Finite Group Databasebeta

← #28402027

Subgroups — #28402027

Order 14464.

322 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
1#20299211C211yesmaximal, characteristic
2#20299206C211yesmaximal, characteristic
3#20298908C211yesmaximal, characteristic, complemented
4#20298904C211yesmaximal, characteristic, complemented
5#20298902C211yesmaximal, characteristic, complemented
6#20298857C211yesmaximal, characteristic
7#20298855C211yesmaximal, characteristic
8#20298840C211yesmaximal, characteristic
9#20298838C211yesmaximal, characteristic
10#20298809C211yesmaximal, characteristic, complemented
11#20298808C211yesmaximal, characteristic, complemented
12#20298807C211yesmaximal, characteristic, complemented
13#20298807C211yesmaximal, characteristic, complemented
14#20298623C211yesmaximal, characteristic
15#479×C113C211yesmaximal, characteristic, complemented
16C2×Dic452C2211yescharacteristic
17C2×Dic452C2211yescharacteristic
18C2×#14268637C2211yescharacteristic
19C2×#14268637C2211yescharacteristic
20C2×#14268630C2211yescharacteristic
21C2×C8×D113C2211yescharacteristic
22#16813622C2211yescharacteristic
23#16813620C2211yescharacteristic
24#16813617—21no—
25#16813617—21no—
26#16813617—21no—
27#16813616—21no—
28#16813614—21no—
29#16813613—21no—
30#16813613—21no—
31#16813613C2211yescharacteristic
32#16813612—21no—
33#16813602C2211yescharacteristic
34#16813602C2211yescharacteristic
35#16813602C2211yescharacteristic
36#16813598C2211yescharacteristic
37C4×Dic226C2211yescharacteristic
38#16813587C2211yescharacteristic
39#16813587C2211yescharacteristic
40#16813579C2211yescharacteristic
41#16813555C2211yescharacteristic
42#16813553C2211yescharacteristic
43C4⋊#11744751C2211yescharacteristic
44#16813551C2211yescharacteristic
45#16813551C2211yescharacteristic
46#16813547C2211yescharacteristic
47#16813547C2211yescharacteristic
48#16813545C2211yescharacteristic
49#16813545C2211yescharacteristic
50#16813545C2211yescharacteristic
51#16813545C2211yescharacteristic
52#125×C113C2211yescharacteristic
53C4×Q8×C113C2211yescharacteristic
54#107×C113C2211yescharacteristic
55#106×C113C2211yescharacteristic
56C4⋊C8×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58#103×C113C2211yescharacteristic
59C2×Dic226C2311yescharacteristic
60C2×Dic226C2311yescharacteristic
61C2×Dic226C2311yescharacteristic
62C2×C4×D113C2311yescharacteristic
63Dic452—41no—
64Dic452—41no—
65#14268637—41no—
66#14268637—41no—
67#14268630—41no—
68C2×#11744751C2311yescharacteristic
69C2×#11744751C2311yescharacteristic
70C8×D113—41no—
71C4⋊Dic113—21no—
72C4⋊Dic113—21no—
73C4⋊Dic113—21no—
74C4⋊Dic113—21no—
75C4⋊Dic113—21no—
76C4⋊Dic113—21no—
77C4⋊Dic113C2311yescharacteristic
78#14268626—21no—
79#14268626—21no—
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83#14268626—21no—
84#14268626—21no—
85#14268626D411yescharacteristic
86#14268626D411yescharacteristic
87#14268624—21no—
88#14268624—21no—
89#14268624—21no—
90#14268624—21no—
91#14268624D411yescharacteristic
92#14268624D411yescharacteristic
93C4×Dic113—21no—
94C4×Dic113—21no—
95C4×Dic113—21no—
96C4×Dic113C2311yescharacteristic
97C2×Q8×C113C2311yescharacteristic
98C2×C8×C113C2311yescharacteristic
99C2×C8×C113C2311yescharacteristic
100C4⋊C4×C113—21no—
101C4⋊C4×C113—21no—
102C4⋊C4×C113—21no—
103C4⋊C4×C113C2311yescharacteristic
104C4⋊C4×C113C2311yescharacteristic
105C4⋊C4×C113C2311yescharacteristic
106C42×C113—21no—
107C42×C113C2311yescharacteristic
108C22×D113C2×D411yescharacteristic
109Q8×C113—21no—
110Q8×C113—21no—
111C2×C4×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×Dic113C2×D411yescharacteristic
123C2×Dic113C2×D411yescharacteristic
124C2×Dic113C2×D411yescharacteristic
125C4×D113—21no—
126C4×D113—21no—
127Dic226—21no—
128Dic226—21no—
129Dic226—21no—
130Dic226—21no—
131Dic226—21no—
132Dic226—21no—
133C8×C113—21no—
134C8×C113—21no—
135#11744751—21no—
136#11744751—21no—
137C22×C113C22×D411yescharacteristic
138C2×D113—21no—
139C2×D113—21no—
140C2×D113—21no—
141C4×C113—21no—
142C4×C113—21no—
143C4×C113—41no—
144C4×C113—41no—
145C4×C113—41no—
146C4×C113—41no—
147C4×C113H(5,𝔽2)11yescharacteristic
148C4×C1132−1+411yescharacteristic
149Dic113—21no—
150Dic113—21no—
151Dic113—21no—
152Dic113—41no—
153Dic113—41no—
154Dic113—41no—
155Dic113—41no—
156C2×C113#53711yescharacteristic
157C2×C113#57811yescharacteristic
158C2×C113#57811yescharacteristic
159D113—41no—
160#3261—1131nomaximal, Sylow
161C113#326111yescharacteristic, complemented, Sylow
162#541—1131no—
163#541—1131no—
164#479—1131no—
165#479—1131no—
166#479—1131no—
167#479D11311yescharacteristic, complemented
168#470—1131no—
169#470—1131no—
170#467—1131no—
171#467—1131no—
172#462—1131no—
173#462—1131no—
174#462—1131no—
175#462—1131no—
176#424—1131no—
177C2×Q16—1131no—
178C2×Q16—1131no—
179C2×Q16—1131no—
180C2×Q16—1131no—
181C2×M16—1131no—
182C22×C8—1131no—
183C4⋊Q8—1131no—
184C4⋊Q8—1131no—
185#126—2261no—
186#126—2261no—
187#126—2261no—
188#126—2261no—
189#125—1131no—
190#125—2261no—
191#125—2261no—
192#125—2261no—
193#125—2261no—
194#125C2×D11311yescharacteristic
195C22⋊Q8—1131no—
196C22⋊Q8—1131no—
197C22⋊Q8—1131no—
198C22⋊Q8—1131no—
199C4×Q8—1131no—
200C4×Q8—1131no—
201C4×Q8—1131no—
202C4×Q8C2×D11311yescharacteristic
203#117—1131no—
204#107—1131no—
205#107C2×D11311yescharacteristic
206#106—1131no—
207#106C2×D11311yescharacteristic
208C4⋊C8—1131no—
209C4⋊C8—1131no—
210C4⋊C8—1131no—
211C4⋊C8C2×D11311yescharacteristic
212#103—1131no—
213#103—1131no—
214#103—1131no—
215#103—1131no—
216#103—1131no—
217#103—1131no—
218#103C2×D11311yescharacteristic
219#103C2×D11311yescharacteristic
220C2×Q8—1131no—
221C2×Q8—1131no—
222C2×Q8—1131no—
223C2×Q8C22×D11311yescharacteristic
224C22×C4—1131no—
225Q16—4521no—
226Q16—4521no—
227Q16—4521no—
228Q16—4521no—
229M16—4521no—
230C2×C8—1131no—
231C2×C8—1131no—
232C2×C8—4521no—
233C2×C8C22×D11311yescharacteristic
234C2×C8C22×D11311yescharacteristic
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—1131no—
239C4⋊C4—1131no—
240C4⋊C4—1131no—
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⋊C4—2261no—
251C4⋊C4—2261no—
252C4⋊C4—2261no—
253C4⋊C4—2261no—
254C4⋊C4C22×D11311yescharacteristic
255C4⋊C4C22×D11311yescharacteristic
256C4⋊C4C22×D11311yescharacteristic
257C22⋊C4—1131no—
258C22⋊C4—1131no—
259C22⋊C4—2261no—
260C22⋊C4—2261no—
261C22⋊C4—2261no—
262C22⋊C4—2261no—
263C42—21no—
264C42—1131no—
265C42—2261no—
266C42—2261no—
267C42—2261no—
268C42C22×D11311yescharacteristic
269C23—1131no—
270Q8—21no—
271Q8—21no—
272Q8—2261no—
273Q8—2261no—
274Q8—2261no—
275Q8—2261no—
276Q8—2261no—
277Q8—2261no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—1131no—
283C2×C4—1131no—
284C2×C4—1131no—
285C2×C4—2261no—
286C2×C4—2261no—
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—2261no—
299C22—2261no—
300C22—2261no—
301C22C2×D4×D11311yescharacteristic
302C4—21no—
303C4—21no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—4521no—
309C4—4521no—
310C4—4521no—
311C4—4521no—
312C4—2261no—
313C4—2261no—
314C4—2261no—
315C4#1681366811yescharacteristic
316C4#1681367011yescharacteristic
317C2—4521no—
318C2#2029917811yescharacteristic
319C2#2029941211yescharacteristic
320C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#479×C113C2
socleC22×C113C22×D4
prime radicalC22×D113C2×D4
hypercenter#479D113
hypocenterC113#3261
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
3. #20298908C2semidirect
4. #20298904C2semidirect
5. #20298902C2semidirect
10. #20298809C2semidirect
11. #20298808C2semidirect
12. #20298807C2semidirect
13. #20298807C2semidirect
15. #479×C113C2semidirect
161. C113#3261semidirect
167. #479D113semidirect

Maximal subgroups

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

subgroupindex
#202992112
#202992062
#202989082
#202989042
#202989022
#202988572
#202988552
#202988402
#202988382
#202988092
#202988082
#202988072
#202986232
#479×C1132
#3261113