Finite Group Databasebeta

← #34059944

Subgroups — #34059944

Order 19072.

252 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 62 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#23750645C212yesmaximal, complemented
2#23750471C212yesmaximal, complemented
3#23750469C212yesmaximal
4C2×#18011868C211yesmaximal, characteristic
5#18011978—22no—
6C22⋊#11924753C2214yes—
7#18011966—22no—
8C22×C4×D149C411yescharacteristic
9#18011868—22no—
10#18011868—22no—
11C2×#14558715C411yescharacteristic
12C2×#14558715C2211yescharacteristic
13C2×#14558713C411yescharacteristic
14C2×#14558713C2211yescharacteristic
15C2×C4×Dic149C2211yescharacteristic
16C2×C42×C149C411yescharacteristic
17C2×#11924753—24no—
18C23×D149C2×C411yescharacteristic
19C22×Dic149C2×C411yescharacteristic
20C22×Dic149C2×C411yescharacteristic
21C22×Dic149C2311yescharacteristic
22C2×C4×D149—22no—
23C2×C4×D149—22no—
24C2×C4×D149—21no—
25C2×C4×D149—21no—
26#14558715—22no—
27#14558715—22no—
28#14558713—22no—
29#14558713—22no—
30C4×Dic149D412yes—
31C4×Dic149D412yes—
32C22×C4×C149C2×C411yescharacteristic
33C22×C4×C149C2×C411yescharacteristic
34C22×C4×C149C2×C411yescharacteristic
35C42×C149—21no—
36C42×C149—21no—
37#11924753—44no—
38C22×D149—21no—
39C22×D149—21no—
40C22×D149—41no—
41C22×D149—41no—
42C22×D149M1612yes—
43C2×Dic149—21no—
44C2×Dic149—21no—
45C2×Dic149—41no—
46C2×Dic149—41no—
47C2×Dic149C22⋊C412yes—
48C2×Dic149M1612yes—
49C2×Dic149C2×D412yes—
50C4×D149—24no—
51C4×D149—24no—
52C23×C149C22×C411yescharacteristic
53C2×C4×C149—21no—
54C2×C4×C149—21no—
55C2×C4×C149—21no—
56C2×C4×C149—21no—
57C2×C4×C149—41no—
58C2×C4×C149—41no—
59C2×C4×C149C22⋊C411yescharacteristic
60C2×C4×C149C22⋊C411yescharacteristic
61C22×C149—21no—
62C22×C149—21no—
63C22×C149C2×C22⋊C411yescharacteristic
64C22×C149C2×M1611yescharacteristic
65C22×C149C2×M1611yescharacteristic
66C2×D149—22no—
67C2×D149—42no—
68C2×D149—41no—
69C2×D149—41no—
70C2×D149—42no—
71C4×C149—21no—
72C4×C149—21no—
73C4×C149—41no—
74C4×C149—41no—
75Dic149—22no—
76Dic149—22no—
77Dic149—22no—
78C2×C149—21no—
79C2×C149—21no—
80C2×C149#40711yescharacteristic
81C2×C149#41011yescharacteristic
82C2×C149#41311yescharacteristic
83D149—42no—
84C149#146411yescharacteristic, complemented, Sylow
85#1464—1491nomaximal, Sylow
86C2×#117—1491no—
87#432—1492no—
88#324—1492no—
89#323—1492no—
90C23×C4—1491no—
91#117—2982no—
92#117—2982no—
93C2×C4⋊C4—1491no—
94C2×C4⋊C4—1491no—
95C2×C22⋊C4—1491no—
96C2×C22⋊C4—1491no—
97C2×C42—1491no—
98C2×C42#1059701011yescharacteristic
99C4⋊C8—2982no—
100C22⋊C8—1494no—
101#97—2982no—
102C24—1491no—
103C22×C4—2982no—
104C22×C4—2982no—
105C22×C4—2981no—
106C22×C4—2981no—
107C22×C4—1491no—
108C22×C4—1491no—
109C22×C4—1491no—
110C22×C4C2×#1059701011yescharacteristic
111C22×C4C2×#1059701011yescharacteristic
112C22×C4C2×#1059701011yescharacteristic
113C2×C8—2984no—
114C4⋊C4—2982no—
115C4⋊C4—2982no—
116C22⋊C4—2982no—
117C22⋊C4—2982no—
118C42—21no—
119C42—21no—
120C42—1492no—
121C42—1492no—
122C23—2981no—
123C23—2981no—
124C23—5961no—
125C23—5961no—
126C23—1492no—
127C23C22×#1059701011yescharacteristic
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—2984no—
135C2×C4—2984no—
136C2×C4—2981no—
137C2×C4—2981no—
138C2×C4—5961no—
139C2×C4—5961no—
140C2×C4—1492no—
141C2×C4—1492no—
142C2×C4—1492no—
143C2×C4C22⋊#1059701011yescharacteristic
144C2×C4C22⋊#1059701011yescharacteristic
145C8—5964no—
146C22—21no—
147C22—21no—
148C22—2982no—
149C22—5962no—
150C22—5962no—
151C22—5961no—
152C22—5961no—
153C22C2×C22⋊#1059701011yescharacteristic
154C22D149⋊M1611yescharacteristic
155C22D149⋊M1611yescharacteristic
156C4—21no—
157C4—21no—
158C4—41no—
159C4—41no—
160C4—2982no—
161C4—2982no—
162C4—2982no—
163C2—21no—
164C2—21no—
165C2—5962no—
166C2#2375059711yescharacteristic
167C2#2375060411yescharacteristic
168C2#2375061111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC23×C149C22×C4
FrattiniC23C22×#10597010
FittingC2×C42×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC23×D149C2×C4
cosocleC22×Dic149C23
hypercenterC2×C42#10597010
hypocenterC149#1464
LCSG ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. #23750645C2semidirect
2. #23750471C2semidirect
84. C149#1464semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237506452
#237504712
#237504692
C2×#180118682
#1464149