Finite Group Databasebeta

← #21435252

Subgroups — #21435252

Order 7552.

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

normal subgroups only

This group has 326 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
2#16837957C211yesmaximal, characteristic
3#16837807C211yesmaximal, characteristic, complemented
4#16837798C211yesmaximal, characteristic, complemented
5#16837752C211yesmaximal, characteristic, complemented
6#16837742C214yesmaximal
7#16837711C214yesmaximal, complemented
8#16837453C211yesmaximal, characteristic
9C59×#487C211yesmaximal, characteristic, complemented
10#14273727C2211yescharacteristic
11#14273727C2211yescharacteristic
12#14273718—21no—
13#14273718C2212yes—
14#14273707—21no—
15#14273707—21no—
16#14273703—21no—
17#14273703C2212yes—
18Q8×Dic59—21no—
19Q8×Dic59C2212yes—
20#14273692—21no—
21#14273692—21no—
22#14273685—21no—
23#14273685C2212yes—
24C42×D59C2211yescharacteristic
25#14273661C2214yes—
26#14273658C2214yes—
27Dic59⋊C8C2212yes—
28#14273651C2214yes—
29(C2×D59)⋊C8C2212yes—
30C4×C59⋊C8C2211yescharacteristic
31C4⋊Q8×C59C2211yescharacteristic
32C4⋊Q8×C59C2211yescharacteristic
33#103×C59C2214yes—
34C4×C8×C59C2211yescharacteristic
35C2×Q8×C59—21no—
36C2×Q8×C59C2312yes—
37C2×C4×D59D411yescharacteristic
38C2×C4×D59D411yescharacteristic
39C2×C4×D59C2311yescharacteristic
40C2×Dic118—21no—
41C2×Dic118—21no—
42C2×C8×C59C2312yes—
43C4⋊C4×C59—21no—
44C4⋊C4×C59—21no—
45C4⋊C4×C59—21no—
46C4⋊C4×C59C2312yes—
47C42×C59C2311yescharacteristic
48(C2×D59)⋊C4—22no—
49(C2×D59)⋊C4—22no—
50C4⋊Dic59—21no—
51C4⋊Dic59—21no—
52C4⋊Dic59—22no—
53C4⋊Dic59—22no—
54C4⋊Dic59C2312yes—
55C4⋊Dic59C2312yes—
56Dic59⋊C4—22no—
57Dic59⋊C4—22no—
58C4×Dic59—22no—
59C4×Dic59—22no—
60C4×Dic59D411yescharacteristic
61C4×Dic59D411yescharacteristic
62C4×Dic59C2311yescharacteristic
63C2×C59⋊C8C2312yes—
64C22×D59C2×D411yescharacteristic
65Q8×C59—24no—
66Q8×C59—42no—
67C2×C4×C59—22no—
68C2×C4×C59—22no—
69C2×C4×C59C2×D411yescharacteristic
70C2×C4×C59C2×D411yescharacteristic
71C2×C4×C59C2411yescharacteristic
72C2×Dic59—22no—
73C2×Dic59—22no—
74C2×Dic59C2×D411yescharacteristic
75C2×Dic59C2×D411yescharacteristic
76C2×Dic59C2×D411yescharacteristic
77C4×D59—22no—
78C4×D59—22no—
79C4×D59—22no—
80Dic118—42no—
81Dic118—42no—
82C8×C59—22no—
83C59⋊C8—22no—
84C22×C59C22×D411yescharacteristic
85C2×D59—21no—
86C2×D59—21no—
87C2×D59—21no—
88C4×C59—42no—
89C4×C59—42no—
90C4×C59#13512yes—
91C4×C59#13712yes—
92C4×C592−1+412yes—
93Dic59—21no—
94Dic59—21no—
95Dic59—21no—
96Dic59—42no—
97Dic59—42no—
98#3231—591nomaximal, Sylow
99C2×C59#53611yescharacteristic
100C2×C59C2×#13511yescharacteristic
101C2×C59C2×#13711yescharacteristic
102D59—41no—
103#533—591no—
104#533—591no—
105#500—591no—
106#498—591no—
107#487—591no—
108#487D5911yescharacteristic, complemented
109#485—594no—
110#479—594no—
111#431—591no—
112C59#323111yescharacteristic, complemented, Sylow
113C4⋊Q8—591no—
114C4⋊Q8—591no—
115C4⋊Q8C2×D5911yescharacteristic
116C4⋊Q8C2×D5911yescharacteristic
117#125—592no—
118#125—1181no—
119C22⋊Q8—592no—
120C22⋊Q8—1181no—
121C22⋊Q8—1181no—
122C22⋊Q8—1181no—
123C4×Q8—592no—
124C4×Q8—1181no—
125C4×Q8—1181no—
126C4×Q8—1181no—
127#117—592no—
128#117—1181no—
129C2×C42—591no—
130#107—594no—
131#106—594no—
132C4⋊C8—592no—
133#103—594no—
134#103C2×D5914yes—
135C22⋊C8—592no—
136C4×C8—591no—
137C4×C8C2×D5911yescharacteristic
138C2×Q8—21no—
139C2×Q8—1181no—
140C2×Q8—1181no—
141C2×Q8C22×D5912yes—
142C22×C4—591no—
143C22×C4—591no—
144C22×C4—591no—
145C2×C8—592no—
146C2×C8C22×D5912yes—
147C4⋊C4—21no—
148C4⋊C4—21no—
149C4⋊C4—21no—
150C4⋊C4—592no—
151C4⋊C4—592no—
152C4⋊C4—1182no—
153C4⋊C4—1182no—
154C4⋊C4—1182no—
155C4⋊C4—1182no—
156C4⋊C4—1181no—
157C4⋊C4—1181no—
158C4⋊C4C22×D5912yes—
159C22⋊C4—1182no—
160C22⋊C4—1182no—
161C42—591no—
162C42—591no—
163C42—591no—
164C42—1182no—
165C42—1182no—
166C42C22×D5911yescharacteristic
167C23—591no—
168Q8—24no—
169Q8—42no—
170Q8—2362no—
171Q8—2362no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—591no—
175C2×C4—591no—
176C2×C4—591no—
177C2×C4—1182no—
178C2×C4—1182no—
179C2×C4—1182no—
180C2×C4—1182no—
181C2×C4—1182no—
182C2×C4D4×D5911yescharacteristic
183C2×C4D4×D5911yescharacteristic
184C2×C4C23×D5911yescharacteristic
185C8—22no—
186C8—1182no—
187C22—1181no—
188C22—1181no—
189C22—1181no—
190C22C2×D4×D5911yescharacteristic
191C4—42no—
192C4—42no—
193C4—1181no—
194C4—1181no—
195C4—1181no—
196C4—2362no—
197C4—2362no—
198C4#1427375012yes—
199C4#1427375612yes—
200C4#1427377412yes—
201C2—2361no—
202C2#1683797211yescharacteristic
203C2C2×#1427375011yescharacteristic
204C2C2×#1427375611yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#487C2
socleC22×C59C22×D4
hypercenter#487D59
hypocenterC59#3231
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. #16837807C2semidirect
4. #16837798C2semidirect
5. #16837752C2semidirect
7. #16837711C2semidirect
9. C59×#487C2semidirect
108. #487D59semidirect
112. C59#3231semidirect