Finite Group Databasebeta

← C43×#3524 #19132341

Subgroups — C43×#3524 #19132341

Order 5504.

1030 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
1C43×#559C213yesmaximal, complemented
2C43×#557C211yesmaximal, characteristic, complemented
3C43×#555C213yesmaximal, complemented
4C43×#553C213yesmaximal, complemented
5C43×#552C213yesmaximal, complemented
6C43×#550C211yesmaximal, characteristic, complemented
7C43×#548C211yesmaximal, characteristic, complemented
8C43×#548C211yesmaximal, characteristic, complemented
9C43×#542C213yesmaximal, complemented
10C43×#540C213yesmaximal, complemented
11C43×#529C213yesmaximal, complemented
12C43×#529C213yesmaximal, complemented
13C43×#520C211yesmaximal, characteristic, complemented
14C43×#519C211yesmaximal, characteristic, complemented
15C4×#41×C43C211yesmaximal, characteristic, complemented
16C2×#41×C43C2211yescharacteristic
17C2×#41×C43C2211yescharacteristic
18C22×Q8×C43C2211yescharacteristic
19C4⋊Q8×C43C2213yes—
20#127×C43C2213yes—
21#126×C43C2211yescharacteristic
22#126×C43C2213yes—
23#126×C43C2216yes—
24#125×C43C2213yes—
25#125×C43C2213yes—
26#125×C43C2213yes—
27#124×C43C2213yes—
28#124×C43C2213yes—
29#124×C43C2213yes—
30#124×C43C2216yes—
31#123×C43C2216yes—
32#123×C43C2213yes—
33#123×C43C2213yes—
34#123×C43C2216yes—
35C22⋊Q8×C43C2213yes—
36C22⋊Q8×C43C2213yes—
37C22⋊Q8×C43C2213yes—
38#121×C43C2213yes—
39#121×C43C2213yes—
40#121×C43C2213yes—
41#121×C43C2213yes—
42#121×C43C2216yes—
43#121×C43C2213yes—
44C4×Q8×C43C2211yescharacteristic
45C4×Q8×C43C2211yescharacteristic
46C4×Q8×C43C2213yes—
47C4×Q8×C43C2211yescharacteristic
48C4×Q8×C43C2213yes—
49C4×Q8×C43C2211yescharacteristic
50C4×Q8×C43C2213yes—
51C4×D4×C43C2213yes—
52C4×D4×C43C2213yes—
53C4×D4×C43C2213yes—
54C4×D4×C43C2213yes—
55C4×D4×C43C2213yes—
56C4×D4×C43C2213yes—
57C4×D4×C43C2213yes—
58C4×D4×C43C2216yes—
59#117×C43C2213yes—
60#117×C43C2213yes—
61#117×C43C2213yes—
62#117×C43C2213yes—
63#117×C43C2216yes—
64C2×C4⋊C4×C43C2213yes—
65C2×C42×C43C2213yes—
66#41×C43—24no—
67#41×C43—24no—
68C2×Q8×C43—24no—
69C2×Q8×C43C2313yes—
70C2×Q8×C43C2313yes—
71C2×Q8×C43C2311yescharacteristic
72C2×D4×C43C2313yes—
73C2×D4×C43C2313yes—
74C2×D4×C43C2313yes—
75C2×D4×C43C2313yes—
76C2×D4×C43C2316yes—
77C2×D4×C43C2313yes—
78C22×C4×C43C2313yes—
79C22×C4×C43C2313yes—
80C22×C4×C43C2313yes—
81C22×C4×C43C2313yes—
82C22×C4×C43C2313yes—
83C22×C4×C43C2316yes—
84C4⋊C4×C43C2313yes—
85C4⋊C4×C43C2313yes—
86C4⋊C4×C43C2313yes—
87C4⋊C4×C43C2311yescharacteristic
88C4⋊C4×C43C2313yes—
89C4⋊C4×C43C2313yes—
90C4⋊C4×C43C2313yes—
91C4⋊C4×C43C2313yes—
92C4⋊C4×C43C2313yes—
93C4⋊C4×C43C2316yes—
94C4⋊C4×C43C2311yescharacteristic
95C4⋊C4×C43C2313yes—
96C4⋊C4×C43C2313yes—
97C4⋊C4×C43C2311yescharacteristic
98C4⋊C4×C43C2313yes—
99C22⋊C4×C43C2311yescharacteristic
100C22⋊C4×C43C2313yes—
101C22⋊C4×C43C2313yes—
102C22⋊C4×C43C2313yes—
103C22⋊C4×C43C2316yes—
104C22⋊C4×C43C2313yes—
105C22⋊C4×C43C2316yes—
106C22⋊C4×C43C2311yescharacteristic
107C22⋊C4×C43C2313yes—
108C22⋊C4×C43C2311yescharacteristic
109C22⋊C4×C43C2313yes—
110C22⋊C4×C43C2316yes—
111C22⋊C4×C43C2313yes—
112C42×C43C2311yescharacteristic
113C42×C43C2313yes—
114C42×C43C2313yes—
115C42×C43C2313yes—
116C42×C43C2316yes—
117C42×C43C2313yes—
118C42×C43C2313yes—
119C23×C43C2411yescharacteristic
120C23×C43C2413yes—
121C23×C43C2413yes—
122Q8×C43—26no—
123Q8×C43—43no—
124Q8×C43#4114yes—
125D4×C43—26no—
126D4×C43—26no—
127D4×C43—43no—
128D4×C43—43no—
129D4×C43—43no—
130D4×C43—46no—
131C2×C4×C43—26no—
132C2×C4×C43—26no—
133C2×C4×C43—26no—
134C2×C4×C43—43no—
135C2×C4×C43—46no—
136C2×C4×C43—43no—
137C2×C4×C43C2411yescharacteristic
138C2×C4×C43C2411yescharacteristic
139C2×C4×C43C2411yescharacteristic
140C2×C4×C43C2413yes—
141C2×C4×C43C2411yescharacteristic
142C2×C4×C43C2413yes—
143C2×C4×C43C2411yescharacteristic
144C2×C4×C43C2413yes—
145C2×C4×C43C2413yes—
146C2×C4×C43C2413yes—
147C2×C4×C43C2411yescharacteristic
148C2×C4×C43C2413yes—
149C22×C43—21no—
150C22×C43—23no—
151C22×C43—23no—
152C22×C43—23no—
153C22×C43—23no—
154C22×C43—23no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—23no—
158C22×C43C2511yescharacteristic
159C4×C43—21no—
160C4×C43—21no—
161C4×C43—23no—
162C4×C43—21no—
163C4×C43—23no—
164C4×C43—21no—
165C4×C43—23no—
166C4×C43—23no—
167C4×C43—21no—
168C4×C43—23no—
169C4×C43—21no—
170C4×C43C2×#4116yes—
171#3524C4311yesmaximal, characteristic, direct product factor, Sylow
172C2×C43—41no—
173C2×C43—43no—
174C2×C43—43no—
175C2×C43C22×#4111yescharacteristic
176C2×C43#58511yescharacteristic
177C2×C43#58511yescharacteristic
178#559C2×C4313yescomplemented
179#557C2×C4311yescharacteristic, complemented
180#555C2×C4313yescomplemented
181#553C2×C4313yescomplemented
182#552C2×C4313yescomplemented
183#550C2×C4311yescharacteristic, complemented
184#548C2×C4311yescharacteristic, complemented
185#548C2×C4311yescharacteristic, complemented
186#542C2×C4313yescomplemented
187#540C2×C4313yescomplemented
188#529C2×C4313yescomplemented
189#529C2×C4313yescomplemented
190#520C2×C4311yescharacteristic, complemented
191#519C2×C4311yescharacteristic, complemented
192C4×#41C2×C4311yescharacteristic, complemented
193C43#352411yescharacteristic, direct product factor, Sylow
194C2×#41C22×C4311yescharacteristic
195C2×#41C22×C4311yescharacteristic
196C22×Q8C22×C4311yescharacteristic
197C4⋊Q8C22×C4313yes—
198#127C22×C4313yes—
199#126C22×C4311yescharacteristic
200#126C22×C4313yes—
201#126C22×C4316yes—
202#125C22×C4313yes—
203#125C22×C4313yes—
204#125C22×C4313yes—
205#124C22×C4313yes—
206#124C22×C4313yes—
207#124C22×C4313yes—
208#124C22×C4316yes—
209#123C22×C4316yes—
210#123C22×C4313yes—
211#123C22×C4313yes—
212#123C22×C4316yes—
213C22⋊Q8C22×C4313yes—
214C22⋊Q8C22×C4313yes—
215C22⋊Q8C22×C4313yes—
216#121C22×C4313yes—
217#121C22×C4313yes—
218#121C22×C4313yes—
219#121C22×C4313yes—
220#121C22×C4316yes—
221#121C22×C4313yes—
222C4×Q8C22×C4311yescharacteristic
223C4×Q8C22×C4311yescharacteristic
224C4×Q8C22×C4313yes—
225C4×Q8C22×C4311yescharacteristic
226C4×Q8C22×C4313yes—
227C4×Q8C22×C4311yescharacteristic
228C4×Q8C22×C4313yes—
229C4×D4C22×C4313yes—
230C4×D4C22×C4313yes—
231C4×D4C22×C4313yes—
232C4×D4C22×C4313yes—
233C4×D4C22×C4313yes—
234C4×D4C22×C4313yes—
235C4×D4C22×C4313yes—
236C4×D4C22×C4316yes—
237#117C22×C4313yes—
238#117C22×C4313yes—
239#117C22×C4313yes—
240#117C22×C4313yes—
241#117C22×C4316yes—
242C2×C4⋊C4C22×C4313yes—
243C2×C42C22×C4313yes—
244#41—24no—
245#41—24no—
246C2×Q8—24no—
247C2×Q8C23×C4313yes—
248C2×Q8C23×C4313yes—
249C2×Q8C23×C4311yescharacteristic
250C2×D4C23×C4313yes—
251C2×D4C23×C4313yes—
252C2×D4C23×C4313yes—
253C2×D4C23×C4313yes—
254C2×D4C23×C4316yes—
255C2×D4C23×C4313yes—
256C22×C4C23×C4313yes—
257C22×C4C23×C4313yes—
258C22×C4C23×C4313yes—
259C22×C4C23×C4313yes—
260C22×C4C23×C4313yes—
261C22×C4C23×C4316yes—
262C4⋊C4C23×C4313yes—
263C4⋊C4C23×C4313yes—
264C4⋊C4C23×C4313yes—
265C4⋊C4C23×C4311yescharacteristic
266C4⋊C4C23×C4313yes—
267C4⋊C4C23×C4313yes—
268C4⋊C4C23×C4313yes—
269C4⋊C4C23×C4313yes—
270C4⋊C4C23×C4313yes—
271C4⋊C4C23×C4316yes—
272C4⋊C4C23×C4311yescharacteristic
273C4⋊C4C23×C4313yes—
274C4⋊C4C23×C4313yes—
275C4⋊C4C23×C4311yescharacteristic
276C4⋊C4C23×C4313yes—
277C22⋊C4C23×C4311yescharacteristic
278C22⋊C4C23×C4313yes—
279C22⋊C4C23×C4313yes—
280C22⋊C4C23×C4313yes—
281C22⋊C4C23×C4316yes—
282C22⋊C4C23×C4313yes—
283C22⋊C4C23×C4316yes—
284C22⋊C4C23×C4311yescharacteristic
285C22⋊C4C23×C4313yes—
286C22⋊C4C23×C4311yescharacteristic
287C22⋊C4C23×C4313yes—
288C22⋊C4C23×C4316yes—
289C22⋊C4C23×C4313yes—
290C42C23×C4311yescharacteristic
291C42C23×C4313yes—
292C42C23×C4313yes—
293C42C23×C4313yes—
294C42C23×C4316yes—
295C42C23×C4313yes—
296C42C23×C4313yes—
297C23C24×C4311yescharacteristic
298C23C24×C4313yes—
299C23C24×C4313yes—
300Q8—26no—
301Q8—43no—
302Q8#41×C4314yes—
303D4—26no—
304D4—26no—
305D4—43no—
306D4—43no—
307D4—43no—
308D4—46no—
309C2×C4—26no—
310C2×C4—26no—
311C2×C4—26no—
312C2×C4—43no—
313C2×C4—46no—
314C2×C4—43no—
315C2×C4C24×C4311yescharacteristic
316C2×C4C24×C4311yescharacteristic
317C2×C4C24×C4311yescharacteristic
318C2×C4C24×C4313yes—
319C2×C4C24×C4311yescharacteristic
320C2×C4C24×C4313yes—
321C2×C4C24×C4311yescharacteristic
322C2×C4C24×C4313yes—
323C2×C4C24×C4313yes—
324C2×C4C24×C4313yes—
325C2×C4C24×C4311yescharacteristic
326C2×C4C24×C4313yes—
327C22—21no—
328C22—23no—
329C22—23no—
330C22—23no—
331C22—23no—
332C22—23no—
333C22—21no—
334C22—21no—
335C22—23no—
336C22C25×C4311yescharacteristic
337C4—21no—
338C4—21no—
339C4—23no—
340C4—21no—
341C4—23no—
342C4—21no—
343C4—23no—
344C4—23no—
345C4—21no—
346C4—23no—
347C4—21no—
348C4C2×#41×C4316yes—
349C2—41no—
350C2—43no—
351C2—43no—
352C2C22×#41×C4311yescharacteristic
353C2C43×#58511yescharacteristic
354C2C43×#58511yescharacteristic
subgroupG/H
center, socleC22×C43C25
commutator, Frattini, cosocleC22C25×C43
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#559C2semidirect
2. C43×#557C2semidirect
3. C43×#555C2semidirect
4. C43×#553C2semidirect
5. C43×#552C2semidirect
6. C43×#550C2semidirect
7. C43×#548C2semidirect
8. C43×#548C2semidirect
9. C43×#542C2semidirect
10. C43×#540C2semidirect
11. C43×#529C2semidirect
12. C43×#529C2semidirect
13. C43×#520C2semidirect
14. C43×#519C2semidirect
15. C4×#41×C43C2semidirect
171. #3524C43direct (N × H)
178. #559C2×C43semidirect
179. #557C2×C43semidirect
180. #555C2×C43semidirect
181. #553C2×C43semidirect
182. #552C2×C43semidirect
183. #550C2×C43semidirect
184. #548C2×C43semidirect
185. #548C2×C43semidirect
186. #542C2×C43semidirect
187. #540C2×C43semidirect
188. #529C2×C43semidirect
189. #529C2×C43semidirect
190. #520C2×C43semidirect
191. #519C2×C43semidirect
192. C4×#41C2×C43semidirect
193. C43#3524direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#5592
C43×#5572
C43×#5552
C43×#5532
C43×#5522
C43×#5502
C43×#5482
C43×#5422
C43×#5402
C43×#5292
C43×#5202
C43×#5192
C4×#41×C432
#352443