Finite Group Databasebeta

← #21434796

Subgroups — #21434796

Order 7552.

410 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16837953C211yesmaximal, characteristic, complemented
2#16837937C211yesmaximal, characteristic, complemented
3#16837791C211yesmaximal, characteristic, complemented
4#16837768C211yesmaximal, characteristic, complemented
5#16837764C211yesmaximal, characteristic, complemented
6#16837639C212yesmaximal, complemented
7#16837632C212yesmaximal, complemented
8#16837513C212yesmaximal, complemented
9#16837501C212yesmaximal, complemented
10#97×D59C211yesmaximal, characteristic, complemented
11C59×#501C211yesmaximal, characteristic, complemented
12C2×#11745689—21no—
13C2×#11745660C2212yes—
14C2×D472C2212yes—
15C2×C8×D59C2212yes—
16#14273724C2211yescharacteristic
17#14273722—21no—
18#14273716—21no—
19#14273715C2211yescharacteristic
20#14273712—21no—
21#14273707C2211yescharacteristic
22#14273702—21no—
23#14273702C2212yes—
24#14273702C2211yescharacteristic
25#14273692C2211yescharacteristic
26#14273689—21no—
27#14273689—21no—
28#14273689C2211yescharacteristic
29#14273689C2212yes—
30#14273685—21no—
31C42×D59C2211yescharacteristic
32#14273650C2212yes—
33#14273647C2212yes—
34#14273647C2212yes—
35#14273647C2212yes—
36#14273638C2211yescharacteristic
37#14273637C2212yes—
38C4⋊Q8×C59C2211yescharacteristic
39#125×C59C2211yescharacteristic
40#107×C59C2212yes—
41#106×C59C2212yes—
42#97×C59C2211yescharacteristic
43C2×Q8×C59—21no—
44#11745689—44no—
45C2×D236—21no—
46C2×D236—22no—
47C2×D236—21no—
48C2×D236—21no—
49C2×D236C2311yescharacteristic
50C2×D236C2312yes—
51C2×C4×D59—21no—
52C2×C4×D59—22no—
53C2×C4×D59D411yescharacteristic
54C2×C4×D59D411yescharacteristic
55C2×C4×D59C2311yescharacteristic
56C2×Dic118C2311yescharacteristic
57C2×C8×C59C2312yes—
58C4⋊C4×C59—21no—
59C4⋊C4×C59—21no—
60C4⋊C4×C59—21no—
61C4⋊C4×C59C2311yescharacteristic
62C4⋊C4×C59C2312yes—
63C4⋊C4×C59C2311yescharacteristic
64C42×C59C2311yescharacteristic
65(C2×D59)⋊C4—21no—
66(C2×D59)⋊C4—21no—
67(C2×D59)⋊C4—21no—
68(C2×D59)⋊C4—21no—
69(C2×D59)⋊C4—22no—
70(C2×D59)⋊C4—22no—
71(C2×D59)⋊C4—21no—
72C4⋊Dic59—21no—
73Dic59⋊C4—21no—
74C4×Dic59—21no—
75C4×Dic59D411yescharacteristic
76C4×Dic59D411yescharacteristic
77C4×Dic59C2311yescharacteristic
78C2×C59⋊C8C2312yes—
79D472—24no—
80#11745660—24no—
81C8×D59—24no—
82C22×D59—21no—
83C22×D59—22no—
84C22×D59C2×D411yescharacteristic
85Q8×C59—42no—
86C2×C4×C59—21no—
87C2×C4×C59—21no—
88C2×C4×C59—22no—
89C2×C4×C59C2×D411yescharacteristic
90C2×C4×C59C2×D411yescharacteristic
91C2×C4×C59C2411yescharacteristic
92C2×Dic59—21no—
93C2×Dic59C2×D411yescharacteristic
94C2×Dic59C2×D411yescharacteristic
95C2×Dic59C2×D411yescharacteristic
96D236—22no—
97D236—22no—
98D236—22no—
99D236—42no—
100D236—42no—
101D236—42no—
102D236—44no—
103C4×D59—22no—
104C4×D59—22no—
105C4×D59—41no—
106C4×D59—42no—
107C4×D59—44no—
108Dic118—22no—
109C8×C59#4114yescomplemented
110C59⋊C8—22no—
111C22×C59C22×D411yescharacteristic
112C2×D59—21no—
113C2×D59—21no—
114C2×D59—42no—
115C2×D59—41no—
116C2×D59—42no—
117C2×D59—41no—
118C2×D59—41no—
119C2×D59—42no—
120C2×D59AGL(1,ℤ/8)12yes—
121C4×C59—21no—
122C4×C59—21no—
123C4×C59—42no—
124C4×C59—41no—
125C4×C59—41no—
126C4×C59C2×#4112yes—
127Dic59—21no—
128Dic59—21no—
129Dic59—21no—
130Dic59—41no—
131#3180—591nomaximal, Sylow
132C2×C59#53211yescharacteristic
133C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
134C2×C59#57511yescharacteristic
135D59—22no—
136D59—82no—
137D59—81no—
138#532—591no—
139#529—591no—
140#501D5911yescharacteristic, complemented
141#496—591no—
142#490—591no—
143#489—591no—
144#466—592no—
145#465—592no—
146#442—592no—
147#440—592no—
148C2×#97—591no—
149C59#318011yescharacteristic, complemented, Sylow
150C2×#41—1181no—
151C2×SD16—592no—
152C2×D8—592no—
153C22×C8—592no—
154C4⋊Q8C2×D5911yescharacteristic
155#127—591no—
156#126—1181no—
157#125C2×D5911yescharacteristic
158#124—591no—
159#124—1181no—
160#123—1181no—
161C22⋊Q8—591no—
162#121—591no—
163#121—592no—
164#121—1181no—
165C4×Q8—591no—
166C4×D4—591no—
167C4×D4—592no—
168C4×D4—1181no—
169C4×D4—1181no—
170#117—1181no—
171C2×C42—591no—
172#107C2×D5912yes—
173#106C2×D5912yes—
174#103—592no—
175#102—592no—
176#102—592no—
177#102—592no—
178#97—592no—
179#97—591no—
180#97C2×D5911yescharacteristic
181#41—2364no—
182C2×Q8—21no—
183C2×Q8—591no—
184C2×D4—591no—
185C2×D4—592no—
186C2×D4—1181no—
187C2×D4—1182no—
188C2×D4—1181no—
189C2×D4—1181no—
190C22×C4—591no—
191C22×C4—591no—
192C22×C4—591no—
193C22×C4—1181no—
194C22×C4—1182no—
195SD16—1184no—
196D8—1184no—
197C2×C8—592no—
198C2×C8—1184no—
199C2×C8C22×D5912yes—
200C4⋊C4—21no—
201C4⋊C4—21no—
202C4⋊C4—21no—
203C4⋊C4—1181no—
204C4⋊C4—1181no—
205C4⋊C4C22×D5911yescharacteristic
206C4⋊C4C22×D5911yescharacteristic
207C4⋊C4C22×D5912yes—
208C22⋊C4—1181no—
209C22⋊C4—1182no—
210C22⋊C4—1181no—
211C22⋊C4—1182no—
212C22⋊C4—1181no—
213C22⋊C4—1181no—
214C22⋊C4—1181no—
215C42—591no—
216C42—591no—
217C42—591no—
218C42—1181no—
219C42C22×D5911yescharacteristic
220C23—591no—
221C23—1181no—
222C23—1182no—
223Q8—42no—
224Q8—1182no—
225D4—1182no—
226D4—1182no—
227D4—1182no—
228D4—2362no—
229D4—2362no—
230D4—2362no—
231D4—2364no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—591no—
236C2×C4—591no—
237C2×C4—591no—
238C2×C4—1182no—
239C2×C4—1182no—
240C2×C4—1181no—
241C2×C4—2361no—
242C2×C4—2362no—
243C2×C4—2364no—
244C2×C4D4×D5911yescharacteristic
245C2×C4D4×D5911yescharacteristic
246C2×C4C23×D5911yescharacteristic
247C8—1182no—
248C8#1174568914yescomplemented
249C22—592no—
250C22—1181no—
251C22—1181no—
252C22—2362no—
253C22—2361no—
254C22—2361no—
255C22—2362no—
256C22—2361no—
257C22—2362no—
258C22C2×D4×D5911yescharacteristic
259C4—21no—
260C4—21no—
261C4—42no—
262C4—41no—
263C4—41no—
264C4—1181no—
265C4—1181no—
266C4—1181no—
267C4—2361no—
268C4C2×#1174568912yes—
269C2—1182no—
270C2—4722no—
271C2—4721no—
272C2#1683795311yescharacteristic
273C2AGL(1,ℤ/8)×D5911yescharacteristic
274C2#1683820111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#501C2
socleC22×C59C22×D4
hypercenter#501D59
hypocenterC59#3180
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. #16837953C2semidirect
2. #16837937C2semidirect
3. #16837791C2semidirect
4. #16837768C2semidirect
5. #16837764C2semidirect
6. #16837639C2semidirect
7. #16837632C2semidirect
8. #16837513C2semidirect
9. #16837501C2semidirect
10. #97×D59C2semidirect
11. C59×#501C2semidirect
109. C8×C59#41semidirect
140. #501D59semidirect
149. C59#3180semidirect
248. C8#11745689semidirect