Finite Group Databasebeta

← #34060030

Subgroups — #34060030

Order 19072.

316 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 72 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#23750646C211yesmaximal, characteristic, complemented
2C4×#14558745C211yesmaximal, characteristic, complemented
3D4⋊#11924753C214yesmaximal, complemented
4C2×D4×Dic149C211yesmaximal, characteristic
5C2×#14558745—21no—
6C4⋊#11924753C2212yescomplemented
7C22⋊#11924753—21no—
8#18011966—21no—
9#18011966—21no—
10C4×#11924753C2212yescomplemented
11C23×Dic149—21no—
12D4×Dic149—21no—
13D4×Dic149—21no—
14D4×Dic149C412yes—
15D4×Dic149C2212yes—
16C2×C4⋊Dic149C411yescharacteristic
17C2×C22⋊Dic149—21no—
18C2×C4×Dic149C2211yescharacteristic
19C22×D4×C149C411yescharacteristic
20#14558745—24no—
21C2×#11924753—22no—
22C2×#11924753—22no—
23C22×Dic149—22no—
24C22×Dic149—22no—
25C22×Dic149—21no—
26C22×Dic149—44no—
27C22×Dic149D411yescharacteristic
28C22×Dic149D411yescharacteristic
29C4⋊Dic149—21no—
30C4⋊Dic149C2×C412yes—
31C22⋊Dic149—22no—
32C22⋊Dic149—22no—
33C4×Dic149C2×C411yescharacteristic
34C4×Dic149D411yescharacteristic
35C4×Dic149D411yescharacteristic
36C4×Dic149C2311yescharacteristic
37C24×C149—21no—
38C2×D4×C149—24no—
39C2×D4×C149—21no—
40C2×D4×C149C2×C412yes—
41C22×C4×C149C2×C411yescharacteristic
42#11924753—24no—
43#11924753—42no—
44C2×Dic149—22no—
45C2×Dic149—22no—
46C2×Dic149—22no—
47C2×Dic149—44no—
48C2×Dic149—42no—
49C2×Dic149—44no—
50C2×Dic149C22⋊C411yescharacteristic
51C2×Dic149C22⋊C411yescharacteristic
52C2×Dic149C2×D411yescharacteristic
53C2×Dic149C2×D411yescharacteristic
54C23×C149—24no—
55C23×C149—22no—
56C23×C149—42no—
57C23×C149—42no—
58C23×C149C22⋊C411yescharacteristic
59D4×C149—24no—
60D4×C149—22no—
61D4×C149M1614yescomplemented
62C2×C4×C149—22no—
63C2×C4×C149C22⋊C411yescharacteristic
64C2×C4×C149C22×C411yescharacteristic
65C22×C149—21no—
66C22×C149—21no—
67C22×C149—24no—
68C22×C149—48no—
69C22×C149—42no—
70C22×C149—42no—
71C22×C149#10412yes—
72C22×C149C2×C22⋊C411yescharacteristic
73C4×C149—21no—
74C4×C149C2×M1612yes—
75Dic149—21no—
76Dic149—21no—
77Dic149—21no—
78Dic149—42no—
79Dic149AGL(1,ℤ/8)12yes—
80C2×C149—22no—
81C2×C149—44no—
82C2×C149#40711yescharacteristic
83C2×C149#41811yescharacteristic
84C2×C149C2×#10411yescharacteristic
85C149#149011yescharacteristic, complemented, Sylow
86#1490—1491nomaximal, Sylow
87C2×C4×D4—1491no—
88#432—1491no—
89C4×M16—1491no—
90D4⋊C8—1494no—
91C22×D4#1059701011yescharacteristic
92C23×C4—2981no—
93C2×M16—2981no—
94C4×D4—2981no—
95C4×D4—2981no—
96C4×D4—1492no—
97C4×D4—1492no—
98C2×C4⋊C4—1491no—
99C2×C22⋊C4—2981no—
100C2×C42—1491no—
101C4⋊C8—1492no—
102C22⋊C8—2981no—
103#97—2981no—
104#97—2981no—
105C4×C8—1492no—
106C24—21no—
107C2×D4—24no—
108C2×D4—21no—
109C2×D4C2×#1059701012yes—
110C22×C4—2981no—
111C22×C4—2982no—
112C22×C4—2982no—
113C22×C4—5964no—
114C22×C4—1491no—
115C22×C4—1491no—
116C22×C4C2×#1059701011yescharacteristic
117M16—2984no—
118C2×C8—2982no—
119C2×C8—2982no—
120C4⋊C4—2981no—
121C4⋊C4—1492no—
122C22⋊C4—2982no—
123C22⋊C4—2982no—
124C42—1491no—
125C42—1491no—
126C42—1491no—
127C42—1491no—
128C23—24no—
129C23—22no—
130C23—42no—
131C23—42no—
132C23C22⋊#1059701011yescharacteristic
133D4—24no—
134D4—22no—
135D4#1455874514yescomplemented
136C2×C4—22no—
137C2×C4—2982no—
138C2×C4—2982no—
139C2×C4—2982no—
140C2×C4—5964no—
141C2×C4—5962no—
142C2×C4—5964no—
143C2×C4—1491no—
144C2×C4—1491no—
145C2×C4—1491no—
146C2×C4—1491no—
147C2×C4C22⋊#1059701011yescharacteristic
148C2×C4C22×#1059701011yescharacteristic
149C8—2984no—
150C8—5962no—
151C22—21no—
152C22—21no—
153C22—24no—
154C22—48no—
155C22—42no—
156C22—42no—
157C22#1801197512yes—
158C22C2×C22⋊#1059701011yescharacteristic
159C4—21no—
160C4—2981no—
161C4—2981no—
162C4—2981no—
163C4—5962no—
164C4—1492no—
165C4C2×#1455874512yes—
166C2—22no—
167C2—44no—
168C2#2375059511yescharacteristic
169C2#2375061711yescharacteristic
170C2C2×#1801197511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting, prime radicalC22×D4×C149C4
socleC22×C149C2×C22⋊C4
cosocleC4×Dic149C23
hypercenterC22×D4#10597010
hypocenterC149#1490
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #23750646C2semidirect
2. C4×#14558745C2semidirect
3. D4⋊#11924753C2semidirect
6. C4⋊#11924753C22semidirect
10. C4×#11924753C22semidirect
61. D4×C149M16semidirect
85. C149#1490semidirect
135. D4#14558745semidirect

Maximal subgroups

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

subgroupindex
#237506462
C4×#145587452
D4⋊#119247532
C2×D4×Dic1492
#1490149