Finite Group Databasebeta

← #15672430

Subgroups — #15672430

Order 2944.

208 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 49 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#13093014C211yesmaximal, characteristic
2#13092753C211yesmaximal, characteristic, complemented
3#13092736C211yesmaximal, characteristic
4#13092356C211yesmaximal, characteristic, complemented
5#13092155C211yesmaximal, characteristic, complemented
6#13092152C211yesmaximal, characteristic
7C23×#324C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×C23C2211yescharacteristic
9#10625101C2211yescharacteristic
10#10625100—21no—
11C4×C22⋊D23—21no—
12C2×C4⋊Dic23C2211yescharacteristic
13#10625095C2211yescharacteristic
14#10625069—21no—
15#10625067—21no—
16#10625065—21no—
17#10625060—21no—
18C23×C22⋊C8C2211yescharacteristic
19C23×C22⋊C8C2211yescharacteristic
20C23⋊#95—21no—
21C23⋊#95—21no—
22C23⋊#95C2211yescharacteristic
23#10625003—21no—
24#10625000—21no—
25#10624999—21no—
26#10624998—21no—
27C22×C4×C23D411yescharacteristic
28C22×C4×C23D411yescharacteristic
29C22×C4×C23C2311yescharacteristic
30C2×C22⋊D23—21no—
31C22×Dic23—21no—
32C22×Dic23—21no—
33C2×D92D411yescharacteristic
34C2×C4×D23—21no—
35C2×Dic46D411yescharacteristic
36C2×C8×C23—21no—
37C2×C8×C23—21no—
38C4⋊C4×C23—21no—
39C4⋊C4×C23—21no—
40C22⋊Dic23—21no—
41(C2×D23)⋊C4—21no—
42(C2×D23)⋊C4—21no—
43(C2×D23)⋊C4—21no—
44(C2×D23)⋊C4—21no—
45C4⋊Dic23—21no—
46C4⋊Dic23—21no—
47C4⋊Dic23D411yescharacteristic
48C4⋊Dic23D411yescharacteristic
49Dic23⋊C4—21no—
50Dic23⋊C4—21no—
51Dic23⋊C4—21no—
52Dic23⋊C4—21no—
53C4×Dic23—21no—
54C23×C23C2×D411yescharacteristic
55C22×D23—21no—
56C2×C4×C23—21no—
57C2×C4×C23—21no—
58C2×C4×C23—21no—
59C2×C4×C23—21no—
60C2×C4×C23—41no—
61C2×C4×C23—41no—
62C2×C4×C23C2×D411yescharacteristic
63C2×C4×C23C2×D411yescharacteristic
64C22⋊D23—41no—
65C22⋊D23—41no—
66C2×Dic23—21no—
67C2×Dic23—21no—
68C2×Dic23—21no—
69C2×Dic23—41no—
70C2×Dic23—41no—
71C2×Dic23—42no—
72C2×Dic23—41no—
73C2×Dic23—41no—
74D92—41no—
75C4×D23—81no—
76Dic46—41no—
77C8×C23—41no—
78C8×C23—41no—
79#1615—231nomaximal, Sylow
80C22×C23—21no—
81C22×C23—21no—
82C22×C23#12011yescharacteristic
83C22×C23#13511yescharacteristic
84C22×C23#13711yescharacteristic
85C2×D23—41no—
86C2×D23—41no—
87C2×D23—41no—
88C4×C23—21no—
89C4×C23—21no—
90C4×C23—41no—
91C4×C23—41no—
92Dic23—41no—
93Dic23—41no—
94Dic23—41no—
95Dic23—81no—
96Dic23—81no—
97#539—231no—
98#484—231no—
99#481—231no—
100#400—231no—
101#328—231no—
102#327—231no—
103#324D2311yescharacteristic, complemented
104C2×C23—21no—
105C2×C23—21no—
106C2×C23#45211yescharacteristic
107C2×C23#45411yescharacteristic
108C2×C23#45811yescharacteristic
109D23—81no—
110#126—461no—
111#125—461no—
112#123—461no—
113#123—461no—
114C22⋊Q8—231no—
115C22⋊Q8—461no—
116#121—231no—
117C4×D4—461no—
118C2×C4⋊C4—231no—
119C2×C4⋊C4C2×D2311yescharacteristic
120#107—461no—
121#106—461no—
122#103—461no—
123#102—461no—
124C22⋊C8C2×D2311yescharacteristic
125C22⋊C8C2×D2311yescharacteristic
126#95—231no—
127#95—461no—
128#95—461no—
129C23#161511yescharacteristic, complemented, Sylow
130C2×Q8—231no—
131C2×D4—231no—
132C2×D4—461no—
133C22×C4—461no—
134C22×C4—461no—
135C22×C4—461no—
136C22×C4D9211yescharacteristic
137C22×C4D9211yescharacteristic
138C22×C4C22×D2311yescharacteristic
139C2×C8—21no—
140C2×C8—21no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—231no—
144C4⋊C4—231no—
145C4⋊C4—461no—
146C4⋊C4—461no—
147C4⋊C4—461no—
148C4⋊C4—461no—
149C4⋊C4—461no—
150C4⋊C4—461no—
151C22⋊C4—461no—
152C22⋊C4—461no—
153C22⋊C4—461no—
154C22⋊C4—461no—
155C22⋊C4—461no—
156C42—461no—
157C23—461no—
158C23C2×D9211yescharacteristic
159Q8—921no—
160D4—921no—
161D4—921no—
162D4—921no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—461no—
170C2×C4—461no—
171C2×C4—461no—
172C2×C4—921no—
173C2×C4—921no—
174C2×C4—922no—
175C2×C4—921no—
176C2×C4—921no—
177C2×C4—1841no—
178C2×C4D4×D2311yescharacteristic
179C2×C4D4×D2311yescharacteristic
180C8—41no—
181C8—41no—
182C22—21no—
183C22—21no—
184C22—921no—
185C22—921no—
186C22—921no—
187C22#1062505311yescharacteristic
188C22#1062507511yescharacteristic
189C22#1062508011yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—921no—
195C4—921no—
196C4—921no—
197C4—1841no—
198C4—1841no—
199C2—21no—
200C2—21no—
201C2—1841no—
202C2#1309258111yescharacteristic
203C2#1309259211yescharacteristic
204C2#1309260811yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#324C2
socleC22×C23#120
prime radical#10625101C22
hypercenter#324D23
hypocenterC23#1615
LCSG ▷ C22×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #13092753C2semidirect
4. #13092356C2semidirect
5. #13092155C2semidirect
7. C23×#324C2semidirect
103. #324D23semidirect
129. C23#1615semidirect

Maximal subgroups

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

subgroupindex
#130930142
#130927532
#130927362
#130923562
#130921552
#130921522
C23×#3242
#161523