Finite Group Databasebeta

← #28400798

Subgroups — #28400798

Order 14464.

370 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299215C211yesmaximal, characteristic
2#20299075C211yesmaximal, characteristic, complemented
3#20298939C211yesmaximal, characteristic, complemented
4#20298892C211yesmaximal, characteristic, complemented
5#20298882C211yesmaximal, characteristic, complemented
6#20298819C211yesmaximal, characteristic, complemented
7#20298819C211yesmaximal, characteristic, complemented
8#20298756C211yesmaximal, characteristic, complemented
9#20298736C211yesmaximal, characteristic
10#20298704C211yesmaximal, characteristic, complemented
11#20298695C211yesmaximal, characteristic, complemented
12#20298692C211yesmaximal, characteristic, complemented
13#20298689C211yesmaximal, characteristic, complemented
14#20298656C211yesmaximal, characteristic, complemented
15#482×C113C211yesmaximal, characteristic
16C22×Dic226C2211yescharacteristic
17C2×Dic452C2211yescharacteristic
18C2×Dic452C2211yescharacteristic
19C2×#14268635C2211yescharacteristic
20C2×#14268635C2211yescharacteristic
21#16813621C2211yescharacteristic
22#16813615—21no—
23#16813609—21no—
24#16813609C2211yescharacteristic
25#16813603—21no—
26#16813601C2211yescharacteristic
27#16813599—21no—
28C4×Dic226—21no—
29C4×Dic226—21no—
30#16813587C2211yescharacteristic
31#16813587C2211yescharacteristic
32#16813587C2211yescharacteristic
33#16813587C2211yescharacteristic
34#16813587C2211yescharacteristic
35D4×Dic113C2211yescharacteristic
36#16813581C2211yescharacteristic
37#16813578—21no—
38#16813578—21no—
39#16813555C2211yescharacteristic
40#16813553C2211yescharacteristic
41#16813551C2211yescharacteristic
42#16813551C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813547C2211yescharacteristic
45#16813545C2211yescharacteristic
46#16813545C2211yescharacteristic
47#16813545C2211yescharacteristic
48#16813545C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813532C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52#121×C113C2211yescharacteristic
53#117×C113C2211yescharacteristic
54#107×C113C2211yescharacteristic
55#106×C113C2211yescharacteristic
56#102×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58C22⋊C8×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226—22no—
61C2×Dic226—22no—
62C2×Dic226—21no—
63C2×Dic226C2311yescharacteristic
64C2×Dic226C2311yescharacteristic
65C2×Dic226C2311yescharacteristic
66C22×Dic113—21no—
67C22×Dic113—21no—
68Dic452—22no—
69Dic452—22no—
70#14268635—22no—
71#14268635—22no—
72C2×#11744751C2311yescharacteristic
73C2×#11744751C2311yescharacteristic
74C4⋊Dic113D411yescharacteristic
75C4⋊Dic113D411yescharacteristic
76C4⋊Dic113C2311yescharacteristic
77#14268626—21no—
78#14268626—21no—
79#14268626—21no—
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83#14268626—21no—
84C22⋊Dic113—21no—
85C22⋊Dic113—21no—
86C22⋊Dic113—21no—
87C22⋊Dic113—21no—
88C22⋊Dic113D411yescharacteristic
89C22⋊Dic113D411yescharacteristic
90C4×Dic113—21no—
91C4×Dic113—21no—
92C4×Dic113—21no—
93C4×Dic113—21no—
94C4×Dic113—21no—
95C4×Dic113C2311yescharacteristic
96C4×Dic113C2311yescharacteristic
97C2×D4×C113—21no—
98C2×D4×C113C2311yescharacteristic
99C22×C4×C113C2311yescharacteristic
100C2×C8×C113C2311yescharacteristic
101C2×C8×C113C2311yescharacteristic
102C4⋊C4×C113C2311yescharacteristic
103C4⋊C4×C113C2311yescharacteristic
104C4⋊C4×C113C2311yescharacteristic
105C22⋊C4×C113—21no—
106C22⋊C4×C113—21no—
107C42×C113—21no—
108C23×C113—21no—
109C23×C113C2×D411yescharacteristic
110D4×C113—21no—
111D4×C113—21no—
112D4×C113—81no—
113C2×C4×C113—21no—
114C2×C4×C113—21no—
115C2×C4×C113—21no—
116C2×C4×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113C2×D411yescharacteristic
119C2×C4×C113C2411yescharacteristic
120C2×Dic113—24no—
121C2×Dic113—21no—
122C2×Dic113—21no—
123C2×Dic113—21no—
124C2×Dic113—21no—
125C2×Dic113—81no—
126C2×Dic113C2×D411yescharacteristic
127C2×Dic113C2×D411yescharacteristic
128C2×Dic113C2×D411yescharacteristic
129C2×Dic113C2×D411yescharacteristic
130Dic226—24no—
131Dic226—21no—
132Dic226—21no—
133Dic226—21no—
134Dic226—21no—
135Dic226—81no—
136Dic226#4112yes—
137Dic226#4112yes—
138C8×C113—21no—
139C8×C113—21no—
140#11744751—21no—
141#11744751—21no—
142C22×C113—21no—
143C22×C113—21no—
144C22×C113—21no—
145C22×C113—41no—
146C22×C113—41no—
147C22×C113—41no—
148C22×C113C22×D411yescharacteristic
149C4×C113—21no—
150C4×C113—41no—
151C4×C113—41no—
152C4×C113—41no—
153C4×C113C2×#4111yescharacteristic
154C4×C113C2×#4111yescharacteristic
155Dic113—22no—
156Dic113—22no—
157Dic113—21no—
158Dic113—21no—
159Dic113—21no—
160Dic113—21no—
161Dic113—41no—
162Dic113—41no—
163C2×C113—41no—
164C2×C113—81no—
165C2×C113#52511yescharacteristic
166C2×C113#57711yescharacteristic
167C2×C113#57811yescharacteristic
168#3121—1131nomaximal, Sylow
169C113#312111yescharacteristic, complemented, Sylow
170#542—1131no—
171#519—1131no—
172#485—1131no—
173#482D11311yescharacteristic
174#477—1131no—
175#475—1131no—
176#464—1131no—
177#464—1131no—
178#451—1131no—
179#448—1131no—
180#441—1131no—
181#440—1131no—
182C4×Q16—1131no—
183C4×SD16—1131no—
184#433—1131no—
185C22×Q8—1131no—
186C2×Q16—1131no—
187C2×Q16—1131no—
188C2×SD16—1131no—
189C2×SD16—1131no—
190C4⋊Q8—1131no—
191#126—2261no—
192#124—1131no—
193#124—2261no—
194#123—2261no—
195C22⋊Q8—1131no—
196C22⋊Q8—2261no—
197#121C2×D11311yescharacteristic
198C4×Q8—1131no—
199C4×Q8—1131no—
200C4×Q8—1131no—
201C4×Q8—1131no—
202C4×Q8—1131no—
203C4×Q8—2261no—
204C4×Q8—2261no—
205C4×D4—1131no—
206#117—1131no—
207#117—2261no—
208#117—2261no—
209#117C2×D11311yescharacteristic
210#107—1131no—
211#107C2×D11311yescharacteristic
212#106—1131no—
213#106C2×D11311yescharacteristic
214C4⋊C8—1131no—
215C4⋊C8—1131no—
216#103—1131no—
217#103—1131no—
218#103—1131no—
219#103—1131no—
220#103—1131no—
221#103—1131no—
222#102C2×D11311yescharacteristic
223#102C2×D11311yescharacteristic
224C22⋊C8—1131no—
225C22⋊C8C2×D11311yescharacteristic
226#97—1131no—
227C4×C8—1131no—
228C2×Q8—1131no—
229C2×Q8—1131no—
230C2×Q8—1131no—
231C2×Q8—2261no—
232C2×Q8—2262no—
233C2×Q8—2262no—
234C2×Q8—2261no—
235C2×D4—21no—
236C2×D4C22×D11311yescharacteristic
237C22×C4—2261no—
238C22×C4—2261no—
239C22×C4C22×D11311yescharacteristic
240Q16—2262no—
241Q16—2262no—
242SD16—2262no—
243SD16—2262no—
244C2×C8—1131no—
245C2×C8—1131no—
246C2×C8C22×D11311yescharacteristic
247C2×C8C22×D11311yescharacteristic
248C4⋊C4—1131no—
249C4⋊C4—1131no—
250C4⋊C4—1131no—
251C4⋊C4—2261no—
252C4⋊C4—2261no—
253C4⋊C4—2261no—
254C4⋊C4—2261no—
255C4⋊C4—2261no—
256C4⋊C4—2261no—
257C4⋊C4—2261no—
258C4⋊C4C22×D11311yescharacteristic
259C4⋊C4C22×D11311yescharacteristic
260C4⋊C4C22×D11311yescharacteristic
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4—1131no—
264C22⋊C4—1131no—
265C22⋊C4—2261no—
266C22⋊C4—2261no—
267C22⋊C4—2261no—
268C22⋊C4—2261no—
269C42—21no—
270C42—1131no—
271C42—1131no—
272C42—2261no—
273C42—2261no—
274C42—2261no—
275C42—2261no—
276C42—2261no—
277C23—21no—
278C23D4×D11311yescharacteristic
279Q8—1132no—
280Q8—1132no—
281Q8—9041no—
282Q8—2264no—
283Q8—2261no—
284Q8—2261no—
285Q8—2261no—
286Q8—2261no—
287D4—21no—
288D4—21no—
289D4—81no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—1131no—
296C2×C4—1131no—
297C2×C4—1131no—
298C2×C4—1131no—
299C2×C4—9041no—
300C2×C4—2261no—
301C2×C4—2261no—
302C2×C4—2264no—
303C2×C4—2261no—
304C2×C4—2261no—
305C2×C4D4×D11311yescharacteristic
306C2×C4C23×D11311yescharacteristic
307C8—21no—
308C8—21no—
309C8—2261no—
310C8—2261no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22C2×D4×D11311yescharacteristic
318C4—21no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—4521no—
323C4—4521no—
324C4—2262no—
325C4—2262no—
326C4—2261no—
327C4—2261no—
328C4—2261no—
329C4—2261no—
330C4#41×D11311yescharacteristic
331C4#41×D11311yescharacteristic
332C2—41no—
333C2—81no—
334C2#2029910611yescharacteristic
335C2#2029940811yescharacteristic
336C2#2029941211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#482×C113C2
socleC22×C113C22×D4
prime radical#121×C113C22
hypercenter#482D113
hypocenterC113#3121
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #20299075C2semidirect
3. #20298939C2semidirect
4. #20298892C2semidirect
5. #20298882C2semidirect
6. #20298819C2semidirect
7. #20298819C2semidirect
8. #20298756C2semidirect
10. #20298704C2semidirect
11. #20298695C2semidirect
12. #20298692C2semidirect
13. #20298689C2semidirect
14. #20298656C2semidirect
169. C113#3121semidirect

Maximal subgroups

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

subgroupindex
#202992152
#202990752
#202989392
#202988922
#202988822
#202988192
#202987562
#202987362
#202987042
#202986952
#202986922
#202986892
#202986562
#482×C1132
#3121113