Finite Group Databasebeta

← #21425517

Subgroups — #21425517

Order 7552.

222 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 79 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×#14273651C211yesmaximal, characteristic
2#16837309C211yesmaximal, characteristic
3#16837267C211yesmaximal, characteristic
4#16837165C211yesmaximal, characteristic
5#16837164C211yesmaximal, characteristic
6#16837156C211yesmaximal, characteristic
7C2×#103×C59C211yesmaximal, characteristic
8C22×C59⋊C8C2211yescharacteristic
9C2×C4⋊Dic59C2211yescharacteristic
10C2×C4⋊Dic59C2211yescharacteristic
11C2×C4×Dic59C2211yescharacteristic
12#14273651—22no—
13C59⋊#95—21no—
14C59⋊#95—21no—
15C59⋊#95—21no—
16C59⋊#95—21no—
17C22×Q8×C59C2211yescharacteristic
18C22×C8×C59C2211yescharacteristic
19C2×C4⋊C4×C59C2211yescharacteristic
20#103×C59—22no—
21C2×Q8×C59—21no—
22C2×Q8×C59—21no—
23C2×Q8×C59—21no—
24C2×Q8×C59—21no—
25C2×Q8×C59—21no—
26C2×Q8×C59D412yes—
27C22×C4×C59—21no—
28C22×C4×C59—21no—
29C22×C4×C59C2311yescharacteristic
30C22×Dic59—21no—
31C22×Dic59—21no—
32C22×Dic59D411yescharacteristic
33C22×Dic59D411yescharacteristic
34C2×C8×C59—21no—
35C2×C8×C59—21no—
36C2×C8×C59—21no—
37C4⋊C4×C59—21no—
38C4⋊C4×C59—21no—
39C4⋊Dic59—21no—
40C4⋊Dic59—21no—
41C4⋊Dic59—21no—
42C4⋊Dic59—21no—
43C4×Dic59—21no—
44C4×Dic59—21no—
45C2×C59⋊C8—21no—
46C2×C59⋊C8—21no—
47C2×C59⋊C8—21no—
48C23×C59C2×D411yescharacteristic
49Q8×C59—22no—
50Q8×C59—22no—
51Q8×C59—41no—
52Q8×C59—41no—
53C2×C4×C59—22no—
54C2×C4×C59—41no—
55C2×C4×C59—41no—
56C2×C4×C59—41no—
57C2×C4×C59—41no—
58C2×C4×C59—41no—
59C2×C4×C59C2×D411yescharacteristic
60C2×C4×C59#4111yescharacteristic
61C2×C4×C59#4111yescharacteristic
62C2×C4×C59#4111yescharacteristic
63C2×C4×C59#4111yescharacteristic
64C2×C4×C59#4111yescharacteristic
65C2×Dic59—21no—
66C2×Dic59—21no—
67C2×Dic59—21no—
68C2×Dic59—21no—
69C2×Dic59—21no—
70C2×Dic59—21no—
71C2×Dic59—41no—
72C2×Dic59—41no—
73C2×Dic59—41no—
74C2×Dic59—41no—
75C2×Dic59—41no—
76C2×Dic59—41no—
77C8×C59—41no—
78C59⋊C8—41no—
79C22×C59#12111yescharacteristic
80C22×C59#12311yescharacteristic
81C22×C59#12411yescharacteristic
82C22×C59#13511yescharacteristic
83C22×C59#13511yescharacteristic
84C22×C59#13711yescharacteristic
85C22×C59#13711yescharacteristic
86C4×C59—42no—
87C4×C59—81no—
88C4×C59#12311yescharacteristic
89C4×C59#12311yescharacteristic
90C4×C59#12611yescharacteristic
91C4×C59#12611yescharacteristic
92Dic59—41no—
93Dic59—41no—
94Dic59—81no—
95Dic59—81no—
96#2074—591nomaximal, Sylow
97C2×C59#39711yescharacteristic
98C2×C59#46411yescharacteristic
99C2×C59#46411yescharacteristic
100C2×C59#48511yescharacteristic
101C2×C59#48511yescharacteristic
102C2×C59#48811yescharacteristic
103C2×C59#49111yescharacteristic
104C2×#103—591no—
105C2×#103D5911yescharacteristic
106#391—591no—
107#382—591no—
108#340—591no—
109#340—591no—
110#336—591no—
111C59#207411yescharacteristic, complemented, Sylow
112C22×Q8C2×D5911yescharacteristic
113C22×C8—591no—
114C22×C8C2×D5911yescharacteristic
115C2×C4⋊C4—591no—
116C2×C4⋊C4—591no—
117C2×C4⋊C4C2×D5911yescharacteristic
118C2×C42—591no—
119#103—22no—
120#103—1182no—
121#95—1181no—
122#95—1181no—
123#95—1181no—
124#95—1181no—
125C2×Q8—21no—
126C2×Q8—21no—
127C2×Q8—21no—
128C2×Q8—21no—
129C2×Q8—21no—
130C2×Q8C22⋊D5912yes—
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—591no—
134C22×C4—591no—
135C22×C4—1181no—
136C22×C4—1181no—
137C22×C4C22×D5911yescharacteristic
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—21no—
141C2×C8—1181no—
142C2×C8—1181no—
143C2×C8—1181no—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—1181no—
147C4⋊C4—1181no—
148C4⋊C4—1181no—
149C4⋊C4—1181no—
150C42—1181no—
151C42—1181no—
152C23D4×D5911yescharacteristic
153Q8—22no—
154Q8—22no—
155Q8—41no—
156Q8—41no—
157C2×C4—22no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—1181no—
164C2×C4—1181no—
165C2×C4—1181no—
166C2×C4—1181no—
167C2×C4—1181no—
168C2×C4—1181no—
169C2×C4—2361no—
170C2×C4—2361no—
171C2×C4—2361no—
172C2×C4—2361no—
173C2×C4—2361no—
174C2×C4—2361no—
175C2×C4#1174568511yescharacteristic
176C2×C4#1174568511yescharacteristic
177C2×C4#1174568711yescharacteristic
178C2×C4#1174568711yescharacteristic
179C2×C4#1174568711yescharacteristic
180C2×C4C2×C22⋊D5911yescharacteristic
181C8—41no—
182C8—2361no—
183C22#1427369911yescharacteristic
184C22#1427370911yescharacteristic
185C22#1427371311yescharacteristic
186C22#1427374811yescharacteristic
187C22#1427375011yescharacteristic
188C22#1427375611yescharacteristic
189C22#1427375911yescharacteristic
190C4—42no—
191C4—81no—
192C4—4721no—
193C4—4721no—
194C4—2361no—
195C4—2361no—
196C4#1427370811yescharacteristic
197C4#1427371011yescharacteristic
198C4#1427372011yescharacteristic
199C4#1427372011yescharacteristic
200C2#1683733011yescharacteristic
201C2#1683762211yescharacteristic
202C2#1683762611yescharacteristic
203C2#1683774111yescharacteristic
204C2#1683774211yescharacteristic
205C2#1683775811yescharacteristic
206C2#1683776911yescharacteristic
subgroupG/H
centerC23D4×D59
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC2×#103×C59C2
socleC23×C59C2×D4
hypercenterC2×#103D59
hypocenterC59#2074
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
111. C59#2074semidirect