Finite Group Databasebeta

← C43×#3111 #19131928

Subgroups — C43×#3111 #19131928

Order 5504.

392 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#529C211yesmaximal, characteristic, complemented
2C4×#41×C43C211yesmaximal, characteristic, complemented
3C43×#485C211yesmaximal, characteristic, complemented
4C43×#482C211yesmaximal, characteristic, complemented
5C43×#479C211yesmaximal, characteristic, complemented
6C43×#478C211yesmaximal, characteristic, complemented
7C43×#464C211yesmaximal, characteristic, complemented
8C43×#463C211yesmaximal, characteristic, complemented
9C43×#452C211yesmaximal, characteristic, complemented
10C43×#449C211yesmaximal, characteristic
11C43×#442C211yesmaximal, characteristic, complemented
12C43×#441C211yesmaximal, characteristic, complemented
13C43×#440C211yesmaximal, characteristic, complemented
14C43×#440C211yesmaximal, characteristic, complemented
15C43×#432C211yesmaximal, characteristic, complemented
16C2×#41×C43C2211yescharacteristic
17C2×Q16×C43C2211yescharacteristic
18C2×SD16×C43C2211yescharacteristic
19C2×SD16×C43C2211yescharacteristic
20C2×D8×C43C2211yescharacteristic
21#126×C43—21no—
22#125×C43C2211yescharacteristic
23#124×C43C2211yescharacteristic
24#123×C43—21no—
25C22⋊Q8×C43C2211yescharacteristic
26#121×C43C2211yescharacteristic
27C4×Q8×C43C2211yescharacteristic
28C4×Q8×C43C2211yescharacteristic
29C4×Q8×C43C2211yescharacteristic
30C4×D4×C43—21no—
31C4×D4×C43—21no—
32C4×D4×C43—21no—
33C4×D4×C43C2211yescharacteristic
34C4×D4×C43C2211yescharacteristic
35C4×D4×C43C2211yescharacteristic
36#117×C43—21no—
37#117×C43—21no—
38#117×C43C2211yescharacteristic
39C2×C42×C43—21no—
40C2×C42×C43C2211yescharacteristic
41#107×C43C2211yescharacteristic
42#107×C43C2211yescharacteristic
43#106×C43C2211yescharacteristic
44#106×C43C2211yescharacteristic
45C4⋊C8×C43C2211yescharacteristic
46C4⋊C8×C43C2211yescharacteristic
47#103×C43C2211yescharacteristic
48#103×C43C2211yescharacteristic
49#103×C43C2211yescharacteristic
50#103×C43C2211yescharacteristic
51#102×C43C2211yescharacteristic
52#102×C43C2211yescharacteristic
53#102×C43C2211yescharacteristic
54#102×C43C2211yescharacteristic
55C22⋊C8×C43C2211yescharacteristic
56C22⋊C8×C43C2211yescharacteristic
57#97×C43C2211yescharacteristic
58#97×C43C2211yescharacteristic
59#41×C43—22no—
60#41×C43—22no—
61C2×Q8×C43C2311yescharacteristic
62C2×Q8×C43C2311yescharacteristic
63C2×D4×C43—21no—
64C2×D4×C43—21no—
65C2×D4×C43C2311yescharacteristic
66C2×D4×C43C2311yescharacteristic
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43—21no—
70C22×C4×C43—21no—
71C22×C4×C43D411yescharacteristic
72C22×C4×C43D411yescharacteristic
73C22×C4×C43C2311yescharacteristic
74Q16×C43—22no—
75SD16×C43—22no—
76SD16×C43—22no—
77D8×C43—22no—
78C2×C8×C43C2311yescharacteristic
79C2×C8×C43C2311yescharacteristic
80C2×C8×C43C2311yescharacteristic
81C2×C8×C43C2311yescharacteristic
82C4⋊C4×C43—21no—
83C4⋊C4×C43—21no—
84C4⋊C4×C43—21no—
85C4⋊C4×C43—21no—
86C4⋊C4×C43—21no—
87C4⋊C4×C43—21no—
88C4⋊C4×C43C2311yescharacteristic
89C4⋊C4×C43C2311yescharacteristic
90C4⋊C4×C43C2311yescharacteristic
91C4⋊C4×C43C2311yescharacteristic
92C22⋊C4×C43—21no—
93C22⋊C4×C43—21no—
94C22⋊C4×C43—21no—
95C22⋊C4×C43—21no—
96C22⋊C4×C43—21no—
97C22⋊C4×C43—21no—
98C22⋊C4×C43—21no—
99C22⋊C4×C43—21no—
100C42×C43—21no—
101C42×C43—21no—
102C42×C43—21no—
103C42×C43—21no—
104C42×C43D411yescharacteristic
105C42×C43D411yescharacteristic
106C42×C43C2311yescharacteristic
107C42×C43C2311yescharacteristic
108C23×C43—21no—
109C23×C43—21no—
110C23×C43C2×D411yescharacteristic
111Q8×C43—21no—
112Q8×C43—21no—
113Q8×C43—21no—
114Q8×C43#4112yes—
115D4×C43—24no—
116D4×C43—21no—
117D4×C43—21no—
118D4×C43—21no—
119D4×C43—42no—
120D4×C43#4112yes—
121C2×C4×C43—24no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—42no—
133C2×C4×C43—42no—
134C2×C4×C43—42no—
135C2×C4×C43C2×D411yescharacteristic
136C2×C4×C43C2×D411yescharacteristic
137C2×C4×C43C2×D411yescharacteristic
138C2×C4×C43C2×D411yescharacteristic
139C2×C4×C43C2×D411yescharacteristic
140C2×C4×C43C2411yescharacteristic
141C8×C43—21no—
142C8×C43—21no—
143C8×C43—21no—
144C8×C43—21no—
145C22×C43—22no—
146C22×C43—21no—
147C22×C43—21no—
148C22×C43—21no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43—41no—
152C22×C43—41no—
153C22×C43—41no—
154C22×C43C22×D411yescharacteristic
155C4×C43—21no—
156C4×C43—22no—
157C4×C43—21no—
158C4×C43—21no—
159C4×C43—21no—
160C4×C43—21no—
161C4×C43—41no—
162C4×C43—41no—
163C4×C43—41no—
164C4×C43—41no—
165C4×C43—41no—
166C4×C43C2×#4111yescharacteristic
167C4×C43C2×#4111yescharacteristic
168#3111C4311yesmaximal, characteristic, direct product factor, Sylow
169C2×C43—41no—
170C2×C43—42no—
171C2×C43—81no—
172C2×C43#52511yescharacteristic
173C2×C43#57511yescharacteristic
174C2×C43#57511yescharacteristic
175#529C2×C4311yescharacteristic, complemented
176C4×#41C2×C4311yescharacteristic, complemented
177#485C2×C4311yescharacteristic, complemented
178#482C2×C4311yescharacteristic, complemented
179#479C2×C4311yescharacteristic, complemented
180#478C2×C4311yescharacteristic, complemented
181#464C2×C4311yescharacteristic, complemented
182#463C2×C4311yescharacteristic, complemented
183#452C2×C4311yescharacteristic, complemented
184#449C2×C4311yescharacteristic
185#442C2×C4311yescharacteristic, complemented
186#441C2×C4311yescharacteristic, complemented
187#440C2×C4311yescharacteristic, complemented
188#440C2×C4311yescharacteristic, complemented
189#432C2×C4311yescharacteristic, complemented
190C43#311111yescharacteristic, direct product factor, Sylow
191C2×#41C22×C4311yescharacteristic
192C2×Q16C22×C4311yescharacteristic
193C2×SD16C22×C4311yescharacteristic
194C2×SD16C22×C4311yescharacteristic
195C2×D8C22×C4311yescharacteristic
196#126—21no—
197#125C22×C4311yescharacteristic
198#124C22×C4311yescharacteristic
199#123—21no—
200C22⋊Q8C22×C4311yescharacteristic
201#121C22×C4311yescharacteristic
202C4×Q8C22×C4311yescharacteristic
203C4×Q8C22×C4311yescharacteristic
204C4×Q8C22×C4311yescharacteristic
205C4×D4—21no—
206C4×D4—21no—
207C4×D4—21no—
208C4×D4C22×C4311yescharacteristic
209C4×D4C22×C4311yescharacteristic
210C4×D4C22×C4311yescharacteristic
211#117—21no—
212#117—21no—
213#117C22×C4311yescharacteristic
214C2×C42—21no—
215C2×C42C22×C4311yescharacteristic
216#107C22×C4311yescharacteristic
217#107C22×C4311yescharacteristic
218#106C22×C4311yescharacteristic
219#106C22×C4311yescharacteristic
220C4⋊C8C22×C4311yescharacteristic
221C4⋊C8C22×C4311yescharacteristic
222#103C22×C4311yescharacteristic
223#103C22×C4311yescharacteristic
224#103C22×C4311yescharacteristic
225#103C22×C4311yescharacteristic
226#102C22×C4311yescharacteristic
227#102C22×C4311yescharacteristic
228#102C22×C4311yescharacteristic
229#102C22×C4311yescharacteristic
230C22⋊C8C22×C4311yescharacteristic
231C22⋊C8C22×C4311yescharacteristic
232#97C22×C4311yescharacteristic
233#97C22×C4311yescharacteristic
234#41—22no—
235#41—22no—
236C2×Q8C23×C4311yescharacteristic
237C2×Q8C23×C4311yescharacteristic
238C2×D4—21no—
239C2×D4—21no—
240C2×D4C23×C4311yescharacteristic
241C2×D4C23×C4311yescharacteristic
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4D4×C4311yescharacteristic
247C22×C4D4×C4311yescharacteristic
248C22×C4C23×C4311yescharacteristic
249Q16—22no—
250SD16—22no—
251SD16—22no—
252D8—22no—
253C2×C8C23×C4311yescharacteristic
254C2×C8C23×C4311yescharacteristic
255C2×C8C23×C4311yescharacteristic
256C2×C8C23×C4311yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4C23×C4311yescharacteristic
264C4⋊C4C23×C4311yescharacteristic
265C4⋊C4C23×C4311yescharacteristic
266C4⋊C4C23×C4311yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C42—21no—
276C42—21no—
277C42—21no—
278C42—21no—
279C42D4×C4311yescharacteristic
280C42D4×C4311yescharacteristic
281C42C23×C4311yescharacteristic
282C42C23×C4311yescharacteristic
283C23—21no—
284C23—21no—
285C23C2×D4×C4311yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8#41×C4312yes—
290D4—24no—
291D4—21no—
292D4—21no—
293D4—21no—
294D4—42no—
295D4#41×C4312yes—
296C2×C4—24no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4C2×D4×C4311yescharacteristic
311C2×C4C2×D4×C4311yescharacteristic
312C2×C4C2×D4×C4311yescharacteristic
313C2×C4C2×D4×C4311yescharacteristic
314C2×C4C2×D4×C4311yescharacteristic
315C2×C4C24×C4311yescharacteristic
316C8—21no—
317C8—21no—
318C8—21no—
319C8—21no—
320C22—21no—
321C22—22no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22C22×D4×C4311yescharacteristic
330C4—21no—
331C4—22no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4C2×#41×C4311yescharacteristic
342C4C2×#41×C4311yescharacteristic
343C2—41no—
344C2—42no—
345C2—81no—
346C2C43×#52511yescharacteristic
347C2C43×#57511yescharacteristic
348C2C43×#57511yescharacteristic
subgroupG/H
center, socleC22×C43C22×D4
commutator, Frattini, cosocleC2×C4C24×C43
prime radicalC43×#449C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#529C2semidirect
2. C4×#41×C43C2semidirect
3. C43×#485C2semidirect
4. C43×#482C2semidirect
5. C43×#479C2semidirect
6. C43×#478C2semidirect
7. C43×#464C2semidirect
8. C43×#463C2semidirect
9. C43×#452C2semidirect
11. C43×#442C2semidirect
12. C43×#441C2semidirect
13. C43×#440C2semidirect
14. C43×#440C2semidirect
15. C43×#432C2semidirect
168. #3111C43direct (N × H)
175. #529C2×C43semidirect
176. C4×#41C2×C43semidirect
177. #485C2×C43semidirect
178. #482C2×C43semidirect
179. #479C2×C43semidirect
180. #478C2×C43semidirect
181. #464C2×C43semidirect
182. #463C2×C43semidirect
183. #452C2×C43semidirect
185. #442C2×C43semidirect
186. #441C2×C43semidirect
187. #440C2×C43semidirect
188. #440C2×C43semidirect
189. #432C2×C43semidirect
190. C43#3111direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#5292
C4×#41×C432
C43×#4852
C43×#4822
C43×#4792
C43×#4782
C43×#4642
C43×#4632
C43×#4522
C43×#4492
C43×#4422
C43×#4412
C43×#4402
C43×#4322
#311143