Finite Group Databasebeta

← #21436416

Subgroups — #21436416

Order 7552.

430 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838071C211yesmaximal, characteristic, complemented
2#16838052C211yesmaximal, characteristic, complemented
3#16837747C211yesmaximal, characteristic, complemented
4#16837721C211yesmaximal, characteristic, complemented
5#16837719C211yesmaximal, characteristic, complemented
6#16837685C211yesmaximal, characteristic, complemented
7#16837653C211yesmaximal, characteristic, complemented
8#16837652C211yesmaximal, characteristic, complemented
9#16837595C211yesmaximal, characteristic, complemented
10#16837546C211yesmaximal, characteristic, complemented
11SD16×Dic59C211yesmaximal, characteristic, complemented
12#16837477C211yesmaximal, characteristic, complemented
13#16837403C211yesmaximal, characteristic, complemented
14#16837402C211yesmaximal, characteristic, complemented
15C59×#449C211yesmaximal, characteristic, complemented
16C2×#11745689C2211yescharacteristic
17C2×#11745687—21no—
18C2×#11745669C2211yescharacteristic
19C2×#11745664C2211yescharacteristic
20C2×#11745659C2211yescharacteristic
21#14273726C2211yescharacteristic
22#14273723—21no—
23#14273723C2211yescharacteristic
24#14273709—21no—
25#14273708—21no—
26#14273704—21no—
27#14273701—21no—
28#14273701C2211yescharacteristic
29#14273698—21no—
30#14273698C2211yescharacteristic
31#14273698C2211yescharacteristic
32Q8×Dic59C2211yescharacteristic
33D4×Dic59C2211yescharacteristic
34C4×C22⋊D59—21no—
35C4×C22⋊D59C2211yescharacteristic
36C2×C4⋊Dic59C2211yescharacteristic
37C4⋊C4×D59C2211yescharacteristic
38#14273659C2211yescharacteristic
39#14273659C2211yescharacteristic
40#14273658C2211yescharacteristic
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—
75C22×Dic59—21no—
76#11745689—22no—
77#11745689—41no—
78#11745687—44no—
79C2×D236—21no—
80C2×D236C2311yescharacteristic
81C2×C4×D59—21no—
82C2×C4×D59—21no—
83C2×C4×D59C2311yescharacteristic
84C2×Dic118—21no—
85SD16×C59—22no—
86D8×C59—41no—
87C2×C8×C59C2311yescharacteristic
88C2×C8×C59C2311yescharacteristic
89C4⋊C4×C59C2311yescharacteristic
90C22⋊C4×C59—21no—
91C22⋊Dic59—21no—
92C22⋊Dic59—21no—
93C22⋊Dic59—21no—
94C22⋊Dic59D411yescharacteristic
95#11745669—41no—
96(C2×D59)⋊C4—21no—
97(C2×D59)⋊C4D411yescharacteristic
98C4⋊Dic59—21no—
99C4⋊Dic59—21no—
100C4⋊Dic59C2311yescharacteristic
101C4⋊Dic59C2311yescharacteristic
102C4⋊Dic59C2311yescharacteristic
103Dic59⋊C4—21no—
104Dic59⋊C4—21no—
105Dic59⋊C4D411yescharacteristic
106C4×Dic59—21no—
107C4×Dic59C2311yescharacteristic
108#11745664—41no—
109C2×C59⋊C8C2311yescharacteristic
110C2×C59⋊C8C2311yescharacteristic
111#11745659—41no—
112C23×C59—21no—
113C23×C59—21no—
114C23×C59C2×D411yescharacteristic
115C22×D59—21no—
116C22×D59C2×D411yescharacteristic
117Q8×C59—21no—
118Q8×C59#4112yescomplemented
119D4×C59—21no—
120D4×C59—21no—
121D4×C59—21no—
122D4×C59—21no—
123D4×C59—42no—
124D4×C59—42no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—42no—
130C2×C4×C59C2×D411yescharacteristic
131C2×C4×C59C2411yescharacteristic
132C22⋊D59—22no—
133C22⋊D59—42no—
134C22⋊D59—42no—
135C22⋊D59—81no—
136C22⋊D59—81no—
137C22⋊D59—81no—
138C2×Dic59—21no—
139C2×Dic59—21no—
140C2×Dic59—21no—
141C2×Dic59—42no—
142C2×Dic59—42no—
143C2×Dic59C2×D411yescharacteristic
144C2×Dic59C2×D411yescharacteristic
145C2×Dic59C2×D411yescharacteristic
146D236—21no—
147D236—21no—
148D236—42no—
149C4×D59—21no—
150C4×D59—21no—
151C4×D59—42no—
152C4×D59—42no—
153Dic118—42no—
154C8×C59—21no—
155C8×C59—21no—
156C59⋊C8—21no—
157C59⋊C8—21no—
158C22×C59—21no—
159C22×C59—21no—
160C22×C59—21no—
161C22×C59—41no—
162C22×C59—41no—
163C22×C59—41no—
164C22×C59—41no—
165C22×C59—41no—
166C22×C59—41no—
167C22×C59C22×D411yescharacteristic
168C2×D59—21no—
169C2×D59—21no—
170C2×D59—21no—
171C2×D59—41no—
172C2×D59—41no—
173C2×D59—41no—
174C4×C59—22no—
175C4×C59—21no—
176C4×C59—41no—
177C4×C59C2×#4111yescharacteristic
178C4×C59H(5,𝔽2)11yescharacteristic
179Dic59—21no—
180Dic59—21no—
181Dic59—41no—
182Dic59—41no—
183Dic59—41no—
184Dic59AGL(1,ℤ/8)12yes—
185#3332—591nomaximal, Sylow
186C2×C59—41no—
187C2×C59—81no—
188C2×C59—81no—
189C2×C59#54611yescharacteristic
190C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C59#57711yescharacteristic
192D59—41no—
193D59—81no—
194#550—591no—
195#547—591no—
196#486—591no—
197#481—591no—
198#481—591no—
199#475—591no—
200#469—591no—
201#469—591no—
202#459—591no—
203#449—591no—
204#449D5911yescharacteristic, complemented
205C4×SD16—591no—
206#436—591no—
207#417—591no—
208#417—591no—
209C59#333211yescharacteristic, complemented, Sylow
210C2×#41—591no—
211C2×#41—1181no—
212C2×#41C2×D5911yescharacteristic
213C2×SD16C2×D5911yescharacteristic
214C2×D8—591no—
215C2×D8C2×D5911yescharacteristic
216C2×M16—591no—
217C2×M16—591no—
218C4⋊Q8—591no—
219#127—591no—
220#127—1181no—
221#123—1181no—
222#123—1181no—
223C22⋊Q8—1181no—
224#121—591no—
225#121—591no—
226#121—591no—
227#121—1181no—
228#121—1181no—
229#121C2×D5911yescharacteristic
230C4×Q8—591no—
231C4×D4—591no—
232C4×D4—591no—
233C4×D4—1181no—
234C2×C4⋊C4—591no—
235C2×C4⋊C4—591no—
236#106—591no—
237#106—591no—
238#106—591no—
239C4⋊C8—591no—
240#103—591no—
241#103—591no—
242#103C2×D5911yescharacteristic
243#102—591no—
244#102—591no—
245#102—591no—
246#102—591no—
247#102—591no—
248#102—591no—
249#102C2×D5911yescharacteristic
250C22⋊C8—591no—
251C22⋊C8C2×D5911yescharacteristic
252C4×C8—591no—
253#41—22no—
254#41—41no—
255#41—1182no—
256#41—2361no—
257#41—2364no—
258C2×Q8—1181no—
259C2×Q8C22×D5911yescharacteristic
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—591no—
263C2×D4—591no—
264C2×D4—1181no—
265C2×D4—1181no—
266C2×D4—1181no—
267C2×D4—1181no—
268C2×D4—1181no—
269C2×D4—1181no—
270C2×D4C22×D5911yescharacteristic
271C2×D4C22×D5911yescharacteristic
272C22×C4—21no—
273C22×C4—591no—
274C22×C4—1181no—
275C22×C4—1181no—
276C22×C4—1181no—
277C22×C4—1181no—
278C22×C4C22×D5911yescharacteristic
279SD16—22no—
280D8—41no—
281D8—2361no—
282M16—2361no—
283M16—2361no—
284C2×C8—591no—
285C2×C8—591no—
286C2×C8C22×D5911yescharacteristic
287C2×C8C22×D5911yescharacteristic
288C4⋊C4—591no—
289C4⋊C4—591no—
290C4⋊C4—591no—
291C4⋊C4—591no—
292C4⋊C4—1181no—
293C4⋊C4—1181no—
294C4⋊C4—1181no—
295C4⋊C4—1181no—
296C4⋊C4C22×D5911yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—591no—
299C22⋊C4—591no—
300C22⋊C4—1181no—
301C22⋊C4—1181no—
302C22⋊C4—1181no—
303C22⋊C4—1181no—
304C42—591no—
305C42—1181no—
306C23—21no—
307C23—21no—
308C23—591no—
309C23—1181no—
310C23D4×D5911yescharacteristic
311Q8—21no—
312Q8—2362no—
313Q8#1174568712yescomplemented
314D4—21no—
315D4—21no—
316D4—21no—
317D4—21no—
318D4—42no—
319D4—42no—
320D4—1182no—
321D4—1181no—
322D4—1181no—
323D4—4721no—
324D4—4721no—
325D4—4721no—
326D4—2362no—
327D4—2362no—
328D4—2362no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—42no—
334C2×C4—591no—
335C2×C4—591no—
336C2×C4—591no—
337C2×C4—1181no—
338C2×C4—1181no—
339C2×C4—1181no—
340C2×C4—1181no—
341C2×C4—1181no—
342C2×C4—2362no—
343C2×C4—2362no—
344C2×C4—2362no—
345C2×C4—2362no—
346C2×C4D4×D5911yescharacteristic
347C2×C4C23×D5911yescharacteristic
348C8—21no—
349C8—21no—
350C8—1181no—
351C8—1181no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—1181no—
362C22—1181no—
363C22—1181no—
364C22—2361no—
365C22—2361no—
366C22—2361no—
367C22C2×D4×D5911yescharacteristic
368C4—21no—
369C4—22no—
370C4—41no—
371C4—592no—
372C4—1181no—
373C4—1181no—
374C4—2361no—
375C4—2361no—
376C4—2361no—
377C4C2×#1174568711yescharacteristic
378C4#1427377211yescharacteristic
379C2—41no—
380C2—81no—
381C2—81no—
382C2—4721no—
383C2—2361no—
384C2#1683803911yescharacteristic
385C2AGL(1,ℤ/8)×D5911yescharacteristic
386C2#1683820911yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#449C2
socleC22×C59C22×D4
hypercenter#449D59
hypocenterC59#3332
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. #16838071C2semidirect
2. #16838052C2semidirect
3. #16837747C2semidirect
4. #16837721C2semidirect
5. #16837719C2semidirect
6. #16837685C2semidirect
7. #16837653C2semidirect
8. #16837652C2semidirect
9. #16837595C2semidirect
10. #16837546C2semidirect
11. SD16×Dic59C2semidirect
12. #16837477C2semidirect
13. #16837403C2semidirect
14. #16837402C2semidirect
15. C59×#449C2semidirect
118. Q8×C59#41semidirect
204. #449D59semidirect
209. C59#3332semidirect
313. Q8#11745687semidirect