Finite Group Databasebeta

← #28401581

Subgroups — #28401581

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#20299148C211yesmaximal, characteristic
2#20298990C212yesmaximal, complemented
3#20298960C212yesmaximal, complemented
4#20298808C212yesmaximal, complemented
5#20298798C212yesmaximal, complemented
6#20298758C214yesmaximal, complemented
7#20298655C211yesmaximal, characteristic, complemented
8#533×C113C211yesmaximal, characteristic, complemented
9C2×#14268647C2212yes—
10C2×#14268637C2214yes—
11C2×#14268634C2214yes—
12#16813622C2211yescharacteristic
13#16813619C2211yescharacteristic
14#16813610C2212yes—
15#16813596—21no—
16#16813596—21no—
17C4×D452—21no—
18C4×D452—21no—
19C4⋊#11744751C2212yes—
20#16813545C2214yes—
21#16813542C2214yes—
22C22⋊#11744751C2212yes—
23#16813533C2212yes—
24C4⋊Q8×C113C2211yescharacteristic
25C4⋊Q8×C113C2211yescharacteristic
26#125×C113—21no—
27C22⋊Q8×C113—21no—
28C22⋊Q8×C113C2212yes—
29C4×Q8×C113—21no—
30C4×Q8×C113C2212yes—
31#117×C113—21no—
32C2×C42×C113C2211yescharacteristic
33#14268647—44no—
34C2×Dic226C2312yes—
35C2×D452—21no—
36C2×D452—21no—
37C2×D452C2312yes—
38C2×C22⋊D113—22no—
39C2×C4×D113—22no—
40#14268637—44no—
41#14268634—44no—
42C2×#11744751C2314yes—
43C4⋊Dic113—21no—
44C4⋊Dic113—21no—
45#14268624—22no—
46#14268624—22no—
47C2×Q8×C113—21no—
48C2×Q8×C113C2312yes—
49C22×C4×C113D411yescharacteristic
50C22×C4×C113D411yescharacteristic
51C22×C4×C113C2311yescharacteristic
52C4⋊C4×C113—21no—
53C4⋊C4×C113—21no—
54C4⋊C4×C113—21no—
55C4⋊C4×C113—22no—
56C4⋊C4×C113—22no—
57C4⋊C4×C113C2312yes—
58C22⋊C4×C113—22no—
59C42×C113—22no—
60C42×C113D411yescharacteristic
61C42×C113D411yescharacteristic
62C42×C113C2311yescharacteristic
63C42×C113C2311yescharacteristic
64C23×C113C2×D411yescharacteristic
65C22×D113—22no—
66Q8×C113—22no—
67Q8×C113—22no—
68Q8×C113—42no—
69C2×C4×C113—22no—
70C2×C4×C113—22no—
71C2×C4×C113—22no—
72C2×C4×C113—22no—
73C2×C4×C113—41no—
74C2×C4×C113C2×D411yescharacteristic
75C2×C4×C113C2×D411yescharacteristic
76C2×C4×C113C2×D411yescharacteristic
77C2×C4×C113C2×D411yescharacteristic
78C2×C4×C113C2×D411yescharacteristic
79C2×C4×C113C2411yescharacteristic
80C22⋊D113—44no—
81C2×Dic113—22no—
82D452—24no—
83D452—42no—
84D452—42no—
85C4×D113—44no—
86Dic226—24no—
87#11744751—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—42no—
100C4×C113—42no—
101C4×C113#13712yes—
102C4×C113H(5,𝔽2)12yes—
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#533D11311yescharacteristic, complemented
112#532—1131no—
113#497—1132no—
114#489—1132no—
115#462—1132no—
116#460—1132no—
117#452—1134no—
118#432—1131no—
119C2×#41—1132no—
120C2×Q16—1134no—
121C2×SD16—1134no—
122C4⋊Q8—1131no—
123C4⋊Q8C2×D11311yescharacteristic
124C4⋊Q8C2×D11311yescharacteristic
125#127—1131no—
126#125—21no—
127#124—1132no—
128C22⋊Q8—21no—
129C22⋊Q8C2×D11312yes—
130#121—2261no—
131#121—2261no—
132C4×Q8—21no—
133C4×Q8C2×D11312yes—
134C4×D4—2261no—
135C4×D4—2261no—
136#117—21no—
137C2×C42C2×D11311yescharacteristic
138C4⋊C8—1132no—
139#103—1134no—
140#102—1134no—
141C22⋊C8—1132no—
142#97—1132no—
143#41—4524no—
144C2×Q8—21no—
145C2×Q8—1132no—
146C2×Q8C22×D11312yes—
147C2×D4—1132no—
148C2×D4—2262no—
149C2×D4—2261no—
150C2×D4—2261no—
151C22×C4—2262no—
152C22×C4C22⋊D11311yescharacteristic
153C22×C4C22⋊D11311yescharacteristic
154C22×C4C22×D11311yescharacteristic
155Q16—4524no—
156SD16—4524no—
157C2×C8—1134no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—22no—
162C4⋊C4—22no—
163C4⋊C4—2261no—
164C4⋊C4—2261no—
165C4⋊C4C22×D11312yes—
166C22⋊C4—22no—
167C22⋊C4—2262no—
168C22⋊C4—2262no—
169C42—22no—
170C42C22⋊D11311yescharacteristic
171C42C22⋊D11311yescharacteristic
172C42C22×D11311yescharacteristic
173C42C22×D11311yescharacteristic
174C23—2262no—
175C23C2×C22⋊D11311yescharacteristic
176Q8—22no—
177Q8—22no—
178Q8—42no—
179Q8—2264no—
180D4—4522no—
181D4—4524no—
182D4—4522no—
183D4—2264no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—41no—
189C2×C4—4524no—
190C2×C4—2262no—
191C2×C4C2×C22⋊D11311yescharacteristic
192C2×C4C2×C22⋊D11311yescharacteristic
193C2×C4C2×C22⋊D11311yescharacteristic
194C2×C4C2×C22⋊D11311yescharacteristic
195C2×C4C2×C22⋊D11311yescharacteristic
196C2×C4C23×D11311yescharacteristic
197C8—2264no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—4522no—
202C22—4522no—
203C22—4522no—
204C22C22×C22⋊D11311yescharacteristic
205C4—21no—
206C4—21no—
207C4—21no—
208C4—21no—
209C4—42no—
210C4—42no—
211C4—4522no—
212C4#1681365312yes—
213C4#1681366812yes—
214C2—41no—
215C2—9042no—
216C2#2029916211yescharacteristic
217C2C2×#1681365311yescharacteristic
218C2#2029939611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#533×C113C2
socleC22×C113C22×D4
prime radical#20299148C2
hypercenter#533D113
hypocenterC113#3216
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #20298990C2semidirect
3. #20298960C2semidirect
4. #20298808C2semidirect
5. #20298798C2semidirect
6. #20298758C2semidirect
7. #20298655C2semidirect
8. #533×C113C2semidirect
110. C113#3216semidirect
111. #533D113semidirect

Maximal subgroups

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

subgroupindex
#202991482
#202989902
#202989602
#202988082
#202987982
#202987582
#202986552
#533×C1132
#3216113