Finite Group Databasebeta

← C43×#17084 #24937101

Subgroups — C43×#17084 #24937101

Order 11008.

1698 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#395C211yesmaximal, characteristic, complemented
2C2×C43×#394C211yesmaximal, characteristic
3C2×C43×#394C212yesmaximal
4C2×C43×#393C212yesmaximal, complemented
5C43×#1445C211yesmaximal, characteristic, complemented
6C43×#1441C212yesmaximal, complemented
7C43×#1440C212yesmaximal, complemented
8C43×#1439C212yesmaximal, complemented
9C43×#1439C212yesmaximal, complemented
10C23×Q8×C43C2211yescharacteristic
11C23×D4×C43C2211yescharacteristic
12C22×C4⋊C4×C43C2212yes—
13C22×C4⋊C4×C43C2212yes—
14C22×C4⋊C4×C43C2211yescharacteristic
15C22×C22⋊C4×C43C2212yes—
16C22×C22⋊C4×C43C2212yes—
17C22×C22⋊C4×C43C2212yes—
18C22×C22⋊C4×C43C2212yes—
19C22×C22⋊C4×C43C2212yes—
20C22×C22⋊C4×C43C2212yes—
21C43×#395—24no—
22C43×#394—24no—
23C43×#394—28no—
24C43×#393—28no—
25C2×#95×C43C2212yes—
26C2×#95×C43C2212yes—
27C2×#95×C43C2212yes—
28C2×#95×C43C2211yescharacteristic
29C2×#95×C43C2212yes—
30C2×#95×C43C2211yescharacteristic
31C2×#95×C43C2212yes—
32C2×#95×C43C2211yescharacteristic
33C2×#95×C43C2212yes—
34C2×#95×C43C2211yescharacteristic
35C25×C43C2312yes—
36C22×Q8×C43—24no—
37C22×Q8×C43—22no—
38C22×Q8×C43—42no—
39C22×Q8×C43—41no—
40C22×Q8×C43—41no—
41C22×D4×C43—24no—
42C22×D4×C43—22no—
43C22×D4×C43—41no—
44C22×D4×C43—42no—
45C22×D4×C43—41no—
46C23×C4×C43C2312yes—
47C23×C4×C43C2312yes—
48C23×C4×C43C2311yescharacteristic
49C23×C4×C43C2312yes—
50C23×C4×C43C2312yes—
51C23×C4×C43C2311yescharacteristic
52C23×C4×C43C2311yescharacteristic
53C23×C4×C43C2312yes—
54C2×C4⋊C4×C43—24no—
55C2×C4⋊C4×C43—24no—
56C2×C4⋊C4×C43—24no—
57C2×C4⋊C4×C43—41no—
58C2×C4⋊C4×C43—41no—
59C2×C4⋊C4×C43—42no—
60C2×C4⋊C4×C43—42no—
61C2×C4⋊C4×C43—42no—
62C2×C4⋊C4×C43D414yes—
63C2×C22⋊C4×C43—24no—
64C2×C22⋊C4×C43—24no—
65C2×C22⋊C4×C43—24no—
66C2×C22⋊C4×C43—24no—
67C2×C22⋊C4×C43—24no—
68C2×C22⋊C4×C43—24no—
69C2×C22⋊C4×C43—24no—
70C2×C22⋊C4×C43—24no—
71C2×C22⋊C4×C43—24no—
72C2×C22⋊C4×C43—42no—
73C2×C22⋊C4×C43—42no—
74C2×C22⋊C4×C43—42no—
75C2×C22⋊C4×C43—42no—
76C2×C22⋊C4×C43—42no—
77C2×C22⋊C4×C43—42no—
78C2×C22⋊C4×C43—42no—
79C2×C22⋊C4×C43—42no—
80C2×C22⋊C4×C43D418yes—
81#95×C43—24no—
82#95×C43—24no—
83#95×C43—24no—
84#95×C43—24no—
85#95×C43—22no—
86#95×C43—22no—
87#95×C43—24no—
88#95×C43—41no—
89#95×C43—42no—
90#95×C43—41no—
91C24×C43—22no—
92C24×C43—22no—
93C24×C43—22no—
94C24×C43—22no—
95C24×C43—22no—
96C24×C43—22no—
97C24×C43—22no—
98C24×C43—22no—
99C24×C43—22no—
100C24×C43—22no—
101C24×C43—22no—
102C24×C43—22no—
103C24×C43—22no—
104C24×C43—22no—
105C24×C43C2×D414yes—
106C24×C43C2411yescharacteristic
107C2×Q8×C43—44no—
108C2×Q8×C43—48no—
109C2×Q8×C43—48no—
110C2×Q8×C43—44no—
111C2×Q8×C43—44no—
112C2×D4×C43—44no—
113C2×D4×C43—48no—
114C2×D4×C43—48no—
115C2×D4×C43—44no—
116C2×D4×C43—44no—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43—22no—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
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—21no—
133C22×C4×C43—21no—
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—21no—
145C22×C4×C43—22no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—22no—
149C22×C4×C43—21no—
150C22×C4×C43—22no—
151C22×C4×C43—22no—
152C22×C4×C43—22no—
153C22×C4×C43—22no—
154C22×C4×C43—22no—
155C22×C4×C43—22no—
156C22×C4×C43—22no—
157C22×C4×C43—22no—
158C22×C4×C43—22no—
159C22×C4×C43—22no—
160C22×C4×C43—22no—
161C22×C4×C43C2×D414yes—
162C22×C4×C43C2×D412yes—
163C22×C4×C43C2×D412yes—
164C22×C4×C43C2×D414yes—
165C22×C4×C43C2×D412yes—
166C22×C4×C43#4114yes—
167C4⋊C4×C43—44no—
168C4⋊C4×C43—48no—
169C4⋊C4×C43—48no—
170C22⋊C4×C43—48no—
171C22⋊C4×C43—48no—
172C22⋊C4×C43—48no—
173C22⋊C4×C43—48no—
174C22⋊C4×C43—48no—
175C22⋊C4×C43—48no—
176C23×C43—24no—
177C23×C43—24no—
178C23×C43—24no—
179C23×C43—24no—
180C23×C43—24no—
181C23×C43—24no—
182C23×C43—24no—
183C23×C43—42no—
184C23×C43—42no—
185C23×C43—42no—
186C23×C43—42no—
187C23×C43—42no—
188C23×C43—42no—
189C23×C43—42no—
190C23×C43—42no—
191C23×C43—42no—
192C23×C43—42no—
193C23×C43—42no—
194C23×C43—42no—
195C23×C43—42no—
196C23×C43—42no—
197C23×C43—42no—
198C23×C43—42no—
199C23×C43—42no—
200C23×C43—42no—
201C23×C43—42no—
202C23×C43—42no—
203C23×C43—42no—
204C23×C43—42no—
205C23×C43—42no—
206C23×C43—42no—
207C23×C43—42no—
208C23×C43—42no—
209C23×C43—42no—
210C23×C43—42no—
211C23×C43C22×D411yescharacteristic
212C23×C43C22×D412yes—
213C23×C43C2×#4112yes—
214C23×C43H(5,𝔽2)11yescharacteristic
215C23×C43H(5,𝔽2)12yes—
216C23×C43H(5,𝔽2)11yescharacteristic
217C23×C43H(5,𝔽2)12yes—
218C23×C432−1+412yes—
219C23×C432−1+412yes—
220Q8×C43—416no—
221D4×C43—416no—
222C2×C4×C43—24no—
223C2×C4×C43—24no—
224C2×C4×C43—22no—
225C2×C4×C43—22no—
226C2×C4×C43—22no—
227C2×C4×C43—22no—
228C2×C4×C43—22no—
229C2×C4×C43—24no—
230C2×C4×C43—24no—
231C2×C4×C43—24no—
232C2×C4×C43—24no—
233C2×C4×C43—24no—
234C2×C4×C43—24no—
235C2×C4×C43—24no—
236C2×C4×C43—24no—
237C2×C4×C43—24no—
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—41no—
248C2×C4×C43—41no—
249C2×C4×C43—42no—
250C2×C4×C43—42no—
251C2×C4×C43—41no—
252C2×C4×C43—42no—
253C2×C4×C43—41no—
254C2×C4×C43—42no—
255C2×C4×C43—42no—
256C2×C4×C43—42no—
257C2×C4×C43—42no—
258C2×C4×C43—42no—
259C2×C4×C43—42no—
260C2×C4×C43—42no—
261C2×C4×C43—42no—
262C2×C4×C43—42no—
263C2×C4×C43—42no—
264C2×C4×C43—42no—
265C2×C4×C43—42no—
266C2×C4×C43—42no—
267C2×C4×C43—42no—
268C2×C4×C43—42no—
269C2×C4×C43—42no—
270C2×C4×C43—42no—
271C2×C4×C43—42no—
272#17084C4311yesmaximal, characteristic, direct product factor, Sylow
273C22×C43—44no—
274C22×C43—44no—
275C22×C43—44no—
276C22×C43—44no—
277C22×C43—44no—
278C22×C43—44no—
279C22×C43—44no—
280C22×C43—82no—
281C22×C43—82no—
282C22×C43—82no—
283C22×C43—82no—
284C22×C43—82no—
285C22×C43—82no—
286C22×C43—82no—
287C22×C43—82no—
288C22×C43#53411yescharacteristic
289C22×C43#53412yes—
290C22×C43#53511yescharacteristic
291C22×C43#53611yescharacteristic
292C22×C43#53612yes—
293C22×C43#53712yes—
294C22×C43#53812yes—
295C22×C43#54212yes—
296C22×C43#54212yes—
297C22×C43D4211yescharacteristic
298C22×C43D4212yes—
299C22×C43#54612yes—
300C22×C43#54712yes—
301C22×C43#54812yes—
302C22×C43#55511yescharacteristic
303C22×C43H(3,𝔽4)11yescharacteristic
304C22×C43#56212yes—
305C22×C43#56212yes—
306C22×C43#56212yes—
307C22×C43#56312yes—
308C22×C43#56311yescharacteristic
309C4×C43—42no—
310C4×C43—44no—
311C4×C43—42no—
312C4×C43—44no—
313C4×C43—42no—
314C4×C43—44no—
315C4×C43—82no—
316C4×C43—82no—
317C2×#395C2×C4311yescharacteristic, complemented
318C2×#394C2×C4311yescharacteristic
319C2×#394C2×C4312yes—
320C2×#393C2×C4312yescomplemented
321#1445C2×C4311yescharacteristic, complemented
322#1441C2×C4312yescomplemented
323#1440C2×C4312yescomplemented
324#1439C2×C4312yescomplemented
325#1439C2×C4312yescomplemented
326C2×C43—84no—
327C2×C43#267212yes—
328C2×C43#267412yes—
329C2×C43#267612yes—
330C2×C43#267911yescharacteristic
331C2×C43#268612yes—
332C2×C43#273111yescharacteristic
333C2×C43#281412yes—
334C2×C43#281611yescharacteristic
335C2×C43#283212yes—
336C23×Q8C22×C4311yescharacteristic
337C23×D4C22×C4311yescharacteristic
338C22×C4⋊C4C22×C4312yes—
339C22×C4⋊C4C22×C4312yes—
340C22×C4⋊C4C22×C4311yescharacteristic
341C22×C22⋊C4C22×C4312yes—
342C22×C22⋊C4C22×C4312yes—
343C22×C22⋊C4C22×C4312yes—
344C22×C22⋊C4C22×C4312yes—
345C22×C22⋊C4C22×C4312yes—
346C22×C22⋊C4C22×C4312yes—
347#395—24no—
348#394—24no—
349#394—28no—
350#393—28no—
351C2×#95C22×C4312yes—
352C2×#95C22×C4312yes—
353C2×#95C22×C4312yes—
354C2×#95C22×C4311yescharacteristic
355C2×#95C22×C4312yes—
356C2×#95C22×C4311yescharacteristic
357C2×#95C22×C4312yes—
358C2×#95C22×C4311yescharacteristic
359C2×#95C22×C4312yes—
360C2×#95C22×C4311yescharacteristic
361C43#1708411yescharacteristic, direct product factor, Sylow
362C25C23×C4312yes—
363C22×Q8—24no—
364C22×Q8—22no—
365C22×Q8—42no—
366C22×Q8—41no—
367C22×Q8—41no—
368C22×D4—24no—
369C22×D4—22no—
370C22×D4—42no—
371C22×D4—41no—
372C22×D4—41no—
373C23×C4C23×C4312yes—
374C23×C4C23×C4312yes—
375C23×C4C23×C4311yescharacteristic
376C23×C4C23×C4312yes—
377C23×C4C23×C4312yes—
378C23×C4C23×C4311yescharacteristic
379C23×C4C23×C4311yescharacteristic
380C23×C4C23×C4312yes—
381C2×C4⋊C4—24no—
382C2×C4⋊C4—24no—
383C2×C4⋊C4—24no—
384C2×C4⋊C4—41no—
385C2×C4⋊C4—41no—
386C2×C4⋊C4—42no—
387C2×C4⋊C4—42no—
388C2×C4⋊C4—42no—
389C2×C4⋊C4D4×C4314yes—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—42no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—42no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4D4×C4318yes—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—22no—
413#95—22no—
414#95—24no—
415#95—41no—
416#95—42no—
417#95—41no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24C2×D4×C4314yes—
433C24C24×C4311yescharacteristic
434C2×Q8—44no—
435C2×Q8—48no—
436C2×Q8—48no—
437C2×Q8—44no—
438C2×Q8—44no—
439C2×D4—48no—
440C2×D4—44no—
441C2×D4—44no—
442C2×D4—48no—
443C2×D4—44no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4C2×D4×C4314yes—
489C22×C4C2×D4×C4312yes—
490C22×C4C2×D4×C4312yes—
491C22×C4C2×D4×C4314yes—
492C22×C4C2×D4×C4312yes—
493C22×C4#41×C4314yes—
494C4⋊C4—44no—
495C4⋊C4—48no—
496C4⋊C4—48no—
497C22⋊C4—48no—
498C22⋊C4—48no—
499C22⋊C4—48no—
500C22⋊C4—48no—
501C22⋊C4—48no—
502C22⋊C4—48no—
503C23—24no—
504C23—24no—
505C23—24no—
506C23—24no—
507C23—24no—
508C23—24no—
509C23—24no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23C22×D4×C4311yescharacteristic
539C23C22×D4×C4312yes—
540C23C2×#41×C4312yes—
541C23H(5,𝔽2)×C4311yescharacteristic
542C23H(5,𝔽2)×C4312yes—
543C23H(5,𝔽2)×C4311yescharacteristic
544C23H(5,𝔽2)×C4312yes—
545C232−1+4×C4312yes—
546C232−1+4×C4312yes—
547Q8—416no—
548D4—416no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—41no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C22—44no—
600C22—44no—
601C22—44no—
602C22—44no—
603C22—44no—
604C22—44no—
605C22—44no—
606C22—82no—
607C22—82no—
608C22—82no—
609C22—82no—
610C22—82no—
611C22—82no—
612C22—82no—
613C22—82no—
614C22C43×#53412yes—
615C22C43×#53411yescharacteristic
616C22C43×#53511yescharacteristic
617C22C43×#53612yes—
618C22C43×#53611yescharacteristic
619C22C43×#53712yes—
620C22C43×#53812yes—
621C22C43×#54212yes—
622C22C43×#54212yes—
623C22D42×C4311yescharacteristic
624C22D42×C4312yes—
625C22C43×#54612yes—
626C22C43×#54712yes—
627C22C43×#54812yes—
628C22C43×#55511yescharacteristic
629C22C43×H(3,𝔽4)11yescharacteristic
630C22C43×#56212yes—
631C22C43×#56212yes—
632C22C43×#56212yes—
633C22C43×#56312yes—
634C22C43×#56311yescharacteristic
635C4—44no—
636C4—42no—
637C4—44no—
638C4—42no—
639C4—44no—
640C4—42no—
641C4—82no—
642C4—82no—
643C2—84no—
644C2C43×#267212yes—
645C2C43×#267412yes—
646C2C43×#267612yes—
647C2C43×#267911yescharacteristic
648C2C43×#268612yes—
649C2C43×#273111yescharacteristic
650C2C43×#281412yes—
651C2C43×#281611yescharacteristic
652C2C43×#283212yes—
subgroupG/H
center, socleC24×C43C24
commutator, Frattini, cosocleC24C24×C43
prime radicalC23×D4×C43C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#395C2semidirect
4. C2×C43×#393C2semidirect
5. C43×#1445C2semidirect
6. C43×#1441C2semidirect
7. C43×#1440C2semidirect
8. C43×#1439C2semidirect
9. C43×#1439C2semidirect
272. #17084C43direct (N × H)
317. C2×#395C2×C43semidirect
320. C2×#393C2×C43semidirect
321. #1445C2×C43semidirect
322. #1441C2×C43semidirect
323. #1440C2×C43semidirect
324. #1439C2×C43semidirect
325. #1439C2×C43semidirect
361. C43#17084direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#3952
C2×C43×#3942
C2×C43×#3932
C43×#14452
C43×#14412
C43×#14402
C43×#14392
#1708443