Finite Group Databasebeta

← #34060035

Subgroups — #34060035

Order 19072.

252 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 68 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#23750646C211yesmaximal, characteristic
2C4×#14558745C211yesmaximal, characteristic
3#23750475C214yesmaximal, complemented
4C2×#18011876C211yesmaximal, characteristic
5C2×#14558745—21no—
6C4⋊#11924753C2212yes—
7C22⋊#11924753—21no—
8#18011966—21no—
9#18011966—21no—
10C4×#11924753C2212yes—
11C22×Dic298C411yescharacteristic
12#18011876—21no—
13#18011876—21no—
14#18011876C412yes—
15#18011876C2212yes—
16C2×#14558715—21no—
17C2×C4×Dic149—21no—
18C2×C4×Dic149C2211yescharacteristic
19C2×C4⋊C4×C149C411yescharacteristic
20#14558745—24no—
21C2×#11924753—22no—
22C2×#11924753—22no—
23C2×Dic298—24no—
24C2×Dic298—21no—
25C2×Dic298C2×C412yes—
26C22×Dic149—21no—
27C22×Dic149D411yescharacteristic
28C22×Dic149D411yescharacteristic
29#14558715—22no—
30#14558715—22no—
31C4×Dic149—22no—
32C4×Dic149—22no—
33C4×Dic149C2×C411yescharacteristic
34C4×Dic149D411yescharacteristic
35C4×Dic149D411yescharacteristic
36C4×Dic149C2311yescharacteristic
37C22×C4×C149—21no—
38C22×C4×C149C2×C411yescharacteristic
39C4⋊C4×C149—21no—
40C4⋊C4×C149C2×C412yes—
41#11924753—24no—
42#11924753—42no—
43Dic298—24no—
44Dic298—22no—
45Dic298M1614yescomplemented
46C2×Dic149—24no—
47C2×Dic149—22no—
48C2×Dic149—22no—
49C2×Dic149—22no—
50C2×Dic149C22⋊C411yescharacteristic
51C2×Dic149C22⋊C411yescharacteristic
52C2×Dic149C2×D411yescharacteristic
53C2×Dic149C2×D411yescharacteristic
54C23×C149C22⋊C411yescharacteristic
55C2×C4×C149—22no—
56C2×C4×C149—22no—
57C2×C4×C149—42no—
58C2×C4×C149C22⋊C411yescharacteristic
59C2×C4×C149C22×C411yescharacteristic
60C22×C149—21no—
61C22×C149—21no—
62C22×C149#10412yes—
63C22×C149C2×C22⋊C411yescharacteristic
64C4×C149—21no—
65C4×C149—42no—
66C4×C149C2×M1612yes—
67Dic149—24no—
68Dic149—21no—
69Dic149—21no—
70Dic149—21no—
71Dic149#13712yes—
72C2×C149—22no—
73C2×C149#40711yescharacteristic
74C2×C149#41911yescharacteristic
75C2×C149C2×#10411yescharacteristic
76C149#149111yescharacteristic, complemented, Sylow
77#1491—1491nomaximal, Sylow
78C2×C4×Q8—1491no—
79#432—1491no—
80C4×M16—1491no—
81Q8⋊C8—1494no—
82C22×Q8—1491no—
83C2×M16—2981no—
84C4×Q8—2981no—
85C4×Q8—2981no—
86C4×Q8—1492no—
87C4×Q8—1492no—
88C2×C4⋊C4—2981no—
89C2×C4⋊C4#1059701011yescharacteristic
90C2×C42—2981no—
91C2×C42—1491no—
92C4⋊C8—1492no—
93C22⋊C8—2981no—
94#97—2981no—
95#97—2981no—
96C4×C8—1492no—
97C2×Q8—2984no—
98C2×Q8—2981no—
99C2×Q8—1492no—
100C22×C4—21no—
101C22×C4—2981no—
102C22×C4—1491no—
103C22×C4—1491no—
104C22×C4C2×#1059701011yescharacteristic
105M16—2984no—
106C2×C8—2982no—
107C2×C8—2982no—
108C4⋊C4—21no—
109C4⋊C4—2982no—
110C4⋊C4—2982no—
111C4⋊C4C2×#1059701012yes—
112C42—2982no—
113C42—2982no—
114C42—1491no—
115C42—1491no—
116C42—1491no—
117C42—1491no—
118C23C22⋊#1059701011yescharacteristic
119Q8—2984no—
120Q8—2982no—
121Q8—1494no—
122C2×C4—22no—
123C2×C4—22no—
124C2×C4—42no—
125C2×C4—2984no—
126C2×C4—2982no—
127C2×C4—2982no—
128C2×C4—2982no—
129C2×C4—1491no—
130C2×C4—1491no—
131C2×C4—1491no—
132C2×C4—1491no—
133C2×C4C22⋊#1059701011yescharacteristic
134C2×C4C22×#1059701011yescharacteristic
135C8—2984no—
136C8—5962no—
137C22—21no—
138C22—21no—
139C22#1801197512yes—
140C22C2×C22⋊#1059701011yescharacteristic
141C4—21no—
142C4—42no—
143C4—2984no—
144C4—2981no—
145C4—2981no—
146C4—2981no—
147C4—1492no—
148C4D149⋊M1612yes—
149C2—22no—
150C2#2375059711yescharacteristic
151C2#2375061811yescharacteristic
152C2C2×#1801197511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC2×C4⋊C4×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC23×C149C22⋊C4
cosocleC4×Dic149C23
hypercenterC2×C4⋊C4#10597010
hypocenterC149#1491
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #23750475C2semidirect
45. Dic298M16semidirect
76. C149#1491semidirect

Maximal subgroups

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

subgroupindex
#237506462
C4×#145587452
#237504752
C2×#180118762
#1491149