Finite Group Databasebeta

← #37524862

Subgroups — #37524862

Order 22932.

152 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 20 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#26039564C211yesmaximal, characteristic, complemented
2#26039562C211yesmaximal, characteristic, complemented
3#26039556C211yesmaximal, characteristic, complemented
4D13×#64418C311yesmaximal, characteristic, complemented
5#21439625—31nomaximal
6#19153212C2211yescharacteristic, complemented, Hall
7C13⋊#64418C2×C311yescharacteristic, complemented
8C13×#64418C2×C311yescharacteristic, complemented
9D13×#3862C2×C311yescharacteristic, complemented
10#16838473D311yescharacteristic, complemented
11#16838458—31no—
12#16838456—31no—
13C7×#10587717—21no—
14C7×D7×D13—31noHall
15C13×#3862C22×C311yescharacteristic, complemented
16#14274263C2×D311yescharacteristic, complemented
17C7×#63271—21no—
18C2×#64418⋊C3—131nomaximal, Hall
19ΓL(1,𝔽8)×D13⋊C3—141no—
20C7×D91—31no—
21C7×C13×D7—31no—
22C72×D13C3×D311yescharacteristic, complemented
23C2×#10587716—211no—
24#10587716⋊C2—211no—
25C2×ΓL(1,𝔽8)2—131no—
26#64418⋊C3—131no—
27#64418⋊C3—261no—
28ΓL(1,𝔽8)×C13⋊C3—141no—
29C72×C13C2×C3×D311yescharacteristic, complemented, Hall
30C2×#64423—391no—
31C2×#64418—131no—
32C2×#63270—211no—
33#10587722—211no—
34#10587720—211no—
35#10587717—21no—
36#10587716—141no—
37#10587716—211no—
38#10587716—421no—
39#10587716—421no—
40ΓL(1,𝔽8)×D13—141no—
41C7×D13⋊C3—141no—
42D3×D13⋊C3—491nomaximal, Hall
43ΓL(1,𝔽8)2—261noHall
44C2×C7×D13—211no—
45D7×D13—31no—
46C2×#3862—131no—
47C2×#3861—131no—
48C2×C7×ΓL(1,𝔽8)—261no—
49#64423—391no—
50#64423—781no—
51#64418—131no—
52#64418D13⋊C311yescharacteristic, complemented
53#63271—21no—
54#63270—141no—
55#63270—421no—
56#63270—421no—
57C7×C13⋊C3—141no—
58C13×ΓL(1,𝔽8)—141no—
59C3⋊(D13⋊C3)—491no—
60D3×C13⋊C3—491no—
61C3×D13⋊C3—981no—
62C2×C7×D7—391noHall
63C2×C7×C13—211no—
64D91—31no—
65C7×D13—21no—
66C7×D13—61no—
67C7×D13—61no—
68C7×D13—211no—
69C13×D7—31no—
70D3×D13—491no—
71C2×D13⋊C3—1471no—
72#3862C2×D13⋊C311yescharacteristic, complemented
73#3861—261no—
74C7×ΓL(1,𝔽8)—521no—
75C2×C3×ΓL(1,𝔽8)—1821no—
76C3×C13⋊C3—981noHall
77C2×C72—131no—
78C7×D7—31no—
79C7×D7—391no—
80C7×C13—21no—
81C7×C13—61no—
82C7×C13—61no—
83C22×ΓL(1,𝔽8)—2731no—
84C2×AGL(1,𝔽7)—2731no—
85D39—491no—
86C3×D13—981no—
87D3×C13—491no—
88C2×C13⋊C3—1471no—
89D13⋊C3—141no—
90D13⋊C3—981no—
91D13⋊C3—1471no—
92C3×ΓL(1,𝔽8)—3641no—
93C2×D13—211noHall
94C72D3×D13⋊C311yescharacteristic, complemented, Sylow
95C2×C3×C7—1821no—
96C2×ΓL(1,𝔽8)—2731no—
97C2×ΓL(1,𝔽8)—2731no—
98C2×ΓL(1,𝔽8)—261no—
99C2×ΓL(1,𝔽8)—5461no—
100C2×ΓL(1,𝔽8)—5461no—
101C2×ΓL(1,𝔽8)—1821no—
102C2×ΓL(1,𝔽8)—1821no—
103AGL(1,𝔽7)—2731no—
104AGL(1,𝔽7)—5461no—
105C3×C13—981no—
106C13⋊C3—141no—
107C13⋊C3—981no—
108C2×C3×D3—6371noHall
109C22×C7—2731no—
110C2×D7—391no—
111C2×C13—211no—
112D13—211no—
113D13#64418⋊C311yescharacteristic, complemented
114C3×C7—3641no—
115ΓL(1,𝔽8)—141no—
116ΓL(1,𝔽8)—5461no—
117ΓL(1,𝔽8)—5461no—
118ΓL(1,𝔽8)—521no—
119ΓL(1,𝔽8)—3641no—
120C2×C32—12741no—
121C3×D3—6371no—
122C3×D3—12741no—
123C2×C7—2731no—
124C2×C7—211no—
125C2×C7—261no—
126C2×C7—781no—
127C2×C7—781no—
128D7—31no—
129D7—391no—
130C13C2×#64418⋊C311yescharacteristic, complemented, Sylow
131C22×C3—19111no—
132C2×D3—6371no—
133C32—25481noSylow
134C7—21no—
135C7—61no—
136C7—61no—
137C2×C3—19111no—
138C2×C3—1821no—
139C2×C3—38221no—
140C2×C3—12741no—
141C2×C3—12741no—
142D3—491no—
143D3—6371no—
144C22—2731noSylow
145C3—981no—
146C3—1821no—
147C3—12741no—
148C2—131no—
149C2—2731no—
150C2—211no—
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. #26039564C2semidirect
2. #26039562C2semidirect
3. #26039556C2semidirect
4. D13×#64418C3semidirect
6. #19153212C22semidirect
7. C13⋊#64418C2×C3semidirect
8. C13×#64418C2×C3semidirect
9. D13×#3862C2×C3semidirect
10. #16838473D3semidirect
15. C13×#3862C22×C3semidirect
16. #14274263C2×D3semidirect
22. C72×D13C3×D3semidirect
29. C72×C13C2×C3×D3semidirect
52. #64418D13⋊C3semidirect
72. #3862C2×D13⋊C3semidirect
94. C72D3×D13⋊C3semidirect
113. D13#64418⋊C3semidirect
130. C13C2×#64418⋊C3semidirect

Maximal subgroups

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

subgroupindex
#260395642
#260395622
#260395562
D13×#644183
#214396253
C2×#64418⋊C313
D3×D13⋊C349