Finite Group Databasebeta

← #21435796

Subgroups — #21435796

Order 7552.

504 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14273750C211yesmaximal, characteristic, complemented
2C22×#11745671C211yesmaximal, characteristic, complemented
3#16838063C211yesmaximal, characteristic, complemented
4#16838043C211yesmaximal, characteristic, complemented
5#16837787C211yesmaximal, characteristic, complemented
6#16837634C211yesmaximal, characteristic, complemented
7#16837633C211yesmaximal, characteristic, complemented
8#16837626C211yesmaximal, characteristic, complemented
9#16837620C211yesmaximal, characteristic, complemented
10#16837563C211yesmaximal, characteristic, complemented
11#16837550C211yesmaximal, characteristic, complemented
12#16837538C211yesmaximal, characteristic, complemented
13#16837487C211yesmaximal, characteristic, complemented
14(C22⋊D59)⋊C8C211yesmaximal, characteristic, complemented
15C59×#451C211yesmaximal, characteristic, complemented
16C2×#11745689C2211yescharacteristic
17C2×#11745689C2211yescharacteristic, complemented
18C22×D236C2211yescharacteristic
19#14273750—24no—
20C2×#11745671—24no—
21C2×#11745671C2211yescharacteristic
22C2×#11745671C2211yescharacteristic
23C2×#11745671C2211yescharacteristic
24C2×#11745671C2211yescharacteristic
25C2×#11745671C2211yescharacteristic, complemented
26C2×D472C2211yescharacteristic
27C2×D472C2211yescharacteristic
28C22×C59⋊C8C2211yescharacteristic
29C2×C8×D59C2211yescharacteristic, complemented
30#14273716—21no—
31#14273716C2211yescharacteristic
32#14273716C2211yescharacteristic, complemented
33#14273712—21no—
34#14273703—21no—
35#14273703C2211yescharacteristic, complemented
36#14273702—21no—
37#14273702C2211yescharacteristic
38#14273701—21no—
39#14273701C2211yescharacteristic
40#14273697—21no—
41Q8×Dic59C2211yescharacteristic, complemented
42#14273689C2211yescharacteristic
43C4×C22⋊D59—21no—
44C4×C22⋊D59C2211yescharacteristic
45C22⋊C4×D59—21no—
46#14273658C2211yescharacteristic, complemented
47Dic59⋊C8C2211yescharacteristic, complemented
48#14273651C2211yescharacteristic, complemented
49#14273649C2211yescharacteristic
50#14273649C2211yescharacteristic
51#14273647C2211yescharacteristic, complemented
52(C2×D59)⋊C8C2211yescharacteristic, complemented
53C8×Dic59C2211yescharacteristic, complemented
54C22×Q8×C59C2211yescharacteristic
55C2×Q16×C59C2211yescharacteristic, complemented
56C2×Q16×C59C2211yescharacteristic, complemented
57C22⋊Q8×C59C2211yescharacteristic
58#103×C59C2211yescharacteristic, complemented
59#103×C59C2211yescharacteristic, complemented
60C22⋊C8×C59C2211yescharacteristic
61C23×D59—21no—
62C2×Q8×C59—21no—
63C2×Q8×C59—22no—
64C2×Q8×C59—41no—
65C2×Q8×C59C2311yescharacteristic
66C2×Q8×C59C2311yescharacteristic
67C2×Q8×C59C2311yescharacteristic
68C22×C4×C59—21no—
69C22×C4×C59C2311yescharacteristic
70C2×C22⋊D59—21no—
71C2×C22⋊D59D411yescharacteristic
72#11745689—22no—
73#11745689—22no—
74#11745689—41no—
75#11745689—41no—
76C2×D236—22no—
77C2×D236—21no—
78C2×D236—21no—
79C2×D236—21no—
80C2×D236—21no—
81C2×D236—41no—
82C2×D236C2311yescharacteristic
83C2×D236C2311yescharacteristic
84C2×D236C2311yescharacteristic
85C2×C4×D59—21no—
86C2×C4×D59—21no—
87C2×C4×D59—21no—
88C2×C4×D59C2311yescharacteristic
89Q16×C59—22no—
90Q16×C59—41no—
91C2×C8×C59C2311yescharacteristic
92C2×C8×C59C2311yescharacteristic
93C4⋊C4×C59—21no—
94C4⋊C4×C59C2311yescharacteristic
95C22⋊C4×C59—21no—
96C22⋊Dic59D411yescharacteristic
97#11745671—22no—
98#11745671—22no—
99#11745671—22no—
100#11745671—22no—
101#11745671D414yescomplemented
102(C2×D59)⋊C4—21no—
103(C2×D59)⋊C4—21no—
104(C2×D59)⋊C4—21no—
105(C2×D59)⋊C4—21no—
106(C2×D59)⋊C4—21no—
107(C2×D59)⋊C4—21no—
108(C2×D59)⋊C4—21no—
109(C2×D59)⋊C4—21no—
110(C2×D59)⋊C4D411yescharacteristic
111C4⋊Dic59—21no—
112C4⋊Dic59C2311yescharacteristic
113Dic59⋊C4—21no—
114Dic59⋊C4D411yescharacteristic
115C4×Dic59—21no—
116C4×Dic59C2311yescharacteristic
117C2×C59⋊C8—22no—
118C2×C59⋊C8C2311yescharacteristic
119C2×C59⋊C8C2311yescharacteristic
120D472—22no—
121D472—41no—
122C8×D59—22no—
123C23×C59C2×D411yescharacteristic
124C22×D59—21no—
125C22×D59—21no—
126C22×D59—21no—
127C22×D59—42no—
128C22×D59—42no—
129C22×D59—81no—
130C22×D59C2×D411yescharacteristic
131Q8×C59—21no—
132Q8×C59—21no—
133Q8×C59—21no—
134Q8×C59—21no—
135Q8×C59—21no—
136Q8×C59—42no—
137Q8×C59C2×D412yes—
138C2×C4×C59—21no—
139C2×C4×C59—21no—
140C2×C4×C59—21no—
141C2×C4×C59—21no—
142C2×C4×C59—21no—
143C2×C4×C59—21no—
144C2×C4×C59—42no—
145C2×C4×C59C2×D411yescharacteristic
146C2×C4×C59C2411yescharacteristic
147C22⋊D59—22no—
148C22⋊D59—42no—
149C2×Dic59—21no—
150C2×Dic59C2×D411yescharacteristic
151C2×Dic59C2×D411yescharacteristic
152C2×Dic59C2×D411yescharacteristic
153D236—21no—
154D236—21no—
155D236—21no—
156D236—21no—
157D236—21no—
158D236—42no—
159D236—42no—
160D236—42no—
161D236—81no—
162D236C2×D412yes—
163C4×D59—21no—
164C4×D59—21no—
165C4×D59—42no—
166C4×D59—42no—
167C4×D59—81no—
168C8×C59—21no—
169C8×C59—21no—
170C59⋊C8—21no—
171C59⋊C8C2×D412yes—
172C22×C59—21no—
173C22×C59—21no—
174C22×C59#13512yescomplemented
175C22×C59C22×D411yescharacteristic
176C2×D59—21no—
177C2×D59—22no—
178C2×D59—21no—
179C2×D59—21no—
180C2×D59—41no—
181C2×D59—41no—
182C2×D59—41no—
183C2×D59—41no—
184C2×D59—41no—
185C2×D59—41no—
186C2×D59—41no—
187C2×D59—41no—
188C2×D59—84no—
189C4×C59—22no—
190C4×C59—21no—
191C4×C59—41no—
192C4×C59—41no—
193C4×C59—41no—
194C4×C59C22×D411yescharacteristic
195C4×C59H(5,𝔽2)11yescharacteristic
196Dic59—21no—
197Dic59—21no—
198Dic59—21no—
199Dic59—41no—
200#3282—591nomaximal, Sylow
201C2×C59—22no—
202C2×C59D4211yescharacteristic
203C2×C59C2×#13511yescharacteristic
204C2×C59#57711yescharacteristic
205D59—41no—
206D59—42no—
207D59—81no—
208D59—81no—
209C2×#135—591no—
210C22×SD16—591no—
211#548—591no—
212#546—591no—
213#495—591no—
214#465—591no—
215#465—591no—
216#464—591no—
217#463—591no—
218#452—591no—
219#451D5911yescharacteristic, complemented
220#449—591no—
221#447—591no—
222C4×SD16—591no—
223C8×D4—591no—
224C59#328211yescharacteristic, complemented, Sylow
225C2×#41—591no—
226C2×#41—591no—
227C22×Q8C2×D5911yescharacteristic
228C22×D4—591no—
229#135—1184no—
230C2×Q16C2×D5911yescharacteristic, complemented
231C2×Q16C2×D5911yescharacteristic, complemented
232C2×SD16—591no—
233C2×SD16—591no—
234C2×SD16—591no—
235C2×SD16—591no—
236C2×SD16—591no—
237C2×SD16—1184no—
238C2×D8—591no—
239C2×D8—591no—
240C22×C8—591no—
241C22×C8—591no—
242#124—591no—
243#124—591no—
244#124—1181no—
245#123—1181no—
246C22⋊Q8—591no—
247C22⋊Q8—1181no—
248C22⋊Q8C2×D5911yescharacteristic
249#121—591no—
250#121—591no—
251#121—1181no—
252#121—1181no—
253#120—1181no—
254C4×Q8—591no—
255C4×D4—591no—
256C4×D4—591no—
257C4×D4—1181no—
258C2×C22⋊C4—1181no—
259#106—591no—
260C4⋊C8—591no—
261#103—591no—
262#103C2×D5911yescharacteristic, complemented
263#103C2×D5911yescharacteristic, complemented
264#102—591no—
265#102—591no—
266#102—591no—
267C22⋊C8—591no—
268C22⋊C8C2×D5911yescharacteristic
269C4×C8—591no—
270C24—1181no—
271#41—1182no—
272#41—1182no—
273#41—2361no—
274#41—2361no—
275C2×Q8—21no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8C22×D5911yescharacteristic
279C2×Q8C22×D5911yescharacteristic
280C2×Q8C22×D5911yescharacteristic
281C2×D4—591no—
282C2×D4—591no—
283C2×D4—591no—
284C2×D4—591no—
285C2×D4—1182no—
286C2×D4—1181no—
287C2×D4—1181no—
288C2×D4—1181no—
289C2×D4—1181no—
290C2×D4—1181no—
291C2×D4—2361no—
292C22×C4—21no—
293C22×C4—591no—
294C22×C4—1181no—
295C22×C4—1181no—
296C22×C4—1181no—
297C22×C4C22×D5911yescharacteristic
298Q16—22no—
299Q16—41no—
300SD16—594no—
301SD16—1182no—
302SD16—1182no—
303SD16—1182no—
304SD16—1182no—
305D8—1182no—
306D8—2361no—
307C2×C8—591no—
308C2×C8—591no—
309C2×C8—1182no—
310C2×C8—1182no—
311C2×C8C22×D5911yescharacteristic
312C2×C8C22×D5911yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—591no—
315C4⋊C4—591no—
316C4⋊C4—1181no—
317C4⋊C4—1181no—
318C4⋊C4C22×D5911yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—591no—
321C22⋊C4—591no—
322C22⋊C4—1181no—
323C22⋊C4—1181no—
324C22⋊C4—1181no—
325C22⋊C4—1181no—
326C22⋊C4—1181no—
327C22⋊C4—1181no—
328C22⋊C4—1181no—
329C22⋊C4—1181no—
330C42—591no—
331C42—1181no—
332C23—591no—
333C23—1181no—
334C23—1181no—
335C23—1181no—
336C23—4721no—
337C23—2362no—
338C23—2362no—
339C23D4×D5911yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—21no—
344Q8—21no—
345Q8—42no—
346Q8D4×D5912yes—
347D4—592no—
348D4—1182no—
349D4—1181no—
350D4—1181no—
351D4—1181no—
352D4—1181no—
353D4—1181no—
354D4—4721no—
355D4—2362no—
356D4—2362no—
357D4—2362no—
358D4—2362no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—42no—
366C2×C4—591no—
367C2×C4—591no—
368C2×C4—591no—
369C2×C4—1181no—
370C2×C4—1181no—
371C2×C4—1181no—
372C2×C4—4721no—
373C2×C4—2362no—
374C2×C4—2362no—
375C2×C4D4×D5911yescharacteristic
376C2×C4C23×D5911yescharacteristic
377C8—21no—
378C8—21no—
379C8—592no—
380C8—1181no—
381C22—21no—
382C22—21no—
383C22—1181no—
384C22—1181no—
385C22—1181no—
386C22—1182no—
387C22—4724no—
388C22—2361no—
389C22—2361no—
390C22—2361no—
391C22—2361no—
392C22—2361no—
393C22—2361no—
394C22—2361no—
395C22—2361no—
396C22#1427375012yescomplemented
397C22C2×D4×D5911yescharacteristic
398C4—21no—
399C4—22no—
400C4—41no—
401C4—41no—
402C4—41no—
403C4—1181no—
404C4—1181no—
405C4—1181no—
406C4—2361no—
407C4C2×D4×D5911yescharacteristic
408C4#1427377211yescharacteristic
409C2—22no—
410C2—4721no—
411C2—4721no—
412C2—2361no—
413C2—2362no—
414C2#1683803411yescharacteristic
415C2C2×#1427375011yescharacteristic
416C2#1683821111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#451C2
socleC22×C59C22×D4
hypercenter#451D59
hypocenterC59#3282
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
1. C2×#14273750C2semidirect
2. C22×#11745671C2semidirect
3. #16838063C2semidirect
4. #16838043C2semidirect
5. #16837787C2semidirect
6. #16837634C2semidirect
7. #16837633C2semidirect
8. #16837626C2semidirect
9. #16837620C2semidirect
10. #16837563C2semidirect
11. #16837550C2semidirect
12. #16837538C2semidirect
13. #16837487C2semidirect
14. (C22⋊D59)⋊C8C2semidirect
15. C59×#451C2semidirect
17. C2×#11745689C22semidirect
25. C2×#11745671C22semidirect
29. C2×C8×D59C22semidirect
32. #14273716C22semidirect
35. #14273703C22semidirect
41. Q8×Dic59C22semidirect
46. #14273658C22semidirect
47. Dic59⋊C8C22semidirect
48. #14273651C22semidirect
51. #14273647C22semidirect
52. (C2×D59)⋊C8C22semidirect
53. C8×Dic59C22semidirect
55. C2×Q16×C59C22semidirect
56. C2×Q16×C59C22semidirect
58. #103×C59C22semidirect
59. #103×C59C22semidirect
101. #11745671D4semidirect
174. C22×C59#135semidirect
219. #451D59semidirect
224. C59#3282semidirect
230. C2×Q16C2×D59semidirect
231. C2×Q16C2×D59semidirect
262. #103C2×D59semidirect
263. #103C2×D59semidirect
396. C22#14273750semidirect