Finite Group Databasebeta

← C43×#34346 #24954363

Subgroups — C43×#34346 #24954363

Order 11008.

2442 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#532C211yesmaximal, characteristic
2C43×#2381C212yesmaximal, complemented
3C43×#2380C212yesmaximal, complemented
4C43×#2379C214yesmaximal, complemented
5C43×#2377C218yesmaximal, complemented
6C43×#2297C214yesmaximal, complemented
7C43×#2290C218yesmaximal, complemented
8C43×#2283C212yesmaximal, complemented
9C22×#41×C43C2212yes—
10C43×#532C4116yescomplemented
11C2×C4⋊Q8×C43C2211yescharacteristic
12C2×#127×C43C2211yescharacteristic
13C2×#124×C43C2212yes—
14C2×#121×C43C2214yes—
15C2×C4×D4×C43C2214yes—
16C2×#117×C43C2214yes—
17C22×C42×C43C2214yes—
18C22×C42×C43C2211yescharacteristic
19C43×#391C2218yes—
20C43×#390C2218yes—
21C43×#388C22116yes—
22C43×#387C22116yes—
23C43×#386C2218yes—
24C43×#386C22116yes—
25C43×#386C2218yes—
26C43×#385C22116yes—
27C43×#383C2214yes—
28C43×#382C2214yes—
29C43×#381C2214yes—
30C43×#380C2214yes—
31C4×C4⋊C4×C43C2214yes—
32C4×C22⋊C4×C43C2214yes—
33C4×C22⋊C4×C43C2218yes—
34C43×#376C2214yes—
35C2×#41×C43—44no—
36C2×#41×C43—44no—
37C2×#41×C43C2×C4116yescomplemented
38C22×Q8×C43C2312yes—
39C22×D4×C43C2314yes—
40C22×D4×C43C2314yes—
41C22×D4×C43C2312yes—
42C23×C4×C43C2314yes—
43C23×C4×C43C2311yescharacteristic
44C23×C4×C43C2318yes—
45C23×C4×C43C2312yes—
46C4⋊Q8×C43C2×C418yescomplemented
47#127×C43C2×C418yes—
48#124×C43C2×C4116yescomplemented
49#121×C43C2×C4132yescomplemented
50C4×D4×C43C2×C4132yescomplemented
51#117×C43—48no—
52C2×C4⋊C4×C43C2318yes—
53C2×C4⋊C4×C43C2318yes—
54C2×C4⋊C4×C43C2314yes—
55C2×C22⋊C4×C43C2318yes—
56C2×C22⋊C4×C43C2318yes—
57C2×C22⋊C4×C43C23116yes—
58C2×C22⋊C4×C43C2318yes—
59C2×C42×C43—48no—
60C2×C42×C43C2×C418yescomplemented
61C2×C42×C43C2318yes—
62C2×C42×C43C2318yes—
63C2×C42×C43C2311yescharacteristic
64C2×C42×C43C2311yescharacteristic
65C2×C42×C43C2312yes—
66#95×C43C2318yes—
67#95×C43C2318yes—
68#95×C43C2318yes—
69#95×C43C23116yes—
70#95×C43C2318yes—
71C24×C43C2414yes—
72C24×C43C2411yescharacteristic
73#41×C43—432no—
74C2×Q8×C43—42no—
75C2×Q8×C43—42no—
76C2×Q8×C43C22×C418yes—
77C2×D4×C43—48no—
78C2×D4×C43—42no—
79C2×D4×C43—44no—
80C2×D4×C43—42no—
81C2×D4×C43—44no—
82C2×D4×C43C22×C4116yes—
83C2×D4×C43C22×C4116yes—
84C2×D4×C43C22×C418yes—
85C22×C4×C43—28no—
86C22×C4×C43—28no—
87C22×C4×C43—24no—
88C22×C4×C43—48no—
89C22×C4×C43—44no—
90C22×C4×C43—416no—
91C22×C4×C43C22×C414yes—
92C22×C4×C43C22×C4116yes—
93C22×C4×C43C22×C418yes—
94C22×C4×C43C24116yes—
95C22×C4×C43C2412yes—
96C22×C4×C43C2411yescharacteristic
97C22×C4×C43C2412yes—
98C22×C4×C43C2414yes—
99C22×C4×C43C2411yescharacteristic
100C4⋊C4×C43—48no—
101C4⋊C4×C43—48no—
102C4⋊C4×C43C22×C4116yes—
103C22⋊C4×C43—48no—
104C22⋊C4×C43—416no—
105C22⋊C4×C43—48no—
106C22⋊C4×C43C22×C4132yes—
107C42×C43—216no—
108C42×C43—48no—
109C42×C43C22×C418yes—
110C42×C43C22×C414yes—
111C42×C43C22×C414yes—
112C23×C43—24no—
113C23×C43—24no—
114C23×C43—22no—
115C23×C43—24no—
116C23×C43—216no—
117C23×C43C23×C418yes—
118C23×C43C23×C412yes—
119C23×C43C2511yescharacteristic
120Q8×C43—48no—
121D4×C43—416no—
122D4×C43—48no—
123D4×C43—416no—
124C2×C4×C43—24no—
125C2×C4×C43—24no—
126C2×C4×C43—22no—
127C2×C4×C43—24no—
128C2×C4×C43—24no—
129C2×C4×C43—232no—
130C2×C4×C43—28no—
131C2×C4×C43—216no—
132C2×C4×C43—216no—
133C2×C4×C43—216no—
134C2×C4×C43—48no—
135C2×C4×C43—432no—
136C2×C4×C43C23×C414yes—
137C2×C4×C43C23×C414yes—
138C2×C4×C43C23×C412yes—
139C2×C4×C43C23×C418yes—
140C2×C4×C43C23×C412yes—
141C2×C4×C43H(5,𝔽2)14yes—
142#34346C4311yesmaximal, characteristic, direct product factor, Sylow
143C22×C43—28no—
144C22×C43—22no—
145C22×C43—24no—
146C22×C43—216no—
147C22×C43—48no—
148C22×C43—44no—
149C22×C43—48no—
150C22×C43C24×C411yescharacteristic
151C22×C43C2×H(5,𝔽2)12yes—
152C22×C43#58514yes—
153C4×C43—22no—
154C4×C43—28no—
155C4×C43—24no—
156C4×C43—24no—
157C4×C43—416no—
158C4×C43#51814yes—
159C2×#532C2×C4311yescharacteristic
160#2381C2×C4312yescomplemented
161#2380C2×C4312yescomplemented
162#2379C2×C4314yescomplemented
163#2377C2×C4318yescomplemented
164#2297C2×C4314yescomplemented
165#2290C2×C4318yescomplemented
166#2283C2×C4312yescomplemented
167C2×C43—48no—
168C2×C43—42no—
169C2×C43C2×#51811yescharacteristic
170C2×C43#342812yes—
171C2×C43#352914yes—
172C22×#41C22×C4312yes—
173#532C4×C43116yescomplemented
174C2×C4⋊Q8C22×C4311yescharacteristic
175C2×#127C22×C4311yescharacteristic
176C2×#124C22×C4312yes—
177C2×#121C22×C4314yes—
178C2×C4×D4C22×C4314yes—
179C2×#117C22×C4314yes—
180C22×C42C22×C4314yes—
181C22×C42C22×C4311yescharacteristic
182#391C22×C4318yes—
183#390C22×C4318yes—
184#388C22×C43116yes—
185#387C22×C43116yes—
186#386C22×C4318yes—
187#386C22×C43116yes—
188#386C22×C4318yes—
189#385C22×C43116yes—
190#383C22×C4314yes—
191#382C22×C4314yes—
192#381C22×C4314yes—
193#380C22×C4314yes—
194C4×C4⋊C4C22×C4314yes—
195C4×C22⋊C4C22×C4314yes—
196C4×C22⋊C4C22×C4318yes—
197#376C22×C4314yes—
198C43#3434611yescharacteristic, direct product factor, Sylow
199C2×#41—44no—
200C2×#41—44no—
201C2×#41C2×C4×C43116yescomplemented
202C22×Q8C23×C4312yes—
203C22×D4C23×C4314yes—
204C22×D4C23×C4314yes—
205C22×D4C23×C4312yes—
206C23×C4C23×C4314yes—
207C23×C4C23×C4311yescharacteristic
208C23×C4C23×C4318yes—
209C23×C4C23×C4312yes—
210C4⋊Q8C2×C4×C4318yescomplemented
211#127C2×C4×C4318yes—
212#124C2×C4×C43116yescomplemented
213#121C2×C4×C43132yescomplemented
214C4×D4C2×C4×C43132yescomplemented
215#117—48no—
216C2×C4⋊C4C23×C4318yes—
217C2×C4⋊C4C23×C4318yes—
218C2×C4⋊C4C23×C4314yes—
219C2×C22⋊C4C23×C4318yes—
220C2×C22⋊C4C23×C4318yes—
221C2×C22⋊C4C23×C43116yes—
222C2×C22⋊C4C23×C4318yes—
223C2×C42—48no—
224C2×C42C2×C4×C4318yescomplemented
225C2×C42C23×C4318yes—
226C2×C42C23×C4318yes—
227C2×C42C23×C4312yes—
228C2×C42C23×C4311yescharacteristic
229C2×C42C23×C4311yescharacteristic
230#95C23×C4318yes—
231#95C23×C4318yes—
232#95C23×C4318yes—
233#95C23×C43116yes—
234#95C23×C4318yes—
235C24C24×C4314yes—
236C24C24×C4311yescharacteristic
237#41—432no—
238C2×Q8—42no—
239C2×Q8—42no—
240C2×Q8C22×C4×C4318yes—
241C2×D4—44no—
242C2×D4—44no—
243C2×D4—42no—
244C2×D4—42no—
245C2×D4—48no—
246C2×D4C22×C4×C43116yes—
247C2×D4C22×C4×C43116yes—
248C2×D4C22×C4×C4318yes—
249C22×C4—28no—
250C22×C4—28no—
251C22×C4—24no—
252C22×C4—48no—
253C22×C4—44no—
254C22×C4—416no—
255C22×C4C22×C4×C4314yes—
256C22×C4C22×C4×C43116yes—
257C22×C4C22×C4×C4318yes—
258C22×C4C24×C43116yes—
259C22×C4C24×C4312yes—
260C22×C4C24×C4311yescharacteristic
261C22×C4C24×C4312yes—
262C22×C4C24×C4314yes—
263C22×C4C24×C4311yescharacteristic
264C4⋊C4—48no—
265C4⋊C4—48no—
266C4⋊C4C22×C4×C43116yes—
267C22⋊C4—48no—
268C22⋊C4—48no—
269C22⋊C4—416no—
270C22⋊C4C22×C4×C43132yes—
271C42—216no—
272C42—48no—
273C42C22×C4×C4318yes—
274C42C22×C4×C4314yes—
275C42C22×C4×C4314yes—
276C23—24no—
277C23—24no—
278C23—22no—
279C23—24no—
280C23—216no—
281C23C23×C4×C4318yes—
282C23C23×C4×C4312yes—
283C23C25×C4311yescharacteristic
284Q8—48no—
285D4—48no—
286D4—416no—
287D4—416no—
288C2×C4—24no—
289C2×C4—24no—
290C2×C4—22no—
291C2×C4—24no—
292C2×C4—24no—
293C2×C4—28no—
294C2×C4—232no—
295C2×C4—216no—
296C2×C4—216no—
297C2×C4—216no—
298C2×C4—48no—
299C2×C4—432no—
300C2×C4C23×C4×C4314yes—
301C2×C4C23×C4×C4314yes—
302C2×C4C23×C4×C4312yes—
303C2×C4C23×C4×C4318yes—
304C2×C4C23×C4×C4312yes—
305C2×C4H(5,𝔽2)×C4314yes—
306C22—22no—
307C22—28no—
308C22—24no—
309C22—216no—
310C22—48no—
311C22—48no—
312C22—44no—
313C22C24×C4×C4311yescharacteristic
314C22C2×H(5,𝔽2)×C4312yes—
315C22C43×#58514yes—
316C4—22no—
317C4—28no—
318C4—24no—
319C4—24no—
320C4—416no—
321C4C43×#51814yes—
322C2—42no—
323C2—48no—
324C2C2×C43×#51811yescharacteristic
325C2C43×#342812yes—
326C2C43×#352914yes—
subgroupG/H
centerC22×C4×C43C24
commutatorC22C24×C4×C43
Frattini, cosocleC23C25×C43
socleC23×C43C25
prime radicalC2×C43×#532C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2381C2semidirect
3. C43×#2380C2semidirect
4. C43×#2379C2semidirect
5. C43×#2377C2semidirect
6. C43×#2297C2semidirect
7. C43×#2290C2semidirect
8. C43×#2283C2semidirect
10. C43×#532C4semidirect
37. C2×#41×C43C2×C4semidirect
46. C4⋊Q8×C43C2×C4semidirect
48. #124×C43C2×C4semidirect
49. #121×C43C2×C4semidirect
50. C4×D4×C43C2×C4semidirect
60. C2×C42×C43C2×C4semidirect
142. #34346C43direct (N × H)
160. #2381C2×C43semidirect
161. #2380C2×C43semidirect
162. #2379C2×C43semidirect
163. #2377C2×C43semidirect
164. #2297C2×C43semidirect
165. #2290C2×C43semidirect
166. #2283C2×C43semidirect
173. #532C4×C43semidirect
198. C43#34346direct (N × H)
201. C2×#41C2×C4×C43semidirect
210. C4⋊Q8C2×C4×C43semidirect
212. #124C2×C4×C43semidirect
213. #121C2×C4×C43semidirect
214. C4×D4C2×C4×C43semidirect
224. C2×C42C2×C4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#5322
C43×#23812
C43×#23802
C43×#23792
C43×#23772
C43×#22972
C43×#22902
C43×#22832
#3434643