Finite Group Databasebeta

← #34061335

Subgroups — #34061335

Order 19072.

484 conjugacy classes of subgroups; only the 202 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 202 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
1C2×D149⋊M16C212yesmaximal
2#23750632C218yesmaximal, complemented
3#23750628C214yesmaximal, complemented
4C2×#18011869C211yesmaximal, characteristic
5C2×#14558746C2214yes—
6D149⋊M16—28no—
7C2×#14558745C2214yes—
8C2×D149⋊C8C2214yes—
9#18011978C2218yescomplemented
10C4⋊#11924753C2218yescomplemented
11C22×C4×D149C2211yescharacteristic
12#18011869C414yes—
13#18011869C2214yes—
14C2×C4⋊Dic149C411yescharacteristic
15C2×#14558713C412yes—
16C2×C4×Dic149C2212yes—
17C2×C4⋊C4×C149C411yescharacteristic
18#14558746—28no—
19#14558745—28no—
20D149⋊C8—28no—
21C2×#11924753C2318yes—
22C23×D149C2×C411yescharacteristic
23C22×Dic149C2×C412yes—
24C22×Dic149C2311yescharacteristic
25C2×C4×D149C2×C412yes—
26C2×C4×D149D414yes—
27C2×C4×D149Q814yes—
28C2×C4×D149C2312yes—
29C4⋊Dic149C2×C414yes—
30#14558713C2×C418yes—
31C4×Dic149C2×C414yes—
32C4×Dic149C2314yes—
33C22×C4×C149C2×C412yes—
34C22×C4×C149C2×C411yescharacteristic
35C4⋊C4×C149C2×C414yes—
36#11924753—28no—
37C22×D149—41no—
38C22×D149—41no—
39C22×D149C4⋊C414yes—
40C22×D149C22×C412yes—
41C2×Dic149—42no—
42C2×Dic149C22×C414yes—
43C2×Dic149C22×C411yescharacteristic
44C2×Dic149C2×D412yes—
45C2×Dic149C2×Q812yes—
46C2×Dic149C2411yescharacteristic
47C4×D149C4⋊C418yes—
48C4×D149C2×D414yes—
49C4×D149C2×Q814yes—
50C23×C149C22×C411yescharacteristic
51C2×C4×C149—42no—
52C2×C4×C149C4⋊C414yes—
53C2×C4×C149C22×C414yes—
54C2×C4×C149C22×C412yes—
55C22×C149—21no—
56C22×C149—21no—
57C22×C149C2×C4⋊C412yes—
58C22×C149C23×C411yescharacteristic
59C2×D149—22no—
60C2×D149—22no—
61C2×D149—44no—
62C2×D149C2×C4⋊C414yes—
63C4×C149—24no—
64C4×C149C2×C4⋊C414yes—
65Dic149—24no—
66Dic149C2×C4⋊C412yes—
67Dic149C22×D411yescharacteristic
68Dic149C22×Q811yescharacteristic
69C2×C149—22no—
70C2×C149C22×C4⋊C411yescharacteristic
71C2×C149#56811yescharacteristic
72C2×C149#56811yescharacteristic
73D149—24no—
74C149#290511yescharacteristic, complemented, Sylow
75#2905—1491nomaximal, Sylow
76C22×M16—1492no—
77C2×#117—1491no—
78#424—1498no—
79#423—1494no—
80C23×C4—1491no—
81C2×M16—2988no—
82C2×M16—1494no—
83C2×M16—1494no—
84C22×C8—1494no—
85#117—1494no—
86#117—1494no—
87C2×C4⋊C4—1491no—
88C2×C4⋊C4#1059701011yescharacteristic
89C2×C22⋊C4—1492no—
90C2×C42—1492no—
91C4⋊C8—1498no—
92C4⋊C8—1498no—
93C24—1491no—
94C22×C4—1492no—
95C22×C4—1491no—
96C22×C4—1494no—
97C22×C4—1494no—
98C22×C4—1492no—
99C22×C4—1492no—
100C22×C4C2×#1059701012yes—
101C22×C4C2×#1059701011yescharacteristic
102M16—2988no—
103M16—2988no—
104C2×C8—2988no—
105C2×C8—1498no—
106C4⋊C4—1494no—
107C4⋊C4C2×#1059701014yes—
108C22⋊C4—1498no—
109C42—1494no—
110C42—1494no—
111C23—5961no—
112C23—5961no—
113C23—1492no—
114C23—1494no—
115C23C22×#1059701011yescharacteristic
116C2×C4—42no—
117C2×C4—5962no—
118C2×C4—1494no—
119C2×C4—1492no—
120C2×C4—1492no—
121C2×C4—1491no—
122C2×C4—1491no—
123C2×C4—1498no—
124C2×C4—1494no—
125C2×C4—1494no—
126C2×C4C4⋊#1059701014yes—
127C2×C4C22×#1059701014yes—
128C2×C4C22×#1059701012yes—
129C8—2988no—
130C22—21no—
131C22—21no—
132C22—2982no—
133C22—2982no—
134C22—5964no—
135C22—1494no—
136C22C2×C4⋊#1059701012yes—
137C22C23×#1059701011yescharacteristic
138C4—24no—
139C4—2984no—
140C4—1491no—
141C4—1492no—
142C4—1491no—
143C4C2×C4⋊#1059701014yes—
144C2—22no—
145C2—2984no—
146C2C22×C4⋊#1059701011yescharacteristic
147C2#2375070311yescharacteristic
148C2#2375070511yescharacteristic
subgroupG/H
center, FrattiniC22C23×#10597010
commutator, socleC22×C149C23×C4
FittingC2×C4⋊C4×C149C4
prime radicalC23×D149C2×C4
cosocleC2×Dic149C24
hypercenterC2×C4⋊C4#10597010
hypocenterC149#2905
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #23750632C2semidirect
3. #23750628C2semidirect
9. #18011978C22semidirect
10. C4⋊#11924753C22semidirect
74. C149#2905semidirect

Maximal subgroups

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

subgroupindex
C2×D149⋊M162
#237506322
#237506282
C2×#180118692
#2905149