Finite Group Databasebeta

← C43×#24469 #24944486

Subgroups — C43×#24469 #24944486

Order 11008.

1402 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3489C211yesmaximal, characteristic, complemented
2C43×#3055C211yesmaximal, characteristic, complemented
3C2×C43×#454C211yesmaximal, characteristic, complemented
4C43×#3006C211yesmaximal, characteristic, complemented
5C2×C43×#421C211yesmaximal, characteristic, complemented
6C43×#2620C211yesmaximal, characteristic, complemented
7C43×#2039C211yesmaximal, characteristic, complemented
8C43×#2038C211yesmaximal, characteristic, complemented
9C43×#2006C211yesmaximal, characteristic, complemented
10C43×#2003C211yesmaximal, characteristic, complemented
11C43×#1901C211yesmaximal, characteristic, complemented
12C43×#1897C211yesmaximal, characteristic, complemented
13C43×#1883C211yesmaximal, characteristic, complemented
14C43×#1859C211yesmaximal, characteristic, complemented
15C43×#1793C211yesmaximal, characteristic, complemented
16C2×2−1+4×C43C2211yescharacteristic
17C22×#41×C43C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C43C2211yescharacteristic, complemented
21C22×M16×C43C2211yescharacteristic
22D4×Q8×C43—21no—
23C43×#548—21no—
24C43×#547—21no—
25C43×#547—22no—
26C43×#546—21no—
27C43×#546—22no—
28C43×#537—21no—
29C43×#537C2211yescharacteristic
30C43×#536—21no—
31C43×#536C2211yescharacteristic
32C2×#124×C43C2211yescharacteristic, complemented
33C43×#525—21no—
34C43×#525C2211yescharacteristic
35C2×C22⋊Q8×C43—21no—
36C2×C22⋊Q8×C43C2211yescharacteristic
37C2×#121×C43C2211yescharacteristic
38C43×#520C2211yescharacteristic
39C2×#117×C43C2211yescharacteristic
40C43×#469—21no—
41C43×#468—21no—
42C43×#466—21no—
43C43×#465—21no—
44C43×#454—24no—
45C43×#449—21no—
46C43×#449—21no—
47C43×#448—21no—
48C43×#447—21no—
49C43×#428C2211yescharacteristic, complemented
50C43×#421—24no—
51C2×#104×C43C2211yescharacteristic
52C2×#104×C43C2211yescharacteristic
53C2×#104×C43C2211yescharacteristic
54C2×#104×C43C2211yescharacteristic
55C2×#104×C43C2211yescharacteristic, complemented
56C2×#104×C43C2211yescharacteristic, complemented
57C43×#418C2211yescharacteristic, complemented
58C43×#417C2211yescharacteristic
59C43×#417C2211yescharacteristic
60C43×#417C2211yescharacteristic, complemented
61C2×#101×C43C2211yescharacteristic, complemented
62C2×#101×C43C2211yescharacteristic, complemented
63C43×#407C2211yescharacteristic
64C43×#396—22no—
65C43×#394—22no—
66C43×#391C2211yescharacteristic, complemented
67C43×#390C2211yescharacteristic, complemented
68C43×#384C2211yescharacteristic, complemented
69C43×#343C2211yescharacteristic, complemented
70C43×#343C2211yescharacteristic, complemented
71C43×#339C2211yescharacteristic, complemented
72C43×#339C2211yescharacteristic, complemented
732−1+4×C43—22no—
742−1+4×C43—22no—
752−1+4×C43—41no—
762−1+4×C43—41no—
77C2×#41×C43—21no—
78C2×#41×C43—21no—
79C2×#41×C43—21no—
80C2×#41×C43—22no—
81C2×#41×C43—21no—
82C2×#41×C43—22no—
83C2×#41×C43—22no—
84C2×#41×C43—41no—
85C2×#41×C43—41no—
86C2×#41×C43D411yescharacteristic
87C2×#41×C43D411yescharacteristic
88C2×#41×C43C2311yescharacteristic
89C2×#41×C43C2311yescharacteristic
90C2×#41×C43C2311yescharacteristic
91C22×Q8×C43—21no—
92C22×Q8×C43—21no—
93C22×Q8×C43D411yescharacteristic
94C22×Q8×C43C2311yescharacteristic
95C22×D4×C43—21no—
96C22×D4×C43—21no—
97C22×D4×C43D411yescharacteristic
98C22×D4×C43C2311yescharacteristic
99C23×C4×C43—21no—
100C23×C4×C43C2311yescharacteristic
101AGL(1,ℤ/8)×C43—22no—
102AGL(1,ℤ/8)×C43—22no—
103AGL(1,ℤ/8)×C43—22no—
104AGL(1,ℤ/8)×C43—41no—
105AGL(1,ℤ/8)×C43—41no—
106AGL(1,ℤ/8)×C43—41no—
107C2×SD16×C43—21no—
108C2×SD16×C43—21no—
109C2×SD16×C43—21no—
110C2×D8×C43—21no—
111C2×D8×C43—21no—
112C2×D8×C43—21no—
113C2×M16×C43—21no—
114C2×M16×C43—22no—
115C2×M16×C43—41no—
116C2×M16×C43C2311yescharacteristic
117C2×M16×C43C2311yescharacteristic
118C2×M16×C43C2311yescharacteristic
119C2×M16×C43C2311yescharacteristic
120C22×C8×C43—21no—
121C4⋊Q8×C43—22no—
122C4⋊Q8×C43—21no—
123#124×C43—22no—
124#124×C43—21no—
125#124×C43—22no—
126#124×C43—41no—
127#123×C43—22no—
128#123×C43—22no—
129#123×C43—22no—
130#123×C43—21no—
131#123×C43—22no—
132C22⋊Q8×C43—22no—
133C22⋊Q8×C43—22no—
134C22⋊Q8×C43—22no—
135C22⋊Q8×C43—21no—
136C22⋊Q8×C43—21no—
137C22⋊Q8×C43—21no—
138C22⋊Q8×C43—21no—
139C22⋊Q8×C43—21no—
140C22⋊Q8×C43—21no—
141C22⋊Q8×C43—21no—
142C22⋊Q8×C43—21no—
143C22⋊Q8×C43D411yescharacteristic
144C22⋊Q8×C43D411yescharacteristic
145#121×C43—22no—
146#121×C43—22no—
147#121×C43—22no—
148#121×C43—21no—
149#121×C43—21no—
150#121×C43—22no—
151#121×C43—21no—
152#121×C43—21no—
153#121×C43—21no—
154#121×C43—21no—
155#121×C43D411yescharacteristic
156#121×C43D411yescharacteristic
157#120×C43—22no—
158#120×C43—21no—
159C4×Q8×C43—21no—
160C4×D4×C43—22no—
161C4×D4×C43—22no—
162C4×D4×C43—21no—
163C4×D4×C43—22no—
164C4×D4×C43—21no—
165C4×D4×C43—21no—
166#117×C43—21no—
167#117×C43—22no—
168#117×C43—41no—
169#117×C43C2311yescharacteristic
170C2×C4⋊C4×C43—22no—
171C2×C4⋊C4×C43—21no—
172C2×C4⋊C4×C43—21no—
173C2×C4⋊C4×C43—22no—
174C2×C4⋊C4×C43D412yes—
175C2×C4⋊C4×C43C2311yescharacteristic
176C2×C4⋊C4×C43C2311yescharacteristic
177C2×C22⋊C4×C43—22no—
178C2×C22⋊C4×C43—21no—
179C2×C22⋊C4×C43—21no—
180C2×C22⋊C4×C43—22no—
181C2×C22⋊C4×C43—22no—
182C2×C22⋊C4×C43D412yes—
183C2×C42×C43C2311yescharacteristic
184C2×C42×C43C2311yescharacteristic
185#107×C43—21no—
186#106×C43—21no—
187#104×C43—22no—
188#104×C43—22no—
189#104×C43—22no—
190#104×C43—22no—
191#104×C43—41no—
192#104×C43D414yescomplemented
193#103×C43—21no—
194#103×C43—21no—
195#103×C43—21no—
196#102×C43—21no—
197#102×C43—21no—
198#102×C43—21no—
199#102×C43—21no—
200#102×C43—21no—
201#101×C43—22no—
202#101×C43—41no—
203C22⋊C8×C43—21no—
204C22⋊C8×C43—21no—
205#95×C43—22no—
206C24×C43—21no—
207C24×C43—21no—
208C24×C43C2×D411yescharacteristic
209#41×C43—21no—
210#41×C43—21no—
211#41×C43—22no—
212#41×C43—22no—
213#41×C43—21no—
214#41×C43—21no—
215#41×C43—21no—
216#41×C43—21no—
217#41×C43—21no—
218#41×C43—21no—
219#41×C43—21no—
220#41×C43—21no—
221#41×C43—42no—
222#41×C43—42no—
223#41×C43—41no—
224#41×C43—41no—
225#41×C43—42no—
226#41×C43—42no—
227#41×C43—42no—
228#41×C43—42no—
229#41×C43—44no—
230#41×C43—44no—
231#41×C43—42no—
232#41×C43—42no—
233#41×C43C2×D412yes—
234#41×C43#4112yes—
235C2×Q8×C43—22no—
236C2×Q8×C43—21no—
237C2×Q8×C43—21no—
238C2×Q8×C43—21no—
239C2×Q8×C43—21no—
240C2×Q8×C43—21no—
241C2×Q8×C43—21no—
242C2×Q8×C43—21no—
243C2×Q8×C43—22no—
244C2×Q8×C43—41no—
245C2×Q8×C43—42no—
246C2×Q8×C43—42no—
247C2×Q8×C43—42no—
248C2×Q8×C43—42no—
249C2×Q8×C43C2×D411yescharacteristic
250C2×Q8×C43C2×D411yescharacteristic
251C2×Q8×C43C2×D411yescharacteristic
252C2×D4×C43—22no—
253C2×D4×C43—22no—
254C2×D4×C43—21no—
255C2×D4×C43—21no—
256C2×D4×C43—21no—
257C2×D4×C43—21no—
258C2×D4×C43—21no—
259C2×D4×C43—21no—
260C2×D4×C43—21no—
261C2×D4×C43—21no—
262C2×D4×C43—22no—
263C2×D4×C43—21no—
264C2×D4×C43—21no—
265C2×D4×C43—21no—
266C2×D4×C43—21no—
267C2×D4×C43—21no—
268C2×D4×C43—21no—
269C2×D4×C43—42no—
270C2×D4×C43—42no—
271C2×D4×C43—41no—
272C2×D4×C43—41no—
273C2×D4×C43—41no—
274C2×D4×C43—82no—
275C2×D4×C43C2×D411yescharacteristic
276C2×D4×C43C2×D411yescharacteristic
277C2×D4×C43C2×D411yescharacteristic
278C22×C4×C43—21no—
279C22×C4×C43—21no—
280C22×C4×C43—21no—
281C22×C4×C43—21no—
282C22×C4×C43—21no—
283C22×C4×C43—22no—
284C22×C4×C43—22no—
285C22×C4×C43—22no—
286C22×C4×C43—21no—
287C22×C4×C43—21no—
288C22×C4×C43—21no—
289C22×C4×C43—21no—
290C22×C4×C43—21no—
291C22×C4×C43—21no—
292C22×C4×C43—21no—
293C22×C4×C43—21no—
294C22×C4×C43—42no—
295C22×C4×C43—42no—
296C22×C4×C43C2×D411yescharacteristic
297C22×C4×C43C2×D411yescharacteristic
298C22×C4×C43C2×D411yescharacteristic
299C22×C4×C43C2×D411yescharacteristic
300C22×C4×C43C2×D412yes—
301C22×C4×C43C2×D411yescharacteristic
302C22×C4×C43C2×D412yes—
303C22×C4×C43C2411yescharacteristic
304SD16×C43—42no—
305SD16×C43—42no—
306SD16×C43—42no—
307D8×C43—42no—
308D8×C43—42no—
309D8×C43—42no—
310M16×C43—21no—
311M16×C43—21no—
312M16×C43—21no—
313M16×C43—21no—
314M16×C43—21no—
315M16×C43—21no—
316M16×C43—21no—
317M16×C43—42no—
318M16×C43C2×D412yes—
319C2×C8×C43—21no—
320C2×C8×C43—21no—
321C2×C8×C43—21no—
322C2×C8×C43—21no—
323C2×C8×C43—42no—
324C4⋊C4×C43—22no—
325C4⋊C4×C43—22no—
326C4⋊C4×C43—22no—
327C4⋊C4×C43—22no—
328C4⋊C4×C43—21no—
329C4⋊C4×C43—22no—
330C4⋊C4×C43—22no—
331C4⋊C4×C43—21no—
332C4⋊C4×C43—21no—
333C4⋊C4×C43—21no—
334C4⋊C4×C43—21no—
335C4⋊C4×C43—21no—
336C4⋊C4×C43—42no—
337C4⋊C4×C43—82no—
338C4⋊C4×C43C2×D411yescharacteristic
339C4⋊C4×C43C2×D411yescharacteristic
340C22⋊C4×C43—22no—
341C22⋊C4×C43—22no—
342C22⋊C4×C43—22no—
343C22⋊C4×C43—22no—
344C22⋊C4×C43—22no—
345C22⋊C4×C43—21no—
346C22⋊C4×C43—21no—
347C22⋊C4×C43—21no—
348C22⋊C4×C43—22no—
349C22⋊C4×C43—22no—
350C22⋊C4×C43—21no—
351C22⋊C4×C43—21no—
352C22⋊C4×C43—42no—
353C22⋊C4×C43—44no—
354C22⋊C4×C43—41no—
355C22⋊C4×C43—41no—
356C22⋊C4×C43—82no—
357C42×C43—22no—
358C42×C43—21no—
359C42×C43—21no—
360C42×C43—21no—
361C42×C43—21no—
362C42×C43C2×D412yes—
363C23×C43—21no—
364C23×C43—21no—
365C23×C43—21no—
366C23×C43—21no—
367C23×C43—21no—
368C23×C43—41no—
369C23×C43—41no—
370C23×C43—42no—
371C23×C43—42no—
372C23×C43—42no—
373C23×C43—42no—
374C23×C43—41no—
375C23×C43—41no—
376C23×C43—41no—
377C23×C43—81no—
378C23×C43#12011yescharacteristic
379C23×C43#12011yescharacteristic
380C23×C43C22×D411yescharacteristic
381Q8×C43—21no—
382Q8×C43—21no—
383Q8×C43—21no—
384Q8×C43—21no—
385Q8×C43—21no—
386Q8×C43—42no—
387Q8×C43—44no—
388Q8×C43—41no—
389Q8×C43—41no—
390Q8×C43—41no—
391Q8×C43—41no—
392Q8×C43#12112yes—
393D4×C43—22no—
394D4×C43—22no—
395D4×C43—21no—
396D4×C43—21no—
397D4×C43—21no—
398D4×C43—21no—
399D4×C43—21no—
400D4×C43—42no—
401D4×C43—42no—
402D4×C43—42no—
403D4×C43—42no—
404D4×C43—44no—
405D4×C43—41no—
406D4×C43—41no—
407D4×C43—41no—
408D4×C43—41no—
409D4×C43—41no—
410D4×C43—41no—
411D4×C43—41no—
412D4×C43—41no—
413D4×C43—81no—
414D4×C43—82no—
415D4×C43—82no—
416D4×C43—82no—
417D4×C43#12112yes—
418C2×C4×C43—21no—
419C2×C4×C43—21no—
420C2×C4×C43—21no—
421C2×C4×C43—21no—
422C2×C4×C43—21no—
423C2×C4×C43—21no—
424C2×C4×C43—21no—
425C2×C4×C43—21no—
426C2×C4×C43—21no—
427C2×C4×C43—22no—
428C2×C4×C43—21no—
429C2×C4×C43—21no—
430C2×C4×C43—22no—
431C2×C4×C43—21no—
432C2×C4×C43—22no—
433C2×C4×C43—21no—
434C2×C4×C43—21no—
435C2×C4×C43—22no—
436C2×C4×C43—21no—
437C2×C4×C43—22no—
438C2×C4×C43—22no—
439C2×C4×C43—22no—
440C2×C4×C43—42no—
441C2×C4×C43—42no—
442C2×C4×C43—42no—
443C2×C4×C43—44no—
444C2×C4×C43—41no—
445C2×C4×C43—41no—
446C2×C4×C43—44no—
447C2×C4×C43—41no—
448C2×C4×C43—41no—
449C2×C4×C43—41no—
450C2×C4×C43—41no—
451C2×C4×C43—42no—
452C2×C4×C43—41no—
453C2×C4×C43—42no—
454C2×C4×C43—41no—
455C2×C4×C43—41no—
456C2×C4×C43—41no—
457C2×C4×C43—82no—
458C2×C4×C43#12011yescharacteristic
459C2×C4×C43#12011yescharacteristic
460C2×C4×C43C22×D411yescharacteristic
461C2×C4×C43C22×D411yescharacteristic
462C2×C4×C43C22×D411yescharacteristic
463C2×C4×C43C2×#4111yescharacteristic
464C2×C4×C43H(5,𝔽2)11yescharacteristic
465C2×C4×C43H(5,𝔽2)11yescharacteristic
466C8×C43—22no—
467C8×C43—41no—
468C8×C43—41no—
469C8×C43—41no—
470#24469C4311yesmaximal, characteristic, direct product factor, Sylow
471C22×C43—21no—
472C22×C43—21no—
473C22×C43—21no—
474C22×C43—21no—
475C22×C43—22no—
476C22×C43—21no—
477C22×C43—21no—
478C22×C43—21no—
479C22×C43—21no—
480C22×C43—41no—
481C22×C43—41no—
482C22×C43—41no—
483C22×C43—41no—
484C22×C43—41no—
485C22×C43—41no—
486C22×C43—41no—
487C22×C43—41no—
488C22×C43—81no—
489C22×C43—81no—
490C22×C43—82no—
491C22×C43—82no—
492C22×C43—84no—
493C22×C43—81no—
494C22×C43—81no—
495C22×C43—81no—
496C22×C43C2×#12011yescharacteristic
497C22×C43D4211yescharacteristic
498C22×C43#54611yescharacteristic
499C4×C43—21no—
500C4×C43—21no—
501C4×C43—22no—
502C4×C43—42no—
503C4×C43—42no—
504C4×C43—41no—
505C4×C43—41no—
506C4×C43—41no—
507C4×C43—42no—
508C4×C43—41no—
509C4×C43—81no—
510C4×C43—81no—
511C4×C43C2×#12111yescharacteristic
512C4×C43#53411yescharacteristic
513C4×C43D4211yescharacteristic
514C4×C43#54611yescharacteristic
515#3489C2×C4311yescharacteristic, complemented
516#3055C2×C4311yescharacteristic, complemented
517C2×#454C2×C4311yescharacteristic, complemented
518#3006C2×C4311yescharacteristic, complemented
519C2×#421C2×C4311yescharacteristic, complemented
520#2620C2×C4311yescharacteristic, complemented
521#2039C2×C4311yescharacteristic, complemented
522#2038C2×C4311yescharacteristic, complemented
523#2006C2×C4311yescharacteristic, complemented
524#2003C2×C4311yescharacteristic, complemented
525#1901C2×C4311yescharacteristic, complemented
526#1897C2×C4311yescharacteristic, complemented
527#1883C2×C4311yescharacteristic, complemented
528#1859C2×C4311yescharacteristic, complemented
529#1793C2×C4311yescharacteristic, complemented
530C2×C43—21no—
531C2×C43—21no—
532C2×C43—41no—
533C2×C43—41no—
534C2×C43—42no—
535C2×C43—81no—
536C2×C43—81no—
537C2×C43—161no—
538C2×C43#241011yescharacteristic
539C2×C43#302011yescharacteristic
540C2×C43#302111yescharacteristic
541C2×2−1+4C22×C4311yescharacteristic
542C22×#41C22×C4311yescharacteristic
543C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
544C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
545C2×AGL(1,ℤ/8)C22×C4311yescharacteristic, complemented
546C22×M16C22×C4311yescharacteristic
547D4×Q8—21no—
548#548—21no—
549#547—21no—
550#547—22no—
551#546—21no—
552#546—22no—
553#537—21no—
554#537C22×C4311yescharacteristic
555#536—21no—
556#536C22×C4311yescharacteristic
557C2×#124C22×C4311yescharacteristic, complemented
558#525—21no—
559#525C22×C4311yescharacteristic
560C2×C22⋊Q8—21no—
561C2×C22⋊Q8C22×C4311yescharacteristic
562C2×#121C22×C4311yescharacteristic
563#520C22×C4311yescharacteristic
564C2×#117C22×C4311yescharacteristic
565#469—21no—
566#468—21no—
567#466—21no—
568#465—21no—
569#454—24no—
570#449—21no—
571#449—21no—
572#448—21no—
573#447—21no—
574#428C22×C4311yescharacteristic, complemented
575#421—24no—
576C2×#104C22×C4311yescharacteristic
577C2×#104C22×C4311yescharacteristic
578C2×#104C22×C4311yescharacteristic
579C2×#104C22×C4311yescharacteristic
580C2×#104C22×C4311yescharacteristic, complemented
581C2×#104C22×C4311yescharacteristic, complemented
582#418C22×C4311yescharacteristic, complemented
583#417C22×C4311yescharacteristic
584#417C22×C4311yescharacteristic
585#417C22×C4311yescharacteristic, complemented
586C2×#101C22×C4311yescharacteristic, complemented
587C2×#101C22×C4311yescharacteristic, complemented
588#407C22×C4311yescharacteristic
589#396—22no—
590#394—22no—
591#391C22×C4311yescharacteristic, complemented
592#390C22×C4311yescharacteristic, complemented
593#384C22×C4311yescharacteristic, complemented
594#343C22×C4311yescharacteristic, complemented
595#343C22×C4311yescharacteristic, complemented
596#339C22×C4311yescharacteristic, complemented
597#339C22×C4311yescharacteristic, complemented
598C43#2446911yescharacteristic, direct product factor, Sylow
5992−1+4—22no—
6002−1+4—22no—
6012−1+4—41no—
6022−1+4—41no—
603C2×#41—21no—
604C2×#41—21no—
605C2×#41—21no—
606C2×#41—22no—
607C2×#41—21no—
608C2×#41—22no—
609C2×#41—22no—
610C2×#41—41no—
611C2×#41—41no—
612C2×#41D4×C4311yescharacteristic
613C2×#41D4×C4311yescharacteristic
614C2×#41C23×C4311yescharacteristic
615C2×#41C23×C4311yescharacteristic
616C2×#41C23×C4311yescharacteristic
617C22×Q8—21no—
618C22×Q8—21no—
619C22×Q8D4×C4311yescharacteristic
620C22×Q8C23×C4311yescharacteristic
621C22×D4—21no—
622C22×D4—21no—
623C22×D4D4×C4311yescharacteristic
624C22×D4C23×C4311yescharacteristic
625C23×C4—21no—
626C23×C4C23×C4311yescharacteristic
627AGL(1,ℤ/8)—22no—
628AGL(1,ℤ/8)—22no—
629AGL(1,ℤ/8)—22no—
630AGL(1,ℤ/8)—41no—
631AGL(1,ℤ/8)—41no—
632AGL(1,ℤ/8)—41no—
633C2×SD16—21no—
634C2×SD16—21no—
635C2×SD16—21no—
636C2×D8—21no—
637C2×D8—21no—
638C2×D8—21no—
639C2×M16—21no—
640C2×M16—22no—
641C2×M16—41no—
642C2×M16C23×C4311yescharacteristic
643C2×M16C23×C4311yescharacteristic
644C2×M16C23×C4311yescharacteristic
645C2×M16C23×C4311yescharacteristic
646C22×C8—21no—
647C4⋊Q8—22no—
648C4⋊Q8—21no—
649#124—22no—
650#124—21no—
651#124—22no—
652#124—41no—
653#123—22no—
654#123—22no—
655#123—22no—
656#123—21no—
657#123—22no—
658C22⋊Q8—22no—
659C22⋊Q8—22no—
660C22⋊Q8—22no—
661C22⋊Q8—21no—
662C22⋊Q8—21no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8D4×C4311yescharacteristic
670C22⋊Q8D4×C4311yescharacteristic
671#121—22no—
672#121—22no—
673#121—22no—
674#121—21no—
675#121—21no—
676#121—22no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121D4×C4311yescharacteristic
682#121D4×C4311yescharacteristic
683#120—22no—
684#120—21no—
685C4×Q8—21no—
686C4×D4—22no—
687C4×D4—22no—
688C4×D4—21no—
689C4×D4—22no—
690C4×D4—21no—
691C4×D4—21no—
692#117—21no—
693#117—22no—
694#117—41no—
695#117C23×C4311yescharacteristic
696C2×C4⋊C4—22no—
697C2×C4⋊C4—21no—
698C2×C4⋊C4—21no—
699C2×C4⋊C4—22no—
700C2×C4⋊C4D4×C4312yes—
701C2×C4⋊C4C23×C4311yescharacteristic
702C2×C4⋊C4C23×C4311yescharacteristic
703C2×C22⋊C4—22no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4D4×C4312yes—
709C2×C42C23×C4311yescharacteristic
710C2×C42C23×C4311yescharacteristic
711#107—21no—
712#106—21no—
713#104—22no—
714#104—22no—
715#104—22no—
716#104—22no—
717#104—41no—
718#104D4×C4314yescomplemented
719#103—21no—
720#103—21no—
721#103—21no—
722#102—21no—
723#102—21no—
724#102—21no—
725#102—21no—
726#102—21no—
727#101—22no—
728#101—41no—
729C22⋊C8—21no—
730C22⋊C8—21no—
731#95—22no—
732C24—21no—
733C24—21no—
734C24C2×D4×C4311yescharacteristic
735#41—21no—
736#41—21no—
737#41—22no—
738#41—22no—
739#41—21no—
740#41—21no—
741#41—21no—
742#41—21no—
743#41—21no—
744#41—21no—
745#41—21no—
746#41—21no—
747#41—42no—
748#41—42no—
749#41—41no—
750#41—41no—
751#41—42no—
752#41—42no—
753#41—42no—
754#41—42no—
755#41—44no—
756#41—44no—
757#41—42no—
758#41—42no—
759#41C2×D4×C4312yes—
760#41#41×C4312yes—
761C2×Q8—22no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—22no—
770C2×Q8—41no—
771C2×Q8—42no—
772C2×Q8—42no—
773C2×Q8—42no—
774C2×Q8—42no—
775C2×Q8C2×D4×C4311yescharacteristic
776C2×Q8C2×D4×C4311yescharacteristic
777C2×Q8C2×D4×C4311yescharacteristic
778C2×D4—21no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—22no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—41no—
796C2×D4—42no—
797C2×D4—42no—
798C2×D4—41no—
799C2×D4—41no—
800C2×D4—82no—
801C2×D4C2×D4×C4311yescharacteristic
802C2×D4C2×D4×C4311yescharacteristic
803C2×D4C2×D4×C4311yescharacteristic
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—42no—
821C22×C4—42no—
822C22×C4C2×D4×C4312yes—
823C22×C4C2×D4×C4311yescharacteristic
824C22×C4C2×D4×C4311yescharacteristic
825C22×C4C2×D4×C4311yescharacteristic
826C22×C4C2×D4×C4311yescharacteristic
827C22×C4C2×D4×C4311yescharacteristic
828C22×C4C2×D4×C4312yes—
829C22×C4C24×C4311yescharacteristic
830SD16—42no—
831SD16—42no—
832SD16—42no—
833D8—42no—
834D8—42no—
835D8—42no—
836M16—21no—
837M16—21no—
838M16—21no—
839M16—21no—
840M16—21no—
841M16—21no—
842M16—21no—
843M16—42no—
844M16C2×D4×C4312yes—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—42no—
850C4⋊C4—22no—
851C4⋊C4—22no—
852C4⋊C4—22no—
853C4⋊C4—22no—
854C4⋊C4—21no—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—42no—
863C4⋊C4—82no—
864C4⋊C4C2×D4×C4311yescharacteristic
865C4⋊C4C2×D4×C4311yescharacteristic
866C22⋊C4—22no—
867C22⋊C4—22no—
868C22⋊C4—22no—
869C22⋊C4—22no—
870C22⋊C4—22no—
871C22⋊C4—21no—
872C22⋊C4—22no—
873C22⋊C4—22no—
874C22⋊C4—21no—
875C22⋊C4—21no—
876C22⋊C4—21no—
877C22⋊C4—21no—
878C22⋊C4—44no—
879C22⋊C4—42no—
880C22⋊C4—41no—
881C22⋊C4—41no—
882C22⋊C4—82no—
883C42—22no—
884C42—21no—
885C42—21no—
886C42—21no—
887C42—21no—
888C42C2×D4×C4312yes—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—21no—
894C23—41no—
895C23—41no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—42no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—81no—
904C23#120×C4311yescharacteristic
905C23#120×C4311yescharacteristic
906C23C22×D4×C4311yescharacteristic
907Q8—21no—
908Q8—21no—
909Q8—21no—
910Q8—21no—
911Q8—21no—
912Q8—42no—
913Q8—44no—
914Q8—41no—
915Q8—41no—
916Q8—41no—
917Q8—41no—
918Q8#121×C4312yes—
919D4—22no—
920D4—22no—
921D4—21no—
922D4—21no—
923D4—21no—
924D4—21no—
925D4—21no—
926D4—42no—
927D4—42no—
928D4—42no—
929D4—44no—
930D4—42no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—41no—
938D4—41no—
939D4—81no—
940D4—82no—
941D4—82no—
942D4—82no—
943D4#121×C4312yes—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—22no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—22no—
957C2×C4—21no—
958C2×C4—22no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—22no—
962C2×C4—21no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—42no—
969C2×C4—44no—
970C2×C4—41no—
971C2×C4—44no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—42no—
978C2×C4—41no—
979C2×C4—42no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—82no—
984C2×C4#120×C4311yescharacteristic
985C2×C4#120×C4311yescharacteristic
986C2×C4C22×D4×C4311yescharacteristic
987C2×C4C22×D4×C4311yescharacteristic
988C2×C4C22×D4×C4311yescharacteristic
989C2×C4C2×#41×C4311yescharacteristic
990C2×C4H(5,𝔽2)×C4311yescharacteristic
991C2×C4H(5,𝔽2)×C4311yescharacteristic
992C8—22no—
993C8—41no—
994C8—41no—
995C8—41no—
996C22—21no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—22no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—41no—
1006C22—41no—
1007C22—41no—
1008C22—41no—
1009C22—41no—
1010C22—41no—
1011C22—41no—
1012C22—41no—
1013C22—81no—
1014C22—81no—
1015C22—82no—
1016C22—82no—
1017C22—84no—
1018C22—81no—
1019C22—81no—
1020C22—81no—
1021C22C2×#120×C4311yescharacteristic
1022C22D42×C4311yescharacteristic
1023C22C43×#54611yescharacteristic
1024C4—21no—
1025C4—21no—
1026C4—22no—
1027C4—42no—
1028C4—42no—
1029C4—41no—
1030C4—41no—
1031C4—41no—
1032C4—42no—
1033C4—41no—
1034C4—81no—
1035C4—81no—
1036C4C2×#121×C4311yescharacteristic
1037C4C43×#53411yescharacteristic
1038C4D42×C4311yescharacteristic
1039C4C43×#54611yescharacteristic
1040C2—21no—
1041C2—21no—
1042C2—41no—
1043C2—41no—
1044C2—42no—
1045C2—81no—
1046C2—81no—
1047C2—161no—
1048C2C43×#241011yescharacteristic
1049C2C43×#302011yescharacteristic
1050C2C43×#302111yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
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. C43×#3489C2semidirect
2. C43×#3055C2semidirect
3. C2×C43×#454C2semidirect
4. C43×#3006C2semidirect
5. C2×C43×#421C2semidirect
6. C43×#2620C2semidirect
7. C43×#2039C2semidirect
8. C43×#2038C2semidirect
9. C43×#2006C2semidirect
10. C43×#2003C2semidirect
11. C43×#1901C2semidirect
12. C43×#1897C2semidirect
13. C43×#1883C2semidirect
14. C43×#1859C2semidirect
15. C43×#1793C2semidirect
20. C2×AGL(1,ℤ/8)×C43C22semidirect
32. C2×#124×C43C22semidirect
49. C43×#428C22semidirect
55. C2×#104×C43C22semidirect
56. C2×#104×C43C22semidirect
57. C43×#418C22semidirect
60. C43×#417C22semidirect
61. C2×#101×C43C22semidirect
62. C2×#101×C43C22semidirect
66. C43×#391C22semidirect
67. C43×#390C22semidirect
68. C43×#384C22semidirect
69. C43×#343C22semidirect
70. C43×#343C22semidirect
71. C43×#339C22semidirect
72. C43×#339C22semidirect
192. #104×C43D4semidirect
470. #24469C43direct (N × H)
515. #3489C2×C43semidirect
516. #3055C2×C43semidirect
517. C2×#454C2×C43semidirect
518. #3006C2×C43semidirect
519. C2×#421C2×C43semidirect
520. #2620C2×C43semidirect
521. #2039C2×C43semidirect
522. #2038C2×C43semidirect
523. #2006C2×C43semidirect
524. #2003C2×C43semidirect
525. #1901C2×C43semidirect
526. #1897C2×C43semidirect
527. #1883C2×C43semidirect
528. #1859C2×C43semidirect
529. #1793C2×C43semidirect
545. C2×AGL(1,ℤ/8)C22×C43semidirect
557. C2×#124C22×C43semidirect
574. #428C22×C43semidirect
580. C2×#104C22×C43semidirect
581. C2×#104C22×C43semidirect
582. #418C22×C43semidirect
585. #417C22×C43semidirect
586. C2×#101C22×C43semidirect
587. C2×#101C22×C43semidirect
591. #391C22×C43semidirect
592. #390C22×C43semidirect
593. #384C22×C43semidirect
594. #343C22×C43semidirect
595. #343C22×C43semidirect
596. #339C22×C43semidirect
597. #339C22×C43semidirect
598. C43#24469direct (N × H)
718. #104D4×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#34892
C43×#30552
C2×C43×#4542
C43×#30062
C2×C43×#4212
C43×#26202
C43×#20392
C43×#20382
C43×#20062
C43×#20032
C43×#19012
C43×#18972
C43×#18832
C43×#18592
C43×#17932
#2446943