Finite Group Databasebeta

← C43×#1596 #19130413

Subgroups — C43×#1596 #19130413

Order 5504.

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

normal subgroups only

This group has 316 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
1C43×#543C211yesmaximal, characteristic, complemented
2C43×#450C212yesmaximal, complemented
3C43×#392C211yesmaximal, characteristic
4C43×#328C212yesmaximal, complemented
5C43×#323C211yesmaximal, characteristic, complemented
6C22×D4×C43—21no—
7C22×D4×C43C2211yescharacteristic
8C2×SD16×C43—22no—
9C22⋊Q8×C43—22no—
10C22⋊Q8×C43—21no—
11C22⋊Q8×C43—22no—
12C22⋊Q8×C43C2212yes—
13C2×C22⋊C4×C43—21no—
14C2×C22⋊C4×C43—21no—
15C2×C22⋊C4×C43C2211yescharacteristic
16#102×C43—22no—
17C22⋊C8×C43C2212yes—
18#95×C43C2211yescharacteristic
19C24×C43—21no—
20C24×C43D411yescharacteristic
21C2×Q8×C43—21no—
22C2×Q8×C43D412yescomplemented
23C2×D4×C43—22no—
24C2×D4×C43—42no—
25C2×D4×C43—42no—
26C2×D4×C43—42no—
27C2×D4×C43—42no—
28C22×C4×C43—21no—
29C22×C4×C43—21no—
30C22×C4×C43—21no—
31C22×C4×C43D411yescharacteristic
32C22×C4×C43C2311yescharacteristic
33SD16×C43—44no—
34C2×C8×C43—22no—
35C4⋊C4×C43—21no—
36C4⋊C4×C43—22no—
37C4⋊C4×C43—22no—
38C4⋊C4×C43D412yescomplemented
39C22⋊C4×C43—22no—
40C22⋊C4×C43—22no—
41C22⋊C4×C43—22no—
42C22⋊C4×C43—42no—
43C23×C43—21no—
44C23×C43—21no—
45C23×C43—22no—
46C23×C43—41no—
47C23×C43—41no—
48C23×C43—41no—
49C23×C43—41no—
50C23×C43—41no—
51C23×C43—41no—
52C23×C43—41no—
53C23×C43—41no—
54C23×C43SD1612yescomplemented
55C23×C43C2×D411yescharacteristic
56Q8×C43—42no—
57Q8×C43—81no—
58D4×C43—24no—
59D4×C43—42no—
60D4×C43—48no—
61C2×C4×C43—22no—
62C2×C4×C43—22no—
63C2×C4×C43—21no—
64C2×C4×C43—22no—
65C2×C4×C43—41no—
66C2×C4×C43—41no—
67C2×C4×C43—41no—
68C2×C4×C43—41no—
69C2×C4×C43—81no—
70C2×C4×C43—81no—
71C2×C4×C43C2×D412yes—
72C8×C43—42no—
73C22×C43—21no—
74C22×C43—21no—
75C22×C43—22no—
76C22×C43—42no—
77C22×C43—42no—
78C22×C43—42no—
79C22×C43—41no—
80C22×C43—41no—
81C22×C43—42no—
82C22×C43—81no—
83C22×C43—81no—
84C22×C43—81no—
85C22×C43—81no—
86C22×C43—81no—
87C22×C43#12011yescharacteristic
88C22×C43C2×SD1611yescharacteristic
89C22×C43#13711yescharacteristic
90C4×C43—22no—
91C4×C43—42no—
92C4×C43—41no—
93C4×C43—42no—
94C4×C43—42no—
95#1596C4311yesmaximal, characteristic, direct product factor, Sylow
96C2×C43—21no—
97C2×C43—21no—
98C2×C43—42no—
99C2×C43—82no—
100C2×C43#44811yescharacteristic
101C2×C43#45311yescharacteristic
102C2×C43B(4,𝔽2)11yescharacteristic
103#543C2×C4311yescharacteristic, complemented
104#450C2×C4312yescomplemented
105#392C2×C4311yescharacteristic
106#328C2×C4312yescomplemented
107#323C2×C4311yescharacteristic, complemented
108C43#159611yescharacteristic, direct product factor, Sylow
109C22×D4—21no—
110C22×D4C22×C4311yescharacteristic
111C2×SD16—22no—
112C22⋊Q8—22no—
113C22⋊Q8—21no—
114C22⋊Q8—22no—
115C22⋊Q8C22×C4312yes—
116C2×C22⋊C4—21no—
117C2×C22⋊C4—21no—
118C2×C22⋊C4C22×C4311yescharacteristic
119#102—22no—
120C22⋊C8C22×C4312yes—
121#95C22×C4311yescharacteristic
122C24—21no—
123C24D4×C4311yescharacteristic
124C2×Q8—21no—
125C2×Q8D4×C4312yescomplemented
126C2×D4—22no—
127C2×D4—42no—
128C2×D4—42no—
129C2×D4—42no—
130C2×D4—42no—
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—21no—
134C22×C4D4×C4311yescharacteristic
135C22×C4C23×C4311yescharacteristic
136SD16—44no—
137C2×C8—22no—
138C4⋊C4—21no—
139C4⋊C4—22no—
140C4⋊C4—22no—
141C4⋊C4D4×C4312yescomplemented
142C22⋊C4—22no—
143C22⋊C4—22no—
144C22⋊C4—22no—
145C22⋊C4—42no—
146C23—21no—
147C23—21no—
148C23—22no—
149C23—41no—
150C23—41no—
151C23—41no—
152C23—41no—
153C23—41no—
154C23—41no—
155C23—41no—
156C23—41no—
157C23SD16×C4312yescomplemented
158C23C2×D4×C4311yescharacteristic
159Q8—42no—
160Q8—81no—
161D4—24no—
162D4—42no—
163D4—48no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—81no—
173C2×C4—81no—
174C2×C4C2×D4×C4312yes—
175C8—42no—
176C22—21no—
177C22—21no—
178C22—22no—
179C22—42no—
180C22—42no—
181C22—42no—
182C22—41no—
183C22—41no—
184C22—42no—
185C22—81no—
186C22—81no—
187C22—81no—
188C22—81no—
189C22—81no—
190C22#120×C4311yescharacteristic
191C22C2×SD16×C4311yescharacteristic
192C22#137×C4311yescharacteristic
193C4—22no—
194C4—42no—
195C4—41no—
196C4—42no—
197C4—42no—
198C2—21no—
199C2—21no—
200C2—42no—
201C2—82no—
202C2C43×#44811yescharacteristic
203C2C43×#45311yescharacteristic
204C2C43×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C43#120
commutator, Frattini, cosocleC22×C4C23×C43
prime radicalC43×#392C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C22×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#543C2semidirect
2. C43×#450C2semidirect
4. C43×#328C2semidirect
5. C43×#323C2semidirect
22. C2×Q8×C43D4semidirect
38. C4⋊C4×C43D4semidirect
54. C23×C43SD16semidirect
95. #1596C43direct (N × H)
103. #543C2×C43semidirect
104. #450C2×C43semidirect
106. #328C2×C43semidirect
107. #323C2×C43semidirect
108. C43#1596direct (N × H)
125. C2×Q8D4×C43semidirect
141. C4⋊C4D4×C43semidirect
157. C23SD16×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#5432
C43×#4502
C43×#3922
C43×#3282
C43×#3232
#159643