Finite Group Databasebeta

← #21436005

Subgroups — #21436005

Order 7552.

398 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838102C211yesmaximal, characteristic, complemented
2#16838060C211yesmaximal, characteristic, complemented
3#16837756C211yesmaximal, characteristic, complemented
4#16837742C211yesmaximal, characteristic, complemented
5#16837719C211yesmaximal, characteristic, complemented
6#16837710C211yesmaximal, characteristic, complemented
7#16837635C211yesmaximal, characteristic, complemented
8#16837628C211yesmaximal, characteristic, complemented
9#16837544C211yesmaximal, characteristic, complemented
10#16837539C211yesmaximal, characteristic, complemented
11C4×#11745670C211yesmaximal, characteristic, complemented
12#16837467C211yesmaximal, characteristic, complemented
13#16837395C211yesmaximal, characteristic, complemented
14#103×D59C211yesmaximal, characteristic, complemented
15C59×#463C211yesmaximal, characteristic, complemented
16C2×#11745687C2211yescharacteristic
17C2×Q8×D59C2211yescharacteristic
18C2×#11745670C2211yescharacteristic
19C2×C8×D59C2211yescharacteristic
20C2×C8×D59C2211yescharacteristic
21#14273720—21no—
22#14273719C2211yescharacteristic
23#14273713—21no—
24#14273710—21no—
25#14273704—21no—
26#14273703C2211yescharacteristic
27#14273700—21no—
28#14273700—21no—
29#14273698C2211yescharacteristic
30#14273698C2211yescharacteristic
31#14273698C2211yescharacteristic
32C4×Dic118C2211yescharacteristic
33C4×D236C2211yescharacteristic
34C4×C22⋊D59—21no—
35(C22⋊D59)⋊C4—21no—
36#14273685C2211yescharacteristic
37C4⋊C4×D59C2211yescharacteristic
38#14273661C2211yescharacteristic
39#14273659C2211yescharacteristic
40#14273658C2211yescharacteristic
41#14273652C2211yescharacteristic
42#14273652C2211yescharacteristic
43#14273651C2211yescharacteristic
44#14273651C2211yescharacteristic
45#14273650C2211yescharacteristic
46#14273648C2211yescharacteristic
47#14273648C2211yescharacteristic
48#14273648C2211yescharacteristic
49(C2×D59)⋊C8C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51C4×C59⋊C8C2211yescharacteristic
52C2×SD16×C59C2211yescharacteristic
53C2×D8×C59C2211yescharacteristic
54#124×C59C2211yescharacteristic
55C4×D4×C59C2211yescharacteristic
56C4⋊C8×C59C2211yescharacteristic
57#103×C59C2211yescharacteristic
58#102×C59C2211yescharacteristic
59C2×Q8×C59C2311yescharacteristic
60C2×D4×C59C2311yescharacteristic
61C2×D4×C59C2311yescharacteristic
62C22×C4×C59—21no—
63C2×C22⋊D59—21no—
64C2×C22⋊D59—21no—
65C2×C22⋊D59—21no—
66C2×C22⋊D59—21no—
67C22×Dic59—21no—
68Q8×D59—22no—
69Q8×D59—41no—
70#11745687—22no—
71#11745687—41no—
72C2×D236D411yescharacteristic
73C2×C4×D59—21no—
74C2×C4×D59—21no—
75C2×C4×D59C2311yescharacteristic
76C2×C4×D59C2311yescharacteristic
77C2×Dic118—21no—
78C2×Dic118C2311yescharacteristic
79SD16×C59—41no—
80D8×C59—41no—
81C2×C8×C59C2311yescharacteristic
82C2×C8×C59C2311yescharacteristic
83C4⋊C4×C59C2311yescharacteristic
84C22⋊C4×C59—21no—
85C22⋊C4×C59—21no—
86C22⋊C4×C59—21no—
87C42×C59C2311yescharacteristic
88C22⋊Dic59—21no—
89C22⋊Dic59—21no—
90C22⋊Dic59—21no—
91#11745670—22no—
92(C2×D59)⋊C4—21no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4D411yescharacteristic
95(C2×D59)⋊C4D411yescharacteristic
96C4⋊Dic59D411yescharacteristic
97C4⋊Dic59C2311yescharacteristic
98C4⋊Dic59C2311yescharacteristic
99C4⋊Dic59C2311yescharacteristic
100Dic59⋊C4—21no—
101Dic59⋊C4—21no—
102Dic59⋊C4—21no—
103Dic59⋊C4—21no—
104Dic59⋊C4—21no—
105C4×Dic59—21no—
106C4×Dic59—21no—
107C2×C59⋊C8C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109C8×D59—41no—
110C8×D59—41no—
111C23×C59—21no—
112C23×C59—21no—
113C22×D59C2×D411yescharacteristic
114C22×D59C2×D411yescharacteristic
115Q8×C59—21no—
116Q8×C59—21no—
117D4×C59—21no—
118D4×C59—21no—
119D4×C59—21no—
120D4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—81no—
124C2×C4×C59C2×D411yescharacteristic
125C2×C4×C59C2×D411yescharacteristic
126C2×C4×C59C2411yescharacteristic
127C22⋊D59—42no—
128C22⋊D59—42no—
129C22⋊D59—42no—
130C22⋊D59—81no—
131C2×Dic59—21no—
132C2×Dic59—21no—
133C2×Dic59—21no—
134C2×Dic59—21no—
135C2×Dic59—42no—
136C2×Dic59C2×D411yescharacteristic
137C2×Dic59C2×D411yescharacteristic
138D236—22no—
139C4×D59—21no—
140C4×D59—21no—
141C4×D59—21no—
142C4×D59—21no—
143C4×D59—42no—
144C4×D59—81no—
145Dic118—21no—
146Dic118—42no—
147Dic118#4112yes—
148C8×C59—21no—
149C8×C59—21no—
150C59⋊C8—21no—
151C59⋊C8—21no—
152C22×C59—41no—
153C22×C59—41no—
154C22×C59—41no—
155C22×C59—41no—
156C22×C59—41no—
157C22×C59—41no—
158C22×C59C22×D411yescharacteristic
159C2×D59—21no—
160C2×D59—21no—
161C2×D59—21no—
162C2×D59—21no—
163C2×D59—21no—
164C2×D59#13512yes—
165C4×C59—21no—
166C4×C59—21no—
167C4×C59—41no—
168C4×C59—41no—
169C4×C59C2×#4111yescharacteristic
170C4×C59H(5,𝔽2)11yescharacteristic
171Dic59—22no—
172Dic59—21no—
173Dic59—21no—
174Dic59—41no—
175Dic59—41no—
176Dic59—41no—
177#3301—591nomaximal, Sylow
178C2×C59—81no—
179C2×C59—81no—
180C2×C59#54611yescharacteristic
181C2×C59C2×#13511yescharacteristic
182C2×C59#57711yescharacteristic
183D59—22no—
184D59—41no—
185#553—591no—
186#548—591no—
187#488—591no—
188#485—591no—
189#481—591no—
190#479—591no—
191#466—591no—
192#465—591no—
193#463D5911yescharacteristic, complemented
194#449—591no—
195#448—591no—
196C4×SD16—591no—
197C8×D4—591no—
198#416—591no—
199C2×#103—591no—
200C59#330111yescharacteristic, complemented, Sylow
201C2×#41—591no—
202C22×Q8—591no—
203C2×SD16—591no—
204C2×SD16C2×D5911yescharacteristic
205C2×D8C2×D5911yescharacteristic
206C22×C8—591no—
207C22×C8—591no—
208#126—1181no—
209#125—591no—
210#124—1181no—
211#124C2×D5911yescharacteristic
212#123—1181no—
213C22⋊Q8—591no—
214C22⋊Q8—1181no—
215#121—591no—
216#121—591no—
217#121—591no—
218#121—1181no—
219#121—1181no—
220C4×Q8—591no—
221C4×D4—591no—
222C4×D4—1181no—
223C4×D4—1181no—
224C4×D4C2×D5911yescharacteristic
225#117—591no—
226C2×C4⋊C4—591no—
227#107—591no—
228#106—591no—
229#106—591no—
230C4⋊C8C2×D5911yescharacteristic
231#103—591no—
232#103—591no—
233#103—591no—
234#103—591no—
235#103—591no—
236#103C2×D5911yescharacteristic
237#102—591no—
238#102—591no—
239#102—591no—
240#102C2×D5911yescharacteristic
241C22⋊C8—591no—
242C22⋊C8—591no—
243C4×C8—591no—
244#41—1182no—
245#41—2361no—
246C2×Q8—591no—
247C2×Q8—1181no—
248C2×Q8—1182no—
249C2×Q8—2361no—
250C2×Q8C22×D5911yescharacteristic
251C2×D4—591no—
252C2×D4—1181no—
253C2×D4—1181no—
254C2×D4—1181no—
255C2×D4—1181no—
256C2×D4C22×D5911yescharacteristic
257C2×D4C22×D5911yescharacteristic
258C22×C4—21no—
259C22×C4—591no—
260C22×C4—591no—
261C22×C4—1181no—
262C22×C4—1181no—
263C22×C4—1181no—
264SD16—41no—
265SD16—1182no—
266D8—41no—
267C2×C8—591no—
268C2×C8—591no—
269C2×C8—2361no—
270C2×C8—2361no—
271C2×C8C22×D5911yescharacteristic
272C2×C8C22×D5911yescharacteristic
273C4⋊C4—591no—
274C4⋊C4—591no—
275C4⋊C4—591no—
276C4⋊C4—591no—
277C4⋊C4—1181no—
278C4⋊C4—1181no—
279C4⋊C4—1181no—
280C4⋊C4—1181no—
281C4⋊C4—1181no—
282C4⋊C4C22×D5911yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—591no—
287C22⋊C4—591no—
288C22⋊C4—1181no—
289C22⋊C4—1181no—
290C22⋊C4—1181no—
291C22⋊C4—1181no—
292C22⋊C4—1181no—
293C42—1181no—
294C42—1181no—
295C42C22×D5911yescharacteristic
296C23—21no—
297C23—21no—
298C23—591no—
299C23—591no—
300Q8—21no—
301Q8—21no—
302Q8—592no—
303Q8—1181no—
304Q8—2362no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—1182no—
310D4—4721no—
311D4—2362no—
312D4—2362no—
313D4—2362no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—81no—
317C2×C4—591no—
318C2×C4—591no—
319C2×C4—1181no—
320C2×C4—1181no—
321C2×C4—1181no—
322C2×C4—1181no—
323C2×C4—1181no—
324C2×C4—1181no—
325C2×C4—1181no—
326C2×C4—1181no—
327C2×C4—4721no—
328C2×C4—2362no—
329C2×C4—2362no—
330C2×C4D4×D5911yescharacteristic
331C2×C4D4×D5911yescharacteristic
332C2×C4C23×D5911yescharacteristic
333C8—21no—
334C8—21no—
335C8—1181no—
336C8—1181no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—592no—
344C22—1181no—
345C22—1181no—
346C22—1181no—
347C22—1181no—
348C22—1181no—
349C22C2×D4×D5911yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—1181no—
355C4—1181no—
356C4—1182no—
357C4—2361no—
358C4—2361no—
359C4—2361no—
360C4#41×D5911yescharacteristic
361C4#1427377211yescharacteristic
362C2—81no—
363C2—81no—
364C2—1182no—
365C2—2361no—
366C2#1683804911yescharacteristic
367C2#135×D5911yescharacteristic
368C2#1683821211yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#463C2
socleC22×C59C22×D4
hypercenter#463D59
hypocenterC59#3301
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #16838102C2semidirect
2. #16838060C2semidirect
3. #16837756C2semidirect
4. #16837742C2semidirect
5. #16837719C2semidirect
6. #16837710C2semidirect
7. #16837635C2semidirect
8. #16837628C2semidirect
9. #16837544C2semidirect
10. #16837539C2semidirect
11. C4×#11745670C2semidirect
12. #16837467C2semidirect
13. #16837395C2semidirect
14. #103×D59C2semidirect
15. C59×#463C2semidirect
193. #463D59semidirect
200. C59#3301semidirect