Finite Group Databasebeta

← #28402010

Subgroups — #28402010

Order 14464.

370 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 109 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#20299201C212yesmaximal, complemented
2#20298900C212yesmaximal, complemented
3#20298897C212yesmaximal, complemented
4#20298851C211yesmaximal, characteristic, complemented
5#20298832C212yesmaximal, complemented
6#20298792C212yesmaximal, complemented
7#20298791C212yesmaximal, complemented
8#20298626C211yesmaximal, characteristic, complemented
9#469×C113C211yesmaximal, characteristic, complemented
10C2×D904C2211yescharacteristic
11C2×#14268632C2212yes—
12C22×#11744751C2211yescharacteristic
13#16813618C2212yes—
14#16813613C2212yes—
15#16813606—22no—
16#16813604—22no—
17#16813596C2212yes—
18#16813594—22no—
19#16813593—22no—
20D4×Dic113C2212yes—
21#16813584C2212yes—
22#16813581C2211yescharacteristic
23#16813555C2212yes—
24#16813554C2211yescharacteristic
25#16813551C2212yes—
26#16813551C2212yes—
27#16813544C2212yes—
28#16813543C2212yes—
29#16813542C2212yes—
30C2×D8×C113C2211yescharacteristic
31C2×M16×C113C2211yescharacteristic
32#121×C113C2212yes—
33#106×C113C2211yescharacteristic
34#102×C113C2212yes—
35C2×D452C2312yes—
36C2×C22⋊D113—22no—
37C2×C22⋊D113—22no—
38C2×C22⋊D113—22no—
39C22×Dic113—22no—
40C2×C4×D113—22no—
41D904—41no—
42#14268632—42no—
43C2×#11744751—41no—
44C2×#11744751C2312yes—
45C4⋊Dic113—22no—
46C4⋊Dic113D412yes—
47C4⋊Dic113C2312yes—
48#14268626—22no—
49C22⋊Dic113—22no—
50C22⋊Dic113D411yescharacteristic
51C22⋊Dic113D411yescharacteristic
52#14268624—22no—
53#14268624—22no—
54C4×Dic113C2312yes—
55C2×D4×C113—22no—
56C2×D4×C113C2312yes—
57C22×C4×C113C2311yescharacteristic
58D8×C113—41no—
59M16×C113—41no—
60C2×C8×C113C2311yescharacteristic
61C2×C8×C113C2311yescharacteristic
62C4⋊C4×C113C2312yes—
63C22⋊C4×C113—22no—
64C23×C113—22no—
65C23×C113C2×D411yescharacteristic
66C22×D113—22no—
67D4×C113—22no—
68D4×C113—22no—
69D4×C113—82no—
70C2×C4×C113—21no—
71C2×C4×C113—21no—
72C2×C4×C113—22no—
73C2×C4×C113C2×D411yescharacteristic
74C2×C4×C113C2411yescharacteristic
75C22⋊D113—82no—
76C22⋊D113—82no—
77C22⋊D113—82no—
78C2×Dic113—22no—
79C2×Dic113—82no—
80C2×Dic113C2×D412yes—
81C2×Dic113C2×D412yes—
82D452—22no—
83D452—22no—
84C4×D113—82no—
85C8×C113—21no—
86C8×C113—21no—
87#11744751—22no—
88C22×C113—21no—
89C22×C113—22no—
90C22×C113—42no—
91C22×C113—42no—
92C22×C113—42no—
93C22×C113C22×D411yescharacteristic
94C2×D113—42no—
95C2×D113—42no—
96C2×D113—42no—
97C4×C113—21no—
98C4×C113—42no—
99C4×C113H(5,𝔽2)11yescharacteristic
100C4×C1132−1+411yescharacteristic
101Dic113—22no—
102Dic113—22no—
103Dic113—42no—
104C2×C113—41no—
105C2×C113—82no—
106C2×C113#53711yescharacteristic
107C2×C113#57612yes—
108D113—82no—
109#3259—1131nomaximal, Sylow
110C113#325911yescharacteristic, complemented, Sylow
111#540—1132no—
112#478—1132no—
113#478—1132no—
114#469—1131no—
115#469D11311yescharacteristic, complemented
116#466—1132no—
117#459—1132no—
118#459—1132no—
119#424—1131no—
120C2×D8—1132no—
121C2×D8—1131no—
122C2×D8C2×D11311yescharacteristic
123C2×M16C2×D11311yescharacteristic
124C22×C8—1131no—
125#127—1132no—
126#125—1132no—
127#123—2262no—
128#123—2262no—
129#121—1132no—
130#121—2262no—
131#121—2262no—
132#121C2×D11312yes—
133C4×D4—1132no—
134C4×D4—1132no—
135#117—1131no—
136#107—1132no—
137#106—1131no—
138#106C2×D11311yescharacteristic
139C4⋊C8—1132no—
140C4⋊C8—1132no—
141#102—1132no—
142#102—1132no—
143#102—1132no—
144#102C2×D11312yes—
145C2×D4—22no—
146C2×D4—1132no—
147C2×D4—2262no—
148C2×D4—2262no—
149C2×D4—2262no—
150C2×D4C22×D11312yes—
151C22×C4—2262no—
152C22×C4—2262no—
153C22×C4C22×D11311yescharacteristic
154D8—41no—
155D8—4521no—
156D8—4522no—
157M16—41no—
158C2×C8—1132no—
159C2×C8—4521no—
160C2×C8C22×D11311yescharacteristic
161C2×C8C22×D11311yescharacteristic
162C4⋊C4—1132no—
163C4⋊C4—1132no—
164C4⋊C4—2262no—
165C4⋊C4—2262no—
166C4⋊C4C22×D11312yes—
167C22⋊C4—22no—
168C22⋊C4—1131no—
169C22⋊C4—1131no—
170C22⋊C4—2262no—
171C22⋊C4—2262no—
172C22⋊C4—2262no—
173C42—1132no—
174C23—22no—
175C23—2262no—
176C23D4×D11311yescharacteristic
177D4—22no—
178D4—22no—
179D4—82no—
180D4—9042no—
181D4—9042no—
182D4—9042no—
183D4—2262no—
184D4—2262no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—1132no—
189C2×C4—1132no—
190C2×C4—9042no—
191C2×C4—9042no—
192C2×C4—2262no—
193C2×C4D4×D11311yescharacteristic
194C2×C4C23×D11311yescharacteristic
195C8—21no—
196C8—21no—
197C8—2262no—
198C22—22no—
199C22—21no—
200C22—42no—
201C22—42no—
202C22—42no—
203C22—4522no—
204C22—4522no—
205C22—4522no—
206C22C2×D4×D11311yescharacteristic
207C4—21no—
208C4—42no—
209C4—4522no—
210C4—2262no—
211C4—2262no—
212C4#1681366711yescharacteristic
213C4#1681366911yescharacteristic
214C2—41no—
215C2—82no—
216C2—9042no—
217C2#2029917511yescharacteristic
218C2#2029940212yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#469×C113C2
socleC22×C113C22×D4
hypercenter#469D113
hypocenterC113#3259
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #20299201C2semidirect
2. #20298900C2semidirect
3. #20298897C2semidirect
4. #20298851C2semidirect
5. #20298832C2semidirect
6. #20298792C2semidirect
7. #20298791C2semidirect
8. #20298626C2semidirect
9. #469×C113C2semidirect
110. C113#3259semidirect
115. #469D113semidirect

Maximal subgroups

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

subgroupindex
#202992012
#202989002
#202988972
#202988512
#202988322
#202987922
#202987912
#202986262
#469×C1132
#3259113