Finite Group Databasebeta

← #22598518

Subgroups — #22598518

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#17986473C211yesmaximal, characteristic, complemented
2#17986337C211yesmaximal, characteristic, complemented
3#17986320C211yesmaximal, characteristic, complemented
4#17986286C211yesmaximal, characteristic, complemented
5#17986276C211yesmaximal, characteristic, complemented
6#17986211C211yesmaximal, characteristic, complemented
7#17986211C211yesmaximal, characteristic, complemented
8#17986149C211yesmaximal, characteristic, complemented
9#17986132C211yesmaximal, characteristic
10#17986109C211yesmaximal, characteristic, complemented
11#17986097C211yesmaximal, characteristic, complemented
12C4×#11765852C211yesmaximal, characteristic, complemented
13C4×#11765850C211yesmaximal, characteristic, complemented
14#17986060C211yesmaximal, characteristic, complemented
15#542×C71C211yesmaximal, characteristic, complemented
16C22×D284C2211yescharacteristic
17C2×#11765852C2211yescharacteristic
18C2×#11765852C2211yescharacteristic
19C2×#11765850C2211yescharacteristic
20C2×#11765850C2211yescharacteristic
21C4×D284C2211yescharacteristic
22C4×D284C2211yescharacteristic
23C4×D284C2211yescharacteristic
24C4×D284C2211yescharacteristic
25#14556090—21no—
26#14556090—21no—
27#14556087C2211yescharacteristic
28C22⋊C4×D71—21no—
29C22⋊C4×D71—21no—
30#14556061C2211yescharacteristic, complemented
31#14556061C2211yescharacteristic, complemented
32#14556059C2211yescharacteristic, complemented
33#14556059C2211yescharacteristic, complemented
34C4⋊(C71⋊C8)C2211yescharacteristic, complemented
35C4⋊(C71⋊C8)C2211yescharacteristic, complemented
36#14556052C2211yescharacteristic, complemented
37#14556052C2211yescharacteristic, complemented
38#14556049C2211yescharacteristic, complemented
39#14556049C2211yescharacteristic, complemented
40#14556048C2211yescharacteristic
41#14556048C2211yescharacteristic
42#14556048C2211yescharacteristic
43#14556048C2211yescharacteristic
44C22⋊(C71⋊C8)C2211yescharacteristic
45C22⋊(C71⋊C8)C2211yescharacteristic
46#14556039C2211yescharacteristic, complemented
47C4×C71⋊C8C2211yescharacteristic, complemented
48C4⋊Q8×C71C2211yescharacteristic, complemented
49#126×C71—21no—
50#124×C71—21no—
51#124×C71C2211yescharacteristic, complemented
52#123×C71—21no—
53C22⋊Q8×C71—21no—
54C22⋊Q8×C71C2211yescharacteristic
55#121×C71C2211yescharacteristic
56C4×Q8×C71C2211yescharacteristic, complemented
57C4×D4×C71C2211yescharacteristic, complemented
58#117×C71C2211yescharacteristic
59C23×D71—21no—
60C2×D284—21no—
61C2×D284—22no—
62C2×D284—22no—
63C2×D284C2311yescharacteristic
64C2×D284C2311yescharacteristic
65C2×C4×D71—21no—
66C2×C4×D71—21no—
67C2×C4×D71—21no—
68C2×C4×D71—21no—
69#11765852—22no—
70#11765852—22no—
71#11765850—22no—
72#11765850—22no—
73C2×C71⋊C8C2311yescharacteristic
74C2×C71⋊C8C2311yescharacteristic
75C2×C71⋊C8C2311yescharacteristic
76C2×C71⋊C8C2311yescharacteristic
77C4⋊Dic71C2311yescharacteristic
78C4⋊Dic71C2311yescharacteristic
79C22⋊Dic71—21no—
80(C2×D71)⋊C4—21no—
81(C2×D71)⋊C4—21no—
82(C2×D71)⋊C4—21no—
83(C2×D71)⋊C4—21no—
84C4×Dic71—21no—
85C2×Q8×C71—21no—
86C2×Q8×C71C2311yescharacteristic
87C2×D4×C71—21no—
88C2×D4×C71C2311yescharacteristic
89C22×C4×C71—21no—
90C22×C4×C71C2311yescharacteristic
91C4⋊C4×C71—21no—
92C4⋊C4×C71—21no—
93C4⋊C4×C71—21no—
94C4⋊C4×C71D411yescharacteristic
95C4⋊C4×C71D411yescharacteristic
96C4⋊C4×C71C2311yescharacteristic
97C4⋊C4×C71C2311yescharacteristic
98C22⋊C4×C71—21no—
99C22⋊C4×C71—21no—
100C22⋊C4×C71—21no—
101C22⋊C4×C71—21no—
102C22⋊C4×C71—21no—
103C22⋊C4×C71D411yescharacteristic
104C22⋊C4×C71D411yescharacteristic
105C42×C71—21no—
106C42×C71C2311yescharacteristic
107C42×C71C2311yescharacteristic
108C23×C71—21no—
109C23×C71C2×D411yescharacteristic
110C22×D71—21no—
111C22×D71—21no—
112C22×D71—24no—
113C22×D71—81no—
114C22×D71—81no—
115Q8×C71—21no—
116Q8×C71—21no—
117Q8×C71—81no—
118D4×C71—21no—
119D4×C71—21no—
120D4×C71—81no—
121C2×C4×C71—21no—
122C2×C4×C71—21no—
123C2×C4×C71—21no—
124C2×C4×C71—21no—
125C2×C4×C71—21no—
126C2×C4×C71—81no—
127C2×C4×C71C2×D411yescharacteristic
128C2×C4×C71C2×D411yescharacteristic
129C2×C4×C71C2×D411yescharacteristic
130C2×C4×C71C2×D411yescharacteristic
131C2×C4×C71C2×D411yescharacteristic
132C2×C4×C71C2411yescharacteristic
133C2×Dic71—21no—
134C2×Dic71—21no—
135D284—24no—
136D284—21no—
137D284—21no—
138D284#4112yes—
139D284#4112yes—
140C4×D71—81no—
141C4×D71—81no—
142C4×D71—81no—
143C4×D71—81no—
144C71⋊C8—21no—
145C71⋊C8—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—21no—
164C4×C71—21no—
165C4×C71—21no—
166C4×C71—21no—
167C4×C71—41no—
168C4×C71—41no—
169C4×C71—41no—
170C4×C71C2×#4111yescharacteristic
171C4×C71C2×#4111yescharacteristic
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#542D7111yescharacteristic, complemented
184#518—711no—
185#485—711no—
186#482—711no—
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⋊Q8C2×D7111yescharacteristic, complemented
204#126—21no—
205#124—21no—
206#124C2×D7111yescharacteristic, complemented
207#123—21no—
208C22⋊Q8—21no—
209C22⋊Q8C2×D7111yescharacteristic
210#121C2×D7111yescharacteristic
211C4×Q8C2×D7111yescharacteristic, complemented
212C4×D4—711no—
213C4×D4—711no—
214C4×D4—711no—
215C4×D4—711no—
216C4×D4—1421no—
217C4×D4—1421no—
218C4×D4C2×D7111yescharacteristic, complemented
219#117—711no—
220#117C2×D7111yescharacteristic
221C2×C22⋊C4—1421no—
222C2×C22⋊C4—1421no—
223#107—711no—
224#107—711no—
225#106—711no—
226#106—711no—
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#102—711no—
236#102—711no—
237C22⋊C8—711no—
238C22⋊C8—711no—
239#97—711no—
240C4×C8—711no—
241C24—1421no—
242C2×Q8—21no—
243C2×Q8C22×D7111yescharacteristic
244C2×D4—21no—
245C2×D4—711no—
246C2×D4—711no—
247C2×D4—1422no—
248C2×D4—1422no—
249C2×D4—1421no—
250C2×D4C22×D7111yescharacteristic
251C22×C4—21no—
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×C8—711no—
264C2×C8—711no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—711no—
269C4⋊C4—711no—
270C4⋊C4C22⋊D7111yescharacteristic
271C4⋊C4C22⋊D7111yescharacteristic
272C4⋊C4C22×D7111yescharacteristic
273C4⋊C4C22×D7111yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—1421no—
280C22⋊C4—1421no—
281C22⋊C4—1421no—
282C22⋊C4—1421no—
283C22⋊C4—1421no—
284C22⋊C4C22⋊D7111yescharacteristic
285C22⋊C4C22⋊D7111yescharacteristic
286C42—21no—
287C42—1421no—
288C42C22×D7111yescharacteristic
289C42C22×D7111yescharacteristic
290C23—21no—
291C23—5681no—
292C23—5681no—
293C23—1424no—
294C23—1421no—
295C23—1421no—
296C23C2×C22⋊D7111yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—81no—
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—81no—
314C2×C4—5681no—
315C2×C4—5681no—
316C2×C4—5681no—
317C2×C4—5681no—
318C2×C4—1421no—
319C2×C4—1421no—
320C2×C4C2×C22⋊D7111yescharacteristic
321C2×C4C2×C22⋊D7111yescharacteristic
322C2×C4C2×C22⋊D7111yescharacteristic
323C2×C4C2×C22⋊D7111yescharacteristic
324C2×C4C2×C22⋊D7111yescharacteristic
325C2×C4C23×D7111yescharacteristic
326C8—1421no—
327C8—1421no—
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—
343C22C22×C22⋊D7111yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—2841no—
353C4—2841no—
354C4#41×D7111yescharacteristic
355C4#41×D7111yescharacteristic
356C2—41no—
357C2—81no—
358C2—2842no—
359C2—2842no—
360C2#1798650611yescharacteristic
361C2#1798680211yescharacteristic
362C2#1798680711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#542×C71C2
socleC22×C71C22×D4
hypercenter#542D71
hypocenterC71#3118
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #17986473C2semidirect
2. #17986337C2semidirect
3. #17986320C2semidirect
4. #17986286C2semidirect
5. #17986276C2semidirect
6. #17986211C2semidirect
7. #17986211C2semidirect
8. #17986149C2semidirect
10. #17986109C2semidirect
11. #17986097C2semidirect
12. C4×#11765852C2semidirect
13. C4×#11765850C2semidirect
14. #17986060C2semidirect
15. #542×C71C2semidirect
30. #14556061C22semidirect
31. #14556061C22semidirect
32. #14556059C22semidirect
33. #14556059C22semidirect
34. C4⋊(C71⋊C8)C22semidirect
35. C4⋊(C71⋊C8)C22semidirect
36. #14556052C22semidirect
37. #14556052C22semidirect
38. #14556049C22semidirect
39. #14556049C22semidirect
46. #14556039C22semidirect
47. C4×C71⋊C8C22semidirect
48. C4⋊Q8×C71C22semidirect
51. #124×C71C22semidirect
56. C4×Q8×C71C22semidirect
57. C4×D4×C71C22semidirect
182. C71#3118semidirect
183. #542D71semidirect
203. C4⋊Q8C2×D71semidirect
206. #124C2×D71semidirect
211. C4×Q8C2×D71semidirect
218. C4×D4C2×D71semidirect