Finite Group Databasebeta

← #21435002

Subgroups — #21435002

Order 7552.

402 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16837980C211yesmaximal, characteristic, complemented
2#16837732C211yesmaximal, characteristic, complemented
3#16837730C211yesmaximal, characteristic, complemented
4#16837720C211yesmaximal, characteristic, complemented
5#16837718C211yesmaximal, characteristic, complemented
6#16837658C211yesmaximal, characteristic, complemented
7#16837653C211yesmaximal, characteristic, complemented
8#16837633C211yesmaximal, characteristic, complemented
9#16837629C211yesmaximal, characteristic, complemented
10#16837564C211yesmaximal, characteristic, complemented
11#16837562C211yesmaximal, characteristic, complemented
12#16837547C211yesmaximal, characteristic, complemented
13#16837545C211yesmaximal, characteristic, complemented
14#16837369C211yesmaximal, characteristic, complemented
15C59×#537C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C2×#11745672C2211yescharacteristic
18C2×#11745670C2211yescharacteristic
19C2×#11745671C2211yescharacteristic
20C2×#11745669C2211yescharacteristic
21C2×#11745664C2211yescharacteristic
22C22×C59⋊C8C2211yescharacteristic
23#14273706C2211yescharacteristic
24#14273706C2211yescharacteristic
25#14273703—21no—
26#14273701C2211yescharacteristic
27#14273701C2211yescharacteristic
28#14273699—21no—
29#14273699—21no—
30#14273698—21no—
31C2×C4⋊Dic59C2211yescharacteristic
32#14273658C2211yescharacteristic
33#14273658C2211yescharacteristic
34#14273658C2211yescharacteristic
35#14273658C2211yescharacteristic
36#14273651C2211yescharacteristic
37#14273651C2211yescharacteristic
38#14273650C2211yescharacteristic
39#14273650C2211yescharacteristic
40#14273648C2211yescharacteristic
41#14273648C2211yescharacteristic
42#14273647C2211yescharacteristic
43#14273647C2211yescharacteristic
44C22⋊(C59⋊C8)C2211yescharacteristic
45C22⋊(C59⋊C8)C2211yescharacteristic
46C22⋊(C59⋊C8)C2211yescharacteristic
47C22⋊(C59⋊C8)C2211yescharacteristic
48C2×#41×C59C2211yescharacteristic
49C2×#41×C59C2211yescharacteristic
50C22⋊Q8×C59—21no—
51C22⋊Q8×C59C2211yescharacteristic
52C22⋊Q8×C59C2211yescharacteristic
53#121×C59—21no—
54#121×C59—21no—
55#121×C59—21no—
56#121×C59C2211yescharacteristic
57#121×C59C2211yescharacteristic
58C2×C4⋊C4×C59C2211yescharacteristic
59#41×C59—41no—
60#41×C59—41no—
61#41×C59—41no—
62#41×C59—41no—
63C2×Q8×C59D411yescharacteristic
64C2×Q8×C59C2311yescharacteristic
65C2×D4×C59—21no—
66C2×D4×C59—21no—
67C2×D4×C59—21no—
68C2×D4×C59D411yescharacteristic
69C2×D4×C59D411yescharacteristic
70C2×D4×C59D411yescharacteristic
71C2×D4×C59C2311yescharacteristic
72C22×C4×C59—21no—
73C22×C4×C59—21no—
74C22×C4×C59C2311yescharacteristic
75C22×C4×C59C2311yescharacteristic
76C22×C4×C59C2311yescharacteristic
77C2×C22⋊D59—21no—
78C2×C22⋊D59—21no—
79C2×C22⋊D59—21no—
80C22×Dic59—21no—
81#11745685—41no—
82#11745685—41no—
83C2×D236C2311yescharacteristic
84C2×C4×D59—21no—
85C2×Dic118C2311yescharacteristic
86C4⋊C4×C59—21no—
87C4⋊C4×C59—21no—
88C4⋊C4×C59—21no—
89C4⋊C4×C59C2311yescharacteristic
90C4⋊C4×C59C2311yescharacteristic
91C22⋊C4×C59—21no—
92C22⋊C4×C59—21no—
93C22⋊C4×C59—21no—
94C22⋊C4×C59—21no—
95C22⋊Dic59—21no—
96C22⋊Dic59—21no—
97#11745672—41no—
98#11745671—41no—
99#11745670—41no—
100#11745669—41no—
101(C2×D59)⋊C4—21no—
102(C2×D59)⋊C4—21no—
103C4⋊Dic59—21no—
104C4⋊Dic59C2311yescharacteristic
105C4⋊Dic59C2311yescharacteristic
106Dic59⋊C4—21no—
107Dic59⋊C4—21no—
108#11745664—41no—
109C2×C59⋊C8—41no—
110C2×C59⋊C8C2311yescharacteristic
111C2×C59⋊C8C2311yescharacteristic
112C2×C59⋊C8C2311yescharacteristic
113C2×C59⋊C8C2311yescharacteristic
114C23×C59—21no—
115C23×C59C2×D411yescharacteristic
116C23×C59C2×D411yescharacteristic
117C23×C59C2×D411yescharacteristic
118C22×D59—21no—
119Q8×C59—21no—
120Q8×C59—21no—
121Q8×C59—41no—
122D4×C59—21no—
123D4×C59—21no—
124D4×C59—41no—
125D4×C59—41no—
126D4×C59—41no—
127D4×C59—42no—
128D4×C59—81no—
129D4×C59—81no—
130C2×C4×C59—21no—
131C2×C4×C59—21no—
132C2×C4×C59—21no—
133C2×C4×C59—21no—
134C2×C4×C59—21no—
135C2×C4×C59—21no—
136C2×C4×C59—21no—
137C2×C4×C59—21no—
138C2×C4×C59—21no—
139C2×C4×C59—42no—
140C2×C4×C59—81no—
141C2×C4×C59C2×D411yescharacteristic
142C2×C4×C59C2×D411yescharacteristic
143C2×C4×C59C2×D411yescharacteristic
144C2×C4×C59C2411yescharacteristic
145C22⋊D59—42no—
146C22⋊D59—81no—
147C22⋊D59—81no—
148C2×Dic59—21no—
149C2×Dic59—21no—
150C2×Dic59—21no—
151C2×Dic59—81no—
152D236—21no—
153D236—21no—
154C4×D59—42no—
155Dic118—21no—
156Dic118—21no—
157C59⋊C8—21no—
158C59⋊C8—21no—
159C59⋊C8—21no—
160C59⋊C8—21no—
161C22×C59—21no—
162C22×C59—21no—
163C22×C59—21no—
164C22×C59—21no—
165C22×C59—21no—
166C22×C59—21no—
167C22×C59—21no—
168C22×C59—21no—
169C22×C59—21no—
170C22×C59—41no—
171C22×C59—41no—
172C22×C59—41no—
173C22×C59C22×D411yescharacteristic
174C2×D59—41no—
175C2×D59—41no—
176C2×D59—41no—
177C4×C59—21no—
178C4×C59—21no—
179C4×C59—21no—
180C4×C59—41no—
181C4×C59—41no—
182C4×C59—41no—
183C4×C59H(5,𝔽2)11yescharacteristic
184C4×C59H(5,𝔽2)11yescharacteristic
185Dic59—41no—
186Dic59—41no—
187Dic59—41no—
188#3204—591nomaximal, Sylow
189C2×C59—41no—
190C2×C59—41no—
191C2×C59—41no—
192C2×C59—81no—
193C2×C59#53411yescharacteristic
194C2×C59#57711yescharacteristic
195C2×C59#57711yescharacteristic
196D59—81no—
197#537—591no—
198#537D5911yescharacteristic, complemented
199#483—591no—
200#483—591no—
201#481—591no—
202#481—591no—
203#470—591no—
204#469—591no—
205#465—591no—
206#465—591no—
207#452—591no—
208#452—591no—
209#449—591no—
210#449—591no—
211#408—591no—
212C59#320411yescharacteristic, complemented, Sylow
213C2×#41—591no—
214C2×#41C2×D5911yescharacteristic
215C2×#41C2×D5911yescharacteristic
216C2×Q16—591no—
217C2×SD16—591no—
218C2×SD16—591no—
219C2×D8—591no—
220C2×M16—591no—
221C22×C8—591no—
222C22⋊Q8—21no—
223C22⋊Q8—591no—
224C22⋊Q8—591no—
225C22⋊Q8—1181no—
226C22⋊Q8C2×D5911yescharacteristic
227C22⋊Q8C2×D5911yescharacteristic
228#121—21no—
229#121—21no—
230#121—21no—
231#121—591no—
232#121—591no—
233#121—1181no—
234#121—1181no—
235#121—1181no—
236#121C2×D5911yescharacteristic
237#121C2×D5911yescharacteristic
238C2×C4⋊C4—591no—
239C2×C4⋊C4C2×D5911yescharacteristic
240#106—591no—
241#106—591no—
242#106—591no—
243#106—591no—
244#103—591no—
245#103—591no—
246#103—591no—
247#103—591no—
248#102—591no—
249#102—591no—
250#102—591no—
251#102—591no—
252C22⋊C8—591no—
253C22⋊C8—591no—
254C22⋊C8—591no—
255C22⋊C8—591no—
256#41—41no—
257#41—41no—
258#41—41no—
259#41—41no—
260#41—2361no—
261#41—2361no—
262C2×Q8—591no—
263C2×Q8C22⋊D5911yescharacteristic
264C2×Q8C22×D5911yescharacteristic
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—591no—
269C2×D4—1181no—
270C2×D4—1181no—
271C2×D4—1181no—
272C2×D4C22⋊D5911yescharacteristic
273C2×D4C22⋊D5911yescharacteristic
274C2×D4C22⋊D5911yescharacteristic
275C2×D4C22×D5911yescharacteristic
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—1181no—
279C22×C4—1181no—
280C22×C4C22×D5911yescharacteristic
281C22×C4C22×D5911yescharacteristic
282C22×C4C22×D5911yescharacteristic
283Q16—2361no—
284SD16—2361no—
285SD16—2361no—
286D8—2361no—
287M16—2361no—
288C2×C8—591no—
289C2×C8—591no—
290C2×C8—591no—
291C2×C8—591no—
292C2×C8—2361no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—591no—
297C4⋊C4—591no—
298C4⋊C4—1181no—
299C4⋊C4—1181no—
300C4⋊C4—1181no—
301C4⋊C4C22×D5911yescharacteristic
302C4⋊C4C22×D5911yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—21no—
306C22⋊C4—21no—
307C22⋊C4—1181no—
308C22⋊C4—1181no—
309C22⋊C4—1181no—
310C22⋊C4—1181no—
311C23—21no—
312C23—1181no—
313C23C2×C22⋊D5911yescharacteristic
314C23C2×C22⋊D5911yescharacteristic
315C23C2×C22⋊D5911yescharacteristic
316Q8—21no—
317Q8—21no—
318Q8—41no—
319Q8—1181no—
320Q8—1181no—
321D4—21no—
322D4—21no—
323D4—41no—
324D4—41no—
325D4—41no—
326D4—42no—
327D4—81no—
328D4—81no—
329D4—1181no—
330D4—1181no—
331D4—4721no—
332D4—4721no—
333D4—2362no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—42no—
344C2×C4—81no—
345C2×C4—1181no—
346C2×C4—1181no—
347C2×C4—1181no—
348C2×C4—4721no—
349C2×C4—2362no—
350C2×C4C2×C22⋊D5911yescharacteristic
351C2×C4C2×C22⋊D5911yescharacteristic
352C2×C4C2×C22⋊D5911yescharacteristic
353C2×C4C23×D5911yescharacteristic
354C8—1181no—
355C8—1181no—
356C8—1181no—
357C8—1181no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—2361no—
371C22—2361no—
372C22—2361no—
373C22C22×C22⋊D5911yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—2361no—
381C4—2361no—
382C4—2361no—
383C4#1427377211yescharacteristic
384C4#1427377211yescharacteristic
385C2—41no—
386C2—41no—
387C2—41no—
388C2—81no—
389C2—4721no—
390C2#1683796111yescharacteristic
391C2#1683821011yescharacteristic
392C2#1683821311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#537C2
socleC22×C59C22×D4
hypercenter#537D59
hypocenterC59#3204
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #16837980C2semidirect
2. #16837732C2semidirect
3. #16837730C2semidirect
4. #16837720C2semidirect
5. #16837718C2semidirect
6. #16837658C2semidirect
7. #16837653C2semidirect
8. #16837633C2semidirect
9. #16837629C2semidirect
10. #16837564C2semidirect
11. #16837562C2semidirect
12. #16837547C2semidirect
13. #16837545C2semidirect
14. #16837369C2semidirect
15. C59×#537C2semidirect
198. #537D59semidirect
212. C59#3204semidirect