Finite Group Databasebeta

← C43×#7314 #24927331

Subgroups — C43×#7314 #24927331

Order 11008.

620 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 74 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×#1783C211yesmaximal, characteristic
2C43×#1781C212yesmaximal
3C23×D4×C43C2211yescharacteristic
4C2×#100×C43—22no—
5C2×#99×C43—22no—
6C2×#99×C43C414yescomplemented
7C43×#407C412yescomplemented
8C43×#379—22no—
9C25×C43D411yescharacteristic
10C25×C43Q811yescharacteristic
11C22×D4×C43—42no—
12C22×D4×C43—44no—
13C22×D4×C43C2×C412yes—
14C22×D4×C43D412yes—
15C23×C4×C43C2×C411yescharacteristic
16C2×M16×C43—22no—
17C2×C22⋊C4×C43—24no—
18C2×C22⋊C4×C43—44no—
19#100×C43—44no—
20#99×C43—44no—
21#99×C43—44no—
22C22⋊C8×C43—42no—
23C24×C43—24no—
24C24×C43—41no—
25C24×C43—41no—
26C24×C43—42no—
27C24×C43—82no—
28C24×C43—82no—
29C24×C43C22⋊C412yes—
30C24×C43C4⋊C411yescharacteristic
31C24×C43C4⋊C412yes—
32C2×D4×C43—24no—
33C2×D4×C43—24no—
34C2×D4×C43—24no—
35C2×D4×C43—42no—
36C2×D4×C43—42no—
37C2×D4×C43—42no—
38C2×D4×C43—416no—
39C22×C4×C43—22no—
40C22×C4×C43—42no—
41C22×C4×C43—44no—
42C22×C4×C43C4211yescharacteristic
43C22×C4×C43C22⋊C411yescharacteristic
44M16×C43—44no—
45C2×C8×C43—42no—
46C22⋊C4×C43—44no—
47C22⋊C4×C43—44no—
48C22⋊C4×C43—88no—
49C23×C43—21no—
50C23×C43—22no—
51C23×C43—22no—
52C23×C43—22no—
53C23×C43—22no—
54C23×C43—22no—
55C23×C43—22no—
56C23×C43—42no—
57C23×C43—44no—
58C23×C43—48no—
59C23×C43—44no—
60C23×C43—84no—
61C23×C43—82no—
62C23×C43—82no—
63C23×C43—82no—
64C23×C43—84no—
65C23×C43—82no—
66C23×C43—82no—
67C23×C43—84no—
68C23×C43—82no—
69C23×C43#9511yescharacteristic
70C23×C43#9914yes—
71D4×C43—48no—
72D4×C43—48no—
73C2×C4×C43—22no—
74C2×C4×C43—21no—
75C2×C4×C43—22no—
76C2×C4×C43—44no—
77C2×C4×C43—84no—
78C2×C4×C43—88no—
79C2×C4×C43#9912yes—
80C8×C43—82no—
81#7314C4311yesmaximal, characteristic, direct product factor, Sylow
82C22×C43—24no—
83C22×C43—22no—
84C22×C43—24no—
85C22×C43—41no—
86C22×C43—44no—
87C22×C43—42no—
88C22×C43—41no—
89C22×C43—44no—
90C22×C43—41no—
91C22×C43—42no—
92C22×C43—82no—
93C22×C43—82no—
94C22×C43—82no—
95C22×C43—82no—
96C22×C43—88no—
97C22×C43—88no—
98C22×C43#34211yescharacteristic
99C22×C43#34212yes—
100C4×C43—22no—
101C4×C43—41no—
102C4×C43—164no—
103#1783C2×C4311yescharacteristic
104#1781C2×C4312yes—
105C2×C43—22no—
106C2×C43—21no—
107C2×C43—44no—
108C2×C43—42no—
109C2×C43—82no—
110C2×C43#130411yescharacteristic
111C23×D4C22×C4311yescharacteristic
112C2×#100—22no—
113C2×#99—22no—
114C2×#99C4×C4314yescomplemented
115#407C4×C4312yescomplemented
116#379—22no—
117C43#731411yescharacteristic, direct product factor, Sylow
118C25D4×C4311yescharacteristic
119C25Q8×C4311yescharacteristic
120C22×D4—42no—
121C22×D4—44no—
122C22×D4C2×C4×C4312yes—
123C22×D4D4×C4312yes—
124C23×C4C2×C4×C4311yescharacteristic
125C2×M16—22no—
126C2×C22⋊C4—24no—
127C2×C22⋊C4—44no—
128#100—44no—
129#99—44no—
130#99—44no—
131C22⋊C8—42no—
132C24—24no—
133C24—41no—
134C24—41no—
135C24—42no—
136C24—82no—
137C24—82no—
138C24C22⋊C4×C4312yes—
139C24C4⋊C4×C4311yescharacteristic
140C24C4⋊C4×C4312yes—
141C2×D4—24no—
142C2×D4—24no—
143C2×D4—24no—
144C2×D4—42no—
145C2×D4—42no—
146C2×D4—42no—
147C2×D4—416no—
148C22×C4—22no—
149C22×C4—42no—
150C22×C4—44no—
151C22×C4C42×C4311yescharacteristic
152C22×C4C22⋊C4×C4311yescharacteristic
153M16—44no—
154C2×C8—42no—
155C22⋊C4—44no—
156C22⋊C4—44no—
157C22⋊C4—88no—
158C23—21no—
159C23—22no—
160C23—22no—
161C23—22no—
162C23—22no—
163C23—22no—
164C23—22no—
165C23—42no—
166C23—44no—
167C23—48no—
168C23—44no—
169C23—84no—
170C23—82no—
171C23—82no—
172C23—82no—
173C23—84no—
174C23—82no—
175C23—82no—
176C23—84no—
177C23—82no—
178C23#95×C4311yescharacteristic
179C23#99×C4314yes—
180D4—48no—
181D4—48no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—44no—
186C2×C4—84no—
187C2×C4—88no—
188C2×C4#99×C4312yes—
189C8—82no—
190C22—24no—
191C22—22no—
192C22—24no—
193C22—41no—
194C22—44no—
195C22—44no—
196C22—42no—
197C22—41no—
198C22—41no—
199C22—42no—
200C22—82no—
201C22—82no—
202C22—82no—
203C22—82no—
204C22—88no—
205C22—88no—
206C22C43×#34212yes—
207C22C43×#34211yescharacteristic
208C4—22no—
209C4—41no—
210C4—164no—
211C2—22no—
212C2—21no—
213C2—44no—
214C2—42no—
215C2—82no—
216C2C43×#130411yescharacteristic
subgroupG/H
center, socleC2×C43#1304
commutatorC22×C4C42×C43
Frattini, cosocleC23×D4C22×C43
prime radicalC23×D4×C43C22
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C43 ◁ C23×C43 ◁ C23×D4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
6. C2×#99×C43C4semidirect
7. C43×#407C4semidirect
81. #7314C43direct (N × H)
114. C2×#99C4×C43semidirect
115. #407C4×C43semidirect
117. C43#7314direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#17832
C43×#17812
#731443