Finite Group Databasebeta

← #21437180

Subgroups — #21437180

Order 7552.

380 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838137C211yesmaximal, characteristic, complemented
2#16837792C211yesmaximal, characteristic, complemented
3#16837789C211yesmaximal, characteristic, complemented
4#16837784C211yesmaximal, characteristic, complemented
5#16837624C211yesmaximal, characteristic, complemented
6#16837621C211yesmaximal, characteristic, complemented
7#16837617C211yesmaximal, characteristic, complemented
8#16837614C211yesmaximal, characteristic, complemented
9#16837597C211yesmaximal, characteristic, complemented
10#16837594C211yesmaximal, characteristic, complemented
11#16837533C211yesmaximal, characteristic, complemented
12#16837502C211yesmaximal, characteristic, complemented
13#16837500C211yesmaximal, characteristic, complemented
14C4×#11745669C211yesmaximal, characteristic, complemented
15C59×#559C211yesmaximal, characteristic, complemented
16C2×#11745672C2211yescharacteristic
17C2×#11745670C2211yescharacteristic
18C2×#11745670C2211yescharacteristic
19C2×#11745671C2211yescharacteristic
20C2×#11745671C2211yescharacteristic
21C2×#11745669C2211yescharacteristic
22C2×#11745669C2211yescharacteristic
23C2×#11745669C2211yescharacteristic
24C2×#11745669C2211yescharacteristic
25#14273724C2211yescharacteristic
26#14273716—21no—
27#14273715C2211yescharacteristic
28#14273715C2211yescharacteristic
29#14273712—21no—
30#14273712—21no—
31C4×Dic118C2211yescharacteristic
32C4×D236C2211yescharacteristic
33C4×D236C2211yescharacteristic
34#14273689—21no—
35#14273660C2211yescharacteristic
36C4⋊(C59⋊C8)C2211yescharacteristic
37C4⋊(C59⋊C8)C2211yescharacteristic
38C4⋊(C59⋊C8)C2211yescharacteristic
39#14273651C2211yescharacteristic
40#14273650C2211yescharacteristic
41#14273648C2211yescharacteristic
42#14273648C2211yescharacteristic
43#14273647C2211yescharacteristic
44#14273647C2211yescharacteristic
45#14273638C2211yescharacteristic
46#14273638C2211yescharacteristic
47C4×C59⋊C8C2211yescharacteristic
48#127×C59C2211yescharacteristic
49#124×C59—21no—
50#124×C59C2211yescharacteristic
51#124×C59C2211yescharacteristic
52#123×C59—21no—
53#123×C59—21no—
54C4×Q8×C59C2211yescharacteristic
55C4×Q8×C59C2211yescharacteristic
56C4×D4×C59—21no—
57C4×D4×C59C2211yescharacteristic
58C4×D4×C59C2211yescharacteristic
59C2×Q8×C59D411yescharacteristic
60C2×Q8×C59C2311yescharacteristic
61C2×D4×C59—21no—
62C2×D4×C59—21no—
63C2×D4×C59C2311yescharacteristic
64C2×D4×C59C2311yescharacteristic
65C22×C4×C59—21no—
66C22×C4×C59—21no—
67C2×D236—21no—
68C2×D236—21no—
69C2×D236C2311yescharacteristic
70C2×D236C2311yescharacteristic
71C2×C4×D59—21no—
72C2×C4×D59—21no—
73C2×Dic118C2311yescharacteristic
74C4⋊C4×C59—21no—
75C4⋊C4×C59D411yescharacteristic
76C4⋊C4×C59D411yescharacteristic
77C4⋊C4×C59D411yescharacteristic
78C4⋊C4×C59C2311yescharacteristic
79C22⋊C4×C59—21no—
80C22⋊C4×C59—21no—
81C22⋊C4×C59—21no—
82C22⋊C4×C59—21no—
83C22⋊C4×C59—21no—
84C22⋊C4×C59—21no—
85C42×C59—21no—
86C42×C59C2311yescharacteristic
87C42×C59C2311yescharacteristic
88C42×C59C2311yescharacteristic
89#11745672—41no—
90#11745671—22no—
91#11745671—41no—
92#11745670—22no—
93#11745670—41no—
94#11745669—22no—
95#11745669—41no—
96#11745669—41no—
97#11745669—41no—
98(C2×D59)⋊C4—21no—
99(C2×D59)⋊C4—21no—
100(C2×D59)⋊C4—21no—
101(C2×D59)⋊C4—21no—
102(C2×D59)⋊C4—21no—
103(C2×D59)⋊C4—21no—
104C4⋊Dic59C2311yescharacteristic
105Dic59⋊C4—21no—
106C4×Dic59—21no—
107C2×C59⋊C8C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110C2×C59⋊C8C2311yescharacteristic
111C23×C59—21no—
112C23×C59—21no—
113C22×D59—21no—
114C22×D59—21no—
115Q8×C59—21no—
116Q8×C59—21no—
117Q8×C59—41no—
118D4×C59—21no—
119D4×C59—21no—
120D4×C59—21no—
121D4×C59—21no—
122D4×C59—42no—
123D4×C59—81no—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—81no—
127C2×C4×C59—81no—
128C2×C4×C59C2×D411yescharacteristic
129C2×C4×C59C2×D411yescharacteristic
130C2×C4×C59C2×D411yescharacteristic
131C2×C4×C59C2×D411yescharacteristic
132C2×C4×C59C2×D411yescharacteristic
133C2×C4×C59C2×D411yescharacteristic
134C2×C4×C59C2411yescharacteristic
135C2×Dic59—21no—
136C2×Dic59—21no—
137D236—21no—
138D236—21no—
139D236—21no—
140D236—21no—
141D236—42no—
142D236—81no—
143C4×D59—81no—
144C4×D59—81no—
145Dic118—21no—
146Dic118—21no—
147C59⋊C8—21no—
148C59⋊C8—21no—
149C59⋊C8—21no—
150C59⋊C8#4112yes—
151C22×C59—41no—
152C22×C59—41no—
153C22×C59—41no—
154C22×C59—41no—
155C22×C59—41no—
156C22×C59—41no—
157C22×C59C22×D411yescharacteristic
158C2×D59—41no—
159C2×D59—41no—
160C2×D59—41no—
161C2×D59—41no—
162C2×D59—41no—
163C2×D59—41no—
164C4×C59—21no—
165C4×C59—21no—
166C4×C59—21no—
167C4×C59—21no—
168C4×C59—21no—
169C4×C59—21no—
170C4×C59—41no—
171C4×C59—41no—
172C4×C59C2×#4111yescharacteristic
173C4×C59H(5,𝔽2)11yescharacteristic
174Dic59—41no—
175Dic59—41no—
176#3403—591nomaximal, Sylow
177C2×C59—81no—
178C2×C59—81no—
179C2×C59#55011yescharacteristic
180C2×C59#57511yescharacteristic
181C2×C59#57611yescharacteristic
182D59—81no—
183D59—81no—
184#559—591no—
185#559D5911yescharacteristic, complemented
186#496—591no—
187#496—591no—
188#495—591no—
189#464—591no—
190#464—591no—
191#463—591no—
192#463—591no—
193#459—591no—
194#459—591no—
195#446—591no—
196#440—591no—
197#440—591no—
198C4×D8—591no—
199C59#340311yescharacteristic, complemented, Sylow
200C2×Q16—591no—
201C2×SD16—591no—
202C2×SD16—591no—
203C2×SD16—591no—
204C2×SD16—591no—
205C2×D8—591no—
206C2×D8—591no—
207C2×D8—591no—
208C2×D8—591no—
209#127—591no—
210#127C2×D5911yescharacteristic
211#124—21no—
212#124—591no—
213#124—591no—
214#124—1181no—
215#124C2×D5911yescharacteristic
216#124C2×D5911yescharacteristic
217#123—21no—
218#123—21no—
219#123—1181no—
220#123—1181no—
221C4×Q8—591no—
222C4×Q8C2×D5911yescharacteristic
223C4×Q8C2×D5911yescharacteristic
224C4×D4—21no—
225C4×D4—591no—
226C4×D4—591no—
227C4×D4—1181no—
228C4×D4C2×D5911yescharacteristic
229C4×D4C2×D5911yescharacteristic
230#107—591no—
231C4⋊C8—591no—
232C4⋊C8—591no—
233C4⋊C8—591no—
234#103—591no—
235#103—591no—
236#102—591no—
237#102—591no—
238#102—591no—
239#102—591no—
240#97—591no—
241#97—591no—
242C4×C8—591no—
243C2×Q8—591no—
244C2×Q8C22⋊D5911yescharacteristic
245C2×Q8C22×D5911yescharacteristic
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—591no—
249C2×D4—591no—
250C2×D4—1181no—
251C2×D4—1181no—
252C2×D4C22×D5911yescharacteristic
253C2×D4C22×D5911yescharacteristic
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—1181no—
257C22×C4—1181no—
258Q16—2361no—
259SD16—1182no—
260SD16—1182no—
261SD16—2361no—
262SD16—2361no—
263D8—1182no—
264D8—2361no—
265D8—2361no—
266D8—2361no—
267C2×C8—591no—
268C2×C8—591no—
269C2×C8—591no—
270C2×C8—591no—
271C4⋊C4—21no—
272C4⋊C4—591no—
273C4⋊C4—1181no—
274C4⋊C4C22⋊D5911yescharacteristic
275C4⋊C4C22⋊D5911yescharacteristic
276C4⋊C4C22⋊D5911yescharacteristic
277C4⋊C4C22×D5911yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—1181no—
285C22⋊C4—1181no—
286C22⋊C4—1181no—
287C22⋊C4—1181no—
288C22⋊C4—1181no—
289C22⋊C4—1181no—
290C42—21no—
291C42—1181no—
292C42C22×D5911yescharacteristic
293C42C22×D5911yescharacteristic
294C42C22×D5911yescharacteristic
295C23—21no—
296C23—21no—
297C23—1181no—
298C23—1181no—
299Q8—21no—
300Q8—21no—
301Q8—41no—
302Q8—1181no—
303Q8—1181no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—81no—
310D4—1181no—
311D4—1181no—
312D4—1181no—
313D4—1181no—
314D4—4721no—
315D4—2362no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—1181no—
321C2×C4—1181no—
322C2×C4—4721no—
323C2×C4—4721no—
324C2×C4C2×C22⋊D5911yescharacteristic
325C2×C4C2×C22⋊D5911yescharacteristic
326C2×C4C2×C22⋊D5911yescharacteristic
327C2×C4C2×C22⋊D5911yescharacteristic
328C2×C4C2×C22⋊D5911yescharacteristic
329C2×C4C2×C22⋊D5911yescharacteristic
330C2×C4C23×D5911yescharacteristic
331C8—592no—
332C8—1181no—
333C8—1181no—
334C8—1181no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—2361no—
342C22—2361no—
343C22—2361no—
344C22—2361no—
345C22—2361no—
346C22—2361no—
347C22C22×C22⋊D5911yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—2361no—
357C4—2361no—
358C4#41×D5911yescharacteristic
359C4#1427377311yescharacteristic
360C2—81no—
361C2—81no—
362C2—4721no—
363C2—4721no—
364C2#1683807111yescharacteristic
365C2#1683820011yescharacteristic
366C2#1683820511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#559C2
socleC22×C59C22×D4
hypercenter#559D59
hypocenterC59#3403
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #559

Complements

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

NH ≅ G/Ntype
1. #16838137C2semidirect
2. #16837792C2semidirect
3. #16837789C2semidirect
4. #16837784C2semidirect
5. #16837624C2semidirect
6. #16837621C2semidirect
7. #16837617C2semidirect
8. #16837614C2semidirect
9. #16837597C2semidirect
10. #16837594C2semidirect
11. #16837533C2semidirect
12. #16837502C2semidirect
13. #16837500C2semidirect
14. C4×#11745669C2semidirect
15. C59×#559C2semidirect
185. #559D59semidirect
199. C59#3403semidirect