Finite Group Databasebeta

← C43×#33552 #24953569

Subgroups — C43×#33552 #24953569

Order 11008.

1156 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3533C211yesmaximal, characteristic, complemented
2C43×#3026C211yesmaximal, characteristic, complemented
3C2×C43×#458C211yesmaximal, characteristic, complemented
4C43×#3019C211yesmaximal, characteristic, complemented
5C43×#2201C212yesmaximal, complemented
6C43×#2200C212yesmaximal, complemented
7C43×#2198C212yesmaximal, complemented
8C43×#2197C212yesmaximal, complemented
9C43×#2127C211yesmaximal, characteristic, complemented
10C43×#2121C211yesmaximal, characteristic, complemented
11C2×C43×#352C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C43C2211yescharacteristic
13C43×#575—21no—
14C43×#563C2211yescharacteristic, complemented
15C43×#562—21no—
16C43×#560C2211yescharacteristic, complemented
17C43×#559C2211yescharacteristic, complemented
18C43×#553—21no—
19C43×#552—21no—
20C43×#551—21no—
21C43×#551C2211yescharacteristic, complemented
22C43×#547—21no—
23C43×#546—21no—
24C43×#542—21no—
25C43×#540—21no—
26C43×#539—21no—
27C43×#538—21no—
28C43×#538—21no—
29C43×#535C2211yescharacteristic
30C43×#534—21no—
31C43×#534C2211yescharacteristic
32C43×#525—21no—
33C2×#123×C43—21no—
34C2×#123×C43C2211yescharacteristic
35C43×#458—21no—
36C43×#458—21no—
37C43×#458—21no—
38C43×#458C2212yes—
39C43×#458C2212yes—
40C43×#458C2212yes—
41C43×B(4,𝔽2)—21no—
42C43×B(4,𝔽2)C2212yes—
43C43×#455—21no—
44C43×#455C2212yes—
45C43×#453—21no—
46C43×#453C2212yes—
47C43×#421—21no—
48C2×#100×C43C2211yescharacteristic
49C2×#99×C43—21no—
50C2×#99×C43—21no—
51C2×#99×C43C2211yescharacteristic
52C2×#99×C43C2211yescharacteristic
53C43×#354C2212yescomplemented
54C43×#353C2212yescomplemented
55C43×#352C2212yescomplemented
56C43×#352C2212yescomplemented
57C43×#352C2212yescomplemented
58C43×AΣL(1,𝔽16)C2212yescomplemented
59H(5,𝔽2)×C43—21no—
60H(5,𝔽2)×C43—21no—
61H(5,𝔽2)×C43—21no—
62H(5,𝔽2)×C43—42no—
63H(5,𝔽2)×C43C2312yes—
64C2×#41×C43—21no—
65C2×#41×C43—21no—
66C2×#41×C43—41no—
67C2×#41×C43D411yescharacteristic, complemented
68C22×D4×C43—21no—
69C22×D4×C43—21no—
70C22×D4×C43—41no—
71C22×D4×C43D411yescharacteristic
72C22×D4×C43C2311yescharacteristic
73C23×C4×C43D411yescharacteristic, complemented
74#137×C43—22no—
75#137×C43—41no—
76AGL(1,ℤ/8)×C43—22no—
77AGL(1,ℤ/8)×C43—41no—
78#135×C43—42no—
79C2×M16×C43—21no—
80C4⋊Q8×C43—21no—
81#127×C43D411yescharacteristic, complemented
82#127×C43C2311yescharacteristic
83#126×C43—21no—
84#126×C43—21no—
85#126×C43—21no—
86#126×C43—21no—
87#126×C43—21no—
88#126×C43—21no—
89#125×C43—21no—
90#125×C43—21no—
91#125×C43—21no—
92#124×C43—21no—
93#124×C43—21no—
94#124×C43—21no—
95#124×C43—21no—
96#124×C43D411yescharacteristic, complemented
97#124×C43C2311yescharacteristic
98#123×C43—21no—
99#123×C43—21no—
100#123×C43—21no—
101#123×C43—21no—
102#123×C43—21no—
103#123×C43—21no—
104#123×C43—21no—
105#123×C43—21no—
106#123×C43—21no—
107#123×C43—21no—
108#123×C43—21no—
109#123×C43—21no—
110#123×C43—22no—
111#123×C43—22no—
112#123×C43—22no—
113#123×C43—41no—
114#123×C43—42no—
115#123×C43D411yescharacteristic
116#123×C43D411yescharacteristic, complemented
117#123×C43D411yescharacteristic, complemented
118#123×C43C2311yescharacteristic
119#123×C43C2311yescharacteristic
120#123×C43C2311yescharacteristic
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—
129#121×C43—21no—
130#121×C43—21no—
131#121×C43—21no—
132#121×C43—21no—
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—42no—
142#120×C43—21no—
143#120×C43—21no—
144#120×C43—21no—
145#120×C43—21no—
146#120×C43—22no—
147#120×C43—41no—
148#120×C43D411yescharacteristic
149#120×C43C2311yescharacteristic
150C4×Q8×C43—21no—
151C4×D4×C43—21no—
152C4×D4×C43—21no—
153C4×D4×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—
160#117×C43—21no—
161#117×C43—21no—
162#117×C43—21no—
163#117×C43D411yescharacteristic, complemented
164C2×C4⋊C4×C43—21no—
165C2×C4⋊C4×C43—21no—
166C2×C4⋊C4×C43—41no—
167C2×C22⋊C4×C43—21no—
168C2×C22⋊C4×C43—21no—
169C2×C22⋊C4×C43—21no—
170C2×C22⋊C4×C43—21no—
171C2×C22⋊C4×C43—41no—
172C2×C22⋊C4×C43D411yescharacteristic
173C2×C22⋊C4×C43D411yescharacteristic, complemented
174#104×C43—22no—
175#104×C43—22no—
176#100×C43—21no—
177#100×C43C2312yes—
178#99×C43—21no—
179#99×C43—21no—
180#99×C43—22no—
181#99×C43—22no—
182#99×C43—22no—
183#99×C43—22no—
184#99×C43C2312yes—
185#99×C43C2312yes—
186C24×C43—21no—
187C24×C43—21no—
188C24×C43C2×D411yescharacteristic
189C24×C43C2×D411yescharacteristic
190C24×C43C2×D411yescharacteristic
191#41×C43—22no—
192#41×C43—22no—
193#41×C43—42no—
194#41×C43—41no—
195#41×C43—42no—
196#41×C43—42no—
197#41×C43—41no—
198#41×C43—41no—
199#41×C43—42no—
200#41×C43—41no—
201#41×C43—81no—
202#41×C43—81no—
203C2×Q8×C43—21no—
204C2×Q8×C43—21no—
205C2×Q8×C43—21no—
206C2×Q8×C43C2×D411yescharacteristic
207C2×D4×C43—22no—
208C2×D4×C43—22no—
209C2×D4×C43—21no—
210C2×D4×C43—21no—
211C2×D4×C43—21no—
212C2×D4×C43—21no—
213C2×D4×C43—21no—
214C2×D4×C43—21no—
215C2×D4×C43—21no—
216C2×D4×C43—21no—
217C2×D4×C43—22no—
218C2×D4×C43—22no—
219C2×D4×C43—21no—
220C2×D4×C43—21no—
221C2×D4×C43—21no—
222C2×D4×C43—21no—
223C2×D4×C43—41no—
224C2×D4×C43—41no—
225C2×D4×C43—42no—
226C2×D4×C43—41no—
227C2×D4×C43—41no—
228C2×D4×C43—41no—
229C2×D4×C43—41no—
230C2×D4×C43—42no—
231C2×D4×C43—42no—
232C2×D4×C43—41no—
233C2×D4×C43—41no—
234C2×D4×C43—42no—
235C2×D4×C43—42no—
236C2×D4×C43—41no—
237C2×D4×C43—41no—
238C2×D4×C43—41no—
239C2×D4×C43C2×D411yescharacteristic
240C2×D4×C43C2×D411yescharacteristic
241C2×D4×C43C2×D411yescharacteristic
242C2×D4×C43C2×D411yescharacteristic
243C2×D4×C43C2411yescharacteristic
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×C43—21no—
254C22×C4×C43—21no—
255C22×C4×C43—41no—
256C22×C4×C43—41no—
257C22×C4×C43—41no—
258C22×C4×C43—41no—
259C22×C4×C43—41no—
260C22×C4×C43C2×D411yescharacteristic
261C22×C4×C43C2×D411yescharacteristic
262C22×C4×C43C2×D411yescharacteristic
263C22×C4×C43C2×D411yescharacteristic
264Q16×C43—42no—
265SD16×C43—42no—
266SD16×C43—42no—
267D8×C43—42no—
268M16×C43—22no—
269M16×C43—41no—
270C2×C8×C43—41no—
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—42no—
291C4⋊C4×C43—42no—
292C4⋊C4×C43—42no—
293C22⋊C4×C43—21no—
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—22no—
317C22⋊C4×C43—22no—
318C22⋊C4×C43—41no—
319C22⋊C4×C43—41no—
320C22⋊C4×C43—42no—
321C22⋊C4×C43—42no—
322C22⋊C4×C43—42no—
323C22⋊C4×C43—42no—
324C22⋊C4×C43C2×D411yescharacteristic
325C22⋊C4×C43C2×D411yescharacteristic
326C22⋊C4×C43C2×D411yescharacteristic
327C22⋊C4×C43C2×D411yescharacteristic
328C42×C43—21no—
329C42×C43—21no—
330C42×C43—21no—
331C42×C43—21no—
332C42×C43C2×D411yescharacteristic
333C42×C43C2×D411yescharacteristic
334C23×C43—21no—
335C23×C43—21no—
336C23×C43—21no—
337C23×C43—21no—
338C23×C43—22no—
339C23×C43—22no—
340C23×C43—21no—
341C23×C43—21no—
342C23×C43—41no—
343C23×C43—41no—
344C23×C43—41no—
345C23×C43—41no—
346C23×C43—81no—
347C23×C43—81no—
348C23×C43—81no—
349C23×C43—82no—
350C23×C43—161no—
351C23×C43#12011yescharacteristic
352C23×C43#12011yescharacteristic
353C23×C43#12011yescharacteristic
354C23×C43C22×D411yescharacteristic
355C23×C43C22×D411yescharacteristic
356Q8×C43—22no—
357Q8×C43—41no—
358Q8×C43—41no—
359Q8×C43—81no—
360Q8×C43—81no—
361D4×C43—22no—
362D4×C43—41no—
363D4×C43—41no—
364D4×C43—41no—
365D4×C43—41no—
366D4×C43—41no—
367D4×C43—41no—
368D4×C43—42no—
369D4×C43—42no—
370D4×C43—42no—
371D4×C43—42no—
372D4×C43—42no—
373D4×C43—42no—
374D4×C43—41no—
375D4×C43—41no—
376D4×C43—41no—
377D4×C43—41no—
378D4×C43—81no—
379D4×C43—81no—
380D4×C43—81no—
381D4×C43—81no—
382D4×C43—81no—
383D4×C43—81no—
384D4×C43—81no—
385D4×C43—81no—
386D4×C43—81no—
387D4×C43—162no—
388C2×C4×C43—21no—
389C2×C4×C43—21no—
390C2×C4×C43—22no—
391C2×C4×C43—22no—
392C2×C4×C43—21no—
393C2×C4×C43—21no—
394C2×C4×C43—21no—
395C2×C4×C43—21no—
396C2×C4×C43—21no—
397C2×C4×C43—21no—
398C2×C4×C43—21no—
399C2×C4×C43—21no—
400C2×C4×C43—21no—
401C2×C4×C43—21no—
402C2×C4×C43—42no—
403C2×C4×C43—42no—
404C2×C4×C43—41no—
405C2×C4×C43—41no—
406C2×C4×C43—41no—
407C2×C4×C43—41no—
408C2×C4×C43—41no—
409C2×C4×C43—41no—
410C2×C4×C43—41no—
411C2×C4×C43—41no—
412C2×C4×C43—42no—
413C2×C4×C43—42no—
414C2×C4×C43—81no—
415C2×C4×C43—81no—
416C2×C4×C43—81no—
417C2×C4×C43—81no—
418C2×C4×C43—81no—
419C2×C4×C43—81no—
420C2×C4×C43—81no—
421C2×C4×C43—81no—
422C2×C4×C43—82no—
423C2×C4×C43—161no—
424C2×C4×C43#12011yescharacteristic
425C2×C4×C43C22×D411yescharacteristic
426C8×C43—42no—
427#33552C4311yesmaximal, characteristic, direct product factor, Sylow
428C22×C43—21no—
429C22×C43—21no—
430C22×C43—21no—
431C22×C43—21no—
432C22×C43—41no—
433C22×C43—41no—
434C22×C43—41no—
435C22×C43—41no—
436C22×C43—41no—
437C22×C43—42no—
438C22×C43—41no—
439C22×C43—41no—
440C22×C43—41no—
441C22×C43—41no—
442C22×C43—42no—
443C22×C43—41no—
444C22×C43—41no—
445C22×C43—81no—
446C22×C43—81no—
447C22×C43—81no—
448C22×C43—82no—
449C22×C43—82no—
450C22×C43—82no—
451C22×C43—82no—
452C22×C43—161no—
453C22×C43—161no—
454C22×C43B(4,𝔽2)11yescharacteristic
455C22×C43B(4,𝔽2)11yescharacteristic
456C22×C43C2×#12011yescharacteristic
457C4×C43—21no—
458C4×C43—21no—
459C4×C43—41no—
460C4×C43—41no—
461C4×C43—41no—
462C4×C43—41no—
463C4×C43—41no—
464C4×C43—41no—
465C4×C43—42no—
466C4×C43—41no—
467C4×C43—41no—
468C4×C43—41no—
469C4×C43—41no—
470C4×C43—82no—
471C4×C43—82no—
472#3533C2×C4311yescharacteristic, complemented
473#3026C2×C4311yescharacteristic, complemented
474C2×#458C2×C4311yescharacteristic, complemented
475#3019C2×C4311yescharacteristic, complemented
476#2201C2×C4312yescomplemented
477#2200C2×C4312yescomplemented
478#2198C2×C4312yescomplemented
479#2197C2×C4312yescomplemented
480#2127C2×C4311yescharacteristic, complemented
481#2121C2×C4311yescharacteristic, complemented
482C2×#352C2×C4311yescharacteristic, complemented
483C2×C43—21no—
484C2×C43—21no—
485C2×C43—21no—
486C2×C43—41no—
487C2×C43—41no—
488C2×C43—41no—
489C2×C43—41no—
490C2×C43—81no—
491C2×C43—81no—
492C2×C43—82no—
493C2×C43C2×B(4,𝔽2)11yescharacteristic
494C2×H(5,𝔽2)C22×C4311yescharacteristic
495#575—21no—
496#563C22×C4311yescharacteristic, complemented
497#562—21no—
498#560C22×C4311yescharacteristic, complemented
499#559C22×C4311yescharacteristic, complemented
500#553—21no—
501#552—21no—
502#551—21no—
503#551C22×C4311yescharacteristic, complemented
504#547—21no—
505#546—21no—
506#542—21no—
507#540—21no—
508#539—21no—
509#538—21no—
510#538—21no—
511#535C22×C4311yescharacteristic
512#534—21no—
513#534C22×C4311yescharacteristic
514#525—21no—
515C2×#123—21no—
516C2×#123C22×C4311yescharacteristic
517#458—21no—
518#458—21no—
519#458—21no—
520#458C22×C4312yes—
521#458C22×C4312yes—
522#458C22×C4312yes—
523B(4,𝔽2)—21no—
524B(4,𝔽2)C22×C4312yes—
525#455—21no—
526#455C22×C4312yes—
527#453—21no—
528#453C22×C4312yes—
529#421—21no—
530C2×#100C22×C4311yescharacteristic
531C2×#99—21no—
532C2×#99—21no—
533C2×#99C22×C4311yescharacteristic
534C2×#99C22×C4311yescharacteristic
535#354C22×C4312yescomplemented
536#353C22×C4312yescomplemented
537#352C22×C4312yescomplemented
538#352C22×C4312yescomplemented
539#352C22×C4312yescomplemented
540AΣL(1,𝔽16)C22×C4312yescomplemented
541C43#3355211yescharacteristic, direct product factor, Sylow
542H(5,𝔽2)—21no—
543H(5,𝔽2)—21no—
544H(5,𝔽2)—21no—
545H(5,𝔽2)—42no—
546H(5,𝔽2)C23×C4312yes—
547C2×#41—21no—
548C2×#41—21no—
549C2×#41—41no—
550C2×#41D4×C4311yescharacteristic, complemented
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—41no—
554C22×D4D4×C4311yescharacteristic
555C22×D4C23×C4311yescharacteristic
556C23×C4D4×C4311yescharacteristic, complemented
557#137—22no—
558#137—41no—
559AGL(1,ℤ/8)—22no—
560AGL(1,ℤ/8)—41no—
561#135—42no—
562C2×M16—21no—
563C4⋊Q8—21no—
564#127D4×C4311yescharacteristic, complemented
565#127C23×C4311yescharacteristic
566#126—21no—
567#126—21no—
568#126—21no—
569#126—21no—
570#126—21no—
571#126—21no—
572#125—21no—
573#125—21no—
574#125—21no—
575#124—21no—
576#124—21no—
577#124—21no—
578#124—21no—
579#124D4×C4311yescharacteristic, complemented
580#124C23×C4311yescharacteristic
581#123—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—22no—
594#123—22no—
595#123—22no—
596#123—41no—
597#123—42no—
598#123D4×C4311yescharacteristic
599#123D4×C4311yescharacteristic, complemented
600#123D4×C4311yescharacteristic, complemented
601#123C23×C4311yescharacteristic
602#123C23×C4311yescharacteristic
603#123C23×C4311yescharacteristic
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612#121—21no—
613#121—21no—
614#121—21no—
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—42no—
625#120—21no—
626#120—21no—
627#120—21no—
628#120—21no—
629#120—22no—
630#120—41no—
631#120D4×C4311yescharacteristic
632#120C23×C4311yescharacteristic
633C4×Q8—21no—
634C4×D4—21no—
635C4×D4—21no—
636C4×D4—21no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643#117—21no—
644#117—21no—
645#117—21no—
646#117D4×C4311yescharacteristic, complemented
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—41no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—41no—
655C2×C22⋊C4D4×C4311yescharacteristic
656C2×C22⋊C4D4×C4311yescharacteristic, complemented
657#104—22no—
658#104—22no—
659#100—21no—
660#100C23×C4312yes—
661#99—21no—
662#99—21no—
663#99—22no—
664#99—22no—
665#99—22no—
666#99—22no—
667#99C23×C4312yes—
668#99C23×C4312yes—
669C24—21no—
670C24—21no—
671C24C2×D4×C4311yescharacteristic
672C24C2×D4×C4311yescharacteristic
673C24C2×D4×C4311yescharacteristic
674#41—22no—
675#41—22no—
676#41—42no—
677#41—41no—
678#41—42no—
679#41—42no—
680#41—41no—
681#41—41no—
682#41—42no—
683#41—41no—
684#41—81no—
685#41—81no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8C2×D4×C4311yescharacteristic
690C2×D4—21no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—22no—
696C2×D4—22no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—41no—
707C2×D4—41no—
708C2×D4—42no—
709C2×D4—42no—
710C2×D4—41no—
711C2×D4—41no—
712C2×D4—41no—
713C2×D4—41no—
714C2×D4—42no—
715C2×D4—42no—
716C2×D4—41no—
717C2×D4—41no—
718C2×D4—41no—
719C2×D4—41no—
720C2×D4—41no—
721C2×D4—42no—
722C2×D4C2×D4×C4311yescharacteristic
723C2×D4C2×D4×C4311yescharacteristic
724C2×D4C2×D4×C4311yescharacteristic
725C2×D4C2×D4×C4311yescharacteristic
726C2×D4C24×C4311yescharacteristic
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×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—41no—
739C22×C4—41no—
740C22×C4—41no—
741C22×C4—41no—
742C22×C4—41no—
743C22×C4C2×D4×C4311yescharacteristic
744C22×C4C2×D4×C4311yescharacteristic
745C22×C4C2×D4×C4311yescharacteristic
746C22×C4C2×D4×C4311yescharacteristic
747Q16—42no—
748SD16—42no—
749SD16—42no—
750D8—42no—
751M16—22no—
752M16—41no—
753C2×C8—41no—
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—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—42no—
774C4⋊C4—42no—
775C4⋊C4—42no—
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—22no—
800C22⋊C4—22no—
801C22⋊C4—42no—
802C22⋊C4—41no—
803C22⋊C4—41no—
804C22⋊C4—42no—
805C22⋊C4—42no—
806C22⋊C4—42no—
807C22⋊C4C2×D4×C4311yescharacteristic
808C22⋊C4C2×D4×C4311yescharacteristic
809C22⋊C4C2×D4×C4311yescharacteristic
810C22⋊C4C2×D4×C4311yescharacteristic
811C42—21no—
812C42—21no—
813C42—21no—
814C42—21no—
815C42C2×D4×C4311yescharacteristic
816C42C2×D4×C4311yescharacteristic
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—22no—
822C23—22no—
823C23—21no—
824C23—21no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—81no—
830C23—81no—
831C23—81no—
832C23—82no—
833C23—161no—
834C23#120×C4311yescharacteristic
835C23#120×C4311yescharacteristic
836C23#120×C4311yescharacteristic
837C23C22×D4×C4311yescharacteristic
838C23C22×D4×C4311yescharacteristic
839Q8—22no—
840Q8—41no—
841Q8—41no—
842Q8—81no—
843Q8—81no—
844D4—22no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—42no—
852D4—42no—
853D4—42no—
854D4—42no—
855D4—42no—
856D4—42no—
857D4—41no—
858D4—41no—
859D4—41no—
860D4—41no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—81no—
866D4—81no—
867D4—81no—
868D4—81no—
869D4—81no—
870D4—162no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4—82no—
906C2×C4—161no—
907C2×C4#120×C4311yescharacteristic
908C2×C4C22×D4×C4311yescharacteristic
909C8—42no—
910C22—21no—
911C22—21no—
912C22—21no—
913C22—21no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—42no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—42no—
925C22—41no—
926C22—41no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—82no—
931C22—82no—
932C22—82no—
933C22—82no—
934C22—161no—
935C22—161no—
936C22C43×B(4,𝔽2)11yescharacteristic
937C22C43×B(4,𝔽2)11yescharacteristic
938C22C2×#120×C4311yescharacteristic
939C4—21no—
940C4—21no—
941C4—41no—
942C4—41no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—41no—
947C4—42no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—82no—
953C4—82no—
954C2—21no—
955C2—21no—
956C2—21no—
957C2—41no—
958C2—41no—
959C2—41no—
960C2—41no—
961C2—81no—
962C2—81no—
963C2—82no—
964C2C2×C43×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C43C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C43
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C43 ◁ C23×C43 ◁ C22×D4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3533C2semidirect
2. C43×#3026C2semidirect
3. C2×C43×#458C2semidirect
4. C43×#3019C2semidirect
5. C43×#2201C2semidirect
6. C43×#2200C2semidirect
7. C43×#2198C2semidirect
8. C43×#2197C2semidirect
9. C43×#2127C2semidirect
10. C43×#2121C2semidirect
11. C2×C43×#352C2semidirect
14. C43×#563C22semidirect
16. C43×#560C22semidirect
17. C43×#559C22semidirect
21. C43×#551C22semidirect
53. C43×#354C22semidirect
54. C43×#353C22semidirect
55. C43×#352C22semidirect
56. C43×#352C22semidirect
57. C43×#352C22semidirect
58. C43×AΣL(1,𝔽16)C22semidirect
67. C2×#41×C43D4semidirect
73. C23×C4×C43D4semidirect
81. #127×C43D4semidirect
96. #124×C43D4semidirect
116. #123×C43D4semidirect
117. #123×C43D4semidirect
163. #117×C43D4semidirect
173. C2×C22⋊C4×C43D4semidirect
427. #33552C43direct (N × H)
472. #3533C2×C43semidirect
473. #3026C2×C43semidirect
474. C2×#458C2×C43semidirect
475. #3019C2×C43semidirect
476. #2201C2×C43semidirect
477. #2200C2×C43semidirect
478. #2198C2×C43semidirect
479. #2197C2×C43semidirect
480. #2127C2×C43semidirect
481. #2121C2×C43semidirect
482. C2×#352C2×C43semidirect
496. #563C22×C43semidirect
498. #560C22×C43semidirect
499. #559C22×C43semidirect
503. #551C22×C43semidirect
535. #354C22×C43semidirect
536. #353C22×C43semidirect
537. #352C22×C43semidirect
538. #352C22×C43semidirect
539. #352C22×C43semidirect
540. AΣL(1,𝔽16)C22×C43semidirect
541. C43#33552direct (N × H)
550. C2×#41D4×C43semidirect
556. C23×C4D4×C43semidirect
564. #127D4×C43semidirect
579. #124D4×C43semidirect
599. #123D4×C43semidirect
600. #123D4×C43semidirect
646. #117D4×C43semidirect
656. C2×C22⋊C4D4×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#35332
C43×#30262
C2×C43×#4582
C43×#30192
C43×#22012
C43×#22002
C43×#21982
C43×#21972
C43×#21272
C43×#21212
C2×C43×#3522
#3355243