Finite Group Databasebeta

← C43×#25180 #24945197

Subgroups — C43×#25180 #24945197

Order 11008.

1074 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#472C211yesmaximal, characteristic, complemented
2C43×#3041C211yesmaximal, characteristic, complemented
3C2×C43×#453C211yesmaximal, characteristic, complemented
4C43×#3008C211yesmaximal, characteristic, complemented
5C43×#2946C211yesmaximal, characteristic, complemented
6C43×#2897C211yesmaximal, characteristic, complemented
7C43×#2063C211yesmaximal, characteristic, complemented
8C43×#2051C211yesmaximal, characteristic, complemented
9C43×#2037C211yesmaximal, characteristic, complemented
10C43×#2011C211yesmaximal, characteristic, complemented
11C43×#1978C211yesmaximal, characteristic, complemented
12C43×#1929C211yesmaximal, characteristic, complemented
13C43×#1887C211yesmaximal, characteristic, complemented
14C43×#1883C211yesmaximal, characteristic, complemented
15C43×#1866C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C43C2211yescharacteristic
17C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
20C22×D8×C43C2211yescharacteristic
21C22×D8×C43C2211yescharacteristic, complemented
22C2×#131×C43C2211yescharacteristic
23C43×#535C2211yescharacteristic
24C2×#127×C43C2211yescharacteristic
25C43×#520C2211yescharacteristic
26C43×#518C2211yescharacteristic, complemented
27C43×#472—24no—
28C43×#463—21no—
29C43×#463—21no—
30C43×#459—21no—
31C43×#459—21no—
32C43×#453—24no—
33C43×#449—21no—
34C43×#449—21no—
35C43×#447—21no—
36C43×#447—21no—
37C43×#442—21no—
38C43×#440—21no—
39C4×SD16×C43—21no—
40C4×D8×C43—21no—
41C2×#108×C43C2211yescharacteristic, complemented
42C2×#108×C43C2211yescharacteristic, complemented
43C43×#428C2211yescharacteristic, complemented
44C43×#424C2211yescharacteristic, complemented
45C2×#104×C43C2211yescharacteristic
46C2×#104×C43C2211yescharacteristic
47C43×#418—21no—
48C43×#418C2211yescharacteristic
49C43×#418C2211yescharacteristic
50C43×#418C2211yescharacteristic, complemented
51C43×#417—21no—
52C43×#417C2211yescharacteristic
53C43×#416—21no—
54C43×#416C2211yescharacteristic
55C43×#416C2211yescharacteristic
56C2×#102×C43—21no—
57C2×#102×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic, complemented
59C2×#100×C43C2211yescharacteristic
60C2×#100×C43C2211yescharacteristic, complemented
61C2×#100×C43C2211yescharacteristic, complemented
62C43×#408C2211yescharacteristic
63C43×#405C2211yescharacteristic, complemented
64C43×#390C2211yescharacteristic, complemented
65C43×#343C2211yescharacteristic, complemented
66C43×#339C2211yescharacteristic, complemented
67C43×#339C2211yescharacteristic, complemented
68C43×#336C2211yescharacteristic, complemented
69H(5,𝔽2)×C43—22no—
70H(5,𝔽2)×C43—22no—
71H(5,𝔽2)×C43—22no—
72H(5,𝔽2)×C43—41no—
73C2×#41×C43—21no—
74C2×#41×C43—21no—
75C2×#41×C43C2311yescharacteristic
76C2×#41×C43C2311yescharacteristic
77C22×D4×C43—21no—
78C22×D4×C43—21no—
79C22×D4×C43—41no—
80C22×D4×C43—41no—
81C22×D4×C43C2311yescharacteristic
82C22×D4×C43C2311yescharacteristic
83C22×D4×C43C2311yescharacteristic
84AGL(1,ℤ/8)×C43—22no—
85AGL(1,ℤ/8)×C43—22no—
86AGL(1,ℤ/8)×C43—22no—
87AGL(1,ℤ/8)×C43—22no—
88AGL(1,ℤ/8)×C43—41no—
89AGL(1,ℤ/8)×C43D414yescomplemented
90C2×SD16×C43—21no—
91C2×SD16×C43—21no—
92C2×SD16×C43—21no—
93C2×D8×C43—21no—
94C2×D8×C43—22no—
95C2×D8×C43—21no—
96C2×D8×C43—21no—
97C2×D8×C43—22no—
98C2×D8×C43—21no—
99C2×D8×C43—21no—
100C2×D8×C43—21no—
101C2×D8×C43—21no—
102C2×D8×C43—41no—
103C2×D8×C43—41no—
104#131×C43—22no—
105#131×C43—41no—
106C2×M16×C43—21no—
107C2×M16×C43C2311yescharacteristic
108C2×M16×C43C2311yescharacteristic
109C2×M16×C43C2311yescharacteristic
110C2×M16×C43C2311yescharacteristic
111C22×C8×C43—21no—
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114#127×C43—22no—
115#127×C43—21no—
116#127×C43—22no—
117#124×C43—21no—
118#121×C43—21no—
119#121×C43—21no—
120#120×C43—41no—
121C4×Q8×C43—21no—
122C4×D4×C43—21no—
123C4×D4×C43—21no—
124C4×D4×C43—21no—
125C4×D4×C43—21no—
126C4×D4×C43—21no—
127C4×D4×C43—41no—
128#117×C43—21no—
129#117×C43C2311yescharacteristic
130#117×C43C2311yescharacteristic
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C22⋊C4×C43—41no—
134C2×C22⋊C4×C43—41no—
135C2×C42×C43C2311yescharacteristic
136#108×C43—22no—
137#108×C43—41no—
138#107×C43—21no—
139#106×C43—21no—
140C4⋊C8×C43—21no—
141C4⋊C8×C43—21no—
142#104×C43—22no—
143#104×C43—22no—
144#103×C43—21no—
145#103×C43D411yescharacteristic, complemented
146#103×C43D411yescharacteristic, complemented
147#103×C43D411yescharacteristic, complemented
148#103×C43D411yescharacteristic, complemented
149#102×C43—21no—
150#102×C43—21no—
151#102×C43—21no—
152#102×C43—21no—
153#102×C43—21no—
154#102×C43—21no—
155#102×C43—21no—
156#102×C43—21no—
157#102×C43—21no—
158#102×C43—21no—
159#102×C43—21no—
160#102×C43D411yescharacteristic, complemented
161#102×C43D411yescharacteristic, complemented
162#102×C43D411yescharacteristic, complemented
163#102×C43D411yescharacteristic, complemented
164#100×C43—22no—
165#100×C43—22no—
166#100×C43—22no—
167C22⋊C8×C43—21no—
168C22⋊C8×C43—21no—
169#97×C43—21no—
170C4×C8×C43—21no—
171C24×C43—21no—
172C24×C43—21no—
173C24×C43—21no—
174C24×C43—41no—
175#41×C43—21no—
176#41×C43—21no—
177#41×C43—24no—
178#41×C43—21no—
179#41×C43—21no—
180#41×C43—21no—
181#41×C43—21no—
182#41×C43—42no—
183#41×C43—42no—
184#41×C43—42no—
185#41×C43C2×D412yes—
186#41×C43#4112yes—
187C2×Q8×C43C2×D411yescharacteristic
188C2×Q8×C43C2×D411yescharacteristic
189C2×D4×C43—21no—
190C2×D4×C43—21no—
191C2×D4×C43—21no—
192C2×D4×C43—21no—
193C2×D4×C43—24no—
194C2×D4×C43—21no—
195C2×D4×C43—21no—
196C2×D4×C43—21no—
197C2×D4×C43—21no—
198C2×D4×C43—21no—
199C2×D4×C43—21no—
200C2×D4×C43—21no—
201C2×D4×C43—21no—
202C2×D4×C43—21no—
203C2×D4×C43—21no—
204C2×D4×C43—21no—
205C2×D4×C43—21no—
206C2×D4×C43—21no—
207C2×D4×C43—21no—
208C2×D4×C43—44no—
209C2×D4×C43—41no—
210C2×D4×C43—41no—
211C2×D4×C43—41no—
212C2×D4×C43—41no—
213C2×D4×C43—44no—
214C2×D4×C43—42no—
215C2×D4×C43—42no—
216C2×D4×C43—44no—
217C2×D4×C43—42no—
218C2×D4×C43—82no—
219C2×D4×C43—82no—
220C2×D4×C43C2×D412yes—
221C2×D4×C43C2×D411yescharacteristic
222C2×D4×C43C2×D411yescharacteristic
223C2×D4×C43#4112yes—
224C22×C4×C43—21no—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43—21no—
228C22×C4×C43—41no—
229C22×C4×C43—41no—
230C22×C4×C43—41no—
231C22×C4×C43—41no—
232C22×C4×C43C2411yescharacteristic
233SD16×C43—24no—
234SD16×C43—42no—
235SD16×C43—42no—
236D8×C43—24no—
237D8×C43—42no—
238D8×C43—42no—
239D8×C43—42no—
240D8×C43—42no—
241D8×C43—42no—
242D8×C43—42no—
243M16×C43—21no—
244M16×C43—21no—
245M16×C43—21no—
246M16×C43—21no—
247M16×C43—21no—
248M16×C43—21no—
249M16×C43—21no—
250M16×C43—42no—
251M16×C43C2×D412yes—
252C2×C8×C43—21no—
253C2×C8×C43—21no—
254C2×C8×C43—21no—
255C2×C8×C43—21no—
256C2×C8×C43—21no—
257C2×C8×C43—21no—
258C2×C8×C43—21no—
259C2×C8×C43—21no—
260C2×C8×C43—42no—
261C2×C8×C43C2×D411yescharacteristic
262C2×C8×C43C2×D411yescharacteristic
263C2×C8×C43C2×D411yescharacteristic
264C2×C8×C43C2×D411yescharacteristic
265C4⋊C4×C43—21no—
266C4⋊C4×C43—21no—
267C4⋊C4×C43—41no—
268C4⋊C4×C43C2×D411yescharacteristic
269C4⋊C4×C43C2×D411yescharacteristic
270C4⋊C4×C43C2×D411yescharacteristic
271C4⋊C4×C43C2×D411yescharacteristic
272C22⋊C4×C43—21no—
273C22⋊C4×C43—21no—
274C22⋊C4×C43—41no—
275C22⋊C4×C43—41no—
276C22⋊C4×C43—41no—
277C22⋊C4×C43—41no—
278C22⋊C4×C43—41no—
279C22⋊C4×C43—82no—
280C42×C43—21no—
281C42×C43—21no—
282C42×C43—21no—
283C42×C43—21no—
284C42×C43—41no—
285C23×C43—21no—
286C23×C43—21no—
287C23×C43—22no—
288C23×C43—22no—
289C23×C43—44no—
290C23×C43—41no—
291C23×C43—41no—
292C23×C43—41no—
293C23×C43—41no—
294C23×C43—41no—
295C23×C43—41no—
296C23×C43—41no—
297C23×C43—81no—
298C23×C43—81no—
299C23×C43—81no—
300C23×C43—81no—
301C23×C43—81no—
302C23×C43—81no—
303C23×C43—161no—
304C23×C43—161no—
305C23×C43H(5,𝔽2)11yescharacteristic
306Q8×C43—21no—
307Q8×C43—21no—
308Q8×C43—21no—
309Q8×C43#12112yes—
310D4×C43—22no—
311D4×C43—22no—
312D4×C43—22no—
313D4×C43—21no—
314D4×C43—22no—
315D4×C43—22no—
316D4×C43—21no—
317D4×C43—21no—
318D4×C43—22no—
319D4×C43—44no—
320D4×C43—44no—
321D4×C43—41no—
322D4×C43—41no—
323D4×C43—41no—
324D4×C43—41no—
325D4×C43—41no—
326D4×C43—41no—
327D4×C43—41no—
328D4×C43—41no—
329D4×C43—41no—
330D4×C43—41no—
331D4×C43—88no—
332D4×C43—161no—
333D4×C43—161no—
334D4×C43#12112yes—
335C2×C4×C43—21no—
336C2×C4×C43—22no—
337C2×C4×C43—22no—
338C2×C4×C43—22no—
339C2×C4×C43—21no—
340C2×C4×C43—21no—
341C2×C4×C43—21no—
342C2×C4×C43—21no—
343C2×C4×C43—21no—
344C2×C4×C43—44no—
345C2×C4×C43—41no—
346C2×C4×C43—41no—
347C2×C4×C43—41no—
348C2×C4×C43—41no—
349C2×C4×C43—41no—
350C2×C4×C43—81no—
351C2×C4×C43—161no—
352C2×C4×C43—161no—
353C2×C4×C43—161no—
354C2×C4×C43C22×D411yescharacteristic
355C2×C4×C43C22×D411yescharacteristic
356C2×C4×C43C22×D411yescharacteristic
357C2×C4×C43C2×#4111yescharacteristic
358C2×C4×C43C2×#4111yescharacteristic
359C2×C4×C43H(5,𝔽2)11yescharacteristic
360C8×C43—22no—
361C8×C43—21no—
362C8×C43—21no—
363C8×C43—21no—
364C8×C43—21no—
365C8×C43—41no—
366C8×C43—41no—
367C8×C43—41no—
368#25180C4311yesmaximal, characteristic, direct product factor, Sylow
369C22×C43—21no—
370C22×C43—21no—
371C22×C43—22no—
372C22×C43—41no—
373C22×C43—41no—
374C22×C43—41no—
375C22×C43—42no—
376C22×C43—42no—
377C22×C43—41no—
378C22×C43—41no—
379C22×C43—82no—
380C22×C43—82no—
381C22×C43—82no—
382C22×C43—81no—
383C22×C43—81no—
384C22×C43—81no—
385C22×C43—81no—
386C22×C43—81no—
387C22×C43—81no—
388C22×C43—81no—
389C22×C43—161no—
390C22×C43—161no—
391C22×C43—161no—
392C22×C43—164no—
393C22×C43#53811yescharacteristic
394C22×C43D4211yescharacteristic
395C22×C43#54611yescharacteristic
396C4×C43—22no—
397C4×C43—42no—
398C4×C43—41no—
399C4×C43—41no—
400C4×C43—41no—
401C4×C43—41no—
402C4×C43—41no—
403C4×C43—81no—
404C4×C43C2×#12111yescharacteristic
405C4×C43#52511yescharacteristic
406C4×C43D4211yescharacteristic
407C4×C43#54611yescharacteristic
408C2×#472C2×C4311yescharacteristic, complemented
409#3041C2×C4311yescharacteristic, complemented
410C2×#453C2×C4311yescharacteristic, complemented
411#3008C2×C4311yescharacteristic, complemented
412#2946C2×C4311yescharacteristic, complemented
413#2897C2×C4311yescharacteristic, complemented
414#2063C2×C4311yescharacteristic, complemented
415#2051C2×C4311yescharacteristic, complemented
416#2037C2×C4311yescharacteristic, complemented
417#2011C2×C4311yescharacteristic, complemented
418#1978C2×C4311yescharacteristic, complemented
419#1929C2×C4311yescharacteristic, complemented
420#1887C2×C4311yescharacteristic, complemented
421#1883C2×C4311yescharacteristic, complemented
422#1866C2×C4311yescharacteristic, complemented
423C2×C43—21no—
424C2×C43—21no—
425C2×C43—42no—
426C2×C43—81no—
427C2×C43—82no—
428C2×C43—82no—
429C2×C43—161no—
430C2×C43#242411yescharacteristic
431C2×C43#328811yescharacteristic
432C2×C43#329211yescharacteristic
433C2×H(5,𝔽2)C22×C4311yescharacteristic
434C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
435C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
436C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
437C22×D8C22×C4311yescharacteristic
438C22×D8C22×C4311yescharacteristic, complemented
439C2×#131C22×C4311yescharacteristic
440#535C22×C4311yescharacteristic
441C2×#127C22×C4311yescharacteristic
442#520C22×C4311yescharacteristic
443#518C22×C4311yescharacteristic, complemented
444#472—24no—
445#463—21no—
446#463—21no—
447#459—21no—
448#459—21no—
449#453—24no—
450#449—21no—
451#449—21no—
452#447—21no—
453#447—21no—
454#442—21no—
455#440—21no—
456C4×SD16—21no—
457C4×D8—21no—
458C2×#108C22×C4311yescharacteristic, complemented
459C2×#108C22×C4311yescharacteristic, complemented
460#428C22×C4311yescharacteristic, complemented
461#424C22×C4311yescharacteristic, complemented
462C2×#104C22×C4311yescharacteristic
463C2×#104C22×C4311yescharacteristic
464#418—21no—
465#418C22×C4311yescharacteristic
466#418C22×C4311yescharacteristic
467#418C22×C4311yescharacteristic, complemented
468#417—21no—
469#417C22×C4311yescharacteristic
470#416—21no—
471#416C22×C4311yescharacteristic
472#416C22×C4311yescharacteristic
473C2×#102—21no—
474C2×#102C22×C4311yescharacteristic
475C2×#102C22×C4311yescharacteristic, complemented
476C2×#100C22×C4311yescharacteristic
477C2×#100C22×C4311yescharacteristic, complemented
478C2×#100C22×C4311yescharacteristic, complemented
479#408C22×C4311yescharacteristic
480#405C22×C4311yescharacteristic, complemented
481#390C22×C4311yescharacteristic, complemented
482#343C22×C4311yescharacteristic, complemented
483#339C22×C4311yescharacteristic, complemented
484#339C22×C4311yescharacteristic, complemented
485#336C22×C4311yescharacteristic, complemented
486C43#2518011yescharacteristic, direct product factor, Sylow
487H(5,𝔽2)—22no—
488H(5,𝔽2)—22no—
489H(5,𝔽2)—22no—
490H(5,𝔽2)—41no—
491C2×#41—21no—
492C2×#41—21no—
493C2×#41C23×C4311yescharacteristic
494C2×#41C23×C4311yescharacteristic
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—41no—
498C22×D4—41no—
499C22×D4C23×C4311yescharacteristic
500C22×D4C23×C4311yescharacteristic
501C22×D4C23×C4311yescharacteristic
502AGL(1,ℤ/8)—22no—
503AGL(1,ℤ/8)—22no—
504AGL(1,ℤ/8)—22no—
505AGL(1,ℤ/8)—22no—
506AGL(1,ℤ/8)—41no—
507AGL(1,ℤ/8)D4×C4314yescomplemented
508C2×SD16—21no—
509C2×SD16—21no—
510C2×SD16—21no—
511C2×D8—21no—
512C2×D8—22no—
513C2×D8—21no—
514C2×D8—21no—
515C2×D8—22no—
516C2×D8—21no—
517C2×D8—21no—
518C2×D8—21no—
519C2×D8—21no—
520C2×D8—41no—
521C2×D8—41no—
522#131—22no—
523#131—41no—
524C2×M16—21no—
525C2×M16C23×C4311yescharacteristic
526C2×M16C23×C4311yescharacteristic
527C2×M16C23×C4311yescharacteristic
528C2×M16C23×C4311yescharacteristic
529C22×C8—21no—
530C22×C8C23×C4311yescharacteristic
531C22×C8C23×C4311yescharacteristic
532#127—22no—
533#127—21no—
534#127—22no—
535#124—21no—
536#121—21no—
537#121—21no—
538#120—41no—
539C4×Q8—21no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—41no—
546#117—21no—
547#117C23×C4311yescharacteristic
548#117C23×C4311yescharacteristic
549C2×C4⋊C4—21no—
550C2×C4⋊C4C23×C4311yescharacteristic
551C2×C22⋊C4—41no—
552C2×C22⋊C4—41no—
553C2×C42C23×C4311yescharacteristic
554#108—22no—
555#108—41no—
556#107—21no—
557#106—21no—
558C4⋊C8—21no—
559C4⋊C8—21no—
560#104—22no—
561#104—22no—
562#103—21no—
563#103D4×C4311yescharacteristic, complemented
564#103D4×C4311yescharacteristic, complemented
565#103D4×C4311yescharacteristic, complemented
566#103D4×C4311yescharacteristic, complemented
567#102—21no—
568#102—21no—
569#102—21no—
570#102—21no—
571#102—21no—
572#102—21no—
573#102—21no—
574#102—21no—
575#102—21no—
576#102—21no—
577#102—21no—
578#102D4×C4311yescharacteristic, complemented
579#102D4×C4311yescharacteristic, complemented
580#102D4×C4311yescharacteristic, complemented
581#102D4×C4311yescharacteristic, complemented
582#100—22no—
583#100—22no—
584#100—22no—
585C22⋊C8—21no—
586C22⋊C8—21no—
587#97—21no—
588C4×C8—21no—
589C24—21no—
590C24—21no—
591C24—21no—
592C24—41no—
593#41—21no—
594#41—21no—
595#41—24no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—42no—
601#41—42no—
602#41—42no—
603#41C2×D4×C4312yes—
604#41#41×C4312yes—
605C2×Q8C2×D4×C4311yescharacteristic
606C2×Q8C2×D4×C4311yescharacteristic
607C2×D4—21no—
608C2×D4—24no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—42no—
627C2×D4—41no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—41no—
631C2×D4—42no—
632C2×D4—44no—
633C2×D4—44no—
634C2×D4—42no—
635C2×D4—44no—
636C2×D4—82no—
637C2×D4—82no—
638C2×D4C2×D4×C4312yes—
639C2×D4C2×D4×C4311yescharacteristic
640C2×D4C2×D4×C4311yescharacteristic
641C2×D4#41×C4312yes—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—41no—
647C22×C4—41no—
648C22×C4—41no—
649C22×C4—41no—
650C22×C4C24×C4311yescharacteristic
651SD16—24no—
652SD16—42no—
653SD16—42no—
654D8—24no—
655D8—42no—
656D8—42no—
657D8—42no—
658D8—42no—
659D8—42no—
660D8—42no—
661M16—21no—
662M16—21no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—21no—
668M16—42no—
669M16C2×D4×C4312yes—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—42no—
679C2×C8C2×D4×C4311yescharacteristic
680C2×C8C2×D4×C4311yescharacteristic
681C2×C8C2×D4×C4311yescharacteristic
682C2×C8C2×D4×C4311yescharacteristic
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—41no—
686C4⋊C4C2×D4×C4311yescharacteristic
687C4⋊C4C2×D4×C4311yescharacteristic
688C4⋊C4C2×D4×C4311yescharacteristic
689C4⋊C4C2×D4×C4311yescharacteristic
690C22⋊C4—21no—
691C22⋊C4—21no—
692C22⋊C4—41no—
693C22⋊C4—41no—
694C22⋊C4—41no—
695C22⋊C4—41no—
696C22⋊C4—41no—
697C22⋊C4—82no—
698C42—21no—
699C42—21no—
700C42—21no—
701C42—21no—
702C42—41no—
703C23—21no—
704C23—21no—
705C23—22no—
706C23—22no—
707C23—44no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—81no—
716C23—81no—
717C23—81no—
718C23—81no—
719C23—81no—
720C23—81no—
721C23—161no—
722C23—161no—
723C23H(5,𝔽2)×C4311yescharacteristic
724Q8—21no—
725Q8—21no—
726Q8—21no—
727Q8#121×C4312yes—
728D4—22no—
729D4—22no—
730D4—22no—
731D4—21no—
732D4—22no—
733D4—22no—
734D4—21no—
735D4—21no—
736D4—22no—
737D4—44no—
738D4—44no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—88no—
750D4—161no—
751D4—161no—
752D4#121×C4312yes—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—44no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—81no—
769C2×C4—161no—
770C2×C4—161no—
771C2×C4—161no—
772C2×C4C22×D4×C4311yescharacteristic
773C2×C4C22×D4×C4311yescharacteristic
774C2×C4C22×D4×C4311yescharacteristic
775C2×C4C2×#41×C4311yescharacteristic
776C2×C4C2×#41×C4311yescharacteristic
777C2×C4H(5,𝔽2)×C4311yescharacteristic
778C8—22no—
779C8—21no—
780C8—21no—
781C8—21no—
782C8—21no—
783C8—41no—
784C8—41no—
785C8—41no—
786C22—21no—
787C22—21no—
788C22—22no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—42no—
793C22—42no—
794C22—41no—
795C22—41no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—161no—
807C22—161no—
808C22—161no—
809C22—164no—
810C22C43×#53811yescharacteristic
811C22D42×C4311yescharacteristic
812C22C43×#54611yescharacteristic
813C4—22no—
814C4—42no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4—81no—
821C4C2×#121×C4311yescharacteristic
822C4C43×#52511yescharacteristic
823C4D42×C4311yescharacteristic
824C4C43×#54611yescharacteristic
825C2—21no—
826C2—21no—
827C2—42no—
828C2—81no—
829C2—82no—
830C2—82no—
831C2—161no—
832C2C43×#242411yescharacteristic
833C2C43×#328811yescharacteristic
834C2C43×#329211yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC22×C4C24×C43
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C22×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#472C2semidirect
2. C43×#3041C2semidirect
3. C2×C43×#453C2semidirect
4. C43×#3008C2semidirect
5. C43×#2946C2semidirect
6. C43×#2897C2semidirect
7. C43×#2063C2semidirect
8. C43×#2051C2semidirect
9. C43×#2037C2semidirect
10. C43×#2011C2semidirect
11. C43×#1978C2semidirect
12. C43×#1929C2semidirect
13. C43×#1887C2semidirect
14. C43×#1883C2semidirect
15. C43×#1866C2semidirect
21. C22×D8×C43C22semidirect
26. C43×#518C22semidirect
41. C2×#108×C43C22semidirect
42. C2×#108×C43C22semidirect
43. C43×#428C22semidirect
44. C43×#424C22semidirect
50. C43×#418C22semidirect
58. C2×#102×C43C22semidirect
60. C2×#100×C43C22semidirect
61. C2×#100×C43C22semidirect
63. C43×#405C22semidirect
64. C43×#390C22semidirect
65. C43×#343C22semidirect
66. C43×#339C22semidirect
67. C43×#339C22semidirect
68. C43×#336C22semidirect
89. AGL(1,ℤ/8)×C43D4semidirect
145. #103×C43D4semidirect
146. #103×C43D4semidirect
147. #103×C43D4semidirect
148. #103×C43D4semidirect
160. #102×C43D4semidirect
161. #102×C43D4semidirect
162. #102×C43D4semidirect
163. #102×C43D4semidirect
368. #25180C43direct (N × H)
408. C2×#472C2×C43semidirect
409. #3041C2×C43semidirect
410. C2×#453C2×C43semidirect
411. #3008C2×C43semidirect
412. #2946C2×C43semidirect
413. #2897C2×C43semidirect
414. #2063C2×C43semidirect
415. #2051C2×C43semidirect
416. #2037C2×C43semidirect
417. #2011C2×C43semidirect
418. #1978C2×C43semidirect
419. #1929C2×C43semidirect
420. #1887C2×C43semidirect
421. #1883C2×C43semidirect
422. #1866C2×C43semidirect
438. C22×D8C22×C43semidirect
443. #518C22×C43semidirect
458. C2×#108C22×C43semidirect
459. C2×#108C22×C43semidirect
460. #428C22×C43semidirect
461. #424C22×C43semidirect
467. #418C22×C43semidirect
475. C2×#102C22×C43semidirect
477. C2×#100C22×C43semidirect
478. C2×#100C22×C43semidirect
480. #405C22×C43semidirect
481. #390C22×C43semidirect
482. #343C22×C43semidirect
483. #339C22×C43semidirect
484. #339C22×C43semidirect
485. #336C22×C43semidirect
486. C43#25180direct (N × H)
507. AGL(1,ℤ/8)D4×C43semidirect
563. #103D4×C43semidirect
564. #103D4×C43semidirect
565. #103D4×C43semidirect
566. #103D4×C43semidirect
578. #102D4×C43semidirect
579. #102D4×C43semidirect
580. #102D4×C43semidirect
581. #102D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4722
C43×#30412
C2×C43×#4532
C43×#30082
C43×#29462
C43×#28972
C43×#20632
C43×#20512
C43×#20372
C43×#20112
C43×#19782
C43×#19292
C43×#18872
C43×#18832
C43×#18662
#2518043