Finite Group Databasebeta

← C43×#24402 #24944419

Subgroups — C43×#24402 #24944419

Order 11008.

1358 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#575C211yesmaximal, characteristic, complemented
2C2×C43×#472C211yesmaximal, characteristic, complemented
3C2×C43×#471C211yesmaximal, characteristic, complemented
4C43×#3006C211yesmaximal, characteristic, complemented
5C2×C43×#449C211yesmaximal, characteristic, complemented
6C43×#2880C211yesmaximal, characteristic, complemented
7C43×#2052C211yesmaximal, characteristic, complemented
8C43×#2051C211yesmaximal, characteristic, complemented
9C43×#2019C211yesmaximal, characteristic, complemented
10C43×#2018C211yesmaximal, characteristic, complemented
11C43×#1908C211yesmaximal, characteristic, complemented
12C43×#1907C211yesmaximal, characteristic, complemented
13C43×#1900C211yesmaximal, characteristic, complemented
14C43×#1855C211yesmaximal, characteristic, complemented
15C43×#1785C211yesmaximal, characteristic, complemented
16C22×#41×C43C2211yescharacteristic
17C22×#41×C43C2211yescharacteristic
18C43×#575—24no—
19C43×#575—24no—
20C2×#137×C43—21no—
21C2×#137×C43C2211yescharacteristic
22C2×#137×C43C2211yescharacteristic
23C2×AGL(1,ℤ/8)×C43—21no—
24C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
26C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
28C2×#135×C43—21no—
29C2×#135×C43—21no—
30C22×SD16×C43C2211yescharacteristic, complemented
31C22×D8×C43C2211yescharacteristic, complemented
32C2×#131×C43C2211yescharacteristic
33C2×#131×C43C2211yescharacteristic
34C22×M16×C43C2211yescharacteristic
35C2×#121×C43C2211yescharacteristic
36C43×#472—24no—
37C43×#471—24no—
38C43×#449—21no—
39C43×#449—21no—
40C43×#449—21no—
41C43×#449—21no—
42C43×#449—21no—
43C43×#449—21no—
44C43×#448—21no—
45C43×#447—21no—
46C2×#108×C43C2211yescharacteristic, complemented
47C2×#108×C43C2211yescharacteristic, complemented
48C43×#417C2211yescharacteristic
49C43×#417C2211yescharacteristic
50C2×#103×C43C2211yescharacteristic, complemented
51C2×#102×C43C2211yescharacteristic, complemented
52C2×#101×C43C2211yescharacteristic, complemented
53C2×#101×C43C2211yescharacteristic, complemented
54C2×#100×C43C2211yescharacteristic, complemented
55C2×#100×C43C2211yescharacteristic, complemented
56C2×#100×C43C2211yescharacteristic, complemented
57C2×#100×C43C2211yescharacteristic, complemented
58C43×#408—21no—
59C43×#408—21no—
60C43×#408C2211yescharacteristic
61C43×#408C2211yescharacteristic
62C43×#407—21no—
63C43×#407C2211yescharacteristic
64C43×#407C2211yescharacteristic
65C2×C22⋊C8×C43—21no—
66C2×C22⋊C8×C43C2211yescharacteristic
67C43×#343C2211yescharacteristic, complemented
68C43×#343C2211yescharacteristic, complemented
69C43×#341C2211yescharacteristic, complemented
70C43×#341C2211yescharacteristic, complemented
71C2×#41×C43—21no—
72C2×#41×C43—21no—
73C2×#41×C43—22no—
74C2×#41×C43—22no—
75C2×#41×C43—22no—
76C2×#41×C43—22no—
77C2×#41×C43—21no—
78C2×#41×C43—21no—
79C2×#41×C43—21no—
80C2×#41×C43—21no—
81C2×#41×C43—41no—
82C2×#41×C43—41no—
83C2×#41×C43—41no—
84C2×#41×C43—41no—
85C2×#41×C43D411yescharacteristic
86C2×#41×C43D411yescharacteristic
87C2×#41×C43C2311yescharacteristic
88C2×#41×C43C2311yescharacteristic
89C22×Q8×C43D411yescharacteristic
90C22×Q8×C43C2311yescharacteristic
91C22×D4×C43—21no—
92C22×D4×C43—21no—
93C22×D4×C43—21no—
94C22×D4×C43D411yescharacteristic
95C22×D4×C43C2311yescharacteristic
96C22×D4×C43C2311yescharacteristic
97C23×C4×C43—21no—
98C23×C4×C43—21no—
99C23×C4×C43C2311yescharacteristic
100#137×C43—28no—
101#137×C43—22no—
102#137×C43—22no—
103#137×C43—22no—
104#137×C43D414yescomplemented
105AGL(1,ℤ/8)×C43—28no—
106AGL(1,ℤ/8)×C43—22no—
107AGL(1,ℤ/8)×C43—22no—
108AGL(1,ℤ/8)×C43—22no—
109AGL(1,ℤ/8)×C43—22no—
110AGL(1,ℤ/8)×C43—22no—
111AGL(1,ℤ/8)×C43—41no—
112AGL(1,ℤ/8)×C43—41no—
113AGL(1,ℤ/8)×C43D414yescomplemented
114#135×C43—28no—
115#135×C43—28no—
116C2×Q16×C43—21no—
117C2×Q16×C43—21no—
118C2×SD16×C43—21no—
119C2×SD16×C43—21no—
120C2×SD16×C43—21no—
121C2×SD16×C43—21no—
122C2×SD16×C43—22no—
123C2×SD16×C43—21no—
124C2×SD16×C43—21no—
125C2×SD16×C43—21no—
126C2×SD16×C43—21no—
127C2×SD16×C43—41no—
128C2×D8×C43—21no—
129C2×D8×C43—21no—
130C2×D8×C43—22no—
131C2×D8×C43—21no—
132C2×D8×C43—21no—
133C2×D8×C43—21no—
134C2×D8×C43—21no—
135C2×D8×C43—41no—
136#131×C43—22no—
137#131×C43—22no—
138#131×C43—41no—
139#131×C43—41no—
140C2×M16×C43—21no—
141C2×M16×C43—22no—
142C2×M16×C43—22no—
143C2×M16×C43—21no—
144C2×M16×C43—21no—
145C2×M16×C43C2311yescharacteristic
146C2×M16×C43C2311yescharacteristic
147C2×M16×C43C2311yescharacteristic
148C2×M16×C43C2311yescharacteristic
149C2×M16×C43C2311yescharacteristic
150C2×M16×C43C2311yescharacteristic
151C22×C8×C43—21no—
152C22×C8×C43—21no—
153C22×C8×C43—21no—
154C22×C8×C43C2311yescharacteristic
155C22×C8×C43C2311yescharacteristic
156#121×C43—21no—
157#121×C43—21no—
158#121×C43—21no—
159#121×C43—21no—
160C2×C4⋊C4×C43C2311yescharacteristic
161C2×C22⋊C4×C43—21no—
162#108×C43—22no—
163#108×C43—22no—
164#103×C43—21no—
165#103×C43—21no—
166#103×C43—21no—
167#103×C43—21no—
168#102×C43—21no—
169#102×C43—21no—
170#102×C43—21no—
171#102×C43—21no—
172#101×C43—22no—
173#101×C43—41no—
174#100×C43—22no—
175#100×C43—22no—
176#100×C43—22no—
177#100×C43—41no—
178C22⋊C8×C43—21no—
179C22⋊C8×C43—21no—
180C22⋊C8×C43—21no—
181C22⋊C8×C43—21no—
182C22⋊C8×C43—21no—
183C22⋊C8×C43—21no—
184C22⋊C8×C43—21no—
185C22⋊C8×C43—21no—
186C22⋊C8×C43D411yescharacteristic
187C22⋊C8×C43D411yescharacteristic
188C22⋊C8×C43D411yescharacteristic
189C22⋊C8×C43D411yescharacteristic
190C24×C43—21no—
191C24×C43—21no—
192C24×C43—21no—
193C24×C43#4111yescharacteristic
194#41×C43—21no—
195#41×C43—21no—
196#41×C43—24no—
197#41×C43—24no—
198#41×C43—22no—
199#41×C43—22no—
200#41×C43—21no—
201#41×C43—21no—
202#41×C43—21no—
203#41×C43—21no—
204#41×C43—42no—
205#41×C43—42no—
206#41×C43—41no—
207#41×C43—41no—
208#41×C43—42no—
209#41×C43—42no—
210#41×C43—42no—
211#41×C43—42no—
212#41×C43—42no—
213#41×C43—42no—
214#41×C43—42no—
215#41×C43—42no—
216#41×C43C2×D412yes—
217#41×C43C2×D412yes—
218C2×Q8×C43—21no—
219C2×Q8×C43—21no—
220C2×Q8×C43—22no—
221C2×Q8×C43—21no—
222C2×Q8×C43—21no—
223C2×Q8×C43—21no—
224C2×Q8×C43—21no—
225C2×Q8×C43—41no—
226C2×Q8×C43C2×D412yes—
227C2×Q8×C43C2×D411yescharacteristic
228C2×Q8×C43C2×D411yescharacteristic
229C2×D4×C43—21no—
230C2×D4×C43—21no—
231C2×D4×C43—21no—
232C2×D4×C43—21no—
233C2×D4×C43—21no—
234C2×D4×C43—21no—
235C2×D4×C43—22no—
236C2×D4×C43—21no—
237C2×D4×C43—21no—
238C2×D4×C43—21no—
239C2×D4×C43—21no—
240C2×D4×C43—21no—
241C2×D4×C43—21no—
242C2×D4×C43—21no—
243C2×D4×C43—21no—
244C2×D4×C43—21no—
245C2×D4×C43—21no—
246C2×D4×C43—42no—
247C2×D4×C43—42no—
248C2×D4×C43—42no—
249C2×D4×C43—42no—
250C2×D4×C43—41no—
251C2×D4×C43—41no—
252C2×D4×C43—41no—
253C2×D4×C43—41no—
254C2×D4×C43—41no—
255C2×D4×C43—82no—
256C2×D4×C43C2×D412yes—
257C2×D4×C43C2×D411yescharacteristic
258C2×D4×C43C2×D411yescharacteristic
259C22×C4×C43—21no—
260C22×C4×C43—21no—
261C22×C4×C43—21no—
262C22×C4×C43—21no—
263C22×C4×C43—21no—
264C22×C4×C43—21no—
265C22×C4×C43—21no—
266C22×C4×C43—21no—
267C22×C4×C43—21no—
268C22×C4×C43—21no—
269C22×C4×C43—21no—
270C22×C4×C43—42no—
271C22×C4×C43—42no—
272C22×C4×C43—42no—
273C22×C4×C43—42no—
274C22×C4×C43—41no—
275C22×C4×C43—41no—
276C22×C4×C43C2×D411yescharacteristic
277C22×C4×C43C2×D411yescharacteristic
278C22×C4×C43C2×D411yescharacteristic
279C22×C4×C43C2×D411yescharacteristic
280C22×C4×C43#4111yescharacteristic
281C22×C4×C43C2411yescharacteristic
282Q16×C43—24no—
283Q16×C43—24no—
284SD16×C43—24no—
285SD16×C43—24no—
286SD16×C43—24no—
287SD16×C43—24no—
288SD16×C43—42no—
289SD16×C43—42no—
290SD16×C43—42no—
291SD16×C43—42no—
292D8×C43—24no—
293D8×C43—24no—
294D8×C43—42no—
295D8×C43—42no—
296D8×C43—42no—
297D8×C43—42no—
298M16×C43—24no—
299M16×C43—21no—
300M16×C43—21no—
301M16×C43—21no—
302M16×C43—21no—
303M16×C43—21no—
304M16×C43—21no—
305M16×C43—21no—
306M16×C43—21no—
307M16×C43—21no—
308M16×C43—21no—
309M16×C43—42no—
310M16×C43—42no—
311M16×C43C2×D412yes—
312M16×C43C2×D412yes—
313C2×C8×C43—24no—
314C2×C8×C43—21no—
315C2×C8×C43—21no—
316C2×C8×C43—21no—
317C2×C8×C43—21no—
318C2×C8×C43—21no—
319C2×C8×C43—21no—
320C2×C8×C43—21no—
321C2×C8×C43—21no—
322C2×C8×C43—21no—
323C2×C8×C43—21no—
324C2×C8×C43—42no—
325C2×C8×C43—42no—
326C2×C8×C43C2×D411yescharacteristic
327C2×C8×C43C2×D411yescharacteristic
328C2×C8×C43C2×D411yescharacteristic
329C2×C8×C43C2×D411yescharacteristic
330C4⋊C4×C43—21no—
331C4⋊C4×C43—21no—
332C22⋊C4×C43—41no—
333C22⋊C4×C43—41no—
334C23×C43—21no—
335C23×C43—21no—
336C23×C43—21no—
337C23×C43—21no—
338C23×C43—22no—
339C23×C43—41no—
340C23×C43—41no—
341C23×C43—42no—
342C23×C43—42no—
343C23×C43—41no—
344C23×C43—41no—
345C23×C43—41no—
346C23×C43—41no—
347C23×C43—41no—
348C23×C43—81no—
349C23×C43—81no—
350C23×C43—81no—
351C23×C43—81no—
352C23×C43—81no—
353C23×C43#12111yescharacteristic
354C23×C43#12111yescharacteristic
355C23×C43C2×#4111yescharacteristic
356Q8×C43—21no—
357Q8×C43—21no—
358Q8×C43—22no—
359Q8×C43—21no—
360Q8×C43—22no—
361Q8×C43—42no—
362Q8×C43—41no—
363Q8×C43—41no—
364Q8×C43#12012yes—
365D4×C43—22no—
366D4×C43—22no—
367D4×C43—21no—
368D4×C43—22no—
369D4×C43—21no—
370D4×C43—21no—
371D4×C43—22no—
372D4×C43—42no—
373D4×C43—42no—
374D4×C43—42no—
375D4×C43—44no—
376D4×C43—44no—
377D4×C43—41no—
378D4×C43—41no—
379D4×C43—41no—
380D4×C43—41no—
381D4×C43—41no—
382D4×C43—41no—
383D4×C43—41no—
384D4×C43—41no—
385D4×C43—82no—
386D4×C43—82no—
387D4×C43#12012yes—
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—22no—
396C2×C4×C43—22no—
397C2×C4×C43—21no—
398C2×C4×C43—21no—
399C2×C4×C43—21no—
400C2×C4×C43—21no—
401C2×C4×C43—21no—
402C2×C4×C43—22no—
403C2×C4×C43—42no—
404C2×C4×C43—42no—
405C2×C4×C43—42no—
406C2×C4×C43—44no—
407C2×C4×C43—44no—
408C2×C4×C43—41no—
409C2×C4×C43—41no—
410C2×C4×C43—41no—
411C2×C4×C43—41no—
412C2×C4×C43—41no—
413C2×C4×C43—81no—
414C2×C4×C43#12111yescharacteristic
415C2×C4×C43#12111yescharacteristic
416C2×C4×C43C22×D411yescharacteristic
417C2×C4×C43C22×D411yescharacteristic
418C2×C4×C43C22×D411yescharacteristic
419C2×C4×C43C22×D411yescharacteristic
420C2×C4×C43H(5,𝔽2)11yescharacteristic
421C2×C4×C43H(5,𝔽2)11yescharacteristic
422C8×C43—22no—
423C8×C43—22no—
424C8×C43—21no—
425C8×C43—21no—
426C8×C43—21no—
427C8×C43—21no—
428C8×C43—41no—
429C8×C43—41no—
430C8×C43—41no—
431C8×C43—41no—
432#24402C4311yesmaximal, characteristic, direct product factor, Sylow
433C22×C43—21no—
434C22×C43—21no—
435C22×C43—21no—
436C22×C43—21no—
437C22×C43—22no—
438C22×C43—21no—
439C22×C43—21no—
440C22×C43—21no—
441C22×C43—21no—
442C22×C43—41no—
443C22×C43—41no—
444C22×C43—41no—
445C22×C43—42no—
446C22×C43—41no—
447C22×C43—41no—
448C22×C43—81no—
449C22×C43—81no—
450C22×C43—82no—
451C22×C43—82no—
452C22×C43—84no—
453C22×C43—81no—
454C22×C43—81no—
455C22×C43—81no—
456C22×C43—81no—
457C22×C43—81no—
458C22×C43—161no—
459C22×C43—161no—
460C22×C43C2×#12111yescharacteristic
461C22×C43#54611yescharacteristic
462C22×C43#54611yescharacteristic
463C4×C43—21no—
464C4×C43—21no—
465C4×C43—22no—
466C4×C43—41no—
467C4×C43—42no—
468C4×C43—81no—
469C4×C43C2×#12011yescharacteristic
470C4×C43#53411yescharacteristic
471C4×C43D4211yescharacteristic
472C4×C43D4211yescharacteristic
473C2×#575C2×C4311yescharacteristic, complemented
474C2×#472C2×C4311yescharacteristic, complemented
475C2×#471C2×C4311yescharacteristic, complemented
476#3006C2×C4311yescharacteristic, complemented
477C2×#449C2×C4311yescharacteristic, complemented
478#2880C2×C4311yescharacteristic, complemented
479#2052C2×C4311yescharacteristic, complemented
480#2051C2×C4311yescharacteristic, complemented
481#2019C2×C4311yescharacteristic, complemented
482#2018C2×C4311yescharacteristic, complemented
483#1908C2×C4311yescharacteristic, complemented
484#1907C2×C4311yescharacteristic, complemented
485#1900C2×C4311yescharacteristic, complemented
486#1855C2×C4311yescharacteristic, complemented
487#1785C2×C4311yescharacteristic, complemented
488C2×C43—21no—
489C2×C43—21no—
490C2×C43—41no—
491C2×C43—41no—
492C2×C43—42no—
493C2×C43—81no—
494C2×C43—82no—
495C2×C43—161no—
496C2×C43#241011yescharacteristic
497C2×C43#306711yescharacteristic
498C2×C43#306811yescharacteristic
499C22×#41C22×C4311yescharacteristic
500C22×#41C22×C4311yescharacteristic
501#575—24no—
502#575—24no—
503C2×#137—21no—
504C2×#137C22×C4311yescharacteristic
505C2×#137C22×C4311yescharacteristic
506C2×AGL(1,ℤ/8)—21no—
507C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
508C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
509C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
510C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
511C2×#135—21no—
512C2×#135—21no—
513C22×SD16C22×C4311yescharacteristic, complemented
514C22×D8C22×C4311yescharacteristic, complemented
515C2×#131C22×C4311yescharacteristic
516C2×#131C22×C4311yescharacteristic
517C22×M16C22×C4311yescharacteristic
518C2×#121C22×C4311yescharacteristic
519#472—24no—
520#471—24no—
521#449—21no—
522#449—21no—
523#449—21no—
524#449—21no—
525#449—21no—
526#449—21no—
527#448—21no—
528#447—21no—
529C2×#108C22×C4311yescharacteristic, complemented
530C2×#108C22×C4311yescharacteristic, complemented
531#417C22×C4311yescharacteristic
532#417C22×C4311yescharacteristic
533C2×#103C22×C4311yescharacteristic, complemented
534C2×#102C22×C4311yescharacteristic, complemented
535C2×#101C22×C4311yescharacteristic, complemented
536C2×#101C22×C4311yescharacteristic, complemented
537C2×#100C22×C4311yescharacteristic, complemented
538C2×#100C22×C4311yescharacteristic, complemented
539C2×#100C22×C4311yescharacteristic, complemented
540C2×#100C22×C4311yescharacteristic, complemented
541#408—21no—
542#408—21no—
543#408C22×C4311yescharacteristic
544#408C22×C4311yescharacteristic
545#407—21no—
546#407C22×C4311yescharacteristic
547#407C22×C4311yescharacteristic
548C2×C22⋊C8—21no—
549C2×C22⋊C8C22×C4311yescharacteristic
550#343C22×C4311yescharacteristic, complemented
551#343C22×C4311yescharacteristic, complemented
552#341C22×C4311yescharacteristic, complemented
553#341C22×C4311yescharacteristic, complemented
554C43#2440211yescharacteristic, direct product factor, Sylow
555C2×#41—21no—
556C2×#41—21no—
557C2×#41—22no—
558C2×#41—22no—
559C2×#41—22no—
560C2×#41—22no—
561C2×#41—21no—
562C2×#41—21no—
563C2×#41—21no—
564C2×#41—21no—
565C2×#41—41no—
566C2×#41—41no—
567C2×#41—41no—
568C2×#41—41no—
569C2×#41D4×C4311yescharacteristic
570C2×#41D4×C4311yescharacteristic
571C2×#41C23×C4311yescharacteristic
572C2×#41C23×C4311yescharacteristic
573C22×Q8D4×C4311yescharacteristic
574C22×Q8C23×C4311yescharacteristic
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4D4×C4311yescharacteristic
579C22×D4C23×C4311yescharacteristic
580C22×D4C23×C4311yescharacteristic
581C23×C4—21no—
582C23×C4—21no—
583C23×C4C23×C4311yescharacteristic
584#137—28no—
585#137—22no—
586#137—22no—
587#137—22no—
588#137D4×C4314yescomplemented
589AGL(1,ℤ/8)—28no—
590AGL(1,ℤ/8)—22no—
591AGL(1,ℤ/8)—22no—
592AGL(1,ℤ/8)—22no—
593AGL(1,ℤ/8)—22no—
594AGL(1,ℤ/8)—22no—
595AGL(1,ℤ/8)—41no—
596AGL(1,ℤ/8)—41no—
597AGL(1,ℤ/8)D4×C4314yescomplemented
598#135—28no—
599#135—28no—
600C2×Q16—21no—
601C2×Q16—21no—
602C2×SD16—21no—
603C2×SD16—21no—
604C2×SD16—21no—
605C2×SD16—21no—
606C2×SD16—22no—
607C2×SD16—21no—
608C2×SD16—21no—
609C2×SD16—21no—
610C2×SD16—21no—
611C2×SD16—41no—
612C2×D8—21no—
613C2×D8—21no—
614C2×D8—22no—
615C2×D8—21no—
616C2×D8—21no—
617C2×D8—21no—
618C2×D8—21no—
619C2×D8—41no—
620#131—22no—
621#131—22no—
622#131—41no—
623#131—41no—
624C2×M16—21no—
625C2×M16—22no—
626C2×M16—22no—
627C2×M16—21no—
628C2×M16—21no—
629C2×M16C23×C4311yescharacteristic
630C2×M16C23×C4311yescharacteristic
631C2×M16C23×C4311yescharacteristic
632C2×M16C23×C4311yescharacteristic
633C2×M16C23×C4311yescharacteristic
634C2×M16C23×C4311yescharacteristic
635C22×C8—21no—
636C22×C8—21no—
637C22×C8—21no—
638C22×C8C23×C4311yescharacteristic
639C22×C8C23×C4311yescharacteristic
640#121—21no—
641#121—21no—
642#121—21no—
643#121—21no—
644C2×C4⋊C4C23×C4311yescharacteristic
645C2×C22⋊C4—21no—
646#108—22no—
647#108—22no—
648#103—21no—
649#103—21no—
650#103—21no—
651#103—21no—
652#102—21no—
653#102—21no—
654#102—21no—
655#102—21no—
656#101—22no—
657#101—41no—
658#100—22no—
659#100—22no—
660#100—22no—
661#100—41no—
662C22⋊C8—21no—
663C22⋊C8—21no—
664C22⋊C8—21no—
665C22⋊C8—21no—
666C22⋊C8—21no—
667C22⋊C8—21no—
668C22⋊C8—21no—
669C22⋊C8—21no—
670C22⋊C8D4×C4311yescharacteristic
671C22⋊C8D4×C4311yescharacteristic
672C22⋊C8D4×C4311yescharacteristic
673C22⋊C8D4×C4311yescharacteristic
674C24—21no—
675C24—21no—
676C24—21no—
677C24#41×C4311yescharacteristic
678#41—21no—
679#41—21no—
680#41—24no—
681#41—24no—
682#41—22no—
683#41—22no—
684#41—21no—
685#41—21no—
686#41—21no—
687#41—21no—
688#41—42no—
689#41—42no—
690#41—41no—
691#41—41no—
692#41—42no—
693#41—42no—
694#41—42no—
695#41—42no—
696#41—42no—
697#41—42no—
698#41—42no—
699#41—42no—
700#41C2×D4×C4312yes—
701#41C2×D4×C4312yes—
702C2×Q8—21no—
703C2×Q8—21no—
704C2×Q8—22no—
705C2×Q8—21no—
706C2×Q8—21no—
707C2×Q8—21no—
708C2×Q8—21no—
709C2×Q8—41no—
710C2×Q8C2×D4×C4312yes—
711C2×Q8C2×D4×C4311yescharacteristic
712C2×Q8C2×D4×C4311yescharacteristic
713C2×D4—21no—
714C2×D4—22no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—41no—
731C2×D4—42no—
732C2×D4—42no—
733C2×D4—42no—
734C2×D4—42no—
735C2×D4—41no—
736C2×D4—41no—
737C2×D4—41no—
738C2×D4—41no—
739C2×D4—82no—
740C2×D4C2×D4×C4312yes—
741C2×D4C2×D4×C4311yescharacteristic
742C2×D4C2×D4×C4311yescharacteristic
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—42no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—41no—
759C22×C4—41no—
760C22×C4C2×D4×C4311yescharacteristic
761C22×C4C2×D4×C4311yescharacteristic
762C22×C4C2×D4×C4311yescharacteristic
763C22×C4C2×D4×C4311yescharacteristic
764C22×C4#41×C4311yescharacteristic
765C22×C4C24×C4311yescharacteristic
766Q16—24no—
767Q16—24no—
768SD16—24no—
769SD16—24no—
770SD16—24no—
771SD16—24no—
772SD16—42no—
773SD16—42no—
774SD16—42no—
775SD16—42no—
776D8—24no—
777D8—24no—
778D8—42no—
779D8—42no—
780D8—42no—
781D8—42no—
782M16—24no—
783M16—21no—
784M16—21no—
785M16—21no—
786M16—21no—
787M16—21no—
788M16—21no—
789M16—21no—
790M16—21no—
791M16—21no—
792M16—21no—
793M16—42no—
794M16—42no—
795M16C2×D4×C4312yes—
796M16C2×D4×C4312yes—
797C2×C8—24no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—42no—
809C2×C8—42no—
810C2×C8C2×D4×C4311yescharacteristic
811C2×C8C2×D4×C4311yescharacteristic
812C2×C8C2×D4×C4311yescharacteristic
813C2×C8C2×D4×C4311yescharacteristic
814C4⋊C4—21no—
815C4⋊C4—21no—
816C22⋊C4—41no—
817C22⋊C4—41no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—22no—
823C23—41no—
824C23—41no—
825C23—42no—
826C23—42no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23—81no—
836C23—81no—
837C23#121×C4311yescharacteristic
838C23#121×C4311yescharacteristic
839C23C2×#41×C4311yescharacteristic
840Q8—21no—
841Q8—21no—
842Q8—22no—
843Q8—21no—
844Q8—22no—
845Q8—42no—
846Q8—41no—
847Q8—41no—
848Q8#120×C4312yes—
849D4—22no—
850D4—22no—
851D4—21no—
852D4—22no—
853D4—21no—
854D4—21no—
855D4—22no—
856D4—42no—
857D4—42no—
858D4—42no—
859D4—44no—
860D4—44no—
861D4—41no—
862D4—41no—
863D4—41no—
864D4—41no—
865D4—41no—
866D4—41no—
867D4—41no—
868D4—41no—
869D4—82no—
870D4—82no—
871D4#120×C4312yes—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—22no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—44no—
891C2×C4—44no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—81no—
898C2×C4#121×C4311yescharacteristic
899C2×C4#121×C4311yescharacteristic
900C2×C4C22×D4×C4311yescharacteristic
901C2×C4C22×D4×C4311yescharacteristic
902C2×C4C22×D4×C4311yescharacteristic
903C2×C4C22×D4×C4311yescharacteristic
904C2×C4H(5,𝔽2)×C4311yescharacteristic
905C2×C4H(5,𝔽2)×C4311yescharacteristic
906C8—22no—
907C8—22no—
908C8—21no—
909C8—21no—
910C8—21no—
911C8—21no—
912C8—41no—
913C8—41no—
914C8—41no—
915C8—41no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—22no—
921C22—21no—
922C22—21no—
923C22—21no—
924C22—21no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—42no—
929C22—41no—
930C22—41no—
931C22—81no—
932C22—81no—
933C22—82no—
934C22—82no—
935C22—84no—
936C22—81no—
937C22—81no—
938C22—81no—
939C22—81no—
940C22—81no—
941C22—161no—
942C22—161no—
943C22C2×#121×C4311yescharacteristic
944C22C43×#54611yescharacteristic
945C22C43×#54611yescharacteristic
946C4—21no—
947C4—21no—
948C4—22no—
949C4—41no—
950C4—42no—
951C4—81no—
952C4C2×#120×C4311yescharacteristic
953C4C43×#53411yescharacteristic
954C4D42×C4311yescharacteristic
955C4D42×C4311yescharacteristic
956C2—21no—
957C2—21no—
958C2—41no—
959C2—41no—
960C2—42no—
961C2—81no—
962C2—82no—
963C2—161no—
964C2C43×#241011yescharacteristic
965C2C43×#306711yescharacteristic
966C2C43×#306811yescharacteristic
subgroupG/H
center, socleC22×C43C2×#121
commutator, Frattini, cosocleC22×C4C24×C43
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C23×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#575C2semidirect
2. C2×C43×#472C2semidirect
3. C2×C43×#471C2semidirect
4. C43×#3006C2semidirect
5. C2×C43×#449C2semidirect
6. C43×#2880C2semidirect
7. C43×#2052C2semidirect
8. C43×#2051C2semidirect
9. C43×#2019C2semidirect
10. C43×#2018C2semidirect
11. C43×#1908C2semidirect
12. C43×#1907C2semidirect
13. C43×#1900C2semidirect
14. C43×#1855C2semidirect
15. C43×#1785C2semidirect
30. C22×SD16×C43C22semidirect
31. C22×D8×C43C22semidirect
46. C2×#108×C43C22semidirect
47. C2×#108×C43C22semidirect
50. C2×#103×C43C22semidirect
51. C2×#102×C43C22semidirect
52. C2×#101×C43C22semidirect
53. C2×#101×C43C22semidirect
54. C2×#100×C43C22semidirect
55. C2×#100×C43C22semidirect
56. C2×#100×C43C22semidirect
57. C2×#100×C43C22semidirect
67. C43×#343C22semidirect
68. C43×#343C22semidirect
69. C43×#341C22semidirect
70. C43×#341C22semidirect
104. #137×C43D4semidirect
113. AGL(1,ℤ/8)×C43D4semidirect
432. #24402C43direct (N × H)
473. C2×#575C2×C43semidirect
474. C2×#472C2×C43semidirect
475. C2×#471C2×C43semidirect
476. #3006C2×C43semidirect
477. C2×#449C2×C43semidirect
478. #2880C2×C43semidirect
479. #2052C2×C43semidirect
480. #2051C2×C43semidirect
481. #2019C2×C43semidirect
482. #2018C2×C43semidirect
483. #1908C2×C43semidirect
484. #1907C2×C43semidirect
485. #1900C2×C43semidirect
486. #1855C2×C43semidirect
487. #1785C2×C43semidirect
513. C22×SD16C22×C43semidirect
514. C22×D8C22×C43semidirect
529. C2×#108C22×C43semidirect
530. C2×#108C22×C43semidirect
533. C2×#103C22×C43semidirect
534. C2×#102C22×C43semidirect
535. C2×#101C22×C43semidirect
536. C2×#101C22×C43semidirect
537. C2×#100C22×C43semidirect
538. C2×#100C22×C43semidirect
539. C2×#100C22×C43semidirect
540. C2×#100C22×C43semidirect
550. #343C22×C43semidirect
551. #343C22×C43semidirect
552. #341C22×C43semidirect
553. #341C22×C43semidirect
554. C43#24402direct (N × H)
588. #137D4×C43semidirect
597. AGL(1,ℤ/8)D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#5752
C2×C43×#4722
C2×C43×#4712
C43×#30062
C2×C43×#4492
C43×#28802
C43×#20522
C43×#20512
C43×#20192
C43×#20182
C43×#19082
C43×#19072
C43×#19002
C43×#18552
C43×#17852
#2440243