Finite Group Databasebeta

← C23×#1611 #15669230

Subgroups — C23×#1611 #15669230

Order 2944.

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

normal subgroups only

This group has 210 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
1C23×#544C211yesmaximal, characteristic
2C23×#483C212yesmaximal
3C23×#398C211yesmaximal, characteristic
4C23×#328C212yesmaximal
5C23×#324C211yesmaximal, characteristic
6C23×C4⋊Q8—22no—
7C23×#125—22no—
8C23×C22⋊Q8—21no—
9C23×C22⋊Q8C2212yes—
10C23×#117—21no—
11C2×C4⋊C4×C23—21no—
12C2×C4⋊C4×C23C2211yescharacteristic
13C2×C4⋊C4×C23C2211yescharacteristic
14C23×#106—22no—
15C23×#103—22no—
16C23×C22⋊C8C2212yes—
17C23×#95—21no—
18C23×#95C2211yescharacteristic
19C2×Q8×C23—21no—
20C2×Q8×C23D412yes—
21C22×C4×C23—21no—
22C22×C4×C23—21no—
23C22×C4×C23D411yescharacteristic
24C22×C4×C23D411yescharacteristic
25C22×C4×C23C2311yescharacteristic
26C2×C8×C23—22no—
27C4⋊C4×C23—21no—
28C4⋊C4×C23—21no—
29C4⋊C4×C23—21no—
30C4⋊C4×C23—22no—
31C4⋊C4×C23—22no—
32C4⋊C4×C23—22no—
33C4⋊C4×C23—22no—
34C4⋊C4×C23—42no—
35C4⋊C4×C23D412yes—
36C22⋊C4×C23—22no—
37C42×C23—22no—
38C23×C23C2×D411yescharacteristic
39Q8×C23—42no—
40Q8×C23—81no—
41C2×C4×C23—21no—
42C2×C4×C23—21no—
43C2×C4×C23—22no—
44C2×C4×C23—22no—
45C2×C4×C23—22no—
46C2×C4×C23—21no—
47C2×C4×C23—41no—
48C2×C4×C23—41no—
49C2×C4×C23—41no—
50C2×C4×C23—41no—
51C2×C4×C23—41no—
52C2×C4×C23—41no—
53C2×C4×C23—41no—
54C2×C4×C23SD1612yes—
55C2×C4×C23C2×D412yes—
56C8×C23—42no—
57#1611C2311yesmaximal, characteristic, direct product factor, Sylow
58C22×C23—21no—
59C22×C23—21no—
60C22×C23#12011yescharacteristic
61C22×C23C2×SD1611yescharacteristic
62C22×C23#13711yescharacteristic
63C4×C23—22no—
64C4×C23—22no—
65C4×C23—42no—
66C4×C23—42no—
67C4×C23—41no—
68C4×C23—42no—
69C4×C23—81no—
70#544C2×C2311yescharacteristic
71#483C2×C2312yes—
72#398C2×C2311yescharacteristic
73#328C2×C2312yes—
74#324C2×C2311yescharacteristic
75C2×C23—21no—
76C2×C23—21no—
77C2×C23#44811yescharacteristic
78C2×C23#45611yescharacteristic
79C2×C23#45811yescharacteristic
80C4⋊Q8—22no—
81#125—22no—
82C22⋊Q8—21no—
83C22⋊Q8C22×C2312yes—
84#117—21no—
85C2×C4⋊C4—21no—
86C2×C4⋊C4C22×C2311yescharacteristic
87C2×C4⋊C4C22×C2311yescharacteristic
88#106—22no—
89#103—22no—
90C22⋊C8C22×C2312yes—
91#95—21no—
92#95C22×C2311yescharacteristic
93C23#161111yescharacteristic, direct product factor, Sylow
94C2×Q8—21no—
95C2×Q8D4×C2312yes—
96C22×C4—21no—
97C22×C4—21no—
98C22×C4D4×C2311yescharacteristic
99C22×C4D4×C2311yescharacteristic
100C22×C4C23×C2311yescharacteristic
101C2×C8—22no—
102C4⋊C4—21no—
103C4⋊C4—21no—
104C4⋊C4—21no—
105C4⋊C4—22no—
106C4⋊C4—22no—
107C4⋊C4—22no—
108C4⋊C4—22no—
109C4⋊C4—42no—
110C4⋊C4D4×C2312yes—
111C22⋊C4—22no—
112C42—22no—
113C23C2×D4×C2311yescharacteristic
114Q8—42no—
115Q8—81no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—22no—
119C2×C4—22no—
120C2×C4—22no—
121C2×C4—21no—
122C2×C4—41no—
123C2×C4—41no—
124C2×C4—41no—
125C2×C4—41no—
126C2×C4—41no—
127C2×C4—41no—
128C2×C4—41no—
129C2×C4SD16×C2312yes—
130C2×C4C2×D4×C2312yes—
131C8—42no—
132C22—21no—
133C22—21no—
134C22C23×#12011yescharacteristic
135C22C2×SD16×C2311yescharacteristic
136C22C23×#13711yescharacteristic
137C4—22no—
138C4—22no—
139C4—42no—
140C4—42no—
141C4—41no—
142C4—42no—
143C4—81no—
144C2—21no—
145C2—21no—
146C2C23×#44811yescharacteristic
147C2C23×#45611yescharacteristic
148C2C23×#45811yescharacteristic
subgroupG/H
center, socleC22×C23#120
commutator, Frattini, cosocleC22×C4C23×C23
prime radicalC23×C23C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C23 ◁ C22×C4×C23 ◁ G

Complements

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

NH ≅ G/Ntype
57. #1611C23direct (N × H)
93. C23#1611direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#5442
C23×#4832
C23×#3982
C23×#3282
C23×#3242
#161123