Finite Group Databasebeta

← #15672426

Subgroups — #15672426

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#13092752C211yesmaximal, characteristic, complemented
3#13092735C211yesmaximal, characteristic
4#13092153C211yesmaximal, characteristic, complemented
5#13092150C211yesmaximal, characteristic
6#13092143C211yesmaximal, characteristic, complemented
7C23×#400C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×C23C2211yescharacteristic
9C2×C4⋊C4×C23C2211yescharacteristic
10#10625101C2211yescharacteristic
11#10625100—21no—
12C4×C22⋊D23—21no—
13#10625095C2211yescharacteristic
14#10625069—21no—
15#10625067—21no—
16#10625065—21no—
17#10625060—21no—
18C23×#95—21no—
19C23×#95—21no—
20C23×#95C2211yescharacteristic
21C22⋊(C23⋊C8)C2211yescharacteristic
22C22⋊(C23⋊C8)C2211yescharacteristic
23#10624992—21no—
24#10624991—21no—
25#10624990—21no—
26#10624989—21no—
27C22×C4×C23—21no—
28C22×C4×C23—21no—
29C22×C4×C23D411yescharacteristic
30C22×C4×C23D411yescharacteristic
31C22×C4×C23C2311yescharacteristic
32C2×C22⋊D23—21no—
33C2×D92D411yescharacteristic
34C2×C4×D23—21no—
35C2×Dic46D411yescharacteristic
36C4⋊C4×C23—21no—
37C4⋊C4×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⋊Dic23D411yescharacteristic
46C4⋊Dic23D411yescharacteristic
47Dic23⋊C4—21no—
48Dic23⋊C4—21no—
49Dic23⋊C4—21no—
50Dic23⋊C4—21no—
51C4×Dic23—21no—
52C2×C23⋊C8—21no—
53C2×C23⋊C8—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×C23—41no—
63C2×C4×C23—41no—
64C2×C4×C23—42no—
65C2×C4×C23—41no—
66C2×C4×C23—41no—
67C2×C4×C23C2×D411yescharacteristic
68C2×C4×C23C2×D411yescharacteristic
69C22⋊D23—41no—
70C22⋊D23—41no—
71C2×Dic23—21no—
72C2×Dic23—21no—
73C2×Dic23—21no—
74D92—41no—
75C4×D23—81no—
76Dic46—41no—
77C23⋊C8—41no—
78C23⋊C8—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—
92C4×C23—81no—
93C4×C23—81no—
94Dic23—41no—
95Dic23—41no—
96Dic23—41no—
97#539—231no—
98#484—231no—
99#481—231no—
100#400D2311yescharacteristic, complemented
101#328—231no—
102#327—231no—
103#324—231no—
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⋊C4C2×D2311yescharacteristic
119C2×C4⋊C4C2×D2311yescharacteristic
120#107—461no—
121#106—461no—
122#103—461no—
123#102—461no—
124C22⋊C8—231no—
125C22⋊C8—231no—
126#95—21no—
127#95—21no—
128#95C2×D2311yescharacteristic
129C23#161511yescharacteristic, complemented, Sylow
130C2×Q8—231no—
131C2×D4—231no—
132C2×D4—461no—
133C22×C4—21no—
134C22×C4—21no—
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—231no—
146C4⋊C4—231no—
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×C22⋊D2311yescharacteristic
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—41no—
170C2×C4—41no—
171C2×C4—42no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—461no—
175C2×C4—461no—
176C2×C4—461no—
177C2×C4—1841no—
178C2×C4D4×D2311yescharacteristic
179C2×C4D4×D2311yescharacteristic
180C8—921no—
181C8—921no—
182C22—21no—
183C22—21no—
184C22—921no—
185C22—921no—
186C22—921no—
187C22#1062510811yescharacteristic
188C22#1062511311yescharacteristic
189C22#1062512111yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—81no—
195C4—81no—
196C4—921no—
197C4—921no—
198C4—921no—
199C2—21no—
200C2—21no—
201C2—1841no—
202C2#1309257711yescharacteristic
203C2#1309258911yescharacteristic
204C2#1309260611yescharacteristic
subgroupG/H
centerC22#10625108
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#400C2
socleC22×C23#120
prime radical#10625101C22
hypercenter#400D23
hypocenterC23#1615
LCSG ▷ C22×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #400

Complements

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

NH ≅ G/Ntype
2. #13092752C2semidirect
4. #13092153C2semidirect
6. #13092143C2semidirect
7. C23×#400C2semidirect
100. #400D23semidirect
129. C23#1615semidirect

Maximal subgroups

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

subgroupindex
#130930142
#130927522
#130927352
#130921532
#130921502
#130921432
C23×#4002
#161523