Finite Group Databasebeta

← C43×#18416 #24938433

Subgroups — C43×#18416 #24938433

Order 11008.

978 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3535C211yesmaximal, characteristic, complemented
2C43×#3194C211yesmaximal, characteristic, complemented
3C43×#3187C211yesmaximal, characteristic, complemented
4C43×#2661C211yesmaximal, characteristic, complemented
5C43×#1612C211yesmaximal, characteristic, complemented
6C43×#1611C211yesmaximal, characteristic, complemented
7C43×#1609C211yesmaximal, characteristic, complemented
8C43×#1608C211yesmaximal, characteristic, complemented
9C43×#1600C211yesmaximal, characteristic, complemented
10C43×#1599C211yesmaximal, characteristic, complemented
11C43×#1597C211yesmaximal, characteristic, complemented
12C43×#1596C211yesmaximal, characteristic, complemented
13C43×#1508C211yesmaximal, characteristic, complemented
14C43×#1501C211yesmaximal, characteristic, complemented
15C43×#1468C211yesmaximal, characteristic, complemented
16C43×#563—21no—
17C43×#562—21no—
18C43×#554—21no—
19C43×#552—21no—
20C43×#551—21no—
21C43×#551—21no—
22C43×#547—21no—
23C43×#546—21no—
24C43×#544C2211yescharacteristic
25C43×#543C2211yescharacteristic
26C43×#542—21no—
27C43×#539—21no—
28C43×#539—21no—
29C43×#539C2211yescharacteristic
30C43×#538C2211yescharacteristic
31C43×#536—21no—
32C43×#525C2211yescharacteristic
33C2×#123×C43C2211yescharacteristic
34C2×C22⋊Q8×C43C2211yescharacteristic
35C2×#121×C43C2211yescharacteristic
36C43×#483C2211yescharacteristic
37C43×#483C2211yescharacteristic
38C43×#483C2211yescharacteristic
39C43×#482—21no—
40C43×#481—21no—
41C43×#480C2211yescharacteristic
42C43×#469—21no—
43C43×#468—21no—
44C43×#465—21no—
45C43×#465—21no—
46C43×#450C2211yescharacteristic
47C43×#450C2211yescharacteristic
48C43×#450C2211yescharacteristic
49C43×#449—21no—
50C43×#448—21no—
51C43×#447C2211yescharacteristic
52C43×#407C2211yescharacteristic
53C2×C22⋊C8×C43C2211yescharacteristic
54C43×#398C2211yescharacteristic
55C43×#397C2211yescharacteristic
56C43×#394—21no—
57C43×#394C2211yescharacteristic
58C43×#392—21no—
59C43×#392C2211yescharacteristic
60C43×#390—21no—
61C43×#388—21no—
62C4×C22⋊C4×C43C2211yescharacteristic
63C43×#328C2211yescharacteristic
64C43×#328C2211yescharacteristic
65C43×#328C2211yescharacteristic
66C43×#328C2211yescharacteristic
67C43×#328C2211yescharacteristic
68C43×#328C2211yescharacteristic
69C43×#327C2211yescharacteristic
70C43×#327C2211yescharacteristic
71C43×#324C2211yescharacteristic
72C43×#324C2211yescharacteristic
73C43×#323C2211yescharacteristic
74C43×#323C2211yescharacteristic
75C2×#41×C43—21no—
76C2×#41×C43D411yescharacteristic, complemented
77C22×Q8×C43D411yescharacteristic, complemented
78C22×D4×C43—21no—
79C22×D4×C43—21no—
80C22×D4×C43D411yescharacteristic
81C22×D4×C43C2311yescharacteristic
82C23×C4×C43C2311yescharacteristic
83C2×SD16×C43—21no—
84C2×SD16×C43—21no—
85C2×SD16×C43—21no—
86C2×D8×C43—21no—
87C2×M16×C43—21no—
88C22×C8×C43—21no—
89C4⋊Q8×C43—21no—
90C4⋊Q8×C43—21no—
91C4⋊Q8×C43—21no—
92#126×C43—21no—
93#126×C43—21no—
94#126×C43—21no—
95#126×C43—21no—
96#126×C43—21no—
97#126×C43—21no—
98#125×C43—21no—
99#125×C43—21no—
100#125×C43—21no—
101#125×C43—21no—
102#125×C43—21no—
103#124×C43—21no—
104#124×C43—21no—
105#124×C43—21no—
106#124×C43—21no—
107#123×C43—21no—
108#123×C43—21no—
109#123×C43—21no—
110#123×C43—21no—
111#123×C43—21no—
112#123×C43—21no—
113#123×C43—21no—
114#123×C43—21no—
115#123×C43—21no—
116#123×C43—21no—
117#123×C43—21no—
118#123×C43—21no—
119#123×C43—21no—
120#123×C43—21no—
121C22⋊Q8×C43—21no—
122C22⋊Q8×C43—21no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43—21no—
126C22⋊Q8×C43—21no—
127C22⋊Q8×C43—21no—
128C22⋊Q8×C43—21no—
129C22⋊Q8×C43—21no—
130C22⋊Q8×C43—21no—
131C22⋊Q8×C43—21no—
132C22⋊Q8×C43—21no—
133C22⋊Q8×C43—21no—
134C22⋊Q8×C43—21no—
135C22⋊Q8×C43D411yescharacteristic, complemented
136C22⋊Q8×C43D411yescharacteristic, complemented
137C22⋊Q8×C43D411yescharacteristic, complemented
138C22⋊Q8×C43C2311yescharacteristic
139C22⋊Q8×C43C2311yescharacteristic
140C22⋊Q8×C43C2311yescharacteristic
141#121×C43—21no—
142#121×C43—21no—
143#121×C43—21no—
144#121×C43—21no—
145#121×C43—21no—
146#121×C43—21no—
147#121×C43—21no—
148#121×C43—21no—
149#121×C43D411yescharacteristic, complemented
150#121×C43C2311yescharacteristic
151#120×C43—21no—
152#120×C43—21no—
153C4×Q8×C43—21no—
154C4×D4×C43—21no—
155C4×D4×C43—21no—
156C4×D4×C43—21no—
157C4×D4×C43—21no—
158C4×D4×C43—21no—
159C4×D4×C43—21no—
160C4×D4×C43—21no—
161#117×C43—21no—
162#117×C43—21no—
163#117×C43—21no—
164#117×C43D411yescharacteristic, complemented
165C2×C4⋊C4×C43—21no—
166C2×C4⋊C4×C43—21no—
167C2×C4⋊C4×C43—21no—
168C2×C4⋊C4×C43D411yescharacteristic
169C2×C4⋊C4×C43D411yescharacteristic, complemented
170C2×C4⋊C4×C43C2311yescharacteristic
171C2×C4⋊C4×C43C2311yescharacteristic
172C2×C22⋊C4×C43—21no—
173C2×C22⋊C4×C43—21no—
174C2×C22⋊C4×C43—21no—
175C2×C22⋊C4×C43—21no—
176C2×C22⋊C4×C43—21no—
177C2×C22⋊C4×C43—21no—
178C2×C22⋊C4×C43—21no—
179C2×C22⋊C4×C43—21no—
180C2×C22⋊C4×C43D411yescharacteristic
181C2×C22⋊C4×C43D411yescharacteristic
182C2×C22⋊C4×C43C2311yescharacteristic
183C2×C42×C43—21no—
184#107×C43—21no—
185#106×C43—21no—
186#106×C43—21no—
187#106×C43—21no—
188#103×C43—21no—
189#103×C43—21no—
190#103×C43—21no—
191#102×C43—21no—
192#102×C43—21no—
193#102×C43—21no—
194#102×C43—21no—
195#102×C43—21no—
196C22⋊C8×C43—21no—
197C22⋊C8×C43—21no—
198C22⋊C8×C43C2311yescharacteristic
199C22⋊C8×C43C2311yescharacteristic
200C22⋊C8×C43C2311yescharacteristic
201C22⋊C8×C43C2311yescharacteristic
202#95×C43—21no—
203#95×C43—21no—
204#95×C43C2311yescharacteristic
205#95×C43C2311yescharacteristic
206C24×C43—21no—
207C24×C43C2×D411yescharacteristic
208C24×C43C2×D411yescharacteristic
209#41×C43—82no—
210#41×C43—81no—
211C2×Q8×C43—21no—
212C2×Q8×C43—21no—
213C2×Q8×C43—21no—
214C2×Q8×C43—81no—
215C2×Q8×C43C2×D411yescharacteristic
216C2×Q8×C43C2×D411yescharacteristic
217C2×Q8×C43C2×D411yescharacteristic
218C2×D4×C43—21no—
219C2×D4×C43—21no—
220C2×D4×C43—21no—
221C2×D4×C43—21no—
222C2×D4×C43—21no—
223C2×D4×C43—21no—
224C2×D4×C43—21no—
225C2×D4×C43—21no—
226C2×D4×C43—21no—
227C2×D4×C43—42no—
228C2×D4×C43—41no—
229C2×D4×C43—41no—
230C2×D4×C43—81no—
231C2×D4×C43—81no—
232C2×D4×C43—81no—
233C2×D4×C43—81no—
234C2×D4×C43—81no—
235C2×D4×C43—81no—
236C2×D4×C43C2×D411yescharacteristic
237C22×C4×C43—21no—
238C22×C4×C43—21no—
239C22×C4×C43—21no—
240C22×C4×C43—21no—
241C22×C4×C43—21no—
242C22×C4×C43—21no—
243C22×C4×C43—21no—
244C22×C4×C43—21no—
245C22×C4×C43—21no—
246C22×C4×C43—21no—
247C22×C4×C43—81no—
248C22×C4×C43C2×D411yescharacteristic
249C22×C4×C43C2×D411yescharacteristic
250C22×C4×C43C2×D411yescharacteristic
251C22×C4×C43C2×D411yescharacteristic
252C22×C4×C43C2×D411yescharacteristic
253C22×C4×C43C2×D411yescharacteristic
254C22×C4×C43C2×D411yescharacteristic
255C22×C4×C43C2×D411yescharacteristic
256C22×C4×C43C2411yescharacteristic
257SD16×C43—81no—
258SD16×C43—81no—
259SD16×C43—81no—
260D8×C43—81no—
261M16×C43—81no—
262C2×C8×C43—21no—
263C2×C8×C43—21no—
264C2×C8×C43—21no—
265C2×C8×C43—21no—
266C2×C8×C43—81no—
267C4⋊C4×C43—21no—
268C4⋊C4×C43—21no—
269C4⋊C4×C43—21no—
270C4⋊C4×C43—21no—
271C4⋊C4×C43—21no—
272C4⋊C4×C43—21no—
273C4⋊C4×C43—21no—
274C4⋊C4×C43—21no—
275C4⋊C4×C43—21no—
276C4⋊C4×C43—21no—
277C4⋊C4×C43—21no—
278C4⋊C4×C43—21no—
279C4⋊C4×C43—21no—
280C4⋊C4×C43—21no—
281C4⋊C4×C43—21no—
282C4⋊C4×C43—21no—
283C4⋊C4×C43—21no—
284C4⋊C4×C43—21no—
285C4⋊C4×C43—21no—
286C4⋊C4×C43—21no—
287C4⋊C4×C43—21no—
288C4⋊C4×C43—21no—
289C4⋊C4×C43—21no—
290C4⋊C4×C43—21no—
291C4⋊C4×C43—21no—
292C4⋊C4×C43—81no—
293C4⋊C4×C43C2×D411yescharacteristic
294C4⋊C4×C43C2×D411yescharacteristic
295C4⋊C4×C43C2×D411yescharacteristic
296C4⋊C4×C43C2×D411yescharacteristic
297C22⋊C4×C43—21no—
298C22⋊C4×C43—21no—
299C22⋊C4×C43—21no—
300C22⋊C4×C43—21no—
301C22⋊C4×C43—21no—
302C22⋊C4×C43—21no—
303C22⋊C4×C43—21no—
304C22⋊C4×C43—21no—
305C22⋊C4×C43—21no—
306C22⋊C4×C43—21no—
307C22⋊C4×C43—21no—
308C22⋊C4×C43—21no—
309C22⋊C4×C43—21no—
310C22⋊C4×C43—21no—
311C22⋊C4×C43—21no—
312C22⋊C4×C43—21no—
313C22⋊C4×C43—21no—
314C22⋊C4×C43—21no—
315C22⋊C4×C43—21no—
316C22⋊C4×C43—21no—
317C22⋊C4×C43—21no—
318C22⋊C4×C43—21no—
319C22⋊C4×C43—21no—
320C22⋊C4×C43—42no—
321C22⋊C4×C43—42no—
322C22⋊C4×C43—41no—
323C22⋊C4×C43—41no—
324C22⋊C4×C43—81no—
325C22⋊C4×C43—81no—
326C22⋊C4×C43—81no—
327C42×C43—21no—
328C42×C43—21no—
329C42×C43—21no—
330C42×C43—21no—
331C42×C43—21no—
332C42×C43—81no—
333C23×C43—21no—
334C23×C43—21no—
335C23×C43—21no—
336C23×C43—21no—
337C23×C43—21no—
338C23×C43—21no—
339C23×C43—41no—
340C23×C43—41no—
341C23×C43—41no—
342C23×C43—41no—
343C23×C43—41no—
344C23×C43—41no—
345C23×C43—41no—
346C23×C43—41no—
347C23×C43—41no—
348C23×C43—41no—
349C23×C43—41no—
350C23×C43#12011yescharacteristic
351C23×C43#12011yescharacteristic
352C23×C43C22×D411yescharacteristic
353Q8×C43—41no—
354Q8×C43—41no—
355Q8×C43—41no—
356Q8×C43—81no—
357Q8×C43—81no—
358Q8×C43—81no—
359D4×C43—41no—
360D4×C43—41no—
361D4×C43—41no—
362D4×C43—41no—
363D4×C43—41no—
364D4×C43—42no—
365D4×C43—42no—
366D4×C43—41no—
367D4×C43—41no—
368D4×C43—81no—
369D4×C43—81no—
370D4×C43—81no—
371D4×C43—81no—
372D4×C43—84no—
373D4×C43—82no—
374D4×C43—82no—
375C2×C4×C43—22no—
376C2×C4×C43—21no—
377C2×C4×C43—21no—
378C2×C4×C43—21no—
379C2×C4×C43—21no—
380C2×C4×C43—21no—
381C2×C4×C43—21no—
382C2×C4×C43—21no—
383C2×C4×C43—21no—
384C2×C4×C43—21no—
385C2×C4×C43—21no—
386C2×C4×C43—21no—
387C2×C4×C43—21no—
388C2×C4×C43—41no—
389C2×C4×C43—41no—
390C2×C4×C43—41no—
391C2×C4×C43—41no—
392C2×C4×C43—41no—
393C2×C4×C43—41no—
394C2×C4×C43—41no—
395C2×C4×C43—42no—
396C2×C4×C43—41no—
397C2×C4×C43—41no—
398C2×C4×C43—41no—
399C2×C4×C43—41no—
400C2×C4×C43—41no—
401C2×C4×C43—41no—
402C2×C4×C43—41no—
403C2×C4×C43—41no—
404C2×C4×C43—41no—
405C2×C4×C43—81no—
406C2×C4×C43—81no—
407C2×C4×C43—81no—
408C2×C4×C43—81no—
409C2×C4×C43—81no—
410C2×C4×C43—81no—
411C2×C4×C43#12011yescharacteristic
412C2×C4×C43#12011yescharacteristic
413C2×C4×C43C22×D411yescharacteristic
414C2×C4×C43C22×D411yescharacteristic
415C8×C43—41no—
416C8×C43—41no—
417C8×C43—41no—
418C8×C43—41no—
419#18416C4311yesmaximal, characteristic, direct product factor, Sylow
420C22×C43—21no—
421C22×C43—21no—
422C22×C43—21no—
423C22×C43—21no—
424C22×C43—21no—
425C22×C43—21no—
426C22×C43—21no—
427C22×C43—21no—
428C22×C43—41no—
429C22×C43—41no—
430C22×C43—41no—
431C22×C43—41no—
432C22×C43—41no—
433C22×C43—41no—
434C22×C43—81no—
435C22×C43—81no—
436C22×C43—81no—
437C22×C43—81no—
438C22×C43—81no—
439C22×C43—81no—
440C22×C43—81no—
441C22×C43—81no—
442C22×C43—81no—
443C22×C43—81no—
444C22×C43—81no—
445C22×C43C2×#12011yescharacteristic
446C22×C43#57711yescharacteristic
447C22×C43#57711yescharacteristic
448C4×C43—21no—
449C4×C43—21no—
450C4×C43—21no—
451C4×C43—21no—
452C4×C43—42no—
453C4×C43—41no—
454C4×C43—41no—
455C4×C43—41no—
456C4×C43—41no—
457C4×C43—41no—
458C4×C43—41no—
459C4×C43—41no—
460C4×C43—41no—
461C4×C43—41no—
462C4×C43—41no—
463C4×C43—81no—
464C4×C43—81no—
465#3535C2×C4311yescharacteristic, complemented
466#3194C2×C4311yescharacteristic, complemented
467#3187C2×C4311yescharacteristic, complemented
468#2661C2×C4311yescharacteristic, complemented
469#1612C2×C4311yescharacteristic, complemented
470#1611C2×C4311yescharacteristic, complemented
471#1609C2×C4311yescharacteristic, complemented
472#1608C2×C4311yescharacteristic, complemented
473#1600C2×C4311yescharacteristic, complemented
474#1599C2×C4311yescharacteristic, complemented
475#1597C2×C4311yescharacteristic, complemented
476#1596C2×C4311yescharacteristic, complemented
477#1508C2×C4311yescharacteristic, complemented
478#1501C2×C4311yescharacteristic, complemented
479#1468C2×C4311yescharacteristic, complemented
480C2×C43—21no—
481C2×C43—21no—
482C2×C43—41no—
483C2×C43—41no—
484C2×C43—81no—
485C2×C43—81no—
486C2×C43—161no—
487C2×C43#301011yescharacteristic
488C2×C43#301811yescharacteristic
489C2×C43#302611yescharacteristic
490#563—21no—
491#562—21no—
492#554—21no—
493#552—21no—
494#551—21no—
495#551—21no—
496#547—21no—
497#546—21no—
498#544C22×C4311yescharacteristic
499#543C22×C4311yescharacteristic
500#542—21no—
501#539—21no—
502#539—21no—
503#539C22×C4311yescharacteristic
504#538C22×C4311yescharacteristic
505#536—21no—
506#525C22×C4311yescharacteristic
507C2×#123C22×C4311yescharacteristic
508C2×C22⋊Q8C22×C4311yescharacteristic
509C2×#121C22×C4311yescharacteristic
510#483C22×C4311yescharacteristic
511#483C22×C4311yescharacteristic
512#483C22×C4311yescharacteristic
513#482—21no—
514#481—21no—
515#480C22×C4311yescharacteristic
516#469—21no—
517#468—21no—
518#465—21no—
519#465—21no—
520#450C22×C4311yescharacteristic
521#450C22×C4311yescharacteristic
522#450C22×C4311yescharacteristic
523#449—21no—
524#448—21no—
525#447C22×C4311yescharacteristic
526#407C22×C4311yescharacteristic
527C2×C22⋊C8C22×C4311yescharacteristic
528#398C22×C4311yescharacteristic
529#397C22×C4311yescharacteristic
530#394—21no—
531#394C22×C4311yescharacteristic
532#392—21no—
533#392C22×C4311yescharacteristic
534#390—21no—
535#388—21no—
536C4×C22⋊C4C22×C4311yescharacteristic
537#328C22×C4311yescharacteristic
538#328C22×C4311yescharacteristic
539#328C22×C4311yescharacteristic
540#328C22×C4311yescharacteristic
541#328C22×C4311yescharacteristic
542#328C22×C4311yescharacteristic
543#327C22×C4311yescharacteristic
544#327C22×C4311yescharacteristic
545#324C22×C4311yescharacteristic
546#324C22×C4311yescharacteristic
547#323C22×C4311yescharacteristic
548#323C22×C4311yescharacteristic
549C43#1841611yescharacteristic, direct product factor, Sylow
550C2×#41—21no—
551C2×#41D4×C4311yescharacteristic, complemented
552C22×Q8D4×C4311yescharacteristic, complemented
553C22×D4—21no—
554C22×D4—21no—
555C22×D4D4×C4311yescharacteristic
556C22×D4C23×C4311yescharacteristic
557C23×C4C23×C4311yescharacteristic
558C2×SD16—21no—
559C2×SD16—21no—
560C2×SD16—21no—
561C2×D8—21no—
562C2×M16—21no—
563C22×C8—21no—
564C4⋊Q8—21no—
565C4⋊Q8—21no—
566C4⋊Q8—21no—
567#126—21no—
568#126—21no—
569#126—21no—
570#126—21no—
571#126—21no—
572#126—21no—
573#125—21no—
574#125—21no—
575#125—21no—
576#125—21no—
577#125—21no—
578#124—21no—
579#124—21no—
580#124—21no—
581#124—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—21no—
594#123—21no—
595#123—21no—
596C22⋊Q8—21no—
597C22⋊Q8—21no—
598C22⋊Q8—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8D4×C4311yescharacteristic, complemented
611C22⋊Q8D4×C4311yescharacteristic, complemented
612C22⋊Q8D4×C4311yescharacteristic, complemented
613C22⋊Q8C23×C4311yescharacteristic
614C22⋊Q8C23×C4311yescharacteristic
615C22⋊Q8C23×C4311yescharacteristic
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121D4×C4311yescharacteristic, complemented
625#121C23×C4311yescharacteristic
626#120—21no—
627#120—21no—
628C4×Q8—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632C4×D4—21no—
633C4×D4—21no—
634C4×D4—21no—
635C4×D4—21no—
636#117—21no—
637#117—21no—
638#117—21no—
639#117D4×C4311yescharacteristic, complemented
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4D4×C4311yescharacteristic
644C2×C4⋊C4D4×C4311yescharacteristic, complemented
645C2×C4⋊C4C23×C4311yescharacteristic
646C2×C4⋊C4C23×C4311yescharacteristic
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4D4×C4311yescharacteristic
656C2×C22⋊C4D4×C4311yescharacteristic
657C2×C22⋊C4C23×C4311yescharacteristic
658C2×C42—21no—
659#107—21no—
660#106—21no—
661#106—21no—
662#106—21no—
663#103—21no—
664#103—21no—
665#103—21no—
666#102—21no—
667#102—21no—
668#102—21no—
669#102—21no—
670#102—21no—
671C22⋊C8—21no—
672C22⋊C8—21no—
673C22⋊C8C23×C4311yescharacteristic
674C22⋊C8C23×C4311yescharacteristic
675C22⋊C8C23×C4311yescharacteristic
676C22⋊C8C23×C4311yescharacteristic
677#95—21no—
678#95—21no—
679#95C23×C4311yescharacteristic
680#95C23×C4311yescharacteristic
681C24—21no—
682C24C2×D4×C4311yescharacteristic
683C24C2×D4×C4311yescharacteristic
684#41—82no—
685#41—81no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—81no—
690C2×Q8C2×D4×C4311yescharacteristic
691C2×Q8C2×D4×C4311yescharacteristic
692C2×Q8C2×D4×C4311yescharacteristic
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—42no—
703C2×D4—41no—
704C2×D4—41no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4C2×D4×C4311yescharacteristic
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—81no—
723C22×C4C2×D4×C4311yescharacteristic
724C22×C4C2×D4×C4311yescharacteristic
725C22×C4C2×D4×C4311yescharacteristic
726C22×C4C2×D4×C4311yescharacteristic
727C22×C4C2×D4×C4311yescharacteristic
728C22×C4C2×D4×C4311yescharacteristic
729C22×C4C2×D4×C4311yescharacteristic
730C22×C4C2×D4×C4311yescharacteristic
731C22×C4C24×C4311yescharacteristic
732SD16—81no—
733SD16—81no—
734SD16—81no—
735D8—81no—
736M16—81no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—81no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—81no—
768C4⋊C4C2×D4×C4311yescharacteristic
769C4⋊C4C2×D4×C4311yescharacteristic
770C4⋊C4C2×D4×C4311yescharacteristic
771C4⋊C4C2×D4×C4311yescharacteristic
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—42no—
796C22⋊C4—42no—
797C22⋊C4—41no—
798C22⋊C4—41no—
799C22⋊C4—81no—
800C22⋊C4—81no—
801C22⋊C4—81no—
802C42—21no—
803C42—21no—
804C42—21no—
805C42—21no—
806C42—21no—
807C42—81no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23#120×C4311yescharacteristic
826C23#120×C4311yescharacteristic
827C23C22×D4×C4311yescharacteristic
828Q8—41no—
829Q8—41no—
830Q8—41no—
831Q8—81no—
832Q8—81no—
833Q8—81no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—42no—
840D4—42no—
841D4—41no—
842D4—41no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—84no—
848D4—82no—
849D4—82no—
850C2×C4—22no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—42no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—81no—
881C2×C4—81no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4#120×C4311yescharacteristic
887C2×C4#120×C4311yescharacteristic
888C2×C4C22×D4×C4311yescharacteristic
889C2×C4C22×D4×C4311yescharacteristic
890C8—41no—
891C8—41no—
892C8—41no—
893C8—41no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22C2×#120×C4311yescharacteristic
920C22C43×#57711yescharacteristic
921C22C43×#57711yescharacteristic
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—42no—
927C4—41no—
928C4—41no—
929C4—41no—
930C4—41no—
931C4—41no—
932C4—41no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—81no—
938C4—81no—
939C2—21no—
940C2—21no—
941C2—41no—
942C2—41no—
943C2—81no—
944C2—81no—
945C2—161no—
946C2C43×#301011yescharacteristic
947C2C43×#301811yescharacteristic
948C2C43×#302611yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC22×C4C24×C43
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C23×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3535C2semidirect
2. C43×#3194C2semidirect
3. C43×#3187C2semidirect
4. C43×#2661C2semidirect
5. C43×#1612C2semidirect
6. C43×#1611C2semidirect
7. C43×#1609C2semidirect
8. C43×#1608C2semidirect
9. C43×#1600C2semidirect
10. C43×#1599C2semidirect
11. C43×#1597C2semidirect
12. C43×#1596C2semidirect
13. C43×#1508C2semidirect
14. C43×#1501C2semidirect
15. C43×#1468C2semidirect
76. C2×#41×C43D4semidirect
77. C22×Q8×C43D4semidirect
135. C22⋊Q8×C43D4semidirect
136. C22⋊Q8×C43D4semidirect
137. C22⋊Q8×C43D4semidirect
149. #121×C43D4semidirect
164. #117×C43D4semidirect
169. C2×C4⋊C4×C43D4semidirect
419. #18416C43direct (N × H)
465. #3535C2×C43semidirect
466. #3194C2×C43semidirect
467. #3187C2×C43semidirect
468. #2661C2×C43semidirect
469. #1612C2×C43semidirect
470. #1611C2×C43semidirect
471. #1609C2×C43semidirect
472. #1608C2×C43semidirect
473. #1600C2×C43semidirect
474. #1599C2×C43semidirect
475. #1597C2×C43semidirect
476. #1596C2×C43semidirect
477. #1508C2×C43semidirect
478. #1501C2×C43semidirect
479. #1468C2×C43semidirect
549. C43#18416direct (N × H)
551. C2×#41D4×C43semidirect
552. C22×Q8D4×C43semidirect
610. C22⋊Q8D4×C43semidirect
611. C22⋊Q8D4×C43semidirect
612. C22⋊Q8D4×C43semidirect
624. #121D4×C43semidirect
639. #117D4×C43semidirect
644. C2×C4⋊C4D4×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#35352
C43×#31942
C43×#31872
C43×#26612
C43×#16122
C43×#16112
C43×#16092
C43×#16082
C43×#16002
C43×#15992
C43×#15972
C43×#15962
C43×#15082
C43×#15012
C43×#14682
#1841643