Finite Group Databasebeta

← #22600537

Subgroups — #22600537

Order 9088.

414 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17986693C211yesmaximal, characteristic, complemented
2#17986643C211yesmaximal, characteristic, complemented
3#17986352C211yesmaximal, characteristic, complemented
4#17986340C211yesmaximal, characteristic, complemented
5#17986311C211yesmaximal, characteristic, complemented
6#17986297C211yesmaximal, characteristic, complemented
7#17986251C211yesmaximal, characteristic, complemented
8#17986245C211yesmaximal, characteristic, complemented
9#17986213C211yesmaximal, characteristic, complemented
10#17986145C211yesmaximal, characteristic, complemented
11#17986133C211yesmaximal, characteristic, complemented
12#17986079C211yesmaximal, characteristic, complemented
13#17986075C211yesmaximal, characteristic, complemented
14#17985997C211yesmaximal, characteristic, complemented
15#418×C71C211yesmaximal, characteristic, complemented
16C2×#11765864C2211yescharacteristic
17C2×#11765854C2211yescharacteristic, complemented
18C2×#11765850C2211yescharacteristic
19C2×#11765850C2211yescharacteristic
20C2×#11765848C2211yescharacteristic, complemented
21#14556122—21no—
22#14556119C2211yescharacteristic, complemented
23#14556115C2211yescharacteristic
24#14556110—21no—
25#14556109—21no—
26#14556107C2211yescharacteristic
27#14556103C2211yescharacteristic, complemented
28#14556102C2211yescharacteristic
29#14556101—21no—
30#14556100—21no—
31#14556099C2211yescharacteristic
32#14556097—21no—
33C4×D284—21no—
34D4×Dic71C2211yescharacteristic
35#14556090C2211yescharacteristic, complemented
36C4×C22⋊D71C2211yescharacteristic
37C4⋊C4×D71C2211yescharacteristic, complemented
38C2×C22⋊Dic71—21no—
39#14556062C2211yescharacteristic, complemented
40#14556061C2211yescharacteristic, complemented
41#14556059C2211yescharacteristic, complemented
42Dic71⋊C8C2211yescharacteristic, complemented
43#14556053C2211yescharacteristic, complemented
44#14556051C2211yescharacteristic, complemented
45#14556051C2211yescharacteristic, complemented
46#14556050C2211yescharacteristic, complemented
47#14556049C2211yescharacteristic
48#14556049C2211yescharacteristic
49C22⋊(C71⋊C8)C2211yescharacteristic
50(C2×D71)⋊C8C2211yescharacteristic, complemented
51C8×Dic71C2211yescharacteristic, complemented
52C22×D4×C71C2211yescharacteristic
53C2×M16×C71C2211yescharacteristic
54#117×C71C2211yescharacteristic
55#102×C71C2211yescharacteristic
56#102×C71C2211yescharacteristic
57#102×C71C2211yescharacteristic
58#102×C71C2211yescharacteristic
59#11765864—22no—
60#11765864—41no—
61C2×Dic142C2311yescharacteristic
62C2×D284—21no—
63C2×D284C2311yescharacteristic
64C2×C22⋊D71—21no—
65C2×C22⋊D71—21no—
66C2×C22⋊D71—21no—
67C2×C22⋊D71D411yescharacteristic
68C22×Dic71—21no—
69C22×Dic71—21no—
70C2×C4×D71—21no—
71C2×C4×D71—21no—
72C2×C4×D71C2311yescharacteristic
73#11765854—41no—
74#11765850—22no—
75#11765850—41no—
76#11765848—41no—
77C2×C71⋊C8C2311yescharacteristic
78C2×C71⋊C8C2311yescharacteristic
79C4⋊Dic71—21no—
80C4⋊Dic71C2311yescharacteristic
81C4⋊Dic71C2311yescharacteristic
82Dic71⋊C4—21no—
83Dic71⋊C4—21no—
84Dic71⋊C4—21no—
85Dic71⋊C4D411yescharacteristic
86C22⋊Dic71—21no—
87C22⋊Dic71—21no—
88C22⋊Dic71—21no—
89C22⋊Dic71—21no—
90C22⋊Dic71—21no—
91C22⋊Dic71D411yescharacteristic
92(C2×D71)⋊C4—21no—
93(C2×D71)⋊C4—21no—
94(C2×D71)⋊C4—21no—
95(C2×D71)⋊C4D411yescharacteristic
96C4×Dic71C2311yescharacteristic
97C24×C71—21no—
98C2×D4×C71—22no—
99C2×D4×C71—21no—
100C2×D4×C71—41no—
101C2×D4×C71C2311yescharacteristic
102C2×D4×C71C2311yescharacteristic
103C22×C4×C71C2311yescharacteristic
104M16×C71—41no—
105C2×C8×C71C2311yescharacteristic
106C2×C8×C71C2311yescharacteristic
107C4⋊C4×C71C2311yescharacteristic
108C4⋊C4×C71C2311yescharacteristic
109C22⋊C4×C71—21no—
110C42×C71—21no—
111C23×C71—21no—
112C23×C71—21no—
113C23×C71—42no—
114C23×C71—42no—
115C23×C71—81no—
116C23×C71C2×D411yescharacteristic
117C22×D71—21no—
118C22×D71C2×D411yescharacteristic
119D4×C71—21no—
120D4×C71—21no—
121D4×C71—21no—
122D4×C71—42no—
123D4×C71#4112yes—
124C2×C4×C71—21no—
125C2×C4×C71—21no—
126C2×C4×C71—21no—
127C2×C4×C71—21no—
128C2×C4×C71C2×D411yescharacteristic
129C2×C4×C71C2411yescharacteristic
130C22⋊D71—41no—
131C22⋊D71—42no—
132C22⋊D71—81no—
133C22⋊D71—81no—
134C2×Dic71—21no—
135C2×Dic71—21no—
136C2×Dic71—21no—
137C2×Dic71—42no—
138C2×Dic71—81no—
139C2×Dic71C2×D411yescharacteristic
140C2×Dic71C2×D411yescharacteristic
141C2×Dic71C2×D411yescharacteristic
142D284—21no—
143D284—21no—
144D284—42no—
145C4×D71—21no—
146C4×D71—21no—
147C4×D71—81no—
148C4×D71—81no—
149Dic142—21no—
150Dic142—21no—
151C8×C71—21no—
152C8×C71—21no—
153C71⋊C8—21no—
154C71⋊C8—21no—
155C22×C71—22no—
156C22×C71—21no—
157C22×C71—21no—
158C22×C71—21no—
159C22×C71—41no—
160C22×C71—41no—
161C22×C71—41no—
162C22×C71—41no—
163C22×C71—41no—
164C22×C71—84no—
165C22×C71C22×D411yescharacteristic
166C2×D71—21no—
167C2×D71—21no—
168C2×D71—21no—
169C2×D71—41no—
170C2×D71—41no—
171C2×D71—41no—
172C4×C71—21no—
173C4×C71—41no—
174C4×C71—41no—
175C4×C71C2×#4111yescharacteristic
176C4×C71H(5,𝔽2)11yescharacteristic
177Dic71—21no—
178Dic71—21no—
179Dic71—21no—
180Dic71—41no—
181Dic71—41no—
182Dic71—41no—
183C2×C71—41no—
184C2×C71—42no—
185C2×C71—81no—
186C2×C71#54611yescharacteristic
187C2×C71#57511yescharacteristic
188C2×C71#57611yescharacteristic
189D71—41no—
190D71—81no—
191#3322—711nomaximal, Sylow
192C71#332211yescharacteristic, complemented, Sylow
193#553—711no—
194#546—711no—
195#488—711no—
196#485—711no—
197#480—711no—
198#478—711no—
199#469—711no—
200#468—711no—
201#463—711no—
202#449—711no—
203#447—711no—
204C4×D8—711no—
205#436—711no—
206#418D7111yescharacteristic, complemented
207#417—711no—
208C2×#41—711no—
209C22×D4C2×D7111yescharacteristic
210C2×SD16—711no—
211C2×D8—711no—
212C2×D8—711no—
213C2×M16—711no—
214C2×M16C2×D7111yescharacteristic
215#126—1421no—
216#125—711no—
217#124—711no—
218#123—1421no—
219#123—1421no—
220C22⋊Q8—711no—
221#121—711no—
222#121—711no—
223#121—711no—
224#121—1421no—
225#121—1421no—
226#120—1421no—
227C4×D4—711no—
228C4×D4—711no—
229C4×D4—711no—
230C4×D4—1421no—
231#117C2×D7111yescharacteristic
232C2×C4⋊C4—711no—
233C2×C22⋊C4—1421no—
234#107—711no—
235#107—711no—
236#106—711no—
237C4⋊C8—711no—
238#103—711no—
239#103—711no—
240#103—711no—
241#102—711no—
242#102—711no—
243#102—711no—
244#102C2×D7111yescharacteristic
245#102C2×D7111yescharacteristic
246#102C2×D7111yescharacteristic
247#102C2×D7111yescharacteristic
248C22⋊C8—711no—
249C22⋊C8—711no—
250C4×C8—711no—
251C24—21no—
252#41—2841no—
253#41—1422no—
254C2×Q8—711no—
255C2×D4—22no—
256C2×D4—21no—
257C2×D4—41no—
258C2×D4—711no—
259C2×D4—711no—
260C2×D4—1421no—
261C2×D4—1421no—
262C2×D4—1421no—
263C2×D4—1421no—
264C2×D4C22×D7111yescharacteristic
265C2×D4C22×D7111yescharacteristic
266C22×C4—711no—
267C22×C4—1421no—
268C22×C4—1421no—
269C22×C4—1421no—
270C22×C4—1421no—
271C22×C4C22×D7111yescharacteristic
272SD16—2841no—
273D8—2841no—
274D8—1422no—
275M16—41no—
276M16—2841no—
277C2×C8—711no—
278C2×C8—711no—
279C2×C8C22×D7111yescharacteristic
280C2×C8C22×D7111yescharacteristic
281C4⋊C4—711no—
282C4⋊C4—711no—
283C4⋊C4—711no—
284C4⋊C4—1421no—
285C4⋊C4—1421no—
286C4⋊C4—1421no—
287C4⋊C4—1421no—
288C4⋊C4C22×D7111yescharacteristic
289C4⋊C4C22×D7111yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—711no—
292C22⋊C4—711no—
293C22⋊C4—1421no—
294C22⋊C4—1421no—
295C22⋊C4—1421no—
296C22⋊C4—1421no—
297C22⋊C4—1421no—
298C22⋊C4—1421no—
299C22⋊C4—1421no—
300C22⋊C4—1421no—
301C42—21no—
302C42—711no—
303C23—21no—
304C23—21no—
305C23—42no—
306C23—42no—
307C23—81no—
308C23—711no—
309C23—1421no—
310C23D4×D7111yescharacteristic
311Q8—1421no—
312Q8—1421no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—42no—
317D4—2842no—
318D4—2842no—
319D4—2841no—
320D4—5681no—
321D4—5681no—
322D4—1421no—
323D4—1421no—
324D4#1176586512yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—2842no—
330C2×C4—5681no—
331C2×C4—5681no—
332C2×C4—5681no—
333C2×C4—711no—
334C2×C4—711no—
335C2×C4—711no—
336C2×C4—1421no—
337C2×C4—1421no—
338C2×C4—1421no—
339C2×C4—1421no—
340C2×C4—1421no—
341C2×C4D4×D7111yescharacteristic
342C2×C4C23×D7111yescharacteristic
343C8—21no—
344C8—21no—
345C8—1421no—
346C8—1421no—
347C22—21no—
348C22—22no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—84no—
357C22—2841no—
358C22—2841no—
359C22—2841no—
360C22—1421no—
361C22—1421no—
362C22—1421no—
363C22C2×D4×D7111yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—2841no—
368C4—2841no—
369C4—2841no—
370C4—1421no—
371C4—1421no—
372C4—1421no—
373C4C2×#1176586511yescharacteristic
374C4#1455617311yescharacteristic
375C2—41no—
376C2—42no—
377C2—81no—
378C2—2841no—
379C2—5681no—
380C2#1798663911yescharacteristic
381C2#1798679511yescharacteristic
382C2#1798680311yescharacteristic
subgroupG/H
centerC22C2×D4×D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#418×C71C2
socleC22×C71C22×D4
hypercenter#418D71
hypocenterC71#3322
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #17986693C2semidirect
2. #17986643C2semidirect
3. #17986352C2semidirect
4. #17986340C2semidirect
5. #17986311C2semidirect
6. #17986297C2semidirect
7. #17986251C2semidirect
8. #17986245C2semidirect
9. #17986213C2semidirect
10. #17986145C2semidirect
11. #17986133C2semidirect
12. #17986079C2semidirect
13. #17986075C2semidirect
14. #17985997C2semidirect
15. #418×C71C2semidirect
17. C2×#11765854C22semidirect
20. C2×#11765848C22semidirect
22. #14556119C22semidirect
27. #14556103C22semidirect
35. #14556090C22semidirect
37. C4⋊C4×D71C22semidirect
39. #14556062C22semidirect
40. #14556061C22semidirect
41. #14556059C22semidirect
42. Dic71⋊C8C22semidirect
43. #14556053C22semidirect
44. #14556051C22semidirect
45. #14556051C22semidirect
46. #14556050C22semidirect
50. (C2×D71)⋊C8C22semidirect
51. C8×Dic71C22semidirect
192. C71#3322semidirect
206. #418D71semidirect