Finite Group Databasebeta

← C43×#62813 #24982830

Subgroups — C43×#62813 #24982830

Order 11008.

6930 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3504C218yesmaximal, complemented
2C43×#3503C218yesmaximal, complemented
3C43×#3502C214yesmaximal, complemented
4C43×#3501C2112yesmaximal, complemented
5Q8×#41×C43C2116yesmaximal, complemented
6C43×#3458C216yesmaximal, complemented
7C2×C43×#533C216yesmaximal, complemented
8C43×#3428C212yesmaximal
9C2×C4×#41×C43C211yesmaximal, characteristic
10C22×#41×C43C2211yescharacteristic
11Q82×C43C22116yescomplemented
12C43×#557C22116yescomplemented
13C43×#557C22132yescomplemented
14C43×#554C22148yescomplemented
15C43×#554C22196yescomplemented
16D4×Q8×C43C22148yescomplemented
17C43×#544C22124yes—
18C43×#544C22148yescomplemented
19C43×#543C22124yes—
20C43×#533C2214yes—
21C43×#533C22112yes—
22C43×#533C22124yes—
23C43×#533C22124yescomplemented
24C43×#533C22112yescomplemented
25C43×#533C22112yescomplemented
26C43×#533C22148yescomplemented
27C2×C4⋊Q8×C43C22112yescomplemented
28C2×#125×C43C22112yescomplemented
29C2×C22⋊Q8×C43C22124yes—
30C43×#520C22116yes—
31C43×#519C2214yes—
32C43×#518C22112yes—
33C4×#41×C43C2218yes—
34C4×#41×C43C2214yes—
35C4×#41×C43C2214yes—
36C4×#41×C43C22116yes—
37C2×C4×Q8×C43C2212yes—
38C2×C4×Q8×C43C22124yescomplemented
39C2×C4×D4×C43C2216yes—
40C2×#117×C43C2213yes—
41C2×#117×C43C22112yes—
42C22×C42×C43C2213yes—
43C2×#41×C43Q8116yescomplemented
44C2×#41×C43C2314yes—
45C2×#41×C43C2314yes—
46C22×Q8×C43C23124yes—
47C22×Q8×C43C2311yescharacteristic
48C22×D4×C43C2313yes—
49C23×C4×C43C2316yes—
50C23×C4×C43C2313yes—
51C4⋊Q8×C43C2318yes—
52C4⋊Q8×C43C23124yes—
53C4⋊Q8×C43C23124yes—
54C4⋊Q8×C43C23124yes—
55C4⋊Q8×C43C23196yes—
56#125×C43C2318yes—
57#125×C43C23124yes—
58#125×C43C23148yes—
59#125×C43C23196yes—
60C22⋊Q8×C43C23116yes—
61C22⋊Q8×C43C23148yes—
62C22⋊Q8×C43C23148yes—
63C22⋊Q8×C43C23148yes—
64C22⋊Q8×C43C231192yes—
65C4×Q8×C43C2318yes—
66C4×Q8×C43C2318yes—
67C4×Q8×C43C23116yes—
68C4×Q8×C43C23148yes—
69C4×Q8×C43C23148yes—
70C4×Q8×C43C23148yes—
71C4×Q8×C43C23132yes—
72C4×D4×C43C23124yes—
73C4×D4×C43C23124yes—
74C4×D4×C43C23196yes—
75#117×C43C2318yes—
76#117×C43C23112yes—
77#117×C43C23124yes—
78#117×C43C23112yes—
79#117×C43C23124yes—
80#117×C43C23124yes—
81C2×C4⋊C4×C43C2316yes—
82C2×C4⋊C4×C43C23124yes—
83C2×C4⋊C4×C43C23148yes—
84C2×C4⋊C4×C43C23124yes—
85C2×C22⋊C4×C43C2316yes—
86C2×C22⋊C4×C43C23124yes—
87C2×C42×C43C2311yescharacteristic
88C2×C42×C43C2313yes—
89C2×C42×C43C2316yes—
90C2×C42×C43C23112yes—
91C2×C42×C43C2316yes—
92C2×C42×C43C2316yes—
93C2×C42×C43C23124yes—
94C24×C43C2413yes—
95#41×C43C2×Q8132yescomplemented
96#41×C43C2×Q8132yescomplemented
97C2×Q8×C43—448no—
98C2×Q8×C43C2×Q818yescomplemented
99C2×Q8×C43C24116yes—
100C2×Q8×C43C24148yes—
101C2×Q8×C43C2414yes—
102C2×D4×C43C2×Q8124yescomplemented
103C2×D4×C43C24112yes—
104C22×C4×C43—412no—
105C22×C4×C43C2×Q8124yescomplemented
106C22×C4×C43C2412yes—
107C22×C4×C43C24112yes—
108C22×C4×C43C2416yes—
109C22×C4×C43C24112yes—
110C22×C4×C43C24148yes—
111C22×C4×C43C2416yes—
112C22×C4×C43C2413yes—
113C22×C4×C43C2416yes—
114C22×C4×C43C2411yescharacteristic
115C4⋊C4×C43C24116yes—
116C4⋊C4×C43C24132yes—
117C4⋊C4×C43C24116yes—
118C4⋊C4×C43C24124yes—
119C4⋊C4×C43C24148yes—
120C4⋊C4×C43C24196yes—
121C4⋊C4×C43C24148yes—
122C22⋊C4×C43C24116yes—
123C22⋊C4×C43C24124yes—
124C22⋊C4×C43C24148yes—
125C42×C43C2411yescharacteristic
126C42×C43C2411yescharacteristic
127C42×C43C2416yes—
128C42×C43C24112yes—
129C42×C43C24112yes—
130C42×C43C24148yes—
131C42×C43C2412yes—
132C42×C43C2416yes—
133C42×C43C24116yes—
134C23×C43—46no—
135C23×C43C22×Q8112yes—
136C23×C43C2511yescharacteristic
137C23×C43C2516yes—
138Q8×C43—232no—
139Q8×C43—448no—
140Q8×C43C22×Q8116yes—
141D4×C43C22×Q8148yes—
142C2×C4×C43—24no—
143C2×C4×C43—224no—
144C2×C4×C43—412no—
145C2×C4×C43—46no—
146C2×C4×C43—448no—
147C2×C4×C43C22×Q814yes—
148C2×C4×C43C22×Q8112yes—
149C2×C4×C43C22×Q8124yes—
150C2×C4×C43C22×Q8124yes—
151C2×C4×C43C2512yes—
152C2×C4×C43C25112yes—
153C2×C4×C43C25132yes—
154C2×C4×C43C2516yes—
155C2×C4×C43C2511yescharacteristic
156C2×C4×C43C2512yes—
157C2×C4×C43C2511yescharacteristic
158#62813C4311yesmaximal, characteristic, direct product factor, Sylow
159C22×C43—22no—
160C22×C43—212no—
161C22×C43—412no—
162C22×C43C23×Q812yes—
163C22×C43C23×Q8112yes—
164C22×C43C2611yescharacteristic
165C4×C43—22no—
166C4×C43—212no—
167C4×C43—232no—
168C4×C43C23×Q812yes—
169C4×C43C23×Q812yes—
170C4×C43C23×Q8112yes—
171C4×C43#58514yes—
172#3504C2×C4318yescomplemented
173#3503C2×C4318yescomplemented
174#3502C2×C4314yescomplemented
175#3501C2×C43112yescomplemented
176Q8×#41C2×C43116yescomplemented
177#3458C2×C4316yescomplemented
178C2×#533C2×C4316yescomplemented
179#3428C2×C4312yes—
180C2×C4×#41C2×C4311yescharacteristic
181C2×C43—22no—
182C2×C43—212no—
183C2×C43C24×Q811yescharacteristic
184C2×C43C2×#58512yes—
185C22×#41C22×C4311yescharacteristic
186Q82C22×C43116yescomplemented
187#557C22×C43116yescomplemented
188#557C22×C43132yescomplemented
189#554C22×C43148yescomplemented
190#554C22×C43196yescomplemented
191D4×Q8C22×C43148yescomplemented
192#544C22×C43124yes—
193#544C22×C43148yescomplemented
194#543C22×C43124yes—
195#533C22×C4314yes—
196#533C22×C43112yes—
197#533C22×C43124yes—
198#533C22×C43124yescomplemented
199#533C22×C43112yescomplemented
200#533C22×C43112yescomplemented
201#533C22×C43148yescomplemented
202C2×C4⋊Q8C22×C43112yescomplemented
203C2×#125C22×C43112yescomplemented
204C2×C22⋊Q8C22×C43124yes—
205#520C22×C43116yes—
206#519C22×C4314yes—
207#518C22×C43112yes—
208C4×#41C22×C4318yes—
209C4×#41C22×C4314yes—
210C4×#41C22×C4314yes—
211C4×#41C22×C43116yes—
212C2×C4×Q8C22×C4312yes—
213C2×C4×Q8C22×C43124yescomplemented
214C2×C4×D4C22×C4316yes—
215C2×#117C22×C4313yes—
216C2×#117C22×C43112yes—
217C22×C42C22×C4313yes—
218C43#6281311yescharacteristic, direct product factor, Sylow
219C2×#41Q8×C43116yescomplemented
220C2×#41C23×C4314yes—
221C2×#41C23×C4314yes—
222C22×Q8C23×C43124yes—
223C22×Q8C23×C4311yescharacteristic
224C22×D4C23×C4313yes—
225C23×C4C23×C4316yes—
226C23×C4C23×C4313yes—
227C4⋊Q8C23×C4318yes—
228C4⋊Q8C23×C43124yes—
229C4⋊Q8C23×C43124yes—
230C4⋊Q8C23×C43124yes—
231C4⋊Q8C23×C43196yes—
232#125C23×C4318yes—
233#125C23×C43124yes—
234#125C23×C43148yes—
235#125C23×C43196yes—
236C22⋊Q8C23×C43116yes—
237C22⋊Q8C23×C43148yes—
238C22⋊Q8C23×C43148yes—
239C22⋊Q8C23×C43148yes—
240C22⋊Q8C23×C431192yes—
241C4×Q8C23×C4318yes—
242C4×Q8C23×C4318yes—
243C4×Q8C23×C43116yes—
244C4×Q8C23×C43148yes—
245C4×Q8C23×C43148yes—
246C4×Q8C23×C43148yes—
247C4×Q8C23×C43132yes—
248C4×D4C23×C43124yes—
249C4×D4C23×C43124yes—
250C4×D4C23×C43196yes—
251#117C23×C4318yes—
252#117C23×C43112yes—
253#117C23×C43124yes—
254#117C23×C43112yes—
255#117C23×C43124yes—
256#117C23×C43124yes—
257C2×C4⋊C4C23×C4316yes—
258C2×C4⋊C4C23×C43124yes—
259C2×C4⋊C4C23×C43148yes—
260C2×C4⋊C4C23×C43124yes—
261C2×C22⋊C4C23×C4316yes—
262C2×C22⋊C4C23×C43124yes—
263C2×C42C23×C4313yes—
264C2×C42C23×C43124yes—
265C2×C42C23×C4316yes—
266C2×C42C23×C43112yes—
267C2×C42C23×C4316yes—
268C2×C42C23×C4316yes—
269C2×C42C23×C4311yescharacteristic
270C24C24×C4313yes—
271#41C2×Q8×C43132yescomplemented
272#41C2×Q8×C43132yescomplemented
273C2×Q8—448no—
274C2×Q8C2×Q8×C4318yescomplemented
275C2×Q8C24×C43116yes—
276C2×Q8C24×C43148yes—
277C2×Q8C24×C4314yes—
278C2×D4C2×Q8×C43124yescomplemented
279C2×D4C24×C43112yes—
280C22×C4—412no—
281C22×C4C2×Q8×C43124yescomplemented
282C22×C4C24×C4312yes—
283C22×C4C24×C43112yes—
284C22×C4C24×C4316yes—
285C22×C4C24×C43112yes—
286C22×C4C24×C43148yes—
287C22×C4C24×C4316yes—
288C22×C4C24×C4311yescharacteristic
289C22×C4C24×C4316yes—
290C22×C4C24×C4313yes—
291C4⋊C4C24×C43116yes—
292C4⋊C4C24×C43132yes—
293C4⋊C4C24×C43116yes—
294C4⋊C4C24×C43124yes—
295C4⋊C4C24×C43148yes—
296C4⋊C4C24×C43196yes—
297C4⋊C4C24×C43148yes—
298C22⋊C4C24×C43116yes—
299C22⋊C4C24×C43124yes—
300C22⋊C4C24×C43148yes—
301C42C24×C4312yes—
302C42C24×C4311yescharacteristic
303C42C24×C4311yescharacteristic
304C42C24×C4316yes—
305C42C24×C43116yes—
306C42C24×C4316yes—
307C42C24×C43112yes—
308C42C24×C43112yes—
309C42C24×C43148yes—
310C23—46no—
311C23C22×Q8×C43112yes—
312C23C25×C4311yescharacteristic
313C23C25×C4316yes—
314Q8—232no—
315Q8—448no—
316Q8C22×Q8×C43116yes—
317D4C22×Q8×C43148yes—
318C2×C4—24no—
319C2×C4—224no—
320C2×C4—412no—
321C2×C4—46no—
322C2×C4—448no—
323C2×C4C22×Q8×C4314yes—
324C2×C4C22×Q8×C43112yes—
325C2×C4C22×Q8×C43124yes—
326C2×C4C22×Q8×C43124yes—
327C2×C4C25×C4312yes—
328C2×C4C25×C43112yes—
329C2×C4C25×C43132yes—
330C2×C4C25×C4311yescharacteristic
331C2×C4C25×C4316yes—
332C2×C4C25×C4311yescharacteristic
333C2×C4C25×C4312yes—
334C22—212no—
335C22—22no—
336C22—412no—
337C22C23×Q8×C4312yes—
338C22C23×Q8×C43112yes—
339C22C26×C4311yescharacteristic
340C4—22no—
341C4—212no—
342C4—232no—
343C4C23×Q8×C4312yes—
344C4C23×Q8×C4312yes—
345C4C23×Q8×C43112yes—
346C4C43×#58514yes—
347C2—22no—
348C2—212no—
349C2C24×Q8×C4311yescharacteristic
350C2C2×C43×#58512yes—
subgroupG/H
centerC2×C4×C43C25
commutator, Frattini, cosocleC22C26×C43
socleC22×C43C26
prime radicalC22×#41×C43C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3504C2semidirect
2. C43×#3503C2semidirect
3. C43×#3502C2semidirect
4. C43×#3501C2semidirect
5. Q8×#41×C43C2semidirect
6. C43×#3458C2semidirect
7. C2×C43×#533C2semidirect
11. Q82×C43C22semidirect
12. C43×#557C22semidirect
13. C43×#557C22semidirect
14. C43×#554C22semidirect
15. C43×#554C22semidirect
16. D4×Q8×C43C22semidirect
18. C43×#544C22semidirect
23. C43×#533C22semidirect
24. C43×#533C22semidirect
25. C43×#533C22semidirect
26. C43×#533C22semidirect
27. C2×C4⋊Q8×C43C22semidirect
28. C2×#125×C43C22semidirect
38. C2×C4×Q8×C43C22semidirect
43. C2×#41×C43Q8semidirect
95. #41×C43C2×Q8semidirect
96. #41×C43C2×Q8semidirect
98. C2×Q8×C43C2×Q8semidirect
102. C2×D4×C43C2×Q8semidirect
105. C22×C4×C43C2×Q8semidirect
158. #62813C43direct (N × H)
172. #3504C2×C43semidirect
173. #3503C2×C43semidirect
174. #3502C2×C43semidirect
175. #3501C2×C43semidirect
176. Q8×#41C2×C43semidirect
177. #3458C2×C43semidirect
178. C2×#533C2×C43semidirect
186. Q82C22×C43semidirect
187. #557C22×C43semidirect
188. #557C22×C43semidirect
189. #554C22×C43semidirect
190. #554C22×C43semidirect
191. D4×Q8C22×C43semidirect
193. #544C22×C43semidirect
198. #533C22×C43semidirect
199. #533C22×C43semidirect
200. #533C22×C43semidirect
201. #533C22×C43semidirect
202. C2×C4⋊Q8C22×C43semidirect
203. C2×#125C22×C43semidirect
213. C2×C4×Q8C22×C43semidirect
218. C43#62813direct (N × H)
219. C2×#41Q8×C43semidirect
271. #41C2×Q8×C43semidirect
272. #41C2×Q8×C43semidirect
274. C2×Q8C2×Q8×C43semidirect
278. C2×D4C2×Q8×C43semidirect
281. C22×C4C2×Q8×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#35042
C43×#35032
C43×#35022
C43×#35012
Q8×#41×C432
C43×#34582
C2×C43×#5332
C43×#34282
C2×C4×#41×C432
#6281343