Finite Group Databasebeta

← #21436893

Subgroups — #21436893

Order 7552.

384 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 115 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#16838138C211yesmaximal, characteristic, complemented
2#16838067C211yesmaximal, characteristic, complemented
3#16837760C212yesmaximal, complemented
4#16837690C212yesmaximal, complemented
5#16837684C211yesmaximal, characteristic, complemented
6#16837616C212yesmaximal, complemented
7#16837594C211yesmaximal, characteristic
8#16837532C211yesmaximal, characteristic, complemented
9#16837511C212yesmaximal, complemented
10C4×#11745660C211yesmaximal, characteristic, complemented
11C59×#486C211yesmaximal, characteristic, complemented
12C2×Q8×D59—21no—
13C2×#11745660C2211yescharacteristic
14C2×#11745669C2212yes—
15#14273726C2212yes—
16#14273714—21no—
17#14273714C2212yes—
18#14273708—22no—
19#14273705—22no—
20#14273703—21no—
21C4×Dic118C2211yescharacteristic
22C4×Dic118C2211yescharacteristic
23C4×D236C2211yescharacteristic
24D4×Dic59—21no—
25D4×Dic59C2212yes—
26#14273689C2212yes—
27#14273659C2211yescharacteristic
28#14273658C2212yes—
29C4⋊(C59⋊C8)C2211yescharacteristic
30Dic59⋊C8C2212yes—
31#14273652C2211yescharacteristic
32#14273650C2212yes—
33#14273649C2211yescharacteristic
34#14273648C2212yes—
35#14273637C2212yes—
36C4⋊Q8×C59C2211yescharacteristic
37#127×C59C2211yescharacteristic
38#102×C59C2212yes—
39#102×C59C2212yes—
40C4×C8×C59C2211yescharacteristic
41C2×Q8×C59—21no—
42C2×D4×C59—21no—
43C2×D4×C59—21no—
44C2×D4×C59C2312yes—
45C22×Dic59—22no—
46Q8×D59—44no—
47C2×D236C2311yescharacteristic
48C2×C4×D59—21no—
49C2×C4×D59—22no—
50C2×Dic118—22no—
51C2×Dic118D411yescharacteristic
52C2×Dic118C2311yescharacteristic
53C2×C8×C59C2311yescharacteristic
54C2×C8×C59C2311yescharacteristic
55C4⋊C4×C59—21no—
56C4⋊C4×C59C2312yes—
57C42×C59C2311yescharacteristic
58C22⋊Dic59—22no—
59C22⋊Dic59—22no—
60C22⋊Dic59—22no—
61#11745669—24no—
62(C2×D59)⋊C4—21no—
63(C2×D59)⋊C4—22no—
64C4⋊Dic59D411yescharacteristic
65C4⋊Dic59C2311yescharacteristic
66C4⋊Dic59C2311yescharacteristic
67Dic59⋊C4—21no—
68Dic59⋊C4—22no—
69Dic59⋊C4D412yes—
70C4×Dic59—21no—
71C4×Dic59C2312yes—
72C2×C59⋊C8C2312yes—
73#11745660—22no—
74C23×C59—22no—
75C22×D59—21no—
76Q8×C59—42no—
77D4×C59—22no—
78D4×C59—22no—
79D4×C59—42no—
80D4×C59—81no—
81C2×C4×C59—22no—
82C2×C4×C59C2×D411yescharacteristic
83C2×C4×C59C2×D411yescharacteristic
84C2×C4×C59C2411yescharacteristic
85C2×Dic59—21no—
86C2×Dic59—21no—
87C2×Dic59—21no—
88C2×Dic59—82no—
89C2×Dic59C2×D412yes—
90C2×Dic59C2×D412yes—
91D236—21no—
92D236#4112yes—
93C4×D59—44no—
94C4×D59—42no—
95Dic118—22no—
96Dic118—21no—
97Dic118—21no—
98Dic118—44no—
99C8×C59—21no—
100C8×C59—21no—
101C59⋊C8—22no—
102C22×C59—42no—
103C22×C59—42no—
104C22×C59—42no—
105C22×C59C22×D411yescharacteristic
106C2×D59—22no—
107C2×D59—41no—
108C2×D59—41no—
109C4×C59—21no—
110C4×C59—42no—
111C4×C59AGL(1,ℤ/8)12yes—
112C4×C59C2×#4111yescharacteristic
113C4×C592−1+411yescharacteristic
114Dic59—22no—
115Dic59—22no—
116Dic59—41no—
117Dic59—41no—
118Dic59—41no—
119#3373—591nomaximal, Sylow
120C2×C59—82no—
121C2×C59#54811yescharacteristic
122C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
123C2×C59#57711yescharacteristic
124D59—42no—
125#559—591no—
126D4×Q8—591no—
127#489—592no—
128#486D5911yescharacteristic, complemented
129#476—592no—
130#475—591no—
131#463—592no—
132#459—591no—
133#446—591no—
134#442—592no—
135C4×SD16—591no—
136C59#337311yescharacteristic, complemented, Sylow
137C22×Q8—1181no—
138C2×SD16—591no—
139C2×D8—592no—
140C4⋊Q8—592no—
141C4⋊Q8C2×D5911yescharacteristic
142#127C2×D5911yescharacteristic
143#124—592no—
144#124—1181no—
145#123—1182no—
146C22⋊Q8—1182no—
147C22⋊Q8—1181no—
148C4×Q8—591no—
149C4×Q8—591no—
150C4×D4—592no—
151C4×D4—592no—
152C4×D4—591no—
153C4×D4—1181no—
154#106—591no—
155#106—592no—
156C4⋊C8—592no—
157C4⋊C8—591no—
158#103—591no—
159#103—592no—
160#102—592no—
161#102—591no—
162#102C2×D5912yes—
163#102C2×D5912yes—
164#97—592no—
165C4×C8C2×D5911yescharacteristic
166C2×Q8—21no—
167C2×Q8—591no—
168C2×Q8—591no—
169C2×Q8—1182no—
170C2×Q8—2364no—
171C2×D4—21no—
172C2×D4—21no—
173C2×D4—591no—
174C2×D4C22×D5912yes—
175C22×C4—1182no—
176C22×C4—1182no—
177C22×C4—1181no—
178SD16—1182no—
179D8—1184no—
180C2×C8—592no—
181C2×C8C22×D5911yescharacteristic
182C2×C8C22×D5911yescharacteristic
183C4⋊C4—21no—
184C4⋊C4—591no—
185C4⋊C4—592no—
186C4⋊C4—591no—
187C4⋊C4—591no—
188C4⋊C4—1182no—
189C4⋊C4—1181no—
190C4⋊C4C22×D5912yes—
191C22⋊C4—1182no—
192C22⋊C4—1182no—
193C22⋊C4—1182no—
194C22⋊C4—1182no—
195C22⋊C4—1181no—
196C42—592no—
197C42—1181no—
198C42C22×D5911yescharacteristic
199C23—22no—
200C23—1181no—
201Q8—42no—
202Q8—1182no—
203Q8—1181no—
204Q8—1181no—
205Q8—2364no—
206D4—22no—
207D4—22no—
208D4—42no—
209D4—81no—
210D4—592no—
211D4—1181no—
212C2×C4—22no—
213C2×C4—592no—
214C2×C4—592no—
215C2×C4—1181no—
216C2×C4—1181no—
217C2×C4—1181no—
218C2×C4—4722no—
219C2×C4—2364no—
220C2×C4—2362no—
221C2×C4D4×D5911yescharacteristic
222C2×C4D4×D5911yescharacteristic
223C2×C4C23×D5911yescharacteristic
224C8—21no—
225C8—21no—
226C8—1182no—
227C22—42no—
228C22—42no—
229C22—42no—
230C22—1182no—
231C22—2361no—
232C22—2361no—
233C22C2×D4×D5911yescharacteristic
234C4—21no—
235C4—42no—
236C4—1182no—
237C4—1182no—
238C4—2361no—
239C4—2361no—
240C4—2361no—
241C4#1427375112yes—
242C4#41×D5911yescharacteristic
243C4#1427377411yescharacteristic
244C2—82no—
245C2—2362no—
246C2#1683806011yescharacteristic
247C2C2×#1427375111yescharacteristic
248C2#1683820811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#486C2
socleC22×C59C22×D4
hypercenter#486D59
hypocenterC59#3373
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #16838138C2semidirect
2. #16838067C2semidirect
3. #16837760C2semidirect
4. #16837690C2semidirect
5. #16837684C2semidirect
6. #16837616C2semidirect
8. #16837532C2semidirect
9. #16837511C2semidirect
10. C4×#11745660C2semidirect
11. C59×#486C2semidirect
128. #486D59semidirect
136. C59#3373semidirect