Finite Group Databasebeta

← C2×#22581788 #31821211

Subgroups — C2×#22581788 #31821211

Order 17792.

5956 conjugacy classes of subgroups; only the 3205 normal subgroups are shown.

normal subgroups only

This group has 5956 conjugacy classes of subgroups — too many to draw. Only its 3205 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
1#22581788C2132yesmaximal, direct product factor
2C2×#17984889C216yesmaximal, complemented
3C2×#17984887C219yesmaximal, complemented
4C22×#14555784C219yesmaximal, complemented
5C2×#41×D139C216yesmaximal, complemented
6C2×H(5,𝔽2)×C139C211yesmaximal, characteristic, complemented
7#17984889C22196yescomplemented
8#17984887C221144yescomplemented
9C2×#14555786C2212yescomplemented
10C2×#14555785C22118yescomplemented
11C2×#14555784C22118yescomplemented
12C2×#14555784C22136yescomplemented
13C2×#14555784C221144yescomplemented
14#41×D139C22196yescomplemented
15C22×Dic278C2219yescomplemented
16C2×Q8×D139C2216yescomplemented
17C22×C22⋊D139C22118yescomplemented
18C2×D4×D139C22118yescomplemented
19C23×Dic139C2216yescomplemented
20C22×C4×D139C2219yescomplemented
21H(5,𝔽2)×C139C22116yescomplemented
22C2×#41×C139C2216yescomplemented
23C22×D4×C139C2219yescomplemented
24C23×D139C2319yes—
25#14555786C23116yescomplemented
26#14555785C231144yescomplemented
27#14555784C231144yescomplemented
28#14555784C231288yescomplemented
29C2×Dic278C23118yes—
30C2×Dic278C23172yescomplemented
31Q8×D139C23148yescomplemented
32C2×D556C2316yes—
33C2×C22⋊D139C23136yes—
34C2×C22⋊D139C231144yescomplemented
35D4×D139C231144yescomplemented
36C22×Dic139C2319yes—
37C22×Dic139C23118yes—
38C22×Dic139C23148yescomplemented
39C2×C4×D139C2316yes—
40C2×C4×D139C23118yes—
41C2×C4×D139C23172yescomplemented
42C24×C139C2316yes—
43#41×C139C23148yescomplemented
44C2×Q8×C139C2312yes—
45C2×D4×C139C23118yes—
46C2×D4×C139C23172yescomplemented
47C22×C4×C139C2319yes—
48C22×D139—418no—
49C22×D139C2416yes—
50C22×D139C24136yes—
51Dic278C24172yes—
52D556C24124yes—
53C22⋊D139C241144yes—
54C2×Dic139C2411yescharacteristic
55C2×Dic139C2419yes—
56C2×Dic139C24136yes—
57C2×Dic139C24172yes—
58C4×D139C24124yes—
59C4×D139C24172yes—
60C23×C139—412no—
61C23×C139C2419yes—
62C23×C139C24124yes—
63Q8×C139C2418yes—
64D4×C139C24172yes—
65C2×C4×C139C2416yes—
66C2×C4×C139C24136yes—
67C22×C139—218no—
68C22×C139—424no—
69C22×C139C25118yes—
70C22×C139C2511yescharacteristic
71C2×D139—212no—
72C2×D139—436no—
73C2×D139C25112yes—
74C4×C139C25112yes—
75Dic139C2512yes—
76Dic139C25118yes—
77C2×C139—218no—
78C2×C139#58512yescomplemented
79C2×C139C2611yescharacteristic
80D139—212no—
81C139C2×#58511yescharacteristic, complemented, Sylow
82C2×#585—1391nomaximal, Sylow
83#585—13932no—
84C2×2−1+4—1396no—
85C2×H(5,𝔽2)—1399no—
86C2×H(5,𝔽2)D13911yescharacteristic, complemented
87C22×#41—1396no—
88C22×#41—1399no—
892−1+4—13996no—
90H(5,𝔽2)—139144no—
91H(5,𝔽2)C2×D139116yescomplemented
92C2×#41—13996no—
93C2×#41—1392no—
94C2×#41—13918no—
95C2×#41—13936no—
96C2×#41—139144no—
97C2×#41—13918no—
98C2×#41C2×D13916yescomplemented
99C22×Q8—1396no—
100C22×Q8—1399no—
101C22×D4—13918no—
102C22×D4—13918no—
103C22×D4C2×D13919yescomplemented
104C23×C4—1396no—
105C23×C4—1399no—
106C24—1399no—
107C24C22×D13916yes—
108#41—13916no—
109#41—139144no—
110#41—139288no—
111#41—139144no—
112#41C22×D139148yescomplemented
113C2×Q8—13948no—
114C2×Q8—13918no—
115C2×Q8—13972no—
116C2×Q8C22×D13912yes—
117C2×D4—13936no—
118C2×D4—139144no—
119C2×D4—139144no—
120C2×D4—1396no—
121C2×D4C22×D139118yes—
122C2×D4C22×D139172yescomplemented
123C22×C4—1399no—
124C22×C4—13918no—
125C22×C4—13948no—
126C22×C4—1396no—
127C22×C4—13918no—
128C22×C4—13972no—
129C22×C4C22×D13919yes—
130C23—412no—
131C23—55618no—
132C23—1396no—
133C23—13936no—
134C23C23×D13919yes—
135C23C23×D139124yes—
136Q8—13972no—
137Q8C23×D13918yes—
138D4—139144no—
139D4—13924no—
140D4C23×D139172yes—
141C2×C4—13936no—
142C2×C4—13972no—
143C2×C4—1391no—
144C2×C4—1399no—
145C2×C4—13924no—
146C2×C4—13972no—
147C2×C4C23×D139136yes—
148C2×C4C23×D13916yes—
149C22—218no—
150C22—424no—
151C22—27812no—
152C22—55636no—
153C22—13912no—
154C22C24×D139118yes—
155C22C24×D13911yescharacteristic
156C4—1392no—
157C4—13918no—
158C4C24×D139112yes—
159C2—218no—
160C2—27812no—
161C2#2258178812yesdirect product factor
162C2C25×D13911yescharacteristic
subgroupG/H
centerC22C24×D139
commutator, cosocleC2×C139C26
FrattiniC2C25×D139
FittingC2×H(5,𝔽2)×C139C2
socleC22×C139C25
hypercenterC2×H(5,𝔽2)D139
hypocenterC139C2×#585
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. #22581788C2direct (N × H)
2. C2×#17984889C2semidirect
3. C2×#17984887C2semidirect
4. C22×#14555784C2semidirect
5. C2×#41×D139C2semidirect
6. C2×H(5,𝔽2)×C139C2semidirect
7. #17984889C22semidirect
8. #17984887C22semidirect
9. C2×#14555786C22semidirect
10. C2×#14555785C22semidirect
11. C2×#14555784C22semidirect
12. C2×#14555784C22semidirect
13. C2×#14555784C22semidirect
14. #41×D139C22semidirect
15. C22×Dic278C22semidirect
16. C2×Q8×D139C22semidirect
17. C22×C22⋊D139C22semidirect
18. C2×D4×D139C22semidirect
19. C23×Dic139C22semidirect
20. C22×C4×D139C22semidirect
21. H(5,𝔽2)×C139C22semidirect
22. C2×#41×C139C22semidirect
23. C22×D4×C139C22semidirect
25. #14555786C23semidirect
26. #14555785C23semidirect
27. #14555784C23semidirect
28. #14555784C23semidirect
30. C2×Dic278C23semidirect
31. Q8×D139C23semidirect
34. C2×C22⋊D139C23semidirect
35. D4×D139C23semidirect
38. C22×Dic139C23semidirect
41. C2×C4×D139C23semidirect
43. #41×C139C23semidirect
46. C2×D4×C139C23semidirect
78. C2×C139#585semidirect
81. C139C2×#585semidirect
86. C2×H(5,𝔽2)D139semidirect
91. H(5,𝔽2)C2×D139semidirect
98. C2×#41C2×D139semidirect
103. C22×D4C2×D139semidirect
112. #41C22×D139semidirect
122. C2×D4C22×D139semidirect
161. C2#22581788direct (N × H)

Maximal subgroups

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

subgroupindex
#225817882
C2×#179848892
C2×#179848872
C22×#145557842
C2×#41×D1392
C2×H(5,𝔽2)×C1392
C2×#585139