Finite Group Databasebeta

← #21436177

Subgroups — #21436177

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#16838109C211yesmaximal, characteristic, complemented
2#16837761C211yesmaximal, characteristic, complemented
3#16837735C211yesmaximal, characteristic, complemented
4#16837713C211yesmaximal, characteristic, complemented
5#16837682C211yesmaximal, characteristic, complemented
6#16837646C211yesmaximal, characteristic, complemented
7#16837641C211yesmaximal, characteristic, complemented
8#16837621C211yesmaximal, characteristic, complemented
9#16837564C211yesmaximal, characteristic, complemented
10#16837553C211yesmaximal, characteristic, complemented
11#16837502C211yesmaximal, characteristic, complemented
12#16837474C211yesmaximal, characteristic, complemented
13#16837403C211yesmaximal, characteristic, complemented
14C2×#14273648C211yesmaximal, characteristic, complemented
15C59×#546C211yesmaximal, characteristic
16C2×#11745672C2211yescharacteristic, complemented
17C2×#11745670C2211yescharacteristic
18C2×#11745670C2211yescharacteristic
19C2×#11745664C2211yescharacteristic, complemented
20C22×C59⋊C8C2211yescharacteristic
21#14273727C2211yescharacteristic, complemented
22#14273718—21no—
23#14273706C2211yescharacteristic
24#14273706C2211yescharacteristic, complemented
25#14273704—21no—
26#14273704—21no—
27C4×Dic118C2211yescharacteristic, complemented
28D4×Dic59—21no—
29C2×C4⋊Dic59C2211yescharacteristic
30C2×C4⋊Dic59C2211yescharacteristic, complemented
31#14273660C2211yescharacteristic, complemented
32#14273660C2211yescharacteristic, complemented
33#14273660C2211yescharacteristic, complemented
34C4⋊(C59⋊C8)C2211yescharacteristic, complemented
35#14273651C2211yescharacteristic, complemented
36#14273651C2211yescharacteristic, complemented
37#14273651C2211yescharacteristic, complemented
38#14273650C2211yescharacteristic, complemented
39#14273648C2211yescharacteristic
40#14273648C2211yescharacteristic
41#14273648C2211yescharacteristic
42#14273648C2211yescharacteristic
43#14273648C2211yescharacteristic
44#14273648C2211yescharacteristic
45C22⋊(C59⋊C8)C2211yescharacteristic
46C22⋊(C59⋊C8)C2211yescharacteristic, complemented
47#14273638C2211yescharacteristic, complemented
48C2×#41×C59C2211yescharacteristic
49C22×D4×C59C2211yescharacteristic
50#124×C59C2211yescharacteristic
51#123×C59—21no—
52C22⋊Q8×C59C2211yescharacteristic
53#121×C59—21no—
54#121×C59C2211yescharacteristic
55#120×C59—21no—
56C4×D4×C59C2211yescharacteristic
57C4×D4×C59C2211yescharacteristic
58C2×C22⋊C4×C59—21no—
59C24×C59—21no—
60#41×C59—22no—
61#41×C59—41no—
62C2×Q8×C59C2311yescharacteristic
63C2×D4×C59—22no—
64C2×D4×C59—21no—
65C2×D4×C59—21no—
66C2×D4×C59—21no—
67C2×D4×C59—41no—
68C2×D4×C59D411yescharacteristic
69C2×D4×C59C2311yescharacteristic
70C2×D4×C59C2311yescharacteristic
71C22×C4×C59—21no—
72C22×C4×C59—21no—
73C22×C4×C59C2311yescharacteristic
74C22×C4×C59C2311yescharacteristic
75C22×Dic59—21no—
76C22×Dic59—21no—
77C2×Dic118—21no—
78C2×Dic118C2311yescharacteristic
79C4⋊C4×C59—21no—
80C4⋊C4×C59D411yescharacteristic
81C4⋊C4×C59C2311yescharacteristic
82C22⋊C4×C59—21no—
83C22⋊C4×C59—21no—
84C22⋊C4×C59—21no—
85C22⋊C4×C59—21no—
86C22⋊C4×C59—21no—
87C22⋊C4×C59D411yescharacteristic
88C22⋊C4×C59D411yescharacteristic
89C42×C59C2311yescharacteristic
90C22⋊Dic59—21no—
91C22⋊Dic59—21no—
92#11745672—41no—
93#11745670—22no—
94#11745670—41no—
95C4⋊Dic59—21no—
96C4⋊Dic59—21no—
97C4⋊Dic59—21no—
98C4⋊Dic59C2311yescharacteristic
99C4⋊Dic59C2311yescharacteristic
100C4⋊Dic59C2311yescharacteristic
101Dic59⋊C4—21no—
102Dic59⋊C4—21no—
103Dic59⋊C4—21no—
104C4×Dic59—21no—
105#11745664—41no—
106C2×C59⋊C8—41no—
107C2×C59⋊C8C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110C2×C59⋊C8C2311yescharacteristic
111C23×C59—21no—
112C23×C59—21no—
113C23×C59—42no—
114C23×C59—42no—
115C23×C59—81no—
116C23×C59C2×D411yescharacteristic
117C23×C59C2×D411yescharacteristic
118Q8×C59—21no—
119Q8×C59—21no—
120D4×C59—22no—
121D4×C59—21no—
122D4×C59—21no—
123D4×C59—21no—
124D4×C59—42no—
125D4×C59—42no—
126D4×C59—81no—
127D4×C59#4112yes—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C2×C4×C59—21no—
132C2×C4×C59—21no—
133C2×C4×C59—21no—
134C2×C4×C59—42no—
135C2×C4×C59—81no—
136C2×C4×C59C2×D411yescharacteristic
137C2×C4×C59C2×D411yescharacteristic
138C2×C4×C59C2×D411yescharacteristic
139C2×C4×C59C2×D411yescharacteristic
140C2×C4×C59C2411yescharacteristic
141C2×Dic59—21no—
142C2×Dic59—21no—
143C2×Dic59—21no—
144C2×Dic59—21no—
145C2×Dic59—81no—
146C2×Dic59—81no—
147Dic118—21no—
148Dic118—21no—
149Dic118—81no—
150C59⋊C8—21no—
151C59⋊C8—21no—
152C59⋊C8—21no—
153C59⋊C8—21no—
154C22×C59—21no—
155C22×C59—21no—
156C22×C59—21no—
157C22×C59—22no—
158C22×C59—21no—
159C22×C59—21no—
160C22×C59—41no—
161C22×C59—41no—
162C22×C59—41no—
163C22×C59—41no—
164C22×C59—41no—
165C22×C59—84no—
166C22×C59#13712yes—
167C22×C59C22×D411yescharacteristic
168C4×C59—21no—
169C4×C59—21no—
170C4×C59—21no—
171C4×C59—21no—
172C4×C59—41no—
173C4×C59—41no—
174C4×C59C2×#4111yescharacteristic
175C4×C59H(5,𝔽2)11yescharacteristic
176Dic59—41no—
177Dic59—41no—
178Dic59—41no—
179Dic59—41no—
180#3314—591nomaximal, Sylow
181C2×C59—22no—
182C2×C59—41no—
183C2×C59—42no—
184C2×C59—81no—
185C2×C59#54611yescharacteristic
186C2×C59C2×#13711yescharacteristic
187C2×C59#57611yescharacteristic
188#554—591no—
189#546D5911yescharacteristic
190#489—591no—
191#484—591no—
192#480—591no—
193#474—591no—
194#468—591no—
195#467—591no—
196#464—591no—
197#452—591no—
198#450—591no—
199#440—591no—
200#435—591no—
201#417—591no—
202C2×#102—591no—
203C59#331411yescharacteristic, complemented, Sylow
204C2×#41C2×D5911yescharacteristic
205C22×D4C2×D5911yescharacteristic
206C2×Q16—591no—
207C2×SD16—591no—
208C2×SD16—591no—
209C2×M16—591no—
210C22×C8—591no—
211C4⋊Q8—591no—
212#125—1181no—
213#124C2×D5911yescharacteristic
214#123—21no—
215C22⋊Q8—591no—
216C22⋊Q8—591no—
217C22⋊Q8—1181no—
218C22⋊Q8—1181no—
219C22⋊Q8C2×D5911yescharacteristic
220#121—21no—
221#121C2×D5911yescharacteristic
222#120—21no—
223C4×Q8—591no—
224C4×D4—1181no—
225C4×D4C2×D5911yescharacteristic
226C4×D4C2×D5911yescharacteristic
227C2×C4⋊C4—591no—
228C2×C4⋊C4—591no—
229C2×C22⋊C4—21no—
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#102—591no—
239#102—591no—
240#102—591no—
241#102—591no—
242#102—591no—
243#102—591no—
244C22⋊C8—591no—
245C22⋊C8—591no—
246#97—591no—
247C24—21no—
248#41—22no—
249#41—41no—
250C2×Q8—591no—
251C2×Q8—1181no—
252C2×Q8C22×D5911yescharacteristic
253C2×D4—22no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—41no—
258C2×D4C22⋊D5911yescharacteristic
259C2×D4C22×D5911yescharacteristic
260C2×D4C22×D5911yescharacteristic
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—1181no—
264C22×C4—1181no—
265C22×C4C22×D5911yescharacteristic
266C22×C4C22×D5911yescharacteristic
267Q16—2361no—
268SD16—1182no—
269SD16—2361no—
270M16—2361no—
271C2×C8—591no—
272C2×C8—591no—
273C2×C8—591no—
274C2×C8—591no—
275C2×C8—2361no—
276C4⋊C4—21no—
277C4⋊C4—591no—
278C4⋊C4—591no—
279C4⋊C4—591no—
280C4⋊C4—1181no—
281C4⋊C4—1181no—
282C4⋊C4—1181no—
283C4⋊C4—1181no—
284C4⋊C4—1181no—
285C4⋊C4—1181no—
286C4⋊C4C22⋊D5911yescharacteristic
287C4⋊C4C22×D5911yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—1181no—
294C22⋊C4—1181no—
295C22⋊C4C22⋊D5911yescharacteristic
296C22⋊C4C22⋊D5911yescharacteristic
297C42—1181no—
298C42C22×D5911yescharacteristic
299C23—21no—
300C23—21no—
301C23—42no—
302C23—42no—
303C23—81no—
304C23C2×C22⋊D5911yescharacteristic
305C23C2×C22⋊D5911yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—1181no—
309Q8—1181no—
310Q8—4721no—
311D4—22no—
312D4—21no—
313D4—21no—
314D4—21no—
315D4—42no—
316D4—42no—
317D4—81no—
318D4#1174568712yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—81no—
327C2×C4—1181no—
328C2×C4—1181no—
329C2×C4—1181no—
330C2×C4—1181no—
331C2×C4—4721no—
332C2×C4—4721no—
333C2×C4C2×C22⋊D5911yescharacteristic
334C2×C4C2×C22⋊D5911yescharacteristic
335C2×C4C2×C22⋊D5911yescharacteristic
336C2×C4C2×C22⋊D5911yescharacteristic
337C2×C4C23×D5911yescharacteristic
338C8—1181no—
339C8—1181no—
340C8—1181no—
341C8—1181no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—22no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—84no—
354C22#1427375712yes—
355C22C22×C22⋊D5911yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—2361no—
363C4—2361no—
364C4—2361no—
365C4—2361no—
366C4C2×#1174568711yescharacteristic
367C4#1427377211yescharacteristic
368C2—22no—
369C2—41no—
370C2—42no—
371C2—81no—
372C2#1683804611yescharacteristic
373C2C2×#1427375711yescharacteristic
374C2#1683820511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#546C2
socleC22×C59C22×D4
hypercenter#546D59
hypocenterC59#3314
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #16838109C2semidirect
2. #16837761C2semidirect
3. #16837735C2semidirect
4. #16837713C2semidirect
5. #16837682C2semidirect
6. #16837646C2semidirect
7. #16837641C2semidirect
8. #16837621C2semidirect
9. #16837564C2semidirect
10. #16837553C2semidirect
11. #16837502C2semidirect
12. #16837474C2semidirect
13. #16837403C2semidirect
14. C2×#14273648C2semidirect
16. C2×#11745672C22semidirect
19. C2×#11745664C22semidirect
21. #14273727C22semidirect
24. #14273706C22semidirect
27. C4×Dic118C22semidirect
30. C2×C4⋊Dic59C22semidirect
31. #14273660C22semidirect
32. #14273660C22semidirect
33. #14273660C22semidirect
34. C4⋊(C59⋊C8)C22semidirect
35. #14273651C22semidirect
36. #14273651C22semidirect
37. #14273651C22semidirect
38. #14273650C22semidirect
46. C22⋊(C59⋊C8)C22semidirect
47. #14273638C22semidirect
203. C59#3314semidirect