Finite Group Databasebeta

← C43×#15849 #24935866

Subgroups — C43×#15849 #24935866

Order 11008.

1522 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#125×C43C211yesmaximal, characteristic
2C2×C43×#395C211yesmaximal, characteristic
3C2×C43×#395C211yesmaximal, characteristic
4C2×C43×#391C211yesmaximal, characteristic
5C43×#1445C211yesmaximal, characteristic
6C43×#1444C212yesmaximal
7C43×#1442C212yesmaximal
8C43×#1441C212yesmaximal
9C43×#1436C212yesmaximal
10C43×#1436C211yesmaximal, characteristic
11C43×#1436C211yesmaximal, characteristic
12C23×Q8×C43C2211yescharacteristic
13C2×#125×C43—24no—
14C2×#125×C43—24no—
15C2×#125×C43—24no—
16C22×C4⋊C4×C43C2211yescharacteristic
17C22×C4⋊C4×C43C2211yescharacteristic
18C22×C4⋊C4×C43C2211yescharacteristic
19C22×C4⋊C4×C43C2212yes—
20C22×C4⋊C4×C43C2212yes—
21C22×C4⋊C4×C43C2211yescharacteristic
22C22×C4⋊C4×C43C2211yescharacteristic
23C22×C4⋊C4×C43C2211yescharacteristic
24C22×C42×C43C2211yescharacteristic
25C22×C42×C43C2211yescharacteristic
26C43×#395—24no—
27C43×#395—24no—
28C43×#391—24no—
29C2×#95×C43C2212yes—
30C2×#95×C43C2211yescharacteristic
31C2×#95×C43C2211yescharacteristic
32C2×#95×C43C2212yes—
33C2×#95×C43C2212yes—
34C2×#95×C43C2212yes—
35C2×#95×C43C2212yes—
36C2×#95×C43C2212yes—
37C2×#95×C43C2212yes—
38C2×#95×C43C2212yes—
39C2×#95×C43C2212yes—
40C2×#95×C43C2212yes—
41C22×Q8×C43—22no—
42C22×Q8×C43—22no—
43C22×Q8×C43—22no—
44C22×Q8×C43—24no—
45C22×Q8×C43—42no—
46C23×C4×C43C2311yescharacteristic
47C23×C4×C43C2311yescharacteristic
48C23×C4×C43C2311yescharacteristic
49C23×C4×C43C2311yescharacteristic
50C23×C4×C43C2311yescharacteristic
51C23×C4×C43C2312yes—
52C23×C4×C43C2312yes—
53C23×C4×C43C2312yes—
54C23×C4×C43C2312yes—
55C23×C4×C43C2311yescharacteristic
56C23×C4×C43C2311yescharacteristic
57#125×C43—232no—
58C2×C4⋊C4×C43—22no—
59C2×C4⋊C4×C43—22no—
60C2×C4⋊C4×C43—22no—
61C2×C4⋊C4×C43—22no—
62C2×C4⋊C4×C43—22no—
63C2×C4⋊C4×C43—22no—
64C2×C4⋊C4×C43—22no—
65C2×C4⋊C4×C43—22no—
66C2×C4⋊C4×C43—22no—
67C2×C4⋊C4×C43—22no—
68C2×C4⋊C4×C43—22no—
69C2×C4⋊C4×C43—22no—
70C2×C4⋊C4×C43—22no—
71C2×C4⋊C4×C43—22no—
72C2×C4⋊C4×C43—22no—
73C2×C4⋊C4×C43—24no—
74C2×C4⋊C4×C43—24no—
75C2×C4⋊C4×C43—24no—
76C2×C4⋊C4×C43—24no—
77C2×C4⋊C4×C43—42no—
78C2×C4⋊C4×C43—42no—
79C2×C4⋊C4×C43D414yes—
80C2×C4⋊C4×C43D414yes—
81C2×C4⋊C4×C43D414yes—
82C2×C42×C43—22no—
83C2×C42×C43—22no—
84C2×C42×C43—22no—
85C2×C42×C43—22no—
86C2×C42×C43—42no—
87#95×C43—24no—
88#95×C43—24no—
89#95×C43—22no—
90#95×C43—22no—
91#95×C43—24no—
92#95×C43—24no—
93#95×C43—24no—
94#95×C43—24no—
95#95×C43—24no—
96#95×C43—42no—
97#95×C43—42no—
98#95×C43Q818yescomplemented
99C24×C43C2411yescharacteristic
100C2×Q8×C43—28no—
101C2×Q8×C43—48no—
102C2×Q8×C43—48no—
103C2×Q8×C43—44no—
104C2×Q8×C43—44no—
105C22×C4×C43—21no—
106C22×C4×C43—21no—
107C22×C4×C43—22no—
108C22×C4×C43—22no—
109C22×C4×C43—22no—
110C22×C4×C43—22no—
111C22×C4×C43—22no—
112C22×C4×C43—22no—
113C22×C4×C43—21no—
114C22×C4×C43—21no—
115C22×C4×C43—21no—
116C22×C4×C43—21no—
117C22×C4×C43—21no—
118C22×C4×C43—21no—
119C22×C4×C43—21no—
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—22no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43—22no—
128C22×C4×C43—22no—
129C22×C4×C43—22no—
130C22×C4×C43—22no—
131C22×C4×C43—22no—
132C22×C4×C43—22no—
133C22×C4×C43—22no—
134C22×C4×C43—22no—
135C22×C4×C43—22no—
136C22×C4×C43—22no—
137C22×C4×C43—22no—
138C22×C4×C43—22no—
139C22×C4×C43—22no—
140C22×C4×C43—22no—
141C22×C4×C43—22no—
142C22×C4×C43—22no—
143C22×C4×C43—22no—
144C22×C4×C43—22no—
145C22×C4×C43—22no—
146C22×C4×C43—22no—
147C22×C4×C43—22no—
148C22×C4×C43—22no—
149C22×C4×C43—22no—
150C22×C4×C43—22no—
151C22×C4×C43—22no—
152C22×C4×C43—22no—
153C22×C4×C43—22no—
154C22×C4×C43C2×D412yes—
155C22×C4×C43C2×D412yes—
156C22×C4×C43C2×D412yes—
157C22×C4×C43C2×D412yes—
158C22×C4×C43C2×D412yes—
159C22×C4×C43C2×D412yes—
160C22×C4×C43C2×D412yes—
161C22×C4×C43C2×D412yes—
162C22×C4×C43C2×D412yes—
163C22×C4×C43C2×Q814yes—
164C22×C4×C43C2×Q814yes—
165C22×C4×C43C2×Q814yes—
166C22×C4×C43#4114yes—
167C22×C4×C43#4114yes—
168C4⋊C4×C43—28no—
169C4⋊C4×C43—28no—
170C4⋊C4×C43—28no—
171C4⋊C4×C43—28no—
172C4⋊C4×C43—28no—
173C4⋊C4×C43—28no—
174C4⋊C4×C43—48no—
175C4⋊C4×C43—48no—
176C42×C43—28no—
177C42×C43—44no—
178C23×C43C22×D411yescharacteristic
179C23×C43C22×D411yescharacteristic
180C23×C43C22×D411yescharacteristic
181C23×C43C22×Q812yes—
182C23×C43C2×#4112yes—
183C23×C43C2×#4112yes—
184C23×C43H(5,𝔽2)12yes—
185C23×C432−1+412yes—
186C23×C432−1+412yes—
187Q8×C43—416no—
188C2×C4×C43—22no—
189C2×C4×C43—22no—
190C2×C4×C43—22no—
191C2×C4×C43—22no—
192C2×C4×C43—24no—
193C2×C4×C43—24no—
194C2×C4×C43—24no—
195C2×C4×C43—24no—
196C2×C4×C43—22no—
197C2×C4×C43—22no—
198C2×C4×C43—22no—
199C2×C4×C43—22no—
200C2×C4×C43—22no—
201C2×C4×C43—24no—
202C2×C4×C43—22no—
203C2×C4×C43—24no—
204C2×C4×C43—22no—
205C2×C4×C43—24no—
206C2×C4×C43—24no—
207C2×C4×C43—24no—
208C2×C4×C43—24no—
209C2×C4×C43—24no—
210C2×C4×C43—24no—
211C2×C4×C43—24no—
212C2×C4×C43—24no—
213C2×C4×C43—24no—
214C2×C4×C43—24no—
215C2×C4×C43—24no—
216C2×C4×C43—24no—
217C2×C4×C43—24no—
218C2×C4×C43—24no—
219C2×C4×C43—42no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—42no—
225C2×C4×C43—42no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—42no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—42no—
232C2×C4×C43—42no—
233C2×C4×C43—42no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43—42no—
237C2×C4×C43—42no—
238C2×C4×C43—42no—
239C2×C4×C43—42no—
240C2×C4×C43—42no—
241C2×C4×C43—42no—
242C2×C4×C43—42no—
243C2×C4×C43—42no—
244C2×C4×C43—42no—
245C2×C4×C43—42no—
246C2×C4×C43—42no—
247C2×C4×C43—42no—
248C2×C4×C43—42no—
249C2×C4×C43#12014yes—
250C2×C4×C43C4⋊Q814yes—
251#15849C4311yesmaximal, characteristic, direct product factor, Sylow
252C22×C43C2×#12011yescharacteristic
253C22×C43#52511yescharacteristic
254C22×C43C2×C4⋊Q811yescharacteristic
255C22×C43#53211yescharacteristic
256C22×C43#53312yes—
257C22×C43#53511yescharacteristic
258C22×C43#53611yescharacteristic
259C22×C43#53611yescharacteristic
260C22×C43#53912yes—
261C22×C43#54112yes—
262C22×C43#54412yes—
263C22×C43#54612yes—
264C22×C43#54612yes—
265C22×C43#54712yes—
266C22×C43#54812yes—
267C22×C43D4×Q812yes—
268C22×C43D4×Q812yes—
269C22×C43#55212yes—
270C22×C43#55412yes—
271C22×C43#55712yes—
272C22×C43#56312yes—
273C4×C43—24no—
274C4×C43—24no—
275C4×C43—42no—
276C4×C43—42no—
277C4×C43—44no—
278C4×C43—42no—
279C4×C43—42no—
280C4×C43—42no—
281C4×C43—44no—
282C4×C43—44no—
283C4×C43—44no—
284C22×#125C2×C4311yescharacteristic
285C2×#395C2×C4311yescharacteristic
286C2×#395C2×C4311yescharacteristic
287C2×#391C2×C4311yescharacteristic
288#1445C2×C4311yescharacteristic
289#1444C2×C4312yes—
290#1442C2×C4312yes—
291#1441C2×C4312yes—
292#1436C2×C4312yes—
293#1436C2×C4311yescharacteristic
294#1436C2×C4311yescharacteristic
295C2×C43#240411yescharacteristic
296C2×C43#243211yescharacteristic
297C2×C43#243411yescharacteristic
298C2×C43#246212yes—
299C2×C43#255012yes—
300C2×C43#255612yes—
301C2×C43#269012yes—
302C2×C43#271312yes—
303C2×C43#272012yes—
304C23×Q8C22×C4311yescharacteristic
305C2×#125—24no—
306C2×#125—24no—
307C2×#125—24no—
308C22×C4⋊C4C22×C4311yescharacteristic
309C22×C4⋊C4C22×C4311yescharacteristic
310C22×C4⋊C4C22×C4311yescharacteristic
311C22×C4⋊C4C22×C4312yes—
312C22×C4⋊C4C22×C4312yes—
313C22×C4⋊C4C22×C4311yescharacteristic
314C22×C4⋊C4C22×C4311yescharacteristic
315C22×C4⋊C4C22×C4311yescharacteristic
316C22×C42C22×C4311yescharacteristic
317C22×C42C22×C4311yescharacteristic
318#395—24no—
319#395—24no—
320#391—24no—
321C2×#95C22×C4312yes—
322C2×#95C22×C4311yescharacteristic
323C2×#95C22×C4311yescharacteristic
324C2×#95C22×C4312yes—
325C2×#95C22×C4312yes—
326C2×#95C22×C4312yes—
327C2×#95C22×C4312yes—
328C2×#95C22×C4312yes—
329C2×#95C22×C4312yes—
330C2×#95C22×C4312yes—
331C2×#95C22×C4312yes—
332C2×#95C22×C4312yes—
333C43#1584911yescharacteristic, direct product factor, Sylow
334C22×Q8—22no—
335C22×Q8—22no—
336C22×Q8—22no—
337C22×Q8—24no—
338C22×Q8—42no—
339C23×C4C23×C4311yescharacteristic
340C23×C4C23×C4311yescharacteristic
341C23×C4C23×C4311yescharacteristic
342C23×C4C23×C4311yescharacteristic
343C23×C4C23×C4311yescharacteristic
344C23×C4C23×C4312yes—
345C23×C4C23×C4312yes—
346C23×C4C23×C4312yes—
347C23×C4C23×C4312yes—
348C23×C4C23×C4311yescharacteristic
349C23×C4C23×C4311yescharacteristic
350#125—232no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—42no—
371C2×C4⋊C4—42no—
372C2×C4⋊C4D4×C4314yes—
373C2×C4⋊C4D4×C4314yes—
374C2×C4⋊C4D4×C4314yes—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—42no—
380#95—24no—
381#95—24no—
382#95—22no—
383#95—22no—
384#95—24no—
385#95—24no—
386#95—24no—
387#95—24no—
388#95—24no—
389#95—42no—
390#95—42no—
391#95Q8×C4318yescomplemented
392C24C24×C4311yescharacteristic
393C2×Q8—28no—
394C2×Q8—48no—
395C2×Q8—48no—
396C2×Q8—44no—
397C2×Q8—44no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4C2×D4×C4312yes—
448C22×C4C2×D4×C4312yes—
449C22×C4C2×D4×C4312yes—
450C22×C4C2×D4×C4312yes—
451C22×C4C2×D4×C4312yes—
452C22×C4C2×D4×C4312yes—
453C22×C4C2×D4×C4312yes—
454C22×C4C2×D4×C4312yes—
455C22×C4C2×D4×C4312yes—
456C22×C4C2×Q8×C4314yes—
457C22×C4C2×Q8×C4314yes—
458C22×C4C2×Q8×C4314yes—
459C22×C4#41×C4314yes—
460C22×C4#41×C4314yes—
461C4⋊C4—28no—
462C4⋊C4—28no—
463C4⋊C4—28no—
464C4⋊C4—28no—
465C4⋊C4—28no—
466C4⋊C4—28no—
467C4⋊C4—48no—
468C4⋊C4—48no—
469C42—28no—
470C42—44no—
471C23C22×D4×C4311yescharacteristic
472C23C22×D4×C4311yescharacteristic
473C23C22×D4×C4311yescharacteristic
474C23C22×Q8×C4312yes—
475C23C2×#41×C4312yes—
476C23C2×#41×C4312yes—
477C23H(5,𝔽2)×C4312yes—
478C232−1+4×C4312yes—
479C232−1+4×C4312yes—
480Q8—416no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—24no—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—22no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4#120×C4314yes—
543C2×C4C4⋊Q8×C4314yes—
544C22C2×#120×C4311yescharacteristic
545C22C43×#52511yescharacteristic
546C22C2×C4⋊Q8×C4311yescharacteristic
547C22C43×#53211yescharacteristic
548C22C43×#53312yes—
549C22C43×#53511yescharacteristic
550C22C43×#53611yescharacteristic
551C22C43×#53611yescharacteristic
552C22C43×#53912yes—
553C22C43×#54112yes—
554C22C43×#54412yes—
555C22C43×#54612yes—
556C22C43×#54612yes—
557C22C43×#54712yes—
558C22C43×#54812yes—
559C22D4×Q8×C4312yes—
560C22D4×Q8×C4312yes—
561C22C43×#55212yes—
562C22C43×#55412yes—
563C22C43×#55712yes—
564C22C43×#56312yes—
565C4—24no—
566C4—24no—
567C4—44no—
568C4—42no—
569C4—42no—
570C4—42no—
571C4—42no—
572C4—42no—
573C4—44no—
574C4—44no—
575C4—44no—
576C2C43×#240411yescharacteristic
577C2C43×#243211yescharacteristic
578C2C43×#243411yescharacteristic
579C2C43×#246212yes—
580C2C43×#255012yes—
581C2C43×#255612yes—
582C2C43×#269012yes—
583C2C43×#271312yes—
584C2C43×#272012yes—
subgroupG/H
center, socle, prime radicalC24×C43C24
commutator, Frattini, cosocleC24C24×C43
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C43 ◁ G

Complements

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

NH ≅ G/Ntype
98. #95×C43Q8semidirect
251. #15849C43direct (N × H)
333. C43#15849direct (N × H)
391. #95Q8×C43semidirect

Maximal subgroups

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

subgroupindex
C22×#125×C432
C2×C43×#3952
C2×C43×#3912
C43×#14452
C43×#14442
C43×#14422
C43×#14412
C43×#14362
#1584943