Finite Group Databasebeta

← #28402720

Subgroups — #28402720

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
2D4×D452C211yesmaximal, characteristic, complemented
3#20298963C211yesmaximal, characteristic, complemented
4#20298924C211yesmaximal, characteristic, complemented
5#20298918C211yesmaximal, characteristic, complemented
6#20298898C211yesmaximal, characteristic, complemented
7#20298850C211yesmaximal, characteristic, complemented
8#20298833C211yesmaximal, characteristic, complemented
9#20298793C211yesmaximal, characteristic, complemented
10#20298730C211yesmaximal, characteristic, complemented
11#20298730C211yesmaximal, characteristic, complemented
12#20298671C211yesmaximal, characteristic, complemented
13#20298601C211yesmaximal, characteristic, complemented
14#102×D113C211yesmaximal, characteristic, complemented
15#442×C113C211yesmaximal, characteristic, complemented
16C22×D452—21no—
17C2×D4×D113C2211yescharacteristic
18C2×D4×D113C2211yescharacteristic
19C2×#14268632C2211yescharacteristic, complemented
20C2×#14268632C2211yescharacteristic, complemented
21C2×#14268630C2211yescharacteristic, complemented
22C2×C8×D113C2211yescharacteristic, complemented
23#16813619C2211yescharacteristic
24#16813615—21no—
25#16813614C2211yescharacteristic, complemented
26#16813605—21no—
27#16813597C2211yescharacteristic
28#16813597C2211yescharacteristic
29#16813596—21no—
30#16813595—21no—
31#16813593C2211yescharacteristic, complemented
32#16813593C2211yescharacteristic, complemented
33#16813592—21no—
34#16813592—21no—
35C4×D452C2211yescharacteristic
36C4×C22⋊D113—21no—
37#16813580C2211yescharacteristic, complemented
38C4⋊C4×D113C2211yescharacteristic, complemented
39#16813555C2211yescharacteristic, complemented
40#16813553C2211yescharacteristic, complemented
41C4⋊#11744751C2211yescharacteristic, complemented
42#16813544C2211yescharacteristic, complemented
43#16813544C2211yescharacteristic, complemented
44#16813544C2211yescharacteristic, complemented
45#16813544C2211yescharacteristic, complemented
46#16813543C2211yescharacteristic
47#16813543C2211yescharacteristic
48#16813542C2211yescharacteristic, complemented
49#16813542C2211yescharacteristic, complemented
50#16813534C2211yescharacteristic, complemented
51#16813534C2211yescharacteristic, complemented
52C2×D8×C113C2211yescharacteristic
53C4×D4×C113C2211yescharacteristic
54C4×D4×C113C2211yescharacteristic, complemented
55#106×C113C2211yescharacteristic, complemented
56#102×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic, complemented
58#97×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60C23×D113—21no—
61C2×D452—21no—
62C2×D452—21no—
63C2×D452—21no—
64C2×D452—21no—
65C2×D452—44no—
66C2×D452D411yescharacteristic
67C2×D452C2311yescharacteristic
68C2×D452C2311yescharacteristic
69C2×C22⋊D113—21no—
70C2×C22⋊D113—21no—
71C2×C22⋊D113—21no—
72C2×C22⋊D113—21no—
73D4×D113—22no—
74D4×D113—22no—
75D4×D113—41no—
76D4×D113—41no—
77C2×C4×D113—21no—
78C2×C4×D113C2311yescharacteristic
79C2×C4×D113C2311yescharacteristic
80#14268632—41no—
81#14268632—41no—
82#14268630—41no—
83C2×#11744751C2311yescharacteristic
84C2×#11744751C2311yescharacteristic
85C8×D113—41no—
86C4⋊Dic113D411yescharacteristic
87C4⋊Dic113C2311yescharacteristic
88C4⋊Dic113C2311yescharacteristic
89#14268626—21no—
90#14268626—21no—
91#14268626—21no—
92C22⋊Dic113—21no—
93C22⋊Dic113—21no—
94#14268624—21no—
95#14268624—21no—
96#14268624—21no—
97#14268624D411yescharacteristic
98#14268624D411yescharacteristic
99C4×Dic113—21no—
100C2×D4×C113C2311yescharacteristic
101C2×D4×C113C2311yescharacteristic
102C22×C4×C113—21no—
103C22×C4×C113—21no—
104D8×C113—22no—
105C2×C8×C113C2311yescharacteristic
106C2×C8×C113C2311yescharacteristic
107C4⋊C4×C113C2311yescharacteristic
108C4⋊C4×C113C2311yescharacteristic
109C22⋊C4×C113—21no—
110C22⋊C4×C113—21no—
111C42×C113C2311yescharacteristic
112C23×C113—21no—
113C23×C113—21no—
114C22×D113—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#4112yes—
128C2×C4×C113—21no—
129C2×C4×C113—21no—
130C2×C4×C113—42no—
131C2×C4×C113—81no—
132C2×C4×C113C2×D411yescharacteristic
133C2×C4×C113C2×D411yescharacteristic
134C2×C4×C113C2411yescharacteristic
135C22⋊D113—42no—
136C22⋊D113—42no—
137C22⋊D113—42no—
138C22⋊D113—81no—
139C2×Dic113—21no—
140C2×Dic113—21no—
141C2×Dic113C2×D411yescharacteristic
142C2×Dic113C2×D411yescharacteristic
143D452—22no—
144D452—21no—
145D452—21no—
146D452—21no—
147D452—21no—
148D452—42no—
149D452—42no—
150D452—42no—
151D452—81no—
152C4×D113—21no—
153C4×D113—21no—
154C4×D113—21no—
155C4×D113—21no—
156C4×D113—81no—
157C8×C113—21no—
158C8×C113—21no—
159#11744751—21no—
160#11744751—21no—
161C22×C113—22no—
162C22×C113—41no—
163C22×C113—41no—
164C22×C113—41no—
165C22×C113—41no—
166C22×C113—41no—
167C22×C113C22×D411yescharacteristic
168C2×D113—21no—
169C2×D113—21no—
170C2×D113—21no—
171C2×D113—21no—
172C2×D113—21no—
173C2×D113—41no—
174C2×D113—41no—
175C2×D113—41no—
176C2×D113—41no—
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×C113—41no—
186C4×C113C2×#4111yescharacteristic
187C4×C113H(5,𝔽2)11yescharacteristic
188Dic113—21no—
189Dic113—21no—
190Dic113—41no—
191Dic113—41no—
192C2×C113—42no—
193C2×C113—81no—
194C2×C113#54611yescharacteristic
195C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
196C2×C113#57611yescharacteristic
197D113—22no—
198D113—41no—
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#442D11311yescharacteristic, complemented
215#435—1131no—
216#418—1131no—
217C2×#102—1131no—
218C22×D4—1131no—
219C22×D4—1131no—
220C22×D4—2261no—
221C2×D8—1131no—
222C2×D8—1131no—
223C2×D8C2×D11311yescharacteristic
224C2×M16—1131no—
225C22×C8—1131no—
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—2261no—
240C4×D4C2×D11311yescharacteristic
241C4×D4C2×D11311yescharacteristic, complemented
242#117—1131no—
243C2×C4⋊C4—1131no—
244#107—1131no—
245#106—1131no—
246#106C2×D11311yescharacteristic, complemented
247C4⋊C8—1131no—
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
257#102C2×D11311yescharacteristic, complemented
258C22⋊C8—1131no—
259C22⋊C8—1131no—
260#97C2×D11311yescharacteristic, complemented
261C24—2261no—
262C24—2261no—
263C2×D4—1131no—
264C2×D4—1131no—
265C2×D4—1131no—
266C2×D4—4524no—
267C2×D4—4521no—
268C2×D4—4521no—
269C2×D4—2261no—
270C2×D4—2261no—
271C2×D4—2261no—
272C2×D4—2261no—
273C2×D4—2261no—
274C2×D4—2261no—
275C2×D4—2262no—
276C2×D4—2262no—
277C2×D4—2261no—
278C2×D4—2261no—
279C2×D4C22×D11311yescharacteristic
280C2×D4C22×D11311yescharacteristic
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—1131no—
284C22×C4—1131no—
285C22×C4—2261no—
286D8—22no—
287D8—4521no—
288D8—4521no—
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—2261no—
299C4⋊C4—2261no—
300C4⋊C4—2261no—
301C4⋊C4C22×D11311yescharacteristic
302C4⋊C4C22×D11311yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—1131no—
306C22⋊C4—1131no—
307C22⋊C4—2261no—
308C22⋊C4—2261no—
309C22⋊C4—2261no—
310C22⋊C4—2261no—
311C22⋊C4—2261no—
312C42—2261no—
313C42C22×D11311yescharacteristic
314C23—21no—
315C23—21no—
316C23—1131no—
317C23—1131no—
318C23—9041no—
319C23—9041no—
320C23—4522no—
321C23—4522no—
322C23—4522no—
323C23—4522no—
324C23—2261no—
325C23—2261no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—9041no—
330D4—9041no—
331D4—4522no—
332D4—4522no—
333D4—4522no—
334D4—4522no—
335D4—4522no—
336D4—4522no—
337D4—2262no—
338D4—2261no—
339D4—2261no—
340D4—2261no—
341D4—2261no—
342D4#1426864712yes—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—42no—
346C2×C4—81no—
347C2×C4—1131no—
348C2×C4—1131no—
349C2×C4—9041no—
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—22no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—1132no—
370C22—9044no—
371C22—9044no—
372C22—4521no—
373C22—4521no—
374C22—4521no—
375C22—4521no—
376C22—4521no—
377C22—4521no—
378C22—2261no—
379C22—2261no—
380C22—2261no—
381C22—2261no—
382C22—2261no—
383C22C2×D4×D11311yescharacteristic
384C4—21no—
385C4—21no—
386C4—41no—
387C4—41no—
388C4—4521no—
389C4—4521no—
390C4—2261no—
391C4—2261no—
392C4C2×#1426864711yescharacteristic
393C4#1681366811yescharacteristic
394C2—42no—
395C2—81no—
396C2—9041no—
397C2—9041no—
398C2—4521no—
399C2—2262no—
400C2#2029924411yescharacteristic
401C2AGL(1,ℤ/8)×D11311yescharacteristic
402C2#2029940211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#442×C113C2
socleC22×C113C22×D4
hypercenter#442D113
hypocenterC113#3318
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #20299298C2semidirect
2. D4×D452C2semidirect
3. #20298963C2semidirect
4. #20298924C2semidirect
5. #20298918C2semidirect
6. #20298898C2semidirect
7. #20298850C2semidirect
8. #20298833C2semidirect
9. #20298793C2semidirect
10. #20298730C2semidirect
11. #20298730C2semidirect
12. #20298671C2semidirect
13. #20298601C2semidirect
14. #102×D113C2semidirect
15. #442×C113C2semidirect
19. C2×#14268632C22semidirect
20. C2×#14268632C22semidirect
21. C2×#14268630C22semidirect
22. C2×C8×D113C22semidirect
25. #16813614C22semidirect
31. #16813593C22semidirect
32. #16813593C22semidirect
37. #16813580C22semidirect
38. C4⋊C4×D113C22semidirect
39. #16813555C22semidirect
40. #16813553C22semidirect
41. C4⋊#11744751C22semidirect
42. #16813544C22semidirect
43. #16813544C22semidirect
44. #16813544C22semidirect
45. #16813544C22semidirect
48. #16813542C22semidirect
49. #16813542C22semidirect
50. #16813534C22semidirect
51. #16813534C22semidirect
54. C4×D4×C113C22semidirect
55. #106×C113C22semidirect
57. #102×C113C22semidirect
58. #97×C113C22semidirect
202. C113#3318semidirect
214. #442D113semidirect
241. C4×D4C2×D113semidirect
246. #106C2×D113semidirect
257. #102C2×D113semidirect
260. #97C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202992982
D4×D4522
#202989632
#202989242
#202989182
#202988982
#202988502
#202988332
#202987932
#202987302
#202986712
#202986012
#102×D1132
#442×C1132
#3318113