Finite Group Databasebeta

← #34052956

Subgroups — #34052956

Order 19072.

548 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 125 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#23749561C213yesmaximal, complemented
2#23749549C212yesmaximal, complemented
3#23749547C216yesmaximal, complemented
4#23749480C213yesmaximal
5#399×C149C211yesmaximal, characteristic, complemented
6C24×D149C2211yescharacteristic
7C2×C4⋊Dic149C2213yescomplemented
8C2×#14558715C2216yescomplemented
9C2×C22⋊Dic149C2213yes—
10C2×#14558713C2216yes—
11C2×#14558713C2216yes—
12#18011818C2213yescomplemented
13C2×C4⋊C4×C149C2213yescomplemented
14C2×C22⋊C4×C149C2213yes—
15#95×C149C2211yescharacteristic, complemented
16C23×D149—43no—
17C23×D149—43no—
18C23×D149Q814yes—
19C23×D149C2312yes—
20C22×Dic149C2316yes—
21C4⋊Dic149—43no—
22#14558715—46no—
23C22⋊Dic149—43no—
24#14558713—46no—
25#14558713—46no—
26C24×C149C2311yescharacteristic
27C22×C4×C149C2313yes—
28C22×C4×C149C2313yes—
29C4⋊C4×C149—43no—
30C22⋊C4×C149—43no—
31C22×D149—26no—
32C22×D149—26no—
33C22×D149—412no—
34C22×D149—44no—
35C22×D149—412no—
36C22×D149C2×Q814yes—
37C2×Dic149—26no—
38C2×Dic149—26no—
39C2×Dic149—26no—
40C23×C149—23no—
41C23×C149—23no—
42C23×C149C2×Q812yes—
43C23×C149C2411yescharacteristic
44C2×C4×C149—23no—
45C2×C4×C149—23no—
46C2×C4×C149—26no—
47C2×C4×C149—26no—
48C22×C149—26no—
49C22×C149—41no—
50C22×C149—43no—
51C22×C149C22×Q811yescharacteristic
52C22×C149H(5,𝔽2)13yes—
53C22×C149H(5,𝔽2)13yes—
54C2×D149—212no—
55C2×D149—416no—
56C2×D149—42no—
57C2×D149—46no—
58C4×C149—43no—
59C4×C149—43no—
60Dic149—46no—
61C2×C149—42no—
62C2×C149#54313yes—
63C2×C149#56011yescharacteristic
64C2×C149#56013yes—
65D149—44no—
66C149#284211yescharacteristic, complemented, Sylow
67#2842—1491nomaximal, Sylow
68#399—1493no—
69#399D14911yescharacteristic, complemented
70#396—1496no—
71#396—1492no—
72#379—1493no—
73C25—1491no—
74C2×C4⋊C4—1496no—
75C2×C4⋊C4—1493no—
76C2×C4⋊C4C2×D14913yescomplemented
77C2×C22⋊C4—1493no—
78C2×C22⋊C4—1496no—
79C2×C22⋊C4—1496no—
80C2×C22⋊C4C2×D14913yes—
81#95—1493no—
82#95C2×D14911yescharacteristic, complemented
83C24—5963no—
84C24—5963no—
85C24—1492no—
86C24—1494no—
87C24C22×D14911yescharacteristic
88C22×C4—1496no—
89C22×C4C22×D14913yes—
90C22×C4C22×D14913yes—
91C4⋊C4—43no—
92C4⋊C4—5966no—
93C4⋊C4—5963no—
94C22⋊C4—43no—
95C22⋊C4—5966no—
96C22⋊C4—5966no—
97C22⋊C4—5963no—
98C23—23no—
99C23—23no—
100C23—2986no—
101C23—2986no—
102C23—59612no—
103C23—5964no—
104C23—59612no—
105C23—1494no—
106C23Q8×D14912yes—
107C23C23×D14911yescharacteristic
108C2×C4—23no—
109C2×C4—23no—
110C2×C4—26no—
111C2×C4—26no—
112C2×C4—2986no—
113C2×C4—2986no—
114C2×C4—2986no—
115C22—26no—
116C22—41no—
117C22—43no—
118C22—29812no—
119C22—59616no—
120C22—5962no—
121C22—5966no—
122C22C2×Q8×D14911yescharacteristic
123C22#1801195613yes—
124C22#1801195713yes—
125C4—43no—
126C4—43no—
127C4—5966no—
128C2—42no—
129C2—5964no—
130C2#2375025013yes—
131C2#2375036211yescharacteristic
132C2#2375036513yes—
subgroupG/H
center, FrattiniC23C23×D149
commutator, socle, cosocleC23×C149C24
Fitting#399×C149C2
prime radicalC24×D149C22
hypercenter#399D149
hypocenterC149#2842
LCSG ▷ C23×C149 ▷ C149
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. #23749561C2semidirect
2. #23749549C2semidirect
3. #23749547C2semidirect
5. #399×C149C2semidirect
7. C2×C4⋊Dic149C22semidirect
8. C2×#14558715C22semidirect
12. #18011818C22semidirect
13. C2×C4⋊C4×C149C22semidirect
15. #95×C149C22semidirect
66. C149#2842semidirect
69. #399D149semidirect
76. C2×C4⋊C4C2×D149semidirect
82. #95C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237495612
#237495492
#237495472
#237494802
#399×C1492
#2842149