Finite Group Databasebeta

← #22600363

Subgroups — #22600363

Order 9088.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17986689C211yesmaximal, characteristic, complemented
2D4×D284C211yesmaximal, characteristic
3#17986364C211yesmaximal, characteristic, complemented
4#17986324C211yesmaximal, characteristic, complemented
5#17986313C211yesmaximal, characteristic, complemented
6#17986300C211yesmaximal, characteristic, complemented
7#17986245C211yesmaximal, characteristic, complemented
8#17986228C211yesmaximal, characteristic, complemented
9#17986200C211yesmaximal, characteristic, complemented
10#17986152C211yesmaximal, characteristic, complemented
11#17986152C211yesmaximal, characteristic, complemented
12#17986101C211yesmaximal, characteristic, complemented
13#17986005C211yesmaximal, characteristic, complemented
14C2×#14556050C211yesmaximal, characteristic, complemented
15#435×C71C211yesmaximal, characteristic, complemented
16C22×D284C2211yescharacteristic
17C22×D284C2211yescharacteristic
18C2×D4×D71—21no—
19C2×#11765854C2211yescharacteristic
20C2×#11765854C2211yescharacteristic, complemented
21C2×#11765854C2211yescharacteristic, complemented
22#14556125C2211yescharacteristic
23#14556121—21no—
24#14556120C2211yescharacteristic, complemented
25#14556118—21no—
26#14556109—21no—
27#14556107C2211yescharacteristic, complemented
28#14556107C2211yescharacteristic, complemented
29#14556103—21no—
30#14556102C2211yescharacteristic
31#14556102C2211yescharacteristic
32#14556098—21no—
33#14556098—21no—
34C4×Dic142C2211yescharacteristic, complemented
35C4×D284C2211yescharacteristic
36#14556087C2211yescharacteristic, complemented
37#14556084—21no—
38C2×C4⋊Dic71C2211yescharacteristic, complemented
39#14556062C2211yescharacteristic, complemented
40#14556062C2211yescharacteristic, complemented
41#14556060C2211yescharacteristic, complemented
42#14556053C2211yescharacteristic, complemented
43#14556050C2211yescharacteristic
44#14556050C2211yescharacteristic
45#14556050C2211yescharacteristic
46#14556050C2211yescharacteristic, complemented
47#14556050C2211yescharacteristic, complemented
48#14556050C2211yescharacteristic, complemented
49#14556050C2211yescharacteristic, complemented
50#14556050C2211yescharacteristic, complemented
51#14556050C2211yescharacteristic, complemented
52C2×M16×C71C2211yescharacteristic, complemented
53C22×C8×C71C2211yescharacteristic, complemented
54C4×D4×C71C2211yescharacteristic
55C4⋊C8×C71C2211yescharacteristic, complemented
56C22⋊C8×C71C2211yescharacteristic, complemented
57C22⋊C8×C71C2211yescharacteristic, complemented
58#97×C71C2211yescharacteristic, complemented
59C23×D71—21no—
60C23×D71—21no—
61C2×Dic142C2311yescharacteristic
62C2×D284—22no—
63C2×D284—22no—
64C2×D284—21no—
65C2×D284—21no—
66C2×D284—21no—
67C2×D284—21no—
68C2×D284—41no—
69C2×D284—41no—
70C2×D284C2311yescharacteristic
71C2×D284C2311yescharacteristic
72C2×D284C2311yescharacteristic
73C2×C22⋊D71—21no—
74C2×C22⋊D71—21no—
75D4×D71—44no—
76C22×Dic71—21no—
77C2×C4×D71—21no—
78#11765854—22no—
79#11765854—41no—
80#11765854—41no—
81C4⋊Dic71—21no—
82C4⋊Dic71C2311yescharacteristic
83C4⋊Dic71C2311yescharacteristic
84C4⋊Dic71C2311yescharacteristic
85C4⋊Dic71C2311yescharacteristic
86Dic71⋊C4—21no—
87Dic71⋊C4—21no—
88Dic71⋊C4—21no—
89Dic71⋊C4—21no—
90Dic71⋊C4—21no—
91C22⋊Dic71—21no—
92C22⋊Dic71—21no—
93C22⋊Dic71—21no—
94(C2×D71)⋊C4—21no—
95(C2×D71)⋊C4—21no—
96(C2×D71)⋊C4—21no—
97C4×Dic71—21no—
98C4×Dic71—21no—
99C2×D4×C71D411yescharacteristic
100C22×C4×C71C2311yescharacteristic
101C22×C4×C71C2311yescharacteristic
102M16×C71—41no—
103C2×C8×C71—41no—
104C2×C8×C71C2311yescharacteristic
105C2×C8×C71C2311yescharacteristic
106C2×C8×C71C2311yescharacteristic
107C2×C8×C71C2311yescharacteristic
108C4⋊C4×C71D411yescharacteristic
109C22⋊C4×C71D411yescharacteristic
110C22⋊C4×C71D411yescharacteristic
111C42×C71C2311yescharacteristic
112C23×C71C2×D411yescharacteristic
113C23×C71C2×D411yescharacteristic
114C22×D71—21no—
115C22×D71—21no—
116C22×D71—21no—
117C22×D71—42no—
118C22×D71—42no—
119C22×D71—42no—
120C22×D71—42no—
121C22×D71—81no—
122C22×D71—81no—
123D4×C71—22no—
124C2×C4×C71—21no—
125C2×C4×C71—21no—
126C2×C4×C71—21no—
127C2×C4×C71—21no—
128C2×C4×C71C2×D411yescharacteristic
129C2×C4×C71C2×D411yescharacteristic
130C2×C4×C71C2×D411yescharacteristic
131C2×C4×C71C2×D411yescharacteristic
132C2×C4×C71C2411yescharacteristic
133C22⋊D71—42no—
134C22⋊D71—42no—
135C2×Dic71—21no—
136C2×Dic71—21no—
137C2×Dic71—21no—
138C2×Dic71—21no—
139C2×Dic71—21no—
140C2×Dic71—42no—
141D284—21no—
142D284—21no—
143D284—21no—
144D284—21no—
145D284—21no—
146D284—42no—
147D284—42no—
148D284—42no—
149D284—81no—
150D284#4112yes—
151C4×D71—42no—
152Dic142—21no—
153Dic142—21no—
154C8×C71—21no—
155C8×C71—21no—
156C8×C71—21no—
157C8×C71—21no—
158C22×C71—21no—
159C22×C71—21no—
160C22×C71—21no—
161C22×C71—21no—
162C22×C71—21no—
163C22×C71AGL(1,ℤ/8)12yes—
164C22×C71C22×D411yescharacteristic
165C2×D71—22no—
166C2×D71—41no—
167C2×D71—41no—
168C2×D71—41no—
169C2×D71—41no—
170C2×D71—41no—
171C2×D71—41no—
172C2×D71—41no—
173C2×D71—41no—
174C2×D71—84no—
175C2×D71—84no—
176C4×C71—21no—
177C4×C71—21no—
178C4×C71—21no—
179C4×C71—21no—
180C4×C71C2×#4111yescharacteristic
181C4×C71H(5,𝔽2)11yescharacteristic
182Dic71—41no—
183Dic71—41no—
184Dic71—41no—
185Dic71—41no—
186Dic71—41no—
187C2×C71—22no—
188C2×C71—41no—
189C2×C71#54611yescharacteristic
190C2×C71C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C71#57711yescharacteristic
192D71—42no—
193D71—81no—
194D71—81no—
195#3310—711nomaximal, Sylow
196C71#331011yescharacteristic, complemented, Sylow
197#552—711no—
198D42—711no—
199#490—711no—
200#482—711no—
201#480—711no—
202#478—711no—
203#468—711no—
204#465—711no—
205#460—711no—
206#450—711no—
207#450—711no—
208#440—711no—
209#435D7111yescharacteristic, complemented
210#418—711no—
211C2×#102—711no—
212C22×D4—711no—
213C22×D4—711no—
214C22×D4—1421no—
215C2×SD16—711no—
216C2×SD16—711no—
217C2×SD16—711no—
218C2×M16C2×D7111yescharacteristic, complemented
219C22×C8C2×D7111yescharacteristic, complemented
220#127—711no—
221#126—1421no—
222#125—711no—
223#125—1421no—
224#123—1421no—
225C22⋊Q8—711no—
226C22⋊Q8—711no—
227#121—711no—
228#121—711no—
229#121—1421no—
230#120—1421no—
231#120—1421no—
232C4×Q8—711no—
233C4×D4—711no—
234C4×D4C2×D7111yescharacteristic
235#117—711no—
236#117—1421no—
237C2×C4⋊C4—711no—
238#107—711no—
239#107—711no—
240#106—711no—
241C4⋊C8C2×D7111yescharacteristic, complemented
242#103—711no—
243#102—711no—
244#102—711no—
245#102—711no—
246#102—711no—
247#102—711no—
248#102—711no—
249#102—711no—
250#102—711no—
251#102—711no—
252C22⋊C8C2×D7111yescharacteristic, complemented
253C22⋊C8C2×D7111yescharacteristic, complemented
254#97C2×D7111yescharacteristic, complemented
255C24—1421no—
256C24—1421no—
257C2×Q8—711no—
258C2×D4—2841no—
259C2×D4—2841no—
260C2×D4—2844no—
261C2×D4—711no—
262C2×D4—711no—
263C2×D4—711no—
264C2×D4—1422no—
265C2×D4—1422no—
266C2×D4—1421no—
267C2×D4—1421no—
268C2×D4—1421no—
269C2×D4—1421no—
270C2×D4—1421no—
271C2×D4—1421no—
272C2×D4D28411yescharacteristic
273C22×C4—1421no—
274C22×C4—1421no—
275C22×C4C22×D7111yescharacteristic
276C22×C4C22×D7111yescharacteristic
277SD16—2841no—
278SD16—2841no—
279SD16—1422no—
280M16—41no—
281C2×C8—41no—
282C2×C8C22×D7111yescharacteristic
283C2×C8C22×D7111yescharacteristic
284C2×C8C22×D7111yescharacteristic
285C2×C8C22×D7111yescharacteristic
286C4⋊C4—711no—
287C4⋊C4—711no—
288C4⋊C4—711no—
289C4⋊C4—711no—
290C4⋊C4—1421no—
291C4⋊C4—1421no—
292C4⋊C4—1421no—
293C4⋊C4—1421no—
294C4⋊C4—1421no—
295C4⋊C4—1421no—
296C4⋊C4D28411yescharacteristic
297C22⋊C4—1421no—
298C22⋊C4—1421no—
299C22⋊C4—1421no—
300C22⋊C4—1421no—
301C22⋊C4—1421no—
302C22⋊C4—1421no—
303C22⋊C4D28411yescharacteristic
304C22⋊C4D28411yescharacteristic
305C42—1421no—
306C42—1421no—
307C42C22×D7111yescharacteristic
308C23—2842no—
309C23—2842no—
310C23—2842no—
311C23—2842no—
312C23—5681no—
313C23—5681no—
314C23—1421no—
315C23—1421no—
316C23—1421no—
317C23C2×D28411yescharacteristic
318C23C2×D28411yescharacteristic
319Q8—1421no—
320Q8—1421no—
321D4—22no—
322D4—2842no—
323D4—2842no—
324D4—2842no—
325D4—2842no—
326D4—2842no—
327D4—5681no—
328D4—712no—
329D4—1421no—
330D4—1421no—
331D4—1421no—
332D4—1421no—
333D4—1421no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—2842no—
339C2×C4—2842no—
340C2×C4—1421no—
341C2×C4—1421no—
342C2×C4—1421no—
343C2×C4—1421no—
344C2×C4—1421no—
345C2×C4C2×D28411yescharacteristic
346C2×C4C2×D28411yescharacteristic
347C2×C4C2×D28411yescharacteristic
348C2×C4C2×D28411yescharacteristic
349C2×C4C23×D7111yescharacteristic
350C8—21no—
351C8—21no—
352C8—21no—
353C8—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—2841no—
360C22—2841no—
361C22—2841no—
362C22—2841no—
363C22—2841no—
364C22—2841no—
365C22—2841no—
366C22—2841no—
367C22—5684no—
368C22—5684no—
369C22—1422no—
370C22#1455615612yes—
371C22C22×D28411yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—2841no—
377C4—2841no—
378C4—2841no—
379C4—2841no—
380C4—2841no—
381C4#41×D7111yescharacteristic
382C4#1455617311yescharacteristic
383C2—22no—
384C2—41no—
385C2—2842no—
386C2—5681no—
387C2—5681no—
388C2#1798664411yescharacteristic
389C2C2×#1455615611yescharacteristic
390C2#1798681111yescharacteristic
subgroupG/H
centerC22C22×D284
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#435×C71C2
socleC22×C71C22×D4
hypercenter#435D71
hypocenterC71#3310
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #17986689C2semidirect
3. #17986364C2semidirect
4. #17986324C2semidirect
5. #17986313C2semidirect
6. #17986300C2semidirect
7. #17986245C2semidirect
8. #17986228C2semidirect
9. #17986200C2semidirect
10. #17986152C2semidirect
11. #17986152C2semidirect
12. #17986101C2semidirect
13. #17986005C2semidirect
14. C2×#14556050C2semidirect
15. #435×C71C2semidirect
20. C2×#11765854C22semidirect
21. C2×#11765854C22semidirect
24. #14556120C22semidirect
27. #14556107C22semidirect
28. #14556107C22semidirect
34. C4×Dic142C22semidirect
36. #14556087C22semidirect
38. C2×C4⋊Dic71C22semidirect
39. #14556062C22semidirect
40. #14556062C22semidirect
41. #14556060C22semidirect
42. #14556053C22semidirect
46. #14556050C22semidirect
47. #14556050C22semidirect
48. #14556050C22semidirect
49. #14556050C22semidirect
50. #14556050C22semidirect
51. #14556050C22semidirect
52. C2×M16×C71C22semidirect
53. C22×C8×C71C22semidirect
55. C4⋊C8×C71C22semidirect
56. C22⋊C8×C71C22semidirect
57. C22⋊C8×C71C22semidirect
58. #97×C71C22semidirect
196. C71#3310semidirect
209. #435D71semidirect
218. C2×M16C2×D71semidirect
219. C22×C8C2×D71semidirect
241. C4⋊C8C2×D71semidirect
252. C22⋊C8C2×D71semidirect
253. C22⋊C8C2×D71semidirect
254. #97C2×D71semidirect