Finite Group Databasebeta

← C2×#30660667 #45692155

Subgroups — C2×#30660667 #45692155

Order 33516.

280 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 56 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×#22552728C211yesmaximal, characteristic, complemented
2#30660667C212yesmaximal, direct product factor
3C2×#19150309C312yesmaximal, complemented
4C2×C19×#64425C311yesmaximal, characteristic, complemented
5C2×#19150286C311yesmaximal, characteristic, complemented
6#22552728C2211yescharacteristic, complemented, Hall
7C2×C19×#3862C2×C311yescharacteristic, complemented
8C2×#14584115C2×C311yescharacteristic, complemented
9C2×C7×#87705C2×C312yescomplemented
10#19150309C2×C314yescomplemented
11C19×#64425C2×C312yescomplemented
12#19150286C2×C312yescomplemented
13C2×AGL(1,𝔽7)×C19⋊C3—72nomaximal
14C2×C19×C7⋊D7C3211yescharacteristic, complemented, Hall
15C19×#3862C22×C311yescharacteristic, complemented
16#14584115C22×C311yescharacteristic, complemented
17C7×#87705C22×C312yescomplemented
18C2×ΓL(1,𝔽8)×C19⋊C3—72no—
19AGL(1,𝔽7)×C19⋊C3—74no—
20C2×C72×C19C2×C3211yescharacteristic, complemented
21C19×C7⋊D7C2×C3212yescomplemented
22C2×ΓL(1,𝔽8)⋊AGL(1,𝔽7)—191nomaximal, Hall
23C2×#11716326—72no—
24C2×#11716325—72no—
25C2×#11716325—212no—
26C2×C19×AGL(1,𝔽7)—72no—
27C2×D7×C19⋊C3—72no—
28ΓL(1,𝔽8)×C19⋊C3—72no—
29C72×C19C22×C3211yescharacteristic, complemented, Hall
30C2×ΓL(1,𝔽8)2—191no—
31ΓL(1,𝔽8)⋊AGL(1,𝔽7)—192no—
32C2×#87705AGL(1,𝔽7)12yescomplemented
33C2×#87704—72no—
34C2×#87704—212no—
35C2×C19×ΓL(1,𝔽8)—72no—
36C2×C7×C19⋊C3—72no—
37#11716326—74no—
38#11716325—74no—
39#11716325—214no—
40C19×AGL(1,𝔽7)—74no—
41D7×C19⋊C3—74no—
42C22×C3×C19⋊C3—491noHall
43C2×#64425C19⋊C311yescharacteristic, complemented
44C2×#64424—191no—
45C2×ΓL(1,𝔽8)⋊D7—192no—
46C2×D7×C19—72no—
47C2×D7×C19—212no—
48ΓL(1,𝔽8)2—191noHall
49#87705C2×AGL(1,𝔽7)12yescomplemented
50#87704—72no—
51#87704—212no—
52C7×C19⋊C3—72no—
53C19×ΓL(1,𝔽8)—72no—
54C2×C3×C19⋊C3—491no—
55C2×C3×C19⋊C3—492no—
56C2×#3862C2×C19⋊C311yescharacteristic, complemented
57C2×#3861—191no—
58C2×C7×ΓL(1,𝔽8)—192no—
59#64425C2×C19⋊C312yescomplemented
60#64424—192no—
61ΓL(1,𝔽8)⋊D7—194no—
62C2×C7×C19—32no—
63C2×C7×C19C3×AGL(1,𝔽7)12yescomplemented
64D7×C19—74no—
65D7×C19—214no—
66C2×C3×AGL(1,𝔽7)—1332no—
67C22×C3×C19—491no—
68C22×C19⋊C3—492no—
69C22×C19⋊C3—491no—
70C2×C7⋊D7C3×C19⋊C311yescharacteristic, complemented, Hall
71C3×C19⋊C3—491noHall
72#3862C22×C19⋊C311yescharacteristic, complemented
73#3861—191no—
74C7×ΓL(1,𝔽8)—192no—
75C7×C19—32no—
76C7×C19C2×C3×AGL(1,𝔽7)12yescomplemented
77C2×C3×ΓL(1,𝔽8)—1332no—
78C3×AGL(1,𝔽7)—1334no—
79C2×C3×C19—492no—
80C2×C3×C19—491no—
81C2×C19⋊C3—72no—
82C2×C19⋊C3—494no—
83C2×C19⋊C3—492no—
84C2×C19⋊C3—491no—
85C2×C72C2×C3×C19⋊C311yescharacteristic, complemented
86C7⋊D7C2×C3×C19⋊C312yescomplemented
87C2×C3×D7—1332no—
88C2×AGL(1,𝔽7)—72no—
89C2×AGL(1,𝔽7)—1332no—
90C2×AGL(1,𝔽7)—1332no—
91C2×AGL(1,𝔽7)—3992no—
92C22×C19—491noHall
93C3×ΓL(1,𝔽8)—1332no—
94C3×C19—491no—
95C19⋊C3—72no—
96C19⋊C3—491no—
97C72C22×C3×C19⋊C311yescharacteristic, complemented, Sylow
98C2×C3×C7—1332no—
99C3×D7—1334no—
100C2×ΓL(1,𝔽8)—72no—
101C2×ΓL(1,𝔽8)—192no—
102C2×ΓL(1,𝔽8)—1332no—
103C2×ΓL(1,𝔽8)—3992no—
104AGL(1,𝔽7)—74no—
105AGL(1,𝔽7)—1334no—
106AGL(1,𝔽7)—1334no—
107AGL(1,𝔽7)—3994no—
108C2×C19—492no—
109C2×C19ΓL(1,𝔽8)⋊AGL(1,𝔽7)11yescharacteristic, complemented
110C22×C32—9311noHall
111C2×D7—72no—
112C2×D7—212no—
113C3×C7—1332no—
114ΓL(1,𝔽8)—72no—
115ΓL(1,𝔽8)—192no—
116ΓL(1,𝔽8)—1332no—
117ΓL(1,𝔽8)—3992no—
118C19C2×ΓL(1,𝔽8)⋊AGL(1,𝔽7)11yescharacteristic, complemented, Sylow
119C2×C32—9311no—
120C2×C32—9312no—
121C2×C7—32no—
122C2×C7AGL(1,𝔽7)×C19⋊C312yescomplemented
123D7—74no—
124D7—214no—
125C22×C3—491no—
126C22×C3—9312no—
127C22×C3—9311no—
128C32—9311noSylow
129C7—32no—
130C7C2×AGL(1,𝔽7)×C19⋊C312yescomplemented
131C2×C3—492no—
132C2×C3—491no—
133C2×C3—1332no—
134C2×C3—9314no—
135C2×C3—9312no—
136C2×C3—9311no—
137C22—491noSylow
138C3—491no—
139C3—1332no—
140C3—9311no—
141C2—492no—
142C2#3066066711yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2#30660667
commutator, cosocle, hypocenterC72×C19C22×C32
FrattiniC1G
Fitting, socleC2×C72×C19C2×C32
LCSG ▷ C72×C19
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×#22552728C2semidirect
2. #30660667C2direct (N × H)
3. C2×#19150309C3semidirect
4. C2×C19×#64425C3semidirect
5. C2×#19150286C3semidirect
6. #22552728C22semidirect
7. C2×C19×#3862C2×C3semidirect
8. C2×#14584115C2×C3semidirect
9. C2×C7×#87705C2×C3semidirect
10. #19150309C2×C3semidirect
11. C19×#64425C2×C3semidirect
12. #19150286C2×C3semidirect
14. C2×C19×C7⋊D7C32semidirect
15. C19×#3862C22×C3semidirect
16. #14584115C22×C3semidirect
17. C7×#87705C22×C3semidirect
20. C2×C72×C19C2×C32semidirect
21. C19×C7⋊D7C2×C32semidirect
29. C72×C19C22×C32semidirect
32. C2×#87705AGL(1,𝔽7)semidirect
43. C2×#64425C19⋊C3semidirect
49. #87705C2×AGL(1,𝔽7)semidirect
56. C2×#3862C2×C19⋊C3semidirect
59. #64425C2×C19⋊C3semidirect
63. C2×C7×C19C3×AGL(1,𝔽7)semidirect
70. C2×C7⋊D7C3×C19⋊C3semidirect
72. #3862C22×C19⋊C3semidirect
76. C7×C19C2×C3×AGL(1,𝔽7)semidirect
85. C2×C72C2×C3×C19⋊C3semidirect
86. C7⋊D7C2×C3×C19⋊C3semidirect
97. C72C22×C3×C19⋊C3semidirect
109. C2×C19ΓL(1,𝔽8)⋊AGL(1,𝔽7)semidirect
118. C19C2×ΓL(1,𝔽8)⋊AGL(1,𝔽7)semidirect
122. C2×C7AGL(1,𝔽7)×C19⋊C3semidirect
130. C7C2×AGL(1,𝔽7)×C19⋊C3semidirect
142. C2#30660667direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#225527282
#306606672
C2×#191503093
C2×C19×#644253
C2×#191502863
C2×AGL(1,𝔽7)×C19⋊C37
C2×ΓL(1,𝔽8)⋊AGL(1,𝔽7)19