Finite Group Databasebeta

← #21434897

Subgroups — #21434897

Order 7552.

462 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
1C22⋊Q8×D59C211yesmaximal, characteristic, complemented
2#121×D59C211yesmaximal, characteristic
3#16837739C211yesmaximal, characteristic, complemented
4#16837736C211yesmaximal, characteristic, complemented
5#16837717C211yesmaximal, characteristic, complemented
6#16837714C211yesmaximal, characteristic, complemented
7#16837650C211yesmaximal, characteristic, complemented
8#16837648C211yesmaximal, characteristic, complemented
9#16837646C211yesmaximal, characteristic, complemented
10#16837554C211yesmaximal, characteristic, complemented
11#16837551C211yesmaximal, characteristic, complemented
12#16837542C211yesmaximal, characteristic, complemented
13#16837539C211yesmaximal, characteristic, complemented
14#16837365C211yesmaximal, characteristic, complemented
15C59×#468C211yesmaximal, characteristic, complemented
16C2×Q8×D59C2211yescharacteristic, complemented
17C2×D4×D59—21no—
18C2×D4×D59C2211yescharacteristic
19C22×C4×D59C2211yescharacteristic
20C2×#11745660C2211yescharacteristic, complemented
21C2×#11745670C2211yescharacteristic, complemented
22C2×#11745671C2211yescharacteristic, complemented
23C2×#11745664C2211yescharacteristic, complemented
24#14273707C2211yescharacteristic
25#14273706C2211yescharacteristic, complemented
26#14273705—21no—
27#14273704—21no—
28#14273703C2211yescharacteristic
29#14273702C2211yescharacteristic
30#14273701C2211yescharacteristic
31#14273700—21no—
32#14273699—21no—
33#14273698C2211yescharacteristic
34C4⋊C4×D59—21no—
35C4⋊C4×D59C2211yescharacteristic
36C4⋊C4×D59C2211yescharacteristic, complemented
37C22⋊C4×D59—21no—
38C22⋊C4×D59—21no—
39#14273661C2211yescharacteristic, complemented
40#14273660C2211yescharacteristic, complemented
41#14273660C2211yescharacteristic, 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, complemented
51(C2×D59)⋊C8C2211yescharacteristic, complemented
52C2×SD16×C59C2211yescharacteristic, complemented
53C2×M16×C59C2211yescharacteristic, complemented
54C22⋊Q8×C59C2211yescharacteristic, complemented
55#121×C59C2211yescharacteristic
56#107×C59C2211yescharacteristic, complemented
57#103×C59C2211yescharacteristic, complemented
58#102×C59C2211yescharacteristic, complemented
59C23×D59—21no—
60C23×D59D411yescharacteristic
61C2×Q8×C59C2311yescharacteristic
62C2×D4×C59—21no—
63C2×D4×C59C2311yescharacteristic
64C22×C4×C59C2311yescharacteristic
65C2×C22⋊D59—21no—
66C2×C22⋊D59—21no—
67C2×C22⋊D59—21no—
68C22×Dic59D411yescharacteristic
69Q8×D59—41no—
70Q8×D59—41no—
71D4×D59—41no—
72D4×D59—41no—
73D4×D59—44no—
74C2×D236—21no—
75C2×D236C2311yescharacteristic
76C2×C4×D59—21no—
77C2×C4×D59—21no—
78C2×C4×D59—21no—
79C2×C4×D59—41no—
80C2×C4×D59—41no—
81C2×C4×D59D411yescharacteristic
82C2×C4×D59D411yescharacteristic
83C2×C4×D59C2311yescharacteristic
84C2×C4×D59C2311yescharacteristic
85C2×Dic118—21no—
86C2×Dic118C2311yescharacteristic
87SD16×C59—41no—
88M16×C59—41no—
89C2×C8×C59C2311yescharacteristic
90C2×C8×C59C2311yescharacteristic
91C4⋊C4×C59—21no—
92C4⋊C4×C59C2311yescharacteristic
93C4⋊C4×C59C2311yescharacteristic
94C22⋊C4×C59—21no—
95C22⋊C4×C59—21no—
96C22⋊Dic59—21no—
97C22⋊Dic59—21no—
98#11745671—41no—
99#11745670—41no—
100(C2×D59)⋊C4—21no—
101(C2×D59)⋊C4—21no—
102(C2×D59)⋊C4—21no—
103(C2×D59)⋊C4—21no—
104C4⋊Dic59—21no—
105C4⋊Dic59C2311yescharacteristic
106C4⋊Dic59C2311yescharacteristic
107Dic59⋊C4—21no—
108Dic59⋊C4—21no—
109Dic59⋊C4—21no—
110Dic59⋊C4—21no—
111#11745664—41no—
112C2×C59⋊C8C2311yescharacteristic
113C2×C59⋊C8C2311yescharacteristic
114#11745660—41no—
115C23×C59—21no—
116C23×C59C2×D411yescharacteristic
117C22×D59—22no—
118C22×D59—22no—
119C22×D59—21no—
120C22×D59—41no—
121C22×D59—42no—
122C22×D59—42no—
123C22×D59—42no—
124C22×D59C2×D411yescharacteristic
125C22×D59C2×D411yescharacteristic
126Q8×C59—21no—
127Q8×C59—21no—
128D4×C59—21no—
129D4×C59—21no—
130D4×C59—42no—
131C2×C4×C59—21no—
132C2×C4×C59—21no—
133C2×C4×C59—21no—
134C2×C4×C59—21no—
135C2×C4×C59—21no—
136C2×C4×C59C2×D411yescharacteristic
137C2×C4×C59C2411yescharacteristic
138C22⋊D59—42no—
139C22⋊D59—42no—
140C22⋊D59—42no—
141C2×Dic59—21no—
142C2×Dic59—21no—
143C2×Dic59—21no—
144C2×Dic59—41no—
145C2×Dic59C2×D411yescharacteristic
146C2×Dic59C2×D411yescharacteristic
147D236—21no—
148D236—21no—
149D236—42no—
150C4×D59—21no—
151C4×D59—21no—
152C4×D59—21no—
153C4×D59—21no—
154C4×D59—41no—
155C4×D59—41no—
156C4×D59—42no—
157C4×D59—42no—
158C4×D59—42no—
159Dic118—21no—
160Dic118—21no—
161Dic118—42no—
162C8×C59—21no—
163C8×C59—21no—
164C59⋊C8—21no—
165C59⋊C8—21no—
166C22×C59—21no—
167C22×C59—21no—
168C22×C59—21no—
169C22×C59—41no—
170C22×C59—41no—
171C22×C59—41no—
172C22×C59C22×D411yescharacteristic
173C2×D59—21no—
174C2×D59—21no—
175C2×D59—21no—
176C2×D59—21no—
177C2×D59—44no—
178C2×D59—41no—
179C2×D59—41no—
180C2×D59—41no—
181C2×D59—84no—
182C2×D59AGL(1,ℤ/8)12yes—
183C2×D59#13712yes—
184C4×C59—21no—
185C4×C59—41no—
186C4×C59—41no—
187C4×C59—41no—
188C4×C59H(5,𝔽2)11yescharacteristic
189C4×C59H(5,𝔽2)11yescharacteristic
190Dic59—21no—
191Dic59—21no—
192Dic59—41no—
193Dic59—41no—
194Dic59—41no—
195#3193—591nomaximal, Sylow
196C2×C59—41no—
197C2×C59—81no—
198C2×C59#53411yescharacteristic
199C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
200C2×C59C2×#13711yescharacteristic
201D59—22no—
202D59—22no—
203D59—81no—
204C2×C22⋊Q8—591no—
205C2×#121—591no—
206#484—591no—
207#484—591no—
208#480—591no—
209#480—591no—
210#468—591no—
211#468—591no—
212#468—591no—
213#468D5911yescharacteristic, complemented
214#450—591no—
215#450—591no—
216#448—591no—
217#448—591no—
218#407—591no—
219C59#319311yescharacteristic, complemented, Sylow
220C22×Q8—591no—
221C22×D4—591no—
222C22×D4—1181no—
223C23×C4—591no—
224C2×SD16—591no—
225C2×SD16—591no—
226C2×SD16—591no—
227C2×SD16C2×D5911yescharacteristic, complemented
228C2×M16—591no—
229C2×M16C2×D5911yescharacteristic, complemented
230C22⋊Q8—591no—
231C22⋊Q8—591no—
232C22⋊Q8—591no—
233C22⋊Q8—1181no—
234C22⋊Q8—1181no—
235C22⋊Q8C2×D5911yescharacteristic, complemented
236#121—591no—
237#121—591no—
238#121—591no—
239#121—1181no—
240#121—1181no—
241#121C2×D5911yescharacteristic
242C2×C4⋊C4—591no—
243C2×C4⋊C4—591no—
244C2×C4⋊C4—1181no—
245C2×C22⋊C4—1181no—
246C2×C22⋊C4—1181no—
247#107—591no—
248#107—591no—
249#107—591no—
250#107C2×D5911yescharacteristic, complemented
251#103—591no—
252#103—591no—
253#103—591no—
254#103C2×D5911yescharacteristic, complemented
255#102—591no—
256#102—591no—
257#102—591no—
258#102C2×D5911yescharacteristic, complemented
259C22⋊C8—591no—
260C22⋊C8—591no—
261C22⋊C8—591no—
262C22⋊C8—591no—
263C24—591no—
264C24—1181no—
265C2×Q8—591no—
266C2×Q8—1181no—
267C2×Q8—2361no—
268C2×Q8—2361no—
269C2×Q8C22×D5911yescharacteristic
270C2×D4—21no—
271C2×D4—591no—
272C2×D4—1181no—
273C2×D4—1181no—
274C2×D4—1181no—
275C2×D4—1181no—
276C2×D4—2361no—
277C2×D4—2361no—
278C2×D4—2364no—
279C2×D4C22×D5911yescharacteristic
280C22×C4—591no—
281C22×C4—591no—
282C22×C4—591no—
283C22×C4—591no—
284C22×C4—591no—
285C22×C4—1181no—
286C22×C4—1181no—
287C22×C4—1181no—
288C22×C4—2361no—
289C22×C4—2361no—
290C22×C4C22×D5911yescharacteristic
291SD16—41no—
292SD16—2361no—
293SD16—2361no—
294SD16—2361no—
295M16—41no—
296M16—2361no—
297C2×C8—591no—
298C2×C8—591no—
299C2×C8C22×D5911yescharacteristic
300C2×C8C22×D5911yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—591no—
303C4⋊C4—591no—
304C4⋊C4—1181no—
305C4⋊C4—1181no—
306C4⋊C4—1181no—
307C4⋊C4—1181no—
308C4⋊C4—1181no—
309C4⋊C4C22×D5911yescharacteristic
310C4⋊C4C22×D5911yescharacteristic
311C22⋊C4—21no—
312C22⋊C4—21no—
313C22⋊C4—1181no—
314C22⋊C4—1181no—
315C22⋊C4—1181no—
316C22⋊C4—1181no—
317C22⋊C4—1181no—
318C22⋊C4—1181no—
319C23—21no—
320C23—591no—
321C23—591no—
322C23—1182no—
323C23—1182no—
324C23—1181no—
325C23—2361no—
326C23—2362no—
327C23—2362no—
328C23—2362no—
329C23D4×D5911yescharacteristic
330Q8—21no—
331Q8—21no—
332Q8—1181no—
333Q8—1181no—
334Q8—2362no—
335D4—21no—
336D4—21no—
337D4—42no—
338D4—1181no—
339D4—1181no—
340D4—2362no—
341D4—2362no—
342D4—2362no—
343D4—2362no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—591no—
350C2×C4—591no—
351C2×C4—1181no—
352C2×C4—1181no—
353C2×C4—1181no—
354C2×C4—1181no—
355C2×C4—1181no—
356C2×C4—1181no—
357C2×C4—1181no—
358C2×C4—2361no—
359C2×C4—2361no—
360C2×C4—2362no—
361C2×C4—2362no—
362C2×C4—2362no—
363C2×C4—2361no—
364C2×C4D4×D5911yescharacteristic
365C2×C4C23×D5911yescharacteristic
366C8—21no—
367C8—21no—
368C8—1181no—
369C8—1181no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—592no—
377C22—592no—
378C22—1181no—
379C22—1181no—
380C22—1181no—
381C22—1181no—
382C22—4724no—
383C22—2364no—
384C22—2361no—
385C22—2361no—
386C22—2361no—
387C22C2×D4×D5911yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—1181no—
393C4—1181no—
394C4—2361no—
395C4—2361no—
396C4—2361no—
397C4#1427377211yescharacteristic
398C4#1427377311yescharacteristic
399C2—41no—
400C2—81no—
401C2—1182no—
402C2—1182no—
403C2—4721no—
404C2#1683796011yescharacteristic
405C2AGL(1,ℤ/8)×D5911yescharacteristic
406C2#137×D5911yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#468C2
socleC22×C59C22×D4
hypercenter#468D59
hypocenterC59#3193
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. C22⋊Q8×D59C2semidirect
3. #16837739C2semidirect
4. #16837736C2semidirect
5. #16837717C2semidirect
6. #16837714C2semidirect
7. #16837650C2semidirect
8. #16837648C2semidirect
9. #16837646C2semidirect
10. #16837554C2semidirect
11. #16837551C2semidirect
12. #16837542C2semidirect
13. #16837539C2semidirect
14. #16837365C2semidirect
15. C59×#468C2semidirect
16. C2×Q8×D59C22semidirect
20. C2×#11745660C22semidirect
21. C2×#11745670C22semidirect
22. C2×#11745671C22semidirect
23. C2×#11745664C22semidirect
25. #14273706C22semidirect
36. C4⋊C4×D59C22semidirect
39. #14273661C22semidirect
40. #14273660C22semidirect
41. #14273660C22semidirect
42. #14273652C22semidirect
43. #14273651C22semidirect
44. #14273650C22semidirect
45. #14273649C22semidirect
46. #14273648C22semidirect
47. #14273647C22semidirect
50. (C2×D59)⋊C8C22semidirect
51. (C2×D59)⋊C8C22semidirect
52. C2×SD16×C59C22semidirect
53. C2×M16×C59C22semidirect
54. C22⋊Q8×C59C22semidirect
56. #107×C59C22semidirect
57. #103×C59C22semidirect
58. #102×C59C22semidirect
213. #468D59semidirect
219. C59#3193semidirect
227. C2×SD16C2×D59semidirect
229. C2×M16C2×D59semidirect
235. C22⋊Q8C2×D59semidirect
250. #107C2×D59semidirect
254. #103C2×D59semidirect
258. #102C2×D59semidirect