Finite Group Databasebeta

← #21433920

Subgroups — #21433920

Order 7552.

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#16838029C211yesmaximal, characteristic, complemented
2#16837874C211yesmaximal, characteristic
3#16837705C211yesmaximal, characteristic, complemented
4#16837703C211yesmaximal, characteristic, complemented
5#16837702C211yesmaximal, characteristic, complemented
6#16837700C211yesmaximal, characteristic, complemented
7#16837690C211yesmaximal, characteristic, complemented
8#16837689C211yesmaximal, characteristic, complemented
9#16837681C211yesmaximal, characteristic, complemented
10#16837443C211yesmaximal, characteristic, complemented
11#16837439C211yesmaximal, characteristic, complemented
12#16837427C211yesmaximal, characteristic, complemented
13#16837405C211yesmaximal, characteristic
14#102×D59C211yesmaximal, characteristic
15C59×#474C211yesmaximal, characteristic, complemented
16C2×D4×D59C2211yescharacteristic
17C2×#11745659C2211yescharacteristic
18C2×C8×D59C2211yescharacteristic
19#14273726C2211yescharacteristic, complemented
20#14273725—21no—
21#14273719C2211yescharacteristic, complemented
22#14273718C2211yescharacteristic, complemented
23#14273717—21no—
24#14273705—21no—
25#14273703—21no—
26C4×D236C2211yescharacteristic
27D4×Dic59C2211yescharacteristic
28#14273689C2211yescharacteristic
29C4×C22⋊D59—21no—
30(C22⋊D59)⋊C4—21no—
31#14273685C2211yescharacteristic
32#14273685C2211yescharacteristic
33#14273684C2211yescharacteristic
34C4⋊C4×D59C2211yescharacteristic
35C2×(C2×D59)⋊C4—21no—
36C22⋊C4×D59—21no—
37#14273661C2211yescharacteristic, complemented
38#14273660C2211yescharacteristic, complemented
39#14273659C2211yescharacteristic, complemented
40#14273658C2211yescharacteristic, complemented
41#14273658C2211yescharacteristic, complemented
42#14273658C2211yescharacteristic, complemented
43C4⋊(C59⋊C8)C2211yescharacteristic, complemented
44Dic59⋊C8C2211yescharacteristic, complemented
45Dic59⋊C8C2211yescharacteristic, complemented
46#14273649C2211yescharacteristic
47#14273649C2211yescharacteristic
48#14273648C2211yescharacteristic
49#14273648C2211yescharacteristic
50#14273647C2211yescharacteristic
51#14273647C2211yescharacteristic
52C4⋊Q8×C59C2211yescharacteristic, complemented
53C4×D4×C59C2211yescharacteristic
54#107×C59C2211yescharacteristic, complemented
55#107×C59C2211yescharacteristic, complemented
56C4⋊C8×C59C2211yescharacteristic, complemented
57#102×C59C2211yescharacteristic
58#102×C59C2211yescharacteristic
59C23×D59—21no—
60C2×Q8×C59—21no—
61C2×D4×C59C2311yescharacteristic
62C22×C4×C59—21no—
63C2×C22⋊D59—21no—
64C22×Dic59—21no—
65D4×D59—22no—
66D4×D59Q814yescomplemented
67C2×D236C2311yescharacteristic
68C2×C4×D59—21no—
69C2×C4×D59—21no—
70C2×C4×D59—21no—
71C2×C4×D59C2311yescharacteristic
72C2×Dic118—21no—
73C2×C8×C59C2311yescharacteristic
74C2×C8×C59C2311yescharacteristic
75C4⋊C4×C59—21no—
76C4⋊C4×C59C2311yescharacteristic
77C4⋊C4×C59C2311yescharacteristic
78C4⋊C4×C59C2311yescharacteristic
79C22⋊C4×C59—21no—
80C42×C59C2311yescharacteristic
81C22⋊Dic59—21no—
82(C2×D59)⋊C4—21no—
83(C2×D59)⋊C4—21no—
84(C2×D59)⋊C4—21no—
85(C2×D59)⋊C4—21no—
86(C2×D59)⋊C4D411yescharacteristic
87(C2×D59)⋊C4D411yescharacteristic
88C4⋊Dic59—21no—
89C4⋊Dic59C2311yescharacteristic
90C4⋊Dic59C2311yescharacteristic
91C4⋊Dic59C2311yescharacteristic
92Dic59⋊C4—21no—
93Dic59⋊C4—21no—
94Dic59⋊C4—21no—
95Dic59⋊C4—21no—
96Dic59⋊C4—21no—
97Dic59⋊C4D411yescharacteristic
98Dic59⋊C4D411yescharacteristic
99C4×Dic59—21no—
100C4×Dic59—21no—
101C4×Dic59C2311yescharacteristic
102C2×C59⋊C8C2311yescharacteristic
103C2×C59⋊C8C2311yescharacteristic
104#11745659—22no—
105C8×D59—22no—
106C23×C59—21no—
107C22×D59—21no—
108C22×D59—24no—
109C22×D59—81no—
110C22×D59—81no—
111C22×D59C2×D411yescharacteristic
112Q8×C59—81no—
113D4×C59—21no—
114D4×C59C2×Q812yes—
115C2×C4×C59—21no—
116C2×C4×C59—21no—
117C2×C4×C59—21no—
118C2×C4×C59—81no—
119C2×C4×C59C2×D411yescharacteristic
120C2×C4×C59C2×D411yescharacteristic
121C2×C4×C59C2411yescharacteristic
122C22⋊D59—24no—
123C2×Dic59—21no—
124C2×Dic59—21no—
125C2×Dic59—21no—
126C2×Dic59—81no—
127C2×Dic59C2×D411yescharacteristic
128C2×Dic59C2×D411yescharacteristic
129C2×Dic59C2×D411yescharacteristic
130D236—21no—
131D236C2×Q812yes—
132C4×D59—81no—
133C4×D59—81no—
134C4×D59—81no—
135C4×D59C2×Q812yes—
136C4×D59#4112yes—
137Dic118—81no—
138C8×C59—21no—
139C8×C59—21no—
140C59⋊C8—21no—
141C59⋊C8—21no—
142C22×C59—22no—
143C22×C59—41no—
144C22×C59—41no—
145C22×C59C22×D411yescharacteristic
146C2×D59—21no—
147C2×D59—21no—
148C2×D59—22no—
149C2×D59—41no—
150C2×D59—41no—
151C2×D59—84no—
152C2×D59C22⋊Q812yes—
153C4×C59—21no—
154C4×C59—21no—
155C4×C59—41no—
156C4×C59—41no—
157C4×C59—41no—
158C4×C59C22×Q811yescharacteristic
159C4×C59C2×#4111yescharacteristic
160Dic59—21no—
161Dic59—21no—
162Dic59—41no—
163Dic59—41no—
164Dic59—41no—
165Dic59C22⋊Q812yes—
166#3081—591nomaximal, Sylow
167C2×C59—42no—
168C2×C59C2×C22⋊Q811yescharacteristic
169C2×C59#57611yescharacteristic
170C2×C59#57711yescharacteristic
171D59—22no—
172D59—42no—
173#544—591no—
174#518—591no—
175#478—591no—
176#478—591no—
177#478—591no—
178#478—591no—
179#476—591no—
180#476—591no—
181#474—591no—
182#474D5911yescharacteristic, complemented
183#428—591no—
184#427—591no—
185#424—591no—
186#418—591no—
187C2×#102—591no—
188C59#308111yescharacteristic, complemented, Sylow
189C22×D4—591no—
190C2×M16—591no—
191C22×C8—591no—
192C4⋊Q8—591no—
193C4⋊Q8—1181no—
194C4⋊Q8C2×D5911yescharacteristic, complemented
195#125—591no—
196#125—591no—
197#125—1181no—
198C22⋊Q8—1181no—
199C22⋊Q8—1181no—
200C4×D4—591no—
201C4×D4—591no—
202C4×D4—591no—
203C4×D4—1181no—
204C4×D4—1181no—
205C4×D4C2×D5911yescharacteristic
206#117—591no—
207#117—591no—
208#117—591no—
209C2×C4⋊C4—591no—
210C2×C22⋊C4—1181no—
211C2×C22⋊C4—1181no—
212#107—591no—
213#107—591no—
214#107C2×D5911yescharacteristic, complemented
215#107C2×D5911yescharacteristic, complemented
216#106—591no—
217#106—591no—
218#106—591no—
219#106—591no—
220C4⋊C8—591no—
221C4⋊C8—591no—
222C4⋊C8—591no—
223C4⋊C8C2×D5911yescharacteristic, complemented
224#102—591no—
225#102—591no—
226#102—591no—
227#102—591no—
228#102—591no—
229#102—591no—
230#102C2×D5911yescharacteristic
231#102C2×D5911yescharacteristic
232C24—1181no—
233C2×Q8—21no—
234C2×Q8—1181no—
235C2×D4—594no—
236C2×D4—591no—
237C2×D4—1182no—
238C2×D4—1181no—
239C2×D4C22×D5911yescharacteristic
240C22×C4—21no—
241C22×C4—591no—
242C22×C4—1181no—
243C22×C4—1181no—
244C22×C4—1181no—
245C22×C4—1181no—
246M16—1182no—
247C2×C8—591no—
248C2×C8—591no—
249C2×C8—1182no—
250C2×C8C22×D5911yescharacteristic
251C2×C8C22×D5911yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—591no—
254C4⋊C4—591no—
255C4⋊C4—591no—
256C4⋊C4—591no—
257C4⋊C4—591no—
258C4⋊C4—1181no—
259C4⋊C4—1181no—
260C4⋊C4—1181no—
261C4⋊C4—1181no—
262C4⋊C4—1181no—
263C4⋊C4—1181no—
264C4⋊C4C22×D5911yescharacteristic
265C4⋊C4C22×D5911yescharacteristic
266C4⋊C4C22×D5911yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—591no—
269C22⋊C4—591no—
270C22⋊C4—1181no—
271C22⋊C4—1181no—
272C22⋊C4—1181no—
273C22⋊C4—1181no—
274C22⋊C4—1181no—
275C42—591no—
276C42—1181no—
277C42—1181no—
278C42C22×D5911yescharacteristic
279C23—21no—
280C23—591no—
281C23—1184no—
282C23—1181no—
283C23—4721no—
284C23—4721no—
285Q8—81no—
286Q8—4721no—
287D4—21no—
288D4—592no—
289D4—1184no—
290D4—1181no—
291D4Q8×D5912yes—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—81no—
296C2×C4—591no—
297C2×C4—592no—
298C2×C4—592no—
299C2×C4—591no—
300C2×C4—591no—
301C2×C4—1181no—
302C2×C4—1181no—
303C2×C4—1181no—
304C2×C4—4721no—
305C2×C4—4721no—
306C2×C4—4721no—
307C2×C4—4721no—
308C2×C4D4×D5911yescharacteristic
309C2×C4D4×D5911yescharacteristic
310C2×C4C23×D5911yescharacteristic
311C8—21no—
312C8—21no—
313C8—1181no—
314C8—1181no—
315C22—22no—
316C22—41no—
317C22—41no—
318C22—592no—
319C22—1181no—
320C22—1181no—
321C22—1182no—
322C22—4724no—
323C22—2361no—
324C22—2361no—
325C22C2×D4×D5911yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—592no—
332C4—1181no—
333C4—1181no—
334C4—2361no—
335C4—2361no—
336C4—2361no—
337C4C2×Q8×D5911yescharacteristic
338C4#41×D5911yescharacteristic
339C2—42no—
340C2—1182no—
341C2—2362no—
342C2C22⋊Q8×D5911yescharacteristic
343C2#1683820311yescharacteristic
344C2#1683821111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#474C2
socleC22×C59C22×D4
hypercenter#474D59
hypocenterC59#3081
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #16838029C2semidirect
3. #16837705C2semidirect
4. #16837703C2semidirect
5. #16837702C2semidirect
6. #16837700C2semidirect
7. #16837690C2semidirect
8. #16837689C2semidirect
9. #16837681C2semidirect
10. #16837443C2semidirect
11. #16837439C2semidirect
12. #16837427C2semidirect
15. C59×#474C2semidirect
19. #14273726C22semidirect
21. #14273719C22semidirect
22. #14273718C22semidirect
37. #14273661C22semidirect
38. #14273660C22semidirect
39. #14273659C22semidirect
40. #14273658C22semidirect
41. #14273658C22semidirect
42. #14273658C22semidirect
43. C4⋊(C59⋊C8)C22semidirect
44. Dic59⋊C8C22semidirect
45. Dic59⋊C8C22semidirect
52. C4⋊Q8×C59C22semidirect
54. #107×C59C22semidirect
55. #107×C59C22semidirect
56. C4⋊C8×C59C22semidirect
66. D4×D59Q8semidirect
182. #474D59semidirect
188. C59#3081semidirect
194. C4⋊Q8C2×D59semidirect
214. #107C2×D59semidirect
215. #107C2×D59semidirect
223. C4⋊C8C2×D59semidirect