Finite Group Databasebeta

← #21435954

Subgroups — #21435954

Order 7552.

420 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×C22⋊D59C211yesmaximal, characteristic, complemented
2#16838052C211yesmaximal, characteristic
3#16837751C211yesmaximal, characteristic, complemented
4#16837733C211yesmaximal, characteristic, complemented
5#16837731C211yesmaximal, characteristic, complemented
6#16837685C211yesmaximal, characteristic, complemented
7#16837629C211yesmaximal, characteristic, complemented
8#16837628C211yesmaximal, characteristic, complemented
9#16837605C211yesmaximal, characteristic, complemented
10#16837539C211yesmaximal, characteristic, complemented
11SD16×Dic59C211yesmaximal, characteristic, complemented
12(C22⋊D59)⋊C8C211yesmaximal, characteristic, complemented
13C2×#14273651C211yesmaximal, characteristic, complemented
14#103×D59C211yesmaximal, characteristic, complemented
15C59×#448C211yesmaximal, characteristic, complemented
16C2×#11745687—21no—
17C2×Q8×D59C2211yescharacteristic
18C2×#11745670C2211yescharacteristic
19C22×C59⋊C8C2211yescharacteristic
20C2×C8×D59C2211yescharacteristic
21#14273726C2211yescharacteristic
22#14273725—21no—
23#14273725C2211yescharacteristic
24#14273709—21no—
25#14273708—21no—
26#14273706—21no—
27#14273706C2211yescharacteristic
28#14273704—21no—
29#14273703—21no—
30#14273703C2211yescharacteristic
31#14273698C2211yescharacteristic
32Q8×Dic59C2211yescharacteristic
33D4×Dic59C2211yescharacteristic
34C4×C22⋊D59—21no—
35C4×C22⋊D59C2211yescharacteristic
36C2×C4⋊Dic59C2211yescharacteristic
37C4⋊C4×D59C2211yescharacteristic
38#14273659C2211yescharacteristic
39#14273659C2211yescharacteristic
40#14273658C2211yescharacteristic
41Dic59⋊C8C2211yescharacteristic
42#14273652C2211yescharacteristic
43#14273652C2211yescharacteristic
44#14273651C2211yescharacteristic
45#14273651C2211yescharacteristic
46#14273651C2211yescharacteristic
47#14273651C2211yescharacteristic
48#14273650C2211yescharacteristic
49#14273648C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51C8×Dic59C2211yescharacteristic
52C22×Q8×C59C2211yescharacteristic
53C2×SD16×C59C2211yescharacteristic
54C2×SD16×C59C2211yescharacteristic
55#121×C59C2211yescharacteristic
56#103×C59C2211yescharacteristic
57#103×C59C2211yescharacteristic
58C22⋊C8×C59C2211yescharacteristic
59C2×Q8×C59—21no—
60C2×Q8×C59—22no—
61C2×Q8×C59—41no—
62C2×Q8×C59C2311yescharacteristic
63C2×Q8×C59C2311yescharacteristic
64C2×D4×C59—21no—
65C2×D4×C59C2311yescharacteristic
66C22×C4×C59—21no—
67C22×C4×C59C2311yescharacteristic
68C2×C22⋊D59—21no—
69C2×C22⋊D59D411yescharacteristic
70C22×Dic59—21no—
71C22×Dic59—21no—
72Q8×D59—22no—
73Q8×D59—41no—
74#11745687—44no—
75C2×C4×D59—21no—
76C2×C4×D59—21no—
77C2×C4×D59C2311yescharacteristic
78C2×Dic118—21no—
79C2×Dic118—21no—
80C2×Dic118C2311yescharacteristic
81SD16×C59—22no—
82SD16×C59—41no—
83C2×C8×C59C2311yescharacteristic
84C2×C8×C59C2311yescharacteristic
85C4⋊C4×C59C2311yescharacteristic
86C22⋊C4×C59—21no—
87C22⋊Dic59—21no—
88C22⋊Dic59—21no—
89C22⋊Dic59—21no—
90C22⋊Dic59D411yescharacteristic
91#11745670—41no—
92(C2×D59)⋊C4—21no—
93(C2×D59)⋊C4D411yescharacteristic
94C4⋊Dic59—21no—
95C4⋊Dic59—21no—
96C4⋊Dic59C2311yescharacteristic
97C4⋊Dic59C2311yescharacteristic
98C4⋊Dic59C2311yescharacteristic
99Dic59⋊C4—21no—
100Dic59⋊C4—21no—
101Dic59⋊C4—21no—
102Dic59⋊C4—21no—
103Dic59⋊C4—21no—
104Dic59⋊C4—21no—
105Dic59⋊C4D411yescharacteristic
106C4×Dic59—21no—
107C4×Dic59C2311yescharacteristic
108C2×C59⋊C8—41no—
109C2×C59⋊C8C2311yescharacteristic
110C2×C59⋊C8C2311yescharacteristic
111C8×D59—41no—
112C23×C59—21no—
113C23×C59C2×D411yescharacteristic
114C22×D59C2×D411yescharacteristic
115Q8×C59—21no—
116Q8×C59—21no—
117Q8×C59—21no—
118Q8×C59—42no—
119Q8×C59#4112yescomplemented
120D4×C59—21no—
121D4×C59—21no—
122D4×C59—42no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—42no—
129C2×C4×C59C2×D411yescharacteristic
130C2×C4×C59C2411yescharacteristic
131C22⋊D59—42no—
132C22⋊D59SD1614yescomplemented
133C2×Dic59—21no—
134C2×Dic59—21no—
135C2×Dic59—21no—
136C2×Dic59—21no—
137C2×Dic59—42no—
138C2×Dic59—42no—
139C2×Dic59C2×D411yescharacteristic
140C2×Dic59C2×D411yescharacteristic
141C2×Dic59C2×D411yescharacteristic
142C4×D59—21no—
143C4×D59—21no—
144C4×D59—42no—
145C4×D59—42no—
146Dic118—21no—
147Dic118—21no—
148Dic118—42no—
149Dic118—42no—
150C8×C59—21no—
151C8×C59—21no—
152C59⋊C8—21no—
153C59⋊C8—21no—
154C22×C59—21no—
155C22×C59—21no—
156C22×C59—41no—
157C22×C59—41no—
158C22×C59—41no—
159C22×C59C2×SD1612yes—
160C22×C59C22×D411yescharacteristic
161C2×D59—21no—
162C2×D59—21no—
163C2×D59C2×SD1612yes—
164C4×C59—22no—
165C4×C59—21no—
166C4×C59—41no—
167C4×C59—41no—
168C4×C59C2×#4111yescharacteristic
169C4×C59H(5,𝔽2)11yescharacteristic
170Dic59—21no—
171Dic59—21no—
172Dic59—41no—
173Dic59—41no—
174Dic59—41no—
175Dic59—41no—
176Dic59C2×SD1612yes—
177#3298—591nomaximal, Sylow
178C2×C59—22no—
179C2×C59—81no—
180C2×C59#54611yescharacteristic
181C2×C59C22×SD1611yescharacteristic
182C2×C59#57811yescharacteristic
183D59—22no—
184D4×Q8—591no—
185#547—591no—
186#487—591no—
187#483—591no—
188#483—591no—
189#475—591no—
190#465—591no—
191#465—591no—
192#461—591no—
193#448—591no—
194#448D5911yescharacteristic, complemented
195C4×SD16—591no—
196C8×D4—591no—
197C2×#103—591no—
198C2×#103—591no—
199C59#329811yescharacteristic, complemented, Sylow
200C2×#41—1181no—
201C22×Q8—591no—
202C22×Q8C2×D5911yescharacteristic
203C2×SD16—591no—
204C2×SD16C2×D5911yescharacteristic
205C2×SD16C2×D5911yescharacteristic
206C22×C8—591no—
207C22×C8—591no—
208C4⋊Q8—591no—
209C4⋊Q8—591no—
210C4⋊Q8—1181no—
211#123—1181no—
212#123—1181no—
213C22⋊Q8—591no—
214C22⋊Q8—591no—
215C22⋊Q8—1181no—
216C22⋊Q8—1181no—
217C22⋊Q8—1181no—
218#121—591no—
219#121C2×D5911yescharacteristic
220C4×Q8—591no—
221C4×D4—591no—
222C4×D4—591no—
223C4×D4—1181no—
224C2×C4⋊C4—591no—
225C2×C4⋊C4—591no—
226#106—591no—
227#106—591no—
228#106—591no—
229C4⋊C8—591no—
230#103—591no—
231#103—591no—
232#103—591no—
233#103—591no—
234#103—591no—
235#103—591no—
236#103—591no—
237#103C2×D5911yescharacteristic
238#103C2×D5911yescharacteristic
239#102—591no—
240C22⋊C8—591no—
241C22⋊C8C2×D5911yescharacteristic
242C4×C8—591no—
243#41—2364no—
244C2×Q8—21no—
245C2×Q8—22no—
246C2×Q8—41no—
247C2×Q8—591no—
248C2×Q8—1181no—
249C2×Q8—1181no—
250C2×Q8—1182no—
251C2×Q8—2361no—
252C2×Q8C22×D5911yescharacteristic
253C2×Q8C22×D5911yescharacteristic
254C2×D4—21no—
255C2×D4—591no—
256C2×D4—1181no—
257C2×D4C22×D5911yescharacteristic
258C22×C4—21no—
259C22×C4—591no—
260C22×C4—1181no—
261C22×C4—1181no—
262C22×C4—1181no—
263C22×C4—1181no—
264C22×C4C22×D5911yescharacteristic
265SD16—22no—
266SD16—41no—
267SD16—2361no—
268C2×C8—591no—
269C2×C8—591no—
270C2×C8—2361no—
271C2×C8—2361no—
272C2×C8C22×D5911yescharacteristic
273C2×C8C22×D5911yescharacteristic
274C4⋊C4—591no—
275C4⋊C4—591no—
276C4⋊C4—591no—
277C4⋊C4—591no—
278C4⋊C4—1181no—
279C4⋊C4—1181no—
280C4⋊C4—1181no—
281C4⋊C4—1181no—
282C4⋊C4—1181no—
283C4⋊C4—1181no—
284C4⋊C4—1181no—
285C4⋊C4—1181no—
286C4⋊C4C22×D5911yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—591no—
289C22⋊C4—591no—
290C22⋊C4—1181no—
291C22⋊C4—1181no—
292C22⋊C4—1181no—
293C22⋊C4—1181no—
294C42—591no—
295C42—1181no—
296C23—21no—
297C23—591no—
298C23D4×D5911yescharacteristic
299Q8—21no—
300Q8—21no—
301Q8—21no—
302Q8—42no—
303Q8—1181no—
304Q8—1181no—
305Q8—2362no—
306Q8—2362no—
307Q8#1174568712yescomplemented
308D4—21no—
309D4—21no—
310D4—42no—
311D4—594no—
312D4—2362no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—42no—
319C2×C4—591no—
320C2×C4—591no—
321C2×C4—591no—
322C2×C4—1181no—
323C2×C4—1181no—
324C2×C4—1181no—
325C2×C4—1181no—
326C2×C4—1181no—
327C2×C4—1181no—
328C2×C4—2362no—
329C2×C4—2362no—
330C2×C4—2362no—
331C2×C4—2362no—
332C2×C4D4×D5911yescharacteristic
333C2×C4C23×D5911yescharacteristic
334C8—21no—
335C8—21no—
336C8—1181no—
337C8—1181no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—592no—
344C22—1181no—
345C22—1181no—
346C22SD16×D5912yes—
347C22C2×D4×D5911yescharacteristic
348C4—21no—
349C4—22no—
350C4—41no—
351C4—41no—
352C4—592no—
353C4—1181no—
354C4—1181no—
355C4—2361no—
356C4—2361no—
357C4—2361no—
358C4—2361no—
359C4C2×#1174568711yescharacteristic
360C4#1427377211yescharacteristic
361C2—22no—
362C2—81no—
363C2—1182no—
364C2#1683803911yescharacteristic
365C2C2×SD16×D5911yescharacteristic
366C2#1683821811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#448C2
socleC22×C59C22×D4
hypercenter#448D59
hypocenterC59#3298
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. Q8×C22⋊D59C2semidirect
3. #16837751C2semidirect
4. #16837733C2semidirect
5. #16837731C2semidirect
6. #16837685C2semidirect
7. #16837629C2semidirect
8. #16837628C2semidirect
9. #16837605C2semidirect
10. #16837539C2semidirect
11. SD16×Dic59C2semidirect
12. (C22⋊D59)⋊C8C2semidirect
13. C2×#14273651C2semidirect
14. #103×D59C2semidirect
15. C59×#448C2semidirect
119. Q8×C59#41semidirect
132. C22⋊D59SD16semidirect
194. #448D59semidirect
199. C59#3298semidirect
307. Q8#11745687semidirect