Finite Group Databasebeta

← C43×#13421 #24933438

Subgroups — C43×#13421 #24933438

Order 11008.

496 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 90 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×#2724C211yesmaximal, characteristic
2C2×C43×#352C212yesmaximal
3C43×#1890C212yesmaximal
4C43×#1856C211yesmaximal, characteristic
5C43×#1393C211yesmaximal, characteristic
6C2×#123×C43C2212yes—
7C43×#518C2211yescharacteristic
8C43×#428—21no—
9C2×#100×C43C2211yescharacteristic
10C2×#99×C43C2212yes—
11C43×#398—21no—
12C43×#397—22no—
13C43×#390C2211yescharacteristic
14C43×#389—21no—
15C43×#385—22no—
16C43×#381—22no—
17C43×#352—24no—
18C43×#342—22no—
19C43×#339—21no—
20C22×D4×C43C2311yescharacteristic
21C23×C4×C43D412yes—
22C2×M16×C43—21no—
23#123×C43—22no—
24#123×C43—22no—
25#123×C43—22no—
26#123×C43—22no—
27C4×D4×C43—41no—
28C4×D4×C43—41no—
29#117×C43—21no—
30C2×C4⋊C4×C43—21no—
31C2×C4⋊C4×C43—22no—
32C2×C4⋊C4×C43—21no—
33C2×C4⋊C4×C43—21no—
34C2×C4⋊C4×C43D411yescharacteristic
35C2×C22⋊C4×C43—22no—
36C2×C22⋊C4×C43—22no—
37C2×C22⋊C4×C43—22no—
38C2×C22⋊C4×C43—22no—
39C2×C22⋊C4×C43D412yes—
40C2×C42×C43D411yescharacteristic
41#107×C43—41no—
42#106×C43—41no—
43#100×C43—21no—
44#100×C43D412yes—
45#99×C43—22no—
46#99×C43—22no—
47#95×C43—22no—
48#95×C43—22no—
49#95×C43—21no—
50#95×C43—42no—
51#95×C43—42no—
52C24×C43C2×D412yes—
53C2×D4×C43—41no—
54C2×D4×C43—41no—
55C2×D4×C43C2×D411yescharacteristic
56C2×D4×C43#4112yes—
57C2×D4×C43#4111yescharacteristic
58C22×C4×C43—22no—
59C22×C4×C43—22no—
60C22×C4×C43—21no—
61C22×C4×C43—21no—
62C22×C4×C43—22no—
63C22×C4×C43—22no—
64C22×C4×C43—22no—
65C22×C4×C43—22no—
66C22×C4×C43—42no—
67C22×C4×C43—42no—
68C22×C4×C43—42no—
69C22×C4×C43C2×D411yescharacteristic
70M16×C43—22no—
71M16×C43—41no—
72C2×C8×C43—41no—
73C4⋊C4×C43—21no—
74C4⋊C4×C43—21no—
75C4⋊C4×C43—41no—
76C4⋊C4×C43—42no—
77C4⋊C4×C43—42no—
78C4⋊C4×C43—42no—
79C4⋊C4×C43—81no—
80C4⋊C4×C43—81no—
81C22⋊C4×C43—22no—
82C22⋊C4×C43—22no—
83C22⋊C4×C43—42no—
84C22⋊C4×C43—42no—
85C22⋊C4×C43—44no—
86C22⋊C4×C43—41no—
87C22⋊C4×C43—42no—
88C22⋊C4×C43—42no—
89C22⋊C4×C43—42no—
90C42×C43—41no—
91C42×C43—41no—
92C23×C43—22no—
93C23×C43—22no—
94C23×C43—42no—
95C23×C43—42no—
96C23×C43#12011yescharacteristic
97C23×C43#12112yes—
98C23×C43#12312yes—
99D4×C43—41no—
100D4×C43—41no—
101D4×C43—42no—
102C2×C4×C43—21no—
103C2×C4×C43—21no—
104C2×C4×C43—22no—
105C2×C4×C43—41no—
106C2×C4×C43—41no—
107C2×C4×C43—42no—
108C2×C4×C43—42no—
109C2×C4×C43—42no—
110C2×C4×C43—44no—
111C2×C4×C43—42no—
112C2×C4×C43—42no—
113C2×C4×C43—41no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43—42no—
117C2×C4×C43—42no—
118C2×C4×C43—82no—
119C2×C4×C43—82no—
120C2×C4×C43—82no—
121C2×C4×C43—82no—
122C2×C4×C43—82no—
123C2×C4×C43—82no—
124C2×C4×C43#12111yescharacteristic
125C2×C4×C43#12411yescharacteristic
126C8×C43—42no—
127#13421C4311yesmaximal, characteristic, direct product factor, Sylow
128C22×C43—21no—
129C22×C43—21no—
130C22×C43—22no—
131C22×C43—22no—
132C22×C43—42no—
133C22×C43—42no—
134C22×C43—42no—
135C22×C43—42no—
136C22×C43—82no—
137C22×C43#39411yescharacteristic
138C22×C43B(4,𝔽2)11yescharacteristic
139C22×C43#45811yescharacteristic
140C4×C43—21no—
141C4×C43—21no—
142C4×C43—42no—
143C4×C43—82no—
144C4×C43—81no—
145C4×C43—81no—
146C4×C43—81no—
147C4×C43—82no—
148C4×C43—162no—
149#2724C2×C4311yescharacteristic
150C2×#352C2×C4312yes—
151#1890C2×C4312yes—
152#1856C2×C4311yescharacteristic
153#1393C2×C4311yescharacteristic
154C2×C43—21no—
155C2×C43—21no—
156C2×C43—42no—
157C2×C43—42no—
158C2×C43#204411yescharacteristic
159C2×C43#219811yescharacteristic
160C2×C43#220111yescharacteristic
161C2×#123C22×C4312yes—
162#518C22×C4311yescharacteristic
163#428—21no—
164C2×#100C22×C4311yescharacteristic
165C2×#99C22×C4312yes—
166#398—21no—
167#397—22no—
168#390C22×C4311yescharacteristic
169#389—21no—
170#385—22no—
171#381—22no—
172#352—24no—
173#342—22no—
174#339—21no—
175C43#1342111yescharacteristic, direct product factor, Sylow
176C22×D4C23×C4311yescharacteristic
177C23×C4D4×C4312yes—
178C2×M16—21no—
179#123—22no—
180#123—22no—
181#123—22no—
182#123—22no—
183C4×D4—41no—
184C4×D4—41no—
185#117—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4D4×C4311yescharacteristic
191C2×C22⋊C4—22no—
192C2×C22⋊C4—22no—
193C2×C22⋊C4—22no—
194C2×C22⋊C4—22no—
195C2×C22⋊C4D4×C4312yes—
196C2×C42D4×C4311yescharacteristic
197#107—41no—
198#106—41no—
199#100—21no—
200#100D4×C4312yes—
201#99—22no—
202#99—22no—
203#95—22no—
204#95—22no—
205#95—21no—
206#95—42no—
207#95—42no—
208C24C2×D4×C4312yes—
209C2×D4—41no—
210C2×D4—41no—
211C2×D4C2×D4×C4311yescharacteristic
212C2×D4#41×C4311yescharacteristic
213C2×D4#41×C4312yes—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4C2×D4×C4311yescharacteristic
226M16—22no—
227M16—41no—
228C2×C8—41no—
229C4⋊C4—21no—
230C4⋊C4—21no—
231C4⋊C4—41no—
232C4⋊C4—42no—
233C4⋊C4—42no—
234C4⋊C4—42no—
235C4⋊C4—81no—
236C4⋊C4—81no—
237C22⋊C4—22no—
238C22⋊C4—22no—
239C22⋊C4—44no—
240C22⋊C4—42no—
241C22⋊C4—41no—
242C22⋊C4—42no—
243C22⋊C4—42no—
244C22⋊C4—42no—
245C22⋊C4—42no—
246C42—41no—
247C42—41no—
248C23—22no—
249C23—22no—
250C23—42no—
251C23—42no—
252C23#120×C4311yescharacteristic
253C23#121×C4312yes—
254C23#123×C4312yes—
255D4—41no—
256D4—41no—
257D4—42no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—44no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—82no—
275C2×C4—82no—
276C2×C4—82no—
277C2×C4—82no—
278C2×C4—82no—
279C2×C4—82no—
280C2×C4#121×C4311yescharacteristic
281C2×C4#124×C4311yescharacteristic
282C8—42no—
283C22—21no—
284C22—21no—
285C22—22no—
286C22—22no—
287C22—42no—
288C22—42no—
289C22—42no—
290C22—42no—
291C22—82no—
292C22C43×#39411yescharacteristic
293C22C43×B(4,𝔽2)11yescharacteristic
294C22C43×#45811yescharacteristic
295C4—21no—
296C4—21no—
297C4—42no—
298C4—82no—
299C4—81no—
300C4—81no—
301C4—81no—
302C4—82no—
303C4—162no—
304C2—21no—
305C2—21no—
306C2—42no—
307C2—42no—
308C2C43×#204411yescharacteristic
309C2C43×#219811yescharacteristic
310C2C43×#220111yescharacteristic
subgroupG/H
center, socleC22×C43B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C43
prime radicalC22×D4×C43C23
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C23×C43 ◁ C22×D4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
127. #13421C43direct (N × H)
175. C43#13421direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#27242
C2×C43×#3522
C43×#18902
C43×#18562
C43×#13932
#1342143