Finite Group Databasebeta

← #21436089

Subgroups — #21436089

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#16838061C211yesmaximal, characteristic, complemented
2#16838056C211yesmaximal, characteristic, complemented
3#16837762C211yesmaximal, characteristic, complemented
4#16837738C211yesmaximal, characteristic, complemented
5#16837716C211yesmaximal, characteristic, complemented
6#16837698C211yesmaximal, characteristic, complemented
7#16837648C211yesmaximal, characteristic, complemented
8#16837638C211yesmaximal, characteristic, complemented
9#16837618C211yesmaximal, characteristic, complemented
10#16837549C211yesmaximal, characteristic, complemented
11#16837543C211yesmaximal, characteristic, complemented
12#16837504C211yesmaximal, characteristic, complemented
13#16837404C211yesmaximal, characteristic, complemented
14C2×#14273652C211yesmaximal, characteristic, complemented
15C59×#435C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C2×#11745687—21no—
18C22×Dic118C2211yescharacteristic
19C2×#11745660C2211yescharacteristic
20C2×#11745660C2211yescharacteristic
21C2×D472C2211yescharacteristic
22#14273727C2211yescharacteristic
23#14273715C2211yescharacteristic
24#14273713—21no—
25#14273711—21no—
26#14273711—21no—
27#14273707—21no—
28#14273706C2211yescharacteristic
29#14273705—21no—
30#14273701C2211yescharacteristic
31#14273701C2211yescharacteristic
32#14273701C2211yescharacteristic
33#14273699—21no—
34C4×Dic118C2211yescharacteristic
35C4×D236C2211yescharacteristic
36(C22⋊D59)⋊C4—21no—
37C2×C4⋊Dic59C2211yescharacteristic
38C2×C4⋊Dic59C2211yescharacteristic
39#14273661C2211yescharacteristic
40#14273661C2211yescharacteristic
41#14273661C2211yescharacteristic
42#14273652C2211yescharacteristic
43#14273652C2211yescharacteristic
44#14273652C2211yescharacteristic
45#14273652C2211yescharacteristic
46#14273652C2211yescharacteristic
47#14273652C2211yescharacteristic
48#14273649C2211yescharacteristic
49#14273649C2211yescharacteristic
50#14273649C2211yescharacteristic
51#14273649C2211yescharacteristic
52C2×M16×C59C2211yescharacteristic
53C22×C8×C59C2211yescharacteristic
54C4×D4×C59C2211yescharacteristic
55C4⋊C8×C59C2211yescharacteristic
56C22⋊C8×C59C2211yescharacteristic
57C22⋊C8×C59C2211yescharacteristic
58#97×C59C2211yescharacteristic
59C2×D4×C59D411yescharacteristic
60C22×C4×C59C2311yescharacteristic
61C22×C4×C59C2311yescharacteristic
62C2×C22⋊D59—21no—
63C2×C22⋊D59—21no—
64C2×C22⋊D59—21no—
65C2×C22⋊D59—21no—
66C22×Dic59—21no—
67C22×Dic59—21no—
68C22×Dic59—21no—
69#11745687—44no—
70#11745685—22no—
71#11745685—41no—
72C2×D236C2311yescharacteristic
73C2×D236C2311yescharacteristic
74C2×C4×D59—21no—
75C2×C4×D59—21no—
76C2×Dic118—22no—
77C2×Dic118—21no—
78C2×Dic118—21no—
79C2×Dic118—41no—
80C2×Dic118C2311yescharacteristic
81C2×Dic118C2311yescharacteristic
82M16×C59—41no—
83C2×C8×C59—41no—
84C2×C8×C59C2311yescharacteristic
85C2×C8×C59C2311yescharacteristic
86C2×C8×C59C2311yescharacteristic
87C2×C8×C59C2311yescharacteristic
88C4⋊C4×C59D411yescharacteristic
89C22⋊C4×C59D411yescharacteristic
90C22⋊C4×C59D411yescharacteristic
91C42×C59C2311yescharacteristic
92C22⋊Dic59—21no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4—21no—
95(C2×D59)⋊C4—21no—
96(C2×D59)⋊C4—21no—
97(C2×D59)⋊C4—21no—
98(C2×D59)⋊C4—21no—
99C4⋊Dic59—21no—
100C4⋊Dic59—21no—
101C4⋊Dic59—21no—
102C4⋊Dic59C2311yescharacteristic
103C4⋊Dic59C2311yescharacteristic
104C4⋊Dic59C2311yescharacteristic
105C4⋊Dic59C2311yescharacteristic
106Dic59⋊C4—21no—
107Dic59⋊C4—21no—
108C4×Dic59—21no—
109D472—41no—
110#11745660—22no—
111#11745660—41no—
112C23×C59C2×D411yescharacteristic
113C23×C59C2×D411yescharacteristic
114C22×D59—21no—
115C22×D59—21no—
116D4×C59—22no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59C2×D411yescharacteristic
122C2×C4×C59C2×D411yescharacteristic
123C2×C4×C59C2×D411yescharacteristic
124C2×C4×C59C2×D411yescharacteristic
125C2×C4×C59C2411yescharacteristic
126C22⋊D59—42no—
127C22⋊D59—42no—
128C22⋊D59—42no—
129C22⋊D59—42no—
130C2×Dic59—21no—
131C2×Dic59—21no—
132C2×Dic59—21no—
133C2×Dic59—21no—
134C2×Dic59—21no—
135C2×Dic59—21no—
136C2×Dic59—42no—
137C2×Dic59—42no—
138C2×Dic59—42no—
139D236—21no—
140D236—21no—
141D236—21no—
142D236—21no—
143C4×D59—42no—
144C4×D59—42no—
145Dic118—21no—
146Dic118—21no—
147Dic118—21no—
148Dic118—42no—
149Dic118—42no—
150Dic118#4112yescomplemented
151C8×C59—21no—
152C8×C59—21no—
153C8×C59—21no—
154C8×C59—21no—
155C22×C59—21no—
156C22×C59—21no—
157C22×C59—21no—
158C22×C59—21no—
159C22×C59—21no—
160C22×C59AGL(1,ℤ/8)12yes—
161C22×C59C22×D411yescharacteristic
162C2×D59—41no—
163C2×D59—41no—
164C2×D59—41no—
165C2×D59—41no—
166C2×D59—41no—
167C2×D59—41no—
168C4×C59—21no—
169C4×C59—21no—
170C4×C59—21no—
171C4×C59—21no—
172C4×C59C2×#4111yescharacteristic
173C4×C59H(5,𝔽2)11yescharacteristic
174Dic59—22no—
175Dic59—41no—
176Dic59—41no—
177Dic59—41no—
178Dic59—41no—
179Dic59—41no—
180#3308—591nomaximal, Sylow
181C2×C59—22no—
182C2×C59—41no—
183C2×C59#54611yescharacteristic
184C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
185C2×C59#57811yescharacteristic
186D59—81no—
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#440—591no—
200#435D5911yescharacteristic, complemented
201#417—591no—
202C2×#103—591no—
203C59#330811yescharacteristic, complemented, Sylow
204C2×#41—591no—
205C2×#41—1181no—
206C22×Q8—591no—
207C2×SD16—591no—
208C2×SD16—591no—
209C2×D8—591no—
210C2×M16C2×D5911yescharacteristic
211C22×C8C2×D5911yescharacteristic
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×Q8—591no—
225C4×D4—591no—
226C4×D4—1181no—
227C4×D4C2×D5911yescharacteristic
228C2×C4⋊C4—591no—
229C2×C4⋊C4—591no—
230#107—591no—
231#107—591no—
232#107—591no—
233C4⋊C8C2×D5911yescharacteristic
234#103—591no—
235#103—591no—
236#103—591no—
237#103—591no—
238#103—591no—
239#103—591no—
240#102—591no—
241#102—591no—
242#102—591no—
243#102—591no—
244C22⋊C8C2×D5911yescharacteristic
245C22⋊C8C2×D5911yescharacteristic
246#97C2×D5911yescharacteristic
247#41—1182no—
248#41—2361no—
249#41—2364no—
250C2×Q8—591no—
251C2×Q8—591no—
252C2×Q8—1182no—
253C2×Q8—1181no—
254C2×Q8—1181no—
255C2×Q8—2361no—
256C2×D4—591no—
257C2×D4—591no—
258C2×D4—1181no—
259C2×D4—1181no—
260C2×D4—1181no—
261C2×D4—1181no—
262C2×D4D23611yescharacteristic
263C22×C4—1181no—
264C22×C4—1181no—
265C22×C4—1181no—
266C22×C4—1181no—
267C22×C4—1181no—
268C22×C4C22×D5911yescharacteristic
269C22×C4C22×D5911yescharacteristic
270SD16—1182no—
271SD16—2361no—
272D8—2361no—
273M16—41no—
274C2×C8—41no—
275C2×C8C22×D5911yescharacteristic
276C2×C8C22×D5911yescharacteristic
277C2×C8C22×D5911yescharacteristic
278C2×C8C22×D5911yescharacteristic
279C4⋊C4—591no—
280C4⋊C4—591no—
281C4⋊C4—591no—
282C4⋊C4—591no—
283C4⋊C4—1181no—
284C4⋊C4—1181no—
285C4⋊C4—1181no—
286C4⋊C4—1181no—
287C4⋊C4—1181no—
288C4⋊C4D23611yescharacteristic
289C22⋊C4—1181no—
290C22⋊C4—1181no—
291C22⋊C4—1181no—
292C22⋊C4—1181no—
293C22⋊C4—1181no—
294C22⋊C4—1181no—
295C22⋊C4—1181no—
296C22⋊C4D23611yescharacteristic
297C22⋊C4D23611yescharacteristic
298C42—1181no—
299C42C22×D5911yescharacteristic
300C23—1181no—
301C23—1181no—
302C23C2×D23611yescharacteristic
303C23C2×D23611yescharacteristic
304Q8—592no—
305Q8—1181no—
306Q8—1181no—
307Q8—1181no—
308Q8—2362no—
309Q8—2362no—
310D4—22no—
311D4—1181no—
312D4—1181no—
313D4—1181no—
314D4—1181no—
315D4—2362no—
316D4—2362no—
317D4—2362no—
318D4—2362no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—1181no—
324C2×C4—1181no—
325C2×C4—1181no—
326C2×C4—1181no—
327C2×C4—1181no—
328C2×C4—1181no—
329C2×C4—2362no—
330C2×C4—2362no—
331C2×C4—2362no—
332C2×C4—2362no—
333C2×C4—2362no—
334C2×C4C2×D23611yescharacteristic
335C2×C4C2×D23611yescharacteristic
336C2×C4C2×D23611yescharacteristic
337C2×C4C2×D23611yescharacteristic
338C2×C4C23×D5911yescharacteristic
339C8—21no—
340C8—21no—
341C8—21no—
342C8—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—2361no—
349C22—2361no—
350C22—2361no—
351C22—2361no—
352C22—2361no—
353C22—2361no—
354C22#1427375512yes—
355C22C22×D23611yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—1182no—
361C4—2361no—
362C4—2361no—
363C4—2361no—
364C4—2361no—
365C4—2361no—
366C4#41×D5911yescharacteristic
367C4#1427377211yescharacteristic
368C2—22no—
369C2—41no—
370C2—4721no—
371C2—4721no—
372C2#1683804711yescharacteristic
373C2C2×#1427375511yescharacteristic
374C2#1683821911yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#435C2
socleC22×C59C22×D4
hypercenter#435D59
hypocenterC59#3308
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #16838061C2semidirect
2. #16838056C2semidirect
3. #16837762C2semidirect
4. #16837738C2semidirect
5. #16837716C2semidirect
6. #16837698C2semidirect
7. #16837648C2semidirect
8. #16837638C2semidirect
9. #16837618C2semidirect
10. #16837549C2semidirect
11. #16837543C2semidirect
12. #16837504C2semidirect
13. #16837404C2semidirect
14. C2×#14273652C2semidirect
15. C59×#435C2semidirect
150. Dic118#41semidirect
200. #435D59semidirect
203. C59#3308semidirect