Finite Group Databasebeta

← #34059671

Subgroups — #34059671

Order 19072.

146 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 30 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#23750503C211yesmaximal, characteristic
2#23750469C211yesmaximal, characteristic
3#23749551C211yesmaximal, characteristic
4C2×C22⋊#10597010—21no—
5C22⋊#11924753—21no—
6C2×#14558713—21no—
7C2×#14558713C2211yescharacteristic
8#18011818—21no—
9#18011818C411yescharacteristic, complemented
10C2×C4⋊C4×C149C411yescharacteristic, complemented
11C22×#10597010—41no—
12C2×#11924753—41no—
13C22⋊#10597010—22no—
14C22⋊#10597010—41no—
15C23×D149D411yescharacteristic
16C22×Dic149—21no—
17C22×Dic149D411yescharacteristic
18#14558713—41no—
19#14558713—41no—
20#14558713—41no—
21C22×C4×C149—21no—
22C22×C4×C149C2×C411yescharacteristic
23C4⋊C4×C149—41no—
24C2×#10597010—42no—
25C2×#10597010—81no—
26C2×#10597010—81no—
27#11924753—81no—
28C22×D149—21no—
29C22×D149—21no—
30C22×D149—41no—
31C22×D149—41no—
32C22×D149D811yescharacteristic
33C22×D149SD1611yescharacteristic
34C2×Dic149—21no—
35C2×Dic149—41no—
36C2×Dic149—41no—
37C2×Dic149—41no—
38C2×Dic149—41no—
39C23×C149C22⋊C411yescharacteristic
40C2×C4×C149—21no—
41C2×C4×C149—41no—
42C2×C4×C149—41no—
43C2×C4×C149—41no—
44C2×C4×C149—41no—
45C22×C149—21no—
46C22×C149—21no—
47C22×C149#9911yescharacteristic
48C22×C149#10211yescharacteristic
49C22×C149#10411yescharacteristic
50C2×D149—21no—
51C2×D149—21no—
52C2×D149—41no—
53C2×D149—41no—
54C2×D149—41no—
55C2×D149—41no—
56C2×D149—81no—
57#10597010—82no—
58C4×C149—41no—
59C4×C149—81no—
60Dic149—41no—
61Dic149—81no—
62C2×C149—21no—
63C2×C149—21no—
64C2×C149#32711yescharacteristic
65C2×C149#35211yescharacteristic
66C2×C149#35411yescharacteristic
67D149—41no—
68D149—41no—
69C149#134411yescharacteristic, complemented, Sylow
70#1344—1491nomaximal, Sylow
71#397—1491no—
72#342—1491no—
73#323—1491no—
74C2×C4⋊C4#1059701011yescharacteristic, complemented
75C2×C22⋊C4—2981no—
76C2×C22⋊C4—2981no—
77C2×C22⋊C4—1491no—
78C22⋊C8—2981no—
79#95—2981no—
80#95—1491no—
81C24—1491no—
82C22×C4—21no—
83C22×C4—2981no—
84C22×C4—5961no—
85C22×C4—1491no—
86C22×C4C2×#1059701011yescharacteristic
87C2×C8—5961no—
88C4⋊C4—41no—
89C22⋊C4—2982no—
90C22⋊C4—5961no—
91C22⋊C4—5961no—
92C22⋊C4—5961no—
93C22⋊C4—5961no—
94C23—2981no—
95C23—2981no—
96C23—5961no—
97C23—5961no—
98C23—1491no—
99C23—1491no—
100C23C22⋊#1059701011yescharacteristic
101C2×C4—21no—
102C2×C4—41no—
103C2×C4—41no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—2981no—
107C2×C4—5961no—
108C2×C4—5961no—
109C2×C4—5961no—
110C2×C4—5962no—
111C2×C4—5961no—
112C2×C4—11921no—
113C2×C4—11921no—
114C8—11921no—
115C22—21no—
116C22—21no—
117C22—2981no—
118C22—2981no—
119C22—5961no—
120C22—5961no—
121C22—5961no—
122C22—5961no—
123C22—11921no—
124C22#1801196911yescharacteristic
125C22#1801197311yescharacteristic
126C22#1801197511yescharacteristic
127C4—41no—
128C4—81no—
129C4—5961no—
130C4—11921no—
131C4—11922no—
132C2—21no—
133C2—21no—
134C2—5961no—
135C2—5961no—
136C2#2375047611yescharacteristic
137C2#2375052711yescharacteristic
138C2#2375053111yescharacteristic
subgroupG/H
centerC22#18011969
commutatorC22×C4×C149C2×C4
FrattiniC22×C4C2×#10597010
FittingC2×C4⋊C4×C149C4
socleC22×C149#99
prime radicalC23×D149D4
cosocleC2×#14558713C22
hypercenterC2×C4⋊C4#10597010
hypocenterC149#1344
LCSG ▷ C22×C4×C149 ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
9. #18011818C4semidirect
10. C2×C4⋊C4×C149C4semidirect
69. C149#1344semidirect
74. C2×C4⋊C4#10597010semidirect

Maximal subgroups

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

subgroupindex
#237505032
#237504692
#237495512
#1344149