Finite Group Databasebeta

← #21435207

Subgroups — #21435207

Order 7552.

376 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838023C211yesmaximal, characteristic, complemented
2#16837978C211yesmaximal, characteristic, complemented
3#16837796C211yesmaximal, characteristic, complemented
4#16837786C211yesmaximal, characteristic, complemented
5#16837762C211yesmaximal, characteristic, complemented
6#16837753C211yesmaximal, characteristic, complemented
7#16837625C211yesmaximal, characteristic, complemented
8#16837618C211yesmaximal, characteristic, complemented
9#16837613C211yesmaximal, characteristic, complemented
10#16837608C211yesmaximal, characteristic, complemented
11#16837566C211yesmaximal, characteristic, complemented
12#16837560C211yesmaximal, characteristic, complemented
13#16837549C211yesmaximal, characteristic
14#16837543C211yesmaximal, characteristic, complemented
15C59×#433C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C22×Dic118C2211yescharacteristic
18C2×Dic236C2211yescharacteristic
19C2×Dic236C2211yescharacteristic
20C2×Dic236C2211yescharacteristic
21C2×#11745660C2211yescharacteristic
22C2×#11745660C2211yescharacteristic
23C2×#11745660C2211yescharacteristic
24C2×#11745660C2211yescharacteristic
25C2×D472C2211yescharacteristic
26#14273727C2211yescharacteristic
27#14273727C2211yescharacteristic
28#14273727C2211yescharacteristic
29#14273722—21no—
30#14273715C2211yescharacteristic
31#14273715C2211yescharacteristic
32#14273715C2211yescharacteristic
33#14273713—21no—
34#14273711—21no—
35#14273711—21no—
36#14273709—21no—
37#14273707—21no—
38#14273707—21no—
39#14273706C2211yescharacteristic
40#14273705—21no—
41#14273701C2211yescharacteristic
42C4×Dic118C2211yescharacteristic
43C4×D236C2211yescharacteristic
44#14273652C2211yescharacteristic
45#14273652C2211yescharacteristic
46#14273652C2211yescharacteristic
47#14273652C2211yescharacteristic
48#14273652C2211yescharacteristic
49#14273652C2211yescharacteristic
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—41no—
64#11745685—41no—
65C2×D236C2311yescharacteristic
66C2×D236C2311yescharacteristic
67C2×C4×D59—21no—
68C2×C4×D59—21no—
69C2×Dic118—21no—
70C2×Dic118—21no—
71C2×Dic118—41no—
72C2×Dic118—41no—
73C2×Dic118C2311yescharacteristic
74C2×Dic118C2311yescharacteristic
75C2×Dic118C2311yescharacteristic
76C2×Dic118C2311yescharacteristic
77C2×C8×C59C2311yescharacteristic
78C2×C8×C59C2311yescharacteristic
79C2×C8×C59C2311yescharacteristic
80C2×C8×C59C2311yescharacteristic
81C4⋊C4×C59D411yescharacteristic
82C4⋊C4×C59D411yescharacteristic
83C22⋊C4×C59D411yescharacteristic
84C22⋊C4×C59D411yescharacteristic
85C42×C59C2311yescharacteristic
86C42×C59C2311yescharacteristic
87C22⋊Dic59—21no—
88(C2×D59)⋊C4—21no—
89(C2×D59)⋊C4—21no—
90(C2×D59)⋊C4—21no—
91(C2×D59)⋊C4—21no—
92(C2×D59)⋊C4—21no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4—21no—
95(C2×D59)⋊C4—21no—
96C4⋊Dic59—21no—
97C4⋊Dic59—21no—
98C4⋊Dic59—21no—
99C4⋊Dic59—21no—
100C4⋊Dic59—21no—
101C4⋊Dic59C2311yescharacteristic
102C4⋊Dic59C2311yescharacteristic
103Dic59⋊C4—21no—
104Dic59⋊C4—21no—
105C4×Dic59—21no—
106Dic236—41no—
107Dic236—41no—
108Dic236—41no—
109D472—41no—
110#11745660—41no—
111#11745660—41no—
112#11745660—41no—
113#11745660—41no—
114C23×C59C2×D411yescharacteristic
115C22×D59—21no—
116C22×D59—21no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59C2×D411yescharacteristic
120C2×C4×C59C2×D411yescharacteristic
121C2×C4×C59C2×D411yescharacteristic
122C2×C4×C59C2×D411yescharacteristic
123C2×C4×C59C2×D411yescharacteristic
124C2×C4×C59C2411yescharacteristic
125C22⋊D59—42no—
126C22⋊D59—81no—
127C2×Dic59—21no—
128C2×Dic59—21no—
129C2×Dic59—21no—
130C2×Dic59—21no—
131C2×Dic59—21no—
132C2×Dic59—21no—
133C2×Dic59—42no—
134D236—21no—
135D236—21no—
136D236—21no—
137D236—21no—
138C4×D59—42no—
139C4×D59—81no—
140Dic118—21no—
141Dic118—21no—
142Dic118—21no—
143Dic118—21no—
144Dic118—21no—
145Dic118—21no—
146Dic118—21no—
147Dic118—21no—
148Dic118—42no—
149Dic118—81no—
150C8×C59—21no—
151C8×C59—21no—
152C8×C59—21no—
153C8×C59—21no—
154C22×C59—21no—
155C22×C59—21no—
156C22×C59—21no—
157C22×C59C22×D411yescharacteristic
158C2×D59—41no—
159C2×D59—41no—
160C2×D59—41no—
161C2×D59—41no—
162C2×D59—41no—
163C2×D59—41no—
164C4×C59—21no—
165C4×C59—21no—
166C4×C59—21no—
167C4×C59—21no—
168C4×C59—21no—
169C4×C59H(5,𝔽2)11yescharacteristic
170C4×C59H(5,𝔽2)11yescharacteristic
171Dic59—41no—
172Dic59—41no—
173Dic59—41no—
174Dic59—41no—
175Dic59—41no—
176Dic59—41no—
177#3225—591nomaximal, Sylow
178C2×C59—41no—
179C2×C59#53511yescharacteristic
180C2×C59#57711yescharacteristic
181C2×C59#57811yescharacteristic
182D59—81no—
183D59—81no—
184#542—591no—
185#536—591no—
186#497—591no—
187#495—591no—
188#489—591no—
189#487—591no—
190#464—591no—
191#463—591no—
192#462—591no—
193#461—591no—
194#452—591no—
195#451—591no—
196#449—591no—
197#448—591no—
198#433D5911yescharacteristic, complemented
199C59#322511yescharacteristic, complemented, Sylow
200C2×#41—591no—
201C22×Q8—591no—
202C2×Q16—591no—
203C2×Q16—591no—
204C2×Q16—591no—
205C2×SD16—591no—
206C2×SD16—591no—
207C2×SD16—591no—
208C2×SD16—591no—
209C2×D8—591no—
210C4⋊Q8—591no—
211C4⋊Q8—591no—
212C4⋊Q8—591no—
213#126—1181no—
214#124—591no—
215#124—591no—
216#124—591no—
217#124—1181no—
218#123—1181no—
219#123—1181no—
220#123—1181no—
221C22⋊Q8—591no—
222C22⋊Q8—1181no—
223C22⋊Q8—1181no—
224C22⋊Q8—1181no—
225#121—591no—
226C4×Q8—591no—
227C4×D4—591no—
228#117C2×D5911yescharacteristic
229C4⋊C8C2×D5911yescharacteristic
230C4⋊C8C2×D5911yescharacteristic
231#103—591no—
232#103—591no—
233#103—591no—
234#103—591no—
235#103—591no—
236#103—591no—
237#102—591no—
238#102—591no—
239C22⋊C8C2×D5911yescharacteristic
240C22⋊C8C2×D5911yescharacteristic
241#97C2×D5911yescharacteristic
242C4×C8C2×D5911yescharacteristic
243#41—2361no—
244#41—2361no—
245C2×Q8—591no—
246C2×Q8—591no—
247C2×Q8—591no—
248C2×Q8—591no—
249C2×Q8—1181no—
250C2×Q8—1181no—
251C2×Q8—2361no—
252C2×Q8—2361no—
253C2×D4—591no—
254C2×D4—591no—
255C2×D4—1181no—
256C2×D4—1181no—
257C22×C4—1181no—
258C22×C4—1181no—
259C22×C4—1181no—
260C22×C4C22×D5911yescharacteristic
261Q16—2361no—
262Q16—2361no—
263Q16—2361no—
264SD16—2361no—
265SD16—2361no—
266SD16—2361no—
267SD16—2361no—
268D8—2361no—
269C2×C8C22×D5911yescharacteristic
270C2×C8C22×D5911yescharacteristic
271C2×C8C22×D5911yescharacteristic
272C2×C8C22×D5911yescharacteristic
273C4⋊C4—591no—
274C4⋊C4—591no—
275C4⋊C4—1181no—
276C4⋊C4—1181no—
277C4⋊C4—1181no—
278C4⋊C4—1181no—
279C4⋊C4—1181no—
280C4⋊C4—1181no—
281C4⋊C4—1181no—
282C4⋊C4D23611yescharacteristic
283C4⋊C4D23611yescharacteristic
284C22⋊C4—1181no—
285C22⋊C4—1181no—
286C22⋊C4—1181no—
287C22⋊C4—1181no—
288C22⋊C4—1181no—
289C22⋊C4—1181no—
290C22⋊C4—1181no—
291C22⋊C4—1181no—
292C22⋊C4—1181no—
293C22⋊C4D23611yescharacteristic
294C22⋊C4D23611yescharacteristic
295C42—1181no—
296C42C22×D5911yescharacteristic
297C42C22×D5911yescharacteristic
298C23—1181no—
299C23—1181no—
300C23C2×D23611yescharacteristic
301Q8—1181no—
302Q8—1181no—
303Q8—1181no—
304Q8—1181no—
305Q8—1181no—
306Q8—1181no—
307Q8—1181no—
308Q8—1181no—
309Q8—4721no—
310Q8—2362no—
311D4—1181no—
312D4—1181no—
313D4—1181no—
314D4—1181no—
315D4—4721no—
316D4—2362no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—1181no—
320C2×C4—1181no—
321C2×C4—1181no—
322C2×C4—1181no—
323C2×C4—1181no—
324C2×C4—1181no—
325C2×C4—4721no—
326C2×C4—2362no—
327C2×C4—2362no—
328C2×C4C2×D23611yescharacteristic
329C2×C4C2×D23611yescharacteristic
330C2×C4C2×D23611yescharacteristic
331C2×C4C2×D23611yescharacteristic
332C2×C4C2×D23611yescharacteristic
333C2×C4C23×D5911yescharacteristic
334C8—21no—
335C8—21no—
336C8—21no—
337C8—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—2361no—
342C22—2361no—
343C22—2361no—
344C22—2361no—
345C22—2361no—
346C22—2361no—
347C22C22×D23611yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—2361no—
354C4—2361no—
355C4—2361no—
356C4—2361no—
357C4—2361no—
358C4—2361no—
359C4#1427377311yescharacteristic
360C4#1427377311yescharacteristic
361C2—41no—
362C2—4721no—
363C2—4721no—
364C2#1683797111yescharacteristic
365C2#1683821411yescharacteristic
366C2#1683821911yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#433C2
socleC22×C59C22×D4
hypercenter#433D59
hypocenterC59#3225
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. #16837978C2semidirect
3. #16837796C2semidirect
4. #16837786C2semidirect
5. #16837762C2semidirect
6. #16837753C2semidirect
7. #16837625C2semidirect
8. #16837618C2semidirect
9. #16837613C2semidirect
10. #16837608C2semidirect
11. #16837566C2semidirect
12. #16837560C2semidirect
14. #16837543C2semidirect
15. C59×#433C2semidirect
198. #433D59semidirect
199. C59#3225semidirect