Finite Group Databasebeta

← #34044014

Subgroups — #34044014

Order 19072.

196 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 49 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#23749995C211yesmaximal, characteristic, complemented
2#23749984C212yesmaximal, complemented
3#23749367C211yesmaximal, characteristic, complemented
4#23749365C212yesmaximal, complemented
5#562×C149C211yesmaximal, characteristic
6#18011911C2211yescharacteristic
7#18011835—22no—
8#18011834—22no—
9#18011832—22no—
10#18011822C2212yes—
11#18011822C2211yescharacteristic
12#125×C149C2211yescharacteristic
13#124×C149C2212yes—
14#123×C149—22no—
15C22⋊Q8×C149—22no—
16#121×C149—22no—
17C2×Dic298—21no—
18C2×#11924746—22no—
19C2×#11924746—21no—
20C4⋊Dic149—22no—
21C2×Q8×C149D412yes—
22C2×D4×C149—22no—
23C2×D4×C149D412yes—
24C22×C4×C149—22no—
25C4⋊C4×C149—22no—
26C4⋊C4×C149—22no—
27C4⋊C4×C149D412yes—
28C22⋊C4×C149—22no—
29C22⋊C4×C149—22no—
30C22⋊C4×C149—22no—
31C42×C149C2311yescharacteristic
32Dic298—42no—
33C2×Dic149—41no—
34#11924746—41no—
35#11924746—42no—
36C23×C149—22no—
37Q8×C149—42no—
38D4×C149—42no—
39D4×C149—82no—
40C2×C4×C149—22no—
41C2×C4×C149—22no—
42C2×C4×C149—82no—
43C2×C4×C149C2×D411yescharacteristic
44C2×C4×C149C2×D412yes—
45C22×C149—42no—
46C22×C149—42no—
47C22×C149—42no—
48C22×C149#12011yescharacteristic
49C4×C149—21no—
50C4×C149—22no—
51C4×C149—42no—
52C4×C149—42no—
53Dic149—81no—
54C2×C149—82no—
55C2×C149#45411yescharacteristic
56C2×C149#45512yes—
57C149#166211yescharacteristic, complemented, Sylow
58#1662—1491nomaximal, Sylow
59#562D14911yescharacteristic
60#491—1491no—
61#489—1492no—
62#330—1491no—
63#329—1492no—
64C4⋊Q8—1491no—
65#125C2×D14911yescharacteristic
66#124C2×D14912yes—
67#123—22no—
68C22⋊Q8—22no—
69#121—22no—
70#103—2982no—
71#103—2982no—
72#102—2982no—
73#97—1491no—
74#97—1492no—
75C2×Q8—2981no—
76C2×Q8C22⋊D14912yes—
77C2×D4—22no—
78C2×D4C22⋊D14912yes—
79C22×C4—22no—
80C2×C8—2982no—
81C2×C8—2981no—
82C4⋊C4—22no—
83C4⋊C4—22no—
84C4⋊C4—2982no—
85C4⋊C4C22⋊D14912yes—
86C22⋊C4—22no—
87C22⋊C4—22no—
88C22⋊C4—22no—
89C42C22×D14911yescharacteristic
90C23—22no—
91Q8—42no—
92Q8—5962no—
93D4—42no—
94D4—82no—
95C2×C4—22no—
96C2×C4—22no—
97C2×C4—82no—
98C2×C4—5961no—
99C2×C4C2×C22⋊D14911yescharacteristic
100C2×C4C2×C22⋊D14912yes—
101C8—5961no—
102C8—5962no—
103C22—42no—
104C22—42no—
105C22—42no—
106C22#1801188011yescharacteristic
107C4—21no—
108C4—22no—
109C4—42no—
110C4—42no—
111C4—11921no—
112C2—82no—
113C2#2374979811yescharacteristic
114C2#2374980312yes—
subgroupG/H
centerC22#18011880
commutator, cosocleC42×C149C23
FrattiniC42C22×D149
Fitting, prime radical#562×C149C2
socleC22×C149#120
hypercenter#562D149
hypocenterC149#1662
LCSG ▷ C42×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #562

Complements

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

NH ≅ G/Ntype
1. #23749995C2semidirect
2. #23749984C2semidirect
3. #23749367C2semidirect
4. #23749365C2semidirect
57. C149#1662semidirect

Maximal subgroups

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

subgroupindex
#237499952
#237499842
#237493672
#237493652
#562×C1492
#1662149