Finite Group Databasebeta

← C43×#29833 #24949850

Subgroups — C43×#29833 #24949850

Order 11008.

776 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#479C211yesmaximal, characteristic, complemented
2C2×C43×#464C211yesmaximal, characteristic
3C43×#2861C211yesmaximal, characteristic
4C43×#2295C211yesmaximal, characteristic, complemented
5C43×#2068C211yesmaximal, characteristic, complemented
6C43×#2067C211yesmaximal, characteristic
7C43×#2066C211yesmaximal, characteristic, complemented
8C43×#2065C211yesmaximal, characteristic
9C43×#2056C211yesmaximal, characteristic, complemented
10C43×#2056C211yesmaximal, characteristic, complemented
11C43×#2055C211yesmaximal, characteristic
12C43×#2055C211yesmaximal, characteristic
13C43×#1989C211yesmaximal, characteristic, complemented
14C43×#1983C211yesmaximal, characteristic
15C43×#1842C211yesmaximal, characteristic, complemented
16C22×Q16×C43C2211yescharacteristic
17C22×SD16×C43C2211yescharacteristic
18C2×#125×C43C2211yescharacteristic
19C2×#124×C43C2211yescharacteristic
20C2×C4×Q8×C43C2211yescharacteristic
21C43×#479—24no—
22C43×#464—24no—
23C2×#107×C43C2211yescharacteristic
24C2×#106×C43C2211yescharacteristic
25C2×C4⋊C8×C43C2211yescharacteristic
26C2×C4⋊C8×C43C2211yescharacteristic
27C2×C4⋊C8×C43C2211yescharacteristic
28C2×C4⋊C8×C43C2211yescharacteristic
29C2×C4⋊C8×C43C2211yescharacteristic
30C2×C4⋊C8×C43C2211yescharacteristic
31C2×#103×C43C2211yescharacteristic
32C2×#103×C43C2211yescharacteristic
33C2×#103×C43C2211yescharacteristic
34C2×#103×C43C2211yescharacteristic
35C2×#103×C43C2211yescharacteristic
36C2×#102×C43C2211yescharacteristic
37C2×#102×C43C2211yescharacteristic
38C2×#102×C43C2211yescharacteristic
39C43×#391C2211yescharacteristic
40C43×#391C2211yescharacteristic
41C43×#391C2211yescharacteristic
42C43×#391C2211yescharacteristic
43C43×#390C2211yescharacteristic
44C43×#390C2211yescharacteristic
45C43×#389C2211yescharacteristic
46C43×#389C2211yescharacteristic
47C43×#388—21no—
48C43×#388—21no—
49C43×#388—21no—
50C43×#388—21no—
51C43×#387—21no—
52C43×#387—21no—
53C4×C4⋊C4×C43—21no—
54C4×C4⋊C4×C43C2211yescharacteristic
55C43×#376—21no—
56C43×C43C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Q8×C43C2311yescharacteristic
62C22×Q8×C43C2311yescharacteristic
63C22×D4×C43C2311yescharacteristic
64C2×Q16×C43—22no—
65C2×Q16×C43—41no—
66C2×Q16×C43—41no—
67C2×SD16×C43—22no—
68C2×SD16×C43—41no—
69C2×SD16×C43—41no—
70C22×C8×C43C2311yescharacteristic
71C22×C8×C43C2311yescharacteristic
72C22×C8×C43C2311yescharacteristic
73C22×C8×C43C2311yescharacteristic
74#125×C43—22no—
75#125×C43—22no—
76#124×C43—22no—
77#124×C43—22no—
78C4×Q8×C43—22no—
79C4×Q8×C43D414yes—
80C2×C4⋊C4×C43—21no—
81C2×C4⋊C4×C43—21no—
82C2×C4⋊C4×C43—21no—
83C2×C4⋊C4×C43—21no—
84C2×C4⋊C4×C43—21no—
85C2×C4⋊C4×C43C2311yescharacteristic
86C2×C4⋊C4×C43C2311yescharacteristic
87C2×C4⋊C4×C43C2311yescharacteristic
88C2×C4⋊C4×C43C2311yescharacteristic
89C2×C4⋊C4×C43C2311yescharacteristic
90C2×C22⋊C4×C43—21no—
91C2×C22⋊C4×C43—21no—
92C2×C22⋊C4×C43—21no—
93C2×C22⋊C4×C43—21no—
94C2×C22⋊C4×C43—21no—
95C2×C22⋊C4×C43—21no—
96C2×C42×C43—21no—
97C2×C42×C43—21no—
98C2×C42×C43D411yescharacteristic
99C2×C42×C43D411yescharacteristic
100C2×C42×C43D411yescharacteristic
101C2×C42×C43D411yescharacteristic
102C2×C42×C43C2311yescharacteristic
103C2×C42×C43C2311yescharacteristic
104C2×C42×C43C2311yescharacteristic
105#107×C43—22no—
106#106×C43—22no—
107C4⋊C8×C43—22no—
108C4⋊C8×C43—22no—
109C4⋊C8×C43—41no—
110C4⋊C8×C43—41no—
111C4⋊C8×C43—41no—
112C4⋊C8×C43—41no—
113#103×C43—22no—
114#103×C43—22no—
115#103×C43—22no—
116#103×C43—41no—
117#103×C43—41no—
118#102×C43—22no—
119#102×C43—41no—
120#102×C43—41no—
121#95×C43—21no—
122#95×C43—21no—
123#95×C43—21no—
124#95×C43—21no—
125#95×C43—21no—
126#95×C43—21no—
127#95×C43—21no—
128#95×C43—21no—
129#95×C43—21no—
130#95×C43—21no—
131#95×C43—21no—
132C24×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43C2×D412yes—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2411yescharacteristic
165Q16×C43—44no—
166SD16×C43—44no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C4⋊C4×C43—24no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—42no—
190C4⋊C4×C43—42no—
191C4⋊C4×C43—42no—
192C4⋊C4×C43—42no—
193C4⋊C4×C43C2×D412yes—
194C22⋊C4×C43—42no—
195C22⋊C4×C43—42no—
196C22⋊C4×C43—42no—
197C22⋊C4×C43—42no—
198C22⋊C4×C43—42no—
199C22⋊C4×C43—42no—
200C42×C43—24no—
201C42×C43—22no—
202C42×C43—22no—
203C42×C43—21no—
204C42×C43—21no—
205C42×C43—21no—
206C42×C43—21no—
207C42×C43—41no—
208C42×C43—41no—
209C42×C43—42no—
210C42×C43C2×D412yes—
211C42×C43#4112yes—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43C22×D411yescharacteristic
220Q8×C43—22no—
221Q8×C43—22no—
222Q8×C43—41no—
223Q8×C43—41no—
224Q8×C43—41no—
225Q8×C43—41no—
226Q8×C43—41no—
227Q8×C43—41no—
228D4×C43—41no—
229D4×C43—41no—
230D4×C43—41no—
231D4×C43—41no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43#12112yes—
268C2×C4×C43#12112yes—
269C2×C4×C43#13512yes—
270C2×C4×C43#13712yes—
271C2×C4×C43C22×D411yescharacteristic
272C2×C4×C43C2×#4111yescharacteristic
273C2×C4×C43H(5,𝔽2)11yescharacteristic
274C2×C4×C43H(5,𝔽2)11yescharacteristic
275C2×C4×C432−1+411yescharacteristic
276C2×C4×C432−1+411yescharacteristic
277C8×C43—41no—
278C8×C43—41no—
279C8×C43—41no—
280C8×C43—41no—
281#29833C4311yesmaximal, characteristic, direct product factor, Sylow
282C22×C43—81no—
283C22×C43—81no—
284C22×C43—81no—
285C22×C43—81no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43—81no—
289C22×C43C2×#12111yescharacteristic
290C22×C43#53711yescharacteristic
291C22×C43#53711yescharacteristic
292C22×C43C2×#13511yescharacteristic
293C22×C43C2×#13711yescharacteristic
294C22×C43#57511yescharacteristic
295C22×C43#57511yescharacteristic
296C4×C43—22no—
297C4×C43—22no—
298C4×C43—22no—
299C4×C43—22no—
300C4×C43—42no—
301C4×C43—41no—
302C4×C43—41no—
303C4×C43—42no—
304C4×C43—81no—
305C4×C43—81no—
306C4×C43—81no—
307C4×C43—81no—
308C4×C43—81no—
309C4×C43#53511yescharacteristic
310C4×C43#53611yescharacteristic
311C4×C43#54211yescharacteristic
312C4×C43#54211yescharacteristic
313C2×#479C2×C4311yescharacteristic, complemented
314C2×#464C2×C4311yescharacteristic
315#2861C2×C4311yescharacteristic
316#2295C2×C4311yescharacteristic, complemented
317#2068C2×C4311yescharacteristic, complemented
318#2067C2×C4311yescharacteristic
319#2066C2×C4311yescharacteristic, complemented
320#2065C2×C4311yescharacteristic
321#2056C2×C4311yescharacteristic, complemented
322#2056C2×C4311yescharacteristic, complemented
323#2055C2×C4311yescharacteristic
324#2055C2×C4311yescharacteristic
325#1989C2×C4311yescharacteristic, complemented
326#1983C2×C4311yescharacteristic
327#1842C2×C4311yescharacteristic, complemented
328C2×C43—161no—
329C2×C43#262011yescharacteristic
330C2×C43#303511yescharacteristic
331C2×C43#303711yescharacteristic
332C2×C43#324811yescharacteristic
333C2×C43#325011yescharacteristic
334C2×C43#325211yescharacteristic
335C2×C43#325611yescharacteristic
336C22×Q16C22×C4311yescharacteristic
337C22×SD16C22×C4311yescharacteristic
338C2×#125C22×C4311yescharacteristic
339C2×#124C22×C4311yescharacteristic
340C2×C4×Q8C22×C4311yescharacteristic
341#479—24no—
342#464—24no—
343C2×#107C22×C4311yescharacteristic
344C2×#106C22×C4311yescharacteristic
345C2×C4⋊C8C22×C4311yescharacteristic
346C2×C4⋊C8C22×C4311yescharacteristic
347C2×C4⋊C8C22×C4311yescharacteristic
348C2×C4⋊C8C22×C4311yescharacteristic
349C2×C4⋊C8C22×C4311yescharacteristic
350C2×C4⋊C8C22×C4311yescharacteristic
351C2×#103C22×C4311yescharacteristic
352C2×#103C22×C4311yescharacteristic
353C2×#103C22×C4311yescharacteristic
354C2×#103C22×C4311yescharacteristic
355C2×#103C22×C4311yescharacteristic
356C2×#102C22×C4311yescharacteristic
357C2×#102C22×C4311yescharacteristic
358C2×#102C22×C4311yescharacteristic
359#391C22×C4311yescharacteristic
360#391C22×C4311yescharacteristic
361#391C22×C4311yescharacteristic
362#391C22×C4311yescharacteristic
363#390C22×C4311yescharacteristic
364#390C22×C4311yescharacteristic
365#389C22×C4311yescharacteristic
366#389C22×C4311yescharacteristic
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#387—21no—
372#387—21no—
373C4×C4⋊C4—21no—
374C4×C4⋊C4C22×C4311yescharacteristic
375#376—21no—
376C43C22×C4311yescharacteristic
377#340C22×C4311yescharacteristic
378#340C22×C4311yescharacteristic
379#340C22×C4311yescharacteristic
380#340C22×C4311yescharacteristic
381C43#2983311yescharacteristic, direct product factor, Sylow
382C22×Q8C23×C4311yescharacteristic
383C22×Q8C23×C4311yescharacteristic
384C22×D4C23×C4311yescharacteristic
385C2×Q16—22no—
386C2×Q16—41no—
387C2×Q16—41no—
388C2×SD16—22no—
389C2×SD16—41no—
390C2×SD16—41no—
391C22×C8C23×C4311yescharacteristic
392C22×C8C23×C4311yescharacteristic
393C22×C8C23×C4311yescharacteristic
394C22×C8C23×C4311yescharacteristic
395#125—22no—
396#125—22no—
397#124—22no—
398#124—22no—
399C4×Q8—22no—
400C4×Q8D4×C4314yes—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4C23×C4311yescharacteristic
407C2×C4⋊C4C23×C4311yescharacteristic
408C2×C4⋊C4C23×C4311yescharacteristic
409C2×C4⋊C4C23×C4311yescharacteristic
410C2×C4⋊C4C23×C4311yescharacteristic
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C42—21no—
418C2×C42—21no—
419C2×C42D4×C4311yescharacteristic
420C2×C42D4×C4311yescharacteristic
421C2×C42D4×C4311yescharacteristic
422C2×C42D4×C4311yescharacteristic
423C2×C42C23×C4311yescharacteristic
424C2×C42C23×C4311yescharacteristic
425C2×C42C23×C4311yescharacteristic
426#107—22no—
427#106—22no—
428C4⋊C8—22no—
429C4⋊C8—22no—
430C4⋊C8—41no—
431C4⋊C8—41no—
432C4⋊C8—41no—
433C4⋊C8—41no—
434#103—22no—
435#103—22no—
436#103—22no—
437#103—41no—
438#103—41no—
439#102—22no—
440#102—41no—
441#102—41no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95—21no—
453C24—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8C2×D4×C4312yes—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4C2×D4×C4311yescharacteristic
480C22×C4C2×D4×C4311yescharacteristic
481C22×C4C2×D4×C4311yescharacteristic
482C22×C4C2×D4×C4311yescharacteristic
483C22×C4C2×D4×C4311yescharacteristic
484C22×C4C2×D4×C4311yescharacteristic
485C22×C4C24×C4311yescharacteristic
486Q16—44no—
487SD16—44no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C4⋊C4—24no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—42no—
511C4⋊C4—42no—
512C4⋊C4—42no—
513C4⋊C4—42no—
514C4⋊C4C2×D4×C4312yes—
515C22⋊C4—42no—
516C22⋊C4—42no—
517C22⋊C4—42no—
518C22⋊C4—42no—
519C22⋊C4—42no—
520C22⋊C4—42no—
521C42—24no—
522C42—22no—
523C42—22no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—41no—
529C42—41no—
530C42—42no—
531C42C2×D4×C4312yes—
532C42#41×C4312yes—
533C23—41no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23C22×D4×C4311yescharacteristic
541Q8—22no—
542Q8—22no—
543Q8—41no—
544Q8—41no—
545Q8—41no—
546Q8—41no—
547Q8—41no—
548Q8—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—41no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4#121×C4312yes—
589C2×C4#121×C4312yes—
590C2×C4#135×C4312yes—
591C2×C4#137×C4312yes—
592C2×C4C22×D4×C4311yescharacteristic
593C2×C4C2×#41×C4311yescharacteristic
594C2×C4H(5,𝔽2)×C4311yescharacteristic
595C2×C4H(5,𝔽2)×C4311yescharacteristic
596C2×C42−1+4×C4311yescharacteristic
597C2×C42−1+4×C4311yescharacteristic
598C8—41no—
599C8—41no—
600C8—41no—
601C8—41no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22—81no—
608C22—81no—
609C22C2×#121×C4311yescharacteristic
610C22C43×#53711yescharacteristic
611C22C43×#53711yescharacteristic
612C22C2×#135×C4311yescharacteristic
613C22C2×#137×C4311yescharacteristic
614C22C43×#57511yescharacteristic
615C22C43×#57511yescharacteristic
616C4—22no—
617C4—22no—
618C4—22no—
619C4—22no—
620C4—42no—
621C4—41no—
622C4—41no—
623C4—42no—
624C4—81no—
625C4—81no—
626C4—81no—
627C4—81no—
628C4—81no—
629C4C43×#53511yescharacteristic
630C4C43×#53611yescharacteristic
631C4C43×#54211yescharacteristic
632C4C43×#54211yescharacteristic
633C2—161no—
634C2C43×#262011yescharacteristic
635C2C43×#303511yescharacteristic
636C2C43×#303711yescharacteristic
637C2C43×#324811yescharacteristic
638C2C43×#325011yescharacteristic
639C2C43×#325211yescharacteristic
640C2C43×#325611yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC22×D4×C43C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C43×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#479C2semidirect
4. C43×#2295C2semidirect
5. C43×#2068C2semidirect
7. C43×#2066C2semidirect
9. C43×#2056C2semidirect
10. C43×#2056C2semidirect
13. C43×#1989C2semidirect
15. C43×#1842C2semidirect
281. #29833C43direct (N × H)
313. C2×#479C2×C43semidirect
316. #2295C2×C43semidirect
317. #2068C2×C43semidirect
319. #2066C2×C43semidirect
321. #2056C2×C43semidirect
322. #2056C2×C43semidirect
325. #1989C2×C43semidirect
327. #1842C2×C43semidirect
381. C43#29833direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#4792
C2×C43×#4642
C43×#28612
C43×#22952
C43×#20682
C43×#20672
C43×#20662
C43×#20652
C43×#20562
C43×#20552
C43×#19892
C43×#19832
C43×#18422
#2983343