Finite Group Databasebeta

← #21436366

Subgroups — #21436366

Order 7552.

380 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838092C211yesmaximal, characteristic, complemented
2#16838061C211yesmaximal, characteristic
3#16837757C211yesmaximal, characteristic, complemented
4#16837738C211yesmaximal, characteristic, complemented
5#16837727C211yesmaximal, characteristic, complemented
6#16837710C211yesmaximal, characteristic, complemented
7#16837660C211yesmaximal, characteristic, complemented
8#16837648C211yesmaximal, characteristic, complemented
9#16837625C211yesmaximal, characteristic, complemented
10#16837566C211yesmaximal, characteristic, complemented
11#16837560C211yesmaximal, characteristic, complemented
12C4×Dic236C211yesmaximal, characteristic, complemented
13#16837412C211yesmaximal, characteristic, complemented
14#16837404C211yesmaximal, characteristic, complemented
15C59×#436C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C22×Dic118C2211yescharacteristic
18C2×Dic236C2211yescharacteristic
19C2×Dic236C2211yescharacteristic
20C2×#11745660C2211yescharacteristic
21#14273720—21no—
22#14273719C2211yescharacteristic
23#14273717—21no—
24#14273715C2211yescharacteristic
25#14273713—21no—
26#14273708—21no—
27#14273706C2211yescharacteristic
28#14273706C2211yescharacteristic
29#14273706C2211yescharacteristic
30#14273705—21no—
31#14273701C2211yescharacteristic
32#14273699—21no—
33C4×Dic118C2211yescharacteristic
34C4×Dic118C2211yescharacteristic
35(C22⋊D59)⋊C4—21no—
36#14273686C2211yescharacteristic
37#14273683—21no—
38C2×C4⋊Dic59C2211yescharacteristic
39#14273661C2211yescharacteristic
40#14273661C2211yescharacteristic
41#14273659C2211yescharacteristic
42#14273652C2211yescharacteristic
43#14273652C2211yescharacteristic
44#14273652C2211yescharacteristic
45#14273652C2211yescharacteristic
46#14273652C2211yescharacteristic
47#14273652C2211yescharacteristic
48#14273652C2211yescharacteristic
49#14273649C2211yescharacteristic
50#14273649C2211yescharacteristic
51#14273649C2211yescharacteristic
52C2×M16×C59C2211yescharacteristic
53C2×M16×C59C2211yescharacteristic
54C4×D4×C59C2211yescharacteristic
55C4⋊C8×C59C2211yescharacteristic
56C22⋊C8×C59C2211yescharacteristic
57C22⋊C8×C59C2211yescharacteristic
58C4×C8×C59C2211yescharacteristic
59C2×D4×C59D411yescharacteristic
60C22×C4×C59C2311yescharacteristic
61C22×C4×C59C2311yescharacteristic
62C2×C22⋊D59—21no—
63C2×C22⋊D59—21no—
64C22×Dic59—21no—
65C22×Dic59—21no—
66#11745685—22no—
67#11745685—41no—
68C2×D236C2311yescharacteristic
69C2×C4×D59—21no—
70C2×Dic118—22no—
71C2×Dic118—21no—
72C2×Dic118—41no—
73C2×Dic118C2311yescharacteristic
74C2×Dic118C2311yescharacteristic
75C2×Dic118C2311yescharacteristic
76M16×C59—41no—
77M16×C59—41no—
78C2×C8×C59C2311yescharacteristic
79C2×C8×C59C2311yescharacteristic
80C2×C8×C59C2311yescharacteristic
81C2×C8×C59C2311yescharacteristic
82C4⋊C4×C59D411yescharacteristic
83C22⋊C4×C59D411yescharacteristic
84C22⋊C4×C59D411yescharacteristic
85C42×C59C2311yescharacteristic
86C22⋊Dic59—21no—
87C22⋊Dic59—21no—
88C22⋊Dic59—21no—
89C22⋊Dic59—21no—
90(C2×D59)⋊C4—21no—
91(C2×D59)⋊C4—21no—
92(C2×D59)⋊C4—21no—
93C4⋊Dic59—21no—
94C4⋊Dic59C2311yescharacteristic
95C4⋊Dic59C2311yescharacteristic
96C4⋊Dic59C2311yescharacteristic
97C4⋊Dic59C2311yescharacteristic
98Dic59⋊C4—21no—
99Dic59⋊C4—21no—
100Dic59⋊C4—21no—
101Dic59⋊C4—21no—
102Dic59⋊C4—21no—
103Dic59⋊C4—21no—
104Dic59⋊C4—21no—
105C4×Dic59—21no—
106C4×Dic59—21no—
107C4×Dic59—21no—
108Dic236—22no—
109Dic236—41no—
110#11745660—41no—
111C23×C59C2×D411yescharacteristic
112C23×C59C2×D411yescharacteristic
113C22×D59—21no—
114D4×C59—41no—
115C2×C4×C59—21no—
116C2×C4×C59—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×C59C2411yescharacteristic
124C22⋊D59—42no—
125C22⋊D59—42no—
126C2×Dic59—21no—
127C2×Dic59—21no—
128C2×Dic59—21no—
129C2×Dic59—21no—
130C2×Dic59—21no—
131C2×Dic59—21no—
132C2×Dic59—21no—
133C2×Dic59—42no—
134C2×Dic59—42no—
135D236—21no—
136D236—21no—
137C4×D59—42no—
138Dic118—21no—
139Dic118—21no—
140Dic118—21no—
141Dic118—21no—
142Dic118—21no—
143Dic118—42no—
144Dic118#4112yes—
145C8×C59—21no—
146C8×C59—21no—
147C8×C59—21no—
148C8×C59—21no—
149C22×C59—21no—
150C22×C59—21no—
151C22×C59—21no—
152C22×C59—21no—
153C22×C59—21no—
154C22×C59—21no—
155C22×C59C22×D411yescharacteristic
156C2×D59—41no—
157C2×D59—41no—
158C2×D59—41no—
159C4×C59—21no—
160C4×C59—21no—
161C4×C59—21no—
162C4×C59—21no—
163C4×C59C2×#4111yescharacteristic
164C4×C59H(5,𝔽2)11yescharacteristic
165Dic59—22no—
166Dic59—41no—
167Dic59—41no—
168Dic59—41no—
169Dic59—41no—
170Dic59—41no—
171Dic59—41no—
172#3327—591nomaximal, Sylow
173C2×C59—41no—
174C2×C59—41no—
175C2×C59#54611yescharacteristic
176C2×C59#57511yescharacteristic
177C2×C59#57811yescharacteristic
178D59—81no—
179#552—591no—
180#548—591no—
181#488—591no—
182#484—591no—
183#482—591no—
184#479—591no—
185#470—591no—
186#468—591no—
187#464—591no—
188#452—591no—
189#451—591no—
190C4×Q16—591no—
191#436D5911yescharacteristic, complemented
192#419—591no—
193#417—591no—
194C59#332711yescharacteristic, complemented, Sylow
195C2×#41—591no—
196C22×Q8—591no—
197C2×Q16—591no—
198C2×Q16—591no—
199C2×SD16—591no—
200C2×M16C2×D5911yescharacteristic
201C2×M16C2×D5911yescharacteristic
202#126—1181no—
203#125—591no—
204#125—1181no—
205#124—591no—
206#124—1181no—
207#123—1181no—
208C22⋊Q8—591no—
209C22⋊Q8—591no—
210C22⋊Q8—591no—
211C22⋊Q8—1181no—
212#121—591no—
213#121—1181no—
214C4×Q8—591no—
215C4×Q8—591no—
216C4×D4—1181no—
217C4×D4C2×D5911yescharacteristic
218#117—591no—
219#117—1181no—
220C2×C4⋊C4—591no—
221#107—591no—
222#107—591no—
223#106—591no—
224C4⋊C8C2×D5911yescharacteristic
225#103—591no—
226#103—591no—
227#103—591no—
228#103—591no—
229#103—591no—
230#103—591no—
231#103—591no—
232#102—591no—
233#102—591no—
234#102—591no—
235C22⋊C8C2×D5911yescharacteristic
236C22⋊C8C2×D5911yescharacteristic
237C4×C8C2×D5911yescharacteristic
238#41—1182no—
239#41—2361no—
240C2×Q8—591no—
241C2×Q8—591no—
242C2×Q8—591no—
243C2×Q8—1182no—
244C2×Q8—1181no—
245C2×Q8—2361no—
246C2×D4—591no—
247C2×D4—1181no—
248C2×D4—1181no—
249C2×D4D23611yescharacteristic
250C22×C4—1181no—
251C22×C4—1181no—
252C22×C4—1181no—
253C22×C4C22×D5911yescharacteristic
254C22×C4C22×D5911yescharacteristic
255Q16—1182no—
256Q16—2361no—
257SD16—2361no—
258M16—41no—
259M16—41no—
260C2×C8C22×D5911yescharacteristic
261C2×C8C22×D5911yescharacteristic
262C2×C8C22×D5911yescharacteristic
263C2×C8C22×D5911yescharacteristic
264C4⋊C4—591no—
265C4⋊C4—591no—
266C4⋊C4—591no—
267C4⋊C4—591no—
268C4⋊C4—1181no—
269C4⋊C4—1181no—
270C4⋊C4—1181no—
271C4⋊C4—1181no—
272C4⋊C4—1181no—
273C4⋊C4—1181no—
274C4⋊C4—1181no—
275C4⋊C4—1181no—
276C4⋊C4D23611yescharacteristic
277C22⋊C4—1181no—
278C22⋊C4—1181no—
279C22⋊C4—1181no—
280C22⋊C4—1181no—
281C22⋊C4—1181no—
282C22⋊C4—1181no—
283C22⋊C4—1181no—
284C22⋊C4D23611yescharacteristic
285C22⋊C4D23611yescharacteristic
286C42—1181no—
287C42—1181no—
288C42—1181no—
289C42C22×D5911yescharacteristic
290C23—1181no—
291C23C2×D23611yescharacteristic
292C23C2×D23611yescharacteristic
293Q8—592no—
294Q8—1181no—
295Q8—1181no—
296Q8—1181no—
297Q8—1181no—
298Q8—1181no—
299Q8—2362no—
300D4—41no—
301D4—1181no—
302D4—1181no—
303D4—2362no—
304D4—2362no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—1181no—
310C2×C4—1181no—
311C2×C4—1181no—
312C2×C4—1181no—
313C2×C4—1181no—
314C2×C4—1181no—
315C2×C4—1181no—
316C2×C4—2362no—
317C2×C4—2362no—
318C2×C4—2362no—
319C2×C4C2×D23611yescharacteristic
320C2×C4C2×D23611yescharacteristic
321C2×C4C2×D23611yescharacteristic
322C2×C4C2×D23611yescharacteristic
323C2×C4C23×D5911yescharacteristic
324C8—21no—
325C8—21no—
326C8—21no—
327C8—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—2361no—
335C22—2361no—
336C22—2361no—
337C22C22×D23611yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—1182no—
343C4—2361no—
344C4—2361no—
345C4—2361no—
346C4—2361no—
347C4—2361no—
348C4—2361no—
349C4#41×D5911yescharacteristic
350C4#1427377211yescharacteristic
351C2—41no—
352C2—41no—
353C2—4721no—
354C2#1683804711yescharacteristic
355C2#1683820211yescharacteristic
356C2#1683821911yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#436C2
socleC22×C59C22×D4
hypercenter#436D59
hypocenterC59#3327
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. #16838092C2semidirect
3. #16837757C2semidirect
4. #16837738C2semidirect
5. #16837727C2semidirect
6. #16837710C2semidirect
7. #16837660C2semidirect
8. #16837648C2semidirect
9. #16837625C2semidirect
10. #16837566C2semidirect
11. #16837560C2semidirect
12. C4×Dic236C2semidirect
13. #16837412C2semidirect
14. #16837404C2semidirect
15. C59×#436C2semidirect
191. #436D59semidirect
194. C59#3327semidirect