Finite Group Databasebeta

← #34059969

Subgroups — #34059969

Order 19072.

270 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 64 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#23750596C211yesmaximal, characteristic
2D149⋊(C22⋊C8)C211yesmaximal, characteristic
3#23750470C214yesmaximal, complemented
4C2×#18011891C211yesmaximal, characteristic
5C2×#14558746—21no—
6C2×D149⋊C8—21no—
7#18011968—21no—
8#18011968—21no—
9C22⋊#11924753C2212yes—
10C22⋊#11924753C2212yes—
11C22×Dic298C411yescharacteristic
12C22×C4×D149C2211yescharacteristic
13#18011891—21no—
14#18011891—21no—
15#18011891—21no—
16#18011891—21no—
17C2×C4⋊Dic149C2212yes—
18C2×#14558713C412yes—
19C2×C4⋊C4×C149C411yescharacteristic
20#14558746—42no—
21D149⋊C8—42no—
22C2×#11924753—22no—
23C2×#11924753—22no—
24C23×D149C2×C411yescharacteristic
25C2×Dic298—21no—
26C2×Dic298—21no—
27C2×Dic298—42no—
28C22×Dic149C2×C412yes—
29C22×Dic149C2311yescharacteristic
30C2×C4×D149—42no—
31C2×C4×D149D411yescharacteristic
32C2×C4×D149D411yescharacteristic
33C2×C4×D149D411yescharacteristic
34C2×C4×D149D411yescharacteristic
35C4⋊Dic149—22no—
36C4⋊Dic149—22no—
37#14558713—22no—
38#14558713—22no—
39C22×C4×C149C2×C412yes—
40C22×C4×C149C2×C411yescharacteristic
41C4⋊C4×C149—21no—
42C4⋊C4×C149—21no—
43#11924753—42no—
44#11924753—42no—
45C22×D149—22no—
46C22×D149—22no—
47C22×D149—41no—
48C22×D149C22⋊C411yescharacteristic
49C22×D149C22⋊C411yescharacteristic
50Dic298—42no—
51Dic298—42no—
52C2×Dic149—22no—
53C2×Dic149—41no—
54C2×Dic149—42no—
55C2×Dic149C2×D411yescharacteristic
56C2×Dic149C2×D411yescharacteristic
57C4×D149—22no—
58C4×D149—22no—
59C4×D149—41no—
60C4×D149—41no—
61C23×C149C22×C411yescharacteristic
62C2×C4×C149—22no—
63C2×C4×C149—22no—
64C2×C4×C149—24no—
65C2×C4×C149C22⋊C411yescharacteristic
66C2×C4×C149C22⋊C411yescharacteristic
67C22×C149—21no—
68C22×C149—21no—
69C22×C149C2×C22⋊C411yescharacteristic
70C22×C149#13112yes—
71C2×D149—21no—
72C2×D149—21no—
73C2×D149—21no—
74C2×D149—21no—
75C2×D149—21no—
76C2×D149—44no—
77C2×D149#10112yes—
78C4×C149—21no—
79C4×C149—42no—
80C4×C149#9912yes—
81Dic149—21no—
82Dic149—21no—
83Dic149—42no—
84C2×C149—22no—
85C2×C149#40811yescharacteristic
86C2×C149C2×#9911yescharacteristic
87C2×C149C2×#10111yescharacteristic
88D149—22no—
89D149—41no—
90C149#147211yescharacteristic, complemented, Sylow
91#1472—1491nomaximal, Sylow
92C2×C22⋊Q8—1491no—
93#407—1491no—
94C2×C22⋊C8—1491no—
95#324—1494no—
96C22×Q8—1491no—
97C23×C4—1491no—
98C2×M16—2981no—
99C22×C8—2981no—
100C22⋊Q8—2981no—
101C22⋊Q8—2981no—
102C22⋊Q8—2981no—
103C22⋊Q8—2981no—
104C2×C4⋊C4—1492no—
105C2×C4⋊C4#1059701011yescharacteristic
106C2×C22⋊C4—1492no—
107C22⋊C8—2981no—
108C22⋊C8—2981no—
109C22⋊C8—1492no—
110C22⋊C8—1492no—
111C24—1491no—
112C2×Q8—2981no—
113C2×Q8—2981no—
114C2×Q8—5962no—
115C22×C4—5962no—
116C22×C4—1491no—
117C22×C4—1491no—
118C22×C4—1492no—
119C22×C4—1491no—
120C22×C4—1491no—
121C22×C4—1491no—
122C22×C4C2×#1059701012yes—
123C22×C4C2×#1059701011yescharacteristic
124M16—5962no—
125C2×C8—2982no—
126C2×C8—2982no—
127C2×C8—5962no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—2982no—
131C4⋊C4—2982no—
132C22⋊C4—2982no—
133C22⋊C4—2982no—
134C23—2982no—
135C23—2982no—
136C23—5961no—
137C23—1491no—
138C23—1491no—
139C23C22×#1059701011yescharacteristic
140Q8—5962no—
141Q8—5962no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—24no—
145C2×C4—2982no—
146C2×C4—2982no—
147C2×C4—2982no—
148C2×C4—5961no—
149C2×C4—5961no—
150C2×C4—5961no—
151C2×C4—5962no—
152C2×C4—1491no—
153C2×C4—1491no—
154C2×C4C22⋊#1059701011yescharacteristic
155C2×C4C22⋊#1059701011yescharacteristic
156C8—5962no—
157C8—5962no—
158C22—21no—
159C22—21no—
160C22—2981no—
161C22—2981no—
162C22—2981no—
163C22—2981no—
164C22—2981no—
165C22—5964no—
166C22—1492no—
167C22C2×C22⋊#1059701011yescharacteristic
168C22#1801199812yes—
169C4—21no—
170C4—42no—
171C4—2981no—
172C4—2981no—
173C4—5962no—
174C4#1801197012yes—
175C2—22no—
176C2—2982no—
177C2—5961no—
178C2#2375059911yescharacteristic
179C2C2×#1801197011yescharacteristic
180C2D149⋊#10111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC23×C149C22×C4
FrattiniC23C22×#10597010
FittingC2×C4⋊C4×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC23×D149C2×C4
cosocleC22×Dic149C23
hypercenterC2×C4⋊C4#10597010
hypocenterC149#1472
LCSG ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #23750470C2semidirect
90. C149#1472semidirect

Maximal subgroups

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

subgroupindex
#237505962
D149⋊(C22⋊C8)2
#237504702
C2×#180118912
#1472149