Finite Group Databasebeta

← C43×#18002 #24938019

Subgroups — C43×#18002 #24938019

Order 11008.

610 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3102C211yesmaximal, characteristic
2C43×#2970C211yesmaximal, characteristic, complemented
3C43×#2969C211yesmaximal, characteristic, complemented
4C43×#1593C211yesmaximal, characteristic, complemented
5C43×#1592C211yesmaximal, characteristic, complemented
6C43×#1587C211yesmaximal, characteristic, complemented
7C43×#1586C211yesmaximal, characteristic, complemented
8C43×#1585C211yesmaximal, characteristic, complemented
9C43×#1585C211yesmaximal, characteristic, complemented
10C43×#1580C211yesmaximal, characteristic, complemented
11C43×SD16⋊C8C211yesmaximal, characteristic, complemented
12C43×#1572C211yesmaximal, characteristic, complemented
13C43×#1494C211yesmaximal, characteristic, complemented
14C43×#1476C211yesmaximal, characteristic, complemented
15C43×#1451C211yesmaximal, characteristic, complemented
16C43×#529C2211yescharacteristic
17C4×#41×C43C2211yescharacteristic
18C43×#485C411yescharacteristic
19C43×#482C411yescharacteristic
20C43×#479C411yescharacteristic
21C43×#478C411yescharacteristic
22C43×#464C411yescharacteristic
23C43×#463C411yescharacteristic
24C43×#452C411yescharacteristic
25C43×#449C411yescharacteristic
26C43×#446C2211yescharacteristic
27C43×#446C2211yescharacteristic
28C43×#446C2211yescharacteristic
29C8×Q8×C43C2211yescharacteristic
30C4×Q16×C43C2211yescharacteristic
31C4×SD16×C43C2211yescharacteristic
32C4×SD16×C43C2211yescharacteristic
33C4×D8×C43C2211yescharacteristic
34C43×#436—21no—
35C43×#436C2211yescharacteristic
36C43×#435—21no—
37C43×#435—21no—
38C43×#435—21no—
39C8×D4×C43C2211yescharacteristic
40C8×D4×C43C2211yescharacteristic
41C8×D4×C43C2211yescharacteristic
42C43×#433—21no—
43C43×#432—21no—
44C43×#432C2211yescharacteristic
45C43×#431C2211yescharacteristic
46C43×#431C2211yescharacteristic
47C43×#405—21no—
48C4×M16×C43C2211yescharacteristic
49C2×#97×C43—21no—
50C2×C4×C8×C43C2211yescharacteristic
51C43×#335C2211yescharacteristic
52C43×#335C2211yescharacteristic
53C43×#334C2211yescharacteristic
54C43×#334C2211yescharacteristic
55C43×Q8⋊C8C2211yescharacteristic
56C43×Q8⋊C8C2211yescharacteristic
57C43×Q8⋊C8C2211yescharacteristic
58C43×Q8⋊C8C2211yescharacteristic
59C43×D4⋊C8C2211yescharacteristic
60C43×D4⋊C8C2211yescharacteristic
61C43×D4⋊C8C2211yescharacteristic
62C43×D4⋊C8C2211yescharacteristic
63C43×#322C2211yescharacteristic
64C43×#322C2211yescharacteristic
65C43×#322C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×#41×C43C2×C411yescharacteristic
68C2×Q16×C43C2×C411yescharacteristic
69C2×SD16×C43C2×C411yescharacteristic
70C2×SD16×C43C2×C411yescharacteristic
71C2×D8×C43C2×C411yescharacteristic
72C2×M16×C43—21no—
73C2×M16×C43D411yescharacteristic
74C2×M16×C43D411yescharacteristic
75C22×C8×C43—21no—
76C22×C8×C43—21no—
77C22×C8×C43—21no—
78C22×C8×C43—21no—
79#126×C43—21no—
80#125×C43C2×C411yescharacteristic
81#124×C43C2×C411yescharacteristic
82#123×C43—21no—
83C22⋊Q8×C43C2×C411yescharacteristic
84#121×C43C2×C411yescharacteristic
85C4×Q8×C43C2×C411yescharacteristic
86C4×Q8×C43C2311yescharacteristic
87C4×Q8×C43C2311yescharacteristic
88C4×D4×C43—21no—
89C4×D4×C43—21no—
90C4×D4×C43—21no—
91C4×D4×C43C2×C411yescharacteristic
92C4×D4×C43C2311yescharacteristic
93C4×D4×C43C2311yescharacteristic
94#117×C43—21no—
95#117×C43—21no—
96#117×C43C2×C411yescharacteristic
97C2×C42×C43—21no—
98C2×C42×C43C2311yescharacteristic
99#107×C43C2×C411yescharacteristic
100#107×C43C2×C411yescharacteristic
101#106×C43C2×C411yescharacteristic
102#106×C43C2×C411yescharacteristic
103C4⋊C8×C43—21no—
104C4⋊C8×C43—21no—
105C4⋊C8×C43—21no—
106C4⋊C8×C43—21no—
107C4⋊C8×C43C2×C411yescharacteristic
108C4⋊C8×C43C2×C411yescharacteristic
109C4⋊C8×C43C2311yescharacteristic
110C4⋊C8×C43C2311yescharacteristic
111C4⋊C8×C43C2311yescharacteristic
112C4⋊C8×C43C2311yescharacteristic
113#103×C43C2×C411yescharacteristic
114#103×C43C2×C411yescharacteristic
115#103×C43C2×C411yescharacteristic
116#103×C43C2×C411yescharacteristic
117#102×C43C2×C411yescharacteristic
118#102×C43C2×C411yescharacteristic
119#102×C43C2×C411yescharacteristic
120#102×C43C2×C411yescharacteristic
121C22⋊C8×C43—21no—
122C22⋊C8×C43—21no—
123C22⋊C8×C43—21no—
124C22⋊C8×C43—21no—
125C22⋊C8×C43—21no—
126C22⋊C8×C43—21no—
127C22⋊C8×C43C2×C411yescharacteristic
128C22⋊C8×C43C2×C411yescharacteristic
129#97×C43—21no—
130#97×C43—21no—
131#97×C43—21no—
132#97×C43—21no—
133#97×C43D411yescharacteristic
134#97×C43D411yescharacteristic
135C4×C8×C43—21no—
136C4×C8×C43—21no—
137C4×C8×C43—21no—
138C4×C8×C43C2311yescharacteristic
139C4×C8×C43C2311yescharacteristic
140C4×C8×C43C2311yescharacteristic
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144#41×C43—22no—
145#41×C43—41no—
146C2×Q8×C43C22×C411yescharacteristic
147C2×Q8×C43C22×C411yescharacteristic
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43C22×C411yescharacteristic
151C2×D4×C43C22×C411yescharacteristic
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43C22×C411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43#4111yescharacteristic
159Q16×C43—41no—
160SD16×C43—22no—
161SD16×C43—41no—
162D8×C43—22no—
163M16×C43—41no—
164M16×C43—41no—
165M16×C43—42no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—42no—
173C2×C8×C43—42no—
174C2×C8×C43—42no—
175C2×C8×C43—42no—
176C2×C8×C43C22×C411yescharacteristic
177C2×C8×C43C22×C411yescharacteristic
178C2×C8×C43C22×C411yescharacteristic
179C2×C8×C43C22×C411yescharacteristic
180C2×C8×C43C2×D411yescharacteristic
181C2×C8×C43C2×D411yescharacteristic
182C2×C8×C43C2×D411yescharacteristic
183C2×C8×C43C2×D411yescharacteristic
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43C22×C411yescharacteristic
191C4⋊C4×C43C22×C411yescharacteristic
192C4⋊C4×C43C22×C411yescharacteristic
193C4⋊C4×C43C22×C411yescharacteristic
194C22⋊C4×C43—21no—
195C22⋊C4×C43—21no—
196C22⋊C4×C43—21no—
197C22⋊C4×C43—21no—
198C22⋊C4×C43—21no—
199C22⋊C4×C43—21no—
200C22⋊C4×C43—21no—
201C22⋊C4×C43—21no—
202C42×C43—21no—
203C42×C43—21no—
204C42×C43—21no—
205C42×C43—21no—
206C42×C43C22×C411yescharacteristic
207C42×C43C2×D411yescharacteristic
208C42×C43#4111yescharacteristic
209C42×C43C2411yescharacteristic
210C23×C43—21no—
211C23×C43—21no—
212C23×C43C4×D411yescharacteristic
213Q8×C43—21no—
214Q8×C43—21no—
215Q8×C43—21no—
216Q8×C43—21no—
217D4×C43—21no—
218D4×C43—21no—
219D4×C43—21no—
220D4×C43—42no—
221D4×C43—81no—
222D4×C43#13112yes—
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—41no—
234C2×C4×C43—42no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—81no—
240C2×C4×C43C4×D411yescharacteristic
241C2×C4×C43C4×D411yescharacteristic
242C2×C4×C43C4×D411yescharacteristic
243C2×C4×C43C23×C411yescharacteristic
244C2×C4×C43C22×D411yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C8×C43—22no—
247C8×C43—21no—
248C8×C43—21no—
249C8×C43—21no—
250C8×C43—21no—
251C8×C43—21no—
252C8×C43—21no—
253C8×C43—21no—
254C8×C43—21no—
255C8×C43—41no—
256C8×C43—41no—
257C8×C43—41no—
258C8×C43—41no—
259C8×C43—41no—
260#18002C4311yesmaximal, characteristic, direct product factor, Sylow
261C22×C43—22no—
262C22×C43—21no—
263C22×C43—21no—
264C22×C43—21no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43C2×C4×D411yescharacteristic
271C4×C43—21no—
272C4×C43—21no—
273C4×C43—21no—
274C4×C43—21no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43—41no—
279C4×C43—41no—
280C4×C43—41no—
281C4×C43C2×#13111yescharacteristic
282C4×C43#56811yescharacteristic
283C4×C43#57511yescharacteristic
284C4×C43#57511yescharacteristic
285#3102C2×C4311yescharacteristic
286#2970C2×C4311yescharacteristic, complemented
287#2969C2×C4311yescharacteristic, complemented
288#1593C2×C4311yescharacteristic, complemented
289#1592C2×C4311yescharacteristic, complemented
290#1587C2×C4311yescharacteristic, complemented
291#1586C2×C4311yescharacteristic, complemented
292#1585C2×C4311yescharacteristic, complemented
293#1585C2×C4311yescharacteristic, complemented
294#1580C2×C4311yescharacteristic, complemented
295SD16⋊C8C2×C4311yescharacteristic, complemented
296#1572C2×C4311yescharacteristic, complemented
297#1494C2×C4311yescharacteristic, complemented
298#1476C2×C4311yescharacteristic, complemented
299#1451C2×C4311yescharacteristic, complemented
300C2×C43—41no—
301C2×C43—42no—
302C2×C43—81no—
303C2×C43#293311yescharacteristic
304C2×C43#294311yescharacteristic
305C2×C43#295611yescharacteristic
306#529C22×C4311yescharacteristic
307C4×#41C22×C4311yescharacteristic
308#485C4×C4311yescharacteristic
309#482C4×C4311yescharacteristic
310#479C4×C4311yescharacteristic
311#478C4×C4311yescharacteristic
312#464C4×C4311yescharacteristic
313#463C4×C4311yescharacteristic
314#452C4×C4311yescharacteristic
315#449C4×C4311yescharacteristic
316#446C22×C4311yescharacteristic
317#446C22×C4311yescharacteristic
318#446C22×C4311yescharacteristic
319C8×Q8C22×C4311yescharacteristic
320C4×Q16C22×C4311yescharacteristic
321C4×SD16C22×C4311yescharacteristic
322C4×SD16C22×C4311yescharacteristic
323C4×D8C22×C4311yescharacteristic
324#436—21no—
325#436C22×C4311yescharacteristic
326#435—21no—
327#435—21no—
328#435—21no—
329C8×D4C22×C4311yescharacteristic
330C8×D4C22×C4311yescharacteristic
331C8×D4C22×C4311yescharacteristic
332#433—21no—
333#432—21no—
334#432C22×C4311yescharacteristic
335#431C22×C4311yescharacteristic
336#431C22×C4311yescharacteristic
337#405—21no—
338C4×M16C22×C4311yescharacteristic
339C2×#97—21no—
340C2×C4×C8C22×C4311yescharacteristic
341#335C22×C4311yescharacteristic
342#335C22×C4311yescharacteristic
343#334C22×C4311yescharacteristic
344#334C22×C4311yescharacteristic
345Q8⋊C8C22×C4311yescharacteristic
346Q8⋊C8C22×C4311yescharacteristic
347Q8⋊C8C22×C4311yescharacteristic
348Q8⋊C8C22×C4311yescharacteristic
349D4⋊C8C22×C4311yescharacteristic
350D4⋊C8C22×C4311yescharacteristic
351D4⋊C8C22×C4311yescharacteristic
352D4⋊C8C22×C4311yescharacteristic
353#322C22×C4311yescharacteristic
354#322C22×C4311yescharacteristic
355#322C22×C4311yescharacteristic
356#322C22×C4311yescharacteristic
357C43#1800211yescharacteristic, direct product factor, Sylow
358C2×#41C2×C4×C4311yescharacteristic
359C2×Q16C2×C4×C4311yescharacteristic
360C2×SD16C2×C4×C4311yescharacteristic
361C2×SD16C2×C4×C4311yescharacteristic
362C2×D8C2×C4×C4311yescharacteristic
363C2×M16—21no—
364C2×M16D4×C4311yescharacteristic
365C2×M16D4×C4311yescharacteristic
366C22×C8—21no—
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—21no—
370#126—21no—
371#125C2×C4×C4311yescharacteristic
372#124C2×C4×C4311yescharacteristic
373#123—21no—
374C22⋊Q8C2×C4×C4311yescharacteristic
375#121C2×C4×C4311yescharacteristic
376C4×Q8C2×C4×C4311yescharacteristic
377C4×Q8C23×C4311yescharacteristic
378C4×Q8C23×C4311yescharacteristic
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—21no—
382C4×D4C2×C4×C4311yescharacteristic
383C4×D4C23×C4311yescharacteristic
384C4×D4C23×C4311yescharacteristic
385#117—21no—
386#117—21no—
387#117C2×C4×C4311yescharacteristic
388C2×C42—21no—
389C2×C42C23×C4311yescharacteristic
390#107C2×C4×C4311yescharacteristic
391#107C2×C4×C4311yescharacteristic
392#106C2×C4×C4311yescharacteristic
393#106C2×C4×C4311yescharacteristic
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8—21no—
398C4⋊C8C2×C4×C4311yescharacteristic
399C4⋊C8C2×C4×C4311yescharacteristic
400C4⋊C8C23×C4311yescharacteristic
401C4⋊C8C23×C4311yescharacteristic
402C4⋊C8C23×C4311yescharacteristic
403C4⋊C8C23×C4311yescharacteristic
404#103C2×C4×C4311yescharacteristic
405#103C2×C4×C4311yescharacteristic
406#103C2×C4×C4311yescharacteristic
407#103C2×C4×C4311yescharacteristic
408#102C2×C4×C4311yescharacteristic
409#102C2×C4×C4311yescharacteristic
410#102C2×C4×C4311yescharacteristic
411#102C2×C4×C4311yescharacteristic
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8—21no—
415C22⋊C8—21no—
416C22⋊C8—21no—
417C22⋊C8—21no—
418C22⋊C8C2×C4×C4311yescharacteristic
419C22⋊C8C2×C4×C4311yescharacteristic
420#97—21no—
421#97—21no—
422#97—21no—
423#97—21no—
424#97D4×C4311yescharacteristic
425#97D4×C4311yescharacteristic
426C4×C8—21no—
427C4×C8—21no—
428C4×C8—21no—
429C4×C8C23×C4311yescharacteristic
430C4×C8C23×C4311yescharacteristic
431C4×C8C23×C4311yescharacteristic
432C4×C8C23×C4311yescharacteristic
433C4×C8C23×C4311yescharacteristic
434C4×C8C23×C4311yescharacteristic
435#41—22no—
436#41—41no—
437C2×Q8C22×C4×C4311yescharacteristic
438C2×Q8C22×C4×C4311yescharacteristic
439C2×D4—21no—
440C2×D4—21no—
441C2×D4C22×C4×C4311yescharacteristic
442C2×D4C22×C4×C4311yescharacteristic
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4C22×C4×C4311yescharacteristic
448C22×C4C2×D4×C4311yescharacteristic
449C22×C4#41×C4311yescharacteristic
450Q16—41no—
451SD16—22no—
452SD16—41no—
453D8—22no—
454M16—41no—
455M16—41no—
456M16—42no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—42no—
464C2×C8—42no—
465C2×C8—42no—
466C2×C8—42no—
467C2×C8C22×C4×C4311yescharacteristic
468C2×C8C22×C4×C4311yescharacteristic
469C2×C8C22×C4×C4311yescharacteristic
470C2×C8C22×C4×C4311yescharacteristic
471C2×C8C2×D4×C4311yescharacteristic
472C2×C8C2×D4×C4311yescharacteristic
473C2×C8C2×D4×C4311yescharacteristic
474C2×C8C2×D4×C4311yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4C22×C4×C4311yescharacteristic
482C4⋊C4C22×C4×C4311yescharacteristic
483C4⋊C4C22×C4×C4311yescharacteristic
484C4⋊C4C22×C4×C4311yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—21no—
491C22⋊C4—21no—
492C22⋊C4—21no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42C22×C4×C4311yescharacteristic
498C42C2×D4×C4311yescharacteristic
499C42#41×C4311yescharacteristic
500C42C24×C4311yescharacteristic
501C23—21no—
502C23—21no—
503C23C4×D4×C4311yescharacteristic
504Q8—21no—
505Q8—21no—
506Q8—21no—
507Q8—21no—
508D4—21no—
509D4—21no—
510D4—21no—
511D4—42no—
512D4—81no—
513D4#131×C4312yes—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—81no—
531C2×C4C4×D4×C4311yescharacteristic
532C2×C4C4×D4×C4311yescharacteristic
533C2×C4C4×D4×C4311yescharacteristic
534C2×C4C23×C4×C4311yescharacteristic
535C2×C4C22×D4×C4311yescharacteristic
536C2×C4C2×#41×C4311yescharacteristic
537C8—22no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—21no—
542C8—21no—
543C8—21no—
544C8—21no—
545C8—21no—
546C8—41no—
547C8—41no—
548C8—41no—
549C8—41no—
550C8—41no—
551C22—21no—
552C22—22no—
553C22—21no—
554C22—21no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22C2×C4×D4×C4311yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4C2×#131×C4311yescharacteristic
572C4C43×#56811yescharacteristic
573C4C43×#57511yescharacteristic
574C4C43×#57511yescharacteristic
575C2—41no—
576C2—42no—
577C2—81no—
578C2C43×#293311yescharacteristic
579C2C43×#294311yescharacteristic
580C2C43×#295611yescharacteristic
subgroupG/H
centerC2×C4×C43C22×D4
commutatorC2×C4C23×C4×C43
Frattini, cosocleC42C24×C43
socleC22×C43C2×C4×D4
prime radicalC43×#449C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C43 ◁ C4×M16×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2970C2semidirect
3. C43×#2969C2semidirect
4. C43×#1593C2semidirect
5. C43×#1592C2semidirect
6. C43×#1587C2semidirect
7. C43×#1586C2semidirect
8. C43×#1585C2semidirect
9. C43×#1585C2semidirect
10. C43×#1580C2semidirect
11. C43×SD16⋊C8C2semidirect
12. C43×#1572C2semidirect
13. C43×#1494C2semidirect
14. C43×#1476C2semidirect
15. C43×#1451C2semidirect
260. #18002C43direct (N × H)
286. #2970C2×C43semidirect
287. #2969C2×C43semidirect
288. #1593C2×C43semidirect
289. #1592C2×C43semidirect
290. #1587C2×C43semidirect
291. #1586C2×C43semidirect
292. #1585C2×C43semidirect
293. #1585C2×C43semidirect
294. #1580C2×C43semidirect
295. SD16⋊C8C2×C43semidirect
296. #1572C2×C43semidirect
297. #1494C2×C43semidirect
298. #1476C2×C43semidirect
299. #1451C2×C43semidirect
357. C43#18002direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#31022
C43×#29702
C43×#29692
C43×#15932
C43×#15922
C43×#15872
C43×#15862
C43×#15852
C43×#15802
C43×SD16⋊C82
C43×#15722
C43×#14942
C43×#14762
C43×#14512
#1800243