Finite Group Databasebeta

← #21434954

Subgroups — #21434954

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#16837982C211yesmaximal, characteristic, complemented
2#16837971C211yesmaximal, characteristic, complemented
3#16837726C211yesmaximal, characteristic, complemented
4#16837722C211yesmaximal, characteristic, complemented
5#16837717C211yesmaximal, characteristic, complemented
6#16837656C211yesmaximal, characteristic, complemented
7#16837651C211yesmaximal, characteristic, complemented
8#16837639C211yesmaximal, characteristic, complemented
9#16837634C211yesmaximal, characteristic, complemented
10#16837552C211yesmaximal, characteristic, complemented
11#16837550C211yesmaximal, characteristic, complemented
12#16837550C211yesmaximal, characteristic, complemented
13#16837538C211yesmaximal, characteristic, complemented
14#16837367C211yesmaximal, characteristic, complemented
15C59×#485C211yesmaximal, characteristic, complemented
16C2×#11745689C2211yescharacteristic, complemented
17C2×#11745685C2211yescharacteristic
18C22×D236C2211yescharacteristic
19C2×#11745671C2211yescharacteristic
20C2×#11745671C2211yescharacteristic
21C2×D472C2211yescharacteristic
22C2×D472C2211yescharacteristic
23C2×#11745659C2211yescharacteristic, complemented
24C2×C8×D59C2211yescharacteristic, complemented
25#14273724—21no—
26#14273715—21no—
27#14273705—21no—
28#14273703C2211yescharacteristic, complemented
29#14273702—21no—
30#14273702C2211yescharacteristic
31#14273702C2211yescharacteristic
32#14273702C2211yescharacteristic
33#14273702C2211yescharacteristic
34#14273702C2211yescharacteristic, complemented
35#14273701C2211yescharacteristic
36#14273700—21no—
37#14273700—21no—
38#14273697—21no—
39#14273697—21no—
40C4⋊C4×D59C2211yescharacteristic, complemented
41#14273660C2211yescharacteristic, complemented
42#14273658C2211yescharacteristic, complemented
43#14273649C2211yescharacteristic
44#14273649C2211yescharacteristic
45#14273647C2211yescharacteristic
46#14273647C2211yescharacteristic
47#14273647C2211yescharacteristic, complemented
48#14273647C2211yescharacteristic, complemented
49C22⋊(C59⋊C8)C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic, complemented
51(C2×D59)⋊C8C2211yescharacteristic, complemented
52C22⋊Q8×C59C2211yescharacteristic
53#117×C59C2211yescharacteristic
54#107×C59C2211yescharacteristic, complemented
55#106×C59C2211yescharacteristic, complemented
56#103×C59C2211yescharacteristic, complemented
57#103×C59C2211yescharacteristic, complemented
58C22⋊C8×C59C2211yescharacteristic
59C23×D59—21no—
60C2×Q8×C59C2311yescharacteristic
61C22×C4×C59C2311yescharacteristic
62C2×C22⋊D59—21no—
63C2×C22⋊D59D411yescharacteristic
64C2×C22⋊D59D411yescharacteristic
65#11745689—41no—
66#11745689—41no—
67#11745685—41no—
68#11745685—41no—
69C2×D236—21no—
70C2×D236—21no—
71C2×D236—21no—
72C2×D236—21no—
73C2×D236—21no—
74C2×D236—21no—
75C2×D236—21no—
76C2×D236—41no—
77C2×D236—41no—
78C2×D236D411yescharacteristic
79C2×D236C2311yescharacteristic
80C2×D236C2311yescharacteristic
81C2×D236C2311yescharacteristic
82C2×C4×D59—21no—
83C2×C4×D59—21no—
84C2×C4×D59C2311yescharacteristic
85C2×C4×D59C2311yescharacteristic
86C2×Dic118D411yescharacteristic
87C2×C8×C59C2311yescharacteristic
88C2×C8×C59C2311yescharacteristic
89C4⋊C4×C59—21no—
90C4⋊C4×C59C2311yescharacteristic
91C4⋊C4×C59C2311yescharacteristic
92C4⋊C4×C59C2311yescharacteristic
93C22⋊C4×C59—21no—
94C22⋊C4×C59—21no—
95C42×C59—21no—
96#11745671—41no—
97#11745671—41no—
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—
103(C2×D59)⋊C4—21no—
104(C2×D59)⋊C4—21no—
105C4⋊Dic59C2311yescharacteristic
106Dic59⋊C4—21no—
107Dic59⋊C4—21no—
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110D472—41no—
111D472—41no—
112#11745659—41no—
113C8×D59—41no—
114C23×C59C2×D411yescharacteristic
115C22×D59—21no—
116C22×D59—21no—
117C22×D59—21no—
118C22×D59—42no—
119C22×D59—81no—
120C22×D59—81no—
121C22×D59C2×D411yescharacteristic
122C22×D59C2×D411yescharacteristic
123Q8×C59—21no—
124Q8×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C2×C4×C59C2×D411yescharacteristic
132C2×C4×C59C2411yescharacteristic
133C22⋊D59—41no—
134C22⋊D59—41no—
135C22⋊D59—81no—
136C2×Dic59—21no—
137C2×Dic59C2×D411yescharacteristic
138C2×Dic59C2×D411yescharacteristic
139D236—21no—
140D236—21no—
141D236—21no—
142D236—21no—
143D236—21no—
144D236—21no—
145D236—41no—
146D236—42no—
147D236—42no—
148D236—81no—
149D236—81no—
150D236—81no—
151D236—81no—
152D236—81no—
153C4×D59—21no—
154C4×D59—21no—
155C4×D59—21no—
156C4×D59—21no—
157C4×D59—42no—
158C4×D59—81no—
159Dic118—41no—
160C8×C59—21no—
161C8×C59—21no—
162C59⋊C8—21no—
163C59⋊C8—21no—
164C22×C59—21no—
165C22×C59—21no—
166C22×C59—21no—
167C22×C59C22×D411yescharacteristic
168C2×D59—21no—
169C2×D59—21no—
170C2×D59—21no—
171C2×D59—21no—
172C2×D59—21no—
173C2×D59—21no—
174C2×D59—41no—
175C2×D59—41no—
176C2×D59—41no—
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—41no—
186C4×C59—41no—
187C4×C59—41no—
188C4×C59—41no—
189C4×C59H(5,𝔽2)11yescharacteristic
190C4×C59H(5,𝔽2)11yescharacteristic
191Dic59—21no—
192Dic59—21no—
193Dic59—41no—
194#3198—591nomaximal, Sylow
195C2×C59—41no—
196C2×C59#53411yescharacteristic
197C2×C59#57611yescharacteristic
198C2×C59#57711yescharacteristic
199D59—41no—
200D59—41no—
201D59—81no—
202D59—81no—
203D59—81no—
204#537—591no—
205#535—591no—
206#485D5911yescharacteristic, complemented
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×#41—591no—
221C2×#41—591no—
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—591no—
232C22⋊Q8—1181no—
233C22⋊Q8C2×D5911yescharacteristic
234#121—591no—
235#121—591no—
236#121—591no—
237#121—591no—
238#121—591no—
239#121—591no—
240#121—1181no—
241#121—1181no—
242#121—1181no—
243#120—1181no—
244#120—1181no—
245#117C2×D5911yescharacteristic
246C2×C4⋊C4—591no—
247#107—591no—
248#107C2×D5911yescharacteristic, complemented
249#106—591no—
250#106C2×D5911yescharacteristic, complemented
251#103C2×D5911yescharacteristic, complemented
252#103C2×D5911yescharacteristic, complemented
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⋊C8C2×D5911yescharacteristic
263C24—1181no—
264#41—2361no—
265#41—2361no—
266#41—2361no—
267#41—2361no—
268C2×Q8—591no—
269C2×Q8C22×D5911yescharacteristic
270C2×D4—591no—
271C2×D4—591no—
272C2×D4—591no—
273C2×D4—591no—
274C2×D4—591no—
275C2×D4—591no—
276C2×D4—1181no—
277C2×D4—1181no—
278C2×D4—1181no—
279C2×D4—1181no—
280C2×D4—1181no—
281C2×D4—1181no—
282C2×D4—1181no—
283C2×D4—1181no—
284C2×D4—2361no—
285C2×D4—2361no—
286C22×C4—591no—
287C22×C4—591no—
288C22×C4—1181no—
289C22×C4—1181no—
290C22×C4C22×D5911yescharacteristic
291SD16—2361no—
292SD16—2361no—
293D8—2361no—
294D8—2361no—
295M16—2361no—
296C2×C8—591no—
297C2×C8—591no—
298C2×C8—2361no—
299C2×C8C22×D5911yescharacteristic
300C2×C8C22×D5911yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—591no—
303C4⋊C4—1181no—
304C4⋊C4—1181no—
305C4⋊C4C22×D5911yescharacteristic
306C4⋊C4C22×D5911yescharacteristic
307C4⋊C4C22×D5911yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—1181no—
311C22⋊C4—1181no—
312C22⋊C4—1181no—
313C22⋊C4—1181no—
314C22⋊C4—1181no—
315C22⋊C4—1181no—
316C22⋊C4—1181no—
317C42—21no—
318C23—591no—
319C23—591no—
320C23—1181no—
321C23—1181no—
322C23—1181no—
323C23—4721no—
324C23—4721no—
325C23—2362no—
326C23D4×D5911yescharacteristic
327Q8—21no—
328Q8—21no—
329Q8—2361no—
330D4—1181no—
331D4—1181no—
332D4—1181no—
333D4—1181no—
334D4—1181no—
335D4—1181no—
336D4—4721no—
337D4—4721no—
338D4—4721no—
339D4—4721no—
340D4—4721no—
341D4—4721no—
342D4—2361no—
343D4—2362no—
344D4—2362no—
345D4—2361no—
346D4—2361no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—591no—
354C2×C4—591no—
355C2×C4—1181no—
356C2×C4—1181no—
357C2×C4—1181no—
358C2×C4—1181no—
359C2×C4—1181no—
360C2×C4—4721no—
361C2×C4—2362no—
362C2×C4D4×D5911yescharacteristic
363C2×C4C23×D5911yescharacteristic
364C8—21no—
365C8—21no—
366C8—1181no—
367C8—1181no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—1181no—
372C22—1181no—
373C22—1181no—
374C22—1181no—
375C22—1181no—
376C22—1181no—
377C22—4724no—
378C22—2361no—
379C22—2361no—
380C22—2361no—
381C22—2361no—
382C22—2361no—
383C22—2361no—
384C22—2361no—
385C22—2361no—
386C22—2361no—
387C22C2×D4×D5911yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—41no—
393C4—1181no—
394C4—1181no—
395C4—2361no—
396C4#1427377311yescharacteristic
397C4#1427377311yescharacteristic
398C2—41no—
399C2—4721no—
400C2—4721no—
401C2—4721no—
402C2—2361no—
403C2—2361no—
404C2#1683796311yescharacteristic
405C2#1683820411yescharacteristic
406C2#1683821111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#485C2
socleC22×C59C22×D4
hypercenter#485D59
hypocenterC59#3198
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #16837982C2semidirect
2. #16837971C2semidirect
3. #16837726C2semidirect
4. #16837722C2semidirect
5. #16837717C2semidirect
6. #16837656C2semidirect
7. #16837651C2semidirect
8. #16837639C2semidirect
9. #16837634C2semidirect
10. #16837552C2semidirect
11. #16837550C2semidirect
12. #16837550C2semidirect
13. #16837538C2semidirect
14. #16837367C2semidirect
15. C59×#485C2semidirect
16. C2×#11745689C22semidirect
23. C2×#11745659C22semidirect
24. C2×C8×D59C22semidirect
28. #14273703C22semidirect
34. #14273702C22semidirect
40. C4⋊C4×D59C22semidirect
41. #14273660C22semidirect
42. #14273658C22semidirect
47. #14273647C22semidirect
48. #14273647C22semidirect
50. (C2×D59)⋊C8C22semidirect
51. (C2×D59)⋊C8C22semidirect
54. #107×C59C22semidirect
55. #106×C59C22semidirect
56. #103×C59C22semidirect
57. #103×C59C22semidirect
206. #485D59semidirect
219. C59#3198semidirect
248. #107C2×D59semidirect
250. #106C2×D59semidirect
251. #103C2×D59semidirect
252. #103C2×D59semidirect