Finite Group Databasebeta

← C43×#24397 #24944414

Subgroups — C43×#24397 #24944414

Order 11008.

1508 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#537C211yesmaximal, characteristic, complemented
2C2×C43×#469C211yesmaximal, characteristic, complemented
3C2×C43×#465C211yesmaximal, characteristic, complemented
4C2×C43×#449C211yesmaximal, characteristic, complemented
5C2×C43×#408C211yesmaximal, characteristic, complemented
6C43×#2615C211yesmaximal, characteristic, complemented
7C43×#2035C211yesmaximal, characteristic, complemented
8C43×#2034C211yesmaximal, characteristic, complemented
9C43×#2000C211yesmaximal, characteristic, complemented
10C43×#1999C211yesmaximal, characteristic, complemented
11C43×#1894C211yesmaximal, characteristic, complemented
12C43×#1893C211yesmaximal, characteristic, complemented
13C43×#1874C211yesmaximal, characteristic, complemented
14C43×#1853C211yesmaximal, characteristic, complemented
15C43×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C43C2211yescharacteristic
17C22×#41×C43C2211yescharacteristic
18C22×SD16×C43C2211yescharacteristic
19C22×D8×C43C2211yescharacteristic
20C22×M16×C43C2211yescharacteristic
21C23×C8×C43C2211yescharacteristic
22C43×#537—24no—
23C43×#537—24no—
24C2×C22⋊Q8×C43—21no—
25C2×C22⋊Q8×C43C2211yescharacteristic
26C2×C22⋊Q8×C43C2211yescharacteristic
27C2×#121×C43—21no—
28C2×#121×C43—21no—
29C2×#121×C43—21no—
30C2×#121×C43C2211yescharacteristic
31C2×#121×C43C2211yescharacteristic
32C2×#121×C43C2211yescharacteristic
33C2×#121×C43C2211yescharacteristic
34C2×#121×C43C2211yescharacteristic
35C22×C4⋊C4×C43C2211yescharacteristic
36C43×#469—24no—
37C43×#465—24no—
38C43×#449—24no—
39C2×#106×C43C2211yescharacteristic
40C2×#106×C43C2211yescharacteristic
41C2×#103×C43C2211yescharacteristic
42C2×#103×C43C2211yescharacteristic
43C2×#103×C43C2211yescharacteristic
44C2×#102×C43C2211yescharacteristic
45C2×#102×C43C2211yescharacteristic
46C2×#102×C43C2211yescharacteristic
47C2×#102×C43C2211yescharacteristic
48C2×#102×C43C2211yescharacteristic
49C43×#408—24no—
50C2×C22⋊C8×C43C2211yescharacteristic
51C2×C22⋊C8×C43C2211yescharacteristic
52C2×C22⋊C8×C43C2211yescharacteristic
53C2×C22⋊C8×C43C2211yescharacteristic
54C43×#393—21no—
55C43×#392—21no—
56C43×#392—21no—
57C43×#392—21no—
58C43×#380C2211yescharacteristic
59C43×#380C2211yescharacteristic
60C43×#380C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C43×#340C2211yescharacteristic
64C43×#340C2211yescharacteristic
65C2×#41×C43—22no—
66C2×#41×C43—22no—
67C2×#41×C43—22no—
68C2×#41×C43—22no—
69C2×#41×C43—22no—
70C2×#41×C43—22no—
71C2×#41×C43—22no—
72C2×#41×C43—22no—
73C2×#41×C43—41no—
74C2×#41×C43—41no—
75C2×#41×C43—41no—
76C2×#41×C43—41no—
77C22×Q8×C43D411yescharacteristic
78C22×Q8×C43C2311yescharacteristic
79C22×D4×C43—21no—
80C22×D4×C43—21no—
81C22×D4×C43—21no—
82C22×D4×C43—21no—
83C22×D4×C43—21no—
84C22×D4×C43—21no—
85C22×D4×C43D411yescharacteristic
86C22×D4×C43D411yescharacteristic
87C22×D4×C43D411yescharacteristic
88C22×D4×C43C2311yescharacteristic
89C22×D4×C43C2311yescharacteristic
90C23×C4×C43—21no—
91C23×C4×C43—21no—
92C23×C4×C43C2311yescharacteristic
93C23×C4×C43C2311yescharacteristic
94C23×C4×C43C2311yescharacteristic
95C2×SD16×C43—22no—
96C2×SD16×C43—22no—
97C2×SD16×C43—41no—
98C2×D8×C43—22no—
99C2×D8×C43—22no—
100C2×D8×C43—41no—
101C2×M16×C43—22no—
102C2×M16×C43—22no—
103C2×M16×C43—41no—
104C22×C8×C43—22no—
105C22×C8×C43—22no—
106C22×C8×C43—41no—
107C22×C8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C22×C8×C43C2311yescharacteristic
111C22⋊Q8×C43—28no—
112C22⋊Q8×C43—22no—
113C22⋊Q8×C43—22no—
114C22⋊Q8×C43—22no—
115C22⋊Q8×C43D414yescomplemented
116#121×C43—28no—
117#121×C43—28no—
118#121×C43—28no—
119#121×C43—22no—
120#121×C43—22no—
121#121×C43—22no—
122#121×C43—22no—
123#121×C43—22no—
124#121×C43—22no—
125#121×C43—22no—
126#121×C43—41no—
127#121×C43—41no—
128#121×C43D414yescomplemented
129C2×C4⋊C4×C43—21no—
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43—22no—
133C2×C4⋊C4×C43—22no—
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C22⋊C4×C43—21no—
140C2×C22⋊C4×C43—21no—
141C2×C22⋊C4×C43—21no—
142C2×C22⋊C4×C43—21no—
143C2×C22⋊C4×C43—21no—
144C2×C22⋊C4×C43—21no—
145C2×C22⋊C4×C43—21no—
146C2×C22⋊C4×C43—21no—
147C2×C22⋊C4×C43—21no—
148C2×C22⋊C4×C43—21no—
149#106×C43—22no—
150#106×C43—22no—
151#103×C43—22no—
152#103×C43—22no—
153#103×C43—41no—
154#102×C43—22no—
155#102×C43—22no—
156#102×C43—22no—
157#102×C43—22no—
158#102×C43—41no—
159C22⋊C8×C43—22no—
160C22⋊C8×C43—22no—
161C22⋊C8×C43—22no—
162C22⋊C8×C43D414yescomplemented
163#95×C43—21no—
164#95×C43—21no—
165#95×C43—21no—
166C24×C43—21no—
167C24×C43—21no—
168C24×C43C2×D411yescharacteristic
169C24×C43C2×D411yescharacteristic
170C24×C43C2×D411yescharacteristic
171#41×C43—44no—
172#41×C43—44no—
173#41×C43—44no—
174#41×C43—44no—
175#41×C43—44no—
176#41×C43—44no—
177#41×C43—44no—
178#41×C43—44no—
179C2×Q8×C43—22no—
180C2×Q8×C43—22no—
181C2×Q8×C43—21no—
182C2×Q8×C43—21no—
183C2×Q8×C43—21no—
184C2×Q8×C43—21no—
185C2×Q8×C43—21no—
186C2×Q8×C43—41no—
187C2×Q8×C43C2×D412yes—
188C2×D4×C43—24no—
189C2×D4×C43—24no—
190C2×D4×C43—22no—
191C2×D4×C43—22no—
192C2×D4×C43—21no—
193C2×D4×C43—22no—
194C2×D4×C43—22no—
195C2×D4×C43—24no—
196C2×D4×C43—22no—
197C2×D4×C43—22no—
198C2×D4×C43—21no—
199C2×D4×C43—21no—
200C2×D4×C43—21no—
201C2×D4×C43—21no—
202C2×D4×C43—21no—
203C2×D4×C43—21no—
204C2×D4×C43—21no—
205C2×D4×C43—21no—
206C2×D4×C43—21no—
207C2×D4×C43—21no—
208C2×D4×C43—41no—
209C2×D4×C43—41no—
210C2×D4×C43—41no—
211C2×D4×C43—42no—
212C2×D4×C43—42no—
213C2×D4×C43—42no—
214C2×D4×C43—42no—
215C2×D4×C43—42no—
216C2×D4×C43—81no—
217C2×D4×C43—81no—
218C2×D4×C43—81no—
219C2×D4×C43—81no—
220C2×D4×C43—81no—
221C2×D4×C43—81no—
222C2×D4×C43—81no—
223C2×D4×C43—81no—
224C2×D4×C43—81no—
225C2×D4×C43—81no—
226C2×D4×C43C2×D412yes—
227C22×C4×C43—21no—
228C22×C4×C43—21no—
229C22×C4×C43—21no—
230C22×C4×C43—21no—
231C22×C4×C43—21no—
232C22×C4×C43—21no—
233C22×C4×C43—21no—
234C22×C4×C43—21no—
235C22×C4×C43—24no—
236C22×C4×C43—24no—
237C22×C4×C43—21no—
238C22×C4×C43—21no—
239C22×C4×C43—21no—
240C22×C4×C43—21no—
241C22×C4×C43—21no—
242C22×C4×C43—21no—
243C22×C4×C43—21no—
244C22×C4×C43—21no—
245C22×C4×C43—21no—
246C22×C4×C43—21no—
247C22×C4×C43—21no—
248C22×C4×C43—21no—
249C22×C4×C43—42no—
250C22×C4×C43—42no—
251C22×C4×C43—81no—
252C22×C4×C43—81no—
253C22×C4×C43C2×D412yes—
254C22×C4×C43C2×D412yes—
255C22×C4×C43C2×D412yes—
256C22×C4×C43C2×D411yescharacteristic
257C22×C4×C43C2×D411yescharacteristic
258C22×C4×C43C2×D411yescharacteristic
259C22×C4×C43#4112yes—
260C22×C4×C43C2411yescharacteristic
261SD16×C43—44no—
262D8×C43—44no—
263M16×C43—44no—
264C2×C8×C43—21no—
265C2×C8×C43—21no—
266C2×C8×C43—21no—
267C2×C8×C43—21no—
268C2×C8×C43—21no—
269C2×C8×C43—21no—
270C2×C8×C43—21no—
271C2×C8×C43—21no—
272C2×C8×C43—21no—
273C2×C8×C43—21no—
274C2×C8×C43—44no—
275C2×C8×C43C2×D412yes—
276C2×C8×C43C2×D412yes—
277C4⋊C4×C43—24no—
278C4⋊C4×C43—24no—
279C4⋊C4×C43—24no—
280C4⋊C4×C43—21no—
281C4⋊C4×C43—21no—
282C4⋊C4×C43—21no—
283C4⋊C4×C43—21no—
284C4⋊C4×C43—21no—
285C4⋊C4×C43—21no—
286C4⋊C4×C43—21no—
287C4⋊C4×C43—21no—
288C4⋊C4×C43C2×D412yes—
289C4⋊C4×C43C2×D412yes—
290C22⋊C4×C43—24no—
291C22⋊C4×C43—24no—
292C22⋊C4×C43—24no—
293C22⋊C4×C43—24no—
294C22⋊C4×C43—42no—
295C22⋊C4×C43—42no—
296C22⋊C4×C43—42no—
297C22⋊C4×C43—81no—
298C22⋊C4×C43—81no—
299C22⋊C4×C43—81no—
300C23×C43—21no—
301C23×C43—21no—
302C23×C43—21no—
303C23×C43—21no—
304C23×C43—21no—
305C23×C43—21no—
306C23×C43—21no—
307C23×C43—21no—
308C23×C43—21no—
309C23×C43—21no—
310C23×C43—21no—
311C23×C43—21no—
312C23×C43—21no—
313C23×C43—22no—
314C23×C43—21no—
315C23×C43—21no—
316C23×C43—21no—
317C23×C43—21no—
318C23×C43—21no—
319C23×C43—21no—
320C23×C43—41no—
321C23×C43—41no—
322C23×C43—41no—
323C23×C43—41no—
324C23×C43—41no—
325C23×C43—41no—
326C23×C43—41no—
327C23×C43—41no—
328C23×C43—41no—
329C23×C43—41no—
330C23×C43—41no—
331C23×C43—41no—
332C23×C43—41no—
333C23×C43#12012yes—
334C23×C43#12112yes—
335C23×C43C22×D411yescharacteristic
336Q8×C43—22no—
337Q8×C43—22no—
338Q8×C43—44no—
339Q8×C43—41no—
340Q8×C43—41no—
341D4×C43—22no—
342D4×C43—22no—
343D4×C43—44no—
344D4×C43—44no—
345D4×C43—44no—
346D4×C43—48no—
347D4×C43—41no—
348D4×C43—41no—
349D4×C43—41no—
350D4×C43—41no—
351D4×C43—41no—
352D4×C43—41no—
353D4×C43—84no—
354D4×C43—84no—
355D4×C43—84no—
356D4×C43—84no—
357D4×C43—84no—
358C2×C4×C43—21no—
359C2×C4×C43—21no—
360C2×C4×C43—21no—
361C2×C4×C43—21no—
362C2×C4×C43—22no—
363C2×C4×C43—22no—
364C2×C4×C43—22no—
365C2×C4×C43—22no—
366C2×C4×C43—22no—
367C2×C4×C43—22no—
368C2×C4×C43—22no—
369C2×C4×C43—22no—
370C2×C4×C43—22no—
371C2×C4×C43—22no—
372C2×C4×C43—22no—
373C2×C4×C43—21no—
374C2×C4×C43—21no—
375C2×C4×C43—21no—
376C2×C4×C43—48no—
377C2×C4×C43—41no—
378C2×C4×C43—41no—
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—41no—
391C2×C4×C43—41no—
392C2×C4×C43—41no—
393C2×C4×C43—41no—
394C2×C4×C43—41no—
395C2×C4×C43—41no—
396C2×C4×C43—84no—
397C2×C4×C43#12012yes—
398C2×C4×C43#12112yes—
399C2×C4×C43C22×D411yescharacteristic
400C2×C4×C43C22×D411yescharacteristic
401C2×C4×C43C22×D411yescharacteristic
402C2×C4×C43C2×#4111yescharacteristic
403C2×C4×C43H(5,𝔽2)11yescharacteristic
404C2×C4×C43H(5,𝔽2)11yescharacteristic
405C8×C43—22no—
406C8×C43—22no—
407C8×C43—41no—
408C8×C43—41no—
409#24397C4311yesmaximal, characteristic, direct product factor, Sylow
410C22×C43—22no—
411C22×C43—22no—
412C22×C43—22no—
413C22×C43—22no—
414C22×C43—22no—
415C22×C43—22no—
416C22×C43—41no—
417C22×C43—41no—
418C22×C43—41no—
419C22×C43—41no—
420C22×C43—41no—
421C22×C43—41no—
422C22×C43—41no—
423C22×C43—41no—
424C22×C43—41no—
425C22×C43—42no—
426C22×C43—41no—
427C22×C43—41no—
428C22×C43—41no—
429C22×C43—42no—
430C22×C43—41no—
431C22×C43—42no—
432C22×C43—41no—
433C22×C43—41no—
434C22×C43—81no—
435C22×C43—81no—
436C22×C43—81no—
437C22×C43—81no—
438C22×C43—81no—
439C22×C43—81no—
440C22×C43—81no—
441C22×C43—81no—
442C22×C43—81no—
443C22×C43—81no—
444C22×C43—81no—
445C22×C43C2×#12011yescharacteristic
446C22×C43C2×#12111yescharacteristic
447C22×C43#53411yescharacteristic
448C22×C43#57611yescharacteristic
449C22×C43#57711yescharacteristic
450C22×C43#57711yescharacteristic
451C22×C43#57711yescharacteristic
452C4×C43—22no—
453C4×C43—22no—
454C4×C43—41no—
455C4×C43—42no—
456C4×C43—42no—
457C4×C43—42no—
458C4×C43—81no—
459C4×C43—81no—
460C4×C43—81no—
461C4×C43D4211yescharacteristic
462C4×C43D4211yescharacteristic
463C4×C43#54611yescharacteristic
464C4×C43#54611yescharacteristic
465C2×#537C2×C4311yescharacteristic, complemented
466C2×#469C2×C4311yescharacteristic, complemented
467C2×#465C2×C4311yescharacteristic, complemented
468C2×#449C2×C4311yescharacteristic, complemented
469C2×#408C2×C4311yescharacteristic, complemented
470#2615C2×C4311yescharacteristic, complemented
471#2035C2×C4311yescharacteristic, complemented
472#2034C2×C4311yescharacteristic, complemented
473#2000C2×C4311yescharacteristic, complemented
474#1999C2×C4311yescharacteristic, complemented
475#1894C2×C4311yescharacteristic, complemented
476#1893C2×C4311yescharacteristic, complemented
477#1874C2×C4311yescharacteristic, complemented
478#1853C2×C4311yescharacteristic, complemented
479#1788C2×C4311yescharacteristic, complemented
480C2×C43—42no—
481C2×C43—42no—
482C2×C43—81no—
483C2×C43—82no—
484C2×C43—161no—
485C2×C43#241011yescharacteristic
486C2×C43#301011yescharacteristic
487C2×C43#301211yescharacteristic
488C2×C43#306011yescharacteristic
489C2×C43#306211yescharacteristic
490C2×C43#319811yescharacteristic
491C2×C43#320411yescharacteristic
492C22×#41C22×C4311yescharacteristic
493C22×#41C22×C4311yescharacteristic
494C22×SD16C22×C4311yescharacteristic
495C22×D8C22×C4311yescharacteristic
496C22×M16C22×C4311yescharacteristic
497C23×C8C22×C4311yescharacteristic
498#537—24no—
499#537—24no—
500C2×C22⋊Q8—21no—
501C2×C22⋊Q8C22×C4311yescharacteristic
502C2×C22⋊Q8C22×C4311yescharacteristic
503C2×#121—21no—
504C2×#121—21no—
505C2×#121—21no—
506C2×#121C22×C4311yescharacteristic
507C2×#121C22×C4311yescharacteristic
508C2×#121C22×C4311yescharacteristic
509C2×#121C22×C4311yescharacteristic
510C2×#121C22×C4311yescharacteristic
511C22×C4⋊C4C22×C4311yescharacteristic
512#469—24no—
513#465—24no—
514#449—24no—
515C2×#106C22×C4311yescharacteristic
516C2×#106C22×C4311yescharacteristic
517C2×#103C22×C4311yescharacteristic
518C2×#103C22×C4311yescharacteristic
519C2×#103C22×C4311yescharacteristic
520C2×#102C22×C4311yescharacteristic
521C2×#102C22×C4311yescharacteristic
522C2×#102C22×C4311yescharacteristic
523C2×#102C22×C4311yescharacteristic
524C2×#102C22×C4311yescharacteristic
525#408—24no—
526C2×C22⋊C8C22×C4311yescharacteristic
527C2×C22⋊C8C22×C4311yescharacteristic
528C2×C22⋊C8C22×C4311yescharacteristic
529C2×C22⋊C8C22×C4311yescharacteristic
530#393—21no—
531#392—21no—
532#392—21no—
533#392—21no—
534#380C22×C4311yescharacteristic
535#380C22×C4311yescharacteristic
536#380C22×C4311yescharacteristic
537#340C22×C4311yescharacteristic
538#340C22×C4311yescharacteristic
539#340C22×C4311yescharacteristic
540#340C22×C4311yescharacteristic
541C43#2439711yescharacteristic, direct product factor, Sylow
542C2×#41—22no—
543C2×#41—22no—
544C2×#41—22no—
545C2×#41—22no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—41no—
551C2×#41—41no—
552C2×#41—41no—
553C2×#41—41no—
554C22×Q8D4×C4311yescharacteristic
555C22×Q8C23×C4311yescharacteristic
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4D4×C4311yescharacteristic
563C22×D4D4×C4311yescharacteristic
564C22×D4D4×C4311yescharacteristic
565C22×D4C23×C4311yescharacteristic
566C22×D4C23×C4311yescharacteristic
567C23×C4—21no—
568C23×C4—21no—
569C23×C4C23×C4311yescharacteristic
570C23×C4C23×C4311yescharacteristic
571C23×C4C23×C4311yescharacteristic
572C2×SD16—22no—
573C2×SD16—22no—
574C2×SD16—41no—
575C2×D8—22no—
576C2×D8—22no—
577C2×D8—41no—
578C2×M16—22no—
579C2×M16—22no—
580C2×M16—41no—
581C22×C8—22no—
582C22×C8—22no—
583C22×C8—41no—
584C22×C8C23×C4311yescharacteristic
585C22×C8C23×C4311yescharacteristic
586C22×C8C23×C4311yescharacteristic
587C22×C8C23×C4311yescharacteristic
588C22⋊Q8—28no—
589C22⋊Q8—22no—
590C22⋊Q8—22no—
591C22⋊Q8—22no—
592C22⋊Q8D4×C4314yescomplemented
593#121—28no—
594#121—28no—
595#121—28no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—22no—
600#121—22no—
601#121—22no—
602#121—22no—
603#121—41no—
604#121—41no—
605#121D4×C4314yescomplemented
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4C23×C4311yescharacteristic
612C2×C4⋊C4C23×C4311yescharacteristic
613C2×C4⋊C4C23×C4311yescharacteristic
614C2×C4⋊C4C23×C4311yescharacteristic
615C2×C4⋊C4C23×C4311yescharacteristic
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626#106—22no—
627#106—22no—
628#103—22no—
629#103—22no—
630#103—41no—
631#102—22no—
632#102—22no—
633#102—22no—
634#102—22no—
635#102—41no—
636C22⋊C8—22no—
637C22⋊C8—22no—
638C22⋊C8—22no—
639C22⋊C8D4×C4314yescomplemented
640#95—21no—
641#95—21no—
642#95—21no—
643C24—21no—
644C24—21no—
645C24C2×D4×C4311yescharacteristic
646C24C2×D4×C4311yescharacteristic
647C24C2×D4×C4311yescharacteristic
648#41—44no—
649#41—44no—
650#41—44no—
651#41—44no—
652#41—44no—
653#41—44no—
654#41—44no—
655#41—44no—
656C2×Q8—22no—
657C2×Q8—22no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—41no—
664C2×Q8C2×D4×C4312yes—
665C2×D4—24no—
666C2×D4—22no—
667C2×D4—22no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—24no—
671C2×D4—24no—
672C2×D4—22no—
673C2×D4—22no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—41no—
686C2×D4—41no—
687C2×D4—41no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—81no—
694C2×D4—81no—
695C2×D4—81no—
696C2×D4—81no—
697C2×D4—81no—
698C2×D4—81no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4C2×D4×C4312yes—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—24no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—24no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—42no—
727C22×C4—42no—
728C22×C4—81no—
729C22×C4—81no—
730C22×C4C2×D4×C4311yescharacteristic
731C22×C4C2×D4×C4311yescharacteristic
732C22×C4C2×D4×C4312yes—
733C22×C4C2×D4×C4312yes—
734C22×C4C2×D4×C4311yescharacteristic
735C22×C4C2×D4×C4312yes—
736C22×C4#41×C4312yes—
737C22×C4C24×C4311yescharacteristic
738SD16—44no—
739D8—44no—
740M16—44no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—44no—
752C2×C8C2×D4×C4312yes—
753C2×C8C2×D4×C4312yes—
754C4⋊C4—24no—
755C4⋊C4—24no—
756C4⋊C4—24no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4C2×D4×C4312yes—
766C4⋊C4C2×D4×C4312yes—
767C22⋊C4—24no—
768C22⋊C4—24no—
769C22⋊C4—24no—
770C22⋊C4—24no—
771C22⋊C4—42no—
772C22⋊C4—42no—
773C22⋊C4—42no—
774C22⋊C4—81no—
775C22⋊C4—81no—
776C22⋊C4—81no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—22no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23#120×C4312yes—
811C23#121×C4312yes—
812C23C22×D4×C4311yescharacteristic
813Q8—22no—
814Q8—22no—
815Q8—44no—
816Q8—41no—
817Q8—41no—
818D4—22no—
819D4—22no—
820D4—44no—
821D4—44no—
822D4—44no—
823D4—48no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—84no—
831D4—84no—
832D4—84no—
833D4—84no—
834D4—84no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—48no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—84no—
874C2×C4#120×C4312yes—
875C2×C4#121×C4312yes—
876C2×C4C22×D4×C4311yescharacteristic
877C2×C4C22×D4×C4311yescharacteristic
878C2×C4C22×D4×C4311yescharacteristic
879C2×C4C2×#41×C4311yescharacteristic
880C2×C4H(5,𝔽2)×C4311yescharacteristic
881C2×C4H(5,𝔽2)×C4311yescharacteristic
882C8—22no—
883C8—22no—
884C8—41no—
885C8—41no—
886C22—22no—
887C22—22no—
888C22—22no—
889C22—22no—
890C22—22no—
891C22—22no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—42no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—42no—
906C22—41no—
907C22—42no—
908C22—41no—
909C22—41no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22C2×#120×C4311yescharacteristic
922C22C2×#121×C4311yescharacteristic
923C22C43×#53411yescharacteristic
924C22C43×#57611yescharacteristic
925C22C43×#57711yescharacteristic
926C22C43×#57711yescharacteristic
927C22C43×#57711yescharacteristic
928C4—22no—
929C4—22no—
930C4—41no—
931C4—42no—
932C4—42no—
933C4—42no—
934C4—81no—
935C4—81no—
936C4—81no—
937C4D42×C4311yescharacteristic
938C4D42×C4311yescharacteristic
939C4C43×#54611yescharacteristic
940C4C43×#54611yescharacteristic
941C2—42no—
942C2—42no—
943C2—81no—
944C2—82no—
945C2—161no—
946C2C43×#241011yescharacteristic
947C2C43×#301011yescharacteristic
948C2C43×#301211yescharacteristic
949C2C43×#306011yescharacteristic
950C2C43×#306211yescharacteristic
951C2C43×#319811yescharacteristic
952C2C43×#320411yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C22×#41×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#537C2semidirect
2. C2×C43×#469C2semidirect
3. C2×C43×#465C2semidirect
4. C2×C43×#449C2semidirect
5. C2×C43×#408C2semidirect
6. C43×#2615C2semidirect
7. C43×#2035C2semidirect
8. C43×#2034C2semidirect
9. C43×#2000C2semidirect
10. C43×#1999C2semidirect
11. C43×#1894C2semidirect
12. C43×#1893C2semidirect
13. C43×#1874C2semidirect
14. C43×#1853C2semidirect
15. C43×#1788C2semidirect
115. C22⋊Q8×C43D4semidirect
128. #121×C43D4semidirect
162. C22⋊C8×C43D4semidirect
409. #24397C43direct (N × H)
465. C2×#537C2×C43semidirect
466. C2×#469C2×C43semidirect
467. C2×#465C2×C43semidirect
468. C2×#449C2×C43semidirect
469. C2×#408C2×C43semidirect
470. #2615C2×C43semidirect
471. #2035C2×C43semidirect
472. #2034C2×C43semidirect
473. #2000C2×C43semidirect
474. #1999C2×C43semidirect
475. #1894C2×C43semidirect
476. #1893C2×C43semidirect
477. #1874C2×C43semidirect
478. #1853C2×C43semidirect
479. #1788C2×C43semidirect
541. C43#24397direct (N × H)
592. C22⋊Q8D4×C43semidirect
605. #121D4×C43semidirect
639. C22⋊C8D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#5372
C2×C43×#4692
C2×C43×#4652
C2×C43×#4492
C2×C43×#4082
C43×#26152
C43×#20352
C43×#20342
C43×#20002
C43×#19992
C43×#18942
C43×#18932
C43×#18742
C43×#18532
C43×#17882
#2439743