Finite Group Databasebeta

← #21434285

Subgroups — #21434285

Order 7552.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838026C211yesmaximal, characteristic, complemented
2#16837874C211yesmaximal, characteristic, complemented
3#16837746C211yesmaximal, characteristic, complemented
4#16837728C211yesmaximal, characteristic, complemented
5#16837679C211yesmaximal, characteristic, complemented
6#16837618C211yesmaximal, characteristic, complemented
7#16837617C211yesmaximal, characteristic, complemented
8#16837554C211yesmaximal, characteristic, complemented
9#16837537C211yesmaximal, characteristic
10#16837513C211yesmaximal, characteristic, complemented
11#16837499C211yesmaximal, characteristic, complemented
12#16837489C211yesmaximal, characteristic, complemented
13#16837482C211yesmaximal, characteristic, complemented
14#16837462C211yesmaximal, characteristic, complemented
15C59×#476C211yesmaximal, characteristic, complemented
16C2×D4×D59C2211yescharacteristic
17C2×#11745660C2211yescharacteristic
18C2×#11745670C2211yescharacteristic
19C2×D472C2211yescharacteristic
20C2×#11745669C2211yescharacteristic
21#14273722—21no—
22#14273716—21no—
23#14273715C2211yescharacteristic, complemented
24#14273712—21no—
25#14273707C2211yescharacteristic
26#14273703—21no—
27#14273702C2211yescharacteristic
28#14273692C2211yescharacteristic, complemented
29C4×D236C2211yescharacteristic
30D4×Dic59C2211yescharacteristic
31#14273689C2211yescharacteristic
32#14273689C2211yescharacteristic, complemented
33C4×C22⋊D59—21no—
34(C22⋊D59)⋊C4—21no—
35#14273685C2211yescharacteristic
36#14273684C2211yescharacteristic
37C2×(C2×D59)⋊C4—21no—
38C22⋊C4×D59—21no—
39#14273660C2211yescharacteristic, complemented
40#14273660C2211yescharacteristic, complemented
41C4⋊(C59⋊C8)C2211yescharacteristic, complemented
42#14273652C2211yescharacteristic, complemented
43#14273650C2211yescharacteristic, complemented
44#14273649C2211yescharacteristic, complemented
45#14273647C2211yescharacteristic
46#14273647C2211yescharacteristic
47#14273647C2211yescharacteristic, complemented
48(C2×D59)⋊C8C2211yescharacteristic
49(C2×D59)⋊C8C2211yescharacteristic
50#14273637C2211yescharacteristic, complemented
51C8×Dic59C2211yescharacteristic, complemented
52C4⋊Q8×C59C2211yescharacteristic, complemented
53C4×D4×C59C2211yescharacteristic
54#106×C59C2211yescharacteristic, complemented
55#106×C59C2211yescharacteristic, complemented
56C4⋊C8×C59C2211yescharacteristic, complemented
57#102×C59C2211yescharacteristic
58#102×C59C2211yescharacteristic
59C23×D59—21no—
60C2×Q8×C59—21no—
61C2×D4×C59C2311yescharacteristic
62C22×C4×C59—21no—
63C2×C22⋊D59—21no—
64C22×Dic59—21no—
65D4×D59—22no—
66D4×D59—22no—
67C2×D236—21no—
68C2×D236C2311yescharacteristic
69C2×D236C2311yescharacteristic
70C2×C4×D59—21no—
71C2×C4×D59—21no—
72C2×C4×D59—21no—
73C2×C4×D59C2311yescharacteristic
74C2×Dic118C2311yescharacteristic
75C2×C8×C59C2311yescharacteristic
76C2×C8×C59C2311yescharacteristic
77C4⋊C4×C59—21no—
78C4⋊C4×C59C2311yescharacteristic
79C4⋊C4×C59C2311yescharacteristic
80C4⋊C4×C59C2311yescharacteristic
81C22⋊C4×C59—21no—
82C42×C59C2311yescharacteristic
83C22⋊Dic59—21no—
84#11745670—22no—
85#11745669—22no—
86(C2×D59)⋊C4—21no—
87(C2×D59)⋊C4—21no—
88(C2×D59)⋊C4—21no—
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)⋊C4D411yescharacteristic
95(C2×D59)⋊C4D411yescharacteristic
96C4⋊Dic59—21no—
97C4⋊Dic59C2311yescharacteristic
98Dic59⋊C4—21no—
99Dic59⋊C4D411yescharacteristic
100Dic59⋊C4D411yescharacteristic
101C4×Dic59—21no—
102C4×Dic59—21no—
103C4×Dic59C2311yescharacteristic
104C2×C59⋊C8C2311yescharacteristic
105C2×C59⋊C8C2311yescharacteristic
106D472—22no—
107#11745660—22no—
108C23×C59—21no—
109C22×D59—21no—
110C22×D59—24no—
111C22×D59—21no—
112C22×D59—81no—
113C22×D59—81no—
114C22×D59C2×D411yescharacteristic
115Q8×C59—81no—
116D4×C59—21no—
117D4×C59#4112yes—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—81no—
122C2×C4×C59C2×D411yescharacteristic
123C2×C4×C59C2×D411yescharacteristic
124C2×C4×C59C2411yescharacteristic
125C22⋊D59—24no—
126C2×Dic59—21no—
127C2×Dic59—21no—
128C2×Dic59—81no—
129C2×Dic59C2×D411yescharacteristic
130C2×Dic59C2×D411yescharacteristic
131C2×Dic59C2×D411yescharacteristic
132D236—21no—
133D236—21no—
134D236—21no—
135D236—81no—
136D236#4112yes—
137C4×D59—21no—
138C4×D59—21no—
139C4×D59—81no—
140C4×D59—81no—
141C4×D59—81no—
142Dic118—21no—
143Dic118—21no—
144C8×C59—21no—
145C8×C59—21no—
146C59⋊C8—21no—
147C59⋊C8—21no—
148C22×C59—22no—
149C22×C59—41no—
150C22×C59—41no—
151C22×C59C22×D411yescharacteristic
152C2×D59—21no—
153C2×D59—22no—
154C2×D59—21no—
155C2×D59—21no—
156C2×D59—41no—
157C2×D59—41no—
158C2×D59—41no—
159C2×D59—41no—
160C2×D59—41no—
161C2×D59—84no—
162C4×C59—21no—
163C4×C59—21no—
164C4×C59—41no—
165C4×C59—41no—
166C4×C59—41no—
167C4×C59C2×#4111yescharacteristic
168C4×C59C2×#4111yescharacteristic
169Dic59—21no—
170Dic59—21no—
171Dic59—21no—
172Dic59—41no—
173Dic59—41no—
174#3118—591nomaximal, Sylow
175C2×C59—42no—
176C2×C59#52511yescharacteristic
177C2×C59#57611yescharacteristic
178C2×C59#57711yescharacteristic
179D59—41no—
180D59—42no—
181D59—81no—
182#542—591no—
183#518—591no—
184#485—591no—
185#482—591no—
186#476D5911yescharacteristic, complemented
187#474—591no—
188#463—591no—
189#463—591no—
190#450—591no—
191#447—591no—
192#442—591no—
193#440—591no—
194C4×SD16—591no—
195C4×D8—591no—
196#433—591no—
197C59#311811yescharacteristic, complemented, Sylow
198C22×D4—591no—
199C2×SD16—591no—
200C2×SD16—591no—
201C2×D8—591no—
202C2×D8—591no—
203C4⋊Q8C2×D5911yescharacteristic, complemented
204#126—1181no—
205#124—591no—
206#124—1181no—
207#123—1181no—
208C22⋊Q8—591no—
209C22⋊Q8—1181no—
210#121—591no—
211C4×Q8—591no—
212C4×D4—591no—
213C4×D4—591no—
214C4×D4—591no—
215C4×D4—591no—
216C4×D4—1181no—
217C4×D4—1181no—
218C4×D4C2×D5911yescharacteristic
219#117—591no—
220#117—591no—
221C2×C22⋊C4—1181no—
222C2×C22⋊C4—1181no—
223#107—591no—
224#107—591no—
225#106C2×D5911yescharacteristic, complemented
226#106C2×D5911yescharacteristic, complemented
227C4⋊C8—591no—
228C4⋊C8C2×D5911yescharacteristic, complemented
229#103—591no—
230#103—591no—
231#102—591no—
232#102—591no—
233#102—591no—
234#102—591no—
235#102C2×D5911yescharacteristic
236#102C2×D5911yescharacteristic
237C22⋊C8—591no—
238C22⋊C8—591no—
239#97—591no—
240C4×C8—591no—
241C24—1181no—
242C2×Q8—21no—
243C2×Q8—591no—
244C2×D4—591no—
245C2×D4—591no—
246C2×D4—1181no—
247C2×D4—1181no—
248C2×D4—1182no—
249C2×D4—1182no—
250C2×D4C22×D5911yescharacteristic
251C22×C4—21no—
252C22×C4—591no—
253C22×C4—1181no—
254C22×C4—1181no—
255C22×C4—1181no—
256C22×C4—1181no—
257SD16—1182no—
258SD16—1182no—
259D8—1182no—
260D8—1182no—
261C2×C8—591no—
262C2×C8—591no—
263C2×C8C22×D5911yescharacteristic
264C2×C8C22×D5911yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—591no—
267C4⋊C4—591no—
268C4⋊C4—591no—
269C4⋊C4—1181no—
270C4⋊C4—1181no—
271C4⋊C4C22×D5911yescharacteristic
272C4⋊C4C22×D5911yescharacteristic
273C4⋊C4C22×D5911yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—591no—
276C22⋊C4—591no—
277C22⋊C4—1181no—
278C22⋊C4—1181no—
279C22⋊C4—1181no—
280C22⋊C4—1181no—
281C22⋊C4—1181no—
282C22⋊C4—1181no—
283C22⋊C4—1181no—
284C22⋊C4—1181no—
285C22⋊C4—1181no—
286C42—591no—
287C42—1181no—
288C42—1181no—
289C42C22×D5911yescharacteristic
290C23—21no—
291C23—591no—
292C23—1184no—
293C23—1181no—
294C23—1181no—
295C23—4721no—
296C23—4721no—
297Q8—81no—
298Q8—1181no—
299Q8—1181no—
300D4—21no—
301D4—592no—
302D4—1184no—
303D4—1181no—
304D4—1181no—
305D4—1181no—
306D4—4721no—
307D4#1174568912yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—591no—
313C2×C4—591no—
314C2×C4—591no—
315C2×C4—1181no—
316C2×C4—1181no—
317C2×C4—1181no—
318C2×C4—1181no—
319C2×C4—4721no—
320C2×C4—4721no—
321C2×C4—4721no—
322C2×C4—4721no—
323C2×C4D4×D5911yescharacteristic
324C2×C4D4×D5911yescharacteristic
325C2×C4C23×D5911yescharacteristic
326C8—21no—
327C8—21no—
328C8—1181no—
329C8—1181no—
330C22—22no—
331C22—41no—
332C22—41no—
333C22—1181no—
334C22—1182no—
335C22—1181no—
336C22—1181no—
337C22—4724no—
338C22—2361no—
339C22—2361no—
340C22—2361no—
341C22—2361no—
342C22—2361no—
343C22C2×D4×D5911yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—1181no—
350C4—1181no—
351C4—1181no—
352C4—2361no—
353C4—2361no—
354C4#41×D5911yescharacteristic
355C4C2×#1174568911yescharacteristic
356C2—42no—
357C2—4721no—
358C2—2361no—
359C2—2362no—
360C2#1683791511yescharacteristic
361C2#1683820611yescharacteristic
362C2#1683820811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#476C2
socleC22×C59C22×D4
hypercenter#476D59
hypocenterC59#3118
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #16838026C2semidirect
2. #16837874C2semidirect
3. #16837746C2semidirect
4. #16837728C2semidirect
5. #16837679C2semidirect
6. #16837618C2semidirect
7. #16837617C2semidirect
8. #16837554C2semidirect
10. #16837513C2semidirect
11. #16837499C2semidirect
12. #16837489C2semidirect
13. #16837482C2semidirect
14. #16837462C2semidirect
15. C59×#476C2semidirect
23. #14273715C22semidirect
28. #14273692C22semidirect
32. #14273689C22semidirect
39. #14273660C22semidirect
40. #14273660C22semidirect
41. C4⋊(C59⋊C8)C22semidirect
42. #14273652C22semidirect
43. #14273650C22semidirect
44. #14273649C22semidirect
47. #14273647C22semidirect
50. #14273637C22semidirect
51. C8×Dic59C22semidirect
52. C4⋊Q8×C59C22semidirect
54. #106×C59C22semidirect
55. #106×C59C22semidirect
56. C4⋊C8×C59C22semidirect
186. #476D59semidirect
197. C59#3118semidirect
203. C4⋊Q8C2×D59semidirect
225. #106C2×D59semidirect
226. #106C2×D59semidirect
228. C4⋊C8C2×D59semidirect