Finite Group Databasebeta

← C43×#25390 #24945407

Subgroups — C43×#25390 #24945407

Order 11008.

1084 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#469C211yesmaximal, characteristic, complemented
2C2×C43×#468C211yesmaximal, characteristic, complemented
3C2×C43×#463C211yesmaximal, characteristic, complemented
4C2×C43×#436C211yesmaximal, characteristic, complemented
5C43×#2540C211yesmaximal, characteristic, complemented
6C43×#2535C211yesmaximal, characteristic, complemented
7C43×#2035C211yesmaximal, characteristic, complemented
8C43×#2033C211yesmaximal, characteristic, complemented
9C43×#2000C211yesmaximal, characteristic, complemented
10C43×#1999C211yesmaximal, characteristic, complemented
11C43×#1958C211yesmaximal, characteristic, complemented
12C43×#1949C211yesmaximal, characteristic, complemented
13C43×#1895C211yesmaximal, characteristic, complemented
14C43×#1894C211yesmaximal, characteristic, complemented
15C4×#102×C43C211yesmaximal, characteristic, complemented
16C22×SD16×C43C2211yescharacteristic
17C22×D8×C43C2211yescharacteristic
18C22×M16×C43C2211yescharacteristic
19C22×M16×C43C2211yescharacteristic
20C2×#124×C43C2211yescharacteristic
21C2×C22⋊Q8×C43C2211yescharacteristic
22C2×C22⋊Q8×C43C2211yescharacteristic
23C2×#121×C43C2211yescharacteristic
24C2×#121×C43C2211yescharacteristic
25C2×#121×C43C2211yescharacteristic
26C2×#121×C43C2211yescharacteristic
27C2×C4×D4×C43C2211yescharacteristic
28C2×C4×D4×C43C2211yescharacteristic
29C43×#469—24no—
30C43×#468—24no—
31C43×#463—24no—
32C43×#436—24no—
33C2×#107×C43C2211yescharacteristic
34C2×#106×C43C2211yescharacteristic
35C2×C4⋊C8×C43C2211yescharacteristic
36C2×#103×C43C2211yescharacteristic
37C2×#103×C43C2211yescharacteristic
38C2×#103×C43C2211yescharacteristic
39C2×#102×C43C2211yescharacteristic
40C2×#102×C43C2211yescharacteristic
41C2×#102×C43C2211yescharacteristic
42C2×#102×C43C2211yescharacteristic
43C2×#102×C43C2211yescharacteristic
44C2×C22⋊C8×C43C2211yescharacteristic
45C2×C22⋊C8×C43C2211yescharacteristic
46C2×C4×C8×C43C2211yescharacteristic
47C43×#399—21no—
48C43×#397—21no—
49C43×#392—21no—
50C43×#392—21no—
51C43×#390—21no—
52C43×#390—21no—
53C43×#386—21no—
54C43×#386—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×C43D411yescharacteristic
69C22×D4×C43C2311yescharacteristic
70C22×D4×C43C2311yescharacteristic
71C23×C4×C43—21no—
72C23×C4×C43C2311yescharacteristic
73C23×C4×C43C2311yescharacteristic
74C2×SD16×C43—22no—
75C2×SD16×C43—22no—
76C2×SD16×C43—41no—
77C2×D8×C43—22no—
78C2×D8×C43—22no—
79C2×D8×C43—41no—
80C2×M16×C43—22no—
81C2×M16×C43—22no—
82C2×M16×C43—22no—
83C2×M16×C43—22no—
84C2×M16×C43—41no—
85C2×M16×C43—41no—
86C22×C8×C43C2311yescharacteristic
87C22×C8×C43C2311yescharacteristic
88C22×C8×C43C2311yescharacteristic
89C22×C8×C43C2311yescharacteristic
90#124×C43—22no—
91#124×C43—22no—
92C22⋊Q8×C43—22no—
93C22⋊Q8×C43—22no—
94C22⋊Q8×C43—41no—
95C22⋊Q8×C43—41no—
96#121×C43—22no—
97#121×C43—22no—
98#121×C43—22no—
99#121×C43—22no—
100#121×C43—41no—
101#121×C43—41no—
102#121×C43—41no—
103#121×C43—41no—
104C4×D4×C43—22no—
105C4×D4×C43—22no—
106C4×D4×C43—22no—
107C4×D4×C43—22no—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43D411yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C22⋊C4×C43—21no—
117C2×C22⋊C4×C43—21no—
118C2×C22⋊C4×C43—21no—
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×C43C2311yescharacteristic
131#107×C43—22no—
132#106×C43—22no—
133C4⋊C8×C43D414yescomplemented
134#103×C43—22no—
135#103×C43—22no—
136#103×C43—41no—
137#102×C43—22no—
138#102×C43—22no—
139#102×C43—22no—
140#102×C43—41no—
141#102×C43D414yescomplemented
142C22⋊C8×C43—22no—
143C22⋊C8×C43—22no—
144C4×C8×C43—22no—
145#95×C43—21no—
146#95×C43—21no—
147#95×C43—21no—
148#95×C43—21no—
149#95×C43—21no—
150C24×C43—21no—
151C24×C43—21no—
152C24×C43C2×D411yescharacteristic
153C24×C43C2×D411yescharacteristic
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×D4×C43—22no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
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—41no—
173C2×D4×C43—41no—
174C2×D4×C43—42no—
175C2×D4×C43—42no—
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—81no—
183C2×D4×C43—81no—
184C2×D4×C43—81no—
185C2×D4×C43—81no—
186C2×D4×C43C2×D412yes—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
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—42no—
206C22×C4×C43—81no—
207C22×C4×C43—81no—
208C22×C4×C43C2×D411yescharacteristic
209C22×C4×C43C2×D411yescharacteristic
210C22×C4×C43C2×D411yescharacteristic
211C22×C4×C43C2×D411yescharacteristic
212C22×C4×C43C2411yescharacteristic
213SD16×C43—44no—
214D8×C43—44no—
215M16×C43—44no—
216M16×C43—44no—
217C2×C8×C43—21no—
218C2×C8×C43—21no—
219C2×C8×C43—21no—
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×C43C2×D412yes—
227C2×C8×C43C2×D412yes—
228C2×C8×C43C2×D412yes—
229C4⋊C4×C43—22no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43—21no—
238C4⋊C4×C43—42no—
239C4⋊C4×C43—42no—
240C4⋊C4×C43C2×D412yes—
241C4⋊C4×C43#4112yes—
242C22⋊C4×C43—22no—
243C22⋊C4×C43—22no—
244C22⋊C4×C43—42no—
245C22⋊C4×C43—42no—
246C22⋊C4×C43—42no—
247C22⋊C4×C43—42no—
248C22⋊C4×C43—42no—
249C22⋊C4×C43—42no—
250C22⋊C4×C43—42no—
251C22⋊C4×C43—42no—
252C22⋊C4×C43—42no—
253C22⋊C4×C43—81no—
254C22⋊C4×C43—81no—
255C42×C43—81no—
256C42×C43C2×D412yes—
257C42×C43#4112yes—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—22no—
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—41no—
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×C43C22×D411yescharacteristic
287Q8×C43—41no—
288Q8×C43—41no—
289Q8×C43—41no—
290Q8×C43—41no—
291D4×C43—22no—
292D4×C43—22no—
293D4×C43—44no—
294D4×C43—41no—
295D4×C43—41no—
296D4×C43—41no—
297D4×C43—41no—
298D4×C43—41no—
299D4×C43—41no—
300D4×C43—84no—
301D4×C43—84no—
302D4×C43—84no—
303D4×C43—84no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—21no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—22no—
312C2×C4×C43—21no—
313C2×C4×C43—22no—
314C2×C4×C43—21no—
315C2×C4×C43—21no—
316C2×C4×C43—41no—
317C2×C4×C43—41no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43—41no—
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—84no—
341C2×C4×C43#12112yes—
342C2×C4×C43#12112yes—
343C2×C4×C43C22×D411yescharacteristic
344C2×C4×C43C22×D411yescharacteristic
345C2×C4×C43C2×#4111yescharacteristic
346C2×C4×C43C2×#4111yescharacteristic
347C2×C4×C43H(5,𝔽2)11yescharacteristic
348C2×C4×C43H(5,𝔽2)11yescharacteristic
349C8×C43—22no—
350C8×C43—22no—
351C8×C43—22no—
352C8×C43—41no—
353#25390C4311yesmaximal, characteristic, direct product factor, Sylow
354C22×C43—41no—
355C22×C43—41no—
356C22×C43—42no—
357C22×C43—41no—
358C22×C43—41no—
359C22×C43—42no—
360C22×C43—41no—
361C22×C43—41no—
362C22×C43—42no—
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—81no—
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×C43C2×#12111yescharacteristic
383C22×C43D4211yescharacteristic
384C22×C43#54611yescharacteristic
385C22×C43#57511yescharacteristic
386C22×C43#57511yescharacteristic
387C22×C43#57611yescharacteristic
388C22×C43#57711yescharacteristic
389C4×C43—22no—
390C4×C43—22no—
391C4×C43—41no—
392C4×C43—41no—
393C4×C43—42no—
394C4×C43—42no—
395C4×C43—81no—
396C4×C43—81no—
397C4×C43—81no—
398C4×C43—81no—
399C4×C43#53211yescharacteristic
400C4×C43#54011yescharacteristic
401C4×C43D4211yescharacteristic
402C4×C43#55011yescharacteristic
403C2×#469C2×C4311yescharacteristic, complemented
404C2×#468C2×C4311yescharacteristic, complemented
405C2×#463C2×C4311yescharacteristic, complemented
406C2×#436C2×C4311yescharacteristic, complemented
407#2540C2×C4311yescharacteristic, complemented
408#2535C2×C4311yescharacteristic, complemented
409#2035C2×C4311yescharacteristic, complemented
410#2033C2×C4311yescharacteristic, complemented
411#2000C2×C4311yescharacteristic, complemented
412#1999C2×C4311yescharacteristic, complemented
413#1958C2×C4311yescharacteristic, complemented
414#1949C2×C4311yescharacteristic, complemented
415#1895C2×C4311yescharacteristic, complemented
416#1894C2×C4311yescharacteristic, complemented
417C4×#102C2×C4311yescharacteristic, complemented
418C2×C43—81no—
419C2×C43—81no—
420C2×C43—82no—
421C2×C43—161no—
422C2×C43#242811yescharacteristic
423C2×C43#305411yescharacteristic
424C2×C43#306211yescharacteristic
425C2×C43#327311yescharacteristic
426C2×C43#327511yescharacteristic
427C2×C43#332211yescharacteristic
428C2×C43#332611yescharacteristic
429C22×SD16C22×C4311yescharacteristic
430C22×D8C22×C4311yescharacteristic
431C22×M16C22×C4311yescharacteristic
432C22×M16C22×C4311yescharacteristic
433C2×#124C22×C4311yescharacteristic
434C2×C22⋊Q8C22×C4311yescharacteristic
435C2×C22⋊Q8C22×C4311yescharacteristic
436C2×#121C22×C4311yescharacteristic
437C2×#121C22×C4311yescharacteristic
438C2×#121C22×C4311yescharacteristic
439C2×#121C22×C4311yescharacteristic
440C2×C4×D4C22×C4311yescharacteristic
441C2×C4×D4C22×C4311yescharacteristic
442#469—24no—
443#468—24no—
444#463—24no—
445#436—24no—
446C2×#107C22×C4311yescharacteristic
447C2×#106C22×C4311yescharacteristic
448C2×C4⋊C8C22×C4311yescharacteristic
449C2×#103C22×C4311yescharacteristic
450C2×#103C22×C4311yescharacteristic
451C2×#103C22×C4311yescharacteristic
452C2×#102C22×C4311yescharacteristic
453C2×#102C22×C4311yescharacteristic
454C2×#102C22×C4311yescharacteristic
455C2×#102C22×C4311yescharacteristic
456C2×#102C22×C4311yescharacteristic
457C2×C22⋊C8C22×C4311yescharacteristic
458C2×C22⋊C8C22×C4311yescharacteristic
459C2×C4×C8C22×C4311yescharacteristic
460#399—21no—
461#397—21no—
462#392—21no—
463#392—21no—
464#390—21no—
465#390—21no—
466#386—21no—
467#386—21no—
468#382C22×C4311yescharacteristic
469#380C22×C4311yescharacteristic
470#380C22×C4311yescharacteristic
471C4×C4⋊C4C22×C4311yescharacteristic
472#340C22×C4311yescharacteristic
473#340C22×C4311yescharacteristic
474#340C22×C4311yescharacteristic
475#340C22×C4311yescharacteristic
476C43#2539011yescharacteristic, direct product factor, Sylow
477C22×Q8C23×C4311yescharacteristic
478C22×D4—21no—
479C22×D4—21no—
480C22×D4—21no—
481C22×D4—21no—
482C22×D4D4×C4311yescharacteristic
483C22×D4C23×C4311yescharacteristic
484C22×D4C23×C4311yescharacteristic
485C23×C4—21no—
486C23×C4C23×C4311yescharacteristic
487C23×C4C23×C4311yescharacteristic
488C2×SD16—22no—
489C2×SD16—22no—
490C2×SD16—41no—
491C2×D8—22no—
492C2×D8—22no—
493C2×D8—41no—
494C2×M16—22no—
495C2×M16—22no—
496C2×M16—22no—
497C2×M16—22no—
498C2×M16—41no—
499C2×M16—41no—
500C22×C8C23×C4311yescharacteristic
501C22×C8C23×C4311yescharacteristic
502C22×C8C23×C4311yescharacteristic
503C22×C8C23×C4311yescharacteristic
504#124—22no—
505#124—22no—
506C22⋊Q8—22no—
507C22⋊Q8—22no—
508C22⋊Q8—41no—
509C22⋊Q8—41no—
510#121—22no—
511#121—22no—
512#121—22no—
513#121—22no—
514#121—41no—
515#121—41no—
516#121—41no—
517#121—41no—
518C4×D4—22no—
519C4×D4—22no—
520C4×D4—22no—
521C4×D4—22no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4D4×C4311yescharacteristic
525C2×C4⋊C4C23×C4311yescharacteristic
526C2×C4⋊C4C23×C4311yescharacteristic
527C2×C4⋊C4C23×C4311yescharacteristic
528C2×C4⋊C4C23×C4311yescharacteristic
529C2×C4⋊C4C23×C4311yescharacteristic
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4D4×C4311yescharacteristic
542C2×C22⋊C4D4×C4311yescharacteristic
543C2×C42—21no—
544C2×C42C23×C4311yescharacteristic
545#107—22no—
546#106—22no—
547C4⋊C8D4×C4314yescomplemented
548#103—22no—
549#103—22no—
550#103—41no—
551#102—22no—
552#102—22no—
553#102—22no—
554#102—41no—
555#102D4×C4314yescomplemented
556C22⋊C8—22no—
557C22⋊C8—22no—
558C4×C8—22no—
559#95—21no—
560#95—21no—
561#95—21no—
562#95—21no—
563#95—21no—
564C24—21no—
565C24—21no—
566C24C2×D4×C4311yescharacteristic
567C24C2×D4×C4311yescharacteristic
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×D4—22no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—41no—
587C2×D4—41no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—81no—
597C2×D4—81no—
598C2×D4—81no—
599C2×D4—81no—
600C2×D4C2×D4×C4312yes—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—42no—
620C22×C4—81no—
621C22×C4—81no—
622C22×C4C2×D4×C4311yescharacteristic
623C22×C4C2×D4×C4311yescharacteristic
624C22×C4C2×D4×C4311yescharacteristic
625C22×C4C2×D4×C4311yescharacteristic
626C22×C4C24×C4311yescharacteristic
627SD16—44no—
628D8—44no—
629M16—44no—
630M16—44no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8C2×D4×C4312yes—
641C2×C8C2×D4×C4312yes—
642C2×C8C2×D4×C4312yes—
643C4⋊C4—22no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—42no—
653C4⋊C4—42no—
654C4⋊C4C2×D4×C4312yes—
655C4⋊C4#41×C4312yes—
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—81no—
668C22⋊C4—81no—
669C42—81no—
670C42C2×D4×C4312yes—
671C42#41×C4312yes—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—22no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23C22×D4×C4311yescharacteristic
701Q8—41no—
702Q8—41no—
703Q8—41no—
704Q8—41no—
705D4—22no—
706D4—22no—
707D4—44no—
708D4—41no—
709D4—41no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—84no—
715D4—84no—
716D4—84no—
717D4—84no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
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—84no—
755C2×C4#121×C4312yes—
756C2×C4#121×C4312yes—
757C2×C4C22×D4×C4311yescharacteristic
758C2×C4C22×D4×C4311yescharacteristic
759C2×C4C2×#41×C4311yescharacteristic
760C2×C4C2×#41×C4311yescharacteristic
761C2×C4H(5,𝔽2)×C4311yescharacteristic
762C2×C4H(5,𝔽2)×C4311yescharacteristic
763C8—22no—
764C8—22no—
765C8—22no—
766C8—41no—
767C22—41no—
768C22—41no—
769C22—42no—
770C22—41no—
771C22—41no—
772C22—42no—
773C22—41no—
774C22—42no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22C2×#121×C4311yescharacteristic
796C22D42×C4311yescharacteristic
797C22C43×#54611yescharacteristic
798C22C43×#57511yescharacteristic
799C22C43×#57511yescharacteristic
800C22C43×#57611yescharacteristic
801C22C43×#57711yescharacteristic
802C4—22no—
803C4—22no—
804C4—41no—
805C4—41no—
806C4—42no—
807C4—42no—
808C4—81no—
809C4—81no—
810C4—81no—
811C4—81no—
812C4C43×#53211yescharacteristic
813C4C43×#54011yescharacteristic
814C4D42×C4311yescharacteristic
815C4C43×#55011yescharacteristic
816C2—81no—
817C2—81no—
818C2—82no—
819C2—161no—
820C2C43×#242811yescharacteristic
821C2C43×#305411yescharacteristic
822C2C43×#306211yescharacteristic
823C2C43×#327311yescharacteristic
824C2C43×#327511yescharacteristic
825C2C43×#332211yescharacteristic
826C2C43×#332611yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
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×#469C2semidirect
2. C2×C43×#468C2semidirect
3. C2×C43×#463C2semidirect
4. C2×C43×#436C2semidirect
5. C43×#2540C2semidirect
6. C43×#2535C2semidirect
7. C43×#2035C2semidirect
8. C43×#2033C2semidirect
9. C43×#2000C2semidirect
10. C43×#1999C2semidirect
11. C43×#1958C2semidirect
12. C43×#1949C2semidirect
13. C43×#1895C2semidirect
14. C43×#1894C2semidirect
15. C4×#102×C43C2semidirect
133. C4⋊C8×C43D4semidirect
141. #102×C43D4semidirect
353. #25390C43direct (N × H)
403. C2×#469C2×C43semidirect
404. C2×#468C2×C43semidirect
405. C2×#463C2×C43semidirect
406. C2×#436C2×C43semidirect
407. #2540C2×C43semidirect
408. #2535C2×C43semidirect
409. #2035C2×C43semidirect
410. #2033C2×C43semidirect
411. #2000C2×C43semidirect
412. #1999C2×C43semidirect
413. #1958C2×C43semidirect
414. #1949C2×C43semidirect
415. #1895C2×C43semidirect
416. #1894C2×C43semidirect
417. C4×#102C2×C43semidirect
476. C43#25390direct (N × H)
547. C4⋊C8D4×C43semidirect
555. #102D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4692
C2×C43×#4682
C2×C43×#4632
C2×C43×#4362
C43×#25402
C43×#25352
C43×#20352
C43×#20332
C43×#20002
C43×#19992
C43×#19582
C43×#19492
C43×#18952
C43×#18942
C4×#102×C432
#2539043