Finite Group Databasebeta

← #21436170

Subgroups — #21436170

Order 7552.

410 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838110C211yesmaximal, characteristic, complemented
2#16838040C211yesmaximal, characteristic
3#16837763C211yesmaximal, characteristic, complemented
4#16837736C211yesmaximal, characteristic, complemented
5#16837716C211yesmaximal, characteristic, complemented
6#16837680C211yesmaximal, characteristic, complemented
7#16837650C211yesmaximal, characteristic, complemented
8#16837640C211yesmaximal, characteristic, complemented
9#16837626C211yesmaximal, characteristic, complemented
10#16837551C211yesmaximal, characteristic, complemented
11#16837503C211yesmaximal, characteristic, complemented
12#16837476C211yesmaximal, characteristic, complemented
13#16837403C211yesmaximal, characteristic, complemented
14#102×D59C211yesmaximal, characteristic, complemented
15C59×#452C211yesmaximal, characteristic, complemented
16C2×D4×D59C2211yescharacteristic
17C2×#11745671C2211yescharacteristic
18C2×#11745664C2211yescharacteristic, complemented
19C2×C8×D59C2211yescharacteristic
20#14273726C2211yescharacteristic, complemented
21#14273717—21no—
22#14273716C2211yescharacteristic
23#14273710—21no—
24#14273707—21no—
25#14273704—21no—
26#14273703C2211yescharacteristic
27#14273703C2211yescharacteristic
28#14273701C2211yescharacteristic
29#14273699—21no—
30#14273695—21no—
31Q8×Dic59C2211yescharacteristic, complemented
32D4×Dic59C2211yescharacteristic
33C4×C22⋊D59C2211yescharacteristic
34(C22⋊D59)⋊C4—21no—
35C2×C4⋊Dic59C2211yescharacteristic, complemented
36C4⋊C4×D59C2211yescharacteristic
37C2×(C2×D59)⋊C4—21no—
38#14273661C2211yescharacteristic, complemented
39#14273661C2211yescharacteristic, complemented
40#14273660C2211yescharacteristic, complemented
41Dic59⋊C8C2211yescharacteristic, complemented
42#14273651C2211yescharacteristic, complemented
43#14273651C2211yescharacteristic, complemented
44#14273651C2211yescharacteristic, complemented
45#14273649C2211yescharacteristic
46#14273649C2211yescharacteristic
47#14273648C2211yescharacteristic
48#14273648C2211yescharacteristic
49#14273647C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51#14273637C2211yescharacteristic, complemented
52C2×#41×C59C2211yescharacteristic
53C2×Q16×C59C2211yescharacteristic, complemented
54C2×SD16×C59C2211yescharacteristic
55C22⋊Q8×C59C2211yescharacteristic, complemented
56#103×C59C2211yescharacteristic, complemented
57#102×C59C2211yescharacteristic
58C22⋊C8×C59C2211yescharacteristic, complemented
59C23×D59—21no—
60#41×C59—22no—
61#41×C59—41no—
62C2×Q8×C59C2311yescharacteristic
63C2×Q8×C59C2311yescharacteristic
64C2×D4×C59—21no—
65C2×D4×C59C2311yescharacteristic
66C22×C4×C59—21no—
67C22×C4×C59C2311yescharacteristic
68C2×C22⋊D59—21no—
69C2×C22⋊D59—21no—
70C2×C22⋊D59D411yescharacteristic
71C22×Dic59—21no—
72C22×Dic59—21no—
73D4×D59—22no—
74D4×D59—41no—
75C2×D236C2311yescharacteristic
76C2×C4×D59—21no—
77C2×C4×D59C2311yescharacteristic
78C2×Dic118—21no—
79Q16×C59—41no—
80SD16×C59—22no—
81C2×C8×C59C2311yescharacteristic
82C2×C8×C59C2311yescharacteristic
83C4⋊C4×C59—21no—
84C4⋊C4×C59C2311yescharacteristic
85C22⋊C4×C59—21no—
86C22⋊Dic59—21no—
87C22⋊Dic59D411yescharacteristic
88#11745671—41no—
89(C2×D59)⋊C4—21no—
90(C2×D59)⋊C4—21no—
91(C2×D59)⋊C4—21no—
92(C2×D59)⋊C4—21no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4D411yescharacteristic
95C4⋊Dic59—21no—
96C4⋊Dic59—21no—
97C4⋊Dic59C2311yescharacteristic
98C4⋊Dic59C2311yescharacteristic
99C4⋊Dic59C2311yescharacteristic
100Dic59⋊C4—21no—
101Dic59⋊C4—21no—
102Dic59⋊C4—21no—
103Dic59⋊C4—21no—
104Dic59⋊C4D411yescharacteristic
105C4×Dic59—21no—
106C4×Dic59C2311yescharacteristic
107#11745664—41no—
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110C8×D59—41no—
111C23×C59—21no—
112C23×C59C2×D411yescharacteristic
113C22×D59—21no—
114C22×D59—42no—
115C22×D59—42no—
116C22×D59—81no—
117C22×D59C2×D411yescharacteristic
118Q8×C59—21no—
119Q8×C59—21no—
120Q8×C59—21no—
121Q8×C59—21no—
122D4×C59—21no—
123D4×C59—42no—
124D4×C59#4112yes—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—42no—
131C2×C4×C59C2×D411yescharacteristic
132C2×C4×C59C2411yescharacteristic
133C22⋊D59—22no—
134C22⋊D59—42no—
135C22⋊D59—81no—
136C2×Dic59—21no—
137C2×Dic59—21no—
138C2×Dic59—21no—
139C2×Dic59—81no—
140C2×Dic59—81no—
141C2×Dic59C2×D411yescharacteristic
142C2×Dic59C2×D411yescharacteristic
143C2×Dic59C2×D411yescharacteristic
144D236—21no—
145D236—21no—
146C4×D59—21no—
147C4×D59—21no—
148C4×D59—81no—
149Dic118—81no—
150C8×C59—21no—
151C8×C59—21no—
152C59⋊C8—21no—
153C59⋊C8—21no—
154C22×C59—22no—
155C22×C59—21no—
156C22×C59—21no—
157C22×C59—21no—
158C22×C59—41no—
159C22×C59—41no—
160C22×C59C22×D411yescharacteristic
161C2×D59—21no—
162C2×D59—21no—
163C2×D59—41no—
164C2×D59—41no—
165C2×D59—41no—
166C2×D59—84no—
167C2×D59#13712yes—
168C4×C59—21no—
169C4×C59—41no—
170C4×C59—41no—
171C4×C59—41no—
172C4×C59C2×#4111yescharacteristic
173C4×C59H(5,𝔽2)11yescharacteristic
174Dic59—21no—
175Dic59—21no—
176Dic59—21no—
177Dic59—41no—
178Dic59—41no—
179Dic59—41no—
180#3314—591nomaximal, Sylow
181C2×C59—42no—
182C2×C59—41no—
183C2×C59#54611yescharacteristic
184C2×C59C2×#13711yescharacteristic
185C2×C59#57611yescharacteristic
186D59—22no—
187D59—81no—
188#554—591no—
189#546—591no—
190#489—591no—
191#484—591no—
192#480—591no—
193#474—591no—
194#468—591no—
195#467—591no—
196#464—591no—
197#452D5911yescharacteristic, complemented
198#450—591no—
199#440—591no—
200#435—591no—
201#417—591no—
202C2×#102—591no—
203C59#331411yescharacteristic, complemented, Sylow
204C2×#41C2×D5911yescharacteristic
205C22×D4—591no—
206C2×Q16C2×D5911yescharacteristic, complemented
207C2×SD16—591no—
208C2×SD16C2×D5911yescharacteristic
209C2×M16—591no—
210C22×C8—591no—
211C4⋊Q8—591no—
212#125—1181no—
213#124—591no—
214#123—1181no—
215C22⋊Q8—591no—
216C22⋊Q8—591no—
217C22⋊Q8—1181no—
218C22⋊Q8—1181no—
219C22⋊Q8C2×D5911yescharacteristic, complemented
220#121—591no—
221#121—1181no—
222#120—1181no—
223C4×Q8—591no—
224C4×D4—591no—
225C4×D4—591no—
226C4×D4—1181no—
227C2×C4⋊C4—591no—
228C2×C4⋊C4—591no—
229C2×C22⋊C4—1181no—
230#107—591no—
231#107—591no—
232#107—591no—
233C4⋊C8—591no—
234#103—591no—
235#103—591no—
236#103—591no—
237#103C2×D5911yescharacteristic, complemented
238#102—591no—
239#102—591no—
240#102—591no—
241#102—591no—
242#102—591no—
243#102C2×D5911yescharacteristic
244C22⋊C8—591no—
245C22⋊C8C2×D5911yescharacteristic, complemented
246#97—591no—
247C24—1181no—
248#41—22no—
249#41—41no—
250C2×Q8—1181no—
251C2×Q8C22×D5911yescharacteristic
252C2×Q8C22×D5911yescharacteristic
253C2×D4—21no—
254C2×D4—591no—
255C2×D4—591no—
256C2×D4—1181no—
257C2×D4—1182no—
258C2×D4—1181no—
259C2×D4—2361no—
260C2×D4C22×D5911yescharacteristic
261C22×C4—21no—
262C22×C4—591no—
263C22×C4—1181no—
264C22×C4—1181no—
265C22×C4—1181no—
266C22×C4C22×D5911yescharacteristic
267Q16—41no—
268SD16—22no—
269SD16—2361no—
270M16—2361no—
271C2×C8—591no—
272C2×C8—591no—
273C2×C8—2361no—
274C2×C8C22×D5911yescharacteristic
275C2×C8C22×D5911yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—591no—
278C4⋊C4—591no—
279C4⋊C4—591no—
280C4⋊C4—591no—
281C4⋊C4—1181no—
282C4⋊C4—1181no—
283C4⋊C4—1181no—
284C4⋊C4—1181no—
285C4⋊C4—1181no—
286C4⋊C4—1181no—
287C4⋊C4C22×D5911yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—591no—
290C22⋊C4—591no—
291C22⋊C4—1181no—
292C22⋊C4—1181no—
293C22⋊C4—1181no—
294C22⋊C4—1181no—
295C22⋊C4—1181no—
296C22⋊C4—1181no—
297C42—591no—
298C42—1181no—
299C23—21no—
300C23—591no—
301C23—1181no—
302C23—4721no—
303C23—2362no—
304C23—2362no—
305C23D4×D5911yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—21no—
309Q8—21no—
310Q8—4721no—
311D4—21no—
312D4—42no—
313D4—1182no—
314D4—1181no—
315D4—1181no—
316D4—4721no—
317D4—2362no—
318D4#1174568712yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—42no—
325C2×C4—591no—
326C2×C4—591no—
327C2×C4—591no—
328C2×C4—1181no—
329C2×C4—1181no—
330C2×C4—1181no—
331C2×C4—1181no—
332C2×C4—1181no—
333C2×C4—4721no—
334C2×C4—4721no—
335C2×C4—4721no—
336C2×C4D4×D5911yescharacteristic
337C2×C4C23×D5911yescharacteristic
338C8—21no—
339C8—21no—
340C8—1181no—
341C8—1181no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—22no—
346C22—41no—
347C22—41no—
348C22—592no—
349C22—1181no—
350C22—1181no—
351C22—4724no—
352C22—2361no—
353C22—2361no—
354C22—2361no—
355C22C2×D4×D5911yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—1181no—
361C4—1181no—
362C4—1181no—
363C4—2361no—
364C4—2361no—
365C4—2361no—
366C4C2×#1174568711yescharacteristic
367C4#1427377211yescharacteristic
368C2—41no—
369C2—42no—
370C2—1182no—
371C2—4721no—
372C2#1683803911yescharacteristic
373C2#137×D5911yescharacteristic
374C2#1683820411yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#452C2
socleC22×C59C22×D4
hypercenter#452D59
hypocenterC59#3314
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #16838110C2semidirect
3. #16837763C2semidirect
4. #16837736C2semidirect
5. #16837716C2semidirect
6. #16837680C2semidirect
7. #16837650C2semidirect
8. #16837640C2semidirect
9. #16837626C2semidirect
10. #16837551C2semidirect
11. #16837503C2semidirect
12. #16837476C2semidirect
13. #16837403C2semidirect
14. #102×D59C2semidirect
15. C59×#452C2semidirect
18. C2×#11745664C22semidirect
20. #14273726C22semidirect
31. Q8×Dic59C22semidirect
35. C2×C4⋊Dic59C22semidirect
38. #14273661C22semidirect
39. #14273661C22semidirect
40. #14273660C22semidirect
41. Dic59⋊C8C22semidirect
42. #14273651C22semidirect
43. #14273651C22semidirect
44. #14273651C22semidirect
51. #14273637C22semidirect
53. C2×Q16×C59C22semidirect
55. C22⋊Q8×C59C22semidirect
56. #103×C59C22semidirect
58. C22⋊C8×C59C22semidirect
197. #452D59semidirect
203. C59#3314semidirect
206. C2×Q16C2×D59semidirect
219. C22⋊Q8C2×D59semidirect
237. #103C2×D59semidirect
245. C22⋊C8C2×D59semidirect