Finite Group Databasebeta

← #37524843

Subgroups — #37524843

Order 22932.

152 conjugacy classes of subgroups; only the 19 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 19 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#26039563C211yesmaximal, characteristic, complemented
2#26039561C211yesmaximal, characteristic, complemented
3#26039518C211yesmaximal, characteristic, complemented
4#64418⋊D13C311yesmaximal, characteristic, complemented
5#21439609—31nomaximal
6#19153211C2211yescharacteristic, complemented, Hall
7C13⋊#64418C2×C311yescharacteristic, complemented
8C13×#64418C2×C311yescharacteristic, complemented
9#16838468—21no—
10#16838459—31no—
11#16838457—31no—
12#16838454C2×C311yescharacteristic, complemented
13#16838447D311yescharacteristic, complemented
14D7×D91—31noHall
15C13×#3862C22×C311yescharacteristic, complemented
16#14274262C2×D311yescharacteristic, complemented
17C7×#63270—21no—
18(#64418⋊C2)⋊C3—131nomaximal, Hall
19ΓL(1,𝔽8)⋊(D13⋊C3)—141no—
20C7⋊D91C3×D311yescharacteristic, complemented
21C7×D91—31no—
22C7×C13×D7—31no—
23C2×#10587723—211no—
24#10587717⋊C2—211no—
25ΓL(1,𝔽8)⋊AGL(1,𝔽7)—131no—
26#64418⋊C3—131no—
27#64418⋊C3—261no—
28ΓL(1,𝔽8)×C13⋊C3—281no—
29C72×C13C2×C3×D311yescharacteristic, complemented, Hall
30#64423⋊C2—391no—
31#64418⋊C2—131no—
32C2×#63271—211no—
33#10587723—141no—
34#10587723—421no—
35#10587723—421no—
36#10587723—421no—
37#10587722—141no—
38#10587721—211no—
39ΓL(1,𝔽8)⋊D13—141no—
40#10587717—211no—
41(C13⋊C3)⋊D7—141no—
42D3×D13⋊C3—491nomaximal, Hall
43ΓL(1,𝔽8)2—261noHall
44C2×D91—211no—
45D7×D13—211no—
46#64425—131no—
47#64424—131no—
48#64423—391no—
49#64423—391no—
50ΓL(1,𝔽8)⋊D7—261no—
51#64418—131no—
52#64418D13⋊C311yescharacteristic, complemented
53#63271—281no—
54#63271—421no—
55#63271—841no—
56#63270—21no—
57C7×C13⋊C3—281no—
58C13×ΓL(1,𝔽8)—141no—
59C3⋊(D13⋊C3)—981no—
60D3×C13⋊C3—981no—
61C3×D13⋊C3—491no—
62D72—391noHall
63C2×C7×C13—211no—
64D91—31no—
65D91—141no—
66D91—421no—
67D91—421no—
68C7×D13—211no—
69C13×D7—31no—
70D3×D13—491no—
71C2×D13⋊C3—1471no—
72#3862C2×D13⋊C311yescharacteristic, complemented
73#3861—131no—
74C7×ΓL(1,𝔽8)—521no—
75C3×AGL(1,𝔽7)—1821no—
76C3×C13⋊C3—1961noHall
77C7⋊D7—131no—
78C7×D7—31no—
79C7×D7—391no—
80C7×C13—21no—
81C7×C13—61no—
82C7×C13—61no—
83C2×AGL(1,𝔽7)—2731no—
84C2×AGL(1,𝔽7)—2731no—
85D39—981no—
86C3×D13—491no—
87D3×C13—981no—
88C2×C13⋊C3—2941no—
89D13⋊C3—2941no—
90D13⋊C3—491no—
91D13⋊C3—981no—
92C3×ΓL(1,𝔽8)—3641no—
93C2×D13—1471noHall
94C72D3×D13⋊C311yescharacteristic, complemented, Sylow
95C3×D7—1821no—
96C2×ΓL(1,𝔽8)—2731no—
97C2×ΓL(1,𝔽8)—5461no—
98AGL(1,𝔽7)—5461no—
99AGL(1,𝔽7)—5461no—
100AGL(1,𝔽7)—5461no—
101AGL(1,𝔽7)—5461no—
102AGL(1,𝔽7)—1821no—
103AGL(1,𝔽7)—1821no—
104AGL(1,𝔽7)—1821no—
105C3×C13—1961no—
106C13⋊C3—281no—
107C13⋊C3—981no—
108C2×C3×D3—6371noHall
109C2×D7—2731no—
110C2×D7—2731no—
111C2×C13—211no—
112D13—211no—
113D13—491no—
114C3×C7—3641no—
115ΓL(1,𝔽8)—281no—
116ΓL(1,𝔽8)—521no—
117ΓL(1,𝔽8)—10921no—
118ΓL(1,𝔽8)—10921no—
119ΓL(1,𝔽8)—3641no—
120C2×C32—6371no—
121C3×D3—12741no—
122C3×D3—12741no—
123C2×C7—2731no—
124C2×C7—211no—
125D7—31no—
126D7—2731no—
127D7—5461no—
128D7—391no—
129D7—1821no—
130C13(#64418⋊C2)⋊C311yescharacteristic, complemented, Sylow
131C22×C3—19111no—
132C2×D3—6371no—
133C32—25481noSylow
134C7—21no—
135C7—31no—
136C7—61no—
137C2×C3—6371no—
138C2×C3—6371no—
139C2×C3—38221no—
140C2×C3—38221no—
141C2×C3—12741no—
142D3—981no—
143D3—12741no—
144C22—19111noSylow
145C3—3641no—
146C3—1961no—
147C3—25481no—
148C2—2731no—
149C2—211no—
150C2—6371no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, cosocle, hypocenterC13×#3862C22×C3
Fitting, socleC72×C13C2×C3×D3
LCSG ▷ C13×#3862
UCSC1

Complements

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

NH ≅ G/Ntype
1. #26039563C2semidirect
2. #26039561C2semidirect
3. #26039518C2semidirect
4. #64418⋊D13C3semidirect
6. #19153211C22semidirect
7. C13⋊#64418C2×C3semidirect
8. C13×#64418C2×C3semidirect
12. #16838454C2×C3semidirect
13. #16838447D3semidirect
15. C13×#3862C22×C3semidirect
16. #14274262C2×D3semidirect
20. C7⋊D91C3×D3semidirect
29. C72×C13C2×C3×D3semidirect
52. #64418D13⋊C3semidirect
72. #3862C2×D13⋊C3semidirect
94. C72D3×D13⋊C3semidirect
130. C13(#64418⋊C2)⋊C3semidirect

Maximal subgroups

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

subgroupindex
#260395632
#260395612
#260395182
#64418⋊D133
#214396093
(#64418⋊C2)⋊C313
D3×D13⋊C349