Finite Group Databasebeta

← C43×#28847 #24948864

Subgroups — C43×#28847 #24948864

Order 11008.

714 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2496C211yesmaximal, characteristic
2C43×#2423C211yesmaximal, characteristic
3C43×#2096C211yesmaximal, characteristic, complemented
4C43×#2084C211yesmaximal, characteristic, complemented
5C43×#2077C211yesmaximal, characteristic
6C43×#2035C211yesmaximal, characteristic
7C43×#1941C211yesmaximal, characteristic, complemented
8C43×#1933C211yesmaximal, characteristic, complemented
9C43×#1920C211yesmaximal, characteristic, complemented
10C43×#1892C211yesmaximal, characteristic
11C43×#1865C211yesmaximal, characteristic, complemented
12C43×#1834C211yesmaximal, characteristic, complemented
13C43×#1807C211yesmaximal, characteristic
14C4×#103×C43C211yesmaximal, characteristic, complemented
15C8×C22⋊C4×C43C211yesmaximal, characteristic
16C23×C8×C43C2211yescharacteristic
17C2×#126×C43—21no—
18C2×C22⋊Q8×C43C2211yescharacteristic
19C2×C4×Q8×C43C2211yescharacteristic
20C2×#106×C43C2211yescharacteristic
21C2×#106×C43C2211yescharacteristic
22C2×#106×C43C2211yescharacteristic
23C2×#106×C43C2211yescharacteristic
24C2×#103×C43C2211yescharacteristic
25C2×#103×C43C2211yescharacteristic
26C2×#103×C43C2211yescharacteristic
27C2×#103×C43C2211yescharacteristic
28C2×C22⋊C8×C43C2211yescharacteristic
29C2×C4×C8×C43C2211yescharacteristic
30C2×C4×C8×C43C2211yescharacteristic
31C43×#400—21no—
32C43×#399—21no—
33C43×#398—21no—
34C43×#397—21no—
35C43×#391C2211yescharacteristic
36C43×#389C2211yescharacteristic
37C43×#389C2211yescharacteristic
38C43×#389C2211yescharacteristic
39C43×#388—21no—
40C43×#387—21no—
41C43×#387—21no—
42C43×#384C2211yescharacteristic
43C43×#384C2211yescharacteristic
44C43×#380C2211yescharacteristic
45C43×#380C2211yescharacteristic
46C43×#380C2211yescharacteristic
47C4×C4⋊C4×C43C2211yescharacteristic
48C4×C22⋊C4×C43C2211yescharacteristic
49C43×#340C2211yescharacteristic
50C43×#340C2211yescharacteristic
51C43×#340C2211yescharacteristic
52C43×#340C2211yescharacteristic
53C43×#340C2211yescharacteristic
54C43×#340C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Q8×C43C2311yescharacteristic
60C23×C4×C43C2311yescharacteristic
61C22×C8×C43—22no—
62C22×C8×C43—22no—
63C22×C8×C43—41no—
64C22×C8×C43C2311yescharacteristic
65C22×C8×C43C2311yescharacteristic
66C22×C8×C43C2311yescharacteristic
67C22×C8×C43C2311yescharacteristic
68#126×C43—44no—
69C22⋊Q8×C43—22no—
70C22⋊Q8×C43—41no—
71C4×Q8×C43—22no—
72C4×Q8×C43—41no—
73C2×C4⋊C4×C43—21no—
74C2×C4⋊C4×C43—21no—
75C2×C4⋊C4×C43—21no—
76C2×C4⋊C4×C43—21no—
77C2×C4⋊C4×C43—21no—
78C2×C4⋊C4×C43—21no—
79C2×C4⋊C4×C43—21no—
80C2×C4⋊C4×C43—21no—
81C2×C4⋊C4×C43—21no—
82C2×C4⋊C4×C43C2311yescharacteristic
83C2×C4⋊C4×C43C2311yescharacteristic
84C2×C4⋊C4×C43C2311yescharacteristic
85C2×C4⋊C4×C43C2311yescharacteristic
86C2×C4⋊C4×C43C2311yescharacteristic
87C2×C4⋊C4×C43C2311yescharacteristic
88C2×C4⋊C4×C43C2311yescharacteristic
89C2×C22⋊C4×C43—21no—
90C2×C22⋊C4×C43—21no—
91C2×C22⋊C4×C43—21no—
92C2×C22⋊C4×C43—21no—
93C2×C22⋊C4×C43D411yescharacteristic
94C2×C22⋊C4×C43D411yescharacteristic
95C2×C42×C43—21no—
96C2×C42×C43—21no—
97C2×C42×C43C2311yescharacteristic
98C2×C42×C43C2311yescharacteristic
99#106×C43—22no—
100#106×C43—22no—
101#106×C43—41no—
102#106×C43—41no—
103#103×C43—22no—
104#103×C43—22no—
105#103×C43—22no—
106#103×C43—22no—
107C22⋊C8×C43—22no—
108C4×C8×C43—22no—
109C4×C8×C43—41no—
110#95×C43—21no—
111#95×C43—21no—
112#95×C43—21no—
113#95×C43—21no—
114#95×C43—21no—
115#95×C43—21no—
116#95×C43—21no—
117#95×C43—21no—
118#95×C43—21no—
119#95×C43D411yescharacteristic
120#95×C43D411yescharacteristic
121C24×C43C2×D411yescharacteristic
122C2×Q8×C43—21no—
123C2×Q8×C43—21no—
124C2×Q8×C43—21no—
125C2×Q8×C43—21no—
126C2×Q8×C43—21no—
127C2×Q8×C43#4112yes—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2411yescharacteristic
148C2×C8×C43—21no—
149C2×C8×C43—21no—
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—44no—
158C2×C8×C43#4112yes—
159C2×C8×C43#4112yes—
160C2×C8×C43#4112yes—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—42no—
176C4⋊C4×C43—42no—
177C4⋊C4×C43—42no—
178C4⋊C4×C43—42no—
179C4⋊C4×C43—42no—
180C4⋊C4×C43—42no—
181C4⋊C4×C43—42no—
182C4⋊C4×C43—81no—
183C4⋊C4×C43—81no—
184C22⋊C4×C43—22no—
185C22⋊C4×C43—42no—
186C22⋊C4×C43—42no—
187C22⋊C4×C43—42no—
188C22⋊C4×C43—81no—
189C22⋊C4×C43SD1614yes—
190C42×C43—21no—
191C42×C43—21no—
192C42×C43—21no—
193C42×C43—21no—
194C42×C43—42no—
195C42×C43—42no—
196C23×C43—21no—
197C23×C43—21no—
198C23×C43—21no—
199C23×C43—21no—
200C23×C43—21no—
201C23×C43—21no—
202C23×C43C2×SD1612yes—
203C23×C43C22×D411yescharacteristic
204Q8×C43—22no—
205Q8×C43—22no—
206Q8×C43—41no—
207Q8×C43—41no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—22no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43C2×SD1612yes—
249C2×C4×C43C2×SD1612yes—
250C2×C4×C43#13512yes—
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C43H(5,𝔽2)11yescharacteristic
256C2×C4×C432−1+411yescharacteristic
257C8×C43—22no—
258C8×C43—22no—
259C8×C43—22no—
260C8×C43—41no—
261#28847C4311yesmaximal, characteristic, direct product factor, Sylow
262C22×C43—22no—
263C22×C43—22no—
264C22×C43—22no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43#53211yescharacteristic
270C22×C43#54611yescharacteristic
271C22×C43#54711yescharacteristic
272C22×C43C22×SD1611yescharacteristic
273C22×C43C2×#13511yescharacteristic
274C22×C43#57711yescharacteristic
275C22×C43#57811yescharacteristic
276C4×C43—22no—
277C4×C43—22no—
278C4×C43—22no—
279C4×C43—41no—
280C4×C43—41no—
281C4×C43—42no—
282C4×C43—81no—
283C4×C43—81no—
284C4×C43—81no—
285C4×C43—81no—
286C4×C43—81no—
287C4×C43—81no—
288C4×C43—81no—
289C4×C43#52911yescharacteristic
290C4×C43#53911yescharacteristic
291C4×C43#55111yescharacteristic
292C4×C43#55211yescharacteristic
293#2496C2×C4311yescharacteristic
294#2423C2×C4311yescharacteristic
295#2096C2×C4311yescharacteristic, complemented
296#2084C2×C4311yescharacteristic, complemented
297#2077C2×C4311yescharacteristic
298#2035C2×C4311yescharacteristic
299#1941C2×C4311yescharacteristic, complemented
300#1933C2×C4311yescharacteristic, complemented
301#1920C2×C4311yescharacteristic, complemented
302#1892C2×C4311yescharacteristic
303#1865C2×C4311yescharacteristic, complemented
304#1834C2×C4311yescharacteristic, complemented
305#1807C2×C4311yescharacteristic
306C4×#103C2×C4311yescharacteristic, complemented
307C8×C22⋊C4C2×C4311yescharacteristic
308C2×C43—42no—
309C2×C43#255311yescharacteristic
310C2×C43#316711yescharacteristic
311C2×C43#317811yescharacteristic
312C2×C43#329811yescharacteristic
313C2×C43#330411yescharacteristic
314C2×C43#333511yescharacteristic
315C2×C43#333611yescharacteristic
316C23×C8C22×C4311yescharacteristic
317C2×#126—21no—
318C2×C22⋊Q8C22×C4311yescharacteristic
319C2×C4×Q8C22×C4311yescharacteristic
320C2×#106C22×C4311yescharacteristic
321C2×#106C22×C4311yescharacteristic
322C2×#106C22×C4311yescharacteristic
323C2×#106C22×C4311yescharacteristic
324C2×#103C22×C4311yescharacteristic
325C2×#103C22×C4311yescharacteristic
326C2×#103C22×C4311yescharacteristic
327C2×#103C22×C4311yescharacteristic
328C2×C22⋊C8C22×C4311yescharacteristic
329C2×C4×C8C22×C4311yescharacteristic
330C2×C4×C8C22×C4311yescharacteristic
331#400—21no—
332#399—21no—
333#398—21no—
334#397—21no—
335#391C22×C4311yescharacteristic
336#389C22×C4311yescharacteristic
337#389C22×C4311yescharacteristic
338#389C22×C4311yescharacteristic
339#388—21no—
340#387—21no—
341#387—21no—
342#384C22×C4311yescharacteristic
343#384C22×C4311yescharacteristic
344#380C22×C4311yescharacteristic
345#380C22×C4311yescharacteristic
346#380C22×C4311yescharacteristic
347C4×C4⋊C4C22×C4311yescharacteristic
348C4×C22⋊C4C22×C4311yescharacteristic
349#340C22×C4311yescharacteristic
350#340C22×C4311yescharacteristic
351#340C22×C4311yescharacteristic
352#340C22×C4311yescharacteristic
353#340C22×C4311yescharacteristic
354#340C22×C4311yescharacteristic
355#340C22×C4311yescharacteristic
356#340C22×C4311yescharacteristic
357#336C22×C4311yescharacteristic
358#336C22×C4311yescharacteristic
359C43#2884711yescharacteristic, direct product factor, Sylow
360C22×Q8C23×C4311yescharacteristic
361C23×C4C23×C4311yescharacteristic
362C22×C8—22no—
363C22×C8—22no—
364C22×C8—41no—
365C22×C8C23×C4311yescharacteristic
366C22×C8C23×C4311yescharacteristic
367C22×C8C23×C4311yescharacteristic
368C22×C8C23×C4311yescharacteristic
369#126—44no—
370C22⋊Q8—22no—
371C22⋊Q8—41no—
372C4×Q8—22no—
373C4×Q8—41no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4C23×C4311yescharacteristic
384C2×C4⋊C4C23×C4311yescharacteristic
385C2×C4⋊C4C23×C4311yescharacteristic
386C2×C4⋊C4C23×C4311yescharacteristic
387C2×C4⋊C4C23×C4311yescharacteristic
388C2×C4⋊C4C23×C4311yescharacteristic
389C2×C4⋊C4C23×C4311yescharacteristic
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4D4×C4311yescharacteristic
395C2×C22⋊C4D4×C4311yescharacteristic
396C2×C42—21no—
397C2×C42—21no—
398C2×C42C23×C4311yescharacteristic
399C2×C42C23×C4311yescharacteristic
400#106—22no—
401#106—22no—
402#106—41no—
403#106—41no—
404#103—22no—
405#103—22no—
406#103—22no—
407#103—22no—
408C22⋊C8—22no—
409C4×C8—22no—
410C4×C8—41no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95D4×C4311yescharacteristic
421#95D4×C4311yescharacteristic
422C24C2×D4×C4311yescharacteristic
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8#41×C4312yes—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4C2×D4×C4311yescharacteristic
444C22×C4C2×D4×C4311yescharacteristic
445C22×C4C2×D4×C4311yescharacteristic
446C22×C4C2×D4×C4311yescharacteristic
447C22×C4C2×D4×C4311yescharacteristic
448C22×C4C24×C4311yescharacteristic
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—44no—
459C2×C8#41×C4312yes—
460C2×C8#41×C4312yes—
461C2×C8#41×C4312yes—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—42no—
477C4⋊C4—42no—
478C4⋊C4—42no—
479C4⋊C4—42no—
480C4⋊C4—42no—
481C4⋊C4—42no—
482C4⋊C4—42no—
483C4⋊C4—81no—
484C4⋊C4—81no—
485C22⋊C4—22no—
486C22⋊C4—42no—
487C22⋊C4—42no—
488C22⋊C4—42no—
489C22⋊C4—81no—
490C22⋊C4SD16×C4314yes—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—42no—
496C42—42no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23—21no—
502C23—21no—
503C23C2×SD16×C4312yes—
504C23C22×D4×C4311yescharacteristic
505Q8—22no—
506Q8—22no—
507Q8—41no—
508Q8—41no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4C2×SD16×C4312yes—
550C2×C4C2×SD16×C4312yes—
551C2×C4#135×C4312yes—
552C2×C4C2×#41×C4311yescharacteristic
553C2×C4C2×#41×C4311yescharacteristic
554C2×C4C2×#41×C4311yescharacteristic
555C2×C4C2×#41×C4311yescharacteristic
556C2×C4H(5,𝔽2)×C4311yescharacteristic
557C2×C42−1+4×C4311yescharacteristic
558C8—22no—
559C8—22no—
560C8—22no—
561C8—41no—
562C22—22no—
563C22—22no—
564C22—22no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22C43×#53211yescharacteristic
570C22C43×#54611yescharacteristic
571C22C43×#54711yescharacteristic
572C22C22×SD16×C4311yescharacteristic
573C22C2×#135×C4311yescharacteristic
574C22C43×#57711yescharacteristic
575C22C43×#57811yescharacteristic
576C4—22no—
577C4—22no—
578C4—22no—
579C4—41no—
580C4—41no—
581C4—42no—
582C4—81no—
583C4—81no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4—81no—
588C4—81no—
589C4C43×#52911yescharacteristic
590C4C43×#53911yescharacteristic
591C4C43×#55111yescharacteristic
592C4C43×#55211yescharacteristic
593C2—42no—
594C2C43×#255311yescharacteristic
595C2C43×#316711yescharacteristic
596C2C43×#317811yescharacteristic
597C2C43×#329811yescharacteristic
598C2C43×#330411yescharacteristic
599C2C43×#333511yescharacteristic
600C2C43×#333611yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC24×C43C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C4×C22⋊C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
3. C43×#2096C2semidirect
4. C43×#2084C2semidirect
7. C43×#1941C2semidirect
8. C43×#1933C2semidirect
9. C43×#1920C2semidirect
11. C43×#1865C2semidirect
12. C43×#1834C2semidirect
14. C4×#103×C43C2semidirect
261. #28847C43direct (N × H)
295. #2096C2×C43semidirect
296. #2084C2×C43semidirect
299. #1941C2×C43semidirect
300. #1933C2×C43semidirect
301. #1920C2×C43semidirect
303. #1865C2×C43semidirect
304. #1834C2×C43semidirect
306. C4×#103C2×C43semidirect
359. C43#28847direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#24962
C43×#24232
C43×#20962
C43×#20842
C43×#20772
C43×#20352
C43×#19412
C43×#19332
C43×#19202
C43×#18922
C43×#18652
C43×#18342
C43×#18072
C4×#103×C432
C8×C22⋊C4×C432
#2884743