Finite Group Databasebeta

← C43×#17109 #24937126

Subgroups — C43×#17109 #24937126

Order 11008.

1634 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#397C212yesmaximal, complemented
2C2×C43×#396C212yesmaximal, complemented
3C2×C43×#394C212yesmaximal
4C43×#1444C211yesmaximal, characteristic, complemented
5C43×#1444C211yesmaximal, characteristic, complemented
6C43×#1441C212yesmaximal, complemented
7C43×#1439C212yesmaximal, complemented
8C43×#1439C212yesmaximal, complemented
9C43×#1438C211yesmaximal, characteristic
10C23×D4×C43C2211yescharacteristic
11C22×C4⋊C4×C43C2212yes—
12C22×C4⋊C4×C43C2211yescharacteristic
13C22×C4⋊C4×C43C2212yes—
14C22×C4⋊C4×C43C2212yes—
15C22×C4⋊C4×C43C2211yescharacteristic
16C22×C22⋊C4×C43C2212yes—
17C22×C22⋊C4×C43C2212yes—
18C22×C22⋊C4×C43C2212yes—
19C22×C22⋊C4×C43C2212yes—
20C22×C22⋊C4×C43C2212yes—
21C22×C22⋊C4×C43C2212yes—
22C43×#397—28no—
23C43×#396—28no—
24C43×#394—28no—
25C2×#95×C43C2212yes—
26C2×#95×C43C2212yes—
27C2×#95×C43C2212yes—
28C2×#95×C43C2212yes—
29C2×#95×C43C2211yescharacteristic
30C2×#95×C43C2211yescharacteristic
31C2×#95×C43C2211yescharacteristic
32C2×#95×C43C2212yes—
33C2×#95×C43C2211yescharacteristic
34C25×C43C2312yes—
35C22×D4×C43—24no—
36C22×D4×C43—22no—
37C22×D4×C43—41no—
38C22×D4×C43—41no—
39C22×D4×C43—42no—
40C23×C4×C43C2312yes—
41C23×C4×C43C2312yes—
42C23×C4×C43C2311yescharacteristic
43C23×C4×C43C2312yes—
44C23×C4×C43C2312yes—
45C23×C4×C43C2312yes—
46C23×C4×C43C2311yescharacteristic
47C23×C4×C43C2311yescharacteristic
48C2×C4⋊C4×C43—24no—
49C2×C4⋊C4×C43—24no—
50C2×C4⋊C4×C43—24no—
51C2×C4⋊C4×C43—24no—
52C2×C4⋊C4×C43—24no—
53C2×C4⋊C4×C43—24no—
54C2×C4⋊C4×C43—41no—
55C2×C4⋊C4×C43—42no—
56C2×C4⋊C4×C43—42no—
57C2×C4⋊C4×C43—42no—
58C2×C4⋊C4×C43—42no—
59C2×C4⋊C4×C43—41no—
60C2×C4⋊C4×C43—42no—
61C2×C22⋊C4×C43—24no—
62C2×C22⋊C4×C43—24no—
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—42no—
71C2×C22⋊C4×C43—42no—
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×C43D418yes—
79#95×C43—24no—
80#95×C43—24no—
81#95×C43—24no—
82#95×C43—24no—
83#95×C43—22no—
84#95×C43—42no—
85#95×C43—41no—
86#95×C43—41no—
87#95×C43D414yescomplemented
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×C43—22no—
98C24×C43—22no—
99C24×C43—22no—
100C24×C43—22no—
101C24×C43—22no—
102C24×C43C2×D414yes—
103C24×C43C2411yescharacteristic
104C2×D4×C43—44no—
105C2×D4×C43—48no—
106C2×D4×C43—48no—
107C2×D4×C43—44no—
108C2×D4×C43—44no—
109C22×C4×C43—22no—
110C22×C4×C43—22no—
111C22×C4×C43—22no—
112C22×C4×C43—22no—
113C22×C4×C43—22no—
114C22×C4×C43—22no—
115C22×C4×C43—22no—
116C22×C4×C43—22no—
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—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
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—21no—
147C22×C4×C43—22no—
148C22×C4×C43—22no—
149C22×C4×C43—22no—
150C22×C4×C43—21no—
151C22×C4×C43—22no—
152C22×C4×C43—22no—
153C22×C4×C43C2×D414yes—
154C22×C4×C43C2×D414yes—
155C22×C4×C43C2×D414yes—
156C22×C4×C43C2×D412yes—
157C22×C4×C43#4112yes—
158C22×C4×C43#4112yes—
159C4⋊C4×C43—44no—
160C4⋊C4×C43—48no—
161C4⋊C4×C43—48no—
162C4⋊C4×C43—48no—
163C4⋊C4×C43—44no—
164C22⋊C4×C43—48no—
165C22⋊C4×C43—48no—
166C22⋊C4×C43—48no—
167C22⋊C4×C43—48no—
168C22⋊C4×C43—48no—
169C22⋊C4×C43—48no—
170C23×C43—24no—
171C23×C43—24no—
172C23×C43—24no—
173C23×C43—24no—
174C23×C43—24no—
175C23×C43—24no—
176C23×C43—24no—
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×C43—42no—
199C23×C43—42no—
200C23×C43—42no—
201C23×C43—42no—
202C23×C43—42no—
203C23×C43—42no—
204C23×C43—42no—
205C23×C43C22×D412yes—
206C23×C43C22×D411yescharacteristic
207C23×C43C2×#4111yescharacteristic
208C23×C43C2×#4111yescharacteristic
209C23×C43H(5,𝔽2)11yescharacteristic
210C23×C43H(5,𝔽2)12yes—
211C23×C43H(5,𝔽2)11yescharacteristic
212C23×C43H(5,𝔽2)12yes—
213C23×C432−1+411yescharacteristic
214C23×C432−1+412yes—
215C23×C432−1+411yescharacteristic
216D4×C43—416no—
217C2×C4×C43—24no—
218C2×C4×C43—24no—
219C2×C4×C43—24no—
220C2×C4×C43—22no—
221C2×C4×C43—24no—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—24no—
225C2×C4×C43—24no—
226C2×C4×C43—24no—
227C2×C4×C43—24no—
228C2×C4×C43—24no—
229C2×C4×C43—24no—
230C2×C4×C43—24no—
231C2×C4×C43—24no—
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—41no—
241C2×C4×C43—41no—
242C2×C4×C43—42no—
243C2×C4×C43—42no—
244C2×C4×C43—42no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—42no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
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—
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—
267#17109C4311yesmaximal, characteristic, direct product factor, Sylow
268C22×C43—44no—
269C22×C43—44no—
270C22×C43—44no—
271C22×C43—44no—
272C22×C43—44no—
273C22×C43—44no—
274C22×C43—44no—
275C22×C43—82no—
276C22×C43—82no—
277C22×C43—82no—
278C22×C43—82no—
279C22×C43—82no—
280C22×C43—82no—
281C22×C43—82no—
282C22×C43—82no—
283C22×C43#53412yes—
284C22×C43#53612yes—
285C22×C43#53712yes—
286C22×C43#53711yescharacteristic
287C22×C43#53712yes—
288C22×C43#53812yes—
289C22×C43#53811yescharacteristic
290C22×C43#53911yescharacteristic
291C22×C43#54212yes—
292C22×C43D4211yescharacteristic
293C22×C43D4212yes—
294C22×C43#54612yes—
295C22×C43#54711yescharacteristic
296C22×C43#54712yes—
297C22×C43#55011yescharacteristic
298C22×C43#55611yescharacteristic
299C22×C43#56011yescharacteristic
300C22×C43#56011yescharacteristic
301C22×C43#56212yes—
302C22×C43#56212yes—
303C22×C43#56311yescharacteristic
304C22×C43#56312yes—
305C22×C43#56311yescharacteristic
306C4×C43—42no—
307C4×C43—44no—
308C4×C43—42no—
309C4×C43—44no—
310C4×C43—42no—
311C4×C43—44no—
312C4×C43—82no—
313C4×C43—82no—
314C2×#397C2×C4312yescomplemented
315C2×#396C2×C4312yescomplemented
316C2×#394C2×C4312yes—
317#1444C2×C4311yescharacteristic, complemented
318#1444C2×C4311yescharacteristic, complemented
319#1441C2×C4312yescomplemented
320#1439C2×C4312yescomplemented
321#1439C2×C4312yescomplemented
322#1438C2×C4311yescharacteristic
323C2×C43—84no—
324C2×C43#266811yescharacteristic
325C2×C43#267212yes—
326C2×C43#267511yescharacteristic
327C2×C43#268011yescharacteristic
328C2×C43#268212yes—
329C2×C43#271512yes—
330C2×C43#272711yescharacteristic
331C2×C43#281412yes—
332C2×C43#282311yescharacteristic
333C2×C43#282611yescharacteristic
334C2×C43#283011yescharacteristic
335C23×D4C22×C4311yescharacteristic
336C22×C4⋊C4C22×C4312yes—
337C22×C4⋊C4C22×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#397—28no—
348#396—28no—
349#394—28no—
350C2×#95C22×C4312yes—
351C2×#95C22×C4312yes—
352C2×#95C22×C4312yes—
353C2×#95C22×C4312yes—
354C2×#95C22×C4311yescharacteristic
355C2×#95C22×C4311yescharacteristic
356C2×#95C22×C4311yescharacteristic
357C2×#95C22×C4312yes—
358C2×#95C22×C4311yescharacteristic
359C43#1710911yescharacteristic, direct product factor, Sylow
360C25C23×C4312yes—
361C22×D4—24no—
362C22×D4—22no—
363C22×D4—41no—
364C22×D4—41no—
365C22×D4—42no—
366C23×C4C23×C4312yes—
367C23×C4C23×C4312yes—
368C23×C4C23×C4311yescharacteristic
369C23×C4C23×C4312yes—
370C23×C4C23×C4312yes—
371C23×C4C23×C4312yes—
372C23×C4C23×C4311yescharacteristic
373C23×C4C23×C4311yescharacteristic
374C2×C4⋊C4—24no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—24no—
380C2×C4⋊C4—41no—
381C2×C4⋊C4—42no—
382C2×C4⋊C4—42no—
383C2×C4⋊C4—42no—
384C2×C4⋊C4—42no—
385C2×C4⋊C4—41no—
386C2×C4⋊C4—42no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
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—42no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—42no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—42no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4D4×C4318yes—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—22no—
410#95—42no—
411#95—41no—
412#95—41no—
413#95D4×C4314yescomplemented
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24C2×D4×C4314yes—
429C24C24×C4311yescharacteristic
430C2×D4—48no—
431C2×D4—44no—
432C2×D4—44no—
433C2×D4—48no—
434C2×D4—44no—
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—21no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
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—21no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
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×C4C2×D4×C4314yes—
480C22×C4C2×D4×C4314yes—
481C22×C4C2×D4×C4314yes—
482C22×C4C2×D4×C4312yes—
483C22×C4#41×C4312yes—
484C22×C4#41×C4312yes—
485C4⋊C4—44no—
486C4⋊C4—48no—
487C4⋊C4—48no—
488C4⋊C4—48no—
489C4⋊C4—44no—
490C22⋊C4—48no—
491C22⋊C4—48no—
492C22⋊C4—48no—
493C22⋊C4—48no—
494C22⋊C4—48no—
495C22⋊C4—48no—
496C23—24no—
497C23—24no—
498C23—24no—
499C23—24no—
500C23—24no—
501C23—24no—
502C23—24no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—42no—
509C23—42no—
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—
531C23C22×D4×C4312yes—
532C23C22×D4×C4311yescharacteristic
533C23C2×#41×C4311yescharacteristic
534C23C2×#41×C4311yescharacteristic
535C23H(5,𝔽2)×C4311yescharacteristic
536C23H(5,𝔽2)×C4312yes—
537C23H(5,𝔽2)×C4311yescharacteristic
538C23H(5,𝔽2)×C4312yes—
539C232−1+4×C4311yescharacteristic
540C232−1+4×C4312yes—
541C232−1+4×C4311yescharacteristic
542D4—416no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
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—41no—
567C2×C4—41no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—42no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
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—
593C22—44no—
594C22—44no—
595C22—44no—
596C22—44no—
597C22—44no—
598C22—44no—
599C22—44no—
600C22—82no—
601C22—82no—
602C22—82no—
603C22—82no—
604C22—82no—
605C22—82no—
606C22—82no—
607C22—82no—
608C22C43×#53412yes—
609C22C43×#53612yes—
610C22C43×#53712yes—
611C22C43×#53712yes—
612C22C43×#53711yescharacteristic
613C22C43×#53811yescharacteristic
614C22C43×#53812yes—
615C22C43×#53911yescharacteristic
616C22C43×#54212yes—
617C22D42×C4311yescharacteristic
618C22D42×C4312yes—
619C22C43×#54612yes—
620C22C43×#54711yescharacteristic
621C22C43×#54712yes—
622C22C43×#55011yescharacteristic
623C22C43×#55611yescharacteristic
624C22C43×#56011yescharacteristic
625C22C43×#56011yescharacteristic
626C22C43×#56212yes—
627C22C43×#56212yes—
628C22C43×#56311yescharacteristic
629C22C43×#56312yes—
630C22C43×#56311yescharacteristic
631C4—42no—
632C4—44no—
633C4—44no—
634C4—42no—
635C4—44no—
636C4—42no—
637C4—82no—
638C4—82no—
639C2—84no—
640C2C43×#266811yescharacteristic
641C2C43×#267212yes—
642C2C43×#267511yescharacteristic
643C2C43×#268011yescharacteristic
644C2C43×#268212yes—
645C2C43×#271512yes—
646C2C43×#272711yescharacteristic
647C2C43×#281412yes—
648C2C43×#282311yescharacteristic
649C2C43×#282611yescharacteristic
650C2C43×#283011yescharacteristic
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×#397C2semidirect
2. C2×C43×#396C2semidirect
4. C43×#1444C2semidirect
5. C43×#1444C2semidirect
6. C43×#1441C2semidirect
7. C43×#1439C2semidirect
8. C43×#1439C2semidirect
87. #95×C43D4semidirect
267. #17109C43direct (N × H)
314. C2×#397C2×C43semidirect
315. C2×#396C2×C43semidirect
317. #1444C2×C43semidirect
318. #1444C2×C43semidirect
319. #1441C2×C43semidirect
320. #1439C2×C43semidirect
321. #1439C2×C43semidirect
359. C43#17109direct (N × H)
413. #95D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#3972
C2×C43×#3962
C2×C43×#3942
C43×#14442
C43×#14412
C43×#14392
C43×#14382
#1710943