Finite Group Databasebeta

← C43×#10284 #24930301

Subgroups — C43×#10284 #24930301

Order 11008.

678 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3226C211yesmaximal, characteristic, complemented
2C43×#3205C211yesmaximal, characteristic
3C43×#2858C211yesmaximal, characteristic, complemented
4C43×#1962C211yesmaximal, characteristic, complemented
5C43×#1546C211yesmaximal, characteristic, complemented
6C43×#1545C211yesmaximal, characteristic, complemented
7C43×#1276C211yesmaximal, characteristic, complemented
8C43×#532C2211yescharacteristic
9C2×C4⋊Q8×C43C2211yescharacteristic
10C2×#127×C43C2211yescharacteristic
11C2×#124×C43—22no—
12C43×#500—21no—
13C43×#493—21no—
14C43×#486—21no—
15C43×#486—21no—
16C43×#480—22no—
17C43×#474—22no—
18C43×#459—22no—
19C43×#447—22no—
20C43×#431C2211yescharacteristic
21C43×#431C2211yescharacteristic
22C43×#423C2211yescharacteristic
23C2×#104×C43—22no—
24C43×#390—22no—
25C43×#390—22no—
26C43×C43C2211yescharacteristic
27C43×#332—22no—
28C43×#331—22no—
29C2×#41×C43—21no—
30C22×Q8×C43—21no—
31C22×D4×C43—21no—
32C22×D4×C43—21no—
33C22×D4×C43D412yes—
34C2×D8×C43—24no—
35C2×M16×C43—21no—
36C4⋊Q8×C43—21no—
37C4⋊Q8×C43—21no—
38C4⋊Q8×C43—21no—
39C4⋊Q8×C43—21no—
40C4⋊Q8×C43D411yescharacteristic
41#127×C43—21no—
42#127×C43—21no—
43#127×C43—21no—
44#127×C43—21no—
45#127×C43D411yescharacteristic
46#124×C43—21no—
47#124×C43—44no—
48#124×C43—44no—
49#121×C43—21no—
50#121×C43—21no—
51C4×D4×C43—21no—
52C4×D4×C43—21no—
53C2×C4⋊C4×C43—21no—
54C2×C4⋊C4×C43D412yes—
55C2×C22⋊C4×C43—28no—
56C2×C42×C43—21no—
57C2×C42×C43—21no—
58C2×C42×C43D412yes—
59C2×C42×C43C2311yescharacteristic
60#107×C43—24no—
61C4⋊C8×C43—21no—
62C4⋊C8×C43—21no—
63C4⋊C8×C43D412yes—
64C4⋊C8×C43D412yes—
65#104×C43—44no—
66#102×C43—24no—
67#102×C43—24no—
68C22⋊C8×C43—21no—
69C22⋊C8×C43—21no—
70C4×C8×C43—21no—
71C4×C8×C43—21no—
72C24×C43—22no—
73#41×C43—42no—
74#41×C43—42no—
75C2×Q8×C43—21no—
76C2×Q8×C43—41no—
77C2×Q8×C43—41no—
78C2×Q8×C43—42no—
79C2×Q8×C43—42no—
80C2×D4×C43—21no—
81C2×D4×C43—22no—
82C2×D4×C43—21no—
83C2×D4×C43—21no—
84C2×D4×C43—22no—
85C2×D4×C43—44no—
86C2×D4×C43—44no—
87C2×D4×C43—41no—
88C2×D4×C43—41no—
89C2×D4×C43—41no—
90C2×D4×C43—41no—
91C2×D4×C43—42no—
92C2×D4×C43—42no—
93C2×D4×C43—41no—
94C22×C4×C43—22no—
95C22×C4×C43—22no—
96C22×C4×C43—41no—
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43C2×D411yescharacteristic
100D8×C43—84no—
101M16×C43—42no—
102C2×C8×C43—22no—
103C2×C8×C43—22no—
104C2×C8×C43—41no—
105C4⋊C4×C43—21no—
106C4⋊C4×C43—22no—
107C4⋊C4×C43—21no—
108C4⋊C4×C43—22no—
109C4⋊C4×C43—41no—
110C4⋊C4×C43—41no—
111C22⋊C4×C43—416no—
112C22⋊C4×C43—41no—
113C22⋊C4×C43—41no—
114C42×C43—22no—
115C42×C43—42no—
116C42×C43—42no—
117C42×C43D814yescomplemented
118C42×C43C2×D411yescharacteristic
119C42×C43C2×D411yescharacteristic
120C42×C43C2×D411yescharacteristic
121C42×C43#4111yescharacteristic
122C23×C43—44no—
123C23×C43—44no—
124C23×C43—41no—
125C23×C43—42no—
126C23×C43—44no—
127C23×C43#12011yescharacteristic
128Q8×C43—42no—
129Q8×C43—82no—
130Q8×C43—81no—
131Q8×C43—81no—
132D4×C43—42no—
133D4×C43—42no—
134D4×C43—44no—
135D4×C43—42no—
136D4×C43—82no—
137D4×C43—82no—
138D4×C43—82no—
139D4×C43—82no—
140D4×C43—82no—
141D4×C43—81no—
142D4×C43—81no—
143C2×C4×C43—22no—
144C2×C4×C43—22no—
145C2×C4×C43—24no—
146C2×C4×C43—42no—
147C2×C4×C43—42no—
148C2×C4×C43—41no—
149C2×C4×C43—42no—
150C2×C4×C43—44no—
151C2×C4×C43—81no—
152C2×C4×C43—81no—
153C2×C4×C43#12011yescharacteristic
154C2×C4×C43#12011yescharacteristic
155C2×C4×C43#12111yescharacteristic
156C2×C4×C43#12111yescharacteristic
157C2×C4×C43#12111yescharacteristic
158C2×C4×C43#12711yescharacteristic
159C2×C4×C43C2×D812yes—
160C2×C4×C43AGL(1,ℤ/8)12yes—
161C8×C43—42no—
162C8×C43—42no—
163C8×C43—81no—
164#10284C4311yesmaximal, characteristic, direct product factor, Sylow
165C22×C43—21no—
166C22×C43—21no—
167C22×C43—88no—
168C22×C43—82no—
169C22×C43—81no—
170C22×C43—82no—
171C22×C43—81no—
172C22×C43—82no—
173C22×C43—81no—
174C22×C43#39211yescharacteristic
175C22×C43#44712yes—
176C4×C43—21no—
177C4×C43—21no—
178C4×C43—44no—
179C4×C43—82no—
180C4×C43—81no—
181C4×C43#45412yes—
182C4×C43#45512yes—
183C4×C43#45912yes—
184C4×C43#49311yescharacteristic
185C4×C43#49611yescharacteristic
186#3226C2×C4311yescharacteristic, complemented
187#3205C2×C4311yescharacteristic
188#2858C2×C4311yescharacteristic, complemented
189#1962C2×C4311yescharacteristic, complemented
190#1546C2×C4311yescharacteristic, complemented
191#1545C2×C4311yescharacteristic, complemented
192#1276C2×C4311yescharacteristic, complemented
193C2×C43—22no—
194C2×C43—161no—
195C2×C43—162no—
196C2×C43#200311yescharacteristic
197C2×C43#200411yescharacteristic
198C2×C43#201111yescharacteristic
199#532C22×C4311yescharacteristic
200C2×C4⋊Q8C22×C4311yescharacteristic
201C2×#127C22×C4311yescharacteristic
202C2×#124—22no—
203#500—21no—
204#493—21no—
205#486—21no—
206#486—21no—
207#480—22no—
208#474—22no—
209#459—22no—
210#447—22no—
211#431C22×C4311yescharacteristic
212#431C22×C4311yescharacteristic
213#423C22×C4311yescharacteristic
214C2×#104—22no—
215#390—22no—
216#390—22no—
217C43C22×C4311yescharacteristic
218#332—22no—
219#331—22no—
220C43#1028411yescharacteristic, direct product factor, Sylow
221C2×#41—21no—
222C22×Q8—21no—
223C22×D4—21no—
224C22×D4—21no—
225C22×D4D4×C4312yes—
226C2×D8—24no—
227C2×M16—21no—
228C4⋊Q8—21no—
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8D4×C4311yescharacteristic
233#127—21no—
234#127—21no—
235#127—21no—
236#127—21no—
237#127D4×C4311yescharacteristic
238#124—21no—
239#124—44no—
240#124—44no—
241#121—21no—
242#121—21no—
243C4×D4—21no—
244C4×D4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4D4×C4312yes—
247C2×C22⋊C4—28no—
248C2×C42—21no—
249C2×C42—21no—
250C2×C42D4×C4312yes—
251C2×C42C23×C4311yescharacteristic
252#107—24no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8D4×C4312yes—
256C4⋊C8D4×C4312yes—
257#104—44no—
258#102—24no—
259#102—24no—
260C22⋊C8—21no—
261C22⋊C8—21no—
262C4×C8—21no—
263C4×C8—21no—
264C24—22no—
265#41—42no—
266#41—42no—
267C2×Q8—21no—
268C2×Q8—41no—
269C2×Q8—41no—
270C2×Q8—42no—
271C2×Q8—42no—
272C2×D4—21no—
273C2×D4—22no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4—22no—
277C2×D4—44no—
278C2×D4—44no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—41no—
282C2×D4—41no—
283C2×D4—41no—
284C2×D4—42no—
285C2×D4—42no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—41no—
289C22×C4C2×D4×C4311yescharacteristic
290C22×C4C2×D4×C4311yescharacteristic
291C22×C4C2×D4×C4311yescharacteristic
292D8—84no—
293M16—42no—
294C2×C8—22no—
295C2×C8—22no—
296C2×C8—41no—
297C4⋊C4—21no—
298C4⋊C4—22no—
299C4⋊C4—21no—
300C4⋊C4—22no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C22⋊C4—416no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C42—22no—
307C42—42no—
308C42—42no—
309C42D8×C4314yescomplemented
310C42C2×D4×C4311yescharacteristic
311C42C2×D4×C4311yescharacteristic
312C42C2×D4×C4311yescharacteristic
313C42#41×C4311yescharacteristic
314C23—44no—
315C23—44no—
316C23—41no—
317C23—42no—
318C23—44no—
319C23#120×C4311yescharacteristic
320Q8—42no—
321Q8—82no—
322Q8—81no—
323Q8—81no—
324D4—42no—
325D4—42no—
326D4—44no—
327D4—42no—
328D4—82no—
329D4—82no—
330D4—82no—
331D4—82no—
332D4—82no—
333D4—81no—
334D4—81no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—24no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—44no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4#120×C4311yescharacteristic
346C2×C4#120×C4311yescharacteristic
347C2×C4#121×C4311yescharacteristic
348C2×C4#121×C4311yescharacteristic
349C2×C4#121×C4311yescharacteristic
350C2×C4#127×C4311yescharacteristic
351C2×C4C2×D8×C4312yes—
352C2×C4AGL(1,ℤ/8)×C4312yes—
353C8—42no—
354C8—42no—
355C8—81no—
356C22—21no—
357C22—21no—
358C22—88no—
359C22—81no—
360C22—82no—
361C22—82no—
362C22—81no—
363C22—81no—
364C22—82no—
365C22C43×#39211yescharacteristic
366C22C43×#44712yes—
367C4—21no—
368C4—21no—
369C4—44no—
370C4—82no—
371C4—81no—
372C4C43×#45412yes—
373C4C43×#45512yes—
374C4C43×#45912yes—
375C4C43×#49311yescharacteristic
376C4C43×#49611yescharacteristic
377C2—22no—
378C2—162no—
379C2—161no—
380C2C43×#200311yescharacteristic
381C2C43×#200411yescharacteristic
382C2C43×#201111yescharacteristic
subgroupG/H
center, socleC22×C43#392
commutator, Frattini, cosocleC2×C42C23×C43
prime radicalC43×#3205C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3226C2semidirect
3. C43×#2858C2semidirect
4. C43×#1962C2semidirect
5. C43×#1546C2semidirect
6. C43×#1545C2semidirect
7. C43×#1276C2semidirect
117. C42×C43D8semidirect
164. #10284C43direct (N × H)
186. #3226C2×C43semidirect
188. #2858C2×C43semidirect
189. #1962C2×C43semidirect
190. #1546C2×C43semidirect
191. #1545C2×C43semidirect
192. #1276C2×C43semidirect
220. C43#10284direct (N × H)
309. C42D8×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#32262
C43×#32052
C43×#28582
C43×#19622
C43×#15462
C43×#15452
C43×#12762
#1028443