Finite Group Databasebeta

← #21423136

Subgroups — #21423136

Order 7552.

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

normal subgroups only

This group has 202 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#16837737C211yesmaximal, characteristic
3#16837340C211yesmaximal, characteristic
4#16837140C211yesmaximal, characteristic
5#16837139C211yesmaximal, characteristic
6#16837127C211yesmaximal, characteristic
7C59×#484C211yesmaximal, characteristic
8#14273726—21no—
9#14273725—21no—
10#14273717—21no—
11#14273717—21no—
12#14273706C2211yescharacteristic
13#14273704—21no—
14#14273683—21no—
15C2×Dic59⋊C4C2211yescharacteristic
16#14273660—21no—
17#14273650—21no—
18C22⋊(C59⋊C8)C2211yescharacteristic
19C59⋊#95—21no—
20C59⋊#95—21no—
21C59⋊#95C2211yescharacteristic
22C22⋊Q8×C59C2211yescharacteristic
23C2×C4⋊C4×C59C2211yescharacteristic
24#107×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—
51C4×Dic59—21no—
52C4×Dic59—21no—
53C2×C59⋊C8—21no—
54C23×C59C2×D411yescharacteristic
55Q8×C59—41no—
56C2×C4×C59—21no—
57C2×C4×C59—21no—
58C2×C4×C59—41no—
59C2×C4×C59—42no—
60C2×C4×C59—41no—
61C2×C4×C59C2×D411yescharacteristic
62C2×C4×C59C2×D411yescharacteristic
63C2×Dic59—21no—
64C2×Dic59—21no—
65C2×Dic59—21no—
66C2×Dic59—21no—
67C2×Dic59—21no—
68C2×Dic59—41no—
69C2×Dic59—41no—
70C2×Dic59—41no—
71C2×Dic59—41no—
72C2×Dic59Q1612yes—
73Dic118—41no—
74Dic118—81no—
75C8×C59—41no—
76C59⋊C8—41no—
77C22×C59—21no—
78C22×C59—21no—
79C22×C59#12011yescharacteristic
80C22×C59C2×Q1611yescharacteristic
81C22×C59#13711yescharacteristic
82C4×C59—21no—
83C4×C59—21no—
84C4×C59—41no—
85C4×C59—41no—
86C4×C59—81no—
87Dic59—22no—
88Dic59—41no—
89Dic59—41no—
90Dic59—41no—
91Dic59—81no—
92#1617—591nomaximal, Sylow
93C2×C59—21no—
94C2×C59—21no—
95C2×C59#45111yescharacteristic
96C2×C59#45411yescharacteristic
97C2×C59#45811yescharacteristic
98#544—591no—
99#484—591no—
100#484D5911yescharacteristic
101#400—591no—
102#328—591no—
103#328—591no—
104#324—591no—
105C59#161711yescharacteristic, complemented, Sylow
106C4⋊Q8—1181no—
107C4⋊Q8—1181no—
108#125—1181no—
109#125—1181no—
110C22⋊Q8—591no—
111C22⋊Q8—1181no—
112C22⋊Q8C2×D5911yescharacteristic
113#117—1181no—
114C2×C4⋊C4—591no—
115C2×C4⋊C4C2×D5911yescharacteristic
116#107—21no—
117#107—1181no—
118#103—21no—
119#103—1181no—
120C22⋊C8—591no—
121C22⋊C8C2×D5911yescharacteristic
122#95—591no—
123#95—1181no—
124#95—1181no—
125C2×Q8—591no—
126C2×Q8—1181no—
127C2×Q8C22⋊D5911yescharacteristic
128C22×C4—21no—
129C22×C4—591no—
130C22×C4—591no—
131C22×C4—1181no—
132C22×C4C22×D5911yescharacteristic
133C2×C8—21no—
134C2×C8—1181no—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—591no—
139C4⋊C4—1181no—
140C4⋊C4—1181no—
141C4⋊C4—1181no—
142C4⋊C4—1181no—
143C4⋊C4—1181no—
144C4⋊C4—1181no—
145C4⋊C4—1181no—
146C4⋊C4—1181no—
147C4⋊C4C22⋊D5911yescharacteristic
148C22⋊C4—21no—
149C22⋊C4—1181no—
150C42—1181no—
151C42—1181no—
152C23D4×D5911yescharacteristic
153Q8—41no—
154Q8—4721no—
155Q8—2361no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—42no—
160C2×C4—41no—
161C2×C4—592no—
162C2×C4—1181no—
163C2×C4—1181no—
164C2×C4—1181no—
165C2×C4—1181no—
166C2×C4—1181no—
167C2×C4—2361no—
168C2×C4—2361no—
169C2×C4—2361no—
170C2×C4—2361no—
171C2×C4D4×D5911yescharacteristic
172C2×C4C2×C22⋊D5911yescharacteristic
173C8—41no—
174C8—2361no—
175C22—21no—
176C22—21no—
177C22#1427369511yescharacteristic
178C22Q16×D5911yescharacteristic
179C22#1427375911yescharacteristic
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—81no—
185C4—1182no—
186C4—4721no—
187C4—2361no—
188C4—2361no—
189C4—2361no—
190C2—21no—
191C2—21no—
192C2#1683755611yescharacteristic
193C2#1683757311yescharacteristic
194C2#1683759111yescharacteristic
subgroupG/H
centerC22#14273695
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC59×#484C2
socleC22×C59#120
hypercenter#484D59
hypocenterC59#1617
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
105. C59#1617semidirect