Finite Group Databasebeta

← C2×#26039564 #37524964

Subgroups — C2×#26039564 #37524964

Order 22932.

152 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 25 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
1C2×#19153212C211yesmaximal, characteristic, complemented
2#26039564C212yesmaximal, direct product factor
3C2×C13×#64418C311yesmaximal, characteristic, complemented
4C2×#16838458—31nomaximal
5#19153212C2211yescharacteristic, complemented, Hall
6C2×C13×#3862C2×C311yescharacteristic, complemented
7C2×#14274263D311yescharacteristic, complemented
8C2×C7×#63271—21no—
9C13×#64418C2×C312yescomplemented
10#16838458—32no—
11C2×C7×C13×D7—31noHall
12C13×#3862C22×C311yescharacteristic, complemented
13#14274263C2×D311yescharacteristic, complemented
14C7×#63271—21no—
15C2×#64418⋊C3—131nomaximal, Hall
16C2×ΓL(1,𝔽8)×C13⋊C3—141no—
17C2×C72×C13C3×D311yescharacteristic, complemented
18C7×C13×D7—32no—
19C22×#63270—211no—
20C2×#10587720—211no—
21C2×ΓL(1,𝔽8)2—131no—
22#64418⋊C3—132no—
23ΓL(1,𝔽8)×C13⋊C3—141no—
24C72×C13C2×C3×D311yescharacteristic, complemented, Hall
25C2×#64423—391no—
26C2×#64418C13⋊C311yescharacteristic, complemented
27C2×#63271—21no—
28C2×#63270—141no—
29C2×#63270—212no—
30C2×#63270—421no—
31C2×#63270—421no—
32C2×C13×ΓL(1,𝔽8)—141no—
33C2×C7×C13⋊C3—141no—
34#10587720—212no—
35C2×D3×C13⋊C3—491nomaximal, Hall
36ΓL(1,𝔽8)2—131noHall
37C22×C7×C13—211no—
38C2×C13×D7—31no—
39C2×#3862C2×C13⋊C311yescharacteristic, complemented
40C2×#3861—131no—
41C2×C7×ΓL(1,𝔽8)—261no—
42#64423—392no—
43#64418C2×C13⋊C312yescomplemented
44#63271—21no—
45#63270—141no—
46#63270—421no—
47#63270—421no—
48C7×C13⋊C3—141no—
49C13×ΓL(1,𝔽8)—141no—
50C2×C3×C13⋊C3—981no—
51D3×C13⋊C3—492no—
52C2×C7×D7—31noHall
53C2×C7×C13—21no—
54C2×C7×C13—61no—
55C2×C7×C13—61no—
56C2×C7×C13—212no—
57C13×D7—32no—
58C2×D3×C13—491no—
59C22×C13⋊C3—1471no—
60#3862C22×C13⋊C311yescharacteristic, complemented
61#3861—131no—
62C7×ΓL(1,𝔽8)—261no—
63C2×C3×ΓL(1,𝔽8)—1821no—
64C3×C13⋊C3—981noHall
65C2×C72D3×C13⋊C311yescharacteristic, complemented
66C7×D7—32no—
67C7×C13—21no—
68C7×C13—61no—
69C7×C13—61no—
70C22×ΓL(1,𝔽8)—2731no—
71C2×AGL(1,𝔽7)—2731no—
72C2×C3×C13—981no—
73D3×C13—492no—
74C2×C13⋊C3—141no—
75C2×C13⋊C3—981no—
76C2×C13⋊C3—1472no—
77C3×ΓL(1,𝔽8)—1821no—
78C22×C13—211noHall
79C72C2×D3×C13⋊C311yescharacteristic, complemented, Sylow
80C2×C3×C7—1821no—
81C2×ΓL(1,𝔽8)—141no—
82C2×ΓL(1,𝔽8)—2732no—
83C2×ΓL(1,𝔽8)—261no—
84C2×ΓL(1,𝔽8)—5461no—
85C2×ΓL(1,𝔽8)—5461no—
86C2×ΓL(1,𝔽8)—1821no—
87AGL(1,𝔽7)—2732no—
88C3×C13—981no—
89C13⋊C3—141no—
90C13⋊C3—981no—
91C2×C3×D3—6371noHall
92C22×C7—211no—
93C2×D7—31no—
94C2×C13—212no—
95C2×C13#64418⋊C311yescharacteristic, complemented
96C3×C7—1821no—
97ΓL(1,𝔽8)—141no—
98ΓL(1,𝔽8)—261no—
99ΓL(1,𝔽8)—5461no—
100ΓL(1,𝔽8)—5461no—
101ΓL(1,𝔽8)—1821no—
102C2×C32—6371no—
103C3×D3—6372no—
104C2×C7—21no—
105C2×C7—61no—
106C2×C7—61no—
107C2×C7—212no—
108D7—32no—
109C13C2×#64418⋊C311yescharacteristic, complemented, Sylow
110C22×C3—19111no—
111C2×D3—491no—
112C32—6371noSylow
113C7—21no—
114C7—61no—
115C7—61no—
116C2×C3—981no—
117C2×C3—19112no—
118C2×C3—1821no—
119C2×C3—12741no—
120D3—492no—
121C22—211noSylow
122C3—981no—
123C3—1821no—
124C3—12741no—
125C2—212no—
126C2#2603956411yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2#26039564
commutator, cosocle, hypocenterC13×#3862C22×C3
FrattiniC1G
Fitting, socleC2×C72×C13C3×D3
LCSG ▷ C13×#3862
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×#19153212C2semidirect
2. #26039564C2direct (N × H)
3. C2×C13×#64418C3semidirect
5. #19153212C22semidirect
6. C2×C13×#3862C2×C3semidirect
7. C2×#14274263D3semidirect
9. C13×#64418C2×C3semidirect
12. C13×#3862C22×C3semidirect
13. #14274263C2×D3semidirect
17. C2×C72×C13C3×D3semidirect
24. C72×C13C2×C3×D3semidirect
26. C2×#64418C13⋊C3semidirect
39. C2×#3862C2×C13⋊C3semidirect
43. #64418C2×C13⋊C3semidirect
60. #3862C22×C13⋊C3semidirect
65. C2×C72D3×C13⋊C3semidirect
79. C72C2×D3×C13⋊C3semidirect
95. C2×C13#64418⋊C3semidirect
109. C13C2×#64418⋊C3semidirect
126. C2#26039564direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191532122
#260395642
C2×C13×#644183
C2×#168384583
C2×#64418⋊C313
C2×D3×C13⋊C349