Finite Group Databasebeta

← #34042846

Subgroups — #34042846

Order 19072.

106 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 106 conjugacy classes of subgroups — too many to draw. Only its 23 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#23749807C211yesmaximal, characteristic
2#23749424C211yesmaximal, characteristic, complemented
3#333×C149C211yesmaximal, characteristic, complemented
4#18011959C411yescharacteristic
5#18011942—21no—
6#18011839—21no—
7#18011830—21no—
8#18011830C411yescharacteristic
9C4⋊Q8×C149C2211yescharacteristic
10C4⋊C8×C149—21no—
11#14558737—41no—
12#14558736—21no—
13#14558736—41no—
14Q8×D149—41no—
15#14558726—41no—
16#14558723—41no—
17#14558720—21no—
18#14558720—41no—
19C2×Q8×C149C2×C411yescharacteristic
20C2×Q8×C149D411yescharacteristic
21C2×C8×C149—41no—
22C4⋊C4×C149—41no—
23C42×C149D411yescharacteristic
24Dic298—21no—
25Dic298—41no—
26D596—21no—
27D596—41no—
28C22⋊D149—41no—
29C4×D149—41no—
30C4×D149—42no—
31#11924746—41no—
32#11924746—81no—
33Q8×C149—41no—
34Q8×C149—41no—
35C2×C4×C149—21no—
36C2×C4×C149—21no—
37C2×C4×C149—21no—
38C2×C4×C149C22⋊C411yescharacteristic
39C8×C149—81no—
40C22×C149#9911yescharacteristic
41C2×D149—41no—
42C4×C149—21no—
43C4×C149—21no—
44C4×C149—21no—
45C4×C149—41no—
46C4×C149—41no—
47Dic149—41no—
48C2×C149—21no—
49C2×C149AΣL(1,𝔽16)11yescharacteristic
50D149—81no—
51C149#140511yescharacteristic, complemented, Sylow
52#1405—1491nomaximal, Sylow
53#456—1491no—
54#356—1491no—
55#333D14911yescharacteristic, complemented
562−1+4—1491no—
57#137—2981no—
58C4⋊Q8C2×D14911yescharacteristic
59C4⋊C8—21no—
60#104—2981no—
61#101—2981no—
62#101—1491no—
63#41—2981no—
64#41—5961no—
65#41—5961no—
66C2×Q8—5961no—
67C2×Q8C4×D14911yescharacteristic
68C2×Q8D59611yescharacteristic
69Q16—5961no—
70SD16—5961no—
71M16—2981no—
72M16—5961no—
73C2×C8—41no—
74C4⋊C4—41no—
75C42C22⋊D14911yescharacteristic
76Q8—41no—
77Q8—41no—
78Q8—2981no—
79Q8—5961no—
80D4—2981no—
81D4—5961no—
82D4—5961no—
83C2×C4—21no—
84C2×C4—21no—
85C2×C4—21no—
86C2×C4—5961no—
87C2×C4—5962no—
88C2×C4#1455871311yescharacteristic
89C8—81no—
90C8—5961no—
91C8—11921no—
92C22—5961no—
93C22#1801182511yescharacteristic
94C4—21no—
95C4—21no—
96C4—21no—
97C4—41no—
98C4—41no—
99C4—5961no—
100C2—21no—
101C2—11921no—
102C2#2374941311yescharacteristic
subgroupG/H
centerC2#23749413
commutatorC2×Q8×C149C2×C4
FrattiniC4⋊Q8C2×D149
Fitting#333×C149C2
socleC2×C149AΣL(1,𝔽16)
prime radical#18011959C4
cosocleC4⋊Q8×C149C22
hypercenter#333D149
hypocenterC149#1405
LCSG ▷ C2×Q8×C149 ▷ C2×C4×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #23749424C2semidirect
3. #333×C149C2semidirect
51. C149#1405semidirect
55. #333D149semidirect

Maximal subgroups

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

subgroupindex
#237498072
#237494242
#333×C1492
#1405149