Finite Group Databasebeta

← #34044015

Subgroups — #34044015

Order 19072.

196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 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#23750373C211yesmaximal, characteristic
2#23749995C211yesmaximal, characteristic, complemented
3#23749985C212yesmaximal, complemented
4#23749364C212yesmaximal, complemented
5#330×C149C211yesmaximal, characteristic, complemented
6#18011911C2211yescharacteristic
7#18011899C2212yes—
8#18011896—22no—
9#18011889—22no—
10#18011886—22no—
11#18011836—22no—
12#18011834—22no—
13#18011833—22no—
14#18011822C2211yescharacteristic
15#125×C149C2211yescharacteristic
16#97×C149C2212yes—
17C2×Dic298—21no—
18C2×Dic298D412yes—
19C2×D596—22no—
20C2×D596D412yes—
21C2×C4×D149—22no—
22C2×#11924746—21no—
23C4⋊Dic149—22no—
24#14558715—22no—
25#14558713—22no—
26#14558713—22no—
27#14558713—22no—
28C2×C8×C149—22no—
29C4⋊C4×C149—22no—
30C4⋊C4×C149D412yes—
31C42×C149C2311yescharacteristic
32C22×D149—22no—
33Dic298—42no—
34Dic298—42no—
35D596—42no—
36D596—82no—
37C2×Dic149—22no—
38C2×Dic149—41no—
39C4×D149—82no—
40#11924746—41no—
41C2×C4×C149—22no—
42C2×C4×C149C2×D412yes—
43C2×C4×C149C2×D411yescharacteristic
44C8×C149—42no—
45C22×C149#12011yescharacteristic
46C2×D149—42no—
47C2×D149—42no—
48C2×D149—42no—
49C4×C149—21no—
50C4×C149—22no—
51C4×C149—42no—
52Dic149—42no—
53Dic149—81no—
54C2×C149#45411yescharacteristic
55C2×C149#45512yes—
56D149—82no—
57C149#166211yescharacteristic, complemented, Sylow
58#1662—1491nomaximal, Sylow
59#562—1491no—
60#491—1491no—
61#489—1492no—
62#330D14911yescharacteristic, complemented
63#329—1492no—
64C4⋊Q8—1491no—
65#125C2×D14911yescharacteristic
66#124—1492no—
67#123—2982no—
68C22⋊Q8—2982no—
69#121—2982no—
70#103—2982no—
71#103—2982no—
72#102—2982no—
73#97—1491no—
74#97C2×D14912yes—
75C2×Q8—2981no—
76C2×Q8—1492no—
77C2×D4—2982no—
78C2×D4—1492no—
79C22×C4—2982no—
80C2×C8—22no—
81C2×C8—2981no—
82C4⋊C4—22no—
83C4⋊C4—2982no—
84C4⋊C4—2982no—
85C4⋊C4D59612yes—
86C22⋊C4—2982no—
87C22⋊C4—2982no—
88C22⋊C4—2982no—
89C42C22×D14911yescharacteristic
90C23—2982no—
91Q8—5962no—
92Q8—5962no—
93D4—5962no—
94D4—11922no—
95C2×C4—22no—
96C2×C4—2982no—
97C2×C4—5961no—
98C2×C4—11922no—
99C2×C4D4×D14912yes—
100C2×C4C2×D59611yescharacteristic
101C8—42no—
102C8—5961no—
103C22—5962no—
104C22—5962no—
105C22—5962no—
106C22#1801188111yescharacteristic
107C4—21no—
108C4—22no—
109C4—42no—
110C4—5962no—
111C4—11921no—
112C2—11922no—
113C2#2374980011yescharacteristic
114C2#2374980412yes—
subgroupG/H
centerC22#18011881
commutator, cosocleC42×C149C23
FrattiniC42C22×D149
Fitting#330×C149C2
socleC22×C149#120
prime radical#23750373C2
hypercenter#330D149
hypocenterC149#1662
LCSG ▷ C42×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #23749995C2semidirect
3. #23749985C2semidirect
4. #23749364C2semidirect
5. #330×C149C2semidirect
57. C149#1662semidirect
62. #330D149semidirect

Maximal subgroups

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

subgroupindex
#237503732
#237499952
#237499852
#237493642
#330×C1492
#1662149