Finite Group Databasebeta

← #28403660

Subgroups — #28403660

Order 14464.

380 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 113 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#20299331C212yesmaximal, complemented
2#20298986C212yesmaximal, complemented
3#20298982C211yesmaximal, characteristic, complemented
4#20298819C212yesmaximal, complemented
5#20298813C212yesmaximal, complemented
6#20298792C212yesmaximal, complemented
7#20298728C211yesmaximal, characteristic, complemented
8#20298697C212yesmaximal, complemented
9C4×D8×C113C211yesmaximal, characteristic, complemented
10C2×Dic452C2211yescharacteristic
11C2×#14268636C2212yes—
12C2×#14268635C2212yes—
13C2×D904C2211yescharacteristic
14C2×#14268632C2212yes—
15#16813618C2212yes—
16#16813610C2212yes—
17#16813609C2212yes—
18#16813608—22no—
19#16813605—22no—
20#16813604—22no—
21C4×Dic226C2211yescharacteristic
22#16813587C2212yes—
23#16813584C2212yes—
24C4×C22⋊D113—22no—
25C4⋊#11744751C2211yescharacteristic
26#16813551C2212yes—
27#16813545C2212yes—
28#16813542C2212yes—
29#16813532C2212yes—
30C2×D8×C113C2211yescharacteristic
31C4×D4×C113C2212yes—
32#107×C113C2211yescharacteristic
33#102×C113C2212yes—
34C4×C8×C113C2211yescharacteristic
35C2×Dic226D411yescharacteristic
36C2×Dic226C2312yes—
37C2×D452C2312yes—
38C2×C22⋊D113—22no—
39C2×C22⋊D113—22no—
40C2×C4×D113—22no—
41Dic452—41no—
42#14268636—24no—
43#14268635—42no—
44D904—41no—
45#14268632—42no—
46C2×#11744751C2312yes—
47C4⋊Dic113D411yescharacteristic
48#14268626—22no—
49#14268626D412yes—
50C22⋊Dic113—22no—
51C22⋊Dic113—22no—
52#14268624—22no—
53#14268624—22no—
54#14268624—22no—
55C4×Dic113—22no—
56C4×Dic113C2312yes—
57C2×D4×C113C2312yes—
58C22×C4×C113—22no—
59D8×C113—22no—
60C2×C8×C113C2311yescharacteristic
61C2×C8×C113C2311yescharacteristic
62C4⋊C4×C113C2312yes—
63C22⋊C4×C113—22no—
64C42×C113C2311yescharacteristic
65C23×C113—22no—
66C22×D113—22no—
67D4×C113—22no—
68D4×C113—22no—
69C2×C4×C113—22no—
70C2×C4×C113—82no—
71C2×C4×C113C2×D411yescharacteristic
72C2×C4×C113C2×D411yescharacteristic
73C2×C4×C113C2411yescharacteristic
74C22⋊D113—44no—
75C22⋊D113—82no—
76C2×Dic113—22no—
77C2×Dic113C2×D412yes—
78C2×Dic113C2×D412yes—
79D452—22no—
80D452—22no—
81C4×D113—82no—
82Dic226—22no—
83Dic226—22no—
84Dic226—41no—
85C8×C113—21no—
86C8×C113#4112yes—
87#11744751—22no—
88C22×C113—42no—
89C22×C113—42no—
90C22×C113—42no—
91C22×C113C22×D411yescharacteristic
92C2×D113—42no—
93C2×D113—42no—
94C2×D113—42no—
95C4×C113—21no—
96C4×C113—21no—
97C4×C113—42no—
98C4×C113C2×#4111yescharacteristic
99C4×C113H(5,𝔽2)11yescharacteristic
100Dic113—22no—
101Dic113—22no—
102Dic113—42no—
103C2×C113—82no—
104C2×C113#55011yescharacteristic
105C2×C113#57511yescharacteristic
106C2×C113#57611yescharacteristic
107D113—82no—
108#3403—1131nomaximal, Sylow
109C113#340311yescharacteristic, complemented, Sylow
110#559—1132no—
111#496—1132no—
112#495—1131no—
113#464—1132no—
114#463—1132no—
115#459—1132no—
116#446—1131no—
117#440—1132no—
118C4×D8D11311yescharacteristic, complemented
119C2×Q16—1131no—
120C2×SD16—1132no—
121C2×SD16—1132no—
122C2×D8—1132no—
123C2×D8—1131no—
124C2×D8C2×D11311yescharacteristic
125#127—1132no—
126#124—1132no—
127#124—1132no—
128#124—2262no—
129#123—2262no—
130#123—2262no—
131C4×Q8—1131no—
132C4×Q8—1132no—
133C4×D4—1132no—
134C4×D4—2262no—
135C4×D4C2×D11312yes—
136#107C2×D11311yescharacteristic
137C4⋊C8—1132no—
138C4⋊C8—1131no—
139#103—1132no—
140#102—1132no—
141#102C2×D11312yes—
142#97—1132no—
143C4×C8C2×D11311yescharacteristic
144C2×Q8—1131no—
145C2×Q8—1132no—
146C2×D4—1132no—
147C2×D4—2262no—
148C2×D4—2262no—
149C2×D4C22×D11312yes—
150C22×C4—22no—
151C22×C4—2262no—
152Q16—4521no—
153SD16—4522no—
154SD16—2264no—
155D8—22no—
156D8—4521no—
157D8—4522no—
158C2×C8—1132no—
159C2×C8C22×D11311yescharacteristic
160C2×C8C22×D11311yescharacteristic
161C4⋊C4—1132no—
162C4⋊C4—1131no—
163C4⋊C4—2262no—
164C4⋊C4C22×D11312yes—
165C22⋊C4—22no—
166C22⋊C4—2262no—
167C22⋊C4—2262no—
168C22⋊C4—2262no—
169C22⋊C4—2262no—
170C22⋊C4—2262no—
171C42—1132no—
172C42—2262no—
173C42C22×D11311yescharacteristic
174C23—22no—
175C23—2262no—
176Q8—4521no—
177Q8—2262no—
178Q8—2262no—
179D4—22no—
180D4—22no—
181D4—9042no—
182D4—4524no—
183D4—2262no—
184D4—2262no—
185C2×C4—22no—
186C2×C4—82no—
187C2×C4—1132no—
188C2×C4—1132no—
189C2×C4—9042no—
190C2×C4—2262no—
191C2×C4D4×D11311yescharacteristic
192C2×C4D4×D11311yescharacteristic
193C2×C4C23×D11311yescharacteristic
194C8—21no—
195C8—2262no—
196C8#1426864712yes—
197C22—42no—
198C22—42no—
199C22—42no—
200C22—4522no—
201C22—4522no—
202C22—4522no—
203C22C2×D4×D11311yescharacteristic
204C4—21no—
205C4—21no—
206C4—42no—
207C4—4522no—
208C4—2262no—
209C4—2262no—
210C4C2×#1426864711yescharacteristic
211C4#1681366811yescharacteristic
212C2—82no—
213C2—9042no—
214C2#2029926911yescharacteristic
215C2#2029939511yescharacteristic
216C2#2029939911yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC4×D8×C113C2
socleC22×C113C22×D4
hypercenterC4×D8D113
hypocenterC113#3403
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #20299331C2semidirect
2. #20298986C2semidirect
3. #20298982C2semidirect
4. #20298819C2semidirect
5. #20298813C2semidirect
6. #20298792C2semidirect
7. #20298728C2semidirect
8. #20298697C2semidirect
9. C4×D8×C113C2semidirect
109. C113#3403semidirect
118. C4×D8D113semidirect

Maximal subgroups

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

subgroupindex
#202993312
#202989862
#202989822
#202988192
#202988132
#202987922
#202987282
#202986972
C4×D8×C1132
#3403113