Finite Group Databasebeta

← #28402717

Subgroups — #28402717

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#20299294C211yesmaximal, characteristic, complemented
2D4×D452C211yesmaximal, characteristic, complemented
3#20298963C211yesmaximal, characteristic, complemented
4#20298923C211yesmaximal, characteristic, complemented
5#20298917C211yesmaximal, characteristic, complemented
6#20298899C211yesmaximal, characteristic, complemented
7#20298851C211yesmaximal, characteristic, complemented
8#20298834C211yesmaximal, characteristic, complemented
9#20298794C211yesmaximal, characteristic, complemented
10#20298734C211yesmaximal, characteristic, complemented
11#20298734C211yesmaximal, characteristic, complemented
12#20298711C211yesmaximal, characteristic, complemented
13#20298604C211yesmaximal, characteristic, complemented
14C2×#16813544C211yesmaximal, characteristic, complemented
15#435×C113C211yesmaximal, characteristic, complemented
16C22×D452C2211yescharacteristic
17C22×D452C2211yescharacteristic
18C2×D4×D113—21no—
19C2×D904C2211yescharacteristic
20C2×D904C2211yescharacteristic, complemented
21C2×D904C2211yescharacteristic, complemented
22#16813619C2211yescharacteristic
23#16813617—21no—
24#16813614C2211yescharacteristic, complemented
25#16813604—21no—
26#16813597—21no—
27#16813596C2211yescharacteristic
28#16813596C2211yescharacteristic
29#16813596C2211yescharacteristic, complemented
30#16813596C2211yescharacteristic, complemented
31#16813594—21no—
32#16813592—21no—
33#16813592—21no—
34C4×D452C2211yescharacteristic
35C4×D452C2211yescharacteristic, complemented
36#16813582—21no—
37#16813581C2211yescharacteristic, complemented
38C2×C4⋊Dic113C2211yescharacteristic, complemented
39#16813556C2211yescharacteristic, complemented
40#16813554C2211yescharacteristic, complemented
41#16813554C2211yescharacteristic, complemented
42#16813544C2211yescharacteristic
43#16813544C2211yescharacteristic
44#16813544C2211yescharacteristic
45#16813544C2211yescharacteristic, complemented
46#16813544C2211yescharacteristic, complemented
47#16813544C2211yescharacteristic, complemented
48#16813544C2211yescharacteristic, complemented
49#16813544C2211yescharacteristic, complemented
50#16813544C2211yescharacteristic, complemented
51#16813544C2211yescharacteristic, complemented
52C2×M16×C113C2211yescharacteristic, complemented
53C22×C8×C113C2211yescharacteristic, complemented
54C4×D4×C113C2211yescharacteristic
55C4⋊C8×C113C2211yescharacteristic, complemented
56C22⋊C8×C113C2211yescharacteristic, complemented
57C22⋊C8×C113C2211yescharacteristic, complemented
58#97×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60C23×D113—21no—
61C2×D452—22no—
62C2×D452—22no—
63C2×D452—21no—
64C2×D452—21no—
65C2×D452—21no—
66C2×D452—21no—
67C2×D452—41no—
68C2×D452—41no—
69C2×D452C2311yescharacteristic
70C2×D452C2311yescharacteristic
71C2×D452C2311yescharacteristic
72C2×D452C2311yescharacteristic
73C2×C22⋊D113—21no—
74C2×C22⋊D113—21no—
75C2×C22⋊D113—21no—
76C2×C22⋊D113—21no—
77D4×D113—44no—
78C22×Dic113—21no—
79C2×C4×D113—21no—
80C2×C4×D113—21no—
81D904—22no—
82D904—41no—
83D904—41no—
84C4⋊Dic113—21no—
85C4⋊Dic113C2311yescharacteristic
86C4⋊Dic113C2311yescharacteristic
87C4⋊Dic113C2311yescharacteristic
88C4⋊Dic113C2311yescharacteristic
89#14268626—21no—
90#14268626—21no—
91C22⋊Dic113—21no—
92#14268624—21no—
93#14268624—21no—
94#14268624—21no—
95#14268624—21no—
96#14268624—21no—
97#14268624—21no—
98C4×Dic113—21no—
99C2×D4×C113D411yescharacteristic
100C22×C4×C113C2311yescharacteristic
101C22×C4×C113C2311yescharacteristic
102M16×C113—41no—
103C2×C8×C113—41no—
104C2×C8×C113C2311yescharacteristic
105C2×C8×C113C2311yescharacteristic
106C2×C8×C113C2311yescharacteristic
107C2×C8×C113C2311yescharacteristic
108C4⋊C4×C113D411yescharacteristic
109C22⋊C4×C113D411yescharacteristic
110C22⋊C4×C113D411yescharacteristic
111C42×C113C2311yescharacteristic
112C23×C113C2×D411yescharacteristic
113C23×C113C2×D411yescharacteristic
114C22×D113—21no—
115C22×D113—21no—
116C22×D113—21no—
117C22×D113—21no—
118C22×D113—42no—
119C22×D113—42no—
120C22×D113—42no—
121C22×D113—42no—
122C22×D113—81no—
123C22×D113—81no—
124D4×C113—22no—
125C2×C4×C113—21no—
126C2×C4×C113—21no—
127C2×C4×C113—21no—
128C2×C4×C113—21no—
129C2×C4×C113C2×D411yescharacteristic
130C2×C4×C113C2×D411yescharacteristic
131C2×C4×C113C2×D411yescharacteristic
132C2×C4×C113C2×D411yescharacteristic
133C2×C4×C113C2411yescharacteristic
134C22⋊D113—42no—
135C22⋊D113—42no—
136C22⋊D113—42no—
137C22⋊D113—81no—
138C2×Dic113—21no—
139C2×Dic113—21no—
140C2×Dic113—21no—
141C2×Dic113—21no—
142C2×Dic113—81no—
143D452—21no—
144D452—21no—
145D452—21no—
146D452—21no—
147D452—21no—
148D452—21no—
149D452—21no—
150D452—42no—
151D452—42no—
152D452—42no—
153D452—81no—
154D452#4112yes—
155C4×D113—42no—
156C4×D113—81no—
157C8×C113—21no—
158C8×C113—21no—
159C8×C113—21no—
160C8×C113—21no—
161C22×C113—21no—
162C22×C113—21no—
163C22×C113—21no—
164C22×C113—21no—
165C22×C113—21no—
166C22×C113AGL(1,ℤ/8)12yes—
167C22×C113C22×D411yescharacteristic
168C2×D113—22no—
169C2×D113—41no—
170C2×D113—41no—
171C2×D113—41no—
172C2×D113—41no—
173C2×D113—41no—
174C2×D113—41no—
175C2×D113—41no—
176C2×D113—41no—
177C2×D113—41no—
178C2×D113—41no—
179C2×D113—41no—
180C2×D113—84no—
181C2×D113—84no—
182C4×C113—21no—
183C4×C113—21no—
184C4×C113—21no—
185C4×C113—21no—
186C4×C113C2×#4111yescharacteristic
187C4×C113H(5,𝔽2)11yescharacteristic
188Dic113—41no—
189Dic113—41no—
190Dic113—41no—
191Dic113—41no—
192C2×C113—22no—
193C2×C113—41no—
194C2×C113#54611yescharacteristic
195C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
196C2×C113#57611yescharacteristic
197D113—42no—
198D113—81no—
199D113—81no—
200D113—81no—
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#459—1131no—
212#447—1131no—
213#447—1131no—
214#442—1131no—
215#435D11311yescharacteristic, complemented
216#418—1131no—
217C2×#102—1131no—
218C22×D4—1131no—
219C22×D4—1131no—
220C22×D4—2261no—
221C2×D8—1131no—
222C2×D8—1131no—
223C2×D8—1131no—
224C2×M16C2×D11311yescharacteristic, complemented
225C22×C8C2×D11311yescharacteristic, complemented
226#127—1131no—
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
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#102—1131no—
257#102—1131no—
258C22⋊C8C2×D11311yescharacteristic, complemented
259C22⋊C8C2×D11311yescharacteristic, complemented
260#97C2×D11311yescharacteristic, complemented
261C24—2261no—
262C24—2261no—
263C2×D4—1131no—
264C2×D4—1131no—
265C2×D4—1131no—
266C2×D4—1131no—
267C2×D4—4521no—
268C2×D4—4521no—
269C2×D4—4524no—
270C2×D4—2262no—
271C2×D4—2262no—
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×D4D45211yescharacteristic
281C22×C4—2261no—
282C22×C4—2261no—
283C22×C4—2261no—
284C22×C4C22×D11311yescharacteristic
285C22×C4C22×D11311yescharacteristic
286D8—4521no—
287D8—4521no—
288D8—2262no—
289M16—41no—
290C2×C8—41no—
291C2×C8C22×D11311yescharacteristic
292C2×C8C22×D11311yescharacteristic
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⋊C4D45211yescharacteristic
303C22⋊C4—2261no—
304C22⋊C4—2261no—
305C22⋊C4—2261no—
306C22⋊C4—2261no—
307C22⋊C4—2261no—
308C22⋊C4—2261no—
309C22⋊C4—2261no—
310C22⋊C4D45211yescharacteristic
311C22⋊C4D45211yescharacteristic
312C42—2261no—
313C42C22×D11311yescharacteristic
314C23—9041no—
315C23—9041no—
316C23—4522no—
317C23—4522no—
318C23—4522no—
319C23—4522no—
320C23—2261no—
321C23—2261no—
322C23—2261no—
323C23—2261no—
324C23C2×D45211yescharacteristic
325C23C2×D45211yescharacteristic
326D4—22no—
327D4—1132no—
328D4—9041no—
329D4—9041no—
330D4—4522no—
331D4—4522no—
332D4—4522no—
333D4—4522no—
334D4—4522no—
335D4—4522no—
336D4—2261no—
337D4—2261no—
338D4—2261no—
339D4—2261no—
340D4—2261no—
341D4—2261no—
342D4—2261no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—9041no—
348C2×C4—9041no—
349C2×C4—4522no—
350C2×C4—2261no—
351C2×C4—2261no—
352C2×C4—2261no—
353C2×C4—2261no—
354C2×C4C2×D45211yescharacteristic
355C2×C4C2×D45211yescharacteristic
356C2×C4C2×D45211yescharacteristic
357C2×C4C2×D45211yescharacteristic
358C2×C4C23×D11311yescharacteristic
359C8—21no—
360C8—21no—
361C8—21no—
362C8—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—9044no—
369C22—9044no—
370C22—4521no—
371C22—4521no—
372C22—4521no—
373C22—4521no—
374C22—4521no—
375C22—4521no—
376C22—4521no—
377C22—4521no—
378C22—4521no—
379C22—4521no—
380C22—4521no—
381C22—2262no—
382C22#1681365012yes—
383C22C22×D45211yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—4521no—
389C4—4521no—
390C4—4521no—
391C4—4521no—
392C4#41×D11311yescharacteristic
393C4#1681366711yescharacteristic
394C2—22no—
395C2—41no—
396C2—9041no—
397C2—9041no—
398C2—9041no—
399C2—4522no—
400C2#2029924311yescharacteristic
401C2C2×#1681365011yescharacteristic
402C2#2029940311yescharacteristic
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#435×C113C2
socleC22×C113C22×D4
hypercenter#435D113
hypocenterC113#3318
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #20299294C2semidirect
2. D4×D452C2semidirect
3. #20298963C2semidirect
4. #20298923C2semidirect
5. #20298917C2semidirect
6. #20298899C2semidirect
7. #20298851C2semidirect
8. #20298834C2semidirect
9. #20298794C2semidirect
10. #20298734C2semidirect
11. #20298734C2semidirect
12. #20298711C2semidirect
13. #20298604C2semidirect
14. C2×#16813544C2semidirect
15. #435×C113C2semidirect
20. C2×D904C22semidirect
21. C2×D904C22semidirect
24. #16813614C22semidirect
29. #16813596C22semidirect
30. #16813596C22semidirect
35. C4×D452C22semidirect
37. #16813581C22semidirect
38. C2×C4⋊Dic113C22semidirect
39. #16813556C22semidirect
40. #16813554C22semidirect
41. #16813554C22semidirect
45. #16813544C22semidirect
46. #16813544C22semidirect
47. #16813544C22semidirect
48. #16813544C22semidirect
49. #16813544C22semidirect
50. #16813544C22semidirect
51. #16813544C22semidirect
52. C2×M16×C113C22semidirect
53. C22×C8×C113C22semidirect
55. C4⋊C8×C113C22semidirect
56. C22⋊C8×C113C22semidirect
57. C22⋊C8×C113C22semidirect
58. #97×C113C22semidirect
202. C113#3318semidirect
215. #435D113semidirect
224. C2×M16C2×D113semidirect
225. C22×C8C2×D113semidirect
247. C4⋊C8C2×D113semidirect
258. C22⋊C8C2×D113semidirect
259. C22⋊C8C2×D113semidirect
260. #97C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202992942
D4×D4522
#202989632
#202989232
#202989172
#202988992
#202988512
#202988342
#202987942
#202987342
#202987112
#202986042
C2×#168135442
#435×C1132
#3318113