Finite Group Databasebeta

← #15672417

Subgroups — #15672417

Order 2944.

288 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 57 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#13092733C212yesmaximal, complemented
2#13092353C211yesmaximal, characteristic, complemented
3#13092151C212yesmaximal, complemented
4#13092141C211yesmaximal, characteristic, complemented
5C23×#534C211yesmaximal, characteristic
6C22×D4×C23—21no—
7C23×#123—22no—
8C23×#121—21no—
9C23×#121C2212yes—
10C23×#120—22no—
11C2×C22⋊C4×C23C2211yescharacteristic
12C2×C22⋊Dic23—21no—
13C2×C4⋊Dic23C2211yescharacteristic, complemented
14C2×Dic23⋊C4—21no—
15#10625014—22no—
16C23⋊#95C2211yescharacteristic, complemented
17C22⋊(C23⋊C8)C2212yescomplemented
18#10624990—22no—
19C24×C23—21no—
20C24×C23D411yescharacteristic
21C2×D4×C23—22no—
22C2×D4×C23—22no—
23C2×D4×C23—21no—
24C2×D4×C23—42no—
25C2×D4×C23—42no—
26C2×D4×C23D412yes—
27C22×C4×C23—21no—
28C22×C4×C23D411yescharacteristic
29C22×C4×C23C2311yescharacteristic
30C22×Dic23—21no—
31C22×Dic23—21no—
32C4⋊C4×C23—21no—
33C4⋊C4×C23D412yes—
34C22⋊C4×C23—22no—
35C22⋊C4×C23—22no—
36C22⋊C4×C23—22no—
37C22⋊Dic23—42no—
38C4⋊Dic23—22no—
39Dic23⋊C4—42no—
40C2×C23⋊C8—22no—
41C23×C23—21no—
42C23×C23—21no—
43C23×C23—22no—
44C23×C23—41no—
45C23×C23—41no—
46C23×C23—42no—
47C23×C23—81no—
48C23×C23—81no—
49C23×C23SD1612yes—
50C23×C23C2×D411yescharacteristic
51D4×C23—42no—
52D4×C23—44no—
53D4×C23—42no—
54D4×C23—42no—
55D4×C23—81no—
56C2×C4×C23—21no—
57C2×C4×C23—22no—
58C2×C4×C23—41no—
59C2×C4×C23—42no—
60C2×C4×C23—41no—
61C2×C4×C23C2×D412yes—
62C2×Dic23—22no—
63C2×Dic23—41no—
64C2×Dic23—41no—
65C2×Dic23—41no—
66C2×Dic23—41no—
67C2×Dic23—41no—
68C23⋊C8—42no—
69#1613—231nomaximal, Sylow
70C22×C23—21no—
71C22×C23—21no—
72C22×C23—22no—
73C22×C23—42no—
74C22×C23—41no—
75C22×C23—41no—
76C22×C23—42no—
77C22×C23—42no—
78C22×C23—42no—
79C22×C23—81no—
80C22×C23—84no—
81C22×C23#12011yescharacteristic
82C22×C23C2×SD1611yescharacteristic
83C22×C23AGL(1,ℤ/8)11yescharacteristic
84C4×C23—22no—
85C4×C23—42no—
86C4×C23—41no—
87Dic23—42no—
88Dic23—81no—
89#534D2311yescharacteristic
90#481—232no—
91#399—231no—
92#327—232no—
93#323—231no—
94C2×C23—21no—
95C2×C23—21no—
96C2×C23—42no—
97C2×C23—82no—
98C2×C23#45011yescharacteristic
99C2×C23#45311yescharacteristic
100C2×C23#45811yescharacteristic
101C22×D4—21no—
102#123—22no—
103#121—21no—
104#121C2×D2312yes—
105#120—22no—
106C2×C4⋊C4—231no—
107C2×C4⋊C4—461no—
108C2×C22⋊C4—461no—
109C2×C22⋊C4C2×D2311yescharacteristic
110#106—462no—
111#102—462no—
112C22⋊C8—232no—
113#95—231no—
114C23#161311yescharacteristic, complemented, Sylow
115C24—21no—
116C24C22⋊D2311yescharacteristic
117C2×D4—22no—
118C2×D4—22no—
119C2×D4—21no—
120C2×D4—42no—
121C2×D4—42no—
122C2×D4C22⋊D2312yes—
123C22×C4—21no—
124C22×C4—461no—
125C22×C4—461no—
126C22×C4C22⋊D2311yescharacteristic
127C22×C4C22×D2311yescharacteristic
128C2×C8—462no—
129C4⋊C4—21no—
130C4⋊C4—462no—
131C4⋊C4—922no—
132C4⋊C4C22⋊D2312yes—
133C22⋊C4—22no—
134C22⋊C4—22no—
135C22⋊C4—22no—
136C22⋊C4—922no—
137C23—21no—
138C23—21no—
139C23—22no—
140C23—41no—
141C23—41no—
142C23—42no—
143C23—81no—
144C23—81no—
145C23#6727312yes—
146C23C2×C22⋊D2311yescharacteristic
147D4—42no—
148D4—44no—
149D4—42no—
150D4—42no—
151D4—81no—
152C2×C4—21no—
153C2×C4—22no—
154C2×C4—41no—
155C2×C4—42no—
156C2×C4—41no—
157C2×C4—462no—
158C2×C4—921no—
159C2×C4—921no—
160C2×C4—921no—
161C2×C4—921no—
162C2×C4—921no—
163C2×C4C2×C22⋊D2312yes—
164C8—922no—
165C22—21no—
166C22—21no—
167C22—22no—
168C22—42no—
169C22—41no—
170C22—41no—
171C22—42no—
172C22—42no—
173C22—42no—
174C22—81no—
175C22—84no—
176C22#1062510311yescharacteristic
177C22C2×#6727311yescharacteristic
178C22#1062512411yescharacteristic
179C4—22no—
180C4—42no—
181C4—41no—
182C4—922no—
183C4—1841no—
184C2—21no—
185C2—21no—
186C2—42no—
187C2—82no—
188C2#1309256811yescharacteristic
189C2#1309258511yescharacteristic
190C2#1309260711yescharacteristic
subgroupG/H
centerC22#10625124
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
Fitting, prime radicalC23×#534C2
socleC22×C23#120
hypercenter#534D23
hypocenterC23#1613
LCSG ▷ C22×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #534

Complements

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

NH ≅ G/Ntype
1. #13092733C2semidirect
2. #13092353C2semidirect
3. #13092151C2semidirect
4. #13092141C2semidirect
13. C2×C4⋊Dic23C22semidirect
16. C23⋊#95C22semidirect
17. C22⋊(C23⋊C8)C22semidirect
114. C23#1613semidirect

Maximal subgroups

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

subgroupindex
#130927332
#130923532
#130921512
#130921412
C23×#5342
#161323