Finite Group Databasebeta

← C43×#14641 #24934658

Subgroups — C43×#14641 #24934658

Order 11008.

1486 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#394C211yesmaximal, characteristic
2C43×#1445C211yesmaximal, characteristic, complemented
3C43×#1442C212yesmaximal, complemented
4C43×#1440C212yesmaximal, complemented
5C43×#1439C212yesmaximal, complemented
6C43×#1439C212yesmaximal, complemented
7C43×#1438C212yesmaximal
8C43×#1437C212yesmaximal, complemented
9C43×#1436C211yesmaximal, characteristic, complemented
10C23×D4×C43C2211yescharacteristic
11C22×C4⋊C4×C43C2212yes—
12C22×C4⋊C4×C43C2211yescharacteristic
13C22×C22⋊C4×C43C2212yes—
14C22×C22⋊C4×C43C2212yes—
15C22×C22⋊C4×C43C2212yes—
16C22×C22⋊C4×C43C2212yes—
17C22×C22⋊C4×C43C2212yes—
18C22×C22⋊C4×C43C2212yes—
19C22×C42×C43C2211yescharacteristic
20C43×#394C418yescomplemented
21C2×#95×C43C2212yes—
22C2×#95×C43C2212yes—
23C2×#95×C43C2211yescharacteristic
24C2×#95×C43C2212yes—
25C2×#95×C43C2212yes—
26C2×#95×C43C2212yes—
27C2×#95×C43C2212yes—
28C2×#95×C43C2211yescharacteristic
29C2×#95×C43C2212yes—
30C2×#95×C43C2211yescharacteristic
31C2×#95×C43C2211yescharacteristic
32C25×C43C2312yes—
33C22×D4×C43—42no—
34C22×D4×C43—42no—
35C22×D4×C43—41no—
36C22×D4×C43—41no—
37C22×D4×C43C2×C414yes—
38C23×C4×C43C2312yes—
39C23×C4×C43C2312yes—
40C23×C4×C43C2312yes—
41C23×C4×C43C2311yescharacteristic
42C23×C4×C43C2311yescharacteristic
43C23×C4×C43C2312yes—
44C23×C4×C43C2311yescharacteristic
45C23×C4×C43C2312yes—
46C2×C4⋊C4×C43—41no—
47C2×C4⋊C4×C43—41no—
48C2×C4⋊C4×C43—42no—
49C2×C4⋊C4×C43—42no—
50C2×C4⋊C4×C43—42no—
51C2×C4⋊C4×C43C2×C414yes—
52C2×C22⋊C4×C43—24no—
53C2×C22⋊C4×C43—24no—
54C2×C22⋊C4×C43—42no—
55C2×C22⋊C4×C43—42no—
56C2×C22⋊C4×C43—42no—
57C2×C22⋊C4×C43—42no—
58C2×C22⋊C4×C43—42no—
59C2×C22⋊C4×C43—42no—
60C2×C22⋊C4×C43—42no—
61C2×C22⋊C4×C43—42no—
62C2×C22⋊C4×C43—42no—
63C2×C22⋊C4×C43—42no—
64C2×C22⋊C4×C43—42no—
65C2×C22⋊C4×C43—42no—
66C2×C22⋊C4×C43—42no—
67C2×C22⋊C4×C43—42no—
68C2×C22⋊C4×C43C2×C418yes—
69C2×C22⋊C4×C43C2×C418yes—
70C2×C42×C43—42no—
71C2×C42×C43—41no—
72#95×C43—24no—
73#95×C43—42no—
74#95×C43—42no—
75#95×C43—42no—
76#95×C43—42no—
77#95×C43—42no—
78#95×C43—41no—
79#95×C43—41no—
80#95×C43—41no—
81#95×C43—42no—
82#95×C43C2×C414yes—
83C24×C43—22no—
84C24×C43—22no—
85C24×C43—22no—
86C24×C43—22no—
87C24×C43—22no—
88C24×C43—22no—
89C24×C43—22no—
90C24×C43—22no—
91C24×C43—22no—
92C24×C43—22no—
93C24×C43—22no—
94C24×C43—22no—
95C24×C43—22no—
96C24×C43—22no—
97C24×C43C22×C414yes—
98C24×C43C2411yescharacteristic
99C2×D4×C43—48no—
100C2×D4×C43—44no—
101C2×D4×C43—48no—
102C2×D4×C43—44no—
103C2×D4×C43—44no—
104C22×C4×C43—22no—
105C22×C4×C43—22no—
106C22×C4×C43—22no—
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—22no—
114C22×C4×C43—21no—
115C22×C4×C43—21no—
116C22×C4×C43—21no—
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—21no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
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×C43C22×C414yes—
150C22×C4×C43C22×C412yes—
151C22×C4×C43C22×C412yes—
152C22×C4×C43C22×C412yes—
153C22×C4×C43#4114yes—
154C4⋊C4×C43—44no—
155C4⋊C4×C43—48no—
156C22⋊C4×C43—48no—
157C22⋊C4×C43—48no—
158C22⋊C4×C43—48no—
159C22⋊C4×C43—48no—
160C22⋊C4×C43—48no—
161C22⋊C4×C43—48no—
162C42×C43—44no—
163C23×C43—24no—
164C23×C43—24no—
165C23×C43—24no—
166C23×C43—24no—
167C23×C43—24no—
168C23×C43—24no—
169C23×C43—24no—
170C23×C43—42no—
171C23×C43—42no—
172C23×C43—42no—
173C23×C43—42no—
174C23×C43—42no—
175C23×C43—42no—
176C23×C43—42no—
177C23×C43—42no—
178C23×C43—42no—
179C23×C43—42no—
180C23×C43—42no—
181C23×C43—42no—
182C23×C43—42no—
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×C43C23×C411yescharacteristic
199C23×C43C2×#4112yes—
200C23×C43H(5,𝔽2)11yescharacteristic
201C23×C43H(5,𝔽2)12yes—
202C23×C43H(5,𝔽2)12yes—
203C23×C43H(5,𝔽2)11yescharacteristic
204C23×C43H(5,𝔽2)12yes—
205C23×C43H(5,𝔽2)12yes—
206C23×C432−1+412yes—
207D4×C43—416no—
208C2×C4×C43—22no—
209C2×C4×C43—22no—
210C2×C4×C43—24no—
211C2×C4×C43—24no—
212C2×C4×C43—24no—
213C2×C4×C43—22no—
214C2×C4×C43—22no—
215C2×C4×C43—22no—
216C2×C4×C43—24no—
217C2×C4×C43—24no—
218C2×C4×C43—24no—
219C2×C4×C43—24no—
220C2×C4×C43—24no—
221C2×C4×C43—42no—
222C2×C4×C43—42no—
223C2×C4×C43—42no—
224C2×C4×C43—42no—
225C2×C4×C43—42no—
226C2×C4×C43—41no—
227C2×C4×C43—42no—
228C2×C4×C43—42no—
229C2×C4×C43—41no—
230C2×C4×C43—42no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
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—42no—
250C2×C4×C43—42no—
251C2×C4×C43—42no—
252C2×C4×C43—42no—
253C2×C4×C43—42no—
254C2×C4×C43—42no—
255C2×C4×C43—42no—
256C2×C4×C43—42no—
257C2×C4×C43—42no—
258#14641C4311yesmaximal, characteristic, direct product factor, Sylow
259C22×C43—44no—
260C22×C43—44no—
261C22×C43—44no—
262C22×C43—44no—
263C22×C43—44no—
264C22×C43—44no—
265C22×C43—44no—
266C22×C43—82no—
267C22×C43—82no—
268C22×C43—82no—
269C22×C43—82no—
270C22×C43—82no—
271C22×C43—82no—
272C22×C43—82no—
273C22×C43—82no—
274C22×C43C4×#4111yescharacteristic
275C22×C43#51811yescharacteristic
276C22×C43#51811yescharacteristic
277C22×C43#51812yes—
278C22×C43#52012yes—
279C22×C43#53812yes—
280C22×C43#53812yes—
281C22×C43#53912yes—
282C22×C43#54012yes—
283C22×C43#54012yes—
284C22×C43#54212yes—
285C22×C43#56012yes—
286C22×C43#56012yes—
287C22×C43#56012yes—
288C22×C43#56011yescharacteristic
289C22×C43H(3,𝔽4)11yescharacteristic
290C22×C43H(3,𝔽4)11yescharacteristic
291C22×C43#56212yes—
292C22×C43#56212yes—
293C22×C43#56212yes—
294C22×C43#56311yescharacteristic
295C4×C43—44no—
296C4×C43—42no—
297C4×C43—42no—
298C4×C43—42no—
299C4×C43—44no—
300C4×C43—82no—
301C4×C43—82no—
302C4×C43—82no—
303C2×#394C2×C4311yescharacteristic
304#1445C2×C4311yescharacteristic, complemented
305#1442C2×C4312yescomplemented
306#1440C2×C4312yescomplemented
307#1439C2×C4312yescomplemented
308#1439C2×C4312yescomplemented
309#1438C2×C4312yes—
310#1437C2×C4312yescomplemented
311#1436C2×C4311yescharacteristic, complemented
312C2×C43—84no—
313C2×C43#233311yescharacteristic
314C2×C43#233512yes—
315C2×C43#237511yescharacteristic
316C2×C43#237712yes—
317C2×C43#237911yescharacteristic
318C2×C43#282412yes—
319C2×C43#282812yes—
320C2×C43#282912yes—
321C2×C43#283712yes—
322C23×D4C22×C4311yescharacteristic
323C22×C4⋊C4C22×C4312yes—
324C22×C4⋊C4C22×C4311yescharacteristic
325C22×C22⋊C4C22×C4312yes—
326C22×C22⋊C4C22×C4312yes—
327C22×C22⋊C4C22×C4312yes—
328C22×C22⋊C4C22×C4312yes—
329C22×C22⋊C4C22×C4312yes—
330C22×C22⋊C4C22×C4312yes—
331C22×C42C22×C4311yescharacteristic
332#394C4×C4318yescomplemented
333C2×#95C22×C4312yes—
334C2×#95C22×C4312yes—
335C2×#95C22×C4311yescharacteristic
336C2×#95C22×C4312yes—
337C2×#95C22×C4312yes—
338C2×#95C22×C4312yes—
339C2×#95C22×C4312yes—
340C2×#95C22×C4311yescharacteristic
341C2×#95C22×C4312yes—
342C2×#95C22×C4311yescharacteristic
343C2×#95C22×C4311yescharacteristic
344C43#1464111yescharacteristic, direct product factor, Sylow
345C25C23×C4312yes—
346C22×D4—42no—
347C22×D4—42no—
348C22×D4—41no—
349C22×D4—41no—
350C22×D4C2×C4×C4314yes—
351C23×C4C23×C4312yes—
352C23×C4C23×C4312yes—
353C23×C4C23×C4312yes—
354C23×C4C23×C4311yescharacteristic
355C23×C4C23×C4312yes—
356C23×C4C23×C4311yescharacteristic
357C23×C4C23×C4311yescharacteristic
358C23×C4C23×C4312yes—
359C2×C4⋊C4—41no—
360C2×C4⋊C4—41no—
361C2×C4⋊C4—42no—
362C2×C4⋊C4—42no—
363C2×C4⋊C4—42no—
364C2×C4⋊C4C2×C4×C4314yes—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4C2×C4×C4318yes—
382C2×C22⋊C4C2×C4×C4318yes—
383C2×C42—42no—
384C2×C42—41no—
385#95—24no—
386#95—42no—
387#95—42no—
388#95—42no—
389#95—42no—
390#95—42no—
391#95—41no—
392#95—41no—
393#95—41no—
394#95—42no—
395#95C2×C4×C4314yes—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24C22×C4×C4314yes—
411C24C24×C4311yescharacteristic
412C2×D4—44no—
413C2×D4—48no—
414C2×D4—48no—
415C2×D4—44no—
416C2×D4—44no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—21no—
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×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4C22×C4×C4314yes—
463C22×C4C22×C4×C4312yes—
464C22×C4C22×C4×C4312yes—
465C22×C4C22×C4×C4312yes—
466C22×C4#41×C4314yes—
467C4⋊C4—44no—
468C4⋊C4—48no—
469C22⋊C4—48no—
470C22⋊C4—48no—
471C22⋊C4—48no—
472C22⋊C4—48no—
473C22⋊C4—48no—
474C22⋊C4—48no—
475C42—44no—
476C23—24no—
477C23—24no—
478C23—24no—
479C23—24no—
480C23—24no—
481C23—24no—
482C23—24no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23C23×C4×C4311yescharacteristic
512C23C2×#41×C4312yes—
513C23H(5,𝔽2)×C4311yescharacteristic
514C23H(5,𝔽2)×C4312yes—
515C23H(5,𝔽2)×C4312yes—
516C23H(5,𝔽2)×C4311yescharacteristic
517C23H(5,𝔽2)×C4312yes—
518C23H(5,𝔽2)×C4312yes—
519C232−1+4×C4312yes—
520D4—416no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—41no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—41no—
544C2×C4—42no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C22—44no—
572C22—44no—
573C22—44no—
574C22—44no—
575C22—44no—
576C22—44no—
577C22—44no—
578C22—82no—
579C22—82no—
580C22—82no—
581C22—82no—
582C22—82no—
583C22—82no—
584C22—82no—
585C22—82no—
586C22C4×#41×C4311yescharacteristic
587C22C43×#51811yescharacteristic
588C22C43×#51811yescharacteristic
589C22C43×#51812yes—
590C22C43×#52012yes—
591C22C43×#53812yes—
592C22C43×#53812yes—
593C22C43×#53912yes—
594C22C43×#54012yes—
595C22C43×#54012yes—
596C22C43×#54212yes—
597C22C43×#56012yes—
598C22C43×#56011yescharacteristic
599C22C43×#56012yes—
600C22C43×#56012yes—
601C22C43×H(3,𝔽4)11yescharacteristic
602C22C43×H(3,𝔽4)11yescharacteristic
603C22C43×#56212yes—
604C22C43×#56212yes—
605C22C43×#56212yes—
606C22C43×#56311yescharacteristic
607C4—42no—
608C4—42no—
609C4—42no—
610C4—44no—
611C4—44no—
612C4—82no—
613C4—82no—
614C4—82no—
615C2—84no—
616C2C43×#233311yescharacteristic
617C2C43×#233512yes—
618C2C43×#237511yescharacteristic
619C2C43×#237712yes—
620C2C43×#237911yescharacteristic
621C2C43×#282412yes—
622C2C43×#282812yes—
623C2C43×#282912yes—
624C2C43×#283712yes—
subgroupG/H
center, socleC24×C43C24
commutatorC23C23×C4×C43
Frattini, cosocleC24C24×C43
prime radicalC23×D4×C43C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#1445C2semidirect
3. C43×#1442C2semidirect
4. C43×#1440C2semidirect
5. C43×#1439C2semidirect
6. C43×#1439C2semidirect
8. C43×#1437C2semidirect
9. C43×#1436C2semidirect
20. C43×#394C4semidirect
258. #14641C43direct (N × H)
304. #1445C2×C43semidirect
305. #1442C2×C43semidirect
306. #1440C2×C43semidirect
307. #1439C2×C43semidirect
308. #1439C2×C43semidirect
310. #1437C2×C43semidirect
311. #1436C2×C43semidirect
332. #394C4×C43semidirect
344. C43#14641direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#3942
C43×#14452
C43×#14422
C43×#14402
C43×#14392
C43×#14382
C43×#14372
C43×#14362
#1464143