Finite Group Databasebeta

← #15672445

Subgroups — #15672445

Order 2944.

240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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#13092750C211yesmaximal, characteristic, complemented
2#13092733C211yesmaximal, characteristic, complemented
3#13092353C211yesmaximal, characteristic, complemented
4#13092154C211yesmaximal, characteristic, complemented
5#13092151C211yesmaximal, characteristic, complemented
6#13092141C211yesmaximal, characteristic, complemented
7C23×#538C211yesmaximal, characteristic
8C23×#126—21no—
9C23×#124—21no—
10C23×#123—21no—
11C23×C22⋊Q8C2211yescharacteristic
12C23×#121—21no—
13C23×#121C2211yescharacteristic
14C23×#120—21no—
15C4×D4×C23—21no—
16C2×C22⋊C4×C23C2211yescharacteristic
17C2×C22⋊Dic23—21no—
18C2×C4⋊Dic23C2211yescharacteristic
19C2×Dic23⋊C4—21no—
20#10625017—21no—
21#10625014—21no—
22C23⋊#95C2211yescharacteristic
23C22⋊(C23⋊C8)C2211yescharacteristic
24C22⋊(C23⋊C8)C2211yescharacteristic
25#10624990—21no—
26#10624989—21no—
27C24×C23D411yescharacteristic
28C2×Q8×C23D411yescharacteristic
29C2×D4×C23—21no—
30C2×D4×C23—21no—
31C2×D4×C23—21no—
32C2×D4×C23D411yescharacteristic
33C22×C4×C23—21no—
34C22×C4×C23D411yescharacteristic
35C22×C4×C23C2311yescharacteristic
36C22×Dic23—21no—
37C22×Dic23—21no—
38C4⋊C4×C23—21no—
39C4⋊C4×C23—21no—
40C4⋊C4×C23D411yescharacteristic
41C4⋊C4×C23D411yescharacteristic
42C22⋊C4×C23—21no—
43C22⋊C4×C23—21no—
44C22⋊C4×C23—21no—
45C22⋊C4×C23—21no—
46C22⋊C4×C23—21no—
47C22⋊C4×C23—21no—
48C22⋊C4×C23—21no—
49C42×C23—21no—
50C22⋊Dic23—42no—
51C4⋊Dic23—21no—
52C4⋊Dic23—21no—
53Dic23⋊C4—42no—
54C2×C23⋊C8—21no—
55C2×C23⋊C8—21no—
56C23×C23—21no—
57C23×C23—21no—
58C23×C23—21no—
59C23×C23—21no—
60C23×C23—41no—
61C23×C23—41no—
62C23×C23C2×D411yescharacteristic
63Q8×C23—41no—
64D4×C23—41no—
65D4×C23—41no—
66D4×C23—41no—
67D4×C23—81no—
68D4×C23—81no—
69C2×C4×C23—21no—
70C2×C4×C23—21no—
71C2×C4×C23—21no—
72C2×C4×C23—21no—
73C2×C4×C23—41no—
74C2×C4×C23—41no—
75C2×C4×C23—81no—
76C2×C4×C23C2×D411yescharacteristic
77C2×C4×C23C2×D411yescharacteristic
78C2×Dic23—22no—
79C2×Dic23—41no—
80C2×Dic23—41no—
81C2×Dic23—41no—
82C2×Dic23—41no—
83C2×Dic23—41no—
84C23⋊C8—41no—
85C23⋊C8—41no—
86#1618—231nomaximal, Sylow
87C22×C23—21no—
88C22×C23—21no—
89C22×C23—42no—
90C22×C23—41no—
91C22×C23—41no—
92C22×C23—41no—
93C22×C23—41no—
94C22×C23—41no—
95C22×C23—41no—
96C22×C23—81no—
97C22×C23#12011yescharacteristic
98C22×C23#13511yescharacteristic
99C22×C23#13711yescharacteristic
100C4×C23—21no—
101C4×C23—21no—
102C4×C23—41no—
103C4×C23—41no—
104C4×C23—41no—
105C4×C23—41no—
106Dic23—42no—
107Dic23—81no—
108#538D2311yescharacteristic
109#484—231no—
110#481—231no—
111#399—231no—
112#328—231no—
113#327—231no—
114#323—231no—
115C2×C23—21no—
116C2×C23—21no—
117C2×C23—81no—
118C2×C23—81no—
119C2×C23#45211yescharacteristic
120C2×C23#45311yescharacteristic
121C2×C23#45811yescharacteristic
122#126—21no—
123#124—21no—
124#123—21no—
125C22⋊Q8C2×D2311yescharacteristic
126#121—21no—
127#121C2×D2311yescharacteristic
128#120—21no—
129C4×D4—21no—
130C2×C4⋊C4—231no—
131C2×C4⋊C4—461no—
132C2×C22⋊C4—461no—
133C2×C22⋊C4C2×D2311yescharacteristic
134#107—461no—
135#106—461no—
136#103—461no—
137#102—461no—
138C22⋊C8—231no—
139C22⋊C8—231no—
140#95—231no—
141C23#161811yescharacteristic, complemented, Sylow
142C24C22⋊D2311yescharacteristic
143C2×Q8C22⋊D2311yescharacteristic
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4C22⋊D2311yescharacteristic
148C22×C4—21no—
149C22×C4—461no—
150C22×C4—461no—
151C22×C4C22⋊D2311yescharacteristic
152C22×C4C22×D2311yescharacteristic
153C2×C8—461no—
154C2×C8—461no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—461no—
158C4⋊C4—461no—
159C4⋊C4—922no—
160C4⋊C4C22⋊D2311yescharacteristic
161C4⋊C4C22⋊D2311yescharacteristic
162C22⋊C4—21no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—21no—
166C22⋊C4—21no—
167C22⋊C4—21no—
168C22⋊C4—21no—
169C22⋊C4—922no—
170C42—21no—
171C23—21no—
172C23—21no—
173C23—21no—
174C23—21no—
175C23—41no—
176C23—41no—
177C23C2×C22⋊D2311yescharacteristic
178Q8—41no—
179D4—41no—
180D4—41no—
181D4—41no—
182D4—81no—
183D4—81no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—81no—
191C2×C4—462no—
192C2×C4—921no—
193C2×C4—921no—
194C2×C4—921no—
195C2×C4—921no—
196C2×C4—921no—
197C2×C4C2×C22⋊D2311yescharacteristic
198C2×C4C2×C22⋊D2311yescharacteristic
199C8—921no—
200C8—921no—
201C22—21no—
202C22—21no—
203C22—42no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—41no—
209C22—41no—
210C22—81no—
211C22#1062512111yescharacteristic
212C22#1062512211yescharacteristic
213C22#1062512411yescharacteristic
214C4—21no—
215C4—21no—
216C4—41no—
217C4—41no—
218C4—41no—
219C4—41no—
220C4—922no—
221C4—1841no—
222C2—21no—
223C2—21no—
224C2—81no—
225C2—81no—
226C2#1309257911yescharacteristic
227C2#1309258511yescharacteristic
228C2#1309260711yescharacteristic
subgroupG/H
centerC22#10625124
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
Fitting, prime radicalC23×#538C2
socleC22×C23#120
hypercenter#538D23
hypocenterC23#1618
LCSG ▷ C22×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #538

Complements

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

NH ≅ G/Ntype
1. #13092750C2semidirect
2. #13092733C2semidirect
3. #13092353C2semidirect
4. #13092154C2semidirect
5. #13092151C2semidirect
6. #13092141C2semidirect
141. C23#1618semidirect

Maximal subgroups

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

subgroupindex
#130927502
#130927332
#130923532
#130921542
#130921512
#130921412
C23×#5382
#161823