Finite Group Databasebeta

← C43×#28957 #24948974

Subgroups — C43×#28957 #24948974

Order 11008.

678 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2507C211yesmaximal, characteristic, complemented
2C43×#2454C211yesmaximal, characteristic
3C43×#2093C211yesmaximal, characteristic
4C43×#2087C211yesmaximal, characteristic, complemented
5C43×#2065C211yesmaximal, characteristic
6C43×#2059C211yesmaximal, characteristic, complemented
7C43×#1992C211yesmaximal, characteristic, complemented
8C43×#1943C211yesmaximal, characteristic, complemented
9C43×#1942C211yesmaximal, characteristic, complemented
10C43×#1936C211yesmaximal, characteristic
11C43×#1934C211yesmaximal, characteristic
12C43×#1918C211yesmaximal, characteristic, complemented
13C43×#1862C211yesmaximal, characteristic
14C43×#1770C211yesmaximal, characteristic, complemented
15C43×#1762C211yesmaximal, characteristic
16C2×#125×C43C2211yescharacteristic
17C2×C4×D4×C43C2211yescharacteristic
18C2×#107×C43C2211yescharacteristic
19C2×#107×C43C2211yescharacteristic
20C2×#107×C43C2211yescharacteristic
21C2×#106×C43C2211yescharacteristic
22C2×C4⋊C8×C43C2211yescharacteristic
23C2×#102×C43C2211yescharacteristic
24C2×#102×C43C2211yescharacteristic
25C2×#102×C43C2211yescharacteristic
26C2×#102×C43C2211yescharacteristic
27C2×#97×C43C2211yescharacteristic
28C2×#97×C43C2211yescharacteristic
29C2×C4×C8×C43C2211yescharacteristic
30C43×#399—21no—
31C43×#398—21no—
32C43×#398—21no—
33C43×#396—21no—
34C43×#390C2211yescharacteristic
35C43×#390C2211yescharacteristic
36C43×#389—21no—
37C43×#389C2211yescharacteristic
38C43×#389C2211yescharacteristic
39C43×#389C2211yescharacteristic
40C43×#389C2211yescharacteristic
41C43×#389C2211yescharacteristic
42C43×#389C2211yescharacteristic
43C43×#387—21no—
44C43×#385—21no—
45C43×#384C2211yescharacteristic
46C43×#380—21no—
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×D4×C43C2311yescharacteristic
60C23×C4×C43—21no—
61C22×C8×C43C2311yescharacteristic
62C22×C8×C43C2311yescharacteristic
63C22×C8×C43C2311yescharacteristic
64C22×C8×C43C2311yescharacteristic
65#125×C43—22no—
66#125×C43—41no—
67C4×D4×C43—22no—
68C4×D4×C43—41no—
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×C43—21no—
76C2×C4⋊C4×C43—21no—
77C2×C4⋊C4×C43—21no—
78C2×C4⋊C4×C43—21no—
79C2×C4⋊C4×C43D411yescharacteristic
80C2×C4⋊C4×C43D411yescharacteristic
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×C4⋊C4×C43C2311yescharacteristic
88C2×C22⋊C4×C43—21no—
89C2×C22⋊C4×C43—21no—
90C2×C22⋊C4×C43—21no—
91C2×C22⋊C4×C43—21no—
92C2×C22⋊C4×C43—21no—
93C2×C42×C43—21no—
94C2×C42×C43C2311yescharacteristic
95C2×C42×C43C2311yescharacteristic
96C2×C42×C43C2311yescharacteristic
97#107×C43—22no—
98#107×C43—22no—
99#107×C43—22no—
100#106×C43—41no—
101C4⋊C8×C43—22no—
102#102×C43—22no—
103#102×C43—22no—
104#102×C43—41no—
105#102×C43Q814yes—
106#97×C43—41no—
107#97×C43—41no—
108C4×C8×C43—22no—
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—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×C43—42no—
133C22×C4×C43—42no—
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×C43C2×Q812yes—
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—41no—
168C4⋊C4×C43—42no—
169C4⋊C4×C43—42no—
170C4⋊C4×C43—42no—
171C4⋊C4×C43—81no—
172C4⋊C4×C43—81no—
173C4⋊C4×C43—81no—
174C4⋊C4×C43—81no—
175C4⋊C4×C43—81no—
176C4⋊C4×C43—81no—
177C4⋊C4×C43—81no—
178C4⋊C4×C43C2×Q812yes—
179C4⋊C4×C43#4112yes—
180C22⋊C4×C43—42no—
181C22⋊C4×C43—42no—
182C22⋊C4×C43—81no—
183C22⋊C4×C43—81no—
184C22⋊C4×C43—81no—
185C42×C43—21no—
186C42×C43—21no—
187C42×C43—21no—
188C42×C43—21no—
189C42×C43—21no—
190C42×C43—21no—
191C42×C43—81no—
192C23×C43—22no—
193C23×C43—41no—
194C23×C43—41no—
195C23×C43—41no—
196C23×C43—41no—
197C23×C43—41no—
198C23×C43—41no—
199C23×C43C22×D411yescharacteristic
200D4×C43—22no—
201D4×C43—22no—
202D4×C43—41no—
203D4×C43—41no—
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—22no—
212C2×C4×C43—22no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
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—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—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—84no—
243C2×C4×C43#13712yes—
244C2×C4×C43C22×Q811yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43H(5,𝔽2)11yescharacteristic
249C2×C4×C432−1+411yescharacteristic
250C8×C43—22no—
251C8×C43—22no—
252C8×C43—22no—
253C8×C43—41no—
254#28957C4311yesmaximal, characteristic, direct product factor, Sylow
255C22×C43—42no—
256C22×C43—42no—
257C22×C43—42no—
258C22×C43—81no—
259C22×C43—81no—
260C22×C43—81no—
261C22×C43—81no—
262C22×C43#53211yescharacteristic
263C22×C43#54611yescharacteristic
264C22×C43D4×Q811yescharacteristic
265C22×C43C2×#13711yescharacteristic
266C22×C43#57511yescharacteristic
267C22×C43#57611yescharacteristic
268C22×C43#57611yescharacteristic
269C4×C43—22no—
270C4×C43—41no—
271C4×C43—41no—
272C4×C43—42no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43—41no—
276C4×C43—42no—
277C4×C43—81no—
278C4×C43—81no—
279C4×C43—81no—
280C4×C43—81no—
281C4×C43—81no—
282C4×C43#53311yescharacteristic
283C4×C43#53911yescharacteristic
284C4×C43#55211yescharacteristic
285C4×C43#55411yescharacteristic
286#2507C2×C4311yescharacteristic, complemented
287#2454C2×C4311yescharacteristic
288#2093C2×C4311yescharacteristic
289#2087C2×C4311yescharacteristic, complemented
290#2065C2×C4311yescharacteristic
291#2059C2×C4311yescharacteristic, complemented
292#1992C2×C4311yescharacteristic, complemented
293#1943C2×C4311yescharacteristic, complemented
294#1942C2×C4311yescharacteristic, complemented
295#1936C2×C4311yescharacteristic
296#1934C2×C4311yescharacteristic
297#1918C2×C4311yescharacteristic, complemented
298#1862C2×C4311yescharacteristic
299#1770C2×C4311yescharacteristic, complemented
300#1762C2×C4311yescharacteristic
301C2×C43—82no—
302C2×C43#255611yescharacteristic
303C2×C43#317611yescharacteristic
304C2×C43#318111yescharacteristic
305C2×C43#332211yescharacteristic
306C2×C43#333311yescharacteristic
307C2×C43#338511yescharacteristic
308C2×C43#338911yescharacteristic
309C2×#125C22×C4311yescharacteristic
310C2×C4×D4C22×C4311yescharacteristic
311C2×#107C22×C4311yescharacteristic
312C2×#107C22×C4311yescharacteristic
313C2×#107C22×C4311yescharacteristic
314C2×#106C22×C4311yescharacteristic
315C2×C4⋊C8C22×C4311yescharacteristic
316C2×#102C22×C4311yescharacteristic
317C2×#102C22×C4311yescharacteristic
318C2×#102C22×C4311yescharacteristic
319C2×#102C22×C4311yescharacteristic
320C2×#97C22×C4311yescharacteristic
321C2×#97C22×C4311yescharacteristic
322C2×C4×C8C22×C4311yescharacteristic
323#399—21no—
324#398—21no—
325#398—21no—
326#396—21no—
327#390C22×C4311yescharacteristic
328#390C22×C4311yescharacteristic
329#389—21no—
330#389C22×C4311yescharacteristic
331#389C22×C4311yescharacteristic
332#389C22×C4311yescharacteristic
333#389C22×C4311yescharacteristic
334#389C22×C4311yescharacteristic
335#389C22×C4311yescharacteristic
336#387—21no—
337#385—21no—
338#384C22×C4311yescharacteristic
339#380—21no—
340C4×C4⋊C4C22×C4311yescharacteristic
341C4×C4⋊C4C22×C4311yescharacteristic
342#340C22×C4311yescharacteristic
343#340C22×C4311yescharacteristic
344#340C22×C4311yescharacteristic
345#340C22×C4311yescharacteristic
346#340C22×C4311yescharacteristic
347#340C22×C4311yescharacteristic
348#340C22×C4311yescharacteristic
349#340C22×C4311yescharacteristic
350#336C22×C4311yescharacteristic
351#336C22×C4311yescharacteristic
352C43#2895711yescharacteristic, direct product factor, Sylow
353C22×D4C23×C4311yescharacteristic
354C23×C4—21no—
355C22×C8C23×C4311yescharacteristic
356C22×C8C23×C4311yescharacteristic
357C22×C8C23×C4311yescharacteristic
358C22×C8C23×C4311yescharacteristic
359#125—22no—
360#125—41no—
361C4×D4—22no—
362C4×D4—41no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
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⋊C4D4×C4311yescharacteristic
374C2×C4⋊C4D4×C4311yescharacteristic
375C2×C4⋊C4C23×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×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C42—21no—
388C2×C42C23×C4311yescharacteristic
389C2×C42C23×C4311yescharacteristic
390C2×C42C23×C4311yescharacteristic
391#107—22no—
392#107—22no—
393#107—22no—
394#106—41no—
395C4⋊C8—22no—
396#102—22no—
397#102—22no—
398#102—41no—
399#102Q8×C4314yes—
400#97—41no—
401#97—41no—
402C4×C8—22no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95D4×C4311yescharacteristic
411#95D4×C4311yescharacteristic
412C24—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4C2×Q8×C4312yes—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—81no—
429C22×C4C2×D4×C4311yescharacteristic
430C22×C4C2×D4×C4311yescharacteristic
431C22×C4C2×D4×C4311yescharacteristic
432C22×C4C2×D4×C4311yescharacteristic
433C22×C4C2×D4×C4311yescharacteristic
434C22×C4C2×D4×C4311yescharacteristic
435C22×C4C24×C4311yescharacteristic
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8C2×Q8×C4312yes—
446C2×C8#41×C4312yes—
447C2×C8#41×C4312yes—
448C4⋊C4—22no—
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—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—41no—
462C4⋊C4—42no—
463C4⋊C4—42no—
464C4⋊C4—42no—
465C4⋊C4—81no—
466C4⋊C4—81no—
467C4⋊C4—81no—
468C4⋊C4—81no—
469C4⋊C4—81no—
470C4⋊C4—81no—
471C4⋊C4—81no—
472C4⋊C4C2×Q8×C4312yes—
473C4⋊C4#41×C4312yes—
474C22⋊C4—42no—
475C22⋊C4—42no—
476C22⋊C4—81no—
477C22⋊C4—81no—
478C22⋊C4—81no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—81no—
486C23—22no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23C22×D4×C4311yescharacteristic
494D4—22no—
495D4—22no—
496D4—41no—
497D4—41no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
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—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—84no—
537C2×C4#137×C4312yes—
538C2×C4C22×Q8×C4311yescharacteristic
539C2×C4C2×#41×C4311yescharacteristic
540C2×C4C2×#41×C4311yescharacteristic
541C2×C4C2×#41×C4311yescharacteristic
542C2×C4H(5,𝔽2)×C4311yescharacteristic
543C2×C42−1+4×C4311yescharacteristic
544C8—22no—
545C8—22no—
546C8—22no—
547C8—41no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22C43×#53211yescharacteristic
556C22C43×#54611yescharacteristic
557C22D4×Q8×C4311yescharacteristic
558C22C2×#137×C4311yescharacteristic
559C22C43×#57511yescharacteristic
560C22C43×#57611yescharacteristic
561C22C43×#57611yescharacteristic
562C4—22no—
563C4—42no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—42no—
568C4—41no—
569C4—41no—
570C4—81no—
571C4—81no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4C43×#53311yescharacteristic
576C4C43×#53911yescharacteristic
577C4C43×#55211yescharacteristic
578C4C43×#55411yescharacteristic
579C2—82no—
580C2C43×#255611yescharacteristic
581C2C43×#317611yescharacteristic
582C2C43×#318111yescharacteristic
583C2C43×#332211yescharacteristic
584C2C43×#333311yescharacteristic
585C2C43×#338511yescharacteristic
586C2C43×#338911yescharacteristic
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×#2507C2semidirect
4. C43×#2087C2semidirect
6. C43×#2059C2semidirect
7. C43×#1992C2semidirect
8. C43×#1943C2semidirect
9. C43×#1942C2semidirect
12. C43×#1918C2semidirect
14. C43×#1770C2semidirect
254. #28957C43direct (N × H)
286. #2507C2×C43semidirect
289. #2087C2×C43semidirect
291. #2059C2×C43semidirect
292. #1992C2×C43semidirect
293. #1943C2×C43semidirect
294. #1942C2×C43semidirect
297. #1918C2×C43semidirect
299. #1770C2×C43semidirect
352. C43#28957direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#25072
C43×#24542
C43×#20932
C43×#20872
C43×#20652
C43×#20592
C43×#19922
C43×#19432
C43×#19422
C43×#19362
C43×#19342
C43×#19182
C43×#18622
C43×#17702
C43×#17622
#2895743