Finite Group Databasebeta

← #22599203

Subgroups — #22599203

Order 9088.

442 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17986566C211yesmaximal, characteristic, complemented
2#17986565C211yesmaximal, characteristic, complemented
3#17986324C211yesmaximal, characteristic, complemented
4#17986322C211yesmaximal, characteristic, complemented
5#17986321C211yesmaximal, characteristic, complemented
6#17986320C211yesmaximal, characteristic, complemented
7#17986251C211yesmaximal, characteristic, complemented
8#17986249C211yesmaximal, characteristic, complemented
9#17986234C211yesmaximal, characteristic, complemented
10#17986232C211yesmaximal, characteristic, complemented
11#17986133C211yesmaximal, characteristic, complemented
12#17986131C211yesmaximal, characteristic, complemented
13#17986131C211yesmaximal, characteristic, complemented
14#17985964C211yesmaximal, characteristic, complemented
15#447×C71C211yesmaximal, characteristic, complemented
16C2×#11765865C2211yescharacteristic
17C2×D4×D71C2211yescharacteristic, complemented
18C2×#11765850C2211yescharacteristic
19C2×#11765850C2211yescharacteristic
20C2×#11765848C2211yescharacteristic, complemented
21C2×C8×D71C2211yescharacteristic, complemented
22#14556124—21no—
23#14556124—21no—
24#14556115—21no—
25#14556114—21no—
26#14556103C2211yescharacteristic, complemented
27#14556102C2211yescharacteristic
28#14556099C2211yescharacteristic
29#14556099C2211yescharacteristic
30#14556099C2211yescharacteristic, complemented
31#14556099C2211yescharacteristic, complemented
32#14556099C2211yescharacteristic, complemented
33#14556098—21no—
34#14556097—21no—
35#14556097—21no—
36#14556096—21no—
37#14556087C2211yescharacteristic, complemented
38#14556086C2211yescharacteristic, complemented
39#14556062C2211yescharacteristic, complemented
40#14556061C2211yescharacteristic, complemented
41#14556060C2211yescharacteristic, complemented
42#14556059C2211yescharacteristic, complemented
43#14556050C2211yescharacteristic, complemented
44#14556050C2211yescharacteristic, complemented
45#14556049C2211yescharacteristic, complemented
46#14556049C2211yescharacteristic, complemented
47#14556049C2211yescharacteristic, complemented
48#14556049C2211yescharacteristic, complemented
49C22⋊(C71⋊C8)C2211yescharacteristic, complemented
50(C2×D71)⋊C8C2211yescharacteristic, complemented
51(C2×D71)⋊C8C2211yescharacteristic, complemented
52C22×D4×C71C2211yescharacteristic, complemented
53C2×D8×C71C2211yescharacteristic
54C2×D8×C71C2211yescharacteristic
55#121×C71C2211yescharacteristic
56#102×C71C2211yescharacteristic, complemented
57#102×C71C2211yescharacteristic, complemented
58C22⋊C8×C71C2211yescharacteristic, complemented
59C23×D71—21no—
60#11765865—41no—
61#11765865—41no—
62C2×Dic142D411yescharacteristic
63C2×D284—21no—
64C2×D284D411yescharacteristic
65C2×D284C2311yescharacteristic
66C2×C22⋊D71—21no—
67C2×C22⋊D71—21no—
68C2×C22⋊D71—21no—
69C2×C22⋊D71—21no—
70C2×C22⋊D71—21no—
71C2×C22⋊D71—21no—
72C2×C22⋊D71—21no—
73C2×C22⋊D71D411yescharacteristic
74C2×C22⋊D71D411yescharacteristic
75D4×D71—41no—
76D4×D71—41no—
77C2×C4×D71C2311yescharacteristic
78C2×C4×D71C2311yescharacteristic
79#11765850—41no—
80#11765850—41no—
81#11765848—41no—
82C2×C71⋊C8C2311yescharacteristic
83C2×C71⋊C8C2311yescharacteristic
84C8×D71—41no—
85C4⋊Dic71C2311yescharacteristic
86C4⋊Dic71C2311yescharacteristic
87C4⋊Dic71C2311yescharacteristic
88C22⋊Dic71—21no—
89C22⋊Dic71—21no—
90C22⋊Dic71—21no—
91C22⋊Dic71—21no—
92C22⋊Dic71—21no—
93C22⋊Dic71—21no—
94(C2×D71)⋊C4—21no—
95(C2×D71)⋊C4—21no—
96(C2×D71)⋊C4—21no—
97C4×Dic71—21no—
98C4×Dic71—21no—
99C24×C71—21no—
100C2×D4×C71—21no—
101C2×D4×C71—21no—
102C2×D4×C71—41no—
103C2×D4×C71—41no—
104C2×D4×C71C2311yescharacteristic
105C2×D4×C71C2311yescharacteristic
106C2×D4×C71C2311yescharacteristic
107C22×C4×C71C2311yescharacteristic
108D8×C71—41no—
109D8×C71—41no—
110C2×C8×C71C2311yescharacteristic
111C2×C8×C71C2311yescharacteristic
112C4⋊C4×C71C2311yescharacteristic
113C22⋊C4×C71—21no—
114C23×C71—21no—
115C23×C71—21no—
116C23×C71—21no—
117C23×C71—42no—
118C23×C71—81no—
119C23×C71—81no—
120C23×C71C2×D411yescharacteristic
121C22×D71—21no—
122C22×D71—42no—
123C22×D71—81no—
124C22×D71—81no—
125C22×D71C2×D411yescharacteristic
126C22×D71C2×D411yescharacteristic
127D4×C71—21no—
128D4×C71—21no—
129D4×C71—21no—
130D4×C71—21no—
131D4×C71—21no—
132D4×C71—21no—
133D4×C71—42no—
134D4×C71—81no—
135C2×C4×C71—21no—
136C2×C4×C71—21no—
137C2×C4×C71—21no—
138C2×C4×C71C2×D411yescharacteristic
139C2×C4×C71C2411yescharacteristic
140C22⋊D71—41no—
141C22⋊D71—41no—
142C22⋊D71—42no—
143C22⋊D71—81no—
144C22⋊D71—81no—
145C22⋊D71—81no—
146C22⋊D71—81no—
147C22⋊D71—81no—
148C22⋊D71—81no—
149C2×Dic71—21no—
150C2×Dic71—21no—
151C2×Dic71—21no—
152C2×Dic71C2×D411yescharacteristic
153C2×Dic71C2×D411yescharacteristic
154D284—21no—
155D284—21no—
156D284—41no—
157D284—81no—
158C4×D71—21no—
159C4×D71—21no—
160C4×D71—21no—
161C4×D71—21no—
162Dic142—41no—
163C8×C71—21no—
164C8×C71—21no—
165C71⋊C8—21no—
166C71⋊C8—21no—
167C22×C71—21no—
168C22×C71—21no—
169C22×C71—21no—
170C22×C71—41no—
171C22×C71—41no—
172C22×C71—41no—
173C22×C71—41no—
174C22×C71—41no—
175C22×C71—41no—
176C22×C71—41no—
177C22×C71—41no—
178C22×C71—41no—
179C22×C71—84no—
180C22×C71C22×D411yescharacteristic
181C2×D71—21no—
182C2×D71—21no—
183C2×D71—21no—
184C2×D71—21no—
185C2×D71—21no—
186C2×D71—21no—
187C2×D71—41no—
188C2×D71—41no—
189C2×D71—41no—
190C2×D71—84no—
191C4×C71—21no—
192C4×C71—41no—
193C4×C71H(5,𝔽2)11yescharacteristic
194C4×C71H(5,𝔽2)11yescharacteristic
195Dic71—21no—
196Dic71—21no—
197Dic71—41no—
198Dic71—41no—
199Dic71—41no—
200C2×C71—41no—
201C2×C71—81no—
202C2×C71—81no—
203C2×C71—81no—
204C2×C71#53411yescharacteristic
205C2×C71#57611yescharacteristic
206C2×C71#57611yescharacteristic
207D71—41no—
208D71—41no—
209D71—81no—
210#3199—711nomaximal, Sylow
211C71#319911yescharacteristic, complemented, Sylow
212#535—711no—
213#535—711no—
214#482—711no—
215#482—711no—
216#482—711no—
217#482—711no—
218#469—711no—
219#469—711no—
220#466—711no—
221#466—711no—
222#447—711no—
223#447—711no—
224#447—711no—
225#447D7111yescharacteristic, complemented
226#408—711no—
227C2×#41—711no—
228C22×D4—711no—
229C22×D4C2×D7111yescharacteristic, complemented
230C2×D8—711no—
231C2×D8—711no—
232C2×D8C2×D7111yescharacteristic
233C2×D8C2×D7111yescharacteristic
234C2×M16—711no—
235C22×C8—711no—
236#127—1421no—
237#127—1421no—
238#124—1421no—
239#124—1421no—
240#121—711no—
241#121—711no—
242#121—711no—
243#121—711no—
244#121—711no—
245#121—711no—
246#121—711no—
247#121C2×D7111yescharacteristic
248#120—1421no—
249#120—1421no—
250#120—1421no—
251#120—1421no—
252#117—711no—
253#117—711no—
254#107—711no—
255#107—711no—
256#106—711no—
257#106—711no—
258#102—711no—
259#102—711no—
260#102—711no—
261#102—711no—
262#102—711no—
263#102—711no—
264#102C2×D7111yescharacteristic, complemented
265#102C2×D7111yescharacteristic, complemented
266C22⋊C8—711no—
267C22⋊C8—711no—
268C22⋊C8—711no—
269C22⋊C8C2×D7111yescharacteristic, complemented
270C24—21no—
271C24—1421no—
272#41—2841no—
273#41—2841no—
274C2×Q8—711no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—2841no—
280C2×D4—2841no—
281C2×D4—711no—
282C2×D4—711no—
283C2×D4—711no—
284C2×D4—711no—
285C2×D4—1421no—
286C2×D4—1421no—
287C2×D4—1421no—
288C2×D4—1421no—
289C2×D4—1421no—
290C2×D4—1421no—
291C2×D4—1421no—
292C2×D4—1421no—
293C2×D4C22×D7111yescharacteristic
294C2×D4C22×D7111yescharacteristic
295C2×D4C22×D7111yescharacteristic
296C22×C4—711no—
297C22×C4—711no—
298C22×C4C22×D7111yescharacteristic
299D8—41no—
300D8—41no—
301D8—2841no—
302D8—2841no—
303M16—2841no—
304C2×C8—2841no—
305C2×C8—711no—
306C2×C8—711no—
307C2×C8C22×D7111yescharacteristic
308C2×C8C22×D7111yescharacteristic
309C4⋊C4—711no—
310C4⋊C4—711no—
311C4⋊C4—711no—
312C4⋊C4C22×D7111yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—1421no—
315C22⋊C4—1421no—
316C22⋊C4—1421no—
317C22⋊C4—1421no—
318C22⋊C4—1421no—
319C22⋊C4—1421no—
320C22⋊C4—1421no—
321C22⋊C4—1421no—
322C22⋊C4—1421no—
323C42—1421no—
324C42—1421no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—42no—
329C23—81no—
330C23—81no—
331C23—2842no—
332C23—5681no—
333C23—5681no—
334C23—711no—
335C23—711no—
336C23—1421no—
337C23D4×D7111yescharacteristic
338Q8—2841no—
339D4—21no—
340D4—21no—
341D4—21no—
342D4—21no—
343D4—21no—
344D4—21no—
345D4—42no—
346D4—81no—
347D4—2841no—
348D4—2841no—
349D4—2841no—
350D4—2842no—
351D4—5681no—
352D4—5681no—
353D4—5681no—
354D4—5681no—
355D4—5681no—
356D4—5681no—
357D4—5681no—
358D4—1421no—
359D4—1421no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—711no—
364C2×C4—711no—
365C2×C4—1421no—
366C2×C4—1421no—
367C2×C4—1421no—
368C2×C4—1421no—
369C2×C4—1421no—
370C2×C4—1421no—
371C2×C4—1421no—
372C2×C4D4×D7111yescharacteristic
373C2×C4C23×D7111yescharacteristic
374C8—21no—
375C8—21no—
376C8—1421no—
377C8—1421no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—84no—
391C22—2841no—
392C22—2841no—
393C22—2841no—
394C22—5684no—
395C22—1421no—
396C22—1421no—
397C22—1421no—
398C22—1421no—
399C22—1421no—
400C22—1421no—
401C22C2×D4×D7111yescharacteristic
402C4—21no—
403C4—41no—
404C4—2841no—
405C4—2841no—
406C4—2841no—
407C4—1421no—
408C4—1421no—
409C4#1455617311yescharacteristic
410C4#1455617311yescharacteristic
411C2—41no—
412C2—81no—
413C2—81no—
414C2—81no—
415C2—2841no—
416C2—2841no—
417C2—5681no—
418C2#1798655911yescharacteristic
419C2#1798680011yescharacteristic
420C2#1798680311yescharacteristic
subgroupG/H
centerC22C2×D4×D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#447×C71C2
socleC22×C71C22×D4
hypercenter#447D71
hypocenterC71#3199
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #17986566C2semidirect
2. #17986565C2semidirect
3. #17986324C2semidirect
4. #17986322C2semidirect
5. #17986321C2semidirect
6. #17986320C2semidirect
7. #17986251C2semidirect
8. #17986249C2semidirect
9. #17986234C2semidirect
10. #17986232C2semidirect
11. #17986133C2semidirect
12. #17986131C2semidirect
13. #17986131C2semidirect
14. #17985964C2semidirect
15. #447×C71C2semidirect
17. C2×D4×D71C22semidirect
20. C2×#11765848C22semidirect
21. C2×C8×D71C22semidirect
26. #14556103C22semidirect
30. #14556099C22semidirect
31. #14556099C22semidirect
32. #14556099C22semidirect
37. #14556087C22semidirect
38. #14556086C22semidirect
39. #14556062C22semidirect
40. #14556061C22semidirect
41. #14556060C22semidirect
42. #14556059C22semidirect
43. #14556050C22semidirect
44. #14556050C22semidirect
45. #14556049C22semidirect
46. #14556049C22semidirect
47. #14556049C22semidirect
48. #14556049C22semidirect
49. C22⋊(C71⋊C8)C22semidirect
50. (C2×D71)⋊C8C22semidirect
51. (C2×D71)⋊C8C22semidirect
52. C22×D4×C71C22semidirect
56. #102×C71C22semidirect
57. #102×C71C22semidirect
58. C22⋊C8×C71C22semidirect
211. C71#3199semidirect
225. #447D71semidirect
229. C22×D4C2×D71semidirect
264. #102C2×D71semidirect
265. #102C2×D71semidirect
269. C22⋊C8C2×D71semidirect