Finite Group Databasebeta

← #21432243

Subgroups — #21432243

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#16837331C212yesmaximal, complemented
2#16837329C212yesmaximal, complemented
3#16837324C212yesmaximal, complemented
4#16837322C211yesmaximal, characteristic, complemented
5#16837319C212yesmaximal
6#16837315C212yesmaximal, complemented
7#16837303C211yesmaximal, characteristic
8#16837288C212yesmaximal, complemented
9C59×#398C211yesmaximal, characteristic, complemented
10C22×Dic118C2211yescharacteristic
11C22×D236C2211yescharacteristic
12C2×C4⋊Dic59C2212yes—
13C2×Dic59⋊C4C2212yes—
14C2×(C2×D59)⋊C4C2212yes—
15C2×(C2×D59)⋊C4C2212yes—
16C2×(C2×D59)⋊C4C2212yes—
17C2×(C2×D59)⋊C4C2212yes—
18C2×(C2×D59)⋊C4C2212yes—
19C2×(C2×D59)⋊C4C2212yes—
20C2×C4×Dic59C2211yescharacteristic
21C59⋊#95C2212yes—
22C59⋊#95C2212yes—
23C59⋊#95C2212yes—
24C59⋊#95C2212yes—
25C59⋊#95C2211yescharacteristic
26C2×C4⋊C4×C59C2212yes—
27C2×C4⋊C4×C59C2211yescharacteristic
28C2×C4⋊C4×C59C2211yescharacteristic
29#95×C59C2212yes—
30#95×C59C2211yescharacteristic
31C23×D59C2312yes—
32C22×C4×C59C2312yes—
33C22×C4×C59C2311yescharacteristic
34C22×C4×C59C2312yes—
35C22×C4×C59C2311yescharacteristic
36C22×C4×C59C2311yescharacteristic
37C22×Dic59C2312yes—
38C22×Dic59C2312yes—
39C22×Dic59C2312yes—
40C2×D236—22no—
41C2×D236—41no—
42C2×D236—41no—
43C2×Dic118—42no—
44C2×Dic118—41no—
45C4⋊C4×C59—24no—
46C4⋊C4×C59—41no—
47C4⋊C4×C59—41no—
48(C2×D59)⋊C4—42no—
49(C2×D59)⋊C4—42no—
50(C2×D59)⋊C4—42no—
51(C2×D59)⋊C4—42no—
52(C2×D59)⋊C4—42no—
53(C2×D59)⋊C4—42no—
54C4⋊Dic59—42no—
55Dic59⋊C4—42no—
56C4×Dic59—41no—
57C23×C59C2411yescharacteristic
58C22×D59—22no—
59C22×D59—22no—
60C22×D59—22no—
61C22×D59—22no—
62C22×D59—22no—
63C22×D59—22no—
64C22×D59—22no—
65C2×C4×C59—21no—
66C2×C4×C59—21no—
67C2×C4×C59—22no—
68C2×C4×C59—22no—
69C2×C4×C59—22no—
70C2×C4×C59—22no—
71C2×C4×C59—22no—
72C2×C4×C59—22no—
73C2×C4×C59—22no—
74C2×C4×C59—21no—
75C2×C4×C59—21no—
76C2×C4×C59—22no—
77C2×C4×C59#4112yes—
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—
87D236—44no—
88Dic118—44no—
89C22×C59C2×#4111yescharacteristic
90C22×C59H(5,𝔽2)11yescharacteristic
91C22×C59H(5,𝔽2)11yescharacteristic
92C22×C59H(5,𝔽2)12yes—
93C22×C592−1+412yes—
94C2×D59—42no—
95C2×D59—42no—
96C2×D59—42no—
97C2×D59—42no—
98C2×D59—42no—
99C2×D59—42no—
100C2×D59—42no—
101C4×C59—22no—
102C4×C59—42no—
103C4×C59—42no—
104C4×C59—41no—
105C4×C59—41no—
106Dic59—42no—
107Dic59—42no—
108Dic59—42no—
109#2830—591nomaximal, Sylow
110C2×C59#53811yescharacteristic
111C2×C59#54212yes—
112C2×C59#56011yescharacteristic
113C2×C59#56212yes—
114C2×C59#56311yescharacteristic
115D59—82no—
116#398D5911yescharacteristic, complemented
117#397—592no—
118#397—592no—
119#396—592no—
120#395—591no—
121#394—592no—
122#393—592no—
123#390—591no—
124#387—592no—
125C59#283011yescharacteristic, complemented, Sylow
126C22×Q8—591no—
127C22×D4—591no—
128C2×C4⋊C4—592no—
129C2×C4⋊C4—592no—
130C2×C4⋊C4C2×D5912yes—
131C2×C4⋊C4C2×D5911yescharacteristic
132C2×C4⋊C4C2×D5911yescharacteristic
133C2×C22⋊C4—592no—
134C2×C22⋊C4—592no—
135C2×C22⋊C4—592no—
136C2×C22⋊C4—592no—
137C2×C22⋊C4—592no—
138C2×C22⋊C4—592no—
139C2×C42—591no—
140#95—592no—
141#95—592no—
142#95—592no—
143#95—592no—
144#95—591no—
145#95C2×D5912yes—
146#95C2×D5911yescharacteristic
147C24—592no—
148C2×Q8—2361no—
149C2×Q8—2362no—
150C2×D4—1182no—
151C2×D4—2361no—
152C2×D4—2361no—
153C22×C4—592no—
154C22×C4—592no—
155C22×C4—592no—
156C22×C4C22×D5912yes—
157C22×C4C22×D5911yescharacteristic
158C22×C4C22×D5912yes—
159C22×C4C22×D5911yescharacteristic
160C22×C4C22×D5911yescharacteristic
161C4⋊C4—24no—
162C4⋊C4—41no—
163C4⋊C4—41no—
164C4⋊C4—2362no—
165C4⋊C4—2362no—
166C22⋊C4—2362no—
167C22⋊C4—2362no—
168C22⋊C4—2362no—
169C22⋊C4—2362no—
170C22⋊C4—2362no—
171C22⋊C4—2362no—
172C42—2361no—
173C23—1182no—
174C23—1182no—
175C23—1182no—
176C23—1182no—
177C23—1182no—
178C23—1182no—
179C23—1182no—
180C23C23×D5911yescharacteristic
181Q8—2364no—
182D4—2364no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
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#1174568712yes—
205C22—2362no—
206C22—2362no—
207C22—2362no—
208C22—2362no—
209C22—2362no—
210C22—2362no—
211C22—2362no—
212C22C2×#1174568711yescharacteristic
213C22#1427377211yescharacteristic
214C22#1427377311yescharacteristic
215C22#1427377312yes—
216C22#1427377512yes—
217C4—22no—
218C4—42no—
219C4—42no—
220C4—41no—
221C4—41no—
222C4—2362no—
223C4—2362no—
224C4—2362no—
225C2—4722no—
226C2#1683798911yescharacteristic
227C2#1683802512yes—
228C2#1683814211yescharacteristic
229C2#1683815012yes—
230C2#1683815111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#398C2
hypercenter#398D59
hypocenterC59#2830
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. #16837331C2semidirect
2. #16837329C2semidirect
3. #16837324C2semidirect
4. #16837322C2semidirect
6. #16837315C2semidirect
8. #16837288C2semidirect
9. C59×#398C2semidirect
116. #398D59semidirect
125. C59#2830semidirect