Finite Group Databasebeta

← #21434934

Subgroups — #21434934

Order 7552.

418 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16837915C211yesmaximal, characteristic, complemented
2#16837912C211yesmaximal, characteristic, complemented
3#16837745C211yesmaximal, characteristic, complemented
4#16837742C211yesmaximal, characteristic, complemented
5#16837729C211yesmaximal, characteristic, complemented
6#16837724C211yesmaximal, characteristic, complemented
7#16837658C211yesmaximal, characteristic, complemented
8#16837653C211yesmaximal, characteristic, complemented
9#16837648C211yesmaximal, characteristic, complemented
10#16837567C211yesmaximal, characteristic, complemented
11#16837561C211yesmaximal, characteristic, complemented
12#16837548C211yesmaximal, characteristic, complemented
13#16837546C211yesmaximal, characteristic, complemented
14#16837365C211yesmaximal, characteristic, complemented
15C59×#468C211yesmaximal, characteristic, complemented
16C2×#11745689C2211yescharacteristic
17C2×#11745687C2211yescharacteristic
18C22×C4×D59C2211yescharacteristic
19C2×#11745672C2211yescharacteristic, complemented
20C2×#11745660C2211yescharacteristic, complemented
21C2×#11745669C2211yescharacteristic, complemented
22C2×#11745664C2211yescharacteristic
23#14273712—21no—
24#14273709—21no—
25#14273707C2211yescharacteristic
26#14273706C2211yescharacteristic
27#14273703C2211yescharacteristic
28#14273702C2211yescharacteristic
29#14273701C2211yescharacteristic
30#14273698C2211yescharacteristic
31#14273697—21no—
32#14273695—21no—
33D4×Dic59—21no—
34#14273689—21no—
35(C22⋊D59)⋊C4—21no—
36(C22⋊D59)⋊C4—21no—
37#14273685C2211yescharacteristic
38#14273685C2211yescharacteristic
39#14273661C2211yescharacteristic, complemented
40#14273658C2211yescharacteristic, complemented
41#14273658C2211yescharacteristic, complemented
42#14273652C2211yescharacteristic, complemented
43#14273651C2211yescharacteristic, complemented
44#14273650C2211yescharacteristic, complemented
45#14273649C2211yescharacteristic, complemented
46#14273648C2211yescharacteristic, complemented
47#14273647C2211yescharacteristic, complemented
48(C2×D59)⋊C8C2211yescharacteristic
49(C2×D59)⋊C8C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51(C2×D59)⋊C8C2211yescharacteristic
52C2×SD16×C59C2211yescharacteristic, complemented
53C2×M16×C59C2211yescharacteristic
54C22⋊Q8×C59C2211yescharacteristic
55#121×C59C2211yescharacteristic
56#107×C59C2211yescharacteristic, complemented
57#103×C59C2211yescharacteristic, complemented
58#102×C59C2211yescharacteristic, complemented
59C23×D59D411yescharacteristic
60C2×Q8×C59C2311yescharacteristic
61C2×D4×C59—21no—
62C2×D4×C59C2311yescharacteristic
63C22×C4×C59C2311yescharacteristic
64C2×C22⋊D59—21no—
65C2×C22⋊D59—21no—
66C2×C22⋊D59—21no—
67C22×Dic59—21no—
68C22×Dic59D411yescharacteristic
69#11745689—41no—
70#11745689—41no—
71#11745687—41no—
72#11745687—41no—
73C2×D236—21no—
74C2×D236—21no—
75C2×D236C2311yescharacteristic
76C2×C4×D59—21no—
77C2×C4×D59—41no—
78C2×C4×D59—41no—
79C2×C4×D59D411yescharacteristic
80C2×C4×D59D411yescharacteristic
81C2×C4×D59C2311yescharacteristic
82C2×C4×D59C2311yescharacteristic
83C2×Dic118C2311yescharacteristic
84SD16×C59—41no—
85M16×C59—41no—
86C2×C8×C59C2311yescharacteristic
87C2×C8×C59C2311yescharacteristic
88C4⋊C4×C59—21no—
89C4⋊C4×C59C2311yescharacteristic
90C4⋊C4×C59C2311yescharacteristic
91C22⋊C4×C59—21no—
92C22⋊C4×C59—21no—
93C22⋊Dic59—21no—
94C22⋊Dic59—21no—
95#11745672—41no—
96#11745669—41no—
97(C2×D59)⋊C4—21no—
98(C2×D59)⋊C4—21no—
99(C2×D59)⋊C4—21no—
100(C2×D59)⋊C4—21no—
101(C2×D59)⋊C4—21no—
102(C2×D59)⋊C4—21no—
103C4⋊Dic59—21no—
104C4⋊Dic59C2311yescharacteristic
105C4⋊Dic59C2311yescharacteristic
106Dic59⋊C4—21no—
107Dic59⋊C4—21no—
108C4×Dic59—21no—
109C4×Dic59—21no—
110#11745664—41no—
111C2×C59⋊C8C2311yescharacteristic
112C2×C59⋊C8C2311yescharacteristic
113#11745660—41no—
114C23×C59—21no—
115C23×C59C2×D411yescharacteristic
116C22×D59—21no—
117C22×D59—41no—
118C22×D59—41no—
119C22×D59—41no—
120C22×D59C2×D411yescharacteristic
121C22×D59C2×D411yescharacteristic
122Q8×C59—21no—
123Q8×C59—21no—
124D4×C59—21no—
125D4×C59—21no—
126D4×C59—42no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C2×C4×C59—21no—
132C2×C4×C59C2×D411yescharacteristic
133C2×C4×C59C2411yescharacteristic
134C22⋊D59—42no—
135C22⋊D59—42no—
136C22⋊D59—42no—
137C2×Dic59—21no—
138C2×Dic59—21no—
139C2×Dic59—21no—
140C2×Dic59—41no—
141C2×Dic59—42no—
142C2×Dic59C2×D411yescharacteristic
143C2×Dic59C2×D411yescharacteristic
144D236—21no—
145D236—21no—
146D236—42no—
147D236—42no—
148C4×D59—21no—
149C4×D59—21no—
150C4×D59—21no—
151C4×D59—21no—
152C4×D59—41no—
153C4×D59—41no—
154C4×D59—42no—
155Dic118—21no—
156Dic118—21no—
157C8×C59—21no—
158C8×C59—21no—
159C59⋊C8—21no—
160C59⋊C8—21no—
161C22×C59—21no—
162C22×C59—21no—
163C22×C59—21no—
164C22×C59—41no—
165C22×C59—41no—
166C22×C59—41no—
167C22×C59C22×D411yescharacteristic
168C2×D59—21no—
169C2×D59—21no—
170C2×D59—21no—
171C2×D59—21no—
172C2×D59—21no—
173C2×D59—21no—
174C2×D59—44no—
175C2×D59—41no—
176C2×D59—41no—
177C2×D59—41no—
178C4×C59—21no—
179C4×C59—41no—
180C4×C59—41no—
181C4×C59—41no—
182C4×C59H(5,𝔽2)11yescharacteristic
183C4×C59H(5,𝔽2)11yescharacteristic
184Dic59—21no—
185Dic59—21no—
186Dic59—41no—
187Dic59—41no—
188Dic59—41no—
189#3197—591nomaximal, Sylow
190C2×C59—41no—
191C2×C59—81no—
192C2×C59#53411yescharacteristic
193C2×C59#57511yescharacteristic
194C2×C59#57511yescharacteristic
195D59—41no—
196D59—41no—
197D59—81no—
198#525—591no—
199#525—591no—
200#485—591no—
201#485—591no—
202#482—591no—
203#482—591no—
204#470—591no—
205#469—591no—
206#468—591no—
207#468D5911yescharacteristic, complemented
208#452—591no—
209#452—591no—
210#449—591no—
211#449—591no—
212#407—591no—
213C59#319711yescharacteristic, complemented, Sylow
214C2×#41—591no—
215C2×#41—591no—
216C23×C4—591no—
217C2×Q16—591no—
218C2×SD16—591no—
219C2×SD16C2×D5911yescharacteristic, complemented
220C2×D8—591no—
221C2×M16—591no—
222C2×M16C2×D5911yescharacteristic
223#123—1181no—
224#123—1181no—
225C22⋊Q8—591no—
226C22⋊Q8—591no—
227C22⋊Q8—591no—
228C22⋊Q8C2×D5911yescharacteristic
229#121—591no—
230#121—591no—
231#121—591no—
232#121C2×D5911yescharacteristic
233#120—1181no—
234#120—1181no—
235C4×D4—1181no—
236C4×D4—1181no—
237C4×D4—1181no—
238C4×D4—1181no—
239#117—591no—
240#117—591no—
241#107—591no—
242#107C2×D5911yescharacteristic, complemented
243#106—591no—
244#106—591no—
245#103—591no—
246#103—591no—
247#103—591no—
248#103C2×D5911yescharacteristic, complemented
249#102—591no—
250#102—591no—
251#102—591no—
252#102C2×D5911yescharacteristic, complemented
253C22⋊C8—591no—
254C22⋊C8—591no—
255C22⋊C8—591no—
256C22⋊C8—591no—
257C24—591no—
258#41—2361no—
259#41—2361no—
260#41—2361no—
261#41—2361no—
262C2×Q8—591no—
263C2×Q8C22×D5911yescharacteristic
264C2×D4—21no—
265C2×D4—591no—
266C2×D4—1181no—
267C2×D4—1181no—
268C2×D4—1181no—
269C2×D4—1181no—
270C2×D4—1181no—
271C2×D4C22×D5911yescharacteristic
272C22×C4—591no—
273C22×C4—591no—
274C22×C4—591no—
275C22×C4—591no—
276C22×C4—591no—
277C22×C4—1181no—
278C22×C4—1181no—
279C22×C4—2361no—
280C22×C4—2361no—
281C22×C4C22×D5911yescharacteristic
282Q16—2361no—
283SD16—41no—
284SD16—2361no—
285D8—2361no—
286M16—41no—
287M16—2361no—
288C2×C8—591no—
289C2×C8—591no—
290C2×C8C22×D5911yescharacteristic
291C2×C8C22×D5911yescharacteristic
292C4⋊C4—21no—
293C4⋊C4—591no—
294C4⋊C4—591no—
295C4⋊C4—1181no—
296C4⋊C4—1181no—
297C4⋊C4—1181no—
298C4⋊C4C22×D5911yescharacteristic
299C4⋊C4C22×D5911yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—1181no—
303C22⋊C4—1181no—
304C22⋊C4—1181no—
305C22⋊C4—1181no—
306C22⋊C4—1181no—
307C22⋊C4—1181no—
308C22⋊C4—1181no—
309C22⋊C4—1181no—
310C42—1181no—
311C42—1181no—
312C23—21no—
313C23—591no—
314C23—591no—
315C23—1181no—
316C23—2361no—
317C23—2361no—
318C23—2361no—
319C23D4×D5911yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—1181no—
323Q8—1181no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—1181no—
328D4—1181no—
329D4—2362no—
330D4—2362no—
331D4—2362no—
332D4—2362no—
333D4—2362no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—591no—
340C2×C4—591no—
341C2×C4—1181no—
342C2×C4—1181no—
343C2×C4—1181no—
344C2×C4—1181no—
345C2×C4—1181no—
346C2×C4—1181no—
347C2×C4—1181no—
348C2×C4—2361no—
349C2×C4—2361no—
350C2×C4—2362no—
351C2×C4—2361no—
352C2×C4—2362no—
353C2×C4D4×D5911yescharacteristic
354C2×C4C23×D5911yescharacteristic
355C8—21no—
356C8—21no—
357C8—1181no—
358C8—1181no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—1181no—
366C22—1181no—
367C22—1181no—
368C22—1181no—
369C22—1181no—
370C22—1181no—
371C22—2364no—
372C22—2361no—
373C22—2361no—
374C22—2361no—
375C22C2×D4×D5911yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—1181no—
381C4—1181no—
382C4—2361no—
383C4—2361no—
384C4—2361no—
385C4#1427377211yescharacteristic
386C4#1427377311yescharacteristic
387C2—41no—
388C2—81no—
389C2—4721no—
390C2—2361no—
391C2—2361no—
392C2#1683796011yescharacteristic
393C2#1683819811yescharacteristic
394C2#1683820111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#468C2
socleC22×C59C22×D4
hypercenter#468D59
hypocenterC59#3197
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #16837915C2semidirect
2. #16837912C2semidirect
3. #16837745C2semidirect
4. #16837742C2semidirect
5. #16837729C2semidirect
6. #16837724C2semidirect
7. #16837658C2semidirect
8. #16837653C2semidirect
9. #16837648C2semidirect
10. #16837567C2semidirect
11. #16837561C2semidirect
12. #16837548C2semidirect
13. #16837546C2semidirect
14. #16837365C2semidirect
15. C59×#468C2semidirect
19. C2×#11745672C22semidirect
20. C2×#11745660C22semidirect
21. C2×#11745669C22semidirect
39. #14273661C22semidirect
40. #14273658C22semidirect
41. #14273658C22semidirect
42. #14273652C22semidirect
43. #14273651C22semidirect
44. #14273650C22semidirect
45. #14273649C22semidirect
46. #14273648C22semidirect
47. #14273647C22semidirect
52. C2×SD16×C59C22semidirect
56. #107×C59C22semidirect
57. #103×C59C22semidirect
58. #102×C59C22semidirect
207. #468D59semidirect
213. C59#3197semidirect
219. C2×SD16C2×D59semidirect
242. #107C2×D59semidirect
248. #103C2×D59semidirect
252. #102C2×D59semidirect