Finite Group Databasebeta

← #21436282

Subgroups — #21436282

Order 7552.

392 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#16838117C211yesmaximal, characteristic, complemented
2#16837761C211yesmaximal, characteristic, complemented
3#16837740C211yesmaximal, characteristic, complemented
4#16837723C211yesmaximal, characteristic, complemented
5#16837687C211yesmaximal, characteristic, complemented
6#16837653C211yesmaximal, characteristic, complemented
7#16837633C211yesmaximal, characteristic, complemented
8#16837614C211yesmaximal, characteristic, complemented
9#16837547C211yesmaximal, characteristic, complemented
10#16837541C211yesmaximal, characteristic, complemented
11#16837500C211yesmaximal, characteristic, complemented
12#16837474C211yesmaximal, characteristic, complemented
13#16837411C211yesmaximal, characteristic, complemented
14#16837398C211yesmaximal, characteristic, complemented
15C59×#548C211yesmaximal, characteristic, complemented
16C2×#11745671C2211yescharacteristic
17C2×#11745671C2211yescharacteristic
18C2×#11745669C2211yescharacteristic
19C2×#11745664C2211yescharacteristic
20C22×C59⋊C8C2211yescharacteristic
21#14273727C2211yescharacteristic
22#14273713—21no—
23#14273713—21no—
24#14273701C2211yescharacteristic
25#14273701C2211yescharacteristic
26#14273698—21no—
27C4×D236C2211yescharacteristic
28#14273686C2211yescharacteristic
29#14273686C2211yescharacteristic
30#14273685—21no—
31#14273660C2211yescharacteristic
32#14273658C2211yescharacteristic
33#14273658C2211yescharacteristic
34C4⋊(C59⋊C8)C2211yescharacteristic
35#14273651C2211yescharacteristic
36#14273651C2211yescharacteristic
37#14273651C2211yescharacteristic
38#14273651C2211yescharacteristic
39#14273651C2211yescharacteristic
40#14273651C2211yescharacteristic
41#14273648C2211yescharacteristic
42#14273648C2211yescharacteristic
43#14273648C2211yescharacteristic
44#14273647C2211yescharacteristic
45C22⋊(C59⋊C8)C2211yescharacteristic
46C22⋊(C59⋊C8)C2211yescharacteristic
47#14273638C2211yescharacteristic
48C2×#41×C59C2211yescharacteristic
49C22×Q8×C59C2211yescharacteristic
50#124×C59—21no—
51#124×C59C2211yescharacteristic
52C22⋊Q8×C59—21no—
53C22⋊Q8×C59C2211yescharacteristic
54#121×C59—21no—
55#121×C59C2211yescharacteristic
56C4×Q8×C59C2211yescharacteristic
57C4×D4×C59—21no—
58C4×D4×C59C2211yescharacteristic
59#41×C59—22no—
60#41×C59—41no—
61C2×Q8×C59—21no—
62C2×Q8×C59—22no—
63C2×Q8×C59—41no—
64C2×Q8×C59C2311yescharacteristic
65C2×Q8×C59C2311yescharacteristic
66C2×D4×C59—21no—
67C2×D4×C59—21no—
68C2×D4×C59D411yescharacteristic
69C2×D4×C59C2311yescharacteristic
70C22×C4×C59—21no—
71C22×C4×C59—21no—
72C22×C4×C59C2311yescharacteristic
73C22×C4×C59C2311yescharacteristic
74C2×C22⋊D59—21no—
75C2×C22⋊D59—21no—
76C2×D236C2311yescharacteristic
77C2×C4×D59—21no—
78C2×Dic118—21no—
79C4⋊C4×C59—21no—
80C4⋊C4×C59—21no—
81C4⋊C4×C59D411yescharacteristic
82C4⋊C4×C59C2311yescharacteristic
83C22⋊C4×C59—21no—
84C22⋊C4×C59—21no—
85C22⋊C4×C59—21no—
86C22⋊C4×C59—21no—
87C22⋊C4×C59D411yescharacteristic
88C22⋊C4×C59D411yescharacteristic
89C42×C59—21no—
90C42×C59C2311yescharacteristic
91C22⋊Dic59—21no—
92C22⋊Dic59—21no—
93#11745671—22no—
94#11745671—41no—
95#11745669—41no—
96(C2×D59)⋊C4—21no—
97(C2×D59)⋊C4—21no—
98(C2×D59)⋊C4—21no—
99C4⋊Dic59—21no—
100C4⋊Dic59C2311yescharacteristic
101C4⋊Dic59C2311yescharacteristic
102C4⋊Dic59C2311yescharacteristic
103C4×Dic59—21no—
104C4×Dic59—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—
115Q8×C59—21no—
116Q8×C59—21no—
117Q8×C59—21no—
118Q8×C59—42no—
119Q8×C59#4112yes—
120D4×C59—21no—
121D4×C59—21no—
122D4×C59—41no—
123D4×C59—42no—
124D4×C59—42no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C2×C4×C59—21no—
132C2×C4×C59—42no—
133C2×C4×C59—42no—
134C2×C4×C59C2×D411yescharacteristic
135C2×C4×C59C2×D411yescharacteristic
136C2×C4×C59C2×D411yescharacteristic
137C2×C4×C59C2×D411yescharacteristic
138C2×C4×C59C2411yescharacteristic
139C22⋊D59—81no—
140C22⋊D59—81no—
141C2×Dic59—21no—
142C2×Dic59—21no—
143C2×Dic59—21no—
144D236—21no—
145D236—21no—
146C4×D59—42no—
147Dic118—81no—
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—41no—
163C2×D59—41no—
164C2×D59—41no—
165C4×C59—21no—
166C4×C59—21no—
167C4×C59—22no—
168C4×C59—21no—
169C4×C59—21no—
170C4×C59—41no—
171C4×C59—41no—
172C4×C59C2×#4111yescharacteristic
173C4×C59H(5,𝔽2)11yescharacteristic
174Dic59—41no—
175Dic59—41no—
176Dic59—41no—
177#3321—591nomaximal, Sylow
178C2×C59—41no—
179C2×C59—41no—
180C2×C59—81no—
181C2×C59#54611yescharacteristic
182C2×C59#57511yescharacteristic
183C2×C59#57711yescharacteristic
184D59—81no—
185#555—591no—
186#548D5911yescharacteristic, complemented
187#489—591no—
188#485—591no—
189#482—591no—
190#475—591no—
191#469—591no—
192#465—591no—
193#463—591no—
194#449—591no—
195#448—591no—
196#440—591no—
197#435—591no—
198#419—591no—
199#416—591no—
200C59#332111yescharacteristic, complemented, Sylow
201C2×#41C2×D5911yescharacteristic
202C22×Q8C2×D5911yescharacteristic
203C2×SD16—591no—
204C2×SD16—591no—
205C2×D8—591no—
206C2×M16—591no—
207C22×C8—591no—
208C4⋊Q8—591no—
209#124—21no—
210#124—1181no—
211#124—1181no—
212#124C2×D5911yescharacteristic
213C22⋊Q8—21no—
214C22⋊Q8C2×D5911yescharacteristic
215#121—21no—
216#121—591no—
217#121—591no—
218#121—1181no—
219#121C2×D5911yescharacteristic
220C4×Q8C2×D5911yescharacteristic
221C4×D4—21no—
222C4×D4—591no—
223C4×D4C2×D5911yescharacteristic
224#117—591no—
225#117—591no—
226#117—1181no—
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—22no—
245#41—41no—
246C2×Q8—21no—
247C2×Q8—22no—
248C2×Q8—41no—
249C2×Q8—1181no—
250C2×Q8C22×D5911yescharacteristic
251C2×Q8C22×D5911yescharacteristic
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—591no—
255C2×D4—1181no—
256C2×D4—1181no—
257C2×D4C22⋊D5911yescharacteristic
258C2×D4C22×D5911yescharacteristic
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—1181no—
262C22×C4C22×D5911yescharacteristic
263C22×C4C22×D5911yescharacteristic
264SD16—1182no—
265SD16—2361no—
266D8—2361no—
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—591no—
276C4⋊C4—591no—
277C4⋊C4—591no—
278C4⋊C4—1181no—
279C4⋊C4C22⋊D5911yescharacteristic
280C4⋊C4C22×D5911yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—1181no—
286C22⋊C4—1181no—
287C22⋊C4—1181no—
288C22⋊C4—1181no—
289C22⋊C4—1181no—
290C22⋊C4C22⋊D5911yescharacteristic
291C22⋊C4C22⋊D5911yescharacteristic
292C42—21no—
293C42—1181no—
294C42—1181no—
295C42C22×D5911yescharacteristic
296C23—21no—
297C23—1181no—
298C23C2×C22⋊D5911yescharacteristic
299C23C2×C22⋊D5911yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—42no—
304Q8—4721no—
305Q8#1174568712yes—
306D4—21no—
307D4—21no—
308D4—41no—
309D4—42no—
310D4—42no—
311D4—1181no—
312D4—1181no—
313D4—4721no—
314D4—4721no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—1181no—
325C2×C4—1181no—
326C2×C4—1181no—
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—2361no—
347C22—2361no—
348C22—2361no—
349C22C22×C22⋊D5911yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—22no—
355C4—41no—
356C4—41no—
357C4—2361no—
358C4—2361no—
359C4—2361no—
360C4C2×#1174568711yescharacteristic
361C4#1427377211yescharacteristic
362C2—41no—
363C2—41no—
364C2—81no—
365C2—4721no—
366C2#1683804611yescharacteristic
367C2#1683820011yescharacteristic
368C2#1683821011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#548C2
socleC22×C59C22×D4
hypercenter#548D59
hypocenterC59#3321
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #16838117C2semidirect
2. #16837761C2semidirect
3. #16837740C2semidirect
4. #16837723C2semidirect
5. #16837687C2semidirect
6. #16837653C2semidirect
7. #16837633C2semidirect
8. #16837614C2semidirect
9. #16837547C2semidirect
10. #16837541C2semidirect
11. #16837500C2semidirect
12. #16837474C2semidirect
13. #16837411C2semidirect
14. #16837398C2semidirect
15. C59×#548C2semidirect
186. #548D59semidirect
200. C59#3321semidirect