Finite Group Databasebeta

← #28402305

Subgroups — #28402305

Order 14464.

494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 133 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×#16813643C212yesmaximal, complemented
2#20299270C211yesmaximal, characteristic, complemented
3#20299252C211yesmaximal, characteristic, complemented
4#20298971C211yesmaximal, characteristic, complemented
5#20298828C212yesmaximal, complemented
6#20298808C211yesmaximal, characteristic, complemented
7#20298793C211yesmaximal, characteristic, complemented
8#20298763C212yesmaximal, complemented
9#20298744C212yesmaximal, complemented
10C8×D452C211yesmaximal, characteristic, complemented
11C4×SD16×C113C211yesmaximal, characteristic, complemented
12C2×#14268648C2212yes—
13C2×#14268646C2212yes—
14#16813643—28no—
15C2×#14268637C2212yes—
16C2×#14268636C2212yes—
17C2×#14268636C2212yes—
18C2×#14268632C2212yes—
19C2×C8×D113C2212yes—
20#16813622C2211yescharacteristic
21#16813619—21no—
22#16813619C2211yescharacteristic
23#16813606—22no—
24#16813602C2212yes—
25#16813597—22no—
26#16813597C2212yes—
27#16813596—21no—
28C4×D452—21no—
29C4×D452C2211yescharacteristic
30C2×C4⋊Dic113—21no—
31C4⋊#11744751C2211yescharacteristic
32#16813545C2212yes—
33#16813542C2212yes—
34#16813534C2212yes—
35C2×SD16×C113C2211yescharacteristic
36C4×Q8×C113C2211yescharacteristic
37C4×D4×C113C2211yescharacteristic
38#106×C113C2211yescharacteristic
39#103×C113C2211yescharacteristic
40#102×C113C2211yescharacteristic
41C4×C8×C113C2211yescharacteristic
42#14268648—24no—
43#14268648—42no—
44#14268646—24no—
45#14268646—42no—
46C2×Dic226C2312yes—
47C2×D452—22no—
48C2×D452—21no—
49C2×D452—22no—
50C2×D452—21no—
51C2×D452D411yescharacteristic
52C2×D452C2312yes—
53C2×C22⋊D113—22no—
54C22×Dic113—22no—
55C2×C4×D113—22no—
56C2×C4×D113C2312yes—
57#14268637—24no—
58#14268636—24no—
59#14268636—42no—
60#14268632—24no—
61C2×#11744751C2312yes—
62C8×D113—24no—
63C4⋊Dic113—21no—
64C4⋊Dic113—21no—
65C4⋊Dic113—22no—
66C4⋊Dic113D411yescharacteristic
67#14268624—22no—
68#14268624—22no—
69#14268624D412yes—
70C2×Q8×C113C2311yescharacteristic
71C2×D4×C113C2311yescharacteristic
72C22×C4×C113—21no—
73SD16×C113D414yescomplemented
74C2×C8×C113C2311yescharacteristic
75C2×C8×C113C2311yescharacteristic
76C4⋊C4×C113—21no—
77C4⋊C4×C113C2311yescharacteristic
78C4⋊C4×C113C2311yescharacteristic
79C22⋊C4×C113—21no—
80C42×C113—21no—
81C42×C113C2311yescharacteristic
82C23×C113—21no—
83C22×D113—22no—
84C22×D113C2×D412yes—
85Q8×C113—21no—
86Q8×C113C2×D412yes—
87D4×C113—21no—
88D4×C113C2×D412yes—
89C2×C4×C113—21no—
90C2×C4×C113—21no—
91C2×C4×C113—21no—
92C2×C4×C113—42no—
93C2×C4×C113C2×D411yescharacteristic
94C2×C4×C113C2×D411yescharacteristic
95C2×C4×C113C2411yescharacteristic
96C22⋊D113—44no—
97C2×Dic113—22no—
98C2×Dic113—44no—
99C2×Dic113C2×D412yes—
100D452—22no—
101D452—22no—
102D452—22no—
103D452—44no—
104D452—42no—
105D452—81no—
106D452—82no—
107C4×D113—22no—
108C4×D113—22no—
109C4×D113—44no—
110Dic226—22no—
111Dic226—22no—
112C8×C113—21no—
113C8×C113C2×D412yes—
114#11744751—22no—
115C22×C113—22no—
116C22×C113—41no—
117C22×C113—41no—
118C22×C113C22×D411yescharacteristic
119C2×D113—22no—
120C2×D113—22no—
121C2×D113—22no—
122C2×D113—42no—
123C2×D113—42no—
124C2×D113—42no—
125C4×C113—22no—
126C4×C113—21no—
127C4×C113—41no—
128C4×C113—41no—
129C4×C113#13512yescomplemented
130C4×C113C22×D411yescharacteristic
131C4×C113H(5,𝔽2)11yescharacteristic
132Dic113—22no—
133Dic113—42no—
134C2×C113—42no—
135C2×C113D4211yescharacteristic
136C2×C113C2×#13511yescharacteristic
137C2×C113#57711yescharacteristic
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#462—1131no—
148#459—1131no—
149#452—1132no—
150#449—1132no—
151C4×SD16D11311yescharacteristic, complemented
152C8×D4—1131no—
153C2×#41—1132no—
154C2×#41—1132no—
155#135—2268no—
156C2×Q16—1132no—
157C2×SD16—1132no—
158C2×SD16—1132no—
159C2×SD16C2×D11311yescharacteristic
160C2×D8—1132no—
161C22×C8—1132no—
162C4⋊Q8—1131no—
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—2261no—
173C4×D4C2×D11311yescharacteristic
174C2×C4⋊C4—2261no—
175#106C2×D11311yescharacteristic
176C4⋊C8—1131no—
177#103—1132no—
178#103C2×D11311yescharacteristic
179#102—1132no—
180#102C2×D11311yescharacteristic
181C22⋊C8—1132no—
182C4×C8C2×D11311yescharacteristic
183#41—4522no—
184#41—4522no—
185#41—2264no—
186#41—2264no—
187C2×Q8—1132no—
188C2×Q8C22×D11311yescharacteristic
189C2×D4—1131no—
190C2×D4—1132no—
191C2×D4—2262no—
192C2×D4—2262no—
193C2×D4—2262no—
194C2×D4—2261no—
195C2×D4—2261no—
196C2×D4C22×D11311yescharacteristic
197C22×C4—21no—
198C22×C4—1132no—
199C22×C4—2262no—
200C22×C4—2262no—
201Q16—2264no—
202SD16—4522no—
203SD16—2264no—
204SD16D45214yescomplemented
205D8—2264no—
206C2×C8—1132no—
207C2×C8—2264no—
208C2×C8C22×D11311yescharacteristic
209C2×C8C22×D11311yescharacteristic
210C4⋊C4—21no—
211C4⋊C4—1131no—
212C4⋊C4—2262no—
213C4⋊C4—2261no—
214C4⋊C4—2261no—
215C4⋊C4C22×D11311yescharacteristic
216C4⋊C4C22×D11311yescharacteristic
217C22⋊C4—21no—
218C22⋊C4—1132no—
219C22⋊C4—2262no—
220C22⋊C4—2262no—
221C42—21no—
222C42C22×D11311yescharacteristic
223C23—21no—
224C23—1132no—
225C23—2262no—
226Q8—21no—
227Q8—2262no—
228Q8—2262no—
229Q8C2×D45212yes—
230D4—21no—
231D4—9041no—
232D4—9042no—
233D4—4524no—
234D4—4524no—
235D4—4522no—
236D4—2262no—
237D4—2262no—
238D4—2262no—
239D4C2×D45212yes—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—42no—
244C2×C4—1132no—
245C2×C4—4524no—
246C2×C4—4524no—
247C2×C4—2262no—
248C2×C4—2262no—
249C2×C4—2262no—
250C2×C4D4×D11311yescharacteristic
251C2×C4D4×D11311yescharacteristic
252C2×C4C23×D11311yescharacteristic
253C8—21no—
254C8—2262no—
255C8C2×D45212yes—
256C22—22no—
257C22—41no—
258C22—41no—
259C22—4522no—
260C22—4522no—
261C22—4522no—
262C22—2262no—
263C22—2262no—
264C22—2262no—
265C22C2×D4×D11311yescharacteristic
266C4—21no—
267C4—22no—
268C4—41no—
269C4—41no—
270C4—4522no—
271C4—2262no—
272C4#1681364312yescomplemented
273C4C22×D45211yescharacteristic
274C4#1681366811yescharacteristic
275C2—42no—
276C2—9042no—
277C2—4522no—
278C2D4×D45211yescharacteristic
279C2C2×#1681364311yescharacteristic
280C2#2029940511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC4×SD16×C113C2
socleC22×C113C22×D4
hypercenterC4×SD16D113
hypocenterC113#3284
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#16813643C2semidirect
2. #20299270C2semidirect
3. #20299252C2semidirect
4. #20298971C2semidirect
5. #20298828C2semidirect
6. #20298808C2semidirect
7. #20298793C2semidirect
8. #20298763C2semidirect
9. #20298744C2semidirect
10. C8×D452C2semidirect
11. C4×SD16×C113C2semidirect
73. SD16×C113D4semidirect
129. C4×C113#135semidirect
141. C113#3284semidirect
151. C4×SD16D113semidirect
204. SD16D452semidirect
272. C4#16813643semidirect

Maximal subgroups

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

subgroupindex
C2×#168136432
#202992702
#202992522
#202989712
#202988282
#202988082
#202987932
#202987632
#202987442
C8×D4522
C4×SD16×C1132
#3284113