Finite Group Databasebeta

← C2×C11×C5⋊#64422 #44568795

Subgroups — C2×C11×C5⋊#64422 #44568795

Order 32340.

168 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 58 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×C5×C11×#3862C211yesmaximal, characteristic, complemented
2C11×C5⋊#64422C212yesmaximal, direct product factor
3C2×C7×C11×D35C311yesmaximal, characteristic, complemented, Hall
4C5×C11×#3862C2211yescharacteristic, complemented, Hall
5C2×C11×#64422—51nomaximal, Hall
6C7×C11×D35C2×C312yescomplemented
7C2×C5×C72×C11C2×C311yescharacteristic, complemented
8C2×D5×C11×ΓL(1,𝔽8)—71nomaximal
9C2×C11×C5⋊AGL(1,𝔽7)—71nomaximal
10C2×C11×#3862D511yescharacteristic, complemented
11C11×#64422—52no—
12C2×C5⋊#64422C1111yesmaximal, characteristic, direct product factor, Hall
13C5×C72×C11C22×C311yescharacteristic, complemented, Hall
14C11×C5⋊AGL(1,𝔽7)—72no—
15D5×C11×ΓL(1,𝔽8)—72no—
16C2×C5×C11×ΓL(1,𝔽8)—71no—
17C2×C5×C11×ΓL(1,𝔽8)—71no—
18C2×C7×C11×D7—51noHall
19C11×#3862C2×D511yescharacteristic, complemented, Hall
20C2×C11×D35ΓL(1,𝔽8)11yescharacteristic, complemented
21C2×C7×D5×C11—71no—
22C2×C5×#3862C2×C1111yescharacteristic, complemented
23C5⋊#64422C2×C1112yesdirect product factor
24C5×C11×ΓL(1,𝔽8)—71no—
25C5×C11×ΓL(1,𝔽8)—71no—
26C2×C72×C11C3×D511yescharacteristic, complemented
27C7×C11×D7—52no—
28C2×C7×D35C3×C1111yescharacteristic, complemented, Hall
29C22×C11×ΓL(1,𝔽8)—351no—
30C2×C11×AGL(1,𝔽7)—351no—
31C2×C5×C7×C11—61no—
32C2×C5×C7×C11AGL(1,𝔽7)11yescharacteristic, complemented
33C2×C5×C7×C11C2×ΓL(1,𝔽8)11yescharacteristic, complemented
34C11×D35C2×ΓL(1,𝔽8)12yescomplemented
35C7×D5×C11—72no—
36C5×#3862C22×C1111yescharacteristic, complemented, Hall
37C2×C3×D5×C11—491noHall
38C2×#64422—51noHall
39C72×C11C2×C3×D511yescharacteristic, complemented, Hall
40C2×C5×C72C2×C3×C1111yescharacteristic, complemented
41C7×D35C2×C3×C1112yescomplemented
42C2×C11×ΓL(1,𝔽8)—71no—
43C2×C11×ΓL(1,𝔽8)—71no—
44C2×C11×ΓL(1,𝔽8)—352no—
45C11×AGL(1,𝔽7)—352no—
46C2×C5⋊AGL(1,𝔽7)—71no—
47C2×D5×ΓL(1,𝔽8)—71no—
48C5×C7×C11—61no—
49C5×C7×C11C2×AGL(1,𝔽7)11yescharacteristic, complemented
50C5×C7×C11C22×ΓL(1,𝔽8)11yescharacteristic, complemented
51C2×C3×C5×C11—491no—
52C3×D5×C11—492no—
53C22×C7×C11—351no—
54C2×C11×D7—51no—
55C2×#3862D5×C1111yescharacteristic, complemented
56#64422—52no—
57C5×C72C22×C3×C1111yescharacteristic, complemented, Hall
58C11×ΓL(1,𝔽8)—71no—
59C11×ΓL(1,𝔽8)—71no—
60C2×D5×C11—71noHall
61C2×C5×ΓL(1,𝔽8)—71no—
62C2×C5×ΓL(1,𝔽8)—71no—
63C5⋊AGL(1,𝔽7)—72no—
64D5×ΓL(1,𝔽8)—72no—
65C2×C7×D7—51noHall
66C3×C5×C11—491noHall
67C2×C7×C11—61no—
68C2×C7×C11—352no—
69C2×C7×C11D5×ΓL(1,𝔽8)11yescharacteristic, complemented
70C2×C7×C11C5⋊AGL(1,𝔽7)11yescharacteristic, complemented
71C11×D7—52no—
72#3862C2×D5×C1111yescharacteristic, complemented, Hall
73C2×D35C11×ΓL(1,𝔽8)11yescharacteristic, complemented
74C2×C7×D5—71no—
75C22×C3×C11—2451noHall
76C2×C5×C11#6442211yescharacteristic, complemented
77D5×C11—72no—
78C5×ΓL(1,𝔽8)—71no—
79C5×ΓL(1,𝔽8)—71no—
80C2×C72C3×D5×C1111yescharacteristic, complemented
81C7×D7—52no—
82C22×ΓL(1,𝔽8)—351no—
83C2×AGL(1,𝔽7)—351no—
84C7×C11—61no—
85C7×C11C2×D5×ΓL(1,𝔽8)11yescharacteristic, complemented
86C7×C11C2×C5⋊AGL(1,𝔽7)11yescharacteristic, complemented
87C2×C5×C7—61no—
88C2×C5×C7C11×AGL(1,𝔽7)11yescharacteristic, complemented
89C2×C5×C7C2×C11×ΓL(1,𝔽8)11yescharacteristic, complemented
90D35C2×C11×ΓL(1,𝔽8)12yescomplemented
91C7×D5—72no—
92C2×C3×C11—491no—
93C2×C3×C11—2452no—
94C2×C3×D5—491noHall
95C5×C11C2×#6442211yescharacteristic, complemented, Hall
96C72C2×C3×D5×C1111yescharacteristic, complemented, Sylow
97C22×C11—351noHall
98C2×ΓL(1,𝔽8)—71no—
99C2×ΓL(1,𝔽8)—71no—
100C2×ΓL(1,𝔽8)—352no—
101AGL(1,𝔽7)—352no—
102C5×C7—61no—
103C5×C7C2×C11×AGL(1,𝔽7)11yescharacteristic, complemented
104C5×C7C22×C11×ΓL(1,𝔽8)11yescharacteristic, complemented
105C3×C11—491noHall
106C2×C3×C5—491no—
107C3×D5—492no—
108C22×C7—351no—
109C2×D7—51no—
110C2×C11—352no—
111C2×C11C5⋊#6442211yescharacteristic, direct product factor
112ΓL(1,𝔽8)—71no—
113ΓL(1,𝔽8)—71no—
114C2×D5—71noHall
115C3×C5—491noHall
116C2×C7—61no—
117C2×C7—352no—
118C2×C7D5×C11×ΓL(1,𝔽8)11yescharacteristic, complemented
119C2×C7C11×C5⋊AGL(1,𝔽7)11yescharacteristic, complemented
120D7—52no—
121C22×C3—2451noHall
122C11C2×C5⋊#6442211yescharacteristic, direct product factor, Sylow
123C2×C5C11×#6442211yescharacteristic, complemented
124D5—72no—
125C7—61no—
126C7C2×C11×C5⋊AGL(1,𝔽7)11yescharacteristic, complemented
127C7C2×D5×C11×ΓL(1,𝔽8)11yescharacteristic, complemented
128C2×C3—491no—
129C2×C3—2452no—
130C5C2×C11×#6442211yescharacteristic, complemented, Sylow
131C22—351noSylow
132C3—491noSylow
133C2—352no—
134C2C11×C5⋊#6442211yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C11C5⋊#64422
commutator, cosocle, hypocenterC5×C72C22×C3×C11
FrattiniC1G
Fitting, socleC2×C5×C72×C11C2×C3
LCSG ▷ C5×C72
UCSC1 ◁ C2×C11

Complements

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

NH ≅ G/Ntype
1. C2×C5×C11×#3862C2semidirect
2. C11×C5⋊#64422C2direct (N × H)
3. C2×C7×C11×D35C3semidirect
4. C5×C11×#3862C22semidirect
6. C7×C11×D35C2×C3semidirect
7. C2×C5×C72×C11C2×C3semidirect
10. C2×C11×#3862D5semidirect
12. C2×C5⋊#64422C11direct (N × H)
13. C5×C72×C11C22×C3semidirect
19. C11×#3862C2×D5semidirect
20. C2×C11×D35ΓL(1,𝔽8)semidirect
22. C2×C5×#3862C2×C11semidirect
23. C5⋊#64422C2×C11direct (N × H)
26. C2×C72×C11C3×D5semidirect
28. C2×C7×D35C3×C11semidirect
32. C2×C5×C7×C11AGL(1,𝔽7)semidirect
33. C2×C5×C7×C11C2×ΓL(1,𝔽8)semidirect
34. C11×D35C2×ΓL(1,𝔽8)semidirect
36. C5×#3862C22×C11semidirect
39. C72×C11C2×C3×D5semidirect
40. C2×C5×C72C2×C3×C11semidirect
41. C7×D35C2×C3×C11semidirect
49. C5×C7×C11C2×AGL(1,𝔽7)semidirect
50. C5×C7×C11C22×ΓL(1,𝔽8)semidirect
55. C2×#3862D5×C11semidirect
57. C5×C72C22×C3×C11semidirect
69. C2×C7×C11D5×ΓL(1,𝔽8)semidirect
70. C2×C7×C11C5⋊AGL(1,𝔽7)semidirect
72. #3862C2×D5×C11semidirect
73. C2×D35C11×ΓL(1,𝔽8)semidirect
76. C2×C5×C11#64422semidirect
80. C2×C72C3×D5×C11semidirect
85. C7×C11C2×D5×ΓL(1,𝔽8)semidirect
86. C7×C11C2×C5⋊AGL(1,𝔽7)semidirect
88. C2×C5×C7C11×AGL(1,𝔽7)semidirect
89. C2×C5×C7C2×C11×ΓL(1,𝔽8)semidirect
90. D35C2×C11×ΓL(1,𝔽8)semidirect
95. C5×C11C2×#64422semidirect
96. C72C2×C3×D5×C11semidirect
103. C5×C7C2×C11×AGL(1,𝔽7)semidirect
104. C5×C7C22×C11×ΓL(1,𝔽8)semidirect
111. C2×C11C5⋊#64422direct (N × H)
118. C2×C7D5×C11×ΓL(1,𝔽8)semidirect
119. C2×C7C11×C5⋊AGL(1,𝔽7)semidirect
122. C11C2×C5⋊#64422direct (N × H)
123. C2×C5C11×#64422semidirect
126. C7C2×C11×C5⋊AGL(1,𝔽7)semidirect
127. C7C2×D5×C11×ΓL(1,𝔽8)semidirect
130. C5C2×C11×#64422semidirect
134. C2C11×C5⋊#64422direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×C11×#38622
C11×C5⋊#644222
C2×C7×C11×D353
C2×C11×#644225
C2×D5×C11×ΓL(1,𝔽8)7
C2×C11×C5⋊AGL(1,𝔽7)7
C2×C5⋊#6442211