Finite Group Databasebeta

← C43×#36607 #24956624

Subgroups — C43×#36607 #24956624

Order 11008.

2524 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2847C213yesmaximal, complemented
2C43×#2569C213yesmaximal, complemented
3C43×#2543C213yesmaximal, complemented
4C43×#2510C216yesmaximal, complemented
5C43×#2444C216yesmaximal, complemented
6C43×#2364C213yesmaximal, complemented
7C43×#2353C213yesmaximal, complemented
8C4×#120×C43C213yesmaximal, complemented
9C22×#95×C43C211yesmaximal, characteristic, complemented
10C24×C4×C43C2213yes—
11C2×#121×C43C2213yes—
12C2×#121×C43C2216yes—
13C2×#120×C43C2213yes—
14C2×C4×D4×C43C2213yes—
15C2×C4×D4×C43C2216yes—
16C43×#401C2212yescomplemented
17C43×#400C2216yescomplemented
18C43×#398C2213yescomplemented
19C43×#397C2216yescomplemented
20C43×#397C2213yescomplemented
21C43×#394C2213yescomplemented
22C43×#392C2211yescharacteristic, complemented
23C43×#388C2216yescomplemented
24C43×#388C2216yescomplemented
25C43×#387C2216yescomplemented
26C43×#387C2216yescomplemented
27C43×#386C2216yes—
28C43×#386C2216yes—
29C43×#386C2216yes—
30C43×#386C2213yes—
31C43×#386C2216yes—
32C43×#386C2216yescomplemented
33C43×#385C2216yes—
34C43×#385C2213yes—
35C43×#383C2213yescomplemented
36C43×#381C2213yescomplemented
37C43×#380C2213yes—
38C43×#380C2216yes—
39C43×#379C2211yescharacteristic
40C4×C22⋊C4×C43C2216yes—
41C4×C22⋊C4×C43C2213yes—
42C4×C22⋊C4×C43C2213yescomplemented
43C43×#376C2211yescharacteristic, complemented
44C2×#95×C43C2213yes—
45C2×#95×C43C2216yes—
46C2×#95×C43C2213yes—
47C25×C43C2311yescharacteristic
48C22×D4×C43C2313yes—
49C22×D4×C43C2316yes—
50C22×D4×C43C2313yes—
51C23×C4×C43—212no—
52C23×C4×C43—412no—
53C23×C4×C43C2316yes—
54C23×C4×C43C2316yes—
55C23×C4×C43C2313yes—
56C23×C4×C43C2313yes—
57C23×C4×C43C2313yes—
58#121×C43—212no—
59#121×C43—412no—
60#120×C43—212no—
61C4×D4×C43—212no—
62C4×D4×C43—412no—
63C2×C4⋊C4×C43C2313yes—
64C2×C4⋊C4×C43C2313yes—
65C2×C4⋊C4×C43C2316yes—
66C2×C4⋊C4×C43C2316yes—
67C2×C22⋊C4×C43C2313yes—
68C2×C22⋊C4×C43C2313yes—
69C2×C22⋊C4×C43C2313yes—
70C2×C22⋊C4×C43C2316yes—
71C2×C22⋊C4×C43C2313yes—
72C2×C22⋊C4×C43C2316yes—
73C2×C22⋊C4×C43C2316yes—
74C2×C22⋊C4×C43C2316yes—
75C2×C22⋊C4×C43C2316yes—
76C2×C42×C43C2313yes—
77C2×C42×C43C2316yes—
78#95×C43C2311yescharacteristic
79#95×C43C2313yes—
80#95×C43C2316yes—
81#95×C43C2311yescharacteristic
82#95×C43C2313yes—
83#95×C43C2312yes—
84#95×C43C2313yes—
85#95×C43C2316yes—
86#95×C43C2316yes—
87#95×C43C2316yes—
88#95×C43C2313yes—
89#95×C43C2316yes—
90#95×C43C2316yes—
91C24×C43—26no—
92C24×C43—26no—
93C24×C43#4114yes—
94C24×C43C2413yes—
95C24×C43C2413yes—
96C2×D4×C43—26no—
97C2×D4×C43—26no—
98C2×D4×C43—26no—
99C2×D4×C43—212no—
100C2×D4×C43—212no—
101C2×D4×C43—212no—
102C2×D4×C43—26no—
103C2×D4×C43—46no—
104C22×C4×C43—212no—
105C22×C4×C43—212no—
106C22×C4×C43—26no—
107C22×C4×C43—26no—
108C22×C4×C43—212no—
109C22×C4×C43—212no—
110C22×C4×C43—46no—
111C22×C4×C43—46no—
112C22×C4×C43—46no—
113C22×C4×C43—46no—
114C22×C4×C43—46no—
115C22×C4×C43—448no—
116C22×C4×C43#41112yes—
117C22×C4×C43C2416yes—
118C22×C4×C43C2411yescharacteristic
119C22×C4×C43C2413yes—
120C22×C4×C43C2416yes—
121C22×C4×C43C2413yes—
122C22×C4×C43C2413yes—
123C22×C4×C43C2413yes—
124C4⋊C4×C43—26no—
125C4⋊C4×C43—26no—
126C4⋊C4×C43—46no—
127C4⋊C4×C43—46no—
128C22⋊C4×C43—26no—
129C22⋊C4×C43—212no—
130C22⋊C4×C43—26no—
131C22⋊C4×C43—212no—
132C22⋊C4×C43—26no—
133C22⋊C4×C43—26no—
134C22⋊C4×C43—46no—
135C22⋊C4×C43—46no—
136C22⋊C4×C43—46no—
137C42×C43—26no—
138C42×C43—46no—
139C23×C43—224no—
140C23×C43—28no—
141C23×C43—224no—
142C23×C43—26no—
143C23×C43—26no—
144C23×C43—23no—
145C23×C43—26no—
146C23×C43—23no—
147C23×C43—26no—
148C23×C43—23no—
149C23×C43C2×#4116yes—
150C23×C43C2×#4116yes—
151C23×C43H(5,𝔽2)16yes—
152C23×C43C2511yescharacteristic
153D4×C43—412no—
154D4×C43—424no—
155D4×C43—86no—
156C2×C4×C43—26no—
157C2×C4×C43—26no—
158C2×C4×C43—23no—
159C2×C4×C43—23no—
160C2×C4×C43—23no—
161C2×C4×C43—26no—
162C2×C4×C43—23no—
163C2×C4×C43—26no—
164C2×C4×C43—26no—
165C2×C4×C43—26no—
166C2×C4×C43—26no—
167C2×C4×C43—23no—
168C2×C4×C43—26no—
169C2×C4×C43—26no—
170C2×C4×C43—412no—
171C2×C4×C43—424no—
172C2×C4×C43—424no—
173C2×C4×C43—412no—
174C2×C4×C43—86no—
175C2×C4×C43C2×#4116yes—
176C2×C4×C43C2×#4116yes—
177#36607C4311yesmaximal, characteristic, direct product factor, Sylow
178C22×C43—232no—
179C22×C43—26no—
180C22×C43—212no—
181C22×C43—26no—
182C22×C43—212no—
183C22×C43—43no—
184C22×C43—43no—
185C22×C43—46no—
186C22×C43—43no—
187C22×C43—46no—
188C22×C43#553112yes—
189C22×C43C22×#4113yes—
190C22×C43C22×#4111yescharacteristic
191C22×C43C2×H(5,𝔽2)13yes—
192C4×C43—26no—
193C4×C43—26no—
194C4×C43—41no—
195C4×C43—43no—
196C4×C43—46no—
197C4×C43—46no—
198C4×C43—43no—
199#2847C2×C4313yescomplemented
200#2569C2×C4313yescomplemented
201#2543C2×C4313yescomplemented
202#2510C2×C4316yescomplemented
203#2444C2×C4316yescomplemented
204#2364C2×C4313yescomplemented
205#2353C2×C4313yescomplemented
206C4×#120C2×C4313yescomplemented
207C22×#95C2×C4311yescharacteristic, complemented
208C2×C43—212no—
209C2×C43—83no—
210C2×C43#344411yescharacteristic
211C2×C43C2×#55313yes—
212C2×C43#349013yes—
213C24×C4C22×C4313yes—
214C2×#121C22×C4313yes—
215C2×#121C22×C4316yes—
216C2×#120C22×C4313yes—
217C2×C4×D4C22×C4313yes—
218C2×C4×D4C22×C4316yes—
219#401C22×C4312yescomplemented
220#400C22×C4316yescomplemented
221#398C22×C4313yescomplemented
222#397C22×C4316yescomplemented
223#397C22×C4313yescomplemented
224#394C22×C4313yescomplemented
225#392C22×C4311yescharacteristic, complemented
226#388C22×C4316yescomplemented
227#388C22×C4316yescomplemented
228#387C22×C4316yescomplemented
229#387C22×C4316yescomplemented
230#386C22×C4316yes—
231#386C22×C4316yes—
232#386C22×C4316yes—
233#386C22×C4313yes—
234#386C22×C4316yes—
235#386C22×C4316yescomplemented
236#385C22×C4316yes—
237#385C22×C4313yes—
238#383C22×C4313yescomplemented
239#381C22×C4313yescomplemented
240#380C22×C4313yes—
241#380C22×C4316yes—
242#379C22×C4311yescharacteristic
243C4×C22⋊C4C22×C4313yes—
244C4×C22⋊C4C22×C4316yes—
245C4×C22⋊C4C22×C4313yescomplemented
246#376C22×C4311yescharacteristic, complemented
247C2×#95C22×C4313yes—
248C2×#95C22×C4313yes—
249C2×#95C22×C4316yes—
250C43#3660711yescharacteristic, direct product factor, Sylow
251C25C23×C4311yescharacteristic
252C22×D4C23×C4313yes—
253C22×D4C23×C4316yes—
254C22×D4C23×C4313yes—
255C23×C4—212no—
256C23×C4—412no—
257C23×C4C23×C4316yes—
258C23×C4C23×C4316yes—
259C23×C4C23×C4313yes—
260C23×C4C23×C4313yes—
261C23×C4C23×C4313yes—
262#121—212no—
263#121—412no—
264#120—212no—
265C4×D4—212no—
266C4×D4—412no—
267C2×C4⋊C4C23×C4313yes—
268C2×C4⋊C4C23×C4313yes—
269C2×C4⋊C4C23×C4316yes—
270C2×C4⋊C4C23×C4316yes—
271C2×C22⋊C4C23×C4313yes—
272C2×C22⋊C4C23×C4313yes—
273C2×C22⋊C4C23×C4313yes—
274C2×C22⋊C4C23×C4313yes—
275C2×C22⋊C4C23×C4316yes—
276C2×C22⋊C4C23×C4316yes—
277C2×C22⋊C4C23×C4316yes—
278C2×C22⋊C4C23×C4316yes—
279C2×C22⋊C4C23×C4316yes—
280C2×C42C23×C4313yes—
281C2×C42C23×C4316yes—
282#95C23×C4311yescharacteristic
283#95C23×C4313yes—
284#95C23×C4316yes—
285#95C23×C4311yescharacteristic
286#95C23×C4313yes—
287#95C23×C4312yes—
288#95C23×C4313yes—
289#95C23×C4316yes—
290#95C23×C4316yes—
291#95C23×C4316yes—
292#95C23×C4313yes—
293#95C23×C4316yes—
294#95C23×C4316yes—
295C24—26no—
296C24—26no—
297C24#41×C4314yes—
298C24C24×C4313yes—
299C24C24×C4313yes—
300C2×D4—26no—
301C2×D4—26no—
302C2×D4—212no—
303C2×D4—212no—
304C2×D4—212no—
305C2×D4—26no—
306C2×D4—26no—
307C2×D4—46no—
308C22×C4—26no—
309C22×C4—212no—
310C22×C4—212no—
311C22×C4—212no—
312C22×C4—212no—
313C22×C4—26no—
314C22×C4—46no—
315C22×C4—46no—
316C22×C4—46no—
317C22×C4—46no—
318C22×C4—46no—
319C22×C4—448no—
320C22×C4#41×C43112yes—
321C22×C4C24×C4316yes—
322C22×C4C24×C4311yescharacteristic
323C22×C4C24×C4313yes—
324C22×C4C24×C4316yes—
325C22×C4C24×C4313yes—
326C22×C4C24×C4313yes—
327C22×C4C24×C4313yes—
328C4⋊C4—26no—
329C4⋊C4—26no—
330C4⋊C4—46no—
331C4⋊C4—46no—
332C22⋊C4—26no—
333C22⋊C4—26no—
334C22⋊C4—212no—
335C22⋊C4—26no—
336C22⋊C4—26no—
337C22⋊C4—212no—
338C22⋊C4—46no—
339C22⋊C4—46no—
340C22⋊C4—46no—
341C42—26no—
342C42—46no—
343C23—224no—
344C23—28no—
345C23—224no—
346C23—26no—
347C23—26no—
348C23—23no—
349C23—26no—
350C23—23no—
351C23—26no—
352C23—23no—
353C23C2×#41×C4316yes—
354C23C2×#41×C4316yes—
355C23H(5,𝔽2)×C4316yes—
356C23C25×C4311yescharacteristic
357D4—412no—
358D4—424no—
359D4—86no—
360C2×C4—26no—
361C2×C4—26no—
362C2×C4—23no—
363C2×C4—23no—
364C2×C4—23no—
365C2×C4—26no—
366C2×C4—23no—
367C2×C4—26no—
368C2×C4—26no—
369C2×C4—26no—
370C2×C4—26no—
371C2×C4—23no—
372C2×C4—26no—
373C2×C4—26no—
374C2×C4—412no—
375C2×C4—424no—
376C2×C4—424no—
377C2×C4—412no—
378C2×C4—86no—
379C2×C4C2×#41×C4316yes—
380C2×C4C2×#41×C4316yes—
381C22—232no—
382C22—26no—
383C22—212no—
384C22—26no—
385C22—212no—
386C22—43no—
387C22—43no—
388C22—46no—
389C22—43no—
390C22—46no—
391C22C43×#553112yes—
392C22C22×#41×C4313yes—
393C22C22×#41×C4311yescharacteristic
394C22C2×H(5,𝔽2)×C4313yes—
395C4—26no—
396C4—26no—
397C4—41no—
398C4—43no—
399C4—46no—
400C4—46no—
401C4—43no—
402C2—212no—
403C2—83no—
404C2C43×#344411yescharacteristic
405C2C2×C43×#55313yes—
406C2C43×#349013yes—
subgroupG/H
center, socleC23×C43C25
commutator, Frattini, cosocleC23C25×C43
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#2847C2semidirect
2. C43×#2569C2semidirect
3. C43×#2543C2semidirect
4. C43×#2510C2semidirect
5. C43×#2444C2semidirect
6. C43×#2364C2semidirect
7. C43×#2353C2semidirect
8. C4×#120×C43C2semidirect
9. C22×#95×C43C2semidirect
16. C43×#401C22semidirect
17. C43×#400C22semidirect
18. C43×#398C22semidirect
19. C43×#397C22semidirect
20. C43×#397C22semidirect
21. C43×#394C22semidirect
22. C43×#392C22semidirect
23. C43×#388C22semidirect
24. C43×#388C22semidirect
25. C43×#387C22semidirect
26. C43×#387C22semidirect
32. C43×#386C22semidirect
35. C43×#383C22semidirect
36. C43×#381C22semidirect
42. C4×C22⋊C4×C43C22semidirect
43. C43×#376C22semidirect
177. #36607C43direct (N × H)
199. #2847C2×C43semidirect
200. #2569C2×C43semidirect
201. #2543C2×C43semidirect
202. #2510C2×C43semidirect
203. #2444C2×C43semidirect
204. #2364C2×C43semidirect
205. #2353C2×C43semidirect
206. C4×#120C2×C43semidirect
207. C22×#95C2×C43semidirect
219. #401C22×C43semidirect
220. #400C22×C43semidirect
221. #398C22×C43semidirect
222. #397C22×C43semidirect
223. #397C22×C43semidirect
224. #394C22×C43semidirect
225. #392C22×C43semidirect
226. #388C22×C43semidirect
227. #388C22×C43semidirect
228. #387C22×C43semidirect
229. #387C22×C43semidirect
235. #386C22×C43semidirect
238. #383C22×C43semidirect
239. #381C22×C43semidirect
245. C4×C22⋊C4C22×C43semidirect
246. #376C22×C43semidirect
250. C43#36607direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#28472
C43×#25692
C43×#25432
C43×#25102
C43×#24442
C43×#23642
C43×#23532
C4×#120×C432
C22×#95×C432
#3660743