Finite Group Databasebeta

← #21434358

Subgroups — #21434358

Order 7552.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838023C211yesmaximal, characteristic, complemented
2#16837737C211yesmaximal, characteristic, complemented
3#16837715C211yesmaximal, characteristic, complemented
4#16837697C211yesmaximal, characteristic, complemented
5#16837682C211yesmaximal, characteristic, complemented
6#16837624C211yesmaximal, characteristic, complemented
7#16837617C211yesmaximal, characteristic, complemented
8#16837564C211yesmaximal, characteristic, complemented
9#16837547C211yesmaximal, characteristic
10#16837502C211yesmaximal, characteristic, complemented
11#16837500C211yesmaximal, characteristic, complemented
12C4×#11745672C211yesmaximal, characteristic, complemented
13C4×#11745669C211yesmaximal, characteristic, complemented
14#16837463C211yesmaximal, characteristic, complemented
15C59×#520C211yesmaximal, characteristic, complemented
16C2×#11745672C2211yescharacteristic
17C2×#11745670C2211yescharacteristic
18C2×#11745671C2211yescharacteristic
19C2×#11745669C2211yescharacteristic
20#14273727C2211yescharacteristic
21#14273722—21no—
22#14273715C2211yescharacteristic
23#14273713—21no—
24#14273709—21no—
25#14273706C2211yescharacteristic
26#14273705—21no—
27#14273701C2211yescharacteristic
28C4×Dic118C2211yescharacteristic
29C4×D236C2211yescharacteristic
30#14273660C2211yescharacteristic
31#14273660C2211yescharacteristic
32#14273660C2211yescharacteristic
33#14273660C2211yescharacteristic
34C4⋊(C59⋊C8)C2211yescharacteristic
35C4⋊(C59⋊C8)C2211yescharacteristic
36#14273651C2211yescharacteristic
37#14273651C2211yescharacteristic
38#14273650C2211yescharacteristic
39#14273650C2211yescharacteristic
40#14273648C2211yescharacteristic
41#14273648C2211yescharacteristic
42#14273647C2211yescharacteristic
43#14273647C2211yescharacteristic
44C22⋊(C59⋊C8)C2211yescharacteristic
45C22⋊(C59⋊C8)C2211yescharacteristic
46#14273638C2211yescharacteristic
47C4×C59⋊C8C2211yescharacteristic
48C2×#41×C59C2211yescharacteristic
49C4×Q8×C59C2211yescharacteristic
50C4×Q8×C59C2211yescharacteristic
51C4×D4×C59—21no—
52C4×D4×C59—21no—
53C4×D4×C59C2211yescharacteristic
54C4×D4×C59C2211yescharacteristic
55#117×C59—21no—
56#117×C59C2211yescharacteristic
57C2×C4⋊C4×C59—21no—
58C2×C4⋊C4×C59C2211yescharacteristic
59#41×C59—22no—
60#41×C59—22no—
61C2×Q8×C59C2311yescharacteristic
62C2×D4×C59—21no—
63C2×D4×C59C2311yescharacteristic
64C22×C4×C59—21no—
65C22×C4×C59—21no—
66C22×C4×C59—21no—
67C22×C4×C59—21no—
68C22×C4×C59C2311yescharacteristic
69C2×C22⋊D59—21no—
70C2×D236C2311yescharacteristic
71C2×C4×D59—21no—
72C2×Dic118—21no—
73C2×Dic118C2311yescharacteristic
74C4⋊C4×C59—21no—
75C4⋊C4×C59—21no—
76C4⋊C4×C59—21no—
77C4⋊C4×C59D411yescharacteristic
78C4⋊C4×C59D411yescharacteristic
79C4⋊C4×C59C2311yescharacteristic
80C4⋊C4×C59C2311yescharacteristic
81C22⋊C4×C59—21no—
82C22⋊C4×C59—21no—
83C22⋊C4×C59D411yescharacteristic
84C22⋊C4×C59D411yescharacteristic
85C42×C59—21no—
86C42×C59—21no—
87C42×C59C2311yescharacteristic
88C42×C59C2311yescharacteristic
89C22⋊Dic59—21no—
90#11745672—22no—
91#11745671—22no—
92#11745670—22no—
93#11745669—22no—
94(C2×D59)⋊C4—21no—
95(C2×D59)⋊C4—21no—
96(C2×D59)⋊C4—21no—
97(C2×D59)⋊C4—21no—
98C4⋊Dic59—21no—
99C4⋊Dic59C2311yescharacteristic
100C4⋊Dic59C2311yescharacteristic
101Dic59⋊C4—21no—
102Dic59⋊C4—21no—
103C4×Dic59—21no—
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#4112yes—
113D4×C59—24no—
114D4×C59—21no—
115D4×C59#4112yes—
116C2×C4×C59—24no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—81no—
123C2×C4×C59—81no—
124C2×C4×C59—81no—
125C2×C4×C59C2×D411yescharacteristic
126C2×C4×C59C2×D411yescharacteristic
127C2×C4×C59C2×D411yescharacteristic
128C2×C4×C59C2×D411yescharacteristic
129C2×C4×C59C2×D411yescharacteristic
130C2×C4×C59C2411yescharacteristic
131C22⋊D59—81no—
132C2×Dic59—21no—
133C2×Dic59—21no—
134C2×Dic59—21no—
135D236—21no—
136D236—21no—
137C4×D59—81no—
138Dic118—21no—
139Dic118—21no—
140Dic118—81no—
141C59⋊C8—21no—
142C59⋊C8—21no—
143C59⋊C8—21no—
144C59⋊C8—21no—
145C22×C59—21no—
146C22×C59—22no—
147C22×C59—21no—
148C22×C59—21no—
149C22×C59—41no—
150C22×C59—41no—
151C22×C59C22×D411yescharacteristic
152C2×D59—41no—
153C2×D59—41no—
154C2×D59—41no—
155C4×C59—21no—
156C4×C59—22no—
157C4×C59—21no—
158C4×C59—21no—
159C4×C59—21no—
160C4×C59—21no—
161C4×C59—41no—
162C4×C59—41no—
163C4×C59C2×#4111yescharacteristic
164C4×C59C2×#4111yescharacteristic
165Dic59—41no—
166Dic59—41no—
167Dic59—41no—
168#3124—591nomaximal, Sylow
169C2×C59—41no—
170C2×C59—42no—
171C2×C59#52511yescharacteristic
172C2×C59#57611yescharacteristic
173C2×C59#57811yescharacteristic
174D59—81no—
175#542—591no—
176#520D5911yescharacteristic, complemented
177#484—591no—
178#480—591no—
179#477—591no—
180#474—591no—
181#464—591no—
182#463—591no—
183#452—591no—
184#449—591no—
185#440—591no—
186#440—591no—
187C4×Q16—591no—
188C4×D8—591no—
189#433—591no—
190C59#312411yescharacteristic, complemented, Sylow
191C2×#41C2×D5911yescharacteristic
192C2×Q16—591no—
193C2×SD16—591no—
194C2×SD16—591no—
195C2×D8—591no—
196C4⋊Q8—591no—
197#126—1181no—
198#124—591no—
199#124—1181no—
200#123—1181no—
201C22⋊Q8—591no—
202C22⋊Q8—1181no—
203#121—591no—
204C4×Q8—591no—
205C4×Q8C2×D5911yescharacteristic
206C4×Q8C2×D5911yescharacteristic
207C4×D4—21no—
208C4×D4—21no—
209C4×D4—591no—
210C4×D4C2×D5911yescharacteristic
211C4×D4C2×D5911yescharacteristic
212#117—21no—
213#117C2×D5911yescharacteristic
214C2×C4⋊C4—21no—
215C2×C4⋊C4C2×D5911yescharacteristic
216#107—591no—
217#107—591no—
218#107—591no—
219#107—591no—
220C4⋊C8—591no—
221C4⋊C8—591no—
222#103—591no—
223#103—591no—
224#103—591no—
225#103—591no—
226#102—591no—
227#102—591no—
228#102—591no—
229#102—591no—
230C22⋊C8—591no—
231C22⋊C8—591no—
232#97—591no—
233C4×C8—591no—
234#41—22no—
235#41—22no—
236C2×Q8—591no—
237C2×Q8—1181no—
238C2×Q8C22×D5911yescharacteristic
239C2×D4—21no—
240C2×D4—591no—
241C2×D4—1181no—
242C2×D4C22×D5911yescharacteristic
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—1181no—
248C22×C4C22×D5911yescharacteristic
249Q16—1182no—
250SD16—1182no—
251SD16—1182no—
252D8—1182no—
253C2×C8—591no—
254C2×C8—591no—
255C2×C8—591no—
256C2×C8—591no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—591no—
261C4⋊C4—591no—
262C4⋊C4—1181no—
263C4⋊C4—1181no—
264C4⋊C4—1181no—
265C4⋊C4C22⋊D5911yescharacteristic
266C4⋊C4C22⋊D5911yescharacteristic
267C4⋊C4C22×D5911yescharacteristic
268C4⋊C4C22×D5911yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—1181no—
272C22⋊C4—1181no—
273C22⋊C4—1181no—
274C22⋊C4—1181no—
275C22⋊C4—1181no—
276C22⋊C4C22⋊D5911yescharacteristic
277C22⋊C4C22⋊D5911yescharacteristic
278C42—21no—
279C42—21no—
280C42—1181no—
281C42C22×D5911yescharacteristic
282C42C22×D5911yescharacteristic
283C23—21no—
284C23—1181no—
285C23C2×C22⋊D5911yescharacteristic
286Q8—21no—
287Q8—1181no—
288Q8—1181no—
289Q8—4721no—
290Q8#1174568512yes—
291D4—24no—
292D4—21no—
293D4—1181no—
294D4—1181no—
295D4—4721no—
296D4#1174568512yes—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—1181no—
307C2×C4—1181no—
308C2×C4—1181no—
309C2×C4—4721no—
310C2×C4C2×C22⋊D5911yescharacteristic
311C2×C4C2×C22⋊D5911yescharacteristic
312C2×C4C2×C22⋊D5911yescharacteristic
313C2×C4C2×C22⋊D5911yescharacteristic
314C2×C4C2×C22⋊D5911yescharacteristic
315C2×C4C23×D5911yescharacteristic
316C8—1181no—
317C8—1181no—
318C8—1181no—
319C8—1181no—
320C22—21no—
321C22—22no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—2361no—
327C22—2361no—
328C22—2361no—
329C22C22×C22⋊D5911yescharacteristic
330C4—21no—
331C4—22no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—41no—
337C4—41no—
338C4—2361no—
339C4—2361no—
340C4—2361no—
341C4C2×#1174568511yescharacteristic
342C4C2×#1174568511yescharacteristic
343C2—41no—
344C2—42no—
345C2—4721no—
346C2#1683791311yescharacteristic
347C2#1683820511yescharacteristic
348C2#1683821711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#520C2
socleC22×C59C22×D4
hypercenter#520D59
hypocenterC59#3124
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #16838023C2semidirect
2. #16837737C2semidirect
3. #16837715C2semidirect
4. #16837697C2semidirect
5. #16837682C2semidirect
6. #16837624C2semidirect
7. #16837617C2semidirect
8. #16837564C2semidirect
10. #16837502C2semidirect
11. #16837500C2semidirect
12. C4×#11745672C2semidirect
13. C4×#11745669C2semidirect
14. #16837463C2semidirect
15. C59×#520C2semidirect
176. #520D59semidirect
190. C59#3124semidirect