Finite Group Databasebeta

← #21422593

Subgroups — #21422593

Order 7552.

240 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 71 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#16837954C211yesmaximal, characteristic
2#16837452C211yesmaximal, characteristic
3#16837253C211yesmaximal, characteristic
4#16837140C211yesmaximal, characteristic
5#16837139C211yesmaximal, characteristic
6#16837138C211yesmaximal, characteristic
7C59×#328C211yesmaximal, characteristic
8#14273726C411yescharacteristic, complemented
9#14273725C411yescharacteristic, complemented
10#14273717—21no—
11#14273706C2211yescharacteristic
12#14273704—21no—
13Q8×Dic59C411yescharacteristic, complemented
14#14273692—21no—
15#14273692C411yescharacteristic, complemented
16#14273683—21no—
17C2×Dic59⋊C4—21no—
18C2×C4×Dic59—21no—
19C2×C4×Dic59C2211yescharacteristic
20Dic59⋊C8—21no—
21C22⋊(C59⋊C8)C2211yescharacteristic
22C8×Dic59—21no—
23C59⋊#95C2211yescharacteristic
24C22⋊Q8×C59C2211yescharacteristic
25C22⋊C8×C59C2211yescharacteristic
26#95×C59C2211yescharacteristic
27C2×Q8×C59C2×C411yescharacteristic
28C22×C4×C59—21no—
29C22×C4×C59C2311yescharacteristic
30C22×Dic59—21no—
31C22×Dic59D411yescharacteristic
32C22×Dic59D411yescharacteristic
33C2×Dic118—21no—
34C2×Dic118C2×C411yescharacteristic
35C2×C8×C59—21no—
36C4⋊C4×C59—21no—
37C4⋊C4×C59C2×C411yescharacteristic
38C22⋊C4×C59—21no—
39C22⋊Dic59—21no—
40C4⋊Dic59—21no—
41C4⋊Dic59C2×C411yescharacteristic
42Dic59⋊C4—24no—
43Dic59⋊C4—21no—
44Dic59⋊C4—21no—
45Dic59⋊C4—21no—
46Dic59⋊C4—21no—
47Dic59⋊C4—21no—
48C4×Dic59—21no—
49C4×Dic59—21no—
50C4×Dic59—42no—
51C4×Dic59C2×C411yescharacteristic
52C4×Dic59C2×C411yescharacteristic
53C4×Dic59D411yescharacteristic
54C4×Dic59D411yescharacteristic
55C2×C59⋊C8—21no—
56C23×C59C2×D411yescharacteristic
57Q8×C59—41no—
58C2×C4×C59—22no—
59C2×C4×C59—21no—
60C2×C4×C59—21no—
61C2×C4×C59—41no—
62C2×C4×C59—41no—
63C2×C4×C59—41no—
64C2×C4×C59C22×C411yescharacteristic
65C2×C4×C59C2×D411yescharacteristic
66C2×Dic59—22no—
67C2×Dic59—22no—
68C2×Dic59—21no—
69C2×Dic59—21no—
70C2×Dic59—41no—
71C2×Dic59—41no—
72C2×Dic59C22⋊C411yescharacteristic
73C2×Dic59C22⋊C411yescharacteristic
74C2×Dic59C22⋊C411yescharacteristic
75C2×Dic59C22⋊C411yescharacteristic
76C2×Dic59SD1612yes—
77C2×Dic59Q1612yes—
78Dic118—42no—
79Dic118—41no—
80C8×C59—41no—
81C59⋊C8—41no—
82C22×C59—21no—
83C22×C59—21no—
84C22×C59C2×C22⋊C411yescharacteristic
85C22×C59C2×SD1611yescharacteristic
86C22×C59C2×Q1611yescharacteristic
87C4×C59—21no—
88C4×C59—21no—
89C4×C59—42no—
90C4×C59—41no—
91C4×C59—41no—
92Dic59—21no—
93Dic59—42no—
94Dic59—41no—
95Dic59—41no—
96Dic59#10312yes—
97Dic59#10312yes—
98Dic59#10412yes—
99#1503—591nomaximal, Sylow
100C2×C59—21no—
101C2×C59—21no—
102C2×C59#41011yescharacteristic
103C2×C59C2×#10311yescharacteristic
104C2×C59C2×#10411yescharacteristic
105#533—591no—
106#431—591no—
107C4×C4⋊C4—591no—
108#328—591no—
109#328—591no—
110#328—591no—
111#328D5911yescharacteristic
112C59#150311yescharacteristic, complemented, Sylow
113C4⋊Q8—591no—
114C4⋊Q8—591no—
115#125—1181no—
116C22⋊Q8—591no—
117C22⋊Q8—1181no—
118C22⋊Q8C2×D5911yescharacteristic
119C4×Q8—591no—
120C4×Q8—591no—
121C4×Q8—1181no—
122#117—1181no—
123C2×C4⋊C4—1181no—
124C2×C42—591no—
125C2×C42—1181no—
126C4⋊C8—1181no—
127C22⋊C8—591no—
128C22⋊C8C2×D5911yescharacteristic
129C4×C8—1181no—
130#95—591no—
131#95C2×D5911yescharacteristic
132C2×Q8—591no—
133C2×Q8—1181no—
134C2×Q8C4×D5911yescharacteristic
135C22×C4—21no—
136C22×C4—591no—
137C22×C4—591no—
138C22×C4—1181no—
139C22×C4C22×D5911yescharacteristic
140C2×C8—21no—
141C2×C8—1181no—
142C4⋊C4—21no—
143C4⋊C4—591no—
144C4⋊C4—1181no—
145C4⋊C4—1181no—
146C4⋊C4—1181no—
147C4⋊C4—1181no—
148C4⋊C4—1181no—
149C4⋊C4—1184no—
150C4⋊C4—1181no—
151C4⋊C4C4×D5911yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—1181no—
154C42—591no—
155C42—591no—
156C42—591no—
157C42—591no—
158C42—1181no—
159C42—1181no—
160C42—2362no—
161C23D4×D5911yescharacteristic
162Q8—41no—
163Q8—2361no—
164Q8—2362no—
165C2×C4—22no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—591no—
172C2×C4—591no—
173C2×C4—591no—
174C2×C4—592no—
175C2×C4—592no—
176C2×C4—591no—
177C2×C4—1182no—
178C2×C4—1182no—
179C2×C4—1181no—
180C2×C4—1181no—
181C2×C4—2361no—
182C2×C4—2361no—
183C2×C4C2×C4×D5911yescharacteristic
184C2×C4D4×D5911yescharacteristic
185C8—41no—
186C8—2361no—
187C22—21no—
188C22—21no—
189C22C22⋊C4×D5911yescharacteristic
190C22SD16×D5911yescharacteristic
191C22Q16×D5911yescharacteristic
192C4—21no—
193C4—21no—
194C4—42no—
195C4—41no—
196C4—41no—
197C4—592no—
198C4—592no—
199C4—592no—
200C4—1181no—
201C4—2362no—
202C4—2361no—
203C4—2361no—
204C2—21no—
205C2—21no—
206C2#1683737411yescharacteristic
207C2#103×D5911yescharacteristic
208C2#104×D5911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D59
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#328C2
socleC22×C59C2×C22⋊C4
hypercenter#328D59
hypocenterC59#1503
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
8. #14273726C4semidirect
9. #14273725C4semidirect
13. Q8×Dic59C4semidirect
15. #14273692C4semidirect
112. C59#1503semidirect