Finite Group Databasebeta

← #21435229

Subgroups — #21435229

Order 7552.

370 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 117 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#16837957C211yesmaximal, characteristic, complemented
2#16837950C211yesmaximal, characteristic
3#16837805C211yesmaximal, characteristic, complemented
4#16837800C211yesmaximal, characteristic, complemented
5#16837748C211yesmaximal, characteristic, complemented
6#16837725C214yesmaximal, complemented
7#16837704C214yesmaximal, complemented
8#16837453C211yesmaximal, characteristic, complemented
9C59×#486C211yesmaximal, characteristic, complemented
10C2×#11745687—21no—
11#14273727C2211yescharacteristic
12#14273727C2211yescharacteristic
13#14273718C2212yes—
14#14273714—21no—
15#14273707—21no—
16#14273703—21no—
17#14273698—21no—
18#14273698C2212yes—
19Q8×Dic59—21no—
20#14273692—21no—
21D4×Dic59—21no—
22D4×Dic59C2212yes—
23#14273685C2212yes—
24C42×D59C2211yescharacteristic
25#14273660C2214yes—
26#14273659C2214yes—
27Dic59⋊C8C2212yes—
28#14273648C2214yes—
29(C2×D59)⋊C8C2212yes—
30C4×C59⋊C8C2211yescharacteristic
31C4⋊Q8×C59C2211yescharacteristic
32#127×C59C2211yescharacteristic
33#102×C59C2214yes—
34C4×C8×C59C2211yescharacteristic
35C2×Q8×C59—21no—
36C2×D4×C59—21no—
37C2×D4×C59—21no—
38C2×D4×C59C2312yes—
39C2×C22⋊D59—22no—
40C22×Dic59—22no—
41#11745687—44no—
42C2×C4×D59D411yescharacteristic
43C2×C4×D59D411yescharacteristic
44C2×C4×D59C2311yescharacteristic
45C2×Dic118—21no—
46C2×Dic118—21no—
47C2×C8×C59C2312yes—
48C4⋊C4×C59—21no—
49C4⋊C4×C59C2312yes—
50C42×C59C2311yescharacteristic
51C22⋊Dic59—22no—
52C22⋊Dic59—22no—
53(C2×D59)⋊C4—22no—
54C4⋊Dic59—21no—
55C4⋊Dic59—21no—
56C4⋊Dic59—22no—
57C4⋊Dic59C2312yes—
58C4⋊Dic59C2312yes—
59Dic59⋊C4—22no—
60C4×Dic59—22no—
61C4×Dic59D411yescharacteristic
62C4×Dic59D411yescharacteristic
63C4×Dic59C2311yescharacteristic
64C2×C59⋊C8C2312yes—
65C23×C59—22no—
66C22×D59C2×D411yescharacteristic
67Q8×C59—42no—
68D4×C59—24no—
69D4×C59—42no—
70D4×C59—42no—
71C2×C4×C59—22no—
72C2×C4×C59C2×D411yescharacteristic
73C2×C4×C59C2×D411yescharacteristic
74C2×C4×C59C2411yescharacteristic
75C22⋊D59—44no—
76C2×Dic59—22no—
77C2×Dic59—22no—
78C2×Dic59—44no—
79C2×Dic59C2×D411yescharacteristic
80C2×Dic59C2×D411yescharacteristic
81C2×Dic59C2×D411yescharacteristic
82C4×D59—22no—
83C4×D59—22no—
84C4×D59—22no—
85Dic118—42no—
86Dic118—42no—
87C8×C59—22no—
88C59⋊C8—22no—
89C22×C59—42no—
90C22×C59—42no—
91C22×C59—42no—
92C22×C59C22×D411yescharacteristic
93C2×D59—21no—
94C2×D59—21no—
95C2×D59—21no—
96C4×C59—42no—
97C4×C59#13512yes—
98C4×C59AGL(1,ℤ/8)12yes—
99C4×C592−1+412yes—
100Dic59—21no—
101Dic59—21no—
102Dic59—21no—
103Dic59—42no—
104Dic59—42no—
105#3228—591nomaximal, Sylow
106C2×C59—82no—
107C2×C59#53611yescharacteristic
108C2×C59C2×#13511yescharacteristic
109C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
110D59—41no—
111#533—591no—
112#532—591no—
113#500—591no—
114#498—591no—
115#486—591no—
116#486D5911yescharacteristic, complemented
117#482—594no—
118#478—594no—
119#431—591no—
120C59#322811yescharacteristic, complemented, Sylow
121C2×#41—1181no—
122C4⋊Q8—591no—
123C4⋊Q8—591no—
124C4⋊Q8C2×D5911yescharacteristic
125#127C2×D5911yescharacteristic
126#125—592no—
127#124—1181no—
128C22⋊Q8—1181no—
129C22⋊Q8—1181no—
130#121—592no—
131#121—1181no—
132C4×Q8—1181no—
133C4×Q8—1181no—
134C4×D4—592no—
135C4×D4—1181no—
136#117—592no—
137C2×C42—591no—
138#107—594no—
139#106—594no—
140C4⋊C8—592no—
141#102—594no—
142#102C2×D5914yes—
143C22⋊C8—592no—
144C4×C8—591no—
145C4×C8C2×D5911yescharacteristic
146#41—2364no—
147C2×Q8—21no—
148C2×Q8—1181no—
149C2×Q8—1181no—
150C2×D4—21no—
151C2×D4—21no—
152C2×D4—1182no—
153C2×D4C22×D5912yes—
154C22×C4—591no—
155C22×C4—591no—
156C22×C4—591no—
157C22×C4—1182no—
158C2×C8—592no—
159C2×C8C22×D5912yes—
160C4⋊C4—21no—
161C4⋊C4—592no—
162C4⋊C4—592no—
163C4⋊C4—1182no—
164C4⋊C4—1182no—
165C4⋊C4—1181no—
166C4⋊C4—1181no—
167C4⋊C4C22×D5912yes—
168C22⋊C4—1182no—
169C22⋊C4—1182no—
170C22⋊C4—1182no—
171C42—591no—
172C42—591no—
173C42—591no—
174C42—1182no—
175C42C22×D5911yescharacteristic
176C23—22no—
177C23—591no—
178Q8—42no—
179Q8—2362no—
180Q8—2362no—
181D4—24no—
182D4—42no—
183D4—42no—
184D4—2364no—
185C2×C4—22no—
186C2×C4—591no—
187C2×C4—591no—
188C2×C4—591no—
189C2×C4—1182no—
190C2×C4—1182no—
191C2×C4—1182no—
192C2×C4—1182no—
193C2×C4—1182no—
194C2×C4—2364no—
195C2×C4D4×D5911yescharacteristic
196C2×C4D4×D5911yescharacteristic
197C2×C4C23×D5911yescharacteristic
198C8—22no—
199C8—1182no—
200C22—42no—
201C22—42no—
202C22—42no—
203C22—1181no—
204C22—1181no—
205C22—1181no—
206C22C2×D4×D5911yescharacteristic
207C4—42no—
208C4—1181no—
209C4—1181no—
210C4—1181no—
211C4—2362no—
212C4—2362no—
213C4#1427374812yes—
214C4#1427375112yes—
215C4#1427377412yes—
216C2—82no—
217C2—2361no—
218C2#1683797211yescharacteristic
219C2C2×#1427374811yescharacteristic
220C2C2×#1427375111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#486C2
socleC22×C59C22×D4
hypercenter#486D59
hypocenterC59#3228
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. #16837957C2semidirect
3. #16837805C2semidirect
4. #16837800C2semidirect
5. #16837748C2semidirect
6. #16837725C2semidirect
7. #16837704C2semidirect
8. #16837453C2semidirect
9. C59×#486C2semidirect
116. #486D59semidirect
120. C59#3228semidirect