Finite Group Databasebeta

← #28401275

Subgroups — #28401275

Order 14464.

410 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 115 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#20299127C211yesmaximal, characteristic, complemented
3#20299004C211yesmaximal, characteristic, complemented
4#20298988C211yesmaximal, characteristic, complemented
5#20298963C211yesmaximal, characteristic, complemented
6#20298833C212yesmaximal, complemented
7#20298830C212yesmaximal, complemented
8#20298707C212yesmaximal, complemented
9#20298701C212yesmaximal, complemented
10#97×D113C211yesmaximal, characteristic, complemented
11#489×C113C211yesmaximal, characteristic, complemented
12C2×#14268648—21no—
13C2×#14268634C2212yes—
14C2×#14268632C2212yes—
15C2×C8×D113C2212yes—
16#16813619C2211yescharacteristic
17#16813615—21no—
18#16813614C2211yescharacteristic
19#16813611—21no—
20#16813604—21no—
21#16813598C2211yescharacteristic
22#16813597—21no—
23#16813597C2212yes—
24#16813593C2211yescharacteristic
25Q8×Dic113C2211yescharacteristic
26D4×Dic113C2211yescharacteristic
27#16813584—21no—
28#16813584C2212yes—
29#16813582—21no—
30#16813578—21no—
31C42×D113C2211yescharacteristic
32#16813555C2212yes—
33#16813553C2212yes—
34#16813544C2212yes—
35#16813544C2212yes—
36#16813533C2211yescharacteristic
37#16813532C2212yes—
38C4⋊Q8×C113C2211yescharacteristic
39#124×C113C2211yescharacteristic
40#103×C113C2212yes—
41#102×C113C2212yes—
42#97×C113C2211yescharacteristic
43#14268648—44no—
44C2×D452—22no—
45C2×D452—21no—
46C2×D452—21no—
47C2×D452C2312yes—
48C2×C22⋊D113—21no—
49C22×Dic113—21no—
50C2×C4×D113—22no—
51C2×C4×D113D411yescharacteristic
52C2×C4×D113D411yescharacteristic
53C2×C4×D113C2311yescharacteristic
54#14268634—24no—
55#14268632—24no—
56C2×#11744751C2312yes—
57C8×D113—24no—
58C4⋊Dic113—21no—
59C4⋊Dic113C2311yescharacteristic
60C4⋊Dic113C2311yescharacteristic
61#14268626—21no—
62#14268626—21no—
63#14268626—21no—
64C22⋊Dic113—21no—
65C22⋊Dic113—21no—
66#14268624—21no—
67#14268624—22no—
68#14268624—22no—
69C4×Dic113—21no—
70C4×Dic113D411yescharacteristic
71C4×Dic113D411yescharacteristic
72C4×Dic113C2311yescharacteristic
73C2×Q8×C113—21no—
74C2×Q8×C113C2311yescharacteristic
75C2×D4×C113C2311yescharacteristic
76C2×C8×C113C2312yes—
77C4⋊C4×C113—21no—
78C4⋊C4×C113C2312yes—
79C22⋊C4×C113—21no—
80C22⋊C4×C113—21no—
81C42×C113C2311yescharacteristic
82C23×C113—21no—
83C22×D113—22no—
84C22×D113C2×D411yescharacteristic
85Q8×C113—22no—
86Q8×C113—42no—
87D4×C113—22no—
88C2×C4×C113—21no—
89C2×C4×C113—22no—
90C2×C4×C113C2×D411yescharacteristic
91C2×C4×C113C2×D411yescharacteristic
92C2×C4×C113C2411yescharacteristic
93C22⋊D113—42no—
94C2×Dic113—21no—
95C2×Dic113—21no—
96C2×Dic113—42no—
97C2×Dic113C2×D411yescharacteristic
98C2×Dic113C2×D411yescharacteristic
99C2×Dic113C2×D411yescharacteristic
100D452—22no—
101D452—22no—
102D452—42no—
103D452—42no—
104D452—44no—
105C4×D113—22no—
106C4×D113—22no—
107C4×D113—41no—
108C4×D113—44no—
109C8×C113—22no—
110#11744751#4114yescomplemented
111C22×C113—41no—
112C22×C113—41no—
113C22×C113—41no—
114C22×C113C22×D411yescharacteristic
115C2×D113—21no—
116C2×D113—21no—
117C2×D113—42no—
118C2×D113—42no—
119C2×D113—42no—
120C2×D113AGL(1,ℤ/8)12yes—
121C4×C113—21no—
122C4×C113—21no—
123C4×C113—41no—
124C4×C113—42no—
125C4×C113C2×#4112yes—
126Dic113—21no—
127Dic113—21no—
128Dic113—21no—
129Dic113—41no—
130Dic113—41no—
131C2×C113—81no—
132C2×C113#53211yescharacteristic
133C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
134C2×C113#57511yescharacteristic
135D113—22no—
136D113—82no—
137#3180—1131nomaximal, Sylow
138C113#318011yescharacteristic, complemented, Sylow
139#532—1131no—
140#529—1131no—
141#501—1131no—
142#496—1131no—
143#490—1131no—
144#489D11311yescharacteristic, complemented
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#125—1131no—
158#124—2261no—
159#124C2×D11311yescharacteristic
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#107—1132no—
173#106—1132no—
174#103C2×D11312yes—
175#102—1132no—
176#102—1132no—
177#102C2×D11312yes—
178#97—1132no—
179#97—1131no—
180#97C2×D11311yescharacteristic
181#41—4524no—
182C2×Q8—21no—
183C2×Q8C22×D11311yescharacteristic
184C2×D4—1132no—
185C2×D4—2262no—
186C2×D4—2261no—
187C2×D4—2261no—
188C2×D4—2261no—
189C2×D4C22×D11311yescharacteristic
190C22×C4—1131no—
191C22×C4—1131no—
192C22×C4—1131no—
193C22×C4—2262no—
194C22×C4—2261no—
195SD16—2264no—
196D8—2264no—
197C2×C8—1132no—
198C2×C8—2264no—
199C2×C8C22×D11312yes—
200C4⋊C4—21no—
201C4⋊C4—1131no—
202C4⋊C4—1131no—
203C4⋊C4—2261no—
204C4⋊C4—2261no—
205C4⋊C4—2261no—
206C4⋊C4—2261no—
207C4⋊C4C22×D11312yes—
208C22⋊C4—21no—
209C22⋊C4—21no—
210C22⋊C4—2262no—
211C22⋊C4—2262no—
212C22⋊C4—2261no—
213C22⋊C4—2261no—
214C22⋊C4—2261no—
215C42—1131no—
216C42—1131no—
217C42—1131no—
218C42—2261no—
219C42C22×D11311yescharacteristic
220C23—21no—
221C23—1131no—
222C23—2262no—
223Q8—22no—
224Q8—42no—
225D4—22no—
226D4—4522no—
227D4—4522no—
228D4—4524no—
229D4—4522no—
230D4—2262no—
231D4—2262no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—1131no—
235C2×C4—1131no—
236C2×C4—1131no—
237C2×C4—4521no—
238C2×C4—4524no—
239C2×C4—4522no—
240C2×C4—2262no—
241C2×C4—2261no—
242C2×C4—2261no—
243C2×C4—2262no—
244C2×C4D4×D11311yescharacteristic
245C2×C4D4×D11311yescharacteristic
246C2×C4C23×D11311yescharacteristic
247C8—22no—
248C8—1134no—
249C22—41no—
250C22—41no—
251C22—41no—
252C22—1132no—
253C22—4522no—
254C22—4522no—
255C22—4522no—
256C22—2261no—
257C22—2261no—
258C22C2×D4×D11311yescharacteristic
259C4—21no—
260C4—21no—
261C4—42no—
262C4—41no—
263C4—4521no—
264C4—4521no—
265C4—2261no—
266C4—2261no—
267C4—2261no—
268C4#41×D11312yes—
269C2—81no—
270C2—9042no—
271C2—2262no—
272C2#2029914711yescharacteristic
273C2AGL(1,ℤ/8)×D11311yescharacteristic
274C2#2029939711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#489×C113C2
socleC22×C113C22×D4
hypercenter#489D113
hypocenterC113#3180
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #20299149C2semidirect
2. #20299127C2semidirect
3. #20299004C2semidirect
4. #20298988C2semidirect
5. #20298963C2semidirect
6. #20298833C2semidirect
7. #20298830C2semidirect
8. #20298707C2semidirect
9. #20298701C2semidirect
10. #97×D113C2semidirect
11. #489×C113C2semidirect
110. #11744751#41semidirect
138. C113#3180semidirect
144. #489D113semidirect

Maximal subgroups

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

subgroupindex
#202991492
#202991272
#202990042
#202989882
#202989632
#202988332
#202988302
#202987072
#202987012
#97×D1132
#489×C1132
#3180113