Finite Group Databasebeta

← #21436347

Subgroups — #21436347

Order 7552.

392 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838096C211yesmaximal, characteristic, complemented
2#16838058C211yesmaximal, characteristic, complemented
3#16837755C211yesmaximal, characteristic, complemented
4#16837734C211yesmaximal, characteristic, complemented
5#16837708C211yesmaximal, characteristic, complemented
6#16837653C211yesmaximal, characteristic, complemented
7#16837649C211yesmaximal, characteristic, complemented
8#16837616C211yesmaximal, characteristic, complemented
9#16837548C211yesmaximal, characteristic, complemented
10#16837543C211yesmaximal, characteristic, complemented
11#16837489C211yesmaximal, characteristic, complemented
12#16837477C211yesmaximal, characteristic, complemented
13#16837410C211yesmaximal, characteristic, complemented
14#16837400C211yesmaximal, characteristic, complemented
15C59×#482C211yesmaximal, characteristic, complemented
16C2×#11745687C2211yescharacteristic
17C22×Dic118C2211yescharacteristic
18C2×#11745660C2211yescharacteristic
19C2×#11745660C2211yescharacteristic
20C2×#11745669C2211yescharacteristic
21C2×#11745664C2211yescharacteristic
22C2×#11745659C2211yescharacteristic
23#14273721—21no—
24#14273718C2211yescharacteristic
25#14273714C2211yescharacteristic
26#14273713—21no—
27#14273709—21no—
28#14273707C2211yescharacteristic
29#14273704—21no—
30#14273702C2211yescharacteristic
31#14273701C2211yescharacteristic
32#14273700—21no—
33#14273699—21no—
34#14273692C2211yescharacteristic
35C4×D236—21no—
36D4×Dic59—21no—
37#14273689C2211yescharacteristic
38C4×C22⋊D59C2211yescharacteristic
39C4⋊C4×D59C2211yescharacteristic
40#14273658C2211yescharacteristic
41Dic59⋊C8C2211yescharacteristic
42#14273652C2211yescharacteristic
43#14273652C2211yescharacteristic
44#14273650C2211yescharacteristic
45#14273650C2211yescharacteristic
46#14273650C2211yescharacteristic
47#14273650C2211yescharacteristic
48#14273648C2211yescharacteristic
49#14273647C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51C8×Dic59C2211yescharacteristic
52#121×C59C2211yescharacteristic
53#117×C59C2211yescharacteristic
54#107×C59C2211yescharacteristic
55#106×C59C2211yescharacteristic
56#102×C59C2211yescharacteristic
57#102×C59C2211yescharacteristic
58C22⋊C8×C59C2211yescharacteristic
59C2×D4×C59—21no—
60C2×D4×C59C2311yescharacteristic
61C22×C4×C59C2311yescharacteristic
62C2×C22⋊D59—21no—
63C2×C22⋊D59—21no—
64C2×C22⋊D59D411yescharacteristic
65C22×Dic59—21no—
66C22×Dic59—21no—
67#11745687—22no—
68#11745687—41no—
69C2×D236—21no—
70C2×D236C2311yescharacteristic
71C2×C4×D59—21no—
72C2×C4×D59—21no—
73C2×C4×D59C2311yescharacteristic
74C2×Dic118—22no—
75C2×Dic118—21no—
76C2×Dic118—41no—
77C2×Dic118C2311yescharacteristic
78C2×Dic118C2311yescharacteristic
79C2×C8×C59C2311yescharacteristic
80C2×C8×C59C2311yescharacteristic
81C4⋊C4×C59C2311yescharacteristic
82C4⋊C4×C59C2311yescharacteristic
83C4⋊C4×C59C2311yescharacteristic
84C22⋊C4×C59—21no—
85C22⋊C4×C59—21no—
86C42×C59—21no—
87C22⋊Dic59—21no—
88C22⋊Dic59—21no—
89C22⋊Dic59D411yescharacteristic
90#11745669—41no—
91(C2×D59)⋊C4—21no—
92(C2×D59)⋊C4—21no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4—21no—
95(C2×D59)⋊C4D411yescharacteristic
96C4⋊Dic59—21no—
97C4⋊Dic59—21no—
98C4⋊Dic59C2311yescharacteristic
99Dic59⋊C4—21no—
100Dic59⋊C4—21no—
101Dic59⋊C4—21no—
102Dic59⋊C4D411yescharacteristic
103C4×Dic59—21no—
104C4×Dic59C2311yescharacteristic
105#11745664—41no—
106C2×C59⋊C8C2311yescharacteristic
107C2×C59⋊C8C2311yescharacteristic
108#11745660—22no—
109#11745660—41no—
110#11745659—41no—
111C23×C59—21no—
112C23×C59C2×D411yescharacteristic
113C22×D59—21no—
114C22×D59C2×D411yescharacteristic
115D4×C59—21no—
116D4×C59—21no—
117D4×C59—42no—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59C2×D411yescharacteristic
124C2×C4×C59C2411yescharacteristic
125C22⋊D59—41no—
126C22⋊D59—42no—
127C22⋊D59—81no—
128C2×Dic59—21no—
129C2×Dic59—21no—
130C2×Dic59—21no—
131C2×Dic59—42no—
132C2×Dic59—42no—
133C2×Dic59C2×D411yescharacteristic
134C2×Dic59C2×D411yescharacteristic
135C2×Dic59C2×D411yescharacteristic
136D236—21no—
137D236—21no—
138D236—42no—
139C4×D59—21no—
140C4×D59—21no—
141C4×D59—81no—
142C4×D59—81no—
143Dic118—21no—
144Dic118—21no—
145Dic118—21no—
146Dic118—42no—
147Dic118#4112yes—
148C8×C59—21no—
149C8×C59—21no—
150C59⋊C8—21no—
151C59⋊C8—21no—
152C22×C59—21no—
153C22×C59—21no—
154C22×C59—21no—
155C22×C59—41no—
156C22×C59—41no—
157C22×C59—41no—
158C22×C59C22×D411yescharacteristic
159C2×D59—21no—
160C2×D59—21no—
161C2×D59—21no—
162C2×D59—41no—
163C2×D59—41no—
164C2×D59—41no—
165C4×C59—21no—
166C4×C59—41no—
167C4×C59—41no—
168C4×C59—41no—
169C4×C59C2×#4111yescharacteristic
170C4×C59H(5,𝔽2)11yescharacteristic
171Dic59—22no—
172Dic59—21no—
173Dic59—21no—
174Dic59—21no—
175Dic59—41no—
176Dic59—41no—
177#3326—591nomaximal, Sylow
178C2×C59—41no—
179C2×C59—81no—
180C2×C59#54611yescharacteristic
181C2×C59#57511yescharacteristic
182C2×C59#57711yescharacteristic
183D59—41no—
184D59—81no—
185#553—591no—
186#548—591no—
187#488—591no—
188#483—591no—
189#482D5911yescharacteristic, complemented
190#479—591no—
191#469—591no—
192#468—591no—
193#463—591no—
194#449—591no—
195#448—591no—
196C4×SD16—591no—
197#436—591no—
198#419—591no—
199#417—591no—
200C59#332611yescharacteristic, complemented, Sylow
201C2×#41—591no—
202C22×Q8—591no—
203C2×SD16—591no—
204C2×SD16—591no—
205C2×D8—591no—
206C2×M16—591no—
207C2×M16—591no—
208#126—1181no—
209#125—591no—
210#124—591no—
211#124—1181no—
212#123—1181no—
213C22⋊Q8—591no—
214C22⋊Q8—1181no—
215#121—591no—
216#121—591no—
217#121—1181no—
218#121—1181no—
219#121C2×D5911yescharacteristic
220C4×Q8—591no—
221C4×D4—591no—
222C4×D4—591no—
223C4×D4—1181no—
224C4×D4—1181no—
225#117C2×D5911yescharacteristic
226C2×C4⋊C4—591no—
227#107C2×D5911yescharacteristic
228#106—591no—
229#106C2×D5911yescharacteristic
230C4⋊C8—591no—
231#103—591no—
232#103—591no—
233#103—591no—
234#103—591no—
235#103—591no—
236#103—591no—
237#102—591no—
238#102—591no—
239#102C2×D5911yescharacteristic
240#102C2×D5911yescharacteristic
241C22⋊C8—591no—
242C22⋊C8C2×D5911yescharacteristic
243C4×C8—591no—
244#41—1182no—
245#41—2361no—
246C2×Q8—591no—
247C2×Q8—591no—
248C2×Q8—1182no—
249C2×Q8—1181no—
250C2×Q8—2361no—
251C2×D4—21no—
252C2×D4—591no—
253C2×D4—591no—
254C2×D4—1181no—
255C2×D4—1181no—
256C2×D4—1181no—
257C2×D4C22×D5911yescharacteristic
258C22×C4—591no—
259C22×C4—1181no—
260C22×C4—1181no—
261C22×C4—1181no—
262C22×C4—1181no—
263C22×C4C22×D5911yescharacteristic
264SD16—1182no—
265SD16—2361no—
266D8—2361no—
267M16—2361no—
268M16—2361no—
269C2×C8—591no—
270C2×C8—591no—
271C2×C8C22×D5911yescharacteristic
272C2×C8C22×D5911yescharacteristic
273C4⋊C4—591no—
274C4⋊C4—591no—
275C4⋊C4—1181no—
276C4⋊C4—1181no—
277C4⋊C4—1181no—
278C4⋊C4—1181no—
279C4⋊C4—1181no—
280C4⋊C4C22×D5911yescharacteristic
281C4⋊C4C22×D5911yescharacteristic
282C4⋊C4C22×D5911yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—591no—
286C22⋊C4—591no—
287C22⋊C4—1181no—
288C22⋊C4—1181no—
289C22⋊C4—1181no—
290C22⋊C4—1181no—
291C22⋊C4—1181no—
292C22⋊C4—1181no—
293C42—21no—
294C42—591no—
295C42—1181no—
296C23—21no—
297C23—591no—
298C23—1181no—
299C23D4×D5911yescharacteristic
300Q8—592no—
301Q8—1181no—
302Q8—1181no—
303Q8—1181no—
304Q8—2362no—
305D4—21no—
306D4—21no—
307D4—42no—
308D4—1181no—
309D4—1181no—
310D4—4721no—
311D4—2362no—
312D4—2361no—
313D4—2362no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—591no—
320C2×C4—591no—
321C2×C4—591no—
322C2×C4—1181no—
323C2×C4—1181no—
324C2×C4—1181no—
325C2×C4—1181no—
326C2×C4—1181no—
327C2×C4—4721no—
328C2×C4—4721no—
329C2×C4—2362no—
330C2×C4—2362no—
331C2×C4D4×D5911yescharacteristic
332C2×C4C23×D5911yescharacteristic
333C8—21no—
334C8—21no—
335C8—1181no—
336C8—1181no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—1181no—
344C22—1181no—
345C22—1181no—
346C22—2361no—
347C22—2361no—
348C22—2361no—
349C22C2×D4×D5911yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—1181no—
355C4—1181no—
356C4—1181no—
357C4—1182no—
358C4—2361no—
359C4—2361no—
360C4#41×D5911yescharacteristic
361C4#1427377311yescharacteristic
362C2—41no—
363C2—81no—
364C2—4721no—
365C2—2361no—
366C2#1683804411yescharacteristic
367C2#1683819811yescharacteristic
368C2#1683820911yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#482C2
socleC22×C59C22×D4
hypercenter#482D59
hypocenterC59#3326
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #16838096C2semidirect
2. #16838058C2semidirect
3. #16837755C2semidirect
4. #16837734C2semidirect
5. #16837708C2semidirect
6. #16837653C2semidirect
7. #16837649C2semidirect
8. #16837616C2semidirect
9. #16837548C2semidirect
10. #16837543C2semidirect
11. #16837489C2semidirect
12. #16837477C2semidirect
13. #16837410C2semidirect
14. #16837400C2semidirect
15. C59×#482C2semidirect
189. #482D59semidirect
200. C59#3326semidirect