Finite Group Databasebeta

← #15672893

Subgroups — #15672893

Order 2944.

160 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 55 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#13092704C211yesmaximal, characteristic
2#13092619C211yesmaximal, characteristic
3#13092496C211yesmaximal, characteristic
4#13092170C211yesmaximal, characteristic, complemented
5#13092166C211yesmaximal, characteristic, complemented
6#13092163C211yesmaximal, characteristic, complemented
7C23×#498C211yesmaximal, characteristic, complemented
8C23×C4⋊Q8C2211yescharacteristic
9C23×C4⋊Q8C2211yescharacteristic
10C2×#67274—21no—
11C2×#67262—21no—
12C4×D92C2211yescharacteristic
13C23×#106—21no—
14C23×#106—21no—
15C4×C8×C23C2211yescharacteristic
16#10625017—21no—
17(C2×D23)⋊C8—21no—
18#10624991—21no—
19#10624990—21no—
20C4⋊(C23⋊C8)C2211yescharacteristic
21C4⋊(C23⋊C8)C2211yescharacteristic
22C4⋊(C23⋊C8)C2211yescharacteristic
23C2×Q8×C23—21no—
24C2×Q8×C23—21no—
25C2×D92D411yescharacteristic
26C2×C4×D23—21no—
27C2×C8×C23D411yescharacteristic
28C2×C8×C23D411yescharacteristic
29C4⋊C4×C23—21no—
30C4⋊C4×C23—21no—
31C4⋊C4×C23—21no—
32C4⋊C4×C23—21no—
33C42×C23C2311yescharacteristic
34#67274—42no—
35(C2×D23)⋊C4—21no—
36C4⋊Dic23D411yescharacteristic
37C2×C23⋊C8—21no—
38C2×C23⋊C8—21no—
39C2×C23⋊C8—21no—
40#67262—42no—
41C22×D23—21no—
42Q8×C23—41no—
43Q8×C23—41no—
44Q8×C23—81no—
45C2×C4×C23—41no—
46C2×C4×C23—41no—
47C2×C4×C23C2×D411yescharacteristic
48C2×C4×C23C2×D411yescharacteristic
49C2×C4×C23#4111yescharacteristic
50C2×Dic23—21no—
51D92—21no—
52D92—21no—
53C4×D23—41no—
54C4×D23—41no—
55C8×C23—21no—
56C8×C23SD1612yescomplemented
57C23⋊C8—41no—
58C23⋊C8—41no—
59C23⋊C8—41no—
60#1691—231nomaximal, Sylow
61C22×C23#12111yescharacteristic
62C2×D23—41no—
63C2×D23—41no—
64C2×D23—41no—
65C4×C23—21no—
66C4×C23—81no—
67C4×C23—81no—
68C4×C23C2×SD1611yescharacteristic
69C4×C23AGL(1,ℤ/8)11yescharacteristic
70C4×C23#13711yescharacteristic
71C4×C23#13711yescharacteristic
72Dic23—41no—
73#498D2311yescharacteristic, complemented
74#476—231no—
75#461—231no—
76#436—231no—
77#335—231no—
78#333—231no—
79#332—231no—
80C2×C23#46111yescharacteristic
81C2×C23#46811yescharacteristic
82C2×C23#47111yescharacteristic
83D23—81no—
84C2×SD16—461no—
85C2×M16—461no—
86C4⋊Q8C2×D2311yescharacteristic
87C4⋊Q8C2×D2311yescharacteristic
88C4×D4—231no—
89#106—21no—
90#106—21no—
91#106—461no—
92C4⋊C8—231no—
93C4⋊C8—231no—
94C4⋊C8—231no—
95#103—461no—
96#102—461no—
97C22⋊C8—461no—
98C4×C8C2×D2311yescharacteristic
99C23#169111yescharacteristic, complemented, Sylow
100C2×Q8—21no—
101C2×Q8—21no—
102C2×D4—231no—
103C22×C4—461no—
104SD16—922no—
105M16—922no—
106C2×C8—461no—
107C2×C8—461no—
108C2×C8—461no—
109C2×C8C22⋊D2311yescharacteristic
110C2×C8C22⋊D2311yescharacteristic
111C4⋊C4—21no—
112C4⋊C4—21no—
113C4⋊C4—21no—
114C4⋊C4—21no—
115C4⋊C4—231no—
116C22⋊C4—461no—
117C42C22×D2311yescharacteristic
118C23—461no—
119Q8—41no—
120Q8—41no—
121Q8—81no—
122D4—461no—
123D4—461no—
124C2×C4—41no—
125C2×C4—41no—
126C2×C4—461no—
127C2×C4—921no—
128C2×C4—921no—
129C2×C4D4×D2311yescharacteristic
130C2×C4#6729011yescharacteristic
131C2×C4C2×C22⋊D2311yescharacteristic
132C8—21no—
133C8—921no—
134C8—921no—
135C8—921no—
136C8#6727412yescomplemented
137C22—921no—
138C22—921no—
139C22—921no—
140C22#1062510911yescharacteristic
141C4—21no—
142C4—81no—
143C4—81no—
144C4—921no—
145C4#1062508511yescharacteristic
146C4#1062508611yescharacteristic
147C4C2×#6727411yescharacteristic
148C4#1062511311yescharacteristic
149C2—1841no—
150C2#1309261911yescharacteristic
151C2#1309266011yescharacteristic
152C2#1309267711yescharacteristic
subgroupG/H
centerC22#10625109
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#498C2
socleC22×C23#121
prime radicalC2×D92D4
hypercenter#498D23
hypocenterC23#1691
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
4. #13092170C2semidirect
5. #13092166C2semidirect
6. #13092163C2semidirect
7. C23×#498C2semidirect
56. C8×C23SD16semidirect
73. #498D23semidirect
99. C23#1691semidirect
136. C8#67274semidirect

Maximal subgroups

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

subgroupindex
#130927042
#130926192
#130924962
#130921702
#130921662
#130921632
C23×#4982
#169123