Finite Group Databasebeta

← C43×#24458 #24944475

Subgroups — C43×#24458 #24944475

Order 11008.

1328 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#577C211yesmaximal, characteristic
2C2×C43×#473C211yesmaximal, characteristic, complemented
3C43×#3046C211yesmaximal, characteristic, complemented
4C2×C43×#455C211yesmaximal, characteristic, complemented
5C43×#3011C211yesmaximal, characteristic, complemented
6C43×#2897C211yesmaximal, characteristic, complemented
7C43×#2051C211yesmaximal, characteristic, complemented
8C43×#2046C211yesmaximal, characteristic, complemented
9C43×#2015C211yesmaximal, characteristic, complemented
10C43×#2003C211yesmaximal, characteristic, complemented
11C43×#1908C211yesmaximal, characteristic, complemented
12C43×#1882C211yesmaximal, characteristic, complemented
13C43×#1876C211yesmaximal, characteristic, complemented
14C43×#1866C211yesmaximal, characteristic, complemented
15C43×#1793C211yesmaximal, characteristic, complemented
16C2×2−1+4×C43C2211yescharacteristic
17C2×H(5,𝔽2)×C43C2211yescharacteristic
18C43×#577—24no—
19C43×#577—24no—
20C2×#137×C43—21no—
21C2×#137×C43C2211yescharacteristic
22C2×#137×C43C2211yescharacteristic
23C2×#137×C43C2211yescharacteristic
24C2×AGL(1,ℤ/8)×C43—21no—
25C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
26C2×#135×C43—21no—
27C2×#135×C43C2211yescharacteristic
28C22×Q16×C43C2211yescharacteristic, complemented
29C22×SD16×C43—21no—
30C22×SD16×C43C2211yescharacteristic
31C2×#131×C43C2211yescharacteristic
32C2×#131×C43C2211yescharacteristic
33C43×#536C2211yescharacteristic, complemented
34C2×#124×C43C2211yescharacteristic
35C43×#520C2211yescharacteristic
36C43×#473—24no—
37C43×#464—21no—
38C43×#463—21no—
39C43×#462—21no—
40C43×#461—21no—
41C43×#455—24no—
42C43×#452—21no—
43C43×#452—21no—
44C43×#451—21no—
45C43×#451—21no—
46C2×#108×C43C2211yescharacteristic, complemented
47C43×#424C2211yescharacteristic, complemented
48C2×#104×C43C2211yescharacteristic
49C2×#104×C43C2211yescharacteristic
50C2×#104×C43C2211yescharacteristic, complemented
51C43×#419C2211yescharacteristic, complemented
52C43×#418—21no—
53C43×#418C2211yescharacteristic
54C43×#417—21no—
55C43×#417C2211yescharacteristic
56C43×#417C2211yescharacteristic, complemented
57C43×#416—21no—
58C43×#416C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic, complemented
60C2×#102×C43—21no—
61C2×#102×C43C2211yescharacteristic
62C2×#101×C43C2211yescharacteristic, complemented
63C2×#101×C43C2211yescharacteristic, complemented
64C2×#100×C43C2211yescharacteristic
65C43×#408C2211yescharacteristic, complemented
66C43×#391C2211yescharacteristic, complemented
67C43×#343C2211yescharacteristic, complemented
68C43×#341C2211yescharacteristic, complemented
69C43×#339C2211yescharacteristic, complemented
70C43×#336C2211yescharacteristic, complemented
712−1+4×C43—22no—
722−1+4×C43—22no—
732−1+4×C43—22no—
742−1+4×C43—41no—
75H(5,𝔽2)×C43—22no—
76H(5,𝔽2)×C43—22no—
77H(5,𝔽2)×C43—41no—
78H(5,𝔽2)×C43D414yes—
79C2×#41×C43—21no—
80C2×#41×C43—21no—
81C2×#41×C43—21no—
82C2×#41×C43—21no—
83C2×#41×C43—41no—
84C2×#41×C43C2311yescharacteristic
85C2×#41×C43C2311yescharacteristic
86C2×#41×C43C2311yescharacteristic
87C22×Q8×C43—21no—
88C22×Q8×C43—21no—
89C22×Q8×C43C2311yescharacteristic
90C22×Q8×C43C2311yescharacteristic
91C22×D4×C43—21no—
92C22×D4×C43—21no—
93C22×D4×C43—41no—
94C22×D4×C43C2311yescharacteristic
95#137×C43—28no—
96#137×C43—22no—
97#137×C43—22no—
98#137×C43—22no—
99#137×C43—22no—
100#137×C43—22no—
101#137×C43D414yes—
102AGL(1,ℤ/8)×C43—28no—
103AGL(1,ℤ/8)×C43—22no—
104AGL(1,ℤ/8)×C43—22no—
105#135×C43—28no—
106#135×C43—22no—
107#135×C43—22no—
108C2×Q16×C43—21no—
109C2×Q16×C43—22no—
110C2×Q16×C43—21no—
111C2×Q16×C43—21no—
112C2×Q16×C43—21no—
113C2×Q16×C43—21no—
114C2×Q16×C43—41no—
115C2×Q16×C43D411yescharacteristic
116C2×SD16×C43—28no—
117C2×SD16×C43—21no—
118C2×SD16×C43—22no—
119C2×SD16×C43—21no—
120C2×SD16×C43—22no—
121C2×SD16×C43—21no—
122C2×SD16×C43—21no—
123C2×SD16×C43—21no—
124C2×SD16×C43—21no—
125C2×SD16×C43D411yescharacteristic
126C2×SD16×C43D411yescharacteristic
127C2×D8×C43—21no—
128C2×D8×C43D411yescharacteristic
129#131×C43—22no—
130#131×C43—22no—
131#131×C43—22no—
132#131×C43—41no—
133C2×M16×C43—21no—
134C2×M16×C43—21no—
135C2×M16×C43C2311yescharacteristic
136C2×M16×C43C2311yescharacteristic
137C2×M16×C43C2311yescharacteristic
138C2×M16×C43C2311yescharacteristic
139C22×C8×C43—21no—
140C22×C8×C43—21no—
141C22×C8×C43C2311yescharacteristic
142C22×C8×C43C2311yescharacteristic
143C4⋊Q8×C43—21no—
144#124×C43—22no—
145#124×C43—21no—
146#124×C43—41no—
147#123×C43—41no—
148C22⋊Q8×C43—21no—
149C22⋊Q8×C43—21no—
150C4×Q8×C43—21no—
151C4×D4×C43—21no—
152C4×D4×C43—41no—
153#117×C43—21no—
154#117×C43C2311yescharacteristic
155C2×C4⋊C4×C43—21no—
156C2×C4⋊C4×C43C2311yescharacteristic
157C2×C22⋊C4×C43—41no—
158C2×C42×C43C2311yescharacteristic
159#108×C43—22no—
160C4⋊C8×C43—21no—
161C4⋊C8×C43—21no—
162#104×C43—22no—
163#104×C43—22no—
164#104×C43—41no—
165#103×C43—21no—
166#103×C43—21no—
167#103×C43—21no—
168#103×C43—21no—
169#103×C43—21no—
170#103×C43—21no—
171#103×C43D411yescharacteristic
172#103×C43D411yescharacteristic
173#102×C43—21no—
174#102×C43—21no—
175#102×C43—21no—
176#102×C43—21no—
177#102×C43—21no—
178#102×C43—21no—
179#102×C43D411yescharacteristic
180#102×C43D411yescharacteristic
181#101×C43—22no—
182#101×C43—22no—
183#100×C43—22no—
184C22⋊C8×C43—21no—
185C22⋊C8×C43—21no—
186#95×C43—41no—
187C24×C43—21no—
188C24×C43—41no—
189#41×C43—21no—
190#41×C43—21no—
191#41×C43—21no—
192#41×C43—21no—
193#41×C43—24no—
194#41×C43—24no—
195#41×C43—24no—
196#41×C43—21no—
197#41×C43—21no—
198#41×C43—21no—
199#41×C43—21no—
200#41×C43—42no—
201#41×C43—44no—
202#41×C43—42no—
203#41×C43—42no—
204#41×C43—42no—
205#41×C43—44no—
206#41×C43—42no—
207#41×C43C2×D412yes—
208#41×C43C2×D412yes—
209#41×C43C2×D412yes—
210#41×C43#4112yes—
211C2×Q8×C43—21no—
212C2×Q8×C43—24no—
213C2×Q8×C43—21no—
214C2×Q8×C43—21no—
215C2×Q8×C43—21no—
216C2×Q8×C43—21no—
217C2×Q8×C43—21no—
218C2×Q8×C43—21no—
219C2×Q8×C43—21no—
220C2×Q8×C43—21no—
221C2×Q8×C43—21no—
222C2×Q8×C43—21no—
223C2×Q8×C43—41no—
224C2×Q8×C43—42no—
225C2×Q8×C43—42no—
226C2×Q8×C43—42no—
227C2×Q8×C43C2×D412yes—
228C2×Q8×C43C2×D411yescharacteristic
229C2×Q8×C43C2×D411yescharacteristic
230C2×Q8×C43C2×D411yescharacteristic
231C2×D4×C43—21no—
232C2×D4×C43—21no—
233C2×D4×C43—21no—
234C2×D4×C43—21no—
235C2×D4×C43—24no—
236C2×D4×C43—24no—
237C2×D4×C43—21no—
238C2×D4×C43—21no—
239C2×D4×C43—21no—
240C2×D4×C43—21no—
241C2×D4×C43—41no—
242C2×D4×C43—41no—
243C2×D4×C43—41no—
244C2×D4×C43—44no—
245C2×D4×C43—42no—
246C2×D4×C43—42no—
247C2×D4×C43—44no—
248C2×D4×C43C2×D412yes—
249C2×D4×C43C2×D411yescharacteristic
250C2×D4×C43C2×D411yescharacteristic
251C2×D4×C43C2×D411yescharacteristic
252C22×C4×C43—21no—
253C22×C4×C43—21no—
254C22×C4×C43—21no—
255C22×C4×C43—21no—
256C22×C4×C43—21no—
257C22×C4×C43—21no—
258C22×C4×C43—21no—
259C22×C4×C43—41no—
260C22×C4×C43—41no—
261C22×C4×C43—41no—
262C22×C4×C43—41no—
263C22×C4×C43C2411yescharacteristic
264Q16×C43—24no—
265Q16×C43—22no—
266Q16×C43—42no—
267Q16×C43—42no—
268Q16×C43—42no—
269Q16×C43—42no—
270SD16×C43—24no—
271SD16×C43—24no—
272SD16×C43—24no—
273SD16×C43—22no—
274SD16×C43—22no—
275SD16×C43—24no—
276SD16×C43—42no—
277SD16×C43—42no—
278D8×C43—24no—
279D8×C43—22no—
280M16×C43—24no—
281M16×C43—21no—
282M16×C43—21no—
283M16×C43—21no—
284M16×C43—21no—
285M16×C43—21no—
286M16×C43—21no—
287M16×C43—21no—
288M16×C43—42no—
289M16×C43C2×D412yes—
290C2×C8×C43—24no—
291C2×C8×C43—21no—
292C2×C8×C43—21no—
293C2×C8×C43—21no—
294C2×C8×C43—21no—
295C2×C8×C43—21no—
296C2×C8×C43—21no—
297C2×C8×C43—21no—
298C2×C8×C43—21no—
299C2×C8×C43—42no—
300C2×C8×C43C2×D411yescharacteristic
301C2×C8×C43C2×D411yescharacteristic
302C2×C8×C43C2×D411yescharacteristic
303C2×C8×C43C2×D411yescharacteristic
304C4⋊C4×C43—21no—
305C4⋊C4×C43—21no—
306C4⋊C4×C43—41no—
307C4⋊C4×C43—41no—
308C4⋊C4×C43—41no—
309C4⋊C4×C43C2×D411yescharacteristic
310C4⋊C4×C43C2×D411yescharacteristic
311C22⋊C4×C43—21no—
312C22⋊C4×C43—41no—
313C22⋊C4×C43—41no—
314C22⋊C4×C43—41no—
315C22⋊C4×C43—44no—
316C42×C43—21no—
317C42×C43—21no—
318C42×C43—21no—
319C42×C43—41no—
320C23×C43—21no—
321C23×C43—21no—
322C23×C43—21no—
323C23×C43—22no—
324C23×C43—44no—
325C23×C43—41no—
326C23×C43—41no—
327C23×C43—81no—
328C23×C43—81no—
329C23×C43—161no—
330C23×C43—161no—
331C23×C43H(5,𝔽2)11yescharacteristic
332Q8×C43—21no—
333Q8×C43—21no—
334Q8×C43—22no—
335Q8×C43—21no—
336Q8×C43—22no—
337Q8×C43—21no—
338Q8×C43—44no—
339Q8×C43—41no—
340Q8×C43—41no—
341Q8×C43—41no—
342Q8×C43—41no—
343Q8×C43—41no—
344Q8×C43—41no—
345Q8×C43#12012yes—
346Q8×C43#12112yes—
347D4×C43—22no—
348D4×C43—22no—
349D4×C43—22no—
350D4×C43—22no—
351D4×C43—21no—
352D4×C43—22no—
353D4×C43—22no—
354D4×C43—21no—
355D4×C43—21no—
356D4×C43—21no—
357D4×C43—44no—
358D4×C43—44no—
359D4×C43—44no—
360D4×C43—41no—
361D4×C43—41no—
362D4×C43—41no—
363D4×C43—41no—
364D4×C43#12012yes—
365D4×C43#12112yes—
366C2×C4×C43—21no—
367C2×C4×C43—21no—
368C2×C4×C43—22no—
369C2×C4×C43—22no—
370C2×C4×C43—22no—
371C2×C4×C43—22no—
372C2×C4×C43—21no—
373C2×C4×C43—21no—
374C2×C4×C43—21no—
375C2×C4×C43—22no—
376C2×C4×C43—44no—
377C2×C4×C43—44no—
378C2×C4×C43—44no—
379C2×C4×C43—41no—
380C2×C4×C43—41no—
381C2×C4×C43—41no—
382C2×C4×C43—41no—
383C2×C4×C43—41no—
384C2×C4×C43—41no—
385C2×C4×C43—41no—
386C2×C4×C43—41no—
387C2×C4×C43—41no—
388C2×C4×C43—41no—
389C2×C4×C43—41no—
390C2×C4×C43—81no—
391C2×C4×C43—161no—
392C2×C4×C43C22×D411yescharacteristic
393C2×C4×C43C22×D411yescharacteristic
394C2×C4×C43C22×D411yescharacteristic
395C2×C4×C43C22×D411yescharacteristic
396C2×C4×C43C2×#4111yescharacteristic
397C2×C4×C43H(5,𝔽2)11yescharacteristic
398C8×C43—21no—
399C8×C43—22no—
400C8×C43—21no—
401C8×C43—21no—
402C8×C43—21no—
403C8×C43—41no—
404C8×C43—41no—
405C8×C43—41no—
406#24458C4311yesmaximal, characteristic, direct product factor, Sylow
407C22×C43—21no—
408C22×C43—21no—
409C22×C43—22no—
410C22×C43—22no—
411C22×C43—41no—
412C22×C43—41no—
413C22×C43—41no—
414C22×C43—41no—
415C22×C43—42no—
416C22×C43—41no—
417C22×C43—41no—
418C22×C43—41no—
419C22×C43—82no—
420C22×C43—81no—
421C22×C43—81no—
422C22×C43—161no—
423C22×C43—164no—
424C22×C43#53411yescharacteristic
425C22×C43D4211yescharacteristic
426C22×C43#54611yescharacteristic
427C4×C43—22no—
428C4×C43—22no—
429C4×C43—41no—
430C4×C43—42no—
431C4×C43—41no—
432C4×C43—41no—
433C4×C43—81no—
434C4×C43—81no—
435C4×C43—81no—
436C4×C43C2×#12011yescharacteristic
437C4×C43C2×#12111yescharacteristic
438C4×C43D4211yescharacteristic
439C4×C43#54611yescharacteristic
440C2×#577C2×C4311yescharacteristic
441C2×#473C2×C4311yescharacteristic, complemented
442#3046C2×C4311yescharacteristic, complemented
443C2×#455C2×C4311yescharacteristic, complemented
444#3011C2×C4311yescharacteristic, complemented
445#2897C2×C4311yescharacteristic, complemented
446#2051C2×C4311yescharacteristic, complemented
447#2046C2×C4311yescharacteristic, complemented
448#2015C2×C4311yescharacteristic, complemented
449#2003C2×C4311yescharacteristic, complemented
450#1908C2×C4311yescharacteristic, complemented
451#1882C2×C4311yescharacteristic, complemented
452#1876C2×C4311yescharacteristic, complemented
453#1866C2×C4311yescharacteristic, complemented
454#1793C2×C4311yescharacteristic, complemented
455C2×C43—21no—
456C2×C43—21no—
457C2×C43—42no—
458C2×C43—42no—
459C2×C43—81no—
460C2×C43—82no—
461C2×C43#241011yescharacteristic
462C2×C43#328911yescharacteristic
463C2×C43#329011yescharacteristic
464C2×2−1+4C22×C4311yescharacteristic
465C2×H(5,𝔽2)C22×C4311yescharacteristic
466#577—24no—
467#577—24no—
468C2×#137—21no—
469C2×#137C22×C4311yescharacteristic
470C2×#137C22×C4311yescharacteristic
471C2×#137C22×C4311yescharacteristic
472C2×AGL(1,ℤ/8)—21no—
473C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
474C2×#135—21no—
475C2×#135C22×C4311yescharacteristic
476C22×Q16C22×C4311yescharacteristic, complemented
477C22×SD16—21no—
478C22×SD16C22×C4311yescharacteristic
479C2×#131C22×C4311yescharacteristic
480C2×#131C22×C4311yescharacteristic
481#536C22×C4311yescharacteristic, complemented
482C2×#124C22×C4311yescharacteristic
483#520C22×C4311yescharacteristic
484#473—24no—
485#464—21no—
486#463—21no—
487#462—21no—
488#461—21no—
489#455—24no—
490#452—21no—
491#452—21no—
492#451—21no—
493#451—21no—
494C2×#108C22×C4311yescharacteristic, complemented
495#424C22×C4311yescharacteristic, complemented
496C2×#104C22×C4311yescharacteristic
497C2×#104C22×C4311yescharacteristic
498C2×#104C22×C4311yescharacteristic, complemented
499#419C22×C4311yescharacteristic, complemented
500#418—21no—
501#418C22×C4311yescharacteristic
502#417—21no—
503#417C22×C4311yescharacteristic
504#417C22×C4311yescharacteristic, complemented
505#416—21no—
506#416C22×C4311yescharacteristic
507C2×#103C22×C4311yescharacteristic, complemented
508C2×#102—21no—
509C2×#102C22×C4311yescharacteristic
510C2×#101C22×C4311yescharacteristic, complemented
511C2×#101C22×C4311yescharacteristic, complemented
512C2×#100C22×C4311yescharacteristic
513#408C22×C4311yescharacteristic, complemented
514#391C22×C4311yescharacteristic, complemented
515#343C22×C4311yescharacteristic, complemented
516#341C22×C4311yescharacteristic, complemented
517#339C22×C4311yescharacteristic, complemented
518#336C22×C4311yescharacteristic, complemented
519C43#2445811yescharacteristic, direct product factor, Sylow
5202−1+4—22no—
5212−1+4—22no—
5222−1+4—22no—
5232−1+4—41no—
524H(5,𝔽2)—22no—
525H(5,𝔽2)—22no—
526H(5,𝔽2)—41no—
527H(5,𝔽2)D4×C4314yes—
528C2×#41—21no—
529C2×#41—21no—
530C2×#41—21no—
531C2×#41—21no—
532C2×#41—41no—
533C2×#41C23×C4311yescharacteristic
534C2×#41C23×C4311yescharacteristic
535C2×#41C23×C4311yescharacteristic
536C22×Q8—21no—
537C22×Q8—21no—
538C22×Q8C23×C4311yescharacteristic
539C22×Q8C23×C4311yescharacteristic
540C22×D4—21no—
541C22×D4—21no—
542C22×D4—41no—
543C22×D4C23×C4311yescharacteristic
544#137—28no—
545#137—22no—
546#137—22no—
547#137—22no—
548#137—22no—
549#137—22no—
550#137D4×C4314yes—
551AGL(1,ℤ/8)—28no—
552AGL(1,ℤ/8)—22no—
553AGL(1,ℤ/8)—22no—
554#135—28no—
555#135—22no—
556#135—22no—
557C2×Q16—21no—
558C2×Q16—22no—
559C2×Q16—21no—
560C2×Q16—21no—
561C2×Q16—21no—
562C2×Q16—21no—
563C2×Q16—41no—
564C2×Q16D4×C4311yescharacteristic
565C2×SD16—28no—
566C2×SD16—21no—
567C2×SD16—22no—
568C2×SD16—21no—
569C2×SD16—22no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16—21no—
573C2×SD16—21no—
574C2×SD16D4×C4311yescharacteristic
575C2×SD16D4×C4311yescharacteristic
576C2×D8—21no—
577C2×D8D4×C4311yescharacteristic
578#131—22no—
579#131—22no—
580#131—22no—
581#131—41no—
582C2×M16—21no—
583C2×M16—21no—
584C2×M16C23×C4311yescharacteristic
585C2×M16C23×C4311yescharacteristic
586C2×M16C23×C4311yescharacteristic
587C2×M16C23×C4311yescharacteristic
588C22×C8—21no—
589C22×C8—21no—
590C22×C8C23×C4311yescharacteristic
591C22×C8C23×C4311yescharacteristic
592C4⋊Q8—21no—
593#124—22no—
594#124—21no—
595#124—41no—
596#123—41no—
597C22⋊Q8—21no—
598C22⋊Q8—21no—
599C4×Q8—21no—
600C4×D4—21no—
601C4×D4—41no—
602#117—21no—
603#117C23×C4311yescharacteristic
604C2×C4⋊C4—21no—
605C2×C4⋊C4C23×C4311yescharacteristic
606C2×C22⋊C4—41no—
607C2×C42C23×C4311yescharacteristic
608#108—22no—
609C4⋊C8—21no—
610C4⋊C8—21no—
611#104—22no—
612#104—22no—
613#104—41no—
614#103—21no—
615#103—21no—
616#103—21no—
617#103—21no—
618#103—21no—
619#103—21no—
620#103D4×C4311yescharacteristic
621#103D4×C4311yescharacteristic
622#102—21no—
623#102—21no—
624#102—21no—
625#102—21no—
626#102—21no—
627#102—21no—
628#102D4×C4311yescharacteristic
629#102D4×C4311yescharacteristic
630#101—22no—
631#101—22no—
632#100—22no—
633C22⋊C8—21no—
634C22⋊C8—21no—
635#95—41no—
636C24—21no—
637C24—41no—
638#41—21no—
639#41—21no—
640#41—21no—
641#41—21no—
642#41—24no—
643#41—24no—
644#41—24no—
645#41—21no—
646#41—21no—
647#41—21no—
648#41—21no—
649#41—42no—
650#41—44no—
651#41—42no—
652#41—42no—
653#41—42no—
654#41—44no—
655#41—42no—
656#41C2×D4×C4312yes—
657#41C2×D4×C4312yes—
658#41C2×D4×C4312yes—
659#41#41×C4312yes—
660C2×Q8—21no—
661C2×Q8—24no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8—41no—
673C2×Q8—42no—
674C2×Q8—42no—
675C2×Q8—42no—
676C2×Q8C2×D4×C4312yes—
677C2×Q8C2×D4×C4311yescharacteristic
678C2×Q8C2×D4×C4311yescharacteristic
679C2×Q8C2×D4×C4311yescharacteristic
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—24no—
683C2×D4—24no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—41no—
693C2×D4—41no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—41no—
697C2×D4C2×D4×C4312yes—
698C2×D4C2×D4×C4311yescharacteristic
699C2×D4C2×D4×C4311yescharacteristic
700C2×D4C2×D4×C4311yescharacteristic
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—41no—
709C22×C4—41no—
710C22×C4—41no—
711C22×C4—41no—
712C22×C4C24×C4311yescharacteristic
713Q16—24no—
714Q16—22no—
715Q16—42no—
716Q16—42no—
717Q16—42no—
718Q16—42no—
719SD16—24no—
720SD16—24no—
721SD16—24no—
722SD16—22no—
723SD16—22no—
724SD16—24no—
725SD16—42no—
726SD16—42no—
727D8—24no—
728D8—22no—
729M16—24no—
730M16—21no—
731M16—21no—
732M16—21no—
733M16—21no—
734M16—21no—
735M16—21no—
736M16—21no—
737M16—42no—
738M16C2×D4×C4312yes—
739C2×C8—24no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—42no—
749C2×C8C2×D4×C4311yescharacteristic
750C2×C8C2×D4×C4311yescharacteristic
751C2×C8C2×D4×C4311yescharacteristic
752C2×C8C2×D4×C4311yescharacteristic
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—41no—
756C4⋊C4—41no—
757C4⋊C4—41no—
758C4⋊C4C2×D4×C4311yescharacteristic
759C4⋊C4C2×D4×C4311yescharacteristic
760C22⋊C4—21no—
761C22⋊C4—41no—
762C22⋊C4—41no—
763C22⋊C4—41no—
764C22⋊C4—44no—
765C42—21no—
766C42—21no—
767C42—21no—
768C42—41no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—22no—
773C23—44no—
774C23—41no—
775C23—41no—
776C23—81no—
777C23—81no—
778C23—161no—
779C23—161no—
780C23H(5,𝔽2)×C4311yescharacteristic
781Q8—21no—
782Q8—21no—
783Q8—22no—
784Q8—21no—
785Q8—22no—
786Q8—21no—
787Q8—44no—
788Q8—41no—
789Q8—41no—
790Q8—41no—
791Q8—41no—
792Q8—41no—
793Q8—41no—
794Q8#120×C4312yes—
795Q8#121×C4312yes—
796D4—22no—
797D4—22no—
798D4—22no—
799D4—22no—
800D4—21no—
801D4—22no—
802D4—22no—
803D4—21no—
804D4—21no—
805D4—21no—
806D4—44no—
807D4—44no—
808D4—44no—
809D4—41no—
810D4—41no—
811D4—41no—
812D4—41no—
813D4#120×C4312yes—
814D4#121×C4312yes—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—22no—
825C2×C4—44no—
826C2×C4—44no—
827C2×C4—44no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—81no—
840C2×C4—161no—
841C2×C4C22×D4×C4311yescharacteristic
842C2×C4C22×D4×C4311yescharacteristic
843C2×C4C22×D4×C4311yescharacteristic
844C2×C4C22×D4×C4311yescharacteristic
845C2×C4C2×#41×C4311yescharacteristic
846C2×C4H(5,𝔽2)×C4311yescharacteristic
847C8—21no—
848C8—22no—
849C8—21no—
850C8—21no—
851C8—21no—
852C8—41no—
853C8—41no—
854C8—41no—
855C22—21no—
856C22—21no—
857C22—22no—
858C22—22no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—42no—
865C22—41no—
866C22—41no—
867C22—82no—
868C22—81no—
869C22—81no—
870C22—161no—
871C22—164no—
872C22C43×#53411yescharacteristic
873C22D42×C4311yescharacteristic
874C22C43×#54611yescharacteristic
875C4—22no—
876C4—22no—
877C4—41no—
878C4—42no—
879C4—41no—
880C4—41no—
881C4—81no—
882C4—81no—
883C4—81no—
884C4C2×#120×C4311yescharacteristic
885C4C2×#121×C4311yescharacteristic
886C4D42×C4311yescharacteristic
887C4C43×#54611yescharacteristic
888C2—21no—
889C2—21no—
890C2—42no—
891C2—42no—
892C2—81no—
893C2—82no—
894C2C43×#241011yescharacteristic
895C2C43×#328911yescharacteristic
896C2C43×#329011yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC2×C43×#577C2
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
2. C2×C43×#473C2semidirect
3. C43×#3046C2semidirect
4. C2×C43×#455C2semidirect
5. C43×#3011C2semidirect
6. C43×#2897C2semidirect
7. C43×#2051C2semidirect
8. C43×#2046C2semidirect
9. C43×#2015C2semidirect
10. C43×#2003C2semidirect
11. C43×#1908C2semidirect
12. C43×#1882C2semidirect
13. C43×#1876C2semidirect
14. C43×#1866C2semidirect
15. C43×#1793C2semidirect
28. C22×Q16×C43C22semidirect
33. C43×#536C22semidirect
46. C2×#108×C43C22semidirect
47. C43×#424C22semidirect
50. C2×#104×C43C22semidirect
51. C43×#419C22semidirect
56. C43×#417C22semidirect
59. C2×#103×C43C22semidirect
62. C2×#101×C43C22semidirect
63. C2×#101×C43C22semidirect
65. C43×#408C22semidirect
66. C43×#391C22semidirect
67. C43×#343C22semidirect
68. C43×#341C22semidirect
69. C43×#339C22semidirect
70. C43×#336C22semidirect
406. #24458C43direct (N × H)
441. C2×#473C2×C43semidirect
442. #3046C2×C43semidirect
443. C2×#455C2×C43semidirect
444. #3011C2×C43semidirect
445. #2897C2×C43semidirect
446. #2051C2×C43semidirect
447. #2046C2×C43semidirect
448. #2015C2×C43semidirect
449. #2003C2×C43semidirect
450. #1908C2×C43semidirect
451. #1882C2×C43semidirect
452. #1876C2×C43semidirect
453. #1866C2×C43semidirect
454. #1793C2×C43semidirect
476. C22×Q16C22×C43semidirect
481. #536C22×C43semidirect
494. C2×#108C22×C43semidirect
495. #424C22×C43semidirect
498. C2×#104C22×C43semidirect
499. #419C22×C43semidirect
504. #417C22×C43semidirect
507. C2×#103C22×C43semidirect
510. C2×#101C22×C43semidirect
511. C2×#101C22×C43semidirect
513. #408C22×C43semidirect
514. #391C22×C43semidirect
515. #343C22×C43semidirect
516. #341C22×C43semidirect
517. #339C22×C43semidirect
518. #336C22×C43semidirect
519. C43#24458direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#5772
C2×C43×#4732
C43×#30462
C2×C43×#4552
C43×#30112
C43×#28972
C43×#20512
C43×#20462
C43×#20152
C43×#20032
C43×#19082
C43×#18822
C43×#18762
C43×#18662
C43×#17932
#2445843