Finite Group Databasebeta

← #28403309

Subgroups — #28403309

Order 14464.

338 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×Dic226C211yesmaximal, characteristic, complemented
2#20299317C211yesmaximal, characteristic
3#20298957C211yesmaximal, characteristic
4#20298956C211yesmaximal, characteristic
5#20298947C211yesmaximal, characteristic, complemented
6#20298886C211yesmaximal, characteristic
7#20298884C211yesmaximal, characteristic, complemented
8#20298881C211yesmaximal, characteristic, complemented
9#20298818C211yesmaximal, characteristic
10#20298806C211yesmaximal, characteristic, complemented
11#20298727C211yesmaximal, characteristic, complemented
12#20298705C211yesmaximal, characteristic, complemented
13#20298703C211yesmaximal, characteristic, complemented
14SD16×Dic113C211yesmaximal, characteristic
15#464×C113C211yesmaximal, characteristic
16C2×#14268637C2211yescharacteristic
17#16813622—21no—
18#16813622C2211yescharacteristic
19#16813621—21no—
20#16813621—21no—
21#16813621C2211yescharacteristic
22#16813621C2211yescharacteristic
23#16813620C2211yescharacteristic
24#16813615—21no—
25#16813615—21no—
26#16813609C2211yescharacteristic
27#16813599—21no—
28Q8×Dic113C2211yescharacteristic
29Q8×Dic113C2211yescharacteristic
30Q8×Dic113C2211yescharacteristic
31C4×Dic226—21no—
32C4×Dic226C2211yescharacteristic
33C4×Dic226C2211yescharacteristic
34D4×Dic113C2211yescharacteristic
35#16813578—21no—
36#16813554C2211yescharacteristic
37#16813554C2211yescharacteristic
38#16813553C2211yescharacteristic
39#16813551C2211yescharacteristic
40#16813551C2211yescharacteristic
41#16813547C2211yescharacteristic
42#16813547C2211yescharacteristic
43#16813546C2211yescharacteristic
44#16813546C2211yescharacteristic
45#16813546C2211yescharacteristic
46#16813545C2211yescharacteristic
47#16813543C2211yescharacteristic
48#16813543C2211yescharacteristic
49#16813533C2211yescharacteristic
50#16813532C2211yescharacteristic
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×Dic226—21no—
61C2×Dic226—21no—
62C2×Dic226D411yescharacteristic
63C2×Dic226C2311yescharacteristic
64C22×Dic113—21no—
65#14268637—22no—
66C2×#11744751C2311yescharacteristic
67C2×#11744751C2311yescharacteristic
68C4⋊Dic113—21no—
69C4⋊Dic113—21no—
70C4⋊Dic113—21no—
71C4⋊Dic113—21no—
72C4⋊Dic113D411yescharacteristic
73C4⋊Dic113C2311yescharacteristic
74C4⋊Dic113C2311yescharacteristic
75C4⋊Dic113C2311yescharacteristic
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—81no—
131Dic226—81no—
132Dic226—81no—
133C8×C113—21no—
134C8×C113—21no—
135#11744751—21no—
136#11744751—21no—
137C22×C113—41no—
138C22×C113—41no—
139C22×C113—41no—
140C22×C113C22×D411yescharacteristic
141C4×C113—22no—
142C4×C113—21no—
143C4×C113—21no—
144C4×C113—41no—
145C4×C113—41no—
146C4×C113C2×#4111yescharacteristic
147C4×C1132−1+411yescharacteristic
148Dic113—21no—
149Dic113—21no—
150Dic113—21no—
151Dic113—41no—
152Dic113—41no—
153Dic113—41no—
154Dic113—41no—
155Dic113#13712yes—
156C2×C113—81no—
157C2×C113#54811yescharacteristic
158C2×C113C2×#13711yescharacteristic
159C2×C113#57711yescharacteristic
160#3369—1131nomaximal, Sylow
161C113#336911yescharacteristic, complemented, Sylow
162Q82—1131no—
163#556—1131no—
164#489—1131no—
165#489—1131no—
166#487—1131no—
167#476—1131no—
168#475—1131no—
169#475—1131no—
170#464—1131no—
171#464D11311yescharacteristic
172#462—1131no—
173#446—1131no—
174#441—1131no—
175#441—1131no—
176C4×SD16—1131no—
177C2×Q16—1131no—
178C2×Q16C2×D11311yescharacteristic
179C2×SD16C2×D11311yescharacteristic
180C4⋊Q8—1131no—
181C4⋊Q8—1131no—
182C4⋊Q8—1131no—
183C4⋊Q8—1131no—
184C4⋊Q8—2261no—
185C4⋊Q8—2261no—
186C4⋊Q8—2261no—
187#126—2261no—
188#126—2261no—
189#124—1131no—
190#124C2×D11311yescharacteristic
191C22⋊Q8—2261no—
192C4×Q8—1131no—
193C4×Q8—1131no—
194C4×Q8—1131no—
195C4×Q8—1131no—
196C4×Q8—1131no—
197C4×Q8—2261no—
198C4×Q8C2×D11311yescharacteristic
199C4×D4—1131no—
200#117—2261no—
201#106—1131no—
202#106—1131no—
203#106—1131no—
204C4⋊C8—1131no—
205C4⋊C8—1131no—
206C4⋊C8C2×D11311yescharacteristic
207#103—1131no—
208#103—1131no—
209#103—1131no—
210#103—1131no—
211#103—1131no—
212#103—1131no—
213#103C2×D11311yescharacteristic
214#102—1131no—
215#102—1131no—
216#102C2×D11311yescharacteristic
217#97—1131no—
218#97—1131no—
219C4×C8—1131no—
220C2×Q8—1131no—
221C2×Q8—1131no—
222C2×Q8—2261no—
223C2×Q8—2261no—
224C2×Q8—2261no—
225C2×Q8C22×D11311yescharacteristic
226C2×Q8C22×D11311yescharacteristic
227C2×D4C22×D11311yescharacteristic
228C22×C4—2261no—
229Q16—22no—
230Q16—2262no—
231SD16—22no—
232C2×C8—1131no—
233C2×C8—1131no—
234C2×C8C22×D11311yescharacteristic
235C2×C8C22×D11311yescharacteristic
236C4⋊C4—21no—
237C4⋊C4—1131no—
238C4⋊C4—1131no—
239C4⋊C4—1131no—
240C4⋊C4—1131no—
241C4⋊C4—1131no—
242C4⋊C4—1131no—
243C4⋊C4—2261no—
244C4⋊C4—2261no—
245C4⋊C4—2261no—
246C4⋊C4—2261no—
247C4⋊C4—2261no—
248C4⋊C4—2261no—
249C4⋊C4—2261no—
250C4⋊C4—2261no—
251C4⋊C4—2261no—
252C4⋊C4C22×D11311yescharacteristic
253C22⋊C4—21no—
254C22⋊C4—21no—
255C22⋊C4—2261no—
256C22⋊C4—2261no—
257C22⋊C4—2261no—
258C42—21no—
259C42—1131no—
260C42—1131no—
261C42—2261no—
262C42—2261no—
263C42—2261no—
264C42—2261no—
265C42C22×D11311yescharacteristic
266C23—21no—
267Q8—21no—
268Q8—21no—
269Q8—21no—
270Q8—9041no—
271Q8—9041no—
272Q8—9041no—
273Q8—2262no—
274Q8—2261no—
275Q8—2261no—
276Q8#1426864612yes—
277D4—21no—
278D4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—1131no—
283C2×C4—1131no—
284C2×C4—1131no—
285C2×C4—1131no—
286C2×C4—4522no—
287C2×C4—2261no—
288C2×C4—2261no—
289C2×C4—2261no—
290C2×C4—2261no—
291C2×C4D4×D11311yescharacteristic
292C2×C4D4×D11311yescharacteristic
293C2×C4C23×D11311yescharacteristic
294C8—21no—
295C8—21no—
296C8—2261no—
297C8—2261no—
298C22—41no—
299C22—41no—
300C22—41no—
301C22C2×D4×D11311yescharacteristic
302C4—21no—
303C4—21no—
304C4—22no—
305C4—41no—
306C4—41no—
307C4—1132no—
308C4—4521no—
309C4—4521no—
310C4—4521no—
311C4—4521no—
312C4—2261no—
313C4—2261no—
314C4—2261no—
315C4C2×#1426864611yescharacteristic
316C4#1681366911yescharacteristic
317C2—81no—
318C2#2029925411yescharacteristic
319C2#137×D11311yescharacteristic
320C2#2029940511yescharacteristic
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#3369
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. Q8×Dic226C2semidirect
5. #20298947C2semidirect
7. #20298884C2semidirect
8. #20298881C2semidirect
10. #20298806C2semidirect
11. #20298727C2semidirect
12. #20298705C2semidirect
13. #20298703C2semidirect
161. C113#3369semidirect

Maximal subgroups

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

subgroupindex
Q8×Dic2262
#202993172
#202989572
#202989562
#202989472
#202988862
#202988842
#202988812
#202988182
#202988062
#202987272
#202987052
#202987032
SD16×Dic1132
#464×C1132
#3369113