Finite Group Databasebeta

← #21436536

Subgroups — #21436536

Order 7552.

376 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838056C211yesmaximal, characteristic
2#16837812C211yesmaximal, characteristic, complemented
3#16837735C211yesmaximal, characteristic, complemented
4#16837730C211yesmaximal, characteristic, complemented
5#16837726C211yesmaximal, characteristic, complemented
6#16837715C211yesmaximal, characteristic, complemented
7#16837699C211yesmaximal, characteristic, complemented
8#16837697C211yesmaximal, characteristic, complemented
9#16837650C211yesmaximal, characteristic, complemented
10#16837633C211yesmaximal, characteristic, complemented
11#16837500C211yesmaximal, characteristic, complemented
12#16837474C211yesmaximal, characteristic, complemented
13#16837445C211yesmaximal, characteristic, complemented
14C2×#14273660C211yesmaximal, characteristic, complemented
15C59×#552C211yesmaximal, characteristic, complemented
16C2×#11745687—21no—
17C2×#11745671C2211yescharacteristic
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#14273660C2211yescharacteristic
33#14273660C2211yescharacteristic
34#14273660C2211yescharacteristic
35#14273658C2211yescharacteristic
36#14273658C2211yescharacteristic
37#14273658C2211yescharacteristic
38C4⋊(C59⋊C8)C2211yescharacteristic
39#14273651C2211yescharacteristic
40#14273651C2211yescharacteristic
41#14273651C2211yescharacteristic
42#14273647C2211yescharacteristic
43#14273647C2211yescharacteristic
44#14273647C2211yescharacteristic
45C22⋊(C59⋊C8)C2211yescharacteristic
46C22⋊(C59⋊C8)C2211yescharacteristic
47#14273638C2211yescharacteristic
48#126×C59—21no—
49#125×C59—21no—
50#125×C59C2211yescharacteristic
51#123×C59—21no—
52C22⋊Q8×C59C2211yescharacteristic
53C22⋊Q8×C59C2211yescharacteristic
54C4×Q8×C59C2211yescharacteristic
55C4×D4×C59C2211yescharacteristic
56#117×C59—21no—
57#117×C59C2211yescharacteristic
58C2×C4⋊C4×C59C2211yescharacteristic
59C2×Q8×C59C2311yescharacteristic
60C2×D4×C59D411yescharacteristic
61C22×C4×C59—21no—
62C22×C4×C59C2311yescharacteristic
63C22×C4×C59C2311yescharacteristic
64C2×C22⋊D59—21no—
65C2×C22⋊D59—21no—
66C22×Dic59—21no—
67C22×Dic59—21no—
68#11745687—44no—
69C2×D236C2311yescharacteristic
70C2×C4×D59—21no—
71C2×Dic118—21no—
72C4⋊C4×C59—21no—
73C4⋊C4×C59—21no—
74C4⋊C4×C59—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×C59D411yescharacteristic
86C22⋊C4×C59D411yescharacteristic
87C42×C59—21no—
88C42×C59—21no—
89C42×C59C2311yescharacteristic
90#11745671—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×C59C2×D411yescharacteristic
107C23×C59C2×D411yescharacteristic
108C22×D59—21no—
109Q8×C59—21no—
110Q8×C59—21no—
111D4×C59—22no—
112C2×C4×C59—21no—
113C2×C4×C59—21no—
114C2×C4×C59—21no—
115C2×C4×C59—21no—
116C2×C4×C59—21no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—42no—
121C2×C4×C59C2×D411yescharacteristic
122C2×C4×C59C2×D411yescharacteristic
123C2×C4×C59C2×D411yescharacteristic
124C2×C4×C59C2×D411yescharacteristic
125C2×C4×C59C2411yescharacteristic
126C22⋊D59—42no—
127C22⋊D59—42no—
128C2×Dic59—21no—
129C2×Dic59—21no—
130C2×Dic59—21no—
131C2×Dic59—42no—
132C2×Dic59—42no—
133D236—21no—
134D236—21no—
135C4×D59—42no—
136Dic118—42no—
137C59⋊C8—21no—
138C59⋊C8—21no—
139C59⋊C8—21no—
140C59⋊C8#4112yescomplemented
141C22×C59—21no—
142C22×C59—21no—
143C22×C59—21no—
144C22×C59—21no—
145C22×C59—21no—
146C22×C59AGL(1,ℤ/8)12yes—
147C22×C59C22×D411yescharacteristic
148C2×D59—41no—
149C2×D59—41no—
150C2×D59—41no—
151C4×C59—21no—
152C4×C59—21no—
153C4×C59—21no—
154C4×C59—21no—
155C4×C59—41no—
156C4×C59—41no—
157C4×C59—41no—
158C4×C59—41no—
159C4×C59C2×#4111yescharacteristic
160C4×C592−1+411yescharacteristic
161Dic59—41no—
162Dic59—41no—
163Dic59—41no—
164#3343—591nomaximal, Sylow
165C2×C59—22no—
166C2×C59—41no—
167C2×C59#54711yescharacteristic
168C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
169C2×C59#57811yescharacteristic
170D59—81no—
171#552D5911yescharacteristic, complemented
172#547—591no—
173#501—591no—
174#484—591no—
175#483—591no—
176#482—591no—
177#480—591no—
178#478—591no—
179#477—591no—
180#468—591no—
181#465—591no—
182#440—591no—
183#435—591no—
184#428—591no—
185C2×#107—591no—
186C59#334311yescharacteristic, complemented, Sylow
187C2×#41—1181no—
188C2×SD16—591no—
189C2×M16—591no—
190C22×C8—591no—
191C4⋊Q8—591no—
192#126—21no—
193#125—21no—
194#125C2×D5911yescharacteristic
195#123—21no—
196#123—1181no—
197#123—1181no—
198C22⋊Q8—1181no—
199C22⋊Q8C2×D5911yescharacteristic
200C22⋊Q8C2×D5911yescharacteristic
201#121—591no—
202#121—591no—
203C4×Q8C2×D5911yescharacteristic
204C4×D4—591no—
205C4×D4C2×D5911yescharacteristic
206#117—21no—
207#117C2×D5911yescharacteristic
208C2×C4⋊C4—591no—
209C2×C4⋊C4—591no—
210C2×C4⋊C4C2×D5911yescharacteristic
211#107—591no—
212#107—591no—
213#107—591no—
214#107—591no—
215#107—591no—
216#107—591no—
217#106—591no—
218#106—591no—
219#106—591no—
220C4⋊C8—591no—
221#103—591no—
222#103—591no—
223#103—591no—
224#102—591no—
225#102—591no—
226#102—591no—
227C22⋊C8—591no—
228C22⋊C8—591no—
229#97—591no—
230#41—2364no—
231C2×Q8—1181no—
232C2×Q8C22×D5911yescharacteristic
233C2×D4—591no—
234C2×D4—1181no—
235C2×D4—1181no—
236C2×D4C22⋊D5911yescharacteristic
237C22×C4—21no—
238C22×C4—1181no—
239C22×C4—1181no—
240C22×C4—1181no—
241C22×C4C22×D5911yescharacteristic
242C22×C4C22×D5911yescharacteristic
243SD16—1182no—
244M16—1182no—
245C2×C8—591no—
246C2×C8—591no—
247C2×C8—591no—
248C2×C8—591no—
249C2×C8—1182no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—591no—
257C4⋊C4—591no—
258C4⋊C4—591no—
259C4⋊C4—1181no—
260C4⋊C4—1181no—
261C4⋊C4—1181no—
262C4⋊C4C22⋊D5911yescharacteristic
263C4⋊C4C22×D5911yescharacteristic
264C4⋊C4C22×D5911yescharacteristic
265C4⋊C4C22×D5911yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—1181no—
270C22⋊C4—1181no—
271C22⋊C4—1181no—
272C22⋊C4C22⋊D5911yescharacteristic
273C22⋊C4C22⋊D5911yescharacteristic
274C42—21no—
275C42—21no—
276C42C22×D5911yescharacteristic
277C23—1181no—
278C23C2×C22⋊D5911yescharacteristic
279C23C2×C22⋊D5911yescharacteristic
280Q8—21no—
281Q8—21no—
282Q8—2362no—
283D4—22no—
284D4—1181no—
285D4—1181no—
286D4—2362no—
287D4—2362no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—42no—
297C2×C4—1181no—
298C2×C4—1181no—
299C2×C4—1181no—
300C2×C4—2362no—
301C2×C4—2362no—
302C2×C4—2362no—
303C2×C4C2×C22⋊D5911yescharacteristic
304C2×C4C2×C22⋊D5911yescharacteristic
305C2×C4C2×C22⋊D5911yescharacteristic
306C2×C4C2×C22⋊D5911yescharacteristic
307C2×C4C23×D5911yescharacteristic
308C8—592no—
309C8—1181no—
310C8—1181no—
311C8—1181no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—2361no—
318C22—2361no—
319C22—2361no—
320C22#1427375212yes—
321C22C22×C22⋊D5911yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—2361no—
331C4—2361no—
332C4—2361no—
333C4#41×D5911yescharacteristic
334C4#1427377411yescharacteristic
335C2—22no—
336C2—41no—
337C2—4721no—
338C2#1683805111yescharacteristic
339C2C2×#1427375211yescharacteristic
340C2#1683821711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#552C2
socleC22×C59C22×D4
hypercenter#552D59
hypocenterC59#3343
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #16837812C2semidirect
3. #16837735C2semidirect
4. #16837730C2semidirect
5. #16837726C2semidirect
6. #16837715C2semidirect
7. #16837699C2semidirect
8. #16837697C2semidirect
9. #16837650C2semidirect
10. #16837633C2semidirect
11. #16837500C2semidirect
12. #16837474C2semidirect
13. #16837445C2semidirect
14. C2×#14273660C2semidirect
15. C59×#552C2semidirect
140. C59⋊C8#41semidirect
171. #552D59semidirect
186. C59#3343semidirect