Finite Group Databasebeta

← C43×#20781 #24940798

Subgroups — C43×#20781 #24940798

Order 11008.

758 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#117×C43C211yesmaximal, characteristic
2C43×#1839C212yesmaximal, complemented
3C43×#1832C212yesmaximal, complemented
4C43×#1817C212yesmaximal
5C43×#1798C212yesmaximal
6C43×#1767C211yesmaximal, characteristic, complemented
7C4×C4⋊C8×C43C211yesmaximal, characteristic, complemented
8C43×#1750C212yesmaximal
9C43×#1746C212yesmaximal, complemented
10C2×#117×C43C2211yescharacteristic
11C2×#117×C43C2211yescharacteristic
12C22×C42×C43C2211yescharacteristic
13C2×C4⋊C8×C43C2212yes—
14C2×C4⋊C8×C43C2212yes—
15C2×C22⋊C8×C43C2214yes—
16C2×#97×C43C2212yes—
17C2×C4×C8×C43C2212yes—
18C4×C4⋊C4×C43C412yes—
19C4×C4⋊C4×C43C412yes—
20C4×C22⋊C4×C43C412yes—
21C4×C22⋊C4×C43C412yes—
22C43×#376C2211yescharacteristic
23C43×#376C2211yescharacteristic
24C43×C43C2211yescharacteristic
25C43×C43C2211yescharacteristic
26C43×#336C2214yes—
27C43×#336C2212yes—
28C43×#336C2212yes—
29C43×#336C2214yes—
30C43×#336C2214yes—
31C23×C4×C43C2×C412yes—
32C23×C4×C43C2311yescharacteristic
33C22×C8×C43C2314yes—
34C22×C8×C43C2314yes—
35#117×C43—22no—
36#117×C43—22no—
37#117×C43—24no—
38C2×C4⋊C4×C43C2×C412yes—
39C2×C4⋊C4×C43C2×C411yescharacteristic
40C2×C4⋊C4×C43C2×C411yescharacteristic
41C2×C22⋊C4×C43C2×C412yes—
42C2×C22⋊C4×C43C2×C411yescharacteristic
43C2×C22⋊C4×C43C2×C411yescharacteristic
44C2×C42×C43—24no—
45C2×C42×C43C2×C412yes—
46C2×C42×C43C2×C412yes—
47C2×C42×C43C2×C412yes—
48C2×C42×C43C2×C412yes—
49C2×C42×C43C2×C412yes—
50C2×C42×C43C2311yescharacteristic
51C2×C42×C43C2311yescharacteristic
52C2×C42×C43C2311yescharacteristic
53C2×C42×C43C2311yescharacteristic
54C2×C42×C43C2311yescharacteristic
55C2×C42×C43C2311yescharacteristic
56C4⋊C8×C43—24no—
57C4⋊C8×C43—24no—
58C22⋊C8×C43—28no—
59#97×C43—24no—
60C4×C8×C43—24no—
61#95×C43C2×C412yes—
62#95×C43C2×C412yes—
63#95×C43C2×C412yes—
64#95×C43C2×C412yes—
65C24×C43C22×C411yescharacteristic
66C22×C4×C43—22no—
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43—24no—
70C22×C4×C43—24no—
71C22×C4×C43—42no—
72C22×C4×C43C22×C412yes—
73C22×C4×C43C22×C411yescharacteristic
74C22×C4×C43C22×C412yes—
75C22×C4×C43C22×C411yescharacteristic
76C22×C4×C43C22×C411yescharacteristic
77C22×C4×C43C22×C412yes—
78C22×C4×C43C22×C411yescharacteristic
79C22×C4×C43C22×C411yescharacteristic
80C22×C4×C43C22×C412yes—
81C22×C4×C43#4114yes—
82C22×C4×C43C2411yescharacteristic
83C2×C8×C43—24no—
84C2×C8×C43—24no—
85C2×C8×C43—24no—
86C2×C8×C43—24no—
87C2×C8×C43—24no—
88C2×C8×C43—24no—
89C4⋊C4×C43—22no—
90C4⋊C4×C43—22no—
91C4⋊C4×C43—24no—
92C22⋊C4×C43—22no—
93C22⋊C4×C43—22no—
94C22⋊C4×C43—24no—
95C42×C43—24no—
96C42×C43—24no—
97C42×C43—24no—
98C42×C43—22no—
99C42×C43—22no—
100C42×C43—22no—
101C42×C43—21no—
102C42×C43—21no—
103C42×C43—42no—
104C42×C43—42no—
105C42×C43#4112yes—
106C42×C43#4112yes—
107C42×C43#4114yes—
108C23×C43—21no—
109C23×C43—21no—
110C23×C43—22no—
111C23×C43—22no—
112C23×C43#11712yes—
113C23×C43C23×C411yescharacteristic
114C2×C4×C43—22no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—22no—
118C2×C4×C43—22no—
119C2×C4×C43—22no—
120C2×C4×C43—22no—
121C2×C4×C43—22no—
122C2×C4×C43—24no—
123C2×C4×C43—24no—
124C2×C4×C43—22no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—22no—
128C2×C4×C43—22no—
129C2×C4×C43—22no—
130C2×C4×C43—22no—
131C2×C4×C43—22no—
132C2×C4×C43—22no—
133C2×C4×C43—22no—
134C2×C4×C43—48no—
135C2×C4×C43#11712yes—
136C2×C4×C43#11712yes—
137C2×C4×C43#11712yes—
138C2×C4×C43#11714yes—
139C2×C4×C43#13114yes—
140C2×C4×C43C2×#4112yes—
141C2×C4×C43C2×#4112yes—
142C2×C4×C43C2×#4111yescharacteristic
143C2×C4×C43C2×#4111yescharacteristic
144C8×C43—44no—
145C8×C43—44no—
146#20781C4311yesmaximal, characteristic, direct product factor, Sylow
147C22×C43—24no—
148C22×C43—22no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43—42no—
152C22×C43C2×#11711yescharacteristic
153C22×C43C2×#11711yescharacteristic
154C22×C43C2×#11711yescharacteristic
155C22×C43C2×#13112yes—
156C22×C43#56812yes—
157C4×C43—22no—
158C4×C43—22no—
159C4×C43—24no—
160C4×C43—24no—
161C4×C43—22no—
162C4×C43—41no—
163C4×C43—41no—
164C4×C43—42no—
165C4×C43—42no—
166C4×C43#52912yes—
167C4×C43#52912yes—
168C4×#117C2×C4311yescharacteristic
169#1839C2×C4312yescomplemented
170#1832C2×C4312yescomplemented
171#1817C2×C4312yes—
172#1798C2×C4312yes—
173#1767C2×C4311yescharacteristic, complemented
174C4×C4⋊C8C2×C4311yescharacteristic, complemented
175#1750C2×C4312yes—
176#1746C2×C4312yescomplemented
177C2×C43—42no—
178C2×C43#228311yescharacteristic
179C2×C43#292211yescharacteristic
180C2×C43#292311yescharacteristic
181C2×C43#292412yes—
182C2×C43#292512yes—
183C2×#117C22×C4311yescharacteristic
184C2×#117C22×C4311yescharacteristic
185C22×C42C22×C4311yescharacteristic
186C2×C4⋊C8C22×C4312yes—
187C2×C4⋊C8C22×C4312yes—
188C2×C22⋊C8C22×C4314yes—
189C2×#97C22×C4312yes—
190C2×C4×C8C22×C4312yes—
191C4×C4⋊C4C4×C4312yes—
192C4×C4⋊C4C4×C4312yes—
193C4×C22⋊C4C4×C4312yes—
194C4×C22⋊C4C4×C4312yes—
195#376C22×C4311yescharacteristic
196#376C22×C4311yescharacteristic
197C43C22×C4311yescharacteristic
198C43C22×C4311yescharacteristic
199#336C22×C4314yes—
200#336C22×C4314yes—
201#336C22×C4312yes—
202#336C22×C4312yes—
203#336C22×C4314yes—
204C43#2078111yescharacteristic, direct product factor, Sylow
205C23×C4C2×C4×C4312yes—
206C23×C4C23×C4311yescharacteristic
207C22×C8C23×C4314yes—
208C22×C8C23×C4314yes—
209#117—22no—
210#117—22no—
211#117—24no—
212C2×C4⋊C4C2×C4×C4311yescharacteristic
213C2×C4⋊C4C2×C4×C4311yescharacteristic
214C2×C4⋊C4C2×C4×C4312yes—
215C2×C22⋊C4C2×C4×C4311yescharacteristic
216C2×C22⋊C4C2×C4×C4311yescharacteristic
217C2×C22⋊C4C2×C4×C4312yes—
218C2×C42—24no—
219C2×C42C2×C4×C4312yes—
220C2×C42C2×C4×C4312yes—
221C2×C42C2×C4×C4312yes—
222C2×C42C2×C4×C4312yes—
223C2×C42C2×C4×C4312yes—
224C2×C42C23×C4311yescharacteristic
225C2×C42C23×C4311yescharacteristic
226C2×C42C23×C4311yescharacteristic
227C2×C42C23×C4311yescharacteristic
228C2×C42C23×C4311yescharacteristic
229C2×C42C23×C4311yescharacteristic
230C4⋊C8—24no—
231C4⋊C8—24no—
232C22⋊C8—28no—
233#97—24no—
234C4×C8—24no—
235#95C2×C4×C4312yes—
236#95C2×C4×C4312yes—
237#95C2×C4×C4312yes—
238#95C2×C4×C4312yes—
239C24C22×C4×C4311yescharacteristic
240C22×C4—22no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—24no—
244C22×C4—24no—
245C22×C4—42no—
246C22×C4C22×C4×C4312yes—
247C22×C4C22×C4×C4311yescharacteristic
248C22×C4C22×C4×C4312yes—
249C22×C4C22×C4×C4311yescharacteristic
250C22×C4C22×C4×C4311yescharacteristic
251C22×C4C22×C4×C4312yes—
252C22×C4C22×C4×C4311yescharacteristic
253C22×C4C22×C4×C4311yescharacteristic
254C22×C4C22×C4×C4312yes—
255C22×C4#41×C4314yes—
256C22×C4C24×C4311yescharacteristic
257C2×C8—24no—
258C2×C8—24no—
259C2×C8—24no—
260C2×C8—24no—
261C2×C8—24no—
262C2×C8—24no—
263C4⋊C4—22no—
264C4⋊C4—22no—
265C4⋊C4—24no—
266C22⋊C4—22no—
267C22⋊C4—22no—
268C22⋊C4—24no—
269C42—24no—
270C42—24no—
271C42—24no—
272C42—22no—
273C42—22no—
274C42—22no—
275C42—21no—
276C42—21no—
277C42—42no—
278C42—42no—
279C42#41×C4312yes—
280C42#41×C4312yes—
281C42#41×C4314yes—
282C23—21no—
283C23—21no—
284C23—22no—
285C23—22no—
286C23#117×C4312yes—
287C23C23×C4×C4311yescharacteristic
288C2×C4—22no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—24no—
297C2×C4—24no—
298C2×C4—22no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—48no—
309C2×C4#117×C4312yes—
310C2×C4#117×C4312yes—
311C2×C4#117×C4312yes—
312C2×C4#117×C4314yes—
313C2×C4#131×C4314yes—
314C2×C4C2×#41×C4312yes—
315C2×C4C2×#41×C4312yes—
316C2×C4C2×#41×C4311yescharacteristic
317C2×C4C2×#41×C4311yescharacteristic
318C8—44no—
319C8—44no—
320C22—24no—
321C22—22no—
322C22—41no—
323C22—41no—
324C22—42no—
325C22C2×#117×C4311yescharacteristic
326C22C2×#117×C4311yescharacteristic
327C22C2×#117×C4311yescharacteristic
328C22C2×#131×C4312yes—
329C22C43×#56812yes—
330C4—22no—
331C4—22no—
332C4—24no—
333C4—24no—
334C4—22no—
335C4—41no—
336C4—41no—
337C4—42no—
338C4—42no—
339C4C43×#52912yes—
340C4C43×#52912yes—
341C2—42no—
342C2C43×#228311yescharacteristic
343C2C43×#292211yescharacteristic
344C2C43×#292311yescharacteristic
345C2C43×#292412yes—
346C2C43×#292512yes—
subgroupG/H
centerC22×C4×C43C24
commutatorC23C23×C4×C43
Frattini, cosocleC22×C4C24×C43
socleC23×C43C23×C4
prime radicalC24×C43C22×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#1839C2semidirect
3. C43×#1832C2semidirect
6. C43×#1767C2semidirect
7. C4×C4⋊C8×C43C2semidirect
9. C43×#1746C2semidirect
146. #20781C43direct (N × H)
169. #1839C2×C43semidirect
170. #1832C2×C43semidirect
173. #1767C2×C43semidirect
174. C4×C4⋊C8C2×C43semidirect
176. #1746C2×C43semidirect
204. C43#20781direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#117×C432
C43×#18392
C43×#18322
C43×#18172
C43×#17982
C43×#17672
C4×C4⋊C8×C432
C43×#17502
C43×#17462
#2078143