Finite Group Databasebeta

← #21422696

Subgroups — #21422696

Order 7552.

212 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 61 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#125×D59C211yesmaximal, characteristic
2#16837457C211yesmaximal, characteristic
3#16837354C211yesmaximal, characteristic
4#16837144C211yesmaximal, characteristic, complemented
5#16837143C211yesmaximal, characteristic, complemented
6#16837143C211yesmaximal, characteristic, complemented
7C59×#330C211yesmaximal, characteristic, complemented
8C2×#11745659—21no—
9#14273719C2211yescharacteristic
10#14273718C411yescharacteristic
11#14273718C411yescharacteristic
12#14273717—21no—
13#14273717—21no—
14C4⋊C4×D59—21no—
15C4⋊C4×D59—21no—
16C4⋊C4×D59C411yescharacteristic
17C4⋊C4×D59C411yescharacteristic
18C42×D59C2211yescharacteristic
19Dic59⋊C8—21no—
20(C2×D59)⋊C8—21no—
21#14273638C2211yescharacteristic
22#14273638C2211yescharacteristic
23C8×Dic59—21no—
24#125×C59C2211yescharacteristic
25#97×C59C2211yescharacteristic
26#97×C59C2211yescharacteristic
27C2×C4×D59—21no—
28C2×C4×D59—21no—
29C2×C4×D59C2×C411yescharacteristic
30C2×C4×D59D411yescharacteristic
31C2×C4×D59D411yescharacteristic
32C2×C8×C59—21no—
33C2×C8×C59—21no—
34C4⋊C4×C59—21no—
35C4⋊C4×C59—21no—
36C4⋊C4×C59C2×C411yescharacteristic
37C4⋊C4×C59C2×C411yescharacteristic
38C42×C59C2311yescharacteristic
39C4⋊Dic59—21no—
40C4⋊Dic59—21no—
41C4⋊Dic59C2×C411yescharacteristic
42C4⋊Dic59C2×C411yescharacteristic
43Dic59⋊C4—21no—
44Dic59⋊C4—21no—
45Dic59⋊C4—21no—
46Dic59⋊C4—21no—
47Dic59⋊C4—21no—
48Dic59⋊C4—21no—
49C4×Dic59C2×C411yescharacteristic
50C4×Dic59D411yescharacteristic
51C4×Dic59D411yescharacteristic
52C2×C59⋊C8—21no—
53C2×C59⋊C8—21no—
54#11745659—24no—
55C22×D59C22⋊C411yescharacteristic
56C2×C4×C59—21no—
57C2×C4×C59—21no—
58C2×C4×C59C22×C411yescharacteristic
59C2×C4×C59C2×D411yescharacteristic
60C2×C4×C59C2×D411yescharacteristic
61C2×Dic59—21no—
62C2×Dic59—21no—
63C2×Dic59C22⋊C411yescharacteristic
64C2×Dic59C22⋊C411yescharacteristic
65C2×Dic59C22⋊C411yescharacteristic
66C4×D59—22no—
67C4×D59—22no—
68C4×D59—41no—
69C4×D59—42no—
70C4×D59—42no—
71C8×C59—22no—
72C8×C59—41no—
73C59⋊C8—22no—
74C59⋊C8—41no—
75C22×C59C2×C22⋊C411yescharacteristic
76C2×D59—21no—
77C2×D59—21no—
78C2×D59#10412yes—
79C4×C59—21no—
80C4×C59—21no—
81C4×C59—21no—
82C4×C59—41no—
83C4×C59—41no—
84Dic59—21no—
85Dic59—21no—
86Dic59—41no—
87Dic59—41no—
88Dic59#10112yes—
89#1528—591nomaximal, Sylow
90C2×C59C2×#10111yescharacteristic
91C2×C59C2×#10411yescharacteristic
92C2×C59#42111yescharacteristic
93D59—22no—
94C2×#125—591no—
95#432—591no—
96C4×M16—591no—
97#330—591no—
98#330—591no—
99#330—591no—
100#330D5911yescharacteristic, complemented
101C59#152811yescharacteristic, complemented, Sylow
102C2×M16—1181no—
103#125—591no—
104#125—591no—
105#125—591no—
106#125—1181no—
107#125—1181no—
108#125C2×D5911yescharacteristic
109C2×C4⋊C4—591no—
110C2×C4⋊C4—591no—
111C2×C4⋊C4—1181no—
112C2×C4⋊C4—1181no—
113C2×C42—591no—
114C4⋊C8—1181no—
115C22⋊C8—1181no—
116#97—591no—
117#97—591no—
118#97C2×D5911yescharacteristic
119#97C2×D5911yescharacteristic
120C4×C8—1181no—
121C22×C4—591no—
122C22×C4—591no—
123C22×C4—591no—
124C22×C4—1181no—
125C22×C4—1181no—
126M16—1184no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—1181no—
130C2×C8—1181no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—591no—
134C4⋊C4—591no—
135C4⋊C4—1181no—
136C4⋊C4—1181no—
137C4⋊C4—1181no—
138C4⋊C4—1181no—
139C4⋊C4—1181no—
140C4⋊C4—1181no—
141C4⋊C4—1181no—
142C4⋊C4—1181no—
143C4⋊C4C4×D5911yescharacteristic
144C4⋊C4C4×D5911yescharacteristic
145C42—591no—
146C42—591no—
147C42—591no—
148C42C22×D5911yescharacteristic
149C23—591no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—591no—
153C2×C4—591no—
154C2×C4—591no—
155C2×C4—1182no—
156C2×C4—1182no—
157C2×C4—1181no—
158C2×C4—1181no—
159C2×C4—2361no—
160C2×C4—2362no—
161C2×C4—2362no—
162C2×C4C2×C4×D5911yescharacteristic
163C2×C4D4×D5911yescharacteristic
164C2×C4D4×D5911yescharacteristic
165C8—22no—
166C8—41no—
167C8—1182no—
168C8—2361no—
169C22—592no—
170C22—1181no—
171C22—1181no—
172C22C22⋊C4×D5911yescharacteristic
173C4—21no—
174C4—21no—
175C4—21no—
176C4—41no—
177C4—41no—
178C4—592no—
179C4—1181no—
180C4—1181no—
181C4—2361no—
182C4—2361no—
183C2—1182no—
184C2#101×D5911yescharacteristic
185C2#104×D5911yescharacteristic
186C2#1683741711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D59
commutatorC2×C4×C59C22×C4
FrattiniC42C22×D59
FittingC59×#330C2
socleC22×C59C2×C22⋊C4
hypercenter#330D59
hypocenterC59#1528
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
4. #16837144C2semidirect
5. #16837143C2semidirect
6. #16837143C2semidirect
7. C59×#330C2semidirect
100. #330D59semidirect
101. C59#1528semidirect