Finite Group Databasebeta

← C13⋊C3×#64418⋊C2 #37524867

Subgroups — C13⋊C3×#64418⋊C2 #37524867

Order 22932.

152 conjugacy classes of subgroups; only the 24 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 24 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
1C13⋊C3×#64418C211yesmaximal, characteristic, complemented
2C13⋊C3×#64418C211yesmaximal, characteristic, complemented
3C13⋊C3×#64425C211yesmaximal, characteristic, complemented
4C13×#64418⋊C2C311yesmaximal, characteristic, complemented
5D72×C13⋊C3—31nomaximal
6C13⋊C3×#3862C2211yescharacteristic, complemented, Hall
7C13×#64418C2×C311yescharacteristic, complemented
8C13×#64418C2×C311yescharacteristic, complemented
9C13⋊C3×C7⋊D7D311yescharacteristic, complemented
10#16838453—21no—
11C13×#64425C2×C311yescharacteristic, complemented
12C7×D7×C13⋊C3—31no—
13C7×D7×C13⋊C3—31no—
14C13×D72—31noHall
15C13⋊#3862—21no—
16C13×#3862C22×C311yescharacteristic, complemented
17C72×C13⋊C3C2×D311yescharacteristic, complemented
18C3×#64418⋊C2—131nomaximal, Hall
19C13⋊C3×AGL(1,𝔽7)—141no—
20C13×C7⋊D7C3×D311yescharacteristic, complemented
21C7×C13×D7—31no—
22C7×C13×D7—31no—
23C2×D7×C13⋊C3—211no—
24C2×D7×C13⋊C3—211no—
25C3×#64425—131no—
26C3×#64418—131no—
27C3×#64418—131no—
28ΓL(1,𝔽8)×C13⋊C3—281no—
29C72×C13C2×C3×D311yescharacteristic, complemented, Hall
30C3×D72—391no—
31#64418⋊C2C13⋊C311yescharacteristic, direct product factor
32C2×C7×C13⋊C3—211no—
33C2×C7×C13⋊C3—211no—
34#10587721—141no—
35#10587720—141no—
36C13×AGL(1,𝔽7)—141no—
37D7×C13⋊C3—31no—
38D7×C13⋊C3—31no—
39D7×C13⋊C3—141no—
40D7×C13⋊C3—211no—
41D7×C13⋊C3—421no—
42C2×D3×C13⋊C3—491nomaximal, Hall
43C3×#3862—131noHall
44C2×C13×D7—211no—
45C2×C13×D7—211no—
46C3×C7⋊D7—131no—
47C3×C7×D7—391no—
48C3×C7×D7—391no—
49#64425—261no—
50#64425C2×C13⋊C311yescharacteristic, complemented
51#64418C2×C13⋊C311yescharacteristic, complemented
52#64418C2×C13⋊C311yescharacteristic, complemented
53#63271—281no—
54#63270—281no—
55C7×C13⋊C3—21no—
56C7×C13⋊C3—31no—
57C7×C13⋊C3—61no—
58C13×ΓL(1,𝔽8)—281no—
59C2×C3×C13⋊C3—491no—
60D3×C13⋊C3—981no—
61D3×C13⋊C3—981no—
62D72—31noHall
63C2×C7×C13—211no—
64C2×C7×C13—211no—
65C13×D7—31no—
66C13×D7—31no—
67C13×D7—141no—
68C13×D7—421no—
69C13×D7—421no—
70C2×D3×C13—491no—
71C22×C13⋊C3—1471no—
72C3×C72—131no—
73#3862—261no—
74#3862C22×C13⋊C311yescharacteristic, complemented
75C3×AGL(1,𝔽7)—1821no—
76C3×C13⋊C3—1961noHall
77C7⋊D7D3×C13⋊C311yescharacteristic, complemented
78C7×D7—31no—
79C7×D7—31no—
80C7×C13—21no—
81C7×C13—61no—
82C7×C13—61no—
83C2×C3×D7—2731no—
84C2×C3×D7—2731no—
85C2×C3×C13—491no—
86D3×C13—981no—
87D3×C13—981no—
88C2×C13⋊C3—211no—
89C2×C13⋊C3—211no—
90C2×C13⋊C3—491no—
91C2×C13⋊C3—981no—
92C3×ΓL(1,𝔽8)—3641no—
93C22×C13—1471noHall
94C72C2×D3×C13⋊C311yescharacteristic, complemented, Sylow
95C2×C3×C7—2731no—
96C2×C3×C7—2731no—
97C3×D7—5461no—
98C3×D7—5461no—
99C3×D7—391no—
100C3×D7—391no—
101C3×D7—1821no—
102AGL(1,𝔽7)—141no—
103AGL(1,𝔽7)—1821no—
104AGL(1,𝔽7)—1821no—
105C3×C13—1961no—
106C13⋊C3—1961no—
107C13⋊C3#64418⋊C211yescharacteristic, direct product factor
108C2×C3×D3—6371noHall
109C2×D7—211no—
110C2×D7—211no—
111C2×C13—211no—
112C2×C13—211no—
113C2×C13—491no—
114C3×C7—261no—
115C3×C7—781no—
116C3×C7—781no—
117ΓL(1,𝔽8)—281no—
118ΓL(1,𝔽8)—3641no—
119ΓL(1,𝔽8)—3641no—
120C2×C32—6371no—
121C3×D3—6371no—
122C3×D3—12741no—
123C2×C7—211no—
124C2×C7—211no—
125D7—31no—
126D7—31no—
127D7—141no—
128D7—421no—
129D7—421no—
130C13C3×#64418⋊C211yescharacteristic, complemented, Sylow
131C22×C3—19111no—
132C2×D3—491no—
133C32—25481noSylow
134C7—21no—
135C7—61no—
136C7—61no—
137C2×C3—2731no—
138C2×C3—2731no—
139C2×C3—491no—
140C2×C3—6371no—
141C2×C3—12741no—
142D3—981no—
143D3—981no—
144C22—1471noSylow
145C3—131no—
146C3—1961no—
147C3—25481no—
148C2—211no—
149C2—211no—
150C2—491no—
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. C13⋊C3×#64418C2semidirect
2. C13⋊C3×#64418C2semidirect
3. C13⋊C3×#64425C2semidirect
4. C13×#64418⋊C2C3semidirect
6. C13⋊C3×#3862C22semidirect
7. C13×#64418C2×C3semidirect
8. C13×#64418C2×C3semidirect
9. C13⋊C3×C7⋊D7D3semidirect
11. C13×#64425C2×C3semidirect
16. C13×#3862C22×C3semidirect
17. C72×C13⋊C3C2×D3semidirect
20. C13×C7⋊D7C3×D3semidirect
29. C72×C13C2×C3×D3semidirect
31. #64418⋊C2C13⋊C3direct (N × H)
50. #64425C2×C13⋊C3semidirect
51. #64418C2×C13⋊C3semidirect
52. #64418C2×C13⋊C3semidirect
74. #3862C22×C13⋊C3semidirect
77. C7⋊D7D3×C13⋊C3semidirect
94. C72C2×D3×C13⋊C3semidirect
107. C13⋊C3#64418⋊C2direct (N × H)
130. C13C3×#64418⋊C2semidirect

Maximal subgroups

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

subgroupindex
C13⋊C3×#644182
C13⋊C3×#644252
C13×#64418⋊C23
D72×C13⋊C33
C3×#64418⋊C213
C2×D3×C13⋊C349