Finite Group Databasebeta

← #21434778

Subgroups — #21434778

Order 7552.

374 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838021C211yesmaximal, characteristic, complemented
2#16838008C211yesmaximal, characteristic, complemented
3#16837812C211yesmaximal, characteristic, complemented
4#16837792C211yesmaximal, characteristic, complemented
5#16837749C211yesmaximal, characteristic, complemented
6#16837654C211yesmaximal, characteristic, complemented
7#16837651C211yesmaximal, characteristic, complemented
8#16837637C211yesmaximal, characteristic, complemented
9#16837634C211yesmaximal, characteristic, complemented
10#16837511C211yesmaximal, characteristic, complemented
11#16837505C211yesmaximal, characteristic, complemented
12#16837487C211yesmaximal, characteristic, complemented
13#16837482C211yesmaximal, characteristic, complemented
14#16837356C211yesmaximal, characteristic, complemented
15C59×#488C211yesmaximal, characteristic, complemented
16C2×#11745671C2211yescharacteristic
17C2×#11745671C2211yescharacteristic
18C2×#11745669C2211yescharacteristic
19C2×#11745669C2211yescharacteristic
20C2×#11745659C2211yescharacteristic
21C2×C8×D59C2211yescharacteristic
22#14273727C2211yescharacteristic
23#14273724C2211yescharacteristic
24#14273720—21no—
25#14273713—21no—
26#14273712—21no—
27#14273712—21no—
28#14273711—21no—
29#14273704—21no—
30#14273703C2211yescharacteristic
31#14273702—21no—
32#14273702—21no—
33#14273702C2211yescharacteristic
34#14273702C2211yescharacteristic
35#14273698C2211yescharacteristic
36Q8×Dic59C2211yescharacteristic
37D4×Dic59C2211yescharacteristic
38#14273689C2211yescharacteristic
39#14273689C2211yescharacteristic
40#14273684C2211yescharacteristic
41#14273660C2211yescharacteristic
42#14273660C2211yescharacteristic
43#14273658C2211yescharacteristic
44#14273658C2211yescharacteristic
45#14273649C2211yescharacteristic
46#14273649C2211yescharacteristic
47#14273649C2211yescharacteristic
48#14273649C2211yescharacteristic
49#14273638C2211yescharacteristic
50#14273637C2211yescharacteristic
51C8×Dic59C2211yescharacteristic
52#125×C59C2211yescharacteristic
53#124×C59C2211yescharacteristic
54#103×C59C2211yescharacteristic
55#103×C59C2211yescharacteristic
56#102×C59C2211yescharacteristic
57#102×C59C2211yescharacteristic
58C4×C8×C59C2211yescharacteristic
59C2×Q8×C59C2311yescharacteristic
60C2×D4×C59C2311yescharacteristic
61C2×C22⋊D59—21no—
62C22×Dic59—21no—
63C2×D236—21no—
64C2×D236—21no—
65C2×D236—21no—
66C2×D236—21no—
67C2×D236C2311yescharacteristic
68C2×D236C2311yescharacteristic
69C2×C4×D59—21no—
70C2×C4×D59—21no—
71C2×C4×D59C2311yescharacteristic
72C2×Dic118—21no—
73C2×C8×C59C2311yescharacteristic
74C2×C8×C59C2311yescharacteristic
75C4⋊C4×C59—21no—
76C4⋊C4×C59—21no—
77C4⋊C4×C59C2311yescharacteristic
78C4⋊C4×C59C2311yescharacteristic
79C22⋊C4×C59—21no—
80C22⋊C4×C59—21no—
81C42×C59C2311yescharacteristic
82C22⋊Dic59—21no—
83C22⋊Dic59—21no—
84#11745671—22no—
85#11745671—22no—
86#11745669—22no—
87#11745669—22no—
88(C2×D59)⋊C4—21no—
89(C2×D59)⋊C4—21no—
90(C2×D59)⋊C4—21no—
91(C2×D59)⋊C4—21no—
92(C2×D59)⋊C4—21no—
93(C2×D59)⋊C4D411yescharacteristic
94(C2×D59)⋊C4D411yescharacteristic
95C4⋊Dic59—21no—
96C4⋊Dic59—21no—
97C4⋊Dic59C2311yescharacteristic
98C4⋊Dic59C2311yescharacteristic
99Dic59⋊C4—21no—
100Dic59⋊C4D411yescharacteristic
101Dic59⋊C4D411yescharacteristic
102C4×Dic59—21no—
103C4×Dic59C2311yescharacteristic
104C2×C59⋊C8C2311yescharacteristic
105C2×C59⋊C8C2311yescharacteristic
106#11745659—22no—
107C8×D59—22no—
108C23×C59—21no—
109C22×D59—21no—
110C22×D59—21no—
111C22×D59C2×D411yescharacteristic
112Q8×C59—21no—
113Q8×C59—21no—
114D4×C59—21no—
115D4×C59—21no—
116C2×C4×C59—21no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59C2×D411yescharacteristic
120C2×C4×C59C2×D411yescharacteristic
121C2×C4×C59C2411yescharacteristic
122C22⋊D59—81no—
123C2×Dic59—21no—
124C2×Dic59—21no—
125C2×Dic59—81no—
126C2×Dic59C2×D411yescharacteristic
127C2×Dic59C2×D411yescharacteristic
128C2×Dic59C2×D411yescharacteristic
129D236—21no—
130D236—21no—
131D236—21no—
132D236—21no—
133D236—81no—
134D236—81no—
135D236—81no—
136D236—81no—
137C4×D59—21no—
138C4×D59—21no—
139C4×D59—81no—
140C4×D59—81no—
141Dic118—81no—
142C8×C59—21no—
143C8×C59—21no—
144C59⋊C8#4112yes—
145C59⋊C8#4112yes—
146C22×C59—41no—
147C22×C59—41no—
148C22×C59—41no—
149C22×C59C22×D411yescharacteristic
150C2×D59—21no—
151C2×D59—21no—
152C2×D59—21no—
153C2×D59—41no—
154C2×D59—41no—
155C2×D59—41no—
156C2×D59—41no—
157C2×D59—41no—
158C2×D59—41no—
159C4×C59—21no—
160C4×C59—21no—
161C4×C59—41no—
162C4×C59—41no—
163C4×C59—41no—
164C4×C59C2×#4111yescharacteristic
165C4×C59C2×#4111yescharacteristic
166Dic59—21no—
167Dic59—21no—
168Dic59—21no—
169Dic59—41no—
170Dic59—41no—
171#3179—591nomaximal, Sylow
172C2×C59—81no—
173C2×C59#53211yescharacteristic
174C2×C59#57611yescharacteristic
175C2×C59#57711yescharacteristic
176D59—41no—
177D59—81no—
178D59—81no—
179#542—591no—
180#540—591no—
181#501—591no—
182#496—591no—
183#488D5911yescharacteristic, complemented
184#486—591no—
185#469—591no—
186#468—591no—
187#466—591no—
188#465—591no—
189#442—591no—
190#440—591no—
191C4×SD16—591no—
192C4×D8—591no—
193#405—591no—
194C59#317911yescharacteristic, complemented, Sylow
195C2×SD16—591no—
196C2×SD16—591no—
197C2×D8—591no—
198C2×D8—591no—
199C2×M16—591no—
200C22×C8—591no—
201C4⋊Q8—591no—
202#127—591no—
203#126—1181no—
204#125C2×D5911yescharacteristic
205#124—1181no—
206#124C2×D5911yescharacteristic
207#123—1181no—
208#123—1181no—
209#123—1181no—
210C22⋊Q8—591no—
211C22⋊Q8—1181no—
212#121—591no—
213#121—591no—
214#121—591no—
215#121—1181no—
216#121—1181no—
217C4×Q8—591no—
218C4×D4—591no—
219C4×D4—591no—
220C4×D4—591no—
221#117—591no—
222#107—591no—
223#107—591no—
224#106—591no—
225#106—591no—
226#103C2×D5911yescharacteristic
227#103C2×D5911yescharacteristic
228#102—591no—
229#102—591no—
230#102—591no—
231#102—591no—
232#102C2×D5911yescharacteristic
233#102C2×D5911yescharacteristic
234#97—591no—
235#97—591no—
236C4×C8—591no—
237C4×C8C2×D5911yescharacteristic
238C2×Q8—1181no—
239C2×Q8C22×D5911yescharacteristic
240C2×D4—591no—
241C2×D4—591no—
242C2×D4—1181no—
243C2×D4—1181no—
244C2×D4—1181no—
245C2×D4—1181no—
246C2×D4—1181no—
247C2×D4C22×D5911yescharacteristic
248C22×C4—591no—
249C22×C4—1181no—
250C22×C4—1181no—
251C22×C4—1181no—
252SD16—1182no—
253SD16—1182no—
254D8—1182no—
255D8—1182no—
256M16—1182no—
257C2×C8—591no—
258C2×C8—591no—
259C2×C8—1182no—
260C2×C8C22×D5911yescharacteristic
261C2×C8C22×D5911yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—591no—
265C4⋊C4—591no—
266C4⋊C4—591no—
267C4⋊C4—591no—
268C4⋊C4—1181no—
269C4⋊C4—1181no—
270C4⋊C4—1181no—
271C4⋊C4C22×D5911yescharacteristic
272C4⋊C4C22×D5911yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—591no—
276C22⋊C4—591no—
277C22⋊C4—1181no—
278C22⋊C4—1181no—
279C22⋊C4—1181no—
280C22⋊C4—1181no—
281C22⋊C4—1181no—
282C22⋊C4—1181no—
283C22⋊C4—1181no—
284C42—591no—
285C42—1181no—
286C42C22×D5911yescharacteristic
287C23—21no—
288C23—591no—
289C23—1181no—
290C23—1181no—
291Q8—21no—
292Q8—21no—
293Q8—4721no—
294D4—21no—
295D4—21no—
296D4—1181no—
297D4—1181no—
298D4—1181no—
299D4—1181no—
300D4—4721no—
301D4—4721no—
302D4—4721no—
303D4—4721no—
304D4—4721no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—591no—
309C2×C4—591no—
310C2×C4—591no—
311C2×C4—1181no—
312C2×C4—1181no—
313C2×C4—1181no—
314C2×C4—1181no—
315C2×C4—4721no—
316C2×C4—4721no—
317C2×C4—4721no—
318C2×C4D4×D5911yescharacteristic
319C2×C4D4×D5911yescharacteristic
320C2×C4C23×D5911yescharacteristic
321C8—21no—
322C8—21no—
323C8—592no—
324C8—592no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—1181no—
329C22—1181no—
330C22—1181no—
331C22—2361no—
332C22—2361no—
333C22—2361no—
334C22—2361no—
335C22—2361no—
336C22—2361no—
337C22C2×D4×D5911yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—1181no—
344C4—1181no—
345C4—1181no—
346C4—2361no—
347C4—2361no—
348C4#41×D5911yescharacteristic
349C4#41×D5911yescharacteristic
350C2—81no—
351C2—4721no—
352C2—4721no—
353C2—2361no—
354C2#1683795111yescharacteristic
355C2#1683820411yescharacteristic
356C2#1683820911yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#488C2
socleC22×C59C22×D4
hypercenter#488D59
hypocenterC59#3179
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #16838021C2semidirect
2. #16838008C2semidirect
3. #16837812C2semidirect
4. #16837792C2semidirect
5. #16837749C2semidirect
6. #16837654C2semidirect
7. #16837651C2semidirect
8. #16837637C2semidirect
9. #16837634C2semidirect
10. #16837511C2semidirect
11. #16837505C2semidirect
12. #16837487C2semidirect
13. #16837482C2semidirect
14. #16837356C2semidirect
15. C59×#488C2semidirect
183. #488D59semidirect
194. C59#3179semidirect