Finite Group Databasebeta

← #21436031

Subgroups — #21436031

Order 7552.

396 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838120C211yesmaximal, characteristic, complemented
2#16838071C211yesmaximal, characteristic
3#16837747C211yesmaximal, characteristic, complemented
4#16837726C211yesmaximal, characteristic, complemented
5#16837725C211yesmaximal, characteristic, complemented
6#16837685C211yesmaximal, characteristic, complemented
7#16837631C211yesmaximal, characteristic, complemented
8#16837630C211yesmaximal, characteristic, complemented
9#16837601C211yesmaximal, characteristic, complemented
10#16837567C211yesmaximal, characteristic, complemented
11#16837564C211yesmaximal, characteristic, complemented
12#16837494C211yesmaximal, characteristic, complemented
13C8×C22⋊D59C211yesmaximal, characteristic, complemented
14#16837397C211yesmaximal, characteristic, complemented
15C59×#416C211yesmaximal, characteristic, complemented
16C2×#11745689C2211yescharacteristic
17C2×#11745672C2211yescharacteristic
18C2×#11745660C2211yescharacteristic
19C2×#11745670C2211yescharacteristic
20C2×C8×D59C2211yescharacteristic
21#14273726C2211yescharacteristic
22#14273723—21no—
23#14273723C2211yescharacteristic
24#14273721—21no—
25#14273720—21no—
26#14273713—21no—
27#14273707C2211yescharacteristic
28#14273706C2211yescharacteristic
29#14273701—21no—
30#14273701C2211yescharacteristic
31#14273698—21no—
32#14273698C2211yescharacteristic
33Q8×Dic59C2211yescharacteristic
34C4×Dic118—21no—
35#14273692C2211yescharacteristic
36C4×C22⋊D59—21no—
37C4×C22⋊D59C2211yescharacteristic
38#14273685C2211yescharacteristic
39#14273660C2211yescharacteristic
40#14273659C2211yescharacteristic
41#14273658C2211yescharacteristic
42Dic59⋊C8C2211yescharacteristic
43#14273652C2211yescharacteristic
44#14273651C2211yescharacteristic
45#14273649C2211yescharacteristic
46#14273648C2211yescharacteristic
47#14273647C2211yescharacteristic
48#14273647C2211yescharacteristic
49C22⋊(C59⋊C8)C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51C8×Dic59C2211yescharacteristic
52C2×#41×C59C2211yescharacteristic
53C22×C8×C59C2211yescharacteristic
54#117×C59C2211yescharacteristic
55#103×C59C2211yescharacteristic
56#103×C59C2211yescharacteristic
57#102×C59C2211yescharacteristic
58#102×C59C2211yescharacteristic
59#41×C59—22no—
60#41×C59—41no—
61C2×Q8×C59C2311yescharacteristic
62C2×D4×C59—21no—
63C2×D4×C59C2311yescharacteristic
64C22×C4×C59—21no—
65C22×C4×C59C2311yescharacteristic
66C2×C22⋊D59—21no—
67C2×C22⋊D59—21no—
68C2×C22⋊D59—21no—
69C2×C22⋊D59—21no—
70C2×C22⋊D59D411yescharacteristic
71#11745689—22no—
72#11745689—41no—
73C2×D236—21no—
74C2×D236C2311yescharacteristic
75C2×C4×D59—21no—
76C2×C4×D59C2311yescharacteristic
77C2×Dic118—21no—
78C2×Dic118C2311yescharacteristic
79C2×C8×C59—41no—
80C2×C8×C59C2311yescharacteristic
81C2×C8×C59C2311yescharacteristic
82C4⋊C4×C59C2311yescharacteristic
83C4⋊C4×C59C2311yescharacteristic
84C22⋊C4×C59—21no—
85C42×C59—21no—
86C22⋊Dic59—21no—
87C22⋊Dic59—21no—
88C22⋊Dic59D411yescharacteristic
89#11745672—22no—
90#11745670—41no—
91(C2×D59)⋊C4—21no—
92(C2×D59)⋊C4—21no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4D411yescharacteristic
95C4⋊Dic59—21no—
96C4⋊Dic59—21no—
97C4⋊Dic59C2311yescharacteristic
98C4⋊Dic59C2311yescharacteristic
99Dic59⋊C4—21no—
100Dic59⋊C4—21no—
101Dic59⋊C4—21no—
102Dic59⋊C4D411yescharacteristic
103C4×Dic59—21no—
104C4×Dic59—21no—
105C4×Dic59—21no—
106C4×Dic59C2311yescharacteristic
107C2×C59⋊C8C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109#11745660—41no—
110C8×D59—41no—
111C23×C59—21no—
112C23×C59C2×D411yescharacteristic
113C22×D59—21no—
114C22×D59C2×D411yescharacteristic
115Q8×C59—21no—
116Q8×C59#4112yes—
117D4×C59—21no—
118D4×C59—21no—
119D4×C59—42no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59—42no—
126C2×C4×C59C2×D411yescharacteristic
127C2×C4×C59C2411yescharacteristic
128C22⋊D59—22no—
129C22⋊D59—42no—
130C22⋊D59—81no—
131C22⋊D59—81no—
132C22⋊D59—81no—
133C2×Dic59—21no—
134C2×Dic59—21no—
135C2×Dic59—21no—
136C2×Dic59C2×D411yescharacteristic
137C2×Dic59C2×D411yescharacteristic
138C2×Dic59C2×D411yescharacteristic
139D236—21no—
140D236—21no—
141D236—42no—
142C4×D59—21no—
143C4×D59—21no—
144C4×D59—42no—
145Dic118—21no—
146Dic118—21no—
147Dic118—42no—
148C8×C59—21no—
149C8×C59—21no—
150C59⋊C8—21no—
151C59⋊C8—21no—
152C22×C59—21no—
153C22×C59—21no—
154C22×C59—21no—
155C22×C59—41no—
156C22×C59—41no—
157C22×C59—41no—
158C22×C59C22×D411yescharacteristic
159C2×D59—21no—
160C2×D59—21no—
161C2×D59—21no—
162C2×D59—41no—
163C2×D59—41no—
164C2×D59—41no—
165C4×C59—22no—
166C4×C59—21no—
167C4×C59—41no—
168C4×C59—41no—
169C4×C59C2×#4111yescharacteristic
170C4×C59H(5,𝔽2)11yescharacteristic
171Dic59—21no—
172Dic59—21no—
173Dic59—41no—
174Dic59—41no—
175Dic59—41no—
176Dic59#13512yes—
177#3304—591nomaximal, Sylow
178C2×C59—41no—
179C2×C59—81no—
180C2×C59#54611yescharacteristic
181C2×C59C2×#13511yescharacteristic
182C2×C59#57711yescharacteristic
183D59—41no—
184D59—81no—
185#556—591no—
186#550—591no—
187#486—591no—
188#482—591no—
189#482—591no—
190#475—591no—
191#465—591no—
192#465—591no—
193#460—591no—
194#452—591no—
195#452—591no—
196C4×Q16—591no—
197C8×D4—591no—
198#416—591no—
199#416D5911yescharacteristic, complemented
200C59#330411yescharacteristic, complemented, Sylow
201C2×#41—591no—
202C2×#41C2×D5911yescharacteristic
203C2×Q16—591no—
204C2×SD16—591no—
205C2×SD16—591no—
206C22×C8—591no—
207C22×C8C2×D5911yescharacteristic
208C4⋊Q8—591no—
209#127—591no—
210#127—1181no—
211#126—1181no—
212#126—1181no—
213#124—1181no—
214C22⋊Q8—591no—
215C22⋊Q8—591no—
216#121—591no—
217#121—591no—
218#121—1181no—
219#121—1181no—
220C4×Q8—591no—
221C4×Q8—591no—
222C4×Q8—1181no—
223C4×D4—591no—
224C4×D4—1181no—
225#117—591no—
226#117C2×D5911yescharacteristic
227#107—591no—
228#106—591no—
229#106—591no—
230C4⋊C8—591no—
231#103—591no—
232#103—591no—
233#103C2×D5911yescharacteristic
234#103C2×D5911yescharacteristic
235#102—591no—
236#102—591no—
237#102—591no—
238#102—591no—
239#102C2×D5911yescharacteristic
240#102C2×D5911yescharacteristic
241C22⋊C8—591no—
242C22⋊C8—591no—
243C4×C8—591no—
244#41—22no—
245#41—41no—
246#41—1182no—
247#41—2361no—
248C2×Q8—591no—
249C2×Q8—1181no—
250C2×Q8C22×D5911yescharacteristic
251C2×D4—21no—
252C2×D4—591no—
253C2×D4—591no—
254C2×D4—1181no—
255C2×D4—1181no—
256C2×D4—1181no—
257C2×D4—1181no—
258C2×D4—1181no—
259C2×D4C22×D5911yescharacteristic
260C22×C4—21no—
261C22×C4—591no—
262C22×C4—1181no—
263C22×C4C22×D5911yescharacteristic
264Q16—1182no—
265SD16—2361no—
266SD16—2361no—
267C2×C8—41no—
268C2×C8—591no—
269C2×C8—591no—
270C2×C8—2361no—
271C2×C8C22×D5911yescharacteristic
272C2×C8C22×D5911yescharacteristic
273C4⋊C4—591no—
274C4⋊C4—591no—
275C4⋊C4—591no—
276C4⋊C4—1181no—
277C4⋊C4—1181no—
278C4⋊C4—1181no—
279C4⋊C4—1181no—
280C4⋊C4—1181no—
281C4⋊C4C22×D5911yescharacteristic
282C4⋊C4C22×D5911yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—591no—
285C22⋊C4—591no—
286C22⋊C4—1181no—
287C22⋊C4—1181no—
288C22⋊C4—1181no—
289C22⋊C4—1181no—
290C22⋊C4—1181no—
291C42—21no—
292C42—591no—
293C42—1181no—
294C42—1181no—
295C42—1181no—
296C23—21no—
297C23—591no—
298C23—1181no—
299C23D4×D5911yescharacteristic
300Q8—21no—
301Q8—1181no—
302Q8—1181no—
303Q8—2362no—
304Q8#1174568512yes—
305D4—21no—
306D4—21no—
307D4—42no—
308D4—1182no—
309D4—1181no—
310D4—1181no—
311D4—4721no—
312D4—4721no—
313D4—4721no—
314D4—2362no—
315D4—2362no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—591no—
323C2×C4—591no—
324C2×C4—591no—
325C2×C4—1181no—
326C2×C4—1181no—
327C2×C4—1181no—
328C2×C4—1181no—
329C2×C4—1181no—
330C2×C4—2362no—
331C2×C4D4×D5911yescharacteristic
332C2×C4C23×D5911yescharacteristic
333C8—21no—
334C8—21no—
335C8—1181no—
336C8—1181no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—1181no—
344C22—1181no—
345C22—1181no—
346C22—2361no—
347C22—2361no—
348C22—2361no—
349C22C2×D4×D5911yescharacteristic
350C4—21no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—592no—
355C4—1181no—
356C4—1181no—
357C4—2361no—
358C4—2361no—
359C4—2361no—
360C4C2×#1174568511yescharacteristic
361C4#1427377211yescharacteristic
362C2—41no—
363C2—81no—
364C2—4721no—
365C2—2361no—
366C2#1683804211yescharacteristic
367C2#135×D5911yescharacteristic
368C2#1683820911yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#416C2
socleC22×C59C22×D4
hypercenter#416D59
hypocenterC59#3304
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #16838120C2semidirect
3. #16837747C2semidirect
4. #16837726C2semidirect
5. #16837725C2semidirect
6. #16837685C2semidirect
7. #16837631C2semidirect
8. #16837630C2semidirect
9. #16837601C2semidirect
10. #16837567C2semidirect
11. #16837564C2semidirect
12. #16837494C2semidirect
13. C8×C22⋊D59C2semidirect
14. #16837397C2semidirect
15. C59×#416C2semidirect
199. #416D59semidirect
200. C59#3304semidirect