Finite Group Databasebeta

← C43×#26192 #24946209

Subgroups — C43×#26192 #24946209

Order 11008.

734 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3097C211yesmaximal, characteristic, complemented
2C43×#3046C211yesmaximal, characteristic
3C43×#2951C211yesmaximal, characteristic
4C43×#2912C211yesmaximal, characteristic, complemented
5C43×#2097C211yesmaximal, characteristic, complemented
6C43×#2089C211yesmaximal, characteristic, complemented
7C43×#2079C211yesmaximal, characteristic, complemented
8C43×#2038C211yesmaximal, characteristic, complemented
9C43×#1930C211yesmaximal, characteristic, complemented
10C43×#1922C211yesmaximal, characteristic, complemented
11C43×#1908C211yesmaximal, characteristic, complemented
12C43×#1882C211yesmaximal, characteristic, complemented
13C43×#1876C211yesmaximal, characteristic
14C43×#1860C211yesmaximal, characteristic, complemented
15C43×#1860C211yesmaximal, characteristic, complemented
16C2×#137×C43C2211yescharacteristic
17C2×#135×C43C2211yescharacteristic
18C2×#131×C43C2211yescharacteristic
19C43×#536C2211yescharacteristic
20C43×#520C2211yescharacteristic
21C43×#520C2211yescharacteristic
22C43×#520C2211yescharacteristic
23C43×#485—21no—
24C43×#485—21no—
25C43×#484—21no—
26C43×#483—21no—
27C43×#464—21no—
28C43×#463—21no—
29C43×#462—21no—
30C43×#461—21no—
31C43×#440—21no—
32C43×#440—21no—
33C4×Q16×C43—21no—
34C4×D8×C43—21no—
35C43×#428—21no—
36C43×#428—21no—
37C43×#428C2211yescharacteristic
38C43×#428C2211yescharacteristic
39C43×#428C2211yescharacteristic
40C43×#427—21no—
41C43×#427C2211yescharacteristic
42C2×#107×C43C2211yescharacteristic
43C2×#106×C43—21no—
44C2×#106×C43C2211yescharacteristic
45C43×#424C2211yescharacteristic
46C2×#104×C43C2211yescharacteristic
47C2×#104×C43C2211yescharacteristic
48C43×#419C2211yescharacteristic
49C43×#417C2211yescharacteristic
50C43×#417C2211yescharacteristic
51C43×#417C2211yescharacteristic
52C2×#103×C43C2211yescharacteristic
53C2×#103×C43C2211yescharacteristic
54C2×#101×C43C2211yescharacteristic
55C43×#408C2211yescharacteristic
56C43×#405C2211yescharacteristic
57C43×#391C2211yescharacteristic
58C43×#382C2211yescharacteristic
59C43×#343C2211yescharacteristic
60C43×#343C2211yescharacteristic
61C43×#343C2211yescharacteristic
62C43×#341C2211yescharacteristic
63C43×#341C2211yescharacteristic
64C43×#339C2211yescharacteristic
65C43×#339C2211yescharacteristic
66C43×#336C2211yescharacteristic
67C2×#41×C43C2311yescharacteristic
68C2×#41×C43C2311yescharacteristic
69C22×Q8×C43C2311yescharacteristic
70#137×C43—22no—
71#137×C43—22no—
72#135×C43—22no—
73#135×C43—22no—
74C2×Q16×C43—21no—
75C2×Q16×C43D411yescharacteristic
76C2×SD16×C43—21no—
77C2×SD16×C43D411yescharacteristic
78C2×SD16×C43D411yescharacteristic
79C2×D8×C43D411yescharacteristic
80#131×C43—22no—
81#131×C43—22no—
82C2×M16×C43—21no—
83C2×M16×C43C2311yescharacteristic
84C2×M16×C43C2311yescharacteristic
85C2×M16×C43C2311yescharacteristic
86C2×M16×C43C2311yescharacteristic
87C22×C8×C43—21no—
88C22×C8×C43C2311yescharacteristic
89C22×C8×C43C2311yescharacteristic
90C4⋊Q8×C43—21no—
91#124×C43—21no—
92#123×C43—41no—
93C22⋊Q8×C43—21no—
94C22⋊Q8×C43—21no—
95C4×Q8×C43—21no—
96C4×Q8×C43—21no—
97C4×Q8×C43—21no—
98C4×D4×C43—21no—
99C4×D4×C43—21no—
100C4×D4×C43—21no—
101C4×D4×C43—41no—
102C4×D4×C43—41no—
103C4×D4×C43—41no—
104#117×C43—21no—
105#117×C43—21no—
106#117×C43—21no—
107#117×C43C2311yescharacteristic
108#117×C43C2311yescharacteristic
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C42×C43C2311yescharacteristic
116#107×C43—21no—
117#107×C43—21no—
118#107×C43—21no—
119#107×C43—21no—
120#107×C43—21no—
121#107×C43D411yescharacteristic
122#107×C43D411yescharacteristic
123#106×C43—21no—
124#106×C43—21no—
125#106×C43—21no—
126#106×C43—21no—
127#106×C43—21no—
128#106×C43D411yescharacteristic
129#106×C43D411yescharacteristic
130C4⋊C8×C43—21no—
131C4⋊C8×C43—21no—
132#104×C43—22no—
133#104×C43—22no—
134#103×C43—21no—
135#103×C43—21no—
136#103×C43—21no—
137#103×C43—21no—
138#103×C43—21no—
139#103×C43—21no—
140#103×C43—21no—
141#103×C43—21no—
142#103×C43—21no—
143#102×C43—21no—
144#102×C43—21no—
145#102×C43—21no—
146#101×C43—22no—
147C22⋊C8×C43—21no—
148C22⋊C8×C43—21no—
149#97×C43—21no—
150C4×C8×C43—21no—
151#95×C43—41no—
152#95×C43—41no—
153#41×C43—21no—
154#41×C43—21no—
155#41×C43—21no—
156#41×C43—21no—
157#41×C43—21no—
158#41×C43—21no—
159#41×C43#4112yes—
160#41×C43#4112yes—
161C2×Q8×C43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×Q8×C43—21no—
166C2×Q8×C43—21no—
167C2×Q8×C43C2×D411yescharacteristic
168C2×Q8×C43C2×D411yescharacteristic
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43C2×D411yescharacteristic
172C2×D4×C43C2×D411yescharacteristic
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—41no—
181C22×C4×C43—41no—
182C22×C4×C43—41no—
183C22×C4×C43C2411yescharacteristic
184Q16×C43—22no—
185Q16×C43—42no—
186SD16×C43—22no—
187SD16×C43—22no—
188SD16×C43—42no—
189D8×C43—22no—
190M16×C43—24no—
191M16×C43—21no—
192M16×C43—21no—
193M16×C43—21no—
194M16×C43—21no—
195M16×C43—21no—
196M16×C43—21no—
197M16×C43—21no—
198M16×C43#4112yes—
199C2×C8×C43—24no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43C2×D411yescharacteristic
209C2×C8×C43C2×D411yescharacteristic
210C2×C8×C43C2×D411yescharacteristic
211C2×C8×C43C2×D411yescharacteristic
212C4⋊C4×C43—21no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43—21no—
215C4⋊C4×C43—21no—
216C4⋊C4×C43—21no—
217C4⋊C4×C43—21no—
218C4⋊C4×C43—41no—
219C4⋊C4×C43—41no—
220C4⋊C4×C43—41no—
221C4⋊C4×C43—41no—
222C4⋊C4×C43—41no—
223C4⋊C4×C43C2×D411yescharacteristic
224C4⋊C4×C43C2×D411yescharacteristic
225C4⋊C4×C43C2×D411yescharacteristic
226C4⋊C4×C43C2×D411yescharacteristic
227C22⋊C4×C43—21no—
228C22⋊C4×C43—21no—
229C22⋊C4×C43—41no—
230C22⋊C4×C43—41no—
231C22⋊C4×C43—41no—
232C22⋊C4×C43—41no—
233C22⋊C4×C43—41no—
234C42×C43—21no—
235C42×C43—21no—
236C42×C43—21no—
237C42×C43—21no—
238C42×C43—41no—
239C42×C43—41no—
240C42×C43—41no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43H(5,𝔽2)11yescharacteristic
244Q8×C43—21no—
245Q8×C43—21no—
246Q8×C43—21no—
247Q8×C43—41no—
248Q8×C43—41no—
249Q8×C43—41no—
250Q8×C43—41no—
251Q8×C43#12312yes—
252D4×C43—22no—
253D4×C43—22no—
254D4×C43—21no—
255D4×C43—21no—
256D4×C43—21no—
257D4×C43—41no—
258D4×C43—41no—
259D4×C43#12312yes—
260C2×C4×C43—21no—
261C2×C4×C43—22no—
262C2×C4×C43—22no—
263C2×C4×C43—21no—
264C2×C4×C43—21no—
265C2×C4×C43—21no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—41no—
269C2×C4×C43—41no—
270C2×C4×C43—41no—
271C2×C4×C43—41no—
272C2×C4×C43—41no—
273C2×C4×C43—41no—
274C2×C4×C43—41no—
275C2×C4×C43—41no—
276C2×C4×C43—41no—
277C2×C4×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43—81no—
280C2×C4×C43—81no—
281C2×C4×C43—81no—
282C2×C4×C43—161no—
283C2×C4×C43—161no—
284C2×C4×C43—161no—
285C2×C4×C43C22×D411yescharacteristic
286C2×C4×C43C22×D411yescharacteristic
287C2×C4×C43C2×#4111yescharacteristic
288C2×C4×C43C2×#4111yescharacteristic
289C2×C4×C43C2×#4111yescharacteristic
290C2×C4×C432−1+411yescharacteristic
291C8×C43—21no—
292C8×C43—21no—
293C8×C43—21no—
294C8×C43—22no—
295C8×C43—21no—
296C8×C43—41no—
297C8×C43—41no—
298C8×C43—41no—
299#26192C4311yesmaximal, characteristic, direct product factor, Sylow
300C22×C43—21no—
301C22×C43—21no—
302C22×C43—22no—
303C22×C43—41no—
304C22×C43—41no—
305C22×C43—41no—
306C22×C43—41no—
307C22×C43—41no—
308C22×C43#53911yescharacteristic
309C22×C43D4211yescharacteristic
310C22×C43#55311yescharacteristic
311C4×C43—22no—
312C4×C43—41no—
313C4×C43—41no—
314C4×C43—41no—
315C4×C43—41no—
316C4×C43—41no—
317C4×C43—81no—
318C4×C43—81no—
319C4×C43—81no—
320C4×C43—81no—
321C4×C43—81no—
322C4×C43C2×#12311yescharacteristic
323C4×C43#52511yescharacteristic
324C4×C43#54711yescharacteristic
325C4×C43#54811yescharacteristic
326#3097C2×C4311yescharacteristic, complemented
327#3046C2×C4311yescharacteristic
328#2951C2×C4311yescharacteristic
329#2912C2×C4311yescharacteristic, complemented
330#2097C2×C4311yescharacteristic, complemented
331#2089C2×C4311yescharacteristic, complemented
332#2079C2×C4311yescharacteristic, complemented
333#2038C2×C4311yescharacteristic, complemented
334#1930C2×C4311yescharacteristic, complemented
335#1922C2×C4311yescharacteristic, complemented
336#1908C2×C4311yescharacteristic, complemented
337#1882C2×C4311yescharacteristic, complemented
338#1876C2×C4311yescharacteristic
339#1860C2×C4311yescharacteristic, complemented
340#1860C2×C4311yescharacteristic, complemented
341C2×C43—21no—
342C2×C43—21no—
343C2×C43—42no—
344C2×C43—81no—
345C2×C43#244311yescharacteristic
346C2×C43#328911yescharacteristic
347C2×C43#329011yescharacteristic
348C2×#137C22×C4311yescharacteristic
349C2×#135C22×C4311yescharacteristic
350C2×#131C22×C4311yescharacteristic
351#536C22×C4311yescharacteristic
352#520C22×C4311yescharacteristic
353#520C22×C4311yescharacteristic
354#520C22×C4311yescharacteristic
355#485—21no—
356#485—21no—
357#484—21no—
358#483—21no—
359#464—21no—
360#463—21no—
361#462—21no—
362#461—21no—
363#440—21no—
364#440—21no—
365C4×Q16—21no—
366C4×D8—21no—
367#428—21no—
368#428—21no—
369#428C22×C4311yescharacteristic
370#428C22×C4311yescharacteristic
371#428C22×C4311yescharacteristic
372#427—21no—
373#427C22×C4311yescharacteristic
374C2×#107C22×C4311yescharacteristic
375C2×#106—21no—
376C2×#106C22×C4311yescharacteristic
377#424C22×C4311yescharacteristic
378C2×#104C22×C4311yescharacteristic
379C2×#104C22×C4311yescharacteristic
380#419C22×C4311yescharacteristic
381#417C22×C4311yescharacteristic
382#417C22×C4311yescharacteristic
383#417C22×C4311yescharacteristic
384C2×#103C22×C4311yescharacteristic
385C2×#103C22×C4311yescharacteristic
386C2×#101C22×C4311yescharacteristic
387#408C22×C4311yescharacteristic
388#405C22×C4311yescharacteristic
389#391C22×C4311yescharacteristic
390#382C22×C4311yescharacteristic
391#343C22×C4311yescharacteristic
392#343C22×C4311yescharacteristic
393#343C22×C4311yescharacteristic
394#341C22×C4311yescharacteristic
395#341C22×C4311yescharacteristic
396#339C22×C4311yescharacteristic
397#339C22×C4311yescharacteristic
398#336C22×C4311yescharacteristic
399C43#2619211yescharacteristic, direct product factor, Sylow
400C2×#41C23×C4311yescharacteristic
401C2×#41C23×C4311yescharacteristic
402C22×Q8C23×C4311yescharacteristic
403#137—22no—
404#137—22no—
405#135—22no—
406#135—22no—
407C2×Q16—21no—
408C2×Q16D4×C4311yescharacteristic
409C2×SD16—21no—
410C2×SD16D4×C4311yescharacteristic
411C2×SD16D4×C4311yescharacteristic
412C2×D8D4×C4311yescharacteristic
413#131—22no—
414#131—22no—
415C2×M16—21no—
416C2×M16C23×C4311yescharacteristic
417C2×M16C23×C4311yescharacteristic
418C2×M16C23×C4311yescharacteristic
419C2×M16C23×C4311yescharacteristic
420C22×C8—21no—
421C22×C8C23×C4311yescharacteristic
422C22×C8C23×C4311yescharacteristic
423C4⋊Q8—21no—
424#124—21no—
425#123—41no—
426C22⋊Q8—21no—
427C22⋊Q8—21no—
428C4×Q8—21no—
429C4×Q8—21no—
430C4×Q8—21no—
431C4×D4—21no—
432C4×D4—21no—
433C4×D4—21no—
434C4×D4—41no—
435C4×D4—41no—
436C4×D4—41no—
437#117—21no—
438#117—21no—
439#117—21no—
440#117C23×C4311yescharacteristic
441#117C23×C4311yescharacteristic
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4C23×C4311yescharacteristic
446C2×C4⋊C4C23×C4311yescharacteristic
447C2×C4⋊C4C23×C4311yescharacteristic
448C2×C42C23×C4311yescharacteristic
449#107—21no—
450#107—21no—
451#107—21no—
452#107—21no—
453#107—21no—
454#107D4×C4311yescharacteristic
455#107D4×C4311yescharacteristic
456#106—21no—
457#106—21no—
458#106—21no—
459#106—21no—
460#106—21no—
461#106D4×C4311yescharacteristic
462#106D4×C4311yescharacteristic
463C4⋊C8—21no—
464C4⋊C8—21no—
465#104—22no—
466#104—22no—
467#103—21no—
468#103—21no—
469#103—21no—
470#103—21no—
471#103—21no—
472#103—21no—
473#103—21no—
474#103—21no—
475#103—21no—
476#102—21no—
477#102—21no—
478#102—21no—
479#101—22no—
480C22⋊C8—21no—
481C22⋊C8—21no—
482#97—21no—
483C4×C8—21no—
484#95—41no—
485#95—41no—
486#41—21no—
487#41—21no—
488#41—21no—
489#41—21no—
490#41—21no—
491#41—21no—
492#41#41×C4312yes—
493#41#41×C4312yes—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8C2×D4×C4311yescharacteristic
501C2×Q8C2×D4×C4311yescharacteristic
502C2×D4—21no—
503C2×D4—21no—
504C2×D4C2×D4×C4311yescharacteristic
505C2×D4C2×D4×C4311yescharacteristic
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4C24×C4311yescharacteristic
517Q16—22no—
518Q16—42no—
519SD16—22no—
520SD16—22no—
521SD16—42no—
522D8—22no—
523M16—24no—
524M16—21no—
525M16—21no—
526M16—21no—
527M16—21no—
528M16—21no—
529M16—21no—
530M16—21no—
531M16#41×C4312yes—
532C2×C8—24no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8C2×D4×C4311yescharacteristic
542C2×C8C2×D4×C4311yescharacteristic
543C2×C8C2×D4×C4311yescharacteristic
544C2×C8C2×D4×C4311yescharacteristic
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—41no—
552C4⋊C4—41no—
553C4⋊C4—41no—
554C4⋊C4—41no—
555C4⋊C4—41no—
556C4⋊C4C2×D4×C4311yescharacteristic
557C4⋊C4C2×D4×C4311yescharacteristic
558C4⋊C4C2×D4×C4311yescharacteristic
559C4⋊C4C2×D4×C4311yescharacteristic
560C22⋊C4—21no—
561C22⋊C4—21no—
562C22⋊C4—41no—
563C22⋊C4—41no—
564C22⋊C4—41no—
565C22⋊C4—41no—
566C22⋊C4—41no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—41no—
572C42—41no—
573C42—41no—
574C23—21no—
575C23—21no—
576C23H(5,𝔽2)×C4311yescharacteristic
577Q8—21no—
578Q8—21no—
579Q8—21no—
580Q8—41no—
581Q8—41no—
582Q8—41no—
583Q8—41no—
584Q8#123×C4312yes—
585D4—22no—
586D4—22no—
587D4—21no—
588D4—21no—
589D4—21no—
590D4—41no—
591D4—41no—
592D4#123×C4312yes—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—81no—
613C2×C4—81no—
614C2×C4—81no—
615C2×C4—161no—
616C2×C4—161no—
617C2×C4—161no—
618C2×C4C22×D4×C4311yescharacteristic
619C2×C4C22×D4×C4311yescharacteristic
620C2×C4C2×#41×C4311yescharacteristic
621C2×C4C2×#41×C4311yescharacteristic
622C2×C4C2×#41×C4311yescharacteristic
623C2×C42−1+4×C4311yescharacteristic
624C8—21no—
625C8—21no—
626C8—21no—
627C8—22no—
628C8—21no—
629C8—41no—
630C8—41no—
631C8—41no—
632C22—21no—
633C22—21no—
634C22—22no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22C43×#53911yescharacteristic
641C22D42×C4311yescharacteristic
642C22C43×#55311yescharacteristic
643C4—22no—
644C4—41no—
645C4—41no—
646C4—41no—
647C4—41no—
648C4—41no—
649C4—81no—
650C4—81no—
651C4—81no—
652C4—81no—
653C4—81no—
654C4C2×#123×C4311yescharacteristic
655C4C43×#52511yescharacteristic
656C4C43×#54711yescharacteristic
657C4C43×#54811yescharacteristic
658C2—21no—
659C2—21no—
660C2—42no—
661C2—81no—
662C2C43×#244311yescharacteristic
663C2C43×#328911yescharacteristic
664C2C43×#329011yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC2×#135×C43C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C22×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3097C2semidirect
4. C43×#2912C2semidirect
5. C43×#2097C2semidirect
6. C43×#2089C2semidirect
7. C43×#2079C2semidirect
8. C43×#2038C2semidirect
9. C43×#1930C2semidirect
10. C43×#1922C2semidirect
11. C43×#1908C2semidirect
12. C43×#1882C2semidirect
14. C43×#1860C2semidirect
15. C43×#1860C2semidirect
299. #26192C43direct (N × H)
326. #3097C2×C43semidirect
329. #2912C2×C43semidirect
330. #2097C2×C43semidirect
331. #2089C2×C43semidirect
332. #2079C2×C43semidirect
333. #2038C2×C43semidirect
334. #1930C2×C43semidirect
335. #1922C2×C43semidirect
336. #1908C2×C43semidirect
337. #1882C2×C43semidirect
339. #1860C2×C43semidirect
340. #1860C2×C43semidirect
399. C43#26192direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#30972
C43×#30462
C43×#29512
C43×#29122
C43×#20972
C43×#20892
C43×#20792
C43×#20382
C43×#19302
C43×#19222
C43×#19082
C43×#18822
C43×#18762
C43×#18602
#2619243