Finite Group Databasebeta

← #21434790

Subgroups — #21434790

Order 7552.

410 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16837949C211yesmaximal, characteristic, complemented
2#16837939C211yesmaximal, characteristic, complemented
3#16837810C211yesmaximal, characteristic, complemented
4#16837788C211yesmaximal, characteristic, complemented
5#16837765C211yesmaximal, characteristic, complemented
6#16837763C211yesmaximal, characteristic, complemented
7#16837639C211yesmaximal, characteristic, complemented
8#16837637C211yesmaximal, characteristic, complemented
9#16837634C211yesmaximal, characteristic, complemented
10#16837628C211yesmaximal, characteristic, complemented
11#16837515C211yesmaximal, characteristic, complemented
12#16837512C211yesmaximal, characteristic, complemented
13#16837500C211yesmaximal, characteristic, complemented
14#97×D59C211yesmaximal, characteristic, complemented
15C59×#440C211yesmaximal, characteristic, complemented
16C2×#11745685—21no—
17C2×#11745671C2211yescharacteristic
18C2×D472C2211yescharacteristic
19C2×#11745669C2211yescharacteristic
20C2×C8×D59C2211yescharacteristic
21C2×C8×D59C2211yescharacteristic
22#14273726C2211yescharacteristic
23#14273723C2211yescharacteristic
24#14273722—21no—
25#14273718C2211yescharacteristic
26#14273716C2211yescharacteristic
27#14273713—21no—
28#14273712—21no—
29#14273703C2211yescharacteristic
30#14273702C2211yescharacteristic
31#14273702C2211yescharacteristic
32#14273700—21no—
33#14273698C2211yescharacteristic
34C4×D236—21no—
35C4×D236C2211yescharacteristic
36C4×D236C2211yescharacteristic
37C4×C22⋊D59—21no—
38#14273684—21no—
39C42×D59C2211yescharacteristic
40#14273660C2211yescharacteristic
41#14273659C2211yescharacteristic
42#14273658C2211yescharacteristic
43#14273651C2211yescharacteristic
44#14273649C2211yescharacteristic
45#14273649C2211yescharacteristic
46#14273648C2211yescharacteristic
47#14273647C2211yescharacteristic
48#14273647C2211yescharacteristic
49#14273638C2211yescharacteristic
50#14273637C2211yescharacteristic
51#14273637C2211yescharacteristic
52C2×SD16×C59C2211yescharacteristic
53C4×Q8×C59C2211yescharacteristic
54C4×D4×C59C2211yescharacteristic
55#107×C59C2211yescharacteristic
56#103×C59C2211yescharacteristic
57#102×C59C2211yescharacteristic
58#97×C59C2211yescharacteristic
59C2×Q8×C59C2311yescharacteristic
60C2×D4×C59C2311yescharacteristic
61C22×C4×C59—21no—
62C2×C22⋊D59—21no—
63C2×C22⋊D59—21no—
64C2×C22⋊D59—21no—
65#11745685—44no—
66C2×D236—21no—
67C2×D236—21no—
68C2×D236C2311yescharacteristic
69C2×D236C2311yescharacteristic
70C2×C4×D59—21no—
71C2×C4×D59—21no—
72C2×C4×D59D411yescharacteristic
73C2×C4×D59D411yescharacteristic
74C2×C4×D59C2311yescharacteristic
75C2×Dic118—21no—
76SD16×C59—22no—
77C2×C8×C59C2311yescharacteristic
78C2×C8×C59C2311yescharacteristic
79C4⋊C4×C59—21no—
80C4⋊C4×C59C2311yescharacteristic
81C4⋊C4×C59C2311yescharacteristic
82C22⋊C4×C59—21no—
83C42×C59—21no—
84C42×C59C2311yescharacteristic
85C22⋊Dic59—21no—
86#11745671—22no—
87#11745669—22no—
88(C2×D59)⋊C4—21no—
89(C2×D59)⋊C4—21no—
90(C2×D59)⋊C4—21no—
91(C2×D59)⋊C4—21no—
92(C2×D59)⋊C4—21no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4—21no—
95C4⋊Dic59—21no—
96C4⋊Dic59C2311yescharacteristic
97C4⋊Dic59C2311yescharacteristic
98Dic59⋊C4—21no—
99Dic59⋊C4—21no—
100Dic59⋊C4—21no—
101C4×Dic59D411yescharacteristic
102C4×Dic59D411yescharacteristic
103C4×Dic59C2311yescharacteristic
104C2×C59⋊C8C2311yescharacteristic
105C2×C59⋊C8C2311yescharacteristic
106D472—22no—
107C8×D59—22no—
108C8×D59—22no—
109C23×C59—21no—
110C22×D59—21no—
111C22×D59—21no—
112C22×D59C2×D411yescharacteristic
113Q8×C59—21no—
114Q8×C59—21no—
115D4×C59—21no—
116D4×C59—21no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—42no—
121C2×C4×C59C2×D411yescharacteristic
122C2×C4×C59C2×D411yescharacteristic
123C2×C4×C59C2411yescharacteristic
124C22⋊D59—42no—
125C22⋊D59—42no—
126C22⋊D59—42no—
127C2×Dic59—21no—
128C2×Dic59—21no—
129C2×Dic59C2×D411yescharacteristic
130C2×Dic59C2×D411yescharacteristic
131C2×Dic59C2×D411yescharacteristic
132D236—21no—
133D236—21no—
134D236—21no—
135D236—21no—
136D236—42no—
137D236—42no—
138C4×D59—22no—
139C4×D59—21no—
140C4×D59—21no—
141C4×D59—41no—
142C4×D59—42no—
143C4×D59—42no—
144Dic118—42no—
145C8×C59—21no—
146C8×C59#4112yescomplemented
147C59⋊C8—21no—
148C59⋊C8#4112yescomplemented
149C22×C59—41no—
150C22×C59—41no—
151C22×C59—41no—
152C22×C59C22×D411yescharacteristic
153C2×D59—21no—
154C2×D59—21no—
155C2×D59—41no—
156C2×D59—41no—
157C2×D59—41no—
158C2×D59—41no—
159C2×D59—41no—
160C2×D59—41no—
161C2×D59AGL(1,ℤ/8)12yes—
162C4×C59—21no—
163C4×C59—21no—
164C4×C59—41no—
165C4×C59—41no—
166C4×C59—41no—
167C4×C59C2×#4111yescharacteristic
168C4×C59C2×#4111yescharacteristic
169Dic59—21no—
170Dic59—21no—
171Dic59—21no—
172Dic59—41no—
173Dic59—41no—
174#3180—591nomaximal, Sylow
175C2×C59—81no—
176C2×C59#53211yescharacteristic
177C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
178C2×C59#57511yescharacteristic
179D59—22no—
180D59—81no—
181D59—81no—
182#532—591no—
183#529—591no—
184#501—591no—
185#496—591no—
186#490—591no—
187#489—591no—
188#466—591no—
189#466—591no—
190#465—591no—
191#465—591no—
192#442—591no—
193#442—591no—
194#440—591no—
195#440D5911yescharacteristic, complemented
196C2×#97—591no—
197C59#318011yescharacteristic, complemented, Sylow
198C2×#41—1181no—
199C2×SD16—591no—
200C2×SD16C2×D5911yescharacteristic
201C2×D8—591no—
202C2×D8—591no—
203C22×C8—591no—
204C22×C8—591no—
205C4⋊Q8—591no—
206#127—591no—
207#126—1181no—
208#125—591no—
209#124—591no—
210#124—1181no—
211#123—1181no—
212C22⋊Q8—591no—
213#121—591no—
214#121—591no—
215#121—591no—
216#121—1181no—
217C4×Q8C2×D5911yescharacteristic
218C4×D4—591no—
219C4×D4—591no—
220C4×D4—1181no—
221C4×D4—1181no—
222C4×D4C2×D5911yescharacteristic
223#117—1181no—
224C2×C42—591no—
225#107—591no—
226#107C2×D5911yescharacteristic
227#106—591no—
228#106—591no—
229#103—591no—
230#103C2×D5911yescharacteristic
231#102—591no—
232#102—591no—
233#102—591no—
234#102—591no—
235#102—591no—
236#102C2×D5911yescharacteristic
237#97—591no—
238#97—591no—
239#97—591no—
240#97C2×D5911yescharacteristic
241#41—2364no—
242C2×Q8—1181no—
243C2×Q8C22×D5911yescharacteristic
244C2×D4—591no—
245C2×D4—591no—
246C2×D4—1181no—
247C2×D4—1181no—
248C2×D4—1181no—
249C2×D4—1181no—
250C2×D4—1181no—
251C2×D4C22×D5911yescharacteristic
252C22×C4—21no—
253C22×C4—591no—
254C22×C4—591no—
255C22×C4—591no—
256C22×C4—1181no—
257C22×C4—1181no—
258SD16—22no—
259SD16—1182no—
260D8—1182no—
261D8—1182no—
262C2×C8—591no—
263C2×C8—591no—
264C2×C8—1182no—
265C2×C8—1182no—
266C2×C8C22×D5911yescharacteristic
267C2×C8C22×D5911yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—591no—
270C4⋊C4—591no—
271C4⋊C4—1181no—
272C4⋊C4—1181no—
273C4⋊C4—1181no—
274C4⋊C4—1181no—
275C4⋊C4C22×D5911yescharacteristic
276C4⋊C4C22×D5911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—1181no—
279C22⋊C4—1181no—
280C22⋊C4—1181no—
281C22⋊C4—1181no—
282C22⋊C4—1181no—
283C22⋊C4—1181no—
284C22⋊C4—1181no—
285C22⋊C4—1181no—
286C42—21no—
287C42—591no—
288C42—591no—
289C42—591no—
290C42C22×D5911yescharacteristic
291C23—21no—
292C23—591no—
293C23—1181no—
294C23—1181no—
295Q8—21no—
296Q8—21no—
297Q8—2362no—
298D4—21no—
299D4—21no—
300D4—1181no—
301D4—1181no—
302D4—1181no—
303D4—1181no—
304D4—2362no—
305D4—2362no—
306D4—2362no—
307D4—2362no—
308D4—2362no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—591no—
314C2×C4—591no—
315C2×C4—591no—
316C2×C4—1182no—
317C2×C4—1181no—
318C2×C4—1181no—
319C2×C4—1181no—
320C2×C4—1181no—
321C2×C4—2361no—
322C2×C4—2362no—
323C2×C4—2362no—
324C2×C4D4×D5911yescharacteristic
325C2×C4D4×D5911yescharacteristic
326C2×C4C23×D5911yescharacteristic
327C8—21no—
328C8—592no—
329C8—1181no—
330C8#1174568512yescomplemented
331C22—41no—
332C22—41no—
333C22—41no—
334C22—592no—
335C22—1181no—
336C22—1181no—
337C22—2361no—
338C22—2361no—
339C22—2361no—
340C22—2361no—
341C22—2361no—
342C22—2361no—
343C22C2×D4×D5911yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—1181no—
350C4—1181no—
351C4—1181no—
352C4—2361no—
353C4—2361no—
354C4#41×D5911yescharacteristic
355C4C2×#1174568511yescharacteristic
356C2—81no—
357C2—1182no—
358C2—4721no—
359C2—4721no—
360C2#1683794911yescharacteristic
361C2AGL(1,ℤ/8)×D5911yescharacteristic
362C2#1683820111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#440C2
socleC22×C59C22×D4
hypercenter#440D59
hypocenterC59#3180
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #16837949C2semidirect
2. #16837939C2semidirect
3. #16837810C2semidirect
4. #16837788C2semidirect
5. #16837765C2semidirect
6. #16837763C2semidirect
7. #16837639C2semidirect
8. #16837637C2semidirect
9. #16837634C2semidirect
10. #16837628C2semidirect
11. #16837515C2semidirect
12. #16837512C2semidirect
13. #16837500C2semidirect
14. #97×D59C2semidirect
15. C59×#440C2semidirect
146. C8×C59#41semidirect
148. C59⋊C8#41semidirect
195. #440D59semidirect
197. C59#3180semidirect
330. C8#11745685semidirect