Finite Group Databasebeta

← #21435166

Subgroups — #21435166

Order 7552.

396 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#16838012C211yesmaximal, characteristic, complemented
2#16837966C211yesmaximal, characteristic
3#16837795C211yesmaximal, characteristic, complemented
4#16837773C211yesmaximal, characteristic, complemented
5#16837765C211yesmaximal, characteristic, complemented
6#16837758C211yesmaximal, characteristic, complemented
7#16837627C211yesmaximal, characteristic, complemented
8#16837626C211yesmaximal, characteristic, complemented
9#16837601C211yesmaximal, characteristic, complemented
10#16837600C211yesmaximal, characteristic, complemented
11#16837564C211yesmaximal, characteristic, complemented
12#16837555C211yesmaximal, characteristic, complemented
13#16837552C211yesmaximal, characteristic, complemented
14#16837460C211yesmaximal, characteristic, complemented
15C59×#452C211yesmaximal, characteristic, complemented
16C22×D236C2211yescharacteristic
17C2×#11745672C2211yescharacteristic, complemented
18C2×#11745660C2211yescharacteristic
19C2×#11745660C2211yescharacteristic
20C2×#11745670C2211yescharacteristic, complemented
21C2×#11745671C2211yescharacteristic
22C2×#11745671C2211yescharacteristic
23#14273725C2211yescharacteristic, complemented
24#14273723C2211yescharacteristic
25#14273723C2211yescharacteristic
26#14273720—21no—
27#14273720—21no—
28#14273718—21no—
29#14273718C2211yescharacteristic, complemented
30#14273717—21no—
31#14273716C2211yescharacteristic
32#14273716C2211yescharacteristic
33#14273706C2211yescharacteristic
34#14273701—21no—
35#14273701—21no—
36#14273695—21no—
37#14273695—21no—
38Q8×Dic59C2211yescharacteristic, complemented
39#14273692C2211yescharacteristic, complemented
40#14273686C2211yescharacteristic
41Dic59⋊C8C2211yescharacteristic, complemented
42Dic59⋊C8C2211yescharacteristic, complemented
43#14273651C2211yescharacteristic, complemented
44#14273649C2211yescharacteristic
45#14273649C2211yescharacteristic
46#14273648C2211yescharacteristic, complemented
47#14273647C2211yescharacteristic
48#14273647C2211yescharacteristic
49C22⋊(C59⋊C8)C2211yescharacteristic
50#14273637C2211yescharacteristic, complemented
51C8×Dic59C2211yescharacteristic, complemented
52C2×#41×C59C2211yescharacteristic
53C2×Q16×C59C2211yescharacteristic, complemented
54C2×SD16×C59C2211yescharacteristic, complemented
55C22⋊Q8×C59C2211yescharacteristic
56#103×C59C2211yescharacteristic, complemented
57#102×C59C2211yescharacteristic, complemented
58C22⋊C8×C59C2211yescharacteristic
59C23×D59—21no—
60#41×C59—41no—
61#41×C59—41no—
62C2×Q8×C59C2311yescharacteristic
63C2×Q8×C59C2311yescharacteristic
64C2×D4×C59—21no—
65C2×D4×C59C2311yescharacteristic
66C22×C4×C59—21no—
67C22×C4×C59C2311yescharacteristic
68C2×C22⋊D59—21no—
69C2×C22⋊D59—21no—
70C2×C22⋊D59—21no—
71C2×C22⋊D59—21no—
72C2×D236—21no—
73C2×D236—41no—
74C2×D236—41no—
75C2×D236C2311yescharacteristic
76C2×D236C2311yescharacteristic
77C2×Dic118C2311yescharacteristic
78Q16×C59—41no—
79SD16×C59—41no—
80C2×C8×C59C2311yescharacteristic
81C2×C8×C59C2311yescharacteristic
82C4⋊C4×C59—21no—
83C4⋊C4×C59C2311yescharacteristic
84C22⋊C4×C59—21no—
85C22⋊Dic59—21no—
86C22⋊Dic59D411yescharacteristic
87C22⋊Dic59D411yescharacteristic
88#11745672—41no—
89#11745671—41no—
90#11745671—41no—
91#11745670—41no—
92(C2×D59)⋊C4—21no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4—21no—
95(C2×D59)⋊C4—21no—
96C4⋊Dic59—21no—
97C4⋊Dic59—21no—
98C4⋊Dic59D411yescharacteristic
99C4⋊Dic59D411yescharacteristic
100C4⋊Dic59C2311yescharacteristic
101Dic59⋊C4—21no—
102Dic59⋊C4—21no—
103Dic59⋊C4—21no—
104Dic59⋊C4—21no—
105Dic59⋊C4—21no—
106C4×Dic59—21no—
107C4×Dic59—21no—
108C4×Dic59C2311yescharacteristic
109C4×Dic59C2311yescharacteristic
110C2×C59⋊C8C2311yescharacteristic
111C2×C59⋊C8C2311yescharacteristic
112#11745660—41no—
113#11745660—41no—
114C23×C59—21no—
115C23×C59C2×D411yescharacteristic
116C22×D59—21no—
117C22×D59—21no—
118C22×D59—42no—
119C22×D59—81no—
120C22×D59—81no—
121Q8×C59—21no—
122Q8×C59—21no—
123Q8×C59—21no—
124Q8×C59—21no—
125D4×C59—21no—
126D4×C59—21no—
127D4×C59—42no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C2×C4×C59—21no—
132C2×C4×C59—21no—
133C2×C4×C59—42no—
134C2×C4×C59C2×D411yescharacteristic
135C2×C4×C59C2411yescharacteristic
136C22⋊D59—81no—
137C22⋊D59—81no—
138C22⋊D59—81no—
139C22⋊D59—81no—
140C2×Dic59—21no—
141C2×Dic59—21no—
142C2×Dic59C2×D411yescharacteristic
143C2×Dic59C2×D411yescharacteristic
144C2×Dic59C2×D411yescharacteristic
145C2×Dic59C2×D411yescharacteristic
146D236—21no—
147D236—21no—
148D236—21no—
149D236—21no—
150D236—42no—
151Dic118—21no—
152Dic118—21no—
153C8×C59—21no—
154C8×C59—21no—
155C59⋊C8—21no—
156C59⋊C8—21no—
157C22×C59—21no—
158C22×C59—21no—
159C22×C59—21no—
160C22×C59—41no—
161C22×C59—41no—
162C22×C59—41no—
163C22×C59C22×D411yescharacteristic
164C2×D59—41no—
165C2×D59—41no—
166C2×D59—41no—
167C2×D59—41no—
168C2×D59—41no—
169C2×D59—41no—
170C2×D59—84no—
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—21no—
180Dic59—21no—
181Dic59—41no—
182Dic59—41no—
183#3222—591nomaximal, Sylow
184C2×C59—41no—
185C2×C59—81no—
186C2×C59#53511yescharacteristic
187C2×C59#57711yescharacteristic
188C2×C59#57711yescharacteristic
189D59—81no—
190D59—81no—
191#541—591no—
192#535—591no—
193#497—591no—
194#492—591no—
195#490—591no—
196#488—591no—
197#464—591no—
198#464—591no—
199#460—591no—
200#460—591no—
201#452—591no—
202#452D5911yescharacteristic, complemented
203#450—591no—
204#450—591no—
205#433—591no—
206C59#322211yescharacteristic, complemented, Sylow
207C2×#41C2×D5911yescharacteristic
208C22×D4—591no—
209C2×Q16—591no—
210C2×Q16C2×D5911yescharacteristic, complemented
211C2×SD16—591no—
212C2×SD16—591no—
213C2×SD16—591no—
214C2×SD16—591no—
215C2×SD16—591no—
216C2×SD16C2×D5911yescharacteristic, complemented
217C4⋊Q8—591no—
218#127—591no—
219#127—591no—
220#126—1181no—
221#126—1181no—
222#125—591no—
223#125—1181no—
224#125—1181no—
225#124—591no—
226#124—591no—
227C22⋊Q8—591no—
228C22⋊Q8C2×D5911yescharacteristic
229#121—1181no—
230#121—1181no—
231#120—1181no—
232#120—1181no—
233C4×Q8—591no—
234C4×Q8—591no—
235#117—591no—
236C4⋊C8—591no—
237C4⋊C8—591no—
238#103—591no—
239#103C2×D5911yescharacteristic, complemented
240#102—591no—
241#102—591no—
242#102—591no—
243#102—591no—
244#102—591no—
245#102C2×D5911yescharacteristic, complemented
246C22⋊C8—591no—
247C22⋊C8C2×D5911yescharacteristic
248#97—591no—
249C4×C8—591no—
250C24—1181no—
251#41—41no—
252#41—41no—
253C2×Q8—591no—
254C2×Q8C22×D5911yescharacteristic
255C2×Q8C22×D5911yescharacteristic
256C2×D4—21no—
257C2×D4—591no—
258C2×D4—591no—
259C2×D4—1181no—
260C2×D4—1181no—
261C2×D4—1181no—
262C2×D4—1181no—
263C2×D4—1181no—
264C2×D4—2361no—
265C2×D4—2361no—
266C2×D4C22×D5911yescharacteristic
267C22×C4—21no—
268C22×C4C22×D5911yescharacteristic
269Q16—41no—
270Q16—2361no—
271SD16—41no—
272SD16—2361no—
273SD16—2361no—
274SD16—2361no—
275SD16—2361no—
276SD16—2361no—
277C2×C8—591no—
278C2×C8—591no—
279C2×C8C22×D5911yescharacteristic
280C2×C8C22×D5911yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—591no—
283C4⋊C4—591no—
284C4⋊C4—591no—
285C4⋊C4—1181no—
286C4⋊C4—1181no—
287C4⋊C4—1181no—
288C4⋊C4—1181no—
289C4⋊C4—1181no—
290C4⋊C4—1181no—
291C4⋊C4—1181no—
292C4⋊C4C22×D5911yescharacteristic
293C22⋊C4—21no—
294C22⋊C4—591no—
295C22⋊C4—591no—
296C22⋊C4—1181no—
297C22⋊C4—1181no—
298C22⋊C4—1181no—
299C22⋊C4—1181no—
300C22⋊C4—1181no—
301C42—591no—
302C42—591no—
303C42—1181no—
304C42—1181no—
305C23—21no—
306C23—1181no—
307C23—1181no—
308C23—4721no—
309C23—4721no—
310C23—2362no—
311C23D4×D5911yescharacteristic
312Q8—21no—
313Q8—21no—
314Q8—21no—
315Q8—21no—
316Q8—1181no—
317Q8—1181no—
318D4—21no—
319D4—21no—
320D4—42no—
321D4—1181no—
322D4—1181no—
323D4—1181no—
324D4—1181no—
325D4—4721no—
326D4—4721no—
327D4—4721no—
328D4—4721no—
329D4—2362no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—42no—
336C2×C4—591no—
337C2×C4—591no—
338C2×C4—591no—
339C2×C4—591no—
340C2×C4—1181no—
341C2×C4—1181no—
342C2×C4D4×D5911yescharacteristic
343C2×C4C23×D5911yescharacteristic
344C8—21no—
345C8—21no—
346C8—1181no—
347C8—1181no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—4724no—
355C22—2361no—
356C22—2361no—
357C22—2361no—
358C22—2361no—
359C22—2361no—
360C22—2361no—
361C22C2×D4×D5911yescharacteristic
362C4—21no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—1181no—
367C4—1181no—
368C4—1181no—
369C4—1181no—
370C4—2361no—
371C4—2361no—
372C4#1427377211yescharacteristic
373C4#1427377211yescharacteristic
374C2—41no—
375C2—81no—
376C2—4721no—
377C2—4721no—
378C2#1683796711yescharacteristic
379C2#1683820911yescharacteristic
380C2#1683821111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#452C2
socleC22×C59C22×D4
hypercenter#452D59
hypocenterC59#3222
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
1. #16838012C2semidirect
3. #16837795C2semidirect
4. #16837773C2semidirect
5. #16837765C2semidirect
6. #16837758C2semidirect
7. #16837627C2semidirect
8. #16837626C2semidirect
9. #16837601C2semidirect
10. #16837600C2semidirect
11. #16837564C2semidirect
12. #16837555C2semidirect
13. #16837552C2semidirect
14. #16837460C2semidirect
15. C59×#452C2semidirect
17. C2×#11745672C22semidirect
20. C2×#11745670C22semidirect
23. #14273725C22semidirect
29. #14273718C22semidirect
38. Q8×Dic59C22semidirect
39. #14273692C22semidirect
41. Dic59⋊C8C22semidirect
42. Dic59⋊C8C22semidirect
43. #14273651C22semidirect
46. #14273648C22semidirect
50. #14273637C22semidirect
51. C8×Dic59C22semidirect
53. C2×Q16×C59C22semidirect
54. C2×SD16×C59C22semidirect
56. #103×C59C22semidirect
57. #102×C59C22semidirect
202. #452D59semidirect
206. C59#3222semidirect
210. C2×Q16C2×D59semidirect
216. C2×SD16C2×D59semidirect
239. #103C2×D59semidirect
245. #102C2×D59semidirect