Finite Group Databasebeta

← #15671942

Subgroups — #15671942

Order 2944.

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

normal subgroups only

This group has 252 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#13092962C211yesmaximal, characteristic
2#13092471C211yesmaximal, characteristic, complemented
3#13092284C211yesmaximal, characteristic, complemented
4#13092152C211yesmaximal, characteristic, complemented
5#13092151C211yesmaximal, characteristic, complemented
6#13092150C211yesmaximal, characteristic, complemented
7C23×#327C211yesmaximal, characteristic, complemented
8C2×#67290—21no—
9C23×#121C2211yescharacteristic
10#10625111C411yescharacteristic, complemented
11#10625110—21no—
12D4×Dic23C411yescharacteristic, complemented
13#10625101C2211yescharacteristic
14C2×C4×Dic23C2211yescharacteristic
15#10625064C411yescharacteristic, complemented
16#10625059C411yescharacteristic, complemented
17#10625056—21no—
18(C22⋊D23)⋊C4—21no—
19C23×C22⋊C8C2211yescharacteristic
20C23×#95C2211yescharacteristic
21C23⋊#95—21no—
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
31C2×C22⋊D23—21no—
32C2×C22⋊D23—21no—
33C2×C22⋊D23—21no—
34C22×Dic23—21no—
35C22×Dic23—21no—
36C22×Dic23D411yescharacteristic
37C22×Dic23D411yescharacteristic
38#67290—42no—
39#67290—42no—
40C2×D92C2×C411yescharacteristic
41C2×C4×D23—21no—
42C2×Dic46—21no—
43C2×C8×C23—21no—
44C4⋊C4×C23C2×C411yescharacteristic
45C22⋊C4×C23—21no—
46C22⋊Dic23—21no—
47(C2×D23)⋊C4—21no—
48(C2×D23)⋊C4—21no—
49C4⋊Dic23C2×C411yescharacteristic
50Dic23⋊C4—21no—
51C4×Dic23C2×C411yescharacteristic
52C4×Dic23C2×C411yescharacteristic
53C4×Dic23D411yescharacteristic
54C4×Dic23D411yescharacteristic
55C2×C23⋊C8—21no—
56C23×C23—21no—
57C23×C23C2×D411yescharacteristic
58C22×D23—21no—
59D4×C23—41no—
60D4×C23—41no—
61D4×C23—41no—
62C2×C4×C23—21no—
63C2×C4×C23—41no—
64C2×C4×C23—41no—
65C2×C4×C23—41no—
66C2×C4×C23—41no—
67C2×C4×C23C22×C411yescharacteristic
68C2×C4×C23C2×D411yescharacteristic
69C22⋊D23—42no—
70C22⋊D23—42no—
71C22⋊D23—41no—
72C22⋊D23—41no—
73C2×Dic23—21no—
74C2×Dic23—21no—
75C2×Dic23—21no—
76C2×Dic23—41no—
77C2×Dic23—42no—
78C2×Dic23—41no—
79C2×Dic23—41no—
80C2×Dic23—41no—
81C2×Dic23C22⋊C411yescharacteristic
82C2×Dic23C22⋊C411yescharacteristic
83C2×Dic23C22⋊C411yescharacteristic
84C2×Dic23C22⋊C411yescharacteristic
85D92—41no—
86C4×D23—42no—
87Dic46—42no—
88C8×C23—41no—
89C23⋊C8—41no—
90#1514—231nomaximal, Sylow
91C22×C23—21no—
92C22×C23—21no—
93C22×C23—41no—
94C22×C23—41no—
95C22×C23—41no—
96C22×C23C2×C22⋊C411yescharacteristic
97C22×C23AGL(1,ℤ/8)11yescharacteristic
98C22×C23AGL(1,ℤ/8)11yescharacteristic
99C2×D23—41no—
100C2×D23—41no—
101C2×D23—41no—
102C4×C23—21no—
103C4×C23—21no—
104C4×C23—41no—
105C4×C23—81no—
106Dic23—21no—
107Dic23—21no—
108Dic23—21no—
109Dic23—21no—
110Dic23—41no—
111Dic23—81no—
112#532—231no—
113#432—231no—
114#383—231no—
115#327—231no—
116#327—231no—
117#327—231no—
118#327D2311yescharacteristic, complemented
119C2×C23—21no—
120C2×C23—21no—
121C2×C23—81no—
122C2×C23#41011yescharacteristic
123C2×C23#41811yescharacteristic
124C2×C23#42111yescharacteristic
125D23—81no—
126C2×#41—461no—
127C4⋊Q8—231no—
128#127—231no—
129#124—461no—
130#121—231no—
131#121—461no—
132#121C2×D2311yescharacteristic
133C4×D4—231no—
134C4×D4—231no—
135C4×D4—461no—
136C2×C42—231no—
137C4⋊C8—461no—
138C22⋊C8—231no—
139C22⋊C8C2×D2311yescharacteristic
140#97—461no—
141#95—231no—
142#95—461no—
143#95—461no—
144#95C2×D2311yescharacteristic
145C23#151411yescharacteristic, complemented, Sylow
146#41—922no—
147#41—922no—
148C2×Q8—461no—
149C2×D4—21no—
150C2×D4—231no—
151C2×D4—461no—
152C2×D4—461no—
153C2×D4—461no—
154C2×D4C4×D2311yescharacteristic
155C22×C4—21no—
156C22×C4—231no—
157C22×C4—231no—
158C22×C4—461no—
159C22×C4—461no—
160C22×C4—461no—
161C22×C4C22×D2311yescharacteristic
162C2×C8—21no—
163C2×C8—461no—
164C4⋊C4—231no—
165C4⋊C4—461no—
166C4⋊C4C4×D2311yescharacteristic
167C22⋊C4—21no—
168C22⋊C4—461no—
169C22⋊C4—461no—
170C22⋊C4—461no—
171C42—231no—
172C42—231no—
173C42—231no—
174C42—231no—
175C23—21no—
176C23—461no—
177C23D4×D2311yescharacteristic
178Q8—922no—
179D4—41no—
180D4—41no—
181D4—41no—
182D4—921no—
183D4—922no—
184D4—922no—
185D4—921no—
186D4—921no—
187C2×C4—21no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—231no—
193C2×C4—231no—
194C2×C4—231no—
195C2×C4—231no—
196C2×C4—461no—
197C2×C4—461no—
198C2×C4—461no—
199C2×C4—922no—
200C2×C4—921no—
201C2×C4—922no—
202C2×C4—921no—
203C2×C4—921no—
204C2×C4—921no—
205C2×C4C2×C4×D2311yescharacteristic
206C2×C4D4×D2311yescharacteristic
207C8—41no—
208C8—921no—
209C22—21no—
210C22—21no—
211C22—41no—
212C22—41no—
213C22—41no—
214C22—921no—
215C22—921no—
216C22—921no—
217C22C22⋊C4×D2311yescharacteristic
218C22#1062508211yescharacteristic
219C22#1062508511yescharacteristic
220C4—21no—
221C4—21no—
222C4—41no—
223C4—81no—
224C4—461no—
225C4—461no—
226C4—461no—
227C4—461no—
228C4—921no—
229C4—1841no—
230C2—21no—
231C2—21no—
232C2—81no—
233C2—1841no—
234C2#1309238911yescharacteristic
235C2#1309242011yescharacteristic
236C2#1309243211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D23
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#327C2
socleC22×C23C2×C22⋊C4
prime radical#13092962C2
cosocleC22×C4×C23C23
hypercenter#327D23
hypocenterC23#1514
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. #13092284C2semidirect
4. #13092152C2semidirect
5. #13092151C2semidirect
6. #13092150C2semidirect
7. C23×#327C2semidirect
10. #10625111C4semidirect
12. D4×Dic23C4semidirect
15. #10625064C4semidirect
16. #10625059C4semidirect
118. #327D23semidirect
145. C23#1514semidirect

Maximal subgroups

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

subgroupindex
#130929622
#130924712
#130922842
#130921522
#130921512
#130921502
C23×#3272
#151423