Finite Group Databasebeta

← C2×C43×#2314 #24954064

Subgroups — C2×C43×#2314 #24954064

Order 11008.

2678 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#117×C43C211yesmaximal, characteristic
2C43×#2314C2116yesmaximal, direct product factor
3C2×C43×#388C214yesmaximal
4C2×C43×#387C214yesmaximal, complemented
5C2×C43×#384C211yesmaximal, characteristic, complemented
6C2×C43×#382C211yesmaximal, characteristic, complemented
7C2×C43×#380C212yesmaximal
8C2×C4×C4⋊C4×C43C212yesmaximal, complemented
9C24×C4×C43C2211yescharacteristic
10C2×#117×C43C4116yescomplemented
11C2×#117×C43C2218yes—
12C22×C4⋊C4×C43C2212yes—
13C22×C4⋊C4×C43C2212yes—
14C22×C4⋊C4×C43C2214yes—
15C22×C4⋊C4×C43C2212yes—
16C22×C22⋊C4×C43C2214yes—
17C22×C22⋊C4×C43C2212yes—
18C22×C42×C43C2214yes—
19C22×C42×C43C2211yescharacteristic
20C22×C42×C43C2211yescharacteristic
21C43×#388C22132yes—
22C43×#387C22132yescomplemented
23C43×#384C2218yescomplemented
24C43×#382C2218yescomplemented
25C43×#380C22116yes—
26C4×C4⋊C4×C43C22116yescomplemented
27C2×#95×C43C2214yes—
28C2×#95×C43C2214yes—
29C2×#95×C43C2214yes—
30C25×C43C2311yescharacteristic
31C23×C4×C43—24no—
32C23×C4×C43—24no—
33C23×C4×C43C2×C418yes—
34C23×C4×C43C2314yes—
35C23×C4×C43C2314yes—
36C23×C4×C43C2314yes—
37C23×C4×C43C2312yes—
38C23×C4×C43C2312yes—
39C23×C4×C43C2311yescharacteristic
40C23×C4×C43C2311yescharacteristic
41#117×C43C2×C4164yescomplemented
42C2×C4⋊C4×C43—28no—
43C2×C4⋊C4×C43—28no—
44C2×C4⋊C4×C43—48no—
45C2×C4⋊C4×C43C2×C4116yes—
46C2×C4⋊C4×C43C2318yes—
47C2×C4⋊C4×C43C2318yes—
48C2×C4⋊C4×C43C23116yes—
49C2×C4⋊C4×C43C2318yes—
50C2×C22⋊C4×C43—48no—
51C2×C22⋊C4×C43C2×C4116yes—
52C2×C22⋊C4×C43C23116yes—
53C2×C22⋊C4×C43C2318yes—
54C2×C42×C43—48no—
55C2×C42×C43C2×C418yes—
56C2×C42×C43C2×C418yes—
57C2×C42×C43C23116yes—
58C2×C42×C43C2314yes—
59C2×C42×C43C2314yes—
60#95×C43C23116yes—
61#95×C43C23116yes—
62#95×C43C23116yes—
63C24×C43—22no—
64C24×C43—22no—
65C24×C43—24no—
66C24×C43—24no—
67C24×C43C22×C414yes—
68C24×C43C2412yes—
69C24×C43C2411yescharacteristic
70C22×C4×C43—232no—
71C22×C4×C43—28no—
72C22×C4×C43—28no—
73C22×C4×C43—22no—
74C22×C4×C43—22no—
75C22×C4×C43—28no—
76C22×C4×C43—28no—
77C22×C4×C43—24no—
78C22×C4×C43—24no—
79C22×C4×C43—28no—
80C22×C4×C43—28no—
81C22×C4×C43—28no—
82C22×C4×C43—24no—
83C22×C4×C43—24no—
84C22×C4×C43—28no—
85C22×C4×C43C22×C418yes—
86C22×C4×C43C22×C418yes—
87C22×C4×C43C22×C414yes—
88C22×C4×C43C22×C4116yes—
89C22×C4×C43C22×C414yes—
90C22×C4×C43#4114yes—
91C22×C4×C43#4114yes—
92C22×C4×C43C2418yes—
93C22×C4×C43C2418yes—
94C22×C4×C43C2412yes—
95C22×C4×C43C2414yes—
96C22×C4×C43C2414yes—
97C22×C4×C43C2412yes—
98C4⋊C4×C43—216no—
99C4⋊C4×C43—216no—
100C4⋊C4×C43—416no—
101C4⋊C4×C43C22×C4132yes—
102C22⋊C4×C43—416no—
103C22⋊C4×C43C22×C4132yes—
104C42×C43—416no—
105C42×C43C22×C4116yes—
106C42×C43C22×C4116yes—
107C23×C43—28no—
108C23×C43—216no—
109C23×C43—22no—
110C23×C43—22no—
111C23×C43—24no—
112C23×C43—24no—
113C23×C43—44no—
114C23×C43—44no—
115C23×C43—48no—
116C23×C43C23×C414yes—
117C23×C43C23×C412yes—
118C23×C43C2×#4112yes—
119C23×C43C2×#4112yes—
120C23×C43H(5,𝔽2)14yes—
121C23×C432−1+414yes—
122C23×C43C2511yescharacteristic
123C2×C4×C43—28no—
124C2×C4×C43—216no—
125C2×C4×C43—216no—
126C2×C4×C43—22no—
127C2×C4×C43—22no—
128C2×C4×C43—24no—
129C2×C4×C43—24no—
130C2×C4×C43—24no—
131C2×C4×C43—24no—
132C2×C4×C43—232no—
133C2×C4×C43—28no—
134C2×C4×C43—28no—
135C2×C4×C43—28no—
136C2×C4×C43—28no—
137C2×C4×C43—28no—
138C2×C4×C43—28no—
139C2×C4×C43—416no—
140C2×C4×C43—416no—
141C2×C4×C43#117116yes—
142C2×C4×C43C23×C418yes—
143C2×C4×C43C23×C418yes—
144C2×C4×C43C23×C414yes—
145C2×C4×C43C23×C414yes—
146C2×C4×C43C2×#4114yes—
147C2×C4×C43C2×#4114yes—
148C2×#2314C4311yesmaximal, characteristic, direct product factor, Sylow
149C22×C43—24no—
150C22×C43—28no—
151C22×C43—416no—
152C22×C43—42no—
153C22×C43—42no—
154C22×C43—44no—
155C22×C43C2×#11714yes—
156C22×C43#52018yes—
157C22×C43#54014yes—
158C22×C43#54114yes—
159C22×C43#54218yes—
160C22×C43C24×C411yescharacteristic
161C22×C43C22×#4111yescharacteristic
162C22×C43C22×#4111yescharacteristic
163C22×C43C2×H(5,𝔽2)12yes—
164C22×C43C2×2−1+412yes—
165C4×C43—24no—
166C4×C43—28no—
167C4×C43—28no—
168C4×C43—48no—
169C4×C43—48no—
170C4×C43C2×#11718yes—
171C22×#117C2×C4311yescharacteristic
172#2314C2×C43116yesdirect product factor
173C2×#388C2×C4314yes—
174C2×#387C2×C4314yescomplemented
175C2×#384C2×C4311yescharacteristic, complemented
176C2×#382C2×C4311yescharacteristic, complemented
177C2×#380C2×C4312yes—
178C2×C4×C4⋊C4C2×C4312yescomplemented
179C2×C43—44no—
180C2×C43#231418yesdirect product factor
181C2×C43C22×#11711yescharacteristic
182C2×C43C2×#52012yes—
183C2×C43C2×#54011yescharacteristic
184C2×C43C2×#54111yescharacteristic
185C2×C43C2×#54212yes—
186C24×C4C22×C4311yescharacteristic
187C2×#117C4×C43116yescomplemented
188C2×#117C22×C4318yes—
189C22×C4⋊C4C22×C4312yes—
190C22×C4⋊C4C22×C4312yes—
191C22×C4⋊C4C22×C4314yes—
192C22×C4⋊C4C22×C4312yes—
193C22×C22⋊C4C22×C4314yes—
194C22×C22⋊C4C22×C4312yes—
195C22×C42C22×C4314yes—
196C22×C42C22×C4311yescharacteristic
197C22×C42C22×C4311yescharacteristic
198#388C22×C43132yes—
199#387C22×C43132yescomplemented
200#384C22×C4318yescomplemented
201#382C22×C4318yescomplemented
202#380C22×C43116yes—
203C4×C4⋊C4C22×C43116yescomplemented
204C2×#95C22×C4314yes—
205C2×#95C22×C4314yes—
206C2×#95C22×C4314yes—
207C43C2×#231411yescharacteristic, direct product factor, Sylow
208C25C23×C4311yescharacteristic
209C23×C4—24no—
210C23×C4—24no—
211C23×C4C2×C4×C4318yes—
212C23×C4C23×C4314yes—
213C23×C4C23×C4314yes—
214C23×C4C23×C4312yes—
215C23×C4C23×C4312yes—
216C23×C4C23×C4311yescharacteristic
217C23×C4C23×C4314yes—
218C23×C4C23×C4311yescharacteristic
219#117C2×C4×C43164yescomplemented
220C2×C4⋊C4—28no—
221C2×C4⋊C4—28no—
222C2×C4⋊C4—48no—
223C2×C4⋊C4C2×C4×C43116yes—
224C2×C4⋊C4C23×C4318yes—
225C2×C4⋊C4C23×C4318yes—
226C2×C4⋊C4C23×C43116yes—
227C2×C4⋊C4C23×C4318yes—
228C2×C22⋊C4—48no—
229C2×C22⋊C4C2×C4×C43116yes—
230C2×C22⋊C4C23×C43116yes—
231C2×C22⋊C4C23×C4318yes—
232C2×C42—48no—
233C2×C42C2×C4×C4318yes—
234C2×C42C2×C4×C4318yes—
235C2×C42C23×C43116yes—
236C2×C42C23×C4314yes—
237C2×C42C23×C4314yes—
238#95C23×C43116yes—
239#95C23×C43116yes—
240#95C23×C43116yes—
241C24—22no—
242C24—22no—
243C24—24no—
244C24—24no—
245C24C22×C4×C4314yes—
246C24C24×C4312yes—
247C24C24×C4311yescharacteristic
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—24no—
251C22×C4—24no—
252C22×C4—24no—
253C22×C4—24no—
254C22×C4—232no—
255C22×C4—28no—
256C22×C4—28no—
257C22×C4—28no—
258C22×C4—28no—
259C22×C4—28no—
260C22×C4—28no—
261C22×C4—28no—
262C22×C4—28no—
263C22×C4C22×C4×C4318yes—
264C22×C4C22×C4×C4318yes—
265C22×C4C22×C4×C4314yes—
266C22×C4C22×C4×C43116yes—
267C22×C4C22×C4×C4314yes—
268C22×C4#41×C4314yes—
269C22×C4#41×C4314yes—
270C22×C4C24×C4318yes—
271C22×C4C24×C4318yes—
272C22×C4C24×C4312yes—
273C22×C4C24×C4314yes—
274C22×C4C24×C4314yes—
275C22×C4C24×C4312yes—
276C4⋊C4—216no—
277C4⋊C4—216no—
278C4⋊C4—416no—
279C4⋊C4C22×C4×C43132yes—
280C22⋊C4—416no—
281C22⋊C4C22×C4×C43132yes—
282C42—416no—
283C42C22×C4×C43116yes—
284C42C22×C4×C43116yes—
285C23—28no—
286C23—216no—
287C23—22no—
288C23—22no—
289C23—24no—
290C23—24no—
291C23—44no—
292C23—44no—
293C23—48no—
294C23C23×C4×C4314yes—
295C23C23×C4×C4312yes—
296C23C2×#41×C4312yes—
297C23C2×#41×C4312yes—
298C23H(5,𝔽2)×C4314yes—
299C232−1+4×C4314yes—
300C23C25×C4311yescharacteristic
301C2×C4—28no—
302C2×C4—216no—
303C2×C4—216no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—24no—
307C2×C4—24no—
308C2×C4—24no—
309C2×C4—24no—
310C2×C4—232no—
311C2×C4—28no—
312C2×C4—28no—
313C2×C4—28no—
314C2×C4—28no—
315C2×C4—28no—
316C2×C4—28no—
317C2×C4—416no—
318C2×C4—416no—
319C2×C4#117×C43116yes—
320C2×C4C23×C4×C4318yes—
321C2×C4C23×C4×C4318yes—
322C2×C4C23×C4×C4314yes—
323C2×C4C23×C4×C4314yes—
324C2×C4C2×#41×C4314yes—
325C2×C4C2×#41×C4314yes—
326C22—24no—
327C22—28no—
328C22—42no—
329C22—42no—
330C22—44no—
331C22—416no—
332C22C2×#117×C4314yes—
333C22C43×#52018yes—
334C22C43×#54014yes—
335C22C43×#54114yes—
336C22C43×#54218yes—
337C22C24×C4×C4311yescharacteristic
338C22C22×#41×C4311yescharacteristic
339C22C22×#41×C4311yescharacteristic
340C22C2×H(5,𝔽2)×C4312yes—
341C22C2×2−1+4×C4312yes—
342C4—24no—
343C4—28no—
344C4—28no—
345C4—48no—
346C4—48no—
347C4C2×#117×C4318yes—
348C2—44no—
349C2C43×#231418yesdirect product factor
350C2C22×#117×C4311yescharacteristic
351C2C2×C43×#52012yes—
352C2C2×C43×#54011yescharacteristic
353C2C2×C43×#54111yescharacteristic
354C2C2×C43×#54212yes—
subgroupG/H
center, socleC24×C43C24
commutatorC22C24×C4×C43
Frattini, cosocleC23C25×C43
prime radicalC25×C43C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2314C2direct (N × H)
4. C2×C43×#387C2semidirect
5. C2×C43×#384C2semidirect
6. C2×C43×#382C2semidirect
8. C2×C4×C4⋊C4×C43C2semidirect
10. C2×#117×C43C4semidirect
22. C43×#387C22semidirect
23. C43×#384C22semidirect
24. C43×#382C22semidirect
26. C4×C4⋊C4×C43C22semidirect
41. #117×C43C2×C4semidirect
148. C2×#2314C43direct (N × H)
172. #2314C2×C43direct (N × H)
174. C2×#387C2×C43semidirect
175. C2×#384C2×C43semidirect
176. C2×#382C2×C43semidirect
178. C2×C4×C4⋊C4C2×C43semidirect
180. C2×C43#2314direct (N × H)
187. C2×#117C4×C43semidirect
199. #387C22×C43semidirect
200. #384C22×C43semidirect
201. #382C22×C43semidirect
203. C4×C4⋊C4C22×C43semidirect
207. C43C2×#2314direct (N × H)
219. #117C2×C4×C43semidirect
349. C2C43×#2314direct (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×#23142
C2×C43×#3882
C2×C43×#3872
C2×C43×#3842
C2×C43×#3822
C2×C43×#3802
C2×C4×C4⋊C4×C432
C2×#231443