Finite Group Databasebeta

← C43×#13850 #24933867

Subgroups — C43×#13850 #24933867

Order 11008.

1790 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
1C22×C4×Q8×C43C211yesmaximal, characteristic
2C2×C4×C4⋊C4×C43C211yesmaximal, characteristic
3C2×C43×#376C211yesmaximal, characteristic
4C43×#1446C212yesmaximal
5C43×#1445C212yesmaximal
6C43×#1441C214yesmaximal
7C4×#95×C43C214yesmaximal
8C23×Q8×C43C2211yescharacteristic
9C2×C4×Q8×C43—24no—
10C2×C4×Q8×C43—24no—
11C2×C4×Q8×C43C418yescomplemented
12C22×C4⋊C4×C43C2212yes—
13C22×C4⋊C4×C43C2212yes—
14C22×C4⋊C4×C43C2211yescharacteristic
15C22×C42×C43C2212yes—
16C22×C42×C43C2212yes—
17C22×C42×C43C2212yes—
18C22×C42×C43C2211yescharacteristic
19C4×C4⋊C4×C43—24no—
20C43×#376—24no—
21C2×#95×C43C2218yes—
22C2×#95×C43C2218yes—
23C2×#95×C43C2212yes—
24C2×#95×C43C2212yes—
25C2×#95×C43C2212yes—
26C22×Q8×C43—22no—
27C22×Q8×C43—22no—
28C22×Q8×C43—28no—
29C22×Q8×C43C2×C414yes—
30C23×C4×C43C2312yes—
31C23×C4×C43C2314yes—
32C23×C4×C43C2314yes—
33C23×C4×C43C2311yescharacteristic
34C23×C4×C43C2311yescharacteristic
35C23×C4×C43C2312yes—
36C23×C4×C43C2311yescharacteristic
37C4×Q8×C43—232no—
38C2×C4⋊C4×C43—24no—
39C2×C4⋊C4×C43—24no—
40C2×C4⋊C4×C43—22no—
41C2×C4⋊C4×C43—22no—
42C2×C4⋊C4×C43—24no—
43C2×C4⋊C4×C43—28no—
44C2×C4⋊C4×C43C2×C414yes—
45C2×C4⋊C4×C43C2×C418yes—
46C2×C42×C43—24no—
47C2×C42×C43—24no—
48C2×C42×C43—24no—
49C2×C42×C43—24no—
50C2×C42×C43—24no—
51C2×C42×C43—28no—
52C2×C42×C43C2×C418yes—
53C2×C42×C43C2×C414yes—
54C2×C42×C43D414yes—
55C2×C42×C43D414yes—
56C2×C42×C43Q818yescomplemented
57#95×C43—24no—
58#95×C43—24no—
59#95×C43—24no—
60#95×C43—216no—
61#95×C43—216no—
62C24×C43C2411yescharacteristic
63C2×Q8×C43—216no—
64C2×Q8×C43—216no—
65C2×Q8×C43—28no—
66C2×Q8×C43—216no—
67C22×C4×C43—22no—
68C22×C4×C43—22no—
69C22×C4×C43—24no—
70C22×C4×C43—24no—
71C22×C4×C43—22no—
72C22×C4×C43—22no—
73C22×C4×C43—24no—
74C22×C4×C43—24no—
75C22×C4×C43—24no—
76C22×C4×C43—28no—
77C22×C4×C43—28no—
78C22×C4×C43—28no—
79C22×C4×C43—28no—
80C22×C4×C43—24no—
81C22×C4×C43—28no—
82C22×C4×C43—24no—
83C22×C4×C43C22×C414yes—
84C22×C4×C43C22×C412yes—
85C22×C4×C43C22×C412yes—
86C22×C4×C43C22×C414yes—
87C22×C4×C43C22×C412yes—
88C22×C4×C43C2×D412yes—
89C22×C4×C43C2×D412yes—
90C22×C4×C43C2×D412yes—
91C22×C4×C43C2×D412yes—
92C22×C4×C43C2×D412yes—
93C22×C4×C43C2×D412yes—
94C22×C4×C43C2×Q818yes—
95C22×C4×C43C2×Q814yes—
96C22×C4×C43#4118yes—
97C22×C4×C43#4118yes—
98C22×C4×C43#4114yes—
99C4⋊C4×C43—216no—
100C4⋊C4×C43—216no—
101C4⋊C4×C43—28no—
102C42×C43—216no—
103C42×C43—216no—
104C42×C43—48no—
105C42×C43C22⋊C4116yes—
106C23×C43C23×C411yescharacteristic
107C23×C43C22×D411yescharacteristic
108C23×C43C22×D411yescharacteristic
109C23×C43C22×Q812yes—
110C23×C43C2×#4114yes—
111C23×C43C2×#4112yes—
112C23×C43C2×#4114yes—
113Q8×C43—232no—
114C2×C4×C43—24no—
115C2×C4×C43—24no—
116C2×C4×C43—24no—
117C2×C4×C43—24no—
118C2×C4×C43—24no—
119C2×C4×C43—24no—
120C2×C4×C43—24no—
121C2×C4×C43—28no—
122C2×C4×C43—28no—
123C2×C4×C43—24no—
124C2×C4×C43—24no—
125C2×C4×C43—28no—
126C2×C4×C43—28no—
127C2×C4×C43—28no—
128C2×C4×C43—216no—
129C2×C4×C43—216no—
130C2×C4×C43—44no—
131C2×C4×C43—44no—
132C2×C4×C43—44no—
133C2×C4×C43—44no—
134C2×C4×C43—48no—
135C2×C4×C43—48no—
136C2×C4×C43—44no—
137C2×C4×C43—44no—
138C2×C4×C43C2×C22⋊C414yes—
139C2×C4×C43C2×C22⋊C414yes—
140C2×C4×C43C2×C22⋊C414yes—
141C2×C4×C43#11718yes—
142C2×C4×C43C4×Q818yes—
143C2×C4×C43C22⋊Q818yes—
144C2×C4×C43#12414yes—
145C2×C4×C43C4⋊Q814yes—
146#13850C4311yesmaximal, characteristic, direct product factor, Sylow
147C22×C43C22×C22⋊C411yescharacteristic
148C22×C43C2×#11712yes—
149C22×C43C2×C4×Q812yes—
150C22×C43C4×#4112yes—
151C22×C43C2×C22⋊Q812yes—
152C22×C43#52512yes—
153C22×C43#52512yes—
154C22×C43#52512yes—
155C22×C43C2×#12411yescharacteristic
156C22×C43#52918yes—
157C22×C43C2×C4⋊Q811yescharacteristic
158C22×C43#53212yes—
159C22×C43#53318yes—
160C4×C43—24no—
161C4×C43—28no—
162C4×C43—24no—
163C4×C43—48no—
164C4×C43—48no—
165C4×C43—44no—
166C4×C43#39118yes—
167C22×C4×Q8C2×C4311yescharacteristic
168C2×C4×C4⋊C4C2×C4311yescharacteristic
169C2×#376C2×C4311yescharacteristic
170#1446C2×C4312yes—
171#1445C2×C4312yes—
172#1441C2×C4314yes—
173C4×#95C2×C4314yes—
174C2×C43#228011yescharacteristic
175C2×C43C2×#39111yescharacteristic
176C2×C43#229514yes—
177C2×C43#229711yescharacteristic
178C2×C43#239614yes—
179C2×C43#239812yes—
180C2×C43#239912yes—
181C23×Q8C22×C4311yescharacteristic
182C2×C4×Q8—24no—
183C2×C4×Q8—24no—
184C2×C4×Q8C4×C4318yescomplemented
185C22×C4⋊C4C22×C4312yes—
186C22×C4⋊C4C22×C4312yes—
187C22×C4⋊C4C22×C4311yescharacteristic
188C22×C42C22×C4312yes—
189C22×C42C22×C4312yes—
190C22×C42C22×C4312yes—
191C22×C42C22×C4311yescharacteristic
192C4×C4⋊C4—24no—
193#376—24no—
194C2×#95C22×C4318yes—
195C2×#95C22×C4318yes—
196C2×#95C22×C4312yes—
197C2×#95C22×C4312yes—
198C2×#95C22×C4312yes—
199C43#1385011yescharacteristic, direct product factor, Sylow
200C22×Q8—22no—
201C22×Q8—22no—
202C22×Q8—28no—
203C22×Q8C2×C4×C4314yes—
204C23×C4C23×C4312yes—
205C23×C4C23×C4314yes—
206C23×C4C23×C4314yes—
207C23×C4C23×C4311yescharacteristic
208C23×C4C23×C4311yescharacteristic
209C23×C4C23×C4312yes—
210C23×C4C23×C4311yescharacteristic
211C4×Q8—232no—
212C2×C4⋊C4—24no—
213C2×C4⋊C4—24no—
214C2×C4⋊C4—22no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—24no—
217C2×C4⋊C4—28no—
218C2×C4⋊C4C2×C4×C4314yes—
219C2×C4⋊C4C2×C4×C4318yes—
220C2×C42—24no—
221C2×C42—24no—
222C2×C42—24no—
223C2×C42—24no—
224C2×C42—24no—
225C2×C42—28no—
226C2×C42C2×C4×C4318yes—
227C2×C42C2×C4×C4314yes—
228C2×C42D4×C4314yes—
229C2×C42D4×C4314yes—
230C2×C42Q8×C4318yescomplemented
231#95—24no—
232#95—24no—
233#95—24no—
234#95—216no—
235#95—216no—
236C24C24×C4311yescharacteristic
237C2×Q8—216no—
238C2×Q8—216no—
239C2×Q8—28no—
240C2×Q8—216no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—24no—
244C22×C4—24no—
245C22×C4—24no—
246C22×C4—24no—
247C22×C4—24no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—28no—
251C22×C4—28no—
252C22×C4—28no—
253C22×C4—28no—
254C22×C4—24no—
255C22×C4—28no—
256C22×C4—24no—
257C22×C4C22×C4×C4314yes—
258C22×C4C22×C4×C4312yes—
259C22×C4C22×C4×C4312yes—
260C22×C4C22×C4×C4314yes—
261C22×C4C22×C4×C4312yes—
262C22×C4C2×D4×C4312yes—
263C22×C4C2×D4×C4312yes—
264C22×C4C2×D4×C4312yes—
265C22×C4C2×D4×C4312yes—
266C22×C4C2×D4×C4312yes—
267C22×C4C2×D4×C4312yes—
268C22×C4C2×Q8×C4318yes—
269C22×C4C2×Q8×C4314yes—
270C22×C4#41×C4318yes—
271C22×C4#41×C4318yes—
272C22×C4#41×C4314yes—
273C4⋊C4—216no—
274C4⋊C4—216no—
275C4⋊C4—28no—
276C42—216no—
277C42—216no—
278C42—48no—
279C42C22⋊C4×C43116yes—
280C23C23×C4×C4311yescharacteristic
281C23C22×D4×C4311yescharacteristic
282C23C22×D4×C4311yescharacteristic
283C23C22×Q8×C4312yes—
284C23C2×#41×C4314yes—
285C23C2×#41×C4312yes—
286C23C2×#41×C4314yes—
287Q8—232no—
288C2×C4—24no—
289C2×C4—24no—
290C2×C4—24no—
291C2×C4—24no—
292C2×C4—24no—
293C2×C4—24no—
294C2×C4—24no—
295C2×C4—28no—
296C2×C4—28no—
297C2×C4—24no—
298C2×C4—24no—
299C2×C4—28no—
300C2×C4—28no—
301C2×C4—28no—
302C2×C4—216no—
303C2×C4—216no—
304C2×C4—44no—
305C2×C4—44no—
306C2×C4—44no—
307C2×C4—44no—
308C2×C4—48no—
309C2×C4—48no—
310C2×C4—44no—
311C2×C4—44no—
312C2×C4C2×C22⋊C4×C4314yes—
313C2×C4C2×C22⋊C4×C4314yes—
314C2×C4C2×C22⋊C4×C4314yes—
315C2×C4#117×C4318yes—
316C2×C4C4×Q8×C4318yes—
317C2×C4C22⋊Q8×C4318yes—
318C2×C4#124×C4314yes—
319C2×C4C4⋊Q8×C4314yes—
320C22C22×C22⋊C4×C4311yescharacteristic
321C22C2×#117×C4312yes—
322C22C2×C4×Q8×C4312yes—
323C22C4×#41×C4312yes—
324C22C2×C22⋊Q8×C4312yes—
325C22C43×#52512yes—
326C22C43×#52512yes—
327C22C43×#52512yes—
328C22C2×#124×C4311yescharacteristic
329C22C43×#52918yes—
330C22C2×C4⋊Q8×C4311yescharacteristic
331C22C43×#53212yes—
332C22C43×#53318yes—
333C4—24no—
334C4—28no—
335C4—24no—
336C4—48no—
337C4—48no—
338C4—44no—
339C4C43×#39118yes—
340C2C43×#228011yescharacteristic
341C2C2×C43×#39111yescharacteristic
342C2C43×#229514yes—
343C2C43×#229711yescharacteristic
344C2C43×#239614yes—
345C2C43×#239812yes—
346C2C43×#239912yes—
subgroupG/H
centerC23×C4×C43C23
commutatorC23C23×C4×C43
Frattini, cosocleC24C24×C43
socle, prime radicalC24×C43C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
11. C2×C4×Q8×C43C4semidirect
56. C2×C42×C43Q8semidirect
146. #13850C43direct (N × H)
184. C2×C4×Q8C4×C43semidirect
199. C43#13850direct (N × H)
230. C2×C42Q8×C43semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Q8×C432
C2×C4×C4⋊C4×C432
C2×C43×#3762
C43×#14462
C43×#14452
C43×#14412
C4×#95×C432
#1385043