Finite Group Databasebeta

← #21435205

Subgroups — #21435205

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#16837794C211yesmaximal, characteristic, complemented
3#16837784C211yesmaximal, characteristic, complemented
4#16837761C211yesmaximal, characteristic, complemented
5#16837752C211yesmaximal, characteristic, complemented
6#16837621C211yesmaximal, characteristic, complemented
7#16837614C211yesmaximal, characteristic, complemented
8#16837609C211yesmaximal, characteristic, complemented
9#16837604C211yesmaximal, characteristic, complemented
10#16837564C211yesmaximal, characteristic, complemented
11#16837558C211yesmaximal, characteristic, complemented
12#16837547C211yesmaximal, characteristic
13#16837541C211yesmaximal, characteristic, complemented
14#16837463C211yesmaximal, characteristic, complemented
15C59×#536C211yesmaximal, characteristic, complemented
16C2×#11745672C2211yescharacteristic
17C2×#11745672C2211yescharacteristic
18C2×#11745672C2211yescharacteristic
19C2×#11745670C2211yescharacteristic
20C2×#11745671C2211yescharacteristic
21C2×#11745671C2211yescharacteristic
22C2×#11745671C2211yescharacteristic
23C2×#11745669C2211yescharacteristic
24#14273727C2211yescharacteristic
25#14273722—21no—
26#14273715C2211yescharacteristic
27#14273713—21no—
28#14273709—21no—
29#14273706C2211yescharacteristic
30#14273705—21no—
31#14273701C2211yescharacteristic
32C4×Dic118C2211yescharacteristic
33C4×D236C2211yescharacteristic
34C4⋊(C59⋊C8)C2211yescharacteristic
35C4⋊(C59⋊C8)C2211yescharacteristic
36#14273651C2211yescharacteristic
37#14273651C2211yescharacteristic
38#14273651C2211yescharacteristic
39#14273651C2211yescharacteristic
40#14273651C2211yescharacteristic
41#14273651C2211yescharacteristic
42#14273648C2211yescharacteristic
43#14273648C2211yescharacteristic
44C22⋊(C59⋊C8)C2211yescharacteristic
45C22⋊(C59⋊C8)C2211yescharacteristic
46#14273638C2211yescharacteristic
47C4×C59⋊C8C2211yescharacteristic
48C2×#41×C59C2211yescharacteristic
49C22×Q8×C59C2211yescharacteristic
50C4⋊Q8×C59C2211yescharacteristic
51C4⋊Q8×C59C2211yescharacteristic
52#124×C59C2211yescharacteristic
53#124×C59C2211yescharacteristic
54#123×C59—21no—
55#123×C59—21no—
56C22⋊Q8×C59—21no—
57C22⋊Q8×C59—21no—
58#117×C59C2211yescharacteristic
59#41×C59—41no—
60#41×C59—41no—
61C2×Q8×C59—21no—
62C2×Q8×C59—41no—
63C2×Q8×C59—41no—
64C2×Q8×C59C2311yescharacteristic
65C2×Q8×C59C2311yescharacteristic
66C2×Q8×C59C2311yescharacteristic
67C2×D4×C59—21no—
68C2×D4×C59C2311yescharacteristic
69C22×C4×C59—21no—
70C22×C4×C59—21no—
71C22×C4×C59C2311yescharacteristic
72C2×C22⋊D59—21no—
73C2×D236C2311yescharacteristic
74C2×C4×D59—21no—
75C2×Dic118—21no—
76C2×Dic118C2311yescharacteristic
77C4⋊C4×C59—21no—
78C4⋊C4×C59—21no—
79C4⋊C4×C59—21no—
80C4⋊C4×C59—21no—
81C4⋊C4×C59D411yescharacteristic
82C4⋊C4×C59D411yescharacteristic
83C22⋊C4×C59—21no—
84C22⋊C4×C59—21no—
85C22⋊C4×C59—21no—
86C22⋊C4×C59—21no—
87C22⋊C4×C59D411yescharacteristic
88C22⋊C4×C59D411yescharacteristic
89C42×C59C2311yescharacteristic
90C42×C59C2311yescharacteristic
91C22⋊Dic59—21no—
92#11745672—41no—
93#11745672—41no—
94#11745672—41no—
95#11745671—41no—
96#11745671—41no—
97#11745671—41no—
98#11745670—41no—
99#11745669—41no—
100(C2×D59)⋊C4—21no—
101(C2×D59)⋊C4—21no—
102(C2×D59)⋊C4—21no—
103(C2×D59)⋊C4—21no—
104C4⋊Dic59—21no—
105C4⋊Dic59C2311yescharacteristic
106C4⋊Dic59C2311yescharacteristic
107Dic59⋊C4—21no—
108Dic59⋊C4—21no—
109C4×Dic59—21no—
110C2×C59⋊C8C2311yescharacteristic
111C2×C59⋊C8C2311yescharacteristic
112C2×C59⋊C8C2311yescharacteristic
113C2×C59⋊C8C2311yescharacteristic
114C23×C59—21no—
115C23×C59C2×D411yescharacteristic
116C22×D59—21no—
117Q8×C59—21no—
118Q8×C59—21no—
119Q8×C59—21no—
120Q8×C59—21no—
121Q8×C59—21no—
122Q8×C59—21no—
123Q8×C59—42no—
124D4×C59—21no—
125D4×C59—21no—
126D4×C59—42no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C2×C4×C59—21no—
132C2×C4×C59—42no—
133C2×C4×C59—42no—
134C2×C4×C59C2×D411yescharacteristic
135C2×C4×C59C2×D411yescharacteristic
136C2×C4×C59C2×D411yescharacteristic
137C2×C4×C59C2×D411yescharacteristic
138C2×C4×C59C2×D411yescharacteristic
139C2×C4×C59C2411yescharacteristic
140C22⋊D59—81no—
141C2×Dic59—21no—
142C2×Dic59—21no—
143C2×Dic59—21no—
144D236—21no—
145D236—21no—
146C4×D59—81no—
147Dic118—21no—
148Dic118—21no—
149Dic118—81no—
150C59⋊C8—21no—
151C59⋊C8—21no—
152C59⋊C8—21no—
153C59⋊C8—21no—
154C22×C59—21no—
155C22×C59—21no—
156C22×C59—21no—
157C22×C59—41no—
158C22×C59—41no—
159C22×C59—41no—
160C22×C59C22×D411yescharacteristic
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×C59—41no—
170C4×C59—41no—
171C4×C59—41no—
172C4×C59H(5,𝔽2)11yescharacteristic
173C4×C59H(5,𝔽2)11yescharacteristic
174Dic59—41no—
175Dic59—41no—
176Dic59—41no—
177#3225—591nomaximal, Sylow
178C2×C59—41no—
179C2×C59—81no—
180C2×C59#53511yescharacteristic
181C2×C59#57711yescharacteristic
182C2×C59#57811yescharacteristic
183D59—81no—
184#542—591no—
185#536D5911yescharacteristic, complemented
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#433—591no—
199C59#322511yescharacteristic, complemented, Sylow
200C2×#41C2×D5911yescharacteristic
201C22×Q8C2×D5911yescharacteristic
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⋊Q8C2×D5911yescharacteristic
212C4⋊Q8C2×D5911yescharacteristic
213#126—1181no—
214#124—591no—
215#124—1181no—
216#124C2×D5911yescharacteristic
217#124C2×D5911yescharacteristic
218#123—21no—
219#123—21no—
220#123—1181no—
221C22⋊Q8—21no—
222C22⋊Q8—21no—
223C22⋊Q8—591no—
224C22⋊Q8—1181no—
225#121—591no—
226C4×Q8—591no—
227C4×D4—591no—
228#117C2×D5911yescharacteristic
229C4⋊C8—591no—
230C4⋊C8—591no—
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⋊C8—591no—
240C22⋊C8—591no—
241#97—591no—
242C4×C8—591no—
243#41—41no—
244#41—41no—
245C2×Q8—21no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—591no—
249C2×Q8—1181no—
250C2×Q8C22×D5911yescharacteristic
251C2×Q8C22×D5911yescharacteristic
252C2×Q8C22×D5911yescharacteristic
253C2×D4—21no—
254C2×D4—591no—
255C2×D4—1181no—
256C2×D4C22×D5911yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—1181no—
260C22×C4C22×D5911yescharacteristic
261Q16—2361no—
262Q16—2361no—
263Q16—2361no—
264SD16—2361no—
265SD16—2361no—
266SD16—2361no—
267SD16—2361no—
268D8—2361no—
269C2×C8—591no—
270C2×C8—591no—
271C2×C8—591no—
272C2×C8—591no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—591no—
278C4⋊C4—591no—
279C4⋊C4—1181no—
280C4⋊C4—1181no—
281C4⋊C4—1181no—
282C4⋊C4C22⋊D5911yescharacteristic
283C4⋊C4C22⋊D5911yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—1181no—
289C22⋊C4—1181no—
290C22⋊C4—1181no—
291C22⋊C4—1181no—
292C22⋊C4—1181no—
293C22⋊C4C22⋊D5911yescharacteristic
294C22⋊C4C22⋊D5911yescharacteristic
295C42—1181no—
296C42C22×D5911yescharacteristic
297C42C22×D5911yescharacteristic
298C23—21no—
299C23—1181no—
300C23C2×C22⋊D5911yescharacteristic
301Q8—21no—
302Q8—21no—
303Q8—21no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—42no—
308Q8—1181no—
309Q8—1181no—
310Q8—4721no—
311D4—21no—
312D4—21no—
313D4—42no—
314D4—1181no—
315D4—1181no—
316D4—4721no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—1181no—
325C2×C4—1181no—
326C2×C4—1181no—
327C2×C4—4721no—
328C2×C4C2×C22⋊D5911yescharacteristic
329C2×C4C2×C22⋊D5911yescharacteristic
330C2×C4C2×C22⋊D5911yescharacteristic
331C2×C4C2×C22⋊D5911yescharacteristic
332C2×C4C2×C22⋊D5911yescharacteristic
333C2×C4C23×D5911yescharacteristic
334C8—1181no—
335C8—1181no—
336C8—1181no—
337C8—1181no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—2361no—
345C22—2361no—
346C22—2361no—
347C22C22×C22⋊D5911yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—2361no—
357C4—2361no—
358C4—2361no—
359C4#1427377211yescharacteristic
360C4#1427377211yescharacteristic
361C2—41no—
362C2—81no—
363C2—4721no—
364C2#1683796911yescharacteristic
365C2#1683821011yescharacteristic
366C2#1683821711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#536C2
socleC22×C59C22×D4
hypercenter#536D59
hypocenterC59#3225
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ #117 ◁ #536

Complements

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

NH ≅ G/Ntype
1. #16838023C2semidirect
2. #16837794C2semidirect
3. #16837784C2semidirect
4. #16837761C2semidirect
5. #16837752C2semidirect
6. #16837621C2semidirect
7. #16837614C2semidirect
8. #16837609C2semidirect
9. #16837604C2semidirect
10. #16837564C2semidirect
11. #16837558C2semidirect
13. #16837541C2semidirect
14. #16837463C2semidirect
15. C59×#536C2semidirect
185. #536D59semidirect
199. C59#3225semidirect