Finite Group Databasebeta

← #22598693

Subgroups — #22598693

Order 9088.

404 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17986629C211yesmaximal, characteristic, complemented
2#17986567C211yesmaximal, characteristic
3#17986365C211yesmaximal, characteristic, complemented
4#17986362C211yesmaximal, characteristic, complemented
5#17986360C211yesmaximal, characteristic, complemented
6#17986358C211yesmaximal, characteristic, complemented
7#17986355C211yesmaximal, characteristic, complemented
8#17986346C211yesmaximal, characteristic, complemented
9#17986344C211yesmaximal, characteristic, complemented
10#17986002C211yesmaximal, characteristic, complemented
11#17985999C211yesmaximal, characteristic, complemented
12#17985994C211yesmaximal, characteristic, complemented
13#102×D71C211yesmaximal, characteristic, complemented
14#17985953C211yesmaximal, characteristic, complemented
15#488×C71C211yesmaximal, characteristic, complemented
16C2×#11765866C2211yescharacteristic
17C2×D4×D71C2211yescharacteristic
18C2×#11765848C2211yescharacteristic
19C2×C8×D71C2211yescharacteristic
20#14556128C2211yescharacteristic, complemented
21#14556127—21no—
22#14556127C2211yescharacteristic, complemented
23#14556125C2211yescharacteristic
24#14556124C2211yescharacteristic
25#14556119C2211yescharacteristic, complemented
26#14556118—21no—
27#14556117C2211yescharacteristic
28#14556108—21no—
29#14556106—21no—
30#14556101—21no—
31#14556101—21no—
32#14556098—21no—
33#14556098—21no—
34#14556086C2211yescharacteristic
35#14556085C2211yescharacteristic
36C4⋊C4×D71C2211yescharacteristic
37#14556052C2211yescharacteristic, complemented
38#14556052C2211yescharacteristic, complemented
39#14556050C2211yescharacteristic
40#14556050C2211yescharacteristic
41#14556050C2211yescharacteristic, complemented
42#14556050C2211yescharacteristic, complemented
43#14556049C2211yescharacteristic
44#14556049C2211yescharacteristic
45#14556048C2211yescharacteristic
46#14556048C2211yescharacteristic
47#14556048C2211yescharacteristic, complemented
48#14556048C2211yescharacteristic, complemented
49#14556039C2211yescharacteristic, complemented
50#14556038C2211yescharacteristic, complemented
51C8×Dic71C2211yescharacteristic, 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—22no—
62C2×Dic142—21no—
63C2×Dic142—21no—
64C2×D284—21no—
65C2×D284—21no—
66C2×D284—21no—
67C2×D284C2311yescharacteristic
68C2×D284C2311yescharacteristic
69C2×C22⋊D71—21no—
70C2×C22⋊D71—21no—
71C2×C22⋊D71—21no—
72D4×D71—22no—
73D4×D71—22no—
74C2×C4×D71—21no—
75C2×C4×D71—21no—
76C2×C4×D71C2311yescharacteristic
77#11765848—22no—
78C2×C71⋊C8C2311yescharacteristic
79C2×C71⋊C8C2311yescharacteristic
80C8×D71—22no—
81C4⋊Dic71—21no—
82C4⋊Dic71—21no—
83C4⋊Dic71C2311yescharacteristic
84C4⋊Dic71C2311yescharacteristic
85Dic71⋊C4—21no—
86Dic71⋊C4—21no—
87Dic71⋊C4—21no—
88Dic71⋊C4D411yescharacteristic
89Dic71⋊C4D411yescharacteristic
90(C2×D71)⋊C4—21no—
91(C2×D71)⋊C4—21no—
92(C2×D71)⋊C4—21no—
93(C2×D71)⋊C4D411yescharacteristic
94(C2×D71)⋊C4D411yescharacteristic
95C4×Dic71—21no—
96C4×Dic71C2311yescharacteristic
97C2×Q8×C71C2311yescharacteristic
98C2×D4×C71C2311yescharacteristic
99C2×C8×C71C2311yescharacteristic
100C2×C8×C71C2311yescharacteristic
101C4⋊C4×C71—21no—
102C4⋊C4×C71—21no—
103C4⋊C4×C71C2311yescharacteristic
104C4⋊C4×C71C2311yescharacteristic
105C22⋊C4×C71—21no—
106C22⋊C4×C71—21no—
107C42×C71C2311yescharacteristic
108C23×C71—21no—
109C22×D71—21no—
110C22×D71—21no—
111C22×D71—42no—
112C22×D71—81no—
113C22×D71—81no—
114C22×D71C2×D411yescharacteristic
115Q8×C71—21no—
116Q8×C71—21no—
117D4×C71—21no—
118D4×C71—21no—
119C2×C4×C71—21no—
120C2×C4×C71—21no—
121C2×C4×C71—21no—
122C2×C4×C71C2×D411yescharacteristic
123C2×C4×C71C2×D411yescharacteristic
124C2×C4×C71C2411yescharacteristic
125C22⋊D71—42no—
126C22⋊D71—81no—
127C22⋊D71—81no—
128C2×Dic71—21no—
129C2×Dic71—21no—
130C2×Dic71C2×D411yescharacteristic
131C2×Dic71C2×D411yescharacteristic
132C2×Dic71C2×D411yescharacteristic
133D284—21no—
134D284—21no—
135D284—21no—
136D284—21no—
137D284—42no—
138D284—81no—
139D284—81no—
140C4×D71—42no—
141C4×D71—81no—
142C4×D71#4112yes—
143C4×D71#4112yes—
144Dic142—81no—
145Dic142—81no—
146C8×C71—21no—
147C8×C71—21no—
148C71⋊C8—21no—
149C71⋊C8—21no—
150C22×C71—41no—
151C22×C71—41no—
152C22×C71—41no—
153C22×C71C22×D411yescharacteristic
154C2×D71—21no—
155C2×D71—21no—
156C2×D71—41no—
157C2×D71—41no—
158C2×D71—41no—
159C2×D71—41no—
160C2×D71—41no—
161C2×D71—41no—
162C2×D71—84no—
163C2×D71#12412yes—
164C4×C71—21no—
165C4×C71—21no—
166C4×C71—41no—
167C4×C71—41no—
168C4×C71—41no—
169C4×C71C2×#4111yescharacteristic
170C4×C71C2×#4111yescharacteristic
171Dic71—21no—
172Dic71—21no—
173Dic71—41no—
174Dic71—41no—
175Dic71#12412yes—
176C2×C71—81no—
177C2×C71C2×#12411yescharacteristic
178C2×C71#57611yescharacteristic
179C2×C71#57711yescharacteristic
180D71—22no—
181D71—81no—
182D71—81no—
183#3136—711nomaximal, Sylow
184C71#313611yescharacteristic, complemented, Sylow
185#544—711no—
186#535—711no—
187#490—711no—
188#490—711no—
189#489—711no—
190#489—711no—
191#488—711no—
192#488D7111yescharacteristic, complemented
193#486—711no—
194#486—711no—
195#418—711no—
196#417—711no—
197#416—711no—
198C2×#102—711no—
199#405—711no—
200C2×#41—711no—
201C22×D4—711no—
202C2×M16—711no—
203C22×C8—711no—
204C4⋊Q8—711no—
205C4⋊Q8—711no—
206C4⋊Q8—1421no—
207#127—711no—
208#127—711no—
209#125—711no—
210#125—1421no—
211#125C2×D7111yescharacteristic, complemented
212#124—711no—
213#124C2×D7111yescharacteristic
214C22⋊Q8—1421no—
215C22⋊Q8—1421no—
216#121—1421no—
217#121—1421no—
218#120—1421no—
219#120—1421no—
220#117—711no—
221#117—711no—
222C2×C4⋊C4—711no—
223#103—711no—
224#103—711no—
225#103C2×D7111yescharacteristic, complemented
226#103C2×D7111yescharacteristic, complemented
227#102—711no—
228#102—711no—
229#102—711no—
230#102—711no—
231#102—711no—
232#102—711no—
233#102—711no—
234#102—711no—
235#102—711no—
236#102—711no—
237#102C2×D7111yescharacteristic
238#102C2×D7111yescharacteristic
239#97—711no—
240#97—711no—
241C4×C8—711no—
242C4×C8C2×D7111yescharacteristic, complemented
243C24—1421no—
244#41—1422no—
245#41—1422no—
246C2×Q8—1421no—
247C2×Q8—1421no—
248C2×Q8C22×D7111yescharacteristic
249C2×D4—711no—
250C2×D4—711no—
251C2×D4—1421no—
252C2×D4—1422no—
253C2×D4—1422no—
254C2×D4—1421no—
255C2×D4—1421no—
256C2×D4—1421no—
257C2×D4—1421no—
258C2×D4—1421no—
259C2×D4C22×D7111yescharacteristic
260C22×C4—711no—
261C22×C4—1421no—
262C22×C4—1421no—
263M16—1422no—
264C2×C8—711no—
265C2×C8—711no—
266C2×C8—1422no—
267C2×C8C22×D7111yescharacteristic
268C2×C8C22×D7111yescharacteristic
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—711no—
272C4⋊C4—711no—
273C4⋊C4—711no—
274C4⋊C4—711no—
275C4⋊C4—1421no—
276C4⋊C4—1421no—
277C4⋊C4—1421no—
278C4⋊C4—1421no—
279C4⋊C4—1421no—
280C4⋊C4C22×D7111yescharacteristic
281C4⋊C4C22×D7111yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—711no—
285C22⋊C4—711no—
286C22⋊C4—1421no—
287C22⋊C4—1421no—
288C22⋊C4—1421no—
289C42—711no—
290C42—1421no—
291C42C22×D7111yescharacteristic
292C23—21no—
293C23—2842no—
294C23—5681no—
295C23—5681no—
296C23—711no—
297C23—1421no—
298C23—1421no—
299Q8—21no—
300Q8—21no—
301Q8—5681no—
302Q8—5681no—
303D4—21no—
304D4—21no—
305D4—2842no—
306D4—2842no—
307D4—5681no—
308D4—5681no—
309D4—5681no—
310D4—5681no—
311D4—1421no—
312D4—1421no—
313D4—1421no—
314D4—1421no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—2842no—
319C2×C4—5681no—
320C2×C4—711no—
321C2×C4—712no—
322C2×C4—712no—
323C2×C4—711no—
324C2×C4—711no—
325C2×C4—1421no—
326C2×C4—1421no—
327C2×C4D4×D7111yescharacteristic
328C2×C4D4×D7111yescharacteristic
329C2×C4C23×D7111yescharacteristic
330C8—21no—
331C8—21no—
332C8—1421no—
333C8—1421no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—2841no—
338C22—2841no—
339C22—2841no—
340C22—2841no—
341C22—2841no—
342C22—2841no—
343C22—5684no—
344C22—712no—
345C22—1421no—
346C22—1421no—
347C22C2×D4×D7111yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—2841no—
354C4—2841no—
355C4—712no—
356C4—1421no—
357C4—1421no—
358C4#41×D7111yescharacteristic
359C4#41×D7111yescharacteristic
360C2—81no—
361C2—5681no—
362C2—5681no—
363C2—1422no—
364C2#124×D7111yescharacteristic
365C2#1798680111yescharacteristic
366C2#1798680611yescharacteristic
subgroupG/H
centerC22C2×D4×D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#488×C71C2
socleC22×C71C22×D4
hypercenter#488D71
hypocenterC71#3136
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. #17986629C2semidirect
3. #17986365C2semidirect
4. #17986362C2semidirect
5. #17986360C2semidirect
6. #17986358C2semidirect
7. #17986355C2semidirect
8. #17986346C2semidirect
9. #17986344C2semidirect
10. #17986002C2semidirect
11. #17985999C2semidirect
12. #17985994C2semidirect
13. #102×D71C2semidirect
14. #17985953C2semidirect
15. #488×C71C2semidirect
20. #14556128C22semidirect
22. #14556127C22semidirect
25. #14556119C22semidirect
37. #14556052C22semidirect
38. #14556052C22semidirect
41. #14556050C22semidirect
42. #14556050C22semidirect
47. #14556048C22semidirect
48. #14556048C22semidirect
49. #14556039C22semidirect
50. #14556038C22semidirect
51. C8×Dic71C22semidirect
52. #125×C71C22semidirect
54. #103×C71C22semidirect
55. #103×C71C22semidirect
58. C4×C8×C71C22semidirect
184. C71#3136semidirect
192. #488D71semidirect
211. #125C2×D71semidirect
225. #103C2×D71semidirect
226. #103C2×D71semidirect
242. C4×C8C2×D71semidirect