Finite Group Databasebeta

← C43×#18434 #24938451

Subgroups — C43×#18434 #24938451

Order 11008.

982 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3560C211yesmaximal, characteristic, complemented
2C43×#3213C211yesmaximal, characteristic, complemented
3C43×#3211C211yesmaximal, characteristic, complemented
4C43×#2662C211yesmaximal, characteristic, complemented
5C43×#1606C211yesmaximal, characteristic, complemented
6C43×#1604C211yesmaximal, characteristic, complemented
7C43×#1603C211yesmaximal, characteristic, complemented
8C43×#1601C211yesmaximal, characteristic, complemented
9C43×#1600C211yesmaximal, characteristic, complemented
10C43×#1598C211yesmaximal, characteristic, complemented
11C43×#1597C211yesmaximal, characteristic, complemented
12C43×#1595C211yesmaximal, characteristic, complemented
13C43×#1509C211yesmaximal, characteristic, complemented
14C43×#1502C211yesmaximal, characteristic, complemented
15C43×#1473C211yesmaximal, characteristic, complemented
16C43×#563—21no—
17C43×#560—21no—
18C43×#553—21no—
19C43×#553—21no—
20C43×#551—21no—
21C43×#547—21no—
22C43×#546—21no—
23C43×#546—21no—
24C43×#542—21no—
25C43×#539—21no—
26C43×#539C2211yescharacteristic
27C43×#538—21no—
28C43×#538—21no—
29C43×#538C2211yescharacteristic
30C43×#537C2211yescharacteristic
31C43×#534C2211yescharacteristic
32C43×#532C2211yescharacteristic
33C43×#529C2211yescharacteristic
34C2×#126×C43C2211yescharacteristic
35C2×#124×C43C2211yescharacteristic, complemented
36C43×#496—21no—
37C43×#495—21no—
38C43×#489—21no—
39C43×#488—21no—
40C43×#464—21no—
41C43×#463—21no—
42C43×#463—21no—
43C43×#463—21no—
44C43×#451C2211yescharacteristic, complemented
45C43×#450C2211yescharacteristic, complemented
46C43×#448C2211yescharacteristic
47C43×#448C2211yescharacteristic
48C43×#448C2211yescharacteristic, complemented
49C43×#447C2211yescharacteristic
50C43×#447C2211yescharacteristic
51C43×#447C2211yescharacteristic, complemented
52C43×#432C2211yescharacteristic, complemented
53C43×#431C2211yescharacteristic, complemented
54C43×#396—21no—
55C43×#395C2211yescharacteristic, complemented
56C43×#394—21no—
57C43×#394C2211yescharacteristic, complemented
58C43×#393C2211yescharacteristic
59C43×#392C2211yescharacteristic
60C43×#390—21no—
61C43×#388—21no—
62C4×C4⋊C4×C43C2211yescharacteristic, complemented
63C43×#328C2211yescharacteristic, complemented
64C43×#328C2211yescharacteristic, complemented
65C43×#327C2211yescharacteristic
66C43×#327C2211yescharacteristic
67C43×#327C2211yescharacteristic
68C43×#327C2211yescharacteristic
69C43×#327C2211yescharacteristic, complemented
70C43×#327C2211yescharacteristic, complemented
71C43×#324C2211yescharacteristic, complemented
72C43×#324C2211yescharacteristic, complemented
73C43×#323C2211yescharacteristic
74C43×#323C2211yescharacteristic
75C2×#41×C43—21no—
76C2×#41×C43—21no—
77C22×Q8×C43C2311yescharacteristic
78C22×D4×C43—21no—
79C22×D4×C43—21no—
80C22×D4×C43C2311yescharacteristic
81C2×Q16×C43—21no—
82C2×SD16×C43—21no—
83C2×SD16×C43—21no—
84C2×SD16×C43—21no—
85C2×SD16×C43—21no—
86C2×D8×C43—21no—
87C2×D8×C43—21no—
88C2×D8×C43—21no—
89C4⋊Q8×C43—21no—
90C4⋊Q8×C43D411yescharacteristic, complemented
91#127×C43D411yescharacteristic, complemented
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#126×C43—21no—
99#126×C43—21no—
100#126×C43—21no—
101#125×C43—21no—
102#125×C43—21no—
103#125×C43D411yescharacteristic, complemented
104#124×C43—21no—
105#124×C43—21no—
106#124×C43—21no—
107#124×C43—21no—
108#124×C43—21no—
109#124×C43—21no—
110#124×C43—21no—
111#124×C43—21no—
112#124×C43D411yescharacteristic, complemented
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—
121#123×C43—21no—
122#123×C43—21no—
123#123×C43—21no—
124#123×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×C43C2311yescharacteristic
133#121×C43—21no—
134#121×C43—21no—
135#121×C43—21no—
136#121×C43—21no—
137#121×C43—21no—
138#121×C43—21no—
139#121×C43—21no—
140#121×C43—21no—
141#121×C43—21no—
142#121×C43—21no—
143#121×C43—21no—
144#121×C43—21no—
145#121×C43C2311yescharacteristic
146#121×C43C2311yescharacteristic
147#121×C43C2311yescharacteristic
148#120×C43—21no—
149#120×C43—21no—
150#120×C43—21no—
151#120×C43—21no—
152#120×C43—21no—
153C4×Q8×C43D411yescharacteristic, complemented
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—
161C4×D4×C43—21no—
162C4×D4×C43D411yescharacteristic, complemented
163C4×D4×C43D411yescharacteristic, complemented
164C4×D4×C43D411yescharacteristic, complemented
165#117×C43—21no—
166#117×C43—21no—
167C2×C4⋊C4×C43—21no—
168C2×C4⋊C4×C43—21no—
169C2×C4⋊C4×C43—21no—
170C2×C4⋊C4×C43D411yescharacteristic
171C2×C4⋊C4×C43D411yescharacteristic
172C2×C4⋊C4×C43C2311yescharacteristic
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×C43—21no—
181C2×C22⋊C4×C43D411yescharacteristic
182C2×C22⋊C4×C43D411yescharacteristic
183C2×C22⋊C4×C43C2311yescharacteristic
184C2×C42×C43—21no—
185C2×C42×C43C2311yescharacteristic
186C4⋊C8×C43—21no—
187C4⋊C8×C43—21no—
188#103×C43—21no—
189#103×C43—21no—
190#103×C43—21no—
191#103×C43—21no—
192#102×C43—21no—
193#102×C43—21no—
194#102×C43—21no—
195#102×C43—21no—
196C22⋊C8×C43C2311yescharacteristic
197C22⋊C8×C43C2311yescharacteristic
198C22⋊C8×C43C2311yescharacteristic
199C22⋊C8×C43C2311yescharacteristic
200#97×C43—21no—
201C4×C8×C43—21no—
202#95×C43—21no—
203#95×C43—21no—
204#95×C43C2311yescharacteristic
205#95×C43C2311yescharacteristic
206C24×C43—21no—
207C24×C43—21no—
208C24×C43C2×D411yescharacteristic
209#41×C43—81no—
210#41×C43—81no—
211#41×C43—81no—
212#41×C43—81no—
213C2×Q8×C43—21no—
214C2×Q8×C43—21no—
215C2×Q8×C43—21no—
216C2×Q8×C43—21no—
217C2×Q8×C43—81no—
218C2×Q8×C43C2×D411yescharacteristic
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—21no—
228C2×D4×C43—21no—
229C2×D4×C43—21no—
230C2×D4×C43—21no—
231C2×D4×C43—21no—
232C2×D4×C43—21no—
233C2×D4×C43—42no—
234C2×D4×C43—81no—
235C2×D4×C43—81no—
236C2×D4×C43—81no—
237C2×D4×C43—81no—
238C2×D4×C43—81no—
239C2×D4×C43C2×D411yescharacteristic
240C2×D4×C43C2×D411yescharacteristic
241C2×D4×C43C2×D411yescharacteristic
242C22×C4×C43—21no—
243C22×C4×C43—21no—
244C22×C4×C43—21no—
245C22×C4×C43—21no—
246C22×C4×C43—21no—
247C22×C4×C43—21no—
248C22×C4×C43—21no—
249C22×C4×C43—21no—
250C22×C4×C43—21no—
251C22×C4×C43—21no—
252C22×C4×C43—21no—
253C22×C4×C43C2×D411yescharacteristic
254C22×C4×C43C2×D411yescharacteristic
255C22×C4×C43C2×D411yescharacteristic
256C22×C4×C43C2×D411yescharacteristic
257C22×C4×C43C2×D411yescharacteristic
258C22×C4×C43C2411yescharacteristic
259Q16×C43—81no—
260SD16×C43—81no—
261SD16×C43—81no—
262SD16×C43—81no—
263SD16×C43—81no—
264D8×C43—81no—
265D8×C43—81no—
266D8×C43—81no—
267C2×C8×C43—21no—
268C2×C8×C43—21no—
269C2×C8×C43—21no—
270C2×C8×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—42no—
289C4⋊C4×C43—81no—
290C4⋊C4×C43C2×D411yescharacteristic
291C4⋊C4×C43C2×D411yescharacteristic
292C4⋊C4×C43C2×D411yescharacteristic
293C4⋊C4×C43C2×D411yescharacteristic
294C22⋊C4×C43—21no—
295C22⋊C4×C43—21no—
296C22⋊C4×C43—21no—
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—42no—
320C22⋊C4×C43—41no—
321C22⋊C4×C43—41no—
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—81no—
331C42×C43C2×D411yescharacteristic
332C42×C43C2×D411yescharacteristic
333C42×C43C2×D411yescharacteristic
334C42×C43C2×D411yescharacteristic
335C23×C43—21no—
336C23×C43—21no—
337C23×C43—21no—
338C23×C43—21no—
339C23×C43—21no—
340C23×C43—21no—
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—81no—
351C23×C43—81no—
352C23×C43—81no—
353C23×C43C22×D411yescharacteristic
354Q8×C43—41no—
355Q8×C43—41no—
356Q8×C43—41no—
357Q8×C43—41no—
358Q8×C43—41no—
359Q8×C43—81no—
360Q8×C43—81no—
361D4×C43—41no—
362D4×C43—41no—
363D4×C43—41no—
364D4×C43—41no—
365D4×C43—41no—
366D4×C43—41no—
367D4×C43—41no—
368D4×C43—41no—
369D4×C43—41no—
370D4×C43—41no—
371D4×C43—41no—
372D4×C43—41no—
373D4×C43—41no—
374D4×C43—81no—
375D4×C43—81no—
376D4×C43—81no—
377D4×C43—81no—
378D4×C43—81no—
379D4×C43—81no—
380D4×C43—81no—
381D4×C43—81no—
382D4×C43—81no—
383D4×C43—84no—
384C2×C4×C43—21no—
385C2×C4×C43—21no—
386C2×C4×C43—22no—
387C2×C4×C43—21no—
388C2×C4×C43—21no—
389C2×C4×C43—21no—
390C2×C4×C43—21no—
391C2×C4×C43—21no—
392C2×C4×C43—21no—
393C2×C4×C43—21no—
394C2×C4×C43—21no—
395C2×C4×C43—21no—
396C2×C4×C43—21no—
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—41no—
406C2×C4×C43—41no—
407C2×C4×C43—41no—
408C2×C4×C43—41no—
409C2×C4×C43—81no—
410C2×C4×C43—81no—
411C2×C4×C43—81no—
412C2×C4×C43—81no—
413C2×C4×C43—81no—
414C2×C4×C43—81no—
415C2×C4×C43—81no—
416C2×C4×C43—81no—
417C2×C4×C43#12011yescharacteristic
418C2×C4×C43#12011yescharacteristic
419C2×C4×C43#12011yescharacteristic
420C2×C4×C43#12011yescharacteristic
421C2×C4×C43C22×D411yescharacteristic
422C2×C4×C43C22×D411yescharacteristic
423C8×C43—41no—
424C8×C43—41no—
425C8×C43—41no—
426C8×C43—41no—
427#18434C4311yesmaximal, characteristic, direct product factor, Sylow
428C22×C43—21no—
429C22×C43—21no—
430C22×C43—41no—
431C22×C43—41no—
432C22×C43—41no—
433C22×C43—41no—
434C22×C43—41no—
435C22×C43—41no—
436C22×C43—41no—
437C22×C43—41no—
438C22×C43—41no—
439C22×C43—41no—
440C22×C43—41no—
441C22×C43—41no—
442C22×C43—81no—
443C22×C43—81no—
444C22×C43—81no—
445C22×C43—81no—
446C22×C43—81no—
447C22×C43—81no—
448C22×C43—81no—
449C22×C43—81no—
450C22×C43—81no—
451C22×C43—162no—
452C22×C43C2×#12011yescharacteristic
453C22×C43#57611yescharacteristic
454C22×C43#57711yescharacteristic
455C4×C43—21no—
456C4×C43—21no—
457C4×C43—21no—
458C4×C43—21no—
459C4×C43—21no—
460C4×C43—21no—
461C4×C43—42no—
462C4×C43—41no—
463C4×C43—41no—
464C4×C43—41no—
465C4×C43—41no—
466C4×C43—41no—
467C4×C43—41no—
468C4×C43—41no—
469C4×C43—41no—
470C4×C43—81no—
471C4×C43—81no—
472#3560C2×C4311yescharacteristic, complemented
473#3213C2×C4311yescharacteristic, complemented
474#3211C2×C4311yescharacteristic, complemented
475#2662C2×C4311yescharacteristic, complemented
476#1606C2×C4311yescharacteristic, complemented
477#1604C2×C4311yescharacteristic, complemented
478#1603C2×C4311yescharacteristic, complemented
479#1601C2×C4311yescharacteristic, complemented
480#1600C2×C4311yescharacteristic, complemented
481#1598C2×C4311yescharacteristic, complemented
482#1597C2×C4311yescharacteristic, complemented
483#1595C2×C4311yescharacteristic, complemented
484#1509C2×C4311yescharacteristic, complemented
485#1502C2×C4311yescharacteristic, complemented
486#1473C2×C4311yescharacteristic, complemented
487C2×C43—21no—
488C2×C43—21no—
489C2×C43—81no—
490C2×C43—81no—
491C2×C43—81no—
492C2×C43—81no—
493C2×C43—161no—
494C2×C43#301211yescharacteristic
495C2×C43#301811yescharacteristic
496C2×C43#302711yescharacteristic
497#563—21no—
498#560—21no—
499#553—21no—
500#553—21no—
501#551—21no—
502#547—21no—
503#546—21no—
504#546—21no—
505#542—21no—
506#539—21no—
507#539C22×C4311yescharacteristic
508#538—21no—
509#538—21no—
510#538C22×C4311yescharacteristic
511#537C22×C4311yescharacteristic
512#534C22×C4311yescharacteristic
513#532C22×C4311yescharacteristic
514#529C22×C4311yescharacteristic
515C2×#126C22×C4311yescharacteristic
516C2×#124C22×C4311yescharacteristic, complemented
517#496—21no—
518#495—21no—
519#489—21no—
520#488—21no—
521#464—21no—
522#463—21no—
523#463—21no—
524#463—21no—
525#451C22×C4311yescharacteristic, complemented
526#450C22×C4311yescharacteristic, complemented
527#448C22×C4311yescharacteristic
528#448C22×C4311yescharacteristic
529#448C22×C4311yescharacteristic, complemented
530#447C22×C4311yescharacteristic
531#447C22×C4311yescharacteristic
532#447C22×C4311yescharacteristic, complemented
533#432C22×C4311yescharacteristic, complemented
534#431C22×C4311yescharacteristic, complemented
535#396—21no—
536#395C22×C4311yescharacteristic, complemented
537#394—21no—
538#394C22×C4311yescharacteristic, complemented
539#393C22×C4311yescharacteristic
540#392C22×C4311yescharacteristic
541#390—21no—
542#388—21no—
543C4×C4⋊C4C22×C4311yescharacteristic, complemented
544#328C22×C4311yescharacteristic, complemented
545#328C22×C4311yescharacteristic, complemented
546#327C22×C4311yescharacteristic
547#327C22×C4311yescharacteristic
548#327C22×C4311yescharacteristic
549#327C22×C4311yescharacteristic
550#327C22×C4311yescharacteristic, complemented
551#327C22×C4311yescharacteristic, complemented
552#324C22×C4311yescharacteristic, complemented
553#324C22×C4311yescharacteristic, complemented
554#323C22×C4311yescharacteristic
555#323C22×C4311yescharacteristic
556C43#1843411yescharacteristic, direct product factor, Sylow
557C2×#41—21no—
558C2×#41—21no—
559C22×Q8C23×C4311yescharacteristic
560C22×D4—21no—
561C22×D4—21no—
562C22×D4C23×C4311yescharacteristic
563C2×Q16—21no—
564C2×SD16—21no—
565C2×SD16—21no—
566C2×SD16—21no—
567C2×SD16—21no—
568C2×D8—21no—
569C2×D8—21no—
570C2×D8—21no—
571C4⋊Q8—21no—
572C4⋊Q8D4×C4311yescharacteristic, complemented
573#127D4×C4311yescharacteristic, complemented
574#126—21no—
575#126—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#126—21no—
580#126—21no—
581#126—21no—
582#126—21no—
583#125—21no—
584#125—21no—
585#125D4×C4311yescharacteristic, complemented
586#124—21no—
587#124—21no—
588#124—21no—
589#124—21no—
590#124—21no—
591#124—21no—
592#124—21no—
593#124—21no—
594#124D4×C4311yescharacteristic, complemented
595#123—21no—
596#123—21no—
597#123—21no—
598#123—21no—
599#123—21no—
600#123—21no—
601#123—21no—
602#123—21no—
603#123—21no—
604#123—21no—
605#123—21no—
606#123—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612C22⋊Q8—21no—
613C22⋊Q8—21no—
614C22⋊Q8C23×C4311yescharacteristic
615#121—21no—
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#121—21no—
625#121—21no—
626#121—21no—
627#121C23×C4311yescharacteristic
628#121C23×C4311yescharacteristic
629#121C23×C4311yescharacteristic
630#120—21no—
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635C4×Q8D4×C4311yescharacteristic, complemented
636C4×D4—21no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4D4×C4311yescharacteristic, complemented
645C4×D4D4×C4311yescharacteristic, complemented
646C4×D4D4×C4311yescharacteristic, complemented
647#117—21no—
648#117—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4D4×C4311yescharacteristic
653C2×C4⋊C4D4×C4311yescharacteristic
654C2×C4⋊C4C23×C4311yescharacteristic
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4D4×C4311yescharacteristic
664C2×C22⋊C4D4×C4311yescharacteristic
665C2×C22⋊C4C23×C4311yescharacteristic
666C2×C42—21no—
667C2×C42C23×C4311yescharacteristic
668C4⋊C8—21no—
669C4⋊C8—21no—
670#103—21no—
671#103—21no—
672#103—21no—
673#103—21no—
674#102—21no—
675#102—21no—
676#102—21no—
677#102—21no—
678C22⋊C8C23×C4311yescharacteristic
679C22⋊C8C23×C4311yescharacteristic
680C22⋊C8C23×C4311yescharacteristic
681C22⋊C8C23×C4311yescharacteristic
682#97—21no—
683C4×C8—21no—
684#95—21no—
685#95—21no—
686#95C23×C4311yescharacteristic
687#95C23×C4311yescharacteristic
688C24—21no—
689C24—21no—
690C24C2×D4×C4311yescharacteristic
691#41—81no—
692#41—81no—
693#41—81no—
694#41—81no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—21no—
698C2×Q8—21no—
699C2×Q8—81no—
700C2×Q8C2×D4×C4311yescharacteristic
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—42no—
716C2×D4—81no—
717C2×D4—81no—
718C2×D4—81no—
719C2×D4—81no—
720C2×D4—81no—
721C2×D4C2×D4×C4311yescharacteristic
722C2×D4C2×D4×C4311yescharacteristic
723C2×D4C2×D4×C4311yescharacteristic
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4C2×D4×C4311yescharacteristic
736C22×C4C2×D4×C4311yescharacteristic
737C22×C4C2×D4×C4311yescharacteristic
738C22×C4C2×D4×C4311yescharacteristic
739C22×C4C2×D4×C4311yescharacteristic
740C22×C4C24×C4311yescharacteristic
741Q16—81no—
742SD16—81no—
743SD16—81no—
744SD16—81no—
745SD16—81no—
746D8—81no—
747D8—81no—
748D8—81no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—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—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—42no—
771C4⋊C4—81no—
772C4⋊C4C2×D4×C4311yescharacteristic
773C4⋊C4C2×D4×C4311yescharacteristic
774C4⋊C4C2×D4×C4311yescharacteristic
775C4⋊C4C2×D4×C4311yescharacteristic
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—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—42no—
802C22⋊C4—41no—
803C22⋊C4—41no—
804C22⋊C4—41no—
805C22⋊C4—41no—
806C22⋊C4—81no—
807C22⋊C4—81no—
808C22⋊C4—81no—
809C42—21no—
810C42—21no—
811C42—21no—
812C42—81no—
813C42C2×D4×C4311yescharacteristic
814C42C2×D4×C4311yescharacteristic
815C42C2×D4×C4311yescharacteristic
816C42C2×D4×C4311yescharacteristic
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23C22×D4×C4311yescharacteristic
836Q8—41no—
837Q8—41no—
838Q8—41no—
839Q8—41no—
840Q8—41no—
841Q8—81no—
842Q8—81no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—84no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—81no—
892C2×C4—81no—
893C2×C4—81no—
894C2×C4—81no—
895C2×C4—81no—
896C2×C4—81no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4#120×C4311yescharacteristic
900C2×C4#120×C4311yescharacteristic
901C2×C4#120×C4311yescharacteristic
902C2×C4#120×C4311yescharacteristic
903C2×C4C22×D4×C4311yescharacteristic
904C2×C4C22×D4×C4311yescharacteristic
905C8—41no—
906C8—41no—
907C8—41no—
908C8—41no—
909C22—21no—
910C22—21no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—162no—
933C22C2×#120×C4311yescharacteristic
934C22C43×#57611yescharacteristic
935C22C43×#57711yescharacteristic
936C4—21no—
937C4—21no—
938C4—21no—
939C4—21no—
940C4—21no—
941C4—21no—
942C4—42no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—41no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—81no—
952C4—81no—
953C2—21no—
954C2—21no—
955C2—81no—
956C2—81no—
957C2—81no—
958C2—81no—
959C2—161no—
960C2C43×#301211yescharacteristic
961C2C43×#301811yescharacteristic
962C2C43×#302711yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC22×C4C24×C43
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3560C2semidirect
2. C43×#3213C2semidirect
3. C43×#3211C2semidirect
4. C43×#2662C2semidirect
5. C43×#1606C2semidirect
6. C43×#1604C2semidirect
7. C43×#1603C2semidirect
8. C43×#1601C2semidirect
9. C43×#1600C2semidirect
10. C43×#1598C2semidirect
11. C43×#1597C2semidirect
12. C43×#1595C2semidirect
13. C43×#1509C2semidirect
14. C43×#1502C2semidirect
15. C43×#1473C2semidirect
35. C2×#124×C43C22semidirect
44. C43×#451C22semidirect
45. C43×#450C22semidirect
48. C43×#448C22semidirect
51. C43×#447C22semidirect
52. C43×#432C22semidirect
53. C43×#431C22semidirect
55. C43×#395C22semidirect
57. C43×#394C22semidirect
62. C4×C4⋊C4×C43C22semidirect
63. C43×#328C22semidirect
64. C43×#328C22semidirect
69. C43×#327C22semidirect
70. C43×#327C22semidirect
71. C43×#324C22semidirect
72. C43×#324C22semidirect
90. C4⋊Q8×C43D4semidirect
91. #127×C43D4semidirect
103. #125×C43D4semidirect
112. #124×C43D4semidirect
153. C4×Q8×C43D4semidirect
162. C4×D4×C43D4semidirect
163. C4×D4×C43D4semidirect
164. C4×D4×C43D4semidirect
427. #18434C43direct (N × H)
472. #3560C2×C43semidirect
473. #3213C2×C43semidirect
474. #3211C2×C43semidirect
475. #2662C2×C43semidirect
476. #1606C2×C43semidirect
477. #1604C2×C43semidirect
478. #1603C2×C43semidirect
479. #1601C2×C43semidirect
480. #1600C2×C43semidirect
481. #1598C2×C43semidirect
482. #1597C2×C43semidirect
483. #1595C2×C43semidirect
484. #1509C2×C43semidirect
485. #1502C2×C43semidirect
486. #1473C2×C43semidirect
516. C2×#124C22×C43semidirect
525. #451C22×C43semidirect
526. #450C22×C43semidirect
529. #448C22×C43semidirect
532. #447C22×C43semidirect
533. #432C22×C43semidirect
534. #431C22×C43semidirect
536. #395C22×C43semidirect
538. #394C22×C43semidirect
543. C4×C4⋊C4C22×C43semidirect
544. #328C22×C43semidirect
545. #328C22×C43semidirect
550. #327C22×C43semidirect
551. #327C22×C43semidirect
552. #324C22×C43semidirect
553. #324C22×C43semidirect
556. C43#18434direct (N × H)
572. C4⋊Q8D4×C43semidirect
573. #127D4×C43semidirect
585. #125D4×C43semidirect
594. #124D4×C43semidirect
635. C4×Q8D4×C43semidirect
644. C4×D4D4×C43semidirect
645. C4×D4D4×C43semidirect
646. C4×D4D4×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#35602
C43×#32132
C43×#32112
C43×#26622
C43×#16062
C43×#16042
C43×#16032
C43×#16012
C43×#16002
C43×#15982
C43×#15972
C43×#15952
C43×#15092
C43×#15022
C43×#14732
#1843443