Finite Group Databasebeta

← #21436567

Subgroups — #21436567

Order 7552.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838096C211yesmaximal, characteristic, complemented
2#16838053C211yesmaximal, characteristic, complemented
3#16837810C211yesmaximal, characteristic, complemented
4#16837726C211yesmaximal, characteristic, complemented
5#16837722C211yesmaximal, characteristic, complemented
6#16837720C211yesmaximal, characteristic, complemented
7#16837717C211yesmaximal, characteristic, complemented
8#16837705C211yesmaximal, characteristic, complemented
9#16837691C211yesmaximal, characteristic, complemented
10#16837655C211yesmaximal, characteristic, complemented
11#16837639C211yesmaximal, characteristic, complemented
12#16837513C211yesmaximal, characteristic, complemented
13#16837471C211yesmaximal, characteristic, complemented
14#106×D59C211yesmaximal, characteristic, complemented
15C59×#428C211yesmaximal, characteristic, complemented
16C2×#11745685—21no—
17C2×D472C2211yescharacteristic
18C2×C8×D59C2211yescharacteristic
19#14273726C2211yescharacteristic
20#14273721—21no—
21#14273718C2211yescharacteristic
22#14273712—21no—
23#14273710—21no—
24#14273709—21no—
25#14273705—21no—
26#14273702C2211yescharacteristic
27#14273702C2211yescharacteristic
28#14273701C2211yescharacteristic
29#14273701C2211yescharacteristic
30#14273700—21no—
31C4×D236—21no—
32#14273689C2211yescharacteristic
33#14273689C2211yescharacteristic
34C4×C22⋊D59C2211yescharacteristic
35C4⋊C4×D59C2211yescharacteristic
36C4⋊C4×D59C2211yescharacteristic
37#14273660C2211yescharacteristic
38#14273659C2211yescharacteristic
39#14273658C2211yescharacteristic
40#14273658C2211yescharacteristic
41#14273658C2211yescharacteristic
42Dic59⋊C8C2211yescharacteristic
43#14273649C2211yescharacteristic
44#14273649C2211yescharacteristic
45#14273647C2211yescharacteristic
46#14273647C2211yescharacteristic
47#14273647C2211yescharacteristic
48#14273647C2211yescharacteristic
49C22⋊(C59⋊C8)C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51#14273637C2211yescharacteristic
52C2×M16×C59C2211yescharacteristic
53#117×C59C2211yescharacteristic
54C2×C4⋊C4×C59C2211yescharacteristic
55#107×C59C2211yescharacteristic
56#107×C59C2211yescharacteristic
57#106×C59C2211yescharacteristic
58#106×C59C2211yescharacteristic
59C22×C4×C59—21no—
60C22×C4×C59C2311yescharacteristic
61C2×C22⋊D59—21no—
62C2×C22⋊D59—21no—
63C2×C22⋊D59D411yescharacteristic
64#11745685—44no—
65C2×D236—21no—
66C2×D236—21no—
67C2×D236C2311yescharacteristic
68C2×D236C2311yescharacteristic
69C2×C4×D59—21no—
70C2×C4×D59—21no—
71C2×C4×D59—21no—
72C2×C4×D59—21no—
73C2×C4×D59C2311yescharacteristic
74C2×Dic118—21no—
75M16×C59—22no—
76C2×C8×C59C2311yescharacteristic
77C2×C8×C59C2311yescharacteristic
78C4⋊C4×C59—21no—
79C4⋊C4×C59C2311yescharacteristic
80C4⋊C4×C59C2311yescharacteristic
81C4⋊C4×C59C2311yescharacteristic
82C4⋊C4×C59C2311yescharacteristic
83C22⋊C4×C59—21no—
84C42×C59—21no—
85C22⋊Dic59D411yescharacteristic
86(C2×D59)⋊C4—21no—
87(C2×D59)⋊C4—21no—
88(C2×D59)⋊C4—21no—
89(C2×D59)⋊C4—21no—
90(C2×D59)⋊C4—21no—
91(C2×D59)⋊C4—21no—
92(C2×D59)⋊C4D411yescharacteristic
93C4⋊Dic59—21no—
94C4⋊Dic59C2311yescharacteristic
95C4⋊Dic59C2311yescharacteristic
96Dic59⋊C4—21no—
97Dic59⋊C4—21no—
98Dic59⋊C4—21no—
99Dic59⋊C4—21no—
100Dic59⋊C4D411yescharacteristic
101C4×Dic59C2311yescharacteristic
102C2×C59⋊C8C2311yescharacteristic
103C2×C59⋊C8C2311yescharacteristic
104D472—22no—
105C8×D59—22no—
106C23×C59C2×D411yescharacteristic
107C22×D59—21no—
108C22×D59—21no—
109C22×D59C2×D411yescharacteristic
110C2×C4×C59—21no—
111C2×C4×C59—21no—
112C2×C4×C59—21no—
113C2×C4×C59—21no—
114C2×C4×C59—21no—
115C2×C4×C59—21no—
116C2×C4×C59—42no—
117C2×C4×C59C2×D411yescharacteristic
118C2×C4×C59C2411yescharacteristic
119C22⋊D59—22no—
120C22⋊D59—42no—
121C22⋊D59—81no—
122C2×Dic59—21no—
123C2×Dic59—21no—
124C2×Dic59C2×D411yescharacteristic
125C2×Dic59C2×D411yescharacteristic
126C2×Dic59C2×D411yescharacteristic
127D236—21no—
128D236—21no—
129D236—21no—
130D236—21no—
131D236—42no—
132D236—42no—
133C4×D59—21no—
134C4×D59—21no—
135C4×D59—42no—
136C4×D59—42no—
137C4×D59—81no—
138C4×D59—81no—
139Dic118—42no—
140C8×C59—21no—
141C8×C59#4112yescomplemented
142C59⋊C8—21no—
143C59⋊C8—21no—
144C22×C59—21no—
145C22×C59—21no—
146C22×C59—21no—
147C22×C59C22×D411yescharacteristic
148C2×D59—21no—
149C2×D59—21no—
150C2×D59—41no—
151C2×D59—41no—
152C2×D59—41no—
153C2×D59—41no—
154C2×D59—41no—
155C2×D59—41no—
156C2×D59AGL(1,ℤ/8)12yes—
157C4×C59—21no—
158C4×C59—41no—
159C4×C59—41no—
160C4×C59—41no—
161C4×C59—41no—
162C4×C59C2×#4111yescharacteristic
163C4×C592−1+411yescharacteristic
164Dic59—21no—
165Dic59—21no—
166Dic59—21no—
167Dic59—41no—
168Dic59—41no—
169#3345—591nomaximal, Sylow
170C2×C59—41no—
171C2×C59#54711yescharacteristic
172C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
173C2×C59#57711yescharacteristic
174D59—22no—
175D59—81no—
176D59—81no—
177#553—591no—
178#547—591no—
179#501—591no—
180#482—591no—
181#481—591no—
182#481—591no—
183#480—591no—
184#478—591no—
185#476—591no—
186#469—591no—
187#466—591no—
188#442—591no—
189#435—591no—
190#428D5911yescharacteristic, complemented
191C2×#106—591no—
192C59#334511yescharacteristic, complemented, Sylow
193C2×#41—1181no—
194C2×D8—591no—
195C2×M16C2×D5911yescharacteristic
196C22×C8—591no—
197C4⋊Q8—591no—
198#126—1181no—
199#125—591no—
200#123—1181no—
201#123—1181no—
202#123—1181no—
203C22⋊Q8—1181no—
204#121—591no—
205#121—591no—
206#121—591no—
207#121—591no—
208#121—1181no—
209C4×D4—591no—
210C4×D4—591no—
211C4×D4—591no—
212C4×D4—1181no—
213#117C2×D5911yescharacteristic
214C2×C4⋊C4—591no—
215C2×C4⋊C4—591no—
216C2×C4⋊C4C2×D5911yescharacteristic
217#107—591no—
218#107C2×D5911yescharacteristic
219#107C2×D5911yescharacteristic
220#106—591no—
221#106—591no—
222#106—591no—
223#106—591no—
224#106C2×D5911yescharacteristic
225#106C2×D5911yescharacteristic
226C4⋊C8—591no—
227#102—591no—
228#102—591no—
229#102—591no—
230#102—591no—
231#102—591no—
232#102—591no—
233C22⋊C8—591no—
234C22⋊C8—591no—
235#97—591no—
236#41—2364no—
237C2×Q8—1181no—
238C2×D4—591no—
239C2×D4—591no—
240C2×D4—591no—
241C2×D4—1181no—
242C2×D4—1181no—
243C2×D4—1181no—
244C2×D4—1181no—
245C22×C4—21no—
246C22×C4—591no—
247C22×C4—1181no—
248C22×C4—1181no—
249C22×C4—1181no—
250C22×C4—1181no—
251C22×C4C22×D5911yescharacteristic
252D8—1182no—
253M16—22no—
254C2×C8—591no—
255C2×C8—591no—
256C2×C8—1182no—
257C2×C8C22×D5911yescharacteristic
258C2×C8C22×D5911yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—591no—
261C4⋊C4—591no—
262C4⋊C4—591no—
263C4⋊C4—1181no—
264C4⋊C4—1181no—
265C4⋊C4—1181no—
266C4⋊C4—1181no—
267C4⋊C4—1181no—
268C4⋊C4C22×D5911yescharacteristic
269C4⋊C4C22×D5911yescharacteristic
270C4⋊C4C22×D5911yescharacteristic
271C4⋊C4C22×D5911yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—591no—
274C22⋊C4—591no—
275C22⋊C4—1181no—
276C22⋊C4—1181no—
277C22⋊C4—1181no—
278C22⋊C4—1181no—
279C22⋊C4—1181no—
280C22⋊C4—1181no—
281C42—21no—
282C42—591no—
283C23—591no—
284C23—1181no—
285C23—1181no—
286C23D4×D5911yescharacteristic
287Q8—2362no—
288D4—1182no—
289D4—1181no—
290D4—1181no—
291D4—1181no—
292D4—1181no—
293D4—4721no—
294D4—2362no—
295D4—2362no—
296D4—2362no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—42no—
304C2×C4—591no—
305C2×C4—591no—
306C2×C4—591no—
307C2×C4—1181no—
308C2×C4—1181no—
309C2×C4—1181no—
310C2×C4—1181no—
311C2×C4—4721no—
312C2×C4—4721no—
313C2×C4—2362no—
314C2×C4—2362no—
315C2×C4D4×D5911yescharacteristic
316C2×C4C23×D5911yescharacteristic
317C8—21no—
318C8—1181no—
319C8—1181no—
320C8#1174568512yescomplemented
321C22—21no—
322C22—21no—
323C22—21no—
324C22—592no—
325C22—1181no—
326C22—1181no—
327C22—2361no—
328C22—2361no—
329C22—2361no—
330C22—2361no—
331C22—2361no—
332C22—2361no—
333C22C2×D4×D5911yescharacteristic
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—1181no—
340C4—1181no—
341C4—1181no—
342C4—2361no—
343C4—2361no—
344C4C2×#1174568511yescharacteristic
345C4#1427377511yescharacteristic
346C2—41no—
347C2—1182no—
348C2—4721no—
349C2—4721no—
350C2#1683805311yescharacteristic
351C2AGL(1,ℤ/8)×D5911yescharacteristic
352C2#1683821111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#428C2
socleC22×C59C22×D4
hypercenter#428D59
hypocenterC59#3345
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
1. #16838096C2semidirect
2. #16838053C2semidirect
3. #16837810C2semidirect
4. #16837726C2semidirect
5. #16837722C2semidirect
6. #16837720C2semidirect
7. #16837717C2semidirect
8. #16837705C2semidirect
9. #16837691C2semidirect
10. #16837655C2semidirect
11. #16837639C2semidirect
12. #16837513C2semidirect
13. #16837471C2semidirect
14. #106×D59C2semidirect
15. C59×#428C2semidirect
141. C8×C59#41semidirect
190. #428D59semidirect
192. C59#3345semidirect
320. C8#11745685semidirect