Finite Group Databasebeta

← #21436182

Subgroups — #21436182

Order 7552.

410 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#16838112C211yesmaximal, characteristic, complemented
2#16838047C211yesmaximal, characteristic
3#16837762C211yesmaximal, characteristic, complemented
4#16837739C211yesmaximal, characteristic, complemented
5#16837717C211yesmaximal, characteristic, complemented
6#16837682C211yesmaximal, characteristic, complemented
7#16837651C211yesmaximal, characteristic, complemented
8#16837642C211yesmaximal, characteristic, complemented
9#16837624C211yesmaximal, characteristic, complemented
10#16837561C211yesmaximal, characteristic, complemented
11#16837551C211yesmaximal, characteristic, complemented
12#16837475C211yesmaximal, characteristic, complemented
13#16837400C211yesmaximal, characteristic, complemented
14#102×D59C211yesmaximal, characteristic, complemented
15C59×#440C211yesmaximal, characteristic, complemented
16C2×#11745687C2211yescharacteristic
17C2×D4×D59C2211yescharacteristic
18C2×#11745672C2211yescharacteristic, complemented
19C2×#11745671C2211yescharacteristic
20C2×#11745659C2211yescharacteristic, complemented
21C2×C8×D59C2211yescharacteristic
22#14273727C2211yescharacteristic, complemented
23#14273719—21no—
24#14273715C2211yescharacteristic
25#14273711—21no—
26#14273707C2211yescharacteristic
27#14273705—21no—
28#14273705—21no—
29#14273703C2211yescharacteristic
30#14273703C2211yescharacteristic, complemented
31#14273702C2211yescharacteristic
32#14273701—21no—
33#14273697—21no—
34C4×D236—21no—
35C4×D236C2211yescharacteristic
36C4⋊C4×D59C2211yescharacteristic
37C4⋊C4×D59C2211yescharacteristic, complemented
38C2×(C2×D59)⋊C4—21no—
39#14273660C2211yescharacteristic, complemented
40#14273660C2211yescharacteristic, complemented
41C4⋊(C59⋊C8)C2211yescharacteristic, complemented
42#14273652C2211yescharacteristic, complemented
43#14273652C2211yescharacteristic, complemented
44#14273650C2211yescharacteristic, complemented
45#14273649C2211yescharacteristic
46#14273649C2211yescharacteristic
47#14273648C2211yescharacteristic
48#14273648C2211yescharacteristic
49#14273647C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51(C2×D59)⋊C8C2211yescharacteristic, complemented
52C2×SD16×C59C2211yescharacteristic
53C4×Q8×C59C2211yescharacteristic, complemented
54C4×D4×C59C2211yescharacteristic
55#107×C59C2211yescharacteristic, complemented
56#103×C59C2211yescharacteristic, complemented
57#102×C59C2211yescharacteristic
58#97×C59C2211yescharacteristic, complemented
59C23×D59—21no—
60C2×Q8×C59C2311yescharacteristic
61C2×D4×C59C2311yescharacteristic
62C22×C4×C59—21no—
63C2×C22⋊D59—21no—
64C2×C22⋊D59—21no—
65C22×Dic59—21no—
66#11745687—22no—
67#11745687—41no—
68D4×D59—22no—
69D4×D59—41no—
70C2×D236—21no—
71C2×D236D411yescharacteristic
72C2×D236C2311yescharacteristic
73C2×C4×D59—21no—
74C2×C4×D59—21no—
75C2×C4×D59C2311yescharacteristic
76C2×C4×D59C2311yescharacteristic
77C2×Dic118—21no—
78C2×Dic118C2311yescharacteristic
79SD16×C59—22no—
80C2×C8×C59C2311yescharacteristic
81C2×C8×C59C2311yescharacteristic
82C4⋊C4×C59—21no—
83C4⋊C4×C59C2311yescharacteristic
84C4⋊C4×C59C2311yescharacteristic
85C22⋊C4×C59—21no—
86C42×C59—21no—
87C42×C59C2311yescharacteristic
88#11745672—41no—
89#11745671—41no—
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)⋊C4—21no—
96(C2×D59)⋊C4D411yescharacteristic
97(C2×D59)⋊C4D411yescharacteristic
98C4⋊Dic59—21no—
99C4⋊Dic59—21no—
100C4⋊Dic59D411yescharacteristic
101C4⋊Dic59C2311yescharacteristic
102C4⋊Dic59C2311yescharacteristic
103Dic59⋊C4—21no—
104Dic59⋊C4—21no—
105Dic59⋊C4—21no—
106Dic59⋊C4—21no—
107C2×C59⋊C8C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109#11745659—41no—
110C8×D59—41no—
111C23×C59—21no—
112C22×D59—21no—
113C22×D59—42no—
114C22×D59—42no—
115C22×D59—81no—
116C22×D59C2×D411yescharacteristic
117C22×D59C2×D411yescharacteristic
118Q8×C59—21no—
119Q8×C59—21no—
120D4×C59—21no—
121D4×C59#4112yes—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59—81no—
126C2×C4×C59C2×D411yescharacteristic
127C2×C4×C59C2×D411yescharacteristic
128C2×C4×C59C2411yescharacteristic
129C22⋊D59—42no—
130C22⋊D59—42no—
131C2×Dic59—21no—
132C2×Dic59—21no—
133C2×Dic59—21no—
134C2×Dic59—42no—
135C2×Dic59C2×D411yescharacteristic
136C2×Dic59C2×D411yescharacteristic
137D236—22no—
138D236—21no—
139D236—21no—
140D236—81no—
141C4×D59—21no—
142C4×D59—21no—
143C4×D59—21no—
144C4×D59—21no—
145C4×D59—81no—
146C4×D59—81no—
147Dic118—21no—
148Dic118—21no—
149Dic118—81no—
150C8×C59—21no—
151C8×C59—21no—
152C59⋊C8—21no—
153C59⋊C8—21no—
154C22×C59—22no—
155C22×C59—41no—
156C22×C59—41no—
157C22×C59C22×D411yescharacteristic
158C2×D59—21no—
159C2×D59—21no—
160C2×D59—21no—
161C2×D59—21no—
162C2×D59—21no—
163C2×D59—41no—
164C2×D59—41no—
165C2×D59—41no—
166C2×D59—84no—
167C2×D59#13712yes—
168C4×C59—21no—
169C4×C59—21no—
170C4×C59—41no—
171C4×C59—41no—
172C4×C59—41no—
173C4×C59C2×#4111yescharacteristic
174C4×C59H(5,𝔽2)11yescharacteristic
175Dic59—21no—
176Dic59—21no—
177Dic59—41no—
178Dic59—41no—
179Dic59—41no—
180#3314—591nomaximal, Sylow
181C2×C59—42no—
182C2×C59#54611yescharacteristic
183C2×C59C2×#13711yescharacteristic
184C2×C59#57611yescharacteristic
185D59—22no—
186D59—41no—
187D59—81no—
188#554—591no—
189#546—591no—
190#489—591no—
191#484—591no—
192#480—591no—
193#474—591no—
194#468—591no—
195#467—591no—
196#464—591no—
197#452—591no—
198#450—591no—
199#440D5911yescharacteristic, complemented
200#435—591no—
201#417—591no—
202C2×#102—591no—
203C59#331411yescharacteristic, complemented, Sylow
204C2×#41—591no—
205C22×D4—591no—
206C2×Q16—591no—
207C2×SD16—591no—
208C2×SD16C2×D5911yescharacteristic
209C2×M16—591no—
210C22×C8—591no—
211C4⋊Q8—591no—
212#125—1181no—
213#124—591no—
214#123—1181no—
215C22⋊Q8—591no—
216C22⋊Q8—591no—
217C22⋊Q8—591no—
218C22⋊Q8—1181no—
219C22⋊Q8—1181no—
220#121—591no—
221#121—1181no—
222#120—1181no—
223C4×Q8C2×D5911yescharacteristic, complemented
224C4×D4—591no—
225C4×D4—1181no—
226C4×D4C2×D5911yescharacteristic
227C2×C4⋊C4—591no—
228C2×C4⋊C4—591no—
229C2×C22⋊C4—1181no—
230#107—591no—
231#107—591no—
232#107C2×D5911yescharacteristic, complemented
233C4⋊C8—591no—
234#103—591no—
235#103—591no—
236#103—591no—
237#103C2×D5911yescharacteristic, complemented
238#102—591no—
239#102—591no—
240#102—591no—
241#102—591no—
242#102—591no—
243#102C2×D5911yescharacteristic
244C22⋊C8—591no—
245C22⋊C8—591no—
246#97C2×D5911yescharacteristic, complemented
247C24—1181no—
248#41—1182no—
249#41—2361no—
250C2×Q8—591no—
251C2×Q8—1181no—
252C2×Q8C22×D5911yescharacteristic
253C2×D4—591no—
254C2×D4—591no—
255C2×D4—1181no—
256C2×D4—1181no—
257C2×D4—1182no—
258C2×D4—1181no—
259C2×D4—2361no—
260C2×D4C22×D5911yescharacteristic
261C22×C4—21no—
262C22×C4—591no—
263C22×C4—591no—
264C22×C4—1181no—
265C22×C4—1181no—
266C22×C4—1181no—
267Q16—2361no—
268SD16—22no—
269SD16—2361no—
270M16—2361no—
271C2×C8—591no—
272C2×C8—591no—
273C2×C8—2361no—
274C2×C8C22×D5911yescharacteristic
275C2×C8C22×D5911yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—591no—
278C4⋊C4—591no—
279C4⋊C4—591no—
280C4⋊C4—1181no—
281C4⋊C4—1181no—
282C4⋊C4—1181no—
283C4⋊C4—1181no—
284C4⋊C4—1181no—
285C4⋊C4—1181no—
286C4⋊C4C22×D5911yescharacteristic
287C4⋊C4C22×D5911yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—591no—
290C22⋊C4—591no—
291C22⋊C4—1181no—
292C22⋊C4—1181no—
293C22⋊C4—1181no—
294C22⋊C4—1181no—
295C22⋊C4—1181no—
296C22⋊C4—1181no—
297C42—21no—
298C42C22×D5911yescharacteristic
299C23—21no—
300C23—591no—
301C23—591no—
302C23—1181no—
303C23—4721no—
304C23—2362no—
305C23—2362no—
306Q8—21no—
307Q8—21no—
308Q8—1181no—
309Q8—1181no—
310Q8—4721no—
311D4—21no—
312D4—1182no—
313D4—1181no—
314D4—1181no—
315D4—4721no—
316D4—2362no—
317D4—2362no—
318D4#1174568512yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—81no—
323C2×C4—591no—
324C2×C4—591no—
325C2×C4—1181no—
326C2×C4—1181no—
327C2×C4—1181no—
328C2×C4—1181no—
329C2×C4—1181no—
330C2×C4—1181no—
331C2×C4—1181no—
332C2×C4—4721no—
333C2×C4—4721no—
334C2×C4—2362no—
335C2×C4D4×D5911yescharacteristic
336C2×C4D4×D5911yescharacteristic
337C2×C4C23×D5911yescharacteristic
338C8—21no—
339C8—21no—
340C8—1181no—
341C8—1181no—
342C22—22no—
343C22—41no—
344C22—41no—
345C22—592no—
346C22—1181no—
347C22—1181no—
348C22—1181no—
349C22—1181no—
350C22—1181no—
351C22—4724no—
352C22—2361no—
353C22—2361no—
354C22—2361no—
355C22C2×D4×D5911yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—1181no—
362C4—1181no—
363C4—2361no—
364C4—2361no—
365C4—2361no—
366C4C2×#1174568511yescharacteristic
367C4#1427377311yescharacteristic
368C2—42no—
369C2—1182no—
370C2—4721no—
371C2—2361no—
372C2#1683804811yescharacteristic
373C2#137×D5911yescharacteristic
374C2#1683820611yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#440C2
socleC22×C59C22×D4
hypercenter#440D59
hypocenterC59#3314
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #16838112C2semidirect
3. #16837762C2semidirect
4. #16837739C2semidirect
5. #16837717C2semidirect
6. #16837682C2semidirect
7. #16837651C2semidirect
8. #16837642C2semidirect
9. #16837624C2semidirect
10. #16837561C2semidirect
11. #16837551C2semidirect
12. #16837475C2semidirect
13. #16837400C2semidirect
14. #102×D59C2semidirect
15. C59×#440C2semidirect
18. C2×#11745672C22semidirect
20. C2×#11745659C22semidirect
22. #14273727C22semidirect
30. #14273703C22semidirect
37. C4⋊C4×D59C22semidirect
39. #14273660C22semidirect
40. #14273660C22semidirect
41. C4⋊(C59⋊C8)C22semidirect
42. #14273652C22semidirect
43. #14273652C22semidirect
44. #14273650C22semidirect
51. (C2×D59)⋊C8C22semidirect
53. C4×Q8×C59C22semidirect
55. #107×C59C22semidirect
56. #103×C59C22semidirect
58. #97×C59C22semidirect
199. #440D59semidirect
203. C59#3314semidirect
223. C4×Q8C2×D59semidirect
232. #107C2×D59semidirect
237. #103C2×D59semidirect
246. #97C2×D59semidirect