Finite Group Databasebeta

← C43×#13779 #24933796

Subgroups — C43×#13779 #24933796

Order 11008.

1582 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#384C211yesmaximal, characteristic
2C2×C43×#382C211yesmaximal, characteristic
3C2×C4×C4⋊C4×C43C212yesmaximal
4C2×C43×#376C211yesmaximal, characteristic
5C43×#1436C218yesmaximal
6C43×C4⋊#95C212yesmaximal
7C22×C4⋊C4×C43C2212yes—
8C22×C4⋊C4×C43C2212yes—
9C22×C4⋊C4×C43C2214yes—
10C22×C42×C43C2211yescharacteristic
11C22×C42×C43C2214yes—
12C22×C42×C43C2211yescharacteristic
13C22×C42×C43C2211yescharacteristic
14C43×#384C418yescomplemented
15C43×#382C418yescomplemented
16C4×C4⋊C4×C43—28no—
17C43×#376C418yescomplemented
18C2×#95×C43C2214yes—
19C2×#95×C43C2218yes—
20C2×#95×C43C2214yes—
21C2×#95×C43C2214yes—
22C23×C4×C43C2314yes—
23C23×C4×C43C2314yes—
24C23×C4×C43C2312yes—
25C23×C4×C43C2312yes—
26C23×C4×C43C2312yes—
27C23×C4×C43C2311yescharacteristic
28C2×C4⋊C4×C43—24no—
29C2×C4⋊C4×C43—24no—
30C2×C4⋊C4×C43—24no—
31C2×C4⋊C4×C43—24no—
32C2×C4⋊C4×C43—48no—
33C2×C4⋊C4×C43C2×C418yes—
34C2×C4⋊C4×C43C2×C418yes—
35C2×C4⋊C4×C43C2×C4116yes—
36C2×C42×C43—22no—
37C2×C42×C43—22no—
38C2×C42×C43—28no—
39C2×C42×C43—48no—
40C2×C42×C43C2×C414yes—
41C2×C42×C43C2×C414yes—
42C2×C42×C43C2×C414yes—
43C2×C42×C43C2×C414yes—
44C2×C42×C43C2×C414yes—
45C2×C42×C43D414yes—
46C2×C42×C43Q814yes—
47#95×C43—28no—
48#95×C43—48no—
49#95×C43C2×C4116yes—
50#95×C43C2×C4116yes—
51C24×C43C2411yescharacteristic
52C22×C4×C43—24no—
53C22×C4×C43—24no—
54C22×C4×C43—22no—
55C22×C4×C43—22no—
56C22×C4×C43—24no—
57C22×C4×C43—24no—
58C22×C4×C43—24no—
59C22×C4×C43—24no—
60C22×C4×C43—24no—
61C22×C4×C43—28no—
62C22×C4×C43—28no—
63C22×C4×C43—28no—
64C22×C4×C43—24no—
65C22×C4×C43—24no—
66C22×C4×C43—28no—
67C22×C4×C43—24no—
68C22×C4×C43C22×C414yes—
69C22×C4×C43C22×C418yes—
70C22×C4×C43C22×C418yes—
71C22×C4×C43C22×C414yes—
72C22×C4×C43C22×C414yes—
73C22×C4×C43C22×C414yes—
74C22×C4×C43C22×C414yes—
75C22×C4×C43C22×C412yes—
76C22×C4×C43C22×C412yes—
77C22×C4×C43C22×C412yes—
78C22×C4×C43C2×D414yes—
79C22×C4×C43C2×D412yes—
80C22×C4×C43C2×Q814yes—
81C22×C4×C43C2×Q812yes—
82C22×C4×C43#4112yes—
83C22×C4×C43#4112yes—
84C4⋊C4×C43—216no—
85C4⋊C4×C43—216no—
86C4⋊C4×C43—416no—
87C42×C43—28no—
88C42×C43—416no—
89C42×C43C42116yescomplemented
90C42×C43C4⋊C4116yescomplemented
91C23×C43C23×C411yescharacteristic
92C23×C43C23×C411yescharacteristic
93C23×C43C23×C411yescharacteristic
94C23×C43C22×D411yescharacteristic
95C23×C43C22×Q811yescharacteristic
96C23×C43C2×#4111yescharacteristic
97C23×C43C2×#4111yescharacteristic
98C23×C43H(5,𝔽2)14yes—
99C23×C432−1+414yes—
100C2×C4×C43—24no—
101C2×C4×C43—24no—
102C2×C4×C43—28no—
103C2×C4×C43—28no—
104C2×C4×C43—28no—
105C2×C4×C43—24no—
106C2×C4×C43—24no—
107C2×C4×C43—28no—
108C2×C4×C43—24no—
109C2×C4×C43—28no—
110C2×C4×C43—28no—
111C2×C4×C43—216no—
112C2×C4×C43—28no—
113C2×C4×C43—216no—
114C2×C4×C43—44no—
115C2×C4×C43—44no—
116C2×C4×C43—44no—
117C2×C4×C43—44no—
118C2×C4×C43—42no—
119C2×C4×C43—48no—
120C2×C4×C43—42no—
121C2×C4×C43—44no—
122C2×C4×C43—48no—
123C2×C4×C43C2×C4218yes—
124C2×C4×C43C2×C4214yes—
125C2×C4×C43C2×C4⋊C418yes—
126C2×C4×C43C2×C4⋊C414yes—
127C2×C4×C43#11714yes—
128C2×C4×C43C4×D414yes—
129C2×C4×C43C4×D414yes—
130C2×C4×C43C4×Q814yes—
131C2×C4×C43C4×Q814yes—
132#13779C4311yesmaximal, characteristic, direct product factor, Sylow
133C22×C43C22×C4211yescharacteristic
134C22×C43C22×C4⋊C411yescharacteristic
135C22×C43C2×#11711yescharacteristic
136C22×C43C2×C4×D411yescharacteristic
137C22×C43C2×C4×D411yescharacteristic
138C22×C43C2×C4×Q811yescharacteristic
139C22×C43C2×C4×Q811yescharacteristic
140C22×C43#51812yes—
141C22×C43#51912yes—
142C22×C43#52014yes—
143C22×C43#52014yes—
144C22×C43#53512yes—
145C22×C43#53612yes—
146C22×C43#54012yes—
147C22×C43#54112yes—
148C22×C43#54214yes—
149C22×C43#54414yes—
150C4×C43—28no—
151C4×C43—28no—
152C4×C43—44no—
153C4×C43—48no—
154C4×C43—48no—
155C4×C43C4×C4⋊C418yes—
156C2×#384C2×C4311yescharacteristic
157C2×#382C2×C4311yescharacteristic
158C2×C4×C4⋊C4C2×C4312yes—
159C2×#376C2×C4311yescharacteristic
160#1436C2×C4318yes—
161C4⋊#95C2×C4312yes—
162C2×C43C2×C4×C4⋊C411yescharacteristic
163C2×C43#227412yes—
164C2×C43#231412yes—
165C2×C43#231712yes—
166C2×C43#232612yes—
167C2×C43#232711yescharacteristic
168C2×C43#232811yescharacteristic
169C2×C43#233012yes—
170C2×C43#233112yes—
171C22×C4⋊C4C22×C4312yes—
172C22×C4⋊C4C22×C4312yes—
173C22×C4⋊C4C22×C4314yes—
174C22×C42C22×C4311yescharacteristic
175C22×C42C22×C4314yes—
176C22×C42C22×C4311yescharacteristic
177C22×C42C22×C4311yescharacteristic
178#384C4×C4318yescomplemented
179#382C4×C4318yescomplemented
180C4×C4⋊C4—28no—
181#376C4×C4318yescomplemented
182C2×#95C22×C4314yes—
183C2×#95C22×C4318yes—
184C2×#95C22×C4314yes—
185C2×#95C22×C4314yes—
186C43#1377911yescharacteristic, direct product factor, Sylow
187C23×C4C23×C4314yes—
188C23×C4C23×C4314yes—
189C23×C4C23×C4312yes—
190C23×C4C23×C4312yes—
191C23×C4C23×C4312yes—
192C23×C4C23×C4311yescharacteristic
193C2×C4⋊C4—24no—
194C2×C4⋊C4—24no—
195C2×C4⋊C4—24no—
196C2×C4⋊C4—24no—
197C2×C4⋊C4—48no—
198C2×C4⋊C4C2×C4×C4318yes—
199C2×C4⋊C4C2×C4×C4318yes—
200C2×C4⋊C4C2×C4×C43116yes—
201C2×C42—22no—
202C2×C42—22no—
203C2×C42—28no—
204C2×C42—48no—
205C2×C42C2×C4×C4314yes—
206C2×C42C2×C4×C4314yes—
207C2×C42C2×C4×C4314yes—
208C2×C42C2×C4×C4314yes—
209C2×C42C2×C4×C4314yes—
210C2×C42D4×C4314yes—
211C2×C42Q8×C4314yes—
212#95—28no—
213#95—48no—
214#95C2×C4×C43116yes—
215#95C2×C4×C43116yes—
216C24C24×C4311yescharacteristic
217C22×C4—24no—
218C22×C4—24no—
219C22×C4—24no—
220C22×C4—24no—
221C22×C4—24no—
222C22×C4—24no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—24no—
226C22×C4—24no—
227C22×C4—24no—
228C22×C4—28no—
229C22×C4—28no—
230C22×C4—28no—
231C22×C4—28no—
232C22×C4—24no—
233C22×C4C22×C4×C4314yes—
234C22×C4C22×C4×C4318yes—
235C22×C4C22×C4×C4318yes—
236C22×C4C22×C4×C4314yes—
237C22×C4C22×C4×C4314yes—
238C22×C4C22×C4×C4314yes—
239C22×C4C22×C4×C4314yes—
240C22×C4C22×C4×C4312yes—
241C22×C4C22×C4×C4312yes—
242C22×C4C22×C4×C4312yes—
243C22×C4C2×D4×C4314yes—
244C22×C4C2×D4×C4312yes—
245C22×C4C2×Q8×C4314yes—
246C22×C4C2×Q8×C4312yes—
247C22×C4#41×C4312yes—
248C22×C4#41×C4312yes—
249C4⋊C4—216no—
250C4⋊C4—216no—
251C4⋊C4—416no—
252C42—28no—
253C42—416no—
254C42C42×C43116yescomplemented
255C42C4⋊C4×C43116yescomplemented
256C23C23×C4×C4311yescharacteristic
257C23C23×C4×C4311yescharacteristic
258C23C23×C4×C4311yescharacteristic
259C23C22×D4×C4311yescharacteristic
260C23C22×Q8×C4311yescharacteristic
261C23C2×#41×C4311yescharacteristic
262C23C2×#41×C4311yescharacteristic
263C23H(5,𝔽2)×C4314yes—
264C232−1+4×C4314yes—
265C2×C4—24no—
266C2×C4—24no—
267C2×C4—28no—
268C2×C4—28no—
269C2×C4—28no—
270C2×C4—24no—
271C2×C4—24no—
272C2×C4—28no—
273C2×C4—24no—
274C2×C4—28no—
275C2×C4—28no—
276C2×C4—216no—
277C2×C4—216no—
278C2×C4—28no—
279C2×C4—44no—
280C2×C4—44no—
281C2×C4—44no—
282C2×C4—44no—
283C2×C4—48no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—48no—
287C2×C4—44no—
288C2×C4C2×C42×C4318yes—
289C2×C4C2×C42×C4314yes—
290C2×C4C2×C4⋊C4×C4318yes—
291C2×C4C2×C4⋊C4×C4314yes—
292C2×C4#117×C4314yes—
293C2×C4C4×D4×C4314yes—
294C2×C4C4×D4×C4314yes—
295C2×C4C4×Q8×C4314yes—
296C2×C4C4×Q8×C4314yes—
297C22C22×C42×C4311yescharacteristic
298C22C22×C4⋊C4×C4311yescharacteristic
299C22C2×#117×C4311yescharacteristic
300C22C2×C4×D4×C4311yescharacteristic
301C22C2×C4×D4×C4311yescharacteristic
302C22C2×C4×Q8×C4311yescharacteristic
303C22C2×C4×Q8×C4311yescharacteristic
304C22C43×#51812yes—
305C22C43×#51912yes—
306C22C43×#52014yes—
307C22C43×#52014yes—
308C22C43×#53512yes—
309C22C43×#53612yes—
310C22C43×#54012yes—
311C22C43×#54112yes—
312C22C43×#54214yes—
313C22C43×#54414yes—
314C4—28no—
315C4—28no—
316C4—48no—
317C4—48no—
318C4—44no—
319C4C4×C4⋊C4×C4318yes—
320C2C2×C4×C4⋊C4×C4311yescharacteristic
321C2C43×#227412yes—
322C2C43×#231412yes—
323C2C43×#231712yes—
324C2C43×#232612yes—
325C2C43×#232711yescharacteristic
326C2C43×#232811yescharacteristic
327C2C43×#233012yes—
328C2C43×#233112yes—
subgroupG/H
center, socle, prime radicalC24×C43C24
commutatorC22C22×C42×C43
Frattini, cosocleC24C24×C43
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C43 ◁ G

Complements

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

NH ≅ G/Ntype
14. C43×#384C4semidirect
15. C43×#382C4semidirect
17. C43×#376C4semidirect
89. C42×C43C42semidirect
90. C42×C43C4⋊C4semidirect
132. #13779C43direct (N × H)
178. #384C4×C43semidirect
179. #382C4×C43semidirect
181. #376C4×C43semidirect
186. C43#13779direct (N × H)
254. C42C42×C43semidirect
255. C42C4⋊C4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#3842
C2×C43×#3822
C2×C4×C4⋊C4×C432
C2×C43×#3762
C43×#14362
C43×C4⋊#952
#1377943