Finite Group Databasebeta

← #21436596

Subgroups — #21436596

Order 7552.

360 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838098C211yesmaximal, characteristic, complemented
2#16837808C211yesmaximal, characteristic, complemented
3#16837726C211yesmaximal, characteristic, complemented
4#16837726C211yesmaximal, characteristic, complemented
5#16837723C211yesmaximal, characteristic, complemented
6#16837713C211yesmaximal, characteristic, complemented
7#16837702C211yesmaximal, characteristic, complemented
8#16837679C211yesmaximal, characteristic, complemented
9#16837653C211yesmaximal, characteristic, complemented
10#16837636C211yesmaximal, characteristic, complemented
11#16837512C211yesmaximal, characteristic, complemented
12#16837474C211yesmaximal, characteristic, complemented
13#16837445C211yesmaximal, characteristic, complemented
14#16837438C211yesmaximal, characteristic, complemented
15C59×#555C211yesmaximal, characteristic, complemented
16C2×#11745669C2211yescharacteristic
17C2×#11745664C2211yescharacteristic
18C22×C59⋊C8C2211yescharacteristic
19#14273722—21no—
20#14273719C2211yescharacteristic
21#14273709—21no—
22#14273701C2211yescharacteristic
23#14273701C2211yescharacteristic
24#14273699—21no—
25C4×D236C2211yescharacteristic
26(C22⋊D59)⋊C4—21no—
27#14273686C2211yescharacteristic
28C2×C4⋊Dic59C2211yescharacteristic
29#14273660C2211yescharacteristic
30#14273660C2211yescharacteristic
31#14273660C2211yescharacteristic
32#14273660C2211yescharacteristic
33#14273660C2211yescharacteristic
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
48C4⋊Q8×C59C2211yescharacteristic
49#124×C59—21no—
50#124×C59—21no—
51#121×C59—21no—
52#121×C59C2211yescharacteristic
53#121×C59C2211yescharacteristic
54C4×D4×C59C2211yescharacteristic
55C4×D4×C59C2211yescharacteristic
56#117×C59—21no—
57#117×C59C2211yescharacteristic
58#117×C59C2211yescharacteristic
59C2×Q8×C59—21no—
60C2×D4×C59—21no—
61C2×D4×C59—21no—
62C2×D4×C59D411yescharacteristic
63C2×D4×C59C2311yescharacteristic
64C22×C4×C59—21no—
65C22×C4×C59C2311yescharacteristic
66C22×C4×C59C2311yescharacteristic
67C2×C22⋊D59—21no—
68C2×C22⋊D59—21no—
69C22×Dic59—21no—
70C2×D236C2311yescharacteristic
71C2×C4×D59—21no—
72C4⋊C4×C59—21no—
73C4⋊C4×C59D411yescharacteristic
74C4⋊C4×C59C2311yescharacteristic
75C4⋊C4×C59C2311yescharacteristic
76C4⋊C4×C59C2311yescharacteristic
77C22⋊C4×C59—21no—
78C22⋊C4×C59—21no—
79C22⋊C4×C59—21no—
80C22⋊C4×C59—21no—
81C22⋊C4×C59—21no—
82C22⋊C4×C59D411yescharacteristic
83C22⋊C4×C59D411yescharacteristic
84C42×C59—21no—
85C42×C59—21no—
86C42×C59C2311yescharacteristic
87C22⋊Dic59—21no—
88#11745669—22no—
89(C2×D59)⋊C4—21no—
90(C2×D59)⋊C4—21no—
91(C2×D59)⋊C4—21no—
92C4⋊Dic59—21no—
93C4⋊Dic59C2311yescharacteristic
94C4⋊Dic59C2311yescharacteristic
95C4⋊Dic59C2311yescharacteristic
96Dic59⋊C4—21no—
97Dic59⋊C4—21no—
98C4×Dic59—21no—
99#11745664—22no—
100C2×C59⋊C8—22no—
101C2×C59⋊C8C2311yescharacteristic
102C2×C59⋊C8C2311yescharacteristic
103C2×C59⋊C8C2311yescharacteristic
104C2×C59⋊C8C2311yescharacteristic
105C23×C59—21no—
106C23×C59C2×D411yescharacteristic
107C23×C59C2×D411yescharacteristic
108C22×D59—21no—
109Q8×C59—81no—
110D4×C59—21no—
111D4×C59—21no—
112D4×C59—41no—
113D4×C59—81no—
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—42no—
123C2×C4×C59C2×D411yescharacteristic
124C2×C4×C59C2×D411yescharacteristic
125C2×C4×C59C2×D411yescharacteristic
126C2×C4×C59C2×D411yescharacteristic
127C2×C4×C59C2411yescharacteristic
128C22⋊D59—42no—
129C22⋊D59—81no—
130C2×Dic59—21no—
131C2×Dic59—21no—
132C2×Dic59—21no—
133C2×Dic59—81no—
134D236—21no—
135D236—21no—
136C4×D59—81no—
137C59⋊C8—21no—
138C59⋊C8—21no—
139C59⋊C8—21no—
140C59⋊C8#4112yes—
141C22×C59—21no—
142C22×C59—21no—
143C22×C59—21no—
144C22×C59—21no—
145C22×C59—21no—
146C22×C59—21no—
147C22×C59—41no—
148C22×C59—41no—
149C22×C59—41no—
150C22×C59C22×D411yescharacteristic
151C2×D59—41no—
152C2×D59—41no—
153C2×D59—41no—
154C4×C59—21no—
155C4×C59—21no—
156C4×C59—21no—
157C4×C59—21no—
158C4×C59—41no—
159C4×C59—41no—
160C4×C59—41no—
161C4×C59C2×#4111yescharacteristic
162C4×C592−1+411yescharacteristic
163Dic59—41no—
164Dic59—41no—
165Dic59—41no—
166#3347—591nomaximal, Sylow
167C2×C59—41no—
168C2×C59—41no—
169C2×C59—81no—
170C2×C59#54711yescharacteristic
171C2×C59#57511yescharacteristic
172C2×C59#57611yescharacteristic
173D59—81no—
174#555D5911yescharacteristic, complemented
175#553—591no—
176#501—591no—
177#482—591no—
178#482—591no—
179#482—591no—
180#480—591no—
181#478—591no—
182#474—591no—
183#469—591no—
184#466—591no—
185#442—591no—
186#435—591no—
187#428—591no—
188#427—591no—
189C59#334711yescharacteristic, complemented, Sylow
190C2×D8—591no—
191C2×M16—591no—
192C22×C8—591no—
193C4⋊Q8C2×D5911yescharacteristic
194#126—1181no—
195#125—591no—
196#124—21no—
197#124—21no—
198#123—1181no—
199#121—21no—
200#121—591no—
201#121—591no—
202#121—1181no—
203#121C2×D5911yescharacteristic
204#121C2×D5911yescharacteristic
205C4×D4—591no—
206C4×D4—1181no—
207C4×D4C2×D5911yescharacteristic
208C4×D4C2×D5911yescharacteristic
209#117—21no—
210#117—591no—
211#117C2×D5911yescharacteristic
212#117C2×D5911yescharacteristic
213C2×C4⋊C4—591no—
214#107—591no—
215#107—591no—
216#107—591no—
217#107—591no—
218#107—591no—
219#106—591no—
220#106—591no—
221#106—591no—
222#106—591no—
223C4⋊C8—591no—
224#102—591no—
225#102—591no—
226#102—591no—
227#102—591no—
228#102—591no—
229#102—591no—
230C22⋊C8—591no—
231C22⋊C8—591no—
232#97—591no—
233C2×Q8—21no—
234C2×D4—21no—
235C2×D4—21no—
236C2×D4—591no—
237C2×D4—1181no—
238C2×D4—1181no—
239C2×D4C22⋊D5911yescharacteristic
240C2×D4C22×D5911yescharacteristic
241C22×C4—21no—
242C22×C4—1181no—
243C22×C4—1181no—
244C22×C4C22×D5911yescharacteristic
245C22×C4C22×D5911yescharacteristic
246D8—1182no—
247M16—1182no—
248C2×C8—591no—
249C2×C8—591no—
250C2×C8—591no—
251C2×C8—591no—
252C2×C8—1182no—
253C4⋊C4—21no—
254C4⋊C4—591no—
255C4⋊C4—591no—
256C4⋊C4—591no—
257C4⋊C4—1181no—
258C4⋊C4—1181no—
259C4⋊C4—1181no—
260C4⋊C4C22⋊D5911yescharacteristic
261C4⋊C4C22×D5911yescharacteristic
262C4⋊C4C22×D5911yescharacteristic
263C4⋊C4C22×D5911yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—1181no—
270C22⋊C4—1181no—
271C22⋊C4—1181no—
272C22⋊C4—1181no—
273C22⋊C4C22⋊D5911yescharacteristic
274C22⋊C4C22⋊D5911yescharacteristic
275C42—21no—
276C42—21no—
277C42—1181no—
278C42C22×D5911yescharacteristic
279C23—21no—
280C23—1181no—
281C23C2×C22⋊D5911yescharacteristic
282C23C2×C22⋊D5911yescharacteristic
283Q8—81no—
284D4—21no—
285D4—21no—
286D4—41no—
287D4—81no—
288D4—81no—
289D4—1181no—
290D4—1181no—
291D4—4721no—
292D4—2362no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—42no—
301C2×C4—1181no—
302C2×C4—1181no—
303C2×C4—1181no—
304C2×C4—4721no—
305C2×C4—4721no—
306C2×C4C2×C22⋊D5911yescharacteristic
307C2×C4C2×C22⋊D5911yescharacteristic
308C2×C4C2×C22⋊D5911yescharacteristic
309C2×C4C2×C22⋊D5911yescharacteristic
310C2×C4C23×D5911yescharacteristic
311C8—592no—
312C8—1181no—
313C8—1181no—
314C8—1181no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—2361no—
325C22—2361no—
326C22—2361no—
327C22C22×C22⋊D5911yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—2361no—
336C4—2361no—
337C4—2361no—
338C4#41×D5911yescharacteristic
339C4#1427377411yescharacteristic
340C2—41no—
341C2—41no—
342C2—81no—
343C2—4721no—
344C2#1683805111yescharacteristic
345C2#1683820011yescharacteristic
346C2#1683820511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#555C2
socleC22×C59C22×D4
hypercenter#555D59
hypocenterC59#3347
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #555

Complements

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

NH ≅ G/Ntype
1. #16838098C2semidirect
2. #16837808C2semidirect
3. #16837726C2semidirect
4. #16837726C2semidirect
5. #16837723C2semidirect
6. #16837713C2semidirect
7. #16837702C2semidirect
8. #16837679C2semidirect
9. #16837653C2semidirect
10. #16837636C2semidirect
11. #16837512C2semidirect
12. #16837474C2semidirect
13. #16837445C2semidirect
14. #16837438C2semidirect
15. C59×#555C2semidirect
174. #555D59semidirect
189. C59#3347semidirect