Finite Group Databasebeta

← #21424552

Subgroups — #21424552

Order 7552.

378 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 89 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
1C2×#14273710C211yesmaximal, characteristic
2C2×#14273686C211yesmaximal, characteristic, complemented
3C2×#14273641C212yesmaximal
4#16837168C212yesmaximal, complemented
5C59×#381C211yesmaximal, characteristic, complemented
6C22×C22⋊D59C2211yescharacteristic
7#14273710—21no—
8#14273710—21no—
9#14273710—22no—
10#14273686—24no—
11C2×C4⋊Dic59—21no—
12C2×Dic59⋊C4C412yescomplemented
13C2×C22⋊Dic59C2211yescharacteristic
14C2×C22⋊Dic59C2212yes—
15C2×(C2×D59)⋊C4C412yescomplemented
16C2×C4×Dic59—21no—
17#14273641—24no—
18C23×C4×C59C2211yescharacteristic
19C2×C22⋊C4×C59C2212yes—
20#95×C59—22no—
21C24×C59C2311yescharacteristic
22C23×D59C2×C411yescharacteristic
23C22×C4×C59—22no—
24C22×C4×C59—22no—
25C22×C4×C59—22no—
26C22×C4×C59C2×C412yes—
27C22×C4×C59D411yescharacteristic
28C22×C4×C59D411yescharacteristic
29C22×C4×C59D412yes—
30C2×C22⋊D59—22no—
31C2×C22⋊D59—21no—
32C2×C22⋊D59—21no—
33C2×C22⋊D59—22no—
34C22×Dic59—22no—
35C22×Dic59C2×C411yescharacteristic
36C22×Dic59C2×C412yes—
37C22⋊C4×C59—22no—
38C22⋊C4×C59—22no—
39C22⋊Dic59—22no—
40C22⋊Dic59—21no—
41C22⋊Dic59—21no—
42C22⋊Dic59D414yes—
43(C2×D59)⋊C4—22no—
44(C2×D59)⋊C4—22no—
45C4⋊Dic59—24no—
46Dic59⋊C4—22no—
47Dic59⋊C4—22no—
48C4×Dic59—24no—
49C23×C59—42no—
50C23×C59C22×C411yescharacteristic
51C23×C59C2×D411yescharacteristic
52C23×C59C2×D412yes—
53C23×C59C2×D411yescharacteristic
54C23×C59#4112yes—
55C22×D59—21no—
56C22×D59—22no—
57C22×D59—42no—
58C2×C4×C59—24no—
59C2×C4×C59—21no—
60C2×C4×C59—21no—
61C2×C4×C59—24no—
62C2×C4×C59—21no—
63C2×C4×C59—21no—
64C2×C4×C59—44no—
65C2×C4×C59—42no—
66C2×C4×C59C22⋊C412yes—
67C2×C4×C59C22⋊C412yes—
68C22⋊D59—41no—
69C22⋊D59—42no—
70C22⋊D59—41no—
71C2×Dic59—21no—
72C2×Dic59—22no—
73C2×Dic59—22no—
74C2×Dic59—24no—
75C2×Dic59—44no—
76C2×Dic59—42no—
77C22×C59—22no—
78C22×C59—22no—
79C22×C59—22no—
80C22×C59—42no—
81C22×C59—42no—
82C22×C59C2×C22⋊C411yescharacteristic
83C22×C59C4×D412yes—
84C22×C59#12011yescharacteristic
85C22×C59#12112yes—
86C22×C59#12311yescharacteristic
87C2×D59—41no—
88C2×D59—42no—
89C2×D59—82no—
90C4×C59—22no—
91C4×C59—22no—
92C4×C59—82no—
93Dic59—44no—
94Dic59—41no—
95Dic59—42no—
96#1899—591nomaximal, Sylow
97C2×C59—21no—
98C2×C59—22no—
99C2×C59—22no—
100C2×C59—21no—
101C2×C59#38611yescharacteristic
102C2×C59#41012yes—
103D59—81no—
104C2×#123—591no—
105C2×#117—591no—
106C2×#99—592no—
107#381D5911yescharacteristic, complemented
108#342—592no—
109C59#189911yescharacteristic, complemented, Sylow
110C22×D4—591no—
111C23×C4C2×D5911yescharacteristic
112#123—1181no—
113#123—1181no—
114#123—1182no—
115#117—1184no—
116C2×C4⋊C4—592no—
117C2×C4⋊C4—1181no—
118C2×C22⋊C4—592no—
119C2×C22⋊C4—591no—
120C2×C22⋊C4—592no—
121C2×C22⋊C4C2×D5912yes—
122C2×C42—1181no—
123#99—1184no—
124#95—22no—
125C24—591no—
126C24C22×D5911yescharacteristic
127C2×D4—1181no—
128C2×D4—1182no—
129C2×D4—1182no—
130C2×D4—1181no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—591no—
135C22×C4—592no—
136C22×C4—1182no—
137C22×C4C4×D5912yes—
138C22×C4D23611yescharacteristic
139C22×C4D23611yescharacteristic
140C22×C4C22⋊D5912yes—
141C4⋊C4—1184no—
142C4⋊C4—1182no—
143C4⋊C4—1182no—
144C22⋊C4—22no—
145C22⋊C4—22no—
146C22⋊C4—594no—
147C22⋊C4—1181no—
148C22⋊C4—1182no—
149C22⋊C4—1181no—
150C22⋊C4—1182no—
151C22⋊C4—1182no—
152C42—1184no—
153C23—42no—
154C23—1182no—
155C23—1181no—
156C23—2362no—
157C23C2×C4×D5911yescharacteristic
158C23C2×D23611yescharacteristic
159C23D4×D5912yes—
160C23#1174568712yes—
161C23C2×C22⋊D5911yescharacteristic
162D4—2361no—
163D4—2362no—
164D4—2361no—
165C2×C4—24no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—24no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—44no—
172C2×C4—42no—
173C2×C4—1182no—
174C2×C4—1181no—
175C2×C4—1182no—
176C2×C4—1184no—
177C2×C4—2364no—
178C2×C4—2362no—
179C2×C4(C2×D59)⋊C412yes—
180C2×C4(C2×D59)⋊C412yes—
181C22—22no—
182C22—22no—
183C22—22no—
184C22—42no—
185C22—42no—
186C22—4722no—
187C22—2361no—
188C22—2362no—
189C22C2×(C2×D59)⋊C411yescharacteristic
190C22(C22⋊D59)⋊C412yes—
191C22#1427369711yescharacteristic
192C22#1427369912yes—
193C22#1427371111yescharacteristic
194C4—22no—
195C4—22no—
196C4—82no—
197C4—2364no—
198C4—2361no—
199C4—2362no—
200C2—22no—
201C2—21no—
202C2—22no—
203C2—21no—
204C2—4721no—
205C2#1683727911yescharacteristic
206C2#1683737512yes—
subgroupG/H
centerC22C2×(C2×D59)⋊C4
commutatorC23×C59C22×C4
FrattiniC24C22×D59
FittingC59×#381C2
socleC22×C59C2×C22⋊C4
hypercenter#381D59
hypocenterC59#1899
LCSG ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×#14273686C2semidirect
4. #16837168C2semidirect
5. C59×#381C2semidirect
12. C2×Dic59⋊C4C4semidirect
15. C2×(C2×D59)⋊C4C4semidirect
107. #381D59semidirect
109. C59#1899semidirect