Finite Group Databasebeta

← #21435501

Subgroups — #21435501

Order 7552.

358 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#16838023C211yesmaximal, characteristic, complemented
2#16837706C211yesmaximal, characteristic, complemented
3#16837699C211yesmaximal, characteristic, complemented
4#16837692C211yesmaximal, characteristic, complemented
5#16837682C211yesmaximal, characteristic, complemented
6#16837653C211yesmaximal, characteristic, complemented
7#16837646C211yesmaximal, characteristic, complemented
8#16837636C211yesmaximal, characteristic, complemented
9#16837629C211yesmaximal, characteristic, complemented
10#16837617C211yesmaximal, characteristic, complemented
11#16837617C211yesmaximal, characteristic, complemented
12#16837599C211yesmaximal, characteristic, complemented
13#16837594C211yesmaximal, characteristic, complemented
14#16837429C211yesmaximal, characteristic, complemented
15C59×#540C211yesmaximal, characteristic, complemented
16C2×#11745670C2211yescharacteristic
17C2×#11745670C2211yescharacteristic
18C2×#11745669C2211yescharacteristic
19C2×#11745669C2211yescharacteristic
20C2×#11745664C2211yescharacteristic
21C22×C59⋊C8C2211yescharacteristic
22#14273727C2211yescharacteristic
23#14273722—21no—
24#14273715C2211yescharacteristic
25#14273713—21no—
26#14273709—21no—
27#14273706C2211yescharacteristic
28#14273705—21no—
29#14273701C2211yescharacteristic
30C4×Dic118C2211yescharacteristic
31C4×D236C2211yescharacteristic
32#14273660C2211yescharacteristic
33#14273660C2211yescharacteristic
34#14273658C2211yescharacteristic
35#14273658C2211yescharacteristic
36C4⋊(C59⋊C8)C2211yescharacteristic
37C4⋊(C59⋊C8)C2211yescharacteristic
38C4⋊(C59⋊C8)C2211yescharacteristic
39C4⋊(C59⋊C8)C2211yescharacteristic
40#14273650C2211yescharacteristic
41#14273650C2211yescharacteristic
42#14273648C2211yescharacteristic
43#14273648C2211yescharacteristic
44#14273648C2211yescharacteristic
45#14273648C2211yescharacteristic
46#14273647C2211yescharacteristic
47#14273647C2211yescharacteristic
48#127×C59C2211yescharacteristic
49#125×C59C2211yescharacteristic
50#123×C59—21no—
51#123×C59—21no—
52#121×C59—21no—
53#121×C59—21no—
54#121×C59C2211yescharacteristic
55#121×C59C2211yescharacteristic
56C4×D4×C59C2211yescharacteristic
57C4×D4×C59C2211yescharacteristic
58#117×C59C2211yescharacteristic
59C2×D4×C59—21no—
60C2×D4×C59—21no—
61C2×D4×C59—21no—
62C2×D4×C59—21no—
63C2×D4×C59C2311yescharacteristic
64C2×D4×C59C2311yescharacteristic
65C22×C4×C59—21no—
66C22×C4×C59—21no—
67C22×C4×C59C2311yescharacteristic
68C2×C22⋊D59—21no—
69C2×D236C2311yescharacteristic
70C2×C4×D59—21no—
71C2×Dic118—21no—
72C2×Dic118C2311yescharacteristic
73C4⋊C4×C59—21no—
74C4⋊C4×C59—21no—
75C4⋊C4×C59D411yescharacteristic
76C4⋊C4×C59D411yescharacteristic
77C4⋊C4×C59C2311yescharacteristic
78C4⋊C4×C59C2311yescharacteristic
79C22⋊C4×C59—21no—
80C22⋊C4×C59—21no—
81C22⋊C4×C59—21no—
82C22⋊C4×C59—21no—
83C22⋊C4×C59D411yescharacteristic
84C22⋊C4×C59D411yescharacteristic
85C42×C59C2311yescharacteristic
86C42×C59C2311yescharacteristic
87C22⋊Dic59—21no—
88#11745670—41no—
89#11745670—41no—
90#11745669—41no—
91#11745669—41no—
92(C2×D59)⋊C4—21no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4—21no—
95(C2×D59)⋊C4—21no—
96C4⋊Dic59—21no—
97C4⋊Dic59C2311yescharacteristic
98C4⋊Dic59C2311yescharacteristic
99Dic59⋊C4—21no—
100Dic59⋊C4—21no—
101C4×Dic59—21no—
102#11745664—41no—
103C2×C59⋊C8—41no—
104C2×C59⋊C8C2311yescharacteristic
105C2×C59⋊C8C2311yescharacteristic
106C2×C59⋊C8C2311yescharacteristic
107C2×C59⋊C8C2311yescharacteristic
108C23×C59—21no—
109C23×C59—21no—
110C23×C59C2×D411yescharacteristic
111C22×D59—21no—
112D4×C59—21no—
113D4×C59—21no—
114D4×C59—21no—
115D4×C59—21no—
116D4×C59—81no—
117D4×C59—81no—
118D4×C59—81no—
119D4×C59—81no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—81no—
125C2×C4×C59—81no—
126C2×C4×C59C2×D411yescharacteristic
127C2×C4×C59C2×D411yescharacteristic
128C2×C4×C59C2×D411yescharacteristic
129C2×C4×C59C2×D411yescharacteristic
130C2×C4×C59C2×D411yescharacteristic
131C2×C4×C59C2411yescharacteristic
132C22⋊D59—81no—
133C2×Dic59—21no—
134C2×Dic59—21no—
135C2×Dic59—21no—
136D236—21no—
137D236—21no—
138C4×D59—81no—
139Dic118—21no—
140Dic118—21no—
141Dic118—81no—
142C59⋊C8—21no—
143C59⋊C8—21no—
144C59⋊C8—21no—
145C59⋊C8—21no—
146C22×C59—21no—
147C22×C59—21no—
148C22×C59—21no—
149C22×C59—41no—
150C22×C59—41no—
151C22×C59—41no—
152C22×C59—41no—
153C22×C59—41no—
154C22×C59—41no—
155C22×C59C22×D411yescharacteristic
156C2×D59—41no—
157C2×D59—41no—
158C2×D59—41no—
159C4×C59—21no—
160C4×C59—21no—
161C4×C59—21no—
162C4×C59—21no—
163C4×C59—21no—
164C4×C59—41no—
165C4×C59—41no—
166C4×C59H(5,𝔽2)11yescharacteristic
167C4×C592−1+411yescharacteristic
168Dic59—41no—
169Dic59—41no—
170Dic59—41no—
171#3257—591nomaximal, Sylow
172C2×C59—41no—
173C2×C59—81no—
174C2×C59—81no—
175C2×C59#53711yescharacteristic
176C2×C59#57611yescharacteristic
177C2×C59#57711yescharacteristic
178D59—81no—
179#542—591no—
180#540D5911yescharacteristic, complemented
181#479—591no—
182#478—591no—
183#476—591no—
184#474—591no—
185#469—591no—
186#468—591no—
187#466—591no—
188#465—591no—
189#463—591no—
190#463—591no—
191#460—591no—
192#459—591no—
193#424—591no—
194C59#325711yescharacteristic, complemented, Sylow
195C2×SD16—591no—
196C2×SD16—591no—
197C2×D8—591no—
198C2×D8—591no—
199C2×M16—591no—
200C22×C8—591no—
201C4⋊Q8—591no—
202#127C2×D5911yescharacteristic
203#126—1181no—
204#125C2×D5911yescharacteristic
205#124—591no—
206#124—1181no—
207#123—21no—
208#123—21no—
209#123—1181no—
210C22⋊Q8—591no—
211C22⋊Q8—1181no—
212#121—21no—
213#121—21no—
214#121—591no—
215#121C2×D5911yescharacteristic
216#121C2×D5911yescharacteristic
217C4×Q8—591no—
218C4×D4—591no—
219C4×D4C2×D5911yescharacteristic
220C4×D4C2×D5911yescharacteristic
221#117C2×D5911yescharacteristic
222#107—591no—
223#107—591no—
224#106—591no—
225#106—591no—
226C4⋊C8—591no—
227C4⋊C8—591no—
228C4⋊C8—591no—
229C4⋊C8—591no—
230#103—591no—
231#103—591no—
232#102—591no—
233#102—591no—
234#102—591no—
235#102—591no—
236#102—591no—
237#102—591no—
238C2×Q8—591no—
239C2×Q8—1181no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—591no—
245C2×D4—1181no—
246C2×D4C22×D5911yescharacteristic
247C2×D4C22×D5911yescharacteristic
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—1181no—
251C22×C4C22×D5911yescharacteristic
252SD16—2361no—
253SD16—2361no—
254D8—2361no—
255D8—2361no—
256M16—2361no—
257C2×C8—591no—
258C2×C8—591no—
259C2×C8—591no—
260C2×C8—591no—
261C2×C8—2361no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—591no—
265C4⋊C4—591no—
266C4⋊C4—1181no—
267C4⋊C4—1181no—
268C4⋊C4—1181no—
269C4⋊C4C22⋊D5911yescharacteristic
270C4⋊C4C22⋊D5911yescharacteristic
271C4⋊C4C22×D5911yescharacteristic
272C4⋊C4C22×D5911yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—1181no—
278C22⋊C4—1181no—
279C22⋊C4—1181no—
280C22⋊C4—1181no—
281C22⋊C4—1181no—
282C22⋊C4C22⋊D5911yescharacteristic
283C22⋊C4C22⋊D5911yescharacteristic
284C42—1181no—
285C42C22×D5911yescharacteristic
286C42C22×D5911yescharacteristic
287C23—21no—
288C23—21no—
289C23—1181no—
290C23C2×C22⋊D5911yescharacteristic
291Q8—1181no—
292Q8—1181no—
293Q8—4721no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—81no—
299D4—81no—
300D4—81no—
301D4—81no—
302D4—1181no—
303D4—1181no—
304D4—4721no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—1181no—
312C2×C4—1181no—
313C2×C4—1181no—
314C2×C4—4721no—
315C2×C4C2×C22⋊D5911yescharacteristic
316C2×C4C2×C22⋊D5911yescharacteristic
317C2×C4C2×C22⋊D5911yescharacteristic
318C2×C4C2×C22⋊D5911yescharacteristic
319C2×C4C2×C22⋊D5911yescharacteristic
320C2×C4C23×D5911yescharacteristic
321C8—1181no—
322C8—1181no—
323C8—1181no—
324C8—1181no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—2361no—
335C22—2361no—
336C22—2361no—
337C22C22×C22⋊D5911yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—2361no—
346C4—2361no—
347C4—2361no—
348C4#1427377311yescharacteristic
349C4#1427377411yescharacteristic
350C2—41no—
351C2—81no—
352C2—81no—
353C2—4721no—
354C2#1683798011yescharacteristic
355C2#1683820511yescharacteristic
356C2#1683821311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#540C2
socleC22×C59C22×D4
hypercenter#540D59
hypocenterC59#3257
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #16838023C2semidirect
2. #16837706C2semidirect
3. #16837699C2semidirect
4. #16837692C2semidirect
5. #16837682C2semidirect
6. #16837653C2semidirect
7. #16837646C2semidirect
8. #16837636C2semidirect
9. #16837629C2semidirect
10. #16837617C2semidirect
11. #16837617C2semidirect
12. #16837599C2semidirect
13. #16837594C2semidirect
14. #16837429C2semidirect
15. C59×#540C2semidirect
180. #540D59semidirect
194. C59#3257semidirect