Finite Group Databasebeta

← #23749519

Subgroups — #23749519

Order 9536.

190 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 69 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
1C2×#14558715C211yesmaximal, characteristic, complemented
2C2×C22⋊Dic149C211yesmaximal, characteristic
3C2×C22⋊Dic149C211yesmaximal, characteristic
4C2×C4×Dic149C211yesmaximal, characteristic, complemented
5#18011818C211yesmaximal, characteristic, complemented
6#18011818C211yesmaximal, characteristic, complemented
7C2×C22⋊C4×C149C211yesmaximal, characteristic
8C22×Dic149C2211yescharacteristic
9C22×Dic149C2211yescharacteristic
10C22×Dic149C2211yescharacteristic
11C22×Dic149C2211yescharacteristic
12#14558715—22no—
13C22⋊Dic149—22no—
14C22⋊Dic149C414yescomplemented
15C4×Dic149—22no—
16C24×C149C2211yescharacteristic
17C22×C4×C149C2211yescharacteristic
18C22×C4×C149C2211yescharacteristic
19C22⋊C4×C149—22no—
20C2×Dic149—21no—
21C2×Dic149—21no—
22C2×Dic149—21no—
23C2×Dic149—21no—
24C2×Dic149—21no—
25C2×Dic149—21no—
26C2×Dic149—21no—
27C2×Dic149—21no—
28C2×Dic149—21no—
29C2×Dic149C2×C412yes—
30C2×Dic149C2×C412yes—
31C2×Dic149D412yes—
32C23×C149—21no—
33C23×C149—21no—
34C23×C149—21no—
35C23×C149—21no—
36C23×C149—21no—
37C23×C149—21no—
38C23×C149C2×C412yes—
39C23×C149C2311yescharacteristic
40C2×C4×C149—21no—
41C2×C4×C149—21no—
42C2×C4×C149—21no—
43C2×C4×C149—21no—
44C2×C4×C149—21no—
45C2×C4×C149D412yes—
46C22×C149—22no—
47C22×C149—22no—
48C22×C149—22no—
49C22×C149—41no—
50C22×C149—41no—
51C22×C149—41no—
52C22×C149—41no—
53C22×C149C22×C411yescharacteristic
54C22×C149C2×D411yescharacteristic
55C22×C149C2×D411yescharacteristic
56C22×C149#4111yescharacteristic
57C22×C149#4111yescharacteristic
58C22×C149#4111yescharacteristic
59C22×C149#4111yescharacteristic
60C4×C149—22no—
61C4×C149—41no—
62Dic149—22no—
63Dic149—22no—
64Dic149—22no—
65Dic149—41no—
66C2×C149—42no—
67C2×C149#11711yescharacteristic
68C2×C149C4×D411yescharacteristic
69C2×C149C4×D411yescharacteristic
70C2×C149#12111yescharacteristic
71C2×C149#12311yescharacteristic
72C2×C149#12411yescharacteristic
73C2×C149#12611yescharacteristic
74C149#38811yescharacteristic, complemented, Sylow
75#388—1491nomaximal, Sylow
76C2×C4⋊C4—1491no—
77C2×C22⋊C4—1491no—
78C2×C22⋊C4—1491no—
79C2×C22⋊C4D14911yescharacteristic
80C2×C42—1491no—
81#95—1491no—
82#95—1491no—
83C24C2×D14911yescharacteristic
84C22×C4—1491no—
85C22×C4—1491no—
86C22×C4—1491no—
87C22×C4—1491no—
88C22×C4C2×D14911yescharacteristic
89C22×C4C2×D14911yescharacteristic
90C4⋊C4—2982no—
91C22⋊C4—22no—
92C22⋊C4—2982no—
93C22⋊C4—1494no—
94C42—2982no—
95C23—21no—
96C23—21no—
97C23—21no—
98C23—21no—
99C23—21no—
100C23—21no—
101C23C4×D14912yes—
102C23C22×D14911yescharacteristic
103C2×C4—21no—
104C2×C4—21no—
105C2×C4—21no—
106C2×C4—21no—
107C2×C4—21no—
108C2×C4—2981no—
109C2×C4—2981no—
110C2×C4—2981no—
111C2×C4—2981no—
112C2×C4—2981no—
113C2×C4—2981no—
114C2×C4—2981no—
115C2×C4—2981no—
116C2×C4—2981no—
117C2×C4—1492no—
118C2×C4—1492no—
119C2×C4—1492no—
120C2×C4C22⋊D14912yes—
121C22—22no—
122C22—22no—
123C22—22no—
124C22—41no—
125C22—41no—
126C22—41no—
127C22—41no—
128C22C2×C4×D14911yescharacteristic
129C22D4×D14911yescharacteristic
130C22C2×C22⋊D14911yescharacteristic
131C22#1455873511yescharacteristic
132C22#1455873511yescharacteristic
133C22#1455873511yescharacteristic
134C22#1455873611yescharacteristic
135C4—22no—
136C4—41no—
137C4—2982no—
138C4—2982no—
139C4—2982no—
140C4—5961no—
141C2—42no—
142C2#1801186711yescharacteristic
143C2#1801187111yescharacteristic
144C2C4×C22⋊D14911yescharacteristic
145C2#1801188311yescharacteristic
146C2#1801189311yescharacteristic
147C2#1801189811yescharacteristic
148C2#1801190411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D149
commutatorC22×C149C22×C4
FittingC2×C22⋊C4×C149C2
socle, cosocleC23×C149C23
prime radicalC24×C149C22
hypercenterC2×C22⋊C4D149
hypocenterC149#388
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#14558715C2semidirect
4. C2×C4×Dic149C2semidirect
5. #18011818C2semidirect
6. #18011818C2semidirect
14. C22⋊Dic149C4semidirect
74. C149#388semidirect