Finite Group Databasebeta

← C2×#23750366 #34058809

Subgroups — C2×#23750366 #34058809

Order 19072.

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#23750366C2116yesmaximal, direct product factor
2C2×#18011908C211yesmaximal, characteristic, complemented
3C2×#18011905C211yesmaximal, characteristic, complemented
4C2×#18011896C213yesmaximal, complemented
5C2×#18011886C213yesmaximal, complemented
6C2×#18011884C213yesmaximal, complemented
7C2×#18011881C213yesmaximal, complemented
8C2×#126×C149C211yesmaximal, characteristic, complemented
9C24×D149C2211yescharacteristic
10C22×D596C2213yes—
11C22×D596C2213yes—
12C22×D596C2213yescomplemented
13C22×C22⋊D149C2213yes—
14C22×C4×D149C2213yescomplemented
15#18011908C2218yescomplemented
16#18011905C2218yescomplemented
17#18011896C22124yescomplemented
18#18011886C22124yescomplemented
19#18011884C22124yescomplemented
20#18011881C22124yescomplemented
21C2×#14558715C2213yescomplemented
22C2×#14558713C2213yes—
23C2×#14558713C2213yes—
24C2×#14558713C2213yescomplemented
25#126×C149C2218yescomplemented
26C2×C4⋊C4×C149C2213yescomplemented
27C2×C22⋊C4×C149C2213yes—
28C2×C42×C149C2211yescharacteristic, complemented
29C23×D149—46no—
30C23×D149C2313yes—
31C23×D149C2311yescharacteristic
32C23×D149C2311yescharacteristic
33C23×D149C2314yes—
34C2×D596—46no—
35C2×D596—46no—
36C2×D596—46no—
37C2×D596C23112yes—
38C2×D596C23112yes—
39C2×D596C23112yescomplemented
40C2×C22⋊D149—46no—
41C2×C22⋊D149C23112yes—
42C22×Dic149C2313yes—
43C2×C4×D149—46no—
44C2×C4×D149C23112yescomplemented
45#14558715C23112yescomplemented
46#14558713C23112yes—
47#14558713C23112yes—
48#14558713C23112yescomplemented
49C24×C149C2311yescharacteristic
50C22×C4×C149C2313yes—
51C22×C4×C149C2313yes—
52C4⋊C4×C149C23112yescomplemented
53C22⋊C4×C149C23112yes—
54C42×C149C2314yescomplemented
55C22×D149—26no—
56C22×D149—26no—
57C22×D149—26no—
58C22×D149—26no—
59C22×D149—26no—
60C22×D149—412no—
61C22×D149—416no—
62C22×D149C2416yes—
63C22×D149C2412yes—
64C22×D149C2412yes—
65D596—412no—
66D596—412no—
67D596—412no—
68C22⋊D149—412no—
69C2×Dic149—26no—
70C2×Dic149C2416yes—
71C4×D149—412no—
72C23×C149—26no—
73C23×C149C2412yes—
74C23×C149C2411yescharacteristic
75C2×C4×C149—26no—
76C2×C4×C149—26no—
77C2×C4×C149C2416yes—
78C2×C4×C149C2416yes—
79C22×C149—26no—
80C22×C149—44no—
81C22×C149H(5,𝔽2)16yes—
82C22×C149C2511yescharacteristic
83C2×D149—26no—
84C2×D149—26no—
85C2×D149—26no—
86C2×D149—26no—
87C2×D149—26no—
88C2×D149—416no—
89C2×D149—412no—
90C2×D149—44no—
91C2×D149—44no—
92C4×C149—26no—
93C4×C149—26no—
94Dic149—26no—
95C2×C149—42no—
96C2×C149#56014yescomplemented
97C2×C149C2×H(5,𝔽2)13yes—
98D149—46no—
99D149—42no—
100D149—42no—
101C149C2×#56011yescharacteristic, complemented, Sylow
102C2×#560—1491nomaximal, Sylow
103#560—14916no—
104C2×#127—1491no—
105C2×#126—1491no—
106C2×#126D14911yescharacteristic, complemented
107C2×#123—1493no—
108C2×#121—1493no—
109C2×#121—1493no—
110C2×#120—1493no—
111C25—1491no—
112C22×D4—1493no—
113C22×D4—1493no—
114C22×D4—1493no—
115C22×D4—1493no—
116C23×C4—1493no—
117#127—1498no—
118#126—1498no—
119#126C2×D14918yescomplemented
120#123—14924no—
121#121—14924no—
122#121—14924no—
123#120—14924no—
124C2×C4⋊C4—1493no—
125C2×C4⋊C4C2×D14913yescomplemented
126C2×C22⋊C4—1493no—
127C2×C22⋊C4—1493no—
128C2×C22⋊C4—1493no—
129C2×C22⋊C4C2×D14913yes—
130C2×C42C2×D14911yescharacteristic, complemented
131C24—5966no—
132C24—1491no—
133C24—1491no—
134C24—1493no—
135C24—1494no—
136C24C22×D14911yescharacteristic
137C2×D4—5966no—
138C2×D4—5966no—
139C2×D4—5966no—
140C2×D4—5966no—
141C2×D4—14912no—
142C2×D4—14912no—
143C2×D4—14912no—
144C2×D4—14912no—
145C22×C4—5966no—
146C22×C4—1493no—
147C22×C4—14912no—
148C22×C4C22×D14913yes—
149C22×C4C22×D14913yes—
150C4⋊C4—14912no—
151C4⋊C4C22×D149112yescomplemented
152C22⋊C4—14912no—
153C22⋊C4—14912no—
154C22⋊C4—14912no—
155C22⋊C4C22×D149112yes—
156C42C22×D14914yescomplemented
157C23—26no—
158C23—2986no—
159C23—2986no—
160C23—2986no—
161C23—2986no—
162C23—2986no—
163C23—59612no—
164C23—59616no—
165C23—1492no—
166C23—1492no—
167C23—1496no—
168C23C23×D14912yes—
169C23C23×D14911yescharacteristic
170D4—59612no—
171D4—59612no—
172D4—59612no—
173D4—59612no—
174C2×C4—26no—
175C2×C4—26no—
176C2×C4—2986no—
177C2×C4—59612no—
178C2×C4—1496no—
179C2×C4C23×D14916yes—
180C2×C4C23×D14916yes—
181C22—26no—
182C22—44no—
183C22—2986no—
184C22—2986no—
185C22—2986no—
186C22—2986no—
187C22—2986no—
188C22—59616no—
189C22—5964no—
190C22—5964no—
191C22—59612no—
192C22#1801195716yes—
193C22C24×D14911yescharacteristic
194C4—26no—
195C4—26no—
196C4—2986no—
197C2—42no—
198C2—5962no—
199C2—5962no—
200C2—5966no—
201C2#2375036614yesdirect product factor
202C2C2×#1801195713yes—
subgroupG/H
centerC23C23×D149
commutator, cosocleC22×C149C25
FrattiniC22C24×D149
FittingC2×#126×C149C2
socleC23×C149C24
hypercenterC2×#126D149
hypocenterC149C2×#560
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #23750366C2direct (N × H)
2. C2×#18011908C2semidirect
3. C2×#18011905C2semidirect
4. C2×#18011896C2semidirect
5. C2×#18011886C2semidirect
6. C2×#18011884C2semidirect
7. C2×#18011881C2semidirect
8. C2×#126×C149C2semidirect
12. C22×D596C22semidirect
14. C22×C4×D149C22semidirect
15. #18011908C22semidirect
16. #18011905C22semidirect
17. #18011896C22semidirect
18. #18011886C22semidirect
19. #18011884C22semidirect
20. #18011881C22semidirect
21. C2×#14558715C22semidirect
24. C2×#14558713C22semidirect
25. #126×C149C22semidirect
26. C2×C4⋊C4×C149C22semidirect
28. C2×C42×C149C22semidirect
39. C2×D596C23semidirect
44. C2×C4×D149C23semidirect
45. #14558715C23semidirect
48. #14558713C23semidirect
52. C4⋊C4×C149C23semidirect
54. C42×C149C23semidirect
96. C2×C149#560semidirect
101. C149C2×#560semidirect
106. C2×#126D149semidirect
119. #126C2×D149semidirect
125. C2×C4⋊C4C2×D149semidirect
130. C2×C42C2×D149semidirect
151. C4⋊C4C22×D149semidirect
156. C42C22×D149semidirect
201. C2#23750366direct (N × H)

Maximal subgroups

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

subgroupindex
#237503662
C2×#180119082
C2×#180119052
C2×#180118962
C2×#180118862
C2×#180118842
C2×#180118812
C2×#126×C1492
C2×#560149