Finite Group Databasebeta

← #21436087

Subgroups — #21436087

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#16838056C211yesmaximal, characteristic, complemented
2#16837761C211yesmaximal, characteristic, complemented
3#16837735C211yesmaximal, characteristic, complemented
4#16837713C211yesmaximal, characteristic, complemented
5#16837697C211yesmaximal, characteristic, complemented
6#16837650C211yesmaximal, characteristic, complemented
7#16837636C211yesmaximal, characteristic, complemented
8#16837614C211yesmaximal, characteristic, complemented
9#16837547C211yesmaximal, characteristic, complemented
10#16837541C211yesmaximal, characteristic, complemented
11#16837500C211yesmaximal, characteristic, complemented
12#16837474C211yesmaximal, characteristic, complemented
13#16837403C211yesmaximal, characteristic, complemented
14C2×#14273651C211yesmaximal, characteristic, complemented
15C59×#548C211yesmaximal, characteristic, complemented
16C2×#11745687—21no—
17C2×#11745671C2211yescharacteristic
18C2×#11745671C2211yescharacteristic
19C2×#11745669C2211yescharacteristic
20C2×#11745664C2211yescharacteristic
21C22×C59⋊C8C2211yescharacteristic
22#14273727C2211yescharacteristic
23#14273711—21no—
24#14273711—21no—
25#14273707—21no—
26#14273701C2211yescharacteristic
27#14273701C2211yescharacteristic
28C4×D236C2211yescharacteristic
29C2×C4⋊Dic59C2211yescharacteristic
30C2×C4⋊Dic59C2211yescharacteristic
31#14273660C2211yescharacteristic
32#14273660C2211yescharacteristic
33#14273660C2211yescharacteristic
34C4⋊(C59⋊C8)C2211yescharacteristic
35#14273651C2211yescharacteristic
36#14273651C2211yescharacteristic
37#14273651C2211yescharacteristic
38#14273651C2211yescharacteristic
39#14273651C2211yescharacteristic
40#14273651C2211yescharacteristic
41#14273648C2211yescharacteristic
42#14273648C2211yescharacteristic
43#14273648C2211yescharacteristic
44#14273647C2211yescharacteristic
45C22⋊(C59⋊C8)C2211yescharacteristic
46C22⋊(C59⋊C8)C2211yescharacteristic
47#14273638C2211yescharacteristic
48C2×#41×C59C2211yescharacteristic
49C22×Q8×C59C2211yescharacteristic
50#124×C59—21no—
51#124×C59C2211yescharacteristic
52C22⋊Q8×C59—21no—
53C22⋊Q8×C59C2211yescharacteristic
54#121×C59—21no—
55#121×C59C2211yescharacteristic
56C4×Q8×C59C2211yescharacteristic
57C4×D4×C59—21no—
58C4×D4×C59C2211yescharacteristic
59#41×C59—22no—
60#41×C59—41no—
61C2×Q8×C59—21no—
62C2×Q8×C59—22no—
63C2×Q8×C59—41no—
64C2×Q8×C59C2311yescharacteristic
65C2×Q8×C59C2311yescharacteristic
66C2×D4×C59—21no—
67C2×D4×C59—21no—
68C2×D4×C59D411yescharacteristic
69C2×D4×C59C2311yescharacteristic
70C22×C4×C59—21no—
71C22×C4×C59—21no—
72C22×C4×C59C2311yescharacteristic
73C22×C4×C59C2311yescharacteristic
74C2×C22⋊D59—21no—
75C2×C22⋊D59—21no—
76C22×Dic59—21no—
77C22×Dic59—21no—
78#11745687—44no—
79C2×D236C2311yescharacteristic
80C2×C4×D59—21no—
81C2×Dic118—21no—
82C4⋊C4×C59—21no—
83C4⋊C4×C59—21no—
84C4⋊C4×C59D411yescharacteristic
85C4⋊C4×C59C2311yescharacteristic
86C22⋊C4×C59—21no—
87C22⋊C4×C59—21no—
88C22⋊C4×C59—21no—
89C22⋊C4×C59—21no—
90C22⋊C4×C59D411yescharacteristic
91C22⋊C4×C59D411yescharacteristic
92C42×C59—21no—
93C42×C59C2311yescharacteristic
94#11745671—22no—
95#11745671—41no—
96#11745669—41no—
97(C2×D59)⋊C4—21no—
98(C2×D59)⋊C4—21no—
99(C2×D59)⋊C4—21no—
100C4⋊Dic59—21no—
101C4⋊Dic59—21no—
102C4⋊Dic59—21no—
103C4⋊Dic59C2311yescharacteristic
104C4⋊Dic59C2311yescharacteristic
105C4⋊Dic59C2311yescharacteristic
106#11745664—41no—
107C2×C59⋊C8—41no—
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110C2×C59⋊C8C2311yescharacteristic
111C2×C59⋊C8C2311yescharacteristic
112C23×C59—21no—
113C23×C59C2×D411yescharacteristic
114C23×C59C2×D411yescharacteristic
115C22×D59—21no—
116Q8×C59—21no—
117Q8×C59—21no—
118Q8×C59—21no—
119Q8×C59—42no—
120Q8×C59#4112yescomplemented
121D4×C59—22no—
122D4×C59—21no—
123D4×C59—21no—
124D4×C59—42no—
125D4×C59—42no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C2×C4×C59—21no—
132C2×C4×C59—21no—
133C2×C4×C59—42no—
134C2×C4×C59—42no—
135C2×C4×C59C2×D411yescharacteristic
136C2×C4×C59C2×D411yescharacteristic
137C2×C4×C59C2×D411yescharacteristic
138C2×C4×C59C2×D411yescharacteristic
139C2×C4×C59C2411yescharacteristic
140C22⋊D59—42no—
141C22⋊D59—42no—
142C2×Dic59—21no—
143C2×Dic59—21no—
144C2×Dic59—21no—
145C2×Dic59—42no—
146C2×Dic59—42no—
147D236—21no—
148D236—21no—
149C4×D59—42no—
150Dic118—42no—
151C59⋊C8—21no—
152C59⋊C8—21no—
153C59⋊C8—21no—
154C59⋊C8—21no—
155C22×C59—21no—
156C22×C59—21no—
157C22×C59—21no—
158C22×C59—21no—
159C22×C59—21no—
160C22×C59—41no—
161C22×C59—41no—
162C22×C59—41no—
163C22×C59AGL(1,ℤ/8)12yes—
164C22×C59C22×D411yescharacteristic
165C2×D59—41no—
166C2×D59—41no—
167C2×D59—41no—
168C4×C59—21no—
169C4×C59—21no—
170C4×C59—22no—
171C4×C59—21no—
172C4×C59—21no—
173C4×C59—41no—
174C4×C59—41no—
175C4×C59C2×#4111yescharacteristic
176C4×C59H(5,𝔽2)11yescharacteristic
177Dic59—41no—
178Dic59—41no—
179Dic59—41no—
180#3308—591nomaximal, Sylow
181C2×C59—22no—
182C2×C59—41no—
183C2×C59—81no—
184C2×C59#54611yescharacteristic
185C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
186C2×C59#57811yescharacteristic
187D59—81no—
188#548D5911yescharacteristic, complemented
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#435—591no—
201#417—591no—
202C2×#103—591no—
203C59#330811yescharacteristic, complemented, Sylow
204C2×#41—1181no—
205C2×#41C2×D5911yescharacteristic
206C22×Q8C2×D5911yescharacteristic
207C2×SD16—591no—
208C2×SD16—591no—
209C2×D8—591no—
210C2×M16—591no—
211C22×C8—591no—
212C4⋊Q8—591no—
213#124—21no—
214#124C2×D5911yescharacteristic
215#123—1181no—
216#123—1181no—
217C22⋊Q8—21no—
218C22⋊Q8—1181no—
219C22⋊Q8C2×D5911yescharacteristic
220#121—21no—
221#121—591no—
222#121—591no—
223#121C2×D5911yescharacteristic
224C4×Q8C2×D5911yescharacteristic
225C4×D4—21no—
226C4×D4—591no—
227C4×D4C2×D5911yescharacteristic
228C2×C4⋊C4—591no—
229C2×C4⋊C4—591no—
230#107—591no—
231#107—591no—
232#107—591no—
233C4⋊C8—591no—
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⋊C8—591no—
245C22⋊C8—591no—
246#97—591no—
247#41—22no—
248#41—41no—
249#41—2364no—
250C2×Q8—21no—
251C2×Q8—22no—
252C2×Q8—41no—
253C2×Q8—1181no—
254C2×Q8C22×D5911yescharacteristic
255C2×Q8C22×D5911yescharacteristic
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—591no—
259C2×D4—1181no—
260C2×D4—1181no—
261C2×D4C22⋊D5911yescharacteristic
262C2×D4C22×D5911yescharacteristic
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—1181no—
266C22×C4—1181no—
267C22×C4—1181no—
268C22×C4C22×D5911yescharacteristic
269C22×C4C22×D5911yescharacteristic
270SD16—1182no—
271SD16—2361no—
272D8—2361no—
273M16—2361no—
274C2×C8—591no—
275C2×C8—591no—
276C2×C8—591no—
277C2×C8—591no—
278C2×C8—2361no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—591no—
282C4⋊C4—591no—
283C4⋊C4—591no—
284C4⋊C4—1181no—
285C4⋊C4—1181no—
286C4⋊C4—1181no—
287C4⋊C4C22⋊D5911yescharacteristic
288C4⋊C4C22×D5911yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—1181no—
294C22⋊C4—1181no—
295C22⋊C4—1181no—
296C22⋊C4C22⋊D5911yescharacteristic
297C22⋊C4C22⋊D5911yescharacteristic
298C42—21no—
299C42C22×D5911yescharacteristic
300C23—21no—
301C23—1181no—
302C23C2×C22⋊D5911yescharacteristic
303C23C2×C22⋊D5911yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—42no—
308Q8—2362no—
309Q8#1174568712yescomplemented
310D4—22no—
311D4—21no—
312D4—21no—
313D4—42no—
314D4—42no—
315D4—1181no—
316D4—1181no—
317D4—2362no—
318D4—2362no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—1181no—
329C2×C4—1181no—
330C2×C4—1181no—
331C2×C4—2362no—
332C2×C4—2362no—
333C2×C4—2362no—
334C2×C4C2×C22⋊D5911yescharacteristic
335C2×C4C2×C22⋊D5911yescharacteristic
336C2×C4C2×C22⋊D5911yescharacteristic
337C2×C4C2×C22⋊D5911yescharacteristic
338C2×C4C23×D5911yescharacteristic
339C8—1181no—
340C8—1181no—
341C8—1181no—
342C8—1181no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—2361no—
352C22—2361no—
353C22—2361no—
354C22#1427375212yes—
355C22C22×C22⋊D5911yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—22no—
361C4—41no—
362C4—41no—
363C4—2361no—
364C4—2361no—
365C4—2361no—
366C4C2×#1174568711yescharacteristic
367C4#1427377211yescharacteristic
368C2—22no—
369C2—41no—
370C2—81no—
371C2—4721no—
372C2#1683804611yescharacteristic
373C2C2×#1427375211yescharacteristic
374C2#1683821711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#548C2
socleC22×C59C22×D4
hypercenter#548D59
hypocenterC59#3308
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #16838056C2semidirect
2. #16837761C2semidirect
3. #16837735C2semidirect
4. #16837713C2semidirect
5. #16837697C2semidirect
6. #16837650C2semidirect
7. #16837636C2semidirect
8. #16837614C2semidirect
9. #16837547C2semidirect
10. #16837541C2semidirect
11. #16837500C2semidirect
12. #16837474C2semidirect
13. #16837403C2semidirect
14. C2×#14273651C2semidirect
15. C59×#548C2semidirect
120. Q8×C59#41semidirect
188. #548D59semidirect
203. C59#3308semidirect
309. Q8#11745687semidirect