Finite Group Databasebeta

← #15671932

Subgroups — #15671932

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#13092948C211yesmaximal, characteristic
2#13092471C211yesmaximal, characteristic, complemented
3#13092281C211yesmaximal, characteristic, complemented
4#13092155C211yesmaximal, characteristic, complemented
5#13092153C211yesmaximal, characteristic, complemented
6#13092151C211yesmaximal, characteristic
7C23×#327C211yesmaximal, characteristic
8C23×#121C2211yescharacteristic
9#10625107C411yescharacteristic, complemented
10#10625106—21no—
11D4×Dic23—21no—
12D4×Dic23C411yescharacteristic, complemented
13#10625095C2211yescharacteristic
14C2×Dic23⋊C4—21no—
15C2×C4×Dic23C2211yescharacteristic
16#10625061C411yescharacteristic, complemented
17#10625058C411yescharacteristic, complemented
18#10625050—21no—
19#10625048—21no—
20C23×C22⋊C8C2211yescharacteristic
21C23×#95C2211yescharacteristic
22C23⋊#95—21no—
23C23⋊#95C2211yescharacteristic
24C22⋊(C23⋊C8)C2211yescharacteristic
25#10624997—21no—
26Dic23⋊C8—21no—
27C2×D4×C23—21no—
28C2×D4×C23C2×C411yescharacteristic
29C22×C4×C23—21no—
30C22×C4×C23C2311yescharacteristic
31C22×Dic23—21no—
32C22×Dic23—21no—
33C22×Dic23D411yescharacteristic
34C22×Dic23D411yescharacteristic
35C2×Dic46C2×C411yescharacteristic
36C2×C8×C23—21no—
37C4⋊C4×C23C2×C411yescharacteristic
38C22⋊C4×C23—21no—
39C22⋊Dic23—21no—
40C22⋊Dic23—21no—
41C22⋊Dic23—21no—
42C22⋊Dic23—21no—
43C4⋊Dic23—21no—
44C4⋊Dic23C2×C411yescharacteristic
45Dic23⋊C4—21no—
46Dic23⋊C4—21no—
47Dic23⋊C4—21no—
48Dic23⋊C4—42no—
49C4×Dic23—21no—
50C4×Dic23C2×C411yescharacteristic
51C4×Dic23C2×C411yescharacteristic
52C4×Dic23D411yescharacteristic
53C4×Dic23D411yescharacteristic
54C2×C23⋊C8—21no—
55C23×C23—21no—
56C23×C23C2×D411yescharacteristic
57D4×C23—41no—
58D4×C23—41no—
59D4×C23—41no—
60C2×C4×C23—21no—
61C2×C4×C23—41no—
62C2×C4×C23—41no—
63C2×C4×C23—41no—
64C2×C4×C23—41no—
65C2×C4×C23C22×C411yescharacteristic
66C2×C4×C23C2×D411yescharacteristic
67C2×Dic23—21no—
68C2×Dic23—21no—
69C2×Dic23—21no—
70C2×Dic23—21no—
71C2×Dic23—41no—
72C2×Dic23—42no—
73C2×Dic23—41no—
74C2×Dic23—41no—
75C2×Dic23—41no—
76C2×Dic23C22⋊C411yescharacteristic
77C2×Dic23C22⋊C411yescharacteristic
78C2×Dic23C22⋊C411yescharacteristic
79C2×Dic23C22⋊C411yescharacteristic
80Dic46—41no—
81C8×C23—41no—
82C23⋊C8—41no—
83#1512—231nomaximal, Sylow
84C22×C23—21no—
85C22×C23—21no—
86C22×C23—41no—
87C22×C23—41no—
88C22×C23—41no—
89C22×C23C2×C22⋊C411yescharacteristic
90C22×C23AGL(1,ℤ/8)11yescharacteristic
91C22×C23#13711yescharacteristic
92C4×C23—21no—
93C4×C23—21no—
94C4×C23—41no—
95C4×C23—81no—
96Dic23—21no—
97Dic23—21no—
98Dic23—21no—
99Dic23—21no—
100Dic23—41no—
101Dic23—41no—
102Dic23—81no—
103#529—231no—
104#432—231no—
105#382—231no—
106#328—231no—
107#328—231no—
108#327—231no—
109#327D2311yescharacteristic
110C2×C23—21no—
111C2×C23—21no—
112C2×C23—81no—
113C2×C23#41011yescharacteristic
114C2×C23#41711yescharacteristic
115C2×C23#42111yescharacteristic
116#126—461no—
117#125—231no—
118#124—231no—
119#123—461no—
120C22⋊Q8—231no—
121#121C2×D2311yescharacteristic
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×Q8—231no—
137C2×D4—21no—
138C2×D4C4×D2311yescharacteristic
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—231no—
148C4⋊C4—461no—
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—21no—
165C23D4×D2311yescharacteristic
166Q8—921no—
167D4—41no—
168D4—41no—
169D4—41no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—231no—
176C2×C4—231no—
177C2×C4—231no—
178C2×C4—231no—
179C2×C4—461no—
180C2×C4—461no—
181C2×C4—461no—
182C2×C4—461no—
183C2×C4—921no—
184C2×C4—922no—
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—41no—
195C22—41no—
196C22—41no—
197C22C22⋊C4×D2311yescharacteristic
198C22#1062508211yescharacteristic
199C22#1062508611yescharacteristic
200C4—21no—
201C4—21no—
202C4—41no—
203C4—81no—
204C4—461no—
205C4—461no—
206C4—461no—
207C4—461no—
208C4—921no—
209C4—921no—
210C4—1841no—
211C2—21no—
212C2—21no—
213C2—81no—
214C2#1309238911yescharacteristic
215C2#1309241511yescharacteristic
216C2#1309243211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D23
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#327C2
socleC22×C23C2×C22⋊C4
prime radicalC23×#121C22
cosocleC22×C4×C23C23
hypercenter#327D23
hypocenterC23#1512
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #13092471C2semidirect
3. #13092281C2semidirect
4. #13092155C2semidirect
5. #13092153C2semidirect
9. #10625107C4semidirect
12. D4×Dic23C4semidirect
16. #10625061C4semidirect
17. #10625058C4semidirect
135. C23#1512semidirect

Maximal subgroups

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

subgroupindex
#130929482
#130924712
#130922812
#130921552
#130921532
#130921512
C23×#3272
#151223