Finite Group Databasebeta

← #21426692

Subgroups — #21426692

Order 7552.

672 conjugacy classes of subgroups; only the 189 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 189 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
1C22×C22⋊Dic59C211yesmaximal, characteristic
2#16837296C214yesmaximal, complemented
3#16837290C214yesmaximal, complemented
4#16837260C212yesmaximal, complemented
5#16837258C211yesmaximal, characteristic
6C22⋊C4×Dic59C212yesmaximal, complemented
7C59×#379C211yesmaximal, characteristic
8C23×Dic59C2211yescharacteristic
9C23×Dic59C2211yescharacteristic
10C2×Dic59⋊C4C2214yescomplemented
11C2×C22⋊Dic59C418yescomplemented
12C2×C22⋊Dic59C2212yes—
13C2×C22⋊Dic59C2212yes—
14C2×C22⋊Dic59C2212yes—
15C2×C22⋊Dic59C2212yes—
16C2×C22⋊Dic59C2212yes—
17C2×C4×Dic59C2214yescomplemented
18C59⋊#95C2214yescomplemented
19C59⋊#95C2214yescomplemented
20C25×C59C2211yescharacteristic
21C2×C22⋊C4×C59C2212yes—
22C2×C22⋊C4×C59C2212yes—
23C2×C22⋊C4×C59C2212yes—
24C24×C59—24no—
25C24×C59—42no—
26C24×C59—42no—
27C24×C59C2×C414yes—
28C24×C59C2311yescharacteristic
29C24×C59C2311yescharacteristic
30C24×C59C2311yescharacteristic
31C22×C4×C59C2314yes—
32C22×Dic59—42no—
33C22×Dic59—42no—
34C22×Dic59C2×C414yes—
35C22×Dic59C2×C414yes—
36C22×Dic59C2314yes—
37C22×Dic59C2312yes—
38C22×Dic59C2312yes—
39C22⋊C4×C59—24no—
40C22⋊C4×C59—42no—
41C22⋊C4×C59—42no—
42C22⋊Dic59—24no—
43C22⋊Dic59—42no—
44C22⋊Dic59—42no—
45C22⋊Dic59C2×C418yes—
46C22⋊Dic59C2×C418yes—
47Dic59⋊C4—44no—
48C4×Dic59—44no—
49C23×C59—22no—
50C23×C59—22no—
51C23×C59—28no—
52C23×C59—22no—
53C23×C59—22no—
54C23×C59—22no—
55C23×C59—22no—
56C23×C59—22no—
57C23×C59—22no—
58C23×C59—44no—
59C23×C59—44no—
60C23×C59—416no—
61C23×C59C22×C412yes—
62C23×C59C22×C412yes—
63C23×C59C22×C412yes—
64C23×C59#4114yes—
65C23×C59C2411yescharacteristic
66C2×C4×C59—24no—
67C2×C4×C59—24no—
68C2×C4×C59—24no—
69C2×Dic59—24no—
70C2×Dic59—24no—
71C2×Dic59—24no—
72C2×Dic59—24no—
73C2×Dic59—24no—
74C2×Dic59—44no—
75C2×Dic59—44no—
76C2×Dic59C22×C414yes—
77C2×Dic59C22×C414yes—
78C22×C59—22no—
79C22×C59—22no—
80C22×C59—28no—
81C22×C59—22no—
82C22×C59—22no—
83C22×C59—22no—
84C22×C59—22no—
85C22×C59—22no—
86C22×C59—22no—
87C22×C59—416no—
88C22×C59—44no—
89C22×C59—44no—
90C22×C59#11714yes—
91C22×C59C23×C411yescharacteristic
92C22×C59C2×#4112yes—
93C22×C59H(5,𝔽2)12yes—
94C22×C59H(5,𝔽2)12yes—
95C4×C59—44no—
96Dic59—24no—
97Dic59—24no—
98Dic59—44no—
99#2312—591nomaximal, Sylow
100C2×C59—24no—
101C2×C59—42no—
102C2×C59—42no—
103C2×C59C2×#11711yescharacteristic
104C2×C59#51811yescharacteristic
105C2×C59#51811yescharacteristic
106C2×C59#53814yes—
107C22×C22⋊C4—591no—
108#388—594no—
109#388—594no—
110#380—592no—
111#379—591no—
112#379D5911yescharacteristic
113C4×C22⋊C4—592no—
114C59#231211yescharacteristic, complemented, Sylow
115C25C2×D5911yescharacteristic
116C23×C4—591no—
117C23×C4—591no—
118C2×C4⋊C4—594no—
119C2×C22⋊C4—598no—
120C2×C22⋊C4—592no—
121C2×C22⋊C4—592no—
122C2×C22⋊C4—592no—
123C2×C22⋊C4—592no—
124C2×C22⋊C4—592no—
125C2×C22⋊C4C2×D5912yes—
126C2×C22⋊C4C2×D5912yes—
127C2×C22⋊C4C2×D5912yes—
128C2×C42—594no—
129#95—594no—
130#95—594no—
131C24—24no—
132C24—42no—
133C24—42no—
134C24C4×D5914yes—
135C24C22×D5911yescharacteristic
136C24C22×D5911yescharacteristic
137C24C22×D5911yescharacteristic
138C22×C4—592no—
139C22×C4—592no—
140C22×C4—594no—
141C22×C4—594no—
142C22×C4—594no—
143C22×C4—2362no—
144C22×C4—2362no—
145C22×C4C22×D5914yes—
146C4⋊C4—2364no—
147C22⋊C4—24no—
148C22⋊C4—42no—
149C22⋊C4—42no—
150C22⋊C4—598no—
151C22⋊C4—598no—
152C22⋊C4—1184no—
153C22⋊C4—2362no—
154C22⋊C4—2362no—
155C42—2364no—
156C23—22no—
157C23—22no—
158C23—28no—
159C23—22no—
160C23—22no—
161C23—22no—
162C23—22no—
163C23—22no—
164C23—22no—
165C23—44no—
166C23—44no—
167C23—416no—
168C23C2×C4×D5912yes—
169C23C2×C4×D5912yes—
170C23C2×C4×D5912yes—
171C23#1174568714yes—
172C23C23×D5911yescharacteristic
173C2×C4—24no—
174C2×C4—24no—
175C2×C4—24no—
176C2×C4—594no—
177C2×C4—594no—
178C2×C4—1184no—
179C2×C4—1184no—
180C2×C4—1184no—
181C2×C4—1184no—
182C2×C4—1184no—
183C2×C4—2364no—
184C2×C4—2364no—
185C22—28no—
186C22—22no—
187C22—22no—
188C22—22no—
189C22—22no—
190C22—22no—
191C22—22no—
192C22—22no—
193C22—22no—
194C22—416no—
195C22—44no—
196C22—44no—
197C22#1427368314yes—
198C22C22×C4×D5911yescharacteristic
199C22C2×#1174568712yes—
200C22#1427377212yes—
201C22#1427377212yes—
202C4—44no—
203C4—1184no—
204C4—1184no—
205C4—2364no—
206C2—24no—
207C2—42no—
208C2—42no—
209C2C2×#1427368311yescharacteristic
210C2#1683787511yescharacteristic
211C2#1683787511yescharacteristic
212C2#1683798714yes—
subgroupG/H
center, FrattiniC23C23×D59
commutatorC22×C59C23×C4
FittingC59×#379C2
socleC23×C59C24
hypercenter#379D59
hypocenterC59#2312
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
2. #16837296C2semidirect
3. #16837290C2semidirect
4. #16837260C2semidirect
6. C22⋊C4×Dic59C2semidirect
10. C2×Dic59⋊C4C22semidirect
11. C2×C22⋊Dic59C4semidirect
17. C2×C4×Dic59C22semidirect
18. C59⋊#95C22semidirect
19. C59⋊#95C22semidirect
114. C59#2312semidirect