Finite Group Databasebeta

← #15673816

Subgroups — #15673816

Order 2944.

342 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 93 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#13093184C211yesmaximal, characteristic, complemented
2#13092401C211yesmaximal, characteristic, complemented
3#13092381C212yesmaximal, complemented
4#13092187C212yesmaximal, complemented
5C23×#525C211yesmaximal, characteristic
6C2×#41×C23C2211yescharacteristic
7C23×C4×C23C2211yescharacteristic
8C23×#123C412yes—
9C23×C22⋊Q8—21no—
10C23×#121—21no—
11C23×#120C412yes—
12C4×D4×C23—22no—
13C23×#117C2211yescharacteristic
14#10625119—24no—
15C2×#67267—22no—
16C2×#67267C2212yes—
17C2×#67267C2212yes—
18#10625018—21no—
19#10625015—21no—
20C22⋊(C23⋊C8)—24no—
21C24×C23C2×C411yescharacteristic
22#41×C23—22no—
23#41×C23—22no—
24C2×Q8×C23D411yescharacteristic
25C2×D4×C23—22no—
26C2×D4×C23C2×C412yes—
27C2×D4×C23D411yescharacteristic
28C22×C4×C23—21no—
29C22×C4×C23—21no—
30C22×C4×C23—22no—
31C22×C4×C23—22no—
32C22×C4×C23C2×C411yescharacteristic
33C22×C4×C23D412yes—
34C22×C4×C23C2311yescharacteristic
35C4⋊C4×C23—22no—
36C4⋊C4×C23—21no—
37C22⋊C4×C23—22no—
38C22⋊C4×C23—22no—
39C22⋊C4×C23C2×C412yes—
40C42×C23—21no—
41#67267—24no—
42#67267—22no—
43#67267—22no—
44#67267—22no—
45#67267—22no—
46C2×C23⋊C8—24no—
47C2×C23⋊C8—22no—
48C2×C23⋊C8D414yescomplemented
49C23×C23—21no—
50C23×C23—22no—
51C23×C23—42no—
52C23×C23C22⋊C412yes—
53C23×C23C22×C411yescharacteristic
54Q8×C23—22no—
55D4×C23—24no—
56D4×C23—22no—
57D4×C23—44no—
58C2×C4×C23—22no—
59C2×C4×C23—22no—
60C2×C4×C23—22no—
61C2×C4×C23—21no—
62C2×C4×C23—22no—
63C2×C4×C23—41no—
64C2×C4×C23—42no—
65C2×C4×C23—41no—
66C2×C4×C23C22⋊C412yes—
67C2×C4×C23C2×D412yes—
68C2×C4×C23C2×D411yescharacteristic
69C2×C4×C23C2×D411yescharacteristic
70C2×C4×C23#4112yes—
71C23⋊C8—24no—
72C23⋊C8—42no—
73#1891—231nomaximal, Sylow
74C22×C23—22no—
75C22×C23—24no—
76C22×C23—22no—
77C22×C23—41no—
78C22×C23—42no—
79C22×C23—41no—
80C22×C23—42no—
81C22×C23—41no—
82C22×C23C2×C22⋊C411yescharacteristic
83C22×C23C4×D412yes—
84C4×C23—22no—
85C4×C23—42no—
86C4×C23—41no—
87C4×C23#12011yescharacteristic
88C4×C23#12112yes—
89C4×C23#12311yescharacteristic
90#568—231no—
91#525D2311yescharacteristic
92#413—231no—
93#407—232no—
94#344—232no—
95C2×C23—21no—
96C2×C23—22no—
97C2×C23—42no—
98C2×C23—42no—
99C2×C23#38611yescharacteristic
100C2×#41C2×D2311yescharacteristic
101C23×C4C2×D2311yescharacteristic
102#131—464no—
103C2×M16—232no—
104C2×M16—232no—
105C2×M16—462no—
106#123Dic2312yes—
107C22⋊Q8—21no—
108#121—21no—
109#120Dic2312yes—
110C4×D4—22no—
111#117C2×D2311yescharacteristic
112#101—461no—
113#100—461no—
114C22⋊C8—464no—
115C23#189111yescharacteristic, complemented, Sylow
116C24C2×Dic2311yescharacteristic
117#41—22no—
118#41—22no—
119C2×Q8C22⋊D2311yescharacteristic
120C2×D4—22no—
121C2×D4C2×Dic2312yes—
122C2×D4C22⋊D2311yescharacteristic
123C22×C4—22no—
124C22×C4—22no—
125C22×C4—21no—
126C22×C4—21no—
127C22×C4C2×Dic2311yescharacteristic
128C22×C4C22⋊D2312yes—
129C22×C4C22×D2311yescharacteristic
130M16—464no—
131M16—462no—
132M16—462no—
133M16—462no—
134M16—462no—
135C2×C8—234no—
136C2×C8—464no—
137C2×C8—462no—
138C4⋊C4—22no—
139C4⋊C4—21no—
140C22⋊C4—22no—
141C22⋊C4—22no—
142C22⋊C4C2×Dic2312yes—
143C42—21no—
144C23—22no—
145C23—21no—
146C23—42no—
147C23C22⋊Dic2312yes—
148C23C22×Dic2311yescharacteristic
149Q8—22no—
150D4—24no—
151D4—22no—
152D4—44no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—42no—
161C2×C4C22⋊Dic2312yes—
162C2×C4D4×D2312yes—
163C2×C4#6729012yes—
164C2×C4C2×C22⋊D2311yescharacteristic
165C2×C4C2×C22⋊D2311yescharacteristic
166C8—464no—
167C8—922no—
168C22—22no—
169C22—24no—
170C22—22no—
171C22—41no—
172C22—42no—
173C22—41no—
174C22—42no—
175C22—41no—
176C22D4×Dic2312yes—
177C22C2×C22⋊Dic2311yescharacteristic
178C4—22no—
179C4—42no—
180C4—41no—
181C4#1062510611yescharacteristic
182C4#1062510811yescharacteristic
183C4#1062511012yes—
184C2—21no—
185C2—22no—
186C2—42no—
187C2—42no—
188C2#1309229711yescharacteristic
subgroupG/H
centerC4#10625108
commutatorC23×C23C22×C4
FrattiniC22×C4C22×D23
Fitting, prime radicalC23×#525C2
socleC2×C23#386
cosocleC22×C4×C23C23
hypercenter#525D23
hypocenterC23#1891
LCSG ▷ C23×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C4 ◁ C22×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #13093184C2semidirect
2. #13092401C2semidirect
3. #13092381C2semidirect
4. #13092187C2semidirect
48. C2×C23⋊C8D4semidirect
115. C23#1891semidirect

Maximal subgroups

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

subgroupindex
#130931842
#130924012
#130923812
#130921872
C23×#5252
#189123