Finite Group Databasebeta

← #21435953

Subgroups — #21435953

Order 7552.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838102C211yesmaximal, characteristic, complemented
2#16838045C211yesmaximal, characteristic, complemented
3#16837756C211yesmaximal, characteristic, complemented
4#16837736C211yesmaximal, characteristic, complemented
5#16837725C211yesmaximal, characteristic, complemented
6#16837703C211yesmaximal, characteristic, complemented
7#16837635C211yesmaximal, characteristic, complemented
8#16837628C211yesmaximal, characteristic, complemented
9#16837546C211yesmaximal, characteristic, complemented
10#16837534C211yesmaximal, characteristic, complemented
11C4×#11745669C211yesmaximal, characteristic, complemented
12#16837467C211yesmaximal, characteristic, complemented
13#16837397C211yesmaximal, characteristic, complemented
14#102×D59C211yesmaximal, characteristic, complemented
15C59×#463C211yesmaximal, characteristic, complemented
16C2×#11745689C2211yescharacteristic
17C2×D4×D59C2211yescharacteristic
18C2×#11745669C2211yescharacteristic
19C2×C8×D59C2211yescharacteristic
20C2×C8×D59C2211yescharacteristic, complemented
21#14273720—21no—
22#14273719C2211yescharacteristic, complemented
23#14273710—21no—
24#14273709—21no—
25#14273703C2211yescharacteristic
26#14273700—21no—
27#14273700—21no—
28#14273698C2211yescharacteristic
29#14273698C2211yescharacteristic
30#14273698C2211yescharacteristic, complemented
31#14273697—21no—
32C4×D236C2211yescharacteristic
33C4×D236C2211yescharacteristic
34C4×C22⋊D59—21no—
35#14273685C2211yescharacteristic, complemented
36C4⋊C4×D59C2211yescharacteristic
37C22⋊C4×D59—21no—
38#14273661C2211yescharacteristic, complemented
39#14273660C2211yescharacteristic, complemented
40#14273659C2211yescharacteristic, complemented
41#14273651C2211yescharacteristic, complemented
42#14273651C2211yescharacteristic, complemented
43#14273649C2211yescharacteristic
44#14273649C2211yescharacteristic
45#14273648C2211yescharacteristic
46#14273648C2211yescharacteristic
47#14273648C2211yescharacteristic, complemented
48#14273647C2211yescharacteristic
49(C2×D59)⋊C8C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic, complemented
51C4×C59⋊C8C2211yescharacteristic, complemented
52C2×SD16×C59C2211yescharacteristic, complemented
53C2×D8×C59C2211yescharacteristic
54#124×C59C2211yescharacteristic
55C4×D4×C59C2211yescharacteristic, complemented
56C4⋊C8×C59C2211yescharacteristic, complemented
57#103×C59C2211yescharacteristic, complemented
58#102×C59C2211yescharacteristic
59C23×D59—21no—
60C2×Q8×C59C2311yescharacteristic
61C2×D4×C59C2311yescharacteristic
62C2×D4×C59C2311yescharacteristic
63C22×C4×C59—21no—
64C2×C22⋊D59—21no—
65C2×C22⋊D59—21no—
66C2×C22⋊D59—21no—
67C2×C22⋊D59—21no—
68#11745689—22no—
69#11745689—41no—
70D4×D59—22no—
71D4×D59—41no—
72C2×D236—21no—
73C2×D236D411yescharacteristic
74C2×D236C2311yescharacteristic
75C2×C4×D59—21no—
76C2×C4×D59—21no—
77C2×C4×D59—21no—
78C2×C4×D59C2311yescharacteristic
79C2×C4×D59C2311yescharacteristic
80SD16×C59—41no—
81D8×C59—41no—
82C2×C8×C59C2311yescharacteristic
83C2×C8×C59C2311yescharacteristic
84C4⋊C4×C59C2311yescharacteristic
85C22⋊C4×C59—21no—
86C22⋊C4×C59—21no—
87C22⋊C4×C59—21no—
88C42×C59C2311yescharacteristic
89C22⋊Dic59—21no—
90C22⋊Dic59—21no—
91C22⋊Dic59—21no—
92#11745669—22no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4—21no—
95(C2×D59)⋊C4—21no—
96(C2×D59)⋊C4D411yescharacteristic
97(C2×D59)⋊C4D411yescharacteristic
98C4⋊Dic59D411yescharacteristic
99C4⋊Dic59C2311yescharacteristic
100C4⋊Dic59C2311yescharacteristic
101C4⋊Dic59C2311yescharacteristic
102Dic59⋊C4—21no—
103Dic59⋊C4—21no—
104Dic59⋊C4—21no—
105Dic59⋊C4—21no—
106C4×Dic59—21no—
107C2×C59⋊C8C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109C8×D59—41no—
110C8×D59—41no—
111C23×C59—21no—
112C23×C59—21no—
113C22×D59—21no—
114C22×D59—42no—
115C22×D59—42no—
116C22×D59—81no—
117C22×D59C2×D411yescharacteristic
118C22×D59C2×D411yescharacteristic
119Q8×C59—21no—
120Q8×C59—21no—
121D4×C59—21no—
122D4×C59—21no—
123D4×C59—21no—
124D4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—81no—
128C2×C4×C59C2×D411yescharacteristic
129C2×C4×C59C2×D411yescharacteristic
130C2×C4×C59C2411yescharacteristic
131C22⋊D59—42no—
132C22⋊D59—42no—
133C22⋊D59—81no—
134C22⋊D59—81no—
135C2×Dic59—21no—
136C2×Dic59—21no—
137C2×Dic59—21no—
138C2×Dic59C2×D411yescharacteristic
139C2×Dic59C2×D411yescharacteristic
140D236—22no—
141D236—21no—
142D236—42no—
143D236#4112yes—
144C4×D59—21no—
145C4×D59—21no—
146C4×D59—21no—
147C4×D59—21no—
148C4×D59—42no—
149C4×D59—81no—
150C4×D59—81no—
151C8×C59—21no—
152C8×C59—21no—
153C59⋊C8—21no—
154C59⋊C8—21no—
155C22×C59—41no—
156C22×C59—41no—
157C22×C59—41no—
158C22×C59—41no—
159C22×C59—41no—
160C22×C59—41no—
161C22×C59C22×D411yescharacteristic
162C2×D59—21no—
163C2×D59—21no—
164C2×D59—21no—
165C2×D59—22no—
166C2×D59—21no—
167C2×D59—21no—
168C2×D59—41no—
169C2×D59—41no—
170C2×D59—84no—
171C2×D59#13512yes—
172C4×C59—21no—
173C4×C59—21no—
174C4×C59—41no—
175C4×C59—41no—
176C4×C59C2×#4111yescharacteristic
177C4×C59H(5,𝔽2)11yescharacteristic
178Dic59—21no—
179Dic59—21no—
180Dic59—41no—
181Dic59—41no—
182Dic59—41no—
183#3297—591nomaximal, Sylow
184C2×C59—81no—
185C2×C59—81no—
186C2×C59#54611yescharacteristic
187C2×C59C2×#13511yescharacteristic
188C2×C59#57611yescharacteristic
189D59—22no—
190D59—41no—
191D59—42no—
192#553—591no—
193#546—591no—
194#488—591no—
195#484—591no—
196#482—591no—
197#478—591no—
198#466—591no—
199#465—591no—
200#463D5911yescharacteristic, complemented
201#449—591no—
202#447—591no—
203C4×D8—591no—
204C8×D4—591no—
205#416—591no—
206C2×#102—591no—
207C59#329711yescharacteristic, complemented, Sylow
208C2×#41—591no—
209C22×D4—591no—
210C2×SD16C2×D5911yescharacteristic, complemented
211C2×D8—591no—
212C2×D8C2×D5911yescharacteristic
213C22×C8—591no—
214C22×C8—591no—
215#126—1181no—
216#125—591no—
217#124C2×D5911yescharacteristic
218#123—1181no—
219#123—1181no—
220C22⋊Q8—591no—
221#121—591no—
222#121—591no—
223#121—591no—
224#121—1181no—
225#121—1181no—
226#120—1181no—
227C4×D4—591no—
228C4×D4—591no—
229C4×D4—1181no—
230C4×D4C2×D5911yescharacteristic, complemented
231#117—591no—
232C2×C4⋊C4—591no—
233C2×C22⋊C4—1181no—
234#107—591no—
235#107—591no—
236#106—591no—
237C4⋊C8C2×D5911yescharacteristic, complemented
238#103—591no—
239#103—591no—
240#103C2×D5911yescharacteristic, complemented
241#102—591no—
242#102—591no—
243#102—591no—
244#102—591no—
245#102—591no—
246#102—591no—
247#102C2×D5911yescharacteristic
248C22⋊C8—591no—
249C22⋊C8—591no—
250C4×C8—591no—
251C24—1181no—
252#41—1182no—
253#41—2361no—
254C2×Q8C22×D5911yescharacteristic
255C2×D4—591no—
256C2×D4—591no—
257C2×D4—1181no—
258C2×D4—1181no—
259C2×D4—1182no—
260C2×D4—1181no—
261C2×D4—1181no—
262C2×D4—1181no—
263C2×D4—2361no—
264C2×D4C22×D5911yescharacteristic
265C2×D4C22×D5911yescharacteristic
266C22×C4—21no—
267C22×C4—591no—
268C22×C4—591no—
269C22×C4—1181no—
270C22×C4—1181no—
271C22×C4—1181no—
272SD16—41no—
273D8—41no—
274D8—1182no—
275C2×C8—591no—
276C2×C8—591no—
277C2×C8—2361no—
278C2×C8—2361no—
279C2×C8C22×D5911yescharacteristic
280C2×C8C22×D5911yescharacteristic
281C4⋊C4—591no—
282C4⋊C4—591no—
283C4⋊C4—591no—
284C4⋊C4—591no—
285C4⋊C4—1181no—
286C4⋊C4—1181no—
287C4⋊C4—1181no—
288C4⋊C4—1181no—
289C4⋊C4C22×D5911yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—591no—
294C22⋊C4—591no—
295C22⋊C4—1181no—
296C22⋊C4—1181no—
297C22⋊C4—1181no—
298C22⋊C4—1181no—
299C22⋊C4—1181no—
300C22⋊C4—1181no—
301C42—1181no—
302C42C22×D5911yescharacteristic
303C23—21no—
304C23—21no—
305C23—591no—
306C23—591no—
307C23—1181no—
308C23—4721no—
309C23—2362no—
310C23—2362no—
311Q8—21no—
312Q8—21no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—592no—
318D4—1182no—
319D4—1181no—
320D4—4721no—
321D4—4721no—
322D4—2362no—
323D4—2362no—
324D4—2362no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—81no—
328C2×C4—591no—
329C2×C4—591no—
330C2×C4—1181no—
331C2×C4—1181no—
332C2×C4—1181no—
333C2×C4—1181no—
334C2×C4—1181no—
335C2×C4—1181no—
336C2×C4—1181no—
337C2×C4—4721no—
338C2×C4—4721no—
339C2×C4—2362no—
340C2×C4D4×D5911yescharacteristic
341C2×C4D4×D5911yescharacteristic
342C2×C4C23×D5911yescharacteristic
343C8—21no—
344C8—21no—
345C8—1181no—
346C8—1181no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—592no—
354C22—1181no—
355C22—1181no—
356C22—1181no—
357C22—1181no—
358C22—1181no—
359C22—1182no—
360C22—4724no—
361C22—2361no—
362C22—2361no—
363C22C2×D4×D5911yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—1181no—
369C4—1181no—
370C4—2361no—
371C4—2361no—
372C4—2361no—
373C4#41×D5911yescharacteristic
374C4#1427377211yescharacteristic
375C2—81no—
376C2—81no—
377C2—1182no—
378C2—2361no—
379C2—2362no—
380C2#1683804911yescharacteristic
381C2#135×D5911yescharacteristic
382C2#1683820611yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#463C2
socleC22×C59C22×D4
hypercenter#463D59
hypocenterC59#3297
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #16838102C2semidirect
2. #16838045C2semidirect
3. #16837756C2semidirect
4. #16837736C2semidirect
5. #16837725C2semidirect
6. #16837703C2semidirect
7. #16837635C2semidirect
8. #16837628C2semidirect
9. #16837546C2semidirect
10. #16837534C2semidirect
11. C4×#11745669C2semidirect
12. #16837467C2semidirect
13. #16837397C2semidirect
14. #102×D59C2semidirect
15. C59×#463C2semidirect
20. C2×C8×D59C22semidirect
22. #14273719C22semidirect
30. #14273698C22semidirect
35. #14273685C22semidirect
38. #14273661C22semidirect
39. #14273660C22semidirect
40. #14273659C22semidirect
41. #14273651C22semidirect
42. #14273651C22semidirect
47. #14273648C22semidirect
50. (C2×D59)⋊C8C22semidirect
51. C4×C59⋊C8C22semidirect
52. C2×SD16×C59C22semidirect
55. C4×D4×C59C22semidirect
56. C4⋊C8×C59C22semidirect
57. #103×C59C22semidirect
200. #463D59semidirect
207. C59#3297semidirect
210. C2×SD16C2×D59semidirect
230. C4×D4C2×D59semidirect
237. C4⋊C8C2×D59semidirect
240. #103C2×D59semidirect