Finite Group Databasebeta

← #15672338

Subgroups — #15672338

Order 2944.

266 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 51 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#13093046C211yesmaximal, characteristic, complemented
2#13092570C211yesmaximal, characteristic
3#13092567C211yesmaximal, characteristic
4#13092335C211yesmaximal, characteristic
5#13092153C211yesmaximal, characteristic, complemented
6#13092142C211yesmaximal, characteristic, complemented
7C23×#328C211yesmaximal, characteristic, complemented
8C22×D92C2211yescharacteristic
9C23×C22⋊Q8C2211yescharacteristic
10#10625115—21no—
11C2×#67274—21no—
12C2×(C2×D23)⋊C4—21no—
13C2×(C2×D23)⋊C4—21no—
14#10625095C2211yescharacteristic
15C2×Dic23⋊C4C2211yescharacteristic
16C2×#67263—21no—
17#10625060—21no—
18#10625060—21no—
19#10625059—21no—
20#10625049—21no—
21#10625048—21no—
22C23×C22⋊C8C2211yescharacteristic
23C23×#95C2211yescharacteristic
24C22⋊(C23⋊C8)C2211yescharacteristic
25#10625003—21no—
26#10624991—21no—
27C23×D23—21no—
28C2×Q8×C23D411yescharacteristic
29C22×C4×C23—21no—
30C22×C4×C23C2311yescharacteristic
31C22×Dic23D411yescharacteristic
32C22×Dic23D411yescharacteristic
33C2×D92—21no—
34C2×D92—21no—
35C2×D92—42no—
36C2×Dic46—21no—
37C2×Dic46D411yescharacteristic
38C2×C8×C23—21no—
39C4⋊C4×C23—21no—
40C4⋊C4×C23D411yescharacteristic
41C22⋊C4×C23—21no—
42C22⋊Dic23—21no—
43#67274—42no—
44(C2×D23)⋊C4—42no—
45(C2×D23)⋊C4—42no—
46C4⋊Dic23—21no—
47C4⋊Dic23D411yescharacteristic
48Dic23⋊C4—21no—
49Dic23⋊C4—21no—
50Dic23⋊C4—21no—
51Dic23⋊C4—21no—
52Dic23⋊C4—21no—
53Dic23⋊C4—21no—
54Dic23⋊C4—21no—
55C4×Dic23—21no—
56C4×Dic23—21no—
57C2×C23⋊C8—21no—
58#67263—42no—
59C23×C23C2×D411yescharacteristic
60C22×D23—22no—
61C22×D23—41no—
62C22×D23—41no—
63C22×D23—41no—
64C22×D23—41no—
65C22×D23—41no—
66C22×D23—41no—
67Q8×C23—41no—
68C2×C4×C23—21no—
69C2×C4×C23—21no—
70C2×C4×C23—41no—
71C2×C4×C23—41no—
72C2×C4×C23—41no—
73C2×C4×C23—41no—
74C2×C4×C23C2×D411yescharacteristic
75C2×C4×C23C2×D411yescharacteristic
76C2×Dic23—21no—
77C2×Dic23—21no—
78C2×Dic23—21no—
79C2×Dic23—21no—
80C2×Dic23—21no—
81C2×Dic23—41no—
82C2×Dic23SD1612yescomplemented
83D92—22no—
84D92—22no—
85D92—41no—
86D92—41no—
87Dic46—41no—
88Dic46—81no—
89C8×C23—41no—
90C23⋊C8—41no—
91#1599—231nomaximal, Sylow
92C22×C23—21no—
93C22×C23—21no—
94C22×C23#12011yescharacteristic
95C22×C23C2×SD1611yescharacteristic
96C22×C23#13711yescharacteristic
97C2×D23—42no—
98C2×D23—42no—
99C2×D23—42no—
100C2×D23—81no—
101C2×D23—81no—
102C2×D23—81no—
103C2×D23—81no—
104C4×C23—21no—
105C4×C23—21no—
106C4×C23—41no—
107C4×C23—41no—
108C4×C23—81no—
109Dic23—22no—
110Dic23—41no—
111Dic23—41no—
112Dic23—41no—
113#544—231no—
114#450—231no—
115#450—231no—
116#394—231no—
117#328—231no—
118#328D2311yescharacteristic, complemented
119#324—231no—
120C2×C23—21no—
121C2×C23—21no—
122C2×C23#44811yescharacteristic
123C2×C23#45411yescharacteristic
124C2×C23B(4,𝔽2)11yescharacteristic
125D23—82no—
126C22×D4—231no—
127C2×SD16—461no—
128C2×SD16—461no—
129C4⋊Q8—461no—
130C4⋊Q8—461no—
131#125—461no—
132#125—461no—
133C22⋊Q8—231no—
134C22⋊Q8—461no—
135C22⋊Q8C2×D2311yescharacteristic
136#117—461no—
137C2×C4⋊C4—231no—
138C2×C22⋊C4—461no—
139C2×C22⋊C4—461no—
140#102—461no—
141#102—461no—
142C22⋊C8—231no—
143C22⋊C8C2×D2311yescharacteristic
144#95C2×D2311yescharacteristic
145C23#159911yescharacteristic, complemented, Sylow
146C24—461no—
147C2×Q8—231no—
148C2×Q8—461no—
149C2×Q8D9211yescharacteristic
150C2×D4—461no—
151C2×D4—461no—
152C2×D4—922no—
153C22×C4—21no—
154C22×C4—231no—
155C22×C4—231no—
156C22×C4C22×D2311yescharacteristic
157SD16—922no—
158SD16—922no—
159C2×C8—21no—
160C2×C8—461no—
161C4⋊C4—21no—
162C4⋊C4—231no—
163C4⋊C4—461no—
164C4⋊C4—461no—
165C4⋊C4—461no—
166C4⋊C4—461no—
167C4⋊C4—461no—
168C4⋊C4—461no—
169C4⋊C4—461no—
170C4⋊C4—461no—
171C4⋊C4D9211yescharacteristic
172C22⋊C4—21no—
173C22⋊C4—461no—
174C22⋊C4—922no—
175C22⋊C4—922no—
176C42—461no—
177C42—461no—
178C23—462no—
179C23—921no—
180C23—921no—
181C23—921no—
182C23—921no—
183C23—921no—
184C23—921no—
185C23D4×D2311yescharacteristic
186Q8—41no—
187Q8—921no—
188Q8—1841no—
189D4—462no—
190D4—462no—
191D4—921no—
192D4—921no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—232no—
200C2×C4—461no—
201C2×C4—461no—
202C2×C4—461no—
203C2×C4—461no—
204C2×C4—461no—
205C2×C4—921no—
206C2×C4C2×D9211yescharacteristic
207C2×C4D4×D2311yescharacteristic
208C8—41no—
209C8—921no—
210C22—21no—
211C22—21no—
212C22—922no—
213C22—922no—
214C22—922no—
215C22—1841no—
216C22—1841no—
217C22—1841no—
218C22—1841no—
219C22#1062505311yescharacteristic
220C22SD16×D2311yescharacteristic
221C22#1062508911yescharacteristic
222C4—21no—
223C4—21no—
224C4—41no—
225C4—41no—
226C4—81no—
227C4—462no—
228C4—921no—
229C4—921no—
230C4—921no—
231C2—21no—
232C2—21no—
233C2—1842no—
234C2#1309255711yescharacteristic
235C2#1309259111yescharacteristic
236C2#1309260511yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#328C2
socleC22×C23#120
prime radicalC22×D92C22
hypercenter#328D23
hypocenterC23#1599
LCSG ▷ C22×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
1. #13093046C2semidirect
5. #13092153C2semidirect
6. #13092142C2semidirect
7. C23×#328C2semidirect
82. C2×Dic23SD16semidirect
118. #328D23semidirect
145. C23#1599semidirect

Maximal subgroups

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

subgroupindex
#130930462
#130925702
#130925672
#130923352
#130921532
#130921422
C23×#3282
#159923