Finite Group Databasebeta

← C2×#31827206 #49135379

Subgroups — C2×#31827206 #49135379

Order 36224.

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#31827206C2116yesmaximal, direct product factor
2C2×#22583607C211yesmaximal, characteristic, complemented
3C2×#22583604C211yesmaximal, characteristic, complemented
4C2×#22583595C213yesmaximal, complemented
5C2×#22583585C213yesmaximal, complemented
6C2×#22583583C213yesmaximal, complemented
7C2×#22583580C213yesmaximal, complemented
8C2×#126×C283C211yesmaximal, characteristic, complemented
9C24×D283C2211yescharacteristic
10C22×D1132C2213yes—
11C22×D1132C2213yes—
12C22×D1132C2213yescomplemented
13C22×C22⋊D283C2213yes—
14C22×C4×D283C2213yescomplemented
15#22583607C2218yescomplemented
16#22583604C2218yescomplemented
17#22583595C22124yescomplemented
18#22583585C22124yescomplemented
19#22583583C22124yescomplemented
20#22583580C22124yescomplemented
21C2×Dic283⋊C4C2213yescomplemented
22C2×(C2×D283)⋊C4C2213yes—
23C2×(C2×D283)⋊C4C2213yes—
24C2×(C2×D283)⋊C4C2213yescomplemented
25#126×C283C2218yescomplemented
26C2×C4⋊C4×C283C2213yescomplemented
27C2×C22⋊C4×C283C2213yes—
28C2×C42×C283C2211yescharacteristic, complemented
29C23×D283—46no—
30C23×D283C2311yescharacteristic
31C23×D283C2311yescharacteristic
32C23×D283C2313yes—
33C23×D283C2314yes—
34C2×D1132—46no—
35C2×D1132—46no—
36C2×D1132—46no—
37C2×D1132C23112yes—
38C2×D1132C23112yes—
39C2×D1132C23112yescomplemented
40C2×C22⋊D283—46no—
41C2×C22⋊D283C23112yes—
42C22×Dic283C2313yes—
43C2×C4×D283—46no—
44C2×C4×D283C23112yescomplemented
45Dic283⋊C4C23112yescomplemented
46(C2×D283)⋊C4C23112yes—
47(C2×D283)⋊C4C23112yes—
48(C2×D283)⋊C4C23112yescomplemented
49C24×C283C2311yescharacteristic
50C22×C4×C283C2313yes—
51C22×C4×C283C2313yes—
52C4⋊C4×C283C23112yescomplemented
53C22⋊C4×C283C23112yes—
54C42×C283C2314yescomplemented
55C22×D283—26no—
56C22×D283—26no—
57C22×D283—26no—
58C22×D283—26no—
59C22×D283—26no—
60C22×D283—412no—
61C22×D283—416no—
62C22×D283C2412yes—
63C22×D283C2412yes—
64C22×D283C2416yes—
65D1132—412no—
66D1132—412no—
67D1132—412no—
68C22⋊D283—412no—
69C2×Dic283—26no—
70C2×Dic283C2416yes—
71C4×D283—412no—
72C23×C283—26no—
73C23×C283C2412yes—
74C23×C283C2411yescharacteristic
75C2×C4×C283—26no—
76C2×C4×C283—26no—
77C2×C4×C283C2416yes—
78C2×C4×C283C2416yes—
79C22×C283—26no—
80C22×C283—44no—
81C22×C283H(5,𝔽2)16yes—
82C22×C283C2511yescharacteristic
83C2×D283—26no—
84C2×D283—26no—
85C2×D283—26no—
86C2×D283—26no—
87C2×D283—26no—
88C2×D283—416no—
89C2×D283—412no—
90C2×D283—44no—
91C2×D283—44no—
92C4×C283—26no—
93C4×C283—26no—
94Dic283—26no—
95C2×C283—42no—
96C2×C283#56014yescomplemented
97C2×C283C2×H(5,𝔽2)13yes—
98D283—46no—
99D283—42no—
100D283—42no—
101C283C2×#56011yescharacteristic, complemented, Sylow
102C2×#560—2831nomaximal, Sylow
103#560—28316no—
104C2×#127—2831no—
105C2×#126—2831no—
106C2×#126D28311yescharacteristic, complemented
107C2×#123—2833no—
108C2×#121—2833no—
109C2×#121—2833no—
110C2×#120—2833no—
111C25—2831no—
112C22×D4—2833no—
113C22×D4—2833no—
114C22×D4—2833no—
115C22×D4—2833no—
116C23×C4—2833no—
117#127—2838no—
118#126—2838no—
119#126C2×D28318yescomplemented
120#123—28324no—
121#121—28324no—
122#121—28324no—
123#120—28324no—
124C2×C4⋊C4—2833no—
125C2×C4⋊C4C2×D28313yescomplemented
126C2×C22⋊C4—2833no—
127C2×C22⋊C4—2833no—
128C2×C22⋊C4—2833no—
129C2×C22⋊C4C2×D28313yes—
130C2×C42C2×D28311yescharacteristic, complemented
131C24—2831no—
132C24—2831no—
133C24—2833no—
134C24—2834no—
135C24—11326no—
136C24C22×D28311yescharacteristic
137C2×D4—28312no—
138C2×D4—28312no—
139C2×D4—28312no—
140C2×D4—28312no—
141C2×D4—11326no—
142C2×D4—11326no—
143C2×D4—11326no—
144C2×D4—11326no—
145C22×C4—2833no—
146C22×C4—28312no—
147C22×C4—11326no—
148C22×C4C22×D28313yes—
149C22×C4C22×D28313yes—
150C4⋊C4—28312no—
151C4⋊C4C22×D283112yescomplemented
152C22⋊C4—28312no—
153C22⋊C4—28312no—
154C22⋊C4—28312no—
155C22⋊C4C22×D283112yes—
156C42C22×D28314yescomplemented
157C23—26no—
158C23—2832no—
159C23—2832no—
160C23—2836no—
161C23—5666no—
162C23—5666no—
163C23—5666no—
164C23—5666no—
165C23—5666no—
166C23—113212no—
167C23—113216no—
168C23C23×D28312yes—
169C23C23×D28311yescharacteristic
170D4—113212no—
171D4—113212no—
172D4—113212no—
173D4—113212no—
174C2×C4—26no—
175C2×C4—26no—
176C2×C4—2836no—
177C2×C4—5666no—
178C2×C4—113212no—
179C2×C4C23×D28316yes—
180C2×C4C23×D28316yes—
181C22—26no—
182C22—44no—
183C22—5666no—
184C22—5666no—
185C22—5666no—
186C22—5666no—
187C22—5666no—
188C22—113216no—
189C22—11324no—
190C22—11324no—
191C22—113212no—
192C22#2258365616yes—
193C22C24×D28311yescharacteristic
194C4—26no—
195C4—26no—
196C4—5666no—
197C2—42no—
198C2—11322no—
199C2—11322no—
200C2—11326no—
201C2#3182720614yesdirect product factor
202C2C2×#2258365613yes—
subgroupG/H
centerC23C23×D283
commutator, cosocleC22×C283C25
FrattiniC22C24×D283
FittingC2×#126×C283C2
socleC23×C283C24
hypercenterC2×#126D283
hypocenterC283C2×#560
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #31827206C2direct (N × H)
2. C2×#22583607C2semidirect
3. C2×#22583604C2semidirect
4. C2×#22583595C2semidirect
5. C2×#22583585C2semidirect
6. C2×#22583583C2semidirect
7. C2×#22583580C2semidirect
8. C2×#126×C283C2semidirect
12. C22×D1132C22semidirect
14. C22×C4×D283C22semidirect
15. #22583607C22semidirect
16. #22583604C22semidirect
17. #22583595C22semidirect
18. #22583585C22semidirect
19. #22583583C22semidirect
20. #22583580C22semidirect
21. C2×Dic283⋊C4C22semidirect
24. C2×(C2×D283)⋊C4C22semidirect
25. #126×C283C22semidirect
26. C2×C4⋊C4×C283C22semidirect
28. C2×C42×C283C22semidirect
39. C2×D1132C23semidirect
44. C2×C4×D283C23semidirect
45. Dic283⋊C4C23semidirect
48. (C2×D283)⋊C4C23semidirect
52. C4⋊C4×C283C23semidirect
54. C42×C283C23semidirect
96. C2×C283#560semidirect
101. C283C2×#560semidirect
106. C2×#126D283semidirect
119. #126C2×D283semidirect
125. C2×C4⋊C4C2×D283semidirect
130. C2×C42C2×D283semidirect
151. C4⋊C4C22×D283semidirect
156. C42C22×D283semidirect
201. C2#31827206direct (N × H)

Maximal subgroups

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

subgroupindex
#318272062
C2×#225836072
C2×#225836042
C2×#225835952
C2×#225835852
C2×#225835832
C2×#225835802
C2×#126×C2832
C2×#560283