Finite Group Databasebeta

← #34042841

Subgroups — #34042841

Order 19072.

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

normal subgroups only

This group has 112 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#23749797C211yesmaximal, characteristic
2#23749365C211yesmaximal, characteristic, complemented
3#354×C149C211yesmaximal, characteristic, complemented
4#18011959C411yescharacteristic, complemented
5#18011937—21no—
6#18011839—21no—
7#18011830C411yescharacteristic, complemented
8#18011822—21no—
9#124×C149C2211yescharacteristic
10#99×C149—21no—
11#14558737—41no—
12#14558736—21no—
13#14558736—41no—
14Q8×D149—41no—
15#14558724—41no—
16#14558721—41no—
17#14558720—21no—
18C2×#11924746—41no—
19C2×Q8×C149C2×C411yescharacteristic
20C2×D4×C149D411yescharacteristic
21C22⋊C4×C149—41no—
22C22⋊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—42no—
33C23×C149—21no—
34Q8×C149—41no—
35D4×C149—41no—
36C2×C4×C149—21no—
37C2×C4×C149—21no—
38C2×C4×C149—81no—
39C2×C4×C149C22⋊C411yescharacteristic
40C22×C149—41no—
41C22×C149—81no—
42C22×C149#9911yescharacteristic
43C2×D149—41no—
44C4×C149—21no—
45C4×C149—41no—
46C4×C149—41no—
47C4×C149—161no—
48Dic149—41no—
49C2×C149—21no—
50C2×C149—81no—
51C2×C149AΣL(1,𝔽16)11yescharacteristic
52D149—81no—
53C149#140411yescharacteristic, complemented, Sylow
54#1404—1491nomaximal, Sylow
55#454—1491no—
56#354D14911yescharacteristic, complemented
57#329—1491no—
582−1+4—1491no—
59AGL(1,ℤ/8)—2981no—
60#124C2×D14911yescharacteristic
61#104—2981no—
62#101—1491no—
63#99—21no—
64#97—2981no—
65#41—2981no—
66#41—5961no—
67#41—5961no—
68C2×Q8—5961no—
69C2×Q8C4×D14911yescharacteristic
70C2×D4C22⋊D14911yescharacteristic
71SD16—5961no—
72D8—5961no—
73M16—2981no—
74C2×C8—5961no—
75C22⋊C4—41no—
76C22⋊C4—41no—
77C42D59611yescharacteristic
78C23—21no—
79Q8—41no—
80Q8—2981no—
81Q8—5961no—
82D4—41no—
83D4—2981no—
84D4—5961no—
85D4—5961no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—81no—
89C2×C4—5961no—
90C2×C4—5962no—
91C2×C4#1455871311yescharacteristic
92C8—5961no—
93C8—5962no—
94C22—41no—
95C22—81no—
96C22—5961no—
97C22#1801182511yescharacteristic
98C4—21no—
99C4—41no—
100C4—41no—
101C4—161no—
102C4—5961no—
103C2—21no—
104C2—81no—
105C2—11921no—
106C2#2374941111yescharacteristic
subgroupG/H
centerC2#23749411
commutatorC2×Q8×C149C2×C4
Frattini#124C2×D149
Fitting#354×C149C2
socleC2×C149AΣL(1,𝔽16)
prime radical#23749797C2
cosocle#124×C149C22
hypercenter#354D149
hypocenterC149#1404
LCSG ▷ C2×Q8×C149 ▷ C2×C4×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #354

Complements

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

NH ≅ G/Ntype
2. #23749365C2semidirect
3. #354×C149C2semidirect
4. #18011959C4semidirect
7. #18011830C4semidirect
53. C149#1404semidirect
56. #354D149semidirect

Maximal subgroups

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

subgroupindex
#237497972
#237493652
#354×C1492
#1404149