Finite Group Databasebeta

← C43×#9979 #24929996

Subgroups — C43×#9979 #24929996

Order 11008.

492 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 102 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×#3189C211yesmaximal, characteristic
2C43×#3095C212yesmaximal
3C43×#1818C211yesmaximal, characteristic
4C43×#1472C212yesmaximal
5C43×#1293C211yesmaximal, characteristic
6C2×C22⋊Q8×C43C2212yes—
7C2×#117×C43C2211yescharacteristic
8C43×#485—24no—
9C43×#484—22no—
10C43×#484—22no—
11C43×#483—22no—
12C43×#467—22no—
13C43×#451—22no—
14C43×#428—22no—
15C43×#419—22no—
16C43×#407C2212yes—
17C2×C22⋊C8×C43C2211yescharacteristic
18C2×C22⋊C8×C43C2211yescharacteristic
19C43×#336—22no—
20C43×#324—24no—
21C22×Q8×C43D412yes—
22C23×C4×C43C2311yescharacteristic
23C2×Q16×C43—22no—
24C2×M16×C43—22no—
25C22×C8×C43—21no—
26C22×C8×C43D412yes—
27C22⋊Q8×C43—22no—
28C22⋊Q8×C43—22no—
29C22⋊Q8×C43—22no—
30C22⋊Q8×C43—22no—
31#117×C43—22no—
32#117×C43—22no—
33C2×C4⋊C4×C43—22no—
34C2×C4⋊C4×C43D411yescharacteristic
35C2×C4⋊C4×C43D411yescharacteristic
36C2×C4⋊C4×C43D412yes—
37C2×C22⋊C4×C43—21no—
38C2×C22⋊C4×C43—22no—
39C2×C42×C43—21no—
40#107×C43—24no—
41#107×C43—22no—
42#106×C43—24no—
43#103×C43—24no—
44#103×C43—24no—
45#103×C43—24no—
46C22⋊C8×C43—22no—
47C22⋊C8×C43—22no—
48C22⋊C8×C43—22no—
49C22⋊C8×C43D414yes—
50C24×C43#4111yescharacteristic
51C2×Q8×C43—22no—
52C2×Q8×C43—22no—
53C2×Q8×C43—44no—
54C22×C4×C43—21no—
55C22×C4×C43—21no—
56C22×C4×C43—22no—
57C22×C4×C43—22no—
58C22×C4×C43—42no—
59C22×C4×C43C2×D412yes—
60C22×C4×C43C2×D411yescharacteristic
61C22×C4×C43C2×D411yescharacteristic
62C22×C4×C43C2×D412yes—
63Q16×C43—82no—
64M16×C43—44no—
65C2×C8×C43—22no—
66C2×C8×C43—24no—
67C2×C8×C43—42no—
68C2×C8×C43—42no—
69C2×C8×C43—41no—
70C4⋊C4×C43—22no—
71C4⋊C4×C43—22no—
72C4⋊C4×C43—22no—
73C4⋊C4×C43—22no—
74C4⋊C4×C43—42no—
75C4⋊C4×C43—42no—
76C22⋊C4×C43—42no—
77C22⋊C4×C43—42no—
78C22⋊C4×C43—42no—
79C42×C43—41no—
80C42×C43—41no—
81C23×C43—22no—
82C23×C43—41no—
83C23×C43—41no—
84C23×C43#12112yes—
85C23×C43#12111yescharacteristic
86Q8×C43—44no—
87Q8×C43—44no—
88C2×C4×C43—22no—
89C2×C4×C43—24no—
90C2×C4×C43—41no—
91C2×C4×C43—42no—
92C2×C4×C43—42no—
93C2×C4×C43—44no—
94C2×C4×C43—41no—
95C2×C4×C43—41no—
96C2×C4×C43—42no—
97C2×C4×C43—42no—
98C2×C4×C43—42no—
99C2×C4×C43—82no—
100C2×C4×C43#12012yes—
101C2×C4×C43#12011yescharacteristic
102C2×C4×C43#12711yescharacteristic
103C8×C43—44no—
104C8×C43—42no—
105C8×C43—81no—
106#9979C4311yesmaximal, characteristic, direct product factor, Sylow
107C22×C43—21no—
108C22×C43—21no—
109C22×C43—22no—
110C22×C43—22no—
111C22×C43—22no—
112C22×C43—82no—
113C22×C43#39211yescharacteristic
114C22×C43#47312yes—
115C4×C43—22no—
116C4×C43—21no—
117C4×C43—81no—
118C4×C43—82no—
119C4×C43—81no—
120C4×C43—82no—
121C4×C43#45812yes—
122#3189C2×C4311yescharacteristic
123#3095C2×C4312yes—
124#1818C2×C4311yescharacteristic
125#1472C2×C4312yes—
126#1293C2×C4311yescharacteristic
127C2×C43—22no—
128C2×C43—42no—
129C2×C43#201711yescharacteristic
130C2×C43#202011yescharacteristic
131C2×C43#202211yescharacteristic
132C2×C22⋊Q8C22×C4312yes—
133C2×#117C22×C4311yescharacteristic
134#485—24no—
135#484—22no—
136#484—22no—
137#483—22no—
138#467—22no—
139#451—22no—
140#428—22no—
141#419—22no—
142#407C22×C4312yes—
143C2×C22⋊C8C22×C4311yescharacteristic
144C2×C22⋊C8C22×C4311yescharacteristic
145#336—22no—
146#324—24no—
147C43#997911yescharacteristic, direct product factor, Sylow
148C22×Q8D4×C4312yes—
149C23×C4C23×C4311yescharacteristic
150C2×Q16—22no—
151C2×M16—22no—
152C22×C8—21no—
153C22×C8D4×C4312yes—
154C22⋊Q8—22no—
155C22⋊Q8—22no—
156C22⋊Q8—22no—
157C22⋊Q8—22no—
158#117—22no—
159#117—22no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4D4×C4311yescharacteristic
162C2×C4⋊C4D4×C4311yescharacteristic
163C2×C4⋊C4D4×C4312yes—
164C2×C22⋊C4—21no—
165C2×C22⋊C4—22no—
166C2×C42—21no—
167#107—24no—
168#107—22no—
169#106—24no—
170#103—24no—
171#103—24no—
172#103—24no—
173C22⋊C8—22no—
174C22⋊C8—22no—
175C22⋊C8—22no—
176C22⋊C8D4×C4314yes—
177C24#41×C4311yescharacteristic
178C2×Q8—22no—
179C2×Q8—22no—
180C2×Q8—44no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—42no—
186C22×C4C2×D4×C4312yes—
187C22×C4C2×D4×C4311yescharacteristic
188C22×C4C2×D4×C4311yescharacteristic
189C22×C4C2×D4×C4312yes—
190Q16—82no—
191M16—44no—
192C2×C8—22no—
193C2×C8—24no—
194C2×C8—42no—
195C2×C8—42no—
196C2×C8—41no—
197C4⋊C4—22no—
198C4⋊C4—22no—
199C4⋊C4—22no—
200C4⋊C4—22no—
201C4⋊C4—42no—
202C4⋊C4—42no—
203C22⋊C4—42no—
204C22⋊C4—42no—
205C22⋊C4—42no—
206C42—41no—
207C42—41no—
208C23—22no—
209C23—41no—
210C23—41no—
211C23#121×C4312yes—
212C23#121×C4311yescharacteristic
213Q8—44no—
214Q8—44no—
215C2×C4—22no—
216C2×C4—24no—
217C2×C4—41no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—44no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—82no—
227C2×C4#120×C4312yes—
228C2×C4#120×C4311yescharacteristic
229C2×C4#127×C4311yescharacteristic
230C8—44no—
231C8—42no—
232C8—81no—
233C22—21no—
234C22—21no—
235C22—22no—
236C22—22no—
237C22—22no—
238C22—82no—
239C22C43×#39211yescharacteristic
240C22C43×#47312yes—
241C4—22no—
242C4—21no—
243C4—81no—
244C4—82no—
245C4—81no—
246C4—82no—
247C4C43×#45812yes—
248C2—22no—
249C2—42no—
250C2C43×#201711yescharacteristic
251C2C43×#202011yescharacteristic
252C2C43×#202211yescharacteristic
subgroupG/H
center, socleC22×C43#392
commutator, Frattini, cosocleC23×C4C23×C43
prime radicalC24×C43#41
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C23×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
106. #9979C43direct (N × H)
147. C43#9979direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#31892
C43×#30952
C43×#18182
C43×#14722
C43×#12932
#997943