Finite Group Databasebeta

← #28401977

Subgroups — #28401977

Order 14464.

354 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#20299135C211yesmaximal, characteristic, complemented
2#20299133C211yesmaximal, characteristic, complemented
3#20298908C211yesmaximal, characteristic, complemented
4#20298901C211yesmaximal, characteristic, complemented
5#20298895C211yesmaximal, characteristic, complemented
6#20298855C211yesmaximal, characteristic, complemented
7#20298852C211yesmaximal, characteristic
8#20298847C211yesmaximal, characteristic, complemented
9#20298845C211yesmaximal, characteristic, complemented
10#20298823C211yesmaximal, characteristic, complemented
11#20298820C211yesmaximal, characteristic, complemented
12#20298816C211yesmaximal, characteristic, complemented
13#20298814C211yesmaximal, characteristic, complemented
14#20298620C211yesmaximal, characteristic, complemented
15#479×C113C211yesmaximal, characteristic, complemented
16C2×#14268637C2211yescharacteristic
17C2×#14268636C2211yescharacteristic
18C2×#14268634C2211yescharacteristic
19C2×D904C2211yescharacteristic
20C2×#14268630C2211yescharacteristic
21C2×#14268630C2211yescharacteristic
22#16813617—21no—
23#16813617—21no—
24#16813613C2211yescharacteristic
25#16813611C2211yescharacteristic
26#16813610C2211yescharacteristic
27#16813607—21no—
28#16813607—21no—
29#16813602C2211yescharacteristic
30#16813598C2211yescharacteristic
31#16813597C2211yescharacteristic
32#16813597C2211yescharacteristic
33#16813587C2211yescharacteristic
34C4×D452—21no—
35C4×D452C2211yescharacteristic
36#16813584—21no—
37#16813584C2211yescharacteristic
38#16813580—21no—
39#16813579—21no—
40C42×D113C2211yescharacteristic
41#16813555C2211yescharacteristic
42#16813553C2211yescharacteristic
43C4⋊#11744751C2211yescharacteristic
44#16813551C2211yescharacteristic
45#16813551C2211yescharacteristic
46#16813547C2211yescharacteristic
47#16813545C2211yescharacteristic
48#16813544C2211yescharacteristic
49#16813542C2211yescharacteristic
50#16813542C2211yescharacteristic
51#16813542C2211yescharacteristic
52#125×C113C2211yescharacteristic
53C4×Q8×C113C2211yescharacteristic
54#107×C113C2211yescharacteristic
55#106×C113C2211yescharacteristic
56C4⋊C8×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58#103×C113C2211yescharacteristic
59C2×Dic226C2311yescharacteristic
60C2×D452—21no—
61C2×D452—21no—
62C2×D452C2311yescharacteristic
63C2×D452C2311yescharacteristic
64C2×C4×D113—21no—
65C2×C4×D113—21no—
66C2×C4×D113D411yescharacteristic
67C2×C4×D113D411yescharacteristic
68C2×C4×D113C2311yescharacteristic
69#14268637—41no—
70#14268636—41no—
71#14268634—41no—
72D904—41no—
73#14268630—41no—
74#14268630—41no—
75C2×#11744751C2311yescharacteristic
76C2×#11744751C2311yescharacteristic
77C4⋊Dic113—21no—
78C4⋊Dic113—21no—
79C4⋊Dic113C2311yescharacteristic
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83#14268624—21no—
84#14268624—21no—
85#14268624—21no—
86#14268624—21no—
87#14268624—21no—
88#14268624—21no—
89#14268624—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93C4×Dic113—21no—
94C4×Dic113D411yescharacteristic
95C4×Dic113D411yescharacteristic
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×D113—21no—
109C22×D113—21no—
110C22×D113C2×D411yescharacteristic
111Q8×C113—21no—
112Q8×C113—21no—
113C2×C4×C113—21no—
114C2×C4×C113—21no—
115C2×C4×C113—21no—
116C2×C4×C113—21no—
117C2×C4×C113C2×D411yescharacteristic
118C2×C4×C113C2×D411yescharacteristic
119C2×C4×C113C2411yescharacteristic
120C2×Dic113—21no—
121C2×Dic113—21no—
122C2×Dic113C2×D411yescharacteristic
123C2×Dic113C2×D411yescharacteristic
124C2×Dic113C2×D411yescharacteristic
125D452—21no—
126D452—21no—
127D452—21no—
128D452—21no—
129D452—42no—
130D452—42no—
131C4×D113—21no—
132C4×D113—21no—
133C4×D113—41no—
134C4×D113—41no—
135C4×D113—42no—
136C4×D113—42no—
137Dic226—21no—
138Dic226—21no—
139C8×C113—21no—
140C8×C113—21no—
141#11744751—21no—
142#11744751—21no—
143C22×C113C22×D411yescharacteristic
144C2×D113—21no—
145C2×D113—21no—
146C2×D113—21no—
147C2×D113—41no—
148C2×D113—41no—
149C2×D113—41no—
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×C113—41no—
159C4×C113H(5,𝔽2)11yescharacteristic
160C4×C1132−1+411yescharacteristic
161Dic113—21no—
162Dic113—21no—
163Dic113—21no—
164Dic113—41no—
165Dic113—41no—
166C2×C113#53711yescharacteristic
167C2×C113#57511yescharacteristic
168C2×C113#57511yescharacteristic
169D113—41no—
170D113—81no—
171D113—81no—
172#3256—1131nomaximal, Sylow
173C113#325611yescharacteristic, complemented, Sylow
174#529—1131no—
175#529—1131no—
176#479—1131no—
177#479D11311yescharacteristic, complemented
178#478—1131no—
179#478—1131no—
180#470—1131no—
181#469—1131no—
182#468—1131no—
183#468—1131no—
184#464—1131no—
185#464—1131no—
186#463—1131no—
187#463—1131no—
188#423—1131no—
189C2×Q16—1131no—
190C2×SD16—1131no—
191C2×SD16—1131no—
192C2×D8—1131no—
193C2×M16—1131no—
194C2×M16—1131no—
195#126—2261no—
196#126—2261no—
197#125—1131no—
198#125C2×D11311yescharacteristic
199#124—1131no—
200#124—1131no—
201#123—2261no—
202#123—2261no—
203C22⋊Q8—1131no—
204C22⋊Q8—1131no—
205#121—1131no—
206#121—1131no—
207C4×Q8—1131no—
208C4×Q8C2×D11311yescharacteristic
209C4×D4—1131no—
210C4×D4—1131no—
211C4×D4—2261no—
212C4×D4—2261no—
213#117—2261no—
214#117—2261no—
215C2×C42—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#103C2×D11311yescharacteristic
227#103C2×D11311yescharacteristic
228#102—1131no—
229#102—1131no—
230#102—1131no—
231#102—1131no—
232C2×Q8—1131no—
233C2×Q8C22×D11311yescharacteristic
234C2×D4—1131no—
235C2×D4—1131no—
236C2×D4—2261no—
237C2×D4—2261no—
238C22×C4—1131no—
239C22×C4—1131no—
240C22×C4—1131no—
241C22×C4—2261no—
242C22×C4—2261no—
243Q16—4521no—
244SD16—4521no—
245SD16—4521no—
246D8—4521no—
247M16—4521no—
248M16—4521no—
249C2×C8—1131no—
250C2×C8—1131no—
251C2×C8C22×D11311yescharacteristic
252C2×C8C22×D11311yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—1131no—
257C4⋊C4—2261no—
258C4⋊C4—2261no—
259C4⋊C4—2261no—
260C4⋊C4—2261no—
261C4⋊C4—2261no—
262C4⋊C4C22×D11311yescharacteristic
263C4⋊C4C22×D11311yescharacteristic
264C4⋊C4C22×D11311yescharacteristic
265C22⋊C4—2261no—
266C22⋊C4—2261no—
267C22⋊C4—2261no—
268C22⋊C4—2261no—
269C22⋊C4—2261no—
270C22⋊C4—2261no—
271C22⋊C4—2261no—
272C22⋊C4—2261no—
273C22⋊C4—2261no—
274C22⋊C4—2261no—
275C42—21no—
276C42—1131no—
277C42—1131no—
278C42—1131no—
279C42—2261no—
280C42C22×D11311yescharacteristic
281C23—1131no—
282C23—2261no—
283C23—2261no—
284Q8—21no—
285Q8—21no—
286Q8—2261no—
287Q8—2261no—
288D4—4522no—
289D4—4522no—
290D4—2261no—
291D4—2261no—
292D4—2261no—
293D4—2261no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—1131no—
299C2×C4—1131no—
300C2×C4—1131no—
301C2×C4—4522no—
302C2×C4—4521no—
303C2×C4—4521no—
304C2×C4—4522no—
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—4521no—
317C22—4521no—
318C22—4521no—
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—41no—
332C4—4521no—
333C4—4521no—
334C4—2261no—
335C4—2261no—
336C4—2261no—
337C4#1681366811yescharacteristic
338C4#1681367011yescharacteristic
339C2—9041no—
340C2—9041no—
341C2—4521no—
342C2#2029917811yescharacteristic
343C2#2029939511yescharacteristic
344C2#2029939711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#479×C113C2
socleC22×C113C22×D4
prime radical#20298852C2
hypercenter#479D113
hypocenterC113#3256
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
1. #20299135C2semidirect
2. #20299133C2semidirect
3. #20298908C2semidirect
4. #20298901C2semidirect
5. #20298895C2semidirect
6. #20298855C2semidirect
8. #20298847C2semidirect
9. #20298845C2semidirect
10. #20298823C2semidirect
11. #20298820C2semidirect
12. #20298816C2semidirect
13. #20298814C2semidirect
14. #20298620C2semidirect
15. #479×C113C2semidirect
173. C113#3256semidirect
177. #479D113semidirect

Maximal subgroups

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

subgroupindex
#202991352
#202991332
#202989082
#202989012
#202988952
#202988552
#202988522
#202988472
#202988452
#202988232
#202988202
#202988162
#202988142
#202986202
#479×C1132
#3256113