Finite Group Databasebeta

← #15674444

Subgroups — #15674444

Order 2944.

370 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 75 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×#10625122C212yesmaximal, complemented
2C2×#10625019C212yesmaximal, complemented
3#13092322C211yesmaximal, characteristic, complemented
4#13092186C211yesmaximal, characteristic, complemented
5C23×#537C211yesmaximal, characteristic
6C2×#41×C23C2212yes—
7C22×Dic46C2211yescharacteristic
8C23×C22⋊Q8—22no—
9C23×#121—22no—
10C23×#121—22no—
11C2×C4⋊C4×C23C2211yescharacteristic
12#10625122—24no—
13#10625122—24no—
14C2×#67275—22no—
15C2×#67273—22no—
16C2×C4×Dic23C2211yescharacteristic
17C2×#67267C2212yes—
18#10625019—24no—
19C23⋊#95—22no—
20#41×C23—22no—
21#41×C23—22no—
22#41×C23—22no—
23#41×C23—22no—
24C2×Q8×C23D412yes—
25C2×D4×C23—22no—
26C2×D4×C23—22no—
27C2×D4×C23D412yes—
28C22×C4×C23—22no—
29C22×C4×C23D412yes—
30C22×C4×C23C2311yescharacteristic
31C22×Dic23—21no—
32C22×Dic23—21no—
33C2×Dic46—22no—
34C2×Dic46—22no—
35C2×Dic46—21no—
36C2×Dic46D412yescomplemented
37C4⋊C4×C23—22no—
38C4⋊C4×C23—22no—
39C22⋊C4×C23—24no—
40#67275—28no—
41#67273—28no—
42C4×Dic23—22no—
43#67267—22no—
44#67267D414yescomplemented
45C2×C23⋊C8—22no—
46C23×C23—22no—
47C23×C23C2×D411yescharacteristic
48Q8×C23—22no—
49Q8×C23—22no—
50D4×C23—22no—
51D4×C23—22no—
52D4×C23—42no—
53D4×C23—42no—
54D4×C23—82no—
55C2×C4×C23—22no—
56C2×C4×C23—22no—
57C2×C4×C23—42no—
58C2×C4×C23—42no—
59C2×C4×C23—42no—
60C2×C4×C23C2×D411yescharacteristic
61C2×C4×C23C2×D412yes—
62C2×C4×C23C2×D412yes—
63C2×C4×C23#4111yescharacteristic
64C2×Dic23—22no—
65C2×Dic23—22no—
66C2×Dic23—41no—
67C2×Dic23—41no—
68C2×Dic23—41no—
69C2×Dic23—41no—
70Dic46—24no—
71Dic46—42no—
72C23⋊C8—24no—
73#2007—231nomaximal, Sylow
74C22×C23—21no—
75C22×C23—21no—
76C22×C23—42no—
77C22×C23—42no—
78C22×C23—42no—
79C22×C23#12011yescharacteristic
80C22×C23#12111yescharacteristic
81C22×C23#12711yescharacteristic
82C4×C23—42no—
83C4×C23—42no—
84C4×C23#12012yes—
85C4×C23#12112yes—
86Dic23—42no—
87Dic23—42no—
88C2×#137—232no—
89#537D2311yescharacteristic
90C2×#104—232no—
91#391—231no—
92#343—231no—
93C2×C23—21no—
94C2×C23—21no—
95C2×C23—82no—
96C2×C23#39211yescharacteristic
97C2×C23#45511yescharacteristic
98C2×C23#45611yescharacteristic
99C2×#41C2×D2312yes—
100C22×Q8—231no—
101#137—464no—
102#137—464no—
103C2×Q16—462no—
104C2×SD16—462no—
105C2×M16—232no—
106C22⋊Q8—22no—
107#121—22no—
108#121—22no—
109C2×C4⋊C4C2×D2311yescharacteristic
110C2×C42—231no—
111#104—464no—
112#95—462no—
113C23#200711yescharacteristic, complemented, Sylow
114#41—22no—
115#41—22no—
116#41—22no—
117#41—22no—
118C2×Q8—232no—
119C2×Q8—461no—
120C2×Q8—462no—
121C2×Q8—462no—
122C2×Q8C22⋊D2312yes—
123C2×D4—22no—
124C2×D4—22no—
125C2×D4C22⋊D2312yes—
126C22×C4—22no—
127C22×C4—461no—
128C22×C4—461no—
129C22×C4C22⋊D2312yes—
130C22×C4C22×D2311yescharacteristic
131Q16—468no—
132SD16—468no—
133M16—234no—
134M16—462no—
135C2×C8—462no—
136C4⋊C4—22no—
137C4⋊C4—22no—
138C22⋊C4—24no—
139C42—462no—
140C23—22no—
141C23C2×C22⋊D2311yescharacteristic
142Q8—22no—
143Q8—22no—
144Q8—464no—
145Q8—922no—
146D4—22no—
147D4—22no—
148D4—42no—
149D4—42no—
150D4—82no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—42no—
154C2×C4—42no—
155C2×C4—42no—
156C2×C4—462no—
157C2×C4—462no—
158C2×C4—921no—
159C2×C4—921no—
160C2×C4—921no—
161C2×C4—921no—
162C2×C4D4×D2311yescharacteristic
163C2×C4D4×D2312yes—
164C2×C4#6729011yescharacteristic
165C2×C4C2×C22⋊D2312yes—
166C8—464no—
167C22—21no—
168C22—21no—
169C22—42no—
170C22—42no—
171C22—42no—
172C22#1062510911yescharacteristic
173C22#1062511111yescharacteristic
174C22#1062512411yescharacteristic
175C4—42no—
176C4—42no—
177C4—922no—
178C4—922no—
179C4#1062510812yes—
180C4#1062511012yes—
181C2—21no—
182C2—21no—
183C2—82no—
184C2#1309232511yescharacteristic
185C2#1309259511yescharacteristic
186C2#1309260011yescharacteristic
subgroupG/H
centerC22#10625124
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
Fitting, prime radicalC23×#537C2
socleC22×C23#120
hypercenter#537D23
hypocenterC23#2007
LCSG ▷ C22×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C2×#10625122C2semidirect
2. C2×#10625019C2semidirect
3. #13092322C2semidirect
4. #13092186C2semidirect
36. C2×Dic46D4semidirect
44. #67267D4semidirect
113. C23#2007semidirect

Maximal subgroups

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

subgroupindex
C2×#106251222
C2×#106250192
#130923222
#130921862
C23×#5372
#200723