Finite Group Databasebeta

← #21435977

Subgroups — #21435977

Order 7552.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838061C211yesmaximal, characteristic
2#16837759C211yesmaximal, characteristic, complemented
3#16837743C211yesmaximal, characteristic, complemented
4#16837715C211yesmaximal, characteristic, complemented
5#16837706C211yesmaximal, characteristic, complemented
6#16837641C211yesmaximal, characteristic, complemented
7#16837633C211yesmaximal, characteristic, complemented
8#16837624C211yesmaximal, characteristic, complemented
9#16837562C211yesmaximal, characteristic, complemented
10#16837557C211yesmaximal, characteristic, complemented
11C4×#11745672C211yesmaximal, characteristic, complemented
12D4×C59⋊C8C211yesmaximal, characteristic, complemented
13#16837396C211yesmaximal, characteristic, complemented
14C2×#14273650C211yesmaximal, characteristic, complemented
15C59×#552C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C22×Dic118C2211yescharacteristic
18C2×#11745672C2211yescharacteristic
19C2×#11745672C2211yescharacteristic
20C2×#11745671C2211yescharacteristic
21C22×C59⋊C8C2211yescharacteristic
22C22×C59⋊C8C2211yescharacteristic
23#14273715C2211yescharacteristic
24#14273713—21no—
25#14273706C2211yescharacteristic
26#14273705—21no—
27#14273701C2211yescharacteristic
28#14273699—21no—
29C4×Dic118C2211yescharacteristic
30(C22⋊D59)⋊C4—21no—
31#14273660C2211yescharacteristic
32#14273660C2211yescharacteristic
33#14273658C2211yescharacteristic
34C4⋊(C59⋊C8)C2211yescharacteristic
35#14273651C2211yescharacteristic
36#14273650C2211yescharacteristic
37#14273650C2211yescharacteristic
38#14273650C2211yescharacteristic
39#14273650C2211yescharacteristic
40#14273650C2211yescharacteristic
41#14273650C2211yescharacteristic
42#14273647C2211yescharacteristic
43#14273647C2211yescharacteristic
44#14273647C2211yescharacteristic
45C22⋊(C59⋊C8)C2211yescharacteristic
46C22⋊(C59⋊C8)C2211yescharacteristic
47C4×C59⋊C8C2211yescharacteristic
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—
67#11745685—22no—
68#11745685—41no—
69C2×D236C2311yescharacteristic
70C2×C4×D59—21no—
71C2×Dic118—22no—
72C2×Dic118—21no—
73C2×Dic118—41no—
74C2×Dic118C2311yescharacteristic
75C2×Dic118C2311yescharacteristic
76C4⋊C4×C59—21no—
77C4⋊C4×C59—21no—
78C4⋊C4×C59—21no—
79C4⋊C4×C59—21no—
80C4⋊C4×C59—21no—
81C4⋊C4×C59—21no—
82C4⋊C4×C59D411yescharacteristic
83C4⋊C4×C59C2311yescharacteristic
84C4⋊C4×C59C2311yescharacteristic
85C4⋊C4×C59C2311yescharacteristic
86C22⋊C4×C59—21no—
87C22⋊C4×C59—21no—
88C22⋊C4×C59—21no—
89C22⋊C4×C59D411yescharacteristic
90C22⋊C4×C59D411yescharacteristic
91C42×C59—21no—
92C42×C59—21no—
93C42×C59C2311yescharacteristic
94C22⋊Dic59—21no—
95#11745672—22no—
96#11745672—41no—
97#11745671—41no—
98(C2×D59)⋊C4—21no—
99(C2×D59)⋊C4—21no—
100(C2×D59)⋊C4—21no—
101C4⋊Dic59C2311yescharacteristic
102Dic59⋊C4—21no—
103Dic59⋊C4—21no—
104C4×Dic59—21no—
105C2×C59⋊C8—41no—
106C2×C59⋊C8—41no—
107C2×C59⋊C8C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110C2×C59⋊C8C2311yescharacteristic
111C23×C59C2×D411yescharacteristic
112C23×C59C2×D411yescharacteristic
113C22×D59—21no—
114Q8×C59—21no—
115Q8×C59—21no—
116D4×C59—22no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59—42no—
126C2×C4×C59C2×D411yescharacteristic
127C2×C4×C59C2×D411yescharacteristic
128C2×C4×C59C2×D411yescharacteristic
129C2×C4×C59C2×D411yescharacteristic
130C2×C4×C59C2411yescharacteristic
131C22⋊D59—42no—
132C22⋊D59—42no—
133C2×Dic59—21no—
134C2×Dic59—21no—
135C2×Dic59—21no—
136C2×Dic59—42no—
137D236—21no—
138D236—21no—
139C4×D59—42no—
140Dic118—21no—
141Dic118—21no—
142Dic118—21no—
143Dic118—42no—
144Dic118#4112yes—
145C59⋊C8—21no—
146C59⋊C8—21no—
147C59⋊C8—21no—
148C59⋊C8—21no—
149C22×C59—21no—
150C22×C59—21no—
151C22×C59—21no—
152C22×C59—21no—
153C22×C59—21no—
154C22×C59#13512yes—
155C22×C59C22×D411yescharacteristic
156C2×D59—41no—
157C2×D59—41no—
158C2×D59—41no—
159C4×C59—21no—
160C4×C59—21no—
161C4×C59—21no—
162C4×C59—21no—
163C4×C59—41no—
164C4×C59—41no—
165C4×C59—41no—
166C4×C59—41no—
167C4×C59C2×#4111yescharacteristic
168C4×C59H(5,𝔽2)11yescharacteristic
169Dic59—22no—
170Dic59—41no—
171Dic59—41no—
172#3300—591nomaximal, Sylow
173C2×C59—22no—
174C2×C59—41no—
175C2×C59#54611yescharacteristic
176C2×C59C2×#13511yescharacteristic
177C2×C59#57811yescharacteristic
178D59—81no—
179#552D5911yescharacteristic, complemented
180#548—591no—
181#488—591no—
182#485—591no—
183#480—591no—
184#479—591no—
185#467—591no—
186#465—591no—
187#464—591no—
188#452—591no—
189#451—591no—
190C4×Q16—591no—
191C8×D4—591no—
192#416—591no—
193C2×#103—591no—
194C59#330011yescharacteristic, complemented, Sylow
195C2×#41—591no—
196C22×Q8—591no—
197C2×Q16—591no—
198C2×Q16—591no—
199C2×SD16—591no—
200C22×C8—591no—
201C22×C8—591no—
202#126—21no—
203#125—21no—
204#125C2×D5911yescharacteristic
205#124—591no—
206#124—1181no—
207#123—21no—
208C22⋊Q8—591no—
209C22⋊Q8—1181no—
210C22⋊Q8C2×D5911yescharacteristic
211C22⋊Q8C2×D5911yescharacteristic
212#121—591no—
213#121—1181no—
214C4×Q8—591no—
215C4×Q8C2×D5911yescharacteristic
216C4×D4—1181no—
217C4×D4C2×D5911yescharacteristic
218#117—21no—
219#117C2×D5911yescharacteristic
220C2×C4⋊C4C2×D5911yescharacteristic
221#107—591no—
222#107—591no—
223#106—591no—
224C4⋊C8—591no—
225#103—591no—
226#103—591no—
227#103—591no—
228#103—591no—
229#103—591no—
230#103—591no—
231#103—591no—
232#102—591no—
233#102—591no—
234#102—591no—
235C22⋊C8—591no—
236C22⋊C8—591no—
237C4×C8—591no—
238#41—1182no—
239#41—2361no—
240C2×Q8—591no—
241C2×Q8—591no—
242C2×Q8—1182no—
243C2×Q8—1181no—
244C2×Q8—2361no—
245C2×Q8C22×D5911yescharacteristic
246C2×D4—591no—
247C2×D4—1181no—
248C2×D4—1181no—
249C2×D4C22⋊D5911yescharacteristic
250C22×C4—21no—
251C22×C4—1181no—
252C22×C4—1181no—
253C22×C4C22×D5911yescharacteristic
254C22×C4C22×D5911yescharacteristic
255Q16—1182no—
256Q16—2361no—
257SD16—2361no—
258C2×C8—591no—
259C2×C8—591no—
260C2×C8—591no—
261C2×C8—591no—
262C2×C8—2361no—
263C2×C8—2361no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—591no—
271C4⋊C4—1181no—
272C4⋊C4—1181no—
273C4⋊C4C22⋊D5911yescharacteristic
274C4⋊C4C22×D5911yescharacteristic
275C4⋊C4C22×D5911yescharacteristic
276C4⋊C4C22×D5911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—1181no—
281C22⋊C4—1181no—
282C22⋊C4—1181no—
283C22⋊C4—1181no—
284C22⋊C4C22⋊D5911yescharacteristic
285C22⋊C4C22⋊D5911yescharacteristic
286C42—21no—
287C42—21no—
288C42—1181no—
289C42C22×D5911yescharacteristic
290C23—1181no—
291C23C2×C22⋊D5911yescharacteristic
292C23C2×C22⋊D5911yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—592no—
296Q8—1181no—
297Q8—1181no—
298Q8—1181no—
299Q8—2362no—
300D4—22no—
301D4—1181no—
302D4—1181no—
303D4—2362no—
304D4—2362no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—1181no—
315C2×C4—1181no—
316C2×C4—1181no—
317C2×C4—2362no—
318C2×C4—2362no—
319C2×C4C2×C22⋊D5911yescharacteristic
320C2×C4C2×C22⋊D5911yescharacteristic
321C2×C4C2×C22⋊D5911yescharacteristic
322C2×C4C2×C22⋊D5911yescharacteristic
323C2×C4C23×D5911yescharacteristic
324C8—1181no—
325C8—1181no—
326C8—1181no—
327C8—1181no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—2361no—
334C22—2361no—
335C22—2361no—
336C22#1427374712yes—
337C22C22×C22⋊D5911yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—1182no—
347C4—2361no—
348C4—2361no—
349C4#41×D5911yescharacteristic
350C4#1427377311yescharacteristic
351C2—22no—
352C2—41no—
353C2—4721no—
354C2#1683804011yescharacteristic
355C2C2×#1427374711yescharacteristic
356C2#1683821711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#552C2
socleC22×C59C22×D4
hypercenter#552D59
hypocenterC59#3300
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. #16837759C2semidirect
3. #16837743C2semidirect
4. #16837715C2semidirect
5. #16837706C2semidirect
6. #16837641C2semidirect
7. #16837633C2semidirect
8. #16837624C2semidirect
9. #16837562C2semidirect
10. #16837557C2semidirect
11. C4×#11745672C2semidirect
12. D4×C59⋊C8C2semidirect
13. #16837396C2semidirect
14. C2×#14273650C2semidirect
15. C59×#552C2semidirect
179. #552D59semidirect
194. C59#3300semidirect