Finite Group Databasebeta

← C43×#3323 #19132140

Subgroups — C43×#3323 #19132140

Order 5504.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#552C211yesmaximal, characteristic, complemented
2C43×#546C211yesmaximal, characteristic
3C43×#488C211yesmaximal, characteristic, complemented
4C43×#485C211yesmaximal, characteristic, complemented
5C43×#481C211yesmaximal, characteristic, complemented
6C43×#478C211yesmaximal, characteristic, complemented
7C43×#470C211yesmaximal, characteristic, complemented
8C43×#468C211yesmaximal, characteristic, complemented
9C43×#464C211yesmaximal, characteristic, complemented
10C43×#452C211yesmaximal, characteristic, complemented
11C43×#450C211yesmaximal, characteristic, complemented
12C4×SD16×C43C211yesmaximal, characteristic, complemented
13C43×#436C211yesmaximal, characteristic, complemented
14C43×#418C211yesmaximal, characteristic, complemented
15C43×#417C211yesmaximal, characteristic, complemented
16C2×#41×C43C2211yescharacteristic
17C22×D4×C43C2211yescharacteristic
18C2×Q16×C43C2211yescharacteristic, complemented
19C2×SD16×C43C2211yescharacteristic
20C2×SD16×C43C2211yescharacteristic
21C2×M16×C43C2211yescharacteristic
22C2×M16×C43C2211yescharacteristic, complemented
23#126×C43—21no—
24#125×C43—21no—
25#125×C43C2211yescharacteristic, complemented
26#124×C43C2211yescharacteristic
27#123×C43—21no—
28#123×C43—21no—
29C22⋊Q8×C43C2211yescharacteristic
30C22⋊Q8×C43C2211yescharacteristic
31C22⋊Q8×C43C2211yescharacteristic, complemented
32#121×C43—21no—
33#121×C43C2211yescharacteristic
34#120×C43—21no—
35C4×Q8×C43C2211yescharacteristic, complemented
36C4×D4×C43C2211yescharacteristic
37C4×D4×C43C2211yescharacteristic
38#117×C43—21no—
39#117×C43C2211yescharacteristic
40C2×C4⋊C4×C43C2211yescharacteristic, complemented
41C2×C22⋊C4×C43—21no—
42#107×C43C2211yescharacteristic, complemented
43#106×C43C2211yescharacteristic, complemented
44#106×C43C2211yescharacteristic, complemented
45C4⋊C8×C43C2211yescharacteristic, complemented
46#103×C43C2211yescharacteristic, complemented
47#103×C43C2211yescharacteristic, complemented
48#103×C43C2211yescharacteristic, complemented
49#103×C43C2211yescharacteristic, complemented
50#102×C43C2211yescharacteristic
51#102×C43C2211yescharacteristic
52#102×C43C2211yescharacteristic
53#102×C43C2211yescharacteristic
54#102×C43C2211yescharacteristic
55#102×C43C2211yescharacteristic
56C22⋊C8×C43C2211yescharacteristic
57C22⋊C8×C43C2211yescharacteristic, complemented
58C4×C8×C43C2211yescharacteristic, complemented
59C24×C43—21no—
60#41×C43—22no—
61#41×C43—41no—
62C2×Q8×C43C2311yescharacteristic
63C2×Q8×C43C2311yescharacteristic
64C2×D4×C43—21no—
65C2×D4×C43—21no—
66C2×D4×C43—21no—
67C2×D4×C43—22no—
68C2×D4×C43—41no—
69C2×D4×C43D411yescharacteristic
70C2×D4×C43C2311yescharacteristic
71C2×D4×C43C2311yescharacteristic
72C22×C4×C43—21no—
73C22×C4×C43—21no—
74C22×C4×C43—21no—
75C22×C4×C43C2311yescharacteristic
76C22×C4×C43C2311yescharacteristic
77Q16×C43—41no—
78SD16×C43—22no—
79SD16×C43—41no—
80M16×C43—41no—
81M16×C43—41no—
82C2×C8×C43C2311yescharacteristic
83C2×C8×C43C2311yescharacteristic
84C2×C8×C43C2311yescharacteristic
85C2×C8×C43C2311yescharacteristic
86C4⋊C4×C43—21no—
87C4⋊C4×C43—21no—
88C4⋊C4×C43—21no—
89C4⋊C4×C43—21no—
90C4⋊C4×C43—21no—
91C4⋊C4×C43—21no—
92C4⋊C4×C43—21no—
93C4⋊C4×C43D411yescharacteristic
94C4⋊C4×C43C2311yescharacteristic
95C4⋊C4×C43C2311yescharacteristic
96C4⋊C4×C43C2311yescharacteristic
97C4⋊C4×C43C2311yescharacteristic
98C22⋊C4×C43—21no—
99C22⋊C4×C43—21no—
100C22⋊C4×C43—21no—
101C22⋊C4×C43—21no—
102C22⋊C4×C43—21no—
103C22⋊C4×C43—21no—
104C22⋊C4×C43—21no—
105C22⋊C4×C43—21no—
106C22⋊C4×C43D411yescharacteristic
107C22⋊C4×C43D411yescharacteristic
108C42×C43—21no—
109C42×C43—21no—
110C42×C43C2311yescharacteristic
111C23×C43—21no—
112C23×C43—21no—
113C23×C43—42no—
114C23×C43—42no—
115C23×C43—81no—
116C23×C43C2×D411yescharacteristic
117C23×C43C2×D411yescharacteristic
118Q8×C43—21no—
119Q8×C43—21no—
120Q8×C43—21no—
121Q8×C43—21no—
122D4×C43—21no—
123D4×C43—21no—
124D4×C43—21no—
125D4×C43—41no—
126D4×C43—42no—
127D4×C43—42no—
128D4×C43—81no—
129D4×C43#4112yes—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—42no—
141C2×C4×C43—42no—
142C2×C4×C43—81no—
143C2×C4×C43C2×D411yescharacteristic
144C2×C4×C43C2×D411yescharacteristic
145C2×C4×C43C2×D411yescharacteristic
146C2×C4×C43C2×D411yescharacteristic
147C2×C4×C43C2411yescharacteristic
148C8×C43—21no—
149C8×C43—21no—
150C8×C43—21no—
151C8×C43—21no—
152C22×C43—22no—
153C22×C43—21no—
154C22×C43—21no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—21no—
159C22×C43—41no—
160C22×C43—41no—
161C22×C43—41no—
162C22×C43—41no—
163C22×C43—41no—
164C22×C43—84no—
165C22×C43C22×D411yescharacteristic
166C4×C43—21no—
167C4×C43—21no—
168C4×C43—21no—
169C4×C43—21no—
170C4×C43—41no—
171C4×C43—41no—
172C4×C43—41no—
173C4×C43—41no—
174C4×C43—41no—
175C4×C43—41no—
176C4×C43C2×#4111yescharacteristic
177C4×C43H(5,𝔽2)11yescharacteristic
178#3323C4311yesmaximal, characteristic, direct product factor, Sylow
179C2×C43—41no—
180C2×C43—41no—
181C2×C43—42no—
182C2×C43—81no—
183C2×C43#54611yescharacteristic
184C2×C43#57511yescharacteristic
185C2×C43#57711yescharacteristic
186#552C2×C4311yescharacteristic, complemented
187#546C2×C4311yescharacteristic
188#488C2×C4311yescharacteristic, complemented
189#485C2×C4311yescharacteristic, complemented
190#481C2×C4311yescharacteristic, complemented
191#478C2×C4311yescharacteristic, complemented
192#470C2×C4311yescharacteristic, complemented
193#468C2×C4311yescharacteristic, complemented
194#464C2×C4311yescharacteristic, complemented
195#452C2×C4311yescharacteristic, complemented
196#450C2×C4311yescharacteristic, complemented
197C4×SD16C2×C4311yescharacteristic, complemented
198#436C2×C4311yescharacteristic, complemented
199#418C2×C4311yescharacteristic, complemented
200#417C2×C4311yescharacteristic, complemented
201C43#332311yescharacteristic, direct product factor, Sylow
202C2×#41C22×C4311yescharacteristic
203C22×D4C22×C4311yescharacteristic
204C2×Q16C22×C4311yescharacteristic, complemented
205C2×SD16C22×C4311yescharacteristic
206C2×SD16C22×C4311yescharacteristic
207C2×M16C22×C4311yescharacteristic
208C2×M16C22×C4311yescharacteristic, complemented
209#126—21no—
210#125—21no—
211#125C22×C4311yescharacteristic, complemented
212#124C22×C4311yescharacteristic
213#123—21no—
214#123—21no—
215C22⋊Q8C22×C4311yescharacteristic
216C22⋊Q8C22×C4311yescharacteristic
217C22⋊Q8C22×C4311yescharacteristic, complemented
218#121—21no—
219#121C22×C4311yescharacteristic
220#120—21no—
221C4×Q8C22×C4311yescharacteristic, complemented
222C4×D4C22×C4311yescharacteristic
223C4×D4C22×C4311yescharacteristic
224#117—21no—
225#117C22×C4311yescharacteristic
226C2×C4⋊C4C22×C4311yescharacteristic, complemented
227C2×C22⋊C4—21no—
228#107C22×C4311yescharacteristic, complemented
229#106C22×C4311yescharacteristic, complemented
230#106C22×C4311yescharacteristic, complemented
231C4⋊C8C22×C4311yescharacteristic, complemented
232#103C22×C4311yescharacteristic, complemented
233#103C22×C4311yescharacteristic, complemented
234#103C22×C4311yescharacteristic, complemented
235#103C22×C4311yescharacteristic, complemented
236#102C22×C4311yescharacteristic
237#102C22×C4311yescharacteristic
238#102C22×C4311yescharacteristic
239#102C22×C4311yescharacteristic
240#102C22×C4311yescharacteristic
241#102C22×C4311yescharacteristic
242C22⋊C8C22×C4311yescharacteristic
243C22⋊C8C22×C4311yescharacteristic, complemented
244C4×C8C22×C4311yescharacteristic, complemented
245C24—21no—
246#41—22no—
247#41—41no—
248C2×Q8C23×C4311yescharacteristic
249C2×Q8C23×C4311yescharacteristic
250C2×D4—22no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—41no—
255C2×D4D4×C4311yescharacteristic
256C2×D4C23×C4311yescharacteristic
257C2×D4C23×C4311yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4C23×C4311yescharacteristic
262C22×C4C23×C4311yescharacteristic
263Q16—41no—
264SD16—22no—
265SD16—41no—
266M16—41no—
267M16—41no—
268C2×C8C23×C4311yescharacteristic
269C2×C8C23×C4311yescharacteristic
270C2×C8C23×C4311yescharacteristic
271C2×C8C23×C4311yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4D4×C4311yescharacteristic
280C4⋊C4C23×C4311yescharacteristic
281C4⋊C4C23×C4311yescharacteristic
282C4⋊C4C23×C4311yescharacteristic
283C4⋊C4C23×C4311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4D4×C4311yescharacteristic
293C22⋊C4D4×C4311yescharacteristic
294C42—21no—
295C42—21no—
296C42C23×C4311yescharacteristic
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23C2×D4×C4311yescharacteristic
303C23C2×D4×C4311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—21no—
308D4—21no—
309D4—21no—
310D4—21no—
311D4—41no—
312D4—42no—
313D4—42no—
314D4—81no—
315D4#41×C4312yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—81no—
329C2×C4C2×D4×C4311yescharacteristic
330C2×C4C2×D4×C4311yescharacteristic
331C2×C4C2×D4×C4311yescharacteristic
332C2×C4C2×D4×C4311yescharacteristic
333C2×C4C24×C4311yescharacteristic
334C8—21no—
335C8—21no—
336C8—21no—
337C8—21no—
338C22—21no—
339C22—21no—
340C22—22no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—84no—
351C22C22×D4×C4311yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4C2×#41×C4311yescharacteristic
363C4H(5,𝔽2)×C4311yescharacteristic
364C2—41no—
365C2—41no—
366C2—42no—
367C2—81no—
368C2C43×#54611yescharacteristic
369C2C43×#57511yescharacteristic
370C2C43×#57711yescharacteristic
subgroupG/H
center, socleC22×C43C22×D4
commutator, Frattini, cosocleC2×C4C24×C43
prime radicalC43×#546C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C4×D4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#552C2semidirect
3. C43×#488C2semidirect
4. C43×#485C2semidirect
5. C43×#481C2semidirect
6. C43×#478C2semidirect
7. C43×#470C2semidirect
8. C43×#468C2semidirect
9. C43×#464C2semidirect
10. C43×#452C2semidirect
11. C43×#450C2semidirect
12. C4×SD16×C43C2semidirect
13. C43×#436C2semidirect
14. C43×#418C2semidirect
15. C43×#417C2semidirect
18. C2×Q16×C43C22semidirect
22. C2×M16×C43C22semidirect
25. #125×C43C22semidirect
31. C22⋊Q8×C43C22semidirect
35. C4×Q8×C43C22semidirect
40. C2×C4⋊C4×C43C22semidirect
42. #107×C43C22semidirect
43. #106×C43C22semidirect
44. #106×C43C22semidirect
45. C4⋊C8×C43C22semidirect
46. #103×C43C22semidirect
47. #103×C43C22semidirect
48. #103×C43C22semidirect
49. #103×C43C22semidirect
57. C22⋊C8×C43C22semidirect
58. C4×C8×C43C22semidirect
178. #3323C43direct (N × H)
186. #552C2×C43semidirect
188. #488C2×C43semidirect
189. #485C2×C43semidirect
190. #481C2×C43semidirect
191. #478C2×C43semidirect
192. #470C2×C43semidirect
193. #468C2×C43semidirect
194. #464C2×C43semidirect
195. #452C2×C43semidirect
196. #450C2×C43semidirect
197. C4×SD16C2×C43semidirect
198. #436C2×C43semidirect
199. #418C2×C43semidirect
200. #417C2×C43semidirect
201. C43#3323direct (N × H)
204. C2×Q16C22×C43semidirect
208. C2×M16C22×C43semidirect
211. #125C22×C43semidirect
217. C22⋊Q8C22×C43semidirect
221. C4×Q8C22×C43semidirect
226. C2×C4⋊C4C22×C43semidirect
228. #107C22×C43semidirect
229. #106C22×C43semidirect
230. #106C22×C43semidirect
231. C4⋊C8C22×C43semidirect
232. #103C22×C43semidirect
233. #103C22×C43semidirect
234. #103C22×C43semidirect
235. #103C22×C43semidirect
243. C22⋊C8C22×C43semidirect
244. C4×C8C22×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#5522
C43×#5462
C43×#4882
C43×#4852
C43×#4812
C43×#4782
C43×#4702
C43×#4682
C43×#4642
C43×#4522
C43×#4502
C4×SD16×C432
C43×#4362
C43×#4182
C43×#4172
#332343