Finite Group Databasebeta

← #15674546

Subgroups — #15674546

Order 2944.

258 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 85 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
1C2×#10625061C211yesmaximal, characteristic
2C2×#10625017C211yesmaximal, characteristic
3#13092324C211yesmaximal, characteristic
4#13092180C211yesmaximal, characteristic
5#13092179C211yesmaximal, characteristic
6#13092171C211yesmaximal, characteristic
7C2×C23×#103C211yesmaximal, characteristic
8C22×Q8×C23C2211yescharacteristic
9C22×C8×C23C2211yescharacteristic
10C2×C4⋊C4×C23C2211yescharacteristic
11C2×C4⋊Dic23—21no—
12C2×C4⋊Dic23C2211yescharacteristic
13C2×C4⋊Dic23C2211yescharacteristic
14C2×Dic23⋊C4—21no—
15C2×C4×Dic23C2211yescharacteristic
16C22×C23⋊C8C2211yescharacteristic
17#10625061—22no—
18#10625061—22no—
19C23×#103—22no—
20#10625017—22no—
21C23⋊#95—21no—
22C23⋊#95—21no—
23C2×Q8×C23—21no—
24C2×Q8×C23—21no—
25C2×Q8×C23—21no—
26C2×Q8×C23—21no—
27C2×Q8×C23—21no—
28C2×Q8×C23Q812yes—
29C22×C4×C23—21no—
30C22×C4×C23—21no—
31C22×C4×C23C2311yescharacteristic
32C22×Dic23—21no—
33C22×Dic23—21no—
34C22×Dic23D411yescharacteristic
35C22×Dic23D411yescharacteristic
36C2×C8×C23—21no—
37C2×C8×C23—21no—
38C2×C8×C23—21no—
39C4⋊C4×C23—21no—
40C4⋊C4×C23D412yes—
41C4⋊Dic23—24no—
42C4⋊Dic23—21no—
43C4⋊Dic23—21no—
44C4⋊Dic23—21no—
45C4⋊Dic23D412yes—
46Dic23⋊C4—24no—
47C4×Dic23—21no—
48C4×Dic23—21no—
49C2×C23⋊C8—21no—
50C2×C23⋊C8—21no—
51C2×C23⋊C8—21no—
52C23×C23C2×D411yescharacteristic
53Q8×C23—22no—
54Q8×C23—22no—
55Q8×C23—41no—
56Q8×C23—41no—
57C2×C4×C23—22no—
58C2×C4×C23—22no—
59C2×C4×C23—41no—
60C2×C4×C23—41no—
61C2×C4×C23—41no—
62C2×C4×C23—41no—
63C2×C4×C23C2×D411yescharacteristic
64C2×C4×C23C2×D411yescharacteristic
65C2×C4×C23C2×Q811yescharacteristic
66C2×C4×C23#4111yescharacteristic
67C2×C4×C23#4111yescharacteristic
68C2×C4×C23#4111yescharacteristic
69C2×Dic23—21no—
70C2×Dic23—21no—
71C2×Dic23—22no—
72C2×Dic23—21no—
73C2×Dic23—21no—
74C2×Dic23—21no—
75C2×Dic23—21no—
76C2×Dic23—41no—
77C2×Dic23—41no—
78C2×Dic23—41no—
79C2×Dic23—41no—
80C2×Dic23—41no—
81C8×C23—41no—
82C23⋊C8—41no—
83#2026—231nomaximal, Sylow
84C22×C23#12011yescharacteristic
85C22×C23C22⋊Q811yescharacteristic
86C22×C23#12411yescharacteristic
87C22×C23#13511yescharacteristic
88C22×C23#13511yescharacteristic
89C22×C23#13711yescharacteristic
90C22×C23#13711yescharacteristic
91C4×C23—42no—
92C4×C23—42no—
93C4×C23C22⋊Q811yescharacteristic
94C4×C23C22⋊Q811yescharacteristic
95C4×C23#12411yescharacteristic
96C4×C23#12411yescharacteristic
97Dic23—41no—
98Dic23—41no—
99Dic23—42no—
100Dic23—81no—
101C2×#125—231no—
102C2×#103—231no—
103C2×#103D2311yescharacteristic
104#391—231no—
105#340—231no—
106#340—231no—
107#336—231no—
108C2×C23#39311yescharacteristic
109C2×C23#45211yescharacteristic
110C2×C23#45211yescharacteristic
111C2×C23#47911yescharacteristic
112C2×C23#47911yescharacteristic
113C2×C23#48811yescharacteristic
114C2×C23#49111yescharacteristic
115C22×Q8C2×D2311yescharacteristic
116C22×C8—231no—
117C22×C8C2×D2311yescharacteristic
118#125—462no—
119#125—462no—
120C2×C4⋊C4—231no—
121C2×C4⋊C4—231no—
122C2×C4⋊C4—461no—
123C2×C4⋊C4—461no—
124C2×C4⋊C4C2×D2311yescharacteristic
125C2×C42—231no—
126#103—22no—
127#103—462no—
128#95—461no—
129#95—461no—
130C23#202611yescharacteristic, complemented, Sylow
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8Dic4612yes—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—231no—
140C22×C4—231no—
141C22×C4—461no—
142C22×C4—461no—
143C22×C4C22×D2311yescharacteristic
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—21no—
147C2×C8—461no—
148C2×C8—461no—
149C2×C8—461no—
150C4⋊C4—21no—
151C4⋊C4—232no—
152C4⋊C4—464no—
153C4⋊C4—464no—
154C4⋊C4—461no—
155C4⋊C4—461no—
156C4⋊C4—461no—
157C4⋊C4C22⋊D2312yes—
158C42—461no—
159C42—461no—
160C23D4×D2311yescharacteristic
161Q8—22no—
162Q8—22no—
163Q8—41no—
164Q8—41no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—461no—
172C2×C4—461no—
173C2×C4—461no—
174C2×C4—461no—
175C2×C4—461no—
176C2×C4—461no—
177C2×C4—462no—
178C2×C4—921no—
179C2×C4—921no—
180C2×C4—921no—
181C2×C4—921no—
182C2×C4—921no—
183C2×C4C2×Dic4611yescharacteristic
184C2×C4#6728811yescharacteristic
185C2×C4D4×D2311yescharacteristic
186C2×C4#6729011yescharacteristic
187C2×C4#6729011yescharacteristic
188C2×C4C2×C22⋊D2311yescharacteristic
189C8—41no—
190C8—921no—
191C22#1062504911yescharacteristic
192C22#1062505611yescharacteristic
193C22#1062508611yescharacteristic
194C22#1062508711yescharacteristic
195C22#1062508911yescharacteristic
196C22#1062509011yescharacteristic
197C22#1062510811yescharacteristic
198C4—42no—
199C4—42no—
200C4—921no—
201C4—921no—
202C4—922no—
203C4—1841no—
204C4#1062504911yescharacteristic
205C4#1062505611yescharacteristic
206C4#1062509511yescharacteristic
207C4#1062510711yescharacteristic
208C2#1309232911yescharacteristic
209C2#1309257611yescharacteristic
210C2#1309257811yescharacteristic
211C2#1309272211yescharacteristic
212C2#1309272611yescharacteristic
213C2#1309277311yescharacteristic
214C2#1309278411yescharacteristic
subgroupG/H
centerC23D4×D23
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC2×C23×#103C2
socle, prime radicalC23×C23C2×D4
hypercenterC2×#103D23
hypocenterC23#2026
LCSG ▷ C22×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
130. C23#2026semidirect

Maximal subgroups

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

subgroupindex
C2×#106250612
C2×#106250172
#130923242
#130921802
#130921792
#130921712
C2×C23×#1032
#202623