Finite Group Databasebeta

← #28402022

Subgroups — #28402022

Order 14464.

346 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299211C211yesmaximal, characteristic, complemented
2#20299199C211yesmaximal, characteristic
3#20298908C211yesmaximal, characteristic, complemented
4#20298904C211yesmaximal, characteristic, complemented
5#20298895C211yesmaximal, characteristic, complemented
6#20298845C211yesmaximal, characteristic, complemented
7#20298843C211yesmaximal, characteristic, complemented
8#20298828C211yesmaximal, characteristic, complemented
9#20298826C211yesmaximal, characteristic, complemented
10#20298804C211yesmaximal, characteristic, complemented
11#20298803C211yesmaximal, characteristic, complemented
12#20298797C211yesmaximal, characteristic, complemented
13#20298797C211yesmaximal, characteristic, complemented
14#20298623C211yesmaximal, characteristic, complemented
15#478×C113C211yesmaximal, characteristic, complemented
16C2×#14268636C2211yescharacteristic
17C2×#14268636C2211yescharacteristic
18C2×#14268635C2211yescharacteristic
19C2×#14268635C2211yescharacteristic
20C2×#14268630C2211yescharacteristic
21C2×C8×D113C2211yescharacteristic
22#16813622C2211yescharacteristic
23#16813618C2211yescharacteristic
24#16813617—21no—
25#16813617—21no—
26#16813613—21no—
27#16813613—21no—
28#16813613C2211yescharacteristic
29#16813605—21no—
30#16813604—21no—
31#16813602C2211yescharacteristic
32#16813602C2211yescharacteristic
33#16813597C2211yescharacteristic
34#16813596—21no—
35#16813595—21no—
36#16813593C2211yescharacteristic
37#16813587C2211yescharacteristic
38#16813587C2211yescharacteristic
39C4×D452C2211yescharacteristic
40#16813579C2211yescharacteristic
41#16813555C2211yescharacteristic
42#16813553C2211yescharacteristic
43C4⋊#11744751C2211yescharacteristic
44#16813551C2211yescharacteristic
45#16813551C2211yescharacteristic
46#16813547C2211yescharacteristic
47#16813547C2211yescharacteristic
48#16813545C2211yescharacteristic
49#16813545C2211yescharacteristic
50#16813542C2211yescharacteristic
51#16813542C2211yescharacteristic
52#125×C113C2211yescharacteristic
53C4×D4×C113C2211yescharacteristic
54#107×C113C2211yescharacteristic
55#106×C113C2211yescharacteristic
56C4⋊C8×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59C2×Dic226C2311yescharacteristic
60C2×Dic226C2311yescharacteristic
61C2×D452—21no—
62C2×D452C2311yescharacteristic
63C2×C22⋊D113—21no—
64C2×C22⋊D113—21no—
65C2×C22⋊D113—21no—
66C2×C4×D113—21no—
67C2×C4×D113C2311yescharacteristic
68#14268636—41no—
69#14268636—41no—
70#14268635—41no—
71#14268635—41no—
72#14268630—41no—
73C2×#11744751C2311yescharacteristic
74C2×#11744751C2311yescharacteristic
75C8×D113—41no—
76C4⋊Dic113—21no—
77C4⋊Dic113—21no—
78C4⋊Dic113—21no—
79C4⋊Dic113—21no—
80C4⋊Dic113—21no—
81C4⋊Dic113C2311yescharacteristic
82#14268626—21no—
83#14268626—21no—
84#14268626—21no—
85#14268626D411yescharacteristic
86#14268626D411yescharacteristic
87C22⋊Dic113—21no—
88#14268624—21no—
89#14268624—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624D411yescharacteristic
93#14268624D411yescharacteristic
94C4×Dic113—21no—
95C4×Dic113—21no—
96C4×Dic113C2311yescharacteristic
97C2×D4×C113C2311yescharacteristic
98C22×C4×C113—21no—
99C2×C8×C113C2311yescharacteristic
100C2×C8×C113C2311yescharacteristic
101C4⋊C4×C113—21no—
102C4⋊C4×C113—21no—
103C4⋊C4×C113C2311yescharacteristic
104C4⋊C4×C113C2311yescharacteristic
105C4⋊C4×C113C2311yescharacteristic
106C22⋊C4×C113—21no—
107C42×C113C2311yescharacteristic
108C23×C113—21no—
109C22×D113—21no—
110C22×D113C2×D411yescharacteristic
111D4×C113—21no—
112D4×C113—21no—
113C2×C4×C113—21no—
114C2×C4×C113—21no—
115C2×C4×C113—21no—
116C2×C4×C113—81no—
117C2×C4×C113C2×D411yescharacteristic
118C2×C4×C113C2×D411yescharacteristic
119C2×C4×C113C2411yescharacteristic
120C22⋊D113—81no—
121C22⋊D113—81no—
122C22⋊D113—81no—
123C2×Dic113—21no—
124C2×Dic113—21no—
125C2×Dic113—21no—
126C2×Dic113C2×D411yescharacteristic
127C2×Dic113C2×D411yescharacteristic
128C2×Dic113C2×D411yescharacteristic
129D452—21no—
130D452—21no—
131D452—81no—
132C4×D113—21no—
133C4×D113—21no—
134C4×D113—81no—
135Dic226—21no—
136Dic226—21no—
137Dic226—21no—
138Dic226—21no—
139C8×C113—21no—
140C8×C113—21no—
141#11744751—21no—
142#11744751—21no—
143C22×C113—41no—
144C22×C113—41no—
145C22×C113—41no—
146C22×C113C22×D411yescharacteristic
147C2×D113—21no—
148C2×D113—21no—
149C2×D113—21no—
150C2×D113—41no—
151C2×D113—41no—
152C2×D113—41no—
153C4×C113—21no—
154C4×C113—21no—
155C4×C113—41no—
156C4×C113—41no—
157C4×C113—41no—
158C4×C113H(5,𝔽2)11yescharacteristic
159C4×C1132−1+411yescharacteristic
160Dic113—21no—
161Dic113—21no—
162Dic113—21no—
163Dic113—41no—
164Dic113—41no—
165Dic113—41no—
166C2×C113—81no—
167C2×C113#53711yescharacteristic
168C2×C113#57711yescharacteristic
169C2×C113#57711yescharacteristic
170D113—41no—
171D113—81no—
172#3260—1131nomaximal, Sylow
173C113#326011yescharacteristic, complemented, Sylow
174#541—1131no—
175#540—1131no—
176#479—1131no—
177#479—1131no—
178#478—1131no—
179#478D11311yescharacteristic, complemented
180#468—1131no—
181#468—1131no—
182#465—1131no—
183#465—1131no—
184#461—1131no—
185#461—1131no—
186#460—1131no—
187#460—1131no—
188#424—1131no—
189C2×SD16—1131no—
190C2×SD16—1131no—
191C2×SD16—1131no—
192C2×SD16—1131no—
193C2×M16—1131no—
194C22×C8—1131no—
195C4⋊Q8—1131no—
196#127—1131no—
197#126—2261no—
198#126—2261no—
199#125—1131no—
200#125—2261no—
201#125—2261no—
202#125C2×D11311yescharacteristic
203#123—2261no—
204#123—2261no—
205C22⋊Q8—1131no—
206C22⋊Q8—1131no—
207#121—1131no—
208#121—1131no—
209#121—2261no—
210#121—2261no—
211C4×Q8—1131no—
212C4×Q8—1131no—
213C4×D4—1131no—
214C4×D4C2×D11311yescharacteristic
215#117—1131no—
216#107—1131no—
217#107C2×D11311yescharacteristic
218#106—1131no—
219#106C2×D11311yescharacteristic
220C4⋊C8—1131no—
221C4⋊C8—1131no—
222C4⋊C8—1131no—
223C4⋊C8C2×D11311yescharacteristic
224#103—1131no—
225#103—1131no—
226#103—1131no—
227#103—1131no—
228#102—1131no—
229#102—1131no—
230#102C2×D11311yescharacteristic
231#102C2×D11311yescharacteristic
232C2×Q8—1131no—
233C2×Q8—1131no—
234C2×D4—1131no—
235C2×D4—2261no—
236C2×D4—2261no—
237C2×D4—2261no—
238C2×D4—2261no—
239C2×D4C22×D11311yescharacteristic
240C22×C4—21no—
241C22×C4—1131no—
242C22×C4—2261no—
243SD16—4521no—
244SD16—4521no—
245SD16—4521no—
246SD16—4521no—
247M16—4521no—
248C2×C8—1131no—
249C2×C8—1131no—
250C2×C8—4521no—
251C2×C8C22×D11311yescharacteristic
252C2×C8C22×D11311yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—1131no—
256C4⋊C4—1131no—
257C4⋊C4—1131no—
258C4⋊C4—2261no—
259C4⋊C4—2261no—
260C4⋊C4—2261no—
261C4⋊C4—2261no—
262C4⋊C4—2261no—
263C4⋊C4—2261no—
264C4⋊C4—2261no—
265C4⋊C4—2261no—
266C4⋊C4C22×D11311yescharacteristic
267C4⋊C4C22×D11311yescharacteristic
268C4⋊C4C22×D11311yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—1131no—
271C22⋊C4—1131no—
272C22⋊C4—2261no—
273C22⋊C4—2261no—
274C22⋊C4—2261no—
275C22⋊C4—2261no—
276C22⋊C4—2261no—
277C42—1131no—
278C42—2261no—
279C42—2261no—
280C42C22×D11311yescharacteristic
281C23—21no—
282C23—1131no—
283C23—2261no—
284Q8—2261no—
285Q8—2261no—
286Q8—2261no—
287Q8—2261no—
288D4—21no—
289D4—21no—
290D4—9041no—
291D4—9041no—
292D4—9041no—
293D4—9041no—
294D4—2261no—
295D4—2261no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—81no—
300C2×C4—1131no—
301C2×C4—1131no—
302C2×C4—1131no—
303C2×C4—9041no—
304C2×C4—2261no—
305C2×C4—2261no—
306C2×C4—2261no—
307C2×C4—2261no—
308C2×C4—2261no—
309C2×C4D4×D11311yescharacteristic
310C2×C4D4×D11311yescharacteristic
311C2×C4C23×D11311yescharacteristic
312C8—21no—
313C8—21no—
314C8—2261no—
315C8—2261no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—4521no—
320C22—4521no—
321C22—4521no—
322C22—2261no—
323C22—2261no—
324C22—2261no—
325C22C2×D4×D11311yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—4521no—
332C4—4521no—
333C4—4521no—
334C4—2261no—
335C4—2261no—
336C4—2261no—
337C4#1681366811yescharacteristic
338C4#1681367011yescharacteristic
339C2—81no—
340C2—9041no—
341C2—4521no—
342C2#2029917811yescharacteristic
343C2#2029940511yescharacteristic
344C2#2029940811yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#478×C113C2
socleC22×C113C22×D4
prime radical#20299199C2
hypercenter#478D113
hypocenterC113#3260
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
1. #20299211C2semidirect
3. #20298908C2semidirect
4. #20298904C2semidirect
5. #20298895C2semidirect
6. #20298845C2semidirect
7. #20298843C2semidirect
8. #20298828C2semidirect
9. #20298826C2semidirect
10. #20298804C2semidirect
11. #20298803C2semidirect
12. #20298797C2semidirect
13. #20298797C2semidirect
14. #20298623C2semidirect
15. #478×C113C2semidirect
173. C113#3260semidirect
179. #478D113semidirect

Maximal subgroups

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

subgroupindex
#202992112
#202991992
#202989082
#202989042
#202988952
#202988452
#202988432
#202988282
#202988262
#202988042
#202988032
#202987972
#202986232
#478×C1132
#3260113