Finite Group Databasebeta

← #15672707

Subgroups — #15672707

Order 2944.

196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 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#13093171C211yesmaximal, characteristic
2#13092823C211yesmaximal, characteristic, complemented
3#13092809C211yesmaximal, characteristic
4#13092159C211yesmaximal, characteristic, complemented
5#13092158C211yesmaximal, characteristic, complemented
6#13092156C211yesmaximal, characteristic
7C23×#501C211yesmaximal, characteristic, complemented
8C23×C4⋊Q8C2211yescharacteristic
9C23×#125C2211yescharacteristic
10C2×#67275—21no—
11C2×#67274—21no—
12#10625069—21no—
13#10625069—21no—
14#10625068—21no—
15#10625067—21no—
16#10625065—21no—
17#10625059—21no—
18#10625046C2211yescharacteristic
19#10625041C2211yescharacteristic
20C23×#107—21no—
21C23×#106—21no—
22C23×#97C2211yescharacteristic
23#10624990—21no—
24#10624989—21no—
25#10624985C2211yescharacteristic
26#10624985C2211yescharacteristic
27C2×Q8×C23—21no—
28C2×D92D411yescharacteristic
29C2×C4×D23—21no—
30C2×Dic46—21no—
31C2×Dic46D411yescharacteristic
32C2×C8×C23—21no—
33C4⋊C4×C23—21no—
34C4⋊C4×C23—21no—
35C4⋊C4×C23—21no—
36C4⋊C4×C23—21no—
37C4⋊C4×C23D411yescharacteristic
38C4⋊C4×C23D411yescharacteristic
39C42×C23C2311yescharacteristic
40#67275—42no—
41#67274—42no—
42(C2×D23)⋊C4—21no—
43(C2×D23)⋊C4—21no—
44(C2×D23)⋊C4—21no—
45(C2×D23)⋊C4—21no—
46(C2×D23)⋊C4—21no—
47C4⋊Dic23—21no—
48C4⋊Dic23D411yescharacteristic
49C4⋊Dic23D411yescharacteristic
50Dic23⋊C4—21no—
51Dic23⋊C4—21no—
52Dic23⋊C4—21no—
53C4×Dic23—21no—
54C2×C23⋊C8—21no—
55C2×C23⋊C8—21no—
56C22×D23—21no—
57Q8×C23—41no—
58Q8×C23—41no—
59C2×C4×C23—21no—
60C2×C4×C23—21no—
61C2×C4×C23—41no—
62C2×C4×C23C2×D411yescharacteristic
63C2×C4×C23C2×D411yescharacteristic
64C2×C4×C23C2×D411yescharacteristic
65C2×Dic23—21no—
66C2×Dic23—21no—
67C2×Dic23—21no—
68D92—41no—
69C4×D23—81no—
70Dic46—41no—
71Dic46—81no—
72C8×C23—22no—
73C23⋊C8—22no—
74C23⋊C8—22no—
75#1660—231nomaximal, Sylow
76C22×C23#12011yescharacteristic
77C2×D23—41no—
78C2×D23—41no—
79C2×D23—41no—
80C4×C23—21no—
81C4×C23—21no—
82C4×C23—21no—
83C4×C23—41no—
84C4×C23—41no—
85C4×C23—81no—
86Dic23—41no—
87Dic23—41no—
88Dic23—41no—
89#563—231no—
90#501—231no—
91#501D2311yescharacteristic, complemented
92#497—231no—
93#330—231no—
94#330—231no—
95#329—231no—
96C2×C23#45311yescharacteristic
97C2×C23#45611yescharacteristic
98C2×C23#45611yescharacteristic
99D23—81no—
100C2×Q16—461no—
101C2×SD16—461no—
102C4⋊Q8—461no—
103C4⋊Q8C2×D2311yescharacteristic
104#126—461no—
105#126—461no—
106#125—231no—
107#125C2×D2311yescharacteristic
108#124—231no—
109#123—461no—
110C22⋊Q8—461no—
111C22⋊Q8—461no—
112#107—21no—
113#107—461no—
114#106—21no—
115#106—461no—
116#97—231no—
117#97—231no—
118#97C2×D2311yescharacteristic
119C23#166011yescharacteristic, complemented, Sylow
120C2×Q8—21no—
121C2×Q8—231no—
122C2×Q8—461no—
123C2×D4—231no—
124C22×C4—461no—
125Q16—922no—
126SD16—922no—
127C2×C8—21no—
128C2×C8—461no—
129C2×C8—461no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—231no—
135C4⋊C4—231no—
136C4⋊C4—461no—
137C4⋊C4—461no—
138C4⋊C4—461no—
139C4⋊C4—461no—
140C4⋊C4C22⋊D2311yescharacteristic
141C4⋊C4C22⋊D2311yescharacteristic
142C22⋊C4—461no—
143C22⋊C4—461no—
144C22⋊C4—461no—
145C22⋊C4—461no—
146C22⋊C4—461no—
147C42—461no—
148C42C22×D2311yescharacteristic
149C23—461no—
150Q8—41no—
151Q8—41no—
152Q8—921no—
153Q8—1841no—
154D4—921no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—41no—
158C2×C4—461no—
159C2×C4—461no—
160C2×C4—461no—
161C2×C4—1841no—
162C2×C4D4×D2311yescharacteristic
163C2×C4D4×D2311yescharacteristic
164C2×C4C2×C22⋊D2311yescharacteristic
165C8—22no—
166C8—462no—
167C8—462no—
168C22—921no—
169C22—921no—
170C22—921no—
171C22#1062510811yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—81no—
178C4—921no—
179C4—921no—
180C4—921no—
181C2—1841no—
182C2#1309258311yescharacteristic
183C2#1309259811yescharacteristic
184C2#1309259911yescharacteristic
subgroupG/H
centerC22#10625108
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#501C2
socleC22×C23#120
prime radicalC2×D92D4
hypercenter#501D23
hypocenterC23#1660
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
2. #13092823C2semidirect
4. #13092159C2semidirect
5. #13092158C2semidirect
7. C23×#501C2semidirect
91. #501D23semidirect
119. C23#1660semidirect

Maximal subgroups

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

subgroupindex
#130931712
#130928232
#130928092
#130921592
#130921582
#130921562
C23×#5012
#166023