Finite Group Databasebeta

← #22600160

Subgroups — #22600160

Order 9088.

462 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17986704C211yesmaximal, characteristic, complemented
2D4×C22⋊D71C211yesmaximal, characteristic
3#17986344C211yesmaximal, characteristic, complemented
4#17986317C211yesmaximal, characteristic, complemented
5#17986316C211yesmaximal, characteristic, complemented
6#17986287C211yesmaximal, characteristic, complemented
7#17986228C211yesmaximal, characteristic, complemented
8#17986227C211yesmaximal, characteristic, complemented
9#17986198C211yesmaximal, characteristic, complemented
10#17986151C211yesmaximal, characteristic, complemented
11#17986150C211yesmaximal, characteristic, complemented
12#17986090C211yesmaximal, characteristic, complemented
13C8×C22⋊D71C211yesmaximal, characteristic, complemented
14#102×D71C211yesmaximal, characteristic, complemented
15C2×#102×C71C211yesmaximal, characteristic, complemented
16C22×C22⋊D71—21no—
17C2×D4×D71C2211yescharacteristic
18C2×#11765854C2211yescharacteristic, complemented
19C2×#11765853C2211yescharacteristic
20C2×#11765853C2211yescharacteristic, complemented
21C2×C8×D71C2211yescharacteristic, complemented
22#14556127C2211yescharacteristic, complemented
23#14556124C2211yescharacteristic
24#14556118—21no—
25#14556108C2211yescharacteristic, complemented
26#14556107—21no—
27#14556107C2211yescharacteristic, complemented
28#14556106—21no—
29#14556102C2211yescharacteristic
30#14556100—21no—
31#14556099C2211yescharacteristic
32#14556097—21no—
33#14556096—21no—
34#14556093C2211yescharacteristic, complemented
35D4×Dic71C2211yescharacteristic
36C4×C22⋊D71—21no—
37C4×C22⋊D71C2211yescharacteristic
38C4⋊C4×D71C2211yescharacteristic, complemented
39#14556060C2211yescharacteristic, complemented
40#14556059C2211yescharacteristic, complemented
41#14556059C2211yescharacteristic, complemented
42Dic71⋊C8C2211yescharacteristic, complemented
43#14556053C2211yescharacteristic, complemented
44#14556050C2211yescharacteristic, complemented
45#14556049C2211yescharacteristic
46#14556049C2211yescharacteristic, complemented
47#14556048C2211yescharacteristic, complemented
48#14556048C2211yescharacteristic, complemented
49C22⋊(C71⋊C8)C2211yescharacteristic, complemented
50(C2×D71)⋊C8C2211yescharacteristic, complemented
51C8×Dic71C2211yescharacteristic, complemented
52C22×D4×C71C2211yescharacteristic
53C22×C8×C71C2211yescharacteristic, complemented
54C2×C4⋊C4×C71C2211yescharacteristic, complemented
55#102×C71C2211yescharacteristic
56#102×C71C2211yescharacteristic
57#102×C71C2211yescharacteristic, complemented
58#102×C71C2211yescharacteristic, complemented
59C23×D71—21no—
60C2×Dic142—21no—
61C2×Dic142C2311yescharacteristic
62C2×D284C2311yescharacteristic
63C2×C22⋊D71—21no—
64C2×C22⋊D71—21no—
65C2×C22⋊D71—21no—
66C2×C22⋊D71—21no—
67C2×C22⋊D71—21no—
68C2×C22⋊D71—44no—
69C2×C22⋊D71D411yescharacteristic
70D4×D71—22no—
71D4×D71—41no—
72C22×Dic71—21no—
73C2×C4×D71—21no—
74C2×C4×D71C2311yescharacteristic
75#11765854—41no—
76#11765853—22no—
77#11765853—41no—
78C2×C71⋊C8C2311yescharacteristic
79C2×C71⋊C8C2311yescharacteristic
80C8×D71—41no—
81C4⋊Dic71—21no—
82C4⋊Dic71C2311yescharacteristic
83C4⋊Dic71C2311yescharacteristic
84Dic71⋊C4—21no—
85Dic71⋊C4—21no—
86Dic71⋊C4—21no—
87Dic71⋊C4—21no—
88Dic71⋊C4D411yescharacteristic
89C22⋊Dic71—21no—
90C22⋊Dic71—21no—
91C22⋊Dic71—21no—
92C22⋊Dic71D411yescharacteristic
93(C2×D71)⋊C4—21no—
94(C2×D71)⋊C4—21no—
95(C2×D71)⋊C4D411yescharacteristic
96C4×Dic71—21no—
97C4×Dic71C2311yescharacteristic
98C24×C71—21no—
99C2×D4×C71—22no—
100C2×D4×C71—21no—
101C2×D4×C71—41no—
102C2×D4×C71C2311yescharacteristic
103C2×D4×C71C2311yescharacteristic
104C22×C4×C71—21no—
105C22×C4×C71C2311yescharacteristic
106C2×C8×C71—41no—
107C2×C8×C71C2311yescharacteristic
108C2×C8×C71C2311yescharacteristic
109C4⋊C4×C71—21no—
110C4⋊C4×C71C2311yescharacteristic
111C4⋊C4×C71C2311yescharacteristic
112C23×C71—21no—
113C23×C71—21no—
114C23×C71—42no—
115C23×C71—42no—
116C23×C71—81no—
117C23×C71C2×D411yescharacteristic
118C22×D71—21no—
119C22×D71—42no—
120C22×D71—42no—
121C22×D71—81no—
122C22×D71C2×D411yescharacteristic
123D4×C71—21no—
124D4×C71—21no—
125D4×C71—21no—
126D4×C71—42no—
127D4×C71#4112yes—
128C2×C4×C71—21no—
129C2×C4×C71—21no—
130C2×C4×C71—21no—
131C2×C4×C71—21no—
132C2×C4×C71—81no—
133C2×C4×C71C2×D411yescharacteristic
134C2×C4×C71C2411yescharacteristic
135C22⋊D71—42no—
136C22⋊D71—42no—
137C22⋊D71—42no—
138C22⋊D71—42no—
139C22⋊D71—81no—
140C22⋊D71SD1614yescomplemented
141C2×Dic71—21no—
142C2×Dic71—21no—
143C2×Dic71—21no—
144C2×Dic71—42no—
145C2×Dic71C2×D411yescharacteristic
146C2×Dic71C2×D411yescharacteristic
147C2×Dic71C2×D411yescharacteristic
148D284—21no—
149D284—21no—
150C4×D71—21no—
151C4×D71—21no—
152C4×D71—81no—
153Dic142—21no—
154Dic142—21no—
155Dic142—81no—
156C8×C71—21no—
157C8×C71—21no—
158C71⋊C8—21no—
159C71⋊C8—21no—
160C22×C71—21no—
161C22×C71—21no—
162C22×C71—22no—
163C22×C71—41no—
164C22×C71—41no—
165C22×C71—41no—
166C22×C71—41no—
167C22×C71—41no—
168C22×C71—84no—
169C22×C71C2×SD1612yes—
170C22×C71C22×D411yescharacteristic
171C2×D71—21no—
172C2×D71—21no—
173C2×D71—41no—
174C2×D71—41no—
175C2×D71—41no—
176C2×D71—84no—
177C2×D71C2×SD1612yes—
178C4×C71—21no—
179C4×C71—41no—
180C4×C71—41no—
181C4×C71C2×#4111yescharacteristic
182C4×C71H(5,𝔽2)11yescharacteristic
183Dic71—21no—
184Dic71—21no—
185Dic71—41no—
186Dic71—41no—
187Dic71—41no—
188Dic71C2×SD1612yes—
189C2×C71—22no—
190C2×C71—42no—
191C2×C71—81no—
192C2×C71#54611yescharacteristic
193C2×C71C22×SD1611yescharacteristic
194C2×C71#57611yescharacteristic
195D71—22no—
196D71—81no—
197#3295—711nomaximal, Sylow
198C71#329511yescharacteristic, complemented, Sylow
199#554—711no—
200D42—711no—
201#486—711no—
202#481—711no—
203#481—711no—
204#476—711no—
205#465—711no—
206#465—711no—
207#460—711no—
208#450—711no—
209#450—711no—
210C4×SD16—711no—
211C8×D4—711no—
212C2×#102—711no—
213C2×#102D7111yescharacteristic, complemented
214C22×D4—711no—
215C22×D4—1421no—
216C22×D4C2×D7111yescharacteristic
217C2×SD16—711no—
218C2×SD16—711no—
219C2×SD16—711no—
220C22×C8—711no—
221C22×C8C2×D7111yescharacteristic, complemented
222C4⋊Q8—711no—
223#127—711no—
224#125—1421no—
225C22⋊Q8—711no—
226C22⋊Q8—711no—
227C22⋊Q8—1421no—
228C22⋊Q8—1421no—
229#121—711no—
230#121—711no—
231#121—1421no—
232#120—1421no—
233#120—1421no—
234C4×Q8—711no—
235C4×D4—711no—
236C4×D4—711no—
237C4×D4—1421no—
238C2×C4⋊C4—711no—
239C2×C4⋊C4C2×D7111yescharacteristic, complemented
240#106—711no—
241#106—711no—
242#106—711no—
243C4⋊C8—711no—
244#103—711no—
245#102—711no—
246#102—711no—
247#102—711no—
248#102—711no—
249#102—711no—
250#102C2×D7111yescharacteristic
251#102C2×D7111yescharacteristic
252#102C2×D7111yescharacteristic, complemented
253#102C2×D7111yescharacteristic, complemented
254C22⋊C8—711no—
255C22⋊C8—711no—
256C4×C8—711no—
257C24—21no—
258C24—1421no—
259C2×Q8—711no—
260C2×Q8—1421no—
261C2×D4—22no—
262C2×D4—21no—
263C2×D4—41no—
264C2×D4—2844no—
265C2×D4—2841no—
266C2×D4—711no—
267C2×D4—711no—
268C2×D4—1421no—
269C2×D4—1421no—
270C2×D4—1421no—
271C2×D4—1421no—
272C2×D4—1421no—
273C2×D4—1422no—
274C2×D4C22×D7111yescharacteristic
275C2×D4C22×D7111yescharacteristic
276C22×C4—21no—
277C22×C4—711no—
278C22×C4—1421no—
279C22×C4—1421no—
280C22×C4C22×D7111yescharacteristic
281SD16—2841no—
282SD16—2841no—
283SD16—1422no—
284C2×C8—41no—
285C2×C8—2841no—
286C2×C8—711no—
287C2×C8—711no—
288C2×C8C22×D7111yescharacteristic
289C2×C8C22×D7111yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—711no—
292C4⋊C4—711no—
293C4⋊C4—711no—
294C4⋊C4—1421no—
295C4⋊C4—1421no—
296C4⋊C4—1421no—
297C4⋊C4—1421no—
298C4⋊C4—1421no—
299C4⋊C4C22×D7111yescharacteristic
300C4⋊C4C22×D7111yescharacteristic
301C22⋊C4—711no—
302C22⋊C4—711no—
303C22⋊C4—1421no—
304C22⋊C4—1421no—
305C22⋊C4—1421no—
306C22⋊C4—1421no—
307C22⋊C4—1421no—
308C42—711no—
309C42—1421no—
310C23—21no—
311C23—21no—
312C23—42no—
313C23—42no—
314C23—81no—
315C23—2842no—
316C23—2842no—
317C23—5681no—
318C23—711no—
319C23—1421no—
320C23D4×D7111yescharacteristic
321Q8—5681no—
322Q8—1421no—
323Q8—1421no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—42no—
328D4—2842no—
329D4—2842no—
330D4—2842no—
331D4—2842no—
332D4—5681no—
333D4—714no—
334D4—1421no—
335D4—1421no—
336D4#1176586512yes—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—81no—
342C2×C4—2842no—
343C2×C4—5681no—
344C2×C4—711no—
345C2×C4—711no—
346C2×C4—711no—
347C2×C4—1421no—
348C2×C4—1421no—
349C2×C4—1421no—
350C2×C4—1421no—
351C2×C4—1421no—
352C2×C4D4×D7111yescharacteristic
353C2×C4C23×D7111yescharacteristic
354C8—21no—
355C8—21no—
356C8—1421no—
357C8—1421no—
358C22—21no—
359C22—21no—
360C22—22no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—84no—
367C22—2841no—
368C22—2841no—
369C22—2841no—
370C22—5684no—
371C22—712no—
372C22—1421no—
373C22—1421no—
374C22SD16×D7112yes—
375C22C2×D4×D7111yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—2841no—
380C4—2841no—
381C4—2841no—
382C4—712no—
383C4—1421no—
384C4—1421no—
385C4C2×#1176586511yescharacteristic
386C4#1455617311yescharacteristic
387C2—22no—
388C2—42no—
389C2—81no—
390C2—5681no—
391C2—1422no—
392C2#1798663911yescharacteristic
393C2C2×SD16×D7111yescharacteristic
394C2#1798680011yescharacteristic
subgroupG/H
centerC22C2×D4×D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
FittingC2×#102×C71C2
socleC22×C71C22×D4
hypercenterC2×#102D71
hypocenterC71#3295
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #17986704C2semidirect
3. #17986344C2semidirect
4. #17986317C2semidirect
5. #17986316C2semidirect
6. #17986287C2semidirect
7. #17986228C2semidirect
8. #17986227C2semidirect
9. #17986198C2semidirect
10. #17986151C2semidirect
11. #17986150C2semidirect
12. #17986090C2semidirect
13. C8×C22⋊D71C2semidirect
14. #102×D71C2semidirect
15. C2×#102×C71C2semidirect
18. C2×#11765854C22semidirect
20. C2×#11765853C22semidirect
21. C2×C8×D71C22semidirect
22. #14556127C22semidirect
25. #14556108C22semidirect
27. #14556107C22semidirect
34. #14556093C22semidirect
38. C4⋊C4×D71C22semidirect
39. #14556060C22semidirect
40. #14556059C22semidirect
41. #14556059C22semidirect
42. Dic71⋊C8C22semidirect
43. #14556053C22semidirect
44. #14556050C22semidirect
46. #14556049C22semidirect
47. #14556048C22semidirect
48. #14556048C22semidirect
49. C22⋊(C71⋊C8)C22semidirect
50. (C2×D71)⋊C8C22semidirect
51. C8×Dic71C22semidirect
53. C22×C8×C71C22semidirect
54. C2×C4⋊C4×C71C22semidirect
57. #102×C71C22semidirect
58. #102×C71C22semidirect
140. C22⋊D71SD16semidirect
198. C71#3295semidirect
213. C2×#102D71semidirect
221. C22×C8C2×D71semidirect
239. C2×C4⋊C4C2×D71semidirect
252. #102C2×D71semidirect
253. #102C2×D71semidirect