Finite Group Databasebeta

← C43×#12705 #24932722

Subgroups — C43×#12705 #24932722

Order 11008.

1186 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 1186 conjugacy classes of subgroups — too many to draw. Only its 146 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3484C211yesmaximal, characteristic
2C43×#2121C214yesmaximal, complemented
3C43×#1783C211yesmaximal, characteristic, complemented
4C43×#1781C211yesmaximal, characteristic, complemented
5C2×H(5,𝔽2)×C43C411yescharacteristic, complemented
6C23×D4×C43C2211yescharacteristic
7C43×#546—24no—
8D42×C43—24no—
9C43×#535—21no—
10C43×#534—21no—
11C43×#534C2212yes—
12C43×#525—21no—
13C2×#120×C43—21no—
14C2×#120×C43C412yescomplemented
15C43×#518C411yescharacteristic, complemented
16C2×#100×C43—21no—
17C2×#100×C43C2212yescomplemented
18C2×#99×C43—21no—
19C2×#99×C43C2212yescomplemented
20C43×#407—21no—
21C43×#379—21no—
22C43×#352—24no—
23C43×AΣL(1,𝔽16)—24no—
24C25×C43C2×C411yescharacteristic
25C25×C43D411yescharacteristic
26H(5,𝔽2)×C43—42no—
27H(5,𝔽2)×C43—42no—
28C2×#41×C43—21no—
29C2×#41×C43—22no—
30C22×D4×C43—21no—
31C22×D4×C43—22no—
32C22×D4×C43—22no—
33C22×D4×C43—22no—
34C22×D4×C43—24no—
35C22×D4×C43—42no—
36C22×D4×C43—42no—
37C22×D4×C43C2×C411yescharacteristic
38C22×D4×C43C2×C412yes—
39C22×D4×C43D411yescharacteristic
40C22×D4×C43D411yescharacteristic
41C22×D4×C43C2311yescharacteristic
42C23×C4×C43D411yescharacteristic
43C2×M16×C43—22no—
44#127×C43—22no—
45#124×C43—22no—
46#123×C43—22no—
47#123×C43—22no—
48#123×C43D414yes—
49C22⋊Q8×C43—22no—
50#121×C43—22no—
51#121×C43—24no—
52#121×C43—24no—
53#121×C43—24no—
54#120×C43—24no—
55#120×C43—22no—
56#120×C43—22no—
57#120×C43—22no—
58#120×C43—22no—
59#120×C43—24no—
60#120×C43D414yes—
61C4×D4×C43—24no—
62C4×D4×C43—24no—
63#117×C43—21no—
64C2×C22⋊C4×C43—22no—
65C2×C22⋊C4×C43—21no—
66C2×C22⋊C4×C43—22no—
67C2×C22⋊C4×C43—22no—
68C2×C22⋊C4×C43—42no—
69C2×C22⋊C4×C43C2×C412yes—
70#100×C43—24no—
71#100×C43—42no—
72#99×C43—24no—
73#99×C43—42no—
74C22⋊C8×C43—42no—
75C24×C43—21no—
76C24×C43—22no—
77C24×C43—22no—
78C24×C43—22no—
79C24×C43—41no—
80C24×C43—41no—
81C24×C43—41no—
82C24×C43—82no—
83C24×C43—82no—
84C24×C43C22⋊C411yescharacteristic
85C24×C43C22⋊C411yescharacteristic
86C24×C43C22⋊C411yescharacteristic
87C24×C43C22⋊C412yescomplemented
88C24×C43C22×C411yescharacteristic
89C24×C43C2×D411yescharacteristic
90#41×C43—42no—
91#41×C43—48no—
92#41×C43—42no—
93C2×Q8×C43—21no—
94C2×D4×C43—24no—
95C2×D4×C43—22no—
96C2×D4×C43—21no—
97C2×D4×C43—24no—
98C2×D4×C43—22no—
99C2×D4×C43—22no—
100C2×D4×C43—22no—
101C2×D4×C43—22no—
102C2×D4×C43—22no—
103C2×D4×C43—22no—
104C2×D4×C43—22no—
105C2×D4×C43—22no—
106C2×D4×C43—22no—
107C2×D4×C43—24no—
108C2×D4×C43—41no—
109C2×D4×C43—41no—
110C2×D4×C43—41no—
111C2×D4×C43—41no—
112C2×D4×C43—42no—
113C2×D4×C43—42no—
114C2×D4×C43—42no—
115C2×D4×C43—416no—
116C2×D4×C43—48no—
117C2×D4×C43—42no—
118C2×D4×C43—84no—
119C2×D4×C43—84no—
120C2×D4×C43C2×D414yes—
121C22×C4×C43—21no—
122C22×C4×C43—22no—
123C22×C4×C43—22no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43—41no—
128C22×C4×C43—42no—
129C22×C4×C43C22⋊C411yescharacteristic
130C22×C4×C43C22⋊C412yescomplemented
131C22×C4×C43C2×D411yescharacteristic
132M16×C43—42no—
133M16×C43—42no—
134C2×C8×C43—42no—
135C4⋊C4×C43—22no—
136C4⋊C4×C43—24no—
137C22⋊C4×C43—24no—
138C22⋊C4×C43—22no—
139C22⋊C4×C43—24no—
140C22⋊C4×C43—24no—
141C22⋊C4×C43—22no—
142C22⋊C4×C43—24no—
143C22⋊C4×C43—42no—
144C22⋊C4×C43—42no—
145C22⋊C4×C43—84no—
146C22⋊C4×C43C22⋊C414yescomplemented
147C42×C43—22no—
148C23×C43—21no—
149C23×C43—21no—
150C23×C43—21no—
151C23×C43—21no—
152C23×C43—21no—
153C23×C43—21no—
154C23×C43—21no—
155C23×C43—21no—
156C23×C43—21no—
157C23×C43—21no—
158C23×C43—22no—
159C23×C43—21no—
160C23×C43—21no—
161C23×C43—42no—
162C23×C43—44no—
163C23×C43—44no—
164C23×C43—44no—
165C23×C43—44no—
166C23×C43—44no—
167C23×C43—42no—
168C23×C43—42no—
169C23×C43—82no—
170C23×C43—82no—
171C23×C43—82no—
172C23×C43—81no—
173C23×C43—81no—
174C23×C43—81no—
175C23×C43—81no—
176C23×C43—82no—
177C23×C43—82no—
178C23×C43—82no—
179C23×C43—82no—
180C23×C43—82no—
181C23×C43—82no—
182C23×C43—82no—
183C23×C43—82no—
184C23×C43#9912yes—
185C23×C43C2×C22⋊C412yes—
186C23×C43C2×C22⋊C411yescharacteristic
187C23×C43#12012yes—
188Q8×C43—42no—
189D4×C43—28no—
190D4×C43—44no—
191D4×C43—44no—
192D4×C43—44no—
193D4×C43—42no—
194D4×C43—44no—
195D4×C43—44no—
196D4×C43—48no—
197D4×C43—42no—
198D4×C43—42no—
199D4×C43—84no—
200D4×C43—84no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—24no—
206C2×C4×C43—22no—
207C2×C4×C43—44no—
208C2×C4×C43—44no—
209C2×C4×C43—42no—
210C2×C4×C43—42no—
211C2×C4×C43—82no—
212C2×C4×C43—82no—
213C2×C4×C43—82no—
214C2×C4×C43—84no—
215C2×C4×C43#9912yes—
216C2×C4×C43#12012yes—
217C8×C43—82no—
218#12705C4311yesmaximal, characteristic, direct product factor, Sylow
219C22×C43—22no—
220C22×C43—22no—
221C22×C43—22no—
222C22×C43—22no—
223C22×C43—22no—
224C22×C43—22no—
225C22×C43—41no—
226C22×C43—42no—
227C22×C43—42no—
228C22×C43—42no—
229C22×C43—41no—
230C22×C43—41no—
231C22×C43—41no—
232C22×C43—42no—
233C22×C43—42no—
234C22×C43—42no—
235C22×C43—44no—
236C22×C43—41no—
237C22×C43—41no—
238C22×C43—42no—
239C22×C43—81no—
240C22×C43—81no—
241C22×C43—81no—
242C22×C43—81no—
243C22×C43—81no—
244C22×C43—81no—
245C22×C43—88no—
246C22×C43—88no—
247C22×C43—162no—
248C22×C43—162no—
249C22×C43#37911yescharacteristic
250C22×C43C2×#9911yescharacteristic
251C22×C43C2×#9911yescharacteristic
252C4×C43—22no—
253C4×C43—22no—
254C4×C43—44no—
255C4×C43—42no—
256C4×C43—162no—
257#3484C2×C4311yescharacteristic
258#2121C2×C4314yescomplemented
259#1783C2×C4311yescharacteristic, complemented
260#1781C2×C4311yescharacteristic, complemented
261C2×C43—21no—
262C2×C43—21no—
263C2×C43—21no—
264C2×C43—42no—
265C2×C43—42no—
266C2×C43—42no—
267C2×C43—42no—
268C2×C43—81no—
269C2×C43—82no—
270C2×C43#178111yescharacteristic
271C2×H(5,𝔽2)C4×C4311yescharacteristic, complemented
272C23×D4C22×C4311yescharacteristic
273#546—24no—
274D42—24no—
275#535—21no—
276#534—21no—
277#534C22×C4312yes—
278#525—21no—
279C2×#120—21no—
280C2×#120C4×C4312yescomplemented
281#518C4×C4311yescharacteristic, complemented
282C2×#100—21no—
283C2×#100C22×C4312yescomplemented
284C2×#99—21no—
285C2×#99C22×C4312yescomplemented
286#407—21no—
287#379—21no—
288#352—24no—
289AΣL(1,𝔽16)—24no—
290C43#1270511yescharacteristic, direct product factor, Sylow
291C25C2×C4×C4311yescharacteristic
292C25D4×C4311yescharacteristic
293H(5,𝔽2)—42no—
294H(5,𝔽2)—42no—
295C2×#41—21no—
296C2×#41—22no—
297C22×D4—21no—
298C22×D4—22no—
299C22×D4—22no—
300C22×D4—22no—
301C22×D4—24no—
302C22×D4—42no—
303C22×D4—42no—
304C22×D4C2×C4×C4311yescharacteristic
305C22×D4C2×C4×C4312yes—
306C22×D4D4×C4311yescharacteristic
307C22×D4D4×C4311yescharacteristic
308C22×D4C23×C4311yescharacteristic
309C23×C4D4×C4311yescharacteristic
310C2×M16—22no—
311#127—22no—
312#124—22no—
313#123—22no—
314#123—22no—
315#123D4×C4314yes—
316C22⋊Q8—22no—
317#121—22no—
318#121—24no—
319#121—24no—
320#121—24no—
321#120—24no—
322#120—22no—
323#120—22no—
324#120—22no—
325#120—22no—
326#120—24no—
327#120D4×C4314yes—
328C4×D4—24no—
329C4×D4—24no—
330#117—21no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4C2×C4×C4312yes—
337#100—24no—
338#100—42no—
339#99—24no—
340#99—42no—
341C22⋊C8—42no—
342C24—21no—
343C24—22no—
344C24—22no—
345C24—22no—
346C24—41no—
347C24—41no—
348C24—41no—
349C24—82no—
350C24—82no—
351C24C22⋊C4×C4311yescharacteristic
352C24C22⋊C4×C4311yescharacteristic
353C24C22⋊C4×C4311yescharacteristic
354C24C22⋊C4×C4312yescomplemented
355C24C22×C4×C4311yescharacteristic
356C24C2×D4×C4311yescharacteristic
357#41—42no—
358#41—48no—
359#41—42no—
360C2×Q8—21no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—24no—
364C2×D4—22no—
365C2×D4—21no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—24no—
371C2×D4—24no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—41no—
376C2×D4—41no—
377C2×D4—41no—
378C2×D4—41no—
379C2×D4—416no—
380C2×D4—48no—
381C2×D4—42no—
382C2×D4—42no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—84no—
386C2×D4—84no—
387C2×D4C2×D4×C4314yes—
388C22×C4—21no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—41no—
395C22×C4—42no—
396C22×C4C22⋊C4×C4311yescharacteristic
397C22×C4C22⋊C4×C4312yescomplemented
398C22×C4C2×D4×C4311yescharacteristic
399M16—42no—
400M16—42no—
401C2×C8—42no—
402C4⋊C4—22no—
403C4⋊C4—24no—
404C22⋊C4—24no—
405C22⋊C4—22no—
406C22⋊C4—24no—
407C22⋊C4—22no—
408C22⋊C4—24no—
409C22⋊C4—24no—
410C22⋊C4—42no—
411C22⋊C4—42no—
412C22⋊C4—84no—
413C22⋊C4C22⋊C4×C4314yescomplemented
414C42—22no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23—22no—
426C23—21no—
427C23—21no—
428C23—42no—
429C23—44no—
430C23—44no—
431C23—44no—
432C23—44no—
433C23—44no—
434C23—42no—
435C23—42no—
436C23—82no—
437C23—82no—
438C23—82no—
439C23—81no—
440C23—81no—
441C23—81no—
442C23—81no—
443C23—82no—
444C23—82no—
445C23—82no—
446C23—82no—
447C23—82no—
448C23—82no—
449C23—82no—
450C23—82no—
451C23#99×C4312yes—
452C23C2×C22⋊C4×C4312yes—
453C23C2×C22⋊C4×C4311yescharacteristic
454C23#120×C4312yes—
455Q8—42no—
456D4—28no—
457D4—44no—
458D4—44no—
459D4—44no—
460D4—42no—
461D4—44no—
462D4—44no—
463D4—48no—
464D4—42no—
465D4—42no—
466D4—84no—
467D4—84no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—24no—
473C2×C4—22no—
474C2×C4—44no—
475C2×C4—44no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—82no—
479C2×C4—82no—
480C2×C4—82no—
481C2×C4—84no—
482C2×C4#99×C4312yes—
483C2×C4#120×C4312yes—
484C8—82no—
485C22—22no—
486C22—22no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—22no—
491C22—41no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—44no—
501C22—42no—
502C22—41no—
503C22—42no—
504C22—41no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22—81no—
509C22—81no—
510C22—81no—
511C22—88no—
512C22—88no—
513C22—162no—
514C22—162no—
515C22C43×#37911yescharacteristic
516C22C2×#99×C4311yescharacteristic
517C22C2×#99×C4311yescharacteristic
518C4—22no—
519C4—22no—
520C4—44no—
521C4—42no—
522C4—162no—
523C2—21no—
524C2—21no—
525C2—21no—
526C2—42no—
527C2—42no—
528C2—42no—
529C2—42no—
530C2—81no—
531C2—82no—
532C2C43×#178111yescharacteristic
subgroupG/H
center, socleC2×C43#1781
commutatorC24C22×C4×C43
Frattini, cosocleC22×D4C23×C43
prime radicalC43×#3484C2
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C43 ◁ C23×C43 ◁ C23×D4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2121C2semidirect
3. C43×#1783C2semidirect
4. C43×#1781C2semidirect
5. C2×H(5,𝔽2)×C43C4semidirect
14. C2×#120×C43C4semidirect
15. C43×#518C4semidirect
17. C2×#100×C43C22semidirect
19. C2×#99×C43C22semidirect
87. C24×C43C22⋊C4semidirect
130. C22×C4×C43C22⋊C4semidirect
146. C22⋊C4×C43C22⋊C4semidirect
218. #12705C43direct (N × H)
258. #2121C2×C43semidirect
259. #1783C2×C43semidirect
260. #1781C2×C43semidirect
271. C2×H(5,𝔽2)C4×C43semidirect
280. C2×#120C4×C43semidirect
281. #518C4×C43semidirect
283. C2×#100C22×C43semidirect
285. C2×#99C22×C43semidirect
290. C43#12705direct (N × H)
354. C24C22⋊C4×C43semidirect
397. C22×C4C22⋊C4×C43semidirect
413. C22⋊C4C22⋊C4×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#34842
C43×#21212
C43×#17832
C43×#17812
#1270543