Finite Group Databasebeta

← #21434819

Subgroups — #21434819

Order 7552.

370 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#16837936C211yesmaximal, characteristic, complemented
2#16837801C211yesmaximal, characteristic, complemented
3#16837784C211yesmaximal, characteristic, complemented
4#16837759C211yesmaximal, characteristic, complemented
5#16837756C211yesmaximal, characteristic, complemented
6#16837658C211yesmaximal, characteristic, complemented
7#16837653C211yesmaximal, characteristic
8#16837650C211yesmaximal, characteristic, complemented
9#16837646C211yesmaximal, characteristic, complemented
10#16837512C211yesmaximal, characteristic, complemented
11#16837507C211yesmaximal, characteristic, complemented
12#16837502C211yesmaximal, characteristic, complemented
13#16837500C211yesmaximal, characteristic, complemented
14C4×#11745664C211yesmaximal, characteristic, complemented
15C59×#529C211yesmaximal, characteristic, complemented
16C2×#11745672C2211yescharacteristic
17C2×#11745670C2211yescharacteristic
18C2×#11745671C2211yescharacteristic
19C2×#11745669C2211yescharacteristic
20C2×#11745664C2211yescharacteristic
21C2×#11745664C2211yescharacteristic
22#14273721—21no—
23#14273719C2211yescharacteristic
24#14273715C2211yescharacteristic
25#14273710—21no—
26#14273706C2211yescharacteristic
27#14273701C2211yescharacteristic
28C4×Dic118C2211yescharacteristic
29C4×D236C2211yescharacteristic
30C4×C22⋊D59—21no—
31#14273684—21no—
32#14273660C2211yescharacteristic
33#14273660C2211yescharacteristic
34#14273658C2211yescharacteristic
35#14273658C2211yescharacteristic
36#14273651C2211yescharacteristic
37#14273651C2211yescharacteristic
38#14273650C2211yescharacteristic
39#14273650C2211yescharacteristic
40#14273648C2211yescharacteristic
41#14273648C2211yescharacteristic
42#14273647C2211yescharacteristic
43#14273647C2211yescharacteristic
44#14273638C2211yescharacteristic
45#14273638C2211yescharacteristic
46C4×C59⋊C8C2211yescharacteristic
47C4×C59⋊C8C2211yescharacteristic
48#126×C59—21no—
49#125×C59C2211yescharacteristic
50#124×C59C2211yescharacteristic
51#123×C59—21no—
52C22⋊Q8×C59C2211yescharacteristic
53#121×C59C2211yescharacteristic
54C4×Q8×C59C2211yescharacteristic
55C4×D4×C59—21no—
56C4×D4×C59C2211yescharacteristic
57#117×C59—21no—
58C2×C42×C59C2211yescharacteristic
59C2×Q8×C59C2311yescharacteristic
60C2×D4×C59—21no—
61C2×D4×C59C2311yescharacteristic
62C22×C4×C59—21no—
63C22×C4×C59D411yescharacteristic
64C22×C4×C59D411yescharacteristic
65C22×C4×C59C2311yescharacteristic
66C2×C22⋊D59—21no—
67C2×D236C2311yescharacteristic
68C2×C4×D59—21no—
69C2×Dic118C2311yescharacteristic
70C4⋊C4×C59—21no—
71C4⋊C4×C59—21no—
72C4⋊C4×C59—21no—
73C4⋊C4×C59—21no—
74C4⋊C4×C59C2311yescharacteristic
75C4⋊C4×C59C2311yescharacteristic
76C22⋊C4×C59—21no—
77C22⋊C4×C59—21no—
78C22⋊C4×C59—21no—
79C22⋊C4×C59—21no—
80C22⋊C4×C59—21no—
81C42×C59—21no—
82C42×C59D411yescharacteristic
83C42×C59D411yescharacteristic
84C42×C59C2311yescharacteristic
85C42×C59C2311yescharacteristic
86C22⋊Dic59—21no—
87#11745672—22no—
88#11745671—22no—
89#11745670—22no—
90#11745669—22no—
91(C2×D59)⋊C4—21no—
92(C2×D59)⋊C4—21no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4—21no—
95C4⋊Dic59C2311yescharacteristic
96C4⋊Dic59C2311yescharacteristic
97Dic59⋊C4—21no—
98Dic59⋊C4—21no—
99Dic59⋊C4—21no—
100Dic59⋊C4—21no—
101C4×Dic59—21no—
102#11745664—22no—
103#11745664—22no—
104C2×C59⋊C8C2311yescharacteristic
105C2×C59⋊C8C2311yescharacteristic
106C2×C59⋊C8C2311yescharacteristic
107C2×C59⋊C8C2311yescharacteristic
108C23×C59—21no—
109C23×C59C2×D411yescharacteristic
110C22×D59—21no—
111Q8×C59—21no—
112Q8×C59—21no—
113D4×C59—21no—
114D4×C59—21no—
115D4×C59—42no—
116C2×C4×C59—21no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—41no—
122C2×C4×C59—41no—
123C2×C4×C59—42no—
124C2×C4×C59C2×D411yescharacteristic
125C2×C4×C59C2×D411yescharacteristic
126C2×C4×C59C2×D411yescharacteristic
127C2×C4×C59C2×D411yescharacteristic
128C2×C4×C59C2×D411yescharacteristic
129C2×C4×C59C2411yescharacteristic
130C22⋊D59—42no—
131C2×Dic59—21no—
132C2×Dic59—21no—
133C2×Dic59—21no—
134D236—21no—
135D236—21no—
136C4×D59—42no—
137Dic118—21no—
138Dic118—21no—
139C59⋊C8—21no—
140C59⋊C8—21no—
141C59⋊C8#4112yes—
142C59⋊C8#4112yes—
143C22×C59—21no—
144C22×C59—21no—
145C22×C59—21no—
146C22×C59—41no—
147C22×C59—41no—
148C22×C59—41no—
149C22×C59C22×D411yescharacteristic
150C2×D59—41no—
151C2×D59—41no—
152C2×D59—41no—
153C4×C59—21no—
154C4×C59—21no—
155C4×C59—21no—
156C4×C59—21no—
157C4×C59—21no—
158C4×C59—41no—
159C4×C59—41no—
160C4×C59—41no—
161C4×C59C2×#4111yescharacteristic
162C4×C59C2×#4111yescharacteristic
163Dic59—41no—
164Dic59—41no—
165Dic59—41no—
166#3183—591nomaximal, Sylow
167C2×C59—41no—
168C2×C59—81no—
169C2×C59#53211yescharacteristic
170C2×C59#57511yescharacteristic
171C2×C59#57511yescharacteristic
172D59—81no—
173#529—591no—
174#529D5911yescharacteristic, complemented
175#499—591no—
176#495—591no—
177#488—591no—
178#488—591no—
179#470—591no—
180#469—591no—
181#468—591no—
182#468—591no—
183#442—591no—
184#441—591no—
185#440—591no—
186#440—591no—
187C4×M16—591no—
188C59#318311yescharacteristic, complemented, Sylow
189C2×Q16—591no—
190C2×SD16—591no—
191C2×SD16—591no—
192C2×D8—591no—
193C2×M16—591no—
194C2×M16—591no—
195#126—21no—
196#126—1181no—
197#125—591no—
198#125C2×D5911yescharacteristic
199#124—591no—
200#124C2×D5911yescharacteristic
201#123—21no—
202#123—1181no—
203C22⋊Q8—591no—
204C22⋊Q8C2×D5911yescharacteristic
205#121—591no—
206#121C2×D5911yescharacteristic
207C4×Q8—591no—
208C4×Q8C2×D5911yescharacteristic
209C4×D4—21no—
210C4×D4—591no—
211C4×D4—1181no—
212C4×D4C2×D5911yescharacteristic
213#117—21no—
214#117—1181no—
215C2×C42C2×D5911yescharacteristic
216#107—591no—
217#107—591no—
218#106—591no—
219#106—591no—
220#103—591no—
221#103—591no—
222#103—591no—
223#103—591no—
224#102—591no—
225#102—591no—
226#102—591no—
227#102—591no—
228#97—591no—
229#97—591no—
230C4×C8—591no—
231C4×C8—591no—
232C2×Q8—591no—
233C2×Q8C22×D5911yescharacteristic
234C2×D4—21no—
235C2×D4—591no—
236C2×D4—1181no—
237C2×D4C22×D5911yescharacteristic
238C22×C4—21no—
239C22×C4—1181no—
240C22×C4C22⋊D5911yescharacteristic
241C22×C4C22⋊D5911yescharacteristic
242C22×C4C22×D5911yescharacteristic
243Q16—1182no—
244SD16—1182no—
245SD16—1182no—
246D8—1182no—
247M16—1182no—
248M16—1182no—
249C2×C8—591no—
250C2×C8—591no—
251C2×C8—591no—
252C2×C8—591no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—591no—
258C4⋊C4—591no—
259C4⋊C4—1181no—
260C4⋊C4—1181no—
261C4⋊C4—1181no—
262C4⋊C4—1181no—
263C4⋊C4C22×D5911yescharacteristic
264C4⋊C4C22×D5911yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—1181no—
271C22⋊C4—1181no—
272C22⋊C4—1181no—
273C22⋊C4—1181no—
274C22⋊C4—1181no—
275C42—21no—
276C42—1181no—
277C42C22⋊D5911yescharacteristic
278C42C22⋊D5911yescharacteristic
279C42C22×D5911yescharacteristic
280C42C22×D5911yescharacteristic
281C23—21no—
282C23—1181no—
283C23C2×C22⋊D5911yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—1181no—
287Q8—1181no—
288D4—21no—
289D4—21no—
290D4—42no—
291D4—1181no—
292D4—1181no—
293D4—2362no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—1181no—
303C2×C4—1181no—
304C2×C4—1181no—
305C2×C4—2362no—
306C2×C4C2×C22⋊D5911yescharacteristic
307C2×C4C2×C22⋊D5911yescharacteristic
308C2×C4C2×C22⋊D5911yescharacteristic
309C2×C4C2×C22⋊D5911yescharacteristic
310C2×C4C2×C22⋊D5911yescharacteristic
311C2×C4C23×D5911yescharacteristic
312C8—592no—
313C8—592no—
314C8—1181no—
315C8—1181no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—2361no—
323C22—2361no—
324C22—2361no—
325C22C22×C22⋊D5911yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—2361no—
335C4—2361no—
336C4—2361no—
337C4#41×D5911yescharacteristic
338C4#41×D5911yescharacteristic
339C2—41no—
340C2—81no—
341C2—4721no—
342C2#1683794811yescharacteristic
343C2#1683820011yescharacteristic
344C2#1683820011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#529C2
socleC22×C59C22×D4
hypercenter#529D59
hypocenterC59#3183
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #16837936C2semidirect
2. #16837801C2semidirect
3. #16837784C2semidirect
4. #16837759C2semidirect
5. #16837756C2semidirect
6. #16837658C2semidirect
8. #16837650C2semidirect
9. #16837646C2semidirect
10. #16837512C2semidirect
11. #16837507C2semidirect
12. #16837502C2semidirect
13. #16837500C2semidirect
14. C4×#11745664C2semidirect
15. C59×#529C2semidirect
174. #529D59semidirect
188. C59#3183semidirect