Finite Group Databasebeta

← #34059591

Subgroups — #34059591

Order 19072.

200 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 46 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#23750596C211yesmaximal, characteristic
2#23750567C211yesmaximal, characteristic
3#23749588C211yesmaximal, characteristic
4C2×#14558746—21no—
5C2×C4⋊#10597010—21no—
6C2×C22⋊#10597010C412yes—
7#18011968—21no—
8C22⋊#11924753C412yescomplemented
9(C2×#10597010)⋊C4—21no—
10C22×C4×D149C2211yescharacteristic
11C2×#14558720C411yescharacteristic, complemented
12#18011823—21no—
13#18011823—21no—
14C2×M16×C149C411yescharacteristic, complemented
15C22×#10597010—22no—
16#14558746—41no—
17#14558746—41no—
18C2×#11924753—22no—
19C4⋊#10597010—41no—
20C4⋊#10597010—41no—
21C22⋊#10597010—42no—
22C23×D149C2×C411yescharacteristic
23C22×Dic149C2×C411yescharacteristic
24C2×C4×D149—41no—
25C2×C4×D149—41no—
26C2×C4×D149D411yescharacteristic
27C2×C4×D149D411yescharacteristic
28C2×C4×D149D411yescharacteristic
29C2×C4×D149Q811yescharacteristic
30#14558720—41no—
31C2×#11924746—21no—
32C22×C4×C149C2×C411yescharacteristic
33M16×C149—41no—
34C2×C8×C149—21no—
35C2×#10597010—42no—
36C2×#10597010—42no—
37C2×#10597010—42no—
38#11924753—42no—
39C22×D149—21no—
40C22×D149—21no—
41C22×D149—41no—
42C22×D149—41no—
43C22×D149C22⋊C411yescharacteristic
44C22×D149C4⋊C411yescharacteristic
45C2×Dic149—41no—
46C2×Dic149C22⋊C411yescharacteristic
47C2×Dic149C4⋊C411yescharacteristic
48C4×D149—21no—
49C4×D149—21no—
50C4×D149—21no—
51C4×D149—21no—
52C4×D149—41no—
53C4×D149—41no—
54#11924746—41no—
55C23×C149C4211yescharacteristic
56C2×C4×C149—21no—
57C2×C4×C149—21no—
58C2×C4×C149C22⋊C411yescharacteristic
59C2×C4×C149C4⋊C411yescharacteristic
60C8×C149—41no—
61C22×C149—21no—
62C22×C149—21no—
63C22×C149—21no—
64C22×C149#9511yescharacteristic
65C2×D149—21no—
66C2×D149—21no—
67C2×D149—21no—
68C2×D149—21no—
69C2×D149—21no—
70C2×D149—42no—
71C2×D149—42no—
72C2×D149#10011yescharacteristic
73C2×D149#10111yescharacteristic
74#10597010—82no—
75C4×C149—21no—
76C4×C149#9911yescharacteristic
77C4×C149#9911yescharacteristic
78Dic149—21no—
79Dic149—21no—
80C2×C149—41no—
81C2×C149#34211yescharacteristic
82C2×C149#34311yescharacteristic
83C2×C149#34411yescharacteristic
84D149—21no—
85D149—21no—
86D149—41no—
87C149#130511yescharacteristic, complemented, Sylow
88#1305—1491nomaximal, Sylow
89#407—1491no—
90#407—1491no—
91#380—1491no—
92C23×C4—1491no—
93C2×M16—2981no—
94C2×M16—1491no—
95C2×M16#1059701011yescharacteristic, complemented
96C2×C4⋊C4—2981no—
97C2×C22⋊C4—1492no—
98C22⋊C8—2981no—
99C22⋊C8—2981no—
100C22⋊C8—2981no—
101C22⋊C8—1492no—
102#95—2981no—
103C24—1491no—
104C22×C4—2982no—
105C22×C4—5961no—
106C22×C4—5961no—
107C22×C4—1491no—
108C22×C4—1491no—
109C22×C4—1491no—
110C22×C4—1491no—
111C22×C4—1491no—
112C22×C4C2×#1059701011yescharacteristic
113M16—41no—
114M16—5961no—
115M16—5961no—
116M16—5961no—
117C2×C8—21no—
118C2×C8—2982no—
119C2×C8—2981no—
120C4⋊C4—5961no—
121C4⋊C4—5961no—
122C22⋊C4—5962no—
123C23—2981no—
124C23—2981no—
125C23—5961no—
126C23—5961no—
127C23—1491no—
128C23—1491no—
129C23C4×#1059701011yescharacteristic
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—2981no—
133C2×C4—2981no—
134C2×C4—2981no—
135C2×C4—2981no—
136C2×C4—5961no—
137C2×C4—5961no—
138C2×C4—5961no—
139C2×C4—5962no—
140C2×C4—5962no—
141C2×C4—5962no—
142C2×C4—1491no—
143C2×C4—1491no—
144C2×C4C22⋊#1059701011yescharacteristic
145C2×C4C4⋊#1059701011yescharacteristic
146C8—41no—
147C8—5962no—
148C8—5961no—
149C22—21no—
150C22—21no—
151C22—21no—
152C22—2981no—
153C22—2981no—
154C22—2981no—
155C22—2981no—
156C22—2981no—
157C22—5962no—
158C22—5962no—
159C22—1491no—
160C22—1491no—
161C22(C2×#10597010)⋊C411yescharacteristic
162C4—21no—
163C4—2981no—
164C4—2981no—
165C4—11922no—
166C4#1801196911yescharacteristic
167C4#1801197011yescharacteristic
168C2—41no—
169C2—2981no—
170C2—2981no—
171C2—5961no—
172C2#2375050311yescharacteristic
173C2#2375050411yescharacteristic
174C2#2375050811yescharacteristic
subgroupG/H
centerC22(C2×#10597010)⋊C4
commutatorC23×C149C42
FrattiniC22×C4C2×#10597010
FittingC2×M16×C149C4
socleC22×C149#95
prime radicalC23×D149C2×C4
cosocleC22×C4×D149C22
hypercenterC2×M16#10597010
hypocenterC149#1305
LCSG ▷ C23×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
8. C22⋊#11924753C4semidirect
11. C2×#14558720C4semidirect
14. C2×M16×C149C4semidirect
87. C149#1305semidirect
95. C2×M16#10597010semidirect

Maximal subgroups

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

subgroupindex
#237505962
#237505672
#237495882
#1305149