Finite Group Databasebeta

← #22598166

Subgroups — #22598166

Order 9088.

398 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17986626C211yesmaximal, characteristic, complemented
2#17986471C211yesmaximal, characteristic
3#17986301C211yesmaximal, characteristic, complemented
4#17986300C211yesmaximal, characteristic, complemented
5#17986299C211yesmaximal, characteristic, complemented
6#17986298C211yesmaximal, characteristic, complemented
7#17986288C211yesmaximal, characteristic, complemented
8#17986277C211yesmaximal, characteristic, complemented
9#17986276C211yesmaximal, characteristic, complemented
10#17986038C211yesmaximal, characteristic, complemented
11#17986034C211yesmaximal, characteristic, complemented
12#17986024C211yesmaximal, characteristic, complemented
13#17986002C211yesmaximal, characteristic
14#102×D71C211yesmaximal, characteristic
15#476×C71C211yesmaximal, characteristic, complemented
16C2×D4×D71C2211yescharacteristic
17C2×#11765848C2211yescharacteristic
18C2×C8×D71C2211yescharacteristic
19#14556127C2211yescharacteristic, complemented
20#14556126—21no—
21#14556120C2211yescharacteristic, complemented
22#14556119C2211yescharacteristic, complemented
23#14556118—21no—
24#14556106—21no—
25#14556104—21no—
26C4×D284C2211yescharacteristic
27D4×Dic71C2211yescharacteristic
28#14556090C2211yescharacteristic
29C4×C22⋊D71—21no—
30(C22⋊D71)⋊C4—21no—
31#14556086C2211yescharacteristic
32#14556086C2211yescharacteristic
33#14556085C2211yescharacteristic
34C4⋊C4×D71C2211yescharacteristic
35C2×(C2×D71)⋊C4—21no—
36C22⋊C4×D71—21no—
37#14556062C2211yescharacteristic, complemented
38#14556061C2211yescharacteristic, complemented
39#14556061C2211yescharacteristic, complemented
40#14556061C2211yescharacteristic, complemented
41#14556060C2211yescharacteristic, complemented
42#14556059C2211yescharacteristic, complemented
43C4⋊(C71⋊C8)C2211yescharacteristic, complemented
44Dic71⋊C8C2211yescharacteristic, complemented
45Dic71⋊C8C2211yescharacteristic, complemented
46#14556050C2211yescharacteristic
47#14556050C2211yescharacteristic
48#14556049C2211yescharacteristic
49#14556049C2211yescharacteristic
50#14556048C2211yescharacteristic
51#14556048C2211yescharacteristic
52C4⋊Q8×C71C2211yescharacteristic, complemented
53C4×D4×C71C2211yescharacteristic
54#106×C71C2211yescharacteristic, complemented
55#106×C71C2211yescharacteristic, complemented
56C4⋊C8×C71C2211yescharacteristic, complemented
57#102×C71C2211yescharacteristic
58#102×C71C2211yescharacteristic
59C23×D71—21no—
60C2×Dic142—21no—
61C2×D284C2311yescharacteristic
62C2×C22⋊D71—21no—
63D4×D71—22no—
64D4×D71Q814yescomplemented
65C22×Dic71—21no—
66C2×C4×D71—21no—
67C2×C4×D71—21no—
68C2×C4×D71—21no—
69C2×C4×D71C2311yescharacteristic
70#11765848—22no—
71C2×C71⋊C8C2311yescharacteristic
72C2×C71⋊C8C2311yescharacteristic
73C8×D71—22no—
74C4⋊Dic71—21no—
75C4⋊Dic71C2311yescharacteristic
76C4⋊Dic71C2311yescharacteristic
77C4⋊Dic71C2311yescharacteristic
78Dic71⋊C4—21no—
79Dic71⋊C4—21no—
80Dic71⋊C4—21no—
81Dic71⋊C4—21no—
82Dic71⋊C4—21no—
83Dic71⋊C4D411yescharacteristic
84Dic71⋊C4D411yescharacteristic
85C22⋊Dic71—21no—
86(C2×D71)⋊C4—21no—
87(C2×D71)⋊C4—21no—
88(C2×D71)⋊C4—21no—
89(C2×D71)⋊C4—21no—
90(C2×D71)⋊C4D411yescharacteristic
91(C2×D71)⋊C4D411yescharacteristic
92C4×Dic71—21no—
93C4×Dic71—21no—
94C4×Dic71C2311yescharacteristic
95C2×Q8×C71—21no—
96C2×D4×C71C2311yescharacteristic
97C22×C4×C71—21no—
98C2×C8×C71C2311yescharacteristic
99C2×C8×C71C2311yescharacteristic
100C4⋊C4×C71—21no—
101C4⋊C4×C71C2311yescharacteristic
102C4⋊C4×C71C2311yescharacteristic
103C4⋊C4×C71C2311yescharacteristic
104C22⋊C4×C71—21no—
105C42×C71C2311yescharacteristic
106C23×C71—21no—
107C22×D71—21no—
108C22×D71—24no—
109C22×D71—81no—
110C22×D71—81no—
111C22×D71C2×D411yescharacteristic
112Q8×C71—81no—
113D4×C71—21no—
114D4×C71C2×Q812yes—
115C2×C4×C71—21no—
116C2×C4×C71—21no—
117C2×C4×C71—21no—
118C2×C4×C71—81no—
119C2×C4×C71C2×D411yescharacteristic
120C2×C4×C71C2×D411yescharacteristic
121C2×C4×C71C2411yescharacteristic
122C22⋊D71—24no—
123C2×Dic71—21no—
124C2×Dic71—21no—
125C2×Dic71—21no—
126C2×Dic71—81no—
127C2×Dic71C2×D411yescharacteristic
128C2×Dic71C2×D411yescharacteristic
129C2×Dic71C2×D411yescharacteristic
130D284—21no—
131D284C2×Q812yes—
132C4×D71—81no—
133C4×D71—81no—
134C4×D71—81no—
135C4×D71C2×Q812yes—
136C4×D71#4112yes—
137Dic142—81no—
138C8×C71—21no—
139C8×C71—21no—
140C71⋊C8—21no—
141C71⋊C8—21no—
142C22×C71—22no—
143C22×C71—41no—
144C22×C71—41no—
145C22×C71C22×D411yescharacteristic
146C2×D71—21no—
147C2×D71—21no—
148C2×D71—22no—
149C2×D71—41no—
150C2×D71—41no—
151C2×D71—84no—
152C2×D71C22⋊Q812yes—
153C4×C71—21no—
154C4×C71—21no—
155C4×C71—41no—
156C4×C71—41no—
157C4×C71—41no—
158C4×C71C22×Q811yescharacteristic
159C4×C71C2×#4111yescharacteristic
160Dic71—21no—
161Dic71—21no—
162Dic71—41no—
163Dic71—41no—
164Dic71—41no—
165Dic71C22⋊Q812yes—
166C2×C71—42no—
167C2×C71C2×C22⋊Q811yescharacteristic
168C2×C71#57611yescharacteristic
169C2×C71#57711yescharacteristic
170D71—22no—
171D71—42no—
172#3081—711nomaximal, Sylow
173C71#308111yescharacteristic, complemented, Sylow
174#544—711no—
175#518—711no—
176#478—711no—
177#478—711no—
178#478—711no—
179#478—711no—
180#476—711no—
181#476D7111yescharacteristic, complemented
182#474—711no—
183#474—711no—
184#428—711no—
185#427—711no—
186#424—711no—
187#418—711no—
188C2×#102—711no—
189C22×D4—711no—
190C2×M16—711no—
191C22×C8—711no—
192C4⋊Q8—711no—
193C4⋊Q8—1421no—
194C4⋊Q8C2×D7111yescharacteristic, complemented
195#125—711no—
196#125—711no—
197#125—1421no—
198C22⋊Q8—1421no—
199C22⋊Q8—1421no—
200C4×D4—711no—
201C4×D4—711no—
202C4×D4—711no—
203C4×D4—1421no—
204C4×D4—1421no—
205C4×D4C2×D7111yescharacteristic
206#117—711no—
207#117—711no—
208#117—711no—
209C2×C4⋊C4—711no—
210C2×C22⋊C4—1421no—
211C2×C22⋊C4—1421no—
212#107—711no—
213#107—711no—
214#107—711no—
215#107—711no—
216#106—711no—
217#106—711no—
218#106C2×D7111yescharacteristic, complemented
219#106C2×D7111yescharacteristic, complemented
220C4⋊C8—711no—
221C4⋊C8—711no—
222C4⋊C8—711no—
223C4⋊C8C2×D7111yescharacteristic, complemented
224#102—711no—
225#102—711no—
226#102—711no—
227#102—711no—
228#102—711no—
229#102—711no—
230#102C2×D7111yescharacteristic
231#102C2×D7111yescharacteristic
232C24—1421no—
233C2×Q8—21no—
234C2×Q8—1421no—
235C2×D4—714no—
236C2×D4—711no—
237C2×D4—1422no—
238C2×D4—1421no—
239C2×D4C22×D7111yescharacteristic
240C22×C4—21no—
241C22×C4—711no—
242C22×C4—1421no—
243C22×C4—1421no—
244C22×C4—1421no—
245C22×C4—1421no—
246M16—1422no—
247C2×C8—711no—
248C2×C8—711no—
249C2×C8—1422no—
250C2×C8C22×D7111yescharacteristic
251C2×C8C22×D7111yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—711no—
254C4⋊C4—711no—
255C4⋊C4—711no—
256C4⋊C4—711no—
257C4⋊C4—711no—
258C4⋊C4—1421no—
259C4⋊C4—1421no—
260C4⋊C4—1421no—
261C4⋊C4—1421no—
262C4⋊C4—1421no—
263C4⋊C4—1421no—
264C4⋊C4C22×D7111yescharacteristic
265C4⋊C4C22×D7111yescharacteristic
266C4⋊C4C22×D7111yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—711no—
269C22⋊C4—711no—
270C22⋊C4—1421no—
271C22⋊C4—1421no—
272C22⋊C4—1421no—
273C22⋊C4—1421no—
274C22⋊C4—1421no—
275C42—711no—
276C42—1421no—
277C42—1421no—
278C42C22×D7111yescharacteristic
279C23—21no—
280C23—5681no—
281C23—5681no—
282C23—711no—
283C23—1424no—
284C23—1421no—
285Q8—81no—
286Q8—5681no—
287D4—21no—
288D4—712no—
289D4—1424no—
290D4—1421no—
291D4Q8×D7112yes—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—81no—
296C2×C4—5681no—
297C2×C4—5681no—
298C2×C4—5681no—
299C2×C4—5681no—
300C2×C4—711no—
301C2×C4—712no—
302C2×C4—712no—
303C2×C4—711no—
304C2×C4—711no—
305C2×C4—1421no—
306C2×C4—1421no—
307C2×C4—1421no—
308C2×C4D4×D7111yescharacteristic
309C2×C4D4×D7111yescharacteristic
310C2×C4C23×D7111yescharacteristic
311C8—21no—
312C8—21no—
313C8—1421no—
314C8—1421no—
315C22—22no—
316C22—41no—
317C22—41no—
318C22—2841no—
319C22—2841no—
320C22—5684no—
321C22—712no—
322C22—1422no—
323C22—1421no—
324C22—1421no—
325C22C2×D4×D7111yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—2841no—
332C4—2841no—
333C4—2841no—
334C4—712no—
335C4—1421no—
336C4—1421no—
337C4C2×Q8×D7111yescharacteristic
338C4#41×D7111yescharacteristic
339C2—42no—
340C2—2842no—
341C2—1422no—
342C2C22⋊Q8×D7111yescharacteristic
343C2#1798680311yescharacteristic
344C2#1798680511yescharacteristic
subgroupG/H
centerC22C2×D4×D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#476×C71C2
socleC22×C71C22×D4
hypercenter#476D71
hypocenterC71#3081
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #17986626C2semidirect
3. #17986301C2semidirect
4. #17986300C2semidirect
5. #17986299C2semidirect
6. #17986298C2semidirect
7. #17986288C2semidirect
8. #17986277C2semidirect
9. #17986276C2semidirect
10. #17986038C2semidirect
11. #17986034C2semidirect
12. #17986024C2semidirect
15. #476×C71C2semidirect
19. #14556127C22semidirect
21. #14556120C22semidirect
22. #14556119C22semidirect
37. #14556062C22semidirect
38. #14556061C22semidirect
39. #14556061C22semidirect
40. #14556061C22semidirect
41. #14556060C22semidirect
42. #14556059C22semidirect
43. C4⋊(C71⋊C8)C22semidirect
44. Dic71⋊C8C22semidirect
45. Dic71⋊C8C22semidirect
52. C4⋊Q8×C71C22semidirect
54. #106×C71C22semidirect
55. #106×C71C22semidirect
56. C4⋊C8×C71C22semidirect
64. D4×D71Q8semidirect
173. C71#3081semidirect
181. #476D71semidirect
194. C4⋊Q8C2×D71semidirect
218. #106C2×D71semidirect
219. #106C2×D71semidirect
223. C4⋊C8C2×D71semidirect