Finite Group Databasebeta

← C2×C43×#2853 #24956635

Subgroups — C2×C43×#2853 #24956635

Order 11008.

3354 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C43C211yesmaximal, characteristic
2C23×C42×C43C211yesmaximal, characteristic, complemented
3C43×#2853C2116yesmaximal, direct product factor
4C2×C43×#388C214yesmaximal, complemented
5C2×C43×#387C214yesmaximal, complemented
6C2×C43×#386C212yesmaximal
7C2×C43×#385C212yesmaximal, complemented
8C2×C43×#381C211yesmaximal, characteristic, complemented
9C23×D4×C43C2211yescharacteristic
10C24×C4×C43C2212yes—
11C24×C4×C43C2211yescharacteristic
12C2×#123×C43—28no—
13C2×#123×C43C2218yes—
14C22×C4⋊C4×C43C2212yes—
15C22×C4⋊C4×C43C2214yes—
16C22×C22⋊C4×C43C2211yescharacteristic
17C22×C22⋊C4×C43C2212yes—
18C22×C22⋊C4×C43C2212yes—
19C22×C22⋊C4×C43C2214yes—
20C22×C42×C43—28no—
21C22×C42×C43C2214yes—
22C22×C42×C43C2218yescomplemented
23C43×#388C22132yescomplemented
24C43×#387C22132yescomplemented
25C43×#386C22116yes—
26C43×#385C22116yescomplemented
27C43×#381C2218yescomplemented
28C2×#95×C43C2214yes—
29C2×#95×C43C2214yes—
30C2×#95×C43C2214yes—
31C25×C43C2311yescharacteristic
32C25×C43C2311yescharacteristic
33C22×D4×C43—24no—
34C22×D4×C43—28no—
35C22×D4×C43C2314yes—
36C23×C4×C43—28no—
37C23×C4×C43—28no—
38C23×C4×C43—216no—
39C23×C4×C43D418yes—
40C23×C4×C43C2318yes—
41C23×C4×C43C2312yes—
42C23×C4×C43C2314yes—
43C23×C4×C43C2311yescharacteristic
44C23×C4×C43C2314yes—
45C23×C4×C43C2312yes—
46C23×C4×C43C2314yes—
47#123×C43—232no—
48C2×C4⋊C4×C43—28no—
49C2×C4⋊C4×C43—216no—
50C2×C4⋊C4×C43C2318yes—
51C2×C4⋊C4×C43C23116yes—
52C2×C22⋊C4×C43—24no—
53C2×C22⋊C4×C43—28no—
54C2×C22⋊C4×C43—28no—
55C2×C22⋊C4×C43—216no—
56C2×C22⋊C4×C43C2314yes—
57C2×C22⋊C4×C43C2318yes—
58C2×C22⋊C4×C43C2318yes—
59C2×C22⋊C4×C43C23116yes—
60C2×C42×C43—216no—
61C2×C42×C43—232no—
62C2×C42×C43C23116yes—
63#95×C43C23116yes—
64#95×C43C23116yes—
65#95×C43C23116yes—
66C24×C43—28no—
67C24×C43—22no—
68C24×C43—28no—
69C24×C43—24no—
70C24×C43C2×D414yes—
71C24×C43#4118yes—
72C24×C43C2412yes—
73C24×C43C2412yes—
74C24×C43C2411yescharacteristic
75C2×D4×C43—28no—
76C2×D4×C43—216no—
77C2×D4×C43—416no—
78C22×C4×C43—264no—
79C22×C4×C43—232no—
80C22×C4×C43—232no—
81C22×C4×C43—216no—
82C22×C4×C43—28no—
83C22×C4×C43—24no—
84C22×C4×C43—22no—
85C22×C4×C43—216no—
86C22×C4×C43—28no—
87C22×C4×C43—28no—
88C22×C4×C43—28no—
89C22×C4×C43—28no—
90C22×C4×C43—28no—
91C22×C4×C43—28no—
92C22×C4×C43—24no—
93C22×C4×C43C2×D418yes—
94C22×C4×C43C2×D4116yes—
95C22×C4×C43#41116yes—
96C22×C4×C43C2418yes—
97C22×C4×C43C2412yes—
98C22×C4×C43C2414yes—
99C22×C4×C43C2414yes—
100C22×C4×C43C2418yes—
101C4⋊C4×C43—216no—
102C4⋊C4×C43—232no—
103C22⋊C4×C43—216no—
104C22⋊C4×C43—232no—
105C22⋊C4×C43—28no—
106C22⋊C4×C43—216no—
107C42×C43—232no—
108C23×C43—216no—
109C23×C43—232no—
110C23×C43—28no—
111C23×C43—22no—
112C23×C43—28no—
113C23×C43—24no—
114C23×C43—44no—
115C23×C43—48no—
116C23×C43—416no—
117C23×C43#123116yes—
118C23×C43C22×D414yes—
119C23×C43C22×D412yes—
120C23×C43C2×#4118yes—
121C23×C43C2×#4114yes—
122C23×C43C2×#4118yes—
123C23×C43C2511yescharacteristic
124D4×C43—416no—
125C2×C4×C43—264no—
126C2×C4×C43—232no—
127C2×C4×C43—216no—
128C2×C4×C43—232no—
129C2×C4×C43—28no—
130C2×C4×C43—28no—
131C2×C4×C43—28no—
132C2×C4×C43—24no—
133C2×C4×C43—22no—
134C2×C4×C43—28no—
135C2×C4×C43—28no—
136C2×C4×C43—28no—
137C2×C4×C43—28no—
138C2×C4×C43—24no—
139C2×C4×C43—44no—
140C2×C4×C43—48no—
141C2×C4×C43—416no—
142C2×C4×C43C22×D418yes—
143C2×C4×C43C2×#41116yes—
144C2×#2853C4311yesmaximal, characteristic, direct product factor, Sylow
145C22×C43—232no—
146C22×C43—28no—
147C22×C43—216no—
148C22×C43—42no—
149C22×C43—44no—
150C22×C43—48no—
151C22×C43—88no—
152C22×C43C2×#12318yes—
153C22×C43C2×#12314yes—
154C22×C43#52518yes—
155C22×C43#529116yes—
156C22×C43C23×D411yescharacteristic
157C22×C43C22×#4112yes—
158C22×C43C22×#4114yes—
159C4×C43—28no—
160C4×C43—216no—
161C4×C43—42no—
162C4×C43—44no—
163C4×C43—48no—
164C22×#123C2×C4311yescharacteristic
165C23×C42C2×C4311yescharacteristic, complemented
166#2853C2×C43116yesdirect product factor
167C2×#388C2×C4314yescomplemented
168C2×#387C2×C4314yescomplemented
169C2×#386C2×C4312yes—
170C2×#385C2×C4312yescomplemented
171C2×#381C2×C4311yescharacteristic, complemented
172C2×C43—28no—
173C2×C43—82no—
174C2×C43#285318yesdirect product factor
175C2×C43C22×#12311yescharacteristic
176C2×C43C2×#52512yes—
177C2×C43C2×#52914yes—
178C23×D4C22×C4311yescharacteristic
179C24×C4C22×C4312yes—
180C24×C4C22×C4311yescharacteristic
181C2×#123—28no—
182C2×#123C22×C4318yes—
183C22×C4⋊C4C22×C4312yes—
184C22×C4⋊C4C22×C4314yes—
185C22×C22⋊C4C22×C4311yescharacteristic
186C22×C22⋊C4C22×C4312yes—
187C22×C22⋊C4C22×C4312yes—
188C22×C22⋊C4C22×C4314yes—
189C22×C42—28no—
190C22×C42C22×C4314yes—
191C22×C42C22×C4318yescomplemented
192#388C22×C43132yescomplemented
193#387C22×C43132yescomplemented
194#386C22×C43116yes—
195#385C22×C43116yescomplemented
196#381C22×C4318yescomplemented
197C2×#95C22×C4314yes—
198C2×#95C22×C4314yes—
199C2×#95C22×C4314yes—
200C43C2×#285311yescharacteristic, direct product factor, Sylow
201C25C23×C4311yescharacteristic
202C25C23×C4311yescharacteristic
203C22×D4—24no—
204C22×D4—28no—
205C22×D4C23×C4314yes—
206C23×C4—28no—
207C23×C4—28no—
208C23×C4—216no—
209C23×C4D4×C4318yes—
210C23×C4C23×C4312yes—
211C23×C4C23×C4314yes—
212C23×C4C23×C4311yescharacteristic
213C23×C4C23×C4318yes—
214C23×C4C23×C4312yes—
215C23×C4C23×C4314yes—
216C23×C4C23×C4314yes—
217#123—232no—
218C2×C4⋊C4—28no—
219C2×C4⋊C4—216no—
220C2×C4⋊C4C23×C4318yes—
221C2×C4⋊C4C23×C43116yes—
222C2×C22⋊C4—24no—
223C2×C22⋊C4—28no—
224C2×C22⋊C4—28no—
225C2×C22⋊C4—216no—
226C2×C22⋊C4C23×C4314yes—
227C2×C22⋊C4C23×C4318yes—
228C2×C22⋊C4C23×C4318yes—
229C2×C22⋊C4C23×C43116yes—
230C2×C42—216no—
231C2×C42—232no—
232C2×C42C23×C43116yes—
233#95C23×C43116yes—
234#95C23×C43116yes—
235#95C23×C43116yes—
236C24—28no—
237C24—22no—
238C24—28no—
239C24—24no—
240C24C2×D4×C4314yes—
241C24#41×C4318yes—
242C24C24×C4312yes—
243C24C24×C4312yes—
244C24C24×C4311yescharacteristic
245C2×D4—28no—
246C2×D4—216no—
247C2×D4—416no—
248C22×C4—264no—
249C22×C4—232no—
250C22×C4—216no—
251C22×C4—28no—
252C22×C4—216no—
253C22×C4—28no—
254C22×C4—28no—
255C22×C4—232no—
256C22×C4—24no—
257C22×C4—22no—
258C22×C4—28no—
259C22×C4—28no—
260C22×C4—28no—
261C22×C4—28no—
262C22×C4—24no—
263C22×C4C2×D4×C4318yes—
264C22×C4C2×D4×C43116yes—
265C22×C4#41×C43116yes—
266C22×C4C24×C4318yes—
267C22×C4C24×C4312yes—
268C22×C4C24×C4314yes—
269C22×C4C24×C4314yes—
270C22×C4C24×C4318yes—
271C4⋊C4—216no—
272C4⋊C4—232no—
273C22⋊C4—28no—
274C22⋊C4—216no—
275C22⋊C4—216no—
276C22⋊C4—232no—
277C42—232no—
278C23—216no—
279C23—232no—
280C23—28no—
281C23—22no—
282C23—28no—
283C23—24no—
284C23—44no—
285C23—48no—
286C23—416no—
287C23#123×C43116yes—
288C23C22×D4×C4314yes—
289C23C22×D4×C4312yes—
290C23C2×#41×C4318yes—
291C23C2×#41×C4314yes—
292C23C2×#41×C4318yes—
293C23C25×C4311yescharacteristic
294D4—416no—
295C2×C4—264no—
296C2×C4—232no—
297C2×C4—216no—
298C2×C4—232no—
299C2×C4—28no—
300C2×C4—28no—
301C2×C4—28no—
302C2×C4—24no—
303C2×C4—22no—
304C2×C4—28no—
305C2×C4—28no—
306C2×C4—28no—
307C2×C4—28no—
308C2×C4—24no—
309C2×C4—44no—
310C2×C4—48no—
311C2×C4—416no—
312C2×C4C22×D4×C4318yes—
313C2×C4C2×#41×C43116yes—
314C22—232no—
315C22—28no—
316C22—216no—
317C22—42no—
318C22—44no—
319C22—48no—
320C22—88no—
321C22C2×#123×C4318yes—
322C22C2×#123×C4314yes—
323C22C43×#52518yes—
324C22C43×#529116yes—
325C22C23×D4×C4311yescharacteristic
326C22C22×#41×C4312yes—
327C22C22×#41×C4314yes—
328C4—28no—
329C4—216no—
330C4—42no—
331C4—44no—
332C4—48no—
333C2—28no—
334C2—82no—
335C2C43×#285318yesdirect product factor
336C2C22×#123×C4311yescharacteristic
337C2C2×C43×#52512yes—
338C2C2×C43×#52914yes—
subgroupG/H
center, socleC24×C43C24
commutator, Frattini, cosocleC23C25×C43
prime radicalC23×D4×C43C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C42×C43C2semidirect
3. C43×#2853C2direct (N × H)
4. C2×C43×#388C2semidirect
5. C2×C43×#387C2semidirect
7. C2×C43×#385C2semidirect
8. C2×C43×#381C2semidirect
22. C22×C42×C43C22semidirect
23. C43×#388C22semidirect
24. C43×#387C22semidirect
26. C43×#385C22semidirect
27. C43×#381C22semidirect
144. C2×#2853C43direct (N × H)
165. C23×C42C2×C43semidirect
166. #2853C2×C43direct (N × H)
167. C2×#388C2×C43semidirect
168. C2×#387C2×C43semidirect
170. C2×#385C2×C43semidirect
171. C2×#381C2×C43semidirect
174. C2×C43#2853direct (N × H)
191. C22×C42C22×C43semidirect
192. #388C22×C43semidirect
193. #387C22×C43semidirect
195. #385C22×C43semidirect
196. #381C22×C43semidirect
200. C43C2×#2853direct (N × H)
335. C2C43×#2853direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#123×C432
C23×C42×C432
C43×#28532
C2×C43×#3882
C2×C43×#3872
C2×C43×#3862
C2×C43×#3852
C2×C43×#3812
C2×#285343