Finite Group Databasebeta

← #15671765

Subgroups — #15671765

Order 2944.

214 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 61 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
1C2×#10625069C211yesmaximal, characteristic
2#13092471C211yesmaximal, characteristic, complemented
3#13092467C211yesmaximal, characteristic, complemented
4#13092143C211yesmaximal, characteristic, complemented
5#13092140C211yesmaximal, characteristic
6#13092140C211yesmaximal, characteristic
7C23×#324C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×C23C2211yescharacteristic
9C2×(C2×D23)⋊C4C411yescharacteristic
10C2×(C2×D23)⋊C4C411yescharacteristic
11C2×(C2×D23)⋊C4C2211yescharacteristic
12C2×C4⋊Dic23C411yescharacteristic
13C2×Dic23⋊C4C411yescharacteristic
14C2×C4×Dic23C2211yescharacteristic
15#10625069—21no—
16#10625069—21no—
17#10625069—21no—
18#10625069—21no—
19C23×C22⋊C8C2211yescharacteristic
20C23×C22⋊C8C2211yescharacteristic
21C22⋊(C23⋊C8)C2211yescharacteristic
22C22⋊(C23⋊C8)C2211yescharacteristic
23#10624997—21no—
24Dic23⋊C8—21no—
25Dic23⋊C8—21no—
26C8×Dic23—21no—
27C23×D23C2×C411yescharacteristic
28C22×C4×C23C2×C411yescharacteristic
29C22×C4×C23C2×C411yescharacteristic
30C22×C4×C23C2311yescharacteristic
31C22×Dic23C2×C411yescharacteristic
32C22×Dic23C2×C411yescharacteristic
33C22×Dic23C2×C411yescharacteristic
34C2×C8×C23—21no—
35C2×C8×C23—21no—
36C4⋊C4×C23—21no—
37C4⋊C4×C23—21no—
38(C2×D23)⋊C4—21no—
39(C2×D23)⋊C4—21no—
40(C2×D23)⋊C4—21no—
41(C2×D23)⋊C4—21no—
42(C2×D23)⋊C4—21no—
43(C2×D23)⋊C4—21no—
44C4⋊Dic23—21no—
45C4⋊Dic23—21no—
46Dic23⋊C4—21no—
47Dic23⋊C4—21no—
48C4×Dic23D411yescharacteristic
49C4×Dic23D411yescharacteristic
50C4×Dic23D411yescharacteristic
51C4×Dic23D411yescharacteristic
52C2×C23⋊C8—21no—
53C2×C23⋊C8—21no—
54C23×C23C22×C411yescharacteristic
55C22×D23—21no—
56C22×D23—21no—
57C22×D23—21no—
58C22×D23—41no—
59C22×D23—41no—
60C2×C4×C23—21no—
61C2×C4×C23—21no—
62C2×C4×C23—21no—
63C2×C4×C23—21no—
64C2×C4×C23—41no—
65C2×C4×C23—41no—
66C2×C4×C23C2×D411yescharacteristic
67C2×C4×C23C2×D411yescharacteristic
68C2×Dic23—21no—
69C2×Dic23—21no—
70C2×Dic23—21no—
71C2×Dic23—41no—
72C2×Dic23—41no—
73C2×Dic23C22⋊C411yescharacteristic
74C2×Dic23C22⋊C411yescharacteristic
75C2×Dic23C22⋊C411yescharacteristic
76C2×Dic23C22⋊C411yescharacteristic
77C8×C23—41no—
78C8×C23—41no—
79C23⋊C8—41no—
80C23⋊C8—41no—
81#1473—231nomaximal, Sylow
82C22×C23—21no—
83C22×C23—21no—
84C22×C23C2×C22⋊C411yescharacteristic
85C22×C23#13111yescharacteristic
86C22×C23#13111yescharacteristic
87C2×D23—41no—
88C2×D23—41no—
89C2×D23—41no—
90C2×D23—81no—
91C2×D23—81no—
92C4×C23—21no—
93C4×C23—21no—
94C4×C23—41no—
95C4×C23—41no—
96Dic23—21no—
97Dic23—21no—
98Dic23—21no—
99Dic23—21no—
100Dic23—41no—
101C2×#126—231no—
102#432—231no—
103#431—231no—
104#324—231no—
105#324D2311yescharacteristic, complemented
106#323—231no—
107#323—231no—
108C2×C23—21no—
109C2×C23—21no—
110C2×C23#40811yescharacteristic
111C2×C23#41011yescharacteristic
112C2×C23#41311yescharacteristic
113D23—81no—
114#126—461no—
115#126—461no—
116#126—461no—
117#126—461no—
118C2×C4⋊C4—231no—
119C2×C4⋊C4—231no—
120C2×C4⋊C4C2×D2311yescharacteristic
121C2×C22⋊C4—231no—
122C2×C22⋊C4—231no—
123C2×C22⋊C4—231no—
124C2×C42—231no—
125C4⋊C8—461no—
126C4⋊C8—461no—
127C22⋊C8—231no—
128C22⋊C8—231no—
129C22⋊C8C2×D2311yescharacteristic
130C22⋊C8C2×D2311yescharacteristic
131#97—461no—
132C4×C8—461no—
133C23#147311yescharacteristic, complemented, Sylow
134C24—231no—
135C22×C4—231no—
136C22×C4—231no—
137C22×C4—231no—
138C22×C4C4×D2311yescharacteristic
139C22×C4C4×D2311yescharacteristic
140C22×C4C22×D2311yescharacteristic
141C2×C8—21no—
142C2×C8—21no—
143C2×C8—461no—
144C2×C8—461no—
145C4⋊C4—21no—
146C4⋊C4—21no—
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—
156C22⋊C4—461no—
157C42—231no—
158C42—231no—
159C42—231no—
160C42—231no—
161C23—461no—
162C23—461no—
163C23—461no—
164C23—921no—
165C23—921no—
166C23C2×C4×D2311yescharacteristic
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—231no—
174C2×C4—231no—
175C2×C4—231no—
176C2×C4—231no—
177C2×C4—461no—
178C2×C4—461no—
179C2×C4—461no—
180C2×C4—921no—
181C2×C4—921no—
182C2×C4D4×D2311yescharacteristic
183C2×C4D4×D2311yescharacteristic
184C8—41no—
185C8—41no—
186C8—921no—
187C8—921no—
188C22—21no—
189C22—21no—
190C22—921no—
191C22—921no—
192C22—921no—
193C22—1841no—
194C22—1841no—
195C22C22⋊C4×D2311yescharacteristic
196C22#1062507211yescharacteristic
197C22#1062507811yescharacteristic
198C4—21no—
199C4—21no—
200C4—41no—
201C4—41no—
202C4—461no—
203C4—461no—
204C4—461no—
205C4—461no—
206C4—921no—
207C2—21no—
208C2—21no—
209C2—1841no—
210C2#1309238211yescharacteristic
211C2#1309238911yescharacteristic
212C2#1309240011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D23
commutatorC23×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#324C2
socleC22×C23C2×C22⋊C4
prime radicalC23×D23C2×C4
cosocleC22×C4×C23C23
hypercenter#324D23
hypocenterC23#1473
LCSG ▷ C23×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #13092471C2semidirect
3. #13092467C2semidirect
4. #13092143C2semidirect
7. C23×#324C2semidirect
105. #324D23semidirect
133. C23#1473semidirect

Maximal subgroups

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

subgroupindex
C2×#106250692
#130924712
#130924672
#130921432
#130921402
C23×#3242
#147323