Finite Group Databasebeta

← C43×#8851 #24928868

Subgroups — C43×#8851 #24928868

Order 11008.

558 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2972C211yesmaximal, characteristic
2C43×#1869C211yesmaximal, characteristic
3C43×#1850C212yesmaximal, complemented
4C4×#99×C43C211yesmaximal, characteristic
5C43×#1282C212yesmaximal, complemented
6C23×C8×C43C2211yescharacteristic
7C2×C4×D4×C43C2211yescharacteristic
8C8×D4×C43—22no—
9C8×D4×C43—22no—
10C43×#431—21no—
11C2×C4⋊C8×C43—22no—
12C2×#99×C43C411yescharacteristic
13C2×#99×C43C411yescharacteristic
14C2×C22⋊C8×C43—21no—
15C2×C22⋊C8×C43—21no—
16C2×C22⋊C8×C43C2211yescharacteristic
17C2×C22⋊C8×C43C2212yes—
18C4×C22⋊C4×C43C2212yes—
19C43×#342C412yes—
20C43×#336—22no—
21C43×#336—21no—
22C22×D4×C43C2×C411yescharacteristic
23C23×C4×C43D411yescharacteristic
24C23×C4×C43C2311yescharacteristic
25C22×C8×C43—21no—
26C22×C8×C43—22no—
27C22×C8×C43—21no—
28C22×C8×C43—21no—
29C22×C8×C43—21no—
30C22×C8×C43—42no—
31C22×C8×C43D412yes—
32C22×C8×C43D412yes—
33C4×D4×C43—22no—
34C4×D4×C43—22no—
35C2×C4⋊C4×C43Q811yescharacteristic
36C2×C22⋊C4×C43C2×C412yes—
37C2×C22⋊C4×C43C2×C411yescharacteristic
38C2×C22⋊C4×C43C2×C412yes—
39C2×C22⋊C4×C43Q811yescharacteristic
40C2×C42×C43—22no—
41C2×C42×C43D411yescharacteristic
42C4⋊C8×C43—21no—
43C4⋊C8×C43—21no—
44C4⋊C8×C43—44no—
45#99×C43—22no—
46#99×C43C814yescomplemented
47C22⋊C8×C43—22no—
48C22⋊C8×C43—22no—
49C22⋊C8×C43—22no—
50C22⋊C8×C43—22no—
51C22⋊C8×C43—42no—
52C4×C8×C43—22no—
53#95×C43—22no—
54C24×C43C4⋊C411yescharacteristic
55C24×C43C22×C411yescharacteristic
56C2×D4×C43—22no—
57C2×D4×C43—22no—
58C2×D4×C43C2×C812yes—
59C2×D4×C43M1612yes—
60C22×C4×C43—21no—
61C22×C4×C43—21no—
62C22×C4×C43—22no—
63C22×C4×C43—22no—
64C22×C4×C43—41no—
65C22×C4×C43—41no—
66C22×C4×C43—41no—
67C22×C4×C43—41no—
68C22×C4×C43C4⋊C411yescharacteristic
69C22×C4×C43C4⋊C411yescharacteristic
70C22×C4×C43C4⋊C411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43C2×D412yes—
73C22×C4×C43C2×Q811yescharacteristic
74C22×C4×C43#4112yes—
75C2×C8×C43—22no—
76C2×C8×C43—24no—
77C2×C8×C43—22no—
78C2×C8×C43—22no—
79C2×C8×C43—42no—
80C2×C8×C43—41no—
81C2×C8×C43—41no—
82C2×C8×C43—42no—
83C2×C8×C43—42no—
84C2×C8×C43—41no—
85C2×C8×C43—41no—
86C2×C8×C43—41no—
87C2×C8×C43—81no—
88C2×C8×C43—81no—
89C4⋊C4×C43—22no—
90C22⋊C4×C43—22no—
91C22⋊C4×C43—22no—
92C22⋊C4×C43—22no—
93C22⋊C4×C43—22no—
94C22⋊C4×C43—22no—
95C22⋊C4×C43C2×C814yescomplemented
96C42×C43—21no—
97C42×C43—21no—
98C42×C43—42no—
99C42×C43—42no—
100C23×C43—21no—
101C23×C43—21no—
102C23×C43—41no—
103C23×C43—41no—
104C23×C43—41no—
105C23×C43—41no—
106C23×C43C4⋊C812yescomplemented
107C23×C43C2×C4⋊C411yescharacteristic
108C23×C43C4×D412yes—
109C23×C43C22×C811yescharacteristic
110C23×C43C2×M1611yescharacteristic
111C23×C43#13112yes—
112D4×C43—24no—
113D4×C43—24no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—22no—
117C2×C4×C43—21no—
118C2×C4×C43—22no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—24no—
123C2×C4×C43—41no—
124C2×C4×C43—42no—
125C2×C4×C43—42no—
126C2×C4×C43—42no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—42no—
132C2×C4×C43—42no—
133C2×C4×C43—42no—
134C2×C4×C43—81no—
135C2×C4×C43C4⋊C812yescomplemented
136C2×C4×C43#12011yescharacteristic
137C2×C4×C43C22⋊Q812yes—
138C2×C4×C43#12311yescharacteristic
139C8×C43—42no—
140C8×C43—42no—
141C8×C43—42no—
142C8×C43—81no—
143#8851C4311yesmaximal, characteristic, direct product factor, Sylow
144C22×C43—21no—
145C22×C43—22no—
146C22×C43—21no—
147C22×C43—22no—
148C22×C43—22no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43—42no—
152C22×C43—42no—
153C22×C43—41no—
154C22×C43—41no—
155C22×C43—81no—
156C22×C43#38511yescharacteristic
157C22×C43C2×C4⋊C811yescharacteristic
158C22×C43#42411yescharacteristic
159C22×C43C8×D412yes—
160C22×C43#43512yes—
161C4×C43—22no—
162C4×C43—21no—
163C4×C43—22no—
164C4×C43—44no—
165C4×C43—41no—
166C4×C43—41no—
167C4×C43—82no—
168C4×C43B(4,𝔽2)11yescharacteristic
169C4×C43#45811yescharacteristic
170#2972C2×C4311yescharacteristic
171#1869C2×C4311yescharacteristic
172#1850C2×C4312yescomplemented
173C4×#99C2×C4311yescharacteristic
174#1282C2×C4312yescomplemented
175C2×C43—22no—
176C2×C43—22no—
177C2×C43—21no—
178C2×C43—21no—
179C2×C43—42no—
180C2×C43#185011yescharacteristic
181C2×C43#186711yescharacteristic
182C2×C43#186811yescharacteristic
183C23×C8C22×C4311yescharacteristic
184C2×C4×D4C22×C4311yescharacteristic
185C8×D4—22no—
186C8×D4—22no—
187#431—21no—
188C2×C4⋊C8—22no—
189C2×#99C4×C4311yescharacteristic
190C2×#99C4×C4311yescharacteristic
191C2×C22⋊C8—21no—
192C2×C22⋊C8—21no—
193C2×C22⋊C8C22×C4311yescharacteristic
194C2×C22⋊C8C22×C4312yes—
195C4×C22⋊C4C22×C4312yes—
196#342C4×C4312yes—
197#336—22no—
198#336—21no—
199C43#885111yescharacteristic, direct product factor, Sylow
200C22×D4C2×C4×C4311yescharacteristic
201C23×C4D4×C4311yescharacteristic
202C23×C4C23×C4311yescharacteristic
203C22×C8—21no—
204C22×C8—22no—
205C22×C8—21no—
206C22×C8—21no—
207C22×C8—21no—
208C22×C8—42no—
209C22×C8D4×C4312yes—
210C22×C8D4×C4312yes—
211C4×D4—22no—
212C4×D4—22no—
213C2×C4⋊C4Q8×C4311yescharacteristic
214C2×C22⋊C4C2×C4×C4312yes—
215C2×C22⋊C4C2×C4×C4311yescharacteristic
216C2×C22⋊C4C2×C4×C4312yes—
217C2×C22⋊C4Q8×C4311yescharacteristic
218C2×C42—22no—
219C2×C42D4×C4311yescharacteristic
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—44no—
223#99—22no—
224#99C8×C4314yescomplemented
225C22⋊C8—22no—
226C22⋊C8—22no—
227C22⋊C8—22no—
228C22⋊C8—22no—
229C22⋊C8—42no—
230C4×C8—22no—
231#95—22no—
232C24C4⋊C4×C4311yescharacteristic
233C24C22×C4×C4311yescharacteristic
234C2×D4—22no—
235C2×D4—22no—
236C2×D4C2×C8×C4312yes—
237C2×D4M16×C4312yes—
238C22×C4—22no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—22no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4C4⋊C4×C4311yescharacteristic
247C22×C4C4⋊C4×C4311yescharacteristic
248C22×C4C4⋊C4×C4311yescharacteristic
249C22×C4C2×D4×C4312yes—
250C22×C4C2×D4×C4311yescharacteristic
251C22×C4C2×Q8×C4311yescharacteristic
252C22×C4#41×C4312yes—
253C2×C8—22no—
254C2×C8—24no—
255C2×C8—22no—
256C2×C8—22no—
257C2×C8—42no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—42no—
261C2×C8—42no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—41no—
265C2×C8—81no—
266C2×C8—81no—
267C4⋊C4—22no—
268C22⋊C4—22no—
269C22⋊C4—22no—
270C22⋊C4—22no—
271C22⋊C4—22no—
272C22⋊C4—22no—
273C22⋊C4C2×C8×C4314yescomplemented
274C42—21no—
275C42—21no—
276C42—42no—
277C42—42no—
278C23—21no—
279C23—21no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23C4⋊C8×C4312yescomplemented
285C23C2×C4⋊C4×C4311yescharacteristic
286C23C4×D4×C4312yes—
287C23C22×C8×C4311yescharacteristic
288C23C2×M16×C4311yescharacteristic
289C23#131×C4312yes—
290D4—24no—
291D4—24no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—22no—
295C2×C4—21no—
296C2×C4—22no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—24no—
301C2×C4—41no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—81no—
313C2×C4C4⋊C8×C4312yescomplemented
314C2×C4#120×C4311yescharacteristic
315C2×C4C22⋊Q8×C4312yes—
316C2×C4#123×C4311yescharacteristic
317C8—42no—
318C8—42no—
319C8—42no—
320C8—81no—
321C22—22no—
322C22—21no—
323C22—22no—
324C22—21no—
325C22—22no—
326C22—41no—
327C22—41no—
328C22—42no—
329C22—42no—
330C22—41no—
331C22—41no—
332C22—81no—
333C22C43×#38511yescharacteristic
334C22C2×C4⋊C8×C4311yescharacteristic
335C22C43×#42411yescharacteristic
336C22C8×D4×C4312yes—
337C22C43×#43512yes—
338C4—22no—
339C4—21no—
340C4—22no—
341C4—44no—
342C4—41no—
343C4—41no—
344C4—82no—
345C4C43×B(4,𝔽2)11yescharacteristic
346C4C43×#45811yescharacteristic
347C2—22no—
348C2—22no—
349C2—21no—
350C2—21no—
351C2—42no—
352C2C43×#185011yescharacteristic
353C2C43×#186711yescharacteristic
354C2C43×#186811yescharacteristic
subgroupG/H
centerC2×C4×C43#120
commutatorC23C22×C8×C43
Frattini, cosocleC23×C4C23×C43
socleC22×C43#385
prime radicalC22×D4×C43C2×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C43 ◁ C23×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
3. C43×#1850C2semidirect
5. C43×#1282C2semidirect
46. #99×C43C8semidirect
95. C22⋊C4×C43C2×C8semidirect
106. C23×C43C4⋊C8semidirect
135. C2×C4×C43C4⋊C8semidirect
143. #8851C43direct (N × H)
172. #1850C2×C43semidirect
174. #1282C2×C43semidirect
199. C43#8851direct (N × H)
224. #99C8×C43semidirect
273. C22⋊C4C2×C8×C43semidirect
284. C23C4⋊C8×C43semidirect
313. C2×C4C4⋊C8×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#29722
C43×#18692
C43×#18502
C4×#99×C432
C43×#12822
#885143