Finite Group Databasebeta

← #21436568

Subgroups — #21436568

Order 7552.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838098C211yesmaximal, characteristic, complemented
2#16838056C211yesmaximal, characteristic, complemented
3#16837811C211yesmaximal, characteristic, complemented
4#16837727C211yesmaximal, characteristic, complemented
5#16837721C211yesmaximal, characteristic, complemented
6#16837721C211yesmaximal, characteristic, complemented
7#16837716C211yesmaximal, characteristic, complemented
8#16837703C211yesmaximal, characteristic, complemented
9#16837693C211yesmaximal, characteristic, complemented
10#16837655C211yesmaximal, characteristic, complemented
11#16837638C211yesmaximal, characteristic, complemented
12#16837515C211yesmaximal, characteristic, complemented
13#16837444C211yesmaximal, characteristic, complemented
14C2×#14273659C211yesmaximal, characteristic, complemented
15C59×#435C211yesmaximal, characteristic, complemented
16C2×#11745687—21no—
17C2×D472C2211yescharacteristic
18#14273727C2211yescharacteristic
19#14273722—21no—
20#14273719C2211yescharacteristic
21#14273711—21no—
22#14273711—21no—
23#14273709—21no—
24#14273707—21no—
25#14273701C2211yescharacteristic
26#14273701C2211yescharacteristic
27#14273701C2211yescharacteristic
28#14273701C2211yescharacteristic
29#14273699—21no—
30C4×D236C2211yescharacteristic
31C4×D236C2211yescharacteristic
32(C22⋊D59)⋊C4—21no—
33#14273686C2211yescharacteristic
34C2×C4⋊Dic59C2211yescharacteristic
35C2×C4⋊Dic59C2211yescharacteristic
36C2×C4⋊Dic59C2211yescharacteristic
37#14273661C2211yescharacteristic
38#14273661C2211yescharacteristic
39#14273661C2211yescharacteristic
40#14273659C2211yescharacteristic
41#14273659C2211yescharacteristic
42#14273659C2211yescharacteristic
43#14273659C2211yescharacteristic
44#14273659C2211yescharacteristic
45#14273659C2211yescharacteristic
46#14273649C2211yescharacteristic
47#14273649C2211yescharacteristic
48#14273649C2211yescharacteristic
49#14273649C2211yescharacteristic
50#14273649C2211yescharacteristic
51#14273649C2211yescharacteristic
52C2×M16×C59C2211yescharacteristic
53C22×C8×C59C2211yescharacteristic
54C4×D4×C59C2211yescharacteristic
55C4⋊C8×C59C2211yescharacteristic
56C22⋊C8×C59C2211yescharacteristic
57C22⋊C8×C59C2211yescharacteristic
58#97×C59C2211yescharacteristic
59C2×D4×C59D411yescharacteristic
60C22×C4×C59C2311yescharacteristic
61C22×C4×C59C2311yescharacteristic
62C2×C22⋊D59—21no—
63C2×C22⋊D59—21no—
64C2×C22⋊D59—21no—
65C2×C22⋊D59—21no—
66C22×Dic59—21no—
67C22×Dic59—21no—
68C22×Dic59—21no—
69#11745687—44no—
70C2×D236C2311yescharacteristic
71C2×D236C2311yescharacteristic
72C2×C4×D59—21no—
73C2×C4×D59—21no—
74C2×Dic118—21no—
75M16×C59—22no—
76C2×C8×C59—22no—
77C2×C8×C59C2311yescharacteristic
78C2×C8×C59C2311yescharacteristic
79C2×C8×C59C2311yescharacteristic
80C2×C8×C59C2311yescharacteristic
81C4⋊C4×C59D411yescharacteristic
82C22⋊C4×C59D411yescharacteristic
83C22⋊C4×C59D411yescharacteristic
84C42×C59C2311yescharacteristic
85C22⋊Dic59—21no—
86(C2×D59)⋊C4—21no—
87(C2×D59)⋊C4—21no—
88(C2×D59)⋊C4—21no—
89(C2×D59)⋊C4—21no—
90(C2×D59)⋊C4—21no—
91(C2×D59)⋊C4—21no—
92C4⋊Dic59—21no—
93C4⋊Dic59—21no—
94C4⋊Dic59—21no—
95C4⋊Dic59—21no—
96C4⋊Dic59C2311yescharacteristic
97C4⋊Dic59C2311yescharacteristic
98C4⋊Dic59C2311yescharacteristic
99C4⋊Dic59C2311yescharacteristic
100C4⋊Dic59C2311yescharacteristic
101C4⋊Dic59C2311yescharacteristic
102Dic59⋊C4—21no—
103Dic59⋊C4—21no—
104C4×Dic59—21no—
105D472—22no—
106C23×C59C2×D411yescharacteristic
107C23×C59C2×D411yescharacteristic
108C22×D59—21no—
109C22×D59—21no—
110D4×C59—22no—
111C2×C4×C59—21no—
112C2×C4×C59—21no—
113C2×C4×C59—21no—
114C2×C4×C59—21no—
115C2×C4×C59C2×D411yescharacteristic
116C2×C4×C59C2×D411yescharacteristic
117C2×C4×C59C2×D411yescharacteristic
118C2×C4×C59C2×D411yescharacteristic
119C2×C4×C59C2411yescharacteristic
120C22⋊D59—42no—
121C22⋊D59—42no—
122C22⋊D59—42no—
123C22⋊D59—81no—
124C2×Dic59—21no—
125C2×Dic59—21no—
126C2×Dic59—21no—
127C2×Dic59—21no—
128C2×Dic59—21no—
129C2×Dic59—21no—
130C2×Dic59—42no—
131C2×Dic59—42no—
132C2×Dic59—81no—
133D236—21no—
134D236—21no—
135D236—21no—
136D236—21no—
137C4×D59—42no—
138C4×D59—81no—
139Dic118—42no—
140C8×C59—21no—
141C8×C59—21no—
142C8×C59—21no—
143C8×C59#4112yescomplemented
144C22×C59—21no—
145C22×C59—21no—
146C22×C59—21no—
147C22×C59—21no—
148C22×C59—21no—
149C22×C59AGL(1,ℤ/8)12yes—
150C22×C59C22×D411yescharacteristic
151C2×D59—41no—
152C2×D59—41no—
153C2×D59—41no—
154C2×D59—41no—
155C2×D59—41no—
156C2×D59—41no—
157C4×C59—21no—
158C4×C59—21no—
159C4×C59—21no—
160C4×C59—21no—
161C4×C59C2×#4111yescharacteristic
162C4×C592−1+411yescharacteristic
163Dic59—41no—
164Dic59—41no—
165Dic59—41no—
166Dic59—41no—
167Dic59—41no—
168Dic59—41no—
169#3345—591nomaximal, Sylow
170C2×C59—22no—
171C2×C59—41no—
172C2×C59#54711yescharacteristic
173C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
174C2×C59#57711yescharacteristic
175D59—81no—
176D59—81no—
177#553—591no—
178#547—591no—
179#501—591no—
180#482—591no—
181#481—591no—
182#481—591no—
183#480—591no—
184#478—591no—
185#476—591no—
186#469—591no—
187#466—591no—
188#442—591no—
189#435D5911yescharacteristic, complemented
190#428—591no—
191C2×#106—591no—
192C59#334511yescharacteristic, complemented, Sylow
193C2×#41—1181no—
194C2×D8—591no—
195C2×M16C2×D5911yescharacteristic
196C22×C8C2×D5911yescharacteristic
197C4⋊Q8—591no—
198#126—1181no—
199#125—591no—
200#123—1181no—
201#123—1181no—
202#123—1181no—
203C22⋊Q8—1181no—
204#121—591no—
205#121—591no—
206#121—591no—
207#121—591no—
208#121—1181no—
209C4×D4—591no—
210C4×D4—591no—
211C4×D4—1181no—
212C4×D4C2×D5911yescharacteristic
213#117—591no—
214C2×C4⋊C4—591no—
215C2×C4⋊C4—591no—
216C2×C4⋊C4—591no—
217#107—591no—
218#107—591no—
219#107—591no—
220#106—591no—
221#106—591no—
222#106—591no—
223#106—591no—
224#106—591no—
225#106—591no—
226C4⋊C8C2×D5911yescharacteristic
227#102—591no—
228#102—591no—
229#102—591no—
230#102—591no—
231#102—591no—
232#102—591no—
233C22⋊C8C2×D5911yescharacteristic
234C22⋊C8C2×D5911yescharacteristic
235#97C2×D5911yescharacteristic
236#41—2364no—
237C2×Q8—1181no—
238C2×D4—591no—
239C2×D4—591no—
240C2×D4—1181no—
241C2×D4—1181no—
242C2×D4—1181no—
243C2×D4—1181no—
244C2×D4D23611yescharacteristic
245C22×C4—1181no—
246C22×C4—1181no—
247C22×C4—1181no—
248C22×C4—1181no—
249C22×C4—1181no—
250C22×C4C22×D5911yescharacteristic
251C22×C4C22×D5911yescharacteristic
252D8—1182no—
253M16—22no—
254C2×C8—22no—
255C2×C8C22×D5911yescharacteristic
256C2×C8C22×D5911yescharacteristic
257C2×C8C22×D5911yescharacteristic
258C2×C8C22×D5911yescharacteristic
259C4⋊C4—591no—
260C4⋊C4—591no—
261C4⋊C4—591no—
262C4⋊C4—591no—
263C4⋊C4—591no—
264C4⋊C4—591no—
265C4⋊C4—1181no—
266C4⋊C4—1181no—
267C4⋊C4—1181no—
268C4⋊C4—1181no—
269C4⋊C4—1181no—
270C4⋊C4—1181no—
271C4⋊C4D23611yescharacteristic
272C22⋊C4—1181no—
273C22⋊C4—1181no—
274C22⋊C4—1181no—
275C22⋊C4—1181no—
276C22⋊C4—1181no—
277C22⋊C4—1181no—
278C22⋊C4—1181no—
279C22⋊C4D23611yescharacteristic
280C22⋊C4D23611yescharacteristic
281C42—1181no—
282C42C22×D5911yescharacteristic
283C23—1181no—
284C23—1181no—
285C23C2×D23611yescharacteristic
286C23C2×D23611yescharacteristic
287Q8—2362no—
288D4—22no—
289D4—1181no—
290D4—1181no—
291D4—1181no—
292D4—1181no—
293D4—4721no—
294D4—2362no—
295D4—2362no—
296D4—2362no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—1181no—
302C2×C4—1181no—
303C2×C4—1181no—
304C2×C4—1181no—
305C2×C4—1181no—
306C2×C4—1181no—
307C2×C4—4721no—
308C2×C4—4721no—
309C2×C4—2362no—
310C2×C4—2362no—
311C2×C4—2362no—
312C2×C4C2×D23611yescharacteristic
313C2×C4C2×D23611yescharacteristic
314C2×C4C2×D23611yescharacteristic
315C2×C4C2×D23611yescharacteristic
316C2×C4C23×D5911yescharacteristic
317C8—21no—
318C8—21no—
319C8—21no—
320C8#1174568712yescomplemented
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—2361no—
327C22—2361no—
328C22—2361no—
329C22—2361no—
330C22—2361no—
331C22—2361no—
332C22#1427375512yes—
333C22C22×D23611yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—2361no—
339C4—2361no—
340C4—2361no—
341C4—2361no—
342C4—2361no—
343C4—2361no—
344C4C2×#1174568711yescharacteristic
345C4#1427377411yescharacteristic
346C2—22no—
347C2—41no—
348C2—4721no—
349C2—4721no—
350C2#1683805611yescharacteristic
351C2C2×#1427375511yescharacteristic
352C2#1683821411yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#435C2
socleC22×C59C22×D4
hypercenter#435D59
hypocenterC59#3345
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #16838098C2semidirect
2. #16838056C2semidirect
3. #16837811C2semidirect
4. #16837727C2semidirect
5. #16837721C2semidirect
6. #16837721C2semidirect
7. #16837716C2semidirect
8. #16837703C2semidirect
9. #16837693C2semidirect
10. #16837655C2semidirect
11. #16837638C2semidirect
12. #16837515C2semidirect
13. #16837444C2semidirect
14. C2×#14273659C2semidirect
15. C59×#435C2semidirect
143. C8×C59#41semidirect
189. #435D59semidirect
192. C59#3345semidirect
320. C8#11745687semidirect