Finite Group Databasebeta

← #22600196

Subgroups — #22600196

Order 9088.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17986701C211yesmaximal, characteristic, complemented
2#17986640C211yesmaximal, characteristic, complemented
3#17986355C211yesmaximal, characteristic, complemented
4#17986332C211yesmaximal, characteristic, complemented
5#17986325C211yesmaximal, characteristic, complemented
6#17986298C211yesmaximal, characteristic, complemented
7#17986234C211yesmaximal, characteristic, complemented
8#17986216C211yesmaximal, characteristic, complemented
9#17986143C211yesmaximal, characteristic, complemented
10#17986132C211yesmaximal, characteristic, complemented
11#17986079C211yesmaximal, characteristic, complemented
12C8×C22⋊D71C211yesmaximal, characteristic, complemented
13#17985994C211yesmaximal, characteristic, complemented
14C2×#14556050C211yesmaximal, characteristic, complemented
15#465×C71C211yesmaximal, characteristic, complemented
16C2×#11765866C2211yescharacteristic
17C22×D284C2211yescharacteristic
18C2×#11765850C2211yescharacteristic
19C2×#11765850C2211yescharacteristic
20C2×C8×D71C2211yescharacteristic, complemented
21#14556121—21no—
22#14556119C2211yescharacteristic, complemented
23#14556117C2211yescharacteristic
24#14556113—21no—
25#14556112—21no—
26#14556103—21no—
27#14556103C2211yescharacteristic
28#14556100—21no—
29#14556099C2211yescharacteristic, complemented
30#14556098—21no—
31D4×Dic71—21no—
32D4×Dic71C2211yescharacteristic, complemented
33#14556090C2211yescharacteristic
34C4×C22⋊D71C2211yescharacteristic
35#14556086C2211yescharacteristic, complemented
36C2×C4⋊Dic71C2211yescharacteristic
37C22⋊C4×D71—21no—
38#14556061C2211yescharacteristic, complemented
39#14556061C2211yescharacteristic, complemented
40Dic71⋊C8C2211yescharacteristic, complemented
41#14556052C2211yescharacteristic, complemented
42#14556052C2211yescharacteristic, complemented
43#14556050C2211yescharacteristic
44#14556050C2211yescharacteristic
45#14556050C2211yescharacteristic
46#14556050C2211yescharacteristic
47#14556048C2211yescharacteristic
48#14556048C2211yescharacteristic
49C22⋊(C71⋊C8)C2211yescharacteristic
50(C2×D71)⋊C8C2211yescharacteristic, complemented
51C8×Dic71C2211yescharacteristic, complemented
52C2×SD16×C71C2211yescharacteristic, complemented
53C22×C8×C71C2211yescharacteristic
54C22⋊Q8×C71C2211yescharacteristic
55#121×C71C2211yescharacteristic
56#106×C71C2211yescharacteristic, complemented
57#103×C71C2211yescharacteristic, complemented
58#102×C71C2211yescharacteristic, complemented
59C23×D71—21no—
60#11765866—22no—
61#11765866—41no—
62C2×D284—22no—
63C2×D284—21no—
64C2×D284—21no—
65C2×D284—21no—
66C2×D284—41no—
67C2×D284C2311yescharacteristic
68C2×D284C2311yescharacteristic
69C2×C22⋊D71—21no—
70C2×C22⋊D71D411yescharacteristic
71C22×Dic71—21no—
72C22×Dic71—21no—
73C2×C4×D71—21no—
74C2×C4×D71—21no—
75C2×C4×D71C2311yescharacteristic
76#11765850—22no—
77#11765850—41no—
78C2×C71⋊C8C2311yescharacteristic
79C2×C71⋊C8C2311yescharacteristic
80C8×D71—41no—
81C4⋊Dic71—21no—
82C4⋊Dic71—21no—
83C4⋊Dic71C2311yescharacteristic
84C4⋊Dic71C2311yescharacteristic
85Dic71⋊C4—21no—
86Dic71⋊C4D411yescharacteristic
87C22⋊Dic71—21no—
88C22⋊Dic71—21no—
89C22⋊Dic71D411yescharacteristic
90(C2×D71)⋊C4—21no—
91(C2×D71)⋊C4—21no—
92(C2×D71)⋊C4—21no—
93(C2×D71)⋊C4—21no—
94(C2×D71)⋊C4—21no—
95(C2×D71)⋊C4D411yescharacteristic
96C4×Dic71—21no—
97C4×Dic71C2311yescharacteristic
98C2×Q8×C71C2311yescharacteristic
99C2×D4×C71—21no—
100C2×D4×C71C2311yescharacteristic
101C22×C4×C71C2311yescharacteristic
102SD16×C71—41no—
103C2×C8×C71—41no—
104C2×C8×C71C2311yescharacteristic
105C2×C8×C71C2311yescharacteristic
106C4⋊C4×C71—21no—
107C4⋊C4×C71C2311yescharacteristic
108C4⋊C4×C71C2311yescharacteristic
109C22⋊C4×C71—21no—
110C22⋊C4×C71—21no—
111C23×C71—21no—
112C23×C71C2×D411yescharacteristic
113C22×D71—21no—
114C22×D71—21no—
115C22×D71—42no—
116C22×D71—42no—
117C22×D71—81no—
118C22×D71C2×D411yescharacteristic
119Q8×C71—21no—
120Q8×C71—21no—
121D4×C71—21no—
122D4×C71—21no—
123D4×C71—42no—
124C2×C4×C71—21no—
125C2×C4×C71—21no—
126C2×C4×C71—21no—
127C2×C4×C71—21no—
128C2×C4×C71—21no—
129C2×C4×C71C2×D411yescharacteristic
130C2×C4×C71C2411yescharacteristic
131C22⋊D71—22no—
132C22⋊D71—81no—
133C2×Dic71—21no—
134C2×Dic71—21no—
135C2×Dic71—81no—
136C2×Dic71—81no—
137C2×Dic71C2×D411yescharacteristic
138C2×Dic71C2×D411yescharacteristic
139C2×Dic71C2×D411yescharacteristic
140D284—21no—
141D284—21no—
142D284—21no—
143D284—42no—
144D284—42no—
145D284—81no—
146D284#4112yes—
147C4×D71—21no—
148C4×D71—21no—
149C4×D71—42no—
150C4×D71—81no—
151C8×C71—21no—
152C8×C71—21no—
153C71⋊C8—21no—
154C71⋊C8—21no—
155C22×C71—21no—
156C22×C71—21no—
157C22×C71—41no—
158C22×C71—41no—
159C22×C71—41no—
160C22×C71#13512yes—
161C22×C71C22×D411yescharacteristic
162C2×D71—21no—
163C2×D71—22no—
164C2×D71—21no—
165C2×D71—21no—
166C2×D71—41no—
167C2×D71—41no—
168C2×D71—41no—
169C2×D71—41no—
170C2×D71—41no—
171C2×D71—84no—
172C4×C71—21no—
173C4×C71—41no—
174C4×C71—41no—
175C4×C71—41no—
176C4×C71C2×#4111yescharacteristic
177C4×C71H(5,𝔽2)11yescharacteristic
178Dic71—21no—
179Dic71—21no—
180Dic71—21no—
181Dic71—41no—
182Dic71—41no—
183C2×C71—22no—
184C2×C71—81no—
185C2×C71#54611yescharacteristic
186C2×C71C2×#13511yescharacteristic
187C2×C71#57611yescharacteristic
188D71—41no—
189D71—42no—
190D71—81no—
191#3297—711nomaximal, Sylow
192C71#329711yescharacteristic, complemented, Sylow
193#553—711no—
194#546—711no—
195#488—711no—
196#484—711no—
197#482—711no—
198#478—711no—
199#466—711no—
200#465D7111yescharacteristic, complemented
201#463—711no—
202#449—711no—
203#447—711no—
204C4×D8—711no—
205C8×D4—711no—
206#416—711no—
207C2×#102—711no—
208C2×#41—711no—
209C22×D4—711no—
210C2×SD16C2×D7111yescharacteristic, complemented
211C2×D8—711no—
212C2×D8—711no—
213C22×C8—711no—
214C22×C8C2×D7111yescharacteristic
215#126—1421no—
216#125—711no—
217#124—711no—
218#123—1421no—
219#123—1421no—
220C22⋊Q8C2×D7111yescharacteristic
221#121—711no—
222#121—711no—
223#121—1421no—
224#121—1421no—
225#121C2×D7111yescharacteristic
226#120—1421no—
227C4×D4—711no—
228C4×D4—711no—
229C4×D4—711no—
230C4×D4—1421no—
231#117—711no—
232C2×C4⋊C4—711no—
233C2×C22⋊C4—1421no—
234#107—711no—
235#107—711no—
236#106C2×D7111yescharacteristic, complemented
237C4⋊C8—711no—
238#103—711no—
239#103—711no—
240#103C2×D7111yescharacteristic, complemented
241#102—711no—
242#102—711no—
243#102—711no—
244#102—711no—
245#102—711no—
246#102—711no—
247#102C2×D7111yescharacteristic, complemented
248C22⋊C8—711no—
249C22⋊C8—711no—
250C4×C8—711no—
251C24—1421no—
252#41—2841no—
253#41—1422no—
254C2×Q8C22×D7111yescharacteristic
255C2×D4—21no—
256C2×D4—2841no—
257C2×D4—711no—
258C2×D4—711no—
259C2×D4—711no—
260C2×D4—1421no—
261C2×D4—1422no—
262C2×D4—1421no—
263C2×D4—1421no—
264C2×D4—1421no—
265C2×D4C22×D7111yescharacteristic
266C22×C4—711no—
267C22×C4—1421no—
268C22×C4—1421no—
269C22×C4—1421no—
270C22×C4—1421no—
271C22×C4C22×D7111yescharacteristic
272SD16—41no—
273D8—2841no—
274D8—1422no—
275C2×C8—41no—
276C2×C8—2841no—
277C2×C8—711no—
278C2×C8—711no—
279C2×C8C22×D7111yescharacteristic
280C2×C8C22×D7111yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—711no—
283C4⋊C4—711no—
284C4⋊C4—711no—
285C4⋊C4—1421no—
286C4⋊C4—1421no—
287C4⋊C4—1421no—
288C4⋊C4C22×D7111yescharacteristic
289C4⋊C4C22×D7111yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—711no—
293C22⋊C4—711no—
294C22⋊C4—1421no—
295C22⋊C4—1421no—
296C22⋊C4—1421no—
297C22⋊C4—1421no—
298C22⋊C4—1421no—
299C22⋊C4—1421no—
300C22⋊C4—1421no—
301C42—711no—
302C42—1421no—
303C23—21no—
304C23—2842no—
305C23—2842no—
306C23—5681no—
307C23—711no—
308C23—1421no—
309C23—1421no—
310C23D4×D7111yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—21no—
314D4—21no—
315D4—42no—
316D4—2842no—
317D4—2842no—
318D4—5681no—
319D4—5681no—
320D4—712no—
321D4—1422no—
322D4—1421no—
323D4—1421no—
324D4—1421no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—2842no—
331C2×C4—5681no—
332C2×C4—5681no—
333C2×C4—5681no—
334C2×C4—711no—
335C2×C4—711no—
336C2×C4—711no—
337C2×C4—1421no—
338C2×C4—1421no—
339C2×C4—1421no—
340C2×C4—1421no—
341C2×C4D4×D7111yescharacteristic
342C2×C4C23×D7111yescharacteristic
343C8—21no—
344C8—21no—
345C8—1421no—
346C8—1421no—
347C22—21no—
348C22—21no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—2841no—
353C22—2841no—
354C22—2841no—
355C22—2841no—
356C22—2841no—
357C22—5684no—
358C22—1422no—
359C22—1421no—
360C22—1421no—
361C22—1421no—
362C22#1455614912yes—
363C22C2×D4×D7111yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—2841no—
369C4—2841no—
370C4—1421no—
371C4—1421no—
372C4—1421no—
373C4#41×D7111yescharacteristic
374C4#1455617311yescharacteristic
375C2—22no—
376C2—81no—
377C2—2842no—
378C2—2841no—
379C2—5681no—
380C2#1798663811yescharacteristic
381C2C2×#1455614911yescharacteristic
382C2#1798680111yescharacteristic
subgroupG/H
centerC22C2×D4×D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#465×C71C2
socleC22×C71C22×D4
hypercenter#465D71
hypocenterC71#3297
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #17986701C2semidirect
2. #17986640C2semidirect
3. #17986355C2semidirect
4. #17986332C2semidirect
5. #17986325C2semidirect
6. #17986298C2semidirect
7. #17986234C2semidirect
8. #17986216C2semidirect
9. #17986143C2semidirect
10. #17986132C2semidirect
11. #17986079C2semidirect
12. C8×C22⋊D71C2semidirect
13. #17985994C2semidirect
14. C2×#14556050C2semidirect
15. #465×C71C2semidirect
20. C2×C8×D71C22semidirect
22. #14556119C22semidirect
29. #14556099C22semidirect
32. D4×Dic71C22semidirect
35. #14556086C22semidirect
38. #14556061C22semidirect
39. #14556061C22semidirect
40. Dic71⋊C8C22semidirect
41. #14556052C22semidirect
42. #14556052C22semidirect
50. (C2×D71)⋊C8C22semidirect
51. C8×Dic71C22semidirect
52. C2×SD16×C71C22semidirect
56. #106×C71C22semidirect
57. #103×C71C22semidirect
58. #102×C71C22semidirect
192. C71#3297semidirect
200. #465D71semidirect
210. C2×SD16C2×D71semidirect
236. #106C2×D71semidirect
240. #103C2×D71semidirect
247. #102C2×D71semidirect