Finite Group Databasebeta

← #21436171

Subgroups — #21436171

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#16838048C211yesmaximal, characteristic
2#16837764C211yesmaximal, characteristic, complemented
3#16837737C211yesmaximal, characteristic, complemented
4#16837715C211yesmaximal, characteristic, complemented
5#16837679C211yesmaximal, characteristic, complemented
6#16837650C211yesmaximal, characteristic, complemented
7#16837641C211yesmaximal, characteristic, complemented
8#16837624C211yesmaximal, characteristic, complemented
9#16837562C211yesmaximal, characteristic, complemented
10#16837552C211yesmaximal, characteristic, complemented
11#16837500C211yesmaximal, characteristic, complemented
12#16837474C211yesmaximal, characteristic, complemented
13#16837401C211yesmaximal, characteristic, complemented
14C2×#14273647C211yesmaximal, characteristic, complemented
15C59×#554C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C22×D236C2211yescharacteristic
18C2×#11745672C2211yescharacteristic, complemented
19C2×#11745671C2211yescharacteristic
20C2×#11745671C2211yescharacteristic
21C2×#11745664C2211yescharacteristic, complemented
22C22×C59⋊C8C2211yescharacteristic
23#14273715C2211yescharacteristic
24#14273712—21no—
25#14273706C2211yescharacteristic
26#14273701C2211yescharacteristic
27#14273700—21no—
28#14273695—21no—
29C4×D236C2211yescharacteristic
30C22⋊C4×D59—21no—
31#14273660C2211yescharacteristic, complemented
32#14273660C2211yescharacteristic, complemented
33#14273660C2211yescharacteristic, complemented
34C4⋊(C59⋊C8)C2211yescharacteristic, complemented
35#14273651C2211yescharacteristic, complemented
36#14273650C2211yescharacteristic, complemented
37#14273650C2211yescharacteristic, complemented
38#14273650C2211yescharacteristic, complemented
39#14273647C2211yescharacteristic
40#14273647C2211yescharacteristic
41#14273647C2211yescharacteristic
42#14273647C2211yescharacteristic
43#14273647C2211yescharacteristic
44#14273647C2211yescharacteristic
45C22⋊(C59⋊C8)C2211yescharacteristic
46C22⋊(C59⋊C8)C2211yescharacteristic, complemented
47#14273638C2211yescharacteristic, complemented
48C4⋊Q8×C59C2211yescharacteristic, complemented
49#125×C59—21no—
50C22⋊Q8×C59—21no—
51C22⋊Q8×C59—21no—
52C22⋊Q8×C59C2211yescharacteristic
53C22⋊Q8×C59C2211yescharacteristic, complemented
54C4×Q8×C59C2211yescharacteristic, complemented
55C4×D4×C59—21no—
56C4×D4×C59C2211yescharacteristic
57C2×C4⋊C4×C59C2211yescharacteristic
58C2×C4⋊C4×C59C2211yescharacteristic, complemented
59C23×D59—21no—
60C2×Q8×C59—21no—
61C2×Q8×C59C2311yescharacteristic
62C2×D4×C59D411yescharacteristic
63C22×C4×C59—21no—
64C22×C4×C59—21no—
65C22×C4×C59C2311yescharacteristic
66C22×C4×C59C2311yescharacteristic
67C2×C22⋊D59—21no—
68C2×C22⋊D59—21no—
69#11745685—22no—
70#11745685—41no—
71C2×D236—22no—
72C2×D236—21no—
73C2×D236—41no—
74C2×D236C2311yescharacteristic
75C2×D236C2311yescharacteristic
76C2×C4×D59—21no—
77C2×C4×D59—21no—
78C2×Dic118C2311yescharacteristic
79C4⋊C4×C59—21no—
80C4⋊C4×C59—21no—
81C4⋊C4×C59—21no—
82C4⋊C4×C59—21no—
83C4⋊C4×C59—21no—
84C4⋊C4×C59—21no—
85C4⋊C4×C59D411yescharacteristic
86C4⋊C4×C59C2311yescharacteristic
87C4⋊C4×C59C2311yescharacteristic
88C4⋊C4×C59C2311yescharacteristic
89C22⋊C4×C59—21no—
90C22⋊C4×C59—21no—
91C22⋊C4×C59D411yescharacteristic
92C22⋊C4×C59D411yescharacteristic
93C42×C59—21no—
94C42×C59C2311yescharacteristic
95C22⋊Dic59—21no—
96#11745672—41no—
97#11745671—22no—
98#11745671—41no—
99(C2×D59)⋊C4—21no—
100(C2×D59)⋊C4—21no—
101(C2×D59)⋊C4—21no—
102(C2×D59)⋊C4—21no—
103C4⋊Dic59C2311yescharacteristic
104Dic59⋊C4—21no—
105#11745664—41no—
106C2×C59⋊C8—41no—
107C2×C59⋊C8C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110C2×C59⋊C8C2311yescharacteristic
111C23×C59C2×D411yescharacteristic
112C23×C59C2×D411yescharacteristic
113C22×D59—21no—
114C22×D59—21no—
115C22×D59—42no—
116C22×D59—42no—
117C22×D59—81no—
118Q8×C59—21no—
119Q8×C59—21no—
120Q8×C59—81no—
121D4×C59—22no—
122C2×C4×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×C59—21no—
130C2×C4×C59—81no—
131C2×C4×C59—81no—
132C2×C4×C59C2×D411yescharacteristic
133C2×C4×C59C2×D411yescharacteristic
134C2×C4×C59C2×D411yescharacteristic
135C2×C4×C59C2×D411yescharacteristic
136C2×C4×C59C2411yescharacteristic
137C22⋊D59—42no—
138C22⋊D59—81no—
139C2×Dic59—21no—
140C2×Dic59—21no—
141D236—21no—
142D236—21no—
143D236—21no—
144D236—42no—
145D236#4112yes—
146C4×D59—42no—
147C4×D59—81no—
148Dic118—21no—
149Dic118—21no—
150C59⋊C8—21no—
151C59⋊C8—21no—
152C59⋊C8—21no—
153C59⋊C8—21no—
154C22×C59—21no—
155C22×C59—21no—
156C22×C59—21no—
157C22×C59—21no—
158C22×C59—21no—
159C22×C59#13712yes—
160C22×C59C22×D411yescharacteristic
161C2×D59—22no—
162C2×D59—41no—
163C2×D59—41no—
164C2×D59—41no—
165C2×D59—41no—
166C2×D59—41no—
167C2×D59—84no—
168C4×C59—21no—
169C4×C59—21no—
170C4×C59—21no—
171C4×C59—21no—
172C4×C59—41no—
173C4×C59—41no—
174C4×C59—41no—
175C4×C59—41no—
176C4×C59C2×#4111yescharacteristic
177C4×C59H(5,𝔽2)11yescharacteristic
178Dic59—41no—
179Dic59—41no—
180#3314—591nomaximal, Sylow
181C2×C59—22no—
182C2×C59—41no—
183C2×C59#54611yescharacteristic
184C2×C59C2×#13711yescharacteristic
185C2×C59#57611yescharacteristic
186D59—42no—
187D59—81no—
188#554D5911yescharacteristic, complemented
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#440—591no—
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×SD16—591no—
209C2×M16—591no—
210C22×C8—591no—
211C4⋊Q8C2×D5911yescharacteristic, complemented
212#125—21no—
213#124—591no—
214#123—1181no—
215C22⋊Q8—21no—
216C22⋊Q8—21no—
217C22⋊Q8—591no—
218C22⋊Q8C2×D5911yescharacteristic
219C22⋊Q8C2×D5911yescharacteristic, complemented
220#121—591no—
221#121—1181no—
222#120—1181no—
223C4×Q8C2×D5911yescharacteristic, complemented
224C4×D4—21no—
225C4×D4—591no—
226C4×D4C2×D5911yescharacteristic
227C2×C4⋊C4C2×D5911yescharacteristic
228C2×C4⋊C4C2×D5911yescharacteristic, complemented
229C2×C22⋊C4—1181no—
230#107—591no—
231#107—591no—
232#107—591no—
233C4⋊C8—591no—
234#103—591no—
235#103—591no—
236#103—591no—
237#103—591no—
238#102—591no—
239#102—591no—
240#102—591no—
241#102—591no—
242#102—591no—
243#102—591no—
244C22⋊C8—591no—
245C22⋊C8—591no—
246#97—591no—
247C24—1181no—
248#41—1182no—
249#41—2361no—
250C2×Q8—21no—
251C2×Q8—591no—
252C2×Q8C22×D5911yescharacteristic
253C2×D4—591no—
254C2×D4—591no—
255C2×D4—1182no—
256C2×D4—1181no—
257C2×D4—1181no—
258C2×D4—1181no—
259C2×D4—2361no—
260C2×D4C22⋊D5911yescharacteristic
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—1181no—
264C22×C4—1181no—
265C22×C4C22×D5911yescharacteristic
266C22×C4C22×D5911yescharacteristic
267Q16—2361no—
268SD16—1182no—
269SD16—2361no—
270M16—2361no—
271C2×C8—591no—
272C2×C8—591no—
273C2×C8—591no—
274C2×C8—591no—
275C2×C8—2361no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—591no—
283C4⋊C4—1181no—
284C4⋊C4C22⋊D5911yescharacteristic
285C4⋊C4C22×D5911yescharacteristic
286C4⋊C4C22×D5911yescharacteristic
287C4⋊C4C22×D5911yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—1181no—
291C22⋊C4—1181no—
292C22⋊C4—1181no—
293C22⋊C4—1181no—
294C22⋊C4—1181no—
295C22⋊C4C22⋊D5911yescharacteristic
296C22⋊C4C22⋊D5911yescharacteristic
297C42—21no—
298C42C22×D5911yescharacteristic
299C23—1181no—
300C23—1181no—
301C23—4721no—
302C23—2362no—
303C23—2362no—
304C23C2×C22⋊D5911yescharacteristic
305C23C2×C22⋊D5911yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—81no—
309Q8—1181no—
310Q8—1181no—
311D4—22no—
312D4—592no—
313D4—1181no—
314D4—1181no—
315D4—1181no—
316D4—4721no—
317D4—2362no—
318D4—2362no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—1181no—
330C2×C4—1181no—
331C2×C4—4721no—
332C2×C4—2362no—
333C2×C4C2×C22⋊D5911yescharacteristic
334C2×C4C2×C22⋊D5911yescharacteristic
335C2×C4C2×C22⋊D5911yescharacteristic
336C2×C4C2×C22⋊D5911yescharacteristic
337C2×C4C23×D5911yescharacteristic
338C8—1181no—
339C8—1181no—
340C8—1181no—
341C8—1181no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—1182no—
348C22—4724no—
349C22—2361no—
350C22—2361no—
351C22—2361no—
352C22—2361no—
353C22—2361no—
354C22#1427375812yes—
355C22C22×C22⋊D5911yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—41no—
363C4—41no—
364C4—2361no—
365C4—2361no—
366C4#41×D5911yescharacteristic
367C4#1427377311yescharacteristic
368C2—22no—
369C2—41no—
370C2—4721no—
371C2—2362no—
372C2#1683804011yescharacteristic
373C2C2×#1427375811yescharacteristic
374C2#1683820511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#554C2
socleC22×C59C22×D4
hypercenter#554D59
hypocenterC59#3314
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #554

Complements

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

NH ≅ G/Ntype
2. #16837764C2semidirect
3. #16837737C2semidirect
4. #16837715C2semidirect
5. #16837679C2semidirect
6. #16837650C2semidirect
7. #16837641C2semidirect
8. #16837624C2semidirect
9. #16837562C2semidirect
10. #16837552C2semidirect
11. #16837500C2semidirect
12. #16837474C2semidirect
13. #16837401C2semidirect
14. C2×#14273647C2semidirect
15. C59×#554C2semidirect
18. C2×#11745672C22semidirect
21. C2×#11745664C22semidirect
31. #14273660C22semidirect
32. #14273660C22semidirect
33. #14273660C22semidirect
34. C4⋊(C59⋊C8)C22semidirect
35. #14273651C22semidirect
36. #14273650C22semidirect
37. #14273650C22semidirect
38. #14273650C22semidirect
46. C22⋊(C59⋊C8)C22semidirect
47. #14273638C22semidirect
48. C4⋊Q8×C59C22semidirect
53. C22⋊Q8×C59C22semidirect
54. C4×Q8×C59C22semidirect
58. C2×C4⋊C4×C59C22semidirect
188. #554D59semidirect
203. C59#3314semidirect
211. C4⋊Q8C2×D59semidirect
219. C22⋊Q8C2×D59semidirect
223. C4×Q8C2×D59semidirect
228. C2×C4⋊C4C2×D59semidirect