Finite Group Databasebeta

← #28401274

Subgroups — #28401274

Order 14464.

410 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 119 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#20299149C211yesmaximal, characteristic, complemented
2#20299133C211yesmaximal, characteristic, complemented
3#20298987C211yesmaximal, characteristic, complemented
4#20298964C211yesmaximal, characteristic, complemented
5#20298960C211yesmaximal, characteristic, complemented
6#20298835C212yesmaximal, complemented
7#20298828C212yesmaximal, complemented
8#20298709C212yesmaximal, complemented
9#20298697C212yesmaximal, complemented
10#97×D113C211yesmaximal, characteristic, complemented
11#501×C113C211yesmaximal, characteristic, complemented
12C2×#14268648—21no—
13C2×#14268636C2212yes—
14C2×D904C2212yes—
15C2×C8×D113C2212yes—
16#16813619C2211yescharacteristic
17#16813617—21no—
18#16813611—21no—
19#16813610C2211yescharacteristic
20#16813607—21no—
21#16813602C2211yescharacteristic
22#16813597—21no—
23#16813597C2212yes—
24#16813597C2211yescharacteristic
25#16813587C2211yescharacteristic
26#16813584—21no—
27#16813584—21no—
28#16813584C2211yescharacteristic
29#16813584C2212yes—
30#16813580—21no—
31C42×D113C2211yescharacteristic
32#16813545C2212yes—
33#16813542C2212yes—
34#16813542C2212yes—
35#16813542C2212yes—
36#16813533C2211yescharacteristic
37#16813532C2212yes—
38C4⋊Q8×C113C2211yescharacteristic
39#125×C113C2211yescharacteristic
40#107×C113C2212yes—
41#106×C113C2212yes—
42#97×C113C2211yescharacteristic
43#14268648—44no—
44C2×Dic226C2311yescharacteristic
45C2×D452—21no—
46C2×D452—22no—
47C2×D452—21no—
48C2×D452—21no—
49C2×D452C2311yescharacteristic
50C2×D452C2312yes—
51C2×C4×D113—21no—
52C2×C4×D113—22no—
53C2×C4×D113D411yescharacteristic
54C2×C4×D113D411yescharacteristic
55C2×C4×D113C2311yescharacteristic
56#14268636—24no—
57D904—24no—
58C2×#11744751C2312yes—
59C8×D113—24no—
60C4⋊Dic113—21no—
61#14268626—21no—
62#14268624—21no—
63#14268624—21no—
64#14268624—21no—
65#14268624—21no—
66#14268624—22no—
67#14268624—22no—
68#14268624—21no—
69C4×Dic113—21no—
70C4×Dic113D411yescharacteristic
71C4×Dic113D411yescharacteristic
72C4×Dic113C2311yescharacteristic
73C2×Q8×C113—21no—
74C2×C8×C113C2312yes—
75C4⋊C4×C113—21no—
76C4⋊C4×C113—21no—
77C4⋊C4×C113—21no—
78C4⋊C4×C113C2312yes—
79C4⋊C4×C113C2311yescharacteristic
80C4⋊C4×C113C2311yescharacteristic
81C42×C113C2311yescharacteristic
82C22×D113—21no—
83C22×D113—22no—
84C22×D113C2×D411yescharacteristic
85Q8×C113—42no—
86C2×C4×C113—21no—
87C2×C4×C113—21no—
88C2×C4×C113—22no—
89C2×C4×C113C2×D411yescharacteristic
90C2×C4×C113C2×D411yescharacteristic
91C2×C4×C113C2411yescharacteristic
92C2×Dic113—21no—
93C2×Dic113C2×D411yescharacteristic
94C2×Dic113C2×D411yescharacteristic
95C2×Dic113C2×D411yescharacteristic
96D452—22no—
97D452—22no—
98D452—22no—
99D452—42no—
100D452—42no—
101D452—42no—
102D452—44no—
103C4×D113—22no—
104C4×D113—22no—
105C4×D113—41no—
106C4×D113—42no—
107C4×D113—44no—
108Dic226—22no—
109C8×C113#4114yescomplemented
110#11744751—22no—
111C22×C113C22×D411yescharacteristic
112C2×D113—21no—
113C2×D113—21no—
114C2×D113—41no—
115C2×D113—42no—
116C2×D113—42no—
117C2×D113—41no—
118C2×D113—41no—
119C2×D113—42no—
120C2×D113AGL(1,ℤ/8)12yes—
121C4×C113—21no—
122C4×C113—21no—
123C4×C113—42no—
124C4×C113—41no—
125C4×C113—41no—
126C4×C113C2×#4112yes—
127Dic113—21no—
128Dic113—21no—
129Dic113—21no—
130Dic113—41no—
131C2×C113#53211yescharacteristic
132C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
133C2×C113#57511yescharacteristic
134D113—22no—
135D113—82no—
136D113—81no—
137#3180—1131nomaximal, Sylow
138C113#318011yescharacteristic, complemented, Sylow
139#532—1131no—
140#529—1131no—
141#501D11311yescharacteristic, complemented
142#496—1131no—
143#490—1131no—
144#489—1131no—
145#466—1132no—
146#465—1132no—
147#442—1132no—
148#440—1132no—
149C2×#97—1131no—
150C2×#41—2261no—
151C2×SD16—1132no—
152C2×D8—1132no—
153C22×C8—1132no—
154C4⋊Q8C2×D11311yescharacteristic
155#127—1131no—
156#126—2261no—
157#125C2×D11311yescharacteristic
158#124—1131no—
159#124—2261no—
160#123—2261no—
161C22⋊Q8—1131no—
162#121—1131no—
163#121—1132no—
164#121—2261no—
165C4×Q8—1131no—
166C4×D4—1131no—
167C4×D4—1132no—
168C4×D4—2261no—
169C4×D4—2261no—
170#117—2261no—
171C2×C42—1131no—
172#107C2×D11312yes—
173#106C2×D11312yes—
174#103—1132no—
175#102—1132no—
176#102—1132no—
177#102—1132no—
178#97—1132no—
179#97—1131no—
180#97C2×D11311yescharacteristic
181#41—4524no—
182C2×Q8—21no—
183C2×Q8—1131no—
184C2×D4—1131no—
185C2×D4—1132no—
186C2×D4—2261no—
187C2×D4—2262no—
188C2×D4—2261no—
189C2×D4—2261no—
190C22×C4—1131no—
191C22×C4—1131no—
192C22×C4—1131no—
193C22×C4—2261no—
194C22×C4—2262no—
195SD16—2264no—
196D8—2264no—
197C2×C8—1132no—
198C2×C8—2264no—
199C2×C8C22×D11312yes—
200C4⋊C4—21no—
201C4⋊C4—21no—
202C4⋊C4—21no—
203C4⋊C4—2261no—
204C4⋊C4—2261no—
205C4⋊C4C22×D11311yescharacteristic
206C4⋊C4C22×D11311yescharacteristic
207C4⋊C4C22×D11312yes—
208C22⋊C4—2261no—
209C22⋊C4—2262no—
210C22⋊C4—2261no—
211C22⋊C4—2262no—
212C22⋊C4—2261no—
213C22⋊C4—2261no—
214C22⋊C4—2261no—
215C42—1131no—
216C42—1131no—
217C42—1131no—
218C42—2261no—
219C42C22×D11311yescharacteristic
220C23—1131no—
221C23—2261no—
222C23—2262no—
223Q8—42no—
224Q8—2262no—
225D4—4522no—
226D4—4522no—
227D4—4524no—
228D4—4522no—
229D4—2262no—
230D4—2262no—
231D4—2262no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—1131no—
236C2×C4—1131no—
237C2×C4—1131no—
238C2×C4—4521no—
239C2×C4—4524no—
240C2×C4—4522no—
241C2×C4—2262no—
242C2×C4—2261no—
243C2×C4—2262no—
244C2×C4D4×D11311yescharacteristic
245C2×C4D4×D11311yescharacteristic
246C2×C4C23×D11311yescharacteristic
247C8—2262no—
248C8#1426864814yescomplemented
249C22—1132no—
250C22—4522no—
251C22—4521no—
252C22—4521no—
253C22—4522no—
254C22—4521no—
255C22—4522no—
256C22—2261no—
257C22—2261no—
258C22C2×D4×D11311yescharacteristic
259C4—21no—
260C4—21no—
261C4—42no—
262C4—41no—
263C4—41no—
264C4—4521no—
265C4—2261no—
266C4—2261no—
267C4—2261no—
268C4C2×#1426864812yes—
269C2—9042no—
270C2—9041no—
271C2—2262no—
272C2#2029914911yescharacteristic
273C2AGL(1,ℤ/8)×D11311yescharacteristic
274C2#2029939711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#501×C113C2
socleC22×C113C22×D4
hypercenter#501D113
hypocenterC113#3180
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. #20299149C2semidirect
2. #20299133C2semidirect
3. #20298987C2semidirect
4. #20298964C2semidirect
5. #20298960C2semidirect
6. #20298835C2semidirect
7. #20298828C2semidirect
8. #20298709C2semidirect
9. #20298697C2semidirect
10. #97×D113C2semidirect
11. #501×C113C2semidirect
109. C8×C113#41semidirect
138. C113#3180semidirect
141. #501D113semidirect
248. C8#14268648semidirect

Maximal subgroups

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

subgroupindex
#202991492
#202991332
#202989872
#202989642
#202989602
#202988352
#202988282
#202987092
#202986972
#97×D1132
#501×C1132
#3180113