Finite Group Databasebeta

← C43×#24140 #24944157

Subgroups — C43×#24140 #24944157

Order 11008.

1556 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3505C211yesmaximal, characteristic, complemented
2C43×#2848C211yesmaximal, characteristic, complemented
3C43×#2847C211yesmaximal, characteristic, complemented
4C4×#120×C43C211yesmaximal, characteristic, complemented
5C43×#2044C212yesmaximal, complemented
6C43×#2021C212yesmaximal, complemented
7C43×#1996C211yesmaximal, characteristic, complemented
8C43×#1964C211yesmaximal, characteristic, complemented
9C43×#1889C212yesmaximal, complemented
10C43×#1867C212yesmaximal, complemented
11C43×#1799C211yesmaximal, characteristic, complemented
12C24×C4×C43C2211yescharacteristic
13C43×#553—21no—
14C43×#553—22no—
15C43×#552—21no—
16C43×#551—22no—
17C43×#548—21no—
18C43×#546—21no—
19C43×#539—21no—
20C43×#538—21no—
21C43×#534C2212yes—
22C43×#529—21no—
23C43×#525—21no—
24C2×C22⋊Q8×C43—21no—
25C2×C22⋊Q8×C43C2211yescharacteristic
26C2×#121×C43—21no—
27C2×#121×C43C2211yescharacteristic
28C2×#120×C43C2211yescharacteristic
29C2×#120×C43C2212yes—
30C43×#518C2212yes—
31C2×C4×D4×C43—21no—
32C2×C4×D4×C43C2211yescharacteristic
33C2×#99×C43C2212yes—
34C2×#99×C43C2212yes—
35C2×#99×C43C2212yes—
36C43×#386—22no—
37C43×#386—21no—
38C43×#386C2212yes—
39C43×#386C2211yescharacteristic
40C43×#385—22no—
41C43×#385—21no—
42C43×#385C2212yes—
43C43×#385C2211yescharacteristic
44C43×#380—21no—
45C43×#380—21no—
46C43×#380C2211yescharacteristic
47C43×#380C2211yescharacteristic
48C43×#379C2212yes—
49C43×#379C2211yescharacteristic
50C4×C22⋊C4×C43—21no—
51C4×C22⋊C4×C43C2211yescharacteristic
52C43×#342C2212yes—
53C43×#342C2212yes—
54C43×#342C2212yes—
55C25×C43C2311yescharacteristic
56C2×#41×C43—21no—
57C22×Q8×C43D411yescharacteristic, complemented
58C22×D4×C43—21no—
59C22×D4×C43—22no—
60C22×D4×C43D411yescharacteristic, complemented
61C22×D4×C43C2311yescharacteristic
62C22×D4×C43C2312yes—
63C23×C4×C43—21no—
64C23×C4×C43—21no—
65C23×C4×C43—21no—
66C23×C4×C43—21no—
67C23×C4×C43—21no—
68C23×C4×C43—21no—
69C23×C4×C43—44no—
70C23×C4×C43D411yescharacteristic, complemented
71C23×C4×C43C2311yescharacteristic
72C23×C4×C43C2311yescharacteristic
73#126×C43—22no—
74#126×C43—22no—
75#126×C43—22no—
76#125×C43—21no—
77#125×C43—22no—
78#124×C43—21no—
79#124×C43—22no—
80#123×C43—22no—
81#123×C43—22no—
82#123×C43—22no—
83#123×C43—22no—
84#123×C43—22no—
85C22⋊Q8×C43—21no—
86C22⋊Q8×C43—22no—
87C22⋊Q8×C43—21no—
88C22⋊Q8×C43—21no—
89C22⋊Q8×C43—21no—
90C22⋊Q8×C43—21no—
91C22⋊Q8×C43—44no—
92#121×C43—21no—
93#121×C43—22no—
94#121×C43—21no—
95#121×C43—21no—
96#121×C43—21no—
97#121×C43—21no—
98#121×C43—22no—
99#121×C43—22no—
100#121×C43—44no—
101#120×C43—22no—
102#120×C43—22no—
103#120×C43—22no—
104#120×C43—22no—
105#120×C43—24no—
106#120×C43—42no—
107C4×Q8×C43—21no—
108C4×D4×C43—22no—
109C4×D4×C43—21no—
110C4×D4×C43—21no—
111C4×D4×C43—21no—
112C4×D4×C43—21no—
113C4×D4×C43—21no—
114C4×D4×C43—22no—
115C4×D4×C43—22no—
116C4×D4×C43—22no—
117C4×D4×C43—22no—
118C4×D4×C43—44no—
119#117×C43—21no—
120#117×C43—22no—
121#117×C43—22no—
122C2×C4⋊C4×C43—21no—
123C2×C4⋊C4×C43—21no—
124C2×C4⋊C4×C43—21no—
125C2×C4⋊C4×C43—22no—
126C2×C4⋊C4×C43D411yescharacteristic, complemented
127C2×C4⋊C4×C43D411yescharacteristic, complemented
128C2×C4⋊C4×C43D411yescharacteristic, complemented
129C2×C4⋊C4×C43D412yescomplemented
130C2×C22⋊C4×C43—22no—
131C2×C22⋊C4×C43—21no—
132C2×C22⋊C4×C43—21no—
133C2×C22⋊C4×C43—22no—
134C2×C22⋊C4×C43—21no—
135C2×C22⋊C4×C43—22no—
136C2×C22⋊C4×C43—22no—
137C2×C22⋊C4×C43—21no—
138C2×C22⋊C4×C43—22no—
139C2×C22⋊C4×C43D411yescharacteristic, complemented
140C2×C22⋊C4×C43D412yescomplemented
141C2×C22⋊C4×C43C2312yes—
142C2×C22⋊C4×C43C2311yescharacteristic
143C2×C22⋊C4×C43C2312yes—
144C2×C22⋊C4×C43C2311yescharacteristic
145C2×C22⋊C4×C43C2312yes—
146C2×C22⋊C4×C43C2311yescharacteristic
147C2×C42×C43—21no—
148C2×C42×C43D411yescharacteristic, complemented
149#99×C43—24no—
150#99×C43—42no—
151#99×C43—42no—
152#95×C43—21no—
153#95×C43—21no—
154#95×C43—21no—
155#95×C43—22no—
156#95×C43—22no—
157#95×C43—21no—
158#95×C43—21no—
159C24×C43—21no—
160C24×C43—21no—
161C24×C43—21no—
162C24×C43—21no—
163C24×C43—21no—
164C24×C43—21no—
165C24×C43—42no—
166C24×C43—42no—
167C24×C43C2×D412yes—
168C24×C43C2×D411yescharacteristic
169C24×C43#4112yescomplemented
170C24×C43C2411yescharacteristic
171#41×C43—82no—
172C2×Q8×C43—21no—
173C2×Q8×C43—21no—
174C2×Q8×C43—42no—
175C2×D4×C43—24no—
176C2×D4×C43—22no—
177C2×D4×C43—22no—
178C2×D4×C43—21no—
179C2×D4×C43—21no—
180C2×D4×C43—21no—
181C2×D4×C43—22no—
182C2×D4×C43—21no—
183C2×D4×C43—22no—
184C2×D4×C43—22no—
185C2×D4×C43—21no—
186C2×D4×C43—21no—
187C2×D4×C43—22no—
188C2×D4×C43—21no—
189C2×D4×C43—22no—
190C2×D4×C43—21no—
191C2×D4×C43—22no—
192C2×D4×C43—44no—
193C2×D4×C43—42no—
194C2×D4×C43—42no—
195C2×D4×C43—44no—
196C2×D4×C43—44no—
197C2×D4×C43—42no—
198C22×C4×C43—24no—
199C22×C4×C43—24no—
200C22×C4×C43—24no—
201C22×C4×C43—22no—
202C22×C4×C43—22no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—22no—
211C22×C4×C43—22no—
212C22×C4×C43—42no—
213C22×C4×C43—42no—
214C22×C4×C43—42no—
215C22×C4×C43—42no—
216C22×C4×C43—42no—
217C22×C4×C43—42no—
218C22×C4×C43—42no—
219C22×C4×C43—42no—
220C22×C4×C43—42no—
221C22×C4×C43—42no—
222C22×C4×C43—42no—
223C22×C4×C43—42no—
224C22×C4×C43—41no—
225C22×C4×C43—41no—
226C22×C4×C43—41no—
227C22×C4×C43—41no—
228C22×C4×C43C2×D411yescharacteristic
229C22×C4×C43C2×D412yes—
230C22×C4×C43C2×D411yescharacteristic
231C22×C4×C43C2×D411yescharacteristic
232C22×C4×C43C2×D411yescharacteristic
233C22×C4×C43C2×D411yescharacteristic
234C22×C4×C43C2×D412yes—
235C22×C4×C43C2×D411yescharacteristic
236C22×C4×C43C2×D412yes—
237C22×C4×C43C2×D411yescharacteristic
238C22×C4×C43C2×D411yescharacteristic
239C22×C4×C43C2×D411yescharacteristic
240C4⋊C4×C43—22no—
241C4⋊C4×C43—22no—
242C4⋊C4×C43—22no—
243C4⋊C4×C43—22no—
244C4⋊C4×C43—21no—
245C4⋊C4×C43—22no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43—21no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43—22no—
251C4⋊C4×C43—21no—
252C4⋊C4×C43—42no—
253C4⋊C4×C43—42no—
254C4⋊C4×C43—42no—
255C4⋊C4×C43—44no—
256C22⋊C4×C43—22no—
257C22⋊C4×C43—22no—
258C22⋊C4×C43—24no—
259C22⋊C4×C43—22no—
260C22⋊C4×C43—22no—
261C22⋊C4×C43—22no—
262C22⋊C4×C43—22no—
263C22⋊C4×C43—22no—
264C22⋊C4×C43—21no—
265C22⋊C4×C43—21no—
266C22⋊C4×C43—22no—
267C22⋊C4×C43—21no—
268C22⋊C4×C43—22no—
269C22⋊C4×C43—21no—
270C22⋊C4×C43—22no—
271C22⋊C4×C43—21no—
272C22⋊C4×C43—22no—
273C22⋊C4×C43—22no—
274C22⋊C4×C43—21no—
275C22⋊C4×C43—22no—
276C22⋊C4×C43—22no—
277C22⋊C4×C43—21no—
278C22⋊C4×C43—44no—
279C22⋊C4×C43—44no—
280C22⋊C4×C43—42no—
281C22⋊C4×C43—42no—
282C22⋊C4×C43—44no—
283C22⋊C4×C43—42no—
284C22⋊C4×C43—44no—
285C22⋊C4×C43#4112yescomplemented
286C42×C43—22no—
287C42×C43—22no—
288C42×C43—21no—
289C42×C43—21no—
290C42×C43—42no—
291C23×C43—22no—
292C23×C43—22no—
293C23×C43—22no—
294C23×C43—22no—
295C23×C43—22no—
296C23×C43—22no—
297C23×C43—22no—
298C23×C43—22no—
299C23×C43—22no—
300C23×C43—21no—
301C23×C43—22no—
302C23×C43—21no—
303C23×C43—21no—
304C23×C43—22no—
305C23×C43—22no—
306C23×C43—41no—
307C23×C43—44no—
308C23×C43—41no—
309C23×C43—41no—
310C23×C43—41no—
311C23×C43—41no—
312C23×C43—41no—
313C23×C43—41no—
314C23×C43—41no—
315C23×C43—44no—
316C23×C43—44no—
317C23×C43—44no—
318C23×C43—41no—
319C23×C43—41no—
320C23×C43—42no—
321C23×C43—42no—
322C23×C43—41no—
323C23×C43—41no—
324C23×C43—41no—
325C23×C43—41no—
326C23×C43C22×D411yescharacteristic
327C23×C43C22×D411yescharacteristic
328C23×C43C22×D411yescharacteristic
329C23×C43C2×#4111yescharacteristic
330C23×C43C2×#4111yescharacteristic
331C23×C43H(5,𝔽2)11yescharacteristic
332C23×C432−1+411yescharacteristic
333Q8×C43—42no—
334Q8×C43—81no—
335D4×C43—48no—
336D4×C43—42no—
337D4×C43—42no—
338D4×C43—41no—
339D4×C43—41no—
340D4×C43—41no—
341D4×C43—42no—
342D4×C43—42no—
343D4×C43—41no—
344D4×C43—42no—
345D4×C43—81no—
346D4×C43—82no—
347D4×C43—82no—
348D4×C43—88no—
349C2×C4×C43—22no—
350C2×C4×C43—22no—
351C2×C4×C43—22no—
352C2×C4×C43—22no—
353C2×C4×C43—22no—
354C2×C4×C43—22no—
355C2×C4×C43—21no—
356C2×C4×C43—22no—
357C2×C4×C43—21no—
358C2×C4×C43—21no—
359C2×C4×C43—22no—
360C2×C4×C43—22no—
361C2×C4×C43—21no—
362C2×C4×C43—22no—
363C2×C4×C43—21no—
364C2×C4×C43—22no—
365C2×C4×C43—22no—
366C2×C4×C43—41no—
367C2×C4×C43—41no—
368C2×C4×C43—41no—
369C2×C4×C43—44no—
370C2×C4×C43—44no—
371C2×C4×C43—44no—
372C2×C4×C43—41no—
373C2×C4×C43—41no—
374C2×C4×C43—41no—
375C2×C4×C43—41no—
376C2×C4×C43—41no—
377C2×C4×C43—41no—
378C2×C4×C43—44no—
379C2×C4×C43—42no—
380C2×C4×C43—41no—
381C2×C4×C43—42no—
382C2×C4×C43—41no—
383C2×C4×C43—42no—
384C2×C4×C43—41no—
385C2×C4×C43—42no—
386C2×C4×C43—42no—
387C2×C4×C43—41no—
388C2×C4×C43—42no—
389C2×C4×C43—42no—
390C2×C4×C43—41no—
391C2×C4×C43—42no—
392C2×C4×C43—42no—
393C2×C4×C43—81no—
394C2×C4×C43—82no—
395C2×C4×C43—82no—
396C2×C4×C43#12011yescharacteristic
397C2×C4×C43#12011yescharacteristic
398C2×C4×C43#12011yescharacteristic
399C2×C4×C43#12011yescharacteristic
400#24140C4311yesmaximal, characteristic, direct product factor, Sylow
401C22×C43—21no—
402C22×C43—21no—
403C22×C43—21no—
404C22×C43—21no—
405C22×C43—21no—
406C22×C43—21no—
407C22×C43—24no—
408C22×C43—24no—
409C22×C43—24no—
410C22×C43—41no—
411C22×C43—41no—
412C22×C43—41no—
413C22×C43—41no—
414C22×C43—42no—
415C22×C43—42no—
416C22×C43—42no—
417C22×C43—42no—
418C22×C43—42no—
419C22×C43—42no—
420C22×C43—42no—
421C22×C43—42no—
422C22×C43—42no—
423C22×C43—42no—
424C22×C43—42no—
425C22×C43—42no—
426C22×C43—42no—
427C22×C43—41no—
428C22×C43—42no—
429C22×C43—41no—
430C22×C43—42no—
431C22×C43—42no—
432C22×C43—41no—
433C22×C43—81no—
434C22×C43—82no—
435C22×C43—82no—
436C22×C43C2×#12011yescharacteristic
437C22×C43#52511yescharacteristic
438C22×C43#53711yescharacteristic
439C22×C43#54611yescharacteristic
440C22×C43#54711yescharacteristic
441C22×C43#54811yescharacteristic
442C22×C43#55011yescharacteristic
443C4×C43—21no—
444C4×C43—21no—
445C4×C43—21no—
446C4×C43—42no—
447C4×C43—41no—
448C4×C43—42no—
449C4×C43—42no—
450C4×C43—41no—
451C4×C43—42no—
452C4×C43—41no—
453C4×C43—42no—
454C4×C43—82no—
455C4×C43—81no—
456C4×C43—82no—
457C4×C43B(4,𝔽2)12yes—
458#3505C2×C4311yescharacteristic, complemented
459#2848C2×C4311yescharacteristic, complemented
460#2847C2×C4311yescharacteristic, complemented
461C4×#120C2×C4311yescharacteristic, complemented
462#2044C2×C4312yescomplemented
463#2021C2×C4312yescomplemented
464#1996C2×C4311yescharacteristic, complemented
465#1964C2×C4311yescharacteristic, complemented
466#1889C2×C4312yescomplemented
467#1867C2×C4312yescomplemented
468#1799C2×C4311yescharacteristic, complemented
469C2×C43—21no—
470C2×C43—21no—
471C2×C43—21no—
472C2×C43—21no—
473C2×C43—21no—
474C2×C43—21no—
475C2×C43—44no—
476C2×C43—81no—
477C2×C43—82no—
478C2×C43#240711yescharacteristic
479C2×C43C2×B(4,𝔽2)11yescharacteristic
480C2×C43#302511yescharacteristic
481C24×C4C22×C4311yescharacteristic
482#553—21no—
483#553—22no—
484#552—21no—
485#551—22no—
486#548—21no—
487#546—21no—
488#539—21no—
489#538—21no—
490#534C22×C4312yes—
491#529—21no—
492#525—21no—
493C2×C22⋊Q8—21no—
494C2×C22⋊Q8C22×C4311yescharacteristic
495C2×#121—21no—
496C2×#121C22×C4311yescharacteristic
497C2×#120C22×C4311yescharacteristic
498C2×#120C22×C4312yes—
499#518C22×C4312yes—
500C2×C4×D4—21no—
501C2×C4×D4C22×C4311yescharacteristic
502C2×#99C22×C4312yes—
503C2×#99C22×C4312yes—
504C2×#99C22×C4312yes—
505#386—22no—
506#386—21no—
507#386C22×C4312yes—
508#386C22×C4311yescharacteristic
509#385—22no—
510#385—21no—
511#385C22×C4312yes—
512#385C22×C4311yescharacteristic
513#380—21no—
514#380—21no—
515#380C22×C4311yescharacteristic
516#380C22×C4311yescharacteristic
517#379C22×C4312yes—
518#379C22×C4311yescharacteristic
519C4×C22⋊C4—21no—
520C4×C22⋊C4C22×C4311yescharacteristic
521#342C22×C4312yes—
522#342C22×C4312yes—
523#342C22×C4312yes—
524C43#2414011yescharacteristic, direct product factor, Sylow
525C25C23×C4311yescharacteristic
526C2×#41—21no—
527C22×Q8D4×C4311yescharacteristic, complemented
528C22×D4—21no—
529C22×D4—22no—
530C22×D4D4×C4311yescharacteristic, complemented
531C22×D4C23×C4311yescharacteristic
532C22×D4C23×C4312yes—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—44no—
540C23×C4D4×C4311yescharacteristic, complemented
541C23×C4C23×C4311yescharacteristic
542C23×C4C23×C4311yescharacteristic
543#126—22no—
544#126—22no—
545#126—22no—
546#125—21no—
547#125—22no—
548#124—21no—
549#124—22no—
550#123—22no—
551#123—22no—
552#123—22no—
553#123—22no—
554#123—22no—
555C22⋊Q8—21no—
556C22⋊Q8—22no—
557C22⋊Q8—21no—
558C22⋊Q8—21no—
559C22⋊Q8—21no—
560C22⋊Q8—21no—
561C22⋊Q8—44no—
562#121—21no—
563#121—22no—
564#121—21no—
565#121—21no—
566#121—21no—
567#121—21no—
568#121—22no—
569#121—22no—
570#121—44no—
571#120—22no—
572#120—22no—
573#120—22no—
574#120—22no—
575#120—24no—
576#120—42no—
577C4×Q8—21no—
578C4×D4—22no—
579C4×D4—21no—
580C4×D4—21no—
581C4×D4—21no—
582C4×D4—21no—
583C4×D4—21no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—44no—
589#117—21no—
590#117—22no—
591#117—22no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4D4×C4311yescharacteristic, complemented
597C2×C4⋊C4D4×C4311yescharacteristic, complemented
598C2×C4⋊C4D4×C4311yescharacteristic, complemented
599C2×C4⋊C4D4×C4312yescomplemented
600C2×C22⋊C4—22no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—22no—
606C2×C22⋊C4—22no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4D4×C4311yescharacteristic, complemented
610C2×C22⋊C4D4×C4312yescomplemented
611C2×C22⋊C4C23×C4312yes—
612C2×C22⋊C4C23×C4311yescharacteristic
613C2×C22⋊C4C23×C4312yes—
614C2×C22⋊C4C23×C4311yescharacteristic
615C2×C22⋊C4C23×C4312yes—
616C2×C22⋊C4C23×C4311yescharacteristic
617C2×C42—21no—
618C2×C42D4×C4311yescharacteristic, complemented
619#99—24no—
620#99—42no—
621#99—42no—
622#95—21no—
623#95—21no—
624#95—21no—
625#95—22no—
626#95—22no—
627#95—21no—
628#95—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—42no—
636C24—42no—
637C24C2×D4×C4312yes—
638C24C2×D4×C4311yescharacteristic
639C24#41×C4312yescomplemented
640C24C24×C4311yescharacteristic
641#41—82no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—42no—
645C2×D4—24no—
646C2×D4—21no—
647C2×D4—22no—
648C2×D4—21no—
649C2×D4—22no—
650C2×D4—22no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—22no—
654C2×D4—21no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—44no—
666C2×D4—44no—
667C2×D4—44no—
668C22×C4—24no—
669C22×C4—24no—
670C22×C4—24no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—41no—
695C22×C4—41no—
696C22×C4—41no—
697C22×C4—41no—
698C22×C4C2×D4×C4311yescharacteristic
699C22×C4C2×D4×C4312yes—
700C22×C4C2×D4×C4311yescharacteristic
701C22×C4C2×D4×C4311yescharacteristic
702C22×C4C2×D4×C4311yescharacteristic
703C22×C4C2×D4×C4311yescharacteristic
704C22×C4C2×D4×C4312yes—
705C22×C4C2×D4×C4311yescharacteristic
706C22×C4C2×D4×C4312yes—
707C22×C4C2×D4×C4311yescharacteristic
708C22×C4C2×D4×C4311yescharacteristic
709C22×C4C2×D4×C4311yescharacteristic
710C4⋊C4—22no—
711C4⋊C4—22no—
712C4⋊C4—22no—
713C4⋊C4—22no—
714C4⋊C4—21no—
715C4⋊C4—22no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—22no—
721C4⋊C4—21no—
722C4⋊C4—42no—
723C4⋊C4—42no—
724C4⋊C4—42no—
725C4⋊C4—44no—
726C22⋊C4—22no—
727C22⋊C4—22no—
728C22⋊C4—24no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—21no—
734C22⋊C4—22no—
735C22⋊C4—21no—
736C22⋊C4—22no—
737C22⋊C4—21no—
738C22⋊C4—22no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—22no—
742C22⋊C4—22no—
743C22⋊C4—22no—
744C22⋊C4—21no—
745C22⋊C4—22no—
746C22⋊C4—22no—
747C22⋊C4—21no—
748C22⋊C4—44no—
749C22⋊C4—42no—
750C22⋊C4—44no—
751C22⋊C4—42no—
752C22⋊C4—44no—
753C22⋊C4—44no—
754C22⋊C4—42no—
755C22⋊C4#41×C4312yescomplemented
756C42—22no—
757C42—22no—
758C42—21no—
759C42—21no—
760C42—42no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—21no—
771C23—22no—
772C23—21no—
773C23—21no—
774C23—22no—
775C23—22no—
776C23—41no—
777C23—44no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—44no—
786C23—44no—
787C23—44no—
788C23—41no—
789C23—41no—
790C23—42no—
791C23—42no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23C22×D4×C4311yescharacteristic
797C23C22×D4×C4311yescharacteristic
798C23C22×D4×C4311yescharacteristic
799C23C2×#41×C4311yescharacteristic
800C23C2×#41×C4311yescharacteristic
801C23H(5,𝔽2)×C4311yescharacteristic
802C232−1+4×C4311yescharacteristic
803Q8—42no—
804Q8—81no—
805D4—48no—
806D4—42no—
807D4—42no—
808D4—41no—
809D4—41no—
810D4—41no—
811D4—42no—
812D4—42no—
813D4—41no—
814D4—42no—
815D4—81no—
816D4—82no—
817D4—82no—
818D4—88no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—21no—
826C2×C4—22no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—21no—
832C2×C4—22no—
833C2×C4—21no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—44no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—44no—
849C2×C4—42no—
850C2×C4—41no—
851C2×C4—42no—
852C2×C4—41no—
853C2×C4—42no—
854C2×C4—41no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—41no—
859C2×C4—42no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—81no—
864C2×C4—82no—
865C2×C4—82no—
866C2×C4#120×C4311yescharacteristic
867C2×C4#120×C4311yescharacteristic
868C2×C4#120×C4311yescharacteristic
869C2×C4#120×C4311yescharacteristic
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—21no—
876C22—24no—
877C22—24no—
878C22—24no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—41no—
897C22—42no—
898C22—41no—
899C22—42no—
900C22—42no—
901C22—41no—
902C22—82no—
903C22—81no—
904C22—82no—
905C22C2×#120×C4311yescharacteristic
906C22C43×#52511yescharacteristic
907C22C43×#53711yescharacteristic
908C22C43×#54611yescharacteristic
909C22C43×#54711yescharacteristic
910C22C43×#54811yescharacteristic
911C22C43×#55011yescharacteristic
912C4—21no—
913C4—21no—
914C4—21no—
915C4—42no—
916C4—41no—
917C4—42no—
918C4—42no—
919C4—41no—
920C4—42no—
921C4—41no—
922C4—42no—
923C4—82no—
924C4—82no—
925C4—81no—
926C4C43×B(4,𝔽2)12yes—
927C2—21no—
928C2—21no—
929C2—21no—
930C2—21no—
931C2—21no—
932C2—21no—
933C2—44no—
934C2—81no—
935C2—82no—
936C2C43×#240711yescharacteristic
937C2C2×C43×B(4,𝔽2)11yescharacteristic
938C2C43×#302511yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC24C24×C43
LCSG ▷ C24 ▷ 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×#3505C2semidirect
2. C43×#2848C2semidirect
3. C43×#2847C2semidirect
4. C4×#120×C43C2semidirect
5. C43×#2044C2semidirect
6. C43×#2021C2semidirect
7. C43×#1996C2semidirect
8. C43×#1964C2semidirect
9. C43×#1889C2semidirect
10. C43×#1867C2semidirect
11. C43×#1799C2semidirect
57. C22×Q8×C43D4semidirect
60. C22×D4×C43D4semidirect
70. C23×C4×C43D4semidirect
126. C2×C4⋊C4×C43D4semidirect
127. C2×C4⋊C4×C43D4semidirect
128. C2×C4⋊C4×C43D4semidirect
129. C2×C4⋊C4×C43D4semidirect
139. C2×C22⋊C4×C43D4semidirect
140. C2×C22⋊C4×C43D4semidirect
148. C2×C42×C43D4semidirect
169. C24×C43#41semidirect
285. C22⋊C4×C43#41semidirect
400. #24140C43direct (N × H)
458. #3505C2×C43semidirect
459. #2848C2×C43semidirect
460. #2847C2×C43semidirect
461. C4×#120C2×C43semidirect
462. #2044C2×C43semidirect
463. #2021C2×C43semidirect
464. #1996C2×C43semidirect
465. #1964C2×C43semidirect
466. #1889C2×C43semidirect
467. #1867C2×C43semidirect
468. #1799C2×C43semidirect
524. C43#24140direct (N × H)
527. C22×Q8D4×C43semidirect
530. C22×D4D4×C43semidirect
540. C23×C4D4×C43semidirect
596. C2×C4⋊C4D4×C43semidirect
597. C2×C4⋊C4D4×C43semidirect
598. C2×C4⋊C4D4×C43semidirect
599. C2×C4⋊C4D4×C43semidirect
609. C2×C22⋊C4D4×C43semidirect
610. C2×C22⋊C4D4×C43semidirect
618. C2×C42D4×C43semidirect
639. C24#41×C43semidirect
755. C22⋊C4#41×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#35052
C43×#28482
C43×#28472
C4×#120×C432
C43×#20442
C43×#20212
C43×#19962
C43×#19642
C43×#18892
C43×#18672
C43×#17992
#2414043