Finite Group Databasebeta

← #22599103

Subgroups — #22599103

Order 9088.

472 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#17986506C211yesmaximal, characteristic, complemented
2#121×D71C211yesmaximal, characteristic, complemented
3#17986333C211yesmaximal, characteristic, complemented
4#17986324C211yesmaximal, characteristic, complemented
5#17986320C211yesmaximal, characteristic, complemented
6#17986316C211yesmaximal, characteristic, complemented
7#17986234C211yesmaximal, characteristic, complemented
8#17986232C211yesmaximal, characteristic, complemented
9#17986231C211yesmaximal, characteristic, complemented
10#17986225C211yesmaximal, characteristic, complemented
11#17986148C211yesmaximal, characteristic, complemented
12#17986144C211yesmaximal, characteristic, complemented
13#17986131C211yesmaximal, characteristic, complemented
14C22⋊C8×D71C211yesmaximal, characteristic, complemented
15#449×C71C211yesmaximal, characteristic, complemented
16C2×D4×D71—21no—
17C2×D4×D71C2211yescharacteristic
18C22×C4×D71C2211yescharacteristic
19C2×#11765852C2211yescharacteristic, complemented
20C2×#11765850C2211yescharacteristic, complemented
21C2×C8×D71C2211yescharacteristic, complemented
22C2×C8×D71C2211yescharacteristic, complemented
23#14556109—21no—
24#14556104C2211yescharacteristic
25#14556104C2211yescharacteristic, complemented
26#14556103C2211yescharacteristic
27#14556102C2211yescharacteristic
28#14556101—21no—
29#14556100—21no—
30#14556099C2211yescharacteristic
31#14556099C2211yescharacteristic
32#14556099C2211yescharacteristic, complemented
33#14556096—21no—
34C4×C22⋊D71—21no—
35C4×C22⋊D71—21no—
36#14556087C2211yescharacteristic, complemented
37C4⋊C4×D71C2211yescharacteristic
38C22⋊C4×D71—21no—
39#14556062C2211yescharacteristic, complemented
40#14556061C2211yescharacteristic, complemented
41#14556060C2211yescharacteristic, complemented
42#14556059C2211yescharacteristic, complemented
43#14556052C2211yescharacteristic, complemented
44#14556050C2211yescharacteristic, complemented
45#14556050C2211yescharacteristic, complemented
46#14556049C2211yescharacteristic, complemented
47#14556049C2211yescharacteristic, complemented
48#14556049C2211yescharacteristic, complemented
49C22⋊(C71⋊C8)C2211yescharacteristic, complemented
50(C2×D71)⋊C8C2211yescharacteristic
51(C2×D71)⋊C8C2211yescharacteristic
52C2×#41×C71C2211yescharacteristic, complemented
53C2×SD16×C71C2211yescharacteristic, complemented
54C2×D8×C71C2211yescharacteristic, complemented
55#121×C71C2211yescharacteristic
56#103×C71C2211yescharacteristic, complemented
57#102×C71C2211yescharacteristic, complemented
58C22⋊C8×C71C2211yescharacteristic, complemented
59C23×D71—21no—
60C23×D71D411yescharacteristic
61C2×D284—21no—
62C2×D284C2311yescharacteristic
63C2×C22⋊D71—21no—
64C2×C22⋊D71—21no—
65C2×C22⋊D71—21no—
66C2×C22⋊D71—21no—
67C2×C22⋊D71—21no—
68D4×D71—41no—
69D4×D71—41no—
70D4×D71—44no—
71C22×Dic71D411yescharacteristic
72C2×C4×D71—21no—
73C2×C4×D71—41no—
74C2×C4×D71—41no—
75C2×C4×D71D411yescharacteristic
76C2×C4×D71D411yescharacteristic
77C2×C4×D71C2311yescharacteristic
78C2×C4×D71C2311yescharacteristic
79#11765852—41no—
80#11765850—41no—
81C2×C71⋊C8C2311yescharacteristic
82C2×C71⋊C8C2311yescharacteristic
83C8×D71—41no—
84C8×D71—41no—
85C4⋊Dic71C2311yescharacteristic
86C4⋊Dic71C2311yescharacteristic
87C4⋊Dic71C2311yescharacteristic
88Dic71⋊C4—21no—
89Dic71⋊C4—21no—
90Dic71⋊C4—21no—
91C22⋊Dic71—21no—
92C22⋊Dic71—21no—
93C22⋊Dic71—21no—
94C22⋊Dic71—21no—
95(C2×D71)⋊C4—21no—
96(C2×D71)⋊C4—21no—
97(C2×D71)⋊C4—21no—
98(C2×D71)⋊C4—21no—
99C4×Dic71—21no—
100#41×C71—41no—
101#41×C71—41no—
102C2×Q8×C71C2311yescharacteristic
103C2×D4×C71—21no—
104C2×D4×C71—21no—
105C2×D4×C71C2311yescharacteristic
106C2×D4×C71C2311yescharacteristic
107C22×C4×C71—21no—
108C22×C4×C71C2311yescharacteristic
109SD16×C71—41no—
110D8×C71—41no—
111C2×C8×C71C2311yescharacteristic
112C2×C8×C71C2311yescharacteristic
113C4⋊C4×C71C2311yescharacteristic
114C22⋊C4×C71—21no—
115C23×C71—21no—
116C23×C71—21no—
117C23×C71C2×D411yescharacteristic
118C22×D71—22no—
119C22×D71—22no—
120C22×D71—21no—
121C22×D71—41no—
122C22×D71—42no—
123C22×D71—42no—
124C22×D71—42no—
125C22×D71C2×D411yescharacteristic
126C22×D71C2×D411yescharacteristic
127Q8×C71—21no—
128Q8×C71—21no—
129D4×C71—21no—
130D4×C71—21no—
131D4×C71—21no—
132D4×C71—21no—
133D4×C71—42no—
134D4×C71—42no—
135C2×C4×C71—21no—
136C2×C4×C71—21no—
137C2×C4×C71—21no—
138C2×C4×C71—21no—
139C2×C4×C71—42no—
140C2×C4×C71C2×D411yescharacteristic
141C2×C4×C71C2411yescharacteristic
142C22⋊D71—42no—
143C22⋊D71—42no—
144C22⋊D71—42no—
145C22⋊D71—42no—
146C22⋊D71—42no—
147C2×Dic71—21no—
148C2×Dic71—21no—
149C2×Dic71—21no—
150C2×Dic71—41no—
151C2×Dic71C2×D411yescharacteristic
152C2×Dic71C2×D411yescharacteristic
153D284—21no—
154D284—21no—
155D284—42no—
156C4×D71—21no—
157C4×D71—21no—
158C4×D71—21no—
159C4×D71—21no—
160C4×D71—41no—
161C4×D71—41no—
162C4×D71—42no—
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—44no—
182C2×D71—41no—
183C2×D71—41no—
184C2×D71—41no—
185C2×D71—84no—
186C2×D71#13512yes—
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×#13511yescharacteristic
203C2×C71C2×AGL(1,ℤ/8)11yescharacteristic
204D71—22no—
205D71—22no—
206D71—81no—
207#3188—711nomaximal, Sylow
208C71#318811yescharacteristic, complemented, Sylow
209#525—711no—
210C2×#121—711no—
211#484—711no—
212#482—711no—
213#482—711no—
214#481—711no—
215#466—711no—
216#466—711no—
217#465—711no—
218#465—711no—
219#450—711no—
220#449—711no—
221#449D7111yescharacteristic, complemented
222#447—711no—
223C2×C22⋊C8—711no—
224C2×#41C2×D7111yescharacteristic, complemented
225C22×D4—711no—
226C22×D4—1421no—
227C23×C4—711no—
228C2×SD16—711no—
229C2×SD16C2×D7111yescharacteristic, complemented
230C2×D8—711no—
231C2×D8C2×D7111yescharacteristic, complemented
232C22×C8—711no—
233C22×C8—711no—
234#123—1421no—
235C22⋊Q8—711no—
236C22⋊Q8—711no—
237#121—711no—
238#121—711no—
239#121—711no—
240#121—711no—
241#121—711no—
242#121—1421no—
243#121—1421no—
244#121C2×D7111yescharacteristic
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#106—711no—
255#103—711no—
256#103C2×D7111yescharacteristic, complemented
257#102—711no—
258#102—711no—
259#102—711no—
260#102—711no—
261#102—711no—
262#102C2×D7111yescharacteristic, complemented
263C22⋊C8—711no—
264C22⋊C8—711no—
265C22⋊C8—711no—
266C22⋊C8C2×D7111yescharacteristic, complemented
267C24—711no—
268C24—1421no—
269#41—41no—
270#41—41no—
271C2×Q8C22×D7111yescharacteristic
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—21no—
287C22×C4—2841no—
288C22×C4—2841no—
289C22×C4—711no—
290C22×C4—711no—
291C22×C4—711no—
292C22×C4—711no—
293C22×C4—711no—
294C22×C4—1421no—
295C22×C4C22×D7111yescharacteristic
296SD16—41no—
297SD16—2841no—
298D8—41no—
299D8—2841no—
300C2×C8—2841no—
301C2×C8—2841no—
302C2×C8—711no—
303C2×C8—711no—
304C2×C8C22×D7111yescharacteristic
305C2×C8C22×D7111yescharacteristic
306C4⋊C4—711no—
307C4⋊C4—711no—
308C4⋊C4—711no—
309C4⋊C4—1421no—
310C4⋊C4—1421no—
311C4⋊C4—1421no—
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—
322C42—1421no—
323C23—21no—
324C23—21no—
325C23—2841no—
326C23—2842no—
327C23—2842no—
328C23—2842no—
329C23—711no—
330C23—711no—
331C23—1422no—
332C23—1422no—
333C23—1421no—
334C23D4×D7111yescharacteristic
335Q8—21no—
336Q8—21no—
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—42no—
356C2×C4—2841no—
357C2×C4—2841no—
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—712no—
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#1455617311yescharacteristic
406C2—41no—
407C2—81no—
408C2—81no—
409C2—5681no—
410C2—1422no—
411C2—1422no—
412C2#1798655911yescharacteristic
413C2#135×D7111yescharacteristic
414C2AGL(1,ℤ/8)×D7111yescharacteristic
subgroupG/H
centerC22C2×D4×D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#449×C71C2
socleC22×C71C22×D4
hypercenter#449D71
hypocenterC71#3188
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #17986506C2semidirect
2. #121×D71C2semidirect
3. #17986333C2semidirect
4. #17986324C2semidirect
5. #17986320C2semidirect
6. #17986316C2semidirect
7. #17986234C2semidirect
8. #17986232C2semidirect
9. #17986231C2semidirect
10. #17986225C2semidirect
11. #17986148C2semidirect
12. #17986144C2semidirect
13. #17986131C2semidirect
14. C22⋊C8×D71C2semidirect
15. #449×C71C2semidirect
19. C2×#11765852C22semidirect
20. C2×#11765850C22semidirect
21. C2×C8×D71C22semidirect
22. C2×C8×D71C22semidirect
25. #14556104C22semidirect
32. #14556099C22semidirect
36. #14556087C22semidirect
39. #14556062C22semidirect
40. #14556061C22semidirect
41. #14556060C22semidirect
42. #14556059C22semidirect
43. #14556052C22semidirect
44. #14556050C22semidirect
45. #14556050C22semidirect
46. #14556049C22semidirect
47. #14556049C22semidirect
48. #14556049C22semidirect
49. C22⋊(C71⋊C8)C22semidirect
52. C2×#41×C71C22semidirect
53. C2×SD16×C71C22semidirect
54. C2×D8×C71C22semidirect
56. #103×C71C22semidirect
57. #102×C71C22semidirect
58. C22⋊C8×C71C22semidirect
208. C71#3188semidirect
221. #449D71semidirect
224. C2×#41C2×D71semidirect
229. C2×SD16C2×D71semidirect
231. C2×D8C2×D71semidirect
256. #103C2×D71semidirect
262. #102C2×D71semidirect
266. C22⋊C8C2×D71semidirect