Finite Group Databasebeta

← C43×#34179 #24954196

Subgroups — C43×#34179 #24954196

Order 11008.

2390 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#117×C43C211yesmaximal, characteristic
2C43×#2347C218yesmaximal, complemented
3C43×#2346C218yesmaximal, complemented
4C43×#2316C212yesmaximal, complemented
5C43×#2312C214yesmaximal
6C43×#2283C214yesmaximal, complemented
7C43×#2280C212yesmaximal
8C43×#2274C212yesmaximal, complemented
9C24×C4×C43C2211yescharacteristic
10C2×#117×C43C4116yescomplemented
11C2×#117×C43C2214yes—
12C2×#117×C43C2214yes—
13C2×#117×C43C2214yes—
14C22×C4⋊C4×C43C2211yescharacteristic
15C22×C4⋊C4×C43C2211yescharacteristic
16C22×C22⋊C4×C43C2212yes—
17C22×C42×C43C2212yes—
18C43×#389C22116yescomplemented
19C43×#388C22132yes—
20C43×#383C2218yescomplemented
21C43×#382C2218yescomplemented
22C43×#381C2214yes—
23C43×#380C2214yes—
24C43×#380C2214yes—
25C43×#380C2218yes—
26C43×#379C2214yes—
27C4×C4⋊C4×C43C22116yescomplemented
28C4×C4⋊C4×C43C2218yescomplemented
29C4×C22⋊C4×C43C2214yes—
30C4×C22⋊C4×C43C2214yes—
31C4×C22⋊C4×C43C2218yes—
32C43×#376C2218yescomplemented
33C25×C43C2311yescharacteristic
34C23×C4×C43—28no—
35C23×C4×C43C2×C418yes—
36C23×C4×C43C2311yescharacteristic
37C23×C4×C43C2312yes—
38C23×C4×C43C2312yes—
39C23×C4×C43C2312yes—
40C23×C4×C43C2312yes—
41C23×C4×C43C2311yescharacteristic
42#117×C43—216no—
43#117×C43C2×C4132yes—
44#117×C43C2×C4132yes—
45C2×C4⋊C4×C43C2×C418yes—
46C2×C4⋊C4×C43C2×C418yes—
47C2×C4⋊C4×C43C2318yes—
48C2×C4⋊C4×C43C23116yes—
49C2×C4⋊C4×C43C2314yes—
50C2×C4⋊C4×C43C2314yes—
51C2×C22⋊C4×C43C2×C4116yes—
52C2×C22⋊C4×C43C2318yes—
53C2×C22⋊C4×C43C2318yes—
54C2×C22⋊C4×C43C2318yes—
55C2×C22⋊C4×C43C2318yes—
56C2×C42×C43C2×C4116yes—
57C2×C42×C43C2318yes—
58C2×C42×C43C23116yes—
59C2×C42×C43C2314yes—
60C2×C42×C43C2314yes—
61#95×C43C2318yes—
62#95×C43C23116yes—
63#95×C43C2318yes—
64#95×C43C23116yes—
65C24×C43—24no—
66C24×C43—42no—
67C24×C43—42no—
68C24×C43C22×C414yes—
69C24×C43C2412yes—
70C24×C43C2411yescharacteristic
71C22×C4×C43—232no—
72C22×C4×C43—28no—
73C22×C4×C43—28no—
74C22×C4×C43—24no—
75C22×C4×C43—44no—
76C22×C4×C43—44no—
77C22×C4×C43C22×C414yes—
78C22×C4×C43C22×C418yes—
79C22×C4×C43C22×C418yes—
80C22×C4×C43C22×C418yes—
81C22×C4×C43C22×C418yes—
82C22×C4×C43C22×C414yes—
83C22×C4×C43#4118yes—
84C22×C4×C43C24116yes—
85C22×C4×C43C2411yescharacteristic
86C22×C4×C43C2411yescharacteristic
87C22×C4×C43C2414yes—
88C22×C4×C43C2414yes—
89C22×C4×C43C2412yes—
90C4⋊C4×C43—216no—
91C4⋊C4×C43—416no—
92C4⋊C4×C43C22×C4116yes—
93C4⋊C4×C43C22×C4116yes—
94C22⋊C4×C43—216no—
95C22⋊C4×C43—48no—
96C22⋊C4×C43—48no—
97C22⋊C4×C43C22×C4132yes—
98C42×C43—216no—
99C42×C43—416no—
100C42×C43C22×C4116yes—
101C42×C43C22×C4116yes—
102C23×C43—22no—
103C23×C43—22no—
104C23×C43—28no—
105C23×C43—24no—
106C23×C43—24no—
107C23×C43—24no—
108C23×C43—44no—
109C23×C43—44no—
110C23×C43—416no—
111C23×C43C23×C414yes—
112C23×C43C23×C412yes—
113C23×C43C2×#4114yes—
114C23×C43C2511yescharacteristic
115C2×C4×C43—28no—
116C2×C4×C43—22no—
117C2×C4×C43—22no—
118C2×C4×C43—28no—
119C2×C4×C43—28no—
120C2×C4×C43—216no—
121C2×C4×C43—216no—
122C2×C4×C43—216no—
123C2×C4×C43—216no—
124C2×C4×C43—216no—
125C2×C4×C43—48no—
126C2×C4×C43—48no—
127C2×C4×C43#117116yes—
128C2×C4×C43C23×C412yes—
129C2×C4×C43C23×C412yes—
130C2×C4×C43C23×C418yes—
131C2×C4×C43C23×C418yes—
132C2×C4×C43C23×C414yes—
133C2×C4×C43C2×#4118yes—
134#34179C4311yesmaximal, characteristic, direct product factor, Sylow
135C22×C43—22no—
136C22×C43—22no—
137C22×C43—28no—
138C22×C43—24no—
139C22×C43—24no—
140C22×C43—24no—
141C22×C43—416no—
142C22×C43—48no—
143C22×C43C2×#11714yes—
144C22×C43C24×C411yescharacteristic
145C22×C43C22×#4112yes—
146C22×C43#58512yes—
147C22×C43#58512yes—
148C4×C43—22no—
149C4×C43—22no—
150C4×C43—28no—
151C4×C43—28no—
152C4×C43—416no—
153C4×C43C2×#11718yes—
154C22×#117C2×C4311yescharacteristic
155#2347C2×C4318yescomplemented
156#2346C2×C4318yescomplemented
157#2316C2×C4312yescomplemented
158#2312C2×C4314yes—
159#2283C2×C4314yescomplemented
160#2280C2×C4312yes—
161#2274C2×C4312yescomplemented
162C2×C43—24no—
163C2×C43—44no—
164C2×C43C22×#11711yescharacteristic
165C2×C43#342811yescharacteristic
166C2×C43#342811yescharacteristic
167C2×C43#349314yes—
168C24×C4C22×C4311yescharacteristic
169C2×#117C4×C43116yescomplemented
170C2×#117C22×C4314yes—
171C2×#117C22×C4314yes—
172C2×#117C22×C4314yes—
173C22×C4⋊C4C22×C4311yescharacteristic
174C22×C4⋊C4C22×C4311yescharacteristic
175C22×C22⋊C4C22×C4312yes—
176C22×C42C22×C4312yes—
177#389C22×C43116yescomplemented
178#388C22×C43132yes—
179#383C22×C4318yescomplemented
180#382C22×C4318yescomplemented
181#381C22×C4314yes—
182#380C22×C4318yes—
183#380C22×C4314yes—
184#380C22×C4314yes—
185#379C22×C4314yes—
186C4×C4⋊C4C22×C43116yescomplemented
187C4×C4⋊C4C22×C4318yescomplemented
188C4×C22⋊C4C22×C4318yes—
189C4×C22⋊C4C22×C4314yes—
190C4×C22⋊C4C22×C4314yes—
191#376C22×C4318yescomplemented
192C43#3417911yescharacteristic, direct product factor, Sylow
193C25C23×C4311yescharacteristic
194C23×C4—28no—
195C23×C4C2×C4×C4318yes—
196C23×C4C23×C4312yes—
197C23×C4C23×C4312yes—
198C23×C4C23×C4311yescharacteristic
199C23×C4C23×C4312yes—
200C23×C4C23×C4312yes—
201C23×C4C23×C4311yescharacteristic
202#117—216no—
203#117C2×C4×C43132yes—
204#117C2×C4×C43132yes—
205C2×C4⋊C4C2×C4×C4318yes—
206C2×C4⋊C4C2×C4×C4318yes—
207C2×C4⋊C4C23×C4318yes—
208C2×C4⋊C4C23×C43116yes—
209C2×C4⋊C4C23×C4314yes—
210C2×C4⋊C4C23×C4314yes—
211C2×C22⋊C4C2×C4×C43116yes—
212C2×C22⋊C4C23×C4318yes—
213C2×C22⋊C4C23×C4318yes—
214C2×C22⋊C4C23×C4318yes—
215C2×C22⋊C4C23×C4318yes—
216C2×C42C2×C4×C43116yes—
217C2×C42C23×C4318yes—
218C2×C42C23×C43116yes—
219C2×C42C23×C4314yes—
220C2×C42C23×C4314yes—
221#95C23×C4318yes—
222#95C23×C43116yes—
223#95C23×C4318yes—
224#95C23×C43116yes—
225C24—24no—
226C24—42no—
227C24—42no—
228C24C22×C4×C4314yes—
229C24C24×C4312yes—
230C24C24×C4311yescharacteristic
231C22×C4—24no—
232C22×C4—232no—
233C22×C4—28no—
234C22×C4—28no—
235C22×C4—44no—
236C22×C4—44no—
237C22×C4C22×C4×C4314yes—
238C22×C4C22×C4×C4318yes—
239C22×C4C22×C4×C4318yes—
240C22×C4C22×C4×C4318yes—
241C22×C4C22×C4×C4318yes—
242C22×C4C22×C4×C4314yes—
243C22×C4#41×C4318yes—
244C22×C4C24×C43116yes—
245C22×C4C24×C4311yescharacteristic
246C22×C4C24×C4311yescharacteristic
247C22×C4C24×C4314yes—
248C22×C4C24×C4314yes—
249C22×C4C24×C4312yes—
250C4⋊C4—216no—
251C4⋊C4—416no—
252C4⋊C4C22×C4×C43116yes—
253C4⋊C4C22×C4×C43116yes—
254C22⋊C4—216no—
255C22⋊C4—48no—
256C22⋊C4—48no—
257C22⋊C4C22×C4×C43132yes—
258C42—216no—
259C42—416no—
260C42C22×C4×C43116yes—
261C42C22×C4×C43116yes—
262C23—22no—
263C23—22no—
264C23—28no—
265C23—24no—
266C23—24no—
267C23—24no—
268C23—44no—
269C23—44no—
270C23—416no—
271C23C23×C4×C4314yes—
272C23C23×C4×C4312yes—
273C23C2×#41×C4314yes—
274C23C25×C4311yescharacteristic
275C2×C4—28no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—28no—
279C2×C4—28no—
280C2×C4—216no—
281C2×C4—216no—
282C2×C4—216no—
283C2×C4—216no—
284C2×C4—216no—
285C2×C4—48no—
286C2×C4—48no—
287C2×C4#117×C43116yes—
288C2×C4C23×C4×C4312yes—
289C2×C4C23×C4×C4312yes—
290C2×C4C23×C4×C4318yes—
291C2×C4C23×C4×C4318yes—
292C2×C4C23×C4×C4314yes—
293C2×C4C2×#41×C4318yes—
294C22—22no—
295C22—22no—
296C22—28no—
297C22—24no—
298C22—24no—
299C22—24no—
300C22—416no—
301C22—48no—
302C22C2×#117×C4314yes—
303C22C24×C4×C4311yescharacteristic
304C22C22×#41×C4312yes—
305C22C43×#58512yes—
306C22C43×#58512yes—
307C4—22no—
308C4—22no—
309C4—28no—
310C4—28no—
311C4—416no—
312C4C2×#117×C4318yes—
313C2—24no—
314C2—44no—
315C2C22×#117×C4311yescharacteristic
316C2C43×#342811yescharacteristic
317C2C43×#342811yescharacteristic
318C2C43×#349314yes—
subgroupG/H
center, socleC23×C43C25
commutatorC22C24×C4×C43
Frattini, cosocleC23C25×C43
prime radicalC25×C43C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2347C2semidirect
3. C43×#2346C2semidirect
4. C43×#2316C2semidirect
6. C43×#2283C2semidirect
8. C43×#2274C2semidirect
10. C2×#117×C43C4semidirect
18. C43×#389C22semidirect
20. C43×#383C22semidirect
21. C43×#382C22semidirect
27. C4×C4⋊C4×C43C22semidirect
28. C4×C4⋊C4×C43C22semidirect
32. C43×#376C22semidirect
134. #34179C43direct (N × H)
155. #2347C2×C43semidirect
156. #2346C2×C43semidirect
157. #2316C2×C43semidirect
159. #2283C2×C43semidirect
161. #2274C2×C43semidirect
169. C2×#117C4×C43semidirect
177. #389C22×C43semidirect
179. #383C22×C43semidirect
180. #382C22×C43semidirect
186. C4×C4⋊C4C22×C43semidirect
187. C4×C4⋊C4C22×C43semidirect
191. #376C22×C43semidirect
192. C43#34179direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#117×C432
C43×#23472
C43×#23462
C43×#23162
C43×#23122
C43×#22832
C43×#22802
C43×#22742
#3417943