Finite Group Databasebeta

← #28403254

Subgroups — #28403254

Order 14464.

336 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299324C211yesmaximal, characteristic, complemented
2#20299317C211yesmaximal, characteristic
3#20298952C211yesmaximal, characteristic
4#20298951C211yesmaximal, characteristic
5#20298947C211yesmaximal, characteristic, complemented
6#20298906C211yesmaximal, characteristic, complemented
7#20298903C211yesmaximal, characteristic, complemented
8#20298876C211yesmaximal, characteristic
9#20298818C211yesmaximal, characteristic
10#20298806C211yesmaximal, characteristic, complemented
11#20298722C211yesmaximal, characteristic, complemented
12Q16×Dic113C211yesmaximal, characteristic, complemented
13C4×#14268637C211yesmaximal, characteristic, complemented
14SD16×Dic113C211yesmaximal, characteristic
15#464×C113C211yesmaximal, characteristic
16C2×#14268637C2211yescharacteristic
17#16813621—21no—
18#16813621C2211yescharacteristic
19#16813620C2211yescharacteristic
20#16813615—21no—
21#16813615—21no—
22#16813614—21no—
23#16813614C2211yescharacteristic
24#16813613—21no—
25#16813613C2211yescharacteristic
26#16813609C2211yescharacteristic
27#16813599—21no—
28Q8×Dic113C2211yescharacteristic
29Q8×Dic113C2211yescharacteristic
30Q8×Dic113C2211yescharacteristic
31C4×Dic226—21no—
32C4×Dic226C2211yescharacteristic
33C4×Dic226C2211yescharacteristic
34D4×Dic113C2211yescharacteristic
35#16813578—21no—
36#16813556C2211yescharacteristic
37#16813555C2211yescharacteristic
38#16813554C2211yescharacteristic
39#16813551C2211yescharacteristic
40#16813551C2211yescharacteristic
41#16813547C2211yescharacteristic
42#16813547C2211yescharacteristic
43#16813546C2211yescharacteristic
44#16813546C2211yescharacteristic
45#16813546C2211yescharacteristic
46#16813545C2211yescharacteristic
47#16813543C2211yescharacteristic
48#16813543C2211yescharacteristic
49C4×#11744751C2211yescharacteristic
50C8×Dic113C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C2×Q16×C113C2211yescharacteristic
53C2×SD16×C113C2211yescharacteristic
54#124×C113C2211yescharacteristic
55C4×Q8×C113C2211yescharacteristic
56C4⋊C8×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226D411yescharacteristic
61C2×Dic226C2311yescharacteristic
62C22×Dic113—21no—
63#14268637—22no—
64C2×#11744751C2311yescharacteristic
65C2×#11744751C2311yescharacteristic
66C4⋊Dic113—21no—
67C4⋊Dic113—21no—
68C4⋊Dic113—21no—
69C4⋊Dic113—21no—
70C4⋊Dic113D411yescharacteristic
71C4⋊Dic113C2311yescharacteristic
72C4⋊Dic113C2311yescharacteristic
73C4⋊Dic113C2311yescharacteristic
74#14268626—21no—
75#14268626—21no—
76#14268626—21no—
77#14268626—21no—
78#14268626—21no—
79#14268626—21no—
80#14268626—21no—
81#14268626D411yescharacteristic
82#14268626D411yescharacteristic
83C22⋊Dic113—21no—
84C22⋊Dic113—21no—
85C22⋊Dic113—21no—
86C4×Dic113—21no—
87C4×Dic113—21no—
88C4×Dic113—21no—
89C4×Dic113—21no—
90C4×Dic113C2311yescharacteristic
91C4×Dic113C2311yescharacteristic
92C2×Q8×C113C2311yescharacteristic
93C2×Q8×C113C2311yescharacteristic
94C2×D4×C113C2311yescharacteristic
95Q16×C113—22no—
96SD16×C113—22no—
97C2×C8×C113C2311yescharacteristic
98C2×C8×C113C2311yescharacteristic
99C4⋊C4×C113—21no—
100C4⋊C4×C113C2311yescharacteristic
101C22⋊C4×C113—21no—
102C22⋊C4×C113—21no—
103C42×C113—21no—
104C42×C113C2311yescharacteristic
105C23×C113—21no—
106Q8×C113—21no—
107Q8×C113—21no—
108Q8×C113—21no—
109Q8×C113#4112yes—
110D4×C113—21no—
111D4×C113—21no—
112C2×C4×C113—21no—
113C2×C4×C113—21no—
114C2×C4×C113—21no—
115C2×C4×C113C2×D411yescharacteristic
116C2×C4×C113C2×D411yescharacteristic
117C2×C4×C113C2411yescharacteristic
118C2×Dic113—21no—
119C2×Dic113—21no—
120C2×Dic113—21no—
121C2×Dic113—21no—
122C2×Dic113—42no—
123C2×Dic113C2×D411yescharacteristic
124C2×Dic113C2×D411yescharacteristic
125C2×Dic113C2×D411yescharacteristic
126C2×Dic113C2×D411yescharacteristic
127Dic226—22no—
128Dic226—21no—
129Dic226—21no—
130Dic226—42no—
131C8×C113—21no—
132C8×C113—21no—
133#11744751—21no—
134#11744751—21no—
135C22×C113—41no—
136C22×C113—41no—
137C22×C113—41no—
138C22×C113C22×D411yescharacteristic
139C4×C113—22no—
140C4×C113—21no—
141C4×C113—21no—
142C4×C113—41no—
143C4×C113—41no—
144C4×C113C2×#4111yescharacteristic
145C4×C1132−1+411yescharacteristic
146Dic113—21no—
147Dic113—21no—
148Dic113—21no—
149Dic113—41no—
150Dic113—41no—
151Dic113—41no—
152Dic113—41no—
153Dic113#13512yes—
154C2×C113—81no—
155C2×C113#54811yescharacteristic
156C2×C113C2×#13511yescharacteristic
157C2×C113#57811yescharacteristic
158#3364—1131nomaximal, Sylow
159C113#336411yescharacteristic, complemented, Sylow
160#557—1131no—
161#556—1131no—
162#488—1131no—
163#488—1131no—
164#487—1131no—
165#479—1131no—
166#479—1131no—
167#474—1131no—
168#464—1131no—
169#464D11311yescharacteristic
170#462—1131no—
171C8×Q8—1131no—
172C4×Q16—1131no—
173C4×Q16—1131no—
174C4×SD16—1131no—
175C2×Q16—1131no—
176C2×Q16C2×D11311yescharacteristic
177C2×SD16C2×D11311yescharacteristic
178C4⋊Q8—1131no—
179C4⋊Q8—1131no—
180C4⋊Q8—2261no—
181#126—2261no—
182#126—2261no—
183#125—1131no—
184#125—1131no—
185#125—2261no—
186#125—2261no—
187#124—1131no—
188#124C2×D11311yescharacteristic
189C22⋊Q8—2261no—
190C4×Q8—1131no—
191C4×Q8—1131no—
192C4×Q8—1131no—
193C4×Q8—1131no—
194C4×Q8—1131no—
195C4×Q8—2261no—
196C4×Q8C2×D11311yescharacteristic
197C4×D4—1131no—
198#117—2261no—
199#107—1131no—
200#107—1131no—
201#106—1131no—
202C4⋊C8—1131no—
203C4⋊C8—1131no—
204C4⋊C8C2×D11311yescharacteristic
205#103—1131no—
206#103—1131no—
207#103—1131no—
208#103—1131no—
209#103—1131no—
210#103—1131no—
211#103C2×D11311yescharacteristic
212#102—1131no—
213#102—1131no—
214#102C2×D11311yescharacteristic
215C4×C8—1131no—
216C4×C8—1131no—
217C4×C8—1131no—
218C2×Q8—1131no—
219C2×Q8—1131no—
220C2×Q8—2261no—
221C2×Q8C22×D11311yescharacteristic
222C2×Q8C22×D11311yescharacteristic
223C2×D4C22×D11311yescharacteristic
224C22×C4—2261no—
225Q16—22no—
226Q16—2262no—
227SD16—22no—
228C2×C8—1131no—
229C2×C8—1131no—
230C2×C8C22×D11311yescharacteristic
231C2×C8C22×D11311yescharacteristic
232C4⋊C4—21no—
233C4⋊C4—1131no—
234C4⋊C4—1131no—
235C4⋊C4—1131no—
236C4⋊C4—1131no—
237C4⋊C4—1131no—
238C4⋊C4—1131no—
239C4⋊C4—2261no—
240C4⋊C4—2261no—
241C4⋊C4—2261no—
242C4⋊C4—2261no—
243C4⋊C4—2261no—
244C4⋊C4—2261no—
245C4⋊C4—2261no—
246C4⋊C4—2261no—
247C4⋊C4—2261no—
248C4⋊C4—2261no—
249C4⋊C4—2261no—
250C4⋊C4C22×D11311yescharacteristic
251C22⋊C4—21no—
252C22⋊C4—21no—
253C22⋊C4—2261no—
254C22⋊C4—2261no—
255C22⋊C4—2261no—
256C42—21no—
257C42—1131no—
258C42—1131no—
259C42—2261no—
260C42—2261no—
261C42—2261no—
262C42—2261no—
263C42C22×D11311yescharacteristic
264C23—21no—
265Q8—21no—
266Q8—21no—
267Q8—21no—
268Q8—4522no—
269Q8—2262no—
270Q8—2261no—
271Q8—2261no—
272Q8#1426864612yes—
273D4—21no—
274D4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—1131no—
279C2×C4—1131no—
280C2×C4—1131no—
281C2×C4—1131no—
282C2×C4—4522no—
283C2×C4—2261no—
284C2×C4—2261no—
285C2×C4—2261no—
286C2×C4—2261no—
287C2×C4D4×D11311yescharacteristic
288C2×C4D4×D11311yescharacteristic
289C2×C4C23×D11311yescharacteristic
290C8—21no—
291C8—21no—
292C8—2261no—
293C8—2261no—
294C22—41no—
295C22—41no—
296C22—41no—
297C22C2×D4×D11311yescharacteristic
298C4—21no—
299C4—21no—
300C4—22no—
301C4—41no—
302C4—41no—
303C4—1132no—
304C4—4521no—
305C4—4521no—
306C4—4521no—
307C4—4521no—
308C4—2261no—
309C4—2261no—
310C4—2261no—
311C4C2×#1426864611yescharacteristic
312C4#1681366911yescharacteristic
313C2—81no—
314C2#2029925411yescharacteristic
315C2#135×D11311yescharacteristic
316C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#464×C113C2
socleC22×C113C22×D4
prime radicalC2×D4×C113C23
hypercenter#464D113
hypocenterC113#3364
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #20299324C2semidirect
5. #20298947C2semidirect
6. #20298906C2semidirect
7. #20298903C2semidirect
10. #20298806C2semidirect
11. #20298722C2semidirect
12. Q16×Dic113C2semidirect
13. C4×#14268637C2semidirect
159. C113#3364semidirect

Maximal subgroups

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

subgroupindex
#202993242
#202993172
#202989522
#202989512
#202989472
#202989062
#202989032
#202988762
#202988182
#202988062
#202987222
Q16×Dic1132
C4×#142686372
SD16×Dic1132
#464×C1132
#3364113