Finite Group Databasebeta

← C2×#14558274 #18008714

Subgroups — C2×#14558274 #18008714

Order 4736.

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#14558274C2116yesmaximal, direct product factor
2C2×#11924533C211yesmaximal, characteristic, complemented
3C2×#11924530C211yesmaximal, characteristic, complemented
4C2×#11924521C213yesmaximal, complemented
5C2×#11924511C213yesmaximal, complemented
6C2×#11924509C213yesmaximal, complemented
7C2×#11924506C213yesmaximal, complemented
8C2×#126×C37C211yesmaximal, characteristic, complemented
9C24×D37C2211yescharacteristic
10C22×D148C2213yes—
11C22×D148C2213yes—
12C22×D148C2213yescomplemented
13C22×C22⋊D37C2213yes—
14C22×C4×D37C2213yescomplemented
15#11924533C2218yescomplemented
16#11924530C2218yescomplemented
17#11924521C22124yescomplemented
18#11924511C22124yescomplemented
19#11924509C22124yescomplemented
20#11924506C22124yescomplemented
21C2×#10596936C2213yescomplemented
22C2×#10596938C2213yes—
23C2×#10596938C2213yes—
24C2×#10596938C2213yescomplemented
25#126×C37C2218yescomplemented
26C2×C4⋊C4×C37C2213yescomplemented
27C2×C22⋊C4×C37C2213yes—
28C2×C42×C37C2211yescharacteristic, complemented
29C24×C37C2311yescharacteristic
30C23×D37—46no—
31C23×D37C2311yescharacteristic
32C23×D37C2311yescharacteristic
33C23×D37C2313yes—
34C23×D37C2314yes—
35C22×C4×C37C2313yes—
36C22×C4×C37C2313yes—
37C2×C22⋊D37—46no—
38C2×C22⋊D37C23112yes—
39C22×Dic37C2313yes—
40C2×D148—46no—
41C2×D148—46no—
42C2×D148—46no—
43C2×D148C23112yes—
44C2×D148C23112yes—
45C2×D148C23112yescomplemented
46C2×C4×D37—46no—
47C2×C4×D37C23112yescomplemented
48C4⋊C4×C37C23112yescomplemented
49C22⋊C4×C37C23112yes—
50C42×C37C2314yescomplemented
51#10596938C23112yes—
52#10596938C23112yes—
53#10596938C23112yescomplemented
54#10596936C23112yescomplemented
55C23×C37—26no—
56C23×C37C2412yes—
57C23×C37C2411yescharacteristic
58C22×D37—26no—
59C22×D37—26no—
60C22×D37—26no—
61C22×D37—26no—
62C22×D37—26no—
63C22×D37—412no—
64C22×D37—416no—
65C22×D37C2412yes—
66C22×D37C2412yes—
67C22×D37C2416yes—
68C2×C4×C37—26no—
69C2×C4×C37—26no—
70C2×C4×C37C2416yes—
71C2×C4×C37C2416yes—
72C22⋊D37—412no—
73C2×Dic37—26no—
74C2×Dic37C2416yes—
75D148—412no—
76D148—412no—
77D148—412no—
78C4×D37—412no—
79C22×C37—26no—
80C22×C37—44no—
81C22×C37H(5,𝔽2)16yes—
82C22×C37C2511yescharacteristic
83C2×D37—26no—
84C2×D37—26no—
85C2×D37—26no—
86C2×D37—26no—
87C2×D37—26no—
88C2×D37—416no—
89C2×D37—412no—
90C2×D37—44no—
91C2×D37—44no—
92C4×C37—26no—
93C4×C37—26no—
94Dic37—26no—
95C2×#560—371nomaximal, Sylow
96C2×C37—42no—
97C2×C37#56014yescomplemented
98C2×C37C2×H(5,𝔽2)13yes—
99D37—46no—
100D37—42no—
101D37—42no—
102#560—3716no—
103C2×#127—371no—
104C2×#126—371no—
105C2×#126D3711yescharacteristic, complemented
106C2×#123—373no—
107C2×#121—373no—
108C2×#121—373no—
109C2×#120—373no—
110C37C2×#56011yescharacteristic, complemented, Sylow
111C25—371no—
112C22×D4—373no—
113C22×D4—373no—
114C22×D4—373no—
115C22×D4—373no—
116C23×C4—373no—
117#127—378no—
118#126—378no—
119#126C2×D3718yescomplemented
120#123—3724no—
121#121—3724no—
122#121—3724no—
123#120—3724no—
124C2×C4⋊C4—373no—
125C2×C4⋊C4C2×D3713yescomplemented
126C2×C22⋊C4—373no—
127C2×C22⋊C4—373no—
128C2×C22⋊C4—373no—
129C2×C22⋊C4C2×D3713yes—
130C2×C42C2×D3711yescharacteristic, complemented
131C24—371no—
132C24—371no—
133C24—373no—
134C24—374no—
135C24—1486no—
136C24C22×D3711yescharacteristic
137C2×D4—3712no—
138C2×D4—3712no—
139C2×D4—3712no—
140C2×D4—3712no—
141C2×D4—1486no—
142C2×D4—1486no—
143C2×D4—1486no—
144C2×D4—1486no—
145C22×C4—373no—
146C22×C4—3712no—
147C22×C4—1486no—
148C22×C4C22×D3713yes—
149C22×C4C22×D3713yes—
150C4⋊C4—3712no—
151C4⋊C4C22×D37112yescomplemented
152C22⋊C4—3712no—
153C22⋊C4—3712no—
154C22⋊C4—3712no—
155C22⋊C4C22×D37112yes—
156C42C22×D3714yescomplemented
157C23—26no—
158C23—372no—
159C23—372no—
160C23—376no—
161C23—746no—
162C23—746no—
163C23—746no—
164C23—746no—
165C23—746no—
166C23—14812no—
167C23—14816no—
168C23C23×D3712yes—
169C23C23×D3711yescharacteristic
170D4—14812no—
171D4—14812no—
172D4—14812no—
173D4—14812no—
174C2×C4—26no—
175C2×C4—26no—
176C2×C4—376no—
177C2×C4—746no—
178C2×C4—14812no—
179C2×C4C23×D3716yes—
180C2×C4C23×D3716yes—
181C22—26no—
182C22—44no—
183C22—746no—
184C22—746no—
185C22—746no—
186C22—746no—
187C22—746no—
188C22—14816no—
189C22—1484no—
190C22—1484no—
191C22—14812no—
192C22#1192458216yes—
193C22C24×D3711yescharacteristic
194C4—26no—
195C4—26no—
196C4—746no—
197C2—42no—
198C2—1482no—
199C2—1482no—
200C2—1486no—
201C2#1455827414yesdirect product factor
202C2C2×#1192458213yes—
subgroupG/H
centerC23C23×D37
commutator, cosocleC22×C37C25
FrattiniC22C24×D37
FittingC2×#126×C37C2
socleC23×C37C24
hypercenterC2×#126D37
hypocenterC37C2×#560
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #14558274C2direct (N × H)
2. C2×#11924533C2semidirect
3. C2×#11924530C2semidirect
4. C2×#11924521C2semidirect
5. C2×#11924511C2semidirect
6. C2×#11924509C2semidirect
7. C2×#11924506C2semidirect
8. C2×#126×C37C2semidirect
12. C22×D148C22semidirect
14. C22×C4×D37C22semidirect
15. #11924533C22semidirect
16. #11924530C22semidirect
17. #11924521C22semidirect
18. #11924511C22semidirect
19. #11924509C22semidirect
20. #11924506C22semidirect
21. C2×#10596936C22semidirect
24. C2×#10596938C22semidirect
25. #126×C37C22semidirect
26. C2×C4⋊C4×C37C22semidirect
28. C2×C42×C37C22semidirect
45. C2×D148C23semidirect
47. C2×C4×D37C23semidirect
48. C4⋊C4×C37C23semidirect
50. C42×C37C23semidirect
53. #10596938C23semidirect
54. #10596936C23semidirect
97. C2×C37#560semidirect
105. C2×#126D37semidirect
110. C37C2×#560semidirect
119. #126C2×D37semidirect
125. C2×C4⋊C4C2×D37semidirect
130. C2×C42C2×D37semidirect
151. C4⋊C4C22×D37semidirect
156. C42C22×D37semidirect
201. C2#14558274direct (N × H)

Maximal subgroups

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

subgroupindex
#145582742
C2×#119245332
C2×#119245302
C2×#119245212
C2×#119245112
C2×#119245092
C2×#119245062
C2×#126×C372
C2×#56037