Finite Group Databasebeta

← C43×#29151 #24949168

Subgroups — C43×#29151 #24949168

Order 11008.

734 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2660C211yesmaximal, characteristic, complemented
2C43×#2326C211yesmaximal, characteristic
3C43×#2026C211yesmaximal, characteristic, complemented
4C43×#2025C211yesmaximal, characteristic
5C43×#2024C211yesmaximal, characteristic, complemented
6C43×#2023C211yesmaximal, characteristic
7C43×#1959C211yesmaximal, characteristic
8C43×#1958C211yesmaximal, characteristic
9C43×#1836C211yesmaximal, characteristic, complemented
10C43×#1834C211yesmaximal, characteristic, complemented
11C43×#1805C211yesmaximal, characteristic, complemented
12C43×#1804C211yesmaximal, characteristic
13C43×#1803C211yesmaximal, characteristic, complemented
14C43×#1802C211yesmaximal, characteristic
15C43×#1768C211yesmaximal, characteristic, complemented
16C2×C4⋊Q8×C43C2211yescharacteristic
17C2×#125×C43C2211yescharacteristic
18C2×#124×C43C2211yescharacteristic
19C2×C4×Q8×C43C2211yescharacteristic
20C2×C4×D4×C43C2211yescharacteristic
21C2×C4⋊C8×C43C2211yescharacteristic
22C2×C4⋊C8×C43C2211yescharacteristic
23C2×#103×C43C2211yescharacteristic
24C2×#103×C43C2211yescharacteristic
25C2×#103×C43C2211yescharacteristic
26C2×#103×C43C2211yescharacteristic
27C2×#102×C43C2211yescharacteristic
28C2×#102×C43C2211yescharacteristic
29C2×#102×C43C2211yescharacteristic
30C2×#102×C43C2211yescharacteristic
31C2×#97×C43C2211yescharacteristic
32C2×C4×C8×C43C2211yescharacteristic
33C43×#398—21no—
34C43×#398—21no—
35C43×#395—21no—
36C43×#395—21no—
37C43×#391C2211yescharacteristic
38C43×#390C2211yescharacteristic
39C43×#388—21no—
40C43×#388—21no—
41C43×#385—21no—
42C43×#385—21no—
43C43×#384C2211yescharacteristic
44C43×#384C2211yescharacteristic
45C43×#384C2211yescharacteristic
46C43×#382C2211yescharacteristic
47C43×#382C2211yescharacteristic
48C43×#376C2211yescharacteristic
49C43×#340C2211yescharacteristic
50C43×#340C2211yescharacteristic
51C43×#340C2211yescharacteristic
52C43×#340C2211yescharacteristic
53C43×#340C2211yescharacteristic
54C43×#340C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Q8×C43—21no—
60C22×Q8×C43C2311yescharacteristic
61C22×D4×C43C2311yescharacteristic
62C23×C4×C43—21no—
63C22×C8×C43C2311yescharacteristic
64C22×C8×C43C2311yescharacteristic
65C22×C8×C43C2311yescharacteristic
66C22×C8×C43C2311yescharacteristic
67C4⋊Q8×C43—41no—
68C4⋊Q8×C43—41no—
69#125×C43—41no—
70#125×C43—41no—
71#124×C43—22no—
72#124×C43Q814yescomplemented
73C4×Q8×C43—22no—
74C4×Q8×C43—22no—
75C4×D4×C43—22no—
76C4×D4×C43—22no—
77C2×C4⋊C4×C43—21no—
78C2×C4⋊C4×C43—21no—
79C2×C4⋊C4×C43—21no—
80C2×C4⋊C4×C43—21no—
81C2×C4⋊C4×C43—21no—
82C2×C4⋊C4×C43—21no—
83C2×C4⋊C4×C43—21no—
84C2×C4⋊C4×C43—21no—
85C2×C4⋊C4×C43—21no—
86C2×C4⋊C4×C43—21no—
87C2×C4⋊C4×C43C2311yescharacteristic
88C2×C4⋊C4×C43C2311yescharacteristic
89C2×C4⋊C4×C43C2311yescharacteristic
90C2×C4⋊C4×C43C2311yescharacteristic
91C2×C4⋊C4×C43C2311yescharacteristic
92C2×C4⋊C4×C43C2311yescharacteristic
93C2×C22⋊C4×C43—21no—
94C2×C22⋊C4×C43—21no—
95C2×C22⋊C4×C43—21no—
96C2×C22⋊C4×C43—21no—
97C2×C22⋊C4×C43—21no—
98C2×C42×C43—21no—
99C2×C42×C43C2311yescharacteristic
100C2×C42×C43C2311yescharacteristic
101C2×C42×C43C2311yescharacteristic
102C4⋊C8×C43—22no—
103C4⋊C8×C43—22no—
104#103×C43—41no—
105#103×C43—41no—
106#103×C43—41no—
107#103×C43—41no—
108#102×C43—41no—
109#102×C43—41no—
110#102×C43—41no—
111#102×C43—41no—
112#97×C43—22no—
113C4×C8×C43—22no—
114#95×C43—21no—
115#95×C43—21no—
116#95×C43—21no—
117#95×C43—21no—
118#95×C43—21no—
119#95×C43—21no—
120#95×C43D411yescharacteristic
121#95×C43D411yescharacteristic
122#95×C43D411yescharacteristic
123#95×C43D411yescharacteristic
124C24×C43—21no—
125C2×Q8×C43—21no—
126C2×Q8×C43—21no—
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—42no—
131C2×Q8×C43—81no—
132C2×Q8×C43—81no—
133C2×Q8×C43C2×Q812yes—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43C2×Q812yes—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—42no—
148C22×C4×C43—81no—
149C22×C4×C43—81no—
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2411yescharacteristic
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—42no—
182C4⋊C4×C43—42no—
183C4⋊C4×C43—42no—
184C4⋊C4×C43—42no—
185C4⋊C4×C43—81no—
186C4⋊C4×C43—81no—
187C4⋊C4×C43—81no—
188C4⋊C4×C43—81no—
189C4⋊C4×C43—81no—
190C4⋊C4×C43—81no—
191C22⋊C4×C43—24no—
192C22⋊C4×C43—24no—
193C22⋊C4×C43—42no—
194C22⋊C4×C43—81no—
195C22⋊C4×C43—81no—
196C42×C43—21no—
197C42×C43—21no—
198C42×C43—42no—
199C42×C43C2×Q812yes—
200C42×C43#4112yes—
201C42×C43#4112yes—
202C42×C43#4112yes—
203C23×C43—22no—
204C23×C43—41no—
205C23×C43—41no—
206C23×C43—41no—
207C23×C43—41no—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43C22×D411yescharacteristic
211Q8×C43—22no—
212Q8×C43—22no—
213Q8×C43—41no—
214Q8×C43—41no—
215Q8×C43—84no—
216D4×C43—22no—
217D4×C43—22no—
218D4×C43—41no—
219D4×C43—41no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—22no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—84no—
256C2×C4×C43C22⋊Q812yes—
257C2×C4×C43C22⋊Q812yes—
258C2×C4×C43#12412yes—
259C2×C4×C43#12412yes—
260C2×C4×C43C22×Q811yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C43C2×#4111yescharacteristic
263C2×C4×C43C2×#4111yescharacteristic
264C2×C4×C43H(5,𝔽2)11yescharacteristic
265C2×C4×C43H(5,𝔽2)11yescharacteristic
266C8×C43—41no—
267C8×C43—41no—
268C8×C43—41no—
269C8×C43—41no—
270#29151C4311yesmaximal, characteristic, direct product factor, Sylow
271C22×C43—42no—
272C22×C43—42no—
273C22×C43—42no—
274C22×C43—81no—
275C22×C43—81no—
276C22×C43—81no—
277C22×C43—81no—
278C22×C43C2×C22⋊Q811yescharacteristic
279C22×C43C2×#12411yescharacteristic
280C22×C43#53511yescharacteristic
281C22×C43#57611yescharacteristic
282C22×C43#57711yescharacteristic
283C22×C43#57711yescharacteristic
284C22×C43#57811yescharacteristic
285C4×C43—22no—
286C4×C43—22no—
287C4×C43—22no—
288C4×C43—22no—
289C4×C43—42no—
290C4×C43—41no—
291C4×C43—41no—
292C4×C43—81no—
293C4×C43—81no—
294C4×C43—81no—
295C4×C43—81no—
296C4×C43—81no—
297C4×C43—81no—
298C4×C43#55411yescharacteristic
299C4×C43#55411yescharacteristic
300C4×C43#55511yescharacteristic
301C4×C43#55511yescharacteristic
302#2660C2×C4311yescharacteristic, complemented
303#2326C2×C4311yescharacteristic
304#2026C2×C4311yescharacteristic, complemented
305#2025C2×C4311yescharacteristic
306#2024C2×C4311yescharacteristic, complemented
307#2023C2×C4311yescharacteristic
308#1959C2×C4311yescharacteristic
309#1958C2×C4311yescharacteristic
310#1836C2×C4311yescharacteristic, complemented
311#1834C2×C4311yescharacteristic, complemented
312#1805C2×C4311yescharacteristic, complemented
313#1804C2×C4311yescharacteristic
314#1803C2×C4311yescharacteristic, complemented
315#1802C2×C4311yescharacteristic
316#1768C2×C4311yescharacteristic, complemented
317C2×C43—82no—
318C2×C43#256311yescharacteristic
319C2×C43#308311yescharacteristic
320C2×C43#308411yescharacteristic
321C2×C43#313611yescharacteristic
322C2×C43#313711yescharacteristic
323C2×C43#322411yescharacteristic
324C2×C43#322511yescharacteristic
325C2×C4⋊Q8C22×C4311yescharacteristic
326C2×#125C22×C4311yescharacteristic
327C2×#124C22×C4311yescharacteristic
328C2×C4×Q8C22×C4311yescharacteristic
329C2×C4×D4C22×C4311yescharacteristic
330C2×C4⋊C8C22×C4311yescharacteristic
331C2×C4⋊C8C22×C4311yescharacteristic
332C2×#103C22×C4311yescharacteristic
333C2×#103C22×C4311yescharacteristic
334C2×#103C22×C4311yescharacteristic
335C2×#103C22×C4311yescharacteristic
336C2×#102C22×C4311yescharacteristic
337C2×#102C22×C4311yescharacteristic
338C2×#102C22×C4311yescharacteristic
339C2×#102C22×C4311yescharacteristic
340C2×#97C22×C4311yescharacteristic
341C2×C4×C8C22×C4311yescharacteristic
342#398—21no—
343#398—21no—
344#395—21no—
345#395—21no—
346#391C22×C4311yescharacteristic
347#390C22×C4311yescharacteristic
348#388—21no—
349#388—21no—
350#385—21no—
351#385—21no—
352#384C22×C4311yescharacteristic
353#384C22×C4311yescharacteristic
354#384C22×C4311yescharacteristic
355#382C22×C4311yescharacteristic
356#382C22×C4311yescharacteristic
357#376C22×C4311yescharacteristic
358#340C22×C4311yescharacteristic
359#340C22×C4311yescharacteristic
360#340C22×C4311yescharacteristic
361#340C22×C4311yescharacteristic
362#340C22×C4311yescharacteristic
363#340C22×C4311yescharacteristic
364#340C22×C4311yescharacteristic
365#340C22×C4311yescharacteristic
366#336C22×C4311yescharacteristic
367#336C22×C4311yescharacteristic
368C43#2915111yescharacteristic, direct product factor, Sylow
369C22×Q8—21no—
370C22×Q8C23×C4311yescharacteristic
371C22×D4C23×C4311yescharacteristic
372C23×C4—21no—
373C22×C8C23×C4311yescharacteristic
374C22×C8C23×C4311yescharacteristic
375C22×C8C23×C4311yescharacteristic
376C22×C8C23×C4311yescharacteristic
377C4⋊Q8—41no—
378C4⋊Q8—41no—
379#125—41no—
380#125—41no—
381#124—22no—
382#124Q8×C4314yescomplemented
383C4×Q8—22no—
384C4×Q8—22no—
385C4×D4—22no—
386C4×D4—22no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4C23×C4311yescharacteristic
398C2×C4⋊C4C23×C4311yescharacteristic
399C2×C4⋊C4C23×C4311yescharacteristic
400C2×C4⋊C4C23×C4311yescharacteristic
401C2×C4⋊C4C23×C4311yescharacteristic
402C2×C4⋊C4C23×C4311yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C42—21no—
409C2×C42C23×C4311yescharacteristic
410C2×C42C23×C4311yescharacteristic
411C2×C42C23×C4311yescharacteristic
412C4⋊C8—22no—
413C4⋊C8—22no—
414#103—41no—
415#103—41no—
416#103—41no—
417#103—41no—
418#102—41no—
419#102—41no—
420#102—41no—
421#102—41no—
422#97—22no—
423C4×C8—22no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95D4×C4311yescharacteristic
431#95D4×C4311yescharacteristic
432#95D4×C4311yescharacteristic
433#95D4×C4311yescharacteristic
434C24—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—42no—
441C2×Q8—81no—
442C2×Q8—81no—
443C2×Q8C2×Q8×C4312yes—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4C2×Q8×C4312yes—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—42no—
458C22×C4—81no—
459C22×C4—81no—
460C22×C4C2×D4×C4311yescharacteristic
461C22×C4C2×D4×C4311yescharacteristic
462C22×C4C2×D4×C4311yescharacteristic
463C22×C4C2×D4×C4311yescharacteristic
464C22×C4C2×D4×C4311yescharacteristic
465C22×C4C2×D4×C4311yescharacteristic
466C22×C4C24×C4311yescharacteristic
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—42no—
492C4⋊C4—42no—
493C4⋊C4—42no—
494C4⋊C4—42no—
495C4⋊C4—81no—
496C4⋊C4—81no—
497C4⋊C4—81no—
498C4⋊C4—81no—
499C4⋊C4—81no—
500C4⋊C4—81no—
501C22⋊C4—24no—
502C22⋊C4—24no—
503C22⋊C4—42no—
504C22⋊C4—81no—
505C22⋊C4—81no—
506C42—21no—
507C42—21no—
508C42—42no—
509C42C2×Q8×C4312yes—
510C42#41×C4312yes—
511C42#41×C4312yes—
512C42#41×C4312yes—
513C23—22no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23C22×D4×C4311yescharacteristic
521Q8—22no—
522Q8—22no—
523Q8—41no—
524Q8—41no—
525Q8—84no—
526D4—22no—
527D4—22no—
528D4—41no—
529D4—41no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—84no—
566C2×C4C22⋊Q8×C4312yes—
567C2×C4C22⋊Q8×C4312yes—
568C2×C4#124×C4312yes—
569C2×C4#124×C4312yes—
570C2×C4C22×Q8×C4311yescharacteristic
571C2×C4C2×#41×C4311yescharacteristic
572C2×C4C2×#41×C4311yescharacteristic
573C2×C4C2×#41×C4311yescharacteristic
574C2×C4H(5,𝔽2)×C4311yescharacteristic
575C2×C4H(5,𝔽2)×C4311yescharacteristic
576C8—41no—
577C8—41no—
578C8—41no—
579C8—41no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22C2×C22⋊Q8×C4311yescharacteristic
588C22C2×#124×C4311yescharacteristic
589C22C43×#53511yescharacteristic
590C22C43×#57611yescharacteristic
591C22C43×#57711yescharacteristic
592C22C43×#57711yescharacteristic
593C22C43×#57811yescharacteristic
594C4—22no—
595C4—22no—
596C4—22no—
597C4—22no—
598C4—41no—
599C4—41no—
600C4—42no—
601C4—81no—
602C4—81no—
603C4—81no—
604C4—81no—
605C4—81no—
606C4—81no—
607C4C43×#55411yescharacteristic
608C4C43×#55411yescharacteristic
609C4C43×#55511yescharacteristic
610C4C43×#55511yescharacteristic
611C2—82no—
612C2C43×#256311yescharacteristic
613C2C43×#308311yescharacteristic
614C2C43×#308411yescharacteristic
615C2C43×#313611yescharacteristic
616C2C43×#313711yescharacteristic
617C2C43×#322411yescharacteristic
618C2C43×#322511yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC22×D4×C43C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C43×#376 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#2660C2semidirect
3. C43×#2026C2semidirect
5. C43×#2024C2semidirect
9. C43×#1836C2semidirect
10. C43×#1834C2semidirect
11. C43×#1805C2semidirect
13. C43×#1803C2semidirect
15. C43×#1768C2semidirect
72. #124×C43Q8semidirect
270. #29151C43direct (N × H)
302. #2660C2×C43semidirect
304. #2026C2×C43semidirect
306. #2024C2×C43semidirect
310. #1836C2×C43semidirect
311. #1834C2×C43semidirect
312. #1805C2×C43semidirect
314. #1803C2×C43semidirect
316. #1768C2×C43semidirect
368. C43#29151direct (N × H)
382. #124Q8×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#26602
C43×#23262
C43×#20262
C43×#20252
C43×#20242
C43×#20232
C43×#19592
C43×#19582
C43×#18362
C43×#18342
C43×#18052
C43×#18042
C43×#18032
C43×#18022
C43×#17682
#2915143