Finite Group Databasebeta

← #21432239

Subgroups — #21432239

Order 7552.

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

normal subgroups only

This group has 408 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#16837332C211yesmaximal, characteristic, complemented
2#16837330C212yesmaximal, complemented
3#16837330C212yesmaximal, complemented
4#16837325C212yesmaximal, complemented
5#16837322C211yesmaximal, characteristic, complemented
6#16837316C212yesmaximal
7#16837314C212yesmaximal, complemented
8#16837286C212yesmaximal, complemented
9C59×#390C211yesmaximal, characteristic
10C22×Dic118C2211yescharacteristic
11C2×C4⋊Dic59C2211yescharacteristic
12C2×Dic59⋊C4C2212yes—
13C2×Dic59⋊C4C2212yes—
14C2×Dic59⋊C4C2212yes—
15C2×C22⋊Dic59C2212yes—
16C2×C22⋊Dic59C2212yes—
17C2×C22⋊Dic59C2212yes—
18C2×C22⋊Dic59C2212yes—
19C59⋊#95C2212yes—
20C59⋊#95C2212yes—
21C59⋊#95C2212yes—
22C59⋊#95C2212yes—
23C59⋊#95C2212yes—
24C59⋊#95C2211yescharacteristic
25C59⋊#95C2211yescharacteristic
26C22×D4×C59C2211yescharacteristic
27C2×C4⋊C4×C59C2211yescharacteristic
28C2×C22⋊C4×C59C2212yes—
29C2×C22⋊C4×C59C2212yes—
30C2×C42×C59C2211yescharacteristic
31C24×C59C2312yes—
32C2×D4×C59—22no—
33C2×D4×C59—41no—
34C2×D4×C59—41no—
35C22×C4×C59C2312yes—
36C22×C4×C59C2311yescharacteristic
37C22×C4×C59C2311yescharacteristic
38C22×C4×C59C2311yescharacteristic
39C22×Dic59C2312yes—
40C22×Dic59C2312yes—
41C22×Dic59C2312yes—
42C22×Dic59C2312yes—
43C2×Dic118—42no—
44C2×Dic118—41no—
45C4⋊C4×C59—41no—
46C22⋊C4×C59—42no—
47C22⋊C4×C59—42no—
48C42×C59—41no—
49C22⋊Dic59—42no—
50C22⋊Dic59—42no—
51C22⋊Dic59—42no—
52C22⋊Dic59—42no—
53C4⋊Dic59—41no—
54Dic59⋊C4—24no—
55Dic59⋊C4—42no—
56Dic59⋊C4—42no—
57C23×C59—22no—
58C23×C59—22no—
59C23×C59—22no—
60C23×C59—22no—
61C23×C59—22no—
62C23×C59—22no—
63C23×C59—22no—
64C23×C59C2411yescharacteristic
65D4×C59—44no—
66C2×C4×C59—21no—
67C2×C4×C59—21no—
68C2×C4×C59—22no—
69C2×C4×C59—22no—
70C2×C4×C59—21no—
71C2×C4×C59—22no—
72C2×C4×C59—22no—
73C2×C4×C59—21no—
74C2×C4×C59—22no—
75C2×C4×C59#4112yes—
76C2×Dic59—22no—
77C2×Dic59—22no—
78C2×Dic59—22no—
79C2×Dic59—22no—
80C2×Dic59—22no—
81C2×Dic59—22no—
82C2×Dic59—22no—
83C2×Dic59—22no—
84C2×Dic59—22no—
85C2×Dic59—22no—
86C2×Dic59—22no—
87C2×Dic59—22no—
88Dic118—44no—
89C22×C59—42no—
90C22×C59—42no—
91C22×C59—42no—
92C22×C59—42no—
93C22×C59—42no—
94C22×C59—42no—
95C22×C59—42no—
96C22×C59C2×#4111yescharacteristic
97C22×C59H(5,𝔽2)11yescharacteristic
98C22×C59H(5,𝔽2)11yescharacteristic
99C22×C59H(5,𝔽2)12yes—
100C22×C592−1+412yes—
101C4×C59—22no—
102C4×C59—41no—
103C4×C59—41no—
104C4×C59—42no—
105Dic59—42no—
106Dic59—42no—
107Dic59—42no—
108Dic59—42no—
109#2830—591nomaximal, Sylow
110C2×C59—82no—
111C2×C59#53811yescharacteristic
112C2×C59#54212yes—
113C2×C59#56011yescharacteristic
114C2×C59#56212yes—
115C2×C59#56311yescharacteristic
116#398—591no—
117#397—592no—
118#397—592no—
119#396—592no—
120#395—591no—
121#394—592no—
122#393—592no—
123#390D5911yescharacteristic
124#387—592no—
125C59#283011yescharacteristic, complemented, Sylow
126C22×Q8—591no—
127C22×D4C2×D5911yescharacteristic
128C2×C4⋊C4—592no—
129C2×C4⋊C4—592no—
130C2×C4⋊C4—592no—
131C2×C4⋊C4—591no—
132C2×C4⋊C4C2×D5911yescharacteristic
133C2×C22⋊C4—592no—
134C2×C22⋊C4—592no—
135C2×C22⋊C4—592no—
136C2×C22⋊C4—592no—
137C2×C22⋊C4C2×D5912yes—
138C2×C22⋊C4C2×D5912yes—
139C2×C42C2×D5911yescharacteristic
140#95—592no—
141#95—592no—
142#95—592no—
143#95—592no—
144#95—592no—
145#95—591no—
146#95—591no—
147C24C22×D5912yes—
148C2×Q8—2362no—
149C2×Q8—2361no—
150C2×D4—22no—
151C2×D4—41no—
152C2×D4—41no—
153C22×C4—592no—
154C22×C4—592no—
155C22×C4—592no—
156C22×C4—592no—
157C22×C4C22×D5912yes—
158C22×C4C22×D5911yescharacteristic
159C22×C4C22×D5911yescharacteristic
160C22×C4C22×D5911yescharacteristic
161C4⋊C4—41no—
162C4⋊C4—1184no—
163C4⋊C4—2362no—
164C4⋊C4—2362no—
165C4⋊C4—2361no—
166C22⋊C4—42no—
167C22⋊C4—42no—
168C22⋊C4—2362no—
169C22⋊C4—2362no—
170C22⋊C4—2362no—
171C22⋊C4—2362no—
172C42—41no—
173C23—22no—
174C23—22no—
175C23—22no—
176C23—22no—
177C23—22no—
178C23—22no—
179C23—22no—
180C23C23×D5911yescharacteristic
181Q8—2364no—
182D4—44no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—1182no—
193C2×C4—1182no—
194C2×C4—1182no—
195C2×C4—1182no—
196C2×C4—1182no—
197C2×C4—1182no—
198C2×C4—1182no—
199C2×C4—1182no—
200C2×C4—1182no—
201C2×C4—1182no—
202C2×C4—1182no—
203C2×C4—1182no—
204C2×C4#1174568512yes—
205C22—42no—
206C22—42no—
207C22—42no—
208C22—42no—
209C22—42no—
210C22—42no—
211C22—42no—
212C22C2×#1174568511yescharacteristic
213C22#1427377211yescharacteristic
214C22#1427377212yes—
215C22#1427377211yescharacteristic
216C22#1427377412yes—
217C4—22no—
218C4—42no—
219C4—41no—
220C4—41no—
221C4—2362no—
222C4—2362no—
223C4—2362no—
224C4—2362no—
225C2—82no—
226C2#1683799011yescharacteristic
227C2#1683801712yes—
228C2#1683813911yescharacteristic
229C2#1683814712yes—
230C2#1683815211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#390C2
hypercenter#390D59
hypocenterC59#2830
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #16837332C2semidirect
2. #16837330C2semidirect
3. #16837330C2semidirect
4. #16837325C2semidirect
5. #16837322C2semidirect
7. #16837314C2semidirect
8. #16837286C2semidirect
125. C59#2830semidirect