Finite Group Databasebeta

← #18008008

Subgroups — #18008008

Order 4736.

1160 conjugacy classes of subgroups; only the 471 normal subgroups are shown.

normal subgroups only

This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 471 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#14558132C216yesmaximal, complemented
2#14558123C216yesmaximal, complemented
3#14558095C213yesmaximal, complemented
4#14558069C216yesmaximal, complemented
5#14558046C216yesmaximal, complemented
6C2×#11924496C213yesmaximal, complemented
7C37×#543C211yesmaximal, characteristic, complemented
8C2×#10596966C2212yescomplemented
9C22×C22⋊D37C2213yes—
10C23×Dic37C2211yescharacteristic
11C22×C4×D37C2213yescomplemented
12#11924531C22112yescomplemented
13#11924527C2216yescomplemented
14#11924525C2216yescomplemented
15#11924521C22112yescomplemented
16#11924520C22112yescomplemented
17#11924512C2216yescomplemented
18#11924511C2216yescomplemented
19#11924510C2216yes—
20#11924510C2216yes—
21#11924506C22112yescomplemented
22Q8×Dic37C2212yescomplemented
23#11924498C2216yescomplemented
24#11924496C22112yescomplemented
25#11924496C22112yescomplemented
26#11924494C2216yescomplemented
27C2×#10596936C2213yescomplemented
28C2×#10596938C2213yescomplemented
29C2×C4×Dic37C2213yescomplemented
30C22⋊Q8×C37C2216yescomplemented
31C22⋊Q8×C37C2216yescomplemented
32C2×C22⋊C4×C37C2213yes—
33C24×C37C2311yescharacteristic
34C23×D37C2313yes—
35C2×Q8×C37C2312yes—
36C2×Q8×C37C2312yes—
37C22×C4×C37C2313yes—
38C22×C4×C37C2313yes—
39C2×C22⋊D37—212no—
40C2×C22⋊D37C23112yes—
41C22×Dic37—42no—
42C22×Dic37C2313yes—
43C22×Dic37C2313yes—
44C22×Dic37C2313yes—
45#10596966—44no—
46C2×D148C2316yes—
47C2×D148C2316yes—
48C2×C4×D37—46no—
49C2×C4×D37C2316yes—
50C2×C4×D37C2316yes—
51C4⋊C4×C37C2316yes—
52C4⋊C4×C37C2316yes—
53C22⋊C4×C37C23112yes—
54#10596938C23112yes—
55#10596938C23112yes—
56#10596938C23112yes—
57C4⋊Dic37C2316yes—
58C4⋊Dic37C2316yes—
59#10596936C23112yes—
60C4×Dic37C2316yes—
61C4×Dic37C2316yes—
62C23×C37—41no—
63C23×C37—41no—
64C23×C37#4114yescomplemented
65C23×C37C2413yes—
66C22×D37—26no—
67C22×D37—43no—
68C22×D37—43no—
69C22×D37C2416yes—
70Q8×C37—42no—
71Q8×C37—42no—
72C2×C4×C37—43no—
73C2×C4×C37—43no—
74C2×C4×C37C2416yes—
75C2×C4×C37C2416yes—
76C22⋊D37—224no—
77C2×Dic37—26no—
78C2×Dic37—26no—
79C2×Dic37—43no—
80C2×Dic37C2413yes—
81C2×Dic37C2416yes—
82C2×Dic37C2411yescharacteristic
83D148—46no—
84D148—46no—
85C4×D37—212no—
86C4×D37—46no—
87C22×C37—23no—
88C22×C37—23no—
89C22×C37—44no—
90C22×C37C2×#4116yes—
91C22×C37C2511yescharacteristic
92C2×D37—26no—
93C2×D37—26no—
94C2×D37—26no—
95C2×D37—412no—
96C4×C37—26no—
97C4×C37—26no—
98Dic37—26no—
99Dic37—23no—
100Dic37H(5,𝔽2)12yes—
101#3459—371nomaximal, Sylow
102C2×C37—26no—
103C2×C37C22×#4111yescharacteristic
104C2×C37C2×H(5,𝔽2)11yescharacteristic
105C2×C37#58511yescharacteristic
106D37—46no—
107#543D3711yescharacteristic, complemented
108#539—376no—
109#538—376no—
110#534—373no—
111#529—376no—
112#525—376no—
113C2×C4×D4—373no—
114C37#345911yescharacteristic, complemented, Sylow
115C2×#41—372no—
116C22×D4—373no—
117C23×C4—371no—
118C23×C4—373no—
119#126—3712no—
120#125—376no—
121#124—376no—
122#123—3712no—
123#123—3712no—
124C22⋊Q8—376no—
125C22⋊Q8C2×D3716yescomplemented
126C22⋊Q8C2×D3716yescomplemented
127#121—376no—
128#121—376no—
129#121—376no—
130#120—3712no—
131C4×Q8—372no—
132C4×D4—376no—
133C4×D4—3712no—
134C4×D4—3712no—
135#117—376no—
136C2×C4⋊C4—373no—
137C2×C22⋊C4—373no—
138C2×C22⋊C4C2×D3713yes—
139C2×C42—373no—
140C24—373no—
141C24C22×D3711yescharacteristic
142#41—1484no—
143C2×Q8C22×D3712yes—
144C2×Q8C22×D3712yes—
145C2×D4—3712no—
146C2×D4—376no—
147C2×D4—376no—
148C2×D4—7412no—
149C22×C4—373no—
150C22×C4—373no—
151C22×C4—373no—
152C22×C4—376no—
153C22×C4—376no—
154C22×C4—1486no—
155C22×C4—1482no—
156C22×C4C22×D3713yes—
157C22×C4C22×D3713yes—
158C4⋊C4—3712no—
159C4⋊C4—376no—
160C4⋊C4—376no—
161C4⋊C4C22×D3716yes—
162C4⋊C4C22×D3716yes—
163C22⋊C4—3712no—
164C22⋊C4—3712no—
165C22⋊C4—3712no—
166C22⋊C4C22×D37112yes—
167C42—376no—
168C42—376no—
169C23—41no—
170C23—41no—
171C23—376no—
172C23—746no—
173C23—1483no—
174C23—1483no—
175C23#1059696614yescomplemented
176C23C23×D3713yes—
177Q8—42no—
178Q8—42no—
179D4—7424no—
180D4—1486no—
181D4—1486no—
182C2×C4—43no—
183C2×C4—43no—
184C2×C4—371no—
185C2×C4—376no—
186C2×C4—373no—
187C2×C4—7412no—
188C2×C4—746no—
189C2×C4—746no—
190C2×C4—1486no—
191C2×C4—1483no—
192C2×C4C23×D3716yes—
193C2×C4C23×D3716yes—
194C22—23no—
195C22—23no—
196C22—44no—
197C22—746no—
198C22—746no—
199C22—746no—
200C22—14812no—
201C22C2×#1059696616yes—
202C22C24×D3711yescharacteristic
203C4—26no—
204C4—26no—
205C4—372no—
206C4—746no—
207C4—743no—
208C2—26no—
209C2—1486no—
210C2C22×#1059696611yescharacteristic
211C2H(5,𝔽2)×D3711yescharacteristic
212C2#1455836811yescharacteristic
subgroupG/H
center, FrattiniC22C24×D37
commutator, socle, cosocleC22×C37C25
FittingC37×#543C2
hypercenter#543D37
hypocenterC37#3459
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ #543

Complements

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

NH ≅ G/Ntype
1. #14558132C2semidirect
2. #14558123C2semidirect
3. #14558095C2semidirect
4. #14558069C2semidirect
5. #14558046C2semidirect
6. C2×#11924496C2semidirect
7. C37×#543C2semidirect
8. C2×#10596966C22semidirect
11. C22×C4×D37C22semidirect
12. #11924531C22semidirect
13. #11924527C22semidirect
14. #11924525C22semidirect
15. #11924521C22semidirect
16. #11924520C22semidirect
17. #11924512C22semidirect
18. #11924511C22semidirect
21. #11924506C22semidirect
22. Q8×Dic37C22semidirect
23. #11924498C22semidirect
24. #11924496C22semidirect
25. #11924496C22semidirect
26. #11924494C22semidirect
27. C2×#10596936C22semidirect
28. C2×#10596938C22semidirect
29. C2×C4×Dic37C22semidirect
30. C22⋊Q8×C37C22semidirect
31. C22⋊Q8×C37C22semidirect
64. C23×C37#41semidirect
107. #543D37semidirect
114. C37#3459semidirect
125. C22⋊Q8C2×D37semidirect
126. C22⋊Q8C2×D37semidirect
175. C23#10596966semidirect

Maximal subgroups

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

subgroupindex
#145581322
#145581232
#145580952
#145580692
#145580462
C2×#119244962
C37×#5432
#345937