Finite Group Databasebeta

← #21435050

Subgroups — #21435050

Order 7552.

394 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16837954C211yesmaximal, characteristic, complemented
2#16837948C211yesmaximal, characteristic
3#16837780C211yesmaximal, characteristic, complemented
4#16837773C211yesmaximal, characteristic, complemented
5#16837751C211yesmaximal, characteristic, complemented
6#16837747C211yesmaximal, characteristic, complemented
7#16837627C211yesmaximal, characteristic, complemented
8#16837626C211yesmaximal, characteristic, complemented
9#16837623C211yesmaximal, characteristic, complemented
10#16837622C211yesmaximal, characteristic, complemented
11#16837566C211yesmaximal, characteristic, complemented
12#16837564C211yesmaximal, characteristic, complemented
13#16837562C211yesmaximal, characteristic, complemented
14#16837452C211yesmaximal, characteristic, complemented
15C59×#452C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C2×Dic236C2211yescharacteristic
18C2×#11745672C2211yescharacteristic
19C2×#11745672C2211yescharacteristic
20C2×#11745660C2211yescharacteristic
21C2×#11745670C2211yescharacteristic
22C2×#11745671C2211yescharacteristic
23#14273726C2211yescharacteristic
24#14273725C2211yescharacteristic
25#14273725C2211yescharacteristic
26#14273723C2211yescharacteristic
27#14273717—21no—
28#14273716C2211yescharacteristic
29#14273714C2211yescharacteristic
30#14273706C2211yescharacteristic
31#14273704—21no—
32#14273699—21no—
33#14273699—21no—
34Q8×Dic59C2211yescharacteristic
35#14273692—21no—
36#14273692C2211yescharacteristic
37C4×C22⋊D59—21no—
38C4×C22⋊D59—21no—
39#14273683—21no—
40C2×C4×Dic59C2211yescharacteristic
41Dic59⋊C8C2211yescharacteristic
42Dic59⋊C8C2211yescharacteristic
43#14273652C2211yescharacteristic
44#14273651C2211yescharacteristic
45#14273650C2211yescharacteristic
46#14273649C2211yescharacteristic
47#14273648C2211yescharacteristic
48#14273647C2211yescharacteristic
49C22⋊(C59⋊C8)C2211yescharacteristic
50C8×Dic59C2211yescharacteristic
51C8×Dic59C2211yescharacteristic
52C2×#41×C59C2211yescharacteristic
53C2×Q16×C59C2211yescharacteristic
54C2×SD16×C59C2211yescharacteristic
55C22⋊Q8×C59C2211yescharacteristic
56#103×C59C2211yescharacteristic
57#102×C59C2211yescharacteristic
58C22⋊C8×C59C2211yescharacteristic
59#41×C59—41no—
60#41×C59—41no—
61C2×Q8×C59C2311yescharacteristic
62C2×Q8×C59C2311yescharacteristic
63C2×D4×C59—21no—
64C2×D4×C59C2311yescharacteristic
65C22×C4×C59—21no—
66C22×C4×C59C2311yescharacteristic
67C2×C22⋊D59—21no—
68C2×C22⋊D59—21no—
69C2×C22⋊D59—21no—
70C22×Dic59D411yescharacteristic
71C22×Dic59D411yescharacteristic
72#11745685—41no—
73#11745685—41no—
74C2×D236C2311yescharacteristic
75C2×C4×D59—21no—
76C2×Dic118—21no—
77C2×Dic118C2311yescharacteristic
78C2×Dic118C2311yescharacteristic
79Q16×C59—41no—
80SD16×C59—41no—
81C2×C8×C59C2311yescharacteristic
82C2×C8×C59C2311yescharacteristic
83C4⋊C4×C59—21no—
84C4⋊C4×C59C2311yescharacteristic
85C22⋊C4×C59—21no—
86C22⋊Dic59—21no—
87C22⋊Dic59—21no—
88C22⋊Dic59—21no—
89#11745672—41no—
90#11745672—41no—
91#11745671—41no—
92#11745670—41no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4—21no—
95C4⋊Dic59—21no—
96C4⋊Dic59C2311yescharacteristic
97Dic59⋊C4—21no—
98Dic59⋊C4—21no—
99Dic59⋊C4—21no—
100Dic59⋊C4—21no—
101Dic59⋊C4—21no—
102Dic59⋊C4—21no—
103Dic59⋊C4—21no—
104C4×Dic59—21no—
105C4×Dic59—21no—
106C4×Dic59D411yescharacteristic
107C4×Dic59D411yescharacteristic
108C4×Dic59C2311yescharacteristic
109C4×Dic59C2311yescharacteristic
110C2×C59⋊C8C2311yescharacteristic
111C2×C59⋊C8C2311yescharacteristic
112Dic236—41no—
113#11745660—41no—
114C23×C59—21no—
115C23×C59C2×D411yescharacteristic
116C22×D59—21no—
117Q8×C59—21no—
118Q8×C59—21no—
119Q8×C59—21no—
120Q8×C59—21no—
121D4×C59—21no—
122D4×C59—21no—
123D4×C59—42no—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—42no—
130C2×C4×C59C2×D411yescharacteristic
131C2×C4×C59C2411yescharacteristic
132C22⋊D59—42no—
133C22⋊D59—42no—
134C22⋊D59—42no—
135C2×Dic59—22no—
136C2×Dic59—22no—
137C2×Dic59—21no—
138C2×Dic59—21no—
139C2×Dic59—21no—
140C2×Dic59C2×D411yescharacteristic
141C2×Dic59C2×D411yescharacteristic
142C2×Dic59C2×D411yescharacteristic
143C2×Dic59C2×D411yescharacteristic
144D236—21no—
145D236—21no—
146C4×D59—42no—
147Dic118—21no—
148Dic118—21no—
149Dic118—21no—
150Dic118—21no—
151Dic118—42no—
152C8×C59—21no—
153C8×C59—21no—
154C59⋊C8—21no—
155C59⋊C8—21no—
156C22×C59—21no—
157C22×C59—21no—
158C22×C59—21no—
159C22×C59—41no—
160C22×C59—41no—
161C22×C59—41no—
162C22×C59C22×D411yescharacteristic
163C2×D59—41no—
164C2×D59—41no—
165C2×D59—41no—
166C4×C59—21no—
167C4×C59—41no—
168C4×C59—41no—
169C4×C59—41no—
170C4×C59H(5,𝔽2)11yescharacteristic
171C4×C59H(5,𝔽2)11yescharacteristic
172Dic59—21no—
173Dic59—21no—
174Dic59—41no—
175Dic59—41no—
176Dic59—41no—
177Dic59#13512yes—
178Dic59#13712yes—
179#3210—591nomaximal, Sylow
180C2×C59—41no—
181C2×C59—81no—
182C2×C59#53511yescharacteristic
183C2×C59C2×#13511yescharacteristic
184C2×C59C2×#13711yescharacteristic
185D59—81no—
186#533—591no—
187#532—591no—
188#494—591no—
189#492—591no—
190#487—591no—
191#486—591no—
192#464—591no—
193#464—591no—
194#464—591no—
195#464—591no—
196#452—591no—
197#452—591no—
198#452—591no—
199#452D5911yescharacteristic, complemented
200#431—591no—
201C59#321011yescharacteristic, complemented, Sylow
202C2×#41—591no—
203C2×#41C2×D5911yescharacteristic
204C2×Q16—591no—
205C2×Q16—591no—
206C2×Q16—591no—
207C2×Q16C2×D5911yescharacteristic
208C2×SD16—591no—
209C2×SD16—591no—
210C2×SD16—591no—
211C2×SD16C2×D5911yescharacteristic
212C4⋊Q8—591no—
213C4⋊Q8—591no—
214C4⋊Q8—591no—
215#127—591no—
216#125—1181no—
217#124—591no—
218#124—591no—
219C22⋊Q8—591no—
220C22⋊Q8—1181no—
221C22⋊Q8C2×D5911yescharacteristic
222#121—1181no—
223#121—1181no—
224C4×Q8—591no—
225C4×Q8—591no—
226C4×Q8—1181no—
227C4×D4—1181no—
228C4×D4—1181no—
229#117—1181no—
230C2×C42—591no—
231C4⋊C8—591no—
232C4⋊C8—591no—
233#103—591no—
234#103—591no—
235#103—591no—
236#103C2×D5911yescharacteristic
237#102—591no—
238#102—591no—
239#102—591no—
240#102C2×D5911yescharacteristic
241C22⋊C8—591no—
242C22⋊C8C2×D5911yescharacteristic
243C4×C8—591no—
244C4×C8—591no—
245#41—41no—
246#41—41no—
247#41—2361no—
248#41—2361no—
249C2×Q8—591no—
250C2×Q8—591no—
251C2×Q8—1181no—
252C2×Q8C22×D5911yescharacteristic
253C2×Q8C22×D5911yescharacteristic
254C2×D4—21no—
255C2×D4—591no—
256C2×D4—1181no—
257C2×D4—1181no—
258C2×D4—1181no—
259C2×D4C22×D5911yescharacteristic
260C22×C4—21no—
261C22×C4—591no—
262C22×C4—591no—
263C22×C4—1181no—
264C22×C4C22×D5911yescharacteristic
265Q16—41no—
266Q16—2361no—
267Q16—2361no—
268Q16—2361no—
269SD16—41no—
270SD16—2361no—
271SD16—2361no—
272SD16—2361no—
273C2×C8—591no—
274C2×C8—591no—
275C2×C8C22×D5911yescharacteristic
276C2×C8C22×D5911yescharacteristic
277C4⋊C4—21no—
278C4⋊C4—591no—
279C4⋊C4—1181no—
280C4⋊C4—1181no—
281C4⋊C4—1181no—
282C4⋊C4—1181no—
283C4⋊C4—1181no—
284C4⋊C4—1181no—
285C4⋊C4—1181no—
286C4⋊C4—1181no—
287C4⋊C4C22×D5911yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—1181no—
290C22⋊C4—1181no—
291C22⋊C4—1181no—
292C22⋊C4—1181no—
293C22⋊C4—1181no—
294C42—591no—
295C42—591no—
296C42—591no—
297C42—591no—
298C42—1181no—
299C42—1181no—
300C23—21no—
301C23—1181no—
302C23D4×D5911yescharacteristic
303Q8—21no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—1181no—
308Q8—1181no—
309Q8—1181no—
310Q8—1181no—
311Q8—2362no—
312D4—21no—
313D4—21no—
314D4—42no—
315D4—1181no—
316D4—1181no—
317D4—2362no—
318D4—2362no—
319D4—2362no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—591no—
327C2×C4—591no—
328C2×C4—591no—
329C2×C4—591no—
330C2×C4—1182no—
331C2×C4—1182no—
332C2×C4—1181no—
333C2×C4—1181no—
334C2×C4—1181no—
335C2×C4—2362no—
336C2×C4D4×D5911yescharacteristic
337C2×C4C23×D5911yescharacteristic
338C8—21no—
339C8—21no—
340C8—1181no—
341C8—1181no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—2361no—
349C22—2361no—
350C22—2361no—
351C22C2×D4×D5911yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—592no—
357C4—592no—
358C4—1181no—
359C4—1181no—
360C4—2361no—
361C4—2361no—
362C4—2361no—
363C4#1427377211yescharacteristic
364C4#1427377211yescharacteristic
365C2—41no—
366C2—81no—
367C2—4721no—
368C2#1683796711yescharacteristic
369C2#135×D5911yescharacteristic
370C2#137×D5911yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#452C2
socleC22×C59C22×D4
hypercenter#452D59
hypocenterC59#3210
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #16837954C2semidirect
3. #16837780C2semidirect
4. #16837773C2semidirect
5. #16837751C2semidirect
6. #16837747C2semidirect
7. #16837627C2semidirect
8. #16837626C2semidirect
9. #16837623C2semidirect
10. #16837622C2semidirect
11. #16837566C2semidirect
12. #16837564C2semidirect
13. #16837562C2semidirect
14. #16837452C2semidirect
15. C59×#452C2semidirect
199. #452D59semidirect
201. C59#3210semidirect