Finite Group Databasebeta

← C43×#25376 #24945393

Subgroups — C43×#25376 #24945393

Order 11008.

1162 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#496C211yesmaximal, characteristic, complemented
2C2×C43×#463C211yesmaximal, characteristic, complemented
3C2×C43×#459C211yesmaximal, characteristic, complemented
4C2×C43×#459C211yesmaximal, characteristic, complemented
5C43×#2544C211yesmaximal, characteristic, complemented
6C43×#2366C211yesmaximal, characteristic, complemented
7C43×#2055C211yesmaximal, characteristic, complemented
8C43×#2054C211yesmaximal, characteristic, complemented
9C43×#2012C211yesmaximal, characteristic, complemented
10C43×#2011C211yesmaximal, characteristic, complemented
11C43×#1983C211yesmaximal, characteristic, complemented
12C43×#1940C211yesmaximal, characteristic, complemented
13C43×#1879C211yesmaximal, characteristic, complemented
14C43×#1877C211yesmaximal, characteristic, complemented
15C43×#1762C211yesmaximal, characteristic, complemented
16C22×SD16×C43C2211yescharacteristic
17C22×SD16×C43C2211yescharacteristic
18C22×D8×C43C2211yescharacteristic
19C22×D8×C43C2211yescharacteristic
20C22×D8×C43C2211yescharacteristic
21C22×D8×C43C2211yescharacteristic
22C2×#127×C43C2211yescharacteristic
23C2×#127×C43C2211yescharacteristic
24C2×#124×C43C2211yescharacteristic
25C2×#124×C43C2211yescharacteristic
26C2×C4×D4×C43—21no—
27C2×C4×D4×C43C2211yescharacteristic
28C2×C4×D4×C43C2211yescharacteristic
29C2×C4×D4×C43C2211yescharacteristic
30C43×#496—24no—
31C43×#463—24no—
32C43×#459—24no—
33C43×#459—24no—
34C2×C4⋊C8×C43C2211yescharacteristic
35C2×C4⋊C8×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×#97×C43C2211yescharacteristic
46C43×#394—21no—
47C43×#394—21no—
48C43×#391C2211yescharacteristic
49C43×#390—21no—
50C43×#390C2211yescharacteristic
51C43×#390C2211yescharacteristic
52C43×#390C2211yescharacteristic
53C43×#386—21no—
54C43×#386—21no—
55C43×#386—21no—
56C43×#386—21no—
57C4×C4⋊C4×C43C2211yescharacteristic
58C4×C4⋊C4×C43C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×Q8×C43C2311yescharacteristic
64C22×D4×C43—21no—
65C22×D4×C43—21no—
66C22×D4×C43—21no—
67C22×D4×C43—21no—
68C22×D4×C43C2311yescharacteristic
69C22×D4×C43C2311yescharacteristic
70C22×D4×C43C2311yescharacteristic
71C22×D4×C43C2311yescharacteristic
72C23×C4×C43—21no—
73C23×C4×C43—21no—
74C23×C4×C43—21no—
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×D8×C43—22no—
82C2×D8×C43—22no—
83C2×D8×C43—22no—
84C2×D8×C43—22no—
85C2×D8×C43—22no—
86C2×D8×C43—22no—
87C2×D8×C43—22no—
88C2×D8×C43—22no—
89C2×D8×C43—41no—
90C2×D8×C43—41no—
91C2×D8×C43—41no—
92C2×D8×C43—41no—
93C22×C8×C43C2311yescharacteristic
94C22×C8×C43C2311yescharacteristic
95C22×C8×C43C2311yescharacteristic
96C22×C8×C43C2311yescharacteristic
97#127×C43—22no—
98#127×C43—22no—
99#127×C43—41no—
100#127×C43D414yescomplemented
101#124×C43—22no—
102#124×C43—22no—
103#124×C43—22no—
104#124×C43—41no—
105C4×D4×C43—22no—
106C4×D4×C43—22no—
107C4×D4×C43—22no—
108C4×D4×C43—22no—
109C4×D4×C43—41no—
110C4×D4×C43—41no—
111C4×D4×C43—44no—
112C2×C4⋊C4×C43D411yescharacteristic
113C2×C4⋊C4×C43D411yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
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×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43—21no—
130C2×C42×C43—21no—
131C2×C42×C43C2311yescharacteristic
132C2×C42×C43C2311yescharacteristic
133C2×C42×C43C2311yescharacteristic
134C4⋊C8×C43—22no—
135C4⋊C8×C43—22no—
136C4⋊C8×C43—22no—
137#103×C43—22no—
138#103×C43—41no—
139#102×C43—22no—
140#102×C43—22no—
141#102×C43—22no—
142#102×C43—22no—
143#102×C43—41no—
144#102×C43D414yescomplemented
145#97×C43—22no—
146#95×C43—21no—
147#95×C43—21no—
148#95×C43—21no—
149#95×C43D411yescharacteristic
150#95×C43D411yescharacteristic
151C24×C43—21no—
152C24×C43—21no—
153C24×C43—21no—
154C24×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×D4×C43—24no—
162C2×D4×C43—24no—
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—21no—
176C2×D4×C43—21no—
177C2×D4×C43—21no—
178C2×D4×C43—21no—
179C2×D4×C43—21no—
180C2×D4×C43—21no—
181C2×D4×C43—21no—
182C2×D4×C43—21no—
183C2×D4×C43—21no—
184C2×D4×C43—42no—
185C2×D4×C43—42no—
186C2×D4×C43—42no—
187C2×D4×C43—42no—
188C2×D4×C43—42no—
189C2×D4×C43—42no—
190C2×D4×C43—81no—
191C2×D4×C43—81no—
192C2×D4×C43—81no—
193C2×D4×C43—81no—
194C2×D4×C43C2×D412yes—
195C2×D4×C43C2×D412yes—
196C2×D4×C43C2×D412yes—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—42no—
202C22×C4×C43—42no—
203C22×C4×C43—42no—
204C22×C4×C43—42no—
205C22×C4×C43—42no—
206C22×C4×C43—81no—
207C22×C4×C43—81no—
208C22×C4×C43—81no—
209C22×C4×C43—81no—
210C22×C4×C43C2×D411yescharacteristic
211C22×C4×C43C2×D411yescharacteristic
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—
219D8×C43—44no—
220D8×C43—44no—
221D8×C43—44no—
222D8×C43—44no—
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—21no—
230C2×C8×C43—21no—
231C2×C8×C43—21no—
232C2×C8×C43—21no—
233C2×C8×C43C2×D412yes—
234C2×C8×C43#4112yes—
235C4⋊C4×C43—22no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43—21no—
238C4⋊C4×C43—21no—
239C4⋊C4×C43—21no—
240C4⋊C4×C43—21no—
241C4⋊C4×C43—41no—
242C4⋊C4×C43C2×D412yes—
243C22⋊C4×C43—42no—
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—81no—
253C22⋊C4×C43—81no—
254C22⋊C4×C43—81no—
255C22⋊C4×C43—81no—
256C42×C43—21no—
257C42×C43—21no—
258C42×C43—21no—
259C42×C43—21no—
260C42×C43—42no—
261C42×C43C2×D412yes—
262C42×C43#4112yes—
263C23×C43—22no—
264C23×C43—22no—
265C23×C43—22no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43—41no—
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×C43—41no—
287C23×C43—41no—
288C23×C43—41no—
289C23×C43—41no—
290C23×C43—41no—
291C23×C43C22×D411yescharacteristic
292Q8×C43—41no—
293Q8×C43—41no—
294Q8×C43—41no—
295Q8×C43—41no—
296D4×C43—22no—
297D4×C43—22no—
298D4×C43—22no—
299D4×C43—22no—
300D4×C43—22no—
301D4×C43—22no—
302D4×C43—48no—
303D4×C43—41no—
304D4×C43—41no—
305D4×C43—41no—
306D4×C43—41no—
307D4×C43—41no—
308D4×C43—41no—
309D4×C43—41no—
310D4×C43—41no—
311D4×C43—41no—
312D4×C43—41no—
313D4×C43—84no—
314D4×C43—84no—
315D4×C43—84no—
316C2×C4×C43—21no—
317C2×C4×C43—21no—
318C2×C4×C43—21no—
319C2×C4×C43—21no—
320C2×C4×C43—21no—
321C2×C4×C43—21no—
322C2×C4×C43—21no—
323C2×C4×C43—21no—
324C2×C4×C43—21no—
325C2×C4×C43—22no—
326C2×C4×C43—21no—
327C2×C4×C43—21no—
328C2×C4×C43—21no—
329C2×C4×C43—21no—
330C2×C4×C43—21no—
331C2×C4×C43—21no—
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—84no—
344C2×C4×C43—84no—
345C2×C4×C43—84no—
346C2×C4×C43#12112yes—
347C2×C4×C43#12112yes—
348C2×C4×C43AGL(1,ℤ/8)12yes—
349C2×C4×C43C22×D411yescharacteristic
350C2×C4×C43C22×D411yescharacteristic
351C2×C4×C43C2×#4111yescharacteristic
352C2×C4×C43C2×#4111yescharacteristic
353C2×C4×C43H(5,𝔽2)11yescharacteristic
354C2×C4×C43H(5,𝔽2)11yescharacteristic
355C8×C43—22no—
356C8×C43—22no—
357C8×C43—41no—
358C8×C43—41no—
359#25376C4311yesmaximal, characteristic, direct product factor, Sylow
360C22×C43—42no—
361C22×C43—42no—
362C22×C43—42no—
363C22×C43—42no—
364C22×C43—42no—
365C22×C43—42no—
366C22×C43—42no—
367C22×C43—42no—
368C22×C43—42no—
369C22×C43—81no—
370C22×C43—81no—
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×C43—81no—
383C22×C43—81no—
384C22×C43—81no—
385C22×C43—81no—
386C22×C43—81no—
387C22×C43—81no—
388C22×C43C2×#12111yescharacteristic
389C22×C43D4211yescharacteristic
390C22×C43#55011yescharacteristic
391C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
392C22×C43#57511yescharacteristic
393C22×C43#57611yescharacteristic
394C22×C43#57611yescharacteristic
395C4×C43—22no—
396C4×C43—22no—
397C4×C43—22no—
398C4×C43—41no—
399C4×C43—42no—
400C4×C43—41no—
401C4×C43—41no—
402C4×C43—81no—
403C4×C43—81no—
404C4×C43—81no—
405C4×C43#53211yescharacteristic
406C4×C43#54011yescharacteristic
407C4×C43D4211yescharacteristic
408C4×C43#54611yescharacteristic
409C2×#496C2×C4311yescharacteristic, complemented
410C2×#463C2×C4311yescharacteristic, complemented
411C2×#459C2×C4311yescharacteristic, complemented
412C2×#459C2×C4311yescharacteristic, complemented
413#2544C2×C4311yescharacteristic, complemented
414#2366C2×C4311yescharacteristic, complemented
415#2055C2×C4311yescharacteristic, complemented
416#2054C2×C4311yescharacteristic, complemented
417#2012C2×C4311yescharacteristic, complemented
418#2011C2×C4311yescharacteristic, complemented
419#1983C2×C4311yescharacteristic, complemented
420#1940C2×C4311yescharacteristic, complemented
421#1879C2×C4311yescharacteristic, complemented
422#1877C2×C4311yescharacteristic, complemented
423#1762C2×C4311yescharacteristic, complemented
424C2×C43—82no—
425C2×C43—82no—
426C2×C43—82no—
427C2×C43—161no—
428C2×C43#242811yescharacteristic
429C2×C43#303611yescharacteristic
430C2×C43#304111yescharacteristic
431C2×C43#326411yescharacteristic
432C2×C43#326811yescharacteristic
433C2×C43#339911yescharacteristic
434C2×C43#340311yescharacteristic
435C22×SD16C22×C4311yescharacteristic
436C22×SD16C22×C4311yescharacteristic
437C22×D8C22×C4311yescharacteristic
438C22×D8C22×C4311yescharacteristic
439C22×D8C22×C4311yescharacteristic
440C22×D8C22×C4311yescharacteristic
441C2×#127C22×C4311yescharacteristic
442C2×#127C22×C4311yescharacteristic
443C2×#124C22×C4311yescharacteristic
444C2×#124C22×C4311yescharacteristic
445C2×C4×D4—21no—
446C2×C4×D4C22×C4311yescharacteristic
447C2×C4×D4C22×C4311yescharacteristic
448C2×C4×D4C22×C4311yescharacteristic
449#496—24no—
450#463—24no—
451#459—24no—
452#459—24no—
453C2×C4⋊C8C22×C4311yescharacteristic
454C2×C4⋊C8C22×C4311yescharacteristic
455C2×C4⋊C8C22×C4311yescharacteristic
456C2×#103C22×C4311yescharacteristic
457C2×#103C22×C4311yescharacteristic
458C2×#102C22×C4311yescharacteristic
459C2×#102C22×C4311yescharacteristic
460C2×#102C22×C4311yescharacteristic
461C2×#102C22×C4311yescharacteristic
462C2×#102C22×C4311yescharacteristic
463C2×#102C22×C4311yescharacteristic
464C2×#97C22×C4311yescharacteristic
465#394—21no—
466#394—21no—
467#391C22×C4311yescharacteristic
468#390—21no—
469#390C22×C4311yescharacteristic
470#390C22×C4311yescharacteristic
471#390C22×C4311yescharacteristic
472#386—21no—
473#386—21no—
474#386—21no—
475#386—21no—
476C4×C4⋊C4C22×C4311yescharacteristic
477C4×C4⋊C4C22×C4311yescharacteristic
478#340C22×C4311yescharacteristic
479#340C22×C4311yescharacteristic
480#336C22×C4311yescharacteristic
481#336C22×C4311yescharacteristic
482C43#2537611yescharacteristic, direct product factor, Sylow
483C22×Q8C23×C4311yescharacteristic
484C22×D4—21no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—21no—
488C22×D4C23×C4311yescharacteristic
489C22×D4C23×C4311yescharacteristic
490C22×D4C23×C4311yescharacteristic
491C22×D4C23×C4311yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—21no—
495C2×SD16—22no—
496C2×SD16—22no—
497C2×SD16—22no—
498C2×SD16—22no—
499C2×SD16—41no—
500C2×SD16—41no—
501C2×D8—22no—
502C2×D8—22no—
503C2×D8—22no—
504C2×D8—22no—
505C2×D8—22no—
506C2×D8—22no—
507C2×D8—22no—
508C2×D8—22no—
509C2×D8—41no—
510C2×D8—41no—
511C2×D8—41no—
512C2×D8—41no—
513C22×C8C23×C4311yescharacteristic
514C22×C8C23×C4311yescharacteristic
515C22×C8C23×C4311yescharacteristic
516C22×C8C23×C4311yescharacteristic
517#127—22no—
518#127—22no—
519#127—41no—
520#127D4×C4314yescomplemented
521#124—22no—
522#124—22no—
523#124—22no—
524#124—41no—
525C4×D4—22no—
526C4×D4—22no—
527C4×D4—22no—
528C4×D4—22no—
529C4×D4—41no—
530C4×D4—41no—
531C4×D4—44no—
532C2×C4⋊C4D4×C4311yescharacteristic
533C2×C4⋊C4D4×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⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C42—21no—
551C2×C42C23×C4311yescharacteristic
552C2×C42C23×C4311yescharacteristic
553C2×C42C23×C4311yescharacteristic
554C4⋊C8—22no—
555C4⋊C8—22no—
556C4⋊C8—22no—
557#103—22no—
558#103—41no—
559#102—22no—
560#102—22no—
561#102—22no—
562#102—22no—
563#102—41no—
564#102D4×C4314yescomplemented
565#97—22no—
566#95—21no—
567#95—21no—
568#95—21no—
569#95D4×C4311yescharacteristic
570#95D4×C4311yescharacteristic
571C24—21no—
572C24—21no—
573C24—21no—
574C24—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×D4—24no—
582C2×D4—24no—
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—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—81no—
611C2×D4—81no—
612C2×D4—81no—
613C2×D4—81no—
614C2×D4C2×D4×C4312yes—
615C2×D4C2×D4×C4312yes—
616C2×D4C2×D4×C4312yes—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—81no—
627C22×C4—81no—
628C22×C4—81no—
629C22×C4—81no—
630C22×C4C2×D4×C4311yescharacteristic
631C22×C4C2×D4×C4311yescharacteristic
632C22×C4C2×D4×C4311yescharacteristic
633C22×C4C2×D4×C4311yescharacteristic
634C22×C4C2×D4×C4311yescharacteristic
635C22×C4C2×D4×C4311yescharacteristic
636C22×C4C24×C4311yescharacteristic
637SD16—44no—
638SD16—44no—
639D8—44no—
640D8—44no—
641D8—44no—
642D8—44no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8C2×D4×C4312yes—
654C2×C8#41×C4312yes—
655C4⋊C4—22no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—41no—
662C4⋊C4C2×D4×C4312yes—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—81no—
673C22⋊C4—81no—
674C22⋊C4—81no—
675C22⋊C4—81no—
676C42—21no—
677C42—21no—
678C42—21no—
679C42—21no—
680C42—42no—
681C42C2×D4×C4312yes—
682C42#41×C4312yes—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—41no—
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—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23C22×D4×C4311yescharacteristic
712Q8—41no—
713Q8—41no—
714Q8—41no—
715Q8—41no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—22no—
720D4—22no—
721D4—22no—
722D4—48no—
723D4—41no—
724D4—41no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—84no—
734D4—84no—
735D4—84no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
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—84no—
764C2×C4—84no—
765C2×C4—84no—
766C2×C4#121×C4312yes—
767C2×C4#121×C4312yes—
768C2×C4AGL(1,ℤ/8)×C4312yes—
769C2×C4C22×D4×C4311yescharacteristic
770C2×C4C22×D4×C4311yescharacteristic
771C2×C4C2×#41×C4311yescharacteristic
772C2×C4C2×#41×C4311yescharacteristic
773C2×C4H(5,𝔽2)×C4311yescharacteristic
774C2×C4H(5,𝔽2)×C4311yescharacteristic
775C8—22no—
776C8—22no—
777C8—41no—
778C8—41no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—81no—
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—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22C2×#121×C4311yescharacteristic
808C22D42×C4311yescharacteristic
809C22C43×#55011yescharacteristic
810C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
811C22C43×#57511yescharacteristic
812C22C43×#57611yescharacteristic
813C22C43×#57611yescharacteristic
814C4—22no—
815C4—22no—
816C4—22no—
817C4—41no—
818C4—42no—
819C4—41no—
820C4—41no—
821C4—81no—
822C4—81no—
823C4—81no—
824C4C43×#53211yescharacteristic
825C4C43×#54011yescharacteristic
826C4D42×C4311yescharacteristic
827C4C43×#54611yescharacteristic
828C2—82no—
829C2—82no—
830C2—82no—
831C2—161no—
832C2C43×#242811yescharacteristic
833C2C43×#303611yescharacteristic
834C2C43×#304111yescharacteristic
835C2C43×#326411yescharacteristic
836C2C43×#326811yescharacteristic
837C2C43×#339911yescharacteristic
838C2C43×#340311yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
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. C2×C43×#496C2semidirect
2. C2×C43×#463C2semidirect
3. C2×C43×#459C2semidirect
4. C2×C43×#459C2semidirect
5. C43×#2544C2semidirect
6. C43×#2366C2semidirect
7. C43×#2055C2semidirect
8. C43×#2054C2semidirect
9. C43×#2012C2semidirect
10. C43×#2011C2semidirect
11. C43×#1983C2semidirect
12. C43×#1940C2semidirect
13. C43×#1879C2semidirect
14. C43×#1877C2semidirect
15. C43×#1762C2semidirect
100. #127×C43D4semidirect
144. #102×C43D4semidirect
359. #25376C43direct (N × H)
409. C2×#496C2×C43semidirect
410. C2×#463C2×C43semidirect
411. C2×#459C2×C43semidirect
412. C2×#459C2×C43semidirect
413. #2544C2×C43semidirect
414. #2366C2×C43semidirect
415. #2055C2×C43semidirect
416. #2054C2×C43semidirect
417. #2012C2×C43semidirect
418. #2011C2×C43semidirect
419. #1983C2×C43semidirect
420. #1940C2×C43semidirect
421. #1879C2×C43semidirect
422. #1877C2×C43semidirect
423. #1762C2×C43semidirect
482. C43#25376direct (N × H)
520. #127D4×C43semidirect
564. #102D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4962
C2×C43×#4632
C2×C43×#4592
C43×#25442
C43×#23662
C43×#20552
C43×#20542
C43×#20122
C43×#20112
C43×#19832
C43×#19402
C43×#18792
C43×#18772
C43×#17622
#2537643