Finite Group Databasebeta

← #21434274

Subgroups — #21434274

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#16837876C211yesmaximal, characteristic, complemented
2#16837740C211yesmaximal, characteristic, complemented
3#16837723C211yesmaximal, characteristic, complemented
4#16837689C211yesmaximal, characteristic, complemented
5#16837679C211yesmaximal, characteristic, complemented
6#16837614C211yesmaximal, characteristic, complemented
7#16837614C211yesmaximal, characteristic, complemented
8#16837552C211yesmaximal, characteristic, complemented
9#16837535C211yesmaximal, characteristic
10#16837512C211yesmaximal, characteristic, complemented
11#16837500C211yesmaximal, characteristic, complemented
12C4×#11745671C211yesmaximal, characteristic, complemented
13C4×#11745669C211yesmaximal, characteristic, complemented
14#16837463C211yesmaximal, characteristic, complemented
15C59×#542C211yesmaximal, characteristic, complemented
16C22×D236C2211yescharacteristic
17C2×#11745671C2211yescharacteristic
18C2×#11745671C2211yescharacteristic
19C2×#11745669C2211yescharacteristic
20C2×#11745669C2211yescharacteristic
21C4×D236C2211yescharacteristic
22C4×D236C2211yescharacteristic
23C4×D236C2211yescharacteristic
24C4×D236C2211yescharacteristic
25#14273689—21no—
26#14273689—21no—
27#14273686C2211yescharacteristic
28C22⋊C4×D59—21no—
29C22⋊C4×D59—21no—
30#14273660C2211yescharacteristic, complemented
31#14273660C2211yescharacteristic, complemented
32#14273658C2211yescharacteristic, complemented
33#14273658C2211yescharacteristic, complemented
34C4⋊(C59⋊C8)C2211yescharacteristic, complemented
35C4⋊(C59⋊C8)C2211yescharacteristic, complemented
36#14273651C2211yescharacteristic, complemented
37#14273651C2211yescharacteristic, complemented
38#14273648C2211yescharacteristic, complemented
39#14273648C2211yescharacteristic, complemented
40#14273647C2211yescharacteristic
41#14273647C2211yescharacteristic
42#14273647C2211yescharacteristic
43#14273647C2211yescharacteristic
44C22⋊(C59⋊C8)C2211yescharacteristic
45C22⋊(C59⋊C8)C2211yescharacteristic
46#14273638C2211yescharacteristic, complemented
47C4×C59⋊C8C2211yescharacteristic, complemented
48C4⋊Q8×C59C2211yescharacteristic, complemented
49#126×C59—21no—
50#124×C59—21no—
51#124×C59C2211yescharacteristic, complemented
52#123×C59—21no—
53C22⋊Q8×C59—21no—
54C22⋊Q8×C59C2211yescharacteristic
55#121×C59C2211yescharacteristic
56C4×Q8×C59C2211yescharacteristic, complemented
57C4×D4×C59C2211yescharacteristic, complemented
58#117×C59C2211yescharacteristic
59C23×D59—21no—
60C2×Q8×C59—21no—
61C2×Q8×C59C2311yescharacteristic
62C2×D4×C59—21no—
63C2×D4×C59C2311yescharacteristic
64C22×C4×C59—21no—
65C22×C4×C59C2311yescharacteristic
66C2×D236—21no—
67C2×D236—22no—
68C2×D236—22no—
69C2×D236C2311yescharacteristic
70C2×D236C2311yescharacteristic
71C2×C4×D59—21no—
72C2×C4×D59—21no—
73C2×C4×D59—21no—
74C2×C4×D59—21no—
75C4⋊C4×C59—21no—
76C4⋊C4×C59—21no—
77C4⋊C4×C59—21no—
78C4⋊C4×C59D411yescharacteristic
79C4⋊C4×C59D411yescharacteristic
80C4⋊C4×C59C2311yescharacteristic
81C4⋊C4×C59C2311yescharacteristic
82C22⋊C4×C59—21no—
83C22⋊C4×C59—21no—
84C22⋊C4×C59—21no—
85C22⋊C4×C59—21no—
86C22⋊C4×C59—21no—
87C22⋊C4×C59D411yescharacteristic
88C22⋊C4×C59D411yescharacteristic
89C42×C59—21no—
90C42×C59C2311yescharacteristic
91C42×C59C2311yescharacteristic
92C22⋊Dic59—21no—
93#11745671—22no—
94#11745671—22no—
95#11745669—22no—
96#11745669—22no—
97(C2×D59)⋊C4—21no—
98(C2×D59)⋊C4—21no—
99(C2×D59)⋊C4—21no—
100(C2×D59)⋊C4—21no—
101C4⋊Dic59C2311yescharacteristic
102C4⋊Dic59C2311yescharacteristic
103C4×Dic59—21no—
104C2×C59⋊C8C2311yescharacteristic
105C2×C59⋊C8C2311yescharacteristic
106C2×C59⋊C8C2311yescharacteristic
107C2×C59⋊C8C2311yescharacteristic
108C23×C59—21no—
109C23×C59C2×D411yescharacteristic
110C22×D59—21no—
111C22×D59—21no—
112C22×D59—24no—
113C22×D59—81no—
114C22×D59—81no—
115Q8×C59—21no—
116Q8×C59—21no—
117Q8×C59—81no—
118D4×C59—21no—
119D4×C59—21no—
120D4×C59—81no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—81no—
127C2×C4×C59C2×D411yescharacteristic
128C2×C4×C59C2×D411yescharacteristic
129C2×C4×C59C2×D411yescharacteristic
130C2×C4×C59C2×D411yescharacteristic
131C2×C4×C59C2×D411yescharacteristic
132C2×C4×C59C2411yescharacteristic
133C2×Dic59—21no—
134C2×Dic59—21no—
135D236—24no—
136D236—21no—
137D236—21no—
138D236#4112yes—
139D236#4112yes—
140C4×D59—81no—
141C4×D59—81no—
142C4×D59—81no—
143C4×D59—81no—
144C59⋊C8—21no—
145C59⋊C8—21no—
146C59⋊C8—21no—
147C59⋊C8—21no—
148C22×C59—21no—
149C22×C59—21no—
150C22×C59—21no—
151C22×C59—41no—
152C22×C59—41no—
153C22×C59—41no—
154C22×C59C22×D411yescharacteristic
155C2×D59—22no—
156C2×D59—22no—
157C2×D59—41no—
158C2×D59—41no—
159C2×D59—41no—
160C2×D59—41no—
161C2×D59—84no—
162C4×C59—21no—
163C4×C59—21no—
164C4×C59—21no—
165C4×C59—21no—
166C4×C59—21no—
167C4×C59—41no—
168C4×C59—41no—
169C4×C59—41no—
170C4×C59C2×#4111yescharacteristic
171C4×C59C2×#4111yescharacteristic
172Dic59—41no—
173Dic59—41no—
174#3118—591nomaximal, Sylow
175C2×C59—41no—
176C2×C59—81no—
177C2×C59#52511yescharacteristic
178C2×C59#57611yescharacteristic
179C2×C59#57711yescharacteristic
180D59—42no—
181D59—42no—
182#542D5911yescharacteristic, complemented
183#518—591no—
184#485—591no—
185#482—591no—
186#476—591no—
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—21no—
205#124—21no—
206#124C2×D5911yescharacteristic, complemented
207#123—21no—
208C22⋊Q8—21no—
209C22⋊Q8C2×D5911yescharacteristic
210#121C2×D5911yescharacteristic
211C4×Q8C2×D5911yescharacteristic, complemented
212C4×D4—591no—
213C4×D4—591no—
214C4×D4—591no—
215C4×D4—591no—
216C4×D4—1181no—
217C4×D4—1181no—
218C4×D4C2×D5911yescharacteristic, complemented
219#117—591no—
220#117C2×D5911yescharacteristic
221C2×C22⋊C4—1181no—
222C2×C22⋊C4—1181no—
223#107—591no—
224#107—591no—
225#106—591no—
226#106—591no—
227C4⋊C8—591no—
228C4⋊C8—591no—
229#103—591no—
230#103—591no—
231#102—591no—
232#102—591no—
233#102—591no—
234#102—591no—
235#102—591no—
236#102—591no—
237C22⋊C8—591no—
238C22⋊C8—591no—
239#97—591no—
240C4×C8—591no—
241C24—1181no—
242C2×Q8—21no—
243C2×Q8C22×D5911yescharacteristic
244C2×D4—21no—
245C2×D4—591no—
246C2×D4—591no—
247C2×D4—1182no—
248C2×D4—1182no—
249C2×D4—1181no—
250C2×D4C22×D5911yescharacteristic
251C22×C4—21no—
252C22×C4—1181no—
253C22×C4—1181no—
254C22×C4—1181no—
255C22×C4—1181no—
256C22×C4C22×D5911yescharacteristic
257SD16—1182no—
258SD16—1182no—
259D8—1182no—
260D8—1182no—
261C2×C8—591no—
262C2×C8—591no—
263C2×C8—591no—
264C2×C8—591no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—591no—
269C4⋊C4—591no—
270C4⋊C4C22⋊D5911yescharacteristic
271C4⋊C4C22⋊D5911yescharacteristic
272C4⋊C4C22×D5911yescharacteristic
273C4⋊C4C22×D5911yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—1181no—
280C22⋊C4—1181no—
281C22⋊C4—1181no—
282C22⋊C4—1181no—
283C22⋊C4—1181no—
284C22⋊C4C22⋊D5911yescharacteristic
285C22⋊C4C22⋊D5911yescharacteristic
286C42—21no—
287C42—1181no—
288C42C22×D5911yescharacteristic
289C42C22×D5911yescharacteristic
290C23—21no—
291C23—1184no—
292C23—1181no—
293C23—1181no—
294C23—4721no—
295C23—4721no—
296C23C2×C22⋊D5911yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—81no—
300D4—21no—
301D4—21no—
302D4—81no—
303D4—592no—
304D4—592no—
305D4—1184no—
306D4—1181no—
307D4—1181no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—81no—
314C2×C4—1181no—
315C2×C4—1181no—
316C2×C4—4721no—
317C2×C4—4721no—
318C2×C4—4721no—
319C2×C4—4721no—
320C2×C4C2×C22⋊D5911yescharacteristic
321C2×C4C2×C22⋊D5911yescharacteristic
322C2×C4C2×C22⋊D5911yescharacteristic
323C2×C4C2×C22⋊D5911yescharacteristic
324C2×C4C2×C22⋊D5911yescharacteristic
325C2×C4C23×D5911yescharacteristic
326C8—1181no—
327C8—1181no—
328C8—1181no—
329C8—1181no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—1182no—
337C22—1182no—
338C22—4724no—
339C22—2361no—
340C22—2361no—
341C22—2361no—
342C22—2361no—
343C22C22×C22⋊D5911yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—2361no—
353C4—2361no—
354C4#41×D5911yescharacteristic
355C4#41×D5911yescharacteristic
356C2—41no—
357C2—81no—
358C2—2362no—
359C2—2362no—
360C2#1683790911yescharacteristic
361C2#1683820511yescharacteristic
362C2#1683821011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#542C2
socleC22×C59C22×D4
hypercenter#542D59
hypocenterC59#3118
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #16837876C2semidirect
2. #16837740C2semidirect
3. #16837723C2semidirect
4. #16837689C2semidirect
5. #16837679C2semidirect
6. #16837614C2semidirect
7. #16837614C2semidirect
8. #16837552C2semidirect
10. #16837512C2semidirect
11. #16837500C2semidirect
12. C4×#11745671C2semidirect
13. C4×#11745669C2semidirect
14. #16837463C2semidirect
15. C59×#542C2semidirect
30. #14273660C22semidirect
31. #14273660C22semidirect
32. #14273658C22semidirect
33. #14273658C22semidirect
34. C4⋊(C59⋊C8)C22semidirect
35. C4⋊(C59⋊C8)C22semidirect
36. #14273651C22semidirect
37. #14273651C22semidirect
38. #14273648C22semidirect
39. #14273648C22semidirect
46. #14273638C22semidirect
47. C4×C59⋊C8C22semidirect
48. C4⋊Q8×C59C22semidirect
51. #124×C59C22semidirect
56. C4×Q8×C59C22semidirect
57. C4×D4×C59C22semidirect
182. #542D59semidirect
197. C59#3118semidirect
203. C4⋊Q8C2×D59semidirect
206. #124C2×D59semidirect
211. C4×Q8C2×D59semidirect
218. C4×D4C2×D59semidirect