Finite Group Databasebeta

← #22600540

Subgroups — #22600540

Order 9088.

414 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#17986702C211yesmaximal, characteristic, complemented
2#17986642C211yesmaximal, characteristic, complemented
3#17986339C211yesmaximal, characteristic, complemented
4#17986311C211yesmaximal, characteristic, complemented
5#17986296C211yesmaximal, characteristic, complemented
6#17986251C211yesmaximal, characteristic, complemented
7#17986248C211yesmaximal, characteristic, complemented
8#17986211C211yesmaximal, characteristic, complemented
9#17986147C211yesmaximal, characteristic, complemented
10#17986134C211yesmaximal, characteristic, complemented
11C4×D568C211yesmaximal, characteristic, complemented
12#17986078C211yesmaximal, characteristic, complemented
13#17986002C211yesmaximal, characteristic, complemented
14#17985999C211yesmaximal, characteristic, complemented
15#488×C71C211yesmaximal, characteristic, complemented
16C2×#11765866C2211yescharacteristic
17C2×D4×D71C2211yescharacteristic
18C2×#11765852C2211yescharacteristic, complemented
19C2×D568C2211yescharacteristic
20C2×#11765850C2211yescharacteristic
21C2×#11765848C2211yescharacteristic
22C2×#11765848C2211yescharacteristic, complemented
23#14556123—21no—
24#14556113—21no—
25#14556110—21no—
26#14556104C2211yescharacteristic
27#14556103—21no—
28#14556103C2211yescharacteristic
29#14556103C2211yescharacteristic, complemented
30#14556101—21no—
31#14556099C2211yescharacteristic
32#14556098—21no—
33C4×D284C2211yescharacteristic
34C4×D284C2211yescharacteristic
35C4×D284C2211yescharacteristic, complemented
36#14556090—21no—
37#14556086C2211yescharacteristic
38C4⋊C4×D71C2211yescharacteristic, complemented
39C22⋊C4×D71—21no—
40#14556062C2211yescharacteristic, complemented
41#14556061C2211yescharacteristic, complemented
42#14556059C2211yescharacteristic, complemented
43C4⋊(C71⋊C8)C2211yescharacteristic, complemented
44#14556052C2211yescharacteristic, complemented
45#14556050C2211yescharacteristic
46#14556050C2211yescharacteristic, complemented
47#14556049C2211yescharacteristic
48#14556048C2211yescharacteristic
49#14556048C2211yescharacteristic
50(C2×D71)⋊C8C2211yescharacteristic
51(C2×D71)⋊C8C2211yescharacteristic, complemented
52#125×C71C2211yescharacteristic, complemented
53#124×C71C2211yescharacteristic
54#103×C71C2211yescharacteristic, complemented
55#103×C71C2211yescharacteristic, complemented
56#102×C71C2211yescharacteristic
57#102×C71C2211yescharacteristic
58C4×C8×C71C2211yescharacteristic, complemented
59C23×D71—21no—
60#11765866—22no—
61#11765866—41no—
62C2×D284—21no—
63C2×D284—21no—
64C2×D284—21no—
65C2×D284D411yescharacteristic
66C2×D284C2311yescharacteristic
67C2×D284C2311yescharacteristic
68C2×C22⋊D71—21no—
69C2×C22⋊D71—21no—
70D4×D71—22no—
71D4×D71—41no—
72C2×C4×D71—21no—
73C2×C4×D71—21no—
74C2×C4×D71—21no—
75C2×C4×D71—21no—
76C2×C4×D71C2311yescharacteristic
77C2×C4×D71C2311yescharacteristic
78#11765852—41no—
79D568—22no—
80#11765850—41no—
81#11765848—41no—
82#11765848—41no—
83C2×C71⋊C8C2311yescharacteristic
84C2×C71⋊C8C2311yescharacteristic
85C4⋊Dic71D411yescharacteristic
86C4⋊Dic71C2311yescharacteristic
87C4⋊Dic71C2311yescharacteristic
88Dic71⋊C4—21no—
89Dic71⋊C4—21no—
90C22⋊Dic71—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—
97(C2×D71)⋊C4D411yescharacteristic
98(C2×D71)⋊C4D411yescharacteristic
99C4×Dic71—21no—
100C2×Q8×C71C2311yescharacteristic
101C2×D4×C71C2311yescharacteristic
102C2×C8×C71C2311yescharacteristic
103C2×C8×C71C2311yescharacteristic
104C4⋊C4×C71—21no—
105C4⋊C4×C71—21no—
106C4⋊C4×C71C2311yescharacteristic
107C4⋊C4×C71C2311yescharacteristic
108C22⋊C4×C71—21no—
109C22⋊C4×C71—21no—
110C42×C71C2311yescharacteristic
111C23×C71—21no—
112C22×D71—21no—
113C22×D71—21no—
114C22×D71—42no—
115C22×D71—42no—
116C22×D71—81no—
117C22×D71C2×D411yescharacteristic
118C22×D71C2×D411yescharacteristic
119Q8×C71—21no—
120Q8×C71—21no—
121D4×C71—21no—
122D4×C71—21no—
123C2×C4×C71—21no—
124C2×C4×C71—21no—
125C2×C4×C71—21no—
126C2×C4×C71C2×D411yescharacteristic
127C2×C4×C71C2×D411yescharacteristic
128C2×C4×C71C2411yescharacteristic
129C22⋊D71—42no—
130C22⋊D71—81no—
131C2×Dic71—21no—
132C2×Dic71—21no—
133C2×Dic71C2×D411yescharacteristic
134C2×Dic71C2×D411yescharacteristic
135D284—21no—
136D284—21no—
137D284—21no—
138D284—41no—
139D284—42no—
140D284—42no—
141D284—81no—
142D284#4112yes—
143C4×D71—21no—
144C4×D71—21no—
145C4×D71—21no—
146C4×D71—21no—
147C4×D71—42no—
148C4×D71—81no—
149C4×D71—81no—
150C4×D71—81no—
151C8×C71—21no—
152C8×C71—21no—
153C71⋊C8—21no—
154C71⋊C8—21no—
155C22×C71—41no—
156C22×C71—41no—
157C22×C71—41no—
158C22×C71C22×D411yescharacteristic
159C2×D71—21no—
160C2×D71—21no—
161C2×D71—22no—
162C2×D71—21no—
163C2×D71—21no—
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—21no—
174C4×C71—41no—
175C4×C71—41no—
176C4×C71—41no—
177C4×C71C2×#4111yescharacteristic
178C4×C71H(5,𝔽2)11yescharacteristic
179Dic71—21no—
180Dic71—21no—
181Dic71—41no—
182Dic71—41no—
183C2×C71—81no—
184C2×C71#54611yescharacteristic
185C2×C71#57511yescharacteristic
186C2×C71#57611yescharacteristic
187D71—41no—
188D71—41no—
189D71—42no—
190D71—81no—
191#3322—711nomaximal, Sylow
192C71#332211yescharacteristic, complemented, Sylow
193#553—711no—
194#546—711no—
195#488D7111yescharacteristic, complemented
196#485—711no—
197#480—711no—
198#478—711no—
199#469—711no—
200#468—711no—
201#463—711no—
202#449—711no—
203#447—711no—
204C4×D8—711no—
205#436—711no—
206#418—711no—
207#417—711no—
208C2×#41—711no—
209C22×D4—711no—
210C2×SD16—711no—
211C2×D8—711no—
212C2×D8—711no—
213C2×M16—711no—
214C2×M16—711no—
215#126—1421no—
216#125C2×D7111yescharacteristic, complemented
217#124C2×D7111yescharacteristic
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—711no—
230C4×D4—1421no—
231#117—711no—
232C2×C4⋊C4—711no—
233C2×C22⋊C4—1421no—
234#107—711no—
235#107—711no—
236#106—711no—
237C4⋊C8—711no—
238#103—711no—
239#103C2×D7111yescharacteristic, complemented
240#103C2×D7111yescharacteristic, complemented
241#102—711no—
242#102—711no—
243#102—711no—
244#102—711no—
245#102—711no—
246#102C2×D7111yescharacteristic
247#102C2×D7111yescharacteristic
248C22⋊C8—711no—
249C22⋊C8—711no—
250C4×C8C2×D7111yescharacteristic, complemented
251C24—1421no—
252#41—2841no—
253#41—1422no—
254C2×Q8C22×D7111yescharacteristic
255C2×D4—2841no—
256C2×D4—711no—
257C2×D4—711no—
258C2×D4—711no—
259C2×D4—1421no—
260C2×D4—1421no—
261C2×D4—1421no—
262C2×D4—1421no—
263C2×D4—1422no—
264C2×D4—1421no—
265C2×D4C22×D7111yescharacteristic
266C22×C4—711no—
267C22×C4—711no—
268C22×C4—1421no—
269C22×C4—1421no—
270C22×C4—1421no—
271C22×C4—1421no—
272SD16—2841no—
273D8—2841no—
274D8—1422no—
275M16—2841no—
276M16—2841no—
277C2×C8—711no—
278C2×C8—711no—
279C2×C8C22×D7111yescharacteristic
280C2×C8C22×D7111yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—711no—
284C4⋊C4—711no—
285C4⋊C4—711no—
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—1421no—
302C42C22×D7111yescharacteristic
303C23—21no—
304C23—2842no—
305C23—2842no—
306C23—5681no—
307C23—711no—
308C23—711no—
309C23—1421no—
310C23—1421no—
311Q8—21no—
312Q8—21no—
313D4—21no—
314D4—21no—
315D4—2841no—
316D4—2842no—
317D4—2842no—
318D4—2842no—
319D4—5681no—
320D4—5681no—
321D4—712no—
322D4—1421no—
323D4—1421no—
324D4—1421no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—2842no—
329C2×C4—5681no—
330C2×C4—5681no—
331C2×C4—5681no—
332C2×C4—711no—
333C2×C4—711no—
334C2×C4—1421no—
335C2×C4—1421no—
336C2×C4—1421no—
337C2×C4—1421no—
338C2×C4—1421no—
339C2×C4—1421no—
340C2×C4D4×D7111yescharacteristic
341C2×C4D4×D7111yescharacteristic
342C2×C4C23×D7111yescharacteristic
343C8—21no—
344C8—21no—
345C8—1421no—
346C8—1421no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—2841no—
351C22—2841no—
352C22—2841no—
353C22—2841no—
354C22—2841no—
355C22—5684no—
356C22—1422no—
357C22—1421no—
358C22—1421no—
359C22—1421no—
360C22—1421no—
361C22—1421no—
362C22—1421no—
363C22C2×D4×D7111yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—2841no—
370C4—2841no—
371C4—1421no—
372C4—1421no—
373C4#41×D7111yescharacteristic
374C4#1455617411yescharacteristic
375C2—81no—
376C2—2842no—
377C2—2841no—
378C2—2841no—
379C2—5681no—
380C2#1798664211yescharacteristic
381C2#1798679611yescharacteristic
382C2#1798680111yescharacteristic
subgroupG/H
centerC22C2×D4×D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#488×C71C2
socleC22×C71C22×D4
hypercenter#488D71
hypocenterC71#3322
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #17986702C2semidirect
2. #17986642C2semidirect
3. #17986339C2semidirect
4. #17986311C2semidirect
5. #17986296C2semidirect
6. #17986251C2semidirect
7. #17986248C2semidirect
8. #17986211C2semidirect
9. #17986147C2semidirect
10. #17986134C2semidirect
11. C4×D568C2semidirect
12. #17986078C2semidirect
13. #17986002C2semidirect
14. #17985999C2semidirect
15. #488×C71C2semidirect
18. C2×#11765852C22semidirect
22. C2×#11765848C22semidirect
29. #14556103C22semidirect
35. C4×D284C22semidirect
38. C4⋊C4×D71C22semidirect
40. #14556062C22semidirect
41. #14556061C22semidirect
42. #14556059C22semidirect
43. C4⋊(C71⋊C8)C22semidirect
44. #14556052C22semidirect
46. #14556050C22semidirect
51. (C2×D71)⋊C8C22semidirect
52. #125×C71C22semidirect
54. #103×C71C22semidirect
55. #103×C71C22semidirect
58. C4×C8×C71C22semidirect
192. C71#3322semidirect
195. #488D71semidirect
216. #125C2×D71semidirect
239. #103C2×D71semidirect
240. #103C2×D71semidirect
250. C4×C8C2×D71semidirect