Finite Group Databasebeta

← C43×#8323 #24928340

Subgroups — C43×#8323 #24928340

Order 11008.

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

normal subgroups only

This group has 930 conjugacy classes of subgroups — too many to draw. Only its 214 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×C43×#519C211yesmaximal, characteristic
2C43×#1479C214yesmaximal, complemented
3C43×#1458C212yesmaximal
4C23×Q8×C43C411yescharacteristic
5C43×#519—28no—
6C2×C4×Q8×C43—22no—
7C2×C4×Q8×C43C412yes—
8C2×C4×Q8×C43C2212yes—
9C2×#117×C43—22no—
10C2×#117×C43C411yescharacteristic
11C2×#117×C43C2211yescharacteristic
12C43×#431C2214yes—
13C43×Q8⋊C8—28no—
14C43×#324—22no—
15C43×#323—22no—
16C22×Q8×C43—24no—
17C22×Q8×C43—24no—
18C22×Q8×C43—21no—
19C22×Q8×C43—22no—
20C22×Q8×C43C814yescomplemented
21C22×Q8×C43C2×C412yes—
22C23×C4×C43—21no—
23C23×C4×C43C2×C411yescharacteristic
24C4×Q8×C43—216no—
25C4×Q8×C43—24no—
26C4×Q8×C43—24no—
27C4×Q8×C43—24no—
28C4×Q8×C43D418yes—
29#117×C43—216no—
30#117×C43—24no—
31#117×C43—24no—
32C2×C4⋊C4×C43—22no—
33C2×C4⋊C4×C43—22no—
34C2×C4⋊C4×C43C2×C412yes—
35C2×C4⋊C4×C43D412yes—
36C2×C22⋊C4×C43—21no—
37C2×C22⋊C4×C43D412yes—
38C2×C42×C43—22no—
39C2×C42×C43—21no—
40C2×C42×C43—22no—
41C2×C42×C43C2×C411yescharacteristic
42C2×C42×C43C2311yescharacteristic
43C4⋊C8×C43—24no—
44C22⋊C8×C43—24no—
45C4×C8×C43—24no—
46C24×C43C22⋊C411yescharacteristic
47C2×Q8×C43—24no—
48C2×Q8×C43—216no—
49C2×Q8×C43—24no—
50C2×Q8×C43—216no—
51C2×Q8×C43—24no—
52C2×Q8×C43—22no—
53C2×Q8×C43—22no—
54C2×Q8×C43—22no—
55C2×Q8×C43C22⋊C414yes—
56C2×Q8×C43C2×C814yes—
57C2×Q8×C43M1614yes—
58C22×C4×C43—24no—
59C22×C4×C43—24no—
60C22×C4×C43—22no—
61C22×C4×C43—22no—
62C22×C4×C43—24no—
63C22×C4×C43—22no—
64C22×C4×C43—22no—
65C22×C4×C43C22⋊C411yescharacteristic
66C22×C4×C43C22⋊C412yes—
67C22×C4×C43C2×C812yes—
68C22×C4×C43M1612yes—
69C22×C4×C43C22×C411yescharacteristic
70C22×C4×C43C2×D412yes—
71C2×C8×C43—44no—
72C4⋊C4×C43—28no—
73C4⋊C4×C43—22no—
74C4⋊C4×C43—28no—
75C4⋊C4×C43—24no—
76C4⋊C4×C43C22⋊C414yes—
77C22⋊C4×C43—24no—
78C22⋊C4×C43—24no—
79C42×C43—28no—
80C42×C43—24no—
81C42×C43—22no—
82C42×C43—28no—
83C42×C43C2×D414yes—
84C23×C43—21no—
85C23×C43—21no—
86C23×C43—42no—
87C23×C43C22⋊C812yes—
88C23×C43C2×C22⋊C411yescharacteristic
89Q8×C43—216no—
90Q8×C43—24no—
91Q8×C43—24no—
92Q8×C43—24no—
93Q8×C43C22⋊C818yes—
94C2×C4×C43—216no—
95C2×C4×C43—24no—
96C2×C4×C43—21no—
97C2×C4×C43—24no—
98C2×C4×C43—24no—
99C2×C4×C43—21no—
100C2×C4×C43—24no—
101C2×C4×C43—24no—
102C2×C4×C43—22no—
103C2×C4×C43—24no—
104C2×C4×C43—42no—
105C2×C4×C43—44no—
106C2×C4×C43—42no—
107C2×C4×C43C22⋊C812yes—
108C2×C4×C43C2×C22⋊C412yes—
109C2×C4×C43#12014yes—
110C2×C4×C43C22×C811yescharacteristic
111C2×C4×C43C2×M1612yes—
112C2×C4×C43C2×M1611yescharacteristic
113C8×C43—84no—
114#8323C4311yesmaximal, characteristic, direct product factor, Sylow
115C22×C43—22no—
116C22×C43—22no—
117C22×C43—42no—
118C22×C43—42no—
119C22×C43—42no—
120C22×C43#37911yescharacteristic
121C22×C43C2×C22⋊C811yescharacteristic
122C22×C43#40711yescharacteristic
123C4×C43—24no—
124C4×C43—28no—
125C4×C43—22no—
126C4×C43—42no—
127C4×C43—44no—
128C4×C43C2×C22⋊C812yes—
129C4×C43#40712yes—
130C2×#519C2×C4311yescharacteristic
131#1479C2×C4314yescomplemented
132#1458C2×C4312yes—
133C2×C43—21no—
134C2×C43—21no—
135C2×C43—42no—
136C2×C43#177911yescharacteristic
137C2×C43#179612yes—
138C23×Q8C4×C4311yescharacteristic
139#519—28no—
140C2×C4×Q8—22no—
141C2×C4×Q8C4×C4312yes—
142C2×C4×Q8C22×C4312yes—
143C2×#117—22no—
144C2×#117C4×C4311yescharacteristic
145C2×#117C22×C4311yescharacteristic
146#431C22×C4314yes—
147Q8⋊C8—28no—
148#324—22no—
149#323—22no—
150C43#832311yescharacteristic, direct product factor, Sylow
151C22×Q8—24no—
152C22×Q8—24no—
153C22×Q8—21no—
154C22×Q8—22no—
155C22×Q8C8×C4314yescomplemented
156C22×Q8C2×C4×C4312yes—
157C23×C4—21no—
158C23×C4C2×C4×C4311yescharacteristic
159C4×Q8—216no—
160C4×Q8—24no—
161C4×Q8—24no—
162C4×Q8—24no—
163C4×Q8D4×C4318yes—
164#117—216no—
165#117—24no—
166#117—24no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4C2×C4×C4312yes—
170C2×C4⋊C4D4×C4312yes—
171C2×C22⋊C4—21no—
172C2×C22⋊C4D4×C4312yes—
173C2×C42—22no—
174C2×C42—21no—
175C2×C42—22no—
176C2×C42C2×C4×C4311yescharacteristic
177C2×C42C23×C4311yescharacteristic
178C4⋊C8—24no—
179C22⋊C8—24no—
180C4×C8—24no—
181C24C22⋊C4×C4311yescharacteristic
182C2×Q8—24no—
183C2×Q8—216no—
184C2×Q8—24no—
185C2×Q8—216no—
186C2×Q8—24no—
187C2×Q8—22no—
188C2×Q8—22no—
189C2×Q8—22no—
190C2×Q8C22⋊C4×C4314yes—
191C2×Q8C2×C8×C4314yes—
192C2×Q8M16×C4314yes—
193C22×C4—24no—
194C22×C4—24no—
195C22×C4—24no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4C22⋊C4×C4311yescharacteristic
201C22×C4C22⋊C4×C4312yes—
202C22×C4C2×C8×C4312yes—
203C22×C4M16×C4312yes—
204C22×C4C22×C4×C4311yescharacteristic
205C22×C4C2×D4×C4312yes—
206C2×C8—44no—
207C4⋊C4—28no—
208C4⋊C4—22no—
209C4⋊C4—28no—
210C4⋊C4—24no—
211C4⋊C4C22⋊C4×C4314yes—
212C22⋊C4—24no—
213C22⋊C4—24no—
214C42—28no—
215C42—24no—
216C42—22no—
217C42—28no—
218C42C2×D4×C4314yes—
219C23—21no—
220C23—21no—
221C23—42no—
222C23C22⋊C8×C4312yes—
223C23C2×C22⋊C4×C4311yescharacteristic
224Q8—216no—
225Q8—24no—
226Q8—24no—
227Q8—24no—
228Q8C22⋊C8×C4318yes—
229C2×C4—216no—
230C2×C4—24no—
231C2×C4—21no—
232C2×C4—24no—
233C2×C4—24no—
234C2×C4—21no—
235C2×C4—24no—
236C2×C4—24no—
237C2×C4—22no—
238C2×C4—24no—
239C2×C4—42no—
240C2×C4—44no—
241C2×C4—42no—
242C2×C4C22⋊C8×C4312yes—
243C2×C4C2×C22⋊C4×C4312yes—
244C2×C4#120×C4314yes—
245C2×C4C22×C8×C4311yescharacteristic
246C2×C4C2×M16×C4312yes—
247C2×C4C2×M16×C4311yescharacteristic
248C8—84no—
249C22—22no—
250C22—22no—
251C22—42no—
252C22—42no—
253C22—42no—
254C22C43×#37911yescharacteristic
255C22C2×C22⋊C8×C4311yescharacteristic
256C22C43×#40711yescharacteristic
257C4—28no—
258C4—22no—
259C4—24no—
260C4—44no—
261C4—42no—
262C4C2×C22⋊C8×C4312yes—
263C4C43×#40712yes—
264C2—21no—
265C2—21no—
266C2—42no—
267C2C43×#177911yescharacteristic
268C2C43×#179612yes—
subgroupG/H
center, socleC22×C43#379
commutatorC2×C4C22×C8×C43
Frattini, cosocleC2×C42C23×C43
prime radicalC24×C43C22⋊C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#1479C2semidirect
20. C22×Q8×C43C8semidirect
114. #8323C43direct (N × H)
131. #1479C2×C43semidirect
150. C43#8323direct (N × H)
155. C22×Q8C8×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#5192
C43×#14792
C43×#14582
#832343