Finite Group Databasebeta

← #21436293

Subgroups — #21436293

Order 7552.

414 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#16838096C211yesmaximal, characteristic, complemented
2#16838046C211yesmaximal, characteristic, complemented
3#16837755C211yesmaximal, characteristic, complemented
4#16837743C211yesmaximal, characteristic, complemented
5#16837714C211yesmaximal, characteristic, complemented
6#16837700C211yesmaximal, characteristic, complemented
7#16837654C211yesmaximal, characteristic, complemented
8#16837648C211yesmaximal, characteristic, complemented
9#16837616C211yesmaximal, characteristic, complemented
10#16837548C211yesmaximal, characteristic, complemented
11#16837536C211yesmaximal, characteristic, complemented
12#16837482C211yesmaximal, characteristic, complemented
13#16837478C211yesmaximal, characteristic, complemented
14#16837400C211yesmaximal, characteristic, complemented
15C59×#418C211yesmaximal, characteristic, complemented
16C2×#11745687C2211yescharacteristic
17C2×#11745660C2211yescharacteristic, complemented
18C2×#11745669C2211yescharacteristic
19C2×#11745669C2211yescharacteristic
20C2×#11745659C2211yescharacteristic, complemented
21#14273721—21no—
22#14273718C2211yescharacteristic, complemented
23#14273714C2211yescharacteristic
24#14273709—21no—
25#14273708—21no—
26#14273706C2211yescharacteristic
27#14273702C2211yescharacteristic, complemented
28#14273701C2211yescharacteristic
29#14273700—21no—
30#14273699—21no—
31#14273698C2211yescharacteristic
32#14273696—21no—
33C4×D236—21no—
34D4×Dic59C2211yescharacteristic
35#14273689C2211yescharacteristic, complemented
36C4×C22⋊D59C2211yescharacteristic
37C4⋊C4×D59C2211yescharacteristic, complemented
38C2×C22⋊Dic59—21no—
39#14273661C2211yescharacteristic, complemented
40#14273660C2211yescharacteristic, complemented
41#14273658C2211yescharacteristic, complemented
42Dic59⋊C8C2211yescharacteristic, complemented
43#14273652C2211yescharacteristic, complemented
44#14273650C2211yescharacteristic, complemented
45#14273650C2211yescharacteristic, complemented
46#14273649C2211yescharacteristic, complemented
47#14273648C2211yescharacteristic
48#14273648C2211yescharacteristic
49C22⋊(C59⋊C8)C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic, complemented
51C8×Dic59C2211yescharacteristic, complemented
52C22×D4×C59C2211yescharacteristic
53C2×M16×C59C2211yescharacteristic
54#117×C59C2211yescharacteristic
55#102×C59C2211yescharacteristic
56#102×C59C2211yescharacteristic
57#102×C59C2211yescharacteristic
58#102×C59C2211yescharacteristic
59C24×C59—21no—
60C2×D4×C59—22no—
61C2×D4×C59—21no—
62C2×D4×C59—41no—
63C2×D4×C59C2311yescharacteristic
64C2×D4×C59C2311yescharacteristic
65C22×C4×C59C2311yescharacteristic
66C2×C22⋊D59—21no—
67C2×C22⋊D59—21no—
68C2×C22⋊D59—21no—
69C2×C22⋊D59D411yescharacteristic
70C22×Dic59—21no—
71C22×Dic59—21no—
72#11745687—22no—
73#11745687—41no—
74C2×D236—21no—
75C2×D236C2311yescharacteristic
76C2×C4×D59—21no—
77C2×C4×D59—21no—
78C2×C4×D59C2311yescharacteristic
79C2×Dic118C2311yescharacteristic
80M16×C59—41no—
81C2×C8×C59C2311yescharacteristic
82C2×C8×C59C2311yescharacteristic
83C4⋊C4×C59C2311yescharacteristic
84C4⋊C4×C59C2311yescharacteristic
85C22⋊C4×C59—21no—
86C42×C59—21no—
87C22⋊Dic59—21no—
88C22⋊Dic59—21no—
89C22⋊Dic59—21no—
90C22⋊Dic59—21no—
91C22⋊Dic59—21no—
92C22⋊Dic59D411yescharacteristic
93#11745669—22no—
94#11745669—41no—
95(C2×D59)⋊C4—21no—
96(C2×D59)⋊C4—21no—
97(C2×D59)⋊C4—21no—
98(C2×D59)⋊C4D411yescharacteristic
99C4⋊Dic59—21no—
100C4⋊Dic59C2311yescharacteristic
101C4⋊Dic59C2311yescharacteristic
102Dic59⋊C4—21no—
103Dic59⋊C4—21no—
104Dic59⋊C4—21no—
105Dic59⋊C4D411yescharacteristic
106C4×Dic59C2311yescharacteristic
107C2×C59⋊C8C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109#11745660—41no—
110#11745659—41no—
111C23×C59—21no—
112C23×C59—21no—
113C23×C59—42no—
114C23×C59—42no—
115C23×C59—81no—
116C23×C59C2×D411yescharacteristic
117C22×D59—21no—
118C22×D59C2×D411yescharacteristic
119D4×C59—21no—
120D4×C59—21no—
121D4×C59—21no—
122D4×C59—42no—
123D4×C59#4112yes—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59C2×D411yescharacteristic
129C2×C4×C59C2411yescharacteristic
130C22⋊D59—41no—
131C22⋊D59—42no—
132C22⋊D59—81no—
133C22⋊D59—81no—
134C2×Dic59—21no—
135C2×Dic59—21no—
136C2×Dic59—21no—
137C2×Dic59—42no—
138C2×Dic59—81no—
139C2×Dic59C2×D411yescharacteristic
140C2×Dic59C2×D411yescharacteristic
141C2×Dic59C2×D411yescharacteristic
142D236—21no—
143D236—21no—
144D236—42no—
145C4×D59—21no—
146C4×D59—21no—
147C4×D59—81no—
148C4×D59—81no—
149Dic118—21no—
150Dic118—21no—
151C8×C59—21no—
152C8×C59—21no—
153C59⋊C8—21no—
154C59⋊C8—21no—
155C22×C59—22no—
156C22×C59—21no—
157C22×C59—21no—
158C22×C59—21no—
159C22×C59—41no—
160C22×C59—41no—
161C22×C59—41no—
162C22×C59—41no—
163C22×C59—41no—
164C22×C59—84no—
165C22×C59C22×D411yescharacteristic
166C2×D59—21no—
167C2×D59—21no—
168C2×D59—21no—
169C2×D59—41no—
170C2×D59—41no—
171C2×D59—41no—
172C4×C59—21no—
173C4×C59—41no—
174C4×C59—41no—
175C4×C59C2×#4111yescharacteristic
176C4×C59H(5,𝔽2)11yescharacteristic
177Dic59—21no—
178Dic59—21no—
179Dic59—21no—
180Dic59—41no—
181Dic59—41no—
182Dic59—41no—
183#3322—591nomaximal, Sylow
184C2×C59—41no—
185C2×C59—42no—
186C2×C59—81no—
187C2×C59#54611yescharacteristic
188C2×C59#57511yescharacteristic
189C2×C59#57611yescharacteristic
190D59—41no—
191D59—81no—
192#553—591no—
193#546—591no—
194#488—591no—
195#485—591no—
196#480—591no—
197#478—591no—
198#469—591no—
199#468—591no—
200#463—591no—
201#449—591no—
202#447—591no—
203C4×D8—591no—
204#436—591no—
205#418D5911yescharacteristic, complemented
206#417—591no—
207C59#332211yescharacteristic, complemented, Sylow
208C2×#41—591no—
209C22×D4C2×D5911yescharacteristic
210C2×SD16—591no—
211C2×D8—591no—
212C2×D8—591no—
213C2×M16—591no—
214C2×M16C2×D5911yescharacteristic
215#126—1181no—
216#125—591no—
217#124—591no—
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—591no—
230C4×D4—1181no—
231#117C2×D5911yescharacteristic
232C2×C4⋊C4—591no—
233C2×C22⋊C4—1181no—
234#107—591no—
235#107—591no—
236#106—591no—
237C4⋊C8—591no—
238#103—591no—
239#103—591no—
240#103—591no—
241#102—591no—
242#102—591no—
243#102—591no—
244#102C2×D5911yescharacteristic
245#102C2×D5911yescharacteristic
246#102C2×D5911yescharacteristic
247#102C2×D5911yescharacteristic
248C22⋊C8—591no—
249C22⋊C8—591no—
250C4×C8—591no—
251C24—21no—
252#41—1182no—
253#41—2361no—
254C2×Q8—591no—
255C2×D4—22no—
256C2×D4—21no—
257C2×D4—41no—
258C2×D4—591no—
259C2×D4—591no—
260C2×D4—1181no—
261C2×D4—1181no—
262C2×D4—1181no—
263C2×D4—1181no—
264C2×D4C22×D5911yescharacteristic
265C2×D4C22×D5911yescharacteristic
266C22×C4—591no—
267C22×C4—1181no—
268C22×C4—1181no—
269C22×C4—1181no—
270C22×C4—1181no—
271C22×C4C22×D5911yescharacteristic
272SD16—2361no—
273D8—1182no—
274D8—2361no—
275M16—41no—
276M16—2361no—
277C2×C8—591no—
278C2×C8—591no—
279C2×C8C22×D5911yescharacteristic
280C2×C8C22×D5911yescharacteristic
281C4⋊C4—591no—
282C4⋊C4—591no—
283C4⋊C4—591no—
284C4⋊C4—1181no—
285C4⋊C4—1181no—
286C4⋊C4—1181no—
287C4⋊C4—1181no—
288C4⋊C4C22×D5911yescharacteristic
289C4⋊C4C22×D5911yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—591no—
292C22⋊C4—591no—
293C22⋊C4—1181no—
294C22⋊C4—1181no—
295C22⋊C4—1181no—
296C22⋊C4—1181no—
297C22⋊C4—1181no—
298C22⋊C4—1181no—
299C22⋊C4—1181no—
300C22⋊C4—1181no—
301C42—21no—
302C42—591no—
303C23—21no—
304C23—21no—
305C23—42no—
306C23—42no—
307C23—81no—
308C23—591no—
309C23—1181no—
310C23D4×D5911yescharacteristic
311Q8—1181no—
312Q8—1181no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—42no—
317D4—1181no—
318D4—1181no—
319D4—4721no—
320D4—4721no—
321D4—2362no—
322D4—2361no—
323D4—2362no—
324D4#1174568512yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—591no—
330C2×C4—591no—
331C2×C4—591no—
332C2×C4—1181no—
333C2×C4—1181no—
334C2×C4—1181no—
335C2×C4—1181no—
336C2×C4—1181no—
337C2×C4—4721no—
338C2×C4—4721no—
339C2×C4—4721no—
340C2×C4—2362no—
341C2×C4D4×D5911yescharacteristic
342C2×C4C23×D5911yescharacteristic
343C8—21no—
344C8—21no—
345C8—1181no—
346C8—1181no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—22no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—84no—
357C22—1181no—
358C22—1181no—
359C22—1181no—
360C22—2361no—
361C22—2361no—
362C22—2361no—
363C22C2×D4×D5911yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—1181no—
368C4—1181no—
369C4—1181no—
370C4—2361no—
371C4—2361no—
372C4—2361no—
373C4C2×#1174568511yescharacteristic
374C4#1427377211yescharacteristic
375C2—41no—
376C2—42no—
377C2—81no—
378C2—4721no—
379C2—2361no—
380C2#1683804211yescharacteristic
381C2#1683819811yescharacteristic
382C2#1683820611yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#418C2
socleC22×C59C22×D4
hypercenter#418D59
hypocenterC59#3322
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #16838096C2semidirect
2. #16838046C2semidirect
3. #16837755C2semidirect
4. #16837743C2semidirect
5. #16837714C2semidirect
6. #16837700C2semidirect
7. #16837654C2semidirect
8. #16837648C2semidirect
9. #16837616C2semidirect
10. #16837548C2semidirect
11. #16837536C2semidirect
12. #16837482C2semidirect
13. #16837478C2semidirect
14. #16837400C2semidirect
15. C59×#418C2semidirect
17. C2×#11745660C22semidirect
20. C2×#11745659C22semidirect
22. #14273718C22semidirect
27. #14273702C22semidirect
35. #14273689C22semidirect
37. C4⋊C4×D59C22semidirect
39. #14273661C22semidirect
40. #14273660C22semidirect
41. #14273658C22semidirect
42. Dic59⋊C8C22semidirect
43. #14273652C22semidirect
44. #14273650C22semidirect
45. #14273650C22semidirect
46. #14273649C22semidirect
50. (C2×D59)⋊C8C22semidirect
51. C8×Dic59C22semidirect
205. #418D59semidirect
207. C59#3322semidirect