Finite Group Databasebeta

← #22600151

Subgroups — #22600151

Order 9088.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17986650C211yesmaximal, characteristic, complemented
2#17986633C211yesmaximal, characteristic, complemented
3#17986344C211yesmaximal, characteristic, complemented
4#17986314C211yesmaximal, characteristic, complemented
5#17986278C211yesmaximal, characteristic, complemented
6#17986236C211yesmaximal, characteristic, complemented
7#17986233C211yesmaximal, characteristic, complemented
8#17986193C211yesmaximal, characteristic, complemented
9#17986135C211yesmaximal, characteristic, complemented
10#17986134C211yesmaximal, characteristic, complemented
11#17986081C211yesmaximal, characteristic, complemented
12(C22⋊D71)⋊C8C211yesmaximal, characteristic, complemented
13C2×#14556048C211yesmaximal, characteristic, complemented
14#102×D71C211yesmaximal, characteristic, complemented
15#480×C71C211yesmaximal, characteristic, complemented
16C2×#11765865—21no—
17C22×D284C2211yescharacteristic
18C2×D4×D71—21no—
19C2×D4×D71C2211yescharacteristic
20C2×D568C2211yescharacteristic
21C2×D568C2211yescharacteristic, complemented
22C2×#11765850C2211yescharacteristic, complemented
23C22×C71⋊C8C2211yescharacteristic, complemented
24C2×C8×D71C2211yescharacteristic, complemented
25#14556127C2211yescharacteristic, complemented
26#14556124C2211yescharacteristic
27#14556113—21no—
28#14556111—21no—
29#14556106—21no—
30#14556103C2211yescharacteristic
31#14556103C2211yescharacteristic, complemented
32#14556102C2211yescharacteristic, complemented
33#14556101—21no—
34#14556098—21no—
35#14556096—21no—
36#14556090C2211yescharacteristic
37#14556090C2211yescharacteristic, complemented
38C4×C22⋊D71C2211yescharacteristic
39C4⋊C4×D71C2211yescharacteristic, complemented
40#14556061C2211yescharacteristic, complemented
41Dic71⋊C8C2211yescharacteristic, complemented
42#14556050C2211yescharacteristic
43#14556050C2211yescharacteristic, complemented
44#14556049C2211yescharacteristic, complemented
45#14556048C2211yescharacteristic
46#14556048C2211yescharacteristic
47#14556048C2211yescharacteristic, complemented
48#14556048C2211yescharacteristic, complemented
49#14556048C2211yescharacteristic, complemented
50(C2×D71)⋊C8C2211yescharacteristic, complemented
51C8×Dic71C2211yescharacteristic, complemented
52#121×C71C2211yescharacteristic
53C2×C4⋊C4×C71C2211yescharacteristic, complemented
54#107×C71C2211yescharacteristic, complemented
55#107×C71C2211yescharacteristic, complemented
56#102×C71C2211yescharacteristic, complemented
57#102×C71C2211yescharacteristic, complemented
58C22⋊C8×C71C2211yescharacteristic, complemented
59C23×D71—21no—
60C23×D71—21no—
61#11765865—44no—
62C2×Dic142—21no—
63C2×D284—22no—
64C2×D284—21no—
65C2×D284—21no—
66C2×D284—21no—
67C2×D284—41no—
68C2×D284C2311yescharacteristic
69C2×D284C2311yescharacteristic
70C2×D284C2311yescharacteristic
71C2×C22⋊D71—21no—
72C2×C22⋊D71—21no—
73C2×C22⋊D71—21no—
74C2×C22⋊D71—21no—
75C2×C22⋊D71D411yescharacteristic
76D4×D71—22no—
77D4×D71—41no—
78D4×D71—44no—
79C2×C4×D71—21no—
80C2×C4×D71—21no—
81C2×C4×D71—21no—
82C2×C4×D71C2311yescharacteristic
83D568—22no—
84D568—41no—
85#11765850—41no—
86C2×C71⋊C8—41no—
87C2×C71⋊C8C2311yescharacteristic
88C2×C71⋊C8C2311yescharacteristic
89C8×D71—41no—
90C4⋊Dic71C2311yescharacteristic
91Dic71⋊C4—21no—
92Dic71⋊C4—21no—
93Dic71⋊C4D411yescharacteristic
94C22⋊Dic71D411yescharacteristic
95(C2×D71)⋊C4—21no—
96(C2×D71)⋊C4—21no—
97(C2×D71)⋊C4—21no—
98(C2×D71)⋊C4—21no—
99(C2×D71)⋊C4—21no—
100(C2×D71)⋊C4D411yescharacteristic
101C4×Dic71C2311yescharacteristic
102C2×D4×C71—21no—
103C2×D4×C71C2311yescharacteristic
104C22×C4×C71—21no—
105C22×C4×C71C2311yescharacteristic
106C2×C8×C71C2311yescharacteristic
107C2×C8×C71C2311yescharacteristic
108C4⋊C4×C71—21no—
109C4⋊C4×C71C2311yescharacteristic
110C4⋊C4×C71C2311yescharacteristic
111C4⋊C4×C71C2311yescharacteristic
112C22⋊C4×C71—21no—
113C23×C71—21no—
114C23×C71C2×D411yescharacteristic
115C22×D71—21no—
116C22×D71—21no—
117C22×D71—21no—
118C22×D71—42no—
119C22×D71—42no—
120C22×D71—42no—
121C22×D71—42no—
122C22×D71—81no—
123C22×D71—81no—
124C22×D71C2×D411yescharacteristic
125D4×C71—21no—
126D4×C71—21no—
127D4×C71—42no—
128C2×C4×C71—21no—
129C2×C4×C71—21no—
130C2×C4×C71—21no—
131C2×C4×C71—21no—
132C2×C4×C71—21no—
133C2×C4×C71—42no—
134C2×C4×C71C2×D411yescharacteristic
135C2×C4×C71C2411yescharacteristic
136C22⋊D71—42no—
137C22⋊D71—42no—
138C22⋊D71—42no—
139C22⋊D71—81no—
140C22⋊D71D814yescomplemented
141C2×Dic71—21no—
142C2×Dic71C2×D411yescharacteristic
143C2×Dic71C2×D411yescharacteristic
144C2×Dic71C2×D411yescharacteristic
145D284—21no—
146D284—21no—
147D284—21no—
148D284—21no—
149D284—21no—
150D284—42no—
151D284—42no—
152D284—42no—
153D284#4112yescomplemented
154C4×D71—21no—
155C4×D71—21no—
156C4×D71—42no—
157C4×D71—42no—
158C4×D71—42no—
159Dic142—42no—
160C8×C71—21no—
161C8×C71—21no—
162C71⋊C8—21no—
163C71⋊C8—21no—
164C22×C71—21no—
165C22×C71—21no—
166C22×C71—41no—
167C22×C71—41no—
168C22×C71—41no—
169C22×C71C2×D812yes—
170C22×C71C22×D411yescharacteristic
171C2×D71—21no—
172C2×D71—21no—
173C2×D71—22no—
174C2×D71—41no—
175C2×D71—41no—
176C2×D71—41no—
177C2×D71—41no—
178C2×D71—41no—
179C2×D71—41no—
180C2×D71—41no—
181C2×D71—41no—
182C2×D71—84no—
183C2×D71—84no—
184C2×D71C2×D812yes—
185C4×C71—21no—
186C4×C71—41no—
187C4×C71—41no—
188C4×C71—41no—
189C4×C71C2×#4111yescharacteristic
190C4×C71H(5,𝔽2)11yescharacteristic
191Dic71—21no—
192Dic71—21no—
193Dic71—41no—
194Dic71C2×D812yes—
195C2×C71—22no—
196C2×C71—81no—
197C2×C71#54611yescharacteristic
198C2×C71C22×D811yescharacteristic
199C2×C71#57711yescharacteristic
200D71—22no—
201D71—42no—
202D71—81no—
203D71—81no—
204#3294—711nomaximal, Sylow
205C71#329411yescharacteristic, complemented, Sylow
206#547—711no—
207D42—711no—
208#486—711no—
209#480—711no—
210#480D7111yescharacteristic, complemented
211#474—711no—
212#466—711no—
213#466—711no—
214#459—711no—
215#447—711no—
216#447—711no—
217C4×D8—711no—
218C8×D4—711no—
219C2×#102—711no—
220C2×#102—711no—
221C2×#41—1421no—
222C22×D4—711no—
223C22×D4—711no—
224C22×D4—1421no—
225C2×D8—711no—
226C2×D8—711no—
227C2×D8—711no—
228C22×C8—711no—
229C22×C8—711no—
230C4⋊Q8—711no—
231#127—711no—
232#123—1421no—
233#123—1421no—
234C22⋊Q8—1421no—
235#121—711no—
236#121—711no—
237#121—711no—
238#121—1421no—
239#121C2×D7111yescharacteristic
240#120—1421no—
241#120—1421no—
242C4×D4—711no—
243C4×D4—711no—
244C4×D4—711no—
245C2×C4⋊C4—711no—
246C2×C4⋊C4C2×D7111yescharacteristic, complemented
247#107—711no—
248#107C2×D7111yescharacteristic, complemented
249#107C2×D7111yescharacteristic, complemented
250C4⋊C8—711no—
251#102—711no—
252#102—711no—
253#102—711no—
254#102—711no—
255#102—711no—
256#102—711no—
257#102—711no—
258#102—711no—
259#102C2×D7111yescharacteristic, complemented
260#102C2×D7111yescharacteristic, complemented
261C22⋊C8—711no—
262C22⋊C8C2×D7111yescharacteristic, complemented
263C4×C8—711no—
264C24—1421no—
265C24—1421no—
266#41—2844no—
267C2×Q8—1421no—
268C2×D4—21no—
269C2×D4—2841no—
270C2×D4—2844no—
271C2×D4—2841no—
272C2×D4—711no—
273C2×D4—711no—
274C2×D4—711no—
275C2×D4—711no—
276C2×D4—1421no—
277C2×D4—1421no—
278C2×D4—1422no—
279C2×D4—1421no—
280C2×D4—1421no—
281C2×D4—1421no—
282C2×D4—1422no—
283C2×D4—1421no—
284C2×D4—1421no—
285C2×D4C22×D7111yescharacteristic
286C22×C4—21no—
287C22×C4—711no—
288C22×C4—1421no—
289C22×C4—1421no—
290C22×C4—1421no—
291C22×C4C22×D7111yescharacteristic
292D8—2841no—
293D8—2841no—
294D8—1422no—
295C2×C8—2841no—
296C2×C8—2841no—
297C2×C8—711no—
298C2×C8—711no—
299C2×C8C22×D7111yescharacteristic
300C2×C8C22×D7111yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—711no—
303C4⋊C4—711no—
304C4⋊C4—1421no—
305C4⋊C4—1421no—
306C4⋊C4C22×D7111yescharacteristic
307C4⋊C4C22×D7111yescharacteristic
308C4⋊C4C22×D7111yescharacteristic
309C22⋊C4—21no—
310C22⋊C4—711no—
311C22⋊C4—711no—
312C22⋊C4—1421no—
313C22⋊C4—1421no—
314C22⋊C4—1421no—
315C22⋊C4—1421no—
316C22⋊C4—1421no—
317C42—711no—
318C23—21no—
319C23—2842no—
320C23—2842no—
321C23—2842no—
322C23—2842no—
323C23—5681no—
324C23—5681no—
325C23—711no—
326C23—1421no—
327C23—1421no—
328C23—1421no—
329C23D4×D7111yescharacteristic
330Q8—2842no—
331D4—21no—
332D4—21no—
333D4—42no—
334D4—2842no—
335D4—2842no—
336D4—2842no—
337D4—2842no—
338D4—2842no—
339D4—2842no—
340D4—5681no—
341D4—714no—
342D4—712no—
343D4—1421no—
344D4—1421no—
345D4—1421no—
346D4—1421no—
347D4—1421no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—42no—
354C2×C4—2842no—
355C2×C4—2842no—
356C2×C4—2842no—
357C2×C4—711no—
358C2×C4—711no—
359C2×C4—711no—
360C2×C4—1421no—
361C2×C4—1421no—
362C2×C4—1421no—
363C2×C4D4×D7111yescharacteristic
364C2×C4C23×D7111yescharacteristic
365C8—21no—
366C8—21no—
367C8—1421no—
368C8—1421no—
369C22—21no—
370C22—21no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—2841no—
375C22—2841no—
376C22—2841no—
377C22—2841no—
378C22—2841no—
379C22—2841no—
380C22—2841no—
381C22—2841no—
382C22—5684no—
383C22—5684no—
384C22—712no—
385C22—1422no—
386C22—1421no—
387C22—1421no—
388C22D8×D7112yes—
389C22C2×D4×D7111yescharacteristic
390C4—21no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—2841no—
395C4—712no—
396C4—1421no—
397C4—1421no—
398C4#41×D7111yescharacteristic
399C4#1455617411yescharacteristic
400C2—22no—
401C2—81no—
402C2—2842no—
403C2—5681no—
404C2—5681no—
405C2—1422no—
406C2#1798664111yescharacteristic
407C2C2×D8×D7111yescharacteristic
408C2#1798680811yescharacteristic
subgroupG/H
centerC22C2×D4×D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#480×C71C2
socleC22×C71C22×D4
hypercenter#480D71
hypocenterC71#3294
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #17986650C2semidirect
2. #17986633C2semidirect
3. #17986344C2semidirect
4. #17986314C2semidirect
5. #17986278C2semidirect
6. #17986236C2semidirect
7. #17986233C2semidirect
8. #17986193C2semidirect
9. #17986135C2semidirect
10. #17986134C2semidirect
11. #17986081C2semidirect
12. (C22⋊D71)⋊C8C2semidirect
13. C2×#14556048C2semidirect
14. #102×D71C2semidirect
15. #480×C71C2semidirect
21. C2×D568C22semidirect
22. C2×#11765850C22semidirect
23. C22×C71⋊C8C22semidirect
24. C2×C8×D71C22semidirect
25. #14556127C22semidirect
31. #14556103C22semidirect
32. #14556102C22semidirect
37. #14556090C22semidirect
39. C4⋊C4×D71C22semidirect
40. #14556061C22semidirect
41. Dic71⋊C8C22semidirect
43. #14556050C22semidirect
44. #14556049C22semidirect
47. #14556048C22semidirect
48. #14556048C22semidirect
49. #14556048C22semidirect
50. (C2×D71)⋊C8C22semidirect
51. C8×Dic71C22semidirect
53. C2×C4⋊C4×C71C22semidirect
54. #107×C71C22semidirect
55. #107×C71C22semidirect
56. #102×C71C22semidirect
57. #102×C71C22semidirect
58. C22⋊C8×C71C22semidirect
140. C22⋊D71D8semidirect
153. D284#41semidirect
205. C71#3294semidirect
210. #480D71semidirect
246. C2×C4⋊C4C2×D71semidirect
248. #107C2×D71semidirect
249. #107C2×D71semidirect
259. #102C2×D71semidirect
260. #102C2×D71semidirect
262. C22⋊C8C2×D71semidirect