Finite Group Databasebeta

← #21436069

Subgroups — #21436069

Order 7552.

394 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#16838105C211yesmaximal, characteristic, complemented
2#16838056C211yesmaximal, characteristic, complemented
3#16837772C211yesmaximal, characteristic, complemented
4#16837745C211yesmaximal, characteristic, complemented
5#16837734C211yesmaximal, characteristic, complemented
6#16837649C211yesmaximal, characteristic, complemented
7#16837632C211yesmaximal, characteristic, complemented
8#16837608C211yesmaximal, characteristic, complemented
9#16837548C211yesmaximal, characteristic, complemented
10#16837548C211yesmaximal, characteristic, complemented
11#16837512C211yesmaximal, characteristic, complemented
12#16837472C211yesmaximal, characteristic, complemented
13#16837400C211yesmaximal, characteristic, complemented
14#16837395C211yesmaximal, characteristic, complemented
15C59×#478C211yesmaximal, characteristic, complemented
16C2×#11745687C2211yescharacteristic
17C2×#11745687C2211yescharacteristic
18C2×#11745660C2211yescharacteristic
19C2×#11745660C2211yescharacteristic
20C2×#11745669C2211yescharacteristic
21C2×#11745659C2211yescharacteristic
22C2×C8×D59C2211yescharacteristic
23#14273727C2211yescharacteristic
24#14273722—21no—
25#14273712—21no—
26#14273711—21no—
27#14273711—21no—
28#14273707C2211yescharacteristic
29#14273707C2211yescharacteristic
30#14273702—21no—
31#14273702C2211yescharacteristic
32#14273702C2211yescharacteristic
33#14273701—21no—
34C4×D236C2211yescharacteristic
35C4×D236C2211yescharacteristic
36#14273689—21no—
37#14273685C2211yescharacteristic
38C2×C4⋊Dic59—21no—
39C4⋊C4×D59C2211yescharacteristic
40#14273658C2211yescharacteristic
41#14273652C2211yescharacteristic
42#14273652C2211yescharacteristic
43#14273650C2211yescharacteristic
44#14273650C2211yescharacteristic
45#14273650C2211yescharacteristic
46#14273650C2211yescharacteristic
47#14273648C2211yescharacteristic
48#14273647C2211yescharacteristic
49(C2×D59)⋊C8C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51#14273638C2211yescharacteristic
52#125×C59C2211yescharacteristic
53C4×D4×C59C2211yescharacteristic
54#107×C59C2211yescharacteristic
55#106×C59C2211yescharacteristic
56C4⋊C8×C59C2211yescharacteristic
57#102×C59C2211yescharacteristic
58#102×C59C2211yescharacteristic
59C2×D4×C59C2311yescharacteristic
60C22×C4×C59—21no—
61C2×C22⋊D59—21no—
62C2×C22⋊D59—21no—
63C22×Dic59—21no—
64C22×Dic59—21no—
65#11745687—22no—
66#11745687—22no—
67#11745687—41no—
68#11745687—41no—
69C2×D236—21no—
70C2×D236—21no—
71C2×D236D411yescharacteristic
72C2×D236C2311yescharacteristic
73C2×C4×D59—21no—
74C2×C4×D59—21no—
75C2×C4×D59C2311yescharacteristic
76C2×C4×D59C2311yescharacteristic
77C2×Dic118C2311yescharacteristic
78C2×Dic118C2311yescharacteristic
79C2×C8×C59C2311yescharacteristic
80C2×C8×C59C2311yescharacteristic
81C4⋊C4×C59—21no—
82C4⋊C4×C59—21no—
83C4⋊C4×C59C2311yescharacteristic
84C4⋊C4×C59C2311yescharacteristic
85C4⋊C4×C59C2311yescharacteristic
86C22⋊C4×C59—21no—
87C42×C59C2311yescharacteristic
88#11745669—22no—
89(C2×D59)⋊C4—21no—
90(C2×D59)⋊C4—21no—
91(C2×D59)⋊C4—21no—
92(C2×D59)⋊C4—21no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4—21no—
95(C2×D59)⋊C4D411yescharacteristic
96(C2×D59)⋊C4D411yescharacteristic
97C4⋊Dic59—21no—
98C4⋊Dic59—21no—
99C4⋊Dic59—21no—
100C4⋊Dic59—21no—
101C4⋊Dic59D411yescharacteristic
102C4⋊Dic59C2311yescharacteristic
103Dic59⋊C4—21no—
104C4×Dic59—21no—
105C2×C59⋊C8C2311yescharacteristic
106C2×C59⋊C8C2311yescharacteristic
107#11745660—41no—
108#11745660—41no—
109#11745659—41no—
110C8×D59—41no—
111C23×C59—21no—
112C22×D59—21no—
113C22×D59C2×D411yescharacteristic
114C22×D59C2×D411yescharacteristic
115D4×C59—21no—
116D4×C59#4112yes—
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×C59C2411yescharacteristic
124C22⋊D59—42no—
125C22⋊D59—42no—
126C2×Dic59—21no—
127C2×Dic59—21no—
128C2×Dic59—21no—
129C2×Dic59—42no—
130C2×Dic59—42no—
131C2×Dic59C2×D411yescharacteristic
132C2×Dic59C2×D411yescharacteristic
133D236—21no—
134D236—21no—
135D236—41no—
136D236—42no—
137D236—81no—
138C4×D59—21no—
139C4×D59—21no—
140C4×D59—21no—
141C4×D59—21no—
142C4×D59—81no—
143C4×D59—81no—
144Dic118—21no—
145Dic118—21no—
146Dic118—21no—
147Dic118—21no—
148C8×C59—21no—
149C8×C59—21no—
150C59⋊C8—21no—
151C59⋊C8—21no—
152C22×C59—22no—
153C22×C59—41no—
154C22×C59—41no—
155C22×C59C22×D411yescharacteristic
156C2×D59—21no—
157C2×D59—21no—
158C2×D59—21no—
159C2×D59—21no—
160C2×D59—21no—
161C2×D59—21no—
162C2×D59—41no—
163C2×D59—41no—
164C2×D59—41no—
165C4×C59—21no—
166C4×C59—21no—
167C4×C59—41no—
168C4×C59—41no—
169C4×C59—41no—
170C4×C59C2×#4111yescharacteristic
171C4×C59H(5,𝔽2)11yescharacteristic
172Dic59—21no—
173Dic59—21no—
174Dic59—41no—
175Dic59—41no—
176Dic59—41no—
177#3307—591nomaximal, Sylow
178C2×C59—42no—
179C2×C59#54611yescharacteristic
180C2×C59#57511yescharacteristic
181C2×C59#57711yescharacteristic
182D59—41no—
183D59—41no—
184D59—81no—
185#553—591no—
186#547—591no—
187#491—591no—
188#485—591no—
189#483—591no—
190#478D5911yescharacteristic, complemented
191#468—591no—
192#465—591no—
193#461—591no—
194#449—591no—
195#449—591no—
196#442—591no—
197#435—591no—
198#417—591no—
199#416—591no—
200C59#330711yescharacteristic, complemented, Sylow
201C2×#41—591no—
202C2×#41—591no—
203C2×SD16—591no—
204C2×SD16—591no—
205C2×D8—591no—
206C2×M16—591no—
207C22×C8—591no—
208C4⋊Q8—591no—
209#126—1181no—
210#125C2×D5911yescharacteristic
211#123—1181no—
212#123—1181no—
213#123—1181no—
214C22⋊Q8—591no—
215C22⋊Q8—591no—
216#121—591no—
217#121—591no—
218#121—1181no—
219#121—1181no—
220C4×D4—591no—
221C4×D4—591no—
222C4×D4—1181no—
223C4×D4C2×D5911yescharacteristic
224#117—591no—
225C2×C4⋊C4—591no—
226C2×C4⋊C4—1181no—
227#107C2×D5911yescharacteristic
228#106—591no—
229#106C2×D5911yescharacteristic
230C4⋊C8C2×D5911yescharacteristic
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⋊C8—591no—
243#97—591no—
244#41—1182no—
245#41—1182no—
246#41—2361no—
247#41—2361no—
248C2×Q8—591no—
249C2×Q8—591no—
250C2×D4—591no—
251C2×D4—591no—
252C2×D4—1181no—
253C2×D4—1181no—
254C2×D4—1181no—
255C2×D4—1181no—
256C2×D4C22×D5911yescharacteristic
257C22×C4—21no—
258C22×C4—591no—
259C22×C4—591no—
260C22×C4—1181no—
261C22×C4—1181no—
262C22×C4—1181no—
263C22×C4—1181no—
264SD16—2361no—
265SD16—2361no—
266D8—1182no—
267M16—2361no—
268C2×C8—591no—
269C2×C8—591no—
270C2×C8—2361no—
271C2×C8C22×D5911yescharacteristic
272C2×C8C22×D5911yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—591no—
276C4⋊C4—591no—
277C4⋊C4—1181no—
278C4⋊C4—1181no—
279C4⋊C4—1181no—
280C4⋊C4—1181no—
281C4⋊C4—1181no—
282C4⋊C4C22×D5911yescharacteristic
283C4⋊C4C22×D5911yescharacteristic
284C4⋊C4C22×D5911yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—591no—
287C22⋊C4—591no—
288C22⋊C4—1181no—
289C22⋊C4—1181no—
290C22⋊C4—1181no—
291C22⋊C4—1181no—
292C22⋊C4—1181no—
293C22⋊C4—1181no—
294C42—1181no—
295C42C22×D5911yescharacteristic
296C23—21no—
297C23—591no—
298C23—591no—
299C23—1181no—
300Q8—1181no—
301Q8—1181no—
302Q8—1181no—
303Q8—1181no—
304D4—21no—
305D4—1181no—
306D4—1181no—
307D4—4721no—
308D4—2361no—
309D4—2362no—
310D4—2362no—
311D4—2362no—
312D4#1174568912yes—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—42no—
317C2×C4—591no—
318C2×C4—591no—
319C2×C4—1181no—
320C2×C4—1181no—
321C2×C4—1181no—
322C2×C4—1181no—
323C2×C4—1181no—
324C2×C4—1181no—
325C2×C4—1181no—
326C2×C4—4721no—
327C2×C4—4721no—
328C2×C4—2362no—
329C2×C4—2362no—
330C2×C4D4×D5911yescharacteristic
331C2×C4D4×D5911yescharacteristic
332C2×C4C23×D5911yescharacteristic
333C8—21no—
334C8—21no—
335C8—1181no—
336C8—1181no—
337C22—22no—
338C22—41no—
339C22—41no—
340C22—1181no—
341C22—1181no—
342C22—1181no—
343C22—1181no—
344C22—1181no—
345C22—1181no—
346C22—2361no—
347C22—2361no—
348C22—2361no—
349C22C2×D4×D5911yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—1181no—
356C4—1181no—
357C4—2361no—
358C4—2361no—
359C4—2361no—
360C4C2×#1174568911yescharacteristic
361C4#1427377311yescharacteristic
362C2—42no—
363C2—4721no—
364C2—2361no—
365C2—2361no—
366C2#1683804311yescharacteristic
367C2#1683819811yescharacteristic
368C2#1683820911yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#478C2
socleC22×C59C22×D4
hypercenter#478D59
hypocenterC59#3307
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #16838105C2semidirect
2. #16838056C2semidirect
3. #16837772C2semidirect
4. #16837745C2semidirect
5. #16837734C2semidirect
6. #16837649C2semidirect
7. #16837632C2semidirect
8. #16837608C2semidirect
9. #16837548C2semidirect
10. #16837548C2semidirect
11. #16837512C2semidirect
12. #16837472C2semidirect
13. #16837400C2semidirect
14. #16837395C2semidirect
15. C59×#478C2semidirect
190. #478D59semidirect
200. C59#3307semidirect