Finite Group Databasebeta

← #21436039

Subgroups — #21436039

Order 7552.

408 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#16838116C211yesmaximal, characteristic, complemented
2#16838071C211yesmaximal, characteristic, complemented
3#16837747C211yesmaximal, characteristic, complemented
4#16837727C211yesmaximal, characteristic, complemented
5#16837725C211yesmaximal, characteristic, complemented
6#16837695C211yesmaximal, characteristic, complemented
7#16837636C211yesmaximal, characteristic, complemented
8#16837635C211yesmaximal, characteristic, complemented
9#16837595C211yesmaximal, characteristic, complemented
10#16837546C211yesmaximal, characteristic, complemented
11SD16×Dic59C211yesmaximal, characteristic, complemented
12(C22⋊D59)⋊C8C211yesmaximal, characteristic, complemented
13#16837398C211yesmaximal, characteristic, complemented
14#16837397C211yesmaximal, characteristic, complemented
15C59×#449C211yesmaximal, characteristic, complemented
16C2×#11745689C2211yescharacteristic
17C2×#11745669C2211yescharacteristic
18C22×C59⋊C8C2211yescharacteristic
19C2×C8×D59C2211yescharacteristic
20#14273726C2211yescharacteristic
21#14273723—21no—
22#14273723C2211yescharacteristic
23#14273714—21no—
24#14273713—21no—
25#14273701—21no—
26#14273701C2211yescharacteristic
27#14273699—21no—
28#14273698—21no—
29#14273698C2211yescharacteristic
30#14273698C2211yescharacteristic
31Q8×Dic59C2211yescharacteristic
32D4×Dic59C2211yescharacteristic
33C4×C22⋊D59—21no—
34C4×C22⋊D59C2211yescharacteristic
35#14273686C2211yescharacteristic
36#14273685C2211yescharacteristic
37#14273683—21no—
38#14273661C2211yescharacteristic
39#14273660C2211yescharacteristic
40#14273659C2211yescharacteristic
41Dic59⋊C8C2211yescharacteristic
42#14273651C2211yescharacteristic
43#14273651C2211yescharacteristic
44#14273649C2211yescharacteristic
45#14273649C2211yescharacteristic
46#14273648C2211yescharacteristic
47#14273648C2211yescharacteristic
48#14273648C2211yescharacteristic
49#14273647C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51C8×Dic59C2211yescharacteristic
52C2×#41×C59C2211yescharacteristic
53C2×SD16×C59C2211yescharacteristic
54C2×D8×C59C2211yescharacteristic
55#121×C59C2211yescharacteristic
56#103×C59C2211yescharacteristic
57#102×C59C2211yescharacteristic
58C22⋊C8×C59C2211yescharacteristic
59#41×C59—22no—
60#41×C59—41no—
61C2×Q8×C59C2311yescharacteristic
62C2×D4×C59—21no—
63C2×D4×C59—21no—
64C2×D4×C59C2311yescharacteristic
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×C22⋊D59—21no—
73C2×C22⋊D59D411yescharacteristic
74C22×Dic59—21no—
75#11745689—22no—
76#11745689—41no—
77C2×D236—21no—
78C2×D236C2311yescharacteristic
79C2×C4×D59—21no—
80C2×C4×D59C2311yescharacteristic
81C2×Dic118—21no—
82SD16×C59—22no—
83D8×C59—41no—
84C2×C8×C59C2311yescharacteristic
85C2×C8×C59C2311yescharacteristic
86C4⋊C4×C59C2311yescharacteristic
87C22⋊C4×C59—21no—
88C22⋊Dic59—21no—
89C22⋊Dic59—21no—
90C22⋊Dic59—21no—
91C22⋊Dic59—21no—
92C22⋊Dic59D411yescharacteristic
93#11745669—41no—
94(C2×D59)⋊C4—21no—
95(C2×D59)⋊C4—21no—
96(C2×D59)⋊C4D411yescharacteristic
97C4⋊Dic59—21no—
98C4⋊Dic59C2311yescharacteristic
99C4⋊Dic59C2311yescharacteristic
100C4⋊Dic59C2311yescharacteristic
101Dic59⋊C4—21no—
102Dic59⋊C4D411yescharacteristic
103C4×Dic59—21no—
104C4×Dic59—21no—
105C4×Dic59—21no—
106C4×Dic59C2311yescharacteristic
107C2×C59⋊C8—41no—
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110C8×D59—41no—
111C23×C59—21no—
112C23×C59—21no—
113C23×C59C2×D411yescharacteristic
114C22×D59—21no—
115C22×D59C2×D411yescharacteristic
116Q8×C59—21no—
117Q8×C59#4112yes—
118D4×C59—21no—
119D4×C59—21no—
120D4×C59—21no—
121D4×C59—21no—
122D4×C59—42no—
123D4×C59—81no—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—42no—
129C2×C4×C59C2×D411yescharacteristic
130C2×C4×C59C2411yescharacteristic
131C22⋊D59—22no—
132C22⋊D59—42no—
133C22⋊D59—81no—
134C22⋊D59—81no—
135C22⋊D59—81no—
136C22⋊D59—81no—
137C2×Dic59—21no—
138C2×Dic59—21no—
139C2×Dic59—21no—
140C2×Dic59—42no—
141C2×Dic59C2×D411yescharacteristic
142C2×Dic59C2×D411yescharacteristic
143C2×Dic59C2×D411yescharacteristic
144D236—21no—
145D236—21no—
146D236—42no—
147C4×D59—21no—
148C4×D59—21no—
149C4×D59—42no—
150Dic118—81no—
151C8×C59—21no—
152C8×C59—21no—
153C59⋊C8—21no—
154C59⋊C8—21no—
155C22×C59—21no—
156C22×C59—21no—
157C22×C59—21no—
158C22×C59—41no—
159C22×C59—41no—
160C22×C59—41no—
161C22×C59—41no—
162C22×C59—41no—
163C22×C59—41no—
164C22×C59C22×D411yescharacteristic
165C2×D59—21no—
166C2×D59—21no—
167C2×D59—21no—
168C2×D59—41no—
169C2×D59—41no—
170C2×D59—41no—
171C4×C59—22no—
172C4×C59—21no—
173C4×C59—41no—
174C4×C59C2×#4111yescharacteristic
175C4×C59H(5,𝔽2)11yescharacteristic
176Dic59—21no—
177Dic59—21no—
178Dic59—41no—
179Dic59—41no—
180Dic59—41no—
181Dic59#13512yes—
182#3305—591nomaximal, Sylow
183C2×C59—41no—
184C2×C59—81no—
185C2×C59—81no—
186C2×C59#54611yescharacteristic
187C2×C59C2×#13511yescharacteristic
188C2×C59#57611yescharacteristic
189D59—41no—
190D59—81no—
191#555—591no—
192#550—591no—
193#486—591no—
194#482—591no—
195#482—591no—
196#477—591no—
197#466—591no—
198#466—591no—
199#459—591no—
200#449—591no—
201#449D5911yescharacteristic, complemented
202C4×SD16—591no—
203C8×D4—591no—
204#416—591no—
205#416—591no—
206C59#330511yescharacteristic, complemented, Sylow
207C2×#41—591no—
208C2×#41C2×D5911yescharacteristic
209C2×SD16C2×D5911yescharacteristic
210C2×D8—591no—
211C2×D8C2×D5911yescharacteristic
212C22×C8—591no—
213C22×C8—591no—
214C4⋊Q8—591no—
215#127—591no—
216#127—1181no—
217#124—1181no—
218#124—1181no—
219#121—591no—
220#121—591no—
221#121—591no—
222#121—1181no—
223#121—1181no—
224#121—1181no—
225#121C2×D5911yescharacteristic
226C4×Q8—591no—
227C4×D4—591no—
228C4×D4—591no—
229C4×D4—1181no—
230#117—591no—
231#117—591no—
232#117—1181no—
233#107—591no—
234#107—591no—
235#106—591no—
236C4⋊C8—591no—
237#103—591no—
238#103—591no—
239#103C2×D5911yescharacteristic
240#102—591no—
241#102—591no—
242#102—591no—
243#102—591no—
244#102—591no—
245#102—591no—
246#102C2×D5911yescharacteristic
247C22⋊C8—591no—
248C22⋊C8C2×D5911yescharacteristic
249C4×C8—591no—
250#41—22no—
251#41—41no—
252#41—1182no—
253#41—2361no—
254C2×Q8—1181no—
255C2×Q8C22×D5911yescharacteristic
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—591no—
259C2×D4—591no—
260C2×D4—1181no—
261C2×D4—1181no—
262C2×D4—1181no—
263C2×D4—1181no—
264C2×D4—1181no—
265C2×D4—1181no—
266C2×D4C22×D5911yescharacteristic
267C2×D4C22×D5911yescharacteristic
268C22×C4—21no—
269C22×C4—591no—
270C22×C4—1181no—
271C22×C4—1181no—
272C22×C4C22×D5911yescharacteristic
273SD16—22no—
274D8—41no—
275D8—2361no—
276C2×C8—591no—
277C2×C8—591no—
278C2×C8—2361no—
279C2×C8—2361no—
280C2×C8C22×D5911yescharacteristic
281C2×C8C22×D5911yescharacteristic
282C4⋊C4—591no—
283C4⋊C4—591no—
284C4⋊C4—591no—
285C4⋊C4—591no—
286C4⋊C4—1181no—
287C4⋊C4—1181no—
288C4⋊C4C22×D5911yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—591no—
291C22⋊C4—591no—
292C22⋊C4—1181no—
293C22⋊C4—1181no—
294C22⋊C4—1181no—
295C22⋊C4—1181no—
296C22⋊C4—1181no—
297C22⋊C4—1181no—
298C42—591no—
299C42—1181no—
300C42—1181no—
301C42—1181no—
302C23—21no—
303C23—21no—
304C23—591no—
305C23—1181no—
306C23D4×D5911yescharacteristic
307Q8—21no—
308Q8—4721no—
309Q8#1174568712yes—
310D4—21no—
311D4—21no—
312D4—21no—
313D4—21no—
314D4—42no—
315D4—81no—
316D4—1182no—
317D4—1181no—
318D4—1181no—
319D4—4721no—
320D4—4721no—
321D4—4721no—
322D4—4721no—
323D4—2362no—
324D4—2362no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—42no—
330C2×C4—591no—
331C2×C4—591no—
332C2×C4—591no—
333C2×C4—1181no—
334C2×C4—1181no—
335C2×C4—1181no—
336C2×C4—1181no—
337C2×C4—1181no—
338C2×C4—2362no—
339C2×C4—2362no—
340C2×C4D4×D5911yescharacteristic
341C2×C4C23×D5911yescharacteristic
342C8—21no—
343C8—21no—
344C8—1181no—
345C8—1181no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—1181no—
356C22—1181no—
357C22—1181no—
358C22—2361no—
359C22—2361no—
360C22—2361no—
361C22C2×D4×D5911yescharacteristic
362C4—21no—
363C4—22no—
364C4—41no—
365C4—592no—
366C4—1181no—
367C4—1181no—
368C4—2361no—
369C4—2361no—
370C4—2361no—
371C4C2×#1174568711yescharacteristic
372C4#1427377211yescharacteristic
373C2—41no—
374C2—81no—
375C2—81no—
376C2—4721no—
377C2—2361no—
378C2#1683803911yescharacteristic
379C2#135×D5911yescharacteristic
380C2#1683820611yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#449C2
socleC22×C59C22×D4
hypercenter#449D59
hypocenterC59#3305
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #16838116C2semidirect
2. #16838071C2semidirect
3. #16837747C2semidirect
4. #16837727C2semidirect
5. #16837725C2semidirect
6. #16837695C2semidirect
7. #16837636C2semidirect
8. #16837635C2semidirect
9. #16837595C2semidirect
10. #16837546C2semidirect
11. SD16×Dic59C2semidirect
12. (C22⋊D59)⋊C8C2semidirect
13. #16837398C2semidirect
14. #16837397C2semidirect
15. C59×#449C2semidirect
201. #449D59semidirect
206. C59#3305semidirect