Finite Group Databasebeta

← #15672420

Subgroups — #15672420

Order 2944.

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

normal subgroups only

This group has 236 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#13093042C211yesmaximal, characteristic
2#13092752C211yesmaximal, characteristic, complemented
3#13092352C211yesmaximal, characteristic
4#13092155C211yesmaximal, characteristic, complemented
5#13092154C211yesmaximal, characteristic, complemented
6#13092140C211yesmaximal, characteristic
7C23×#484C211yesmaximal, characteristic, complemented
8C23×C22⋊Q8C2211yescharacteristic
9C2×C4⋊C4×C23C2211yescharacteristic
10#10625117—21no—
11C2×(C2×D23)⋊C4—21no—
12C2×(C2×D23)⋊C4C2211yescharacteristic
13#10625095C2211yescharacteristic
14C2×Dic23⋊C4—21no—
15#10625068—21no—
16#10625067—21no—
17#10625067—21no—
18C22⋊C4×D23—21no—
19#10625049—21no—
20C23×#107—21no—
21C23×#103—21no—
22C23×C22⋊C8C2211yescharacteristic
23C23⋊#95C2211yescharacteristic
24C22⋊(C23⋊C8)C2211yescharacteristic
25#10624992—21no—
26#10624989—21no—
27C23×D23D411yescharacteristic
28C2×Q8×C23D411yescharacteristic
29C22×C4×C23—21no—
30C22×C4×C23C2311yescharacteristic
31C22×Dic23—21no—
32C22×Dic23D411yescharacteristic
33C2×C4×D23—21no—
34C2×C4×D23—21no—
35C2×Dic46—21no—
36C2×Dic46D411yescharacteristic
37C2×C8×C23—21no—
38C4⋊C4×C23—21no—
39C4⋊C4×C23—21no—
40C4⋊C4×C23—21no—
41C4⋊C4×C23D411yescharacteristic
42C22⋊C4×C23—21no—
43C22⋊Dic23—21no—
44(C2×D23)⋊C4—21no—
45(C2×D23)⋊C4—21no—
46(C2×D23)⋊C4—21no—
47(C2×D23)⋊C4—21no—
48(C2×D23)⋊C4—42no—
49C4⋊Dic23—21no—
50C4⋊Dic23D411yescharacteristic
51Dic23⋊C4—21no—
52Dic23⋊C4—21no—
53Dic23⋊C4—21no—
54Dic23⋊C4—42no—
55C2×C23⋊C8—21no—
56C23×C23C2×D411yescharacteristic
57C22×D23—21no—
58C22×D23—21no—
59C22×D23—41no—
60C22×D23—41no—
61C22×D23Q1612yes—
62Q8×C23—41no—
63C2×C4×C23—21no—
64C2×C4×C23—21no—
65C2×C4×C23—41no—
66C2×C4×C23—41no—
67C2×C4×C23—41no—
68C2×C4×C23—41no—
69C2×C4×C23C2×D411yescharacteristic
70C2×C4×C23C2×D411yescharacteristic
71C2×Dic23—22no—
72C2×Dic23—21no—
73C2×Dic23—21no—
74C2×Dic23—21no—
75C2×Dic23—41no—
76C2×Dic23—41no—
77C2×Dic23—41no—
78C4×D23—81no—
79C4×D23—81no—
80Dic46—41no—
81Dic46—81no—
82C8×C23—41no—
83C23⋊C8—41no—
84#1614—231nomaximal, Sylow
85C22×C23—21no—
86C22×C23—21no—
87C22×C23#12011yescharacteristic
88C22×C23C2×Q1611yescharacteristic
89C22×C23#13711yescharacteristic
90C2×D23—22no—
91C2×D23—41no—
92C2×D23—41no—
93C2×D23—42no—
94C2×D23—81no—
95C4×C23—21no—
96C4×C23—21no—
97C4×C23—41no—
98C4×C23—41no—
99C4×C23—81no—
100Dic23—42no—
101Dic23—41no—
102Dic23—41no—
103Dic23—41no—
104#543—231no—
105#484—231no—
106#484D2311yescharacteristic, complemented
107#399—231no—
108#328—231no—
109#328—231no—
110#323—231no—
111C2×C23—21no—
112C2×C23—21no—
113C2×C23#45111yescharacteristic
114C2×C23#45311yescharacteristic
115C2×C23#45811yescharacteristic
116D23—42no—
117C22⋊Q8—231no—
118C22⋊Q8—461no—
119C22⋊Q8—461no—
120C22⋊Q8—461no—
121C22⋊Q8—461no—
122C22⋊Q8—461no—
123C22⋊Q8C2×D2311yescharacteristic
124C2×C4⋊C4—461no—
125C2×C4⋊C4C2×D2311yescharacteristic
126C2×C22⋊C4—231no—
127C2×C22⋊C4—461no—
128C2×C22⋊C4—461no—
129#107—21no—
130#107—461no—
131#103—21no—
132#103—461no—
133C22⋊C8—231no—
134C22⋊C8C2×D2311yescharacteristic
135#95—231no—
136C23#161411yescharacteristic, complemented, Sylow
137C24—231no—
138C2×Q8—231no—
139C2×Q8—461no—
140C2×Q8C22⋊D2311yescharacteristic
141C22×C4—21no—
142C22×C4—231no—
143C22×C4—461no—
144C22×C4—461no—
145C22×C4—461no—
146C22×C4C22×D2311yescharacteristic
147C2×C8—21no—
148C2×C8—461no—
149C4⋊C4—21no—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—231no—
153C4⋊C4—461no—
154C4⋊C4—461no—
155C4⋊C4—461no—
156C4⋊C4—461no—
157C4⋊C4—922no—
158C4⋊C4C22⋊D2311yescharacteristic
159C22⋊C4—21no—
160C22⋊C4—461no—
161C22⋊C4—461no—
162C22⋊C4—461no—
163C22⋊C4—461no—
164C22⋊C4—461no—
165C22⋊C4—922no—
166C23—232no—
167C23—461no—
168C23—461no—
169C23—921no—
170C23—921no—
171C23D4×D2311yescharacteristic
172Q8—41no—
173Q8—921no—
174Q8—1841no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—462no—
182C2×C4—461no—
183C2×C4—461no—
184C2×C4—461no—
185C2×C4—921no—
186C2×C4—921no—
187C2×C4—921no—
188C2×C4—1841no—
189C2×C4—1841no—
190C2×C4D4×D2311yescharacteristic
191C2×C4C2×C22⋊D2311yescharacteristic
192C8—41no—
193C8—921no—
194C22—21no—
195C22—21no—
196C22—462no—
197C22—922no—
198C22—921no—
199C22—921no—
200C22—1841no—
201C22Q16×D2311yescharacteristic
202C22#1062508911yescharacteristic
203C22#1062510811yescharacteristic
204C4—21no—
205C4—21no—
206C4—41no—
207C4—41no—
208C4—81no—
209C4—922no—
210C4—921no—
211C4—921no—
212C4—921no—
213C2—21no—
214C2—21no—
215C2—922no—
216C2#1309257111yescharacteristic
217C2#1309258311yescharacteristic
218C2#1309260611yescharacteristic
subgroupG/H
centerC22#10625108
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#484C2
socleC22×C23#120
prime radicalC23×D23D4
hypercenter#484D23
hypocenterC23#1614
LCSG ▷ C22×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
2. #13092752C2semidirect
4. #13092155C2semidirect
5. #13092154C2semidirect
7. C23×#484C2semidirect
106. #484D23semidirect
136. C23#1614semidirect

Maximal subgroups

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

subgroupindex
#130930422
#130927522
#130923522
#130921552
#130921542
#130921402
C23×#4842
#161423