Finite Group Databasebeta

← #21434977

Subgroups — #21434977

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#16837975C211yesmaximal, characteristic, complemented
3#16837742C211yesmaximal, characteristic, complemented
4#16837738C211yesmaximal, characteristic, complemented
5#16837730C211yesmaximal, characteristic, complemented
6#16837724C211yesmaximal, characteristic, complemented
7#16837659C211yesmaximal, characteristic, complemented
8#16837645C211yesmaximal, characteristic, complemented
9#16837640C211yesmaximal, characteristic, complemented
10#16837630C211yesmaximal, characteristic, complemented
11#16837564C211yesmaximal, characteristic, complemented
12#16837556C211yesmaximal, characteristic, complemented
13#16837539C211yesmaximal, characteristic, complemented
14#16837367C211yesmaximal, characteristic, complemented
15C59×#452C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C2×Q8×D59C2211yescharacteristic
18C2×#11745672C2211yescharacteristic
19C2×#11745670C2211yescharacteristic
20C2×#11745659C2211yescharacteristic
21C2×C8×D59C2211yescharacteristic
22#14273726—21no—
23#14273713—21no—
24#14273712—21no—
25#14273709—21no—
26#14273707C2211yescharacteristic
27#14273706—21no—
28#14273706C2211yescharacteristic
29#14273703C2211yescharacteristic
30#14273703C2211yescharacteristic
31#14273703C2211yescharacteristic
32#14273701—21no—
33#14273699—21no—
34#14273699—21no—
35#14273698C2211yescharacteristic
36#14273698C2211yescharacteristic
37#14273685C2211yescharacteristic
38C2×C4⋊Dic59C2211yescharacteristic
39#14273661C2211yescharacteristic
40#14273661C2211yescharacteristic
41#14273658C2211yescharacteristic
42#14273658C2211yescharacteristic
43#14273652C2211yescharacteristic
44#14273652C2211yescharacteristic
45#14273651C2211yescharacteristic
46#14273651C2211yescharacteristic
47#14273651C2211yescharacteristic
48#14273648C2211yescharacteristic
49C22⋊(C59⋊C8)C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51(C2×D59)⋊C8C2211yescharacteristic
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⋊D59D411yescharacteristic
70C2×C22⋊D59D411yescharacteristic
71C22×Dic59—21no—
72Q8×D59—41no—
73Q8×D59—41no—
74#11745685—41no—
75#11745685—41no—
76C2×D236D411yescharacteristic
77C2×C4×D59—21no—
78C2×C4×D59C2311yescharacteristic
79C2×C4×D59C2311yescharacteristic
80C2×Dic118—21no—
81C2×Dic118D411yescharacteristic
82C2×Dic118C2311yescharacteristic
83Q16×C59—41no—
84SD16×C59—41no—
85C2×C8×C59C2311yescharacteristic
86C2×C8×C59C2311yescharacteristic
87C4⋊C4×C59—21no—
88C4⋊C4×C59C2311yescharacteristic
89C22⋊C4×C59—21no—
90C22⋊Dic59—21no—
91C22⋊Dic59—21no—
92C22⋊Dic59—21no—
93#11745672—41no—
94#11745670—41no—
95(C2×D59)⋊C4—21no—
96(C2×D59)⋊C4—21no—
97(C2×D59)⋊C4—21no—
98(C2×D59)⋊C4—21no—
99(C2×D59)⋊C4—21no—
100C4⋊Dic59—21no—
101C4⋊Dic59—21no—
102C4⋊Dic59C2311yescharacteristic
103C4⋊Dic59C2311yescharacteristic
104C4⋊Dic59C2311yescharacteristic
105Dic59⋊C4—21no—
106Dic59⋊C4—21no—
107Dic59⋊C4—21no—
108Dic59⋊C4—21no—
109C4×Dic59—21no—
110C2×C59⋊C8C2311yescharacteristic
111C2×C59⋊C8C2311yescharacteristic
112#11745659—41no—
113C8×D59—41no—
114C23×C59—21no—
115C23×C59C2×D411yescharacteristic
116C22×D59C2×D411yescharacteristic
117C22×D59C2×D411yescharacteristic
118Q8×C59—21no—
119Q8×C59—21no—
120Q8×C59—21no—
121Q8×C59—21no—
122D4×C59—21no—
123D4×C59—21no—
124D4×C59—42no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—42no—
131C2×C4×C59C2×D411yescharacteristic
132C2×C4×C59C2411yescharacteristic
133C22⋊D59—41no—
134C22⋊D59—41no—
135C22⋊D59—81no—
136C22⋊D59—81no—
137C2×Dic59—21no—
138C2×Dic59—21no—
139C2×Dic59—21no—
140C2×Dic59—21no—
141C2×Dic59—81no—
142C2×Dic59C2×D411yescharacteristic
143C2×Dic59C2×D411yescharacteristic
144D236—41no—
145C4×D59—21no—
146C4×D59—21no—
147C4×D59—21no—
148C4×D59—21no—
149C4×D59—42no—
150Dic118—21no—
151Dic118—21no—
152Dic118—41no—
153Dic118—42no—
154C8×C59—21no—
155C8×C59—21no—
156C59⋊C8—21no—
157C59⋊C8—21no—
158C22×C59—21no—
159C22×C59—21no—
160C22×C59—21no—
161C22×C59—41no—
162C22×C59—41no—
163C22×C59—41no—
164C22×C59C22×D411yescharacteristic
165C2×D59—21no—
166C2×D59—21no—
167C2×D59—21no—
168C2×D59—21no—
169C2×D59—21no—
170C2×D59—21no—
171C4×C59—21no—
172C4×C59—41no—
173C4×C59—41no—
174C4×C59—41no—
175C4×C59H(5,𝔽2)11yescharacteristic
176C4×C59H(5,𝔽2)11yescharacteristic
177Dic59—21no—
178Dic59—21no—
179Dic59—41no—
180Dic59—41no—
181Dic59—41no—
182Dic59—41no—
183#3201—591nomaximal, Sylow
184C2×C59—41no—
185C2×C59—81no—
186C2×C59#53411yescharacteristic
187C2×C59#57711yescharacteristic
188C2×C59#57811yescharacteristic
189D59—41no—
190D59—41no—
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#452D5911yescharacteristic, complemented
203#451—591no—
204#448—591no—
205#408—591no—
206C59#320111yescharacteristic, complemented, Sylow
207C2×#41—591no—
208C2×#41C2×D5911yescharacteristic
209C22×Q8—591no—
210C2×Q16—591no—
211C2×Q16C2×D5911yescharacteristic
212C2×SD16—591no—
213C2×SD16C2×D5911yescharacteristic
214C2×M16—591no—
215C22×C8—591no—
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—1181no—
226C22⋊Q8C2×D5911yescharacteristic
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#103C2×D5911yescharacteristic
244#102—591no—
245#102C2×D5911yescharacteristic
246C22⋊C8—591no—
247C22⋊C8—591no—
248C22⋊C8—591no—
249C22⋊C8C2×D5911yescharacteristic
250#41—41no—
251#41—41no—
252#41—2361no—
253#41—2361no—
254C2×Q8—591no—
255C2×Q8—591no—
256C2×Q8—1181no—
257C2×Q8—2361no—
258C2×Q8—2361no—
259C2×Q8C22×D5911yescharacteristic
260C2×Q8C22×D5911yescharacteristic
261C2×D4—21no—
262C2×D4—591no—
263C2×D4—591no—
264C2×D4—591no—
265C2×D4—1181no—
266C2×D4—1181no—
267C2×D4C22×D5911yescharacteristic
268C22×C4—21no—
269C22×C4—591no—
270C22×C4—591no—
271C22×C4—1181no—
272C22×C4—1181no—
273C22×C4C22×D5911yescharacteristic
274Q16—41no—
275Q16—2361no—
276SD16—41no—
277SD16—2361no—
278M16—2361no—
279C2×C8—591no—
280C2×C8—591no—
281C2×C8—2361no—
282C2×C8C22×D5911yescharacteristic
283C2×C8C22×D5911yescharacteristic
284C4⋊C4—21no—
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⋊C4C22×D5911yescharacteristic
295C22⋊C4—21no—
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—21no—
306C23—591no—
307C23—591no—
308C23D4×D5911yescharacteristic
309Q8—21no—
310Q8—21no—
311Q8—21no—
312Q8—21no—
313Q8—1181no—
314Q8—1181no—
315Q8—2361no—
316Q8—2362no—
317D4—21no—
318D4—21no—
319D4—42no—
320D4—4721no—
321D4—4721no—
322D4—2361no—
323D4—2361no—
324D4—2361no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—591no—
332C2×C4—591no—
333C2×C4—1181no—
334C2×C4—1181no—
335C2×C4—1181no—
336C2×C4—1181no—
337C2×C4—1181no—
338C2×C4—1181no—
339C2×C4—1181no—
340C2×C4—1181no—
341C2×C4—4721no—
342C2×C4—2362no—
343C2×C4D4×D5911yescharacteristic
344C2×C4C23×D5911yescharacteristic
345C8—21no—
346C8—21no—
347C8—1181no—
348C8—1181no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—1181no—
356C22—1181no—
357C22—1181no—
358C22—1181no—
359C22—1181no—
360C22—1181no—
361C22C2×D4×D5911yescharacteristic
362C4—21no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—1181no—
367C4—1181no—
368C4—2361no—
369C4—2361no—
370C4—2361no—
371C4—2361no—
372C4#1427377211yescharacteristic
373C4#1427377211yescharacteristic
374C2—41no—
375C2—81no—
376C2—2361no—
377C2—2361no—
378C2#1683796211yescharacteristic
379C2#1683821111yescharacteristic
380C2#1683821611yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#452C2
socleC22×C59C22×D4
hypercenter#452D59
hypocenterC59#3201
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
2. #16837975C2semidirect
3. #16837742C2semidirect
4. #16837738C2semidirect
5. #16837730C2semidirect
6. #16837724C2semidirect
7. #16837659C2semidirect
8. #16837645C2semidirect
9. #16837640C2semidirect
10. #16837630C2semidirect
11. #16837564C2semidirect
12. #16837556C2semidirect
13. #16837539C2semidirect
14. #16837367C2semidirect
15. C59×#452C2semidirect
202. #452D59semidirect
206. C59#3201semidirect