Finite Group Databasebeta

← #21432362

Subgroups — #21432362

Order 7552.

348 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 125 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#16837343C212yesmaximal
2#16837341C211yesmaximal, characteristic
3#16837336C212yesmaximal
4#16837335C212yesmaximal
5#16837333C212yesmaximal
6#16837321C212yesmaximal
7#16837271C211yesmaximal, characteristic
8#16837269C212yesmaximal
9C59×#395C211yesmaximal, characteristic
10C2×C4⋊Dic59C2211yescharacteristic
11C2×C4⋊Dic59C2211yescharacteristic
12C2×Dic59⋊C4C2212yes—
13C2×Dic59⋊C4C2212yes—
14C2×Dic59⋊C4C2212yes—
15C2×Dic59⋊C4C2212yes—
16C2×Dic59⋊C4C2212yes—
17C2×C4×Dic59C2211yescharacteristic
18C59⋊#95C2212yes—
19C59⋊#95C2212yes—
20C59⋊#95C2212yes—
21C59⋊#95C2212yes—
22C59⋊#95C2212yes—
23C59⋊#95C2212yes—
24C59⋊#95C2211yescharacteristic
25C59⋊#95C2212yes—
26C22×Q8×C59C2211yescharacteristic
27C2×C4⋊C4×C59C2211yescharacteristic
28C2×C4⋊C4×C59C2212yes—
29#95×C59C2212yes—
30#95×C59C2211yescharacteristic
31C2×Q8×C59—41no—
32C2×Q8×C59—42no—
33C22×C4×C59C2312yes—
34C22×C4×C59C2312yes—
35C22×C4×C59C2311yescharacteristic
36C22×C4×C59C2311yescharacteristic
37C22×C4×C59C2311yescharacteristic
38C22×Dic59C2312yes—
39C22×Dic59C2312yes—
40C22×Dic59C2312yes—
41C22×Dic59C2312yes—
42C4⋊C4×C59—41no—
43C4⋊C4×C59—42no—
44C4⋊Dic59—41no—
45C4⋊Dic59—41no—
46Dic59⋊C4—42no—
47Dic59⋊C4—42no—
48Dic59⋊C4—42no—
49Dic59⋊C4—42no—
50Dic59⋊C4—42no—
51C4×Dic59Q814yescomplemented
52C23×C59C2411yescharacteristic
53Q8×C59—44no—
54C2×C4×C59—21no—
55C2×C4×C59—21no—
56C2×C4×C59—22no—
57C2×C4×C59—22no—
58C2×C4×C59—22no—
59C2×C4×C59—22no—
60C2×C4×C59—22no—
61C2×C4×C59—21no—
62C2×C4×C59—21no—
63C2×C4×C59—22no—
64C2×C4×C59—22no—
65C2×C4×C59—22no—
66C2×C4×C59C2×Q812yes—
67C2×Dic59—22no—
68C2×Dic59—22no—
69C2×Dic59—22no—
70C2×Dic59—22no—
71C2×Dic59—22no—
72C2×Dic59—22no—
73C2×Dic59—22no—
74C2×Dic59—22no—
75C2×Dic59—22no—
76C2×Dic59—24no—
77C2×Dic59C2×Q814yes—
78C22×C59C22×Q811yescharacteristic
79C22×C59H(5,𝔽2)11yescharacteristic
80C22×C59H(5,𝔽2)12yes—
81C22×C592−1+411yescharacteristic
82C22×C592−1+412yes—
83C4×C59—22no—
84C4×C59—41no—
85C4×C59—41no—
86C4×C59—42no—
87C4×C59—42no—
88Dic59—24no—
89Dic59—42no—
90Dic59—42no—
91Dic59—42no—
92#2843—591nomaximal, Sylow
93C2×C59#54412yes—
94C2×C59#54411yescharacteristic
95C2×C59#56011yescharacteristic
96C2×C59#56311yescharacteristic
97C2×C59#56312yes—
98#400—591no—
99#400—592no—
100#398—592no—
101#398—592no—
102#398—592no—
103#395—592no—
104#395D5911yescharacteristic
105#384—591no—
106#383—592no—
107C59#284311yescharacteristic, complemented, Sylow
108C22×Q8C2×D5911yescharacteristic
109C2×C4⋊C4—592no—
110C2×C4⋊C4—592no—
111C2×C4⋊C4—591no—
112C2×C4⋊C4—592no—
113C2×C4⋊C4—592no—
114C2×C4⋊C4—592no—
115C2×C4⋊C4—591no—
116C2×C4⋊C4C2×D5911yescharacteristic
117C2×C4⋊C4C2×D5912yes—
118C2×C42—591no—
119#95—592no—
120#95—592no—
121#95—592no—
122#95—592no—
123#95—592no—
124#95—592no—
125#95—591no—
126#95—592no—
127#95C2×D5912yes—
128#95C2×D5911yescharacteristic
129C2×Q8—41no—
130C2×Q8—42no—
131C22×C4—592no—
132C22×C4—592no—
133C22×C4—592no—
134C22×C4—592no—
135C22×C4C22×D5912yes—
136C22×C4C22×D5912yes—
137C22×C4C22×D5911yescharacteristic
138C22×C4C22×D5911yescharacteristic
139C22×C4C22×D5911yescharacteristic
140C4⋊C4—41no—
141C4⋊C4—42no—
142C4⋊C4—2362no—
143C4⋊C4—2362no—
144C4⋊C4—2362no—
145C4⋊C4—2362no—
146C4⋊C4—2362no—
147C4⋊C4—2361no—
148C4⋊C4—2361no—
149C42—594no—
150C23C23×D5911yescharacteristic
151Q8—44no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—22no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—594no—
165C2×C4—1182no—
166C2×C4—1182no—
167C2×C4—1182no—
168C2×C4—1182no—
169C2×C4—1182no—
170C2×C4—1182no—
171C2×C4—1182no—
172C2×C4—1182no—
173C2×C4—1184no—
174C2×C4—1182no—
175C2×C4Q8×D5912yes—
176C22C2×Q8×D5911yescharacteristic
177C22#1427377211yescharacteristic
178C22#1427377212yes—
179C22#1427377411yescharacteristic
180C22#1427377512yes—
181C4—22no—
182C4—42no—
183C4—41no—
184C4—42no—
185C4—41no—
186C4—1184no—
187C4—2362no—
188C4—2362no—
189C4—2362no—
190C2#1683802912yes—
191C2#1683803111yescharacteristic
192C2#1683814111yescharacteristic
193C2#1683815111yescharacteristic
194C2#1683815312yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#395C2
hypercenter#395D59
hypocenterC59#2843
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
51. C4×Dic59Q8semidirect
107. C59#2843semidirect