Finite Group Databasebeta

← #28403121

Subgroups — #28403121

Order 14464.

348 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299318C211yesmaximal, characteristic, complemented
2#20299294C211yesmaximal, characteristic
3#20299007C211yesmaximal, characteristic, complemented
4#20298940C211yesmaximal, characteristic, complemented
5#20298929C211yesmaximal, characteristic, complemented
6#20298923C211yesmaximal, characteristic, complemented
7#20298923C211yesmaximal, characteristic, complemented
8#20298906C211yesmaximal, characteristic, complemented
9#20298889C211yesmaximal, characteristic, complemented
10#20298844C211yesmaximal, characteristic, complemented
11#20298827C211yesmaximal, characteristic, complemented
12#20298700C211yesmaximal, characteristic, complemented
13#20298640C211yesmaximal, characteristic, complemented
14#20298636C211yesmaximal, characteristic, complemented
15#435×C113C211yesmaximal, characteristic, complemented
16C2×#14268636C2211yescharacteristic
17#16813622C2211yescharacteristic
18#16813617—21no—
19#16813615—21no—
20#16813615—21no—
21#16813614C2211yescharacteristic
22#16813609—21no—
23#16813604—21no—
24#16813601C2211yescharacteristic
25#16813601C2211yescharacteristic
26#16813596C2211yescharacteristic
27#16813596C2211yescharacteristic
28#16813594—21no—
29C4×Dic226C2211yescharacteristic
30#16813587—21no—
31C4×D452C2211yescharacteristic
32#16813582—21no—
33#16813581C2211yescharacteristic
34#16813581C2211yescharacteristic
35#16813581C2211yescharacteristic
36C2×C4⋊Dic113C2211yescharacteristic
37#16813556C2211yescharacteristic
38#16813556C2211yescharacteristic
39#16813556C2211yescharacteristic
40#16813556C2211yescharacteristic
41#16813554C2211yescharacteristic
42#16813554C2211yescharacteristic
43#16813554C2211yescharacteristic
44#16813554C2211yescharacteristic
45#16813554C2211yescharacteristic
46#16813547C2211yescharacteristic
47#16813547C2211yescharacteristic
48#16813547C2211yescharacteristic
49#16813544C2211yescharacteristic
50#16813544C2211yescharacteristic
51#16813544C2211yescharacteristic
52C2×M16×C113C2211yescharacteristic
53C22×C8×C113C2211yescharacteristic
54C4×D4×C113C2211yescharacteristic
55C4⋊C8×C113C2211yescharacteristic
56C22⋊C8×C113C2211yescharacteristic
57C22⋊C8×C113C2211yescharacteristic
58#97×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226C2311yescharacteristic
61C2×D452C2311yescharacteristic
62C2×C22⋊D113—21no—
63C2×C22⋊D113—21no—
64C22×Dic113—21no—
65C2×C4×D113—21no—
66#14268636—22no—
67C4⋊Dic113—21no—
68C4⋊Dic113—21no—
69C4⋊Dic113C2311yescharacteristic
70C4⋊Dic113C2311yescharacteristic
71C4⋊Dic113C2311yescharacteristic
72C4⋊Dic113C2311yescharacteristic
73C4⋊Dic113C2311yescharacteristic
74C4⋊Dic113C2311yescharacteristic
75#14268626—21no—
76#14268626—21no—
77#14268626—21no—
78#14268626—21no—
79#14268626—21no—
80C22⋊Dic113—21no—
81C22⋊Dic113—21no—
82C22⋊Dic113—21no—
83C22⋊Dic113—21no—
84C22⋊Dic113—21no—
85#14268624—21no—
86#14268624—21no—
87#14268624—21no—
88C4×Dic113—21no—
89C4×Dic113—21no—
90C4×Dic113—21no—
91C4×Dic113—21no—
92C2×D4×C113D411yescharacteristic
93C22×C4×C113C2311yescharacteristic
94C22×C4×C113C2311yescharacteristic
95M16×C113—22no—
96C2×C8×C113—22no—
97C2×C8×C113C2311yescharacteristic
98C2×C8×C113C2311yescharacteristic
99C2×C8×C113C2311yescharacteristic
100C2×C8×C113C2311yescharacteristic
101C4⋊C4×C113D411yescharacteristic
102C22⋊C4×C113D411yescharacteristic
103C22⋊C4×C113D411yescharacteristic
104C42×C113C2311yescharacteristic
105C23×C113C2×D411yescharacteristic
106C23×C113C2×D411yescharacteristic
107C22×D113—21no—
108D4×C113—41no—
109C2×C4×C113—21no—
110C2×C4×C113—21no—
111C2×C4×C113—21no—
112C2×C4×C113—21no—
113C2×C4×C113C2×D411yescharacteristic
114C2×C4×C113C2×D411yescharacteristic
115C2×C4×C113C2×D411yescharacteristic
116C2×C4×C113C2×D411yescharacteristic
117C2×C4×C113C2411yescharacteristic
118C22⋊D113—42no—
119C22⋊D113—81no—
120C2×Dic113—21no—
121C2×Dic113—21no—
122C2×Dic113—21no—
123C2×Dic113—21no—
124C2×Dic113—21no—
125C2×Dic113—21no—
126C2×Dic113—21no—
127C2×Dic113—81no—
128D452—21no—
129D452—21no—
130C4×D113—81no—
131Dic226—21no—
132Dic226—21no—
133Dic226—42no—
134C8×C113—21no—
135C8×C113—21no—
136C8×C113—21no—
137C8×C113#4112yes—
138C22×C113—21no—
139C22×C113—21no—
140C22×C113—21no—
141C22×C113—21no—
142C22×C113—21no—
143C22×C113—21no—
144C22×C113C22×D411yescharacteristic
145C2×D113—41no—
146C2×D113—41no—
147C2×D113—41no—
148C4×C113—21no—
149C4×C113—21no—
150C4×C113—21no—
151C4×C113—21no—
152C4×C113C2×#4111yescharacteristic
153C4×C1132−1+411yescharacteristic
154Dic113—41no—
155Dic113—41no—
156Dic113—41no—
157Dic113—41no—
158Dic113—41no—
159Dic113—41no—
160Dic113—41no—
161C2×C113—41no—
162C2×C113—41no—
163C2×C113#54711yescharacteristic
164C2×C113#57511yescharacteristic
165C2×C113#57711yescharacteristic
166D113—81no—
167#3350—1131nomaximal, Sylow
168C113#335011yescharacteristic, complemented, Sylow
169#556—1131no—
170#553—1131no—
171#501—1131no—
172#485—1131no—
173#483—1131no—
174#482—1131no—
175#482—1131no—
176#479—1131no—
177#476—1131no—
178#468—1131no—
179#465—1131no—
180#440—1131no—
181#435D11311yescharacteristic, complemented
182#428—1131no—
183#427—1131no—
184C2×SD16—1131no—
185C2×M16C2×D11311yescharacteristic
186C22×C8C2×D11311yescharacteristic
187C4⋊Q8—1131no—
188#126—2261no—
189#126—2261no—
190#126—2261no—
191#125—1131no—
192#124—2261no—
193#123—2261no—
194C22⋊Q8—1131no—
195C22⋊Q8—1131no—
196#121—1131no—
197#121—1131no—
198#121—2261no—
199C4×Q8—1131no—
200C4×Q8—2261no—
201C4×D4—1131no—
202C4×D4—2261no—
203C4×D4C2×D11311yescharacteristic
204#117—1131no—
205#117—1131no—
206#117—1131no—
207C2×C4⋊C4—1131no—
208#107—1131no—
209#107—1131no—
210#107—1131no—
211#107—1131no—
212#106—1131no—
213#106—1131no—
214#106—1131no—
215#106—1131no—
216#106—1131no—
217C4⋊C8C2×D11311yescharacteristic
218#103—1131no—
219#103—1131no—
220#103—1131no—
221#102—1131no—
222#102—1131no—
223#102—1131no—
224C22⋊C8C2×D11311yescharacteristic
225C22⋊C8C2×D11311yescharacteristic
226#97C2×D11311yescharacteristic
227C2×Q8—1131no—
228C2×Q8—2261no—
229C2×D4—1131no—
230C2×D4—2261no—
231C2×D4—2261no—
232C2×D4D45211yescharacteristic
233C22×C4—2261no—
234C22×C4—2261no—
235C22×C4C22×D11311yescharacteristic
236C22×C4C22×D11311yescharacteristic
237SD16—2262no—
238M16—22no—
239C2×C8—22no—
240C2×C8C22×D11311yescharacteristic
241C2×C8C22×D11311yescharacteristic
242C2×C8C22×D11311yescharacteristic
243C2×C8C22×D11311yescharacteristic
244C4⋊C4—1131no—
245C4⋊C4—1131no—
246C4⋊C4—1131no—
247C4⋊C4—1131no—
248C4⋊C4—1131no—
249C4⋊C4—1131no—
250C4⋊C4—2261no—
251C4⋊C4—2261no—
252C4⋊C4—2261no—
253C4⋊C4—2261no—
254C4⋊C4—2261no—
255C4⋊C4—2261no—
256C4⋊C4—2261no—
257C4⋊C4D45211yescharacteristic
258C22⋊C4—2261no—
259C22⋊C4—2261no—
260C22⋊C4—2261no—
261C22⋊C4—2261no—
262C22⋊C4—2261no—
263C22⋊C4—2261no—
264C22⋊C4—2261no—
265C22⋊C4—2261no—
266C22⋊C4D45211yescharacteristic
267C22⋊C4D45211yescharacteristic
268C42—2261no—
269C42—2261no—
270C42—2261no—
271C42—2261no—
272C42C22×D11311yescharacteristic
273C23—2261no—
274C23C2×D45211yescharacteristic
275C23C2×D45211yescharacteristic
276Q8—4522no—
277Q8—2261no—
278Q8—2261no—
279D4—41no—
280D4—9041no—
281D4—4522no—
282D4—2261no—
283D4—2261no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—9041no—
289C2×C4—9041no—
290C2×C4—2261no—
291C2×C4—2261no—
292C2×C4—2261no—
293C2×C4—2261no—
294C2×C4—2261no—
295C2×C4—2261no—
296C2×C4—2261no—
297C2×C4C2×D45211yescharacteristic
298C2×C4C2×D45211yescharacteristic
299C2×C4C2×D45211yescharacteristic
300C2×C4C2×D45211yescharacteristic
301C2×C4C23×D11311yescharacteristic
302C8—21no—
303C8—21no—
304C8—21no—
305C8#1426864612yes—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—4521no—
313C22—4521no—
314C22—4521no—
315C22C22×D45211yescharacteristic
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—4521no—
321C4—4521no—
322C4—4521no—
323C4—4521no—
324C4—4521no—
325C4—4521no—
326C4—4521no—
327C4C2×#1426864611yescharacteristic
328C4#1681366911yescharacteristic
329C2—41no—
330C2—41no—
331C2—9041no—
332C2#2029925211yescharacteristic
333C2#2029939811yescharacteristic
334C2#2029941011yescharacteristic
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#435×C113C2
socleC22×C113C22×D4
prime radical#20299294C2
hypercenter#435D113
hypocenterC113#3350
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #20299318C2semidirect
3. #20299007C2semidirect
4. #20298940C2semidirect
5. #20298929C2semidirect
6. #20298923C2semidirect
7. #20298923C2semidirect
8. #20298906C2semidirect
9. #20298889C2semidirect
10. #20298844C2semidirect
11. #20298827C2semidirect
12. #20298700C2semidirect
13. #20298640C2semidirect
14. #20298636C2semidirect
15. #435×C113C2semidirect
168. C113#3350semidirect
181. #435D113semidirect

Maximal subgroups

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

subgroupindex
#202993182
#202992942
#202990072
#202989402
#202989292
#202989232
#202989062
#202988892
#202988442
#202988272
#202987002
#202986402
#202986362
#435×C1132
#3350113