Finite Group Databasebeta

← C2×#22581695 #31820524

Subgroups — C2×#22581695 #31820524

Order 17792.

1408 conjugacy classes of subgroups; only the 469 normal subgroups are shown.

normal subgroups only

This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 469 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#22581695C2116yesmaximal, direct product factor
2C2×#17984831C212yesmaximal, complemented
3C2×#17984830C212yesmaximal, complemented
4C2×#17984828C214yesmaximal, complemented
5C2×#17984812C214yesmaximal, complemented
6C2×#17984810C212yesmaximal, complemented
7C2×#124×C139C211yesmaximal, characteristic, complemented
8C24×D139C2212yescomplemented
9C22×Dic278C2212yescomplemented
10C22×D556C2212yes—
11C22×D556C2212yes—
12C22×C22⋊D139C2214yes—
13#17984831C22116yescomplemented
14#17984830C22116yescomplemented
15#17984828C22132yescomplemented
16#17984812C22132yescomplemented
17#17984810C22116yescomplemented
18C2×C22⋊Dic139C2212yescomplemented
19C2×(C2×D139)⋊C4C2214yescomplemented
20C2×(C2×D139)⋊C4C2214yescomplemented
21C2×(C2×D139)⋊C4C2214yescomplemented
22C2×C4×Dic139C2212yescomplemented
23C22×Q8×C139C2211yescharacteristic, complemented
24C22×D4×C139C2211yescharacteristic
25#124×C139C2218yescomplemented
26C2×C22⋊C4×C139C2214yescomplemented
27C2×C42×C139C2211yescharacteristic, complemented
28C23×D139—44no—
29C23×D139—48no—
30C23×D139C2314yes—
31C23×D139C2318yescomplemented
32C2×Dic278—44no—
33C2×Dic278C2318yescomplemented
34C2×D556—44no—
35C2×D556—44no—
36C2×D556C2318yes—
37C2×D556C2318yes—
38C2×C22⋊D139—48no—
39C2×C22⋊D139C23116yes—
40C22×Dic139C2314yes—
41C22⋊Dic139C2318yescomplemented
42(C2×D139)⋊C4C23116yescomplemented
43(C2×D139)⋊C4C23116yescomplemented
44(C2×D139)⋊C4C23116yescomplemented
45C4×Dic139C2318yescomplemented
46C24×C139C2312yes—
47C2×Q8×C139—42no—
48C2×Q8×C139C2314yescomplemented
49C2×D4×C139—42no—
50C2×D4×C139C2314yes—
51C22×C4×C139C2312yes—
52C22×C4×C139C2311yescharacteristic
53C22×C4×C139C2312yes—
54C22⋊C4×C139C23116yescomplemented
55C42×C139C2314yescomplemented
56C22×D139—28no—
57C22×D139—28no—
58C22×D139—28no—
59C22×D139—416no—
60C22×D139—48no—
61C22×D139—432no—
62C22×D139C2418yes—
63Dic278—48no—
64D556—48no—
65D556—48no—
66C22⋊D139—416no—
67C2×Dic139—28no—
68C2×Dic139C2418yes—
69C23×C139—24no—
70C23×C139—28no—
71C23×C139C2414yes—
72C23×C139C2411yescharacteristic
73Q8×C139—44no—
74D4×C139—44no—
75C2×C4×C139—22no—
76C2×C4×C139—24no—
77C2×C4×C139—24no—
78C2×C4×C139C2414yes—
79C2×C4×C139C2412yes—
80C2×C4×C139C2414yes—
81C22×C139—24no—
82C22×C139—28no—
83C22×C139—48no—
84C22×C139H(5,𝔽2)12yes—
85C22×C139H(5,𝔽2)14yes—
86C22×C139C2511yescharacteristic
87C2×D139—28no—
88C2×D139—28no—
89C2×D139—28no—
90C2×D139—432no—
91C2×D139—416no—
92C4×C139—22no—
93C4×C139—24no—
94C4×C139—24no—
95Dic139—28no—
96C2×C139—44no—
97C2×C139H(3,𝔽4)14yescomplemented
98C2×C139C2×H(5,𝔽2)11yescharacteristic
99C2×C139C2×H(5,𝔽2)12yes—
100D139—48no—
101C139C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
102C2×H(3,𝔽4)—1391nomaximal, Sylow
103H(3,𝔽4)—13916no—
104C2×#124—1392no—
105C2×#124—1394no—
106C2×#124—1392no—
107C2×#124D13911yescharacteristic, complemented
108C2×#120—1392no—
109C2×#120—1394no—
110C25—1392no—
111C22×Q8—1392no—
112C22×Q8C2×D13911yescharacteristic, complemented
113C22×D4—1394no—
114C22×D4—1392no—
115C22×D4—1392no—
116C22×D4C2×D13911yescharacteristic
117#124—13916no—
118#124—13932no—
119#124—13916no—
120#124C2×D13918yescomplemented
121#120—13916no—
122#120—13932no—
123C2×C22⋊C4—1392no—
124C2×C22⋊C4—1394no—
125C2×C22⋊C4—1394no—
126C2×C22⋊C4—1394no—
127C2×C22⋊C4C2×D13914yescomplemented
128C2×C42—1392no—
129C2×C42C2×D13911yescharacteristic, complemented
130C24—5564no—
131C24—5568no—
132C24—1394no—
133C24—1398no—
134C24C22×D13912yes—
135C2×Q8—42no—
136C2×Q8—5564no—
137C2×Q8—1398no—
138C2×Q8C22×D13914yescomplemented
139C2×D4—42no—
140C2×D4—5564no—
141C2×D4—5564no—
142C2×D4—5568no—
143C2×D4—13916no—
144C2×D4—1398no—
145C2×D4—1398no—
146C2×D4C22×D13914yes—
147C22×C4—1394no—
148C22×C4C22×D13912yes—
149C22×C4C22×D13911yescharacteristic
150C22×C4C22×D13912yes—
151C22⋊C4—1398no—
152C22⋊C4—13916no—
153C22⋊C4—13916no—
154C22⋊C4—13916no—
155C22⋊C4C22×D139116yescomplemented
156C42—1398no—
157C42C22×D13914yescomplemented
158C23—24no—
159C23—28no—
160C23—2788no—
161C23—2788no—
162C23—2788no—
163C23—5568no—
164C23—55616no—
165C23—55632no—
166C23—1398no—
167C23C23×D13914yes—
168C23C23×D13911yescharacteristic
169Q8—44no—
170Q8—5568no—
171D4—44no—
172D4—5568no—
173D4—5568no—
174D4—55616no—
175C2×C4—22no—
176C2×C4—24no—
177C2×C4—24no—
178C2×C4—2788no—
179C2×C4—1398no—
180C2×C4C23×D13914yes—
181C2×C4C23×D13912yes—
182C2×C4C23×D13914yes—
183C22—24no—
184C22—28no—
185C22—48no—
186C22—2788no—
187C22—2788no—
188C22—2788no—
189C22—55632no—
190C22—55616no—
191C22#1798488712yes—
192C22#1798488814yes—
193C22C24×D13911yescharacteristic
194C4—22no—
195C4—24no—
196C4—24no—
197C4—2788no—
198C2—44no—
199C2—5568no—
200C2#2258169514yesdirect product factor
201C2C2×#1798488711yescharacteristic
202C2C2×#1798488812yes—
subgroupG/H
centerC23C23×D139
commutator, cosocleC22×C139C25
FrattiniC22C24×D139
FittingC2×#124×C139C2
socleC23×C139C24
hypercenterC2×#124D139
hypocenterC139C2×H(3,𝔽4)
LCSG ▷ C22×C139 ▷ C139
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #22581695C2direct (N × H)
2. C2×#17984831C2semidirect
3. C2×#17984830C2semidirect
4. C2×#17984828C2semidirect
5. C2×#17984812C2semidirect
6. C2×#17984810C2semidirect
7. C2×#124×C139C2semidirect
8. C24×D139C22semidirect
9. C22×Dic278C22semidirect
13. #17984831C22semidirect
14. #17984830C22semidirect
15. #17984828C22semidirect
16. #17984812C22semidirect
17. #17984810C22semidirect
18. C2×C22⋊Dic139C22semidirect
19. C2×(C2×D139)⋊C4C22semidirect
20. C2×(C2×D139)⋊C4C22semidirect
21. C2×(C2×D139)⋊C4C22semidirect
22. C2×C4×Dic139C22semidirect
23. C22×Q8×C139C22semidirect
25. #124×C139C22semidirect
26. C2×C22⋊C4×C139C22semidirect
27. C2×C42×C139C22semidirect
31. C23×D139C23semidirect
33. C2×Dic278C23semidirect
41. C22⋊Dic139C23semidirect
42. (C2×D139)⋊C4C23semidirect
43. (C2×D139)⋊C4C23semidirect
44. (C2×D139)⋊C4C23semidirect
45. C4×Dic139C23semidirect
48. C2×Q8×C139C23semidirect
54. C22⋊C4×C139C23semidirect
55. C42×C139C23semidirect
97. C2×C139H(3,𝔽4)semidirect
101. C139C2×H(3,𝔽4)semidirect
107. C2×#124D139semidirect
112. C22×Q8C2×D139semidirect
120. #124C2×D139semidirect
127. C2×C22⋊C4C2×D139semidirect
129. C2×C42C2×D139semidirect
138. C2×Q8C22×D139semidirect
155. C22⋊C4C22×D139semidirect
157. C42C22×D139semidirect
200. C2#22581695direct (N × H)

Maximal subgroups

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

subgroupindex
#225816952
C2×#179848312
C2×#179848302
C2×#179848282
C2×#179848122
C2×#179848102
C2×#124×C1392
C2×H(3,𝔽4)139