Finite Group Databasebeta

← #21434942

Subgroups — #21434942

Order 7552.

422 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16837966C211yesmaximal, characteristic, complemented
2#16837740C211yesmaximal, characteristic, complemented
3#16837723C211yesmaximal, characteristic, complemented
4#16837720C211yesmaximal, characteristic, complemented
5#16837715C211yesmaximal, characteristic, complemented
6#16837653C211yesmaximal, characteristic, complemented
7#16837650C211yesmaximal, characteristic, complemented
8#16837636C211yesmaximal, characteristic, complemented
9#16837633C211yesmaximal, characteristic, complemented
10#16837552C211yesmaximal, characteristic, complemented
11#16837547C211yesmaximal, characteristic, complemented
12#16837547C211yesmaximal, characteristic, complemented
13#16837535C211yesmaximal, characteristic, complemented
14#16837369C211yesmaximal, characteristic, complemented
15C59×#537C211yesmaximal, characteristic, complemented
16C22×D236C2211yescharacteristic
17C2×#11745671C2211yescharacteristic
18C2×#11745671C2211yescharacteristic
19C2×#11745669C2211yescharacteristic
20C2×#11745669C2211yescharacteristic
21C2×#11745664C2211yescharacteristic, complemented
22C22×C59⋊C8C2211yescharacteristic, complemented
23#14273723—21no—
24#14273716—21no—
25#14273701C2211yescharacteristic
26#14273701C2211yescharacteristic
27#14273701C2211yescharacteristic
28#14273701C2211yescharacteristic
29#14273695—21no—
30#14273695—21no—
31#14273686C2211yescharacteristic
32#14273660C2211yescharacteristic, complemented
33#14273660C2211yescharacteristic, complemented
34#14273658C2211yescharacteristic, complemented
35#14273658C2211yescharacteristic, 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
46C22⋊(C59⋊C8)C2211yescharacteristic, complemented
47C22⋊(C59⋊C8)C2211yescharacteristic, complemented
48C2×#41×C59C2211yescharacteristic
49C2×#41×C59C2211yescharacteristic, complemented
50C22⋊Q8×C59—21no—
51C22⋊Q8×C59C2211yescharacteristic
52C22⋊Q8×C59C2211yescharacteristic, complemented
53#121×C59—21no—
54#121×C59—21no—
55#121×C59—21no—
56#121×C59C2211yescharacteristic
57#121×C59C2211yescharacteristic, complemented
58C2×C4⋊C4×C59C2211yescharacteristic, complemented
59C23×D59—21no—
60#41×C59—41no—
61#41×C59—41no—
62#41×C59—41no—
63#41×C59—41no—
64C2×Q8×C59D411yescharacteristic
65C2×Q8×C59C2311yescharacteristic
66C2×D4×C59—21no—
67C2×D4×C59—21no—
68C2×D4×C59—21no—
69C2×D4×C59D411yescharacteristic
70C2×D4×C59D411yescharacteristic
71C2×D4×C59D411yescharacteristic
72C2×D4×C59C2311yescharacteristic
73C22×C4×C59—21no—
74C22×C4×C59—21no—
75C22×C4×C59C2311yescharacteristic
76C22×C4×C59C2311yescharacteristic
77C22×C4×C59C2311yescharacteristic
78C2×C22⋊D59—21no—
79C2×C22⋊D59—21no—
80C2×C22⋊D59—21no—
81C2×C22⋊D59—21no—
82C2×D236—21no—
83C2×D236—41no—
84C2×D236—41no—
85C2×D236C2311yescharacteristic
86C2×D236C2311yescharacteristic
87C4⋊C4×C59—21no—
88C4⋊C4×C59—21no—
89C4⋊C4×C59—21no—
90C4⋊C4×C59C2311yescharacteristic
91C4⋊C4×C59C2311yescharacteristic
92C22⋊C4×C59—21no—
93C22⋊C4×C59—21no—
94C22⋊C4×C59—21no—
95C22⋊C4×C59—21no—
96C22⋊Dic59—21no—
97#11745671—41no—
98#11745671—41no—
99#11745669—41no—
100#11745669—41no—
101(C2×D59)⋊C4—21no—
102(C2×D59)⋊C4—21no—
103(C2×D59)⋊C4—21no—
104(C2×D59)⋊C4—21no—
105C4⋊Dic59C2311yescharacteristic
106C4⋊Dic59C2311yescharacteristic
107C4×Dic59—21no—
108#11745664—41no—
109C2×C59⋊C8—41no—
110C2×C59⋊C8C2311yescharacteristic
111C2×C59⋊C8C2311yescharacteristic
112C2×C59⋊C8C2311yescharacteristic
113C2×C59⋊C8C2311yescharacteristic
114C23×C59—21no—
115C23×C59C2×D411yescharacteristic
116C23×C59C2×D411yescharacteristic
117C23×C59C2×D411yescharacteristic
118C22×D59—21no—
119C22×D59—21no—
120C22×D59—42no—
121C22×D59—81no—
122C22×D59—81no—
123Q8×C59—21no—
124Q8×C59—21no—
125Q8×C59—41no—
126D4×C59—21no—
127D4×C59—21no—
128D4×C59—41no—
129D4×C59—41no—
130D4×C59—41no—
131D4×C59—42no—
132D4×C59—81no—
133D4×C59—81no—
134C2×C4×C59—21no—
135C2×C4×C59—21no—
136C2×C4×C59—21no—
137C2×C4×C59—21no—
138C2×C4×C59—21no—
139C2×C4×C59—21no—
140C2×C4×C59—21no—
141C2×C4×C59—21no—
142C2×C4×C59—21no—
143C2×C4×C59—42no—
144C2×C4×C59—81no—
145C2×C4×C59C2×D411yescharacteristic
146C2×C4×C59C2×D411yescharacteristic
147C2×C4×C59C2×D411yescharacteristic
148C2×C4×C59C2411yescharacteristic
149C22⋊D59—81no—
150C22⋊D59—81no—
151C22⋊D59—81no—
152C22⋊D59—81no—
153C2×Dic59—21no—
154C2×Dic59—21no—
155D236—21no—
156D236—21no—
157D236—21no—
158D236—21no—
159D236—42no—
160C59⋊C8—21no—
161C59⋊C8—21no—
162C59⋊C8—21no—
163C59⋊C8—21no—
164C22×C59—21no—
165C22×C59—21no—
166C22×C59—21no—
167C22×C59—21no—
168C22×C59—21no—
169C22×C59—21no—
170C22×C59—21no—
171C22×C59—21no—
172C22×C59—21no—
173C22×C59—41no—
174C22×C59—41no—
175C22×C59—41no—
176C22×C59C22×D411yescharacteristic
177C2×D59—41no—
178C2×D59—41no—
179C2×D59—41no—
180C2×D59—41no—
181C2×D59—41no—
182C2×D59—41no—
183C2×D59—84no—
184C4×C59—21no—
185C4×C59—21no—
186C4×C59—21no—
187C4×C59—41no—
188C4×C59—41no—
189C4×C59—41no—
190C4×C59H(5,𝔽2)11yescharacteristic
191C4×C59H(5,𝔽2)11yescharacteristic
192Dic59—41no—
193Dic59—41no—
194#3198—591nomaximal, Sylow
195C2×C59—41no—
196C2×C59—41no—
197C2×C59—41no—
198C2×C59—81no—
199C2×C59#53411yescharacteristic
200C2×C59#57611yescharacteristic
201C2×C59#57711yescharacteristic
202D59—81no—
203D59—81no—
204#537D5911yescharacteristic, complemented
205#535—591no—
206#485—591no—
207#482—591no—
208#481—591no—
209#480—591no—
210#469—591no—
211#468—591no—
212#466—591no—
213#465—591no—
214#450—591no—
215#449—591no—
216#449—591no—
217#447—591no—
218#408—591no—
219C59#319811yescharacteristic, complemented, Sylow
220C2×#41C2×D5911yescharacteristic
221C2×#41C2×D5911yescharacteristic, complemented
222C22×D4—591no—
223C2×SD16—591no—
224C2×SD16—591no—
225C2×D8—591no—
226C2×D8—591no—
227C2×M16—591no—
228C22×C8—591no—
229#127—1181no—
230#124—1181no—
231C22⋊Q8—21no—
232C22⋊Q8C2×D5911yescharacteristic
233C22⋊Q8C2×D5911yescharacteristic, complemented
234#121—21no—
235#121—21no—
236#121—21no—
237#121—591no—
238#121—591no—
239#121—591no—
240#121—591no—
241#121C2×D5911yescharacteristic
242#121C2×D5911yescharacteristic, complemented
243#120—1181no—
244#120—1181no—
245#117—591no—
246C2×C4⋊C4C2×D5911yescharacteristic, complemented
247#107—591no—
248#107—591no—
249#106—591no—
250#106—591no—
251#103—591no—
252#103—591no—
253#102—591no—
254#102—591no—
255#102—591no—
256#102—591no—
257#102—591no—
258#102—591no—
259C22⋊C8—591no—
260C22⋊C8—591no—
261C22⋊C8—591no—
262C22⋊C8—591no—
263C24—1181no—
264#41—41no—
265#41—41no—
266#41—41no—
267#41—41no—
268C2×Q8C22⋊D5911yescharacteristic
269C2×Q8C22×D5911yescharacteristic
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—591no—
274C2×D4—591no—
275C2×D4—1181no—
276C2×D4—1181no—
277C2×D4—1181no—
278C2×D4—1181no—
279C2×D4—1181no—
280C2×D4—2361no—
281C2×D4—2361no—
282C2×D4C22⋊D5911yescharacteristic
283C2×D4C22⋊D5911yescharacteristic
284C2×D4C22⋊D5911yescharacteristic
285C2×D4C22×D5911yescharacteristic
286C22×C4—21no—
287C22×C4—21no—
288C22×C4C22×D5911yescharacteristic
289C22×C4C22×D5911yescharacteristic
290C22×C4C22×D5911yescharacteristic
291SD16—2361no—
292SD16—2361no—
293D8—2361no—
294D8—2361no—
295M16—2361no—
296C2×C8—591no—
297C2×C8—591no—
298C2×C8—591no—
299C2×C8—591no—
300C2×C8—2361no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—591no—
305C4⋊C4—591no—
306C4⋊C4C22×D5911yescharacteristic
307C4⋊C4C22×D5911yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—1181no—
313C22⋊C4—1181no—
314C22⋊C4—1181no—
315C22⋊C4—1181no—
316C22⋊C4—1181no—
317C42—1181no—
318C23—21no—
319C23—1181no—
320C23—1181no—
321C23—4721no—
322C23—4721no—
323C23—2362no—
324C23C2×C22⋊D5911yescharacteristic
325C23C2×C22⋊D5911yescharacteristic
326C23C2×C22⋊D5911yescharacteristic
327Q8—21no—
328Q8—21no—
329Q8—41no—
330D4—21no—
331D4—21no—
332D4—41no—
333D4—41no—
334D4—41no—
335D4—42no—
336D4—81no—
337D4—81no—
338D4—1181no—
339D4—1181no—
340D4—1181no—
341D4—1181no—
342D4—4721no—
343D4—4721no—
344D4—4721no—
345D4—4721no—
346D4—2362no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—42no—
357C2×C4—81no—
358C2×C4—1181no—
359C2×C4—1181no—
360C2×C4C2×C22⋊D5911yescharacteristic
361C2×C4C2×C22⋊D5911yescharacteristic
362C2×C4C2×C22⋊D5911yescharacteristic
363C2×C4C23×D5911yescharacteristic
364C8—1181no—
365C8—1181no—
366C8—1181no—
367C8—1181no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—4724no—
381C22—2361no—
382C22—2361no—
383C22—2361no—
384C22—2361no—
385C22—2361no—
386C22—2361no—
387C22C22×C22⋊D5911yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—2361no—
395C4—2361no—
396C4#1427377211yescharacteristic
397C4#1427377211yescharacteristic
398C2—41no—
399C2—41no—
400C2—41no—
401C2—81no—
402C2—4721no—
403C2—4721no—
404C2#1683796111yescharacteristic
405C2#1683820511yescharacteristic
406C2#1683821011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#537C2
socleC22×C59C22×D4
hypercenter#537D59
hypocenterC59#3198
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #16837966C2semidirect
2. #16837740C2semidirect
3. #16837723C2semidirect
4. #16837720C2semidirect
5. #16837715C2semidirect
6. #16837653C2semidirect
7. #16837650C2semidirect
8. #16837636C2semidirect
9. #16837633C2semidirect
10. #16837552C2semidirect
11. #16837547C2semidirect
12. #16837547C2semidirect
13. #16837535C2semidirect
14. #16837369C2semidirect
15. C59×#537C2semidirect
21. C2×#11745664C22semidirect
22. C22×C59⋊C8C22semidirect
32. #14273660C22semidirect
33. #14273660C22semidirect
34. #14273658C22semidirect
35. #14273658C22semidirect
36. #14273651C22semidirect
37. #14273651C22semidirect
38. #14273648C22semidirect
39. #14273648C22semidirect
46. C22⋊(C59⋊C8)C22semidirect
47. C22⋊(C59⋊C8)C22semidirect
49. C2×#41×C59C22semidirect
52. C22⋊Q8×C59C22semidirect
57. #121×C59C22semidirect
58. C2×C4⋊C4×C59C22semidirect
204. #537D59semidirect
219. C59#3198semidirect
221. C2×#41C2×D59semidirect
233. C22⋊Q8C2×D59semidirect
242. #121C2×D59semidirect
246. C2×C4⋊C4C2×D59semidirect