Finite Group Databasebeta

← #22599149

Subgroups — #22599149

Order 9088.

466 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17986509C211yesmaximal, characteristic, complemented
2#121×D71C211yesmaximal, characteristic, complemented
3#17986331C211yesmaximal, characteristic, complemented
4#17986325C211yesmaximal, characteristic, complemented
5#17986321C211yesmaximal, characteristic, complemented
6#17986311C211yesmaximal, characteristic, complemented
7#17986250C211yesmaximal, characteristic, complemented
8#17986245C211yesmaximal, characteristic, complemented
9#17986243C211yesmaximal, characteristic, complemented
10#17986151C211yesmaximal, characteristic, complemented
11#17986145C211yesmaximal, characteristic, complemented
12#17986141C211yesmaximal, characteristic, complemented
13#17986131C211yesmaximal, characteristic, complemented
14#17985962C211yesmaximal, characteristic, complemented
15#469×C71C211yesmaximal, characteristic, complemented
16C2×#11765864C2211yescharacteristic, complemented
17C2×D4×D71—21no—
18C2×D4×D71C2211yescharacteristic
19C22×C4×D71C2211yescharacteristic
20C2×#11765854C2211yescharacteristic, complemented
21C2×#11765853C2211yescharacteristic, complemented
22C2×#11765850C2211yescharacteristic, complemented
23C2×#11765849C2211yescharacteristic, complemented
24#14556110—21no—
25#14556108C2211yescharacteristic
26#14556107C2211yescharacteristic, complemented
27#14556103C2211yescharacteristic
28#14556102C2211yescharacteristic
29#14556101—21no—
30#14556100—21no—
31#14556099C2211yescharacteristic
32#14556099C2211yescharacteristic
33#14556096—21no—
34D4×Dic71—21no—
35(C22⋊D71)⋊C4—21no—
36#14556086C2211yescharacteristic, complemented
37C4⋊C4×D71C2211yescharacteristic
38C22⋊C4×D71—21no—
39#14556062C2211yescharacteristic, complemented
40#14556061C2211yescharacteristic, complemented
41#14556059C2211yescharacteristic, complemented
42#14556053C2211yescharacteristic, complemented
43#14556051C2211yescharacteristic, complemented
44#14556050C2211yescharacteristic, complemented
45#14556049C2211yescharacteristic, complemented
46#14556049C2211yescharacteristic, complemented
47#14556048C2211yescharacteristic, complemented
48(C2×D71)⋊C8C2211yescharacteristic
49(C2×D71)⋊C8C2211yescharacteristic
50(C2×D71)⋊C8C2211yescharacteristic, complemented
51(C2×D71)⋊C8C2211yescharacteristic, complemented
52C2×D8×C71C2211yescharacteristic, complemented
53C2×M16×C71C2211yescharacteristic, complemented
54#121×C71C2211yescharacteristic
55#121×C71C2211yescharacteristic, complemented
56#106×C71C2211yescharacteristic, complemented
57#102×C71C2211yescharacteristic, complemented
58#102×C71C2211yescharacteristic, complemented
59C23×D71—21no—
60C23×D71D411yescharacteristic
61#11765864—41no—
62#11765864—41no—
63C2×Dic142C2311yescharacteristic
64C2×D284—21no—
65C2×D284C2311yescharacteristic
66C2×C22⋊D71—21no—
67C2×C22⋊D71—21no—
68C2×C22⋊D71—21no—
69C2×C22⋊D71—21no—
70C2×C22⋊D71—21no—
71D4×D71—41no—
72D4×D71—41no—
73D4×D71—44no—
74C22×Dic71—21no—
75C22×Dic71D411yescharacteristic
76C2×C4×D71—21no—
77C2×C4×D71—41no—
78C2×C4×D71—41no—
79C2×C4×D71D411yescharacteristic
80C2×C4×D71D411yescharacteristic
81C2×C4×D71C2311yescharacteristic
82C2×C4×D71C2311yescharacteristic
83#11765854—41no—
84#11765853—41no—
85#11765850—41no—
86#11765849—41no—
87C2×C71⋊C8C2311yescharacteristic
88C2×C71⋊C8C2311yescharacteristic
89C4⋊Dic71—21no—
90C4⋊Dic71C2311yescharacteristic
91C4⋊Dic71C2311yescharacteristic
92Dic71⋊C4—21no—
93Dic71⋊C4—21no—
94C22⋊Dic71—21no—
95C22⋊Dic71—21no—
96C22⋊Dic71—21no—
97(C2×D71)⋊C4—21no—
98(C2×D71)⋊C4—21no—
99(C2×D71)⋊C4—21no—
100(C2×D71)⋊C4—21no—
101C4×Dic71—21no—
102C2×D4×C71—21no—
103C2×D4×C71—21no—
104C2×D4×C71C2311yescharacteristic
105C2×D4×C71C2311yescharacteristic
106C22×C4×C71C2311yescharacteristic
107D8×C71—41no—
108M16×C71—41no—
109C2×C8×C71C2311yescharacteristic
110C2×C8×C71C2311yescharacteristic
111C4⋊C4×C71C2311yescharacteristic
112C4⋊C4×C71C2311yescharacteristic
113C22⋊C4×C71—21no—
114C22⋊C4×C71—21no—
115C23×C71—21no—
116C23×C71—21no—
117C23×C71C2×D411yescharacteristic
118C22×D71—22no—
119C22×D71—21no—
120C22×D71—41no—
121C22×D71—41no—
122C22×D71—42no—
123C22×D71—42no—
124C22×D71—42no—
125C22×D71C2×D411yescharacteristic
126C22×D71C2×D411yescharacteristic
127D4×C71—21no—
128D4×C71—21no—
129D4×C71—21no—
130D4×C71—21no—
131D4×C71—42no—
132D4×C71—42no—
133C2×C4×C71—21no—
134C2×C4×C71—21no—
135C2×C4×C71—21no—
136C2×C4×C71—21no—
137C2×C4×C71C2×D411yescharacteristic
138C2×C4×C71C2411yescharacteristic
139C22⋊D71—42no—
140C22⋊D71—42no—
141C22⋊D71—42no—
142C22⋊D71—42no—
143C22⋊D71—42no—
144C2×Dic71—21no—
145C2×Dic71—21no—
146C2×Dic71—21no—
147C2×Dic71—41no—
148C2×Dic71—42no—
149C2×Dic71C2×D411yescharacteristic
150C2×Dic71C2×D411yescharacteristic
151D284—21no—
152D284—21no—
153D284—42no—
154C4×D71—21no—
155C4×D71—21no—
156C4×D71—21no—
157C4×D71—21no—
158C4×D71—41no—
159C4×D71—41no—
160C4×D71—42no—
161Dic142—21no—
162Dic142—21no—
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×C71C22×D411yescharacteristic
177C2×D71—21no—
178C2×D71—21no—
179C2×D71—21no—
180C2×D71—21no—
181C2×D71—21no—
182C2×D71—44no—
183C2×D71—41no—
184C2×D71—41no—
185C2×D71—41no—
186C2×D71—84no—
187C2×D71AGL(1,ℤ/8)12yes—
188C4×C71—21no—
189C4×C71—41no—
190C4×C71—41no—
191C4×C71H(5,𝔽2)11yescharacteristic
192C4×C71H(5,𝔽2)11yescharacteristic
193Dic71—21no—
194Dic71—21no—
195Dic71—41no—
196Dic71—41no—
197Dic71—41no—
198C2×C71—41no—
199C2×C71—81no—
200C2×C71—81no—
201C2×C71#53411yescharacteristic
202C2×C71C2×AGL(1,ℤ/8)11yescharacteristic
203C2×C71#57511yescharacteristic
204D71—22no—
205D71—41no—
206D71—81no—
207#3194—711nomaximal, Sylow
208C71#319411yescharacteristic, complemented, Sylow
209#525—711no—
210C2×#121—711no—
211#483—711no—
212#482—711no—
213#482—711no—
214#480—711no—
215#469—711no—
216#469D7111yescharacteristic, complemented
217#468—711no—
218#468—711no—
219#450—711no—
220#449—711no—
221#449—711no—
222#447—711no—
223#407—711no—
224C2×#41—711no—
225C22×D4—711no—
226C22×D4—1421no—
227C23×C4—711no—
228C2×SD16—711no—
229C2×SD16—711no—
230C2×D8—711no—
231C2×D8C2×D7111yescharacteristic, complemented
232C2×M16—711no—
233C2×M16C2×D7111yescharacteristic, complemented
234#123—1421no—
235C22⋊Q8—711no—
236C22⋊Q8—711no—
237#121—711no—
238#121—711no—
239#121—711no—
240#121—711no—
241#121—1421no—
242#121—1421no—
243#121C2×D7111yescharacteristic
244#121C2×D7111yescharacteristic, complemented
245#120—1421no—
246C4×D4—1421no—
247C4×D4—1421no—
248#117—711no—
249C2×C4⋊C4—711no—
250C2×C22⋊C4—1421no—
251#107—711no—
252#107—711no—
253#106—711no—
254#106C2×D7111yescharacteristic, complemented
255#103—711no—
256#103—711no—
257#102—711no—
258#102—711no—
259#102—711no—
260#102—711no—
261#102C2×D7111yescharacteristic, complemented
262#102C2×D7111yescharacteristic, complemented
263C22⋊C8—711no—
264C22⋊C8—711no—
265C22⋊C8—711no—
266C22⋊C8—711no—
267C24—711no—
268C24—1421no—
269#41—2841no—
270#41—2841no—
271C2×Q8—711no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—2844no—
275C2×D4—2841no—
276C2×D4—2841no—
277C2×D4—711no—
278C2×D4—1421no—
279C2×D4—1421no—
280C2×D4—1421no—
281C2×D4—1421no—
282C2×D4—1421no—
283C2×D4—1421no—
284C2×D4C22×D7111yescharacteristic
285C2×D4C22×D7111yescharacteristic
286C22×C4—2841no—
287C22×C4—2841no—
288C22×C4—711no—
289C22×C4—711no—
290C22×C4—711no—
291C22×C4—711no—
292C22×C4—711no—
293C22×C4—1421no—
294C22×C4—1421no—
295C22×C4C22×D7111yescharacteristic
296SD16—2841no—
297SD16—2841no—
298D8—41no—
299D8—2841no—
300M16—41no—
301M16—2841no—
302C2×C8—711no—
303C2×C8—711no—
304C2×C8C22×D7111yescharacteristic
305C2×C8C22×D7111yescharacteristic
306C4⋊C4—711no—
307C4⋊C4—711no—
308C4⋊C4—1421no—
309C4⋊C4—1421no—
310C4⋊C4—1421no—
311C4⋊C4C22×D7111yescharacteristic
312C4⋊C4C22×D7111yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—1421no—
316C22⋊C4—1421no—
317C22⋊C4—1421no—
318C22⋊C4—1421no—
319C22⋊C4—1421no—
320C22⋊C4—1421no—
321C22⋊C4—1421no—
322C42—1421no—
323C23—21no—
324C23—21no—
325C23—2841no—
326C23—2841no—
327C23—2842no—
328C23—2842no—
329C23—2842no—
330C23—711no—
331C23—711no—
332C23—1422no—
333C23—1421no—
334C23D4×D7111yescharacteristic
335Q8—1421no—
336Q8—1421no—
337D4—21no—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—42no—
342D4—42no—
343D4—2842no—
344D4—2842no—
345D4—2842no—
346D4—2842no—
347D4—2842no—
348D4—2842no—
349D4—1421no—
350D4—1421no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—2841no—
356C2×C4—2841no—
357C2×C4—2842no—
358C2×C4—2842no—
359C2×C4—2841no—
360C2×C4—711no—
361C2×C4—711no—
362C2×C4—1421no—
363C2×C4—1421no—
364C2×C4—1421no—
365C2×C4—1421no—
366C2×C4—1421no—
367C2×C4—1421no—
368C2×C4—1421no—
369C2×C4D4×D7111yescharacteristic
370C2×C4C23×D7111yescharacteristic
371C8—21no—
372C8—21no—
373C8—1421no—
374C8—1421no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—2844no—
385C22—2841no—
386C22—2841no—
387C22—2841no—
388C22—5684no—
389C22—712no—
390C22—1421no—
391C22—1421no—
392C22—1421no—
393C22—1421no—
394C22—1421no—
395C22C2×D4×D7111yescharacteristic
396C4—21no—
397C4—41no—
398C4—41no—
399C4—2841no—
400C4—2841no—
401C4—2841no—
402C4—1421no—
403C4—1421no—
404C4#1455617311yescharacteristic
405C4#1455617411yescharacteristic
406C2—41no—
407C2—81no—
408C2—81no—
409C2—2841no—
410C2—5681no—
411C2—1422no—
412C2#1798655711yescharacteristic
413C2AGL(1,ℤ/8)×D7111yescharacteristic
414C2#1798679511yescharacteristic
subgroupG/H
centerC22C2×D4×D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#469×C71C2
socleC22×C71C22×D4
hypercenter#469D71
hypocenterC71#3194
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #17986509C2semidirect
2. #121×D71C2semidirect
3. #17986331C2semidirect
4. #17986325C2semidirect
5. #17986321C2semidirect
6. #17986311C2semidirect
7. #17986250C2semidirect
8. #17986245C2semidirect
9. #17986243C2semidirect
10. #17986151C2semidirect
11. #17986145C2semidirect
12. #17986141C2semidirect
13. #17986131C2semidirect
14. #17985962C2semidirect
15. #469×C71C2semidirect
16. C2×#11765864C22semidirect
20. C2×#11765854C22semidirect
21. C2×#11765853C22semidirect
22. C2×#11765850C22semidirect
23. C2×#11765849C22semidirect
26. #14556107C22semidirect
36. #14556086C22semidirect
39. #14556062C22semidirect
40. #14556061C22semidirect
41. #14556059C22semidirect
42. #14556053C22semidirect
43. #14556051C22semidirect
44. #14556050C22semidirect
45. #14556049C22semidirect
46. #14556049C22semidirect
47. #14556048C22semidirect
50. (C2×D71)⋊C8C22semidirect
51. (C2×D71)⋊C8C22semidirect
52. C2×D8×C71C22semidirect
53. C2×M16×C71C22semidirect
55. #121×C71C22semidirect
56. #106×C71C22semidirect
57. #102×C71C22semidirect
58. #102×C71C22semidirect
208. C71#3194semidirect
216. #469D71semidirect
231. C2×D8C2×D71semidirect
233. C2×M16C2×D71semidirect
244. #121C2×D71semidirect
254. #106C2×D71semidirect
261. #102C2×D71semidirect
262. #102C2×D71semidirect