Finite Group Databasebeta

← #28403986

Subgroups — #28403986

Order 14464.

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#20299197C216yesmaximal, complemented
2#20299188C216yesmaximal, complemented
3#20299160C213yesmaximal, complemented
4#20299134C216yesmaximal, complemented
5#20299111C216yesmaximal, complemented
6C2×#16813582C213yesmaximal, complemented
7#543×C113C211yesmaximal, characteristic, complemented
8C2×#14268648C2212yescomplemented
9C22×C22⋊D113C2213yes—
10C23×Dic113C2211yescharacteristic
11C22×C4×D113C2213yescomplemented
12#16813617C22112yescomplemented
13#16813613C2216yescomplemented
14#16813611C2216yescomplemented
15#16813607C22112yescomplemented
16#16813606C22112yescomplemented
17#16813598C2216yescomplemented
18#16813597C2216yescomplemented
19#16813596C2216yes—
20#16813596C2216yes—
21#16813592C22112yescomplemented
22Q8×Dic113C2212yescomplemented
23#16813584C2216yescomplemented
24#16813582C22112yescomplemented
25#16813582C22112yescomplemented
26#16813580C2216yescomplemented
27C2×#14268626C2213yescomplemented
28C2×#14268624C2213yescomplemented
29C2×C4×Dic113C2213yescomplemented
30C22⋊Q8×C113C2216yescomplemented
31C22⋊Q8×C113C2216yescomplemented
32C2×C22⋊C4×C113C2213yes—
33C23×D113C2313yes—
34#14268648—44no—
35C2×D452C2316yes—
36C2×D452C2316yes—
37C2×C22⋊D113—212no—
38C2×C22⋊D113C23112yes—
39C22×Dic113—42no—
40C22×Dic113C2313yes—
41C22×Dic113C2313yes—
42C22×Dic113C2313yes—
43C2×C4×D113—46no—
44C2×C4×D113C2316yes—
45C2×C4×D113C2316yes—
46C4⋊Dic113C2316yes—
47C4⋊Dic113C2316yes—
48#14268626C23112yes—
49#14268624C23112yes—
50#14268624C23112yes—
51#14268624C23112yes—
52C4×Dic113C2316yes—
53C4×Dic113C2316yes—
54C24×C113C2311yescharacteristic
55C2×Q8×C113C2312yes—
56C2×Q8×C113C2312yes—
57C22×C4×C113C2313yes—
58C22×C4×C113C2313yes—
59C4⋊C4×C113C2316yes—
60C4⋊C4×C113C2316yes—
61C22⋊C4×C113C23112yes—
62C23×C113—41no—
63C23×C113—41no—
64C23×C113#4114yescomplemented
65C23×C113C2413yes—
66C22×D113—26no—
67C22×D113—43no—
68C22×D113—43no—
69C22×D113C2416yes—
70Q8×C113—42no—
71Q8×C113—42no—
72C2×C4×C113—43no—
73C2×C4×C113—43no—
74C2×C4×C113C2416yes—
75C2×C4×C113C2416yes—
76C22⋊D113—224no—
77C2×Dic113—26no—
78C2×Dic113—26no—
79C2×Dic113—43no—
80C2×Dic113C2413yes—
81C2×Dic113C2416yes—
82C2×Dic113C2411yescharacteristic
83D452—46no—
84D452—46no—
85C4×D113—212no—
86C4×D113—46no—
87C22×C113—23no—
88C22×C113—23no—
89C22×C113—44no—
90C22×C113C2×#4116yes—
91C22×C113C2511yescharacteristic
92C2×D113—26no—
93C2×D113—26no—
94C2×D113—26no—
95C2×D113—412no—
96C4×C113—26no—
97C4×C113—26no—
98Dic113—26no—
99Dic113—23no—
100Dic113H(5,𝔽2)12yes—
101C2×C113—26no—
102C2×C113C22×#4111yescharacteristic
103C2×C113C2×H(5,𝔽2)11yescharacteristic
104C2×C113#58511yescharacteristic
105D113—46no—
106#3459—1131nomaximal, Sylow
107C113#345911yescharacteristic, complemented, Sylow
108#543D11311yescharacteristic, complemented
109#539—1136no—
110#538—1136no—
111#534—1133no—
112#529—1136no—
113#525—1136no—
114C2×C4×D4—1133no—
115C2×#41—1132no—
116C22×D4—1133no—
117C23×C4—1131no—
118C23×C4—1133no—
119#126—11312no—
120#125—1136no—
121#124—1136no—
122#123—11312no—
123#123—11312no—
124C22⋊Q8—1136no—
125C22⋊Q8C2×D11316yescomplemented
126C22⋊Q8C2×D11316yescomplemented
127#121—1136no—
128#121—1136no—
129#121—1136no—
130#120—11312no—
131C4×Q8—1132no—
132C4×D4—1136no—
133C4×D4—11312no—
134C4×D4—11312no—
135#117—1136no—
136C2×C4⋊C4—1133no—
137C2×C22⋊C4—1133no—
138C2×C22⋊C4C2×D11313yes—
139C2×C42—1133no—
140C24—1133no—
141C24C22×D11311yescharacteristic
142#41—4524no—
143C2×Q8C22×D11312yes—
144C2×Q8C22×D11312yes—
145C2×D4—11312no—
146C2×D4—1136no—
147C2×D4—1136no—
148C2×D4—22612no—
149C22×C4—1133no—
150C22×C4—1133no—
151C22×C4—1133no—
152C22×C4—1136no—
153C22×C4—1136no—
154C22×C4—4526no—
155C22×C4—4522no—
156C22×C4C22×D11313yes—
157C22×C4C22×D11313yes—
158C4⋊C4—11312no—
159C4⋊C4—1136no—
160C4⋊C4—1136no—
161C4⋊C4C22×D11316yes—
162C4⋊C4C22×D11316yes—
163C22⋊C4—11312no—
164C22⋊C4—11312no—
165C22⋊C4—11312no—
166C22⋊C4C22×D113112yes—
167C42—1136no—
168C42—1136no—
169C23—41no—
170C23—41no—
171C23—1136no—
172C23—4523no—
173C23—4523no—
174C23—2266no—
175C23#1426864814yescomplemented
176C23C23×D11313yes—
177Q8—42no—
178Q8—42no—
179D4—4526no—
180D4—4526no—
181D4—22624no—
182C2×C4—43no—
183C2×C4—43no—
184C2×C4—1131no—
185C2×C4—1136no—
186C2×C4—1133no—
187C2×C4—4526no—
188C2×C4—4523no—
189C2×C4—22612no—
190C2×C4—2266no—
191C2×C4—2266no—
192C2×C4C23×D11316yes—
193C2×C4C23×D11316yes—
194C22—23no—
195C22—23no—
196C22—44no—
197C22—45212no—
198C22—2266no—
199C22—2266no—
200C22—2266no—
201C22C2×#1426864816yes—
202C22C24×D11311yescharacteristic
203C4—26no—
204C4—26no—
205C4—1132no—
206C4—2266no—
207C4—2263no—
208C2—26no—
209C2—4526no—
210C2C22×#1426864811yescharacteristic
211C2H(5,𝔽2)×D11311yescharacteristic
212C2#2029943311yescharacteristic
subgroupG/H
center, FrattiniC22C24×D113
commutator, socle, cosocleC22×C113C25
Fitting#543×C113C2
hypercenter#543D113
hypocenterC113#3459
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ #543

Complements

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

NH ≅ G/Ntype
1. #20299197C2semidirect
2. #20299188C2semidirect
3. #20299160C2semidirect
4. #20299134C2semidirect
5. #20299111C2semidirect
6. C2×#16813582C2semidirect
7. #543×C113C2semidirect
8. C2×#14268648C22semidirect
11. C22×C4×D113C22semidirect
12. #16813617C22semidirect
13. #16813613C22semidirect
14. #16813611C22semidirect
15. #16813607C22semidirect
16. #16813606C22semidirect
17. #16813598C22semidirect
18. #16813597C22semidirect
21. #16813592C22semidirect
22. Q8×Dic113C22semidirect
23. #16813584C22semidirect
24. #16813582C22semidirect
25. #16813582C22semidirect
26. #16813580C22semidirect
27. C2×#14268626C22semidirect
28. C2×#14268624C22semidirect
29. C2×C4×Dic113C22semidirect
30. C22⋊Q8×C113C22semidirect
31. C22⋊Q8×C113C22semidirect
64. C23×C113#41semidirect
107. C113#3459semidirect
108. #543D113semidirect
125. C22⋊Q8C2×D113semidirect
126. C22⋊Q8C2×D113semidirect
175. C23#14268648semidirect

Maximal subgroups

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

subgroupindex
#202991972
#202991882
#202991602
#202991342
#202991112
C2×#168135822
#543×C1132
#3459113