Finite Group Databasebeta

← #22598519

Subgroups — #22598519

Order 9088.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17986616C211yesmaximal, characteristic, complemented
2#17986473C211yesmaximal, characteristic, complemented
3#17986340C211yesmaximal, characteristic, complemented
4#17986288C211yesmaximal, characteristic, complemented
5#17986278C211yesmaximal, characteristic, complemented
6#17986213C211yesmaximal, characteristic, complemented
7#17986213C211yesmaximal, characteristic, complemented
8#17986152C211yesmaximal, characteristic, complemented
9#17986132C211yesmaximal, characteristic
10#17986108C211yesmaximal, characteristic, complemented
11#17986098C211yesmaximal, characteristic, complemented
12#17986086C211yesmaximal, characteristic, complemented
13#17986079C211yesmaximal, characteristic, complemented
14#17986057C211yesmaximal, characteristic, complemented
15#482×C71C211yesmaximal, characteristic, complemented
16C22×D284C2211yescharacteristic
17C2×#11765854C2211yescharacteristic
18C2×#11765854C2211yescharacteristic
19C2×#11765850C2211yescharacteristic
20C2×#11765850C2211yescharacteristic
21#14556127C2211yescharacteristic, complemented
22#14556121—21no—
23#14556115—21no—
24#14556115C2211yescharacteristic, complemented
25#14556109—21no—
26#14556107C2211yescharacteristic
27#14556105—21no—
28#14556093C2211yescharacteristic, complemented
29C4×D284—21no—
30C4×D284—21no—
31D4×Dic71C2211yescharacteristic, complemented
32#14556090C2211yescharacteristic
33#14556090C2211yescharacteristic
34#14556090C2211yescharacteristic
35#14556090C2211yescharacteristic
36#14556087C2211yescharacteristic
37C22⋊C4×D71—21no—
38C22⋊C4×D71—21no—
39#14556061C2211yescharacteristic, complemented
40#14556059C2211yescharacteristic, complemented
41Dic71⋊C8C2211yescharacteristic, complemented
42Dic71⋊C8C2211yescharacteristic, complemented
43#14556051C2211yescharacteristic, complemented
44#14556051C2211yescharacteristic, complemented
45#14556050C2211yescharacteristic
46#14556050C2211yescharacteristic
47#14556048C2211yescharacteristic
48#14556048C2211yescharacteristic
49C22⋊(C71⋊C8)C2211yescharacteristic
50#14556038C2211yescharacteristic, complemented
51C8×Dic71C2211yescharacteristic, complemented
52#121×C71C2211yescharacteristic
53#117×C71C2211yescharacteristic
54#107×C71C2211yescharacteristic, complemented
55#106×C71C2211yescharacteristic, complemented
56#102×C71C2211yescharacteristic, complemented
57#102×C71C2211yescharacteristic, complemented
58C22⋊C8×C71C2211yescharacteristic
59C23×D71—21no—
60C2×Dic142—21no—
61C2×Dic142C2311yescharacteristic
62C2×D284—21no—
63C2×D284—22no—
64C2×D284—22no—
65C2×D284C2311yescharacteristic
66C2×D284C2311yescharacteristic
67C22×Dic71—21no—
68C2×C4×D71—21no—
69C2×C4×D71—21no—
70C2×C4×D71—21no—
71C2×C4×D71—21no—
72#11765854—22no—
73#11765854—22no—
74#11765850—22no—
75#11765850—22no—
76C2×C71⋊C8C2311yescharacteristic
77C2×C71⋊C8C2311yescharacteristic
78C4⋊Dic71D411yescharacteristic
79C4⋊Dic71D411yescharacteristic
80C4⋊Dic71C2311yescharacteristic
81Dic71⋊C4—21no—
82Dic71⋊C4—21no—
83Dic71⋊C4—21no—
84C22⋊Dic71—21no—
85C22⋊Dic71—21no—
86C22⋊Dic71—21no—
87C22⋊Dic71—21no—
88C22⋊Dic71D411yescharacteristic
89C22⋊Dic71D411yescharacteristic
90(C2×D71)⋊C4—21no—
91(C2×D71)⋊C4—21no—
92(C2×D71)⋊C4—21no—
93(C2×D71)⋊C4—21no—
94C4×Dic71—21no—
95C4×Dic71C2311yescharacteristic
96C4×Dic71C2311yescharacteristic
97C2×D4×C71—21no—
98C2×D4×C71C2311yescharacteristic
99C22×C4×C71C2311yescharacteristic
100C2×C8×C71C2311yescharacteristic
101C2×C8×C71C2311yescharacteristic
102C4⋊C4×C71C2311yescharacteristic
103C4⋊C4×C71C2311yescharacteristic
104C4⋊C4×C71C2311yescharacteristic
105C22⋊C4×C71—21no—
106C22⋊C4×C71—21no—
107C42×C71—21no—
108C23×C71—21no—
109C23×C71C2×D411yescharacteristic
110C22×D71—21no—
111C22×D71—21no—
112C22×D71—24no—
113C22×D71—81no—
114C22×D71—81no—
115D4×C71—21no—
116D4×C71—21no—
117D4×C71—81no—
118C2×C4×C71—21no—
119C2×C4×C71—21no—
120C2×C4×C71—21no—
121C2×C4×C71—21no—
122C2×C4×C71—21no—
123C2×C4×C71C2×D411yescharacteristic
124C2×C4×C71C2411yescharacteristic
125C2×Dic71—21no—
126C2×Dic71—21no—
127C2×Dic71—81no—
128C2×Dic71C2×D411yescharacteristic
129C2×Dic71C2×D411yescharacteristic
130C2×Dic71C2×D411yescharacteristic
131C2×Dic71C2×D411yescharacteristic
132D284—24no—
133D284—21no—
134D284—21no—
135D284#4112yes—
136D284#4112yes—
137C4×D71—81no—
138C4×D71—81no—
139C4×D71—81no—
140C4×D71—81no—
141Dic142—21no—
142Dic142—21no—
143Dic142—81no—
144C8×C71—21no—
145C8×C71—21no—
146C71⋊C8—21no—
147C71⋊C8—21no—
148C22×C71—21no—
149C22×C71—21no—
150C22×C71—21no—
151C22×C71—41no—
152C22×C71—41no—
153C22×C71—41no—
154C22×C71C22×D411yescharacteristic
155C2×D71—22no—
156C2×D71—22no—
157C2×D71—41no—
158C2×D71—41no—
159C2×D71—41no—
160C2×D71—41no—
161C2×D71—84no—
162C4×C71—21no—
163C4×C71—41no—
164C4×C71—41no—
165C4×C71—41no—
166C4×C71C2×#4111yescharacteristic
167C4×C71C2×#4111yescharacteristic
168Dic71—21no—
169Dic71—21no—
170Dic71—21no—
171Dic71—21no—
172Dic71—41no—
173Dic71—41no—
174C2×C71—41no—
175C2×C71—81no—
176C2×C71#52511yescharacteristic
177C2×C71#57611yescharacteristic
178C2×C71#57711yescharacteristic
179D71—42no—
180D71—42no—
181#3118—711nomaximal, Sylow
182C71#311811yescharacteristic, complemented, Sylow
183#542—711no—
184#518—711no—
185#485—711no—
186#482D7111yescharacteristic, complemented
187#476—711no—
188#474—711no—
189#463—711no—
190#463—711no—
191#450—711no—
192#447—711no—
193#442—711no—
194#440—711no—
195C4×SD16—711no—
196C4×D8—711no—
197#433—711no—
198C22×D4—711no—
199C2×SD16—711no—
200C2×SD16—711no—
201C2×D8—711no—
202C2×D8—711no—
203C4⋊Q8—711no—
204#126—1421no—
205#124—711no—
206#124—1421no—
207#123—1421no—
208C22⋊Q8—711no—
209C22⋊Q8—1421no—
210#121C2×D7111yescharacteristic
211C4×Q8—711no—
212C4×D4—711no—
213C4×D4—711no—
214C4×D4—711no—
215C4×D4—711no—
216C4×D4—711no—
217C4×D4—1421no—
218C4×D4—1421no—
219#117—711no—
220#117C2×D7111yescharacteristic
221C2×C22⋊C4—1421no—
222C2×C22⋊C4—1421no—
223#107—711no—
224#107C2×D7111yescharacteristic, complemented
225#106—711no—
226#106C2×D7111yescharacteristic, complemented
227C4⋊C8—711no—
228C4⋊C8—711no—
229#103—711no—
230#103—711no—
231#102—711no—
232#102—711no—
233#102—711no—
234#102—711no—
235#102C2×D7111yescharacteristic, complemented
236#102C2×D7111yescharacteristic, complemented
237C22⋊C8—711no—
238C22⋊C8C2×D7111yescharacteristic
239#97—711no—
240C4×C8—711no—
241C24—1421no—
242C2×Q8—711no—
243C2×Q8—1421no—
244C2×D4—21no—
245C2×D4—711no—
246C2×D4—711no—
247C2×D4—1422no—
248C2×D4—1422no—
249C2×D4—1421no—
250C2×D4C22×D7111yescharacteristic
251C22×C4—1421no—
252C22×C4—1421no—
253C22×C4—1421no—
254C22×C4—1421no—
255C22×C4—1421no—
256C22×C4C22×D7111yescharacteristic
257SD16—1422no—
258SD16—1422no—
259D8—1422no—
260D8—1422no—
261C2×C8—711no—
262C2×C8—711no—
263C2×C8C22×D7111yescharacteristic
264C2×C8C22×D7111yescharacteristic
265C4⋊C4—711no—
266C4⋊C4—711no—
267C4⋊C4—711no—
268C4⋊C4—1421no—
269C4⋊C4—1421no—
270C4⋊C4—1421no—
271C4⋊C4C22×D7111yescharacteristic
272C4⋊C4C22×D7111yescharacteristic
273C4⋊C4C22×D7111yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—711no—
277C22⋊C4—711no—
278C22⋊C4—1421no—
279C22⋊C4—1421no—
280C22⋊C4—1421no—
281C22⋊C4—1421no—
282C22⋊C4—1421no—
283C22⋊C4—1421no—
284C22⋊C4—1421no—
285C22⋊C4—1421no—
286C42—21no—
287C42—711no—
288C42—711no—
289C42—1421no—
290C23—21no—
291C23—5681no—
292C23—5681no—
293C23—1424no—
294C23—1421no—
295C23—1421no—
296C23D4×D7111yescharacteristic
297Q8—5681no—
298Q8—1421no—
299Q8—1421no—
300D4—21no—
301D4—21no—
302D4—81no—
303D4—712no—
304D4—712no—
305D4—1424no—
306D4—1421no—
307D4—1421no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—5681no—
314C2×C4—5681no—
315C2×C4—5681no—
316C2×C4—5681no—
317C2×C4—5681no—
318C2×C4—711no—
319C2×C4—711no—
320C2×C4—711no—
321C2×C4—711no—
322C2×C4—1421no—
323C2×C4—1421no—
324C2×C4D4×D7111yescharacteristic
325C2×C4C23×D7111yescharacteristic
326C8—21no—
327C8—21no—
328C8—1421no—
329C8—1421no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—2841no—
337C22—2841no—
338C22—2841no—
339C22—2841no—
340C22—5684no—
341C22—1422no—
342C22—1422no—
343C22C2×D4×D7111yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—2841no—
349C4—2841no—
350C4—1421no—
351C4—1421no—
352C4—1421no—
353C4—1421no—
354C4#41×D7111yescharacteristic
355C4#41×D7111yescharacteristic
356C2—41no—
357C2—81no—
358C2—2842no—
359C2—2842no—
360C2#1798650711yescharacteristic
361C2#1798680311yescharacteristic
362C2#1798680611yescharacteristic
subgroupG/H
centerC22C2×D4×D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#482×C71C2
socleC22×C71C22×D4
hypercenter#482D71
hypocenterC71#3118
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #17986616C2semidirect
2. #17986473C2semidirect
3. #17986340C2semidirect
4. #17986288C2semidirect
5. #17986278C2semidirect
6. #17986213C2semidirect
7. #17986213C2semidirect
8. #17986152C2semidirect
10. #17986108C2semidirect
11. #17986098C2semidirect
12. #17986086C2semidirect
13. #17986079C2semidirect
14. #17986057C2semidirect
15. #482×C71C2semidirect
21. #14556127C22semidirect
24. #14556115C22semidirect
28. #14556093C22semidirect
31. D4×Dic71C22semidirect
39. #14556061C22semidirect
40. #14556059C22semidirect
41. Dic71⋊C8C22semidirect
42. Dic71⋊C8C22semidirect
43. #14556051C22semidirect
44. #14556051C22semidirect
50. #14556038C22semidirect
51. C8×Dic71C22semidirect
54. #107×C71C22semidirect
55. #106×C71C22semidirect
56. #102×C71C22semidirect
57. #102×C71C22semidirect
182. C71#3118semidirect
186. #482D71semidirect
224. #107C2×D71semidirect
226. #106C2×D71semidirect
235. #102C2×D71semidirect
236. #102C2×D71semidirect