Finite Group Databasebeta

← #34043403

Subgroups — #34043403

Order 19072.

332 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 67 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#127×D149C211yesmaximal, characteristic
2#23749681C212yesmaximal, complemented
3#23749369C211yesmaximal, characteristic, complemented
4#23749368C212yesmaximal, complemented
5#331×C149C211yesmaximal, characteristic, complemented
6C2×D4×D149—22no—
7C2×D4×D149C412yes—
8#18011908C2211yescharacteristic
9#18011907—22no—
10#18011907C412yes—
11C42×D149C2211yescharacteristic
12C4⋊#11924746C2212yescomplemented
13#18011823—22no—
14#18011821—22no—
15#127×C149C2211yescharacteristic
16C4⋊C8×C149C2212yescomplemented
17C23×D149—22no—
18C2×D596—22no—
19C2×D596C2×C412yes—
20C2×C22⋊D149—22no—
21C2×C22⋊D149—24no—
22D4×D149—44no—
23D4×D149—44no—
24D4×D149—44no—
25C2×C4×D149C2×C411yescharacteristic
26C2×C4×D149D412yes—
27C2×#11924746—22no—
28C4×Dic149C2×C411yescharacteristic
29C4×Dic149D412yes—
30C2×D4×C149—22no—
31C2×D4×C149C2×C412yes—
32C2×C8×C149—22no—
33C42×C149C2311yescharacteristic
34C22×D149—22no—
35C22×D149—48no—
36C22×D149—44no—
37C22×D149C22⋊C411yescharacteristic
38D596—42no—
39D596—42no—
40D596—42no—
41C22⋊D149—44no—
42C22⋊D149—48no—
43C2×Dic149C22⋊C411yescharacteristic
44C2×Dic149C22⋊C412yes—
45C4×D149—22no—
46C4×D149—22no—
47C4×D149—22no—
48#11924746—42no—
49C23×C149—22no—
50D4×C149—42no—
51D4×C149—42no—
52D4×C149—42no—
53C2×C4×C149C22×C411yescharacteristic
54C2×C4×C149C2×D412yes—
55C8×C149—42no—
56C22×C149—42no—
57C22×C149—44no—
58C22×C149C2×C22⋊C411yescharacteristic
59C2×D149—22no—
60C2×D149—42no—
61C2×D149—44no—
62C2×D149—88no—
63C2×D149#10012yes—
64C4×C149—21no—
65C4×C149AGL(1,ℤ/8)12yes—
66C4×C149AGL(1,ℤ/8)12yes—
67Dic149—21no—
68Dic149—22no—
69C2×C149—82no—
70C2×C149C2×#10011yescharacteristic
71C2×C149#41812yes—
72D149—22no—
73D149—82no—
74C149#155511yescharacteristic, complemented, Sylow
75#1555—1491nomaximal, Sylow
76C2×#127—1491no—
77#432—1492no—
78#331—1491no—
79#331—1492no—
80#331D14911yescharacteristic, complemented
81C22×D4—2982no—
82C22×D4—1492no—
83#127—2982no—
84#127—1492no—
85#127—1491no—
86#127C2×D14911yescharacteristic
87C2×C42—1491no—
88C4⋊C8—1492no—
89C4⋊C8C2×D14912yescomplemented
90C22⋊C8—2982no—
91#97—2982no—
92C24—2982no—
93C2×D4—22no—
94C2×D4—2982no—
95C2×D4—2984no—
96C2×D4—2982no—
97C2×D4—5964no—
98C2×D4—5964no—
99C2×D4—5964no—
100C2×D4—1492no—
101C2×D4C4×D14912yes—
102C22×C4—1491no—
103C22×C4—1492no—
104C2×C8—22no—
105C2×C8—2982no—
106C42—1491no—
107C42—1492no—
108C42C22×D14911yescharacteristic
109C23—22no—
110C23—2982no—
111C23—5968no—
112C23—5964no—
113C23—1491no—
114D4—42no—
115D4—42no—
116D4—42no—
117D4—5962no—
118D4—5964no—
119D4—5968no—
120D4—5962no—
121D4—5962no—
122C2×C4—2982no—
123C2×C4—2982no—
124C2×C4—2982no—
125C2×C4—1491no—
126C2×C4—1492no—
127C2×C4C2×C4×D14911yescharacteristic
128C2×C4D4×D14912yes—
129C8—42no—
130C8—5962no—
131C22—42no—
132C22—44no—
133C22—2982no—
134C22—5962no—
135C22—5964no—
136C22—1492no—
137C22—11928no—
138C22C22⋊C4×D14911yescharacteristic
139C4—21no—
140C4—2981no—
141C4—2982no—
142C4#1801193512yes—
143C4#1801193812yes—
144C2—82no—
145C2—2982no—
146C2—11922no—
147C2#100×D14911yescharacteristic
148C2#2374962812yes—
subgroupG/H
centerC22C22⋊C4×D149
commutatorC2×C4×C149C22×C4
FrattiniC42C22×D149
Fitting#331×C149C2
socleC22×C149C2×C22⋊C4
prime radical#127×D149C2
cosocleC42×C149C23
hypercenter#331D149
hypocenterC149#1555
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #23749681C2semidirect
3. #23749369C2semidirect
4. #23749368C2semidirect
5. #331×C149C2semidirect
12. C4⋊#11924746C22semidirect
16. C4⋊C8×C149C22semidirect
74. C149#1555semidirect
80. #331D149semidirect
89. C4⋊C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#127×D1492
#237496812
#237493692
#237493682
#331×C1492
#1555149