Finite Group Databasebeta

← C23×#3058 #15670677

Subgroups — C23×#3058 #15670677

Order 2944.

524 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 200 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
1C22×D8×C23C211yesmaximal, characteristic, complemented
2C2×C23×#131C211yesmaximal, characteristic, complemented
3C23×#535C212yesmaximal, complemented
4C23×#469C214yesmaximal, complemented
5C23×#466C214yesmaximal, complemented
6C23×#427C211yesmaximal, characteristic, complemented
7C23×#418C212yesmaximal, complemented
8C2×#41×C23C2211yescharacteristic
9C22×D4×C23C2212yes—
10C2×D8×C23—24no—
11C2×D8×C23C2212yes—
12C2×D8×C23C2212yes—
13C23×#131—24no—
14C2×M16×C23C2211yescharacteristic
15C2×M16×C23C2212yescomplemented
16C22×C8×C23C2211yescharacteristic
17C22×C8×C23C2212yescomplemented
18C23×#127—22no—
19C23×#124—22no—
20C23×#121C2218yescomplemented
21C23×#120—24no—
22C23×#117C2212yes—
23C23×#107C2212yescomplemented
24C23×#106C2212yescomplemented
25C23×#102C2218yescomplemented
26C24×C23—22no—
27#41×C23—22no—
28#41×C23—22no—
29C2×Q8×C23D411yescharacteristic
30C2×D4×C23—28no—
31C2×D4×C23—24no—
32C2×D4×C23—22no—
33C2×D4×C23—24no—
34C2×D4×C23D412yes—
35C2×D4×C23D411yescharacteristic
36C2×D4×C23C2314yes—
37C22×C4×C23C2312yes—
38C22×C4×C23C2311yescharacteristic
39D8×C23—24no—
40D8×C23—24no—
41M16×C23—22no—
42M16×C23—24no—
43C2×C8×C23—24no—
44C2×C8×C23D414yescomplemented
45C2×C8×C23C2312yes—
46C2×C8×C23C2311yescharacteristic
47C2×C8×C23C2311yescharacteristic
48C4⋊C4×C23C2314yes—
49C22⋊C4×C23—22no—
50C22⋊C4×C23—28no—
51C42×C23—22no—
52C23×C23—24no—
53C23×C23—44no—
54C23×C23—84no—
55C23×C23C2×D412yes—
56C23×C23C2×D411yescharacteristic
57Q8×C23—22no—
58D4×C23—24no—
59D4×C23—22no—
60D4×C23—24no—
61D4×C23—24no—
62D4×C23—44no—
63D4×C23—88no—
64C2×C4×C23—22no—
65C2×C4×C23—22no—
66C2×C4×C23—24no—
67C2×C4×C23C2×D412yes—
68C2×C4×C23C2×D411yescharacteristic
69C2×C4×C23C2×D412yes—
70C2×C4×C23#4112yes—
71C2×C4×C23C2411yescharacteristic
72C8×C23—22no—
73C8×C23C2×D412yes—
74C8×C23C2×D412yes—
75#3058C2311yesmaximal, characteristic, direct product factor, Sylow
76C22×C23—22no—
77C22×C23—22no—
78C22×C23—24no—
79C22×C23—44no—
80C22×C23—48no—
81C22×C23—88no—
82C22×C23#12112yes—
83C22×C23C22×D411yescharacteristic
84C4×C23—22no—
85C4×C23—44no—
86C4×C23#12112yes—
87C4×C23C22×D411yescharacteristic
88C4×C23C2×#4111yescharacteristic
89C22×D8C2×C2311yescharacteristic, complemented
90C2×#131C2×C2311yescharacteristic, complemented
91#535C2×C2312yescomplemented
92#469C2×C2314yescomplemented
93#466C2×C2314yescomplemented
94#427C2×C2311yescharacteristic, complemented
95#418C2×C2312yescomplemented
96C2×C23—22no—
97C2×C23—42no—
98C2×C23—84no—
99C2×C23C2×#12111yescharacteristic
100C2×C23#57612yes—
101C2×#41C22×C2311yescharacteristic
102C22×D4C22×C2312yes—
103C2×D8—24no—
104C2×D8C22×C2312yes—
105C2×D8C22×C2312yes—
106#131—24no—
107C2×M16C22×C2311yescharacteristic
108C2×M16C22×C2312yescomplemented
109C22×C8C22×C2311yescharacteristic
110C22×C8C22×C2312yescomplemented
111#127—22no—
112#124—22no—
113#121C22×C2318yescomplemented
114#120—24no—
115#117C22×C2312yes—
116#107C22×C2312yescomplemented
117#106C22×C2312yescomplemented
118#102C22×C2318yescomplemented
119C23#305811yescharacteristic, direct product factor, Sylow
120C24—22no—
121#41—22no—
122#41—22no—
123C2×Q8D4×C2311yescharacteristic
124C2×D4—28no—
125C2×D4—24no—
126C2×D4—22no—
127C2×D4—24no—
128C2×D4D4×C2312yes—
129C2×D4D4×C2311yescharacteristic
130C2×D4C23×C2314yes—
131C22×C4C23×C2312yes—
132C22×C4C23×C2311yescharacteristic
133D8—24no—
134D8—24no—
135M16—22no—
136M16—24no—
137C2×C8—24no—
138C2×C8D4×C2314yescomplemented
139C2×C8C23×C2312yes—
140C2×C8C23×C2311yescharacteristic
141C2×C8C23×C2311yescharacteristic
142C4⋊C4C23×C2314yes—
143C22⋊C4—22no—
144C22⋊C4—28no—
145C42—22no—
146C23—24no—
147C23—44no—
148C23—84no—
149C23C2×D4×C2312yes—
150C23C2×D4×C2311yescharacteristic
151Q8—22no—
152D4—24no—
153D4—22no—
154D4—24no—
155D4—24no—
156D4—44no—
157D4—88no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—24no—
161C2×C4C2×D4×C2312yes—
162C2×C4C2×D4×C2311yescharacteristic
163C2×C4C2×D4×C2312yes—
164C2×C4#41×C2312yes—
165C2×C4C24×C2311yescharacteristic
166C8—22no—
167C8C2×D4×C2312yes—
168C8C2×D4×C2312yes—
169C22—22no—
170C22—24no—
171C22—22no—
172C22—48no—
173C22—44no—
174C22—88no—
175C22C23×#12112yes—
176C22C22×D4×C2311yescharacteristic
177C4—22no—
178C4—44no—
179C4C23×#12112yes—
180C4C22×D4×C2311yescharacteristic
181C4C2×#41×C2311yescharacteristic
182C2—22no—
183C2—42no—
184C2—84no—
185C2C2×C23×#12111yescharacteristic
186C2C23×#57612yes—
subgroupG/H
center, socleC22×C23C22×D4
commutator, Frattini, cosocleC2×C4C24×C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C23 ◁ C2×#41×C23 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×D8×C23C2semidirect
2. C2×C23×#131C2semidirect
3. C23×#535C2semidirect
4. C23×#469C2semidirect
5. C23×#466C2semidirect
6. C23×#427C2semidirect
7. C23×#418C2semidirect
15. C2×M16×C23C22semidirect
17. C22×C8×C23C22semidirect
20. C23×#121C22semidirect
23. C23×#107C22semidirect
24. C23×#106C22semidirect
25. C23×#102C22semidirect
44. C2×C8×C23D4semidirect
75. #3058C23direct (N × H)
89. C22×D8C2×C23semidirect
90. C2×#131C2×C23semidirect
91. #535C2×C23semidirect
92. #469C2×C23semidirect
93. #466C2×C23semidirect
94. #427C2×C23semidirect
95. #418C2×C23semidirect
108. C2×M16C22×C23semidirect
110. C22×C8C22×C23semidirect
113. #121C22×C23semidirect
116. #107C22×C23semidirect
117. #106C22×C23semidirect
118. #102C22×C23semidirect
119. C23#3058direct (N × H)
138. C2×C8D4×C23semidirect

Maximal subgroups

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

subgroupindex
C22×D8×C232
C2×C23×#1312
C23×#5352
C23×#4692
C23×#4662
C23×#4272
C23×#4182
#305823