Finite Group Databasebeta

← #21436066

Subgroups — #21436066

Order 7552.

394 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838057C211yesmaximal, characteristic, complemented
2#16837772C211yesmaximal, characteristic, complemented
3#16837743C211yesmaximal, characteristic, complemented
4#16837732C211yesmaximal, characteristic, complemented
5#16837699C211yesmaximal, characteristic, complemented
6#16837646C211yesmaximal, characteristic, complemented
7#16837629C211yesmaximal, characteristic, complemented
8#16837607C211yesmaximal, characteristic, complemented
9#16837545C211yesmaximal, characteristic, complemented
10#16837545C211yesmaximal, characteristic, complemented
11#16837512C211yesmaximal, characteristic, complemented
12#16837474C211yesmaximal, characteristic, complemented
13#16837401C211yesmaximal, characteristic, complemented
14#16837396C211yesmaximal, characteristic, complemented
15C59×#553C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C2×#11745685C2211yescharacteristic
18C2×#11745670C2211yescharacteristic
19C2×#11745670C2211yescharacteristic
20C2×#11745669C2211yescharacteristic
21C2×#11745664C2211yescharacteristic
22C22×C59⋊C8C2211yescharacteristic
23#14273727C2211yescharacteristic
24#14273709—21no—
25#14273709—21no—
26#14273706C2211yescharacteristic
27#14273706C2211yescharacteristic
28#14273698—21no—
29C4×D236C2211yescharacteristic
30C4⋊C4×D59—21no—
31#14273660C2211yescharacteristic
32#14273658C2211yescharacteristic
33#14273658C2211yescharacteristic
34C4⋊(C59⋊C8)C2211yescharacteristic
35#14273650C2211yescharacteristic
36#14273650C2211yescharacteristic
37#14273650C2211yescharacteristic
38#14273650C2211yescharacteristic
39#14273650C2211yescharacteristic
40#14273650C2211yescharacteristic
41#14273648C2211yescharacteristic
42#14273647C2211yescharacteristic
43#14273647C2211yescharacteristic
44#14273647C2211yescharacteristic
45C22⋊(C59⋊C8)C2211yescharacteristic
46C22⋊(C59⋊C8)C2211yescharacteristic
47#14273638C2211yescharacteristic
48#126×C59—21no—
49#125×C59C2211yescharacteristic
50#123×C59—21no—
51#121×C59—21no—
52#121×C59C2211yescharacteristic
53#121×C59C2211yescharacteristic
54C4×D4×C59—21no—
55C4×D4×C59C2211yescharacteristic
56C4×D4×C59C2211yescharacteristic
57#117×C59C2211yescharacteristic
58C2×C4⋊C4×C59C2211yescharacteristic
59C2×D4×C59—21no—
60C2×D4×C59—21no—
61C2×D4×C59D411yescharacteristic
62C2×D4×C59C2311yescharacteristic
63C22×C4×C59—21no—
64C22×C4×C59—21no—
65C22×C4×C59C2311yescharacteristic
66C22×C4×C59C2311yescharacteristic
67C2×C22⋊D59—21no—
68C2×C22⋊D59—21no—
69#11745685—22no—
70#11745685—22no—
71#11745685—41no—
72#11745685—41no—
73C2×D236C2311yescharacteristic
74C2×C4×D59—21no—
75C2×C4×D59—21no—
76C2×C4×D59—21no—
77C2×Dic118C2311yescharacteristic
78C2×Dic118C2311yescharacteristic
79C4⋊C4×C59—21no—
80C4⋊C4×C59—21no—
81C4⋊C4×C59—21no—
82C4⋊C4×C59D411yescharacteristic
83C4⋊C4×C59C2311yescharacteristic
84C4⋊C4×C59C2311yescharacteristic
85C4⋊C4×C59C2311yescharacteristic
86C22⋊C4×C59—21no—
87C22⋊C4×C59—21no—
88C22⋊C4×C59—21no—
89C22⋊C4×C59—21no—
90C22⋊C4×C59D411yescharacteristic
91C22⋊C4×C59D411yescharacteristic
92C42×C59—21no—
93C42×C59C2311yescharacteristic
94C22⋊Dic59—21no—
95C22⋊Dic59—21no—
96#11745670—41no—
97#11745670—41no—
98#11745669—22no—
99(C2×D59)⋊C4—21no—
100C4⋊Dic59—21no—
101C4⋊Dic59—21no—
102C4⋊Dic59C2311yescharacteristic
103Dic59⋊C4—21no—
104Dic59⋊C4—21no—
105#11745664—41no—
106C2×C59⋊C8—41no—
107C2×C59⋊C8C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110C2×C59⋊C8C2311yescharacteristic
111C23×C59—21no—
112C23×C59C2×D411yescharacteristic
113C23×C59C2×D411yescharacteristic
114C22×D59—21no—
115D4×C59—21no—
116D4×C59—21no—
117D4×C59—41no—
118D4×C59—42no—
119D4×C59—81no—
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—21no—
127C2×C4×C59—81no—
128C2×C4×C59—81no—
129C2×C4×C59C2×D411yescharacteristic
130C2×C4×C59C2×D411yescharacteristic
131C2×C4×C59C2×D411yescharacteristic
132C2×C4×C59C2×D411yescharacteristic
133C2×C4×C59C2411yescharacteristic
134C22⋊D59—42no—
135C22⋊D59—42no—
136C2×Dic59—21no—
137C2×Dic59—21no—
138C2×Dic59—21no—
139D236—21no—
140D236#4112yes—
141C4×D59—42no—
142C4×D59—42no—
143C4×D59—42no—
144Dic118—21no—
145Dic118—21no—
146Dic118—21no—
147Dic118—21no—
148C59⋊C8—21no—
149C59⋊C8—21no—
150C59⋊C8—21no—
151C59⋊C8—21no—
152C22×C59—21no—
153C22×C59—21no—
154C22×C59—21no—
155C22×C59—21no—
156C22×C59—21no—
157C22×C59—21no—
158C22×C59—41no—
159C22×C59—41no—
160C22×C59—41no—
161C22×C59C22×D411yescharacteristic
162C2×D59—22no—
163C2×D59—41no—
164C2×D59—41no—
165C4×C59—21no—
166C4×C59—21no—
167C4×C59—21no—
168C4×C59—21no—
169C4×C59—41no—
170C4×C59—41no—
171C4×C59—41no—
172C4×C59C2×#4111yescharacteristic
173C4×C59H(5,𝔽2)11yescharacteristic
174Dic59—41no—
175Dic59—41no—
176Dic59—41no—
177#3307—591nomaximal, Sylow
178C2×C59—41no—
179C2×C59—41no—
180C2×C59—81no—
181C2×C59#54611yescharacteristic
182C2×C59#57511yescharacteristic
183C2×C59#57711yescharacteristic
184D59—42no—
185#553D5911yescharacteristic, complemented
186#547—591no—
187#491—591no—
188#485—591no—
189#483—591no—
190#478—591no—
191#468—591no—
192#465—591no—
193#461—591no—
194#449—591no—
195#449—591no—
196#442—591no—
197#435—591no—
198#417—591no—
199#416—591no—
200C59#330711yescharacteristic, complemented, Sylow
201C2×#41—591no—
202C2×#41—591no—
203C2×SD16—591no—
204C2×SD16—591no—
205C2×D8—591no—
206C2×M16—591no—
207C22×C8—591no—
208C4⋊Q8—591no—
209#126—21no—
210#125C2×D5911yescharacteristic
211#123—21no—
212#123—1181no—
213#123—1181no—
214C22⋊Q8—591no—
215C22⋊Q8—591no—
216#121—21no—
217#121—1181no—
218#121C2×D5911yescharacteristic
219#121C2×D5911yescharacteristic
220C4×D4—21no—
221C4×D4—591no—
222C4×D4C2×D5911yescharacteristic
223C4×D4C2×D5911yescharacteristic
224#117C2×D5911yescharacteristic
225C2×C4⋊C4—1181no—
226C2×C4⋊C4C2×D5911yescharacteristic
227#107—591no—
228#106—591no—
229#106—591no—
230C4⋊C8—591no—
231#103—591no—
232#103—591no—
233#103—591no—
234#103—591no—
235#103—591no—
236#103—591no—
237#102—591no—
238#102—591no—
239#102—591no—
240#102—591no—
241C22⋊C8—591no—
242C22⋊C8—591no—
243#97—591no—
244#41—1182no—
245#41—1182no—
246#41—2361no—
247#41—2361no—
248C2×Q8—591no—
249C2×Q8—591no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—591no—
253C2×D4—1181no—
254C2×D4—1181no—
255C2×D4C22⋊D5911yescharacteristic
256C2×D4C22×D5911yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—1181no—
260C22×C4—1181no—
261C22×C4—1181no—
262C22×C4C22×D5911yescharacteristic
263C22×C4C22×D5911yescharacteristic
264SD16—2361no—
265SD16—2361no—
266D8—1182no—
267M16—2361no—
268C2×C8—591no—
269C2×C8—591no—
270C2×C8—591no—
271C2×C8—591no—
272C2×C8—2361no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—591no—
277C4⋊C4—1181no—
278C4⋊C4—1181no—
279C4⋊C4—1181no—
280C4⋊C4—1181no—
281C4⋊C4C22⋊D5911yescharacteristic
282C4⋊C4C22×D5911yescharacteristic
283C4⋊C4C22×D5911yescharacteristic
284C4⋊C4C22×D5911yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—1181no—
290C22⋊C4—1181no—
291C22⋊C4—1181no—
292C22⋊C4C22⋊D5911yescharacteristic
293C22⋊C4C22⋊D5911yescharacteristic
294C42—21no—
295C42C22×D5911yescharacteristic
296C23—21no—
297C23—1181no—
298C23C2×C22⋊D5911yescharacteristic
299C23C2×C22⋊D5911yescharacteristic
300Q8—1181no—
301Q8—1181no—
302Q8—1181no—
303Q8—1181no—
304D4—21no—
305D4—21no—
306D4—41no—
307D4—42no—
308D4—81no—
309D4—592no—
310D4—1181no—
311D4—2362no—
312D4—2362no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—1181no—
323C2×C4—1181no—
324C2×C4—1181no—
325C2×C4—2362no—
326C2×C4—2362no—
327C2×C4—2362no—
328C2×C4C2×C22⋊D5911yescharacteristic
329C2×C4C2×C22⋊D5911yescharacteristic
330C2×C4C2×C22⋊D5911yescharacteristic
331C2×C4C2×C22⋊D5911yescharacteristic
332C2×C4C23×D5911yescharacteristic
333C8—1181no—
334C8—1181no—
335C8—1181no—
336C8—1181no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—1182no—
347C22—2361no—
348C22—2361no—
349C22C22×C22⋊D5911yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—2361no—
358C4—2361no—
359C4—2361no—
360C4#41×D5911yescharacteristic
361C4#1427377311yescharacteristic
362C2—41no—
363C2—41no—
364C2—81no—
365C2—2362no—
366C2#1683804011yescharacteristic
367C2#1683820011yescharacteristic
368C2#1683821311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#553C2
socleC22×C59C22×D4
hypercenter#553D59
hypocenterC59#3307
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #16838057C2semidirect
2. #16837772C2semidirect
3. #16837743C2semidirect
4. #16837732C2semidirect
5. #16837699C2semidirect
6. #16837646C2semidirect
7. #16837629C2semidirect
8. #16837607C2semidirect
9. #16837545C2semidirect
10. #16837545C2semidirect
11. #16837512C2semidirect
12. #16837474C2semidirect
13. #16837401C2semidirect
14. #16837396C2semidirect
15. C59×#553C2semidirect
185. #553D59semidirect
200. C59#3307semidirect