Finite Group Databasebeta

← C2×#22581694 #31820522

Subgroups — C2×#22581694 #31820522

Order 17792.

1344 conjugacy classes of subgroups; only the 469 normal subgroups are shown.

normal subgroups only

This group has 1344 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#22581694C2116yesmaximal, direct product factor
2C2×#17984839C211yesmaximal, characteristic, complemented
3C2×#17984836C211yesmaximal, characteristic, complemented
4C2×#17984827C213yesmaximal, complemented
5C2×#17984817C213yesmaximal, complemented
6C2×#17984815C213yesmaximal, complemented
7C2×#17984812C213yesmaximal, complemented
8C2×#126×C139C211yesmaximal, characteristic, complemented
9C24×D139C2211yescharacteristic
10C22×D556C2213yes—
11C22×D556C2213yes—
12C22×D556C2213yescomplemented
13C22×C22⋊D139C2213yes—
14C22×C4×D139C2213yescomplemented
15#17984839C2218yescomplemented
16#17984836C2218yescomplemented
17#17984827C22124yescomplemented
18#17984817C22124yescomplemented
19#17984815C22124yescomplemented
20#17984812C22124yescomplemented
21C2×Dic139⋊C4C2213yescomplemented
22C2×(C2×D139)⋊C4C2213yes—
23C2×(C2×D139)⋊C4C2213yes—
24C2×(C2×D139)⋊C4C2213yescomplemented
25#126×C139C2218yescomplemented
26C2×C4⋊C4×C139C2213yescomplemented
27C2×C22⋊C4×C139C2213yes—
28C2×C42×C139C2211yescharacteristic, complemented
29C23×D139—46no—
30C23×D139C2311yescharacteristic
31C23×D139C2311yescharacteristic
32C23×D139C2313yes—
33C23×D139C2314yes—
34C2×D556—46no—
35C2×D556—46no—
36C2×D556—46no—
37C2×D556C23112yes—
38C2×D556C23112yes—
39C2×D556C23112yescomplemented
40C2×C22⋊D139—46no—
41C2×C22⋊D139C23112yes—
42C22×Dic139C2313yes—
43C2×C4×D139—46no—
44C2×C4×D139C23112yescomplemented
45Dic139⋊C4C23112yescomplemented
46(C2×D139)⋊C4C23112yes—
47(C2×D139)⋊C4C23112yes—
48(C2×D139)⋊C4C23112yescomplemented
49C24×C139C2311yescharacteristic
50C22×C4×C139C2313yes—
51C22×C4×C139C2313yes—
52C4⋊C4×C139C23112yescomplemented
53C22⋊C4×C139C23112yes—
54C42×C139C2314yescomplemented
55C22×D139—26no—
56C22×D139—26no—
57C22×D139—26no—
58C22×D139—26no—
59C22×D139—26no—
60C22×D139—412no—
61C22×D139—416no—
62C22×D139C2412yes—
63C22×D139C2412yes—
64C22×D139C2416yes—
65D556—412no—
66D556—412no—
67D556—412no—
68C22⋊D139—412no—
69C2×Dic139—26no—
70C2×Dic139C2416yes—
71C4×D139—412no—
72C23×C139—26no—
73C23×C139C2412yes—
74C23×C139C2411yescharacteristic
75C2×C4×C139—26no—
76C2×C4×C139—26no—
77C2×C4×C139C2416yes—
78C2×C4×C139C2416yes—
79C22×C139—26no—
80C22×C139—44no—
81C22×C139H(5,𝔽2)16yes—
82C22×C139C2511yescharacteristic
83C2×D139—26no—
84C2×D139—26no—
85C2×D139—26no—
86C2×D139—26no—
87C2×D139—26no—
88C2×D139—416no—
89C2×D139—412no—
90C2×D139—44no—
91C2×D139—44no—
92C4×C139—26no—
93C4×C139—26no—
94Dic139—26no—
95C2×C139—42no—
96C2×C139#56014yescomplemented
97C2×C139C2×H(5,𝔽2)13yes—
98D139—46no—
99D139—42no—
100D139—42no—
101C139C2×#56011yescharacteristic, complemented, Sylow
102C2×#560—1391nomaximal, Sylow
103#560—13916no—
104C2×#127—1391no—
105C2×#126—1391no—
106C2×#126D13911yescharacteristic, complemented
107C2×#123—1393no—
108C2×#121—1393no—
109C2×#121—1393no—
110C2×#120—1393no—
111C25—1391no—
112C22×D4—1393no—
113C22×D4—1393no—
114C22×D4—1393no—
115C22×D4—1393no—
116C23×C4—1393no—
117#127—1398no—
118#126—1398no—
119#126C2×D13918yescomplemented
120#123—13924no—
121#121—13924no—
122#121—13924no—
123#120—13924no—
124C2×C4⋊C4—1393no—
125C2×C4⋊C4C2×D13913yescomplemented
126C2×C22⋊C4—1393no—
127C2×C22⋊C4—1393no—
128C2×C22⋊C4—1393no—
129C2×C22⋊C4C2×D13913yes—
130C2×C42C2×D13911yescharacteristic, complemented
131C24—5566no—
132C24—1391no—
133C24—1391no—
134C24—1393no—
135C24—1394no—
136C24C22×D13911yescharacteristic
137C2×D4—5566no—
138C2×D4—5566no—
139C2×D4—5566no—
140C2×D4—5566no—
141C2×D4—13912no—
142C2×D4—13912no—
143C2×D4—13912no—
144C2×D4—13912no—
145C22×C4—5566no—
146C22×C4—1393no—
147C22×C4—13912no—
148C22×C4C22×D13913yes—
149C22×C4C22×D13913yes—
150C4⋊C4—13912no—
151C4⋊C4C22×D139112yescomplemented
152C22⋊C4—13912no—
153C22⋊C4—13912no—
154C22⋊C4—13912no—
155C22⋊C4C22×D139112yes—
156C42C22×D13914yescomplemented
157C23—26no—
158C23—2786no—
159C23—2786no—
160C23—2786no—
161C23—2786no—
162C23—2786no—
163C23—55612no—
164C23—55616no—
165C23—1392no—
166C23—1392no—
167C23—1396no—
168C23C23×D13912yes—
169C23C23×D13911yescharacteristic
170D4—55612no—
171D4—55612no—
172D4—55612no—
173D4—55612no—
174C2×C4—26no—
175C2×C4—26no—
176C2×C4—2786no—
177C2×C4—55612no—
178C2×C4—1396no—
179C2×C4C23×D13916yes—
180C2×C4C23×D13916yes—
181C22—26no—
182C22—44no—
183C22—2786no—
184C22—2786no—
185C22—2786no—
186C22—2786no—
187C22—2786no—
188C22—55616no—
189C22—5564no—
190C22—5564no—
191C22—55612no—
192C22#1798488816yes—
193C22C24×D13911yescharacteristic
194C4—26no—
195C4—26no—
196C4—2786no—
197C2—42no—
198C2—5562no—
199C2—5562no—
200C2—5566no—
201C2#2258169414yesdirect product factor
202C2C2×#1798488813yes—
subgroupG/H
centerC23C23×D139
commutator, cosocleC22×C139C25
FrattiniC22C24×D139
FittingC2×#126×C139C2
socleC23×C139C24
hypercenterC2×#126D139
hypocenterC139C2×#560
LCSG ▷ C22×C139 ▷ C139
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #22581694C2direct (N × H)
2. C2×#17984839C2semidirect
3. C2×#17984836C2semidirect
4. C2×#17984827C2semidirect
5. C2×#17984817C2semidirect
6. C2×#17984815C2semidirect
7. C2×#17984812C2semidirect
8. C2×#126×C139C2semidirect
12. C22×D556C22semidirect
14. C22×C4×D139C22semidirect
15. #17984839C22semidirect
16. #17984836C22semidirect
17. #17984827C22semidirect
18. #17984817C22semidirect
19. #17984815C22semidirect
20. #17984812C22semidirect
21. C2×Dic139⋊C4C22semidirect
24. C2×(C2×D139)⋊C4C22semidirect
25. #126×C139C22semidirect
26. C2×C4⋊C4×C139C22semidirect
28. C2×C42×C139C22semidirect
39. C2×D556C23semidirect
44. C2×C4×D139C23semidirect
45. Dic139⋊C4C23semidirect
48. (C2×D139)⋊C4C23semidirect
52. C4⋊C4×C139C23semidirect
54. C42×C139C23semidirect
96. C2×C139#560semidirect
101. C139C2×#560semidirect
106. C2×#126D139semidirect
119. #126C2×D139semidirect
125. C2×C4⋊C4C2×D139semidirect
130. C2×C42C2×D139semidirect
151. C4⋊C4C22×D139semidirect
156. C42C22×D139semidirect
201. C2#22581694direct (N × H)

Maximal subgroups

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

subgroupindex
#225816942
C2×#179848392
C2×#179848362
C2×#179848272
C2×#179848172
C2×#179848152
C2×#179848122
C2×#126×C1392
C2×#560139