Finite Group Databasebeta

← #21436081

Subgroups — #21436081

Order 7552.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838061C211yesmaximal, characteristic, complemented
2#16837764C211yesmaximal, characteristic, complemented
3#16837737C211yesmaximal, characteristic, complemented
4#16837715C211yesmaximal, characteristic, complemented
5#16837694C211yesmaximal, characteristic, complemented
6#16837646C211yesmaximal, characteristic, complemented
7#16837636C211yesmaximal, characteristic, complemented
8#16837617C211yesmaximal, characteristic, complemented
9#16837545C211yesmaximal, characteristic, complemented
10#16837540C211yesmaximal, characteristic, complemented
11#16837502C211yesmaximal, characteristic, complemented
12#16837474C211yesmaximal, characteristic, complemented
13#16837401C211yesmaximal, characteristic, complemented
14C2×#14273650C211yesmaximal, characteristic, complemented
15C59×#547C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C22×Dic118C2211yescharacteristic
18C2×#11745670C2211yescharacteristic
19C2×#11745670C2211yescharacteristic
20C2×#11745669C2211yescharacteristic
21C2×#11745664C2211yescharacteristic
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#14273660C2211yescharacteristic
34C4⋊(C59⋊C8)C2211yescharacteristic
35#14273650C2211yescharacteristic
36#14273650C2211yescharacteristic
37#14273650C2211yescharacteristic
38#14273650C2211yescharacteristic
39#14273650C2211yescharacteristic
40#14273650C2211yescharacteristic
41#14273648C2211yescharacteristic
42#14273647C2211yescharacteristic
43#14273647C2211yescharacteristic
44#14273647C2211yescharacteristic
45C22⋊(C59⋊C8)C2211yescharacteristic
46C22⋊(C59⋊C8)C2211yescharacteristic
47#14273638C2211yescharacteristic
48C2×#41×C59—21no—
49C4⋊Q8×C59C2211yescharacteristic
50#123×C59—21no—
51#123×C59—21no—
52C22⋊Q8×C59—21no—
53#121×C59C2211yescharacteristic
54#121×C59C2211yescharacteristic
55C4×D4×C59C2211yescharacteristic
56C4×D4×C59C2211yescharacteristic
57C2×C4⋊C4×C59C2211yescharacteristic
58C2×C4⋊C4×C59C2211yescharacteristic
59#41×C59—44no—
60C2×Q8×C59—21no—
61C2×D4×C59—21no—
62C2×D4×C59—21no—
63C2×D4×C59D411yescharacteristic
64C2×D4×C59C2311yescharacteristic
65C22×C4×C59—21no—
66C22×C4×C59—21no—
67C22×C4×C59—21no—
68C22×C4×C59C2311yescharacteristic
69C22×C4×C59C2311yescharacteristic
70C2×C22⋊D59—21no—
71C2×C22⋊D59—21no—
72C22×Dic59—21no—
73#11745685—22no—
74#11745685—41no—
75C2×D236C2311yescharacteristic
76C2×C4×D59—21no—
77C2×Dic118—22no—
78C2×Dic118—21no—
79C2×Dic118—41no—
80C2×Dic118C2311yescharacteristic
81C2×Dic118C2311yescharacteristic
82C4⋊C4×C59—21no—
83C4⋊C4×C59—21no—
84C4⋊C4×C59—21no—
85C4⋊C4×C59D411yescharacteristic
86C4⋊C4×C59C2311yescharacteristic
87C4⋊C4×C59C2311yescharacteristic
88C4⋊C4×C59C2311yescharacteristic
89C22⋊C4×C59—21no—
90C22⋊C4×C59—21no—
91C22⋊C4×C59—21no—
92C22⋊C4×C59D411yescharacteristic
93C22⋊C4×C59D411yescharacteristic
94C42×C59C2311yescharacteristic
95C22⋊Dic59—21no—
96#11745670—22no—
97#11745670—41no—
98#11745669—41no—
99(C2×D59)⋊C4—21no—
100(C2×D59)⋊C4—21no—
101(C2×D59)⋊C4—21no—
102C4⋊Dic59C2311yescharacteristic
103Dic59⋊C4—21no—
104Dic59⋊C4—21no—
105C4×Dic59—21no—
106#11745664—41no—
107C2×C59⋊C8—41no—
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110C2×C59⋊C8C2311yescharacteristic
111C2×C59⋊C8C2311yescharacteristic
112C23×C59—21no—
113C23×C59C2×D411yescharacteristic
114C23×C59C2×D411yescharacteristic
115C22×D59—21no—
116Q8×C59—42no—
117D4×C59—22no—
118D4×C59—21no—
119D4×C59—21no—
120D4×C59—42no—
121D4×C59—42no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—42no—
130C2×C4×C59—42no—
131C2×C4×C59—42no—
132C2×C4×C59C2×D411yescharacteristic
133C2×C4×C59C2×D411yescharacteristic
134C2×C4×C59C2×D411yescharacteristic
135C2×C4×C59C2×D411yescharacteristic
136C2×C4×C59C2411yescharacteristic
137C22⋊D59—42no—
138C22⋊D59—42no—
139C2×Dic59—21no—
140C2×Dic59—21no—
141C2×Dic59—21no—
142C2×Dic59—42no—
143D236—21no—
144D236—21no—
145C4×D59—42no—
146Dic118—21no—
147Dic118—21no—
148Dic118—21no—
149Dic118—42no—
150Dic118#4112yescomplemented
151C59⋊C8—21no—
152C59⋊C8—21no—
153C59⋊C8—21no—
154C59⋊C8—21no—
155C22×C59—21no—
156C22×C59—21no—
157C22×C59—21no—
158C22×C59—21no—
159C22×C59—21no—
160C22×C59—41no—
161C22×C59—41no—
162C22×C59—41no—
163C22×C59AGL(1,ℤ/8)12yes—
164C22×C59C22×D411yescharacteristic
165C2×D59—41no—
166C2×D59—41no—
167C2×D59—41no—
168C4×C59—21no—
169C4×C59—21no—
170C4×C59—21no—
171C4×C59—21no—
172C4×C59—41no—
173C4×C59—41no—
174C4×C59—41no—
175C4×C59C2×#4111yescharacteristic
176C4×C59H(5,𝔽2)11yescharacteristic
177Dic59—22no—
178Dic59—41no—
179Dic59—41no—
180#3308—591nomaximal, Sylow
181C2×C59—22no—
182C2×C59—41no—
183C2×C59—81no—
184C2×C59#54611yescharacteristic
185C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
186C2×C59#57811yescharacteristic
187D59—81no—
188#548—591no—
189#547D5911yescharacteristic, complemented
190#489—591no—
191#484—591no—
192#480—591no—
193#477—591no—
194#468—591no—
195#466—591no—
196#463—591no—
197#449—591no—
198#448—591no—
199#440—591no—
200#435—591no—
201#417—591no—
202C2×#103—591no—
203C59#330811yescharacteristic, complemented, Sylow
204C2×#41—21no—
205C2×#41—591no—
206C22×Q8—591no—
207C2×SD16—591no—
208C2×SD16—591no—
209C2×D8—591no—
210C2×M16—591no—
211C22×C8—591no—
212C4⋊Q8C2×D5911yescharacteristic
213#124—591no—
214#124—1181no—
215#123—21no—
216#123—21no—
217C22⋊Q8—21no—
218C22⋊Q8—591no—
219C22⋊Q8—1181no—
220#121—591no—
221#121—1181no—
222#121C2×D5911yescharacteristic
223#121C2×D5911yescharacteristic
224C4×Q8—591no—
225C4×D4—1181no—
226C4×D4C2×D5911yescharacteristic
227C4×D4C2×D5911yescharacteristic
228C2×C4⋊C4C2×D5911yescharacteristic
229C2×C4⋊C4C2×D5911yescharacteristic
230#107—591no—
231#107—591no—
232#107—591no—
233C4⋊C8—591no—
234#103—591no—
235#103—591no—
236#103—591no—
237#103—591no—
238#103—591no—
239#103—591no—
240#102—591no—
241#102—591no—
242#102—591no—
243#102—591no—
244C22⋊C8—591no—
245C22⋊C8—591no—
246#97—591no—
247#41—44no—
248#41—1182no—
249#41—2361no—
250C2×Q8—21no—
251C2×Q8—591no—
252C2×Q8—591no—
253C2×Q8—1182no—
254C2×Q8—1181no—
255C2×Q8—2361no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—591no—
259C2×D4—1181no—
260C2×D4—1181no—
261C2×D4C22⋊D5911yescharacteristic
262C2×D4C22×D5911yescharacteristic
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—1181no—
267C22×C4—1181no—
268C22×C4C22×D5911yescharacteristic
269C22×C4C22×D5911yescharacteristic
270SD16—1182no—
271SD16—2361no—
272D8—2361no—
273M16—2361no—
274C2×C8—591no—
275C2×C8—591no—
276C2×C8—591no—
277C2×C8—591no—
278C2×C8—2361no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—591no—
283C4⋊C4—1181no—
284C4⋊C4—1181no—
285C4⋊C4C22⋊D5911yescharacteristic
286C4⋊C4C22×D5911yescharacteristic
287C4⋊C4C22×D5911yescharacteristic
288C4⋊C4C22×D5911yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—1181no—
293C22⋊C4—1181no—
294C22⋊C4—1181no—
295C22⋊C4—1181no—
296C22⋊C4C22⋊D5911yescharacteristic
297C22⋊C4C22⋊D5911yescharacteristic
298C42—1181no—
299C42C22×D5911yescharacteristic
300C23—21no—
301C23—1181no—
302C23C2×C22⋊D5911yescharacteristic
303C23C2×C22⋊D5911yescharacteristic
304Q8—42no—
305Q8—592no—
306Q8—1181no—
307Q8—1181no—
308Q8—1181no—
309Q8—2362no—
310D4—22no—
311D4—21no—
312D4—21no—
313D4—42no—
314D4—42no—
315D4—1181no—
316D4—1181no—
317D4—2362no—
318D4—2362no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—1181no—
330C2×C4—1181no—
331C2×C4—1181no—
332C2×C4—2362no—
333C2×C4—2362no—
334C2×C4C2×C22⋊D5911yescharacteristic
335C2×C4C2×C22⋊D5911yescharacteristic
336C2×C4C2×C22⋊D5911yescharacteristic
337C2×C4C2×C22⋊D5911yescharacteristic
338C2×C4C23×D5911yescharacteristic
339C8—1181no—
340C8—1181no—
341C8—1181no—
342C8—1181no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—2361no—
352C22—2361no—
353C22—2361no—
354C22#1427375312yes—
355C22C22×C22⋊D5911yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—41no—
363C4—1182no—
364C4—2361no—
365C4—2361no—
366C4#41×D5911yescharacteristic
367C4#1427377311yescharacteristic
368C2—22no—
369C2—41no—
370C2—81no—
371C2—4721no—
372C2#1683804011yescharacteristic
373C2C2×#1427375311yescharacteristic
374C2#1683821711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#547C2
socleC22×C59C22×D4
hypercenter#547D59
hypocenterC59#3308
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #16838061C2semidirect
2. #16837764C2semidirect
3. #16837737C2semidirect
4. #16837715C2semidirect
5. #16837694C2semidirect
6. #16837646C2semidirect
7. #16837636C2semidirect
8. #16837617C2semidirect
9. #16837545C2semidirect
10. #16837540C2semidirect
11. #16837502C2semidirect
12. #16837474C2semidirect
13. #16837401C2semidirect
14. C2×#14273650C2semidirect
15. C59×#547C2semidirect
150. Dic118#41semidirect
189. #547D59semidirect
203. C59#3308semidirect