Finite Group Databasebeta

← #28401663

Subgroups — #28401663

Order 14464.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299217C211yesmaximal, characteristic, complemented
2#20299161C211yesmaximal, characteristic, complemented
3#20298980C211yesmaximal, characteristic, complemented
4#20298958C211yesmaximal, characteristic, complemented
5#20298944C211yesmaximal, characteristic, complemented
6#20298818C211yesmaximal, characteristic, complemented
7#20298811C211yesmaximal, characteristic, complemented
8#20298796C211yesmaximal, characteristic, complemented
9#20298791C211yesmaximal, characteristic, complemented
10#20298757C211yesmaximal, characteristic, complemented
11#20298747C211yesmaximal, characteristic, complemented
12#20298740C211yesmaximal, characteristic, complemented
13#20298730C211yesmaximal, characteristic, complemented
14#20298660C211yesmaximal, characteristic, complemented
15#496×C113C211yesmaximal, characteristic, complemented
16C2×#14268646C2211yescharacteristic
17C2×D4×D113C2211yescharacteristic
18C2×#14268637C2211yescharacteristic, complemented
19C2×#14268635C2211yescharacteristic, complemented
20C2×#14268634C2211yescharacteristic
21C2×#14268632C2211yescharacteristic
22#16813622C2211yescharacteristic, complemented
23#16813618C2211yescharacteristic
24#16813615—21no—
25#16813610C2211yescharacteristic
26#16813609C2211yescharacteristic
27#16813608—21no—
28#16813606—21no—
29#16813599—21no—
30#16813598C2211yescharacteristic
31#16813594—21no—
32#16813594—21no—
33#16813593C2211yescharacteristic
34#16813590—21no—
35#16813590—21no—
36Q8×Dic113C2211yescharacteristic, complemented
37D4×Dic113C2211yescharacteristic, complemented
38#16813579C2211yescharacteristic
39#16813551C2211yescharacteristic, complemented
40#16813551C2211yescharacteristic, complemented
41#16813547C2211yescharacteristic, complemented
42#16813547C2211yescharacteristic, complemented
43#16813544C2211yescharacteristic
44#16813544C2211yescharacteristic
45#16813543C2211yescharacteristic
46#16813543C2211yescharacteristic
47#16813543C2211yescharacteristic, complemented
48#16813543C2211yescharacteristic, complemented
49#16813534C2211yescharacteristic
50#16813534C2211yescharacteristic
51C4×#11744751C2211yescharacteristic, complemented
52C2×SD16×C113C2211yescharacteristic
53C2×SD16×C113C2211yescharacteristic, complemented
54C2×D8×C113C2211yescharacteristic
55C2×D8×C113C2211yescharacteristic, complemented
56#127×C113C2211yescharacteristic
57#124×C113C2211yescharacteristic, complemented
58#97×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60#14268646—41no—
61#14268646—41no—
62C2×Dic226—21no—
63C2×Dic226C2311yescharacteristic
64C2×D452C2311yescharacteristic
65C2×C22⋊D113—21no—
66C2×C22⋊D113—21no—
67C2×C22⋊D113—21no—
68C2×C22⋊D113—21no—
69C2×C22⋊D113—21no—
70D4×D113—41no—
71D4×D113—41no—
72C22×Dic113—21no—
73C22×Dic113—21no—
74C2×C4×D113C2311yescharacteristic
75#14268637—41no—
76#14268635—41no—
77#14268634—41no—
78#14268632—41no—
79C2×#11744751C2311yescharacteristic
80C2×#11744751C2311yescharacteristic
81C4⋊Dic113—21no—
82C4⋊Dic113—21no—
83C4⋊Dic113C2311yescharacteristic
84C4⋊Dic113C2311yescharacteristic
85#14268626—21no—
86#14268626D411yescharacteristic
87#14268626D411yescharacteristic
88C22⋊Dic113—21no—
89C22⋊Dic113—21no—
90C22⋊Dic113—21no—
91C22⋊Dic113—21no—
92#14268624—21no—
93#14268624—21no—
94#14268624—21no—
95#14268624D411yescharacteristic
96#14268624D411yescharacteristic
97C4×Dic113—21no—
98C4×Dic113C2311yescharacteristic
99C2×Q8×C113C2311yescharacteristic
100C2×D4×C113—21no—
101C2×D4×C113—21no—
102C2×D4×C113C2311yescharacteristic
103C2×D4×C113C2311yescharacteristic
104C2×D4×C113C2311yescharacteristic
105SD16×C113—41no—
106SD16×C113—41no—
107D8×C113—41no—
108D8×C113—41no—
109C2×C8×C113C2311yescharacteristic
110C2×C8×C113C2311yescharacteristic
111C22⋊C4×C113—21no—
112C22⋊C4×C113—21no—
113C42×C113C2311yescharacteristic
114C23×C113—21no—
115C23×C113—21no—
116C23×C113—21no—
117C22×D113—21no—
118C22×D113—42no—
119C22×D113—81no—
120C22×D113—81no—
121C22×D113C2×D411yescharacteristic
122Q8×C113—21no—
123Q8×C113—21no—
124D4×C113—21no—
125D4×C113—21no—
126D4×C113—21no—
127D4×C113—21no—
128D4×C113—21no—
129D4×C113—21no—
130D4×C113—81no—
131D4×C113—81no—
132C2×C4×C113—21no—
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—
141C2×Dic113—21no—
142C2×Dic113—21no—
143C2×Dic113—21no—
144C2×Dic113—42no—
145C2×Dic113—81no—
146C2×Dic113C2×D411yescharacteristic
147C2×Dic113C2×D411yescharacteristic
148C2×Dic113C2×D411yescharacteristic
149D452—21no—
150D452—21no—
151C4×D113—21no—
152C4×D113—21no—
153Dic226—21no—
154Dic226—21no—
155Dic226—81no—
156C8×C113—21no—
157C8×C113—21no—
158#11744751—21no—
159#11744751—21no—
160C22×C113—41no—
161C22×C113—41no—
162C22×C113—41no—
163C22×C113—41no—
164C22×C113—41no—
165C22×C113—41no—
166C22×C113—41no—
167C22×C113—41no—
168C22×C113—41no—
169C22×C113C22×D411yescharacteristic
170C2×D113—21no—
171C2×D113—21no—
172C2×D113—21no—
173C2×D113—41no—
174C2×D113—41no—
175C2×D113—41no—
176C2×D113—84no—
177C4×C113—21no—
178C4×C113—21no—
179C4×C113—41no—
180C4×C113H(5,𝔽2)11yescharacteristic
181C4×C113H(5,𝔽2)11yescharacteristic
182Dic113—21no—
183Dic113—21no—
184Dic113—21no—
185Dic113—41no—
186Dic113—41no—
187Dic113—41no—
188C2×C113—81no—
189C2×C113—81no—
190C2×C113—81no—
191C2×C113#53511yescharacteristic
192C2×C113#57611yescharacteristic
193C2×C113#57711yescharacteristic
194D113—41no—
195D113—81no—
196#3224—1131nomaximal, Sylow
197C113#322411yescharacteristic, complemented, Sylow
198#542—1131no—
199#535—1131no—
200#496D11311yescharacteristic, complemented
201#495—1131no—
202#489—1131no—
203#486—1131no—
204#464—1131no—
205#463—1131no—
206#460—1131no—
207#459—1131no—
208#452—1131no—
209#450—1131no—
210#449—1131no—
211#447—1131no—
212#433—1131no—
213C2×#41—1131no—
214C22×D4—1131no—
215C2×Q16—1131no—
216C2×SD16—1131no—
217C2×SD16—1131no—
218C2×SD16C2×D11311yescharacteristic
219C2×SD16C2×D11311yescharacteristic, complemented
220C2×D8—1131no—
221C2×D8C2×D11311yescharacteristic
222C2×D8C2×D11311yescharacteristic, complemented
223C4⋊Q8—1131no—
224#127—1131no—
225#127C2×D11311yescharacteristic
226#126—2261no—
227#124—1131no—
228#124—1131no—
229#124—2261no—
230#124C2×D11311yescharacteristic, complemented
231#123—2261no—
232C22⋊Q8—1131no—
233C22⋊Q8—2261no—
234#121—1131no—
235#121—2261no—
236#121—2261no—
237#120—2261no—
238#120—2261no—
239C4×Q8—1131no—
240C4×D4—1131no—
241#117—1131no—
242C4⋊C8—1131no—
243C4⋊C8—1131no—
244#103—1131no—
245#103—1131no—
246#102—1131no—
247#102—1131no—
248#102—1131no—
249#102—1131no—
250#102—1131no—
251#102—1131no—
252C22⋊C8—1131no—
253C22⋊C8—1131no—
254#97C2×D11311yescharacteristic, complemented
255C4×C8—1131no—
256C24—2261no—
257#41—4521no—
258#41—4521no—
259C2×Q8—1131no—
260C2×Q8—2261no—
261C2×Q8C22×D11311yescharacteristic
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—1131no—
265C2×D4—4521no—
266C2×D4—4521no—
267C2×D4—2261no—
268C2×D4—2261no—
269C2×D4—2261no—
270C2×D4—2261no—
271C2×D4—2261no—
272C2×D4C22×D11311yescharacteristic
273C2×D4C22×D11311yescharacteristic
274C2×D4C22×D11311yescharacteristic
275C22×C4—1131no—
276C22×C4—2261no—
277C22×C4—2261no—
278Q16—4521no—
279SD16—41no—
280SD16—41no—
281SD16—4521no—
282SD16—4521no—
283D8—41no—
284D8—41no—
285D8—4521no—
286C2×C8—1131no—
287C2×C8—1131no—
288C2×C8C22×D11311yescharacteristic
289C2×C8C22×D11311yescharacteristic
290C4⋊C4—1131no—
291C4⋊C4—1131no—
292C4⋊C4—1131no—
293C4⋊C4—1131no—
294C4⋊C4—2261no—
295C4⋊C4—2261no—
296C4⋊C4—2261no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—1131no—
300C22⋊C4—1131no—
301C22⋊C4—2261no—
302C22⋊C4—2261no—
303C22⋊C4—2261no—
304C22⋊C4—2261no—
305C22⋊C4—2261no—
306C22⋊C4—2261no—
307C22⋊C4—2261no—
308C42—1131no—
309C42—2261no—
310C42C22×D11311yescharacteristic
311C23—21no—
312C23—21no—
313C23—21no—
314C23—1131no—
315C23—9041no—
316C23—9041no—
317C23—4522no—
318C23—2261no—
319Q8—21no—
320Q8—21no—
321Q8—9041no—
322Q8—2261no—
323Q8—2261no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—81no—
331D4—81no—
332D4—9041no—
333D4—9041no—
334D4—9041no—
335D4—4522no—
336D4—4522no—
337D4—2261no—
338D4—2261no—
339C2×C4—21no—
340C2×C4—1131no—
341C2×C4—1131no—
342C2×C4—1131no—
343C2×C4—9041no—
344C2×C4—4522no—
345C2×C4—2261no—
346C2×C4—2261no—
347C2×C4—2261no—
348C2×C4—2261no—
349C2×C4—2261no—
350C2×C4D4×D11311yescharacteristic
351C2×C4D4×D11311yescharacteristic
352C2×C4C23×D11311yescharacteristic
353C8—21no—
354C8—21no—
355C8—2261no—
356C8—2261no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—9044no—
367C22—4521no—
368C22—4521no—
369C22—4521no—
370C22—2261no—
371C22—2261no—
372C22—2261no—
373C22C2×D4×D11311yescharacteristic
374C4—21no—
375C4—21no—
376C4—41no—
377C4—4521no—
378C4—4521no—
379C4—4521no—
380C4—2261no—
381C4—2261no—
382C4—2261no—
383C4#1681366711yescharacteristic
384C4#1681366711yescharacteristic
385C2—81no—
386C2—81no—
387C2—81no—
388C2—9041no—
389C2—4521no—
390C2#2029916111yescharacteristic
391C2#2029940211yescharacteristic
392C2#2029940811yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#496×C113C2
socleC22×C113C22×D4
hypercenter#496D113
hypocenterC113#3224
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #20299217C2semidirect
2. #20299161C2semidirect
3. #20298980C2semidirect
4. #20298958C2semidirect
5. #20298944C2semidirect
6. #20298818C2semidirect
7. #20298811C2semidirect
8. #20298796C2semidirect
9. #20298791C2semidirect
10. #20298757C2semidirect
11. #20298747C2semidirect
12. #20298740C2semidirect
13. #20298730C2semidirect
14. #20298660C2semidirect
15. #496×C113C2semidirect
18. C2×#14268637C22semidirect
19. C2×#14268635C22semidirect
22. #16813622C22semidirect
36. Q8×Dic113C22semidirect
37. D4×Dic113C22semidirect
39. #16813551C22semidirect
40. #16813551C22semidirect
41. #16813547C22semidirect
42. #16813547C22semidirect
47. #16813543C22semidirect
48. #16813543C22semidirect
51. C4×#11744751C22semidirect
53. C2×SD16×C113C22semidirect
55. C2×D8×C113C22semidirect
57. #124×C113C22semidirect
58. #97×C113C22semidirect
197. C113#3224semidirect
200. #496D113semidirect
219. C2×SD16C2×D113semidirect
222. C2×D8C2×D113semidirect
230. #124C2×D113semidirect
254. #97C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202992172
#202991612
#202989802
#202989582
#202989442
#202988182
#202988112
#202987962
#202987912
#202987572
#202987472
#202987402
#202987302
#202986602
#496×C1132
#3224113