Finite Group Databasebeta

← #34044335

Subgroups — #34044335

Order 19072.

164 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 164 conjugacy classes of subgroups — too many to draw. Only its 57 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#23750028C211yesmaximal, characteristic
2#23749977C211yesmaximal, characteristic
3#23749976C211yesmaximal, characteristic
4#23749975C211yesmaximal, characteristic
5#23749975C211yesmaximal, characteristic
6#23749347C211yesmaximal, characteristic
7#498×C149C211yesmaximal, characteristic
8#18011911C2211yescharacteristic
9#18011911C2211yescharacteristic
10#18011844—22no—
11#18011836—22no—
12#18011835—22no—
13#18011835—22no—
14#18011834—22no—
15C4×#11924746C2211yescharacteristic
16C4×#11924746C2211yescharacteristic
17C4⋊Q8×C149C2211yescharacteristic
18C4⋊Q8×C149C2211yescharacteristic
19#106×C149—22no—
20C4×C8×C149C2211yescharacteristic
21C2×Dic298—21no—
22C2×Dic298—21no—
23C2×#11924746D412yes—
24C2×#11924746D412yes—
25C4⋊Dic149—21no—
26C4⋊Dic149—21no—
27C4⋊Dic149—21no—
28C4⋊Dic149—21no—
29C2×Q8×C149—21no—
30C2×Q8×C149—21no—
31C2×C8×C149D412yes—
32C4⋊C4×C149—21no—
33C4⋊C4×C149—21no—
34C4⋊C4×C149—21no—
35C4⋊C4×C149—21no—
36C42×C149C2311yescharacteristic
37Dic298—42no—
38Dic298—42no—
39C2×Dic149—41no—
40C2×Dic149—41no—
41#11924746—22no—
42#11924746—22no—
43Q8×C149—42no—
44Q8×C149—42no—
45C2×C4×C149—41no—
46C2×C4×C149—41no—
47C2×C4×C149C2×D411yescharacteristic
48C2×C4×C149C2×D411yescharacteristic
49C2×C4×C149C2×D411yescharacteristic
50C8×C149—22no—
51C22×C149#12711yescharacteristic
52C4×C149—81no—
53C4×C149—81no—
54C4×C149#13512yes—
55C4×C149#13712yes—
56C4×C149#13712yes—
57Dic149—81no—
58Dic149—81no—
59C2×C149#49511yescharacteristic
60C2×C149#49711yescharacteristic
61C2×C149#49711yescharacteristic
62C149#171811yescharacteristic, complemented, Sylow
63#1718—1491nomaximal, Sylow
64#500—1491no—
65#498D14911yescharacteristic
66#487—1491no—
67#487—1491no—
68#487—1491no—
69#487—1491no—
70#322—1491no—
71C4⋊Q8—1491no—
72C4⋊Q8—1491no—
73C4⋊Q8C2×D14911yescharacteristic
74C4⋊Q8C2×D14911yescharacteristic
75#107—2982no—
76#106—22no—
77#103—2982no—
78#103—2982no—
79#103—2982no—
80#103—2982no—
81C4×C8—1491no—
82C4×C8—1491no—
83C4×C8C2×D14911yescharacteristic
84C2×Q8—21no—
85C2×Q8—21no—
86C2×Q8—2981no—
87C2×Q8—2981no—
88C2×C8—1492no—
89C2×C8—1492no—
90C2×C8C22⋊D14912yes—
91C4⋊C4—21no—
92C4⋊C4—21no—
93C4⋊C4—21no—
94C4⋊C4—21no—
95C4⋊C4—2981no—
96C4⋊C4—2981no—
97C4⋊C4—2981no—
98C4⋊C4—2981no—
99C42C22×D14911yescharacteristic
100Q8—42no—
101Q8—42no—
102Q8—5962no—
103Q8—5962no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—5961no—
107C2×C4—5961no—
108C2×C4D4×D14911yescharacteristic
109C2×C4D4×D14911yescharacteristic
110C2×C4C2×C22⋊D14911yescharacteristic
111C8—22no—
112C8—2982no—
113C8—2982no—
114C22#1801190711yescharacteristic
115C4—81no—
116C4—81no—
117C4—11921no—
118C4—11921no—
119C4#1801193212yes—
120C4#1801194012yes—
121C4#1801194212yes—
122C2#2375000611yescharacteristic
123C2#2375001611yescharacteristic
124C2#2375001711yescharacteristic
subgroupG/H
centerC22#18011907
commutator, cosocleC42×C149C23
FrattiniC42C22×D149
Fitting#498×C149C2
socle, prime radicalC22×C149#127
hypercenter#498D149
hypocenterC149#1718
LCSG ▷ C42×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
62. C149#1718semidirect

Maximal subgroups

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

subgroupindex
#237500282
#237499772
#237499762
#237499752
#237493472
#498×C1492
#1718149