Finite Group Databasebeta

← #34059593

Subgroups — #34059593

Order 19072.

200 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 44 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#23750597C211yesmaximal, characteristic
2#23750567C211yesmaximal, characteristic
3#23749587C211yesmaximal, characteristic
4C2×#14558745C412yescomplemented
5C2×C4⋊#10597010—21no—
6C2×C22⋊#10597010C412yes—
7#18011968—21no—
8#18011968—21no—
9(C2×#10597010)⋊C4—21no—
10C22×C4×D149C2211yescharacteristic
11C2×#14558719—21no—
12C22⋊#11924746C411yescharacteristic, complemented
13#18011823—21no—
14C22⋊C8×C149C411yescharacteristic, complemented
15C22×#10597010—22no—
16#14558745—42no—
17C2×#11924753—22no—
18C4⋊#10597010—42no—
19C22⋊#10597010—42no—
20C23×D149C2×C411yescharacteristic
21C22×Dic149C2×C411yescharacteristic
22C2×C4×D149—42no—
23C2×C4×D149D411yescharacteristic
24C2×C4×D149D411yescharacteristic
25C2×C4×D149D411yescharacteristic
26C2×C4×D149Q811yescharacteristic
27#14558719—42no—
28C2×#11924746—21no—
29C22×C4×C149C2×C411yescharacteristic
30C2×C8×C149—21no—
31C2×#10597010—42no—
32C2×#10597010—42no—
33C2×#10597010—42no—
34#11924753—42no—
35C22×D149—21no—
36C22×D149—21no—
37C22×D149—41no—
38C22×D149—41no—
39C22×D149C22⋊C411yescharacteristic
40C22×D149C4⋊C411yescharacteristic
41C2×Dic149—22no—
42C2×Dic149C22⋊C411yescharacteristic
43C2×Dic149C4⋊C411yescharacteristic
44C4×D149—22no—
45C4×D149—22no—
46C4×D149—41no—
47C4×D149—41no—
48#11924746—41no—
49C23×C149C4211yescharacteristic
50C2×C4×C149—41no—
51C2×C4×C149C22⋊C411yescharacteristic
52C2×C4×C149C4⋊C411yescharacteristic
53C8×C149—41no—
54C22×C149—21no—
55C22×C149—21no—
56C22×C149—21no—
57C22×C149#9511yescharacteristic
58C2×D149—21no—
59C2×D149—21no—
60C2×D149—21no—
61C2×D149—21no—
62C2×D149—21no—
63C2×D149—42no—
64C2×D149—42no—
65C2×D149#10011yescharacteristic
66C2×D149#10111yescharacteristic
67#10597010—82no—
68C4×C149—21no—
69C4×C149—21no—
70Dic149—21no—
71Dic149#9912yes—
72C2×C149—41no—
73C2×C149#34211yescharacteristic
74C2×C149#34311yescharacteristic
75C2×C149#34411yescharacteristic
76D149—21no—
77D149—21no—
78D149—41no—
79C149#130511yescharacteristic, complemented, Sylow
80#1305—1491nomaximal, Sylow
81#407—1491no—
82#407—1491no—
83#380—1491no—
84C23×C4—1491no—
85C2×M16—2981no—
86C2×M16—1492no—
87C2×C4⋊C4—2981no—
88C2×C22⋊C4—1492no—
89C22⋊C8—2981no—
90C22⋊C8—2981no—
91C22⋊C8—2981no—
92C22⋊C8—1491no—
93C22⋊C8#1059701011yescharacteristic, complemented
94#95—2981no—
95C24—1491no—
96C22×C4—2982no—
97C22×C4—5962no—
98C22×C4—1491no—
99C22×C4—1491no—
100C22×C4—1491no—
101C22×C4—1491no—
102C22×C4—1491no—
103C22×C4C2×#1059701011yescharacteristic
104M16—5962no—
105M16—5962no—
106C2×C8—21no—
107C2×C8—2982no—
108C2×C8—2981no—
109C4⋊C4—5962no—
110C22⋊C4—5962no—
111C23—2981no—
112C23—2981no—
113C23—5961no—
114C23—5961no—
115C23—1491no—
116C23—1491no—
117C23C4×#1059701011yescharacteristic
118C2×C4—41no—
119C2×C4—2982no—
120C2×C4—2982no—
121C2×C4—2982no—
122C2×C4—5961no—
123C2×C4—5961no—
124C2×C4—5962no—
125C2×C4—5962no—
126C2×C4—5962no—
127C2×C4—1491no—
128C2×C4—1491no—
129C2×C4C22⋊#1059701011yescharacteristic
130C2×C4C4⋊#1059701011yescharacteristic
131C8—41no—
132C8—5961no—
133C8—5962no—
134C22—21no—
135C22—21no—
136C22—21no—
137C22—2981no—
138C22—2981no—
139C22—2981no—
140C22—2981no—
141C22—2981no—
142C22—5962no—
143C22—5962no—
144C22—1491no—
145C22—1491no—
146C22(C2×#10597010)⋊C411yescharacteristic
147C4—21no—
148C4—21no—
149C4—2981no—
150C4—1492no—
151C4—11922no—
152C2—41no—
153C2—2981no—
154C2—2981no—
155C2—5961no—
156C2#2375050211yescharacteristic
157C2#2375050411yescharacteristic
158C2#2375050711yescharacteristic
subgroupG/H
centerC22(C2×#10597010)⋊C4
commutatorC23×C149C42
FrattiniC22×C4C2×#10597010
FittingC22⋊C8×C149C4
socleC22×C149#95
prime radicalC23×D149C2×C4
cosocleC22×C4×D149C22
hypercenterC22⋊C8#10597010
hypocenterC149#1305
LCSG ▷ C23×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
4. C2×#14558745C4semidirect
12. C22⋊#11924746C4semidirect
14. C22⋊C8×C149C4semidirect
79. C149#1305semidirect
93. C22⋊C8#10597010semidirect

Maximal subgroups

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

subgroupindex
#237505972
#237505672
#237495872
#1305149