Finite Group Databasebeta

← C43×#24466 #24944483

Subgroups — C43×#24466 #24944483

Order 11008.

1418 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3489C211yesmaximal, characteristic
2C43×#3056C211yesmaximal, characteristic, complemented
3C2×C43×#456C211yesmaximal, characteristic, complemented
4C43×#3007C211yesmaximal, characteristic, complemented
5C22×#104×C43C211yesmaximal, characteristic, complemented
6C43×#2857C211yesmaximal, characteristic, complemented
7C43×#2039C211yesmaximal, characteristic, complemented
8C43×#2038C211yesmaximal, characteristic, complemented
9C43×#2007C211yesmaximal, characteristic, complemented
10C43×#2005C211yesmaximal, characteristic, complemented
11C43×#1901C211yesmaximal, characteristic, complemented
12C43×#1896C211yesmaximal, characteristic, complemented
13C43×#1882C211yesmaximal, characteristic, complemented
14C43×#1859C211yesmaximal, characteristic, complemented
15C43×#1793C211yesmaximal, characteristic, complemented
16C2×2−1+4×C43C2211yescharacteristic
17C22×#41×C43C2211yescharacteristic
18C2×#137×C43C2211yescharacteristic
19C2×#137×C43C2211yescharacteristic
20C2×#137×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×C4⋊Q8×C43C2211yescharacteristic, complemented
33C43×#525—21no—
34C43×#525C2211yescharacteristic
35C2×C22⋊Q8×C43—21no—
36C2×C22⋊Q8×C43C2211yescharacteristic
37C2×C22⋊Q8×C43C2211yescharacteristic
38C43×#520C2211yescharacteristic
39C22×C42×C43C2211yescharacteristic
40C43×#470—21no—
41C43×#468—21no—
42C43×#467—21no—
43C43×#465—21no—
44C43×#456—24no—
45C43×#452—21no—
46C43×#452—21no—
47C43×#451—21no—
48C43×#450—21no—
49C43×#428C2211yescharacteristic, complemented
50C2×#104×C43—24no—
51C2×#104×C43C2211yescharacteristic
52C2×#104×C43C2211yescharacteristic
53C2×#104×C43C2211yescharacteristic
54C2×#104×C43C2211yescharacteristic
55C2×#104×C43C2211yescharacteristic, complemented
56C2×#104×C43C2211yescharacteristic, complemented
57C43×#419C2211yescharacteristic, complemented
58C43×#417C2211yescharacteristic
59C43×#417C2211yescharacteristic
60C43×#417C2211yescharacteristic, complemented
61C2×#101×C43C2211yescharacteristic, complemented
62C2×#101×C43C2211yescharacteristic, complemented
63C43×#407C2211yescharacteristic
64C43×#391C2211yescharacteristic, complemented
65C43×#391C2211yescharacteristic, complemented
66C43×#389—22no—
67C43×#384C2211yescharacteristic, complemented
68C43×#380—22no—
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×Q8×C43C2311yescharacteristic
96C22×D4×C43—21no—
97C22×D4×C43D411yescharacteristic
98C23×C4×C43—21no—
99C23×C4×C43—21no—
100C23×C4×C43C2311yescharacteristic
101#137×C43—22no—
102#137×C43—22no—
103#137×C43—22no—
104#137×C43—41no—
105#137×C43—41no—
106#137×C43—41no—
107C2×Q16×C43—21no—
108C2×Q16×C43—21no—
109C2×Q16×C43—21no—
110C2×SD16×C43—21no—
111C2×SD16×C43—21no—
112C2×SD16×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—
123C4⋊Q8×C43—22no—
124C4⋊Q8×C43—41no—
125#124×C43—22no—
126#124×C43—21no—
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×C43—21no—
144C22⋊Q8×C43—21no—
145C22⋊Q8×C43—21no—
146C22⋊Q8×C43—21no—
147C22⋊Q8×C43D411yescharacteristic
148C22⋊Q8×C43D411yescharacteristic
149#121×C43—22no—
150#121×C43—22no—
151#121×C43—22no—
152#121×C43—21no—
153#121×C43—21no—
154#121×C43—22no—
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×C43C2311yescharacteristic
168C2×C4⋊C4×C43—22no—
169C2×C4⋊C4×C43—21no—
170C2×C4⋊C4×C43—21no—
171C2×C4⋊C4×C43—22no—
172C2×C4⋊C4×C43—22no—
173C2×C4⋊C4×C43D412yes—
174C2×C4⋊C4×C43C2311yescharacteristic
175C2×C4⋊C4×C43C2311yescharacteristic
176C2×C22⋊C4×C43—22no—
177C2×C22⋊C4×C43—21no—
178C2×C22⋊C4×C43D412yes—
179C2×C42×C43—22no—
180C2×C42×C43—21no—
181C2×C42×C43—41no—
182C2×C42×C43C2311yescharacteristic
183C2×C42×C43C2311yescharacteristic
184#107×C43—21no—
185#106×C43—21no—
186#104×C43—22no—
187#104×C43—22no—
188#104×C43—22no—
189#104×C43—22no—
190#104×C43—41no—
191#104×C43D414yescomplemented
192#103×C43—21no—
193#103×C43—21no—
194#103×C43—21no—
195#103×C43—21no—
196#103×C43—21no—
197#102×C43—21no—
198#102×C43—21no—
199#102×C43—21no—
200#101×C43—22no—
201#101×C43—41no—
202C22⋊C8×C43—21no—
203C22⋊C8×C43—21no—
204#95×C43—22no—
205#95×C43—22no—
206C24×C43—21no—
207C24×C43C2×D411yescharacteristic
208#41×C43—21no—
209#41×C43—21no—
210#41×C43—22no—
211#41×C43—22no—
212#41×C43—21no—
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—42no—
221#41×C43—42no—
222#41×C43—41no—
223#41×C43—41no—
224#41×C43—42no—
225#41×C43—42no—
226#41×C43—42no—
227#41×C43—42no—
228#41×C43—44no—
229#41×C43—44no—
230#41×C43—42no—
231#41×C43—42no—
232#41×C43C2×D412yes—
233#41×C43#4112yes—
234C2×Q8×C43—22no—
235C2×Q8×C43—21no—
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—22no—
243C2×Q8×C43—21no—
244C2×Q8×C43—21no—
245C2×Q8×C43—21no—
246C2×Q8×C43—21no—
247C2×Q8×C43—21no—
248C2×Q8×C43—21no—
249C2×Q8×C43—41no—
250C2×Q8×C43—42no—
251C2×Q8×C43—42no—
252C2×Q8×C43—42no—
253C2×Q8×C43—42no—
254C2×Q8×C43C2×D411yescharacteristic
255C2×Q8×C43C2×D411yescharacteristic
256C2×Q8×C43C2×D411yescharacteristic
257C2×D4×C43—22no—
258C2×D4×C43—22no—
259C2×D4×C43—21no—
260C2×D4×C43—21no—
261C2×D4×C43—21no—
262C2×D4×C43—21no—
263C2×D4×C43—21no—
264C2×D4×C43—21no—
265C2×D4×C43—21no—
266C2×D4×C43—21no—
267C2×D4×C43—22no—
268C2×D4×C43—42no—
269C2×D4×C43—42no—
270C2×D4×C43—41no—
271C2×D4×C43C2×D411yescharacteristic
272C2×D4×C43C2×D411yescharacteristic
273C2×D4×C43C2×D411yescharacteristic
274C22×C4×C43—21no—
275C22×C4×C43—21no—
276C22×C4×C43—21no—
277C22×C4×C43—21no—
278C22×C4×C43—21no—
279C22×C4×C43—22no—
280C22×C4×C43—22no—
281C22×C4×C43—24no—
282C22×C4×C43—22no—
283C22×C4×C43—21no—
284C22×C4×C43—21no—
285C22×C4×C43—21no—
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—42no—
293C22×C4×C43—42no—
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
304Q16×C43—42no—
305Q16×C43—42no—
306Q16×C43—42no—
307SD16×C43—42no—
308SD16×C43—42no—
309SD16×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—44no—
337C4⋊C4×C43—44no—
338C4⋊C4×C43—41no—
339C4⋊C4×C43—41no—
340C4⋊C4×C43C2×D411yescharacteristic
341C4⋊C4×C43C2×D411yescharacteristic
342C22⋊C4×C43—22no—
343C22⋊C4×C43—22no—
344C22⋊C4×C43—22no—
345C22⋊C4×C43—22no—
346C22⋊C4×C43—22no—
347C22⋊C4×C43—21no—
348C22⋊C4×C43—21no—
349C22⋊C4×C43—21no—
350C22⋊C4×C43—22no—
351C22⋊C4×C43—22no—
352C22⋊C4×C43—21no—
353C22⋊C4×C43—21no—
354C22⋊C4×C43—41no—
355C22⋊C4×C43—41no—
356C42×C43—22no—
357C42×C43—21no—
358C42×C43—21no—
359C42×C43—21no—
360C42×C43—21no—
361C42×C43—42no—
362C42×C43C2×D412yes—
363C23×C43—21no—
364C23×C43—21no—
365C23×C43—21no—
366C23×C43—22no—
367C23×C43—21no—
368C23×C43—21no—
369C23×C43—41no—
370C23×C43—42no—
371C23×C43—42no—
372C23×C43—81no—
373C23×C43#12011yescharacteristic
374C23×C43#12011yescharacteristic
375C23×C43C22×D411yescharacteristic
376Q8×C43—21no—
377Q8×C43—21no—
378Q8×C43—21no—
379Q8×C43—21no—
380Q8×C43—21no—
381Q8×C43—42no—
382Q8×C43—44no—
383Q8×C43—41no—
384Q8×C43—41no—
385Q8×C43—41no—
386Q8×C43—41no—
387Q8×C43—41no—
388Q8×C43—41no—
389Q8×C43—41no—
390Q8×C43—41no—
391Q8×C43#12112yes—
392D4×C43—22no—
393D4×C43—22no—
394D4×C43—21no—
395D4×C43—21no—
396D4×C43—21no—
397D4×C43—21no—
398D4×C43—21no—
399D4×C43—42no—
400D4×C43—42no—
401D4×C43—42no—
402D4×C43—44no—
403D4×C43—41no—
404D4×C43—41no—
405D4×C43—41no—
406D4×C43—41no—
407D4×C43—42no—
408D4×C43—81no—
409D4×C43—82no—
410D4×C43#12112yes—
411C2×C4×C43—22no—
412C2×C4×C43—22no—
413C2×C4×C43—21no—
414C2×C4×C43—22no—
415C2×C4×C43—21no—
416C2×C4×C43—21no—
417C2×C4×C43—21no—
418C2×C4×C43—21no—
419C2×C4×C43—21no—
420C2×C4×C43—21no—
421C2×C4×C43—21no—
422C2×C4×C43—21no—
423C2×C4×C43—22no—
424C2×C4×C43—21no—
425C2×C4×C43—21no—
426C2×C4×C43—22no—
427C2×C4×C43—22no—
428C2×C4×C43—21no—
429C2×C4×C43—22no—
430C2×C4×C43—21no—
431C2×C4×C43—21no—
432C2×C4×C43—22no—
433C2×C4×C43—21no—
434C2×C4×C43—22no—
435C2×C4×C43—22no—
436C2×C4×C43—42no—
437C2×C4×C43—42no—
438C2×C4×C43—42no—
439C2×C4×C43—48no—
440C2×C4×C43—44no—
441C2×C4×C43—41no—
442C2×C4×C43—44no—
443C2×C4×C43—41no—
444C2×C4×C43—41no—
445C2×C4×C43—41no—
446C2×C4×C43—41no—
447C2×C4×C43—41no—
448C2×C4×C43—42no—
449C2×C4×C43—42no—
450C2×C4×C43—41no—
451C2×C4×C43—41no—
452C2×C4×C43—41no—
453C2×C4×C43—41no—
454C2×C4×C43—82no—
455C2×C4×C43#12011yescharacteristic
456C2×C4×C43#12011yescharacteristic
457C2×C4×C43C22×D411yescharacteristic
458C2×C4×C43C22×D411yescharacteristic
459C2×C4×C43C22×D411yescharacteristic
460C2×C4×C43C2×#4111yescharacteristic
461C2×C4×C43H(5,𝔽2)11yescharacteristic
462C2×C4×C43H(5,𝔽2)11yescharacteristic
463C8×C43—22no—
464C8×C43—41no—
465C8×C43—41no—
466C8×C43—41no—
467#24466C4311yesmaximal, characteristic, direct product factor, Sylow
468C22×C43—21no—
469C22×C43—21no—
470C22×C43—21no—
471C22×C43—21no—
472C22×C43—21no—
473C22×C43—22no—
474C22×C43—21no—
475C22×C43—21no—
476C22×C43—42no—
477C22×C43—42no—
478C22×C43—41no—
479C22×C43—41no—
480C22×C43—41no—
481C22×C43—41no—
482C22×C43—41no—
483C22×C43—41no—
484C22×C43—41no—
485C22×C43—41no—
486C22×C43—84no—
487C22×C43#45612yescomplemented
488C22×C43C2×#12011yescharacteristic
489C22×C43D4211yescharacteristic
490C22×C43#54611yescharacteristic
491C4×C43—24no—
492C4×C43—21no—
493C4×C43—21no—
494C4×C43—22no—
495C4×C43—42no—
496C4×C43—42no—
497C4×C43—41no—
498C4×C43—41no—
499C4×C43—41no—
500C4×C43—42no—
501C4×C43—41no—
502C4×C43—81no—
503C4×C43—81no—
504C4×C43C2×#12111yescharacteristic
505C4×C43#53411yescharacteristic
506C4×C43D4211yescharacteristic
507C4×C43#54611yescharacteristic
508#3489C2×C4311yescharacteristic
509#3056C2×C4311yescharacteristic, complemented
510C2×#456C2×C4311yescharacteristic, complemented
511#3007C2×C4311yescharacteristic, complemented
512C22×#104C2×C4311yescharacteristic, complemented
513#2857C2×C4311yescharacteristic, complemented
514#2039C2×C4311yescharacteristic, complemented
515#2038C2×C4311yescharacteristic, complemented
516#2007C2×C4311yescharacteristic, complemented
517#2005C2×C4311yescharacteristic, complemented
518#1901C2×C4311yescharacteristic, complemented
519#1896C2×C4311yescharacteristic, complemented
520#1882C2×C4311yescharacteristic, complemented
521#1859C2×C4311yescharacteristic, complemented
522#1793C2×C4311yescharacteristic, complemented
523C2×C43—21no—
524C2×C43—22no—
525C2×C43—21no—
526C2×C43—41no—
527C2×C43—42no—
528C2×C43—81no—
529C2×C43—81no—
530C2×C43#241011yescharacteristic
531C2×C43C2×#45611yescharacteristic
532C2×C43#301811yescharacteristic
533C2×2−1+4C22×C4311yescharacteristic
534C22×#41C22×C4311yescharacteristic
535C2×#137C22×C4311yescharacteristic
536C2×#137C22×C4311yescharacteristic
537C2×#137C22×C4311yescharacteristic, complemented
538C22×M16C22×C4311yescharacteristic
539D4×Q8—21no—
540#548—21no—
541#547—21no—
542#547—22no—
543#546—21no—
544#546—22no—
545#537—21no—
546#537C22×C4311yescharacteristic
547#536—21no—
548#536C22×C4311yescharacteristic
549C2×C4⋊Q8C22×C4311yescharacteristic, complemented
550#525—21no—
551#525C22×C4311yescharacteristic
552C2×C22⋊Q8—21no—
553C2×C22⋊Q8C22×C4311yescharacteristic
554C2×C22⋊Q8C22×C4311yescharacteristic
555#520C22×C4311yescharacteristic
556C22×C42C22×C4311yescharacteristic
557#470—21no—
558#468—21no—
559#467—21no—
560#465—21no—
561#456—24no—
562#452—21no—
563#452—21no—
564#451—21no—
565#450—21no—
566#428C22×C4311yescharacteristic, complemented
567C2×#104—24no—
568C2×#104C22×C4311yescharacteristic
569C2×#104C22×C4311yescharacteristic
570C2×#104C22×C4311yescharacteristic
571C2×#104C22×C4311yescharacteristic
572C2×#104C22×C4311yescharacteristic, complemented
573C2×#104C22×C4311yescharacteristic, complemented
574#419C22×C4311yescharacteristic, complemented
575#417C22×C4311yescharacteristic
576#417C22×C4311yescharacteristic
577#417C22×C4311yescharacteristic, complemented
578C2×#101C22×C4311yescharacteristic, complemented
579C2×#101C22×C4311yescharacteristic, complemented
580#407C22×C4311yescharacteristic
581#391C22×C4311yescharacteristic, complemented
582#391C22×C4311yescharacteristic, complemented
583#389—22no—
584#384C22×C4311yescharacteristic, complemented
585#380—22no—
586#343C22×C4311yescharacteristic, complemented
587#343C22×C4311yescharacteristic, complemented
588#339C22×C4311yescharacteristic, complemented
589#339C22×C4311yescharacteristic, complemented
590C43#2446611yescharacteristic, direct product factor, Sylow
5912−1+4—22no—
5922−1+4—22no—
5932−1+4—41no—
5942−1+4—41no—
595C2×#41—21no—
596C2×#41—21no—
597C2×#41—21no—
598C2×#41—22no—
599C2×#41—21no—
600C2×#41—22no—
601C2×#41—22no—
602C2×#41—41no—
603C2×#41—41no—
604C2×#41D4×C4311yescharacteristic
605C2×#41D4×C4311yescharacteristic
606C2×#41C23×C4311yescharacteristic
607C2×#41C23×C4311yescharacteristic
608C2×#41C23×C4311yescharacteristic
609C22×Q8—21no—
610C22×Q8—21no—
611C22×Q8D4×C4311yescharacteristic
612C22×Q8C23×C4311yescharacteristic
613C22×Q8C23×C4311yescharacteristic
614C22×D4—21no—
615C22×D4D4×C4311yescharacteristic
616C23×C4—21no—
617C23×C4—21no—
618C23×C4C23×C4311yescharacteristic
619#137—22no—
620#137—22no—
621#137—22no—
622#137—41no—
623#137—41no—
624#137—41no—
625C2×Q16—21no—
626C2×Q16—21no—
627C2×Q16—21no—
628C2×SD16—21no—
629C2×SD16—21no—
630C2×SD16—21no—
631C2×M16—21no—
632C2×M16—22no—
633C2×M16—41no—
634C2×M16C23×C4311yescharacteristic
635C2×M16C23×C4311yescharacteristic
636C2×M16C23×C4311yescharacteristic
637C2×M16C23×C4311yescharacteristic
638C22×C8—21no—
639C4⋊Q8—22no—
640C4⋊Q8—21no—
641C4⋊Q8—22no—
642C4⋊Q8—41no—
643#124—22no—
644#124—21no—
645#123—22no—
646#123—22no—
647#123—22no—
648#123—21no—
649#123—22no—
650C22⋊Q8—22no—
651C22⋊Q8—22no—
652C22⋊Q8—22no—
653C22⋊Q8—21no—
654C22⋊Q8—21no—
655C22⋊Q8—21no—
656C22⋊Q8—21no—
657C22⋊Q8—21no—
658C22⋊Q8—21no—
659C22⋊Q8—21no—
660C22⋊Q8—21no—
661C22⋊Q8—21no—
662C22⋊Q8—21no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8D4×C4311yescharacteristic
666C22⋊Q8D4×C4311yescharacteristic
667#121—22no—
668#121—22no—
669#121—22no—
670#121—21no—
671#121—21no—
672#121—22no—
673#121D4×C4311yescharacteristic
674#121D4×C4311yescharacteristic
675#120—22no—
676#120—21no—
677C4×Q8—21no—
678C4×D4—22no—
679C4×D4—22no—
680C4×D4—21no—
681C4×D4—22no—
682C4×D4—21no—
683C4×D4—21no—
684#117—21no—
685#117C23×C4311yescharacteristic
686C2×C4⋊C4—22no—
687C2×C4⋊C4—21no—
688C2×C4⋊C4—21no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—22no—
691C2×C4⋊C4D4×C4312yes—
692C2×C4⋊C4C23×C4311yescharacteristic
693C2×C4⋊C4C23×C4311yescharacteristic
694C2×C22⋊C4—22no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4D4×C4312yes—
697C2×C42—22no—
698C2×C42—21no—
699C2×C42—41no—
700C2×C42C23×C4311yescharacteristic
701C2×C42C23×C4311yescharacteristic
702#107—21no—
703#106—21no—
704#104—22no—
705#104—22no—
706#104—22no—
707#104—22no—
708#104—41no—
709#104D4×C4314yescomplemented
710#103—21no—
711#103—21no—
712#103—21no—
713#103—21no—
714#103—21no—
715#102—21no—
716#102—21no—
717#102—21no—
718#101—22no—
719#101—41no—
720C22⋊C8—21no—
721C22⋊C8—21no—
722#95—22no—
723#95—22no—
724C24—21no—
725C24C2×D4×C4311yescharacteristic
726#41—21no—
727#41—21no—
728#41—22no—
729#41—22no—
730#41—21no—
731#41—21no—
732#41—21no—
733#41—21no—
734#41—21no—
735#41—21no—
736#41—21no—
737#41—21no—
738#41—42no—
739#41—42no—
740#41—41no—
741#41—41no—
742#41—42no—
743#41—42no—
744#41—42no—
745#41—42no—
746#41—44no—
747#41—44no—
748#41—42no—
749#41—42no—
750#41C2×D4×C4312yes—
751#41#41×C4312yes—
752C2×Q8—22no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—22no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—41no—
768C2×Q8—42no—
769C2×Q8—42no—
770C2×Q8—42no—
771C2×Q8—42no—
772C2×Q8C2×D4×C4311yescharacteristic
773C2×Q8C2×D4×C4311yescharacteristic
774C2×Q8C2×D4×C4311yescharacteristic
775C2×D4—21no—
776C2×D4—22no—
777C2×D4—22no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—22no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—41no—
787C2×D4—42no—
788C2×D4—42no—
789C2×D4C2×D4×C4311yescharacteristic
790C2×D4C2×D4×C4311yescharacteristic
791C2×D4C2×D4×C4311yescharacteristic
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—24no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—22no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4C2×D4×C4312yes—
815C22×C4C2×D4×C4311yescharacteristic
816C22×C4C2×D4×C4311yescharacteristic
817C22×C4C2×D4×C4311yescharacteristic
818C22×C4C2×D4×C4311yescharacteristic
819C22×C4C2×D4×C4311yescharacteristic
820C22×C4C2×D4×C4312yes—
821C22×C4C24×C4311yescharacteristic
822Q16—42no—
823Q16—42no—
824Q16—42no—
825SD16—42no—
826SD16—42no—
827SD16—42no—
828M16—21no—
829M16—21no—
830M16—21no—
831M16—21no—
832M16—21no—
833M16—21no—
834M16—21no—
835M16—42no—
836M16C2×D4×C4312yes—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8—42no—
842C4⋊C4—22no—
843C4⋊C4—22no—
844C4⋊C4—22no—
845C4⋊C4—22no—
846C4⋊C4—21no—
847C4⋊C4—22no—
848C4⋊C4—22no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—44no—
855C4⋊C4—44no—
856C4⋊C4—41no—
857C4⋊C4—41no—
858C4⋊C4C2×D4×C4311yescharacteristic
859C4⋊C4C2×D4×C4311yescharacteristic
860C22⋊C4—22no—
861C22⋊C4—22no—
862C22⋊C4—22no—
863C22⋊C4—22no—
864C22⋊C4—22no—
865C22⋊C4—21no—
866C22⋊C4—22no—
867C22⋊C4—22no—
868C22⋊C4—21no—
869C22⋊C4—21no—
870C22⋊C4—21no—
871C22⋊C4—21no—
872C22⋊C4—41no—
873C22⋊C4—41no—
874C42—22no—
875C42—21no—
876C42—21no—
877C42—21no—
878C42—21no—
879C42—42no—
880C42C2×D4×C4312yes—
881C23—21no—
882C23—21no—
883C23—21no—
884C23—22no—
885C23—21no—
886C23—21no—
887C23—41no—
888C23—42no—
889C23—42no—
890C23—81no—
891C23#120×C4311yescharacteristic
892C23#120×C4311yescharacteristic
893C23C22×D4×C4311yescharacteristic
894Q8—21no—
895Q8—21no—
896Q8—21no—
897Q8—21no—
898Q8—21no—
899Q8—42no—
900Q8—44no—
901Q8—41no—
902Q8—41no—
903Q8—41no—
904Q8—41no—
905Q8—41no—
906Q8—41no—
907Q8—41no—
908Q8—41no—
909Q8#121×C4312yes—
910D4—22no—
911D4—22no—
912D4—21no—
913D4—21no—
914D4—21no—
915D4—21no—
916D4—21no—
917D4—42no—
918D4—42no—
919D4—42no—
920D4—44no—
921D4—41no—
922D4—41no—
923D4—41no—
924D4—41no—
925D4—42no—
926D4—81no—
927D4—82no—
928D4#121×C4312yes—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—21no—
932C2×C4—22no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—22no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—21no—
947C2×C4—22no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—22no—
951C2×C4—21no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4—42no—
957C2×C4—48no—
958C2×C4—44no—
959C2×C4—41no—
960C2×C4—44no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—82no—
973C2×C4#120×C4311yescharacteristic
974C2×C4#120×C4311yescharacteristic
975C2×C4C22×D4×C4311yescharacteristic
976C2×C4C22×D4×C4311yescharacteristic
977C2×C4C22×D4×C4311yescharacteristic
978C2×C4C2×#41×C4311yescharacteristic
979C2×C4H(5,𝔽2)×C4311yescharacteristic
980C2×C4H(5,𝔽2)×C4311yescharacteristic
981C8—22no—
982C8—41no—
983C8—41no—
984C8—41no—
985C22—21no—
986C22—21no—
987C22—21no—
988C22—21no—
989C22—21no—
990C22—22no—
991C22—21no—
992C22—21no—
993C22—42no—
994C22—42no—
995C22—41no—
996C22—41no—
997C22—41no—
998C22—41no—
999C22—41no—
1000C22—41no—
1001C22—41no—
1002C22—41no—
1003C22—84no—
1004C22C43×#45612yescomplemented
1005C22C2×#120×C4311yescharacteristic
1006C22D42×C4311yescharacteristic
1007C22C43×#54611yescharacteristic
1008C4—24no—
1009C4—21no—
1010C4—21no—
1011C4—22no—
1012C4—42no—
1013C4—42no—
1014C4—41no—
1015C4—41no—
1016C4—41no—
1017C4—42no—
1018C4—41no—
1019C4—81no—
1020C4—81no—
1021C4C2×#121×C4311yescharacteristic
1022C4C43×#53411yescharacteristic
1023C4D42×C4311yescharacteristic
1024C4C43×#54611yescharacteristic
1025C2—21no—
1026C2—22no—
1027C2—21no—
1028C2—41no—
1029C2—42no—
1030C2—81no—
1031C2—81no—
1032C2C43×#241011yescharacteristic
1033C2C2×C43×#45611yescharacteristic
1034C2C43×#301811yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC43×#3489C2
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
2. C43×#3056C2semidirect
3. C2×C43×#456C2semidirect
4. C43×#3007C2semidirect
5. C22×#104×C43C2semidirect
6. C43×#2857C2semidirect
7. C43×#2039C2semidirect
8. C43×#2038C2semidirect
9. C43×#2007C2semidirect
10. C43×#2005C2semidirect
11. C43×#1901C2semidirect
12. C43×#1896C2semidirect
13. C43×#1882C2semidirect
14. C43×#1859C2semidirect
15. C43×#1793C2semidirect
20. C2×#137×C43C22semidirect
32. C2×C4⋊Q8×C43C22semidirect
49. C43×#428C22semidirect
55. C2×#104×C43C22semidirect
56. C2×#104×C43C22semidirect
57. C43×#419C22semidirect
60. C43×#417C22semidirect
61. C2×#101×C43C22semidirect
62. C2×#101×C43C22semidirect
64. C43×#391C22semidirect
65. C43×#391C22semidirect
67. C43×#384C22semidirect
69. C43×#343C22semidirect
70. C43×#343C22semidirect
71. C43×#339C22semidirect
72. C43×#339C22semidirect
191. #104×C43D4semidirect
467. #24466C43direct (N × H)
487. C22×C43#456semidirect
509. #3056C2×C43semidirect
510. C2×#456C2×C43semidirect
511. #3007C2×C43semidirect
512. C22×#104C2×C43semidirect
513. #2857C2×C43semidirect
514. #2039C2×C43semidirect
515. #2038C2×C43semidirect
516. #2007C2×C43semidirect
517. #2005C2×C43semidirect
518. #1901C2×C43semidirect
519. #1896C2×C43semidirect
520. #1882C2×C43semidirect
521. #1859C2×C43semidirect
522. #1793C2×C43semidirect
537. C2×#137C22×C43semidirect
549. C2×C4⋊Q8C22×C43semidirect
566. #428C22×C43semidirect
572. C2×#104C22×C43semidirect
573. C2×#104C22×C43semidirect
574. #419C22×C43semidirect
577. #417C22×C43semidirect
578. C2×#101C22×C43semidirect
579. C2×#101C22×C43semidirect
581. #391C22×C43semidirect
582. #391C22×C43semidirect
584. #384C22×C43semidirect
586. #343C22×C43semidirect
587. #343C22×C43semidirect
588. #339C22×C43semidirect
589. #339C22×C43semidirect
590. C43#24466direct (N × H)
709. #104D4×C43semidirect
1004. C22C43×#456semidirect

Maximal subgroups

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

subgroupindex
C43×#34892
C43×#30562
C2×C43×#4562
C43×#30072
C22×#104×C432
C43×#28572
C43×#20392
C43×#20382
C43×#20072
C43×#20052
C43×#19012
C43×#18962
C43×#18822
C43×#18592
C43×#17932
#2446643