Finite Group Databasebeta

← C43×#24388 #24944405

Subgroups — C43×#24388 #24944405

Order 11008.

1646 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#525C211yesmaximal, characteristic, complemented
2C2×C43×#469C211yesmaximal, characteristic, complemented
3C2×C43×#468C211yesmaximal, characteristic, complemented
4C2×C43×#449C211yesmaximal, characteristic, complemented
5C2×C43×#407C211yesmaximal, characteristic, complemented
6C43×#2847C211yesmaximal, characteristic, complemented
7C43×#2035C211yesmaximal, characteristic, complemented
8C43×#2033C211yesmaximal, characteristic, complemented
9C43×#2000C211yesmaximal, characteristic, complemented
10C43×#1999C211yesmaximal, characteristic, complemented
11C43×#1895C211yesmaximal, characteristic, complemented
12C43×#1894C211yesmaximal, characteristic, complemented
13C43×#1875C211yesmaximal, characteristic, complemented
14C43×#1854C211yesmaximal, characteristic, complemented
15C43×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C43C2211yescharacteristic
17C24×C4×C43C2211yescharacteristic
18C22×SD16×C43C2211yescharacteristic, complemented
19C22×D8×C43C2211yescharacteristic, complemented
20C22×M16×C43C2211yescharacteristic
21C22×M16×C43C2211yescharacteristic
22C43×#525—24no—
23C43×#525—24no—
24C2×#123×C43—21no—
25C2×C22⋊Q8×C43C2211yescharacteristic
26C2×C22⋊Q8×C43C2211yescharacteristic
27C2×#121×C43C2211yescharacteristic
28C2×#121×C43C2211yescharacteristic
29C2×#121×C43C2211yescharacteristic
30C2×#121×C43C2211yescharacteristic
31C2×#121×C43C2211yescharacteristic
32C2×#120×C43—21no—
33C2×#120×C43—21no—
34C2×C4×D4×C43—21no—
35C2×C4×D4×C43—21no—
36C2×#117×C43C2211yescharacteristic
37C43×#469—24no—
38C43×#468—24no—
39C43×#449—24no—
40C2×#107×C43C2211yescharacteristic, complemented
41C2×#106×C43C2211yescharacteristic, complemented
42C2×#103×C43C2211yescharacteristic, complemented
43C2×#103×C43C2211yescharacteristic, complemented
44C2×#103×C43C2211yescharacteristic, complemented
45C2×#102×C43C2211yescharacteristic, complemented
46C2×#102×C43C2211yescharacteristic, complemented
47C2×#102×C43C2211yescharacteristic, complemented
48C2×#102×C43C2211yescharacteristic, complemented
49C2×#102×C43C2211yescharacteristic, complemented
50C43×#407—24no—
51C2×C22⋊C8×C43C2211yescharacteristic
52C2×C22⋊C8×C43C2211yescharacteristic
53C2×C22⋊C8×C43C2211yescharacteristic
54C2×C22⋊C8×C43C2211yescharacteristic
55C43×#386—21no—
56C43×#386—21no—
57C43×#386—21no—
58C43×#380C2211yescharacteristic
59C43×#380C2211yescharacteristic
60C43×#380C2211yescharacteristic
61C43×#340C2211yescharacteristic, complemented
62C43×#340C2211yescharacteristic, complemented
63C43×#340C2211yescharacteristic, complemented
64C43×#340C2211yescharacteristic, complemented
65C25×C43D411yescharacteristic
66C2×#41×C43—22no—
67C2×#41×C43—22no—
68C2×#41×C43—22no—
69C2×#41×C43—22no—
70C2×#41×C43—41no—
71C2×#41×C43—41no—
72C22×Q8×C43C2311yescharacteristic
73C22×D4×C43—21no—
74C22×D4×C43—21no—
75C22×D4×C43—21no—
76C22×D4×C43—21no—
77C22×D4×C43—21no—
78C22×D4×C43—21no—
79C22×D4×C43C2311yescharacteristic
80C22×D4×C43C2311yescharacteristic
81C23×C4×C43—21no—
82C23×C4×C43—22no—
83C23×C4×C43—22no—
84C23×C4×C43—22no—
85C23×C4×C43—22no—
86C23×C4×C43—41no—
87C23×C4×C43—41no—
88C23×C4×C43D411yescharacteristic
89C23×C4×C43D411yescharacteristic
90C23×C4×C43D411yescharacteristic
91C23×C4×C43C2311yescharacteristic
92C23×C4×C43C2311yescharacteristic
93C23×C4×C43C2311yescharacteristic
94C2×SD16×C43—22no—
95C2×SD16×C43—22no—
96C2×SD16×C43—41no—
97C2×D8×C43—22no—
98C2×D8×C43—22no—
99C2×D8×C43—41no—
100C2×M16×C43—22no—
101C2×M16×C43—22no—
102C2×M16×C43—22no—
103C2×M16×C43—22no—
104C2×M16×C43—41no—
105C2×M16×C43—41no—
106C22×C8×C43C2311yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110#123×C43—28no—
111C22⋊Q8×C43—22no—
112C22⋊Q8×C43—22no—
113C22⋊Q8×C43—22no—
114C22⋊Q8×C43D414yescomplemented
115#121×C43—22no—
116#121×C43—22no—
117#121×C43—22no—
118#121×C43—22no—
119#121×C43—22no—
120#121×C43—22no—
121#121×C43—22no—
122#121×C43—41no—
123#121×C43—41no—
124#121×C43D414yescomplemented
125#120×C43—28no—
126#120×C43—44no—
127C4×D4×C43—28no—
128C4×D4×C43—28no—
129#117×C43—22no—
130#117×C43—22no—
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C22⋊C4×C43—21no—
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—
149C2×C42×C43—21no—
150#107×C43—22no—
151#106×C43—22no—
152#103×C43—22no—
153#103×C43—22no—
154#103×C43—41no—
155#102×C43—22no—
156#102×C43—22no—
157#102×C43—22no—
158#102×C43—22no—
159#102×C43—41no—
160C22⋊C8×C43—22no—
161C22⋊C8×C43—22no—
162C22⋊C8×C43—22no—
163C22⋊C8×C43D414yescomplemented
164#95×C43—21no—
165#95×C43—21no—
166#95×C43—21no—
167C24×C43—22no—
168C24×C43—22no—
169C24×C43—22no—
170C24×C43—21no—
171C24×C43—21no—
172C24×C43—41no—
173C24×C43—41no—
174C24×C43—41no—
175C24×C43—41no—
176C24×C43C2×D411yescharacteristic
177C24×C43C2×D411yescharacteristic
178C24×C43C2×D411yescharacteristic
179#41×C43—44no—
180#41×C43—44no—
181#41×C43—44no—
182#41×C43—44no—
183C2×Q8×C43—21no—
184C2×Q8×C43—21no—
185C2×Q8×C43—21no—
186C2×Q8×C43—21no—
187C2×Q8×C43—21no—
188C2×Q8×C43C2×D412yes—
189C2×D4×C43—24no—
190C2×D4×C43—24no—
191C2×D4×C43—21no—
192C2×D4×C43—24no—
193C2×D4×C43—21no—
194C2×D4×C43—21no—
195C2×D4×C43—21no—
196C2×D4×C43—21no—
197C2×D4×C43—21no—
198C2×D4×C43—21no—
199C2×D4×C43—21no—
200C2×D4×C43—21no—
201C2×D4×C43—21no—
202C2×D4×C43—21no—
203C2×D4×C43—42no—
204C2×D4×C43—42no—
205C2×D4×C43—42no—
206C2×D4×C43—42no—
207C2×D4×C43—42no—
208C2×D4×C43—42no—
209C2×D4×C43—42no—
210C2×D4×C43—42no—
211C2×D4×C43—42no—
212C2×D4×C43—42no—
213C2×D4×C43—42no—
214C2×D4×C43—42no—
215C2×D4×C43—42no—
216C2×D4×C43—42no—
217C2×D4×C43—42no—
218C2×D4×C43C2×D412yes—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43—24no—
228C22×C4×C43—22no—
229C22×C4×C43—22no—
230C22×C4×C43—22no—
231C22×C4×C43—22no—
232C22×C4×C43—21no—
233C22×C4×C43—21no—
234C22×C4×C43—21no—
235C22×C4×C43—21no—
236C22×C4×C43—21no—
237C22×C4×C43—21no—
238C22×C4×C43—22no—
239C22×C4×C43—22no—
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—41no—
247C22×C4×C43—41no—
248C22×C4×C43—41no—
249C22×C4×C43—44no—
250C22×C4×C43—44no—
251C22×C4×C43—44no—
252C22×C4×C43—44no—
253C22×C4×C43—42no—
254C22×C4×C43—42no—
255C22×C4×C43C2×D412yes—
256C22×C4×C43C2×D412yes—
257C22×C4×C43C2×D412yes—
258C22×C4×C43C2×D411yescharacteristic
259C22×C4×C43C2×D411yescharacteristic
260C22×C4×C43C2×D411yescharacteristic
261C22×C4×C43#4112yes—
262C22×C4×C43C2411yescharacteristic
263SD16×C43—44no—
264D8×C43—44no—
265M16×C43—44no—
266M16×C43—44no—
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—21no—
275C2×C8×C43—21no—
276C2×C8×C43—21no—
277C2×C8×C43C2×D412yes—
278C2×C8×C43C2×D412yes—
279C4⋊C4×C43—24no—
280C4⋊C4×C43—24no—
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×C43—21no—
289C4⋊C4×C43C2×D412yes—
290C4⋊C4×C43C2×D412yes—
291C22⋊C4×C43—24no—
292C22⋊C4×C43—24no—
293C22⋊C4×C43—24no—
294C22⋊C4×C43—24no—
295C22⋊C4×C43—24no—
296C22⋊C4×C43—42no—
297C22⋊C4×C43—42no—
298C22⋊C4×C43—42no—
299C22⋊C4×C43—42no—
300C22⋊C4×C43—42no—
301C22⋊C4×C43—42no—
302C42×C43—24no—
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—21no—
314C23×C43—21no—
315C23×C43—21no—
316C23×C43—21no—
317C23×C43—21no—
318C23×C43—21no—
319C23×C43—21no—
320C23×C43—21no—
321C23×C43—22no—
322C23×C43—44no—
323C23×C43—44no—
324C23×C43—44no—
325C23×C43—44no—
326C23×C43—44no—
327C23×C43—44no—
328C23×C43—44no—
329C23×C43—41no—
330C23×C43—41no—
331C23×C43—41no—
332C23×C43—41no—
333C23×C43—41no—
334C23×C43—41no—
335C23×C43—41no—
336C23×C43—41no—
337C23×C43—41no—
338C23×C43—41no—
339C23×C43—41no—
340C23×C43—41no—
341C23×C43—41no—
342C23×C43#12012yes—
343C23×C43#12112yes—
344C23×C43AGL(1,ℤ/8)12yes—
345C23×C43C22×D411yescharacteristic
346Q8×C43—22no—
347Q8×C43—22no—
348Q8×C43—41no—
349Q8×C43—41no—
350D4×C43—22no—
351D4×C43—22no—
352D4×C43—48no—
353D4×C43—48no—
354D4×C43—48no—
355D4×C43—41no—
356D4×C43—41no—
357D4×C43—41no—
358D4×C43—41no—
359D4×C43—41no—
360D4×C43—41no—
361D4×C43—84no—
362D4×C43—84no—
363D4×C43—84no—
364C2×C4×C43—21no—
365C2×C4×C43—21no—
366C2×C4×C43—21no—
367C2×C4×C43—21no—
368C2×C4×C43—22no—
369C2×C4×C43—22no—
370C2×C4×C43—22no—
371C2×C4×C43—22no—
372C2×C4×C43—22no—
373C2×C4×C43—22no—
374C2×C4×C43—22no—
375C2×C4×C43—22no—
376C2×C4×C43—22no—
377C2×C4×C43—22no—
378C2×C4×C43—21no—
379C2×C4×C43—22no—
380C2×C4×C43—21no—
381C2×C4×C43—21no—
382C2×C4×C43—44no—
383C2×C4×C43—44no—
384C2×C4×C43—44no—
385C2×C4×C43—48no—
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—41no—
397C2×C4×C43—41no—
398C2×C4×C43—41no—
399C2×C4×C43—41no—
400C2×C4×C43—41no—
401C2×C4×C43—41no—
402C2×C4×C43—41no—
403C2×C4×C43—41no—
404C2×C4×C43—41no—
405C2×C4×C43#12012yes—
406C2×C4×C43#12112yes—
407C2×C4×C43C22×D411yescharacteristic
408C2×C4×C43C22×D411yescharacteristic
409C2×C4×C43C22×D411yescharacteristic
410C2×C4×C43C2×#4111yescharacteristic
411C2×C4×C43H(5,𝔽2)11yescharacteristic
412C2×C4×C43H(5,𝔽2)11yescharacteristic
413C8×C43—22no—
414C8×C43—22no—
415C8×C43—41no—
416C8×C43—41no—
417#24388C4311yesmaximal, characteristic, direct product factor, Sylow
418C22×C43—22no—
419C22×C43—22no—
420C22×C43—22no—
421C22×C43—22no—
422C22×C43—22no—
423C22×C43—22no—
424C22×C43—22no—
425C22×C43—22no—
426C22×C43—22no—
427C22×C43—416no—
428C22×C43—41no—
429C22×C43—41no—
430C22×C43—41no—
431C22×C43—41no—
432C22×C43—41no—
433C22×C43—41no—
434C22×C43—41no—
435C22×C43—41no—
436C22×C43—41no—
437C22×C43—41no—
438C22×C43—41no—
439C22×C43—41no—
440C22×C43—42no—
441C22×C43—42no—
442C22×C43—42no—
443C22×C43—81no—
444C22×C43—81no—
445C22×C43—81no—
446C22×C43—81no—
447C22×C43—81no—
448C22×C43—81no—
449C22×C43—81no—
450C22×C43—81no—
451C22×C43—81no—
452C22×C43—81no—
453C22×C43—81no—
454C22×C43C2×#12011yescharacteristic
455C22×C43C2×#12111yescharacteristic
456C22×C43#53411yescharacteristic
457C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
458C22×C43#57511yescharacteristic
459C22×C43#57511yescharacteristic
460C22×C43#57511yescharacteristic
461C4×C43—22no—
462C4×C43—22no—
463C4×C43—41no—
464C4×C43—42no—
465C4×C43—42no—
466C4×C43—42no—
467C4×C43—81no—
468C4×C43—81no—
469C4×C43—81no—
470C4×C43D4211yescharacteristic
471C4×C43D4211yescharacteristic
472C4×C43#54611yescharacteristic
473C4×C43#54611yescharacteristic
474C2×#525C2×C4311yescharacteristic, complemented
475C2×#469C2×C4311yescharacteristic, complemented
476C2×#468C2×C4311yescharacteristic, complemented
477C2×#449C2×C4311yescharacteristic, complemented
478C2×#407C2×C4311yescharacteristic, complemented
479#2847C2×C4311yescharacteristic, complemented
480#2035C2×C4311yescharacteristic, complemented
481#2033C2×C4311yescharacteristic, complemented
482#2000C2×C4311yescharacteristic, complemented
483#1999C2×C4311yescharacteristic, complemented
484#1895C2×C4311yescharacteristic, complemented
485#1894C2×C4311yescharacteristic, complemented
486#1875C2×C4311yescharacteristic, complemented
487#1854C2×C4311yescharacteristic, complemented
488#1788C2×C4311yescharacteristic, complemented
489C2×C43—42no—
490C2×C43—42no—
491C2×C43—42no—
492C2×C43—82no—
493C2×C43—161no—
494C2×C43#241011yescharacteristic
495C2×C43#300511yescharacteristic
496C2×C43#300611yescharacteristic
497C2×C43#305411yescharacteristic
498C2×C43#305511yescharacteristic
499C2×C43#319411yescharacteristic
500C2×C43#319711yescharacteristic
501C22×#41C22×C4311yescharacteristic
502C24×C4C22×C4311yescharacteristic
503C22×SD16C22×C4311yescharacteristic, complemented
504C22×D8C22×C4311yescharacteristic, complemented
505C22×M16C22×C4311yescharacteristic
506C22×M16C22×C4311yescharacteristic
507#525—24no—
508#525—24no—
509C2×#123—21no—
510C2×C22⋊Q8C22×C4311yescharacteristic
511C2×C22⋊Q8C22×C4311yescharacteristic
512C2×#121C22×C4311yescharacteristic
513C2×#121C22×C4311yescharacteristic
514C2×#121C22×C4311yescharacteristic
515C2×#121C22×C4311yescharacteristic
516C2×#121C22×C4311yescharacteristic
517C2×#120—21no—
518C2×#120—21no—
519C2×C4×D4—21no—
520C2×C4×D4—21no—
521C2×#117C22×C4311yescharacteristic
522#469—24no—
523#468—24no—
524#449—24no—
525C2×#107C22×C4311yescharacteristic, complemented
526C2×#106C22×C4311yescharacteristic, complemented
527C2×#103C22×C4311yescharacteristic, complemented
528C2×#103C22×C4311yescharacteristic, complemented
529C2×#103C22×C4311yescharacteristic, complemented
530C2×#102C22×C4311yescharacteristic, complemented
531C2×#102C22×C4311yescharacteristic, complemented
532C2×#102C22×C4311yescharacteristic, complemented
533C2×#102C22×C4311yescharacteristic, complemented
534C2×#102C22×C4311yescharacteristic, complemented
535#407—24no—
536C2×C22⋊C8C22×C4311yescharacteristic
537C2×C22⋊C8C22×C4311yescharacteristic
538C2×C22⋊C8C22×C4311yescharacteristic
539C2×C22⋊C8C22×C4311yescharacteristic
540#386—21no—
541#386—21no—
542#386—21no—
543#380C22×C4311yescharacteristic
544#380C22×C4311yescharacteristic
545#380C22×C4311yescharacteristic
546#340C22×C4311yescharacteristic, complemented
547#340C22×C4311yescharacteristic, complemented
548#340C22×C4311yescharacteristic, complemented
549#340C22×C4311yescharacteristic, complemented
550C43#2438811yescharacteristic, direct product factor, Sylow
551C25D4×C4311yescharacteristic
552C2×#41—22no—
553C2×#41—22no—
554C2×#41—22no—
555C2×#41—22no—
556C2×#41—41no—
557C2×#41—41no—
558C22×Q8C23×C4311yescharacteristic
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4C23×C4311yescharacteristic
566C22×D4C23×C4311yescharacteristic
567C23×C4—21no—
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—22no—
572C23×C4—41no—
573C23×C4—41no—
574C23×C4D4×C4311yescharacteristic
575C23×C4D4×C4311yescharacteristic
576C23×C4D4×C4311yescharacteristic
577C23×C4C23×C4311yescharacteristic
578C23×C4C23×C4311yescharacteristic
579C23×C4C23×C4311yescharacteristic
580C2×SD16—22no—
581C2×SD16—22no—
582C2×SD16—41no—
583C2×D8—22no—
584C2×D8—22no—
585C2×D8—41no—
586C2×M16—22no—
587C2×M16—22no—
588C2×M16—22no—
589C2×M16—22no—
590C2×M16—41no—
591C2×M16—41no—
592C22×C8C23×C4311yescharacteristic
593C22×C8C23×C4311yescharacteristic
594C22×C8C23×C4311yescharacteristic
595C22×C8C23×C4311yescharacteristic
596#123—28no—
597C22⋊Q8—22no—
598C22⋊Q8—22no—
599C22⋊Q8—22no—
600C22⋊Q8D4×C4314yescomplemented
601#121—22no—
602#121—22no—
603#121—22no—
604#121—22no—
605#121—22no—
606#121—22no—
607#121—22no—
608#121—41no—
609#121—41no—
610#121D4×C4314yescomplemented
611#120—28no—
612#120—44no—
613C4×D4—28no—
614C4×D4—28no—
615#117—22no—
616#117—22no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4C23×C4311yescharacteristic
620C2×C4⋊C4C23×C4311yescharacteristic
621C2×C4⋊C4C23×C4311yescharacteristic
622C2×C4⋊C4C23×C4311yescharacteristic
623C2×C4⋊C4C23×C4311yescharacteristic
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C42—21no—
636#107—22no—
637#106—22no—
638#103—22no—
639#103—22no—
640#103—41no—
641#102—22no—
642#102—22no—
643#102—22no—
644#102—22no—
645#102—41no—
646C22⋊C8—22no—
647C22⋊C8—22no—
648C22⋊C8—22no—
649C22⋊C8D4×C4314yescomplemented
650#95—21no—
651#95—21no—
652#95—21no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—21no—
657C24—21no—
658C24—41no—
659C24—41no—
660C24—41no—
661C24—41no—
662C24C2×D4×C4311yescharacteristic
663C24C2×D4×C4311yescharacteristic
664C24C2×D4×C4311yescharacteristic
665#41—44no—
666#41—44no—
667#41—44no—
668#41—44no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8—21no—
673C2×Q8—21no—
674C2×Q8C2×D4×C4312yes—
675C2×D4—24no—
676C2×D4—24no—
677C2×D4—24no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—42no—
704C2×D4C2×D4×C4312yes—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—24no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—41no—
733C22×C4—41no—
734C22×C4—41no—
735C22×C4—44no—
736C22×C4—44no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—42no—
740C22×C4—42no—
741C22×C4C2×D4×C4311yescharacteristic
742C22×C4C2×D4×C4311yescharacteristic
743C22×C4C2×D4×C4312yes—
744C22×C4C2×D4×C4312yes—
745C22×C4C2×D4×C4311yescharacteristic
746C22×C4C2×D4×C4312yes—
747C22×C4#41×C4312yes—
748C22×C4C24×C4311yescharacteristic
749SD16—44no—
750D8—44no—
751M16—44no—
752M16—44no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—21no—
761C2×C8—21no—
762C2×C8—21no—
763C2×C8C2×D4×C4312yes—
764C2×C8C2×D4×C4312yes—
765C4⋊C4—24no—
766C4⋊C4—24no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4—21no—
775C4⋊C4C2×D4×C4312yes—
776C4⋊C4C2×D4×C4312yes—
777C22⋊C4—24no—
778C22⋊C4—24no—
779C22⋊C4—24no—
780C22⋊C4—24no—
781C22⋊C4—24no—
782C22⋊C4—42no—
783C22⋊C4—42no—
784C22⋊C4—42no—
785C22⋊C4—42no—
786C22⋊C4—42no—
787C22⋊C4—42no—
788C42—24no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—21no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—21no—
807C23—22no—
808C23—44no—
809C23—44no—
810C23—44no—
811C23—44no—
812C23—44no—
813C23—44no—
814C23—44no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23#120×C4312yes—
829C23#121×C4312yes—
830C23AGL(1,ℤ/8)×C4312yes—
831C23C22×D4×C4311yescharacteristic
832Q8—22no—
833Q8—22no—
834Q8—41no—
835Q8—41no—
836D4—22no—
837D4—22no—
838D4—48no—
839D4—48no—
840D4—48no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—84no—
848D4—84no—
849D4—84no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—21no—
865C2×C4—22no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—44no—
869C2×C4—44no—
870C2×C4—44no—
871C2×C4—48no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4#120×C4312yes—
892C2×C4#121×C4312yes—
893C2×C4C22×D4×C4311yescharacteristic
894C2×C4C22×D4×C4311yescharacteristic
895C2×C4C22×D4×C4311yescharacteristic
896C2×C4C2×#41×C4311yescharacteristic
897C2×C4H(5,𝔽2)×C4311yescharacteristic
898C2×C4H(5,𝔽2)×C4311yescharacteristic
899C8—22no—
900C8—22no—
901C8—41no—
902C8—41no—
903C22—22no—
904C22—22no—
905C22—22no—
906C22—22no—
907C22—22no—
908C22—22no—
909C22—22no—
910C22—22no—
911C22—22no—
912C22—416no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—81no—
938C22—81no—
939C22C2×#120×C4311yescharacteristic
940C22C2×#121×C4311yescharacteristic
941C22C43×#53411yescharacteristic
942C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
943C22C43×#57511yescharacteristic
944C22C43×#57511yescharacteristic
945C22C43×#57511yescharacteristic
946C4—22no—
947C4—22no—
948C4—41no—
949C4—42no—
950C4—42no—
951C4—42no—
952C4—81no—
953C4—81no—
954C4—81no—
955C4D42×C4311yescharacteristic
956C4D42×C4311yescharacteristic
957C4C43×#54611yescharacteristic
958C4C43×#54611yescharacteristic
959C2—42no—
960C2—42no—
961C2—42no—
962C2—82no—
963C2—161no—
964C2C43×#241011yescharacteristic
965C2C43×#300511yescharacteristic
966C2C43×#300611yescharacteristic
967C2C43×#305411yescharacteristic
968C2C43×#305511yescharacteristic
969C2C43×#319411yescharacteristic
970C2C43×#319711yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C24×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#525C2semidirect
2. C2×C43×#469C2semidirect
3. C2×C43×#468C2semidirect
4. C2×C43×#449C2semidirect
5. C2×C43×#407C2semidirect
6. C43×#2847C2semidirect
7. C43×#2035C2semidirect
8. C43×#2033C2semidirect
9. C43×#2000C2semidirect
10. C43×#1999C2semidirect
11. C43×#1895C2semidirect
12. C43×#1894C2semidirect
13. C43×#1875C2semidirect
14. C43×#1854C2semidirect
15. C43×#1788C2semidirect
18. C22×SD16×C43C22semidirect
19. C22×D8×C43C22semidirect
40. C2×#107×C43C22semidirect
41. C2×#106×C43C22semidirect
42. C2×#103×C43C22semidirect
43. C2×#103×C43C22semidirect
44. C2×#103×C43C22semidirect
45. C2×#102×C43C22semidirect
46. C2×#102×C43C22semidirect
47. C2×#102×C43C22semidirect
48. C2×#102×C43C22semidirect
49. C2×#102×C43C22semidirect
61. C43×#340C22semidirect
62. C43×#340C22semidirect
63. C43×#340C22semidirect
64. C43×#340C22semidirect
114. C22⋊Q8×C43D4semidirect
124. #121×C43D4semidirect
163. C22⋊C8×C43D4semidirect
417. #24388C43direct (N × H)
474. C2×#525C2×C43semidirect
475. C2×#469C2×C43semidirect
476. C2×#468C2×C43semidirect
477. C2×#449C2×C43semidirect
478. C2×#407C2×C43semidirect
479. #2847C2×C43semidirect
480. #2035C2×C43semidirect
481. #2033C2×C43semidirect
482. #2000C2×C43semidirect
483. #1999C2×C43semidirect
484. #1895C2×C43semidirect
485. #1894C2×C43semidirect
486. #1875C2×C43semidirect
487. #1854C2×C43semidirect
488. #1788C2×C43semidirect
503. C22×SD16C22×C43semidirect
504. C22×D8C22×C43semidirect
525. C2×#107C22×C43semidirect
526. C2×#106C22×C43semidirect
527. C2×#103C22×C43semidirect
528. C2×#103C22×C43semidirect
529. C2×#103C22×C43semidirect
530. C2×#102C22×C43semidirect
531. C2×#102C22×C43semidirect
532. C2×#102C22×C43semidirect
533. C2×#102C22×C43semidirect
534. C2×#102C22×C43semidirect
546. #340C22×C43semidirect
547. #340C22×C43semidirect
548. #340C22×C43semidirect
549. #340C22×C43semidirect
550. C43#24388direct (N × H)
600. C22⋊Q8D4×C43semidirect
610. #121D4×C43semidirect
649. 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×#5252
C2×C43×#4692
C2×C43×#4682
C2×C43×#4492
C2×C43×#4072
C43×#28472
C43×#20352
C43×#20332
C43×#20002
C43×#19992
C43×#18952
C43×#18942
C43×#18752
C43×#18542
C43×#17882
#2438843