Finite Group Databasebeta

← #22598581

Subgroups — #22598581

Order 9088.

418 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17986603C211yesmaximal, characteristic, complemented
2#17986471C211yesmaximal, characteristic, complemented
3#17986322C211yesmaximal, characteristic, complemented
4#17986321C211yesmaximal, characteristic, complemented
5#17986300C211yesmaximal, characteristic, complemented
6#17986299C211yesmaximal, characteristic, complemented
7#17986191C211yesmaximal, characteristic, complemented
8#17986131C211yesmaximal, characteristic, complemented
9#17986131C211yesmaximal, characteristic, complemented
10#17986111C211yesmaximal, characteristic, complemented
11#17986108C211yesmaximal, characteristic, complemented
12D8×Dic71C211yesmaximal, characteristic, complemented
13#17986079C211yesmaximal, characteristic, complemented
14#17986059C211yesmaximal, characteristic, complemented
15#459×C71C211yesmaximal, characteristic, complemented
16C2×D4×D71C2211yescharacteristic
17C2×#11765850C2211yescharacteristic
18C2×#11765850C2211yescharacteristic
19#14556120C2211yescharacteristic, complemented
20#14556109—21no—
21#14556109—21no—
22#14556100—21no—
23#14556100—21no—
24#14556099C2211yescharacteristic
25#14556099C2211yescharacteristic
26C4×D284C2211yescharacteristic
27D4×Dic71C2211yescharacteristic
28D4×Dic71C2211yescharacteristic, complemented
29D4×Dic71C2211yescharacteristic, complemented
30#14556090C2211yescharacteristic
31C4×C22⋊D71—21no—
32(C22⋊D71)⋊C4—21no—
33#14556086C2211yescharacteristic
34#14556085C2211yescharacteristic
35C2×(C2×D71)⋊C4—21no—
36C22⋊C4×D71—21no—
37#14556062C2211yescharacteristic, complemented
38#14556061C2211yescharacteristic, complemented
39#14556060C2211yescharacteristic, complemented
40#14556059C2211yescharacteristic, complemented
41C4⋊(C71⋊C8)C2211yescharacteristic, complemented
42#14556050C2211yescharacteristic
43#14556050C2211yescharacteristic
44#14556049C2211yescharacteristic
45#14556049C2211yescharacteristic
46#14556049C2211yescharacteristic, complemented
47#14556049C2211yescharacteristic, complemented
48(C2×D71)⋊C8C2211yescharacteristic
49(C2×D71)⋊C8C2211yescharacteristic
50#14556038C2211yescharacteristic, complemented
51C8×Dic71C2211yescharacteristic, complemented
52C2×D8×C71C2211yescharacteristic
53C2×D8×C71C2211yescharacteristic
54#127×C71C2211yescharacteristic, complemented
55C4×D4×C71C2211yescharacteristic
56C4⋊C8×C71C2211yescharacteristic, complemented
57#102×C71C2211yescharacteristic, complemented
58#102×C71C2211yescharacteristic, complemented
59C23×D71—21no—
60C2×D284C2311yescharacteristic
61C2×C22⋊D71—21no—
62C2×C22⋊D71—21no—
63C2×C22⋊D71—21no—
64D4×D71—22no—
65D4×D71—22no—
66C22×Dic71—21no—
67C22×Dic71—21no—
68C22×Dic71—21no—
69C2×C4×D71—21no—
70C2×C4×D71—21no—
71C2×C4×D71C2311yescharacteristic
72#11765850—22no—
73#11765850—22no—
74C2×C71⋊C8C2311yescharacteristic
75C2×C71⋊C8C2311yescharacteristic
76C4⋊Dic71C2311yescharacteristic
77C4⋊Dic71C2311yescharacteristic
78C4⋊Dic71C2311yescharacteristic
79Dic71⋊C4—21no—
80Dic71⋊C4—21no—
81Dic71⋊C4D411yescharacteristic
82Dic71⋊C4D411yescharacteristic
83C22⋊Dic71—21no—
84C22⋊Dic71—21no—
85C22⋊Dic71—21no—
86C22⋊Dic71—21no—
87C22⋊Dic71—21no—
88(C2×D71)⋊C4—21no—
89(C2×D71)⋊C4—21no—
90(C2×D71)⋊C4—21no—
91(C2×D71)⋊C4D411yescharacteristic
92(C2×D71)⋊C4D411yescharacteristic
93C4×Dic71—21no—
94C4×Dic71C2311yescharacteristic
95C2×D4×C71—21no—
96C2×D4×C71—21no—
97C2×D4×C71C2311yescharacteristic
98C2×D4×C71C2311yescharacteristic
99C2×D4×C71C2311yescharacteristic
100C22×C4×C71—21no—
101D8×C71—22no—
102D8×C71—22no—
103C2×C8×C71C2311yescharacteristic
104C2×C8×C71C2311yescharacteristic
105C4⋊C4×C71C2311yescharacteristic
106C22⋊C4×C71—21no—
107C42×C71C2311yescharacteristic
108C23×C71—21no—
109C23×C71—21no—
110C23×C71—21no—
111C22×D71—21no—
112C22×D71—24no—
113C22×D71—81no—
114C22×D71—81no—
115C22×D71C2×D411yescharacteristic
116D4×C71—21no—
117D4×C71—21no—
118D4×C71—21no—
119D4×C71—21no—
120D4×C71—21no—
121D4×C71—81no—
122D4×C71—81no—
123D4×C71#4112yes—
124C2×C4×C71—21no—
125C2×C4×C71—81no—
126C2×C4×C71C2×D411yescharacteristic
127C2×C4×C71C2×D411yescharacteristic
128C2×C4×C71C2411yescharacteristic
129C22⋊D71—24no—
130C22⋊D71—81no—
131C22⋊D71—81no—
132C2×Dic71—21no—
133C2×Dic71—21no—
134C2×Dic71—21no—
135C2×Dic71—81no—
136C2×Dic71—81no—
137C2×Dic71—81no—
138C2×Dic71C2×D411yescharacteristic
139C2×Dic71C2×D411yescharacteristic
140C2×Dic71C2×D411yescharacteristic
141D284—21no—
142D284#4112yes—
143C4×D71—21no—
144C4×D71—21no—
145C4×D71—81no—
146C4×D71—81no—
147C8×C71—21no—
148C8×C71—21no—
149C71⋊C8—21no—
150C71⋊C8—21no—
151C22×C71—22no—
152C22×C71—41no—
153C22×C71—41no—
154C22×C71—41no—
155C22×C71—41no—
156C22×C71—41no—
157C22×C71—41no—
158C22×C71—41no—
159C22×C71—41no—
160C22×C71C22×D411yescharacteristic
161C2×D71—21no—
162C2×D71—22no—
163C2×D71—21no—
164C2×D71—21no—
165C2×D71—41no—
166C2×D71—41no—
167C2×D71—84no—
168C4×C71—21no—
169C4×C71—21no—
170C4×C71—41no—
171C4×C71C2×#4111yescharacteristic
172C4×C71C2×#4111yescharacteristic
173Dic71—21no—
174Dic71—21no—
175Dic71—21no—
176Dic71—41no—
177Dic71—41no—
178Dic71—41no—
179C2×C71—42no—
180C2×C71—81no—
181C2×C71—81no—
182C2×C71#52511yescharacteristic
183C2×C71#57611yescharacteristic
184C2×C71#57611yescharacteristic
185D71—41no—
186D71—42no—
187#3122—711nomaximal, Sylow
188C71#312211yescharacteristic, complemented, Sylow
189#540—711no—
190#518—711no—
191#482—711no—
192#482—711no—
193#478—711no—
194#478—711no—
195#459—711no—
196#459D7111yescharacteristic, complemented
197#447—711no—
198#447—711no—
199#442—711no—
200#442—711no—
201C4×D8—711no—
202C4×D8—711no—
203#433—711no—
204C22×D4—711no—
205C2×D8—711no—
206C2×D8—711no—
207C2×D8C2×D7111yescharacteristic
208C2×D8C2×D7111yescharacteristic
209#127C2×D7111yescharacteristic, complemented
210#125—711no—
211#123—1421no—
212#123—1421no—
213#121—711no—
214#121—711no—
215#121—1421no—
216#121—1421no—
217C4×D4—711no—
218C4×D4—711no—
219C4×D4—711no—
220C4×D4—711no—
221C4×D4—711no—
222C4×D4—1421no—
223C4×D4—1421no—
224C4×D4C2×D7111yescharacteristic
225#117—711no—
226#117—711no—
227C2×C22⋊C4—1421no—
228C2×C22⋊C4—1421no—
229#107—711no—
230#107—711no—
231#106—711no—
232#106—711no—
233C4⋊C8—711no—
234C4⋊C8C2×D7111yescharacteristic, complemented
235#102—711no—
236#102—711no—
237#102—711no—
238#102—711no—
239#102—711no—
240#102—711no—
241#102C2×D7111yescharacteristic, complemented
242#102C2×D7111yescharacteristic, complemented
243C22⋊C8—711no—
244C22⋊C8—711no—
245#97—711no—
246C4×C8—711no—
247C24—1421no—
248C2×D4—21no—
249C2×D4—21no—
250C2×D4—711no—
251C2×D4—1421no—
252C2×D4—1422no—
253C2×D4—1421no—
254C2×D4—1421no—
255C2×D4—1422no—
256C2×D4C22×D7111yescharacteristic
257C2×D4C22×D7111yescharacteristic
258C2×D4C22×D7111yescharacteristic
259C22×C4—21no—
260C22×C4—711no—
261C22×C4—1421no—
262C22×C4—1421no—
263C22×C4—1421no—
264C22×C4—1421no—
265C22×C4—1421no—
266D8—22no—
267D8—22no—
268D8—1422no—
269D8—1422no—
270C2×C8—711no—
271C2×C8—711no—
272C2×C8C22×D7111yescharacteristic
273C2×C8C22×D7111yescharacteristic
274C4⋊C4—711no—
275C4⋊C4—711no—
276C4⋊C4—711no—
277C4⋊C4—711no—
278C4⋊C4—711no—
279C4⋊C4—1421no—
280C4⋊C4—1421no—
281C4⋊C4C22×D7111yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—711no—
284C22⋊C4—711no—
285C22⋊C4—1421no—
286C22⋊C4—1421no—
287C22⋊C4—1421no—
288C22⋊C4—1421no—
289C22⋊C4—1421no—
290C22⋊C4—1421no—
291C22⋊C4—1421no—
292C22⋊C4—1421no—
293C42—711no—
294C42—1421no—
295C42C22×D7111yescharacteristic
296C23—21no—
297C23—21no—
298C23—21no—
299C23—5681no—
300C23—5681no—
301C23—711no—
302C23—1424no—
303C23—1421no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—81no—
310D4—81no—
311D4—5681no—
312D4—5681no—
313D4—712no—
314D4—1424no—
315D4—1421no—
316D4#1176586412yes—
317C2×C4—21no—
318C2×C4—81no—
319C2×C4—5681no—
320C2×C4—5681no—
321C2×C4—5681no—
322C2×C4—5681no—
323C2×C4—5681no—
324C2×C4—711no—
325C2×C4—711no—
326C2×C4—711no—
327C2×C4—1421no—
328C2×C4—1421no—
329C2×C4—1421no—
330C2×C4—1421no—
331C2×C4—1421no—
332C2×C4D4×D7111yescharacteristic
333C2×C4D4×D7111yescharacteristic
334C2×C4C23×D7111yescharacteristic
335C8—21no—
336C8—21no—
337C8—1421no—
338C8—1421no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—2841no—
349C22—2841no—
350C22—5684no—
351C22—1421no—
352C22—1422no—
353C22—1421no—
354C22—1421no—
355C22C2×D4×D7111yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—2841no—
360C4—2841no—
361C4—2841no—
362C4—1421no—
363C4—1421no—
364C4—1421no—
365C4#41×D7111yescharacteristic
366C4C2×#1176586411yescharacteristic
367C2—42no—
368C2—81no—
369C2—81no—
370C2—2842no—
371C2—2841no—
372C2#1798650911yescharacteristic
373C2#1798680011yescharacteristic
374C2#1798680311yescharacteristic
subgroupG/H
centerC22C2×D4×D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#459×C71C2
socleC22×C71C22×D4
hypercenter#459D71
hypocenterC71#3122
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #17986603C2semidirect
2. #17986471C2semidirect
3. #17986322C2semidirect
4. #17986321C2semidirect
5. #17986300C2semidirect
6. #17986299C2semidirect
7. #17986191C2semidirect
8. #17986131C2semidirect
9. #17986131C2semidirect
10. #17986111C2semidirect
11. #17986108C2semidirect
12. D8×Dic71C2semidirect
13. #17986079C2semidirect
14. #17986059C2semidirect
15. #459×C71C2semidirect
19. #14556120C22semidirect
28. D4×Dic71C22semidirect
29. D4×Dic71C22semidirect
37. #14556062C22semidirect
38. #14556061C22semidirect
39. #14556060C22semidirect
40. #14556059C22semidirect
41. C4⋊(C71⋊C8)C22semidirect
46. #14556049C22semidirect
47. #14556049C22semidirect
50. #14556038C22semidirect
51. C8×Dic71C22semidirect
54. #127×C71C22semidirect
56. C4⋊C8×C71C22semidirect
57. #102×C71C22semidirect
58. #102×C71C22semidirect
188. C71#3122semidirect
196. #459D71semidirect
209. #127C2×D71semidirect
234. C4⋊C8C2×D71semidirect
241. #102C2×D71semidirect
242. #102C2×D71semidirect