Finite Group Databasebeta

← #21436560

Subgroups — #21436560

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#16838056C211yesmaximal, characteristic, complemented
2#16837812C211yesmaximal, characteristic, complemented
3#16837726C211yesmaximal, characteristic, complemented
4#16837720C211yesmaximal, characteristic, complemented
5#16837718C211yesmaximal, characteristic, complemented
6#16837713C211yesmaximal, characteristic, complemented
7#16837699C211yesmaximal, characteristic, complemented
8#16837692C211yesmaximal, characteristic, complemented
9#16837653C211yesmaximal, characteristic, complemented
10#16837636C211yesmaximal, characteristic, complemented
11#16837512C211yesmaximal, characteristic, complemented
12#16837474C211yesmaximal, characteristic, complemented
13#16837445C211yesmaximal, characteristic, complemented
14C2×#14273658C211yesmaximal, characteristic, complemented
15C59×#553C211yesmaximal, characteristic, complemented
16C2×#11745687—21no—
17C2×#11745669C2211yescharacteristic
18C2×#11745664C2211yescharacteristic
19C22×C59⋊C8C2211yescharacteristic
20#14273727C2211yescharacteristic
21#14273711—21no—
22#14273711—21no—
23#14273707—21no—
24#14273701C2211yescharacteristic
25#14273701C2211yescharacteristic
26C4×D236C2211yescharacteristic
27C2×C4⋊Dic59C2211yescharacteristic
28C2×C4⋊Dic59C2211yescharacteristic
29#14273660C2211yescharacteristic
30#14273660C2211yescharacteristic
31#14273660C2211yescharacteristic
32#14273658C2211yescharacteristic
33#14273658C2211yescharacteristic
34#14273658C2211yescharacteristic
35#14273658C2211yescharacteristic
36#14273658C2211yescharacteristic
37#14273658C2211yescharacteristic
38C4⋊(C59⋊C8)C2211yescharacteristic
39#14273648C2211yescharacteristic
40#14273648C2211yescharacteristic
41#14273648C2211yescharacteristic
42#14273647C2211yescharacteristic
43#14273647C2211yescharacteristic
44#14273647C2211yescharacteristic
45C22⋊(C59⋊C8)C2211yescharacteristic
46C22⋊(C59⋊C8)C2211yescharacteristic
47#14273638C2211yescharacteristic
48#126×C59—21no—
49#125×C59C2211yescharacteristic
50#123×C59—21no—
51#121×C59—21no—
52#121×C59C2211yescharacteristic
53#121×C59C2211yescharacteristic
54C4×D4×C59—21no—
55C4×D4×C59C2211yescharacteristic
56C4×D4×C59C2211yescharacteristic
57#117×C59C2211yescharacteristic
58C2×C4⋊C4×C59C2211yescharacteristic
59C2×D4×C59—21no—
60C2×D4×C59—21no—
61C2×D4×C59D411yescharacteristic
62C2×D4×C59C2311yescharacteristic
63C22×C4×C59—21no—
64C22×C4×C59—21no—
65C22×C4×C59C2311yescharacteristic
66C22×C4×C59C2311yescharacteristic
67C2×C22⋊D59—21no—
68C2×C22⋊D59—21no—
69C22×Dic59—21no—
70C22×Dic59—21no—
71#11745687—44no—
72C2×D236C2311yescharacteristic
73C2×C4×D59—21no—
74C2×Dic118—21no—
75C4⋊C4×C59—21no—
76C4⋊C4×C59—21no—
77C4⋊C4×C59—21no—
78C4⋊C4×C59D411yescharacteristic
79C4⋊C4×C59C2311yescharacteristic
80C4⋊C4×C59C2311yescharacteristic
81C4⋊C4×C59C2311yescharacteristic
82C22⋊C4×C59—21no—
83C22⋊C4×C59—21no—
84C22⋊C4×C59—21no—
85C22⋊C4×C59—21no—
86C22⋊C4×C59D411yescharacteristic
87C22⋊C4×C59D411yescharacteristic
88C42×C59—21no—
89C42×C59C2311yescharacteristic
90#11745669—22no—
91(C2×D59)⋊C4—21no—
92(C2×D59)⋊C4—21no—
93(C2×D59)⋊C4—21no—
94C4⋊Dic59—21no—
95C4⋊Dic59—21no—
96C4⋊Dic59—21no—
97C4⋊Dic59C2311yescharacteristic
98C4⋊Dic59C2311yescharacteristic
99C4⋊Dic59C2311yescharacteristic
100#11745664—22no—
101C2×C59⋊C8—22no—
102C2×C59⋊C8C2311yescharacteristic
103C2×C59⋊C8C2311yescharacteristic
104C2×C59⋊C8C2311yescharacteristic
105C2×C59⋊C8C2311yescharacteristic
106C23×C59—21no—
107C23×C59C2×D411yescharacteristic
108C23×C59C2×D411yescharacteristic
109C22×D59—21no—
110D4×C59—22no—
111D4×C59—21no—
112D4×C59—21no—
113D4×C59—42no—
114D4×C59—81no—
115C2×C4×C59—21no—
116C2×C4×C59—21no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—81no—
123C2×C4×C59—81no—
124C2×C4×C59C2×D411yescharacteristic
125C2×C4×C59C2×D411yescharacteristic
126C2×C4×C59C2×D411yescharacteristic
127C2×C4×C59C2×D411yescharacteristic
128C2×C4×C59C2411yescharacteristic
129C22⋊D59—42no—
130C22⋊D59—42no—
131C2×Dic59—21no—
132C2×Dic59—21no—
133C2×Dic59—21no—
134C2×Dic59—42no—
135C2×Dic59—42no—
136D236—21no—
137D236—21no—
138C4×D59—42no—
139Dic118—42no—
140C59⋊C8—21no—
141C59⋊C8—21no—
142C59⋊C8—21no—
143C59⋊C8#4112yescomplemented
144C22×C59—21no—
145C22×C59—21no—
146C22×C59—21no—
147C22×C59—21no—
148C22×C59—21no—
149C22×C59—41no—
150C22×C59—41no—
151C22×C59—41no—
152C22×C59AGL(1,ℤ/8)12yes—
153C22×C59C22×D411yescharacteristic
154C2×D59—41no—
155C2×D59—41no—
156C2×D59—41no—
157C4×C59—21no—
158C4×C59—21no—
159C4×C59—21no—
160C4×C59—21no—
161C4×C59—41no—
162C4×C59—41no—
163C4×C59—41no—
164C4×C59C2×#4111yescharacteristic
165C4×C592−1+411yescharacteristic
166Dic59—41no—
167Dic59—41no—
168Dic59—41no—
169#3345—591nomaximal, Sylow
170C2×C59—22no—
171C2×C59—41no—
172C2×C59—81no—
173C2×C59#54711yescharacteristic
174C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
175C2×C59#57711yescharacteristic
176D59—81no—
177#553D5911yescharacteristic, complemented
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#428—591no—
191C2×#106—591no—
192C59#334511yescharacteristic, complemented, Sylow
193C2×#41—1181no—
194C2×D8—591no—
195C2×M16—591no—
196C22×C8—591no—
197C4⋊Q8—591no—
198#126—21no—
199#125C2×D5911yescharacteristic
200#123—21no—
201#123—1181no—
202#123—1181no—
203C22⋊Q8—1181no—
204#121—21no—
205#121—591no—
206#121—591no—
207#121C2×D5911yescharacteristic
208#121C2×D5911yescharacteristic
209C4×D4—21no—
210C4×D4—591no—
211C4×D4C2×D5911yescharacteristic
212C4×D4C2×D5911yescharacteristic
213#117C2×D5911yescharacteristic
214C2×C4⋊C4—591no—
215C2×C4⋊C4—591no—
216C2×C4⋊C4C2×D5911yescharacteristic
217#107—591no—
218#107—591no—
219#107—591no—
220#106—591no—
221#106—591no—
222#106—591no—
223#106—591no—
224#106—591no—
225#106—591no—
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—21no—
239C2×D4—21no—
240C2×D4—591no—
241C2×D4—1181no—
242C2×D4—1181no—
243C2×D4C22⋊D5911yescharacteristic
244C2×D4C22×D5911yescharacteristic
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—1181no—
248C22×C4—1181no—
249C22×C4—1181no—
250C22×C4C22×D5911yescharacteristic
251C22×C4C22×D5911yescharacteristic
252D8—1182no—
253M16—1182no—
254C2×C8—591no—
255C2×C8—591no—
256C2×C8—591no—
257C2×C8—591no—
258C2×C8—1182no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—591no—
263C4⋊C4—591no—
264C4⋊C4—591no—
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—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—1181no—
277C22⋊C4—1181no—
278C22⋊C4—1181no—
279C22⋊C4C22⋊D5911yescharacteristic
280C22⋊C4C22⋊D5911yescharacteristic
281C42—21no—
282C42C22×D5911yescharacteristic
283C23—21no—
284C23—1181no—
285C23C2×C22⋊D5911yescharacteristic
286C23C2×C22⋊D5911yescharacteristic
287Q8—2362no—
288D4—22no—
289D4—21no—
290D4—21no—
291D4—42no—
292D4—81no—
293D4—1181no—
294D4—1181no—
295D4—2362no—
296D4—2362no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—1181no—
307C2×C4—1181no—
308C2×C4—1181no—
309C2×C4—2362no—
310C2×C4—2362no—
311C2×C4—2362no—
312C2×C4C2×C22⋊D5911yescharacteristic
313C2×C4C2×C22⋊D5911yescharacteristic
314C2×C4C2×C22⋊D5911yescharacteristic
315C2×C4C2×C22⋊D5911yescharacteristic
316C2×C4C23×D5911yescharacteristic
317C8—592no—
318C8—1181no—
319C8—1181no—
320C8—1181no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—2361no—
330C22—2361no—
331C22—2361no—
332C22#1427375212yes—
333C22C22×C22⋊D5911yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—2361no—
342C4—2361no—
343C4—2361no—
344C4#41×D5911yescharacteristic
345C4#1427377411yescharacteristic
346C2—22no—
347C2—41no—
348C2—81no—
349C2—4721no—
350C2#1683805111yescharacteristic
351C2C2×#1427375211yescharacteristic
352C2#1683821311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#553C2
socleC22×C59C22×D4
hypercenter#553D59
hypocenterC59#3345
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #16838056C2semidirect
2. #16837812C2semidirect
3. #16837726C2semidirect
4. #16837720C2semidirect
5. #16837718C2semidirect
6. #16837713C2semidirect
7. #16837699C2semidirect
8. #16837692C2semidirect
9. #16837653C2semidirect
10. #16837636C2semidirect
11. #16837512C2semidirect
12. #16837474C2semidirect
13. #16837445C2semidirect
14. C2×#14273658C2semidirect
15. C59×#553C2semidirect
143. C59⋊C8#41semidirect
177. #553D59semidirect
192. C59#3345semidirect