Finite Group Databasebeta

← #21434360

Subgroups — #21434360

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#16837882C211yesmaximal, characteristic, complemented
3#16837738C211yesmaximal, characteristic, complemented
4#16837716C211yesmaximal, characteristic, complemented
5#16837698C211yesmaximal, characteristic, complemented
6#16837683C211yesmaximal, characteristic, complemented
7#16837625C211yesmaximal, characteristic, complemented
8#16837618C211yesmaximal, characteristic, complemented
9#16837566C211yesmaximal, characteristic, complemented
10#16837549C211yesmaximal, characteristic
11#16837504C211yesmaximal, characteristic, complemented
12#16837504C211yesmaximal, characteristic, complemented
13C4×Dic236C211yesmaximal, characteristic, complemented
14C4×D472C211yesmaximal, characteristic, complemented
15C59×#433C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C2×Dic236C2211yescharacteristic
18C2×#11745660C2211yescharacteristic
19C2×#11745660C2211yescharacteristic
20C2×D472C2211yescharacteristic
21#14273727C2211yescharacteristic
22#14273722—21no—
23#14273715C2211yescharacteristic
24#14273713—21no—
25#14273709—21no—
26#14273706C2211yescharacteristic
27#14273705—21no—
28#14273701C2211yescharacteristic
29C4×Dic118C2211yescharacteristic
30C4×Dic118C2211yescharacteristic
31C4×Dic118C2211yescharacteristic
32C4×D236C2211yescharacteristic
33C4×D236C2211yescharacteristic
34C4×D236C2211yescharacteristic
35(C22⋊D59)⋊C4—21no—
36(C22⋊D59)⋊C4—21no—
37#14273685—21no—
38C2×C4⋊Dic59C2211yescharacteristic
39C4⋊C4×D59—21no—
40#14273661C2211yescharacteristic
41#14273661C2211yescharacteristic
42#14273661C2211yescharacteristic
43#14273661C2211yescharacteristic
44#14273652C2211yescharacteristic
45#14273652C2211yescharacteristic
46#14273652C2211yescharacteristic
47#14273652C2211yescharacteristic
48#14273649C2211yescharacteristic
49#14273649C2211yescharacteristic
50#14273649C2211yescharacteristic
51#14273649C2211yescharacteristic
52#117×C59C2211yescharacteristic
53C4⋊C8×C59C2211yescharacteristic
54C4⋊C8×C59C2211yescharacteristic
55C22⋊C8×C59C2211yescharacteristic
56C22⋊C8×C59C2211yescharacteristic
57#97×C59C2211yescharacteristic
58C4×C8×C59C2211yescharacteristic
59C22×C4×C59C2311yescharacteristic
60C2×C22⋊D59—21no—
61C2×C22⋊D59—21no—
62C22×Dic59—21no—
63#11745685—22no—
64#11745685—22no—
65C2×D236C2311yescharacteristic
66C2×D236C2311yescharacteristic
67C2×C4×D59—21no—
68C2×C4×D59—21no—
69C2×C4×D59—21no—
70C2×C4×D59—21no—
71C2×Dic118—21no—
72C2×Dic118C2311yescharacteristic
73C2×Dic118C2311yescharacteristic
74C2×C8×C59C2311yescharacteristic
75C2×C8×C59C2311yescharacteristic
76C2×C8×C59C2311yescharacteristic
77C2×C8×C59C2311yescharacteristic
78C4⋊C4×C59D411yescharacteristic
79C4⋊C4×C59D411yescharacteristic
80C22⋊C4×C59D411yescharacteristic
81C22⋊C4×C59D411yescharacteristic
82C42×C59C2311yescharacteristic
83C42×C59C2311yescharacteristic
84C22⋊Dic59—21no—
85(C2×D59)⋊C4—21no—
86(C2×D59)⋊C4—21no—
87(C2×D59)⋊C4—21no—
88(C2×D59)⋊C4—21no—
89(C2×D59)⋊C4—21no—
90(C2×D59)⋊C4—21no—
91C4⋊Dic59—21no—
92C4⋊Dic59—21no—
93C4⋊Dic59C2311yescharacteristic
94C4⋊Dic59C2311yescharacteristic
95C4⋊Dic59C2311yescharacteristic
96C4⋊Dic59C2311yescharacteristic
97Dic59⋊C4—21no—
98Dic59⋊C4—21no—
99Dic59⋊C4—21no—
100Dic59⋊C4—21no—
101C4×Dic59—21no—
102C4×Dic59—21no—
103C4×Dic59—21no—
104Dic236—22no—
105D472—22no—
106#11745660—22no—
107#11745660—22no—
108C23×C59C2×D411yescharacteristic
109C22×D59—21no—
110C22×D59—21no—
111C2×C4×C59—21no—
112C2×C4×C59—21no—
113C2×C4×C59C2×D411yescharacteristic
114C2×C4×C59C2×D411yescharacteristic
115C2×C4×C59C2×D411yescharacteristic
116C2×C4×C59C2×D411yescharacteristic
117C2×C4×C59C2×D411yescharacteristic
118C2×C4×C59C2411yescharacteristic
119C22⋊D59—24no—
120C22⋊D59—81no—
121C2×Dic59—21no—
122C2×Dic59—21no—
123C2×Dic59—21no—
124C2×Dic59—21no—
125C2×Dic59—21no—
126C2×Dic59—21no—
127C2×Dic59—81no—
128D236—21no—
129D236—21no—
130D236—21no—
131D236#4112yes—
132C4×D59—24no—
133C4×D59—81no—
134C4×D59—81no—
135C4×D59—81no—
136Dic118—21no—
137Dic118—21no—
138Dic118—21no—
139Dic118—81no—
140Dic118#4112yes—
141C8×C59—21no—
142C8×C59—21no—
143C8×C59—21no—
144C8×C59—21no—
145C22×C59—21no—
146C22×C59—21no—
147C22×C59—21no—
148C22×C59C22×D411yescharacteristic
149C2×D59—22no—
150C2×D59—41no—
151C2×D59—41no—
152C2×D59—41no—
153C2×D59—41no—
154C2×D59—41no—
155C4×C59—21no—
156C4×C59—21no—
157C4×C59—21no—
158C4×C59—21no—
159C4×C59—21no—
160C4×C59C2×#4111yescharacteristic
161C4×C59C2×#4111yescharacteristic
162Dic59—22no—
163Dic59—41no—
164Dic59—41no—
165Dic59—41no—
166Dic59—41no—
167Dic59—41no—
168#3124—591nomaximal, Sylow
169C2×C59—41no—
170C2×C59#52511yescharacteristic
171C2×C59#57611yescharacteristic
172C2×C59#57811yescharacteristic
173D59—42no—
174D59—81no—
175#542—591no—
176#520—591no—
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#433D5911yescharacteristic, complemented
190C59#312411yescharacteristic, complemented, Sylow
191C2×#41—591no—
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×Q8—591no—
206C4×Q8—591no—
207C4×D4—591no—
208C4×D4—591no—
209C4×D4—591no—
210C4×D4—1181no—
211C4×D4—1181no—
212#117—1181no—
213#117C2×D5911yescharacteristic
214C2×C4⋊C4—591no—
215C2×C4⋊C4—1181no—
216#107—591no—
217#107—591no—
218#107—591no—
219#107—591no—
220C4⋊C8C2×D5911yescharacteristic
221C4⋊C8C2×D5911yescharacteristic
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⋊C8C2×D5911yescharacteristic
231C22⋊C8C2×D5911yescharacteristic
232#97C2×D5911yescharacteristic
233C4×C8C2×D5911yescharacteristic
234#41—1182no—
235#41—1182no—
236C2×Q8—591no—
237C2×Q8—591no—
238C2×Q8—1181no—
239C2×D4—591no—
240C2×D4—591no—
241C2×D4—1181no—
242C2×D4—1181no—
243C22×C4—1181no—
244C22×C4—1181no—
245C22×C4—1181no—
246C22×C4—1181no—
247C22×C4—1181no—
248C22×C4C22×D5911yescharacteristic
249Q16—1182no—
250SD16—1182no—
251SD16—1182no—
252D8—1182no—
253C2×C8C22×D5911yescharacteristic
254C2×C8C22×D5911yescharacteristic
255C2×C8C22×D5911yescharacteristic
256C2×C8C22×D5911yescharacteristic
257C4⋊C4—591no—
258C4⋊C4—591no—
259C4⋊C4—591no—
260C4⋊C4—591no—
261C4⋊C4—1181no—
262C4⋊C4—1181no—
263C4⋊C4—1181no—
264C4⋊C4—1181no—
265C4⋊C4—1181no—
266C4⋊C4—1181no—
267C4⋊C4D23611yescharacteristic
268C4⋊C4D23611yescharacteristic
269C22⋊C4—1181no—
270C22⋊C4—1181no—
271C22⋊C4—1181no—
272C22⋊C4—1181no—
273C22⋊C4—1181no—
274C22⋊C4—1181no—
275C22⋊C4—1181no—
276C22⋊C4D23611yescharacteristic
277C22⋊C4D23611yescharacteristic
278C42—1181no—
279C42—1181no—
280C42—1181no—
281C42C22×D5911yescharacteristic
282C42C22×D5911yescharacteristic
283C23—1181no—
284C23—1181no—
285C23C2×D23611yescharacteristic
286Q8—592no—
287Q8—1181no—
288Q8—1181no—
289Q8—1181no—
290Q8—4721no—
291D4—592no—
292D4—1184no—
293D4—1181no—
294D4—1181no—
295D4—1181no—
296D4—4721no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—1184no—
300C2×C4—1181no—
301C2×C4—1181no—
302C2×C4—1181no—
303C2×C4—1181no—
304C2×C4—1181no—
305C2×C4—1181no—
306C2×C4—4721no—
307C2×C4—4721no—
308C2×C4—4721no—
309C2×C4—4721no—
310C2×C4C2×D23611yescharacteristic
311C2×C4C2×D23611yescharacteristic
312C2×C4C2×D23611yescharacteristic
313C2×C4C2×D23611yescharacteristic
314C2×C4C2×D23611yescharacteristic
315C2×C4C23×D5911yescharacteristic
316C8—21no—
317C8—21no—
318C8—21no—
319C8—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—1182no—
324C22—2361no—
325C22—2361no—
326C22—2361no—
327C22—2361no—
328C22—2361no—
329C22C22×D23611yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—1182no—
336C4—2361no—
337C4—2361no—
338C4—2361no—
339C4—2361no—
340C4—2361no—
341C4#41×D5911yescharacteristic
342C4#41×D5911yescharacteristic
343C2—41no—
344C2—4721no—
345C2—2362no—
346C2#1683791411yescharacteristic
347C2#1683820711yescharacteristic
348C2#1683821911yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#433C2
socleC22×C59C22×D4
hypercenter#433D59
hypocenterC59#3124
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #16838023C2semidirect
2. #16837882C2semidirect
3. #16837738C2semidirect
4. #16837716C2semidirect
5. #16837698C2semidirect
6. #16837683C2semidirect
7. #16837625C2semidirect
8. #16837618C2semidirect
9. #16837566C2semidirect
11. #16837504C2semidirect
12. #16837504C2semidirect
13. C4×Dic236C2semidirect
14. C4×D472C2semidirect
15. C59×#433C2semidirect
189. #433D59semidirect
190. C59#3124semidirect