Finite Group Databasebeta

← #15672919

Subgroups — #15672919

Order 2944.

154 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 51 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#13092820C211yesmaximal, characteristic, complemented
2#13092708C211yesmaximal, characteristic
3#13092704C211yesmaximal, characteristic
4#13092494C211yesmaximal, characteristic
5#13092167C211yesmaximal, characteristic, complemented
6#13092165C211yesmaximal, characteristic, complemented
7C23×#333C211yesmaximal, characteristic, complemented
8C23×C4⋊Q8C2211yescharacteristic
9C2×#67262—21no—
10C4×D92C2211yescharacteristic
11#10625040C2211yescharacteristic
12C23×C4⋊C8C2211yescharacteristic
13C23×C4⋊C8C2211yescharacteristic
14#10625003—21no—
15(C2×D23)⋊C8—21no—
16#10624999—21no—
17#10624991—21no—
18#10624990—21no—
19#10624989—21no—
20#10624989—21no—
21C4⋊(C23⋊C8)C2211yescharacteristic
22C4×C23⋊C8C2211yescharacteristic
23C2×Q8×C23—21no—
24C2×D92D411yescharacteristic
25C2×C4×D23—21no—
26C2×Dic46—21no—
27C2×C8×C23—21no—
28C2×C8×C23—21no—
29C4⋊C4×C23—21no—
30C4⋊C4×C23—21no—
31C42×C23C2311yescharacteristic
32(C2×D23)⋊C4—21no—
33C4⋊Dic23—21no—
34C4⋊Dic23—21no—
35C4⋊Dic23D411yescharacteristic
36C2×C23⋊C8—21no—
37C2×C23⋊C8D411yescharacteristic
38C2×C23⋊C8D411yescharacteristic
39#67262—42no—
40C22×D23—21no—
41Q8×C23—81no—
42C2×C4×C23—41no—
43C2×C4×C23C2×D411yescharacteristic
44C2×C4×C23C2×D411yescharacteristic
45C2×C4×C23#4111yescharacteristic
46C2×Dic23—21no—
47C2×Dic23—41no—
48D92—21no—
49D92—21no—
50C4×D23—41no—
51C4×D23—41no—
52Dic46—81no—
53C8×C23—41no—
54C8×C23—41no—
55C23⋊C8—21no—
56C23⋊C8—41no—
57C23⋊C8SD1612yes—
58#1695—231nomaximal, Sylow
59C22×C23#12111yescharacteristic
60C2×D23—41no—
61C2×D23—41no—
62C2×D23—41no—
63C4×C23—21no—
64C4×C23—81no—
65C4×C23C2×SD1611yescharacteristic
66C4×C23#13711yescharacteristic
67C4×C23#13711yescharacteristic
68C4×C23#13711yescharacteristic
69Dic23—41no—
70Dic23—81no—
71#500—231no—
72#476—231no—
73#476—231no—
74#436—231no—
75#334—231no—
76#333—231no—
77#333D2311yescharacteristic, complemented
78C2×C23#46111yescharacteristic
79C2×C23#47011yescharacteristic
80C2×C23#47211yescharacteristic
81D23—81no—
82C2×M16—461no—
83C4⋊Q8—231no—
84C4⋊Q8C2×D2311yescharacteristic
85C4×D4—231no—
86#107—461no—
87#107—461no—
88#106—461no—
89#106—461no—
90C4⋊C8—231no—
91C4⋊C8C2×D2311yescharacteristic
92C4⋊C8C2×D2311yescharacteristic
93#102—461no—
94#102—461no—
95C22⋊C8—461no—
96C4×C8—231no—
97C23#169511yescharacteristic, complemented, Sylow
98C2×Q8—21no—
99C2×Q8—461no—
100C2×D4—231no—
101C22×C4—461no—
102M16—922no—
103C2×C8—21no—
104C2×C8—21no—
105C2×C8—231no—
106C2×C8—231no—
107C2×C8—461no—
108C4⋊C4—21no—
109C4⋊C4—21no—
110C4⋊C4—231no—
111C4⋊C4—461no—
112C4⋊C4—461no—
113C22⋊C4—461no—
114C42C22×D2311yescharacteristic
115C23—461no—
116Q8—81no—
117Q8—1841no—
118D4—461no—
119D4—461no—
120C2×C4—41no—
121C2×C4—461no—
122C2×C4—921no—
123C2×C4—921no—
124C2×C4—921no—
125C2×C4#6728811yescharacteristic
126C2×C4D4×D2311yescharacteristic
127C2×C4D4×D2311yescharacteristic
128C8—41no—
129C8—41no—
130C8—232no—
131C8—461no—
132C8—921no—
133C22—921no—
134C22—921no—
135C22—921no—
136C22#1062505511yescharacteristic
137C4—21no—
138C4—81no—
139C4—921no—
140C4—1841no—
141C4SD16×D2311yescharacteristic
142C4#1062508611yescharacteristic
143C4#1062508911yescharacteristic
144C4#1062508911yescharacteristic
145C2—1841no—
146C2#1309262111yescharacteristic
147C2#1309267411yescharacteristic
148C2#1309268611yescharacteristic
subgroupG/H
centerC22#10625055
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#333C2
socleC22×C23#121
prime radicalC2×D92D4
hypercenter#333D23
hypocenterC23#1695
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
1. #13092820C2semidirect
5. #13092167C2semidirect
6. #13092165C2semidirect
7. C23×#333C2semidirect
77. #333D23semidirect
97. C23#1695semidirect

Maximal subgroups

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

subgroupindex
#130928202
#130927082
#130927042
#130924942
#130921672
#130921652
C23×#3332
#169523