Finite Group Databasebeta

← C2×#23752953 #34083228

Subgroups — C2×#23752953 #34083228

Order 19328.

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#23752953C2116yesmaximal, direct product factor
2C2×#18012736C211yesmaximal, characteristic, complemented
3C2×#18012733C211yesmaximal, characteristic, complemented
4C2×#18012724C213yesmaximal, complemented
5C2×#18012714C213yesmaximal, complemented
6C2×#18012712C213yesmaximal, complemented
7C2×#18012709C213yesmaximal, complemented
8C2×#126×C151C211yesmaximal, characteristic, complemented
9C24×D151C2211yescharacteristic
10C22×D604C2213yes—
11C22×D604C2213yes—
12C22×D604C2213yescomplemented
13C22×C22⋊D151C2213yes—
14C22×C4×D151C2213yescomplemented
15#18012736C2218yescomplemented
16#18012733C2218yescomplemented
17#18012724C22124yescomplemented
18#18012714C22124yescomplemented
19#18012712C22124yescomplemented
20#18012709C22124yescomplemented
21C2×Dic151⋊C4C2213yescomplemented
22C2×(C2×D151)⋊C4C2213yes—
23C2×(C2×D151)⋊C4C2213yes—
24C2×(C2×D151)⋊C4C2213yescomplemented
25#126×C151C2218yescomplemented
26C2×C4⋊C4×C151C2213yescomplemented
27C2×C22⋊C4×C151C2213yes—
28C2×C42×C151C2211yescharacteristic, complemented
29C23×D151—46no—
30C23×D151C2311yescharacteristic
31C23×D151C2311yescharacteristic
32C23×D151C2313yes—
33C23×D151C2314yes—
34C2×D604—46no—
35C2×D604—46no—
36C2×D604—46no—
37C2×D604C23112yes—
38C2×D604C23112yes—
39C2×D604C23112yescomplemented
40C2×C22⋊D151—46no—
41C2×C22⋊D151C23112yes—
42C22×Dic151C2313yes—
43C2×C4×D151—46no—
44C2×C4×D151C23112yescomplemented
45Dic151⋊C4C23112yescomplemented
46(C2×D151)⋊C4C23112yes—
47(C2×D151)⋊C4C23112yes—
48(C2×D151)⋊C4C23112yescomplemented
49C24×C151C2311yescharacteristic
50C22×C4×C151C2313yes—
51C22×C4×C151C2313yes—
52C4⋊C4×C151C23112yescomplemented
53C22⋊C4×C151C23112yes—
54C42×C151C2314yescomplemented
55C22×D151—26no—
56C22×D151—26no—
57C22×D151—26no—
58C22×D151—26no—
59C22×D151—26no—
60C22×D151—412no—
61C22×D151—416no—
62C22×D151C2412yes—
63C22×D151C2412yes—
64C22×D151C2416yes—
65D604—412no—
66D604—412no—
67D604—412no—
68C22⋊D151—412no—
69C2×Dic151—26no—
70C2×Dic151C2416yes—
71C4×D151—412no—
72C23×C151—26no—
73C23×C151C2412yes—
74C23×C151C2411yescharacteristic
75C2×C4×C151—26no—
76C2×C4×C151—26no—
77C2×C4×C151C2416yes—
78C2×C4×C151C2416yes—
79C22×C151—26no—
80C22×C151—44no—
81C22×C151H(5,𝔽2)16yes—
82C22×C151C2511yescharacteristic
83C2×D151—26no—
84C2×D151—26no—
85C2×D151—26no—
86C2×D151—26no—
87C2×D151—26no—
88C2×D151—416no—
89C2×D151—412no—
90C2×D151—44no—
91C2×D151—44no—
92C4×C151—26no—
93C4×C151—26no—
94Dic151—26no—
95C2×C151—42no—
96C2×C151#56014yescomplemented
97C2×C151C2×H(5,𝔽2)13yes—
98D151—46no—
99D151—42no—
100D151—42no—
101C151C2×#56011yescharacteristic, complemented, Sylow
102C2×#560—1511nomaximal, Sylow
103#560—15116no—
104C2×#127—1511no—
105C2×#126—1511no—
106C2×#126D15111yescharacteristic, complemented
107C2×#123—1513no—
108C2×#121—1513no—
109C2×#121—1513no—
110C2×#120—1513no—
111C25—1511no—
112C22×D4—1513no—
113C22×D4—1513no—
114C22×D4—1513no—
115C22×D4—1513no—
116C23×C4—1513no—
117#127—1518no—
118#126—1518no—
119#126C2×D15118yescomplemented
120#123—15124no—
121#121—15124no—
122#121—15124no—
123#120—15124no—
124C2×C4⋊C4—1513no—
125C2×C4⋊C4C2×D15113yescomplemented
126C2×C22⋊C4—1513no—
127C2×C22⋊C4—1513no—
128C2×C22⋊C4—1513no—
129C2×C22⋊C4C2×D15113yes—
130C2×C42C2×D15111yescharacteristic, complemented
131C24—6046no—
132C24—1511no—
133C24—1511no—
134C24—1513no—
135C24—1514no—
136C24C22×D15111yescharacteristic
137C2×D4—6046no—
138C2×D4—6046no—
139C2×D4—6046no—
140C2×D4—6046no—
141C2×D4—15112no—
142C2×D4—15112no—
143C2×D4—15112no—
144C2×D4—15112no—
145C22×C4—6046no—
146C22×C4—1513no—
147C22×C4—15112no—
148C22×C4C22×D15113yes—
149C22×C4C22×D15113yes—
150C4⋊C4—15112no—
151C4⋊C4C22×D151112yescomplemented
152C22⋊C4—15112no—
153C22⋊C4—15112no—
154C22⋊C4—15112no—
155C22⋊C4C22×D151112yes—
156C42C22×D15114yescomplemented
157C23—26no—
158C23—3026no—
159C23—3026no—
160C23—3026no—
161C23—3026no—
162C23—3026no—
163C23—60412no—
164C23—60416no—
165C23—1512no—
166C23—1512no—
167C23—1516no—
168C23C23×D15112yes—
169C23C23×D15111yescharacteristic
170D4—60412no—
171D4—60412no—
172D4—60412no—
173D4—60412no—
174C2×C4—26no—
175C2×C4—26no—
176C2×C4—3026no—
177C2×C4—60412no—
178C2×C4—1516no—
179C2×C4C23×D15116yes—
180C2×C4C23×D15116yes—
181C22—26no—
182C22—44no—
183C22—3026no—
184C22—3026no—
185C22—3026no—
186C22—3026no—
187C22—3026no—
188C22—60416no—
189C22—6044no—
190C22—6044no—
191C22—60412no—
192C22#1801278516yes—
193C22C24×D15111yescharacteristic
194C4—26no—
195C4—26no—
196C4—3026no—
197C2—42no—
198C2—6042no—
199C2—6042no—
200C2—6046no—
201C2#2375295314yesdirect product factor
202C2C2×#1801278513yes—
subgroupG/H
centerC23C23×D151
commutator, cosocleC22×C151C25
FrattiniC22C24×D151
FittingC2×#126×C151C2
socleC23×C151C24
hypercenterC2×#126D151
hypocenterC151C2×#560
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #23752953C2direct (N × H)
2. C2×#18012736C2semidirect
3. C2×#18012733C2semidirect
4. C2×#18012724C2semidirect
5. C2×#18012714C2semidirect
6. C2×#18012712C2semidirect
7. C2×#18012709C2semidirect
8. C2×#126×C151C2semidirect
12. C22×D604C22semidirect
14. C22×C4×D151C22semidirect
15. #18012736C22semidirect
16. #18012733C22semidirect
17. #18012724C22semidirect
18. #18012714C22semidirect
19. #18012712C22semidirect
20. #18012709C22semidirect
21. C2×Dic151⋊C4C22semidirect
24. C2×(C2×D151)⋊C4C22semidirect
25. #126×C151C22semidirect
26. C2×C4⋊C4×C151C22semidirect
28. C2×C42×C151C22semidirect
39. C2×D604C23semidirect
44. C2×C4×D151C23semidirect
45. Dic151⋊C4C23semidirect
48. (C2×D151)⋊C4C23semidirect
52. C4⋊C4×C151C23semidirect
54. C42×C151C23semidirect
96. C2×C151#560semidirect
101. C151C2×#560semidirect
106. C2×#126D151semidirect
119. #126C2×D151semidirect
125. C2×C4⋊C4C2×D151semidirect
130. C2×C42C2×D151semidirect
151. C4⋊C4C22×D151semidirect
156. C42C22×D151semidirect
201. C2#23752953direct (N × H)

Maximal subgroups

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

subgroupindex
#237529532
C2×#180127362
C2×#180127332
C2×#180127242
C2×#180127142
C2×#180127122
C2×#180127092
C2×#126×C1512
C2×#560151