Finite Group Databasebeta

← #21423110

Subgroups — #21423110

Order 7552.

232 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 53 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#16837730C211yesmaximal, characteristic, complemented
2#16837713C211yesmaximal, characteristic, complemented
3#16837327C211yesmaximal, characteristic, complemented
4#16837139C211yesmaximal, characteristic, complemented
5#16837136C211yesmaximal, characteristic, complemented
6#16837126C211yesmaximal, characteristic, complemented
7C59×#538C211yesmaximal, characteristic
8C2×C4⋊Dic59C2211yescharacteristic
9C2×C22⋊Dic59—21no—
10#14273660—21no—
11#14273658—21no—
12#14273651—21no—
13#14273648—21no—
14C22⋊(C59⋊C8)C2211yescharacteristic
15C22⋊(C59⋊C8)C2211yescharacteristic
16C59⋊#95—21no—
17C59⋊#95C2211yescharacteristic
18#126×C59—21no—
19#124×C59—21no—
20#123×C59—21no—
21C22⋊Q8×C59C2211yescharacteristic
22#121×C59—21no—
23#121×C59C2211yescharacteristic
24#120×C59—21no—
25C4×D4×C59—21no—
26C2×C22⋊C4×C59C2211yescharacteristic
27C24×C59D411yescharacteristic
28C2×Q8×C59D411yescharacteristic
29C2×D4×C59—21no—
30C2×D4×C59—21no—
31C2×D4×C59—21no—
32C2×D4×C59D411yescharacteristic
33C22×C4×C59—21no—
34C22×C4×C59D411yescharacteristic
35C22×C4×C59C2311yescharacteristic
36C22×Dic59—21no—
37C22×Dic59—21no—
38C4⋊C4×C59—21no—
39C4⋊C4×C59—21no—
40C4⋊C4×C59D411yescharacteristic
41C4⋊C4×C59D411yescharacteristic
42C22⋊C4×C59—21no—
43C22⋊C4×C59—21no—
44C22⋊C4×C59—21no—
45C22⋊C4×C59—21no—
46C22⋊C4×C59—21no—
47C22⋊C4×C59—21no—
48C22⋊C4×C59—21no—
49C42×C59—21no—
50C22⋊Dic59—42no—
51C4⋊Dic59—21no—
52C4⋊Dic59—21no—
53C2×C59⋊C8—21no—
54C2×C59⋊C8—21no—
55C23×C59—21no—
56C23×C59—21no—
57C23×C59—21no—
58C23×C59—21no—
59C23×C59—41no—
60C23×C59—41no—
61C23×C59C2×D411yescharacteristic
62Q8×C59—41no—
63D4×C59—41no—
64D4×C59—41no—
65D4×C59—41no—
66D4×C59—81no—
67D4×C59—81no—
68C2×C4×C59—21no—
69C2×C4×C59—21no—
70C2×C4×C59—21no—
71C2×C4×C59—21no—
72C2×C4×C59—41no—
73C2×C4×C59—41no—
74C2×C4×C59—81no—
75C2×C4×C59C2×D411yescharacteristic
76C2×C4×C59C2×D411yescharacteristic
77C2×Dic59—41no—
78C2×Dic59—41no—
79C2×Dic59—41no—
80C2×Dic59—41no—
81C2×Dic59—41no—
82C2×Dic59—41no—
83C59⋊C8—41no—
84C59⋊C8—41no—
85C22×C59—21no—
86C22×C59—21no—
87C22×C59—42no—
88C22×C59—41no—
89C22×C59—41no—
90C22×C59—41no—
91C22×C59—41no—
92C22×C59—41no—
93C22×C59—41no—
94C22×C59—81no—
95C22×C59#12011yescharacteristic
96C22×C59#13511yescharacteristic
97C22×C59AGL(1,ℤ/8)11yescharacteristic
98C4×C59—21no—
99C4×C59—21no—
100C4×C59—41no—
101C4×C59—41no—
102C4×C59—41no—
103C4×C59—41no—
104Dic59—81no—
105Dic59—81no—
106#1612—591nomaximal, Sylow
107C2×C59—21no—
108C2×C59—21no—
109C2×C59—81no—
110C2×C59—81no—
111C2×C59#44911yescharacteristic
112C2×C59#45511yescharacteristic
113C2×C59#45811yescharacteristic
114#538D5911yescharacteristic
115#483—591no—
116#480—591no—
117#397—591no—
118#328—591no—
119#327—591no—
120#323—591no—
121C59#161211yescharacteristic, complemented, Sylow
122#126—21no—
123#124—21no—
124#123—21no—
125C22⋊Q8C2×D5911yescharacteristic
126#121—21no—
127#121C2×D5911yescharacteristic
128#120—21no—
129C4×D4—21no—
130C2×C4⋊C4—591no—
131C2×C22⋊C4—1181no—
132C2×C22⋊C4C2×D5911yescharacteristic
133#107—1181no—
134#106—1181no—
135#103—1181no—
136#102—1181no—
137C22⋊C8—591no—
138C22⋊C8—591no—
139#95—591no—
140#95—1181no—
141C24C22⋊D5911yescharacteristic
142C2×Q8C22⋊D5911yescharacteristic
143C2×D4—21no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4C22⋊D5911yescharacteristic
147C22×C4—21no—
148C22×C4—1181no—
149C22×C4—1181no—
150C22×C4C22⋊D5911yescharacteristic
151C22×C4C22×D5911yescharacteristic
152C2×C8—1181no—
153C2×C8—1181no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—1181no—
157C4⋊C4—1181no—
158C4⋊C4C22⋊D5911yescharacteristic
159C4⋊C4C22⋊D5911yescharacteristic
160C22⋊C4—21no—
161C22⋊C4—21no—
162C22⋊C4—21no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—21no—
166C22⋊C4—21no—
167C22⋊C4—2362no—
168C42—21no—
169C23—21no—
170C23—21no—
171C23—21no—
172C23—21no—
173C23—41no—
174C23—41no—
175C23C2×C22⋊D5911yescharacteristic
176Q8—41no—
177D4—41no—
178D4—41no—
179D4—41no—
180D4—81no—
181D4—81no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—81no—
189C2×C4—2361no—
190C2×C4—2361no—
191C2×C4—2361no—
192C2×C4—2361no—
193C2×C4—2361no—
194C2×C4—2361no—
195C2×C4C2×C22⋊D5911yescharacteristic
196C2×C4C2×C22⋊D5911yescharacteristic
197C8—2361no—
198C8—2361no—
199C22—21no—
200C22—21no—
201C22—42no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—81no—
209C22#1427369611yescharacteristic
210C22#1427374711yescharacteristic
211C22#1427375211yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—41no—
216C4—41no—
217C4—41no—
218C4—4721no—
219C4—4721no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—81no—
224C2#1683754711yescharacteristic
225C2#1683758011yescharacteristic
226C2#1683759211yescharacteristic
subgroupG/H
centerC22#14273696
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC59×#538C2
socleC22×C59#120
hypercenter#538D59
hypocenterC59#1612
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #538

Complements

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

NH ≅ G/Ntype
1. #16837730C2semidirect
2. #16837713C2semidirect
3. #16837327C2semidirect
4. #16837139C2semidirect
5. #16837136C2semidirect
6. #16837126C2semidirect
121. C59#1612semidirect