Finite Group Databasebeta

← #21423102

Subgroups — #21423102

Order 7552.

210 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 51 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#16838031C211yesmaximal, characteristic
2#16837732C211yesmaximal, characteristic
3#16837333C211yesmaximal, characteristic
4#16837140C211yesmaximal, characteristic
5#16837139C211yesmaximal, characteristic
6#16837127C211yesmaximal, characteristic
7C59×#483C211yesmaximal, characteristic
8#14273726—21no—
9#14273725—21no—
10#14273717—21no—
11#14273717—21no—
12#14273706C2211yescharacteristic
13#14273704—21no—
14#14273683—21no—
15C2×Dic59⋊C4—21no—
16C2×Dic59⋊C4C2211yescharacteristic
17#14273658—21no—
18#14273650—21no—
19C22⋊(C59⋊C8)C2211yescharacteristic
20C59⋊#95—21no—
21C59⋊#95C2211yescharacteristic
22C22⋊Q8×C59C2211yescharacteristic
23C2×C4⋊C4×C59C2211yescharacteristic
24#106×C59—21no—
25#103×C59—21no—
26C22⋊C8×C59C2211yescharacteristic
27C2×Q8×C59D411yescharacteristic
28C22×C4×C59—21no—
29C22×C4×C59C2311yescharacteristic
30C22×Dic59—21no—
31C22×Dic59D411yescharacteristic
32C22×Dic59D411yescharacteristic
33C2×Dic118—21no—
34C2×Dic118D411yescharacteristic
35C2×C8×C59—21no—
36C4⋊C4×C59—21no—
37C4⋊C4×C59—21no—
38C4⋊C4×C59—21no—
39C4⋊C4×C59D411yescharacteristic
40C22⋊C4×C59—21no—
41C22⋊Dic59—21no—
42C4⋊Dic59—21no—
43C4⋊Dic59D411yescharacteristic
44Dic59⋊C4—21no—
45Dic59⋊C4—21no—
46Dic59⋊C4—21no—
47Dic59⋊C4—21no—
48Dic59⋊C4—21no—
49Dic59⋊C4—21no—
50Dic59⋊C4—21no—
51Dic59⋊C4—42no—
52C4×Dic59—21no—
53C4×Dic59—21no—
54C2×C59⋊C8—21no—
55C23×C59C2×D411yescharacteristic
56Q8×C59—41no—
57C2×C4×C59—21no—
58C2×C4×C59—21no—
59C2×C4×C59—41no—
60C2×C4×C59—41no—
61C2×C4×C59—41no—
62C2×C4×C59—41no—
63C2×C4×C59C2×D411yescharacteristic
64C2×C4×C59C2×D411yescharacteristic
65C2×Dic59—21no—
66C2×Dic59—21no—
67C2×Dic59—22no—
68C2×Dic59—21no—
69C2×Dic59—21no—
70C2×Dic59—21no—
71C2×Dic59—41no—
72C2×Dic59—41no—
73C2×Dic59—41no—
74C2×Dic59SD1612yes—
75Dic118—41no—
76Dic118—81no—
77C8×C59—41no—
78C59⋊C8—41no—
79C22×C59—21no—
80C22×C59—21no—
81C22×C59#12011yescharacteristic
82C22×C59C2×SD1611yescharacteristic
83C22×C59#13711yescharacteristic
84C4×C59—21no—
85C4×C59—21no—
86C4×C59—41no—
87C4×C59—41no—
88C4×C59—81no—
89Dic59—22no—
90Dic59—42no—
91Dic59—41no—
92Dic59—41no—
93Dic59—41no—
94#1611—591nomaximal, Sylow
95C2×C59—21no—
96C2×C59—21no—
97C2×C59#44811yescharacteristic
98C2×C59#45611yescharacteristic
99C2×C59#45811yescharacteristic
100#544—591no—
101#483—591no—
102#483D5911yescharacteristic
103#398—591no—
104#328—591no—
105#328—591no—
106#324—591no—
107C59#161111yescharacteristic, complemented, Sylow
108C4⋊Q8—1181no—
109C4⋊Q8—1181no—
110#125—1181no—
111#125—1181no—
112C22⋊Q8—591no—
113C22⋊Q8—1181no—
114C22⋊Q8C2×D5911yescharacteristic
115#117—1181no—
116C2×C4⋊C4—591no—
117C2×C4⋊C4—1181no—
118C2×C4⋊C4C2×D5911yescharacteristic
119#106—21no—
120#106—1181no—
121#103—21no—
122#103—1181no—
123C22⋊C8—591no—
124C22⋊C8C2×D5911yescharacteristic
125#95—591no—
126#95—1181no—
127C2×Q8—591no—
128C2×Q8—1181no—
129C2×Q8C22⋊D5911yescharacteristic
130C22×C4—21no—
131C22×C4—591no—
132C22×C4—591no—
133C22×C4—1181no—
134C22×C4C22×D5911yescharacteristic
135C2×C8—21no—
136C2×C8—1181no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—591no—
141C4⋊C4—1181no—
142C4⋊C4—1181no—
143C4⋊C4—1181no—
144C4⋊C4—1181no—
145C4⋊C4—1181no—
146C4⋊C4—1181no—
147C4⋊C4—1181no—
148C4⋊C4—1181no—
149C4⋊C4—2362no—
150C4⋊C4C22⋊D5911yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—1181no—
153C42—1181no—
154C42—1181no—
155C23D4×D5911yescharacteristic
156Q8—41no—
157Q8—4721no—
158Q8—2361no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—592no—
166C2×C4—1181no—
167C2×C4—1181no—
168C2×C4—1182no—
169C2×C4—1181no—
170C2×C4—1181no—
171C2×C4—1181no—
172C2×C4—2361no—
173C2×C4—2361no—
174C2×C4—2361no—
175C2×C4D4×D5911yescharacteristic
176C2×C4C2×C22⋊D5911yescharacteristic
177C8—41no—
178C8—2361no—
179C22—21no—
180C22—21no—
181C22#1427369511yescharacteristic
182C22SD16×D5911yescharacteristic
183C22#1427375611yescharacteristic
184C4—21no—
185C4—21no—
186C4—41no—
187C4—41no—
188C4—81no—
189C4—1182no—
190C4—2362no—
191C4—2361no—
192C4—2361no—
193C4—2361no—
194C2—21no—
195C2—21no—
196C2#1683753911yescharacteristic
197C2#1683758311yescharacteristic
198C2#1683759111yescharacteristic
subgroupG/H
centerC22#14273695
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC59×#483C2
socleC22×C59#120
hypercenter#483D59
hypocenterC59#1611
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
107. C59#1611semidirect