Finite Group Databasebeta

← #34060993

Subgroups — #34060993

Order 19072.

230 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 54 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#23750611C212yesmaximal
2#23750535C214yesmaximal, complemented
3#23750199C211yesmaximal, characteristic
4D149⋊M16—22no—
5#18011972C2214yes—
6#18011971—22no—
7C2×#14558736C2211yescharacteristic
8#18011909C2212yes—
9#18011900C412yes—
10#18011894—22no—
11#18011887—22no—
12#18011870C411yescharacteristic
13C22×Q8×C149C411yescharacteristic
14#14558746—42no—
15#14558745—24no—
16D149⋊C8—42no—
17#14558736—42no—
18C2×Dic298C2311yescharacteristic
19C2×D596C2×C411yescharacteristic
20C2×C22⋊D149D412yes—
21C2×C4×D149D412yes—
22C4⋊Dic149—21no—
23#14558715—24no—
24C22⋊Dic149—21no—
25#14558713—24no—
26C4×Dic149C2×C412yes—
27C2×Q8×C149—21no—
28C2×Q8×C149—42no—
29C2×Q8×C149C2×C412yes—
30C22×C4×C149—21no—
31C22×C4×C149C2×C411yescharacteristic
32#11924753—44no—
33C22×D149C22⋊C412yes—
34Dic298—41no—
35D596—41no—
36C22⋊D149—42no—
37C2×Dic149—22no—
38C2×Dic149C2×D412yes—
39C4×D149—22no—
40C4×D149—22no—
41C23×C149C22⋊C411yescharacteristic
42Q8×C149—42no—
43Q8×C149—42no—
44C2×C4×C149—22no—
45C2×C4×C149—22no—
46C2×C4×C149—42no—
47C2×C4×C149C22⋊C411yescharacteristic
48C2×C4×C149C22×C411yescharacteristic
49C22×C149—21no—
50C22×C149—41no—
51C22×C149C2×C22⋊C411yescharacteristic
52C2×D149—22no—
53C2×D149—42no—
54C4×C149—21no—
55C4×C149—42no—
56C4×C149#9912yes—
57Dic149—22no—
58Dic149—42no—
59C2×C149—21no—
60C2×C149—41no—
61C2×C149C2×#9911yescharacteristic
62D149—42no—
63C149#213511yescharacteristic, complemented, Sylow
64#2135—1491nomaximal, Sylow
65#536—1491no—
66#413—1492no—
67#356—1494no—
68C2×#41—1491no—
69C22×Q8#1059701011yescharacteristic
70C2×M16—2982no—
71C4⋊Q8—1492no—
72#124—1492no—
73#123—2982no—
74C22⋊Q8—2982no—
75#117—1491no—
76#101—1494no—
77#100—2982no—
78#41—5962no—
79C2×Q8—21no—
80C2×Q8—42no—
81C2×Q8—1491no—
82C2×Q8C2×#1059701012yes—
83C2×D4—1492no—
84C2×D4—1491no—
85C22×C4—21no—
86C22×C4—1492no—
87C22×C4C2×#1059701011yescharacteristic
88M16—2984no—
89M16—5962no—
90C2×C8—5962no—
91C4⋊C4—2984no—
92C4⋊C4—2981no—
93C22⋊C4—2984no—
94C22⋊C4—2981no—
95C42—1492no—
96C23—1492no—
97C23C22⋊#1059701011yescharacteristic
98Q8—42no—
99Q8—42no—
100Q8—5961no—
101D4—5961no—
102D4—5962no—
103C2×C4—22no—
104C2×C4—22no—
105C2×C4—42no—
106C2×C4—2982no—
107C2×C4—2982no—
108C2×C4—2982no—
109C2×C4—1492no—
110C2×C4C22⋊#1059701011yescharacteristic
111C2×C4C22×#1059701011yescharacteristic
112C8—5964no—
113C22—21no—
114C22—41no—
115C22—2982no—
116C22—5962no—
117C22C2×C22⋊#1059701011yescharacteristic
118C4—21no—
119C4—42no—
120C4—2982no—
121C4—5962no—
122C4#1801196912yes—
123C2—21no—
124C2—41no—
125C2—5962no—
126C2C2×#1801196911yescharacteristic
subgroupG/H
centerC2C2×#18011969
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC22×Q8×C149C4
socleC2×C149C2×#99
prime radicalC2×#14558736C22
cosocleC2×Dic298C23
hypercenterC22×Q8#10597010
hypocenterC149#2135
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. #23750535C2semidirect
63. C149#2135semidirect

Maximal subgroups

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

subgroupindex
#237506112
#237505352
#237501992
#2135149