Finite Group Databasebeta

← C43×#28965 #24948982

Subgroups — C43×#28965 #24948982

Order 11008.

706 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2508C211yesmaximal, characteristic, complemented
2C43×#2452C211yesmaximal, characteristic
3C43×#2092C211yesmaximal, characteristic
4C43×#2088C211yesmaximal, characteristic, complemented
5C43×#2065C211yesmaximal, characteristic
6C43×#2058C211yesmaximal, characteristic, complemented
7C43×#1993C211yesmaximal, characteristic, complemented
8C43×#1944C211yesmaximal, characteristic, complemented
9C43×#1941C211yesmaximal, characteristic, complemented
10C43×#1936C211yesmaximal, characteristic
11C43×#1936C211yesmaximal, characteristic
12C43×#1918C211yesmaximal, characteristic, complemented
13C43×#1864C211yesmaximal, characteristic
14C43×#1771C211yesmaximal, characteristic, complemented
15C4×#102×C43C211yesmaximal, characteristic
16C2×C4⋊Q8×C43C2211yescharacteristic
17C2×C22⋊Q8×C43—21no—
18C2×C4×D4×C43C2211yescharacteristic
19C2×#107×C43C2211yescharacteristic
20C2×#106×C43C2211yescharacteristic
21C2×#106×C43C2211yescharacteristic
22C2×#106×C43C2211yescharacteristic
23C2×C4⋊C8×C43C2211yescharacteristic
24C2×#102×C43C2211yescharacteristic
25C2×#102×C43C2211yescharacteristic
26C2×#102×C43C2211yescharacteristic
27C2×#102×C43C2211yescharacteristic
28C2×#97×C43C2211yescharacteristic
29C2×#97×C43C2211yescharacteristic
30C2×C4×C8×C43C2211yescharacteristic
31C43×#400—21no—
32C43×#398—21no—
33C43×#396—21no—
34C43×#393—21no—
35C43×#390C2211yescharacteristic
36C43×#390C2211yescharacteristic
37C43×#389C2211yescharacteristic
38C43×#389C2211yescharacteristic
39C43×#389C2211yescharacteristic
40C43×#389C2211yescharacteristic
41C43×#389C2211yescharacteristic
42C43×#389C2211yescharacteristic
43C43×#387—21no—
44C43×#385—21no—
45C43×#382—21no—
46C43×#382C2211yescharacteristic
47C4×C4⋊C4×C43C2211yescharacteristic
48C4×C4⋊C4×C43C2211yescharacteristic
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×D4×C43C2311yescharacteristic
61C23×C4×C43—21no—
62C22×C8×C43C2311yescharacteristic
63C22×C8×C43C2311yescharacteristic
64C22×C8×C43C2311yescharacteristic
65C22×C8×C43C2311yescharacteristic
66C4⋊Q8×C43—22no—
67C4⋊Q8×C43—41no—
68C22⋊Q8×C43—44no—
69C4×D4×C43—22no—
70C4×D4×C43—41no—
71C2×C4⋊C4×C43—21no—
72C2×C4⋊C4×C43—21no—
73C2×C4⋊C4×C43—21no—
74C2×C4⋊C4×C43—21no—
75C2×C4⋊C4×C43—21no—
76C2×C4⋊C4×C43—21no—
77C2×C4⋊C4×C43—21no—
78C2×C4⋊C4×C43D411yescharacteristic
79C2×C4⋊C4×C43D411yescharacteristic
80C2×C4⋊C4×C43C2311yescharacteristic
81C2×C4⋊C4×C43C2311yescharacteristic
82C2×C4⋊C4×C43C2311yescharacteristic
83C2×C4⋊C4×C43C2311yescharacteristic
84C2×C4⋊C4×C43C2311yescharacteristic
85C2×C4⋊C4×C43C2311yescharacteristic
86C2×C4⋊C4×C43C2311yescharacteristic
87C2×C22⋊C4×C43—21no—
88C2×C22⋊C4×C43—21no—
89C2×C22⋊C4×C43—21no—
90C2×C22⋊C4×C43—21no—
91C2×C22⋊C4×C43—21no—
92C2×C42×C43—21no—
93C2×C42×C43C2311yescharacteristic
94C2×C42×C43C2311yescharacteristic
95C2×C42×C43C2311yescharacteristic
96#107×C43—22no—
97#106×C43—22no—
98#106×C43—22no—
99#106×C43—41no—
100C4⋊C8×C43—22no—
101#102×C43—22no—
102#102×C43—22no—
103#102×C43—41no—
104#102×C43Q814yescomplemented
105#97×C43—22no—
106#97×C43—41no—
107C4×C8×C43—41no—
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×C43—21no—
117#95×C43D411yescharacteristic
118#95×C43D411yescharacteristic
119C24×C43—21no—
120C2×Q8×C43—42no—
121C2×Q8×C43—42no—
122C2×Q8×C43—81no—
123C2×D4×C43—21no—
124C2×D4×C43—21no—
125C2×D4×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43C2×Q812yes—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—42no—
137C22×C4×C43—42no—
138C22×C4×C43—81no—
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2411yescharacteristic
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—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43C2×Q812yes—
156C2×C8×C43#4112yes—
157C2×C8×C43#4112yes—
158C4⋊C4×C43—22no—
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—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—41no—
172C4⋊C4×C43—42no—
173C4⋊C4×C43—42no—
174C4⋊C4×C43—42no—
175C4⋊C4×C43—42no—
176C4⋊C4×C43—81no—
177C4⋊C4×C43—81no—
178C4⋊C4×C43—81no—
179C4⋊C4×C43C2×Q812yes—
180C4⋊C4×C43#4112yes—
181C22⋊C4×C43—42no—
182C22⋊C4×C43—42no—
183C22⋊C4×C43—42no—
184C22⋊C4×C43—42no—
185C22⋊C4×C43—81no—
186C42×C43—21no—
187C42×C43—21no—
188C42×C43—21no—
189C42×C43—21no—
190C42×C43—21no—
191C42×C43—21no—
192C42×C43—42no—
193C23×C43—22no—
194C23×C43—41no—
195C23×C43—41no—
196C23×C43—41no—
197C23×C43—41no—
198C23×C43—41no—
199C23×C43—41no—
200C23×C43C22×D411yescharacteristic
201Q8×C43—84no—
202D4×C43—22no—
203D4×C43—22no—
204D4×C43—41no—
205D4×C43—41no—
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—22no—
214C2×C4×C43—22no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
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—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—84no—
245C2×C4×C43AGL(1,ℤ/8)12yes—
246C2×C4×C43C22×Q811yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43H(5,𝔽2)11yescharacteristic
251C2×C4×C432−1+411yescharacteristic
252C8×C43—22no—
253C8×C43—22no—
254C8×C43—22no—
255C8×C43—41no—
256#28965C4311yesmaximal, characteristic, direct product factor, Sylow
257C22×C43—42no—
258C22×C43—42no—
259C22×C43—42no—
260C22×C43—81no—
261C22×C43—81no—
262C22×C43—81no—
263C22×C43—81no—
264C22×C43#53211yescharacteristic
265C22×C43#54611yescharacteristic
266C22×C43D4×Q811yescharacteristic
267C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
268C22×C43#57511yescharacteristic
269C22×C43#57711yescharacteristic
270C22×C43#57711yescharacteristic
271C4×C43—22no—
272C4×C43—42no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43—41no—
276C4×C43—42no—
277C4×C43—41no—
278C4×C43—41no—
279C4×C43—81no—
280C4×C43—81no—
281C4×C43—81no—
282C4×C43—81no—
283C4×C43—81no—
284C4×C43#53311yescharacteristic
285C4×C43#53911yescharacteristic
286C4×C43#55211yescharacteristic
287C4×C43#55411yescharacteristic
288#2508C2×C4311yescharacteristic, complemented
289#2452C2×C4311yescharacteristic
290#2092C2×C4311yescharacteristic
291#2088C2×C4311yescharacteristic, complemented
292#2065C2×C4311yescharacteristic
293#2058C2×C4311yescharacteristic, complemented
294#1993C2×C4311yescharacteristic, complemented
295#1944C2×C4311yescharacteristic, complemented
296#1941C2×C4311yescharacteristic, complemented
297#1936C2×C4311yescharacteristic
298#1936C2×C4311yescharacteristic
299#1918C2×C4311yescharacteristic, complemented
300#1864C2×C4311yescharacteristic
301#1771C2×C4311yescharacteristic, complemented
302C4×#102C2×C4311yescharacteristic
303C2×C43—82no—
304C2×C43#255611yescharacteristic
305C2×C43#317111yescharacteristic
306C2×C43#317311yescharacteristic
307C2×C43#331011yescharacteristic
308C2×C43#332111yescharacteristic
309C2×C43#338411yescharacteristic
310C2×C43#338811yescharacteristic
311C2×C4⋊Q8C22×C4311yescharacteristic
312C2×C22⋊Q8—21no—
313C2×C4×D4C22×C4311yescharacteristic
314C2×#107C22×C4311yescharacteristic
315C2×#106C22×C4311yescharacteristic
316C2×#106C22×C4311yescharacteristic
317C2×#106C22×C4311yescharacteristic
318C2×C4⋊C8C22×C4311yescharacteristic
319C2×#102C22×C4311yescharacteristic
320C2×#102C22×C4311yescharacteristic
321C2×#102C22×C4311yescharacteristic
322C2×#102C22×C4311yescharacteristic
323C2×#97C22×C4311yescharacteristic
324C2×#97C22×C4311yescharacteristic
325C2×C4×C8C22×C4311yescharacteristic
326#400—21no—
327#398—21no—
328#396—21no—
329#393—21no—
330#390C22×C4311yescharacteristic
331#390C22×C4311yescharacteristic
332#389C22×C4311yescharacteristic
333#389C22×C4311yescharacteristic
334#389C22×C4311yescharacteristic
335#389C22×C4311yescharacteristic
336#389C22×C4311yescharacteristic
337#389C22×C4311yescharacteristic
338#387—21no—
339#385—21no—
340#382—21no—
341#382C22×C4311yescharacteristic
342C4×C4⋊C4C22×C4311yescharacteristic
343C4×C4⋊C4C22×C4311yescharacteristic
344#340C22×C4311yescharacteristic
345#340C22×C4311yescharacteristic
346#340C22×C4311yescharacteristic
347#340C22×C4311yescharacteristic
348#340C22×C4311yescharacteristic
349#340C22×C4311yescharacteristic
350#340C22×C4311yescharacteristic
351#340C22×C4311yescharacteristic
352#336C22×C4311yescharacteristic
353#336C22×C4311yescharacteristic
354C43#2896511yescharacteristic, direct product factor, Sylow
355C22×Q8—21no—
356C22×D4C23×C4311yescharacteristic
357C23×C4—21no—
358C22×C8C23×C4311yescharacteristic
359C22×C8C23×C4311yescharacteristic
360C22×C8C23×C4311yescharacteristic
361C22×C8C23×C4311yescharacteristic
362C4⋊Q8—22no—
363C4⋊Q8—41no—
364C22⋊Q8—44no—
365C4×D4—22no—
366C4×D4—41no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4D4×C4311yescharacteristic
375C2×C4⋊C4D4×C4311yescharacteristic
376C2×C4⋊C4C23×C4311yescharacteristic
377C2×C4⋊C4C23×C4311yescharacteristic
378C2×C4⋊C4C23×C4311yescharacteristic
379C2×C4⋊C4C23×C4311yescharacteristic
380C2×C4⋊C4C23×C4311yescharacteristic
381C2×C4⋊C4C23×C4311yescharacteristic
382C2×C4⋊C4C23×C4311yescharacteristic
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C42—21no—
389C2×C42C23×C4311yescharacteristic
390C2×C42C23×C4311yescharacteristic
391C2×C42C23×C4311yescharacteristic
392#107—22no—
393#106—22no—
394#106—22no—
395#106—41no—
396C4⋊C8—22no—
397#102—22no—
398#102—22no—
399#102—41no—
400#102Q8×C4314yescomplemented
401#97—22no—
402#97—41no—
403C4×C8—41no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95D4×C4311yescharacteristic
414#95D4×C4311yescharacteristic
415C24—21no—
416C2×Q8—42no—
417C2×Q8—42no—
418C2×Q8—81no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4C2×Q8×C4312yes—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—81no—
435C22×C4C2×D4×C4311yescharacteristic
436C22×C4C2×D4×C4311yescharacteristic
437C22×C4C2×D4×C4311yescharacteristic
438C22×C4C2×D4×C4311yescharacteristic
439C22×C4C2×D4×C4311yescharacteristic
440C22×C4C2×D4×C4311yescharacteristic
441C22×C4C24×C4311yescharacteristic
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8C2×Q8×C4312yes—
452C2×C8#41×C4312yes—
453C2×C8#41×C4312yes—
454C4⋊C4—22no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—41no—
468C4⋊C4—42no—
469C4⋊C4—42no—
470C4⋊C4—42no—
471C4⋊C4—42no—
472C4⋊C4—81no—
473C4⋊C4—81no—
474C4⋊C4—81no—
475C4⋊C4C2×Q8×C4312yes—
476C4⋊C4#41×C4312yes—
477C22⋊C4—42no—
478C22⋊C4—42no—
479C22⋊C4—42no—
480C22⋊C4—42no—
481C22⋊C4—81no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—42no—
489C23—22no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23C22×D4×C4311yescharacteristic
497Q8—84no—
498D4—22no—
499D4—22no—
500D4—41no—
501D4—41no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—84no—
541C2×C4AGL(1,ℤ/8)×C4312yes—
542C2×C4C22×Q8×C4311yescharacteristic
543C2×C4C2×#41×C4311yescharacteristic
544C2×C4C2×#41×C4311yescharacteristic
545C2×C4C2×#41×C4311yescharacteristic
546C2×C4H(5,𝔽2)×C4311yescharacteristic
547C2×C42−1+4×C4311yescharacteristic
548C8—22no—
549C8—22no—
550C8—22no—
551C8—41no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22C43×#53211yescharacteristic
560C22C43×#54611yescharacteristic
561C22D4×Q8×C4311yescharacteristic
562C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
563C22C43×#57511yescharacteristic
564C22C43×#57711yescharacteristic
565C22C43×#57711yescharacteristic
566C4—22no—
567C4—42no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—42no—
572C4—41no—
573C4—41no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4—81no—
578C4—81no—
579C4C43×#53311yescharacteristic
580C4C43×#53911yescharacteristic
581C4C43×#55211yescharacteristic
582C4C43×#55411yescharacteristic
583C2—82no—
584C2C43×#255611yescharacteristic
585C2C43×#317111yescharacteristic
586C2C43×#317311yescharacteristic
587C2C43×#331011yescharacteristic
588C2C43×#332111yescharacteristic
589C2C43×#338411yescharacteristic
590C2C43×#338811yescharacteristic
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×#2508C2semidirect
4. C43×#2088C2semidirect
6. C43×#2058C2semidirect
7. C43×#1993C2semidirect
8. C43×#1944C2semidirect
9. C43×#1941C2semidirect
12. C43×#1918C2semidirect
14. C43×#1771C2semidirect
104. #102×C43Q8semidirect
256. #28965C43direct (N × H)
288. #2508C2×C43semidirect
291. #2088C2×C43semidirect
293. #2058C2×C43semidirect
294. #1993C2×C43semidirect
295. #1944C2×C43semidirect
296. #1941C2×C43semidirect
299. #1918C2×C43semidirect
301. #1771C2×C43semidirect
354. C43#28965direct (N × H)
400. #102Q8×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#25082
C43×#24522
C43×#20922
C43×#20882
C43×#20652
C43×#20582
C43×#19932
C43×#19442
C43×#19412
C43×#19362
C43×#19182
C43×#18642
C43×#17712
C4×#102×C432
#2896543