Finite Group Databasebeta

← C43×#8833 #24928850

Subgroups — C43×#8833 #24928850

Order 11008.

520 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#423C211yesmaximal, characteristic
2C43×#1797C211yesmaximal, characteristic
3C4×C22⋊C8×C43C211yesmaximal, characteristic
4C2×C43×#334C212yesmaximal, complemented
5C43×#1277C212yesmaximal, complemented
6C22×M16×C43—21no—
7C22×C42×C43C2211yescharacteristic
8C43×#423—24no—
9C2×C4⋊C8×C43—21no—
10C2×C4⋊C8×C43C2211yescharacteristic
11C2×C4⋊C8×C43C2211yescharacteristic
12C2×C4⋊C8×C43C2212yes—
13C2×C22⋊C8×C43—21no—
14C2×C22⋊C8×C43C412yes—
15C2×C4×C8×C43C2212yes—
16C43×#336—21no—
17C43×#336C411yescharacteristic
18C43×#336C411yescharacteristic
19C43×#334—24no—
20C23×C4×C43C2×C411yescharacteristic
21C23×C4×C43D411yescharacteristic
22C23×C4×C43Q811yescharacteristic
23C2×M16×C43—24no—
24C2×M16×C43—42no—
25C2×M16×C43—42no—
26C22×C8×C43—22no—
27C22×C8×C43—21no—
28C22×C8×C43—21no—
29C22×C8×C43C2×C412yes—
30C22×C8×C43C2×C412yes—
31C2×C42×C43—22no—
32C2×C42×C43—22no—
33C2×C42×C43C2×C411yescharacteristic
34C2×C42×C43D411yescharacteristic
35C2×C42×C43Q811yescharacteristic
36C2×C42×C43C2311yescharacteristic
37C4⋊C8×C43—24no—
38C4⋊C8×C43—22no—
39C4⋊C8×C43—22no—
40C4⋊C8×C43—22no—
41C4⋊C8×C43D414yes—
42C22⋊C8×C43—24no—
43C22⋊C8×C43—42no—
44C4×C8×C43—22no—
45C4×C8×C43—22no—
46C24×C43C4⋊C411yescharacteristic
47C22×C4×C43—21no—
48C22×C4×C43—21no—
49C22×C4×C43—21no—
50C22×C4×C43—21no—
51C22×C4×C43—22no—
52C22×C4×C43—22no—
53C22×C4×C43—22no—
54C22×C4×C43—22no—
55C22×C4×C43—21no—
56C22×C4×C43—21no—
57C22×C4×C43—41no—
58C22×C4×C43C4⋊C411yescharacteristic
59C22×C4×C43C4⋊C411yescharacteristic
60C22×C4×C43C4⋊C411yescharacteristic
61C22×C4×C43SD1612yes—
62C22×C4×C43SD1612yes—
63C22×C4×C43C22×C411yescharacteristic
64C22×C4×C43C2×D411yescharacteristic
65C22×C4×C43C2×Q811yescharacteristic
66M16×C43—48no—
67C2×C8×C43—22no—
68C2×C8×C43—22no—
69C2×C8×C43—22no—
70C2×C8×C43—24no—
71C2×C8×C43—22no—
72C2×C8×C43—22no—
73C2×C8×C43—42no—
74C2×C8×C43—42no—
75C2×C8×C43—41no—
76C2×C8×C43—41no—
77C2×C8×C43—41no—
78C2×C8×C43—41no—
79C2×C8×C43—41no—
80C2×C8×C43—41no—
81C2×C8×C43M1614yescomplemented
82C42×C43—22no—
83C42×C43—21no—
84C42×C43—22no—
85C42×C43—21no—
86C42×C43C2×D412yes—
87C42×C43#4112yes—
88C23×C43—21no—
89C23×C43—21no—
90C23×C43—21no—
91C23×C43—21no—
92C23×C43—21no—
93C23×C43—21no—
94C23×C43#10612yes—
95C23×C43C2×C4⋊C411yescharacteristic
96C2×C4×C43—21no—
97C2×C4×C43—21no—
98C2×C4×C43—21no—
99C2×C4×C43—21no—
100C2×C4×C43—21no—
101C2×C4×C43—21no—
102C2×C4×C43—22no—
103C2×C4×C43—22no—
104C2×C4×C43—22no—
105C2×C4×C43—22no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—44no—
110C2×C4×C43—42no—
111C2×C4×C43—42no—
112C2×C4×C43#10612yes—
113C2×C4×C43#10812yes—
114C2×C4×C43C4×D412yes—
115C2×C4×C43#12011yescharacteristic
116C2×C4×C43C22⋊Q812yes—
117C2×C4×C43#12311yescharacteristic
118C2×C4×C43C2×M1612yes—
119C2×C4×C43#13111yescharacteristic
120C2×C4×C43#13111yescharacteristic
121C2×C4×C43C2×SD1611yescharacteristic
122C2×C4×C43C2×SD1611yescharacteristic
123C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C43#13711yescharacteristic
125C8×C43—24no—
126C8×C43—42no—
127C8×C43—44no—
128C8×C43—81no—
129C8×C43—81no—
130#8833C4311yesmaximal, characteristic, direct product factor, Sylow
131C22×C43—22no—
132C22×C43—22no—
133C22×C43—22no—
134C22×C43—41no—
135C22×C43—41no—
136C22×C43—41no—
137C22×C43—41no—
138C22×C43#38511yescharacteristic
139C22×C43#42311yescharacteristic
140C22×C43#42411yescharacteristic
141C22×C43C2×#10611yescharacteristic
142C22×C43#42811yescharacteristic
143C22×C43C2×#10811yescharacteristic
144C22×C43#43011yescharacteristic
145C4×C43—22no—
146C4×C43—22no—
147C4×C43—22no—
148C4×C43—41no—
149C4×C43#43512yes—
150C4×C43#43612yes—
151C4×C43#44811yescharacteristic
152C4×C43#45011yescharacteristic
153C4×C43#48111yescharacteristic
154C4×C43#48311yescharacteristic
155C2×#423C2×C4311yescharacteristic
156#1797C2×C4311yescharacteristic
157C4×C22⋊C8C2×C4311yescharacteristic
158C2×#334C2×C4312yescomplemented
159#1277C2×C4312yescomplemented
160C2×C43—42no—
161C2×C43#156611yescharacteristic
162C2×C43#156911yescharacteristic
163C2×C43#157011yescharacteristic
164C2×C43#157411yescharacteristic
165C2×C43#185111yescharacteristic
166C2×C43#185311yescharacteristic
167C2×C43#185511yescharacteristic
168C22×M16—21no—
169C22×C42C22×C4311yescharacteristic
170#423—24no—
171C2×C4⋊C8—21no—
172C2×C4⋊C8C22×C4311yescharacteristic
173C2×C4⋊C8C22×C4311yescharacteristic
174C2×C4⋊C8C22×C4312yes—
175C2×C22⋊C8—21no—
176C2×C22⋊C8C4×C4312yes—
177C2×C4×C8C22×C4312yes—
178#336—21no—
179#336C4×C4311yescharacteristic
180#336C4×C4311yescharacteristic
181#334—24no—
182C43#883311yescharacteristic, direct product factor, Sylow
183C23×C4C2×C4×C4311yescharacteristic
184C23×C4D4×C4311yescharacteristic
185C23×C4Q8×C4311yescharacteristic
186C2×M16—24no—
187C2×M16—42no—
188C2×M16—42no—
189C22×C8—22no—
190C22×C8—21no—
191C22×C8—21no—
192C22×C8C2×C4×C4312yes—
193C22×C8C2×C4×C4312yes—
194C2×C42—22no—
195C2×C42—22no—
196C2×C42C2×C4×C4311yescharacteristic
197C2×C42D4×C4311yescharacteristic
198C2×C42Q8×C4311yescharacteristic
199C2×C42C23×C4311yescharacteristic
200C4⋊C8—24no—
201C4⋊C8—22no—
202C4⋊C8—22no—
203C4⋊C8—22no—
204C4⋊C8D4×C4314yes—
205C22⋊C8—24no—
206C22⋊C8—42no—
207C4×C8—22no—
208C4×C8—22no—
209C24C4⋊C4×C4311yescharacteristic
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—41no—
221C22×C4C4⋊C4×C4311yescharacteristic
222C22×C4C4⋊C4×C4311yescharacteristic
223C22×C4C4⋊C4×C4311yescharacteristic
224C22×C4SD16×C4312yes—
225C22×C4SD16×C4312yes—
226C22×C4C22×C4×C4311yescharacteristic
227C22×C4C2×D4×C4311yescharacteristic
228C22×C4C2×Q8×C4311yescharacteristic
229M16—48no—
230C2×C8—22no—
231C2×C8—22no—
232C2×C8—22no—
233C2×C8—24no—
234C2×C8—22no—
235C2×C8—22no—
236C2×C8—42no—
237C2×C8—42no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8M16×C4314yescomplemented
245C42—22no—
246C42—21no—
247C42—22no—
248C42—21no—
249C42C2×D4×C4312yes—
250C42#41×C4312yes—
251C23—21no—
252C23—21no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23#106×C4312yes—
258C23C2×C4⋊C4×C4311yescharacteristic
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—44no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4#106×C4312yes—
276C2×C4#108×C4312yes—
277C2×C4C4×D4×C4312yes—
278C2×C4#120×C4311yescharacteristic
279C2×C4C22⋊Q8×C4312yes—
280C2×C4#123×C4311yescharacteristic
281C2×C4C2×M16×C4312yes—
282C2×C4#131×C4311yescharacteristic
283C2×C4#131×C4311yescharacteristic
284C2×C4C2×SD16×C4311yescharacteristic
285C2×C4C2×SD16×C4311yescharacteristic
286C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
287C2×C4#137×C4311yescharacteristic
288C8—24no—
289C8—42no—
290C8—44no—
291C8—81no—
292C8—81no—
293C22—22no—
294C22—22no—
295C22—22no—
296C22—41no—
297C22—41no—
298C22—41no—
299C22—41no—
300C22C43×#38511yescharacteristic
301C22C43×#42311yescharacteristic
302C22C43×#42411yescharacteristic
303C22C2×#106×C4311yescharacteristic
304C22C43×#42811yescharacteristic
305C22C2×#108×C4311yescharacteristic
306C22C43×#43011yescharacteristic
307C4—22no—
308C4—22no—
309C4—22no—
310C4—41no—
311C4C43×#43512yes—
312C4C43×#43612yes—
313C4C43×#44811yescharacteristic
314C4C43×#45011yescharacteristic
315C4C43×#48111yescharacteristic
316C4C43×#48311yescharacteristic
317C2—42no—
318C2C43×#156611yescharacteristic
319C2C43×#156911yescharacteristic
320C2C43×#157011yescharacteristic
321C2C43×#157411yescharacteristic
322C2C43×#185111yescharacteristic
323C2C43×#185311yescharacteristic
324C2C43×#185511yescharacteristic
subgroupG/H
centerC22×C4×C43C2×D4
commutatorC22×C4C22×C4×C43
Frattini, cosocleC2×C42C23×C43
socleC23×C43C2×C4⋊C4
prime radicalC24×C43C4⋊C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C43 ◁ C22×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C43×#334C2semidirect
5. C43×#1277C2semidirect
81. C2×C8×C43M16semidirect
130. #8833C43direct (N × H)
158. C2×#334C2×C43semidirect
159. #1277C2×C43semidirect
182. C43#8833direct (N × H)
244. C2×C8M16×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4232
C43×#17972
C4×C22⋊C8×C432
C2×C43×#3342
C43×#12772
#883343