Finite Group Databasebeta

← #16859123

Subgroups — #16859123

Order 3968.

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#14521648C216yesmaximal, complemented
2#14521639C216yesmaximal, complemented
3#14521611C213yesmaximal, complemented
4#14521585C216yesmaximal, complemented
5#14521562C216yesmaximal, complemented
6C2×(C22⋊D31)⋊C4C213yesmaximal, complemented
7C31×#543C211yesmaximal, characteristic, complemented
8C22×C22⋊D31C2213yes—
9C23×Dic31C2211yescharacteristic
10C2×#92499C2212yescomplemented
11C22×C4×D31C2213yescomplemented
12C31×C22⋊Q8C2216yescomplemented
13C31×C22⋊Q8C2216yescomplemented
14C2×C22⋊C4×C31C2213yes—
15#11758524C2216yescomplemented
16#11758523C2216yescomplemented
17Q8×Dic31C2212yescomplemented
18#11758507C2216yes—
19#11758507C2216yes—
20C2×(C2×D31)⋊C4C2213yescomplemented
21C2×Dic31⋊C4C2213yescomplemented
22C2×C4×Dic31C2213yescomplemented
23#11758475C22112yescomplemented
24#11758472C2216yescomplemented
25#11758471C22112yescomplemented
26#11758470C2216yescomplemented
27#11758469C2216yescomplemented
28#11758467C2216yescomplemented
29#11758463C22112yescomplemented
30#11758459C22112yescomplemented
31(C22⋊D31)⋊C4C22112yescomplemented
32(C22⋊D31)⋊C4C22112yescomplemented
33C24×C31C2311yescharacteristic
34C23×D31C2313yes—
35C2×Q8×C31C2312yes—
36C2×Q8×C31C2312yes—
37C22×C4×C31C2313yes—
38C22×C4×C31C2313yes—
39C2×C22⋊D31—212no—
40C2×C22⋊D31C23112yes—
41C22×Dic31—42no—
42C22×Dic31C2313yes—
43C22×Dic31C2313yes—
44C22×Dic31C2313yes—
45#92499—44no—
46C2×D124C2316yes—
47C2×D124C2316yes—
48C2×C4×D31—46no—
49C2×C4×D31C2316yes—
50C2×C4×D31C2316yes—
51C4⋊C4×C31C2316yes—
52C4⋊C4×C31C2316yes—
53C22⋊C4×C31C23112yes—
54(C2×D31)⋊C4C23112yes—
55(C2×D31)⋊C4C23112yes—
56(C2×D31)⋊C4C23112yes—
57C4⋊Dic31C2316yes—
58C4⋊Dic31C2316yes—
59Dic31⋊C4C23112yes—
60C4×Dic31C2316yes—
61C4×Dic31C2316yes—
62C23×C31—41no—
63C23×C31—41no—
64C23×C31#4114yescomplemented
65C23×C31C2413yes—
66C22×D31—26no—
67C22×D31—43no—
68C22×D31—43no—
69C22×D31C2416yes—
70Q8×C31—42no—
71Q8×C31—42no—
72C2×C4×C31—43no—
73C2×C4×C31—43no—
74C2×C4×C31C2416yes—
75C2×C4×C31C2416yes—
76C22⋊D31—224no—
77C2×Dic31—26no—
78C2×Dic31—26no—
79C2×Dic31—43no—
80C2×Dic31C2413yes—
81C2×Dic31C2416yes—
82C2×Dic31C2411yescharacteristic
83D124—46no—
84D124—46no—
85C4×D31—212no—
86C4×D31—46no—
87#3459—311nomaximal, Sylow
88C22×C31—23no—
89C22×C31—23no—
90C22×C31—44no—
91C22×C31C2×#4116yes—
92C22×C31C2511yescharacteristic
93C2×D31—26no—
94C2×D31—26no—
95C2×D31—26no—
96C2×D31—412no—
97C4×C31—26no—
98C4×C31—26no—
99Dic31—26no—
100Dic31—23no—
101Dic31H(5,𝔽2)12yes—
102#543D3111yescharacteristic, complemented
103#539—316no—
104#538—316no—
105#534—313no—
106#529—316no—
107#525—316no—
108C2×C4×D4—313no—
109C2×C31—26no—
110C2×C31C22×#4111yescharacteristic
111C2×C31C2×H(5,𝔽2)11yescharacteristic
112C2×C31#58511yescharacteristic
113D31—46no—
114C2×#41—312no—
115C22×D4—313no—
116C23×C4—311no—
117C23×C4—313no—
118#126—3112no—
119#125—316no—
120#124—316no—
121#123—3112no—
122#123—3112no—
123C22⋊Q8—316no—
124C22⋊Q8C2×D3116yescomplemented
125C22⋊Q8C2×D3116yescomplemented
126#121—316no—
127#121—316no—
128#121—316no—
129#120—3112no—
130C4×Q8—312no—
131C4×D4—316no—
132C4×D4—3112no—
133C4×D4—3112no—
134#117—316no—
135C2×C4⋊C4—313no—
136C2×C22⋊C4—313no—
137C2×C22⋊C4C2×D3113yes—
138C2×C42—313no—
139C31#345911yescharacteristic, complemented, Sylow
140C24—313no—
141C24C22×D3111yescharacteristic
142#41—1244no—
143C2×Q8C22×D3112yes—
144C2×Q8C22×D3112yes—
145C2×D4—3112no—
146C2×D4—316no—
147C2×D4—316no—
148C2×D4—6212no—
149C22×C4—313no—
150C22×C4—313no—
151C22×C4—313no—
152C22×C4—316no—
153C22×C4—316no—
154C22×C4—1246no—
155C22×C4—1242no—
156C22×C4C22×D3113yes—
157C22×C4C22×D3113yes—
158C4⋊C4—3112no—
159C4⋊C4—316no—
160C4⋊C4—316no—
161C4⋊C4C22×D3116yes—
162C4⋊C4C22×D3116yes—
163C22⋊C4—3112no—
164C22⋊C4—3112no—
165C22⋊C4—3112no—
166C22⋊C4C22×D31112yes—
167C42—316no—
168C42—316no—
169C23—41no—
170C23—41no—
171C23—316no—
172C23—626no—
173C23—1243no—
174C23—1243no—
175C23#9249914yescomplemented
176C23C23×D3113yes—
177Q8—42no—
178Q8—42no—
179D4—6224no—
180D4—1246no—
181D4—1246no—
182C2×C4—43no—
183C2×C4—43no—
184C2×C4—311no—
185C2×C4—316no—
186C2×C4—313no—
187C2×C4—6212no—
188C2×C4—626no—
189C2×C4—626no—
190C2×C4—1246no—
191C2×C4—1243no—
192C2×C4C23×D3116yes—
193C2×C4C23×D3116yes—
194C22—23no—
195C22—23no—
196C22—44no—
197C22—626no—
198C22—626no—
199C22—626no—
200C22—12412no—
201C22C2×#9249916yes—
202C22C24×D3111yescharacteristic
203C4—26no—
204C4—26no—
205C4—312no—
206C4—626no—
207C4—623no—
208C2—26no—
209C2—1246no—
210C2C22×#9249911yescharacteristic
211C2H(5,𝔽2)×D3111yescharacteristic
212C2#1452188411yescharacteristic
subgroupG/H
center, FrattiniC22C24×D31
commutator, socle, cosocleC22×C31C25
FittingC31×#543C2
hypercenter#543D31
hypocenterC31#3459
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ #543

Complements

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

NH ≅ G/Ntype
1. #14521648C2semidirect
2. #14521639C2semidirect
3. #14521611C2semidirect
4. #14521585C2semidirect
5. #14521562C2semidirect
6. C2×(C22⋊D31)⋊C4C2semidirect
7. C31×#543C2semidirect
10. C2×#92499C22semidirect
11. C22×C4×D31C22semidirect
12. C31×C22⋊Q8C22semidirect
13. C31×C22⋊Q8C22semidirect
15. #11758524C22semidirect
16. #11758523C22semidirect
17. Q8×Dic31C22semidirect
20. C2×(C2×D31)⋊C4C22semidirect
21. C2×Dic31⋊C4C22semidirect
22. C2×C4×Dic31C22semidirect
23. #11758475C22semidirect
24. #11758472C22semidirect
25. #11758471C22semidirect
26. #11758470C22semidirect
27. #11758469C22semidirect
28. #11758467C22semidirect
29. #11758463C22semidirect
30. #11758459C22semidirect
31. (C22⋊D31)⋊C4C22semidirect
32. (C22⋊D31)⋊C4C22semidirect
64. C23×C31#41semidirect
102. #543D31semidirect
124. C22⋊Q8C2×D31semidirect
125. C22⋊Q8C2×D31semidirect
139. C31#3459semidirect
175. C23#92499semidirect

Maximal subgroups

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

subgroupindex
#145216482
#145216392
#145216112
#145215852
#145215622
C2×(C22⋊D31)⋊C42
C31×#5432
#345931