Finite Group Databasebeta

← C43×#25402 #24945419

Subgroups — C43×#25402 #24945419

Order 11008.

1120 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#468C211yesmaximal, characteristic, complemented
2C2×C43×#465C211yesmaximal, characteristic, complemented
3C2×C43×#460C211yesmaximal, characteristic, complemented
4C2×C43×#435C211yesmaximal, characteristic, complemented
5C43×#2541C211yesmaximal, characteristic
6C43×#2536C211yesmaximal, characteristic, complemented
7C43×#2034C211yesmaximal, characteristic, complemented
8C43×#2033C211yesmaximal, characteristic, complemented
9C43×#2000C211yesmaximal, characteristic, complemented
10C43×#2000C211yesmaximal, characteristic, complemented
11C43×#1961C211yesmaximal, characteristic, complemented
12C43×#1949C211yesmaximal, characteristic, complemented
13C43×#1895C211yesmaximal, characteristic, complemented
14C43×#1893C211yesmaximal, characteristic, complemented
15C43×#1763C211yesmaximal, characteristic, complemented
16C22×SD16×C43C2211yescharacteristic
17C22×SD16×C43C2211yescharacteristic
18C22×M16×C43C2211yescharacteristic
19C23×C8×C43C2211yescharacteristic
20C2×#127×C43—21no—
21C2×#127×C43C2211yescharacteristic
22C2×C22⋊Q8×C43C2211yescharacteristic
23C2×C22⋊Q8×C43C2211yescharacteristic
24C2×#121×C43C2211yescharacteristic
25C2×#121×C43C2211yescharacteristic
26C2×#121×C43C2211yescharacteristic
27C2×#121×C43C2211yescharacteristic
28C2×C4×Q8×C43C2211yescharacteristic
29C2×C4×D4×C43C2211yescharacteristic
30C43×#468—24no—
31C43×#465—24no—
32C43×#460—24no—
33C43×#435—24no—
34C2×#107×C43C2211yescharacteristic
35C2×#106×C43C2211yescharacteristic
36C2×C4⋊C8×C43C2211yescharacteristic
37C2×#103×C43C2211yescharacteristic
38C2×#103×C43C2211yescharacteristic
39C2×#102×C43C2211yescharacteristic
40C2×#102×C43C2211yescharacteristic
41C2×#102×C43C2211yescharacteristic
42C2×#102×C43C2211yescharacteristic
43C2×#102×C43C2211yescharacteristic
44C2×#102×C43C2211yescharacteristic
45C2×C22⋊C8×C43C2211yescharacteristic
46C2×C22⋊C8×C43C2211yescharacteristic
47C2×#97×C43C2211yescharacteristic
48C43×#398—21no—
49C43×#394—21no—
50C43×#392—21no—
51C43×#392—21no—
52C43×#390—21no—
53C43×#388—21no—
54C43×#388—21no—
55C43×#382C2211yescharacteristic
56C43×#380C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C4×C4⋊C4×C43C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C22×Q8×C43C2311yescharacteristic
64C22×D4×C43—21no—
65C22×D4×C43—21no—
66C22×D4×C43—21no—
67C22×D4×C43—21no—
68C22×D4×C43—21no—
69C22×D4×C43—21no—
70C22×D4×C43D411yescharacteristic
71C22×D4×C43C2311yescharacteristic
72C22×D4×C43C2311yescharacteristic
73C23×C4×C43C2311yescharacteristic
74C23×C4×C43C2311yescharacteristic
75C2×SD16×C43—22no—
76C2×SD16×C43—22no—
77C2×SD16×C43—22no—
78C2×SD16×C43—22no—
79C2×SD16×C43—41no—
80C2×SD16×C43—41no—
81C2×M16×C43—22no—
82C2×M16×C43—22no—
83C2×M16×C43—41no—
84C22×C8×C43—22no—
85C22×C8×C43—22no—
86C22×C8×C43—41no—
87C22×C8×C43C2311yescharacteristic
88C22×C8×C43C2311yescharacteristic
89C22×C8×C43C2311yescharacteristic
90C22×C8×C43C2311yescharacteristic
91#127×C43—22no—
92#127×C43—22no—
93#127×C43—44no—
94C22⋊Q8×C43—22no—
95C22⋊Q8×C43—22no—
96C22⋊Q8×C43—41no—
97C22⋊Q8×C43—41no—
98#121×C43—22no—
99#121×C43—22no—
100#121×C43—22no—
101#121×C43—22no—
102#121×C43—41no—
103#121×C43—41no—
104#121×C43—41no—
105#121×C43—41no—
106C4×Q8×C43—22no—
107C4×Q8×C43—22no—
108C4×D4×C43—22no—
109C4×D4×C43—22no—
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43D411yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C22⋊C4×C43—21no—
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122C2×C22⋊C4×C43—21no—
123C2×C22⋊C4×C43—21no—
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43D411yescharacteristic
128C2×C22⋊C4×C43D411yescharacteristic
129C2×C42×C43—21no—
130C2×C42×C43—21no—
131C2×C42×C43C2311yescharacteristic
132#107×C43—22no—
133#106×C43—22no—
134C4⋊C8×C43D414yescomplemented
135#103×C43—22no—
136#103×C43D414yescomplemented
137#102×C43—22no—
138#102×C43—22no—
139#102×C43—22no—
140#102×C43—22no—
141#102×C43—41no—
142#102×C43—41no—
143C22⋊C8×C43—22no—
144C22⋊C8×C43—22no—
145#97×C43—22no—
146#95×C43—21no—
147#95×C43—21no—
148#95×C43—21no—
149#95×C43—21no—
150#95×C43—21no—
151C24×C43—21no—
152C24×C43—21no—
153C24×C43C2×D411yescharacteristic
154C24×C43C2×D411yescharacteristic
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43C2×D412yes—
161C2×D4×C43—22no—
162C2×D4×C43—22no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43—21no—
174C2×D4×C43—21no—
175C2×D4×C43—41no—
176C2×D4×C43—42no—
177C2×D4×C43—42no—
178C2×D4×C43—42no—
179C2×D4×C43—42no—
180C2×D4×C43—42no—
181C2×D4×C43—42no—
182C2×D4×C43—42no—
183C2×D4×C43—42no—
184C2×D4×C43—42no—
185C2×D4×C43—42no—
186C2×D4×C43—42no—
187C2×D4×C43—42no—
188C2×D4×C43—81no—
189C2×D4×C43—81no—
190C2×D4×C43—81no—
191C2×D4×C43—81no—
192C2×D4×C43—81no—
193C2×D4×C43—81no—
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—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43C2×D411yescharacteristic
213C22×C4×C43C2×D411yescharacteristic
214C22×C4×C43C2×D411yescharacteristic
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2411yescharacteristic
217SD16×C43—44no—
218SD16×C43—44no—
219M16×C43—44no—
220C2×C8×C43—21no—
221C2×C8×C43—21no—
222C2×C8×C43—21no—
223C2×C8×C43—21no—
224C2×C8×C43—21no—
225C2×C8×C43—21no—
226C2×C8×C43—21no—
227C2×C8×C43—21no—
228C2×C8×C43—21no—
229C2×C8×C43—44no—
230C2×C8×C43C2×D412yes—
231C2×C8×C43C2×D412yes—
232C2×C8×C43C2×D412yes—
233C4⋊C4×C43—22no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43—21no—
238C4⋊C4×C43—21no—
239C4⋊C4×C43—21no—
240C4⋊C4×C43—21no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43—42no—
243C4⋊C4×C43—42no—
244C4⋊C4×C43—42no—
245C4⋊C4×C43C2×D412yes—
246C4⋊C4×C43#4112yes—
247C22⋊C4×C43—22no—
248C22⋊C4×C43—22no—
249C22⋊C4×C43—42no—
250C22⋊C4×C43—42no—
251C22⋊C4×C43—42no—
252C22⋊C4×C43—42no—
253C22⋊C4×C43—42no—
254C22⋊C4×C43—42no—
255C22⋊C4×C43—42no—
256C22⋊C4×C43—42no—
257C42×C43—42no—
258C42×C43—42no—
259C42×C43C2×D412yes—
260C42×C43#4112yes—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43—21no—
266C23×C43—21no—
267C23×C43—21no—
268C23×C43—21no—
269C23×C43—21no—
270C23×C43—21no—
271C23×C43—21no—
272C23×C43—21no—
273C23×C43—21no—
274C23×C43—41no—
275C23×C43—41no—
276C23×C43—41no—
277C23×C43—41no—
278C23×C43—41no—
279C23×C43—41no—
280C23×C43—41no—
281C23×C43—41no—
282C23×C43—41no—
283C23×C43—41no—
284C23×C43—41no—
285C23×C43—41no—
286C23×C43—41no—
287C23×C43—41no—
288C23×C43AGL(1,ℤ/8)12yes—
289C23×C43C22×D411yescharacteristic
290Q8×C43—22no—
291Q8×C43—22no—
292Q8×C43—41no—
293Q8×C43—41no—
294D4×C43—44no—
295D4×C43—41no—
296D4×C43—41no—
297D4×C43—41no—
298D4×C43—41no—
299D4×C43—41no—
300D4×C43—41no—
301D4×C43—41no—
302D4×C43—41no—
303D4×C43—84no—
304D4×C43—84no—
305D4×C43—84no—
306D4×C43—84no—
307D4×C43—84no—
308D4×C43—84no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—21no—
313C2×C4×C43—21no—
314C2×C4×C43—21no—
315C2×C4×C43—22no—
316C2×C4×C43—21no—
317C2×C4×C43—21no—
318C2×C4×C43—22no—
319C2×C4×C43—22no—
320C2×C4×C43—21no—
321C2×C4×C43—21no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43—41no—
327C2×C4×C43—41no—
328C2×C4×C43—41no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43—41no—
340C2×C4×C43—41no—
341C2×C4×C43—41no—
342C2×C4×C43—41no—
343C2×C4×C43—41no—
344C2×C4×C43—41no—
345C2×C4×C43#12112yes—
346C2×C4×C43#12112yes—
347C2×C4×C43C22×D411yescharacteristic
348C2×C4×C43C22×D411yescharacteristic
349C2×C4×C43C2×#4111yescharacteristic
350C2×C4×C43C2×#4111yescharacteristic
351C2×C4×C43H(5,𝔽2)11yescharacteristic
352C2×C4×C43H(5,𝔽2)11yescharacteristic
353C8×C43—22no—
354C8×C43—22no—
355C8×C43—22no—
356C8×C43—41no—
357#25402C4311yesmaximal, characteristic, direct product factor, Sylow
358C22×C43—22no—
359C22×C43—22no—
360C22×C43—22no—
361C22×C43—41no—
362C22×C43—41no—
363C22×C43—41no—
364C22×C43—41no—
365C22×C43—41no—
366C22×C43—41no—
367C22×C43—41no—
368C22×C43—41no—
369C22×C43—41no—
370C22×C43—41no—
371C22×C43—41no—
372C22×C43—81no—
373C22×C43—81no—
374C22×C43—81no—
375C22×C43—81no—
376C22×C43—81no—
377C22×C43—81no—
378C22×C43—81no—
379C22×C43—81no—
380C22×C43—81no—
381C22×C43—81no—
382C22×C43—81no—
383C22×C43—81no—
384C22×C43—81no—
385C22×C43—81no—
386C22×C43C2×#12111yescharacteristic
387C22×C43D4211yescharacteristic
388C22×C43#54611yescharacteristic
389C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
390C22×C43#57511yescharacteristic
391C22×C43#57711yescharacteristic
392C22×C43#57711yescharacteristic
393C4×C43—22no—
394C4×C43—22no—
395C4×C43—41no—
396C4×C43—41no—
397C4×C43—42no—
398C4×C43—42no—
399C4×C43—42no—
400C4×C43—81no—
401C4×C43—81no—
402C4×C43—81no—
403C4×C43#53211yescharacteristic
404C4×C43#54011yescharacteristic
405C4×C43D4211yescharacteristic
406C4×C43#55011yescharacteristic
407C2×#468C2×C4311yescharacteristic, complemented
408C2×#465C2×C4311yescharacteristic, complemented
409C2×#460C2×C4311yescharacteristic, complemented
410C2×#435C2×C4311yescharacteristic, complemented
411#2541C2×C4311yescharacteristic
412#2536C2×C4311yescharacteristic, complemented
413#2034C2×C4311yescharacteristic, complemented
414#2033C2×C4311yescharacteristic, complemented
415#2000C2×C4311yescharacteristic, complemented
416#2000C2×C4311yescharacteristic, complemented
417#1961C2×C4311yescharacteristic, complemented
418#1949C2×C4311yescharacteristic, complemented
419#1895C2×C4311yescharacteristic, complemented
420#1893C2×C4311yescharacteristic, complemented
421#1763C2×C4311yescharacteristic, complemented
422C2×C43—42no—
423C2×C43—81no—
424C2×C43—161no—
425C2×C43—161no—
426C2×C43#242811yescharacteristic
427C2×C43#305511yescharacteristic
428C2×C43#305711yescharacteristic
429C2×C43#326511yescharacteristic
430C2×C43#327111yescharacteristic
431C2×C43#331011yescharacteristic
432C2×C43#331711yescharacteristic
433C22×SD16C22×C4311yescharacteristic
434C22×SD16C22×C4311yescharacteristic
435C22×M16C22×C4311yescharacteristic
436C23×C8C22×C4311yescharacteristic
437C2×#127—21no—
438C2×#127C22×C4311yescharacteristic
439C2×C22⋊Q8C22×C4311yescharacteristic
440C2×C22⋊Q8C22×C4311yescharacteristic
441C2×#121C22×C4311yescharacteristic
442C2×#121C22×C4311yescharacteristic
443C2×#121C22×C4311yescharacteristic
444C2×#121C22×C4311yescharacteristic
445C2×C4×Q8C22×C4311yescharacteristic
446C2×C4×D4C22×C4311yescharacteristic
447#468—24no—
448#465—24no—
449#460—24no—
450#435—24no—
451C2×#107C22×C4311yescharacteristic
452C2×#106C22×C4311yescharacteristic
453C2×C4⋊C8C22×C4311yescharacteristic
454C2×#103C22×C4311yescharacteristic
455C2×#103C22×C4311yescharacteristic
456C2×#102C22×C4311yescharacteristic
457C2×#102C22×C4311yescharacteristic
458C2×#102C22×C4311yescharacteristic
459C2×#102C22×C4311yescharacteristic
460C2×#102C22×C4311yescharacteristic
461C2×#102C22×C4311yescharacteristic
462C2×C22⋊C8C22×C4311yescharacteristic
463C2×C22⋊C8C22×C4311yescharacteristic
464C2×#97C22×C4311yescharacteristic
465#398—21no—
466#394—21no—
467#392—21no—
468#392—21no—
469#390—21no—
470#388—21no—
471#388—21no—
472#382C22×C4311yescharacteristic
473#380C22×C4311yescharacteristic
474#380C22×C4311yescharacteristic
475C4×C4⋊C4C22×C4311yescharacteristic
476#340C22×C4311yescharacteristic
477#340C22×C4311yescharacteristic
478#340C22×C4311yescharacteristic
479#340C22×C4311yescharacteristic
480C43#2540211yescharacteristic, direct product factor, Sylow
481C22×Q8C23×C4311yescharacteristic
482C22×D4—21no—
483C22×D4—21no—
484C22×D4—21no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—21no—
488C22×D4D4×C4311yescharacteristic
489C22×D4C23×C4311yescharacteristic
490C22×D4C23×C4311yescharacteristic
491C23×C4C23×C4311yescharacteristic
492C23×C4C23×C4311yescharacteristic
493C2×SD16—22no—
494C2×SD16—22no—
495C2×SD16—22no—
496C2×SD16—22no—
497C2×SD16—41no—
498C2×SD16—41no—
499C2×M16—22no—
500C2×M16—22no—
501C2×M16—41no—
502C22×C8—22no—
503C22×C8—22no—
504C22×C8—41no—
505C22×C8C23×C4311yescharacteristic
506C22×C8C23×C4311yescharacteristic
507C22×C8C23×C4311yescharacteristic
508C22×C8C23×C4311yescharacteristic
509#127—22no—
510#127—22no—
511#127—44no—
512C22⋊Q8—22no—
513C22⋊Q8—22no—
514C22⋊Q8—41no—
515C22⋊Q8—41no—
516#121—22no—
517#121—22no—
518#121—22no—
519#121—22no—
520#121—41no—
521#121—41no—
522#121—41no—
523#121—41no—
524C4×Q8—22no—
525C4×Q8—22no—
526C4×D4—22no—
527C4×D4—22no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4D4×C4311yescharacteristic
532C2×C4⋊C4C23×C4311yescharacteristic
533C2×C4⋊C4C23×C4311yescharacteristic
534C2×C4⋊C4C23×C4311yescharacteristic
535C2×C4⋊C4C23×C4311yescharacteristic
536C2×C4⋊C4C23×C4311yescharacteristic
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4D4×C4311yescharacteristic
546C2×C22⋊C4D4×C4311yescharacteristic
547C2×C42—21no—
548C2×C42—21no—
549C2×C42C23×C4311yescharacteristic
550#107—22no—
551#106—22no—
552C4⋊C8D4×C4314yescomplemented
553#103—22no—
554#103D4×C4314yescomplemented
555#102—22no—
556#102—22no—
557#102—22no—
558#102—22no—
559#102—41no—
560#102—41no—
561C22⋊C8—22no—
562C22⋊C8—22no—
563#97—22no—
564#95—21no—
565#95—21no—
566#95—21no—
567#95—21no—
568#95—21no—
569C24—21no—
570C24—21no—
571C24C2×D4×C4311yescharacteristic
572C24C2×D4×C4311yescharacteristic
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8C2×D4×C4312yes—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—41no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—81no—
607C2×D4—81no—
608C2×D4—81no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4—81no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4C2×D4×C4311yescharacteristic
631C22×C4C2×D4×C4311yescharacteristic
632C22×C4C2×D4×C4311yescharacteristic
633C22×C4C2×D4×C4311yescharacteristic
634C22×C4C24×C4311yescharacteristic
635SD16—44no—
636SD16—44no—
637M16—44no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—44no—
648C2×C8C2×D4×C4312yes—
649C2×C8C2×D4×C4312yes—
650C2×C8C2×D4×C4312yes—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—42no—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4C2×D4×C4312yes—
664C4⋊C4#41×C4312yes—
665C22⋊C4—22no—
666C22⋊C4—22no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C42—42no—
676C42—42no—
677C42C2×D4×C4312yes—
678C42#41×C4312yes—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23AGL(1,ℤ/8)×C4312yes—
707C23C22×D4×C4311yescharacteristic
708Q8—22no—
709Q8—22no—
710Q8—41no—
711Q8—41no—
712D4—44no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—84no—
722D4—84no—
723D4—84no—
724D4—84no—
725D4—84no—
726D4—84no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4#121×C4312yes—
764C2×C4#121×C4312yes—
765C2×C4C22×D4×C4311yescharacteristic
766C2×C4C22×D4×C4311yescharacteristic
767C2×C4C2×#41×C4311yescharacteristic
768C2×C4C2×#41×C4311yescharacteristic
769C2×C4H(5,𝔽2)×C4311yescharacteristic
770C2×C4H(5,𝔽2)×C4311yescharacteristic
771C8—22no—
772C8—22no—
773C8—22no—
774C8—41no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22C2×#121×C4311yescharacteristic
804C22D42×C4311yescharacteristic
805C22C43×#54611yescharacteristic
806C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
807C22C43×#57511yescharacteristic
808C22C43×#57711yescharacteristic
809C22C43×#57711yescharacteristic
810C4—22no—
811C4—22no—
812C4—41no—
813C4—41no—
814C4—42no—
815C4—42no—
816C4—42no—
817C4—81no—
818C4—81no—
819C4—81no—
820C4C43×#53211yescharacteristic
821C4C43×#54011yescharacteristic
822C4D42×C4311yescharacteristic
823C4C43×#55011yescharacteristic
824C2—42no—
825C2—81no—
826C2—161no—
827C2—161no—
828C2C43×#242811yescharacteristic
829C2C43×#305511yescharacteristic
830C2C43×#305711yescharacteristic
831C2C43×#326511yescharacteristic
832C2C43×#327111yescharacteristic
833C2C43×#331011yescharacteristic
834C2C43×#331711yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC43×#2541C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C2×C4×D4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#468C2semidirect
2. C2×C43×#465C2semidirect
3. C2×C43×#460C2semidirect
4. C2×C43×#435C2semidirect
6. C43×#2536C2semidirect
7. C43×#2034C2semidirect
8. C43×#2033C2semidirect
9. C43×#2000C2semidirect
10. C43×#2000C2semidirect
11. C43×#1961C2semidirect
12. C43×#1949C2semidirect
13. C43×#1895C2semidirect
14. C43×#1893C2semidirect
15. C43×#1763C2semidirect
134. C4⋊C8×C43D4semidirect
136. #103×C43D4semidirect
357. #25402C43direct (N × H)
407. C2×#468C2×C43semidirect
408. C2×#465C2×C43semidirect
409. C2×#460C2×C43semidirect
410. C2×#435C2×C43semidirect
412. #2536C2×C43semidirect
413. #2034C2×C43semidirect
414. #2033C2×C43semidirect
415. #2000C2×C43semidirect
416. #2000C2×C43semidirect
417. #1961C2×C43semidirect
418. #1949C2×C43semidirect
419. #1895C2×C43semidirect
420. #1893C2×C43semidirect
421. #1763C2×C43semidirect
480. C43#25402direct (N × H)
552. C4⋊C8D4×C43semidirect
554. #103D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4682
C2×C43×#4652
C2×C43×#4602
C2×C43×#4352
C43×#25412
C43×#25362
C43×#20342
C43×#20332
C43×#20002
C43×#19612
C43×#19492
C43×#18952
C43×#18932
C43×#17632
#2540243