Finite Group Databasebeta

← #20253214

Subgroups — #20253214

Order 6016.

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#15689750C211yesmaximal, characteristic, complemented
2#15689595C211yesmaximal, characteristic
3#15689425C211yesmaximal, characteristic, complemented
4#15689424C211yesmaximal, characteristic, complemented
5#15689423C211yesmaximal, characteristic, complemented
6#15689422C211yesmaximal, characteristic, complemented
7#15689412C211yesmaximal, characteristic, complemented
8#15689401C211yesmaximal, characteristic, complemented
9#15689400C211yesmaximal, characteristic, complemented
10#15689162C211yesmaximal, characteristic, complemented
11#15689158C211yesmaximal, characteristic, complemented
12#15689148C211yesmaximal, characteristic, complemented
13#15689126C211yesmaximal, characteristic
14#102×D47C211yesmaximal, characteristic
15C47×#476C211yesmaximal, characteristic, complemented
16C2×D4×D47C2211yescharacteristic
17C2×#10625324C2211yescharacteristic
18C2×C8×D47C2211yescharacteristic
19#13094023C2211yescharacteristic, complemented
20#13094022—21no—
21#13094016C2211yescharacteristic, complemented
22#13094015C2211yescharacteristic, complemented
23#13094014—21no—
24#13094002—21no—
25#13094000—21no—
26C4×D188C2211yescharacteristic
27D4×Dic47C2211yescharacteristic
28#13093986C2211yescharacteristic
29C4×C22⋊D47—21no—
30(C22⋊D47)⋊C4—21no—
31#13093982C2211yescharacteristic
32#13093982C2211yescharacteristic
33#13093981C2211yescharacteristic
34C4⋊C4×D47C2211yescharacteristic
35C2×(C2×D47)⋊C4—21no—
36C22⋊C4×D47—21no—
37#13093958C2211yescharacteristic, complemented
38#13093957C2211yescharacteristic, complemented
39#13093957C2211yescharacteristic, complemented
40#13093957C2211yescharacteristic, complemented
41#13093956C2211yescharacteristic, complemented
42#13093955C2211yescharacteristic, complemented
43C4⋊(C47⋊C8)C2211yescharacteristic, complemented
44Dic47⋊C8C2211yescharacteristic, complemented
45Dic47⋊C8C2211yescharacteristic, complemented
46#13093946C2211yescharacteristic
47#13093946C2211yescharacteristic
48#13093945C2211yescharacteristic
49#13093945C2211yescharacteristic
50#13093944C2211yescharacteristic
51#13093944C2211yescharacteristic
52C4⋊Q8×C47C2211yescharacteristic, complemented
53C4×D4×C47C2211yescharacteristic
54#106×C47C2211yescharacteristic, complemented
55#106×C47C2211yescharacteristic, complemented
56C4⋊C8×C47C2211yescharacteristic, complemented
57#102×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C23×D47—21no—
60C2×Q8×C47—21no—
61C2×D4×C47C2311yescharacteristic
62C22×C4×C47—21no—
63C2×C22⋊D47—21no—
64C22×Dic47—21no—
65D4×D47—22no—
66D4×D47Q814yescomplemented
67C2×D188C2311yescharacteristic
68C2×C4×D47—21no—
69C2×C4×D47—21no—
70C2×C4×D47—21no—
71C2×C4×D47C2311yescharacteristic
72C2×Dic94—21no—
73C2×C8×C47C2311yescharacteristic
74C2×C8×C47C2311yescharacteristic
75C4⋊C4×C47—21no—
76C4⋊C4×C47C2311yescharacteristic
77C4⋊C4×C47C2311yescharacteristic
78C4⋊C4×C47C2311yescharacteristic
79C22⋊C4×C47—21no—
80C42×C47C2311yescharacteristic
81C22⋊Dic47—21no—
82(C2×D47)⋊C4—21no—
83(C2×D47)⋊C4—21no—
84(C2×D47)⋊C4—21no—
85(C2×D47)⋊C4—21no—
86(C2×D47)⋊C4D411yescharacteristic
87(C2×D47)⋊C4D411yescharacteristic
88C4⋊Dic47—21no—
89C4⋊Dic47C2311yescharacteristic
90C4⋊Dic47C2311yescharacteristic
91C4⋊Dic47C2311yescharacteristic
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4D411yescharacteristic
98Dic47⋊C4D411yescharacteristic
99C4×Dic47—21no—
100C4×Dic47—21no—
101C4×Dic47C2311yescharacteristic
102C2×C47⋊C8C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104#10625324—22no—
105C8×D47—22no—
106C23×C47—21no—
107C22×D47—21no—
108C22×D47—24no—
109C22×D47—81no—
110C22×D47—81no—
111C22×D47C2×D411yescharacteristic
112Q8×C47—81no—
113D4×C47—21no—
114D4×C47C2×Q812yes—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—81no—
119C2×C4×C47C2×D411yescharacteristic
120C2×C4×C47C2×D411yescharacteristic
121C2×C4×C47C2411yescharacteristic
122C22⋊D47—24no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—81no—
127C2×Dic47C2×D411yescharacteristic
128C2×Dic47C2×D411yescharacteristic
129C2×Dic47C2×D411yescharacteristic
130D188—21no—
131D188C2×Q812yes—
132C4×D47—81no—
133C4×D47—81no—
134C4×D47—81no—
135C4×D47C2×Q812yes—
136C4×D47#4112yes—
137Dic94—81no—
138C8×C47—21no—
139C8×C47—21no—
140C47⋊C8—21no—
141C47⋊C8—21no—
142C22×C47—22no—
143C22×C47—41no—
144C22×C47—41no—
145C22×C47C22×D411yescharacteristic
146C2×D47—21no—
147C2×D47—21no—
148C2×D47—22no—
149C2×D47—41no—
150C2×D47—41no—
151C2×D47—84no—
152C2×D47C22⋊Q812yes—
153C4×C47—21no—
154C4×C47—21no—
155C4×C47—41no—
156C4×C47—41no—
157C4×C47—41no—
158C4×C47C22×Q811yescharacteristic
159C4×C47C2×#4111yescharacteristic
160Dic47—21no—
161Dic47—21no—
162Dic47—41no—
163Dic47—41no—
164Dic47—41no—
165Dic47C22⋊Q812yes—
166#3081—471nomaximal, Sylow
167C2×C47—42no—
168C2×C47C2×C22⋊Q811yescharacteristic
169C2×C47#57611yescharacteristic
170C2×C47#57711yescharacteristic
171D47—22no—
172D47—42no—
173#544—471no—
174#518—471no—
175#478—471no—
176#478—471no—
177#478—471no—
178#478—471no—
179#476—471no—
180#476D4711yescharacteristic, complemented
181#474—471no—
182#474—471no—
183#428—471no—
184#427—471no—
185#424—471no—
186#418—471no—
187C2×#102—471no—
188C47#308111yescharacteristic, complemented, Sylow
189C22×D4—471no—
190C2×M16—471no—
191C22×C8—471no—
192C4⋊Q8—471no—
193C4⋊Q8—941no—
194C4⋊Q8C2×D4711yescharacteristic, complemented
195#125—471no—
196#125—471no—
197#125—941no—
198C22⋊Q8—941no—
199C22⋊Q8—941no—
200C4×D4—471no—
201C4×D4—471no—
202C4×D4—471no—
203C4×D4—941no—
204C4×D4—941no—
205C4×D4C2×D4711yescharacteristic
206#117—471no—
207#117—471no—
208#117—471no—
209C2×C4⋊C4—471no—
210C2×C22⋊C4—941no—
211C2×C22⋊C4—941no—
212#107—471no—
213#107—471no—
214#107—471no—
215#107—471no—
216#106—471no—
217#106—471no—
218#106C2×D4711yescharacteristic, complemented
219#106C2×D4711yescharacteristic, complemented
220C4⋊C8—471no—
221C4⋊C8—471no—
222C4⋊C8—471no—
223C4⋊C8C2×D4711yescharacteristic, complemented
224#102—471no—
225#102—471no—
226#102—471no—
227#102—471no—
228#102—471no—
229#102—471no—
230#102C2×D4711yescharacteristic
231#102C2×D4711yescharacteristic
232C24—941no—
233C2×Q8—21no—
234C2×Q8—941no—
235C2×D4—474no—
236C2×D4—471no—
237C2×D4—942no—
238C2×D4—941no—
239C2×D4C22×D4711yescharacteristic
240C22×C4—21no—
241C22×C4—471no—
242C22×C4—941no—
243C22×C4—941no—
244C22×C4—941no—
245C22×C4—941no—
246M16—942no—
247C2×C8—471no—
248C2×C8—471no—
249C2×C8—942no—
250C2×C8C22×D4711yescharacteristic
251C2×C8C22×D4711yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—471no—
254C4⋊C4—471no—
255C4⋊C4—471no—
256C4⋊C4—471no—
257C4⋊C4—471no—
258C4⋊C4—941no—
259C4⋊C4—941no—
260C4⋊C4—941no—
261C4⋊C4—941no—
262C4⋊C4—941no—
263C4⋊C4—941no—
264C4⋊C4C22×D4711yescharacteristic
265C4⋊C4C22×D4711yescharacteristic
266C4⋊C4C22×D4711yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—471no—
269C22⋊C4—471no—
270C22⋊C4—941no—
271C22⋊C4—941no—
272C22⋊C4—941no—
273C22⋊C4—941no—
274C22⋊C4—941no—
275C42—471no—
276C42—941no—
277C42—941no—
278C42C22×D4711yescharacteristic
279C23—21no—
280C23—471no—
281C23—944no—
282C23—941no—
283C23—3761no—
284C23—3761no—
285Q8—81no—
286Q8—3761no—
287D4—21no—
288D4—472no—
289D4—944no—
290D4—941no—
291D4Q8×D4712yes—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—81no—
296C2×C4—471no—
297C2×C4—472no—
298C2×C4—472no—
299C2×C4—471no—
300C2×C4—471no—
301C2×C4—941no—
302C2×C4—941no—
303C2×C4—941no—
304C2×C4—3761no—
305C2×C4—3761no—
306C2×C4—3761no—
307C2×C4—3761no—
308C2×C4D4×D4711yescharacteristic
309C2×C4D4×D4711yescharacteristic
310C2×C4C23×D4711yescharacteristic
311C8—21no—
312C8—21no—
313C8—941no—
314C8—941no—
315C22—22no—
316C22—41no—
317C22—41no—
318C22—472no—
319C22—941no—
320C22—941no—
321C22—942no—
322C22—3764no—
323C22—1881no—
324C22—1881no—
325C22C2×D4×D4711yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—472no—
332C4—941no—
333C4—941no—
334C4—1881no—
335C4—1881no—
336C4—1881no—
337C4C2×Q8×D4711yescharacteristic
338C4#41×D4711yescharacteristic
339C2—42no—
340C2—942no—
341C2—1882no—
342C2C22⋊Q8×D4711yescharacteristic
343C2#1568992711yescharacteristic
344C2#1568992911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#476C2
socleC22×C47C22×D4
hypercenter#476D47
hypocenterC47#3081
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #15689750C2semidirect
3. #15689425C2semidirect
4. #15689424C2semidirect
5. #15689423C2semidirect
6. #15689422C2semidirect
7. #15689412C2semidirect
8. #15689401C2semidirect
9. #15689400C2semidirect
10. #15689162C2semidirect
11. #15689158C2semidirect
12. #15689148C2semidirect
15. C47×#476C2semidirect
19. #13094023C22semidirect
21. #13094016C22semidirect
22. #13094015C22semidirect
37. #13093958C22semidirect
38. #13093957C22semidirect
39. #13093957C22semidirect
40. #13093957C22semidirect
41. #13093956C22semidirect
42. #13093955C22semidirect
43. C4⋊(C47⋊C8)C22semidirect
44. Dic47⋊C8C22semidirect
45. Dic47⋊C8C22semidirect
52. C4⋊Q8×C47C22semidirect
54. #106×C47C22semidirect
55. #106×C47C22semidirect
56. C4⋊C8×C47C22semidirect
66. D4×D47Q8semidirect
180. #476D47semidirect
188. C47#3081semidirect
194. C4⋊Q8C2×D47semidirect
218. #106C2×D47semidirect
219. #106C2×D47semidirect
223. C4⋊C8C2×D47semidirect