Finite Group Databasebeta

← #28401623

Subgroups — #28401623

Order 14464.

420 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299199C211yesmaximal, characteristic, complemented
2#20299161C211yesmaximal, characteristic, complemented
3#20298986C211yesmaximal, characteristic, complemented
4#20298973C211yesmaximal, characteristic, complemented
5#20298961C211yesmaximal, characteristic, complemented
6#20298951C211yesmaximal, characteristic, complemented
7#20298814C211yesmaximal, characteristic, complemented
8#20298813C211yesmaximal, characteristic, complemented
9#20298790C211yesmaximal, characteristic, complemented
10#20298744C211yesmaximal, characteristic, complemented
11#20298740C211yesmaximal, characteristic, complemented
12#20298733C211yesmaximal, characteristic, complemented
13#20298730C211yesmaximal, characteristic, complemented
14#20298658C211yesmaximal, characteristic, complemented
15#459×C113C211yesmaximal, characteristic, complemented
16C2×#14268646C2211yescharacteristic
17C2×D4×D113C2211yescharacteristic
18C2×#14268636C2211yescharacteristic, complemented
19C2×#14268635C2211yescharacteristic, complemented
20C2×D904C2211yescharacteristic
21C2×#14268632C2211yescharacteristic
22C2×#14268632C2211yescharacteristic
23C2×#14268632C2211yescharacteristic, complemented
24#16813618C2211yescharacteristic
25#16813618C2211yescharacteristic, complemented
26#16813613C2211yescharacteristic, complemented
27#16813610C2211yescharacteristic
28#16813609C2211yescharacteristic
29#16813605—21no—
30#16813604—21no—
31#16813597C2211yescharacteristic
32#16813596—21no—
33#16813595—21no—
34#16813594—21no—
35#16813594—21no—
36#16813593C2211yescharacteristic
37#16813590—21no—
38#16813590—21no—
39C4×D452C2211yescharacteristic, complemented
40#16813579C2211yescharacteristic
41C4⋊#11744751C2211yescharacteristic, complemented
42#16813547C2211yescharacteristic, complemented
43#16813545C2211yescharacteristic, complemented
44#16813544C2211yescharacteristic
45#16813543C2211yescharacteristic
46#16813543C2211yescharacteristic, complemented
47#16813542C2211yescharacteristic
48#16813534C2211yescharacteristic
49#16813534C2211yescharacteristic
50#16813532C2211yescharacteristic, complemented
51C8×Dic113C2211yescharacteristic, complemented
52C2×D8×C113C2211yescharacteristic
53C2×D8×C113C2211yescharacteristic, complemented
54#127×C113C2211yescharacteristic
55C4×D4×C113C2211yescharacteristic, complemented
56C4⋊C8×C113C2211yescharacteristic, complemented
57#102×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60#14268646—41no—
61#14268646—41no—
62C2×Dic226C2311yescharacteristic
63C2×D452—21no—
64C2×D452C2311yescharacteristic
65C2×D452C2311yescharacteristic
66C2×C22⋊D113—21no—
67C2×C22⋊D113—21no—
68C2×C22⋊D113—21no—
69C2×C22⋊D113—21no—
70C2×C22⋊D113—21no—
71C2×C22⋊D113—21no—
72C2×C22⋊D113—21no—
73D4×D113—41no—
74D4×D113—41no—
75C22×Dic113—21no—
76C2×C4×D113—21no—
77C2×C4×D113C2311yescharacteristic
78#14268636—41no—
79#14268635—41no—
80D904—41no—
81#14268632—41no—
82#14268632—41no—
83#14268632—41no—
84C2×#11744751C2311yescharacteristic
85C2×#11744751C2311yescharacteristic
86C4⋊Dic113—21no—
87C4⋊Dic113C2311yescharacteristic
88#14268626—21no—
89#14268626D411yescharacteristic
90#14268626D411yescharacteristic
91C22⋊Dic113—21no—
92C22⋊Dic113—21no—
93C22⋊Dic113—21no—
94#14268624—21no—
95#14268624—21no—
96#14268624—21no—
97#14268624—21no—
98#14268624D411yescharacteristic
99#14268624D411yescharacteristic
100C4×Dic113C2311yescharacteristic
101C2×D4×C113—21no—
102C2×D4×C113—21no—
103C2×D4×C113C2311yescharacteristic
104C2×D4×C113C2311yescharacteristic
105C2×D4×C113C2311yescharacteristic
106C22×C4×C113—21no—
107D8×C113—41no—
108D8×C113—41no—
109C2×C8×C113C2311yescharacteristic
110C2×C8×C113C2311yescharacteristic
111C4⋊C4×C113C2311yescharacteristic
112C22⋊C4×C113—21no—
113C42×C113C2311yescharacteristic
114C23×C113—21no—
115C23×C113—21no—
116C23×C113—21no—
117C22×D113—21no—
118C22×D113—21no—
119C22×D113—42no—
120C22×D113—81no—
121C22×D113—81no—
122C22×D113C2×D411yescharacteristic
123D4×C113—21no—
124D4×C113—21no—
125D4×C113—21no—
126D4×C113—21no—
127D4×C113—21no—
128D4×C113—21no—
129D4×C113—81no—
130D4×C113—81no—
131C2×C4×C113—21no—
132C2×C4×C113—81no—
133C2×C4×C113C2×D411yescharacteristic
134C2×C4×C113C2×D411yescharacteristic
135C2×C4×C113C2411yescharacteristic
136C22⋊D113—42no—
137C22⋊D113—42no—
138C22⋊D113—81no—
139C22⋊D113—81no—
140C22⋊D113—81no—
141C22⋊D113—81no—
142C22⋊D113—81no—
143C2×Dic113—21no—
144C2×Dic113—21no—
145C2×Dic113—42no—
146C2×Dic113C2×D411yescharacteristic
147C2×Dic113C2×D411yescharacteristic
148C2×Dic113C2×D411yescharacteristic
149D452—21no—
150D452—21no—
151D452—21no—
152D452—21no—
153D452—81no—
154C4×D113—21no—
155C4×D113—21no—
156C4×D113—81no—
157Dic226—21no—
158Dic226—21no—
159C8×C113—21no—
160C8×C113—21no—
161#11744751—21no—
162#11744751—21no—
163C22×C113—41no—
164C22×C113—41no—
165C22×C113—41no—
166C22×C113—41no—
167C22×C113—41no—
168C22×C113—41no—
169C22×C113—41no—
170C22×C113—41no—
171C22×C113—41no—
172C22×C113C22×D411yescharacteristic
173C2×D113—21no—
174C2×D113—21no—
175C2×D113—21no—
176C2×D113—41no—
177C2×D113—41no—
178C2×D113—41no—
179C2×D113—41no—
180C2×D113—41no—
181C2×D113—41no—
182C2×D113—84no—
183C4×C113—21no—
184C4×C113—21no—
185C4×C113—41no—
186C4×C113H(5,𝔽2)11yescharacteristic
187C4×C113H(5,𝔽2)11yescharacteristic
188Dic113—21no—
189Dic113—21no—
190Dic113—21no—
191Dic113—41no—
192Dic113—41no—
193C2×C113—81no—
194C2×C113—81no—
195C2×C113—81no—
196C2×C113#53511yescharacteristic
197C2×C113#57611yescharacteristic
198C2×C113#57611yescharacteristic
199D113—41no—
200D113—81no—
201D113—81no—
202#3220—1131nomaximal, Sylow
203C113#322011yescharacteristic, complemented, Sylow
204#540—1131no—
205#535—1131no—
206#496—1131no—
207#493—1131no—
208#490—1131no—
209#488—1131no—
210#463—1131no—
211#463—1131no—
212#459—1131no—
213#459D11311yescharacteristic, complemented
214#449—1131no—
215#449—1131no—
216#447—1131no—
217#447—1131no—
218#433—1131no—
219C2×#41—1131no—
220C22×D4—1131no—
221C2×SD16—1131no—
222C2×SD16—1131no—
223C2×D8—1131no—
224C2×D8—1131no—
225C2×D8—1131no—
226C2×D8—1131no—
227C2×D8C2×D11311yescharacteristic
228C2×D8C2×D11311yescharacteristic, complemented
229#127—1131no—
230#127—1131no—
231#127C2×D11311yescharacteristic
232#125—1131no—
233#124—1131no—
234#124—1131no—
235#123—2261no—
236#123—2261no—
237#121—1131no—
238#121—1131no—
239#121—2261no—
240#121—2261no—
241#121—2261no—
242#121—2261no—
243#120—2261no—
244#120—2261no—
245C4×D4—1131no—
246C4×D4C2×D11311yescharacteristic, complemented
247#117—1131no—
248C4⋊C8—1131no—
249C4⋊C8C2×D11311yescharacteristic, complemented
250#103—1131no—
251#103—1131no—
252#102—1131no—
253#102—1131no—
254#102—1131no—
255#102—1131no—
256#102C2×D11311yescharacteristic
257#102C2×D11311yescharacteristic, complemented
258C22⋊C8—1131no—
259C22⋊C8—1131no—
260#97—1131no—
261C4×C8—1131no—
262C24—2261no—
263#41—4521no—
264#41—4521no—
265C2×Q8—1131no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—1131no—
269C2×D4—1131no—
270C2×D4—4521no—
271C2×D4—4521no—
272C2×D4—2261no—
273C2×D4—2261no—
274C2×D4—2261no—
275C2×D4—2261no—
276C2×D4—2261no—
277C2×D4—2261no—
278C2×D4—2261no—
279C2×D4—2261no—
280C2×D4C22×D11311yescharacteristic
281C2×D4C22×D11311yescharacteristic
282C2×D4C22×D11311yescharacteristic
283C22×C4—21no—
284C22×C4—1131no—
285C22×C4—2261no—
286C22×C4—2261no—
287SD16—4521no—
288SD16—4521no—
289D8—41no—
290D8—41no—
291D8—4521no—
292D8—4521no—
293D8—4521no—
294D8—4521no—
295C2×C8—1131no—
296C2×C8—1131no—
297C2×C8C22×D11311yescharacteristic
298C2×C8C22×D11311yescharacteristic
299C4⋊C4—1131no—
300C4⋊C4—1131no—
301C4⋊C4—1131no—
302C4⋊C4—2261no—
303C4⋊C4—2261no—
304C4⋊C4C22×D11311yescharacteristic
305C22⋊C4—21no—
306C22⋊C4—1131no—
307C22⋊C4—1131no—
308C22⋊C4—2261no—
309C22⋊C4—2261no—
310C22⋊C4—2261no—
311C22⋊C4—2261no—
312C22⋊C4—2261no—
313C22⋊C4—2261no—
314C22⋊C4—2261no—
315C42—1131no—
316C42C22×D11311yescharacteristic
317C23—21no—
318C23—21no—
319C23—21no—
320C23—1131no—
321C23—9041no—
322C23—9041no—
323C23—4522no—
324C23—2261no—
325C23—2261no—
326Q8—2261no—
327Q8—2261no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—81no—
335D4—81no—
336D4—9041no—
337D4—9041no—
338D4—9041no—
339D4—9041no—
340D4—9041no—
341D4—9041no—
342D4—4522no—
343D4—4522no—
344D4—2261no—
345D4—2261no—
346D4—2261no—
347D4—2261no—
348C2×C4—21no—
349C2×C4—81no—
350C2×C4—1131no—
351C2×C4—1131no—
352C2×C4—1131no—
353C2×C4—9041no—
354C2×C4—4522no—
355C2×C4—2261no—
356C2×C4—2261no—
357C2×C4—2261no—
358C2×C4—2261no—
359C2×C4D4×D11311yescharacteristic
360C2×C4D4×D11311yescharacteristic
361C2×C4C23×D11311yescharacteristic
362C8—21no—
363C8—21no—
364C8—2261no—
365C8—2261no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—9044no—
376C22—4521no—
377C22—4521no—
378C22—4521no—
379C22—4521no—
380C22—4521no—
381C22—4521no—
382C22—2261no—
383C22—2261no—
384C22—2261no—
385C22C2×D4×D11311yescharacteristic
386C4—21no—
387C4—21no—
388C4—41no—
389C4—4521no—
390C4—4521no—
391C4—2261no—
392C4—2261no—
393C4—2261no—
394C4#1681366711yescharacteristic
395C4#1681366811yescharacteristic
396C2—81no—
397C2—81no—
398C2—81no—
399C2—9041no—
400C2—9041no—
401C2—4521no—
402C2#2029916411yescharacteristic
403C2#2029939911yescharacteristic
404C2#2029940211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#459×C113C2
socleC22×C113C22×D4
hypercenter#459D113
hypocenterC113#3220
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #20299199C2semidirect
2. #20299161C2semidirect
3. #20298986C2semidirect
4. #20298973C2semidirect
5. #20298961C2semidirect
6. #20298951C2semidirect
7. #20298814C2semidirect
8. #20298813C2semidirect
9. #20298790C2semidirect
10. #20298744C2semidirect
11. #20298740C2semidirect
12. #20298733C2semidirect
13. #20298730C2semidirect
14. #20298658C2semidirect
15. #459×C113C2semidirect
18. C2×#14268636C22semidirect
19. C2×#14268635C22semidirect
23. C2×#14268632C22semidirect
25. #16813618C22semidirect
26. #16813613C22semidirect
39. C4×D452C22semidirect
41. C4⋊#11744751C22semidirect
42. #16813547C22semidirect
43. #16813545C22semidirect
46. #16813543C22semidirect
50. #16813532C22semidirect
51. C8×Dic113C22semidirect
53. C2×D8×C113C22semidirect
55. C4×D4×C113C22semidirect
56. C4⋊C8×C113C22semidirect
58. #102×C113C22semidirect
203. C113#3220semidirect
213. #459D113semidirect
228. C2×D8C2×D113semidirect
246. C4×D4C2×D113semidirect
249. C4⋊C8C2×D113semidirect
257. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991992
#202991612
#202989862
#202989732
#202989612
#202989512
#202988142
#202988132
#202987902
#202987442
#202987402
#202987332
#202987302
#202986582
#459×C1132
#3220113