Finite Group Databasebeta

← C23×#1473 #15669092

Subgroups — C23×#1473 #15669092

Order 2944.

214 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 88 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×C23×#126C211yesmaximal, characteristic
2C23×#432C211yesmaximal, characteristic, complemented
3C23×#431C211yesmaximal, characteristic, complemented
4C23×#324C212yesmaximal, complemented
5C23×#323C212yesmaximal
6C23×#126—21no—
7C23×#126—21no—
8C23×#126—21no—
9C23×#126—21no—
10C2×C4⋊C4×C23C411yescharacteristic
11C2×C4⋊C4×C23C411yescharacteristic
12C2×C4⋊C4×C23C2211yescharacteristic
13C2×C22⋊C4×C23C411yescharacteristic
14C2×C22⋊C4×C23C411yescharacteristic
15C2×C22⋊C4×C23C2211yescharacteristic
16C2×C42×C23C2211yescharacteristic
17C23×C4⋊C8—21no—
18C23×C4⋊C8—21no—
19C23×C22⋊C8C2212yes—
20C23×C22⋊C8C2212yes—
21C23×#97—21no—
22C4×C8×C23—21no—
23C24×C23C2×C411yescharacteristic
24C22×C4×C23C2×C411yescharacteristic
25C22×C4×C23C2×C411yescharacteristic
26C22×C4×C23C2×C411yescharacteristic
27C22×C4×C23C2×C411yescharacteristic
28C22×C4×C23C2×C411yescharacteristic
29C22×C4×C23C2311yescharacteristic
30C2×C8×C23—22no—
31C2×C8×C23—22no—
32C4⋊C4×C23—21no—
33C4⋊C4×C23—21no—
34C4⋊C4×C23—21no—
35C4⋊C4×C23—21no—
36C4⋊C4×C23—21no—
37C4⋊C4×C23—21no—
38C22⋊C4×C23—21no—
39C22⋊C4×C23—21no—
40C22⋊C4×C23—21no—
41C22⋊C4×C23—21no—
42C22⋊C4×C23—21no—
43C22⋊C4×C23—21no—
44C42×C23D411yescharacteristic
45C42×C23D411yescharacteristic
46C42×C23D411yescharacteristic
47C42×C23D411yescharacteristic
48C23×C23—21no—
49C23×C23—22no—
50C23×C23—41no—
51C23×C23—41no—
52C23×C23C22×C411yescharacteristic
53C2×C4×C23—22no—
54C2×C4×C23—21no—
55C2×C4×C23—21no—
56C2×C4×C23—21no—
57C2×C4×C23—22no—
58C2×C4×C23—41no—
59C2×C4×C23—41no—
60C2×C4×C23—41no—
61C2×C4×C23—41no—
62C2×C4×C23C22⋊C411yescharacteristic
63C2×C4×C23C22⋊C411yescharacteristic
64C2×C4×C23C22⋊C411yescharacteristic
65C2×C4×C23C22⋊C411yescharacteristic
66C2×C4×C23C2×D411yescharacteristic
67C2×C4×C23C2×D411yescharacteristic
68C8×C23—42no—
69C8×C23—42no—
70#1473C2311yesmaximal, characteristic, direct product factor, Sylow
71C22×C23—21no—
72C22×C23—21no—
73C22×C23—41no—
74C22×C23—41no—
75C22×C23—41no—
76C22×C23—82no—
77C22×C23C2×C22⋊C411yescharacteristic
78C22×C23#13112yes—
79C4×C23—21no—
80C4×C23—21no—
81C4×C23—21no—
82C4×C23—21no—
83C4×C23—21no—
84C4×C23—21no—
85C4×C23—41no—
86C4×C23—41no—
87C4×C23—41no—
88C2×#126C2×C2311yescharacteristic
89#432C2×C2311yescharacteristic, complemented
90#431C2×C2311yescharacteristic, complemented
91#324C2×C2312yescomplemented
92#323C2×C2312yes—
93C2×C23—22no—
94C2×C23—81no—
95C2×C23#40811yescharacteristic
96C2×C23#41011yescharacteristic
97C2×C23#41311yescharacteristic
98#126—21no—
99#126—21no—
100#126—21no—
101#126—21no—
102C2×C4⋊C4C4×C2311yescharacteristic
103C2×C4⋊C4C4×C2311yescharacteristic
104C2×C4⋊C4C22×C2311yescharacteristic
105C2×C22⋊C4C4×C2311yescharacteristic
106C2×C22⋊C4C4×C2311yescharacteristic
107C2×C22⋊C4C22×C2311yescharacteristic
108C2×C42C22×C2311yescharacteristic
109C4⋊C8—21no—
110C4⋊C8—21no—
111C22⋊C8C22×C2312yes—
112C22⋊C8C22×C2312yes—
113#97—21no—
114C4×C8—21no—
115C23#147311yescharacteristic, direct product factor, Sylow
116C24C2×C4×C2311yescharacteristic
117C22×C4C2×C4×C2311yescharacteristic
118C22×C4C2×C4×C2311yescharacteristic
119C22×C4C2×C4×C2311yescharacteristic
120C22×C4C2×C4×C2311yescharacteristic
121C22×C4C2×C4×C2311yescharacteristic
122C22×C4C23×C2311yescharacteristic
123C2×C8—22no—
124C2×C8—22no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C22⋊C4—21no—
132C22⋊C4—21no—
133C22⋊C4—21no—
134C22⋊C4—21no—
135C22⋊C4—21no—
136C22⋊C4—21no—
137C42D4×C2311yescharacteristic
138C42D4×C2311yescharacteristic
139C42D4×C2311yescharacteristic
140C42D4×C2311yescharacteristic
141C23—21no—
142C23—22no—
143C23—41no—
144C23—41no—
145C23C22×C4×C2311yescharacteristic
146C2×C4—22no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—22no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4C22⋊C4×C2311yescharacteristic
156C2×C4C22⋊C4×C2311yescharacteristic
157C2×C4C22⋊C4×C2311yescharacteristic
158C2×C4C22⋊C4×C2311yescharacteristic
159C2×C4C2×D4×C2311yescharacteristic
160C2×C4C2×D4×C2311yescharacteristic
161C8—42no—
162C8—42no—
163C22—21no—
164C22—21no—
165C22—41no—
166C22—41no—
167C22—41no—
168C22—82no—
169C22C2×C22⋊C4×C2311yescharacteristic
170C22C23×#13112yes—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—21no—
177C4—41no—
178C4—41no—
179C4—41no—
180C2—22no—
181C2—81no—
182C2C23×#40811yescharacteristic
183C2C23×#41011yescharacteristic
184C2C23×#41311yescharacteristic
subgroupG/H
center, socleC22×C23C2×C22⋊C4
commutatorC23C22×C4×C23
Frattini, cosocleC22×C4C23×C23
prime radicalC24×C23C2×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C23 ◁ C2×C42×C23 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×#432C2semidirect
3. C23×#431C2semidirect
4. C23×#324C2semidirect
70. #1473C23direct (N × H)
89. #432C2×C23semidirect
90. #431C2×C23semidirect
91. #324C2×C23semidirect
115. C23#1473direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C23×#1262
C23×#4322
C23×#4312
C23×#3242
C23×#3232
#147323