Finite Group Databasebeta

← #28403086

Subgroups — #28403086

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#20299313C211yesmaximal, characteristic
2#20299286C211yesmaximal, characteristic, complemented
3#20299008C211yesmaximal, characteristic, complemented
4#20298942C211yesmaximal, characteristic, complemented
5#20298941C211yesmaximal, characteristic, complemented
6#20298921C211yesmaximal, characteristic, complemented
7#20298915C211yesmaximal, characteristic, complemented
8#20298884C211yesmaximal, characteristic, complemented
9#20298843C211yesmaximal, characteristic, complemented
10#20298826C211yesmaximal, characteristic, complemented
11#20298698C211yesmaximal, characteristic, complemented
12#20298668C211yesmaximal, characteristic, complemented
13#20298639C211yesmaximal, characteristic, complemented
14#20298633C211yesmaximal, characteristic, complemented
15#478×C113C211yesmaximal, characteristic, complemented
16C2×#14268635C2211yescharacteristic
17C2×#14268630C2211yescharacteristic
18C2×C8×D113C2211yescharacteristic
19#16813622C2211yescharacteristic
20#16813617—21no—
21#16813613—21no—
22#16813608—21no—
23#16813608—21no—
24#16813607—21no—
25#16813602C2211yescharacteristic
26#16813602C2211yescharacteristic
27#16813596—21no—
28#16813593C2211yescharacteristic
29#16813593C2211yescharacteristic
30C4×Dic226C2211yescharacteristic
31C4×D452C2211yescharacteristic
32#16813581—21no—
33#16813580—21no—
34#16813580C2211yescharacteristic
35#16813580C2211yescharacteristic
36#16813580C2211yescharacteristic
37C4⋊C4×D113C2211yescharacteristic
38#16813555C2211yescharacteristic
39#16813555C2211yescharacteristic
40#16813555C2211yescharacteristic
41#16813554C2211yescharacteristic
42#16813554C2211yescharacteristic
43#16813553C2211yescharacteristic
44#16813553C2211yescharacteristic
45#16813547C2211yescharacteristic
46#16813547C2211yescharacteristic
47#16813545C2211yescharacteristic
48#16813543C2211yescharacteristic
49#16813534C2211yescharacteristic
50#16813534C2211yescharacteristic
51#16813533C2211yescharacteristic
52#125×C113C2211yescharacteristic
53C4×D4×C113C2211yescharacteristic
54#107×C113C2211yescharacteristic
55#106×C113C2211yescharacteristic
56C4⋊C8×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226C2311yescharacteristic
61C2×D452D411yescharacteristic
62C2×C22⋊D113—21no—
63C2×C22⋊D113—21no—
64C2×C4×D113—21no—
65C2×C4×D113C2311yescharacteristic
66C2×C4×D113C2311yescharacteristic
67#14268635—22no—
68#14268630—22no—
69C2×#11744751C2311yescharacteristic
70C2×#11744751C2311yescharacteristic
71C8×D113—22no—
72C4⋊Dic113—21no—
73C4⋊Dic113—21no—
74C4⋊Dic113—21no—
75C4⋊Dic113D411yescharacteristic
76C4⋊Dic113C2311yescharacteristic
77C4⋊Dic113C2311yescharacteristic
78C4⋊Dic113C2311yescharacteristic
79#14268626—21no—
80#14268626—21no—
81C22⋊Dic113—21no—
82C22⋊Dic113—21no—
83#14268624—21no—
84#14268624—21no—
85#14268624—21no—
86#14268624—21no—
87#14268624—21no—
88#14268624D411yescharacteristic
89#14268624D411yescharacteristic
90C4×Dic113—21no—
91C4×Dic113—21no—
92C4×Dic113—21no—
93C4×Dic113—21no—
94C2×D4×C113C2311yescharacteristic
95C22×C4×C113—21no—
96C2×C8×C113C2311yescharacteristic
97C2×C8×C113C2311yescharacteristic
98C4⋊C4×C113—21no—
99C4⋊C4×C113—21no—
100C4⋊C4×C113C2311yescharacteristic
101C4⋊C4×C113C2311yescharacteristic
102C4⋊C4×C113C2311yescharacteristic
103C22⋊C4×C113—21no—
104C42×C113C2311yescharacteristic
105C23×C113—21no—
106C22×D113C2×D411yescharacteristic
107C22×D113C2×D411yescharacteristic
108D4×C113—21no—
109D4×C113—21no—
110C2×C4×C113—21no—
111C2×C4×C113—21no—
112C2×C4×C113—21no—
113C2×C4×C113—42no—
114C2×C4×C113C2×D411yescharacteristic
115C2×C4×C113C2×D411yescharacteristic
116C2×C4×C113C2411yescharacteristic
117C22⋊D113—81no—
118C22⋊D113—81no—
119C2×Dic113—21no—
120C2×Dic113—21no—
121C2×Dic113—21no—
122C2×Dic113—21no—
123C2×Dic113C2×D411yescharacteristic
124C2×Dic113C2×D411yescharacteristic
125D452—41no—
126C4×D113—21no—
127C4×D113—21no—
128C4×D113—21no—
129C4×D113—21no—
130C4×D113—42no—
131Dic226—21no—
132Dic226—21no—
133Dic226—81no—
134C8×C113—21no—
135C8×C113—21no—
136#11744751—21no—
137#11744751#4112yes—
138C22×C113—41no—
139C22×C113—41no—
140C22×C113—41no—
141C22×C113C22×D411yescharacteristic
142C2×D113—21no—
143C2×D113—21no—
144C2×D113—21no—
145C2×D113—21no—
146C2×D113—21no—
147C2×D113—21no—
148C4×C113—21no—
149C4×C113—21no—
150C4×C113—41no—
151C4×C113—41no—
152C4×C113—41no—
153C4×C113C2×#4111yescharacteristic
154C4×C1132−1+411yescharacteristic
155Dic113—21no—
156Dic113—21no—
157Dic113—41no—
158Dic113—41no—
159Dic113—41no—
160Dic113—41no—
161C2×C113—81no—
162C2×C113#54711yescharacteristic
163C2×C113#57511yescharacteristic
164C2×C113#57711yescharacteristic
165D113—41no—
166D113—41no—
167#3348—1131nomaximal, Sylow
168C113#334811yescharacteristic, complemented, Sylow
169#555—1131no—
170#552—1131no—
171#501—1131no—
172#485—1131no—
173#485—1131no—
174#482—1131no—
175#481—1131no—
176#478D11311yescharacteristic, complemented
177#475—1131no—
178#468—1131no—
179#465—1131no—
180#440—1131no—
181#435—1131no—
182#428—1131no—
183#427—1131no—
184C2×SD16—1131no—
185C2×M16—1131no—
186C22×C8—1131no—
187C4⋊Q8—1131no—
188#126—2261no—
189#125—2261no—
190#125C2×D11311yescharacteristic
191#124—2261no—
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×D4—1131no—
201C4×D4C2×D11311yescharacteristic
202#117—1131no—
203#117—1131no—
204#117—1131no—
205#117—2261no—
206#117—2261no—
207C2×C4⋊C4—1131no—
208#107—1131no—
209#107—1131no—
210#107—1131no—
211#107C2×D11311yescharacteristic
212#106—1131no—
213#106—1131no—
214#106—1131no—
215#106—1131no—
216#106C2×D11311yescharacteristic
217C4⋊C8C2×D11311yescharacteristic
218#103—1131no—
219#103—1131no—
220#103—1131no—
221#102—1131no—
222#102C2×D11311yescharacteristic
223#102C2×D11311yescharacteristic
224C22⋊C8—1131no—
225C22⋊C8—1131no—
226#97—1131no—
227C2×Q8—1131no—
228C2×Q8—2261no—
229C2×D4—1131no—
230C2×D4—2261no—
231C2×D4—2261no—
232C2×D4C22×D11311yescharacteristic
233C22×C4—21no—
234C22×C4—1131no—
235C22×C4—1131no—
236C22×C4—2261no—
237SD16—2262no—
238M16—2262no—
239C2×C8—1131no—
240C2×C8—1131no—
241C2×C8—2262no—
242C2×C8C22×D11311yescharacteristic
243C2×C8C22×D11311yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—21no—
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⋊C4C22×D11311yescharacteristic
256C4⋊C4C22×D11311yescharacteristic
257C4⋊C4C22×D11311yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—1131no—
260C22⋊C4—1131no—
261C22⋊C4—2261no—
262C22⋊C4—2261no—
263C22⋊C4—2261no—
264C22⋊C4—2261no—
265C22⋊C4—2261no—
266C22⋊C4—2261no—
267C22⋊C4—2261no—
268C42—2261no—
269C42—2261no—
270C42—2261no—
271C42—2261no—
272C42C22×D11311yescharacteristic
273C23—21no—
274C23—1131no—
275C23—1131no—
276Q8—9041no—
277Q8—2261no—
278Q8—2261no—
279D4—21no—
280D4—21no—
281D4—9041no—
282D4—9041no—
283D4—4521no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—42no—
288C2×C4—1131no—
289C2×C4—1131no—
290C2×C4—4522no—
291C2×C4—2261no—
292C2×C4—2261no—
293C2×C4—2261no—
294C2×C4—2261no—
295C2×C4—2261no—
296C2×C4—2261no—
297C2×C4—2261no—
298C2×C4—2261no—
299C2×C4D4×D11311yescharacteristic
300C2×C4D4×D11311yescharacteristic
301C2×C4C23×D11311yescharacteristic
302C8—21no—
303C8—21no—
304C8—1132no—
305C8—2261no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22—2261no—
310C22—2261no—
311C22—2261no—
312C22—2261no—
313C22—2261no—
314C22—2261no—
315C22C2×D4×D11311yescharacteristic
316C4—21no—
317C4—21no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—4521no—
322C4—4521no—
323C4—4521no—
324C4—4521no—
325C4—2261no—
326C4—2261no—
327C4#41×D11311yescharacteristic
328C4#1681367011yescharacteristic
329C2—81no—
330C2—4521no—
331C2—4521no—
332C2#2029925011yescharacteristic
333C2#2029939411yescharacteristic
334C2#2029940511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#478×C113C2
socleC22×C113C22×D4
prime radical#20299313C2
hypercenter#478D113
hypocenterC113#3348
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
2. #20299286C2semidirect
3. #20299008C2semidirect
4. #20298942C2semidirect
5. #20298941C2semidirect
6. #20298921C2semidirect
7. #20298915C2semidirect
8. #20298884C2semidirect
9. #20298843C2semidirect
10. #20298826C2semidirect
11. #20298698C2semidirect
12. #20298668C2semidirect
13. #20298639C2semidirect
14. #20298633C2semidirect
15. #478×C113C2semidirect
168. C113#3348semidirect
176. #478D113semidirect

Maximal subgroups

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

subgroupindex
#202993132
#202992862
#202990082
#202989422
#202989412
#202989212
#202989152
#202988842
#202988432
#202988262
#202986982
#202986682
#202986392
#202986332
#478×C1132
#3348113