Finite Group Databasebeta

← C43×#27178 #24947195

Subgroups — C43×#27178 #24947195

Order 11008.

750 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2420C211yesmaximal, characteristic
2C43×#2345C211yesmaximal, characteristic, complemented
3C43×#2101C211yesmaximal, characteristic, complemented
4C43×#2076C211yesmaximal, characteristic, complemented
5C43×#2067C211yesmaximal, characteristic, complemented
6C43×#2034C211yesmaximal, characteristic
7C43×#1949C211yesmaximal, characteristic, complemented
8C43×#1943C211yesmaximal, characteristic, complemented
9C43×#1925C211yesmaximal, characteristic, complemented
10C43×#1924C211yesmaximal, characteristic, complemented
11C43×#1918C211yesmaximal, characteristic, complemented
12C43×#1874C211yesmaximal, characteristic
13C43×#1862C211yesmaximal, characteristic, complemented
14C43×#1852C211yesmaximal, characteristic, complemented
15C43×#1762C211yesmaximal, characteristic, complemented
16C2×#121×C43C2211yescharacteristic
17C2×C4×D4×C43C2211yescharacteristic
18C22×C4⋊C4×C43C2211yescharacteristic
19C2×#107×C43C2211yescharacteristic
20C2×#107×C43C2211yescharacteristic
21C2×#107×C43C2211yescharacteristic
22C2×#106×C43C2211yescharacteristic
23C2×C4⋊C8×C43C2211yescharacteristic
24C2×#102×C43C2211yescharacteristic
25C2×#102×C43C2211yescharacteristic
26C2×#102×C43C2211yescharacteristic
27C2×#102×C43C2211yescharacteristic
28C2×C22⋊C8×C43C2211yescharacteristic
29C2×C22⋊C8×C43C2211yescharacteristic
30C2×#97×C43C2211yescharacteristic
31C43×#397—21no—
32C43×#394—21no—
33C43×#390C2211yescharacteristic
34C43×#389C2211yescharacteristic
35C43×#389C2211yescharacteristic
36C43×#389C2211yescharacteristic
37C43×#387—21no—
38C43×#387—21no—
39C43×#386—21no—
40C43×#382C2211yescharacteristic
41C43×#381—21no—
42C43×#380—21no—
43C43×#380C2211yescharacteristic
44C43×#380C2211yescharacteristic
45C4×C4⋊C4×C43C2211yescharacteristic
46C4×C4⋊C4×C43C2211yescharacteristic
47C4×C22⋊C4×C43—21no—
48C4×C22⋊C4×C43C2211yescharacteristic
49C43×#340C2211yescharacteristic
50C43×#340C2211yescharacteristic
51C43×#340C2211yescharacteristic
52C43×#340C2211yescharacteristic
53C43×#340C2211yescharacteristic
54C43×#340C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×D4×C43—21no—
60C22×D4×C43C2311yescharacteristic
61C23×C4×C43—21no—
62C23×C4×C43—21no—
63C23×C4×C43C2311yescharacteristic
64C22×C8×C43C2311yescharacteristic
65C22×C8×C43C2311yescharacteristic
66C22×C8×C43C2311yescharacteristic
67C22×C8×C43C2311yescharacteristic
68#121×C43—22no—
69#121×C43—41no—
70C4×D4×C43—22no—
71C4×D4×C43—41no—
72C2×C4⋊C4×C43—21no—
73C2×C4⋊C4×C43—22no—
74C2×C4⋊C4×C43—22no—
75C2×C4⋊C4×C43—21no—
76C2×C4⋊C4×C43—21no—
77C2×C4⋊C4×C43—21no—
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×C4⋊C4×C43C2311yescharacteristic
85C2×C22⋊C4×C43—21no—
86C2×C22⋊C4×C43—21no—
87C2×C22⋊C4×C43—21no—
88C2×C22⋊C4×C43—21no—
89C2×C22⋊C4×C43—21no—
90C2×C22⋊C4×C43—21no—
91C2×C22⋊C4×C43D411yescharacteristic
92C2×C22⋊C4×C43D411yescharacteristic
93C2×C42×C43—21no—
94C2×C42×C43—21no—
95C2×C42×C43C2311yescharacteristic
96C2×C42×C43C2311yescharacteristic
97#107×C43—22no—
98#107×C43—22no—
99#107×C43—41no—
100#106×C43—41no—
101C4⋊C8×C43—22no—
102#102×C43—22no—
103#102×C43—22no—
104#102×C43—22no—
105#102×C43—22no—
106C22⋊C8×C43—22no—
107C22⋊C8×C43—41no—
108#97×C43—41no—
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×C43—21no—
117#95×C43—21no—
118#95×C43D411yescharacteristic
119#95×C43D411yescharacteristic
120C24×C43—21no—
121C24×C43C2×D411yescharacteristic
122C2×D4×C43—21no—
123C2×D4×C43—21no—
124C2×D4×C43—21no—
125C2×D4×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43—42no—
128C2×D4×C43—42no—
129C2×D4×C43—81no—
130C2×D4×C43#4112yes—
131C22×C4×C43—24no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—42no—
146C22×C4×C43—42no—
147C22×C4×C43—81no—
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×C43C2411yescharacteristic
156C2×C8×C43—21no—
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#4112yes—
168C4⋊C4×C43—24no—
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—81no—
182C4⋊C4×C43—81no—
183C4⋊C4×C43—81no—
184C4⋊C4×C43#4112yes—
185C4⋊C4×C43#4112yes—
186C22⋊C4×C43—22no—
187C22⋊C4×C43—41no—
188C22⋊C4×C43—42no—
189C22⋊C4×C43—42no—
190C22⋊C4×C43—42no—
191C22⋊C4×C43—81no—
192C22⋊C4×C43—81no—
193C22⋊C4×C43—81no—
194C42×C43—21no—
195C42×C43—21no—
196C42×C43—21no—
197C42×C43—21no—
198C42×C43—81no—
199C42×C43—81no—
200C23×C43—21no—
201C23×C43—21no—
202C23×C43—21no—
203C23×C43—21no—
204C23×C43—21no—
205C23×C43—21no—
206C23×C43—22no—
207C23×C43—41no—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43#13712yes—
214C23×C43C22×D411yescharacteristic
215D4×C43—22no—
216D4×C43—22no—
217D4×C43—41no—
218D4×C43—41no—
219D4×C43—84no—
220C2×C4×C43—21no—
221C2×C4×C43—22no—
222C2×C4×C43—22no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
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—21no—
236C2×C4×C43—21no—
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—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—84no—
261C2×C4×C43—84no—
262C2×C4×C43C2×#4111yescharacteristic
263C2×C4×C43C2×#4111yescharacteristic
264C2×C4×C43C2×#4111yescharacteristic
265C2×C4×C43C2×#4111yescharacteristic
266C2×C4×C43H(5,𝔽2)11yescharacteristic
267C2×C4×C432−1+411yescharacteristic
268C8×C43—22no—
269C8×C43—41no—
270C8×C43—41no—
271C8×C43—41no—
272#27178C4311yesmaximal, characteristic, direct product factor, Sylow
273C22×C43—22no—
274C22×C43—22no—
275C22×C43—22no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—42no—
281C22×C43—42no—
282C22×C43—42no—
283C22×C43—81no—
284C22×C43—81no—
285C22×C43—81no—
286C22×C43—81no—
287C22×C43#52511yescharacteristic
288C22×C43#54611yescharacteristic
289C22×C43#54711yescharacteristic
290C22×C43C2×#13711yescharacteristic
291C22×C43#57511yescharacteristic
292C22×C43#57611yescharacteristic
293C22×C43#57611yescharacteristic
294C4×C43—41no—
295C4×C43—41no—
296C4×C43—42no—
297C4×C43—42no—
298C4×C43—41no—
299C4×C43—41no—
300C4×C43—41no—
301C4×C43—81no—
302C4×C43—81no—
303C4×C43—81no—
304C4×C43—81no—
305C4×C43—81no—
306C4×C43#52911yescharacteristic
307C4×C43#54211yescharacteristic
308C4×C43#55211yescharacteristic
309C4×C43#55311yescharacteristic
310#2420C2×C4311yescharacteristic
311#2345C2×C4311yescharacteristic, complemented
312#2101C2×C4311yescharacteristic, complemented
313#2076C2×C4311yescharacteristic, complemented
314#2067C2×C4311yescharacteristic, complemented
315#2034C2×C4311yescharacteristic
316#1949C2×C4311yescharacteristic, complemented
317#1943C2×C4311yescharacteristic, complemented
318#1925C2×C4311yescharacteristic, complemented
319#1924C2×C4311yescharacteristic, complemented
320#1918C2×C4311yescharacteristic, complemented
321#1874C2×C4311yescharacteristic
322#1862C2×C4311yescharacteristic, complemented
323#1852C2×C4311yescharacteristic, complemented
324#1762C2×C4311yescharacteristic, complemented
325C2×C43—42no—
326C2×C43—82no—
327C2×C43#247011yescharacteristic
328C2×C43#311711yescharacteristic
329C2×C43#312211yescharacteristic
330C2×C43#331411yescharacteristic
331C2×C43#332211yescharacteristic
332C2×C43#334611yescharacteristic
333C2×C43#334711yescharacteristic
334C2×#121C22×C4311yescharacteristic
335C2×C4×D4C22×C4311yescharacteristic
336C22×C4⋊C4C22×C4311yescharacteristic
337C2×#107C22×C4311yescharacteristic
338C2×#107C22×C4311yescharacteristic
339C2×#107C22×C4311yescharacteristic
340C2×#106C22×C4311yescharacteristic
341C2×C4⋊C8C22×C4311yescharacteristic
342C2×#102C22×C4311yescharacteristic
343C2×#102C22×C4311yescharacteristic
344C2×#102C22×C4311yescharacteristic
345C2×#102C22×C4311yescharacteristic
346C2×C22⋊C8C22×C4311yescharacteristic
347C2×C22⋊C8C22×C4311yescharacteristic
348C2×#97C22×C4311yescharacteristic
349#397—21no—
350#394—21no—
351#390C22×C4311yescharacteristic
352#389C22×C4311yescharacteristic
353#389C22×C4311yescharacteristic
354#389C22×C4311yescharacteristic
355#387—21no—
356#387—21no—
357#386—21no—
358#382C22×C4311yescharacteristic
359#381—21no—
360#380—21no—
361#380C22×C4311yescharacteristic
362#380C22×C4311yescharacteristic
363C4×C4⋊C4C22×C4311yescharacteristic
364C4×C4⋊C4C22×C4311yescharacteristic
365C4×C22⋊C4—21no—
366C4×C22⋊C4C22×C4311yescharacteristic
367#340C22×C4311yescharacteristic
368#340C22×C4311yescharacteristic
369#340C22×C4311yescharacteristic
370#340C22×C4311yescharacteristic
371#340C22×C4311yescharacteristic
372#340C22×C4311yescharacteristic
373#340C22×C4311yescharacteristic
374#340C22×C4311yescharacteristic
375#336C22×C4311yescharacteristic
376#336C22×C4311yescharacteristic
377C43#2717811yescharacteristic, direct product factor, Sylow
378C22×D4—21no—
379C22×D4C23×C4311yescharacteristic
380C23×C4—21no—
381C23×C4—21no—
382C23×C4C23×C4311yescharacteristic
383C22×C8C23×C4311yescharacteristic
384C22×C8C23×C4311yescharacteristic
385C22×C8C23×C4311yescharacteristic
386C22×C8C23×C4311yescharacteristic
387#121—22no—
388#121—41no—
389C4×D4—22no—
390C4×D4—41no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
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×C4⋊C4C23×C4311yescharacteristic
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4D4×C4311yescharacteristic
411C2×C22⋊C4D4×C4311yescharacteristic
412C2×C42—21no—
413C2×C42—21no—
414C2×C42C23×C4311yescharacteristic
415C2×C42C23×C4311yescharacteristic
416#107—22no—
417#107—22no—
418#107—41no—
419#106—41no—
420C4⋊C8—22no—
421#102—22no—
422#102—22no—
423#102—22no—
424#102—22no—
425C22⋊C8—22no—
426C22⋊C8—41no—
427#97—41no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95D4×C4311yescharacteristic
438#95D4×C4311yescharacteristic
439C24—21no—
440C24C2×D4×C4311yescharacteristic
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—42no—
447C2×D4—42no—
448C2×D4—81no—
449C2×D4#41×C4312yes—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—24no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—81no—
467C22×C4—81no—
468C22×C4—81no—
469C22×C4C2×D4×C4311yescharacteristic
470C22×C4C2×D4×C4311yescharacteristic
471C22×C4C2×D4×C4311yescharacteristic
472C22×C4C2×D4×C4311yescharacteristic
473C22×C4C2×D4×C4311yescharacteristic
474C22×C4C24×C4311yescharacteristic
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8#41×C4312yes—
487C4⋊C4—24no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—81no—
501C4⋊C4—81no—
502C4⋊C4—81no—
503C4⋊C4#41×C4312yes—
504C4⋊C4#41×C4312yes—
505C22⋊C4—22no—
506C22⋊C4—41no—
507C22⋊C4—42no—
508C22⋊C4—42no—
509C22⋊C4—42no—
510C22⋊C4—81no—
511C22⋊C4—81no—
512C22⋊C4—81no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—21no—
517C42—81no—
518C42—81no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—22no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23#137×C4312yes—
533C23C22×D4×C4311yescharacteristic
534D4—22no—
535D4—22no—
536D4—41no—
537D4—41no—
538D4—84no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
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—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—84no—
580C2×C4—84no—
581C2×C4C2×#41×C4311yescharacteristic
582C2×C4C2×#41×C4311yescharacteristic
583C2×C4C2×#41×C4311yescharacteristic
584C2×C4C2×#41×C4311yescharacteristic
585C2×C4H(5,𝔽2)×C4311yescharacteristic
586C2×C42−1+4×C4311yescharacteristic
587C8—22no—
588C8—41no—
589C8—41no—
590C8—41no—
591C22—22no—
592C22—22no—
593C22—22no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—42no—
599C22—42no—
600C22—42no—
601C22—81no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22C43×#52511yescharacteristic
606C22C43×#54611yescharacteristic
607C22C43×#54711yescharacteristic
608C22C2×#137×C4311yescharacteristic
609C22C43×#57511yescharacteristic
610C22C43×#57611yescharacteristic
611C22C43×#57611yescharacteristic
612C4—41no—
613C4—41no—
614C4—42no—
615C4—42no—
616C4—41no—
617C4—41no—
618C4—41no—
619C4—81no—
620C4—81no—
621C4—81no—
622C4—81no—
623C4—81no—
624C4C43×#52911yescharacteristic
625C4C43×#54211yescharacteristic
626C4C43×#55211yescharacteristic
627C4C43×#55311yescharacteristic
628C2—42no—
629C2—82no—
630C2C43×#247011yescharacteristic
631C2C43×#311711yescharacteristic
632C2C43×#312211yescharacteristic
633C2C43×#331411yescharacteristic
634C2C43×#332211yescharacteristic
635C2C43×#334611yescharacteristic
636C2C43×#334711yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC2×#121×C43C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C4×C22⋊C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2345C2semidirect
3. C43×#2101C2semidirect
4. C43×#2076C2semidirect
5. C43×#2067C2semidirect
7. C43×#1949C2semidirect
8. C43×#1943C2semidirect
9. C43×#1925C2semidirect
10. C43×#1924C2semidirect
11. C43×#1918C2semidirect
13. C43×#1862C2semidirect
14. C43×#1852C2semidirect
15. C43×#1762C2semidirect
272. #27178C43direct (N × H)
311. #2345C2×C43semidirect
312. #2101C2×C43semidirect
313. #2076C2×C43semidirect
314. #2067C2×C43semidirect
316. #1949C2×C43semidirect
317. #1943C2×C43semidirect
318. #1925C2×C43semidirect
319. #1924C2×C43semidirect
320. #1918C2×C43semidirect
322. #1862C2×C43semidirect
323. #1852C2×C43semidirect
324. #1762C2×C43semidirect
377. C43#27178direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#24202
C43×#23452
C43×#21012
C43×#20762
C43×#20672
C43×#20342
C43×#19492
C43×#19432
C43×#19252
C43×#19242
C43×#19182
C43×#18742
C43×#18622
C43×#18522
C43×#17622
#2717843