Finite Group Databasebeta

← #21436092

Subgroups — #21436092

Order 7552.

420 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#16838064C211yesmaximal, characteristic, complemented
2#16838057C211yesmaximal, characteristic, complemented
3#16837762C211yesmaximal, characteristic, complemented
4#16837739C211yesmaximal, characteristic, complemented
5#16837717C211yesmaximal, characteristic, complemented
6#16837697C211yesmaximal, characteristic, complemented
7#16837647C211yesmaximal, characteristic, complemented
8#16837637C211yesmaximal, characteristic, complemented
9#16837617C211yesmaximal, characteristic, complemented
10#16837546C211yesmaximal, characteristic, complemented
11#16837539C211yesmaximal, characteristic, complemented
12#16837475C211yesmaximal, characteristic, complemented
13#16837402C211yesmaximal, characteristic, complemented
14#103×D59C211yesmaximal, characteristic, complemented
15C59×#440C211yesmaximal, characteristic, complemented
16C2×#11745689C2211yescharacteristic
17C2×#11745685—21no—
18C2×Q8×D59C2211yescharacteristic
19C2×#11745670C2211yescharacteristic
20C2×#11745669C2211yescharacteristic
21C2×#11745659C2211yescharacteristic
22C2×C8×D59C2211yescharacteristic
23#14273727C2211yescharacteristic
24#14273715—21no—
25#14273715C2211yescharacteristic
26#14273709—21no—
27#14273709—21no—
28#14273707—21no—
29#14273707C2211yescharacteristic
30#14273706—21no—
31#14273702—21no—
32#14273702C2211yescharacteristic
33#14273698C2211yescharacteristic
34#14273698C2211yescharacteristic
35C4×D236—21no—
36C4×D236C2211yescharacteristic
37C4⋊C4×D59C2211yescharacteristic
38C4⋊C4×D59C2211yescharacteristic
39#14273660C2211yescharacteristic
40#14273660C2211yescharacteristic
41C4⋊(C59⋊C8)C2211yescharacteristic
42#14273652C2211yescharacteristic
43#14273652C2211yescharacteristic
44#14273651C2211yescharacteristic
45#14273651C2211yescharacteristic
46#14273650C2211yescharacteristic
47#14273649C2211yescharacteristic
48#14273649C2211yescharacteristic
49#14273647C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51(C2×D59)⋊C8C2211yescharacteristic
52C2×SD16×C59C2211yescharacteristic
53C4×Q8×C59C2211yescharacteristic
54C4×D4×C59C2211yescharacteristic
55#107×C59C2211yescharacteristic
56#103×C59C2211yescharacteristic
57#102×C59C2211yescharacteristic
58#97×C59C2211yescharacteristic
59C2×Q8×C59C2311yescharacteristic
60C2×D4×C59C2311yescharacteristic
61C22×C4×C59—21no—
62C2×C22⋊D59—21no—
63C2×C22⋊D59—21no—
64#11745689—22no—
65#11745689—41no—
66Q8×D59—22no—
67Q8×D59—41no—
68#11745685—44no—
69C2×D236—21no—
70C2×D236—21no—
71C2×D236D411yescharacteristic
72C2×D236C2311yescharacteristic
73C2×C4×D59—21no—
74C2×C4×D59—21no—
75C2×C4×D59—21no—
76C2×C4×D59—21no—
77C2×C4×D59C2311yescharacteristic
78C2×C4×D59C2311yescharacteristic
79C2×Dic118—21no—
80C2×Dic118—21no—
81C2×Dic118C2311yescharacteristic
82SD16×C59—22no—
83C2×C8×C59C2311yescharacteristic
84C2×C8×C59C2311yescharacteristic
85C4⋊C4×C59—21no—
86C4⋊C4×C59C2311yescharacteristic
87C4⋊C4×C59C2311yescharacteristic
88C22⋊C4×C59—21no—
89C42×C59—21no—
90C42×C59C2311yescharacteristic
91C22⋊Dic59—21no—
92C22⋊Dic59—21no—
93#11745670—41no—
94#11745669—41no—
95(C2×D59)⋊C4—21no—
96(C2×D59)⋊C4—21no—
97(C2×D59)⋊C4—21no—
98(C2×D59)⋊C4—21no—
99(C2×D59)⋊C4D411yescharacteristic
100(C2×D59)⋊C4D411yescharacteristic
101C4⋊Dic59—21no—
102C4⋊Dic59—21no—
103C4⋊Dic59D411yescharacteristic
104C4⋊Dic59C2311yescharacteristic
105C4⋊Dic59C2311yescharacteristic
106Dic59⋊C4—21no—
107Dic59⋊C4—21no—
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110#11745659—41no—
111C8×D59—41no—
112C23×C59—21no—
113C22×D59—21no—
114C22×D59C2×D411yescharacteristic
115C22×D59C2×D411yescharacteristic
116Q8×C59—21no—
117Q8×C59#4112yescomplemented
118D4×C59—21no—
119D4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—42no—
124C2×C4×C59C2×D411yescharacteristic
125C2×C4×C59C2×D411yescharacteristic
126C2×C4×C59C2411yescharacteristic
127C22⋊D59—42no—
128C22⋊D59—42no—
129C2×Dic59—21no—
130C2×Dic59—21no—
131C2×Dic59—21no—
132C2×Dic59C2×D411yescharacteristic
133C2×Dic59C2×D411yescharacteristic
134D236—22no—
135D236—21no—
136D236—21no—
137D236—42no—
138D236—42no—
139C4×D59—21no—
140C4×D59—21no—
141C4×D59—21no—
142C4×D59—21no—
143C4×D59—42no—
144C4×D59—42no—
145C4×D59—42no—
146C4×D59—42no—
147Dic118—21no—
148Dic118—21no—
149Dic118—42no—
150Dic118—42no—
151C8×C59—21no—
152C8×C59—21no—
153C59⋊C8—21no—
154C59⋊C8—21no—
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—41no—
165C2×D59—41no—
166C2×D59—41no—
167C2×D59AGL(1,ℤ/8)12yes—
168C4×C59—22no—
169C4×C59—21no—
170C4×C59—21no—
171C4×C59—41no—
172C4×C59—41no—
173C4×C59C2×#4111yescharacteristic
174C4×C59H(5,𝔽2)11yescharacteristic
175Dic59—21no—
176Dic59—21no—
177Dic59—41no—
178Dic59—41no—
179Dic59—41no—
180#3308—591nomaximal, Sylow
181C2×C59—81no—
182C2×C59#54611yescharacteristic
183C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
184C2×C59#57811yescharacteristic
185D59—22no—
186D59—41no—
187D59—81no—
188#548—591no—
189#547—591no—
190#489—591no—
191#484—591no—
192#480—591no—
193#477—591no—
194#468—591no—
195#466—591no—
196#463—591no—
197#449—591no—
198#448—591no—
199#440D5911yescharacteristic, complemented
200#435—591no—
201#417—591no—
202C2×#103—591no—
203C59#330811yescharacteristic, complemented, Sylow
204C2×#41—591no—
205C2×#41—1181no—
206C22×Q8—591no—
207C2×SD16—591no—
208C2×SD16C2×D5911yescharacteristic
209C2×D8—591no—
210C2×M16—591no—
211C22×C8—591no—
212C4⋊Q8—591no—
213#124—591no—
214#124—1181no—
215#123—1181no—
216#123—1181no—
217C22⋊Q8—591no—
218C22⋊Q8—1181no—
219C22⋊Q8—1181no—
220#121—591no—
221#121—591no—
222#121—591no—
223#121—1181no—
224C4×Q8C2×D5911yescharacteristic
225C4×D4—591no—
226C4×D4—1181no—
227C4×D4C2×D5911yescharacteristic
228C2×C4⋊C4—591no—
229C2×C4⋊C4—591no—
230#107—591no—
231#107—591no—
232#107C2×D5911yescharacteristic
233C4⋊C8—591no—
234#103—591no—
235#103—591no—
236#103—591no—
237#103—591no—
238#103—591no—
239#103C2×D5911yescharacteristic
240#102—591no—
241#102—591no—
242#102—591no—
243#102C2×D5911yescharacteristic
244C22⋊C8—591no—
245C22⋊C8—591no—
246#97C2×D5911yescharacteristic
247#41—1182no—
248#41—2364no—
249#41—2361no—
250C2×Q8—591no—
251C2×Q8—1181no—
252C2×Q8—1181no—
253C2×Q8—1182no—
254C2×Q8—2361no—
255C2×Q8C22×D5911yescharacteristic
256C2×D4—591no—
257C2×D4—591no—
258C2×D4—1181no—
259C2×D4—1181no—
260C2×D4—1181no—
261C2×D4—1181no—
262C2×D4C22×D5911yescharacteristic
263C22×C4—21no—
264C22×C4—591no—
265C22×C4—591no—
266C22×C4—1181no—
267C22×C4—1181no—
268C22×C4—1181no—
269C22×C4—1181no—
270SD16—22no—
271SD16—2361no—
272D8—2361no—
273M16—2361no—
274C2×C8—591no—
275C2×C8—591no—
276C2×C8—2361no—
277C2×C8C22×D5911yescharacteristic
278C2×C8C22×D5911yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—591no—
281C4⋊C4—591no—
282C4⋊C4—591no—
283C4⋊C4—1181no—
284C4⋊C4—1181no—
285C4⋊C4—1181no—
286C4⋊C4—1181no—
287C4⋊C4C22×D5911yescharacteristic
288C4⋊C4C22×D5911yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—591no—
291C22⋊C4—591no—
292C22⋊C4—1181no—
293C22⋊C4—1181no—
294C22⋊C4—1181no—
295C22⋊C4—1181no—
296C22⋊C4—1181no—
297C22⋊C4—1181no—
298C42—21no—
299C42C22×D5911yescharacteristic
300C23—21no—
301C23—591no—
302C23—591no—
303C23—1181no—
304Q8—21no—
305Q8—1181no—
306Q8—1181no—
307Q8—2362no—
308Q8—2362no—
309Q8#1174568512yescomplemented
310D4—21no—
311D4—21no—
312D4—1182no—
313D4—1181no—
314D4—1181no—
315D4—2362no—
316D4—2362no—
317D4—2362no—
318D4—2362no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—591no—
324C2×C4—591no—
325C2×C4—1181no—
326C2×C4—1181no—
327C2×C4—1181no—
328C2×C4—1181no—
329C2×C4—1181no—
330C2×C4—1181no—
331C2×C4—1181no—
332C2×C4—2362no—
333C2×C4—2362no—
334C2×C4—2362no—
335C2×C4—2362no—
336C2×C4D4×D5911yescharacteristic
337C2×C4D4×D5911yescharacteristic
338C2×C4C23×D5911yescharacteristic
339C8—21no—
340C8—21no—
341C8—1181no—
342C8—1181no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—592no—
347C22—1181no—
348C22—1181no—
349C22—1181no—
350C22—1181no—
351C22—1181no—
352C22—2361no—
353C22—2361no—
354C22—2361no—
355C22C2×D4×D5911yescharacteristic
356C4—21no—
357C4—21no—
358C4—22no—
359C4—41no—
360C4—41no—
361C4—1181no—
362C4—1181no—
363C4—2361no—
364C4—2361no—
365C4—2361no—
366C4C2×#1174568511yescharacteristic
367C4#1427377311yescharacteristic
368C2—81no—
369C2—1182no—
370C2—4721no—
371C2—2361no—
372C2#1683804811yescharacteristic
373C2AGL(1,ℤ/8)×D5911yescharacteristic
374C2#1683821811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#440C2
socleC22×C59C22×D4
hypercenter#440D59
hypocenterC59#3308
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #16838064C2semidirect
2. #16838057C2semidirect
3. #16837762C2semidirect
4. #16837739C2semidirect
5. #16837717C2semidirect
6. #16837697C2semidirect
7. #16837647C2semidirect
8. #16837637C2semidirect
9. #16837617C2semidirect
10. #16837546C2semidirect
11. #16837539C2semidirect
12. #16837475C2semidirect
13. #16837402C2semidirect
14. #103×D59C2semidirect
15. C59×#440C2semidirect
117. Q8×C59#41semidirect
199. #440D59semidirect
203. C59#3308semidirect
309. Q8#11745685semidirect