Finite Group Databasebeta

← #23752134

Subgroups — #23752134

Order 9664.

186 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 63 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×C4⋊Dic151C211yesmaximal, characteristic, complemented
2C2×Dic151⋊C4C211yesmaximal, characteristic, complemented
3C2×(C2×D151)⋊C4C211yesmaximal, characteristic
4C2×(C2×D151)⋊C4C211yesmaximal, characteristic
5C2×(C2×D151)⋊C4C211yesmaximal, characteristic
6C151⋊#95C211yesmaximal, characteristic, complemented
7C2×C4⋊C4×C151C211yesmaximal, characteristic, complemented
8C23×D151C2211yescharacteristic
9C22×Dic151C2211yescharacteristic
10C22×Dic151C2211yescharacteristic
11C22×Dic151C2211yescharacteristic
12C4⋊Dic151—22no—
13Dic151⋊C4—22no—
14(C2×D151)⋊C4—22no—
15(C2×D151)⋊C4—22no—
16(C2×D151)⋊C4—22no—
17C22×C4×C151C2211yescharacteristic
18C22×C4×C151C2211yescharacteristic
19C22×C4×C151C2211yescharacteristic
20C4⋊C4×C151—22no—
21C22×D151—21no—
22C22×D151—21no—
23C22×D151—21no—
24C22×D151—21no—
25C22×D151—21no—
26C22×D151—21no—
27C22×D151Q812yes—
28C2×Dic151—21no—
29C2×Dic151—21no—
30C2×Dic151—21no—
31C2×Dic151—21no—
32C2×Dic151—21no—
33C2×Dic151—21no—
34C2×Dic151—21no—
35C2×Dic151—21no—
36C2×Dic151D412yes—
37C23×C151C2311yescharacteristic
38C2×C4×C151—21no—
39C2×C4×C151—21no—
40C2×C4×C151—21no—
41C2×C4×C151—21no—
42C2×C4×C151—21no—
43C2×C4×C151—21no—
44C2×C4×C151—21no—
45C2×C4×C151D412yes—
46C2×C4×C151D412yes—
47C22×C151C2×D411yescharacteristic
48C22×C151C2×D411yescharacteristic
49C22×C151C2×D411yescharacteristic
50C22×C151C2×Q811yescharacteristic
51C22×C151#4111yescharacteristic
52C22×C151#4111yescharacteristic
53C22×C151#4111yescharacteristic
54C2×D151—22no—
55C2×D151—22no—
56C2×D151—22no—
57C2×D151—41no—
58C2×D151—41no—
59C2×D151—41no—
60C2×D151—41no—
61C4×C151—22no—
62C4×C151—22no—
63C4×C151—41no—
64Dic151—22no—
65Dic151—41no—
66Dic151—41no—
67C2×C151#12111yescharacteristic
68C2×C151#12111yescharacteristic
69C2×C151#12111yescharacteristic
70C2×C151C22⋊Q811yescharacteristic
71C2×C151C22⋊Q811yescharacteristic
72C2×C151C22⋊Q811yescharacteristic
73C2×C151#12611yescharacteristic
74D151—42no—
75C151#39611yescharacteristic, complemented, Sylow
76#396—1511nomaximal, Sylow
77C2×C4⋊C4—1511no—
78C2×C4⋊C4—1511no—
79C2×C4⋊C4D15111yescharacteristic, complemented
80C2×C22⋊C4—1511no—
81C2×C22⋊C4—1511no—
82C2×C22⋊C4—1511no—
83#95—1511no—
84C24—1511no—
85C22×C4—1511no—
86C22×C4—1511no—
87C22×C4—1511no—
88C22×C4C2×D15111yescharacteristic
89C22×C4C2×D15111yescharacteristic
90C22×C4C2×D15111yescharacteristic
91C4⋊C4—22no—
92C4⋊C4—3022no—
93C4⋊C4—3022no—
94C22⋊C4—3022no—
95C22⋊C4—3022no—
96C22⋊C4—3022no—
97C23—3021no—
98C23—3021no—
99C23—3021no—
100C23—3021no—
101C23—3021no—
102C23—3021no—
103C23—1512no—
104C23C22×D15111yescharacteristic
105C2×C4—21no—
106C2×C4—21no—
107C2×C4—21no—
108C2×C4—21no—
109C2×C4—21no—
110C2×C4—21no—
111C2×C4—21no—
112C2×C4—3021no—
113C2×C4—3021no—
114C2×C4—3021no—
115C2×C4—3021no—
116C2×C4—3021no—
117C2×C4—3021no—
118C2×C4—3021no—
119C2×C4—3021no—
120C2×C4—1512no—
121C2×C4C22⋊D15112yes—
122C2×C4D60412yes—
123C22—3022no—
124C22—3022no—
125C22—3022no—
126C22—6041no—
127C22—6041no—
128C22—6041no—
129C22—6041no—
130C22D4×D15111yescharacteristic
131C22C2×C22⋊D15111yescharacteristic
132C22C2×D60411yescharacteristic
133C22Q8×D15111yescharacteristic
134C22#1455900311yescharacteristic
135C22#1455900411yescharacteristic
136C22#1455900511yescharacteristic
137C4—22no—
138C4—22no—
139C4—41no—
140C4—3022no—
141C4—6041no—
142C4—6041no—
143C2—6042no—
144C2#1801271111yescharacteristic
145C2#1801271311yescharacteristic
146C2#1801271411yescharacteristic
147C2#1801271511yescharacteristic
148C2#1801271711yescharacteristic
149C2#1801271911yescharacteristic
150C2#1801273411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D151
commutator, socle, cosocleC23×C151C23
FittingC2×C4⋊C4×C151C2
prime radicalC23×D151C22
hypercenterC2×C4⋊C4D151
hypocenterC151#396
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊Dic151C2semidirect
2. C2×Dic151⋊C4C2semidirect
6. C151⋊#95C2semidirect
7. C2×C4⋊C4×C151C2semidirect
75. C151#396semidirect
79. C2×C4⋊C4D151semidirect