Finite Group Databasebeta

← #21436175

Subgroups — #21436175

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#16838107C211yesmaximal, characteristic, complemented
2#16838043C211yesmaximal, characteristic
3#16837763C211yesmaximal, characteristic, complemented
4#16837717C211yesmaximal, characteristic, complemented
5#16837681C211yesmaximal, characteristic, complemented
6#16837649C211yesmaximal, characteristic, complemented
7#16837641C211yesmaximal, characteristic, complemented
8#16837627C211yesmaximal, characteristic, complemented
9#16837567C211yesmaximal, characteristic, complemented
10#16837555C211yesmaximal, characteristic, complemented
11#16837501C211yesmaximal, characteristic, complemented
12#16837470C211yesmaximal, characteristic, complemented
13#16837402C211yesmaximal, characteristic, complemented
14C2×#14273647C211yesmaximal, characteristic, complemented
15C59×#484C211yesmaximal, characteristic, complemented
16C2×#11745689C2211yescharacteristic
17C22×D236C2211yescharacteristic
18C2×#11745672C2211yescharacteristic, complemented
19C2×#11745660C2211yescharacteristic
20C2×#11745660C2211yescharacteristic
21C2×#11745659C2211yescharacteristic, complemented
22C22×C59⋊C8C2211yescharacteristic
23#14273726C2211yescharacteristic, complemented
24#14273717—21no—
25#14273716C2211yescharacteristic
26#14273712—21no—
27#14273707C2211yescharacteristic, complemented
28#14273706—21no—
29#14273706C2211yescharacteristic
30#14273705—21no—
31#14273702—21no—
32#14273702C2211yescharacteristic
33#14273697—21no—
34#14273692C2211yescharacteristic, complemented
35#14273689C2211yescharacteristic
36C4×C22⋊D59—21no—
37C4×C22⋊D59C2211yescharacteristic
38C4⋊C4×D59C2211yescharacteristic, complemented
39C22⋊C4×D59—21no—
40#14273660C2211yescharacteristic, complemented
41Dic59⋊C8C2211yescharacteristic, complemented
42#14273651C2211yescharacteristic, complemented
43#14273650C2211yescharacteristic, complemented
44#14273649C2211yescharacteristic
45#14273649C2211yescharacteristic
46#14273647C2211yescharacteristic
47#14273647C2211yescharacteristic
48#14273647C2211yescharacteristic
49#14273647C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic, complemented
51#14273637C2211yescharacteristic, complemented
52C22⋊Q8×C59C2211yescharacteristic
53C2×C4⋊C4×C59C2211yescharacteristic
54#107×C59C2211yescharacteristic, complemented
55#107×C59C2211yescharacteristic, complemented
56#103×C59C2211yescharacteristic, complemented
57#103×C59C2211yescharacteristic, complemented
58C22⋊C8×C59C2211yescharacteristic
59C23×D59—21no—
60C2×Q8×C59C2311yescharacteristic
61C22×C4×C59—21no—
62C22×C4×C59C2311yescharacteristic
63C2×C22⋊D59D411yescharacteristic
64#11745689—22no—
65#11745689—41no—
66C2×D236—22no—
67C2×D236—21no—
68C2×D236—21no—
69C2×D236—21no—
70C2×D236—41no—
71C2×D236C2311yescharacteristic
72C2×D236C2311yescharacteristic
73C2×C4×D59—21no—
74C2×C4×D59—21no—
75C2×C4×D59—21no—
76C2×C4×D59C2311yescharacteristic
77C2×Dic118—21no—
78C2×Dic118C2311yescharacteristic
79C2×C8×C59C2311yescharacteristic
80C2×C8×C59C2311yescharacteristic
81C4⋊C4×C59—21no—
82C4⋊C4×C59—21no—
83C4⋊C4×C59C2311yescharacteristic
84C4⋊C4×C59C2311yescharacteristic
85C4⋊C4×C59C2311yescharacteristic
86C22⋊C4×C59—21no—
87C22⋊Dic59—21no—
88C22⋊Dic59D411yescharacteristic
89#11745672—41no—
90(C2×D59)⋊C4—21no—
91(C2×D59)⋊C4—21no—
92(C2×D59)⋊C4—21no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4—21no—
95(C2×D59)⋊C4D411yescharacteristic
96C4⋊Dic59—21no—
97C4⋊Dic59C2311yescharacteristic
98Dic59⋊C4—21no—
99Dic59⋊C4—21no—
100Dic59⋊C4—21no—
101Dic59⋊C4—21no—
102Dic59⋊C4D411yescharacteristic
103C4×Dic59—21no—
104C4×Dic59C2311yescharacteristic
105C2×C59⋊C8—41no—
106C2×C59⋊C8C2311yescharacteristic
107C2×C59⋊C8C2311yescharacteristic
108#11745660—22no—
109#11745660—41no—
110#11745659—41no—
111C23×C59C2×D411yescharacteristic
112C22×D59—21no—
113C22×D59—21no—
114C22×D59—42no—
115C22×D59—42no—
116C22×D59—81no—
117C22×D59C2×D411yescharacteristic
118Q8×C59—21no—
119Q8×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—81no—
127C2×C4×C59C2×D411yescharacteristic
128C2×C4×C59C2411yescharacteristic
129C22⋊D59—22no—
130C2×Dic59—21no—
131C2×Dic59—21no—
132C2×Dic59C2×D411yescharacteristic
133C2×Dic59C2×D411yescharacteristic
134C2×Dic59C2×D411yescharacteristic
135D236—21no—
136D236—21no—
137D236—21no—
138D236—42no—
139D236—42no—
140D236—81no—
141D236#4112yes—
142C4×D59—21no—
143C4×D59—21no—
144C4×D59—42no—
145C4×D59—81no—
146C4×D59—81no—
147Dic118—21no—
148Dic118—21no—
149Dic118—81no—
150C8×C59—21no—
151C8×C59—21no—
152C59⋊C8—21no—
153C59⋊C8—21no—
154C22×C59—21no—
155C22×C59—21no—
156C22×C59#13712yes—
157C22×C59C22×D411yescharacteristic
158C2×D59—21no—
159C2×D59—22no—
160C2×D59—21no—
161C2×D59—21no—
162C2×D59—41no—
163C2×D59—41no—
164C2×D59—41no—
165C2×D59—41no—
166C2×D59—41no—
167C2×D59—84no—
168C4×C59—21no—
169C4×C59—41no—
170C4×C59—41no—
171C4×C59—41no—
172C4×C59—41no—
173C4×C59C2×#4111yescharacteristic
174C4×C59H(5,𝔽2)11yescharacteristic
175Dic59—21no—
176Dic59—21no—
177Dic59—21no—
178Dic59—41no—
179Dic59—41no—
180#3314—591nomaximal, Sylow
181C2×C59—22no—
182C2×C59#54611yescharacteristic
183C2×C59C2×#13711yescharacteristic
184C2×C59#57611yescharacteristic
185D59—41no—
186D59—42no—
187D59—81no—
188#554—591no—
189#546—591no—
190#489—591no—
191#484D5911yescharacteristic, complemented
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×#41—591no—
205C22×D4—591no—
206C2×Q16—591no—
207C2×SD16—591no—
208C2×SD16—591no—
209C2×M16—591no—
210C22×C8—591no—
211C4⋊Q8—591no—
212#125—1181no—
213#124—591no—
214#123—1181no—
215C22⋊Q8—591no—
216C22⋊Q8—591no—
217C22⋊Q8—1181no—
218C22⋊Q8—1181no—
219C22⋊Q8C2×D5911yescharacteristic
220#121—591no—
221#121—1181no—
222#120—1181no—
223C4×Q8—591no—
224C4×D4—591no—
225C4×D4—591no—
226C4×D4—1181no—
227C2×C4⋊C4—591no—
228C2×C4⋊C4C2×D5911yescharacteristic
229C2×C22⋊C4—1181no—
230#107—591no—
231#107C2×D5911yescharacteristic, complemented
232#107C2×D5911yescharacteristic, complemented
233C4⋊C8—591no—
234#103—591no—
235#103—591no—
236#103C2×D5911yescharacteristic, complemented
237#103C2×D5911yescharacteristic, complemented
238#102—591no—
239#102—591no—
240#102—591no—
241#102—591no—
242#102—591no—
243#102—591no—
244C22⋊C8—591no—
245C22⋊C8C2×D5911yescharacteristic
246#97—591no—
247C24—1181no—
248#41—1182no—
249#41—2361no—
250C2×Q8—591no—
251C2×Q8—1181no—
252C2×Q8C22×D5911yescharacteristic
253C2×D4—591no—
254C2×D4—591no—
255C2×D4—591no—
256C2×D4—1182no—
257C2×D4—1181no—
258C2×D4—1181no—
259C2×D4—1181no—
260C2×D4—2361no—
261C22×C4—21no—
262C22×C4—591no—
263C22×C4—1181no—
264C22×C4—1181no—
265C22×C4—1181no—
266C22×C4C22×D5911yescharacteristic
267Q16—2361no—
268SD16—1182no—
269SD16—2361no—
270M16—2361no—
271C2×C8—591no—
272C2×C8—591no—
273C2×C8—2361no—
274C2×C8C22×D5911yescharacteristic
275C2×C8C22×D5911yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—591no—
279C4⋊C4—591no—
280C4⋊C4—1181no—
281C4⋊C4—1181no—
282C4⋊C4—1181no—
283C4⋊C4—1181no—
284C4⋊C4—1181no—
285C4⋊C4C22×D5911yescharacteristic
286C4⋊C4C22×D5911yescharacteristic
287C4⋊C4C22×D5911yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—591no—
290C22⋊C4—591no—
291C22⋊C4—1181no—
292C22⋊C4—1181no—
293C22⋊C4—1181no—
294C22⋊C4—1181no—
295C22⋊C4—1181no—
296C22⋊C4—1181no—
297C42—591no—
298C42—1181no—
299C23—591no—
300C23—1181no—
301C23—1181no—
302C23—4721no—
303C23—2362no—
304C23—2362no—
305C23D4×D5911yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—1181no—
309Q8—1181no—
310Q8—4721no—
311D4—592no—
312D4—1182no—
313D4—1181no—
314D4—1181no—
315D4—1181no—
316D4—4721no—
317D4—2362no—
318D4—2362no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—81no—
326C2×C4—591no—
327C2×C4—591no—
328C2×C4—591no—
329C2×C4—1181no—
330C2×C4—1181no—
331C2×C4—1181no—
332C2×C4—1181no—
333C2×C4—4721no—
334C2×C4—4721no—
335C2×C4—2362no—
336C2×C4D4×D5911yescharacteristic
337C2×C4C23×D5911yescharacteristic
338C8—21no—
339C8—21no—
340C8—1181no—
341C8—1181no—
342C22—21no—
343C22—21no—
344C22—1181no—
345C22—1181no—
346C22—1181no—
347C22—1182no—
348C22—4724no—
349C22—2361no—
350C22—2361no—
351C22—2361no—
352C22—2361no—
353C22—2361no—
354C22#1427375912yes—
355C22C2×D4×D5911yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—1181no—
362C4—1181no—
363C4—1181no—
364C4—2361no—
365C4—2361no—
366C4#41×D5911yescharacteristic
367C4#1427377311yescharacteristic
368C2—22no—
369C2—4721no—
370C2—2361no—
371C2—2362no—
372C2#1683804411yescharacteristic
373C2C2×#1427375911yescharacteristic
374C2#1683820611yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#484C2
socleC22×C59C22×D4
hypercenter#484D59
hypocenterC59#3314
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
1. #16838107C2semidirect
3. #16837763C2semidirect
4. #16837717C2semidirect
5. #16837681C2semidirect
6. #16837649C2semidirect
7. #16837641C2semidirect
8. #16837627C2semidirect
9. #16837567C2semidirect
10. #16837555C2semidirect
11. #16837501C2semidirect
12. #16837470C2semidirect
13. #16837402C2semidirect
14. C2×#14273647C2semidirect
15. C59×#484C2semidirect
18. C2×#11745672C22semidirect
21. C2×#11745659C22semidirect
23. #14273726C22semidirect
27. #14273707C22semidirect
34. #14273692C22semidirect
38. C4⋊C4×D59C22semidirect
40. #14273660C22semidirect
41. Dic59⋊C8C22semidirect
42. #14273651C22semidirect
43. #14273650C22semidirect
50. (C2×D59)⋊C8C22semidirect
51. #14273637C22semidirect
54. #107×C59C22semidirect
55. #107×C59C22semidirect
56. #103×C59C22semidirect
57. #103×C59C22semidirect
191. #484D59semidirect
203. C59#3314semidirect
231. #107C2×D59semidirect
232. #107C2×D59semidirect
236. #103C2×D59semidirect
237. #103C2×D59semidirect