Finite Group Databasebeta

← #21436388

Subgroups — #21436388

Order 7552.

386 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838115C211yesmaximal, characteristic
2#16838065C211yesmaximal, characteristic, complemented
3#16837751C211yesmaximal, characteristic, complemented
4#16837746C211yesmaximal, characteristic, complemented
5#16837696C211yesmaximal, characteristic, complemented
6#16837650C211yesmaximal, characteristic, complemented
7#16837649C211yesmaximal, characteristic, complemented
8#16837606C211yesmaximal, characteristic, complemented
9#16837543C211yesmaximal, characteristic, complemented
10#16837542C211yesmaximal, characteristic, complemented
11#16837489C211yesmaximal, characteristic, complemented
12#16837477C211yesmaximal, characteristic, complemented
13#16837410C211yesmaximal, characteristic, complemented
14#16837409C211yesmaximal, characteristic, complemented
15C59×#485C211yesmaximal, characteristic, complemented
16C22×Dic118C2211yescharacteristic
17C2×Q8×D59C2211yescharacteristic
18C2×#11745660C2211yescharacteristic
19C2×#11745660C2211yescharacteristic
20C2×#11745671C2211yescharacteristic
21C2×#11745664C2211yescharacteristic
22C2×#11745659C2211yescharacteristic
23#14273726—21no—
24#14273726C2211yescharacteristic
25#14273725C2211yescharacteristic
26#14273715—21no—
27#14273713—21no—
28#14273707C2211yescharacteristic
29#14273705—21no—
30#14273704—21no—
31#14273702C2211yescharacteristic
32#14273701C2211yescharacteristic
33#14273700—21no—
34#14273692C2211yescharacteristic
35#14273689C2211yescharacteristic
36C4×C22⋊D59C2211yescharacteristic
37(C22⋊D59)⋊C4—21no—
38#14273685C2211yescharacteristic
39#14273684—21no—
40#14273660C2211yescharacteristic
41Dic59⋊C8C2211yescharacteristic
42#14273652C2211yescharacteristic
43#14273652C2211yescharacteristic
44#14273651C2211yescharacteristic
45#14273650C2211yescharacteristic
46#14273650C2211yescharacteristic
47#14273650C2211yescharacteristic
48#14273650C2211yescharacteristic
49#14273647C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51C8×Dic59C2211yescharacteristic
52C22⋊Q8×C59C2211yescharacteristic
53#117×C59C2211yescharacteristic
54#107×C59C2211yescharacteristic
55#106×C59C2211yescharacteristic
56#103×C59C2211yescharacteristic
57#103×C59C2211yescharacteristic
58C22⋊C8×C59C2211yescharacteristic
59C2×Q8×C59C2311yescharacteristic
60C22×C4×C59C2311yescharacteristic
61C2×C22⋊D59—21no—
62C2×C22⋊D59D411yescharacteristic
63C22×Dic59—21no—
64Q8×D59—22no—
65Q8×D59—41no—
66C2×D236—21no—
67C2×D236C2311yescharacteristic
68C2×C4×D59—21no—
69C2×C4×D59—21no—
70C2×C4×D59C2311yescharacteristic
71C2×Dic118—22no—
72C2×Dic118—21no—
73C2×Dic118—21no—
74C2×Dic118—21no—
75C2×Dic118—41no—
76C2×Dic118C2311yescharacteristic
77C2×Dic118C2311yescharacteristic
78C2×C8×C59C2311yescharacteristic
79C2×C8×C59C2311yescharacteristic
80C4⋊C4×C59—21no—
81C4⋊C4×C59C2311yescharacteristic
82C4⋊C4×C59C2311yescharacteristic
83C4⋊C4×C59C2311yescharacteristic
84C22⋊C4×C59—21no—
85C22⋊C4×C59—21no—
86C42×C59—21no—
87C22⋊Dic59D411yescharacteristic
88#11745671—41no—
89(C2×D59)⋊C4—21no—
90(C2×D59)⋊C4—21no—
91(C2×D59)⋊C4—21no—
92(C2×D59)⋊C4—21no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4D411yescharacteristic
95C4⋊Dic59—21no—
96C4⋊Dic59C2311yescharacteristic
97Dic59⋊C4—21no—
98Dic59⋊C4—21no—
99Dic59⋊C4—21no—
100Dic59⋊C4—21no—
101Dic59⋊C4D411yescharacteristic
102C4×Dic59—21no—
103C4×Dic59—21no—
104C4×Dic59C2311yescharacteristic
105#11745664—41no—
106C2×C59⋊C8C2311yescharacteristic
107C2×C59⋊C8C2311yescharacteristic
108#11745660—22no—
109#11745660—41no—
110#11745659—41no—
111C23×C59C2×D411yescharacteristic
112C22×D59—21no—
113C22×D59C2×D411yescharacteristic
114Q8×C59—21no—
115Q8×C59—21no—
116C2×C4×C59—21no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59C2×D411yescharacteristic
123C2×C4×C59C2411yescharacteristic
124C22⋊D59—22no—
125C22⋊D59—81no—
126C2×Dic59—21no—
127C2×Dic59—21no—
128C2×Dic59—21no—
129C2×Dic59—42no—
130C2×Dic59C2×D411yescharacteristic
131C2×Dic59C2×D411yescharacteristic
132C2×Dic59C2×D411yescharacteristic
133D236—21no—
134D236—21no—
135D236—81no—
136C4×D59—21no—
137C4×D59—21no—
138C4×D59—42no—
139C4×D59—42no—
140Dic118—21no—
141Dic118—21no—
142Dic118—21no—
143Dic118—42no—
144Dic118—42no—
145Dic118—81no—
146Dic118#4112yes—
147C8×C59—21no—
148C8×C59—21no—
149C59⋊C8—21no—
150C59⋊C8—21no—
151C22×C59—21no—
152C22×C59—21no—
153C22×C59—21no—
154C22×C59C22×D411yescharacteristic
155C2×D59—21no—
156C2×D59—21no—
157C2×D59—21no—
158C2×D59—41no—
159C2×D59—41no—
160C2×D59—41no—
161C4×C59—21no—
162C4×C59—41no—
163C4×C59—41no—
164C4×C59—41no—
165C4×C59—41no—
166C4×C59C2×#4111yescharacteristic
167C4×C59H(5,𝔽2)11yescharacteristic
168Dic59—22no—
169Dic59—21no—
170Dic59—21no—
171Dic59—41no—
172Dic59—41no—
173Dic59#13712yes—
174#3329—591nomaximal, Sylow
175C2×C59—41no—
176C2×C59#54611yescharacteristic
177C2×C59C2×#13711yescharacteristic
178C2×C59#57711yescharacteristic
179D59—41no—
180D59—81no—
181#555—591no—
182D4×Q8—591no—
183#487—591no—
184#485—591no—
185#485D5911yescharacteristic, complemented
186#477—591no—
187#468—591no—
188#468—591no—
189#461—591no—
190#448—591no—
191#448—591no—
192C4×SD16—591no—
193#436—591no—
194#419—591no—
195#419—591no—
196C59#332911yescharacteristic, complemented, Sylow
197C22×Q8—591no—
198C22×Q8—591no—
199C2×SD16—591no—
200C2×SD16—591no—
201C2×SD16—591no—
202C2×M16—591no—
203C2×M16—591no—
204C4⋊Q8—591no—
205C4⋊Q8—591no—
206C4⋊Q8—1181no—
207#124—1181no—
208#124—1181no—
209C22⋊Q8—591no—
210C22⋊Q8—1181no—
211C22⋊Q8—1181no—
212C22⋊Q8C2×D5911yescharacteristic
213#121—591no—
214#121—591no—
215#121—1181no—
216C4×Q8—591no—
217C4×D4—591no—
218C4×D4—591no—
219C4×D4—1181no—
220#117—591no—
221#117—1181no—
222#117C2×D5911yescharacteristic
223#107—591no—
224#107C2×D5911yescharacteristic
225#106C2×D5911yescharacteristic
226C4⋊C8—591no—
227#103—591no—
228#103—591no—
229#103—591no—
230#103—591no—
231#103—591no—
232#103—591no—
233#103—591no—
234#103C2×D5911yescharacteristic
235#103C2×D5911yescharacteristic
236#102—591no—
237C22⋊C8—591no—
238C22⋊C8C2×D5911yescharacteristic
239C4×C8—591no—
240C2×Q8—591no—
241C2×Q8—591no—
242C2×Q8—1181no—
243C2×Q8—1181no—
244C2×Q8—1182no—
245C2×Q8—1181no—
246C2×Q8—1182no—
247C2×Q8—2361no—
248C2×Q8—2361no—
249C2×Q8C22×D5911yescharacteristic
250C2×D4—591no—
251C2×D4—591no—
252C2×D4—1181no—
253C2×D4—1181no—
254C22×C4—591no—
255C22×C4—1181no—
256C22×C4—1181no—
257C22×C4—1181no—
258C22×C4C22×D5911yescharacteristic
259SD16—1182no—
260SD16—2361no—
261SD16—2361no—
262M16—2361no—
263M16—2361no—
264C2×C8—591no—
265C2×C8—591no—
266C2×C8C22×D5911yescharacteristic
267C2×C8C22×D5911yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—591no—
270C4⋊C4—591no—
271C4⋊C4—1181no—
272C4⋊C4—1181no—
273C4⋊C4—1181no—
274C4⋊C4—1181no—
275C4⋊C4—1181no—
276C4⋊C4C22×D5911yescharacteristic
277C4⋊C4C22×D5911yescharacteristic
278C4⋊C4C22×D5911yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—591no—
282C22⋊C4—591no—
283C22⋊C4—1181no—
284C22⋊C4—1181no—
285C22⋊C4—1181no—
286C22⋊C4—1181no—
287C22⋊C4—1181no—
288C42—21no—
289C42—591no—
290C42—1181no—
291C42—1181no—
292C23—591no—
293C23—1181no—
294C23D4×D5911yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—592no—
298Q8—1181no—
299Q8—1181no—
300Q8—1181no—
301Q8—4721no—
302Q8—2362no—
303Q8—2362no—
304D4—1182no—
305D4—1181no—
306D4—1181no—
307D4—4721no—
308D4—4721no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—591no—
316C2×C4—591no—
317C2×C4—591no—
318C2×C4—1181no—
319C2×C4—1181no—
320C2×C4—1181no—
321C2×C4—1181no—
322C2×C4—1181no—
323C2×C4—2362no—
324C2×C4—2362no—
325C2×C4—2362no—
326C2×C4D4×D5911yescharacteristic
327C2×C4C23×D5911yescharacteristic
328C8—21no—
329C8—21no—
330C8—1181no—
331C8—1181no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—1181no—
336C22—1181no—
337C22—1181no—
338C22—2361no—
339C22—2361no—
340C22—2361no—
341C22C2×D4×D5911yescharacteristic
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—592no—
348C4—1181no—
349C4—1181no—
350C4—1182no—
351C4—2361no—
352C4—2361no—
353C4#41×D5911yescharacteristic
354C4#1427377311yescharacteristic
355C2—41no—
356C2—4721no—
357C2—2361no—
358C2#1683804411yescharacteristic
359C2#137×D5911yescharacteristic
360C2#1683820911yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#485C2
socleC22×C59C22×D4
hypercenter#485D59
hypocenterC59#3329
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
2. #16838065C2semidirect
3. #16837751C2semidirect
4. #16837746C2semidirect
5. #16837696C2semidirect
6. #16837650C2semidirect
7. #16837649C2semidirect
8. #16837606C2semidirect
9. #16837543C2semidirect
10. #16837542C2semidirect
11. #16837489C2semidirect
12. #16837477C2semidirect
13. #16837410C2semidirect
14. #16837409C2semidirect
15. C59×#485C2semidirect
185. #485D59semidirect
196. C59#3329semidirect