Finite Group Databasebeta

← #28401587

Subgroups — #28401587

Order 14464.

390 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 121 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#20299155C211yesmaximal, characteristic, complemented
2#20299148C211yesmaximal, characteristic
3#20298992C212yesmaximal, complemented
4#20298958C212yesmaximal, complemented
5#20298809C212yesmaximal, complemented
6#20298799C212yesmaximal, complemented
7#20298762C214yesmaximal, complemented
8#432×C113C211yesmaximal, characteristic, complemented
9C2×#14268647C2212yes—
10C2×Dic452C2214yes—
11C2×#14268636C2214yes—
12#16813622C2211yescharacteristic
13#16813622C2211yescharacteristic
14#16813622C2211yescharacteristic
15#16813619C2211yescharacteristic
16#16813614—21no—
17#16813610C2212yes—
18#16813601—21no—
19#16813601C2212yes—
20#16813596—21no—
21#16813596—21no—
22C4×Dic226—21no—
23C4×Dic226C2212yes—
24C4×D452—21no—
25C4×D452—21no—
26#16813581—21no—
27#16813547C2214yes—
28#16813544C2214yes—
29C2×C42×C113C2211yescharacteristic
30C4⋊C8×C113C2212yes—
31C22⋊C8×C113C2212yes—
32#97×C113C2212yes—
33#14268647—44no—
34C2×Dic226—21no—
35C2×Dic226C2312yes—
36C2×Dic226C2312yes—
37C2×D452—21no—
38C2×D452—21no—
39C2×D452C2312yes—
40C2×C22⋊D113—22no—
41C2×C4×D113—22no—
42Dic452—44no—
43#14268636—44no—
44C4⋊Dic113—21no—
45C4⋊Dic113—21no—
46C4⋊Dic113—21no—
47C4⋊Dic113—21no—
48C4⋊Dic113—21no—
49C4⋊Dic113C2312yes—
50#14268626—22no—
51#14268626—22no—
52C22⋊Dic113—22no—
53#14268624—22no—
54#14268624—22no—
55C4×Dic113—22no—
56C22×C4×C113D411yescharacteristic
57C22×C4×C113D411yescharacteristic
58C22×C4×C113C2311yescharacteristic
59C2×C8×C113C2314yes—
60C42×C113D411yescharacteristic
61C42×C113D411yescharacteristic
62C42×C113C2311yescharacteristic
63C42×C113C2311yescharacteristic
64C23×C113C2×D411yescharacteristic
65C22×D113—22no—
66C2×C4×C113—22no—
67C2×C4×C113—22no—
68C2×C4×C113—41no—
69C2×C4×C113C2×D411yescharacteristic
70C2×C4×C113C2×D411yescharacteristic
71C2×C4×C113C2×D411yescharacteristic
72C2×C4×C113C2×D411yescharacteristic
73C2×C4×C113C2×D411yescharacteristic
74C2×C4×C113C2411yescharacteristic
75C22⋊D113—44no—
76C2×Dic113—22no—
77C2×Dic113—22no—
78C2×Dic113—22no—
79D452—24no—
80D452—42no—
81D452—42no—
82C4×D113—44no—
83Dic226—22no—
84Dic226—22no—
85Dic226—24no—
86Dic226—42no—
87C8×C113—24no—
88C22×C113—21no—
89C22×C113—21no—
90C22×C113—21no—
91C22×C113C22×D411yescharacteristic
92C2×D113—42no—
93C2×D113—42no—
94C2×D113—42no—
95C4×C113—21no—
96C4×C113—21no—
97C4×C113—21no—
98C4×C113—21no—
99C4×C113#13712yes—
100C4×C113H(5,𝔽2)12yes—
101Dic113—42no—
102Dic113—42no—
103Dic113—42no—
104C2×C113—41no—
105C2×C113#53511yescharacteristic
106C2×C113C2×#13711yescharacteristic
107C2×C113#57511yescharacteristic
108D113—82no—
109#3216—1131nomaximal, Sylow
110C113#321611yescharacteristic, complemented, Sylow
111#533—1131no—
112#532—1131no—
113#497—1132no—
114#489—1132no—
115#462—1132no—
116#460—1132no—
117#452—1134no—
118#432D11311yescharacteristic, complemented
119C2×#41—1132no—
120C2×Q16—1134no—
121C2×SD16—1134no—
122C4⋊Q8—1131no—
123C4⋊Q8—1131no—
124C4⋊Q8—1131no—
125#127—1131no—
126#125—2261no—
127#124—1132no—
128C22⋊Q8—1132no—
129C22⋊Q8—2261no—
130#121—2261no—
131#121—2261no—
132C4×Q8—1132no—
133C4×Q8—2261no—
134C4×D4—2261no—
135C4×D4—2261no—
136#117—2261no—
137C2×C42C2×D11311yescharacteristic
138C4⋊C8C2×D11312yes—
139#103—1134no—
140#102—1134no—
141C22⋊C8C2×D11312yes—
142#97C2×D11312yes—
143#41—4524no—
144C2×Q8—1132no—
145C2×Q8—1132no—
146C2×Q8—2261no—
147C2×D4—1132no—
148C2×D4—2262no—
149C2×D4—2261no—
150C2×D4—2261no—
151C22×C4—2262no—
152C22×C4D45211yescharacteristic
153C22×C4D45211yescharacteristic
154C22×C4C22×D11311yescharacteristic
155Q16—4524no—
156SD16—4524no—
157C2×C8C22×D11314yes—
158C4⋊C4—1132no—
159C4⋊C4—2261no—
160C4⋊C4—2261no—
161C4⋊C4—2261no—
162C4⋊C4—2261no—
163C4⋊C4—2262no—
164C4⋊C4—2262no—
165C4⋊C4—2261no—
166C22⋊C4—2262no—
167C22⋊C4—2262no—
168C22⋊C4—2262no—
169C42—2262no—
170C42D45211yescharacteristic
171C42D45211yescharacteristic
172C42C22×D11311yescharacteristic
173C42C22×D11311yescharacteristic
174C23—2262no—
175C23C2×D45211yescharacteristic
176Q8—4522no—
177Q8—2262no—
178Q8—2262no—
179Q8—2264no—
180D4—4522no—
181D4—4524no—
182D4—4522no—
183D4—2264no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—41no—
187C2×C4—4524no—
188C2×C4—2262no—
189C2×C4—2262no—
190C2×C4—2262no—
191C2×C4C2×D45211yescharacteristic
192C2×C4C2×D45211yescharacteristic
193C2×C4C2×D45211yescharacteristic
194C2×C4C2×D45211yescharacteristic
195C2×C4C2×D45211yescharacteristic
196C2×C4C23×D11311yescharacteristic
197C8—24no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—4522no—
202C22—4522no—
203C22—4522no—
204C22C22×D45211yescharacteristic
205C4—21no—
206C4—21no—
207C4—21no—
208C4—21no—
209C4—4522no—
210C4—4522no—
211C4—4522no—
212C4#1681365512yes—
213C4#1681366812yes—
214C2—41no—
215C2—9042no—
216C2#2029916711yescharacteristic
217C2C2×#1681365511yescharacteristic
218C2#2029939811yescharacteristic
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#432×C113C2
socleC22×C113C22×D4
prime radical#20299148C2
hypercenter#432D113
hypocenterC113#3216
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #20299155C2semidirect
3. #20298992C2semidirect
4. #20298958C2semidirect
5. #20298809C2semidirect
6. #20298799C2semidirect
7. #20298762C2semidirect
8. #432×C113C2semidirect
110. C113#3216semidirect
118. #432D113semidirect

Maximal subgroups

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

subgroupindex
#202991552
#202991482
#202989922
#202989582
#202988092
#202987992
#202987622
#432×C1132
#3216113