Finite Group Databasebeta

← #34059940

Subgroups — #34059940

Order 19072.

312 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 68 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#23750596C212yesmaximal
2#23750471C212yesmaximal, complemented
3#23750470C212yesmaximal, complemented
4C2×C4⋊C4×D149C211yesmaximal, characteristic
5C2×#14558746—22no—
6#18011968—22no—
7C22⋊#11924753C2214yes—
8C22×C4×D149C411yescharacteristic
9C22×C4×D149C411yescharacteristic
10C22×C4×D149C2211yescharacteristic
11C2×C4⋊Dic149C2211yescharacteristic
12C2×#14558715C411yescharacteristic
13C2×#14558715C2211yescharacteristic
14C4⋊C4×D149—22no—
15C4⋊C4×D149—22no—
16C2×C4⋊C4×C149C411yescharacteristic
17#14558746—44no—
18C2×#11924753—24no—
19C23×D149C2×C411yescharacteristic
20C22×Dic149C2×C411yescharacteristic
21C22×Dic149C2×C411yescharacteristic
22C22×Dic149C2311yescharacteristic
23C2×C4×D149—21no—
24C2×C4×D149—21no—
25C2×C4×D149—22no—
26C2×C4×D149—21no—
27C2×C4×D149—21no—
28C2×C4×D149—22no—
29C2×C4×D149—42no—
30C2×C4×D149—42no—
31C2×C4×D149D412yes—
32C2×C4×D149D412yes—
33C4⋊Dic149—22no—
34#14558715—22no—
35#14558715—22no—
36C22×C4×C149C2×C411yescharacteristic
37C22×C4×C149C2×C411yescharacteristic
38C22×C4×C149C2×C411yescharacteristic
39C4⋊C4×C149—22no—
40#11924753—44no—
41C22×D149—21no—
42C22×D149—21no—
43C22×D149—22no—
44C22×D149—22no—
45C22×D149C22⋊C411yescharacteristic
46C22×D149C22⋊C411yescharacteristic
47C2×Dic149—21no—
48C2×Dic149—21no—
49C2×Dic149—21no—
50C2×Dic149—41no—
51C2×Dic149—41no—
52C2×Dic149M1612yescomplemented
53C2×Dic149C2×D412yes—
54C4×D149—24no—
55C4×D149—24no—
56C4×D149—24no—
57C4×D149—42no—
58C4×D149—42no—
59C4×D149—42no—
60C23×C149C22×C411yescharacteristic
61C2×C4×C149—21no—
62C2×C4×C149—21no—
63C2×C4×C149—21no—
64C2×C4×C149—41no—
65C2×C4×C149—41no—
66C2×C4×C149C22⋊C412yes—
67C2×C4×C149M1612yescomplemented
68C22×C149—21no—
69C22×C149—21no—
70C22×C149C2×C22⋊C411yescharacteristic
71C22×C149C2×M1611yescharacteristic
72C22×C149C2×M1611yescharacteristic
73C2×D149—24no—
74C2×D149—24no—
75C2×D149—21no—
76C2×D149—21no—
77C2×D149—21no—
78C2×D149—21no—
79C2×D149#9912yes—
80C2×D149#10112yes—
81C4×C149—22no—
82C4×C149—22no—
83C4×C149—41no—
84Dic149—22no—
85Dic149—22no—
86Dic149—41no—
87C2×C149—21no—
88C2×C149—21no—
89C2×C149#40711yescharacteristic
90C2×C149C2×#9911yescharacteristic
91C2×C149C2×#10111yescharacteristic
92D149—22no—
93D149—22no—
94C149#146311yescharacteristic, complemented, Sylow
95#1463—1491nomaximal, Sylow
96C22×C4⋊C4—1491no—
97#407—1492no—
98#324—1492no—
99#324—1492no—
100C23×C4—1491no—
101C23×C4—1491no—
102C23×C4—1491no—
103C2×M16—2982no—
104C2×C4⋊C4—2982no—
105C2×C4⋊C4—2982no—
106C2×C4⋊C4—1491no—
107C2×C4⋊C4—1491no—
108C2×C4⋊C4—1491no—
109C2×C4⋊C4#1059701011yescharacteristic
110C22⋊C8—2982no—
111C22⋊C8—1494no—
112C24—1491no—
113C22×C4—2981no—
114C22×C4—2981no—
115C22×C4—2982no—
116C22×C4—2981no—
117C22×C4—2981no—
118C22×C4—2982no—
119C22×C4—5962no—
120C22×C4—5962no—
121C22×C4—1491no—
122C22×C4—1492no—
123C22×C4—1491no—
124C22×C4—1491no—
125C22×C4—1492no—
126C22×C4C2×#1059701011yescharacteristic
127C22×C4C2×#1059701011yescharacteristic
128C22×C4C2×#1059701011yescharacteristic
129M16—5964no—
130C2×C8—2984no—
131C4⋊C4—22no—
132C4⋊C4—2982no—
133C4⋊C4—2982no—
134C4⋊C4—2982no—
135C23—2982no—
136C23—2982no—
137C23—2981no—
138C23—2981no—
139C23—1491no—
140C23—1491no—
141C23C22×#1059701011yescharacteristic
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—2984no—
148C2×C4—2984no—
149C2×C4—2984no—
150C2×C4—2981no—
151C2×C4—2981no—
152C2×C4—2981no—
153C2×C4—5962no—
154C2×C4—5962no—
155C2×C4—5962no—
156C2×C4—5961no—
157C2×C4—5961no—
158C2×C4—1492no—
159C2×C4—1492no—
160C2×C4C22⋊#1059701012yes—
161C2×C4#1455874612yescomplemented
162C8—5964no—
163C22—21no—
164C22—21no—
165C22—2984no—
166C22—2984no—
167C22—2981no—
168C22—2981no—
169C22—2981no—
170C22—2981no—
171C22—1492no—
172C22—1492no—
173C22C2×C22⋊#1059701011yescharacteristic
174C22D149⋊M1611yescharacteristic
175C22C2×#1455874611yescharacteristic
176C4—22no—
177C4—22no—
178C4—41no—
179C4—2982no—
180C4—2982no—
181C4—5961no—
182C2—21no—
183C2—21no—
184C2—2982no—
185C2—2982no—
186C2#2375059611yescharacteristic
187C2D149⋊#9911yescharacteristic
188C2D149⋊#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#1463
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
2. #23750471C2semidirect
3. #23750470C2semidirect
52. C2×Dic149M16semidirect
67. C2×C4×C149M16semidirect
94. C149#1463semidirect
161. C2×C4#14558746semidirect

Maximal subgroups

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

subgroupindex
#237505962
#237504712
#237504702
C2×C4⋊C4×D1492
#1463149