Finite Group Databasebeta

← #22600159

Subgroups — #22600159

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#17986707C211yesmaximal, characteristic, complemented
2#17986633C211yesmaximal, characteristic
3#17986344C211yesmaximal, characteristic, complemented
4#17986319C211yesmaximal, characteristic, complemented
5#17986315C211yesmaximal, characteristic, complemented
6#17986288C211yesmaximal, characteristic, complemented
7#17986231C211yesmaximal, characteristic, complemented
8#17986197C211yesmaximal, characteristic, complemented
9#17986149C211yesmaximal, characteristic, complemented
10#17986148C211yesmaximal, characteristic, complemented
11#17986084C211yesmaximal, characteristic, complemented
12C8×C22⋊D71C211yesmaximal, characteristic, complemented
13C2×#14556050C211yesmaximal, characteristic, complemented
14#102×D71C211yesmaximal, characteristic, complemented
15#465×C71C211yesmaximal, characteristic, complemented
16C22×D284C2211yescharacteristic
17C2×D4×D71—21no—
18C2×D4×D71C2211yescharacteristic
19C2×#11765852C2211yescharacteristic
20C2×#11765852C2211yescharacteristic, complemented
21C2×C8×D71C2211yescharacteristic, complemented
22#14556127C2211yescharacteristic, complemented
23#14556124C2211yescharacteristic
24#14556118—21no—
25#14556108—21no—
26#14556105—21no—
27#14556104C2211yescharacteristic, complemented
28#14556103C2211yescharacteristic
29#14556101—21no—
30#14556098—21no—
31#14556096—21no—
32Q8×Dic71C2211yescharacteristic, complemented
33#14556090C2211yescharacteristic
34C4×C22⋊D71C2211yescharacteristic
35(C22⋊D71)⋊C4—21no—
36C2×C4⋊Dic71C2211yescharacteristic, complemented
37C4⋊C4×D71C2211yescharacteristic, complemented
38#14556059C2211yescharacteristic, complemented
39#14556059C2211yescharacteristic, complemented
40Dic71⋊C8C2211yescharacteristic, complemented
41#14556050C2211yescharacteristic
42#14556050C2211yescharacteristic
43#14556050C2211yescharacteristic, complemented
44#14556050C2211yescharacteristic, complemented
45#14556049C2211yescharacteristic, complemented
46#14556049C2211yescharacteristic, complemented
47#14556048C2211yescharacteristic
48#14556048C2211yescharacteristic, complemented
49C22⋊(C71⋊C8)C2211yescharacteristic, complemented
50(C2×D71)⋊C8C2211yescharacteristic, complemented
51C8×Dic71C2211yescharacteristic, complemented
52C2×SD16×C71C2211yescharacteristic, complemented
53C22×C8×C71C2211yescharacteristic, complemented
54C22⋊Q8×C71C2211yescharacteristic, complemented
55#121×C71C2211yescharacteristic
56#106×C71C2211yescharacteristic, complemented
57#103×C71C2211yescharacteristic, complemented
58#102×C71C2211yescharacteristic, complemented
59C23×D71—21no—
60C23×D71—21no—
61C2×Dic142—21no—
62C2×D284—22no—
63C2×D284—21no—
64C2×D284—21no—
65C2×D284—41no—
66C2×D284C2311yescharacteristic
67C2×D284C2311yescharacteristic
68C2×C22⋊D71—21no—
69C2×C22⋊D71—21no—
70C2×C22⋊D71—21no—
71C2×C22⋊D71D411yescharacteristic
72D4×D71—22no—
73D4×D71—41no—
74D4×D71—44no—
75C22×Dic71—21no—
76C2×C4×D71—21no—
77C2×C4×D71—21no—
78C2×C4×D71C2311yescharacteristic
79#11765852—22no—
80#11765852—41no—
81C2×C71⋊C8C2311yescharacteristic
82C2×C71⋊C8C2311yescharacteristic
83C8×D71—41no—
84C4⋊Dic71—21no—
85C4⋊Dic71—21no—
86C4⋊Dic71C2311yescharacteristic
87C4⋊Dic71C2311yescharacteristic
88Dic71⋊C4—21no—
89Dic71⋊C4—21no—
90Dic71⋊C4—21no—
91Dic71⋊C4D411yescharacteristic
92C22⋊Dic71D411yescharacteristic
93(C2×D71)⋊C4—21no—
94(C2×D71)⋊C4—21no—
95(C2×D71)⋊C4—21no—
96(C2×D71)⋊C4D411yescharacteristic
97C4×Dic71—21no—
98C4×Dic71C2311yescharacteristic
99C2×Q8×C71C2311yescharacteristic
100C2×D4×C71—21no—
101C2×D4×C71C2311yescharacteristic
102C22×C4×C71C2311yescharacteristic
103SD16×C71—41no—
104C2×C8×C71—41no—
105C2×C8×C71C2311yescharacteristic
106C2×C8×C71C2311yescharacteristic
107C4⋊C4×C71—21no—
108C4⋊C4×C71C2311yescharacteristic
109C4⋊C4×C71C2311yescharacteristic
110C22⋊C4×C71—21no—
111C22⋊C4×C71—21no—
112C23×C71—21no—
113C23×C71C2×D411yescharacteristic
114C22×D71—21no—
115C22×D71—21no—
116C22×D71—42no—
117C22×D71—42no—
118C22×D71—42no—
119C22×D71—42no—
120C22×D71—81no—
121C22×D71—81no—
122C22×D71C2×D411yescharacteristic
123Q8×C71—21no—
124Q8×C71—21no—
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×C71C2×D411yescharacteristic
134C2×C4×C71C2411yescharacteristic
135C22⋊D71—42no—
136C22⋊D71—42no—
137C22⋊D71—81no—
138C22⋊D71SD1614yescomplemented
139C2×Dic71—21no—
140C2×Dic71—21no—
141C2×Dic71—81no—
142C2×Dic71C2×D411yescharacteristic
143C2×Dic71C2×D411yescharacteristic
144C2×Dic71C2×D411yescharacteristic
145D284—21no—
146D284—21no—
147D284—21no—
148D284—42no—
149D284—42no—
150D284#4112yes—
151C4×D71—21no—
152C4×D71—21no—
153C4×D71—42no—
154C4×D71—81no—
155Dic142—81no—
156C8×C71—21no—
157C8×C71—21no—
158C71⋊C8—21no—
159C71⋊C8—21no—
160C22×C71—21no—
161C22×C71—21no—
162C22×C71—41no—
163C22×C71—41no—
164C22×C71—41no—
165C22×C71C2×SD1612yes—
166C22×C71C22×D411yescharacteristic
167C2×D71—21no—
168C2×D71—21no—
169C2×D71—22no—
170C2×D71—41no—
171C2×D71—41no—
172C2×D71—41no—
173C2×D71—41no—
174C2×D71—41no—
175C2×D71—84no—
176C2×D71—84no—
177C2×D71C2×SD1612yes—
178C4×C71—21no—
179C4×C71—41no—
180C4×C71—41no—
181C4×C71—41no—
182C4×C71C2×#4111yescharacteristic
183C4×C71H(5,𝔽2)11yescharacteristic
184Dic71—21no—
185Dic71—21no—
186Dic71—41no—
187Dic71—41no—
188Dic71C2×SD1612yes—
189C2×C71—22no—
190C2×C71—81no—
191C2×C71#54611yescharacteristic
192C2×C71C22×SD1611yescharacteristic
193C2×C71#57611yescharacteristic
194D71—22no—
195D71—42no—
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#465D7111yescharacteristic, complemented
207#460—711no—
208#450—711no—
209#450—711no—
210C4×SD16—711no—
211C8×D4—711no—
212C2×#102—711no—
213C2×#102—711no—
214C22×D4—711no—
215C22×D4—711no—
216C22×D4—1421no—
217C2×SD16—711no—
218C2×SD16—711no—
219C2×SD16C2×D7111yescharacteristic, complemented
220C22×C8—711no—
221C22×C8C2×D7111yescharacteristic, complemented
222C4⋊Q8—711no—
223#127—711no—
224#125—1421no—
225C22⋊Q8—711no—
226C22⋊Q8—1421no—
227C22⋊Q8—1421no—
228C22⋊Q8C2×D7111yescharacteristic, complemented
229#121—711no—
230#121—1421no—
231#121C2×D7111yescharacteristic
232#120—1421no—
233#120—1421no—
234C4×Q8—711no—
235C4×D4—711no—
236C4×D4—711no—
237C4×D4—1421no—
238C2×C4⋊C4—711no—
239C2×C4⋊C4—711no—
240#106—711no—
241#106—711no—
242#106C2×D7111yescharacteristic, complemented
243C4⋊C8—711no—
244#103C2×D7111yescharacteristic, complemented
245#102—711no—
246#102—711no—
247#102—711no—
248#102—711no—
249#102—711no—
250#102—711no—
251#102—711no—
252#102—711no—
253#102C2×D7111yescharacteristic, complemented
254C22⋊C8—711no—
255C22⋊C8—711no—
256C4×C8—711no—
257C24—1421no—
258C24—1421no—
259C2×Q8—1421no—
260C2×Q8C22×D7111yescharacteristic
261C2×D4—21no—
262C2×D4—2841no—
263C2×D4—2844no—
264C2×D4—2841no—
265C2×D4—711no—
266C2×D4—711no—
267C2×D4—711no—
268C2×D4—1421no—
269C2×D4—1422no—
270C2×D4—1421no—
271C2×D4—1421no—
272C2×D4—1421no—
273C2×D4—1422no—
274C2×D4—1421no—
275C2×D4C22×D7111yescharacteristic
276C22×C4—711no—
277C22×C4—1421no—
278C22×C4—1421no—
279C22×C4—1421no—
280C22×C4C22×D7111yescharacteristic
281SD16—41no—
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—21no—
302C22⋊C4—21no—
303C22⋊C4—711no—
304C22⋊C4—711no—
305C22⋊C4—1421no—
306C22⋊C4—1421no—
307C22⋊C4—1421no—
308C42—711no—
309C42—1421no—
310C23—21no—
311C23—2842no—
312C23—2842no—
313C23—2842no—
314C23—2842no—
315C23—5681no—
316C23—5681no—
317C23—711no—
318C23—1421no—
319C23—1421no—
320C23D4×D7111yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—5681no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—2842no—
328D4—2842no—
329D4—2842no—
330D4—2842no—
331D4—5681no—
332D4—714no—
333D4—712no—
334D4—1421no—
335D4—1421no—
336D4—1421no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—2842no—
343C2×C4—5681no—
344C2×C4—5681no—
345C2×C4—711no—
346C2×C4—711no—
347C2×C4—711no—
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—41no—
361C22—41no—
362C22—41no—
363C22—2841no—
364C22—2841no—
365C22—2841no—
366C22—2841no—
367C22—2841no—
368C22—5684no—
369C22—5684no—
370C22—712no—
371C22—1422no—
372C22—1421no—
373C22—1421no—
374C22SD16×D7112yes—
375C22C2×D4×D7111yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—2841no—
381C4—2841no—
382C4—712no—
383C4—1421no—
384C4—1421no—
385C4#41×D7111yescharacteristic
386C4#1455617311yescharacteristic
387C2—22no—
388C2—81no—
389C2—2842no—
390C2—5681no—
391C2—1422no—
392C2#1798663811yescharacteristic
393C2C2×SD16×D7111yescharacteristic
394C2#1798680111yescharacteristic
subgroupG/H
centerC22C2×D4×D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#465×C71C2
socleC22×C71C22×D4
hypercenter#465D71
hypocenterC71#3295
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. #17986707C2semidirect
3. #17986344C2semidirect
4. #17986319C2semidirect
5. #17986315C2semidirect
6. #17986288C2semidirect
7. #17986231C2semidirect
8. #17986197C2semidirect
9. #17986149C2semidirect
10. #17986148C2semidirect
11. #17986084C2semidirect
12. C8×C22⋊D71C2semidirect
13. C2×#14556050C2semidirect
14. #102×D71C2semidirect
15. #465×C71C2semidirect
20. C2×#11765852C22semidirect
21. C2×C8×D71C22semidirect
22. #14556127C22semidirect
27. #14556104C22semidirect
32. Q8×Dic71C22semidirect
36. C2×C4⋊Dic71C22semidirect
37. C4⋊C4×D71C22semidirect
38. #14556059C22semidirect
39. #14556059C22semidirect
40. Dic71⋊C8C22semidirect
43. #14556050C22semidirect
44. #14556050C22semidirect
45. #14556049C22semidirect
46. #14556049C22semidirect
48. #14556048C22semidirect
49. C22⋊(C71⋊C8)C22semidirect
50. (C2×D71)⋊C8C22semidirect
51. C8×Dic71C22semidirect
52. C2×SD16×C71C22semidirect
53. C22×C8×C71C22semidirect
54. C22⋊Q8×C71C22semidirect
56. #106×C71C22semidirect
57. #103×C71C22semidirect
58. #102×C71C22semidirect
138. C22⋊D71SD16semidirect
198. C71#3295semidirect
206. #465D71semidirect
219. C2×SD16C2×D71semidirect
221. C22×C8C2×D71semidirect
228. C22⋊Q8C2×D71semidirect
242. #106C2×D71semidirect
244. #103C2×D71semidirect
253. #102C2×D71semidirect