Finite Group Databasebeta

← #28402299

Subgroups — #28402299

Order 14464.

494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C2×#16813645C212yesmaximal, complemented
2#20299270C211yesmaximal, characteristic, complemented
3#20299251C211yesmaximal, characteristic, complemented
4#20298972C211yesmaximal, characteristic, complemented
5#20298830C212yesmaximal, complemented
6#20298794C211yesmaximal, characteristic, complemented
7#20298759C212yesmaximal, complemented
8#20298746C212yesmaximal, complemented
9C4×#14268634C211yesmaximal, characteristic, complemented
10#20298663C211yesmaximal, characteristic, complemented
11#462×C113C211yesmaximal, characteristic, complemented
12C2×#14268648C2212yes—
13C2×#14268648C2212yes—
14#16813645—28no—
15C2×#14268634C2212yes—
16C2×#14268634C2212yes—
17C2×#14268634C2211yescharacteristic
18C2×D904C2212yes—
19C2×C8×D113C2212yes—
20#16813619—21no—
21#16813619C2211yescharacteristic
22#16813607—22no—
23#16813598C2212yes—
24#16813597—21no—
25#16813597—22no—
26#16813597C2212yes—
27C4×D452—21no—
28C4×D452C2211yescharacteristic
29C4×D452C2211yescharacteristic
30C4⋊C4×D113—21no—
31#16813553C2211yescharacteristic
32#16813546C2211yescharacteristic
33#16813544C2212yes—
34#16813542C2211yescharacteristic
35#16813534C2212yes—
36C4×#11744751C2211yescharacteristic
37C2×Q16×C113C2212yes—
38C4⋊Q8×C113C2211yescharacteristic
39C4×Q8×C113C2211yescharacteristic
40C4⋊C8×C113C2211yescharacteristic
41#103×C113C2212yes—
42#14268648—24no—
43#14268648—24no—
44#14268648—42no—
45#14268648—42no—
46C2×D452—22no—
47C2×D452—22no—
48C2×D452—21no—
49C2×D452—22no—
50C2×D452—21no—
51C2×D452D411yescharacteristic
52C2×D452C2312yes—
53C2×D452C2311yescharacteristic
54C2×C4×D113—21no—
55C2×C4×D113—22no—
56C2×C4×D113—22no—
57C2×C4×D113C2312yes—
58#14268634—24no—
59#14268634—42no—
60#14268634D414yescomplemented
61D904—24no—
62C2×#11744751C2311yescharacteristic
63C2×#11744751C2311yescharacteristic
64C8×D113—24no—
65C4⋊Dic113D411yescharacteristic
66C4⋊Dic113C2311yescharacteristic
67#14268626—22no—
68#14268624—22no—
69#14268624—21no—
70#14268624—22no—
71#14268624D412yes—
72C2×Q8×C113C2312yes—
73C2×Q8×C113C2311yescharacteristic
74Q16×C113—24no—
75C2×C8×C113C2312yes—
76C4⋊C4×C113—21no—
77C4⋊C4×C113—21no—
78C4⋊C4×C113—21no—
79C4⋊C4×C113C2311yescharacteristic
80C42×C113—21no—
81C42×C113C2311yescharacteristic
82C22×D113—21no—
83C22×D113—22no—
84C22×D113C2×D412yes—
85Q8×C113—21no—
86Q8×C113—22no—
87Q8×C113—22no—
88Q8×C113C2×D412yes—
89C2×C4×C113—21no—
90C2×C4×C113—21no—
91C2×C4×C113—22no—
92C2×C4×C113C2×D411yescharacteristic
93C2×C4×C113C2×D411yescharacteristic
94C2×C4×C113C2411yescharacteristic
95C2×Dic113—21no—
96C2×Dic113C2×D412yes—
97D452—22no—
98D452—22no—
99D452—21no—
100D452—22no—
101D452—44no—
102D452—44no—
103D452—42no—
104D452—81no—
105D452—82no—
106D452C2×D412yes—
107C4×D113—22no—
108C4×D113—22no—
109C4×D113—44no—
110C4×D113—44no—
111C4×D113—42no—
112C8×C113—22no—
113#11744751—21no—
114#11744751C2×D412yes—
115C22×C113C22×D411yescharacteristic
116C2×D113—22no—
117C2×D113—22no—
118C2×D113—22no—
119C2×D113—22no—
120C2×D113—41no—
121C2×D113—41no—
122C2×D113—42no—
123C2×D113—42no—
124C2×D113—42no—
125C4×C113—22no—
126C4×C113—21no—
127C4×C113—42no—
128C4×C113—41no—
129C4×C113#13512yescomplemented
130C4×C113C22×D411yescharacteristic
131C4×C113H(5,𝔽2)11yescharacteristic
132Dic113—22no—
133Dic113—41no—
134C2×C113D4211yescharacteristic
135C2×C113C2×#13511yescharacteristic
136C2×C113#57711yescharacteristic
137D113—42no—
138D113—42no—
139D113—82no—
140#3284—1131nomaximal, Sylow
141C113#328411yescharacteristic, complemented, Sylow
142C2×#135—1132no—
143#550—1131no—
144#547—1131no—
145#492—1131no—
146#465—1132no—
147#462D11311yescharacteristic, complemented
148#459—1131no—
149#452—1132no—
150#449—1132no—
151C4×SD16—1131no—
152C8×D4—1131no—
153C2×#41—1132no—
154C2×#41—1132no—
155#135—2268no—
156C2×Q16C2×D11312yes—
157C2×SD16—1131no—
158C2×SD16—1132no—
159C2×SD16—1132no—
160C2×D8—1132no—
161C22×C8—1132no—
162C4⋊Q8C2×D11311yescharacteristic
163#127—1131no—
164#127—2261no—
165#123—2262no—
166C22⋊Q8—1132no—
167#121—1132no—
168#121—2262no—
169#121—2261no—
170C4×Q8C2×D11311yescharacteristic
171C4×D4—1131no—
172C4×D4—1131no—
173C4×D4—2261no—
174C2×C4⋊C4—2261no—
175#106—1131no—
176C4⋊C8C2×D11311yescharacteristic
177#103—1131no—
178#103C2×D11312yes—
179#102—1132no—
180#102—1131no—
181C22⋊C8—1132no—
182C4×C8—1131no—
183#41—4522no—
184#41—4522no—
185#41—2264no—
186#41—2264no—
187C2×Q8C22×D11312yes—
188C2×Q8C22×D11311yescharacteristic
189C2×D4—1131no—
190C2×D4—1131no—
191C2×D4—1132no—
192C2×D4—2262no—
193C2×D4—2262no—
194C2×D4—2262no—
195C2×D4—2261no—
196C2×D4—2261no—
197C22×C4—1132no—
198C22×C4—2262no—
199C22×C4—2262no—
200C22×C4—2261no—
201Q16—24no—
202SD16—1134no—
203SD16—4522no—
204SD16—2264no—
205D8—2264no—
206C2×C8—1131no—
207C2×C8—1131no—
208C2×C8—2264no—
209C2×C8C22×D11312yes—
210C4⋊C4—21no—
211C4⋊C4—21no—
212C4⋊C4—21no—
213C4⋊C4—1131no—
214C4⋊C4—1131no—
215C4⋊C4—2262no—
216C4⋊C4C22×D11311yescharacteristic
217C22⋊C4—1132no—
218C22⋊C4—2262no—
219C22⋊C4—2262no—
220C22⋊C4—2261no—
221C42—21no—
222C42C22×D11311yescharacteristic
223C23—1132no—
224C23—2262no—
225C23—2261no—
226Q8—21no—
227Q8—22no—
228Q8—22no—
229Q8D4×D11312yes—
230D4—1132no—
231D4—9041no—
232D4—9042no—
233D4—4524no—
234D4—4524no—
235D4—4522no—
236D4—2262no—
237D4—2262no—
238D4—2262no—
239D4—2261no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—1132no—
244C2×C4—4524no—
245C2×C4—4524no—
246C2×C4—4522no—
247C2×C4—2261no—
248C2×C4—2262no—
249C2×C4—2262no—
250C2×C4D4×D11311yescharacteristic
251C2×C4D4×D11311yescharacteristic
252C2×C4C23×D11311yescharacteristic
253C8—22no—
254C8—1132no—
255C8—2261no—
256C22—4522no—
257C22—4522no—
258C22—4522no—
259C22—4521no—
260C22—4521no—
261C22—2262no—
262C22—2262no—
263C22—2262no—
264C22—2262no—
265C22C2×D4×D11311yescharacteristic
266C4—21no—
267C4—22no—
268C4—41no—
269C4—42no—
270C4—4521no—
271C4—2262no—
272C4#1681364512yescomplemented
273C4C2×D4×D11311yescharacteristic
274C4#1681366811yescharacteristic
275C2—9042no—
276C2—4522no—
277C2—4522no—
278C2#2029923211yescharacteristic
279C2C2×#1681364511yescharacteristic
280C2#2029940711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#462×C113C2
socleC22×C113C22×D4
hypercenter#462D113
hypocenterC113#3284
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
1. C2×#16813645C2semidirect
2. #20299270C2semidirect
3. #20299251C2semidirect
4. #20298972C2semidirect
5. #20298830C2semidirect
6. #20298794C2semidirect
7. #20298759C2semidirect
8. #20298746C2semidirect
9. C4×#14268634C2semidirect
10. #20298663C2semidirect
11. #462×C113C2semidirect
60. #14268634D4semidirect
129. C4×C113#135semidirect
141. C113#3284semidirect
147. #462D113semidirect
272. C4#16813645semidirect

Maximal subgroups

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

subgroupindex
C2×#168136452
#202992702
#202992512
#202989722
#202988302
#202987942
#202987592
#202987462
C4×#142686342
#202986632
#462×C1132
#3284113