Finite Group Databasebeta

← C43×#29588 #24949605

Subgroups — C43×#29588 #24949605

Order 11008.

644 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2647C211yesmaximal, characteristic, complemented
2C43×#2319C211yesmaximal, characteristic
3C43×#2099C211yesmaximal, characteristic, complemented
4C43×#2094C211yesmaximal, characteristic
5C43×#2085C211yesmaximal, characteristic, complemented
6C43×#2073C211yesmaximal, characteristic
7C43×#1943C211yesmaximal, characteristic, complemented
8C43×#1941C211yesmaximal, characteristic, complemented
9C43×#1936C211yesmaximal, characteristic
10C43×#1934C211yesmaximal, characteristic
11C43×#1920C211yesmaximal, characteristic, complemented
12C43×#1919C211yesmaximal, characteristic, complemented
13C43×#1864C211yesmaximal, characteristic
14C43×#1862C211yesmaximal, characteristic
15C43×#1746C211yesmaximal, characteristic, complemented
16C2×C4×D4×C43C2211yescharacteristic
17C2×#107×C43C2211yescharacteristic
18C2×#106×C43C2211yescharacteristic
19C2×#106×C43C2211yescharacteristic
20C2×#106×C43C2211yescharacteristic
21C2×#102×C43C2211yescharacteristic
22C2×#102×C43C2211yescharacteristic
23C2×#102×C43C2211yescharacteristic
24C2×#102×C43C2211yescharacteristic
25C2×#97×C43C2211yescharacteristic
26C2×C4×C8×C43C2211yescharacteristic
27C43×#400—21no—
28C43×#400—21no—
29C43×#398—21no—
30C43×#398—21no—
31C43×#390C2211yescharacteristic
32C43×#390C2211yescharacteristic
33C43×#389C2211yescharacteristic
34C43×#389C2211yescharacteristic
35C43×#389C2211yescharacteristic
36C43×#389C2211yescharacteristic
37C43×#389C2211yescharacteristic
38C43×#389C2211yescharacteristic
39C43×#388—21no—
40C43×#388—21no—
41C43×#384C2211yescharacteristic
42C43×#382C2211yescharacteristic
43C43×#381—21no—
44C43×#380—21no—
45C4×C4⋊C4×C43C2211yescharacteristic
46C43×#376C2211yescharacteristic
47C43×#340C2211yescharacteristic
48C43×#340C2211yescharacteristic
49C43×#340C2211yescharacteristic
50C43×#340C2211yescharacteristic
51C43×#340C2211yescharacteristic
52C43×#340C2211yescharacteristic
53C43×#340C2211yescharacteristic
54C43×#340C2211yescharacteristic
55C43×#336C2211yescharacteristic
56C43×#336C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×D4×C43C2311yescharacteristic
60C23×C4×C43—21no—
61C22×C8×C43C2311yescharacteristic
62C22×C8×C43C2311yescharacteristic
63C22×C8×C43C2311yescharacteristic
64C22×C8×C43C2311yescharacteristic
65C4×D4×C43—22no—
66C4×D4×C43—22no—
67C2×C4⋊C4×C43—21no—
68C2×C4⋊C4×C43—21no—
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×C43—21no—
75C2×C4⋊C4×C43C2311yescharacteristic
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×C22⋊C4×C43—21no—
83C2×C22⋊C4×C43—21no—
84C2×C22⋊C4×C43—21no—
85C2×C22⋊C4×C43—21no—
86C2×C22⋊C4×C43—21no—
87C2×C42×C43—21no—
88C2×C42×C43C2311yescharacteristic
89C2×C42×C43C2311yescharacteristic
90C2×C42×C43C2311yescharacteristic
91#107×C43—22no—
92#106×C43—22no—
93#106×C43—22no—
94#106×C43—22no—
95#102×C43—22no—
96#102×C43—22no—
97#102×C43—22no—
98#102×C43—22no—
99#97×C43—22no—
100C4×C8×C43—22no—
101#95×C43—21no—
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×C43D411yescharacteristic
111#95×C43D411yescharacteristic
112#95×C43D411yescharacteristic
113#95×C43D411yescharacteristic
114C24×C43—21no—
115C2×D4×C43—21no—
116C2×D4×C43—21no—
117C2×D4×C43—21no—
118C2×D4×C43—21no—
119C2×D4×C43—21no—
120C2×D4×C43#4112yes—
121C22×C4×C43—24no—
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—81no—
130C22×C4×C43—81no—
131C22×C4×C43C2×D411yescharacteristic
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#4112yes—
149C2×C8×C43#4112yes—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—21no—
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—81no—
164C4⋊C4×C43—81no—
165C4⋊C4×C43—81no—
166C4⋊C4×C43—81no—
167C4⋊C4×C43—81no—
168C4⋊C4×C43—81no—
169C4⋊C4×C43—81no—
170C4⋊C4×C43—81no—
171C4⋊C4×C43#4112yes—
172C22⋊C4×C43—24no—
173C22⋊C4×C43—81no—
174C22⋊C4×C43—81no—
175C22⋊C4×C43—81no—
176C22⋊C4×C43—81no—
177C42×C43—21no—
178C42×C43—21no—
179C42×C43—21no—
180C42×C43—21no—
181C42×C43—21no—
182C42×C43—21no—
183C42×C43—81no—
184C23×C43—22no—
185C23×C43—41no—
186C23×C43—41no—
187C23×C43—41no—
188C23×C43—41no—
189C23×C43—41no—
190C23×C43—41no—
191C23×C43C22×D411yescharacteristic
192D4×C43—22no—
193D4×C43—22no—
194D4×C43—41no—
195D4×C43—41no—
196C2×C4×C43—21no—
197C2×C4×C43—21no—
198C2×C4×C43—22no—
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—21no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
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—84no—
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C2×C4×C432−1+411yescharacteristic
241C2×C4×C432−1+411yescharacteristic
242C8×C43—22no—
243C8×C43—22no—
244C8×C43—41no—
245C8×C43—41no—
246#29588C4311yesmaximal, characteristic, direct product factor, Sylow
247C22×C43—42no—
248C22×C43—42no—
249C22×C43—42no—
250C22×C43—81no—
251C22×C43—81no—
252C22×C43—81no—
253C22×C43—81no—
254C22×C43#52511yescharacteristic
255C22×C43#53211yescharacteristic
256C22×C43#53611yescharacteristic
257C22×C43#57611yescharacteristic
258C22×C43#57711yescharacteristic
259C22×C43#57711yescharacteristic
260C22×C43#57711yescharacteristic
261C4×C43—41no—
262C4×C43—42no—
263C4×C43—41no—
264C4×C43—41no—
265C4×C43—41no—
266C4×C43—41no—
267C4×C43—41no—
268C4×C43—81no—
269C4×C43—81no—
270C4×C43—81no—
271C4×C43—81no—
272C4×C43—81no—
273C4×C43—81no—
274C4×C43#55211yescharacteristic
275C4×C43#55211yescharacteristic
276C4×C43#55211yescharacteristic
277C4×C43#55211yescharacteristic
278#2647C2×C4311yescharacteristic, complemented
279#2319C2×C4311yescharacteristic
280#2099C2×C4311yescharacteristic, complemented
281#2094C2×C4311yescharacteristic
282#2085C2×C4311yescharacteristic, complemented
283#2073C2×C4311yescharacteristic
284#1943C2×C4311yescharacteristic, complemented
285#1941C2×C4311yescharacteristic, complemented
286#1936C2×C4311yescharacteristic
287#1934C2×C4311yescharacteristic
288#1920C2×C4311yescharacteristic, complemented
289#1919C2×C4311yescharacteristic, complemented
290#1864C2×C4311yescharacteristic
291#1862C2×C4311yescharacteristic
292#1746C2×C4311yescharacteristic, complemented
293C2×C43—82no—
294C2×C43#261111yescharacteristic
295C2×C43#311811yescharacteristic
296C2×C43#312511yescharacteristic
297C2×C43#317411yescharacteristic
298C2×C43#317911yescharacteristic
299C2×C43#324111yescharacteristic
300C2×C43#324411yescharacteristic
301C2×C4×D4C22×C4311yescharacteristic
302C2×#107C22×C4311yescharacteristic
303C2×#106C22×C4311yescharacteristic
304C2×#106C22×C4311yescharacteristic
305C2×#106C22×C4311yescharacteristic
306C2×#102C22×C4311yescharacteristic
307C2×#102C22×C4311yescharacteristic
308C2×#102C22×C4311yescharacteristic
309C2×#102C22×C4311yescharacteristic
310C2×#97C22×C4311yescharacteristic
311C2×C4×C8C22×C4311yescharacteristic
312#400—21no—
313#400—21no—
314#398—21no—
315#398—21no—
316#390C22×C4311yescharacteristic
317#390C22×C4311yescharacteristic
318#389C22×C4311yescharacteristic
319#389C22×C4311yescharacteristic
320#389C22×C4311yescharacteristic
321#389C22×C4311yescharacteristic
322#389C22×C4311yescharacteristic
323#389C22×C4311yescharacteristic
324#388—21no—
325#388—21no—
326#384C22×C4311yescharacteristic
327#382C22×C4311yescharacteristic
328#381—21no—
329#380—21no—
330C4×C4⋊C4C22×C4311yescharacteristic
331#376C22×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#336C22×C4311yescharacteristic
341#336C22×C4311yescharacteristic
342#336C22×C4311yescharacteristic
343#336C22×C4311yescharacteristic
344C43#2958811yescharacteristic, direct product factor, Sylow
345C22×D4C23×C4311yescharacteristic
346C23×C4—21no—
347C22×C8C23×C4311yescharacteristic
348C22×C8C23×C4311yescharacteristic
349C22×C8C23×C4311yescharacteristic
350C22×C8C23×C4311yescharacteristic
351C4×D4—22no—
352C4×D4—22no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4C23×C4311yescharacteristic
362C2×C4⋊C4C23×C4311yescharacteristic
363C2×C4⋊C4C23×C4311yescharacteristic
364C2×C4⋊C4C23×C4311yescharacteristic
365C2×C4⋊C4C23×C4311yescharacteristic
366C2×C4⋊C4C23×C4311yescharacteristic
367C2×C4⋊C4C23×C4311yescharacteristic
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C42—21no—
374C2×C42C23×C4311yescharacteristic
375C2×C42C23×C4311yescharacteristic
376C2×C42C23×C4311yescharacteristic
377#107—22no—
378#106—22no—
379#106—22no—
380#106—22no—
381#102—22no—
382#102—22no—
383#102—22no—
384#102—22no—
385#97—22no—
386C4×C8—22no—
387#95—21no—
388#95—21no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95D4×C4311yescharacteristic
397#95D4×C4311yescharacteristic
398#95D4×C4311yescharacteristic
399#95D4×C4311yescharacteristic
400C24—21no—
401C2×D4—21no—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4#41×C4312yes—
407C22×C4—21no—
408C22×C4—24no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—81no—
416C22×C4—81no—
417C22×C4C2×D4×C4311yescharacteristic
418C22×C4C2×D4×C4311yescharacteristic
419C22×C4C2×D4×C4311yescharacteristic
420C22×C4C2×D4×C4311yescharacteristic
421C22×C4C2×D4×C4311yescharacteristic
422C22×C4C2×D4×C4311yescharacteristic
423C22×C4C24×C4311yescharacteristic
424C2×C8—21no—
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#41×C4312yes—
435C2×C8#41×C4312yes—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—21no—
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—81no—
450C4⋊C4—81no—
451C4⋊C4—81no—
452C4⋊C4—81no—
453C4⋊C4—81no—
454C4⋊C4—81no—
455C4⋊C4—81no—
456C4⋊C4—81no—
457C4⋊C4#41×C4312yes—
458C22⋊C4—24no—
459C22⋊C4—81no—
460C22⋊C4—81no—
461C22⋊C4—81no—
462C22⋊C4—81no—
463C42—21no—
464C42—21no—
465C42—21no—
466C42—21no—
467C42—21no—
468C42—21no—
469C42—81no—
470C23—22no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23C22×D4×C4311yescharacteristic
478D4—22no—
479D4—22no—
480D4—41no—
481D4—41no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—22no—
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—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
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—84no—
522C2×C4C2×#41×C4311yescharacteristic
523C2×C4C2×#41×C4311yescharacteristic
524C2×C4C2×#41×C4311yescharacteristic
525C2×C4C2×#41×C4311yescharacteristic
526C2×C42−1+4×C4311yescharacteristic
527C2×C42−1+4×C4311yescharacteristic
528C8—22no—
529C8—22no—
530C8—41no—
531C8—41no—
532C22—42no—
533C22—42no—
534C22—42no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22—81no—
539C22C43×#52511yescharacteristic
540C22C43×#53211yescharacteristic
541C22C43×#53611yescharacteristic
542C22C43×#57611yescharacteristic
543C22C43×#57711yescharacteristic
544C22C43×#57711yescharacteristic
545C22C43×#57711yescharacteristic
546C4—41no—
547C4—42no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—81no—
554C4—81no—
555C4—81no—
556C4—81no—
557C4—81no—
558C4—81no—
559C4C43×#55211yescharacteristic
560C4C43×#55211yescharacteristic
561C4C43×#55211yescharacteristic
562C4C43×#55211yescharacteristic
563C2—82no—
564C2C43×#261111yescharacteristic
565C2C43×#311811yescharacteristic
566C2C43×#312511yescharacteristic
567C2C43×#317411yescharacteristic
568C2C43×#317911yescharacteristic
569C2C43×#324111yescharacteristic
570C2C43×#324411yescharacteristic
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×#2647C2semidirect
3. C43×#2099C2semidirect
5. C43×#2085C2semidirect
7. C43×#1943C2semidirect
8. C43×#1941C2semidirect
11. C43×#1920C2semidirect
12. C43×#1919C2semidirect
15. C43×#1746C2semidirect
246. #29588C43direct (N × H)
278. #2647C2×C43semidirect
280. #2099C2×C43semidirect
282. #2085C2×C43semidirect
284. #1943C2×C43semidirect
285. #1941C2×C43semidirect
288. #1920C2×C43semidirect
289. #1919C2×C43semidirect
292. #1746C2×C43semidirect
344. C43#29588direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#26472
C43×#23192
C43×#20992
C43×#20942
C43×#20852
C43×#20732
C43×#19432
C43×#19412
C43×#19362
C43×#19342
C43×#19202
C43×#19192
C43×#18642
C43×#18622
C43×#17462
#2958843