Finite Group Databasebeta

← #15671934

Subgroups — #15671934

Order 2944.

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

normal subgroups only

This group has 222 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
1#13092953C211yesmaximal, characteristic
2#13092471C211yesmaximal, characteristic, complemented
3#13092281C211yesmaximal, characteristic, complemented
4#13092154C211yesmaximal, characteristic, complemented
5#13092152C211yesmaximal, characteristic
6#13092150C211yesmaximal, characteristic
7C23×#328C211yesmaximal, characteristic, complemented
8C23×C22⋊Q8C2211yescharacteristic
9#10625118C411yescharacteristic, complemented
10Q8×Dic23C411yescharacteristic, complemented
11#10625101C2211yescharacteristic
12C2×Dic23⋊C4—21no—
13C2×C4×Dic23C2211yescharacteristic
14#10625069—21no—
15#10625064C411yescharacteristic, complemented
16#10625063—21no—
17#10625061C411yescharacteristic, complemented
18#10625057—21no—
19(C22⋊D23)⋊C4—21no—
20C23×C22⋊C8C2211yescharacteristic
21C23×#95C2211yescharacteristic
22C23⋊#95—21no—
23C23⋊#95C2211yescharacteristic
24C22⋊(C23⋊C8)C2211yescharacteristic
25#10624997—21no—
26Dic23⋊C8—21no—
27C2×Q8×C23C2×C411yescharacteristic
28C22×C4×C23—21no—
29C22×C4×C23C2311yescharacteristic
30C2×C22⋊D23—21no—
31C22×Dic23—21no—
32C22×Dic23D411yescharacteristic
33C22×Dic23D411yescharacteristic
34C2×D92C2×C411yescharacteristic
35C2×C4×D23—21no—
36C2×C8×C23—21no—
37C4⋊C4×C23—21no—
38C4⋊C4×C23C2×C411yescharacteristic
39C22⋊C4×C23—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—
46C4⋊Dic23C2×C411yescharacteristic
47Dic23⋊C4—21no—
48Dic23⋊C4—42no—
49C4×Dic23—21no—
50C4×Dic23C2×C411yescharacteristic
51C4×Dic23C2×C411yescharacteristic
52C4×Dic23D411yescharacteristic
53C4×Dic23D411yescharacteristic
54C2×C23⋊C8—21no—
55C23×C23C2×D411yescharacteristic
56C22×D23—21no—
57Q8×C23—41no—
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×C23C22×C411yescharacteristic
65C2×C4×C23C2×D411yescharacteristic
66C22⋊D23—41no—
67C22⋊D23—41no—
68C2×Dic23—21no—
69C2×Dic23—21no—
70C2×Dic23—21no—
71C2×Dic23—41no—
72C2×Dic23—41no—
73C2×Dic23—41no—
74C2×Dic23—41no—
75C2×Dic23C22⋊C411yescharacteristic
76C2×Dic23C22⋊C411yescharacteristic
77C2×Dic23C22⋊C411yescharacteristic
78C2×Dic23C22⋊C411yescharacteristic
79D92—41no—
80C4×D23—42no—
81C8×C23—41no—
82C23⋊C8—41no—
83#1512—231nomaximal, Sylow
84C22×C23—21no—
85C22×C23—21no—
86C22×C23C2×C22⋊C411yescharacteristic
87C22×C23AGL(1,ℤ/8)11yescharacteristic
88C22×C23#13711yescharacteristic
89C2×D23—41no—
90C2×D23—41no—
91C2×D23—41no—
92C4×C23—21no—
93C4×C23—21no—
94C4×C23—41no—
95C4×C23—41no—
96C4×C23—81no—
97Dic23—21no—
98Dic23—21no—
99Dic23—21no—
100Dic23—21no—
101Dic23—41no—
102Dic23—81no—
103#529—231no—
104#432—231no—
105#382—231no—
106#328—231no—
107#328D2311yescharacteristic, complemented
108#327—231no—
109#327—231no—
110C2×C23—21no—
111C2×C23—21no—
112C2×C23#41011yescharacteristic
113C2×C23#41711yescharacteristic
114C2×C23#42111yescharacteristic
115D23—81no—
116#126—461no—
117#125—231no—
118#124—231no—
119#123—461no—
120C22⋊Q8C2×D2311yescharacteristic
121#121—231no—
122C4×Q8—231no—
123C4×D4—231no—
124C4×D4—461no—
125#117—461no—
126C2×C4⋊C4—461no—
127C2×C42—231no—
128C4⋊C8—461no—
129C22⋊C8—231no—
130C22⋊C8C2×D2311yescharacteristic
131#97—461no—
132#95—231no—
133#95—461no—
134#95C2×D2311yescharacteristic
135C23#151211yescharacteristic, complemented, Sylow
136C2×Q8C4×D2311yescharacteristic
137C2×D4—231no—
138C2×D4—461no—
139C22×C4—21no—
140C22×C4—231no—
141C22×C4—231no—
142C22×C4—461no—
143C22×C4—461no—
144C22×C4C22×D2311yescharacteristic
145C2×C8—21no—
146C2×C8—461no—
147C4⋊C4—21no—
148C4⋊C4—231no—
149C4⋊C4—461no—
150C4⋊C4—461no—
151C4⋊C4—461no—
152C4⋊C4—922no—
153C4⋊C4C4×D2311yescharacteristic
154C22⋊C4—21no—
155C22⋊C4—461no—
156C22⋊C4—461no—
157C22⋊C4—461no—
158C22⋊C4—461no—
159C42—231no—
160C42—231no—
161C42—231no—
162C42—231no—
163C42—461no—
164C23—461no—
165C23D4×D2311yescharacteristic
166Q8—41no—
167D4—921no—
168D4—921no—
169D4—921no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—231no—
177C2×C4—231no—
178C2×C4—231no—
179C2×C4—231no—
180C2×C4—461no—
181C2×C4—461no—
182C2×C4—461no—
183C2×C4—922no—
184C2×C4—921no—
185C2×C4—921no—
186C2×C4—921no—
187C2×C4—921no—
188C2×C4C2×C4×D2311yescharacteristic
189C2×C4D4×D2311yescharacteristic
190C8—41no—
191C8—921no—
192C22—21no—
193C22—21no—
194C22—921no—
195C22—921no—
196C22—921no—
197C22C22⋊C4×D2311yescharacteristic
198C22#1062508511yescharacteristic
199C22#1062508911yescharacteristic
200C4—21no—
201C4—21no—
202C4—41no—
203C4—41no—
204C4—81no—
205C4—461no—
206C4—461no—
207C4—461no—
208C4—461no—
209C4—921no—
210C4—1841no—
211C2—21no—
212C2—21no—
213C2—1841no—
214C2#1309238911yescharacteristic
215C2#1309241711yescharacteristic
216C2#1309243211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D23
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#328C2
socleC22×C23C2×C22⋊C4
prime radical#10625101C22
cosocleC22×C4×C23C23
hypercenter#328D23
hypocenterC23#1512
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #13092471C2semidirect
3. #13092281C2semidirect
4. #13092154C2semidirect
7. C23×#328C2semidirect
9. #10625118C4semidirect
10. Q8×Dic23C4semidirect
15. #10625064C4semidirect
17. #10625061C4semidirect
107. #328D23semidirect
135. C23#1512semidirect

Maximal subgroups

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

subgroupindex
#130929532
#130924712
#130922812
#130921542
#130921522
#130921502
C23×#3282
#151223