Finite Group Databasebeta

← C43×#33719 #24953736

Subgroups — C43×#33719 #24953736

Order 11008.

834 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
1C2×C43×#510C212yesmaximal, complemented
2C2×C43×#509C212yesmaximal, complemented
3C43×#3147C211yesmaximal, characteristic, complemented
4C2×C43×#495C211yesmaximal, characteristic, complemented
5C43×#2251C212yesmaximal, complemented
6C43×#2250C212yesmaximal, complemented
7C43×#2249C214yesmaximal, complemented
8C4×M32×C43C211yesmaximal, characteristic, complemented
9C2×#135×C43—21no—
10C2×#135×C43C2212yes—
11C22×Q16×C43C2211yescharacteristic
12C22×SD16×C43—21no—
13C22×D8×C43C2211yescharacteristic
14C43×#532—21no—
15C2×#124×C43—21no—
16C43×#510—28no—
17C43×#509—28no—
18C2×Q32×C43C2214yescomplemented
19C2×SD32×C43C2214yes—
20C2×SD32×C43C2214yescomplemented
21C2×D16×C43C2214yes—
22C2×M32×C43C2212yes—
23C43×#495—21no—
24C43×#495—21no—
25C43×#495—21no—
26C43×#495C2212yes—
27C43×#495C2212yes—
28C43×#495C2212yescomplemented
29C43×#494C2211yescharacteristic, complemented
30C43×#493C2211yescharacteristic, complemented
31C43×#492—21no—
32C2×C4×C8×C43C2211yescharacteristic
33C43×#346C2212yescomplemented
34C4×C16×C43C2212yescomplemented
35C2×#41×C43—22no—
36C22×Q8×C43—21no—
37C22×D4×C43—21no—
38#135×C43—24no—
39#135×C43—24no—
40#135×C43—44no—
41C2×Q16×C43—24no—
42C2×Q16×C43—21no—
43C2×Q16×C43—21no—
44C2×Q16×C43C2312yes—
45C2×Q16×C43C2312yes—
46C2×SD16×C43—22no—
47C2×SD16×C43—22no—
48C2×SD16×C43—22no—
49C2×SD16×C43—22no—
50C2×SD16×C43—44no—
51C2×D8×C43—24no—
52C2×D8×C43—21no—
53C2×D8×C43—21no—
54C2×D8×C43C2312yes—
55C2×D8×C43C2312yes—
56C22×C8×C43D411yescharacteristic
57C22×C8×C43C2311yescharacteristic
58C4⋊Q8×C43—21no—
59#127×C43—21no—
60#124×C43—22no—
61#124×C43—22no—
62#124×C43—22no—
63#124×C43—42no—
64#121×C43—42no—
65C4×D4×C43—42no—
66C2×C22⋊C4×C43—42no—
67C2×C42×C43D411yescharacteristic
68Q32×C43—28no—
69SD32×C43—28no—
70SD32×C43—28no—
71D16×C43—28no—
72M32×C43D418yescomplemented
73C2×C16×C43C2314yes—
74C4×C8×C43D411yescharacteristic
75C4×C8×C43D411yescharacteristic
76C4×C8×C43C2311yescharacteristic
77C4×C8×C43C2311yescharacteristic
78C24×C43—41no—
79#41×C43—44no—
80#41×C43—44no—
81C2×Q8×C43—22no—
82C2×Q8×C43—22no—
83C2×Q8×C43—41no—
84C2×Q8×C43—42no—
85C2×Q8×C43—42no—
86C2×D4×C43—22no—
87C2×D4×C43—22no—
88C2×D4×C43—42no—
89C2×D4×C43—41no—
90C2×D4×C43—42no—
91C2×D4×C43—42no—
92C2×D4×C43—42no—
93C22×C4×C43—42no—
94C22×C4×C43—41no—
95C22×C4×C43D812yes—
96C22×C4×C43C2×D411yescharacteristic
97Q16×C43—22no—
98Q16×C43—24no—
99Q16×C43—22no—
100Q16×C43—42no—
101Q16×C43—42no—
102SD16×C43—44no—
103SD16×C43—44no—
104SD16×C43—44no—
105SD16×C43—44no—
106D8×C43—22no—
107D8×C43—24no—
108D8×C43—22no—
109D8×C43—42no—
110D8×C43—42no—
111C2×C8×C43D814yes—
112C2×C8×C43C2×D411yescharacteristic
113C2×C8×C43C2×D414yes—
114C2×C8×C43C2×D411yescharacteristic
115C2×C8×C43C2×D411yescharacteristic
116C2×C8×C43C2411yescharacteristic
117C4⋊C4×C43—42no—
118C22⋊C4×C43—44no—
119C22⋊C4×C43—44no—
120C22⋊C4×C43—44no—
121C42×C43D812yes—
122C42×C43C2×D411yescharacteristic
123C42×C43C2×D411yescharacteristic
124C16×C43C2×D418yes—
125C23×C43—42no—
126C23×C43—42no—
127C23×C43—84no—
128C23×C43—82no—
129C23×C43C2×D811yescharacteristic
130Q8×C43—42no—
131Q8×C43—42no—
132Q8×C43—42no—
133Q8×C43—42no—
134Q8×C43—82no—
135D4×C43—42no—
136D4×C43—42no—
137D4×C43—42no—
138D4×C43—42no—
139D4×C43—84no—
140D4×C43—84no—
141D4×C43—82no—
142C2×C4×C43—42no—
143C2×C4×C43—42no—
144C2×C4×C43—42no—
145C2×C4×C43—82no—
146C2×C4×C43—84no—
147C2×C4×C43#12712yes—
148C2×C4×C43C2×D812yes—
149C2×C4×C43C2×D812yes—
150C2×C4×C43C2×D812yes—
151C2×C4×C43C2×D811yescharacteristic
152C2×C4×C43C22×D411yescharacteristic
153C8×C43#12712yes—
154C8×C43C2×D812yes—
155C8×C43C2×D812yes—
156C8×C43C22×D412yes—
157#33719C4311yesmaximal, characteristic, direct product factor, Sylow
158C22×C43—22no—
159C22×C43—82no—
160C22×C43—82no—
161C22×C43—84no—
162C22×C43—84no—
163C22×C43—164no—
164C22×C43#49312yes—
165C22×C43C22×D811yescharacteristic
166C4×C43—22no—
167C4×C43—22no—
168C4×C43—82no—
169C4×C43—82no—
170C4×C43#49312yes—
171C4×C43C2×#12711yescharacteristic
172C4×C43C22×D811yescharacteristic
173C2×#510C2×C4312yescomplemented
174C2×#509C2×C4312yescomplemented
175#3147C2×C4311yescharacteristic, complemented
176C2×#495C2×C4311yescharacteristic, complemented
177#2251C2×C4312yescomplemented
178#2250C2×C4312yescomplemented
179#2249C2×C4314yescomplemented
180C4×M32C2×C4311yescharacteristic, complemented
181C2×C43—22no—
182C2×C43—162no—
183C2×C43—162no—
184C2×C43C2×#49311yescharacteristic
185C2×C43#341412yes—
186C2×#135—21no—
187C2×#135C22×C4312yes—
188C22×Q16C22×C4311yescharacteristic
189C22×SD16—21no—
190C22×D8C22×C4311yescharacteristic
191#532—21no—
192C2×#124—21no—
193#510—28no—
194#509—28no—
195C2×Q32C22×C4314yescomplemented
196C2×SD32C22×C4314yes—
197C2×SD32C22×C4314yescomplemented
198C2×D16C22×C4314yes—
199C2×M32C22×C4312yes—
200#495—21no—
201#495—21no—
202#495—21no—
203#495C22×C4312yes—
204#495C22×C4312yes—
205#495C22×C4312yescomplemented
206#494C22×C4311yescharacteristic, complemented
207#493C22×C4311yescharacteristic, complemented
208#492—21no—
209C2×C4×C8C22×C4311yescharacteristic
210#346C22×C4312yescomplemented
211C4×C16C22×C4312yescomplemented
212C43#3371911yescharacteristic, direct product factor, Sylow
213C2×#41—22no—
214C22×Q8—21no—
215C22×D4—21no—
216#135—24no—
217#135—24no—
218#135—44no—
219C2×Q16—24no—
220C2×Q16—21no—
221C2×Q16—21no—
222C2×Q16C23×C4312yes—
223C2×Q16C23×C4312yes—
224C2×SD16—22no—
225C2×SD16—22no—
226C2×SD16—22no—
227C2×SD16—22no—
228C2×SD16—44no—
229C2×D8—24no—
230C2×D8—21no—
231C2×D8—21no—
232C2×D8C23×C4312yes—
233C2×D8C23×C4312yes—
234C22×C8D4×C4311yescharacteristic
235C22×C8C23×C4311yescharacteristic
236C4⋊Q8—21no—
237#127—21no—
238#124—22no—
239#124—22no—
240#124—22no—
241#124—42no—
242#121—42no—
243C4×D4—42no—
244C2×C22⋊C4—42no—
245C2×C42D4×C4311yescharacteristic
246Q32—28no—
247SD32—28no—
248SD32—28no—
249D16—28no—
250M32D4×C4318yescomplemented
251C2×C16C23×C4314yes—
252C4×C8D4×C4311yescharacteristic
253C4×C8D4×C4311yescharacteristic
254C4×C8C23×C4311yescharacteristic
255C4×C8C23×C4311yescharacteristic
256C24—41no—
257#41—44no—
258#41—44no—
259C2×Q8—22no—
260C2×Q8—22no—
261C2×Q8—41no—
262C2×Q8—42no—
263C2×Q8—42no—
264C2×D4—22no—
265C2×D4—22no—
266C2×D4—42no—
267C2×D4—42no—
268C2×D4—42no—
269C2×D4—42no—
270C2×D4—41no—
271C22×C4—41no—
272C22×C4—42no—
273C22×C4D8×C4312yes—
274C22×C4C2×D4×C4311yescharacteristic
275Q16—22no—
276Q16—24no—
277Q16—22no—
278Q16—42no—
279Q16—42no—
280SD16—44no—
281SD16—44no—
282SD16—44no—
283SD16—44no—
284D8—22no—
285D8—24no—
286D8—22no—
287D8—42no—
288D8—42no—
289C2×C8D8×C4314yes—
290C2×C8C2×D4×C4311yescharacteristic
291C2×C8C2×D4×C4314yes—
292C2×C8C2×D4×C4311yescharacteristic
293C2×C8C2×D4×C4311yescharacteristic
294C2×C8C24×C4311yescharacteristic
295C4⋊C4—42no—
296C22⋊C4—44no—
297C22⋊C4—44no—
298C22⋊C4—44no—
299C42D8×C4312yes—
300C42C2×D4×C4311yescharacteristic
301C42C2×D4×C4311yescharacteristic
302C16C2×D4×C4318yes—
303C23—42no—
304C23—42no—
305C23—84no—
306C23—82no—
307C23C2×D8×C4311yescharacteristic
308Q8—42no—
309Q8—42no—
310Q8—42no—
311Q8—42no—
312Q8—82no—
313D4—42no—
314D4—42no—
315D4—42no—
316D4—42no—
317D4—84no—
318D4—84no—
319D4—82no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—82no—
324C2×C4—84no—
325C2×C4#127×C4312yes—
326C2×C4C2×D8×C4312yes—
327C2×C4C2×D8×C4312yes—
328C2×C4C2×D8×C4312yes—
329C2×C4C2×D8×C4311yescharacteristic
330C2×C4C22×D4×C4311yescharacteristic
331C8#127×C4312yes—
332C8C2×D8×C4312yes—
333C8C2×D8×C4312yes—
334C8C22×D4×C4312yes—
335C22—22no—
336C22—82no—
337C22—82no—
338C22—84no—
339C22—84no—
340C22—164no—
341C22C43×#49312yes—
342C22C22×D8×C4311yescharacteristic
343C4—22no—
344C4—22no—
345C4—82no—
346C4—82no—
347C4C43×#49312yes—
348C4C2×#127×C4311yescharacteristic
349C4C22×D8×C4311yescharacteristic
350C2—22no—
351C2—162no—
352C2—162no—
353C2C2×C43×#49311yescharacteristic
354C2C43×#341412yes—
subgroupG/H
center, socleC22×C43C22×D8
commutator, Frattini, cosocleC2×C8C24×C43
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ C2×C4×C8×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#510C2semidirect
2. C2×C43×#509C2semidirect
3. C43×#3147C2semidirect
4. C2×C43×#495C2semidirect
5. C43×#2251C2semidirect
6. C43×#2250C2semidirect
7. C43×#2249C2semidirect
8. C4×M32×C43C2semidirect
18. C2×Q32×C43C22semidirect
20. C2×SD32×C43C22semidirect
28. C43×#495C22semidirect
29. C43×#494C22semidirect
30. C43×#493C22semidirect
33. C43×#346C22semidirect
34. C4×C16×C43C22semidirect
72. M32×C43D4semidirect
157. #33719C43direct (N × H)
173. C2×#510C2×C43semidirect
174. C2×#509C2×C43semidirect
175. #3147C2×C43semidirect
176. C2×#495C2×C43semidirect
177. #2251C2×C43semidirect
178. #2250C2×C43semidirect
179. #2249C2×C43semidirect
180. C4×M32C2×C43semidirect
195. C2×Q32C22×C43semidirect
197. C2×SD32C22×C43semidirect
205. #495C22×C43semidirect
206. #494C22×C43semidirect
207. #493C22×C43semidirect
210. #346C22×C43semidirect
211. C4×C16C22×C43semidirect
212. C43#33719direct (N × H)
250. M32D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#5102
C2×C43×#5092
C43×#31472
C2×C43×#4952
C43×#22512
C43×#22502
C43×#22492
C4×M32×C432
#3371943