Finite Group Databasebeta

← #22600192

Subgroups — #22600192

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#17986695C211yesmaximal, characteristic, complemented
2#17986645C211yesmaximal, characteristic, complemented
3#17986354C211yesmaximal, characteristic, complemented
4#17986335C211yesmaximal, characteristic, complemented
5#17986324C211yesmaximal, characteristic, complemented
6#17986300C211yesmaximal, characteristic, complemented
7#17986235C211yesmaximal, characteristic, complemented
8#17986228C211yesmaximal, characteristic, complemented
9#17986215C211yesmaximal, characteristic, complemented
10#17986146C211yesmaximal, characteristic, complemented
11#17986135C211yesmaximal, characteristic, complemented
12C4×D568C211yesmaximal, characteristic, complemented
13#17985996C211yesmaximal, characteristic, complemented
14C2×#14556050C211yesmaximal, characteristic, complemented
15C8×D4×C71C211yesmaximal, characteristic, complemented
16C2×#11765865C2211yescharacteristic
17C22×D284C2211yescharacteristic
18C2×#11765854C2211yescharacteristic, complemented
19C2×D568C2211yescharacteristic
20C2×D568C2211yescharacteristic
21#14556123—21no—
22#14556120C2211yescharacteristic, complemented
23#14556116C2211yescharacteristic
24#14556113—21no—
25#14556110—21no—
26#14556107C2211yescharacteristic
27#14556102C2211yescharacteristic
28#14556102C2211yescharacteristic
29#14556102C2211yescharacteristic, complemented
30#14556101—21no—
31#14556100—21no—
32#14556096—21no—
33C4×D284C2211yescharacteristic
34C4×D284C2211yescharacteristic, complemented
35(C22⋊D71)⋊C4—21no—
36#14556087C2211yescharacteristic, complemented
37C2×C4⋊Dic71C2211yescharacteristic
38C22⋊C4×D71—21no—
39#14556062C2211yescharacteristic, complemented
40#14556062C2211yescharacteristic, complemented
41#14556060C2211yescharacteristic, complemented
42#14556053C2211yescharacteristic, complemented
43#14556053C2211yescharacteristic, complemented
44#14556053C2211yescharacteristic, complemented
45#14556050C2211yescharacteristic
46#14556050C2211yescharacteristic
47#14556050C2211yescharacteristic
48#14556050C2211yescharacteristic
49#14556050C2211yescharacteristic
50#14556050C2211yescharacteristic
51#14556050C2211yescharacteristic, complemented
52C22×C8×C71C2211yescharacteristic
53C22×C8×C71C2211yescharacteristic, complemented
54C4×D4×C71C2211yescharacteristic
55C4⋊C8×C71C2211yescharacteristic, complemented
56C22⋊C8×C71C2211yescharacteristic
57C22⋊C8×C71C2211yescharacteristic, complemented
58C4×C8×C71C2211yescharacteristic, complemented
59C23×D71—21no—
60#11765865—22no—
61#11765865—41no—
62C2×Dic142C2311yescharacteristic
63C2×D284—22no—
64C2×D284—21no—
65C2×D284—41no—
66C2×D284C2311yescharacteristic
67C2×D284C2311yescharacteristic
68C2×D284C2311yescharacteristic
69C2×C22⋊D71—21no—
70C2×C22⋊D71—21no—
71C2×C22⋊D71—21no—
72C2×C22⋊D71—21no—
73C22×Dic71—21no—
74C2×C4×D71—21no—
75C2×C4×D71—21no—
76C2×C4×D71—21no—
77#11765854—41no—
78D568—22no—
79D568—41no—
80C4⋊Dic71—21no—
81C4⋊Dic71C2311yescharacteristic
82C4⋊Dic71C2311yescharacteristic
83C4⋊Dic71C2311yescharacteristic
84C4⋊Dic71C2311yescharacteristic
85Dic71⋊C4—21no—
86Dic71⋊C4—21no—
87Dic71⋊C4—21no—
88C22⋊Dic71—21no—
89C22⋊Dic71—21no—
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)⋊C4—21no—
96(C2×D71)⋊C4—21no—
97C4×Dic71—21no—
98C2×D4×C71D411yescharacteristic
99C22×C4×C71C2311yescharacteristic
100C22×C4×C71C2311yescharacteristic
101C2×C8×C71—41no—
102C2×C8×C71—41no—
103C2×C8×C71C2311yescharacteristic
104C2×C8×C71C2311yescharacteristic
105C2×C8×C71C2311yescharacteristic
106C2×C8×C71C2311yescharacteristic
107C4⋊C4×C71D411yescharacteristic
108C22⋊C4×C71D411yescharacteristic
109C22⋊C4×C71D411yescharacteristic
110C42×C71C2311yescharacteristic
111C23×C71C2×D411yescharacteristic
112C23×C71C2×D411yescharacteristic
113C22×D71—21no—
114C22×D71—21no—
115C22×D71—21no—
116C22×D71—42no—
117C22×D71—42no—
118C22×D71—81no—
119D4×C71—22no—
120C2×C4×C71—21no—
121C2×C4×C71—21no—
122C2×C4×C71—21no—
123C2×C4×C71—21no—
124C2×C4×C71C2×D411yescharacteristic
125C2×C4×C71C2×D411yescharacteristic
126C2×C4×C71C2×D411yescharacteristic
127C2×C4×C71C2×D411yescharacteristic
128C2×C4×C71C2411yescharacteristic
129C22⋊D71—42no—
130C22⋊D71—42no—
131C22⋊D71—81no—
132C22⋊D71—81no—
133C2×Dic71—21no—
134C2×Dic71—21no—
135C2×Dic71—21no—
136C2×Dic71—21no—
137C2×Dic71—21no—
138C2×Dic71—81no—
139D284—21no—
140D284—21no—
141D284—21no—
142D284—21no—
143D284—21no—
144D284—42no—
145D284#4112yes—
146C4×D71—42no—
147C4×D71—81no—
148C4×D71—81no—
149Dic142—21no—
150Dic142—21no—
151C8×C71—21no—
152C8×C71—21no—
153C8×C71—21no—
154C8×C71—21no—
155C22×C71—21no—
156C22×C71—21no—
157C22×C71—21no—
158C22×C71—21no—
159C22×C71—21no—
160C22×C71#13512yes—
161C22×C71C22×D411yescharacteristic
162C2×D71—22no—
163C2×D71—41no—
164C2×D71—41no—
165C2×D71—41no—
166C2×D71—41no—
167C2×D71—41no—
168C2×D71—41no—
169C2×D71—41no—
170C2×D71—41no—
171C2×D71—84no—
172C4×C71—21no—
173C4×C71—21no—
174C4×C71—21no—
175C4×C71—21no—
176C4×C71C2×#4111yescharacteristic
177C4×C71H(5,𝔽2)11yescharacteristic
178Dic71—41no—
179Dic71—41no—
180Dic71—41no—
181Dic71—41no—
182Dic71—41no—
183C2×C71—22no—
184C2×C71—41no—
185C2×C71#54611yescharacteristic
186C2×C71C2×#13511yescharacteristic
187C2×C71#57611yescharacteristic
188D71—42no—
189D71—81no—
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#465—711no—
201#463—711no—
202#449—711no—
203#447—711no—
204C4×D8—711no—
205C8×D4D7111yescharacteristic, complemented
206#416—711no—
207C2×#102—711no—
208C2×#41—711no—
209C22×D4—711no—
210C2×SD16—711no—
211C2×D8—711no—
212C2×D8—711no—
213C22×C8C2×D7111yescharacteristic
214C22×C8C2×D7111yescharacteristic, complemented
215#126—1421no—
216#125—711no—
217#124—711no—
218#123—1421no—
219#123—1421no—
220C22⋊Q8—711no—
221#121—711no—
222#121—711no—
223#121—711no—
224#121—1421no—
225#121—1421no—
226#120—1421no—
227C4×D4—711no—
228C4×D4—711no—
229C4×D4—1421no—
230C4×D4C2×D7111yescharacteristic
231#117—711no—
232C2×C4⋊C4—711no—
233C2×C22⋊C4—1421no—
234#107—711no—
235#107—711no—
236#106—711no—
237C4⋊C8C2×D7111yescharacteristic, complemented
238#103—711no—
239#103—711no—
240#103—711no—
241#102—711no—
242#102—711no—
243#102—711no—
244#102—711no—
245#102—711no—
246#102—711no—
247#102—711no—
248C22⋊C8C2×D7111yescharacteristic
249C22⋊C8C2×D7111yescharacteristic, complemented
250C4×C8C2×D7111yescharacteristic, complemented
251C24—1421no—
252#41—2841no—
253#41—1422no—
254C2×Q8—711no—
255C2×D4—2841no—
256C2×D4—711no—
257C2×D4—711no—
258C2×D4—711no—
259C2×D4—1422no—
260C2×D4—1421no—
261C2×D4—1421no—
262C2×D4—1421no—
263C2×D4—1421no—
264C2×D4—1421no—
265C2×D4D28411yescharacteristic
266C22×C4—1421no—
267C22×C4—1421no—
268C22×C4—1421no—
269C22×C4—1421no—
270C22×C4C22×D7111yescharacteristic
271C22×C4C22×D7111yescharacteristic
272SD16—2841no—
273D8—2841no—
274D8—1422no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8C22×D7111yescharacteristic
278C2×C8C22×D7111yescharacteristic
279C2×C8C22×D7111yescharacteristic
280C2×C8C22×D7111yescharacteristic
281C4⋊C4—711no—
282C4⋊C4—711no—
283C4⋊C4—711no—
284C4⋊C4—711no—
285C4⋊C4—1421no—
286C4⋊C4—1421no—
287C4⋊C4—1421no—
288C4⋊C4—1421no—
289C4⋊C4D28411yescharacteristic
290C22⋊C4—1421no—
291C22⋊C4—1421no—
292C22⋊C4—1421no—
293C22⋊C4—1421no—
294C22⋊C4—1421no—
295C22⋊C4—1421no—
296C22⋊C4—1421no—
297C22⋊C4—1421no—
298C22⋊C4—1421no—
299C22⋊C4D28411yescharacteristic
300C22⋊C4D28411yescharacteristic
301C42—1421no—
302C42C22×D7111yescharacteristic
303C23—2842no—
304C23—2842no—
305C23—5681no—
306C23—1421no—
307C23—1421no—
308C23—1421no—
309C23C2×D28411yescharacteristic
310C23C2×D28411yescharacteristic
311Q8—1421no—
312Q8—1421no—
313D4—22no—
314D4—2842no—
315D4—2842no—
316D4—2842no—
317D4—5681no—
318D4—5681no—
319D4—712no—
320D4—1421no—
321D4—1421no—
322D4—1421no—
323D4—1421no—
324D4—1421no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—2842no—
330C2×C4—5681no—
331C2×C4—5681no—
332C2×C4—5681no—
333C2×C4—1421no—
334C2×C4—1421no—
335C2×C4—1421no—
336C2×C4—1421no—
337C2×C4—1421no—
338C2×C4C2×D28411yescharacteristic
339C2×C4C2×D28411yescharacteristic
340C2×C4C2×D28411yescharacteristic
341C2×C4C2×D28411yescharacteristic
342C2×C4C23×D7111yescharacteristic
343C8—21no—
344C8—21no—
345C8—21no—
346C8—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—2841no—
353C22—2841no—
354C22—2841no—
355C22—2841no—
356C22—2841no—
357C22—2841no—
358C22—2841no—
359C22—2841no—
360C22—5684no—
361C22—1422no—
362C22#1455615012yes—
363C22C22×D28411yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—2841no—
369C4—2841no—
370C4—2841no—
371C4—2841no—
372C4—2841no—
373C4#41×D7111yescharacteristic
374C4#1455617311yescharacteristic
375C2—22no—
376C2—41no—
377C2—2842no—
378C2—5681no—
379C2—5681no—
380C2#1798664411yescharacteristic
381C2C2×#1455615011yescharacteristic
382C2#1798680411yescharacteristic
subgroupG/H
centerC22C22×D284
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
FittingC8×D4×C71C2
socleC22×C71C22×D4
hypercenterC8×D4D71
hypocenterC71#3297
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #17986695C2semidirect
2. #17986645C2semidirect
3. #17986354C2semidirect
4. #17986335C2semidirect
5. #17986324C2semidirect
6. #17986300C2semidirect
7. #17986235C2semidirect
8. #17986228C2semidirect
9. #17986215C2semidirect
10. #17986146C2semidirect
11. #17986135C2semidirect
12. C4×D568C2semidirect
13. #17985996C2semidirect
14. C2×#14556050C2semidirect
15. C8×D4×C71C2semidirect
18. C2×#11765854C22semidirect
22. #14556120C22semidirect
29. #14556102C22semidirect
34. C4×D284C22semidirect
36. #14556087C22semidirect
39. #14556062C22semidirect
40. #14556062C22semidirect
41. #14556060C22semidirect
42. #14556053C22semidirect
43. #14556053C22semidirect
44. #14556053C22semidirect
51. #14556050C22semidirect
53. C22×C8×C71C22semidirect
55. C4⋊C8×C71C22semidirect
57. C22⋊C8×C71C22semidirect
58. C4×C8×C71C22semidirect
192. C71#3297semidirect
205. C8×D4D71semidirect
214. C22×C8C2×D71semidirect
237. C4⋊C8C2×D71semidirect
249. C22⋊C8C2×D71semidirect
250. C4×C8C2×D71semidirect