C2×C4×C23—21no—
65C2×C4×C23—21no—
66C2×C4×C23—21no—
67C2×C4×C23—41no—
68C2×C4×C23—41no—
69C2×C4×C23—81no—
70C2×C4×C23C2×D411yescharacteristic
71C2×C4×C23C2×D411yescharacteristic
72C2×Dic23—41no—
73C2×Dic23—41no—
74C2×Dic23—42no—
75C2×Dic23—41no—
76C2×Dic23—41no—
77C23⋊C8—41no—
78C23⋊C8—41no—
79#1615—231nomaximal, Sylow
80C22×C23—21no—
81C22×C23—21no—
82C22×C23—41no—
83C22×C23—41no—
84C22×C23—41no—
85C22×C23#12011yescharacteristic
86C22×C23#13511yescharacteristic
87C22×C23#13711yescharacteristic
88C4×C23—21no—
89C4×C23—21no—
90C4×C23—41no—
91C4×C23—41no—
92C4×C23—41no—
93C4×C23—41no—
94C4×C23—41no—
95Dic23—81no—
96Dic23—81no—
97#539D2311yescharacteristic
98#484—231no—
99#481—231no—
100#400—231no—
101#328—231no—
102#327—231no—
103#324—231no—
104C2×C23—21no—
105C2×C23—21no—
106C2×C23—81no—
107C2×C23#45211yescharacteristic
108C2×C23#45411yescharacteristic
109C2×C23#45811yescharacteristic
110#126—21no—
111#125—21no—
112#123—21no—
113#123—21no—
114C22⋊Q8—21no—
115C22⋊Q8C2×D2311yescharacteristic
116#121C2×D2311yescharacteristic
117C4×D4—21no—
118C2×C4⋊C4—231no—
119C2×C4⋊C4C2×D2311yescharacteristic
120#107—461no—
121#106—461no—
122#103—461no—
123#102—461no—
124C22⋊C8—231no—
125C22⋊C8—231no—
126#95—231no—
127#95—461no—
128#95—461no—
129C23#161511yescharacteristic, complemented, Sylow
130C2×Q8C22⋊D2311yescharacteristic
131C2×D4—21no—
132C2×D4C22⋊D2311yescharacteristic
133C22×C4—21no—
134C22×C4—461no—
135C22×C4—461no—
136C22×C4C22⋊D2311yescharacteristic
137C22×C4C22⋊D2311yescharacteristic
138C22×C4C22×D2311yescharacteristic
139C2×C8—461no—
140C2×C8—461no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—21no—
147C4⋊C4—461no—
148C4⋊C4—461no—
149C4⋊C4C22⋊D2311yescharacteristic
150C4⋊C4C22⋊D2311yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—21no—
153C22⋊C4—21no—
154C22⋊C4—21no—
155C22⋊C4—21no—
156C42—21no—
157C23—21no—
158C23C2×C22⋊D2311yescharacteristic
159Q8—41no—
160D4—41no—
161D4—41no—
162D4—41no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—81no—
173C2×C4—921no—
174C2×C4—921no—
175C2×C4—922no—
176C2×C4—921no—
177C2×C4—921no—
178C2×C4C2×C22⋊D2311yescharacteristic
179C2×C4C2×C22⋊D2311yescharacteristic
180C8—921no—
181C8—921no—
182C22—21no—
183C22—21no—
184C22—41no—
185C22—41no—
186C22—41no—
187C22#1062512111yescharacteristic
188C22#1062512211yescharacteristic
189C22#1062512411yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—41no—
195C4—41no—
196C4—41no—
197C4—1841no—
198C4—1841no—
199C2—21no—
200C2—21no—
201C2—81no—
202C2#1309257911yescharacteristic
203C2#1309259011yescharacteristic
204C2#1309260711yescharacteristic
subgroupG/H
centerC22#10625124
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#539C2
socleC22×C23#120
prime radicalC23×#121C22
hypercenter#539D23
hypocenterC23#1615
LCSG ▷ C22×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #539

Complements

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

NH ≅ G/Ntype
1. #13092750C2semidirect
3. #13092356C2semidirect
4. #13092154C2semidirect
6. #13092143C2semidirect
129. C23#1615semidirect

Maximal subgroups

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

subgroupindex
#130927502
#130927332
#130923562
#130921542
#130921512
#130921432
C23×#5392
#161523