Finite Group Databasebeta

← #22600423

Subgroups — #22600423

Order 9088.

410 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#17986706C211yesmaximal, characteristic, complemented
2#17986645C211yesmaximal, characteristic
3#17986359C211yesmaximal, characteristic, complemented
4#17986335C211yesmaximal, characteristic, complemented
5#17986313C211yesmaximal, characteristic, complemented
6#17986280C211yesmaximal, characteristic, complemented
7#17986245C211yesmaximal, characteristic, complemented
8#17986240C211yesmaximal, characteristic, complemented
9#17986222C211yesmaximal, characteristic, complemented
10#17986163C211yesmaximal, characteristic, complemented
11#17986152C211yesmaximal, characteristic, complemented
12#17986101C211yesmaximal, characteristic, complemented
13#17986001C211yesmaximal, characteristic, complemented
14C2×#14556050C211yesmaximal, characteristic, complemented
15#435×C71C211yesmaximal, characteristic, complemented
16C2×#11765865C2211yescharacteristic
17C22×D284C2211yescharacteristic
18C2×Dic284C2211yescharacteristic, complemented
19C2×#11765854C2211yescharacteristic
20C2×#11765854C2211yescharacteristic
21#14556128C2211yescharacteristic, complemented
22#14556119—21no—
23#14556116C2211yescharacteristic
24#14556113—21no—
25#14556107C2211yescharacteristic
26#14556107C2211yescharacteristic
27#14556107C2211yescharacteristic, complemented
28#14556105—21no—
29#14556105—21no—
30#14556102C2211yescharacteristic
31#14556101—21no—
32#14556096—21no—
33C4×Dic142C2211yescharacteristic, complemented
34C4×D284C2211yescharacteristic
35D4×Dic71—21no—
36C2×C4⋊Dic71C2211yescharacteristic
37C2×C4⋊Dic71C2211yescharacteristic, complemented
38C22⋊C4×D71—21no—
39#14556062C2211yescharacteristic, complemented
40#14556062C2211yescharacteristic, complemented
41#14556062C2211yescharacteristic, complemented
42#14556053C2211yescharacteristic, complemented
43#14556053C2211yescharacteristic, complemented
44#14556053C2211yescharacteristic, complemented
45#14556053C2211yescharacteristic, complemented
46#14556050C2211yescharacteristic
47#14556050C2211yescharacteristic
48#14556050C2211yescharacteristic
49#14556050C2211yescharacteristic
50#14556050C2211yescharacteristic
51#14556050C2211yescharacteristic
52C2×M16×C71C2211yescharacteristic, complemented
53C22×C8×C71C2211yescharacteristic
54C4×D4×C71C2211yescharacteristic
55C4⋊C8×C71C2211yescharacteristic, complemented
56C22⋊C8×C71C2211yescharacteristic
57C22⋊C8×C71C2211yescharacteristic, complemented
58#97×C71C2211yescharacteristic, complemented
59C23×D71—21no—
60#11765865—22no—
61#11765865—41no—
62C2×Dic142—21no—
63C2×Dic142C2311yescharacteristic
64C2×Dic142C2311yescharacteristic
65C2×D284—22no—
66C2×D284—21no—
67C2×D284—41no—
68C2×D284C2311yescharacteristic
69C2×D284C2311yescharacteristic
70C2×C22⋊D71—21no—
71C2×C22⋊D71—21no—
72C22×Dic71—21no—
73C22×Dic71—21no—
74C2×C4×D71—21no—
75C2×C4×D71—21no—
76Dic284—41no—
77#11765854—22no—
78#11765854—41no—
79C4⋊Dic71—21no—
80C4⋊Dic71—21no—
81C4⋊Dic71—21no—
82C4⋊Dic71C2311yescharacteristic
83C4⋊Dic71C2311yescharacteristic
84C4⋊Dic71C2311yescharacteristic
85C4⋊Dic71C2311yescharacteristic
86Dic71⋊C4—21no—
87Dic71⋊C4—21no—
88Dic71⋊C4—21no—
89Dic71⋊C4—21no—
90C22⋊Dic71—21no—
91C22⋊Dic71—21no—
92C22⋊Dic71—21no—
93(C2×D71)⋊C4—21no—
94(C2×D71)⋊C4—21no—
95(C2×D71)⋊C4—21no—
96(C2×D71)⋊C4—21no—
97C4×Dic71—21no—
98C2×D4×C71D411yescharacteristic
99C22×C4×C71C2311yescharacteristic
100C22×C4×C71C2311yescharacteristic
101M16×C71—41no—
102C2×C8×C71—41no—
103C2×C8×C71C2311yescharacteristic
104C2×C8×C71C2311yescharacteristic
105C2×C8×C71C2311yescharacteristic
106C2×C8×C71C2311yescharacteristic
107C4⋊C4×C71D411yescharacteristic
108C22⋊C4×C71D411yescharacteristic
109C22⋊C4×C71D411yescharacteristic
110C42×C71C2311yescharacteristic
111C23×C71C2×D411yescharacteristic
112C23×C71C2×D411yescharacteristic
113C22×D71—21no—
114C22×D71—21no—
115C22×D71—42no—
116C22×D71—42no—
117C22×D71—81no—
118D4×C71—22no—
119C2×C4×C71—21no—
120C2×C4×C71—21no—
121C2×C4×C71—21no—
122C2×C4×C71—21no—
123C2×C4×C71C2×D411yescharacteristic
124C2×C4×C71C2×D411yescharacteristic
125C2×C4×C71C2×D411yescharacteristic
126C2×C4×C71C2×D411yescharacteristic
127C2×C4×C71C2411yescharacteristic
128C22⋊D71—42no—
129C22⋊D71—81no—
130C2×Dic71—21no—
131C2×Dic71—21no—
132C2×Dic71—21no—
133C2×Dic71—21no—
134C2×Dic71—21no—
135C2×Dic71—21no—
136C2×Dic71—81no—
137C2×Dic71—81no—
138D284—21no—
139D284—21no—
140D284—21no—
141D284—42no—
142D284#4112yes—
143C4×D71—42no—
144C4×D71—81no—
145Dic142—21no—
146Dic142—21no—
147Dic142—21no—
148Dic142—21no—
149Dic142—81no—
150C8×C71—21no—
151C8×C71—21no—
152C8×C71—21no—
153C8×C71—21no—
154C22×C71—21no—
155C22×C71—21no—
156C22×C71—21no—
157C22×C71—21no—
158C22×C71—21no—
159C22×C71#13712yes—
160C22×C71C22×D411yescharacteristic
161C2×D71—22no—
162C2×D71—41no—
163C2×D71—41no—
164C2×D71—41no—
165C2×D71—41no—
166C2×D71—41no—
167C2×D71—84no—
168C4×C71—21no—
169C4×C71—21no—
170C4×C71—21no—
171C4×C71—21no—
172C4×C71C2×#4111yescharacteristic
173C4×C71H(5,𝔽2)11yescharacteristic
174Dic71—41no—
175Dic71—41no—
176Dic71—41no—
177Dic71—41no—
178Dic71—41no—
179Dic71—41no—
180C2×C71—22no—
181C2×C71—41no—
182C2×C71#54611yescharacteristic
183C2×C71C2×#13711yescharacteristic
184C2×C71#57611yescharacteristic
185D71—42no—
186D71—81no—
187#3314—711nomaximal, Sylow
188C71#331411yescharacteristic, complemented, Sylow
189#554—711no—
190#546—711no—
191#489—711no—
192#484—711no—
193#480—711no—
194#474—711no—
195#468—711no—
196#467—711no—
197#464—711no—
198#452—711no—
199#450—711no—
200#440—711no—
201#435D7111yescharacteristic, complemented
202#417—711no—
203C2×#102—711no—
204C2×#41—711no—
205C22×D4—711no—
206C2×Q16—711no—
207C2×SD16—711no—
208C2×SD16—711no—
209C2×M16C2×D7111yescharacteristic, complemented
210C22×C8C2×D7111yescharacteristic
211C4⋊Q8—711no—
212#125—1421no—
213#124—711no—
214#123—1421no—
215C22⋊Q8—711no—
216C22⋊Q8—711no—
217C22⋊Q8—711no—
218C22⋊Q8—1421no—
219C22⋊Q8—1421no—
220#121—711no—
221#121—1421no—
222#120—1421no—
223C4×Q8—711no—
224C4×D4—711no—
225C4×D4—1421no—
226C4×D4C2×D7111yescharacteristic
227C2×C4⋊C4—711no—
228C2×C4⋊C4—711no—
229C2×C22⋊C4—1421no—
230#107—711no—
231#107—711no—
232#107—711no—
233C4⋊C8C2×D7111yescharacteristic, complemented
234#103—711no—
235#103—711no—
236#103—711no—
237#103—711no—
238#102—711no—
239#102—711no—
240#102—711no—
241#102—711no—
242#102—711no—
243#102—711no—
244C22⋊C8C2×D7111yescharacteristic
245C22⋊C8C2×D7111yescharacteristic, complemented
246#97C2×D7111yescharacteristic, complemented
247C24—1421no—
248#41—2841no—
249#41—1422no—
250C2×Q8—711no—
251C2×Q8—711no—
252C2×Q8—1421no—
253C2×D4—2841no—
254C2×D4—711no—
255C2×D4—711no—
256C2×D4—1422no—
257C2×D4—1421no—
258C2×D4—1421no—
259C2×D4—1421no—
260C2×D4D28411yescharacteristic
261C22×C4—1421no—
262C22×C4—1421no—
263C22×C4—1421no—
264C22×C4—1421no—
265C22×C4C22×D7111yescharacteristic
266C22×C4C22×D7111yescharacteristic
267Q16—2841no—
268SD16—2841no—
269SD16—1422no—
270M16—41no—
271C2×C8—41no—
272C2×C8C22×D7111yescharacteristic
273C2×C8C22×D7111yescharacteristic
274C2×C8C22×D7111yescharacteristic
275C2×C8C22×D7111yescharacteristic
276C4⋊C4—711no—
277C4⋊C4—711no—
278C4⋊C4—711no—
279C4⋊C4—711no—
280C4⋊C4—1421no—
281C4⋊C4—1421no—
282C4⋊C4—1421no—
283C4⋊C4—1421no—
284C4⋊C4—1421no—
285C4⋊C4—1421no—
286C4⋊C4—1421no—
287C4⋊C4D28411yescharacteristic
288C22⋊C4—1421no—
289C22⋊C4—1421no—
290C22⋊C4—1421no—
291C22⋊C4—1421no—
292C22⋊C4—1421no—
293C22⋊C4—1421no—
294C22⋊C4—1421no—
295C22⋊C4D28411yescharacteristic
296C22⋊C4D28411yescharacteristic
297C42—1421no—
298C42C22×D7111yescharacteristic
299C23—2842no—
300C23—2842no—
301C23—5681no—
302C23—1421no—
303C23—1421no—
304C23C2×D28411yescharacteristic
305C23C2×D28411yescharacteristic
306Q8—5681no—
307Q8—1421no—
308Q8—1421no—
309Q8—1421no—
310Q8—1421no—
311D4—22no—
312D4—2842no—
313D4—2842no—
314D4—5681no—
315D4—712no—
316D4—1421no—
317D4—1421no—
318D4—1421no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—2842no—
324C2×C4—5681no—
325C2×C4—5681no—
326C2×C4—5681no—
327C2×C4—1421no—
328C2×C4—1421no—
329C2×C4—1421no—
330C2×C4—1421no—
331C2×C4—1421no—
332C2×C4—1421no—
333C2×C4C2×D28411yescharacteristic
334C2×C4C2×D28411yescharacteristic
335C2×C4C2×D28411yescharacteristic
336C2×C4C2×D28411yescharacteristic
337C2×C4C23×D7111yescharacteristic
338C8—21no—
339C8—21no—
340C8—21no—
341C8—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—2841no—
348C22—2841no—
349C22—2841no—
350C22—2841no—
351C22—2841no—
352C22—5684no—
353C22—1422no—
354C22#1455616112yes—
355C22C22×D28411yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—2841no—
361C4—2841no—
362C4—2841no—
363C4—2841no—
364C4—2841no—
365C4—2841no—
366C4#41×D7111yescharacteristic
367C4#1455617311yescharacteristic
368C2—22no—
369C2—41no—
370C2—2842no—
371C2—5681no—
372C2#1798664411yescharacteristic
373C2C2×#1455616111yescharacteristic
374C2#1798680411yescharacteristic
subgroupG/H
centerC22C22×D284
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#435×C71C2
socleC22×C71C22×D4
hypercenter#435D71
hypocenterC71#3314
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #17986706C2semidirect
3. #17986359C2semidirect
4. #17986335C2semidirect
5. #17986313C2semidirect
6. #17986280C2semidirect
7. #17986245C2semidirect
8. #17986240C2semidirect
9. #17986222C2semidirect
10. #17986163C2semidirect
11. #17986152C2semidirect
12. #17986101C2semidirect
13. #17986001C2semidirect
14. C2×#14556050C2semidirect
15. #435×C71C2semidirect
18. C2×Dic284C22semidirect
21. #14556128C22semidirect
27. #14556107C22semidirect
33. C4×Dic142C22semidirect
37. C2×C4⋊Dic71C22semidirect
39. #14556062C22semidirect
40. #14556062C22semidirect
41. #14556062C22semidirect
42. #14556053C22semidirect
43. #14556053C22semidirect
44. #14556053C22semidirect
45. #14556053C22semidirect
52. C2×M16×C71C22semidirect
55. C4⋊C8×C71C22semidirect
57. C22⋊C8×C71C22semidirect
58. #97×C71C22semidirect
188. C71#3314semidirect
201. #435D71semidirect
209. C2×M16C2×D71semidirect
233. C4⋊C8C2×D71semidirect
245. C22⋊C8C2×D71semidirect
246. #97C2×D71semidirect