Finite Group Databasebeta

← #28402722

Subgroups — #28402722

Order 14464.

462 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299298C211yesmaximal, characteristic, complemented
2#20299233C211yesmaximal, characteristic, complemented
3#20298962C211yesmaximal, characteristic, complemented
4#20298920C211yesmaximal, characteristic, complemented
5#20298915C211yesmaximal, characteristic, complemented
6#20298899C211yesmaximal, characteristic, complemented
7#20298848C211yesmaximal, characteristic, complemented
8#20298831C211yesmaximal, characteristic, complemented
9#20298730C211yesmaximal, characteristic, complemented
10#20298730C211yesmaximal, characteristic, complemented
11#20298708C211yesmaximal, characteristic, complemented
12#20298668C211yesmaximal, characteristic, complemented
13#20298601C211yesmaximal, characteristic, complemented
14#102×D113C211yesmaximal, characteristic, complemented
15#459×C113C211yesmaximal, characteristic, complemented
16C2×D4×D113—21no—
17C2×D4×D113C2211yescharacteristic
18C2×D4×D113C2211yescharacteristic
19C2×#14268632C2211yescharacteristic
20C2×#14268630C2211yescharacteristic, complemented
21C2×C8×D113C2211yescharacteristic, complemented
22#16813615—21no—
23#16813614C2211yescharacteristic, complemented
24#16813605—21no—
25#16813595—21no—
26#16813593—21no—
27#16813593C2211yescharacteristic
28#16813593C2211yescharacteristic
29#16813593C2211yescharacteristic, complemented
30#16813593C2211yescharacteristic, complemented
31#16813590—21no—
32#16813590—21no—
33C4×D452C2211yescharacteristic
34C4×D452C2211yescharacteristic
35C4×C22⋊D113—21no—
36#16813580C2211yescharacteristic, complemented
37C4⋊C4×D113C2211yescharacteristic, complemented
38#16813556C2211yescharacteristic, complemented
39#16813554C2211yescharacteristic, complemented
40#16813553C2211yescharacteristic, complemented
41#16813544C2211yescharacteristic
42#16813544C2211yescharacteristic
43#16813543C2211yescharacteristic, complemented
44#16813543C2211yescharacteristic, complemented
45#16813543C2211yescharacteristic, complemented
46#16813543C2211yescharacteristic, complemented
47#16813543C2211yescharacteristic, complemented
48#16813542C2211yescharacteristic
49#16813534C2211yescharacteristic, complemented
50#16813534C2211yescharacteristic, complemented
51#16813533C2211yescharacteristic, complemented
52C2×D8×C113C2211yescharacteristic, complemented
53C2×D8×C113C2211yescharacteristic, complemented
54#127×C113C2211yescharacteristic
55C4×D4×C113C2211yescharacteristic, complemented
56C4⋊C8×C113C2211yescharacteristic, complemented
57#102×C113C2211yescharacteristic, complemented
58#102×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60C23×D113—21no—
61C2×D452D411yescharacteristic
62C2×D452C2311yescharacteristic
63C2×C22⋊D113—21no—
64C2×C22⋊D113—21no—
65C2×C22⋊D113—21no—
66C2×C22⋊D113—21no—
67C2×C22⋊D113—21no—
68C2×C22⋊D113—21no—
69D4×D113—22no—
70D4×D113—22no—
71D4×D113—41no—
72D4×D113—41no—
73D4×D113—44no—
74C2×C4×D113—21no—
75C2×C4×D113—21no—
76C2×C4×D113C2311yescharacteristic
77C2×C4×D113C2311yescharacteristic
78#14268632—22no—
79#14268630—41no—
80C2×#11744751C2311yescharacteristic
81C2×#11744751C2311yescharacteristic
82C8×D113—41no—
83C4⋊Dic113D411yescharacteristic
84C4⋊Dic113C2311yescharacteristic
85C4⋊Dic113C2311yescharacteristic
86C4⋊Dic113C2311yescharacteristic
87#14268626—21no—
88#14268626—21no—
89#14268626—21no—
90C22⋊Dic113—21no—
91C22⋊Dic113—21no—
92C22⋊Dic113—21no—
93C22⋊Dic113—21no—
94#14268624—21no—
95#14268624—21no—
96#14268624D411yescharacteristic
97#14268624D411yescharacteristic
98C4×Dic113—21no—
99C2×D4×C113—21no—
100C2×D4×C113—21no—
101C2×D4×C113C2311yescharacteristic
102C2×D4×C113C2311yescharacteristic
103C2×D4×C113C2311yescharacteristic
104C22×C4×C113—21no—
105D8×C113—41no—
106D8×C113—41no—
107C2×C8×C113C2311yescharacteristic
108C2×C8×C113C2311yescharacteristic
109C4⋊C4×C113C2311yescharacteristic
110C22⋊C4×C113—21no—
111C42×C113C2311yescharacteristic
112C23×C113—21no—
113C23×C113—21no—
114C23×C113—21no—
115C22×D113—21no—
116C22×D113—42no—
117C22×D113—42no—
118C22×D113—42no—
119C22×D113—42no—
120C22×D113—81no—
121C22×D113—81no—
122C22×D113C2×D411yescharacteristic
123C22×D113C2×D411yescharacteristic
124D4×C113—21no—
125D4×C113—21no—
126D4×C113—21no—
127D4×C113—21no—
128D4×C113—21no—
129D4×C113—21no—
130D4×C113—42no—
131D4×C113—81no—
132C2×C4×C113—21no—
133C2×C4×C113—81no—
134C2×C4×C113C2×D411yescharacteristic
135C2×C4×C113C2×D411yescharacteristic
136C2×C4×C113C2411yescharacteristic
137C22⋊D113—42no—
138C22⋊D113—42no—
139C22⋊D113—42no—
140C22⋊D113—42no—
141C22⋊D113—42no—
142C22⋊D113—81no—
143C2×Dic113—21no—
144C2×Dic113—21no—
145C2×Dic113—21no—
146C2×Dic113C2×D411yescharacteristic
147C2×Dic113C2×D411yescharacteristic
148D452—22no—
149D452—21no—
150D452#4112yes—
151C4×D113—21no—
152C4×D113—21no—
153C4×D113—21no—
154C4×D113—21no—
155C4×D113—42no—
156C4×D113—81no—
157C8×C113—21no—
158C8×C113—21no—
159#11744751—21no—
160#11744751—21no—
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×C113—41no—
170C22×C113C22×D411yescharacteristic
171C2×D113—21no—
172C2×D113—21no—
173C2×D113—21no—
174C2×D113—22no—
175C2×D113—21no—
176C2×D113—21no—
177C2×D113—41no—
178C2×D113—41no—
179C2×D113—84no—
180C2×D113—84no—
181C2×D113AGL(1,ℤ/8)12yes—
182C4×C113—21no—
183C4×C113—21no—
184C4×C113—41no—
185C4×C113C2×#4111yescharacteristic
186C4×C113H(5,𝔽2)11yescharacteristic
187Dic113—21no—
188Dic113—21no—
189Dic113—41no—
190Dic113—41no—
191Dic113—41no—
192C2×C113—81no—
193C2×C113—81no—
194C2×C113—81no—
195C2×C113#54611yescharacteristic
196C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
197C2×C113#57611yescharacteristic
198D113—22no—
199D113—41no—
200D113—42no—
201#3318—1131nomaximal, Sylow
202C113#331811yescharacteristic, complemented, Sylow
203#553—1131no—
204D42—1131no—
205#490—1131no—
206#482—1131no—
207#481—1131no—
208#478—1131no—
209#469—1131no—
210#466—1131no—
211#459D11311yescharacteristic, complemented
212#447—1131no—
213#447—1131no—
214#442—1131no—
215#435—1131no—
216#418—1131no—
217C2×#102—1131no—
218C22×D4—1131no—
219C22×D4—1131no—
220C22×D4—2261no—
221C2×D8—1131no—
222C2×D8C2×D11311yescharacteristic, complemented
223C2×D8C2×D11311yescharacteristic, complemented
224C2×M16—1131no—
225C22×C8—1131no—
226#127C2×D11311yescharacteristic
227#126—2261no—
228#125—1131no—
229#123—2261no—
230#121—1131no—
231#121—1131no—
232#121—1131no—
233#121—1131no—
234#121—2261no—
235#121—2261no—
236#120—2261no—
237#120—2261no—
238C4×D4—1131no—
239C4×D4—1131no—
240C4×D4—2261no—
241C4×D4C2×D11311yescharacteristic, complemented
242#117—1131no—
243C2×C4⋊C4—1131no—
244#107—1131no—
245#106—1131no—
246#106—1131no—
247C4⋊C8C2×D11311yescharacteristic, complemented
248#102—1131no—
249#102—1131no—
250#102—1131no—
251#102—1131no—
252#102—1131no—
253#102—1131no—
254#102—1131no—
255#102—1131no—
256#102C2×D11311yescharacteristic, complemented
257#102C2×D11311yescharacteristic, complemented
258C22⋊C8—1131no—
259C22⋊C8—1131no—
260#97—1131no—
261C24—2261no—
262C24—2261no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—1131no—
266C2×D4—1131no—
267C2×D4—4524no—
268C2×D4—4521no—
269C2×D4—4521no—
270C2×D4—2261no—
271C2×D4—2261no—
272C2×D4—2262no—
273C2×D4—2262no—
274C2×D4—2261no—
275C2×D4—2261no—
276C2×D4—2261no—
277C2×D4—2261no—
278C2×D4C22×D11311yescharacteristic
279C2×D4C22×D11311yescharacteristic
280C2×D4C22×D11311yescharacteristic
281C22×C4—21no—
282C22×C4—1131no—
283C22×C4—1131no—
284C22×C4—2261no—
285C22×C4—2261no—
286D8—41no—
287D8—41no—
288D8—2262no—
289M16—4521no—
290C2×C8—1131no—
291C2×C8—1131no—
292C2×C8—4521no—
293C2×C8C22×D11311yescharacteristic
294C2×C8C22×D11311yescharacteristic
295C4⋊C4—1131no—
296C4⋊C4—1131no—
297C4⋊C4—1131no—
298C4⋊C4—1131no—
299C4⋊C4—2261no—
300C4⋊C4—2261no—
301C4⋊C4—2261no—
302C4⋊C4C22×D11311yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—1131no—
305C22⋊C4—1131no—
306C22⋊C4—2261no—
307C22⋊C4—2261no—
308C22⋊C4—2261no—
309C22⋊C4—2261no—
310C22⋊C4—2261no—
311C22⋊C4—2261no—
312C42—2261no—
313C42C22×D11311yescharacteristic
314C23—21no—
315C23—21no—
316C23—21no—
317C23—1131no—
318C23—1131no—
319C23—9041no—
320C23—9041no—
321C23—4522no—
322C23—4522no—
323C23—4522no—
324C23—4522no—
325C23—2261no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—42no—
333D4—81no—
334D4—1132no—
335D4—9041no—
336D4—4522no—
337D4—4522no—
338D4—4522no—
339D4—4522no—
340D4—4522no—
341D4—2262no—
342D4—2261no—
343C2×C4—21no—
344C2×C4—81no—
345C2×C4—1131no—
346C2×C4—1131no—
347C2×C4—9041no—
348C2×C4—4522no—
349C2×C4—2261no—
350C2×C4—2261no—
351C2×C4—2261no—
352C2×C4—2261no—
353C2×C4—2261no—
354C2×C4—2261no—
355C2×C4—2261no—
356C2×C4D4×D11311yescharacteristic
357C2×C4D4×D11311yescharacteristic
358C2×C4C23×D11311yescharacteristic
359C8—21no—
360C8—21no—
361C8—2261no—
362C8—2261no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—1132no—
373C22—9044no—
374C22—9044no—
375C22—4521no—
376C22—4521no—
377C22—2261no—
378C22—2261no—
379C22—2261no—
380C22—2262no—
381C22—2261no—
382C22—2261no—
383C22C2×D4×D11311yescharacteristic
384C4—21no—
385C4—21no—
386C4—41no—
387C4—4521no—
388C4—4521no—
389C4—4521no—
390C4—2261no—
391C4—2261no—
392C4#41×D11311yescharacteristic
393C4#1681366711yescharacteristic
394C2—81no—
395C2—81no—
396C2—81no—
397C2—4522no—
398C2—4521no—
399C2—2262no—
400C2#2029924511yescharacteristic
401C2AGL(1,ℤ/8)×D11311yescharacteristic
402C2#2029939911yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#459×C113C2
socleC22×C113C22×D4
hypercenter#459D113
hypocenterC113#3318
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. #20299298C2semidirect
2. #20299233C2semidirect
3. #20298962C2semidirect
4. #20298920C2semidirect
5. #20298915C2semidirect
6. #20298899C2semidirect
7. #20298848C2semidirect
8. #20298831C2semidirect
9. #20298730C2semidirect
10. #20298730C2semidirect
11. #20298708C2semidirect
12. #20298668C2semidirect
13. #20298601C2semidirect
14. #102×D113C2semidirect
15. #459×C113C2semidirect
20. C2×#14268630C22semidirect
21. C2×C8×D113C22semidirect
23. #16813614C22semidirect
29. #16813593C22semidirect
30. #16813593C22semidirect
36. #16813580C22semidirect
37. C4⋊C4×D113C22semidirect
38. #16813556C22semidirect
39. #16813554C22semidirect
40. #16813553C22semidirect
43. #16813543C22semidirect
44. #16813543C22semidirect
45. #16813543C22semidirect
46. #16813543C22semidirect
47. #16813543C22semidirect
49. #16813534C22semidirect
50. #16813534C22semidirect
51. #16813533C22semidirect
52. C2×D8×C113C22semidirect
53. C2×D8×C113C22semidirect
55. C4×D4×C113C22semidirect
56. C4⋊C8×C113C22semidirect
57. #102×C113C22semidirect
58. #102×C113C22semidirect
202. C113#3318semidirect
211. #459D113semidirect
222. C2×D8C2×D113semidirect
223. C2×D8C2×D113semidirect
241. C4×D4C2×D113semidirect
247. C4⋊C8C2×D113semidirect
256. #102C2×D113semidirect
257. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202992982
#202992332
#202989622
#202989202
#202989152
#202988992
#202988482
#202988312
#202987302
#202987082
#202986682
#202986012
#102×D1132
#459×C1132
#3318113