Finite Group Databasebeta

← C43×#26094 #24946111

Subgroups — C43×#26094 #24946111

Order 11008.

678 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2570C211yesmaximal, characteristic, complemented
2C43×#2357C211yesmaximal, characteristic
3C43×#2093C211yesmaximal, characteristic
4C43×#2092C211yesmaximal, characteristic
5C43×#2065C211yesmaximal, characteristic
6C43×#2065C211yesmaximal, characteristic
7C43×#1949C211yesmaximal, characteristic, complemented
8C43×#1949C211yesmaximal, characteristic, complemented
9C43×#1948C211yesmaximal, characteristic, complemented
10C43×#1939C211yesmaximal, characteristic, complemented
11C43×#1921C211yesmaximal, characteristic, complemented
12C43×#1918C211yesmaximal, characteristic, complemented
13C43×#1846C211yesmaximal, characteristic, complemented
14C43×#1804C211yesmaximal, characteristic
15C4×#102×C43C211yesmaximal, characteristic
16C2×C4×D4×C43C2211yescharacteristic
17C2×#107×C43C2211yescharacteristic
18C2×#107×C43C2211yescharacteristic
19C2×#107×C43C2211yescharacteristic
20C2×#106×C43C2211yescharacteristic
21C2×#106×C43C2211yescharacteristic
22C2×#106×C43C2211yescharacteristic
23C2×C4⋊C8×C43C2211yescharacteristic
24C2×C4⋊C8×C43C2211yescharacteristic
25C2×C4⋊C8×C43C2211yescharacteristic
26C2×#102×C43C2211yescharacteristic
27C2×#102×C43C2211yescharacteristic
28C2×#102×C43C2211yescharacteristic
29C2×#102×C43C2211yescharacteristic
30C2×C4×C8×C43C2211yescharacteristic
31C43×#400—21no—
32C43×#398—21no—
33C43×#390C2211yescharacteristic
34C43×#390C2211yescharacteristic
35C43×#389C2211yescharacteristic
36C43×#389C2211yescharacteristic
37C43×#388—21no—
38C43×#388—21no—
39C43×#387—21no—
40C43×#387—21no—
41C43×#384C2211yescharacteristic
42C43×#382C2211yescharacteristic
43C43×#382C2211yescharacteristic
44C43×#382C2211yescharacteristic
45C43×#381—21no—
46C4×C4⋊C4×C43C2211yescharacteristic
47C4×C4⋊C4×C43C2211yescharacteristic
48C4×C4⋊C4×C43C2211yescharacteristic
49C4×C4⋊C4×C43C2211yescharacteristic
50C4×C22⋊C4×C43—21no—
51C43×#340C2211yescharacteristic
52C43×#340C2211yescharacteristic
53C43×#340C2211yescharacteristic
54C43×#340C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
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×C43Q814yes—
67C2×C4⋊C4×C43—21no—
68C2×C4⋊C4×C43—21no—
69C2×C4⋊C4×C43—21no—
70C2×C4⋊C4×C43—21no—
71C2×C4⋊C4×C43D411yescharacteristic
72C2×C4⋊C4×C43D411yescharacteristic
73C2×C4⋊C4×C43C2311yescharacteristic
74C2×C4⋊C4×C43C2311yescharacteristic
75C2×C4⋊C4×C43C2311yescharacteristic
76C2×C4⋊C4×C43C2311yescharacteristic
77C2×C4⋊C4×C43C2311yescharacteristic
78C2×C4⋊C4×C43C2311yescharacteristic
79C2×C4⋊C4×C43C2311yescharacteristic
80C2×C22⋊C4×C43—21no—
81C2×C22⋊C4×C43—21no—
82C2×C22⋊C4×C43—21no—
83C2×C22⋊C4×C43—21no—
84C2×C22⋊C4×C43—21no—
85C2×C42×C43—21no—
86C2×C42×C43—21no—
87C2×C42×C43—21no—
88C2×C42×C43C2311yescharacteristic
89C2×C42×C43C2311yescharacteristic
90C2×C42×C43C2311yescharacteristic
91#107×C43—22no—
92#107×C43—22no—
93#107×C43—41no—
94#106×C43—41no—
95#106×C43—41no—
96#106×C43—41no—
97C4⋊C8×C43—22no—
98C4⋊C8×C43—22no—
99C4⋊C8×C43—22no—
100#102×C43—22no—
101#102×C43—22no—
102#102×C43—41no—
103#102×C43—41no—
104C4×C8×C43—22no—
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—
114#95×C43—21no—
115#95×C43—21no—
116#95×C43D411yescharacteristic
117#95×C43D411yescharacteristic
118C24×C43—21no—
119C2×D4×C43—21no—
120C2×D4×C43—21no—
121C2×D4×C43—21no—
122C2×D4×C43—21no—
123C2×D4×C43—21no—
124C2×D4×C43C2×Q812yes—
125C22×C4×C43—24no—
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×C43—21no—
133C22×C4×C43—81no—
134C22×C4×C43—81no—
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2411yescharacteristic
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—
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43#4112yes—
153C2×C8×C43#4112yes—
154C4⋊C4×C43—22no—
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—41no—
169C4⋊C4×C43—42no—
170C4⋊C4×C43—42no—
171C4⋊C4×C43—81no—
172C4⋊C4×C43—81no—
173C4⋊C4×C43C2×Q812yes—
174C22⋊C4×C43—24no—
175C22⋊C4×C43—42no—
176C22⋊C4×C43—42no—
177C22⋊C4×C43—81no—
178C22⋊C4×C43—81no—
179C42×C43—21no—
180C42×C43—21no—
181C42×C43—21no—
182C42×C43—21no—
183C42×C43—81no—
184C42×C43—81no—
185C42×C43—81no—
186C42×C43C2×Q812yes—
187C42×C43#4112yes—
188C23×C43—22no—
189C23×C43—41no—
190C23×C43—41no—
191C23×C43—41no—
192C23×C43—41no—
193C23×C43—41no—
194C23×C43—41no—
195C23×C43C22×D411yescharacteristic
196D4×C43—22no—
197D4×C43—22no—
198D4×C43—41no—
199D4×C43—41no—
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—22no—
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—21no—
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—41no—
236C2×C4×C43—84no—
237C2×C4×C43C22⋊Q812yes—
238C2×C4×C43C22⋊Q812yes—
239C2×C4×C43#13512yes—
240C2×C4×C43C22×Q811yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43H(5,𝔽2)11yescharacteristic
245C2×C4×C432−1+411yescharacteristic
246C8×C43—22no—
247C8×C43—22no—
248C8×C43—41no—
249C8×C43—41no—
250#26094C4311yesmaximal, characteristic, direct product factor, Sylow
251C22×C43—42no—
252C22×C43—42no—
253C22×C43—42no—
254C22×C43—81no—
255C22×C43—81no—
256C22×C43—81no—
257C22×C43—81no—
258C22×C43C2×C22⋊Q811yescharacteristic
259C22×C43#54711yescharacteristic
260C22×C43#55011yescharacteristic
261C22×C43C2×#13511yescharacteristic
262C22×C43#57511yescharacteristic
263C22×C43#57611yescharacteristic
264C22×C43#57711yescharacteristic
265C4×C43—22no—
266C4×C43—22no—
267C4×C43—22no—
268C4×C43—42no—
269C4×C43—41no—
270C4×C43—41no—
271C4×C43—41no—
272C4×C43—81no—
273C4×C43—81no—
274C4×C43—81no—
275C4×C43—81no—
276C4×C43—81no—
277C4×C43—81no—
278C4×C43#53311yescharacteristic
279C4×C43#54411yescharacteristic
280C4×C43#55211yescharacteristic
281C4×C43#55311yescharacteristic
282#2570C2×C4311yescharacteristic, complemented
283#2357C2×C4311yescharacteristic
284#2093C2×C4311yescharacteristic
285#2092C2×C4311yescharacteristic
286#2065C2×C4311yescharacteristic
287#2065C2×C4311yescharacteristic
288#1949C2×C4311yescharacteristic, complemented
289#1949C2×C4311yescharacteristic, complemented
290#1948C2×C4311yescharacteristic, complemented
291#1939C2×C4311yescharacteristic, complemented
292#1921C2×C4311yescharacteristic, complemented
293#1918C2×C4311yescharacteristic, complemented
294#1846C2×C4311yescharacteristic, complemented
295#1804C2×C4311yescharacteristic
296C4×#102C2×C4311yescharacteristic
297C2×C43—82no—
298C2×C43#244111yescharacteristic
299C2×C43#307611yescharacteristic
300C2×C43#308111yescharacteristic
301C2×C43#333711yescharacteristic
302C2×C43#335511yescharacteristic
303C2×C43#339611yescharacteristic
304C2×C43#340111yescharacteristic
305C2×C4×D4C22×C4311yescharacteristic
306C2×#107C22×C4311yescharacteristic
307C2×#107C22×C4311yescharacteristic
308C2×#107C22×C4311yescharacteristic
309C2×#106C22×C4311yescharacteristic
310C2×#106C22×C4311yescharacteristic
311C2×#106C22×C4311yescharacteristic
312C2×C4⋊C8C22×C4311yescharacteristic
313C2×C4⋊C8C22×C4311yescharacteristic
314C2×C4⋊C8C22×C4311yescharacteristic
315C2×#102C22×C4311yescharacteristic
316C2×#102C22×C4311yescharacteristic
317C2×#102C22×C4311yescharacteristic
318C2×#102C22×C4311yescharacteristic
319C2×C4×C8C22×C4311yescharacteristic
320#400—21no—
321#398—21no—
322#390C22×C4311yescharacteristic
323#390C22×C4311yescharacteristic
324#389C22×C4311yescharacteristic
325#389C22×C4311yescharacteristic
326#388—21no—
327#388—21no—
328#387—21no—
329#387—21no—
330#384C22×C4311yescharacteristic
331#382C22×C4311yescharacteristic
332#382C22×C4311yescharacteristic
333#382C22×C4311yescharacteristic
334#381—21no—
335C4×C4⋊C4C22×C4311yescharacteristic
336C4×C4⋊C4C22×C4311yescharacteristic
337C4×C4⋊C4C22×C4311yescharacteristic
338C4×C4⋊C4C22×C4311yescharacteristic
339C4×C22⋊C4—21no—
340#340C22×C4311yescharacteristic
341#340C22×C4311yescharacteristic
342#340C22×C4311yescharacteristic
343#340C22×C4311yescharacteristic
344#340C22×C4311yescharacteristic
345#340C22×C4311yescharacteristic
346#336C22×C4311yescharacteristic
347#336C22×C4311yescharacteristic
348C43#2609411yescharacteristic, direct product factor, Sylow
349C22×D4C23×C4311yescharacteristic
350C23×C4—21no—
351C22×C8C23×C4311yescharacteristic
352C22×C8C23×C4311yescharacteristic
353C22×C8C23×C4311yescharacteristic
354C22×C8C23×C4311yescharacteristic
355C4×D4—22no—
356C4×D4Q8×C4314yes—
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×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C42—21no—
376C2×C42—21no—
377C2×C42—21no—
378C2×C42C23×C4311yescharacteristic
379C2×C42C23×C4311yescharacteristic
380C2×C42C23×C4311yescharacteristic
381#107—22no—
382#107—22no—
383#107—41no—
384#106—41no—
385#106—41no—
386#106—41no—
387C4⋊C8—22no—
388C4⋊C8—22no—
389C4⋊C8—22no—
390#102—22no—
391#102—22no—
392#102—41no—
393#102—41no—
394C4×C8—22no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95D4×C4311yescharacteristic
407#95D4×C4311yescharacteristic
408C24—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4C2×Q8×C4312yes—
415C22×C4—21no—
416C22×C4—24no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—81no—
424C22×C4—81no—
425C22×C4C2×D4×C4311yescharacteristic
426C22×C4C2×D4×C4311yescharacteristic
427C22×C4C2×D4×C4311yescharacteristic
428C22×C4C2×D4×C4311yescharacteristic
429C22×C4C2×D4×C4311yescharacteristic
430C22×C4C2×D4×C4311yescharacteristic
431C22×C4C24×C4311yescharacteristic
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8#41×C4312yes—
443C2×C8#41×C4312yes—
444C4⋊C4—22no—
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—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—41no—
459C4⋊C4—42no—
460C4⋊C4—42no—
461C4⋊C4—81no—
462C4⋊C4—81no—
463C4⋊C4C2×Q8×C4312yes—
464C22⋊C4—24no—
465C22⋊C4—42no—
466C22⋊C4—42no—
467C22⋊C4—81no—
468C22⋊C4—81no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—21no—
473C42—81no—
474C42—81no—
475C42—81no—
476C42C2×Q8×C4312yes—
477C42#41×C4312yes—
478C23—22no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23C22×D4×C4311yescharacteristic
486D4—22no—
487D4—22no—
488D4—41no—
489D4—41no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
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—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—84no—
527C2×C4C22⋊Q8×C4312yes—
528C2×C4C22⋊Q8×C4312yes—
529C2×C4#135×C4312yes—
530C2×C4C22×Q8×C4311yescharacteristic
531C2×C4C2×#41×C4311yescharacteristic
532C2×C4C2×#41×C4311yescharacteristic
533C2×C4C2×#41×C4311yescharacteristic
534C2×C4H(5,𝔽2)×C4311yescharacteristic
535C2×C42−1+4×C4311yescharacteristic
536C8—22no—
537C8—22no—
538C8—41no—
539C8—41no—
540C22—42no—
541C22—42no—
542C22—42no—
543C22—81no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22C2×C22⋊Q8×C4311yescharacteristic
548C22C43×#54711yescharacteristic
549C22C43×#55011yescharacteristic
550C22C2×#135×C4311yescharacteristic
551C22C43×#57511yescharacteristic
552C22C43×#57611yescharacteristic
553C22C43×#57711yescharacteristic
554C4—22no—
555C4—22no—
556C4—22no—
557C4—41no—
558C4—41no—
559C4—42no—
560C4—41no—
561C4—81no—
562C4—81no—
563C4—81no—
564C4—81no—
565C4—81no—
566C4—81no—
567C4C43×#53311yescharacteristic
568C4C43×#54411yescharacteristic
569C4C43×#55211yescharacteristic
570C4C43×#55311yescharacteristic
571C2—82no—
572C2C43×#244111yescharacteristic
573C2C43×#307611yescharacteristic
574C2C43×#308111yescharacteristic
575C2C43×#333711yescharacteristic
576C2C43×#335511yescharacteristic
577C2C43×#339611yescharacteristic
578C2C43×#340111yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC22×D4×C43C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C4×C4⋊C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#2570C2semidirect
7. C43×#1949C2semidirect
8. C43×#1949C2semidirect
9. C43×#1948C2semidirect
10. C43×#1939C2semidirect
11. C43×#1921C2semidirect
12. C43×#1918C2semidirect
13. C43×#1846C2semidirect
250. #26094C43direct (N × H)
282. #2570C2×C43semidirect
288. #1949C2×C43semidirect
289. #1949C2×C43semidirect
290. #1948C2×C43semidirect
291. #1939C2×C43semidirect
292. #1921C2×C43semidirect
293. #1918C2×C43semidirect
294. #1846C2×C43semidirect
348. C43#26094direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#25702
C43×#23572
C43×#20932
C43×#20922
C43×#20652
C43×#19492
C43×#19482
C43×#19392
C43×#19212
C43×#19182
C43×#18462
C43×#18042
C4×#102×C432
#2609443