Finite Group Databasebeta

← #21434930

Subgroups — #21434930

Order 7552.

414 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16837914C211yesmaximal, characteristic
2C22⋊Q8×D59C211yesmaximal, characteristic, complemented
3#16837743C211yesmaximal, characteristic, complemented
4#16837739C211yesmaximal, characteristic, complemented
5#16837722C211yesmaximal, characteristic, complemented
6#16837661C211yesmaximal, characteristic, complemented
7#16837659C211yesmaximal, characteristic, complemented
8#16837651C211yesmaximal, characteristic, complemented
9#16837649C211yesmaximal, characteristic, complemented
10#16837566C211yesmaximal, characteristic, complemented
11#16837562C211yesmaximal, characteristic, complemented
12#16837559C211yesmaximal, characteristic, complemented
13#16837542C211yesmaximal, characteristic, complemented
14#16837364C211yesmaximal, characteristic, complemented
15C59×#485C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C2×Q8×D59C2211yescharacteristic
18C22×C4×D59C2211yescharacteristic
19C2×Dic236C2211yescharacteristic, complemented
20C2×#11745672C2211yescharacteristic, complemented
21C2×#11745660C2211yescharacteristic, complemented
22C2×#11745671C2211yescharacteristic, complemented
23C2×#11745659C2211yescharacteristic
24C2×#11745659C2211yescharacteristic
25#14273711—21no—
26#14273707C2211yescharacteristic
27#14273707C2211yescharacteristic
28#14273707C2211yescharacteristic
29#14273706C2211yescharacteristic
30#14273705—21no—
31#14273704—21no—
32#14273703C2211yescharacteristic
33#14273702C2211yescharacteristic
34#14273702C2211yescharacteristic
35#14273697—21no—
36C4×D236—21no—
37C4×D236—21no—
38C4⋊C4×D59—21no—
39C4⋊C4×D59C2211yescharacteristic
40C22⋊C4×D59—21no—
41#14273660C2211yescharacteristic, complemented
42#14273658C2211yescharacteristic, complemented
43#14273652C2211yescharacteristic, complemented
44#14273650C2211yescharacteristic, complemented
45#14273650C2211yescharacteristic, complemented
46#14273650C2211yescharacteristic, complemented
47#14273649C2211yescharacteristic, complemented
48#14273647C2211yescharacteristic, complemented
49C22⋊(C59⋊C8)C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51(C2×D59)⋊C8C2211yescharacteristic
52C22⋊Q8×C59C2211yescharacteristic
53#117×C59C2211yescharacteristic
54#107×C59C2211yescharacteristic, complemented
55#106×C59C2211yescharacteristic, complemented
56#103×C59C2211yescharacteristic, complemented
57#103×C59C2211yescharacteristic, complemented
58C22⋊C8×C59C2211yescharacteristic
59C23×D59D411yescharacteristic
60C2×Q8×C59C2311yescharacteristic
61C22×C4×C59C2311yescharacteristic
62C2×C22⋊D59—21no—
63C22×Dic59D411yescharacteristic
64Q8×D59—41no—
65Q8×D59—41no—
66#11745685—41no—
67#11745685—41no—
68C2×D236—21no—
69C2×D236—21no—
70C2×D236C2311yescharacteristic
71C2×C4×D59—21no—
72C2×C4×D59—21no—
73C2×C4×D59—21no—
74C2×C4×D59—41no—
75C2×C4×D59—41no—
76C2×C4×D59D411yescharacteristic
77C2×C4×D59D411yescharacteristic
78C2×C4×D59C2311yescharacteristic
79C2×C4×D59C2311yescharacteristic
80C2×Dic118—21no—
81C2×Dic118C2311yescharacteristic
82C2×Dic118C2311yescharacteristic
83C2×C8×C59C2311yescharacteristic
84C2×C8×C59C2311yescharacteristic
85C4⋊C4×C59—21no—
86C4⋊C4×C59C2311yescharacteristic
87C4⋊C4×C59C2311yescharacteristic
88C4⋊C4×C59C2311yescharacteristic
89C22⋊C4×C59—21no—
90C22⋊C4×C59—21no—
91C42×C59—21no—
92C22⋊Dic59—21no—
93#11745672—41no—
94#11745671—41no—
95(C2×D59)⋊C4—21no—
96(C2×D59)⋊C4—21no—
97(C2×D59)⋊C4—21no—
98(C2×D59)⋊C4—21no—
99(C2×D59)⋊C4—21no—
100(C2×D59)⋊C4—21no—
101C4⋊Dic59—21no—
102C4⋊Dic59—21no—
103C4⋊Dic59—21no—
104C4⋊Dic59C2311yescharacteristic
105Dic59⋊C4—21no—
106Dic59⋊C4—21no—
107Dic59⋊C4—21no—
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110Dic236—41no—
111#11745660—41no—
112#11745659—41no—
113#11745659—41no—
114C23×C59C2×D411yescharacteristic
115C22×D59—22no—
116C22×D59—21no—
117C22×D59—41no—
118C22×D59—41no—
119C22×D59C2×D411yescharacteristic
120C22×D59C2×D411yescharacteristic
121Q8×C59—21no—
122Q8×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×C59C2×D411yescharacteristic
130C2×C4×C59C2411yescharacteristic
131C22⋊D59—42no—
132C2×Dic59—21no—
133C2×Dic59—21no—
134C2×Dic59—21no—
135C2×Dic59—41no—
136C2×Dic59C2×D411yescharacteristic
137C2×Dic59C2×D411yescharacteristic
138D236—21no—
139D236—21no—
140D236—42no—
141D236—42no—
142C4×D59—21no—
143C4×D59—21no—
144C4×D59—21no—
145C4×D59—21no—
146C4×D59—41no—
147C4×D59—41no—
148C4×D59—42no—
149C4×D59—42no—
150C4×D59—42no—
151Dic118—21no—
152Dic118—21no—
153Dic118—21no—
154Dic118—21no—
155Dic118—42no—
156C8×C59—21no—
157C8×C59—21no—
158C59⋊C8—21no—
159C59⋊C8—21no—
160C22×C59—21no—
161C22×C59—21no—
162C22×C59—21no—
163C22×C59C22×D411yescharacteristic
164C2×D59—21no—
165C2×D59—21no—
166C2×D59—21no—
167C2×D59—21no—
168C2×D59—21no—
169C2×D59—44no—
170C2×D59—41no—
171C2×D59—41no—
172C2×D59—41no—
173C2×D59#13712yes—
174C4×C59—21no—
175C4×C59—41no—
176C4×C59—41no—
177C4×C59—41no—
178C4×C59—41no—
179C4×C59H(5,𝔽2)11yescharacteristic
180C4×C59H(5,𝔽2)11yescharacteristic
181Dic59—21no—
182Dic59—21no—
183Dic59—41no—
184Dic59—41no—
185Dic59—41no—
186#3196—591nomaximal, Sylow
187C2×C59—41no—
188C2×C59#53411yescharacteristic
189C2×C59C2×#13711yescharacteristic
190C2×C59#57511yescharacteristic
191D59—22no—
192D59—41no—
193D59—81no—
194#525—591no—
195C2×C22⋊Q8—591no—
196#485—591no—
197#485D5911yescharacteristic, complemented
198#484—591no—
199#481—591no—
200#470—591no—
201#470—591no—
202#468—591no—
203#468—591no—
204#452—591no—
205#452—591no—
206#451—591no—
207#448—591no—
208#407—591no—
209C59#319611yescharacteristic, complemented, Sylow
210C2×#41—591no—
211C22×Q8—591no—
212C23×C4—591no—
213C2×Q16—591no—
214C2×Q16—591no—
215C2×SD16—591no—
216C2×SD16—591no—
217C2×M16—591no—
218C2×M16—591no—
219#123—1181no—
220C22⋊Q8—591no—
221C22⋊Q8—591no—
222C22⋊Q8—591no—
223C22⋊Q8—591no—
224C22⋊Q8—591no—
225C22⋊Q8—1181no—
226C22⋊Q8—1181no—
227C22⋊Q8C2×D5911yescharacteristic
228#121—591no—
229#121—591no—
230#120—1181no—
231C4×D4—1181no—
232C4×D4—1181no—
233#117C2×D5911yescharacteristic
234C2×C4⋊C4—591no—
235C2×C4⋊C4—1181no—
236C2×C22⋊C4—1181no—
237#107—591no—
238#107C2×D5911yescharacteristic, complemented
239#106—591no—
240#106C2×D5911yescharacteristic, complemented
241#103—591no—
242#103—591no—
243#103—591no—
244#103—591no—
245#103C2×D5911yescharacteristic, complemented
246#103C2×D5911yescharacteristic, complemented
247#102—591no—
248#102—591no—
249C22⋊C8—591no—
250C22⋊C8—591no—
251C22⋊C8—591no—
252C22⋊C8C2×D5911yescharacteristic
253C24—591no—
254#41—2361no—
255#41—2361no—
256C2×Q8—591no—
257C2×Q8—591no—
258C2×Q8—1181no—
259C2×Q8—2361no—
260C2×Q8—2361no—
261C2×Q8C22×D5911yescharacteristic
262C2×D4—591no—
263C2×D4—1181no—
264C2×D4—1181no—
265C2×D4—1181no—
266C22×C4—591no—
267C22×C4—591no—
268C22×C4—591no—
269C22×C4—591no—
270C22×C4—591no—
271C22×C4—1181no—
272C22×C4—1181no—
273C22×C4—1181no—
274C22×C4—2361no—
275C22×C4—2361no—
276C22×C4C22×D5911yescharacteristic
277Q16—2361no—
278Q16—2361no—
279SD16—2361no—
280SD16—2361no—
281M16—2361no—
282M16—2361no—
283C2×C8—591no—
284C2×C8—591no—
285C2×C8C22×D5911yescharacteristic
286C2×C8C22×D5911yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—591no—
289C4⋊C4—1181no—
290C4⋊C4—1181no—
291C4⋊C4—1181no—
292C4⋊C4—1181no—
293C4⋊C4—1181no—
294C4⋊C4—1181no—
295C4⋊C4C22×D5911yescharacteristic
296C4⋊C4C22×D5911yescharacteristic
297C4⋊C4C22×D5911yescharacteristic
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—1181no—
301C22⋊C4—1181no—
302C22⋊C4—1181no—
303C22⋊C4—1181no—
304C22⋊C4—1181no—
305C22⋊C4—1181no—
306C22⋊C4—1181no—
307C42—21no—
308C23—591no—
309C23—591no—
310C23—1182no—
311C23—1181no—
312C23—2361no—
313C23—2361no—
314C23D4×D5911yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—1181no—
318Q8—1181no—
319Q8—1181no—
320Q8—1181no—
321Q8—2362no—
322D4—1181no—
323D4—1181no—
324D4—2362no—
325D4—2362no—
326D4—2362no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—591no—
334C2×C4—591no—
335C2×C4—1181no—
336C2×C4—1181no—
337C2×C4—1181no—
338C2×C4—1181no—
339C2×C4—1181no—
340C2×C4—1181no—
341C2×C4—1181no—
342C2×C4—2361no—
343C2×C4—2361no—
344C2×C4—2362no—
345C2×C4—2362no—
346C2×C4—2362no—
347C2×C4—2361no—
348C2×C4D4×D5911yescharacteristic
349C2×C4C23×D5911yescharacteristic
350C8—21no—
351C8—21no—
352C8—1181no—
353C8—1181no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—592no—
358C22—1181no—
359C22—1181no—
360C22—1181no—
361C22—1181no—
362C22—1181no—
363C22—2364no—
364C22—2361no—
365C22—2361no—
366C22—2361no—
367C22C2×D4×D5911yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4—1181no—
374C4—1181no—
375C4—2361no—
376C4—2361no—
377C4—2361no—
378C4#1427377311yescharacteristic
379C4#1427377311yescharacteristic
380C2—41no—
381C2—1182no—
382C2—4721no—
383C2—2361no—
384C2#1683796311yescharacteristic
385C2#137×D5911yescharacteristic
386C2#1683819911yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#485C2
socleC22×C59C22×D4
hypercenter#485D59
hypocenterC59#3196
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
2. C22⋊Q8×D59C2semidirect
3. #16837743C2semidirect
4. #16837739C2semidirect
5. #16837722C2semidirect
6. #16837661C2semidirect
7. #16837659C2semidirect
8. #16837651C2semidirect
9. #16837649C2semidirect
10. #16837566C2semidirect
11. #16837562C2semidirect
12. #16837559C2semidirect
13. #16837542C2semidirect
14. #16837364C2semidirect
15. C59×#485C2semidirect
19. C2×Dic236C22semidirect
20. C2×#11745672C22semidirect
21. C2×#11745660C22semidirect
22. C2×#11745671C22semidirect
41. #14273660C22semidirect
42. #14273658C22semidirect
43. #14273652C22semidirect
44. #14273650C22semidirect
45. #14273650C22semidirect
46. #14273650C22semidirect
47. #14273649C22semidirect
48. #14273647C22semidirect
54. #107×C59C22semidirect
55. #106×C59C22semidirect
56. #103×C59C22semidirect
57. #103×C59C22semidirect
197. #485D59semidirect
209. C59#3196semidirect
238. #107C2×D59semidirect
240. #106C2×D59semidirect
245. #103C2×D59semidirect
246. #103C2×D59semidirect