Finite Group Databasebeta

← #28402009

Subgroups — #28402009

Order 14464.

370 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 117 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#20299203C211yesmaximal, characteristic, complemented
2#20298898C212yesmaximal, complemented
3#20298895C212yesmaximal, complemented
4#20298849C212yesmaximal, complemented
5#20298832C212yesmaximal, complemented
6#20298793C212yesmaximal, complemented
7#20298790C212yesmaximal, complemented
8#20298625C211yesmaximal, characteristic, complemented
9#540×C113C211yesmaximal, characteristic, complemented
10C2×#14268632C2212yes—
11C2×#14268632C2212yes—
12C2×#14268631C2211yescharacteristic
13C22×#11744751C2211yescharacteristic
14#16813619C2211yescharacteristic
15#16813614C2211yescharacteristic
16#16813607—22no—
17#16813596C2212yes—
18#16813595—22no—
19C4×D452C2212yes—
20#16813555C2212yes—
21#16813553C2212yes—
22C4⋊#11744751C2212yes—
23C4⋊#11744751C2212yes—
24#16813543C2212yes—
25#16813543C2212yes—
26#16813542C2212yes—
27#16813542C2212yes—
28#127×C113C2211yescharacteristic
29#125×C113C2211yescharacteristic
30#123×C113—22no—
31#121×C113—22no—
32#121×C113C2212yes—
33C4×D4×C113C2212yes—
34#117×C113C2211yescharacteristic
35C2×D452—22no—
36C2×D452C2312yes—
37C2×C22⋊D113—22no—
38C2×C4×D113—22no—
39#14268632—42no—
40#14268632—42no—
41#14268631—41no—
42C2×#11744751—41no—
43C2×#11744751C2312yes—
44C2×#11744751C2312yes—
45C4⋊Dic113C2312yes—
46#14268626—22no—
47#14268624—22no—
48#14268624—22no—
49C2×D4×C113—22no—
50C2×D4×C113—22no—
51C2×D4×C113C2312yes—
52C22×C4×C113—22no—
53C22×C4×C113C2311yescharacteristic
54C4⋊C4×C113—22no—
55C4⋊C4×C113D412yes—
56C4⋊C4×C113C2312yes—
57C22⋊C4×C113—22no—
58C22⋊C4×C113—22no—
59C22⋊C4×C113D412yes—
60C42×C113C2311yescharacteristic
61C42×C113C2311yescharacteristic
62C23×C113—22no—
63C23×C113C2×D411yescharacteristic
64C22×D113—22no—
65D4×C113—22no—
66D4×C113—22no—
67D4×C113—82no—
68D4×C113—82no—
69C2×C4×C113—21no—
70C2×C4×C113—21no—
71C2×C4×C113—22no—
72C2×C4×C113—82no—
73C2×C4×C113C2×D412yes—
74C2×C4×C113C2×D412yes—
75C2×C4×C113C2×D411yescharacteristic
76C2×C4×C113C2411yescharacteristic
77C22⋊D113—82no—
78C2×Dic113—22no—
79D452—22no—
80D452—22no—
81D452—82no—
82C4×D113—82no—
83#11744751—22no—
84#11744751—22no—
85C22×C113—21no—
86C22×C113—22no—
87C22×C113—42no—
88C22×C113—42no—
89C22×C113—42no—
90C22×C113C22×D411yescharacteristic
91C2×D113—42no—
92C2×D113—42no—
93C2×D113—42no—
94C4×C113—21no—
95C4×C113—22no—
96C4×C113—22no—
97C4×C113—42no—
98C4×C113H(5,𝔽2)11yescharacteristic
99C4×C1132−1+411yescharacteristic
100Dic113—42no—
101C2×C113—41no—
102C2×C113—82no—
103C2×C113#53711yescharacteristic
104C2×C113#57612yes—
105D113—82no—
106#3259—1131nomaximal, Sylow
107C113#325911yescharacteristic, complemented, Sylow
108#540—1131no—
109#540D11311yescharacteristic, complemented
110#478—1132no—
111#478—1132no—
112#469—1132no—
113#466—1132no—
114#459—1132no—
115#459—1132no—
116#424—1131no—
117C2×D8—1132no—
118C2×D8—1132no—
119C2×M16—1131no—
120C22×C8—1131no—
121#127—1131no—
122#127C2×D11311yescharacteristic
123#125—1131no—
124#125C2×D11311yescharacteristic
125#123—22no—
126#123—2262no—
127#121—22no—
128#121—1132no—
129#121—2262no—
130#121C2×D11312yes—
131C4×D4—1132no—
132C4×D4C2×D11312yes—
133#117C2×D11311yescharacteristic
134#107—1132no—
135#106—1132no—
136C4⋊C8—1132no—
137C4⋊C8—1132no—
138#102—1132no—
139#102—1132no—
140#102—1132no—
141#102—1132no—
142C2×D4—22no—
143C2×D4—22no—
144C2×D4—1132no—
145C2×D4—2262no—
146C2×D4—2262no—
147C2×D4C22×D11312yes—
148C22×C4—22no—
149C22×C4—2262no—
150C22×C4C22×D11311yescharacteristic
151D8—4522no—
152D8—4522no—
153M16—4521no—
154C2×C8—1132no—
155C2×C8—1132no—
156C2×C8—4521no—
157C4⋊C4—22no—
158C4⋊C4—1132no—
159C4⋊C4—2262no—
160C4⋊C4C22⋊D11312yes—
161C4⋊C4C22×D11312yes—
162C22⋊C4—22no—
163C22⋊C4—22no—
164C22⋊C4—2262no—
165C22⋊C4—2262no—
166C22⋊C4C22⋊D11312yes—
167C42C22×D11311yescharacteristic
168C42C22×D11311yescharacteristic
169C23—22no—
170C23—2262no—
171C23C2×C22⋊D11311yescharacteristic
172D4—22no—
173D4—22no—
174D4—82no—
175D4—82no—
176D4—9042no—
177D4—9042no—
178D4—2262no—
179D4—2262no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—82no—
184C2×C4—9042no—
185C2×C4—2262no—
186C2×C4C2×C22⋊D11312yes—
187C2×C4C2×C22⋊D11312yes—
188C2×C4C2×C22⋊D11311yescharacteristic
189C2×C4C23×D11311yescharacteristic
190C8—2262no—
191C8—2262no—
192C22—22no—
193C22—21no—
194C22—42no—
195C22—42no—
196C22—42no—
197C22—4522no—
198C22—4522no—
199C22—4522no—
200C22C22×C22⋊D11311yescharacteristic
201C4—22no—
202C4—22no—
203C4—21no—
204C4—42no—
205C4—4522no—
206C4#1681366811yescharacteristic
207C4#1681366911yescharacteristic
208C2—41no—
209C2—82no—
210C2—9042no—
211C2#2029917611yescharacteristic
212C2#2029940112yes—
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#540×C113C2
socleC22×C113C22×D4
hypercenter#540D113
hypocenterC113#3259
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #20299203C2semidirect
2. #20298898C2semidirect
3. #20298895C2semidirect
4. #20298849C2semidirect
5. #20298832C2semidirect
6. #20298793C2semidirect
7. #20298790C2semidirect
8. #20298625C2semidirect
9. #540×C113C2semidirect
107. C113#3259semidirect
109. #540D113semidirect

Maximal subgroups

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

subgroupindex
#202992032
#202988982
#202988952
#202988492
#202988322
#202987932
#202987902
#202986252
#540×C1132
#3259113