Finite Group Databasebeta

← #21434980

Subgroups — #21434980

Order 7552.

390 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16837980C211yesmaximal, characteristic
2#16837973C211yesmaximal, characteristic, complemented
3#16837744C211yesmaximal, characteristic, complemented
4#16837738C211yesmaximal, characteristic, complemented
5#16837733C211yesmaximal, characteristic, complemented
6#16837727C211yesmaximal, characteristic, complemented
7#16837660C211yesmaximal, characteristic, complemented
8#16837648C211yesmaximal, characteristic, complemented
9#16837643C211yesmaximal, characteristic, complemented
10#16837631C211yesmaximal, characteristic, complemented
11#16837566C211yesmaximal, characteristic, complemented
12#16837566C211yesmaximal, characteristic, complemented
13#16837560C211yesmaximal, characteristic, complemented
14#16837543C211yesmaximal, characteristic, complemented
15C59×#408C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C22×Dic118C2211yescharacteristic
18C2×Dic236C2211yescharacteristic
19C2×Dic236C2211yescharacteristic
20C2×#11745660C2211yescharacteristic
21C2×#11745660C2211yescharacteristic
22#14273725—21no—
23#14273714—21no—
24#14273708—21no—
25#14273708—21no—
26#14273706C2211yescharacteristic
27#14273706C2211yescharacteristic
28#14273706C2211yescharacteristic
29#14273706C2211yescharacteristic
30#14273706C2211yescharacteristic
31#14273706C2211yescharacteristic
32#14273703—21no—
33#14273701C2211yescharacteristic
34#14273701C2211yescharacteristic
35#14273699—21no—
36#14273699—21no—
37#14273698—21no—
38#14273686C2211yescharacteristic
39C2×C4⋊Dic59C2211yescharacteristic
40#14273661C2211yescharacteristic
41#14273661C2211yescharacteristic
42#14273659C2211yescharacteristic
43#14273659C2211yescharacteristic
44#14273652C2211yescharacteristic
45#14273652C2211yescharacteristic
46#14273652C2211yescharacteristic
47#14273652C2211yescharacteristic
48#14273652C2211yescharacteristic
49#14273652C2211yescharacteristic
50#14273649C2211yescharacteristic
51#14273649C2211yescharacteristic
52C2×#41×C59C2211yescharacteristic
53C2×M16×C59C2211yescharacteristic
54C22×C8×C59C2211yescharacteristic
55C22⋊C8×C59C2211yescharacteristic
56C22⋊C8×C59C2211yescharacteristic
57C22⋊C8×C59C2211yescharacteristic
58C22⋊C8×C59C2211yescharacteristic
59#41×C59—41no—
60#41×C59—41no—
61C2×Q8×C59D411yescharacteristic
62C2×D4×C59D411yescharacteristic
63C2×D4×C59D411yescharacteristic
64C2×D4×C59D411yescharacteristic
65C22×C4×C59C2311yescharacteristic
66C22×C4×C59C2311yescharacteristic
67C22×C4×C59C2311yescharacteristic
68C2×C22⋊D59—21no—
69C2×C22⋊D59—21no—
70C2×C22⋊D59—21no—
71C22×Dic59—21no—
72C22×Dic59—21no—
73#11745685—41no—
74#11745685—41no—
75C2×D236C2311yescharacteristic
76C2×C4×D59—21no—
77C2×Dic118—21no—
78C2×Dic118—41no—
79C2×Dic118—41no—
80C2×Dic118C2311yescharacteristic
81C2×Dic118C2311yescharacteristic
82C2×Dic118C2311yescharacteristic
83M16×C59—41no—
84C2×C8×C59—41no—
85C2×C8×C59C2311yescharacteristic
86C2×C8×C59C2311yescharacteristic
87C2×C8×C59C2311yescharacteristic
88C2×C8×C59C2311yescharacteristic
89C22⋊Dic59—21no—
90C22⋊Dic59—21no—
91C22⋊Dic59—21no—
92C22⋊Dic59—21no—
93C22⋊Dic59—21no—
94C22⋊Dic59—21no—
95C22⋊Dic59—21no—
96(C2×D59)⋊C4—21no—
97(C2×D59)⋊C4—21no—
98C4⋊Dic59—21no—
99C4⋊Dic59C2311yescharacteristic
100C4⋊Dic59C2311yescharacteristic
101C4⋊Dic59C2311yescharacteristic
102C4⋊Dic59C2311yescharacteristic
103Dic59⋊C4—21no—
104Dic59⋊C4—21no—
105Dic59⋊C4—21no—
106Dic59⋊C4—21no—
107Dic59⋊C4—21no—
108Dic59⋊C4—21no—
109C4×Dic59—21no—
110Dic236—41no—
111Dic236—41no—
112#11745660—41no—
113#11745660—41no—
114C23×C59C2×D411yescharacteristic
115C23×C59C2×D411yescharacteristic
116C23×C59C2×D411yescharacteristic
117C22×D59—21no—
118Q8×C59—41no—
119D4×C59—41no—
120D4×C59—41no—
121D4×C59—41no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59C2×D411yescharacteristic
129C2×C4×C59C2×D411yescharacteristic
130C2×C4×C59C2×D411yescharacteristic
131C2×C4×C59C2411yescharacteristic
132C22⋊D59—42no—
133C22⋊D59—81no—
134C22⋊D59—81no—
135C2×Dic59—21no—
136C2×Dic59—21no—
137C2×Dic59—21no—
138C2×Dic59—21no—
139C2×Dic59—21no—
140C2×Dic59—21no—
141C2×Dic59—21no—
142C2×Dic59—42no—
143C2×Dic59—81no—
144D236—21no—
145D236—21no—
146C4×D59—42no—
147Dic118—21no—
148Dic118—21no—
149Dic118—21no—
150Dic118—21no—
151Dic118—21no—
152Dic118—21no—
153Dic118—42no—
154C8×C59—21no—
155C8×C59—21no—
156C8×C59—21no—
157C8×C59—21no—
158C22×C59—21no—
159C22×C59—21no—
160C22×C59—21no—
161C22×C59—21no—
162C22×C59—21no—
163C22×C59—21no—
164C22×C59—21no—
165C22×C59—21no—
166C22×C59—21no—
167C22×C59C22×D411yescharacteristic
168C2×D59—41no—
169C2×D59—41no—
170C2×D59—41no—
171C4×C59—21no—
172C4×C59—21no—
173C4×C59—21no—
174C4×C59H(5,𝔽2)11yescharacteristic
175C4×C59H(5,𝔽2)11yescharacteristic
176Dic59—41no—
177Dic59—41no—
178Dic59—41no—
179Dic59—41no—
180Dic59—41no—
181Dic59—41no—
182Dic59—41no—
183#3201—591nomaximal, Sylow
184C2×C59—41no—
185C2×C59—41no—
186C2×C59—41no—
187C2×C59#53411yescharacteristic
188C2×C59#57711yescharacteristic
189C2×C59#57811yescharacteristic
190D59—81no—
191#537—591no—
192#536—591no—
193#485—591no—
194#484—591no—
195#483—591no—
196#482—591no—
197#470—591no—
198#468—591no—
199#467—591no—
200#465—591no—
201#452—591no—
202#452—591no—
203#451—591no—
204#448—591no—
205#408D5911yescharacteristic, complemented
206C59#320111yescharacteristic, complemented, Sylow
207C2×#41—591no—
208C2×#41C2×D5911yescharacteristic
209C22×Q8—591no—
210C2×Q16—591no—
211C2×Q16—591no—
212C2×SD16—591no—
213C2×SD16—591no—
214C2×M16C2×D5911yescharacteristic
215C22×C8C2×D5911yescharacteristic
216C4⋊Q8—1181no—
217#124—1181no—
218#123—1181no—
219#123—1181no—
220C22⋊Q8—591no—
221C22⋊Q8—591no—
222C22⋊Q8—591no—
223C22⋊Q8—591no—
224C22⋊Q8—591no—
225C22⋊Q8—591no—
226C22⋊Q8—1181no—
227#121—591no—
228#121—591no—
229#121—1181no—
230#121—1181no—
231#121—1181no—
232#117—591no—
233C2×C4⋊C4—591no—
234#107—591no—
235#107—591no—
236#106—591no—
237#106—591no—
238#103—591no—
239#103—591no—
240#103—591no—
241#103—591no—
242#103—591no—
243#103—591no—
244#102—591no—
245#102—591no—
246C22⋊C8C2×D5911yescharacteristic
247C22⋊C8C2×D5911yescharacteristic
248C22⋊C8C2×D5911yescharacteristic
249C22⋊C8C2×D5911yescharacteristic
250#41—41no—
251#41—41no—
252#41—2361no—
253#41—2361no—
254C2×Q8—591no—
255C2×Q8—591no—
256C2×Q8—591no—
257C2×Q8—1181no—
258C2×Q8—2361no—
259C2×Q8—2361no—
260C2×Q8D23611yescharacteristic
261C2×D4—591no—
262C2×D4—1181no—
263C2×D4—1181no—
264C2×D4—1181no—
265C2×D4D23611yescharacteristic
266C2×D4D23611yescharacteristic
267C2×D4D23611yescharacteristic
268C22×C4—1181no—
269C22×C4—1181no—
270C22×C4—1181no—
271C22×C4C22×D5911yescharacteristic
272C22×C4C22×D5911yescharacteristic
273C22×C4C22×D5911yescharacteristic
274Q16—2361no—
275Q16—2361no—
276SD16—2361no—
277SD16—2361no—
278M16—41no—
279C2×C8—41no—
280C2×C8C22×D5911yescharacteristic
281C2×C8C22×D5911yescharacteristic
282C2×C8C22×D5911yescharacteristic
283C2×C8C22×D5911yescharacteristic
284C4⋊C4—591no—
285C4⋊C4—591no—
286C4⋊C4—591no—
287C4⋊C4—591no—
288C4⋊C4—1181no—
289C4⋊C4—1181no—
290C4⋊C4—1181no—
291C4⋊C4—1181no—
292C4⋊C4—1181no—
293C4⋊C4—1181no—
294C4⋊C4—1181no—
295C22⋊C4—1181no—
296C22⋊C4—1181no—
297C22⋊C4—1181no—
298C22⋊C4—1181no—
299C22⋊C4—1181no—
300C22⋊C4—1181no—
301C22⋊C4—1181no—
302C22⋊C4—1181no—
303C22⋊C4—1181no—
304C42—1181no—
305C23—1181no—
306C23C2×D23611yescharacteristic
307C23C2×D23611yescharacteristic
308C23C2×D23611yescharacteristic
309Q8—41no—
310Q8—1181no—
311Q8—1181no—
312Q8—1181no—
313Q8—1181no—
314Q8—1181no—
315Q8—1181no—
316Q8—2362no—
317D4—41no—
318D4—41no—
319D4—41no—
320D4—1181no—
321D4—1181no—
322D4—4721no—
323D4—4721no—
324D4—2362no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—1181no—
332C2×C4—1181no—
333C2×C4—1181no—
334C2×C4—1181no—
335C2×C4—1181no—
336C2×C4—1181no—
337C2×C4—1181no—
338C2×C4—4721no—
339C2×C4—2362no—
340C2×C4—2362no—
341C2×C4C2×D23611yescharacteristic
342C2×C4C2×D23611yescharacteristic
343C2×C4C2×D23611yescharacteristic
344C2×C4C23×D5911yescharacteristic
345C8—21no—
346C8—21no—
347C8—21no—
348C8—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—2361no—
359C22—2361no—
360C22—2361no—
361C22C22×D23611yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—2361no—
366C4—2361no—
367C4—2361no—
368C4—2361no—
369C4—2361no—
370C4—2361no—
371C4—2361no—
372C4#1427377211yescharacteristic
373C4#1427377211yescharacteristic
374C2—41no—
375C2—41no—
376C2—41no—
377C2—4721no—
378C2#1683796411yescharacteristic
379C2#1683821411yescharacteristic
380C2#1683821911yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#408C2
socleC22×C59C22×D4
hypercenter#408D59
hypocenterC59#3201
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
2. #16837973C2semidirect
3. #16837744C2semidirect
4. #16837738C2semidirect
5. #16837733C2semidirect
6. #16837727C2semidirect
7. #16837660C2semidirect
8. #16837648C2semidirect
9. #16837643C2semidirect
10. #16837631C2semidirect
11. #16837566C2semidirect
12. #16837566C2semidirect
13. #16837560C2semidirect
14. #16837543C2semidirect
15. C59×#408C2semidirect
205. #408D59semidirect
206. C59#3201semidirect