Finite Group Databasebeta

← C43×#29947 #24949964

Subgroups — C43×#29947 #24949964

Order 11008.

616 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2628C211yesmaximal, characteristic
2C43×#2314C211yesmaximal, characteristic
3C43×#2100C211yesmaximal, characteristic, complemented
4C43×#2099C211yesmaximal, characteristic, complemented
5C43×#2085C211yesmaximal, characteristic, complemented
6C43×#2085C211yesmaximal, characteristic, complemented
7C43×#2077C211yesmaximal, characteristic
8C43×#2077C211yesmaximal, characteristic
9C43×#2076C211yesmaximal, characteristic
10C43×#2075C211yesmaximal, characteristic
11C43×#1988C211yesmaximal, characteristic, complemented
12C43×#1987C211yesmaximal, characteristic, complemented
13C43×#1949C211yesmaximal, characteristic, complemented
14C43×#1949C211yesmaximal, characteristic, complemented
15C43×#1798C211yesmaximal, characteristic
16C2×C4⋊Q8×C43C2211yescharacteristic
17C2×#117×C43C2211yescharacteristic
18C2×#107×C43C2211yescharacteristic
19C2×#107×C43C2211yescharacteristic
20C2×#106×C43C2211yescharacteristic
21C2×#106×C43C2211yescharacteristic
22C2×C4⋊C8×C43C2211yescharacteristic
23C2×C4⋊C8×C43C2211yescharacteristic
24C2×C22⋊C8×C43C2211yescharacteristic
25C2×C22⋊C8×C43C2211yescharacteristic
26C43×#400—21no—
27C43×#399—21no—
28C43×#395—21no—
29C43×#393—21no—
30C43×#389C2211yescharacteristic
31C43×#389C2211yescharacteristic
32C43×#388—21no—
33C43×#388—21no—
34C43×#387—21no—
35C43×#387—21no—
36C43×#384C2211yescharacteristic
37C43×#382C2211yescharacteristic
38C43×#382C2211yescharacteristic
39C43×#380C2211yescharacteristic
40C43×#380C2211yescharacteristic
41C43×#380C2211yescharacteristic
42C43×#380C2211yescharacteristic
43C4×C4⋊C4×C43C2211yescharacteristic
44C4×C4⋊C4×C43C2211yescharacteristic
45C43×#340C2211yescharacteristic
46C43×#340C2211yescharacteristic
47C43×#340C2211yescharacteristic
48C43×#340C2211yescharacteristic
49C43×#340C2211yescharacteristic
50C43×#340C2211yescharacteristic
51C43×#340C2211yescharacteristic
52C43×#340C2211yescharacteristic
53C43×#340C2211yescharacteristic
54C43×#340C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Q8×C43—21no—
60C23×C4×C43C2311yescharacteristic
61C22×C8×C43C2311yescharacteristic
62C22×C8×C43C2311yescharacteristic
63C22×C8×C43C2311yescharacteristic
64C22×C8×C43C2311yescharacteristic
65C4⋊Q8×C43—22no—
66C4⋊Q8×C43—22no—
67#117×C43—22no—
68#117×C43—22no—
69C2×C4⋊C4×C43—21no—
70C2×C4⋊C4×C43—21no—
71C2×C4⋊C4×C43—21no—
72C2×C4⋊C4×C43—21no—
73C2×C4⋊C4×C43—21no—
74C2×C4⋊C4×C43D411yescharacteristic
75C2×C4⋊C4×C43D411yescharacteristic
76C2×C4⋊C4×C43C2311yescharacteristic
77C2×C4⋊C4×C43C2311yescharacteristic
78C2×C4⋊C4×C43C2311yescharacteristic
79C2×C4⋊C4×C43C2311yescharacteristic
80C2×C4⋊C4×C43C2311yescharacteristic
81C2×C4⋊C4×C43C2311yescharacteristic
82C2×C4⋊C4×C43C2311yescharacteristic
83C2×C4⋊C4×C43C2311yescharacteristic
84C2×C22⋊C4×C43—21no—
85C2×C22⋊C4×C43—21no—
86C2×C22⋊C4×C43—21no—
87C2×C22⋊C4×C43—21no—
88C2×C22⋊C4×C43D411yescharacteristic
89C2×C22⋊C4×C43D411yescharacteristic
90C2×C42×C43—21no—
91C2×C42×C43—21no—
92C2×C42×C43C2311yescharacteristic
93C2×C42×C43C2311yescharacteristic
94#107×C43—41no—
95#107×C43—41no—
96#106×C43—41no—
97#106×C43—41no—
98C4⋊C8×C43—22no—
99C4⋊C8×C43—22no—
100C22⋊C8×C43—41no—
101C22⋊C8×C43—41no—
102#95×C43—21no—
103#95×C43—21no—
104#95×C43—21no—
105#95×C43—21no—
106#95×C43—21no—
107#95×C43—21no—
108#95×C43—21no—
109#95×C43—21no—
110#95×C43—21no—
111#95×C43—21no—
112#95×C43—21no—
113#95×C43—21no—
114C24×C43C2×D411yescharacteristic
115C2×Q8×C43—42no—
116C2×Q8×C43—81no—
117C2×Q8×C43—81no—
118C22×C4×C43—21no—
119C22×C4×C43—21no—
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2411yescharacteristic
138C2×C8×C43—21no—
139C2×C8×C43—21no—
140C2×C8×C43—21no—
141C2×C8×C43—21no—
142C2×C8×C43—21no—
143C2×C8×C43—21no—
144C2×C8×C43—21no—
145C2×C8×C43—21no—
146C2×C8×C43—21no—
147C2×C8×C43—21no—
148C2×C8×C43—21no—
149C2×C8×C43—21no—
150C4⋊C4×C43—22no—
151C4⋊C4×C43—22no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—42no—
169C4⋊C4×C43—81no—
170C4⋊C4×C43—81no—
171C4⋊C4×C43—81no—
172C4⋊C4×C43—81no—
173C22⋊C4×C43—22no—
174C22⋊C4×C43—22no—
175C22⋊C4×C43—81no—
176C22⋊C4×C43—81no—
177C22⋊C4×C43—81no—
178C22⋊C4×C43—81no—
179C42×C43—21no—
180C42×C43—21no—
181C42×C43—81no—
182C42×C43—81no—
183C42×C43#4112yes—
184C42×C43#4112yes—
185C23×C43—21no—
186C23×C43—21no—
187C23×C43—21no—
188C23×C43—21no—
189C23×C43—21no—
190C23×C43—21no—
191C23×C43—21no—
192C23×C43C22×D411yescharacteristic
193Q8×C43—84no—
194C2×C4×C43—21no—
195C2×C4×C43—21no—
196C2×C4×C43—21no—
197C2×C4×C43—21no—
198C2×C4×C43—21no—
199C2×C4×C43—21no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43#12312yes—
236C2×C4×C43#12312yes—
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C2×C4×C43H(5,𝔽2)11yescharacteristic
240C2×C4×C432−1+411yescharacteristic
241C2×C4×C432−1+411yescharacteristic
242C2×C4×C432−1+411yescharacteristic
243C8×C43—41no—
244C8×C43—41no—
245C8×C43—41no—
246C8×C43—41no—
247#29947C4311yesmaximal, characteristic, direct product factor, Sylow
248C22×C43—41no—
249C22×C43—41no—
250C22×C43—41no—
251C22×C43—41no—
252C22×C43—41no—
253C22×C43—41no—
254C22×C43—41no—
255C22×C43C2×#12311yescharacteristic
256C22×C43#53611yescharacteristic
257C22×C43#53711yescharacteristic
258C22×C43#57611yescharacteristic
259C22×C43#57711yescharacteristic
260C22×C43#57711yescharacteristic
261C22×C43#57811yescharacteristic
262C4×C43—22no—
263C4×C43—22no—
264C4×C43—41no—
265C4×C43—41no—
266C4×C43—41no—
267C4×C43—81no—
268C4×C43—81no—
269C4×C43—81no—
270C4×C43—81no—
271C4×C43—81no—
272C4×C43—81no—
273C4×C43—81no—
274C4×C43—81no—
275C4×C43#54111yescharacteristic
276C4×C43#54111yescharacteristic
277C4×C43#54211yescharacteristic
278C4×C43#54211yescharacteristic
279#2628C2×C4311yescharacteristic
280#2314C2×C4311yescharacteristic
281#2100C2×C4311yescharacteristic, complemented
282#2099C2×C4311yescharacteristic, complemented
283#2085C2×C4311yescharacteristic, complemented
284#2085C2×C4311yescharacteristic, complemented
285#2077C2×C4311yescharacteristic
286#2077C2×C4311yescharacteristic
287#2076C2×C4311yescharacteristic
288#2075C2×C4311yescharacteristic
289#1988C2×C4311yescharacteristic, complemented
290#1987C2×C4311yescharacteristic, complemented
291#1949C2×C4311yescharacteristic, complemented
292#1949C2×C4311yescharacteristic, complemented
293#1798C2×C4311yescharacteristic
294C2×C43—81no—
295C2×C43#262511yescharacteristic
296C2×C43#309611yescharacteristic
297C2×C43#309711yescharacteristic
298C2×C43#324111yescharacteristic
299C2×C43#324211yescharacteristic
300C2×C43#326211yescharacteristic
301C2×C43#326311yescharacteristic
302C2×C4⋊Q8C22×C4311yescharacteristic
303C2×#117C22×C4311yescharacteristic
304C2×#107C22×C4311yescharacteristic
305C2×#107C22×C4311yescharacteristic
306C2×#106C22×C4311yescharacteristic
307C2×#106C22×C4311yescharacteristic
308C2×C4⋊C8C22×C4311yescharacteristic
309C2×C4⋊C8C22×C4311yescharacteristic
310C2×C22⋊C8C22×C4311yescharacteristic
311C2×C22⋊C8C22×C4311yescharacteristic
312#400—21no—
313#399—21no—
314#395—21no—
315#393—21no—
316#389C22×C4311yescharacteristic
317#389C22×C4311yescharacteristic
318#388—21no—
319#388—21no—
320#387—21no—
321#387—21no—
322#384C22×C4311yescharacteristic
323#382C22×C4311yescharacteristic
324#382C22×C4311yescharacteristic
325#380C22×C4311yescharacteristic
326#380C22×C4311yescharacteristic
327#380C22×C4311yescharacteristic
328#380C22×C4311yescharacteristic
329C4×C4⋊C4C22×C4311yescharacteristic
330C4×C4⋊C4C22×C4311yescharacteristic
331#340C22×C4311yescharacteristic
332#340C22×C4311yescharacteristic
333#340C22×C4311yescharacteristic
334#340C22×C4311yescharacteristic
335#340C22×C4311yescharacteristic
336#340C22×C4311yescharacteristic
337#340C22×C4311yescharacteristic
338#340C22×C4311yescharacteristic
339#340C22×C4311yescharacteristic
340#340C22×C4311yescharacteristic
341#340C22×C4311yescharacteristic
342#340C22×C4311yescharacteristic
343#336C22×C4311yescharacteristic
344#336C22×C4311yescharacteristic
345C43#2994711yescharacteristic, direct product factor, Sylow
346C22×Q8—21no—
347C23×C4C23×C4311yescharacteristic
348C22×C8C23×C4311yescharacteristic
349C22×C8C23×C4311yescharacteristic
350C22×C8C23×C4311yescharacteristic
351C22×C8C23×C4311yescharacteristic
352C4⋊Q8—22no—
353C4⋊Q8—22no—
354#117—22no—
355#117—22no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4D4×C4311yescharacteristic
362C2×C4⋊C4D4×C4311yescharacteristic
363C2×C4⋊C4C23×C4311yescharacteristic
364C2×C4⋊C4C23×C4311yescharacteristic
365C2×C4⋊C4C23×C4311yescharacteristic
366C2×C4⋊C4C23×C4311yescharacteristic
367C2×C4⋊C4C23×C4311yescharacteristic
368C2×C4⋊C4C23×C4311yescharacteristic
369C2×C4⋊C4C23×C4311yescharacteristic
370C2×C4⋊C4C23×C4311yescharacteristic
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4D4×C4311yescharacteristic
376C2×C22⋊C4D4×C4311yescharacteristic
377C2×C42—21no—
378C2×C42—21no—
379C2×C42C23×C4311yescharacteristic
380C2×C42C23×C4311yescharacteristic
381#107—41no—
382#107—41no—
383#106—41no—
384#106—41no—
385C4⋊C8—22no—
386C4⋊C8—22no—
387C22⋊C8—41no—
388C22⋊C8—41no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—21no—
401C24C2×D4×C4311yescharacteristic
402C2×Q8—42no—
403C2×Q8—81no—
404C2×Q8—81no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
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×C4C2×D4×C4311yescharacteristic
420C22×C4C2×D4×C4311yescharacteristic
421C22×C4C2×D4×C4311yescharacteristic
422C22×C4C2×D4×C4311yescharacteristic
423C22×C4C2×D4×C4311yescharacteristic
424C22×C4C24×C4311yescharacteristic
425C2×C8—21no—
426C2×C8—21no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—42no—
456C4⋊C4—81no—
457C4⋊C4—81no—
458C4⋊C4—81no—
459C4⋊C4—81no—
460C22⋊C4—22no—
461C22⋊C4—22no—
462C22⋊C4—81no—
463C22⋊C4—81no—
464C22⋊C4—81no—
465C22⋊C4—81no—
466C42—21no—
467C42—21no—
468C42—81no—
469C42—81no—
470C42#41×C4312yes—
471C42#41×C4312yes—
472C23—21no—
473C23—21no—
474C23—21no—
475C23—21no—
476C23—21no—
477C23—21no—
478C23—21no—
479C23C22×D4×C4311yescharacteristic
480Q8—84no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4#123×C4312yes—
523C2×C4#123×C4312yes—
524C2×C4C2×#41×C4311yescharacteristic
525C2×C4C2×#41×C4311yescharacteristic
526C2×C4H(5,𝔽2)×C4311yescharacteristic
527C2×C42−1+4×C4311yescharacteristic
528C2×C42−1+4×C4311yescharacteristic
529C2×C42−1+4×C4311yescharacteristic
530C8—41no—
531C8—41no—
532C8—41no—
533C8—41no—
534C22—41no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22C2×#123×C4311yescharacteristic
542C22C43×#53611yescharacteristic
543C22C43×#53711yescharacteristic
544C22C43×#57611yescharacteristic
545C22C43×#57711yescharacteristic
546C22C43×#57711yescharacteristic
547C22C43×#57811yescharacteristic
548C4—22no—
549C4—22no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—81no—
554C4—81no—
555C4—81no—
556C4—81no—
557C4—81no—
558C4—81no—
559C4—81no—
560C4—81no—
561C4C43×#54111yescharacteristic
562C4C43×#54111yescharacteristic
563C4C43×#54211yescharacteristic
564C4C43×#54211yescharacteristic
565C2—81no—
566C2C43×#262511yescharacteristic
567C2C43×#309611yescharacteristic
568C2C43×#309711yescharacteristic
569C2C43×#324111yescharacteristic
570C2C43×#324211yescharacteristic
571C2C43×#326211yescharacteristic
572C2C43×#326311yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC24×C43C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C2×#117×C43 ◁ G

Complements

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

NH ≅ G/Ntype
3. C43×#2100C2semidirect
4. C43×#2099C2semidirect
5. C43×#2085C2semidirect
6. C43×#2085C2semidirect
11. C43×#1988C2semidirect
12. C43×#1987C2semidirect
13. C43×#1949C2semidirect
14. C43×#1949C2semidirect
247. #29947C43direct (N × H)
281. #2100C2×C43semidirect
282. #2099C2×C43semidirect
283. #2085C2×C43semidirect
284. #2085C2×C43semidirect
289. #1988C2×C43semidirect
290. #1987C2×C43semidirect
291. #1949C2×C43semidirect
292. #1949C2×C43semidirect
345. C43#29947direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#26282
C43×#23142
C43×#21002
C43×#20992
C43×#20852
C43×#20772
C43×#20762
C43×#20752
C43×#19882
C43×#19872
C43×#19492
C43×#17982
#2994743