Finite Group Databasebeta

← #34059792

Subgroups — #34059792

Order 19072.

162 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 40 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#23750611C211yesmaximal, characteristic
2#23750604C211yesmaximal, characteristic
3#23749593C211yesmaximal, characteristic
4D149⋊M16—21no—
5#18011990—21no—
6#18011972C412yescomplemented
7#18011971—21no—
8#18011970C412yes—
9#18011969—21no—
10C2×#14558736C2211yescharacteristic
11C22×#11924746C411yescharacteristic, complemented
12#18011823—21no—
13#18011823—21no—
14C2×M16×C149C411yescharacteristic, complemented
15#14558746—41no—
16#14558745—22no—
17D149⋊C8—41no—
18C4⋊#10597010—41no—
19C22⋊#10597010—22no—
20C4×#10597010—41no—
21#14558736—41no—
22#14558736—41no—
23C2×Dic298C2×C411yescharacteristic
24C2×D596C2×C411yescharacteristic
25C2×C22⋊D149D411yescharacteristic
26C2×C22⋊D149Q811yescharacteristic
27C2×C4×D149D411yescharacteristic
28C2×C4×D149D411yescharacteristic
29C2×#11924746—21no—
30C2×#11924746—41no—
31C22×C4×C149C2×C411yescharacteristic
32M16×C149—41no—
33C2×C8×C149—21no—
34C2×#10597010—42no—
35#11924753—42no—
36C22×D149C22⋊C411yescharacteristic
37C22×D149C4⋊C411yescharacteristic
38Dic298—41no—
39D596—41no—
40C22⋊D149—41no—
41C22⋊D149—41no—
42C2×Dic149C22⋊C411yescharacteristic
43C2×Dic149C4⋊C411yescharacteristic
44C4×D149—21no—
45C4×D149—21no—
46C4×D149—21no—
47C4×D149—21no—
48#11924746—41no—
49C23×C149C4⋊C411yescharacteristic
50C2×C4×C149—21no—
51C2×C4×C149—21no—
52C2×C4×C149C4211yescharacteristic
53C2×C4×C149C22⋊C411yescharacteristic
54C8×C149—41no—
55C22×C149—21no—
56C22×C149—41no—
57C22×C149#9511yescharacteristic
58C2×D149—21no—
59C2×D149—21no—
60C2×D149—41no—
61C2×D149—41no—
62#10597010—82no—
63C4×C149—21no—
64C4×C149#9911yescharacteristic
65C4×C149#9911yescharacteristic
66Dic149—21no—
67Dic149—21no—
68C2×C149—21no—
69C2×C149—41no—
70C2×C149#34211yescharacteristic
71D149—41no—
72D149—41no—
73C149#139511yescharacteristic, complemented, Sylow
74#1395—1491nomaximal, Sylow
75#413—1491no—
76#410—1491no—
77#408—1491no—
78C2×#41—1491no—
79C2×M16—2981no—
80C2×M16#1059701011yescharacteristic, complemented
81C22×C8—1491no—
82#117—2981no—
83#101—1492no—
84#100—2981no—
85#99—2981no—
86#99—1492no—
87C22⋊C8—2981no—
88C22⋊C8—2981no—
89#41—5961no—
90#41—5961no—
91C2×Q8—1491no—
92C2×D4—1491no—
93C2×D4—1491no—
94C2×D4—1491no—
95C22×C4—1491no—
96C22×C4—1491no—
97C22×C4C2×#1059701011yescharacteristic
98M16—41no—
99M16—2982no—
100M16—5961no—
101C2×C8—21no—
102C2×C8—2981no—
103C2×C8—5961no—
104C2×C8—5961no—
105C4⋊C4—5961no—
106C22⋊C4—2982no—
107C42—5961no—
108C23—1491no—
109C23—1491no—
110C23C4⋊#1059701011yescharacteristic
111Q8—5961no—
112D4—5961no—
113D4—5961no—
114D4—5961no—
115C2×C4—21no—
116C2×C4—21no—
117C2×C4—2981no—
118C2×C4—2981no—
119C2×C4—2981no—
120C2×C4—2981no—
121C2×C4—5962no—
122C2×C4—1491no—
123C2×C4—1491no—
124C2×C4C4×#1059701011yescharacteristic
125C2×C4C22⋊#1059701011yescharacteristic
126C8—41no—
127C8—5962no—
128C8—5961no—
129C22—21no—
130C22—41no—
131C22—2981no—
132C22—2981no—
133C22—5961no—
134C22—5961no—
135C22(C2×#10597010)⋊C411yescharacteristic
136C4—21no—
137C4—2981no—
138C4—2981no—
139C4—11922no—
140C4#1801196911yescharacteristic
141C4#1801197011yescharacteristic
142C2—21no—
143C2—41no—
144C2—5961no—
145C2—5961no—
146C2#2375050311yescharacteristic
subgroupG/H
centerC4#18011969
commutatorC2×C4×C149C42
FrattiniC22×C4C2×#10597010
FittingC2×M16×C149C4
socleC2×C149#342
prime radical, cosocleC2×#14558736C22
hypercenterC2×M16#10597010
hypocenterC149#1395
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
6. #18011972C4semidirect
11. C22×#11924746C4semidirect
14. C2×M16×C149C4semidirect
73. C149#1395semidirect
80. C2×M16#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506112
#237506042
#237495932
#1395149