Finite Group Databasebeta

← C2×H(5,𝔽2)×D139 #31821204

Subgroups — C2×H(5,𝔽2)×D139 #31821204

Order 17792.

6560 conjugacy classes of subgroups; only the 3213 normal subgroups are shown.

normal subgroups only

This group has 6560 conjugacy classes of subgroups — too many to draw. Only its 3213 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×#17984888C216yesmaximal, complemented
2C2×#17984887C219yesmaximal, complemented
3H(5,𝔽2)×D139C2132yesmaximal, direct product factor
4C2×#41×D139C216yesmaximal, complemented
5C22×D4×D139C219yesmaximal, complemented
6C2×H(5,𝔽2)×C139C211yesmaximal, characteristic, complemented
7C24×D139C2216yescomplemented
8#17984888C22196yescomplemented
9#17984887C221144yescomplemented
10C2×#14555786C2216yescomplemented
11C2×#14555785C22118yescomplemented
12C2×#14555784C22118yescomplemented
13#41×D139C22196yescomplemented
14C2×Q8×D139C2212yescomplemented
15C22×D556C2219yescomplemented
16C22×C22⋊D139C22118yescomplemented
17C2×D4×D139C22118yescomplemented
18C2×D4×D139C221144yescomplemented
19C2×D4×D139C22136yescomplemented
20C22×C4×D139C2219yescomplemented
21H(5,𝔽2)×C139C22116yescomplemented
22C2×#41×C139C2216yescomplemented
23C22×D4×C139C2219yescomplemented
24C23×D139—424no—
25C23×D139C2319yes—
26C23×D139C23118yescomplemented
27C23×D139C23148yescomplemented
28#14555786C23148yescomplemented
29#14555785C231144yescomplemented
30#14555784C231144yescomplemented
31C2×Dic278C2316yescomplemented
32Q8×D139C23116yescomplemented
33C2×D556C23118yescomplemented
34C2×D556C23172yescomplemented
35C2×C22⋊D139C23136yescomplemented
36C2×C22⋊D139C231144yescomplemented
37D4×D139C231144yescomplemented
38D4×D139C231288yescomplemented
39C22×Dic139C2319yescomplemented
40C2×C4×D139C2316yes—
41C2×C4×D139C23118yescomplemented
42C2×C4×D139C23172yescomplemented
43C24×C139C2316yescomplemented
44#41×C139C23148yescomplemented
45C2×Q8×C139C2312yescomplemented
46C2×D4×C139C23118yescomplemented
47C2×D4×C139C23172yescomplemented
48C22×C4×C139C2319yescomplemented
49C22×D139—236no—
50C22×D139—496no—
51C22×D139—436no—
52C22×D139C24136yes—
53C22×D139C2419yes—
54C22×D139C2411yescharacteristic
55C22×D139C24172yescomplemented
56Dic278C24124yescomplemented
57D556C24172yescomplemented
58C22⋊D139C241144yescomplemented
59C2×Dic139C2416yes—
60C2×Dic139C24136yescomplemented
61C4×D139C24124yes—
62C4×D139C24172yescomplemented
63C23×C139—412no—
64C23×C139C2419yes—
65C23×C139C24124yescomplemented
66Q8×C139C2418yescomplemented
67D4×C139C24172yescomplemented
68C2×C4×C139C2416yes—
69C2×C4×C139C24136yescomplemented
70C22×C139—218no—
71C22×C139—424no—
72C22×C139C25118yes—
73C22×C139C2511yescharacteristic
74C2×D139—218no—
75C2×D139—272no—
76C2×D139—472no—
77C2×D139H(5,𝔽2)14yesdirect product factor
78C2×D139C25118yes—
79C2×D139C2512yes—
80C4×C139C25112yes—
81Dic139C25112yes—
82C2×C139—218no—
83C2×C139C2×H(5,𝔽2)12yescomplemented
84C2×C139C2611yescharacteristic
85D139—218no—
86D139C2×H(5,𝔽2)14yesdirect product factor
87C139C22×H(5,𝔽2)11yescharacteristic, complemented, Sylow
88C22×H(5,𝔽2)—1391nomaximal, Sylow
89C2×H(5,𝔽2)—13932no—
90C2×H(5,𝔽2)—1396no—
91C2×H(5,𝔽2)—1399no—
92C2×H(5,𝔽2)D13911yescharacteristic, direct product factor
93C22×#41—1396no—
94C23×D4—1399no—
95C25—1396no—
96H(5,𝔽2)—13996no—
97H(5,𝔽2)—139144no—
98H(5,𝔽2)C2×D139116yesdirect product factor
99C2×#41—13996no—
100C2×#41—1396no—
101C2×#41—13918no—
102C2×#41—13918no—
103C2×#41C2×D13916yescomplemented
104C22×Q8—1392no—
105C22×D4—13918no—
106C22×D4—13918no—
107C22×D4—13936no—
108C22×D4—139144no—
109C22×D4—1399no—
110C22×D4C2×D13919yescomplemented
111C23×C4—1399no—
112C24—55624no—
113C24—1399no—
114C24—13918no—
115C24—13948no—
116C24C22×D13916yescomplemented
117#41—13948no—
118#41—139144no—
119#41—139144no—
120#41C22×D139148yescomplemented
121C2×Q8—13916no—
122C2×Q8—1396no—
123C2×Q8C22×D13912yescomplemented
124C2×D4—13936no—
125C2×D4—139144no—
126C2×D4—139144no—
127C2×D4—139288no—
128C2×D4—13918no—
129C2×D4—13972no—
130C2×D4C22×D139118yescomplemented
131C2×D4C22×D139172yescomplemented
132C22×C4—1399no—
133C22×C4—1396no—
134C22×C4—13918no—
135C22×C4—13972no—
136C22×C4C22×D13919yescomplemented
137C23—412no—
138C23—27836no—
139C23—55636no—
140C23—55696no—
141C23—13936no—
142C23—1399no—
143C23—13972no—
144C23—1391no—
145C23C23×D13919yes—
146C23C23×D139124yescomplemented
147Q8—13924no—
148Q8C23×D13918yescomplemented
149D4—139144no—
150D4—13972no—
151D4C23×D139172yescomplemented
152C2×C4—13936no—
153C2×C4—1396no—
154C2×C4—13924no—
155C2×C4—13972no—
156C2×C4C23×D13916yes—
157C2×C4C23×D139136yescomplemented
158C22—218no—
159C22—424no—
160C22—27872no—
161C22—27818no—
162C22—55672no—
163C22—13918no—
164C22—1394no—
165C22—1392no—
166C22C24×D139118yes—
167C22C24×D13911yescharacteristic
168C4—13912no—
169C4C24×D139112yes—
170C2—218no—
171C2—27818no—
172C2—1394no—
173C2H(5,𝔽2)×D13912yesdirect product factor
174C2C25×D13911yescharacteristic
subgroupG/H
centerC22C24×D139
commutator, cosocleC2×C139C26
FrattiniC2C25×D139
FittingC2×H(5,𝔽2)×C139C2
socleC22×C139C25
hypercenterC2×H(5,𝔽2)D139
hypocenterC139C22×H(5,𝔽2)
LCSG ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C2×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. C2×#17984888C2semidirect
2. C2×#17984887C2semidirect
3. H(5,𝔽2)×D139C2direct (N × H)
4. C2×#41×D139C2semidirect
5. C22×D4×D139C2semidirect
6. C2×H(5,𝔽2)×C139C2semidirect
7. C24×D139C22semidirect
8. #17984888C22semidirect
9. #17984887C22semidirect
10. C2×#14555786C22semidirect
11. C2×#14555785C22semidirect
12. C2×#14555784C22semidirect
13. #41×D139C22semidirect
14. C2×Q8×D139C22semidirect
15. C22×D556C22semidirect
16. C22×C22⋊D139C22semidirect
17. C2×D4×D139C22semidirect
18. C2×D4×D139C22semidirect
19. C2×D4×D139C22semidirect
20. C22×C4×D139C22semidirect
21. H(5,𝔽2)×C139C22semidirect
22. C2×#41×C139C22semidirect
23. C22×D4×C139C22semidirect
26. C23×D139C23semidirect
27. C23×D139C23semidirect
28. #14555786C23semidirect
29. #14555785C23semidirect
30. #14555784C23semidirect
31. C2×Dic278C23semidirect
32. Q8×D139C23semidirect
33. C2×D556C23semidirect
34. C2×D556C23semidirect
35. C2×C22⋊D139C23semidirect
36. C2×C22⋊D139C23semidirect
37. D4×D139C23semidirect
38. D4×D139C23semidirect
39. C22×Dic139C23semidirect
41. C2×C4×D139C23semidirect
42. C2×C4×D139C23semidirect
43. C24×C139C23semidirect
44. #41×C139C23semidirect
45. C2×Q8×C139C23semidirect
46. C2×D4×C139C23semidirect
47. C2×D4×C139C23semidirect
48. C22×C4×C139C23semidirect
55. C22×D139C24semidirect
56. Dic278C24semidirect
57. D556C24semidirect
58. C22⋊D139C24semidirect
60. C2×Dic139C24semidirect
62. C4×D139C24semidirect
65. C23×C139C24semidirect
66. Q8×C139C24semidirect
67. D4×C139C24semidirect
69. C2×C4×C139C24semidirect
77. C2×D139H(5,𝔽2)direct (N × H)
83. C2×C139C2×H(5,𝔽2)semidirect
86. D139C2×H(5,𝔽2)direct (N × H)
87. C139C22×H(5,𝔽2)semidirect
92. C2×H(5,𝔽2)D139direct (N × H)
98. H(5,𝔽2)C2×D139direct (N × H)
103. C2×#41C2×D139semidirect
110. C22×D4C2×D139semidirect
116. C24C22×D139semidirect
120. #41C22×D139semidirect
123. C2×Q8C22×D139semidirect
130. C2×D4C22×D139semidirect
131. C2×D4C22×D139semidirect
136. C22×C4C22×D139semidirect
146. C23C23×D139semidirect
148. Q8C23×D139semidirect
151. D4C23×D139semidirect
157. C2×C4C23×D139semidirect
173. C2H(5,𝔽2)×D139direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179848882
C2×#179848872
H(5,𝔽2)×D1392
C2×#41×D1392
C22×D4×D1392
C2×H(5,𝔽2)×C1392
C22×H(5,𝔽2)139