Finite Group Databasebeta

← C43×#24899 #24944916

Subgroups — C43×#24899 #24944916

Order 11008.

1070 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#449C211yesmaximal, characteristic
2C2×C4×D8×C43C211yesmaximal, characteristic, complemented
3C43×#2422C211yesmaximal, characteristic, complemented
4C43×#2339C211yesmaximal, characteristic, complemented
5C43×#2095C211yesmaximal, characteristic, complemented
6C43×#2076C211yesmaximal, characteristic, complemented
7C43×#2055C211yesmaximal, characteristic, complemented
8C43×#2033C211yesmaximal, characteristic, complemented
9C43×#1933C211yesmaximal, characteristic, complemented
10C43×#1923C211yesmaximal, characteristic, complemented
11C43×#1879C211yesmaximal, characteristic, complemented
12C43×#1877C211yesmaximal, characteristic, complemented
13C43×#1862C211yesmaximal, characteristic, complemented
14C43×#1802C211yesmaximal, characteristic, complemented
15C43×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C43C2211yescharacteristic
17C22×SD16×C43C2211yescharacteristic
18C22×D8×C43C2211yescharacteristic
19C2×#123×C43—21no—
20C2×#121×C43C2211yescharacteristic
21C2×C4×D4×C43C2211yescharacteristic
22C2×C4×D4×C43C2211yescharacteristic
23C2×C4×D4×C43C2211yescharacteristic
24C43×#449—24no—
25C4×D8×C43—24no—
26C2×#107×C43C2211yescharacteristic
27C2×#107×C43C2211yescharacteristic
28C2×C4⋊C8×C43C2211yescharacteristic
29C2×#103×C43C2211yescharacteristic
30C2×#103×C43C2211yescharacteristic
31C2×#103×C43C2211yescharacteristic
32C2×#102×C43C2211yescharacteristic
33C2×#102×C43C2211yescharacteristic
34C2×#102×C43C2211yescharacteristic
35C2×#102×C43C2211yescharacteristic
36C2×#102×C43C2211yescharacteristic
37C2×C22⋊C8×C43C2211yescharacteristic
38C2×C22⋊C8×C43C2211yescharacteristic
39C2×C4×C8×C43C2211yescharacteristic
40C43×#397—21no—
41C43×#394—21no—
42C43×#391C2211yescharacteristic
43C43×#391C2211yescharacteristic
44C43×#390C2211yescharacteristic
45C43×#389C2211yescharacteristic
46C43×#386—21no—
47C43×#386—21no—
48C43×#385—21no—
49C43×#384C2211yescharacteristic
50C43×#381—21no—
51C43×#380C2211yescharacteristic
52C43×#380C2211yescharacteristic
53C4×C22⋊C4×C43C2211yescharacteristic
54C2×#95×C43—21no—
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C2×#41×C43—22no—
62C2×#41×C43—22no—
63C2×#41×C43—22no—
64C2×#41×C43—22no—
65C2×#41×C43—41no—
66C2×#41×C43—41no—
67C22×Q8×C43C2311yescharacteristic
68C22×D4×C43—21no—
69C22×D4×C43—21no—
70C22×D4×C43C2311yescharacteristic
71C22×D4×C43C2311yescharacteristic
72C23×C4×C43—21no—
73C23×C4×C43—21no—
74C23×C4×C43—21no—
75C23×C4×C43—21no—
76C23×C4×C43C2311yescharacteristic
77C2×SD16×C43—22no—
78C2×SD16×C43—22no—
79C2×SD16×C43—41no—
80C2×D8×C43—22no—
81C2×D8×C43—22no—
82C2×D8×C43D414yes—
83C22×C8×C43C2311yescharacteristic
84C22×C8×C43C2311yescharacteristic
85C22×C8×C43C2311yescharacteristic
86C22×C8×C43C2311yescharacteristic
87#123×C43—44no—
88#121×C43—22no—
89#121×C43—41no—
90C4×D4×C43—22no—
91C4×D4×C43—22no—
92C4×D4×C43—22no—
93C4×D4×C43—41no—
94C4×D4×C43—41no—
95C4×D4×C43—41no—
96C2×C4⋊C4×C43—21no—
97C2×C4⋊C4×C43—21no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43C2311yescharacteristic
100C2×C4⋊C4×C43C2311yescharacteristic
101C2×C4⋊C4×C43C2311yescharacteristic
102C2×C4⋊C4×C43C2311yescharacteristic
103C2×C4⋊C4×C43C2311yescharacteristic
104C2×C22⋊C4×C43—21no—
105C2×C22⋊C4×C43—21no—
106C2×C22⋊C4×C43—21no—
107C2×C22⋊C4×C43—21no—
108C2×C22⋊C4×C43—21no—
109C2×C22⋊C4×C43—21no—
110C2×C22⋊C4×C43—21no—
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43D411yescharacteristic
113C2×C22⋊C4×C43D411yescharacteristic
114C2×C42×C43C2311yescharacteristic
115C2×C42×C43C2311yescharacteristic
116#107×C43—22no—
117#107×C43—41no—
118C4⋊C8×C43—41no—
119#103×C43—22no—
120#103×C43—22no—
121#103×C43—41no—
122#102×C43—22no—
123#102×C43—22no—
124#102×C43—22no—
125#102×C43—22no—
126#102×C43—41no—
127C22⋊C8×C43—22no—
128C22⋊C8×C43—41no—
129C4×C8×C43—22no—
130#95×C43—21no—
131#95×C43—21no—
132#95×C43—21no—
133#95×C43—21no—
134#95×C43—21no—
135#95×C43—21no—
136#95×C43—21no—
137#95×C43D411yescharacteristic
138#95×C43D411yescharacteristic
139C24×C43—21no—
140C24×C43—21no—
141C24×C43C2×D411yescharacteristic
142#41×C43—44no—
143#41×C43—44no—
144#41×C43—44no—
145#41×C43—44no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43#4112yes—
152C2×D4×C43—24no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—42no—
162C2×D4×C43—42no—
163C2×D4×C43—42no—
164C2×D4×C43—42no—
165C2×D4×C43—81no—
166C2×D4×C43C2×D412yes—
167C2×D4×C43C2×D412yes—
168C2×D4×C43#4112yes—
169C2×D4×C43#4112yes—
170C22×C4×C43—24no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—42no—
184C22×C4×C43—42no—
185C22×C4×C43—42no—
186C22×C4×C43—42no—
187C22×C4×C43—42no—
188C22×C4×C43—42no—
189C22×C4×C43—42no—
190C22×C4×C43—42no—
191C22×C4×C43—81no—
192C22×C4×C43—81no—
193C22×C4×C43—81no—
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2411yescharacteristic
200SD16×C43—44no—
201D8×C43—28no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C2×C8×C43—21no—
213C2×C8×C43C2×D412yes—
214C4⋊C4×C43—21no—
215C4⋊C4×C43—21no—
216C4⋊C4×C43—21no—
217C4⋊C4×C43—21no—
218C4⋊C4×C43—21no—
219C4⋊C4×C43—21no—
220C4⋊C4×C43—21no—
221C4⋊C4×C43—21no—
222C4⋊C4×C43—21no—
223C4⋊C4×C43—21no—
224C4⋊C4×C43—42no—
225C4⋊C4×C43—42no—
226C4⋊C4×C43—81no—
227C22⋊C4×C43—22no—
228C22⋊C4×C43—22no—
229C22⋊C4×C43—42no—
230C22⋊C4×C43—42no—
231C22⋊C4×C43—42no—
232C22⋊C4×C43—42no—
233C22⋊C4×C43—42no—
234C22⋊C4×C43—42no—
235C22⋊C4×C43—42no—
236C22⋊C4×C43—81no—
237C42×C43—21no—
238C42×C43—21no—
239C42×C43—21no—
240C42×C43—21no—
241C23×C43—22no—
242C23×C43—22no—
243C23×C43—22no—
244C23×C43—21no—
245C23×C43—22no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43C22×D411yescharacteristic
263Q8×C43—22no—
264Q8×C43—22no—
265Q8×C43—41no—
266Q8×C43—41no—
267D4×C43—22no—
268D4×C43—22no—
269D4×C43—22no—
270D4×C43—22no—
271D4×C43—22no—
272D4×C43—48no—
273D4×C43—41no—
274D4×C43—41no—
275D4×C43—84no—
276D4×C43#12314yescomplemented
277C2×C4×C43—21no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
281C2×C4×C43—21no—
282C2×C4×C43—22no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—48no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43—41no—
307C2×C4×C43—41no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43—41no—
313C2×C4×C43—84no—
314C2×C4×C43—84no—
315C2×C4×C43—84no—
316C2×C4×C43#13512yes—
317C2×C4×C43AGL(1,ℤ/8)12yes—
318C2×C4×C43C22×D411yescharacteristic
319C2×C4×C43C2×#4111yescharacteristic
320C2×C4×C43C2×#4111yescharacteristic
321C2×C4×C43C2×#4111yescharacteristic
322C2×C4×C43H(5,𝔽2)11yescharacteristic
323C2×C4×C43H(5,𝔽2)11yescharacteristic
324C8×C43—22no—
325C8×C43—41no—
326C8×C43—41no—
327C8×C43—41no—
328#24899C4311yesmaximal, characteristic, direct product factor, Sylow
329C22×C43—24no—
330C22×C43—42no—
331C22×C43—42no—
332C22×C43—42no—
333C22×C43—42no—
334C22×C43—42no—
335C22×C43—42no—
336C22×C43—41no—
337C22×C43—41no—
338C22×C43—41no—
339C22×C43—41no—
340C22×C43—42no—
341C22×C43—41no—
342C22×C43—42no—
343C22×C43—41no—
344C22×C43—42no—
345C22×C43—41no—
346C22×C43—81no—
347C22×C43—81no—
348C22×C43—81no—
349C22×C43—81no—
350C22×C43#52511yescharacteristic
351C22×C43D4211yescharacteristic
352C22×C43#54611yescharacteristic
353C22×C43C2×#13511yescharacteristic
354C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
355C22×C43#57611yescharacteristic
356C22×C43#57811yescharacteristic
357C4×C43—22no—
358C4×C43—22no—
359C4×C43—41no—
360C4×C43—41no—
361C4×C43—42no—
362C4×C43—41no—
363C4×C43—81no—
364C4×C43—81no—
365C4×C43—81no—
366C4×C43—81no—
367C4×C43—81no—
368C4×C43C2×#12311yescharacteristic
369C4×C43#53811yescharacteristic
370C4×C43#54611yescharacteristic
371C4×C43#55111yescharacteristic
372C2×#449C2×C4311yescharacteristic
373C2×C4×D8C2×C4311yescharacteristic, complemented
374#2422C2×C4311yescharacteristic, complemented
375#2339C2×C4311yescharacteristic, complemented
376#2095C2×C4311yescharacteristic, complemented
377#2076C2×C4311yescharacteristic, complemented
378#2055C2×C4311yescharacteristic, complemented
379#2033C2×C4311yescharacteristic, complemented
380#1933C2×C4311yescharacteristic, complemented
381#1923C2×C4311yescharacteristic, complemented
382#1879C2×C4311yescharacteristic, complemented
383#1877C2×C4311yescharacteristic, complemented
384#1862C2×C4311yescharacteristic, complemented
385#1802C2×C4311yescharacteristic, complemented
386#1788C2×C4311yescharacteristic, complemented
387C2×C43—44no—
388C2×C43—81no—
389C2×C43—82no—
390C2×C43#241811yescharacteristic
391C2×C43#310611yescharacteristic
392C2×C43#312411yescharacteristic
393C2×C43#326411yescharacteristic
394C2×C43#328311yescharacteristic
395C2×C43#329711yescharacteristic
396C2×C43#333011yescharacteristic
397C22×#41C22×C4311yescharacteristic
398C22×SD16C22×C4311yescharacteristic
399C22×D8C22×C4311yescharacteristic
400C2×#123—21no—
401C2×#121C22×C4311yescharacteristic
402C2×C4×D4C22×C4311yescharacteristic
403C2×C4×D4C22×C4311yescharacteristic
404C2×C4×D4C22×C4311yescharacteristic
405#449—24no—
406C4×D8—24no—
407C2×#107C22×C4311yescharacteristic
408C2×#107C22×C4311yescharacteristic
409C2×C4⋊C8C22×C4311yescharacteristic
410C2×#103C22×C4311yescharacteristic
411C2×#103C22×C4311yescharacteristic
412C2×#103C22×C4311yescharacteristic
413C2×#102C22×C4311yescharacteristic
414C2×#102C22×C4311yescharacteristic
415C2×#102C22×C4311yescharacteristic
416C2×#102C22×C4311yescharacteristic
417C2×#102C22×C4311yescharacteristic
418C2×C22⋊C8C22×C4311yescharacteristic
419C2×C22⋊C8C22×C4311yescharacteristic
420C2×C4×C8C22×C4311yescharacteristic
421#397—21no—
422#394—21no—
423#391C22×C4311yescharacteristic
424#391C22×C4311yescharacteristic
425#390C22×C4311yescharacteristic
426#389C22×C4311yescharacteristic
427#386—21no—
428#386—21no—
429#385—21no—
430#384C22×C4311yescharacteristic
431#381—21no—
432#380C22×C4311yescharacteristic
433#380C22×C4311yescharacteristic
434C4×C22⋊C4C22×C4311yescharacteristic
435C2×#95—21no—
436#340C22×C4311yescharacteristic
437#340C22×C4311yescharacteristic
438#340C22×C4311yescharacteristic
439#340C22×C4311yescharacteristic
440#336C22×C4311yescharacteristic
441#336C22×C4311yescharacteristic
442C43#2489911yescharacteristic, direct product factor, Sylow
443C2×#41—22no—
444C2×#41—22no—
445C2×#41—22no—
446C2×#41—22no—
447C2×#41—41no—
448C2×#41—41no—
449C22×Q8C23×C4311yescharacteristic
450C22×D4—21no—
451C22×D4—21no—
452C22×D4C23×C4311yescharacteristic
453C22×D4C23×C4311yescharacteristic
454C23×C4—21no—
455C23×C4—21no—
456C23×C4—21no—
457C23×C4—21no—
458C23×C4C23×C4311yescharacteristic
459C2×SD16—22no—
460C2×SD16—22no—
461C2×SD16—41no—
462C2×D8—22no—
463C2×D8—22no—
464C2×D8D4×C4314yes—
465C22×C8C23×C4311yescharacteristic
466C22×C8C23×C4311yescharacteristic
467C22×C8C23×C4311yescharacteristic
468C22×C8C23×C4311yescharacteristic
469#123—44no—
470#121—22no—
471#121—41no—
472C4×D4—22no—
473C4×D4—22no—
474C4×D4—22no—
475C4×D4—41no—
476C4×D4—41no—
477C4×D4—41no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4C23×C4311yescharacteristic
482C2×C4⋊C4C23×C4311yescharacteristic
483C2×C4⋊C4C23×C4311yescharacteristic
484C2×C4⋊C4C23×C4311yescharacteristic
485C2×C4⋊C4C23×C4311yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4D4×C4311yescharacteristic
495C2×C22⋊C4D4×C4311yescharacteristic
496C2×C42C23×C4311yescharacteristic
497C2×C42C23×C4311yescharacteristic
498#107—22no—
499#107—41no—
500C4⋊C8—41no—
501#103—22no—
502#103—22no—
503#103—41no—
504#102—22no—
505#102—22no—
506#102—22no—
507#102—22no—
508#102—41no—
509C22⋊C8—22no—
510C22⋊C8—41no—
511C4×C8—22no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95D4×C4311yescharacteristic
520#95D4×C4311yescharacteristic
521C24—21no—
522C24—21no—
523C24C2×D4×C4311yescharacteristic
524#41—44no—
525#41—44no—
526#41—44no—
527#41—44no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8#41×C4312yes—
534C2×D4—24no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—81no—
548C2×D4C2×D4×C4312yes—
549C2×D4C2×D4×C4312yes—
550C2×D4#41×C4312yes—
551C2×D4#41×C4312yes—
552C22×C4—24no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—81no—
574C22×C4—81no—
575C22×C4—81no—
576C22×C4C2×D4×C4311yescharacteristic
577C22×C4C2×D4×C4311yescharacteristic
578C22×C4C2×D4×C4311yescharacteristic
579C22×C4C2×D4×C4311yescharacteristic
580C22×C4C2×D4×C4311yescharacteristic
581C22×C4C24×C4311yescharacteristic
582SD16—44no—
583D8—28no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8C2×D4×C4312yes—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4—81no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—42no—
612C22⋊C4—42no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C22⋊C4—42no—
618C22⋊C4—81no—
619C42—21no—
620C42—21no—
621C42—21no—
622C42—21no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—21no—
627C23—22no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23C22×D4×C4311yescharacteristic
645Q8—22no—
646Q8—22no—
647Q8—41no—
648Q8—41no—
649D4—22no—
650D4—22no—
651D4—22no—
652D4—22no—
653D4—22no—
654D4—48no—
655D4—41no—
656D4—41no—
657D4—84no—
658D4#123×C4314yescomplemented
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—48no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—84no—
696C2×C4—84no—
697C2×C4—84no—
698C2×C4#135×C4312yes—
699C2×C4AGL(1,ℤ/8)×C4312yes—
700C2×C4C22×D4×C4311yescharacteristic
701C2×C4C2×#41×C4311yescharacteristic
702C2×C4C2×#41×C4311yescharacteristic
703C2×C4C2×#41×C4311yescharacteristic
704C2×C4H(5,𝔽2)×C4311yescharacteristic
705C2×C4H(5,𝔽2)×C4311yescharacteristic
706C8—22no—
707C8—41no—
708C8—41no—
709C8—41no—
710C22—24no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—42no—
721C22—42no—
722C22—41no—
723C22—41no—
724C22—42no—
725C22—41no—
726C22—41no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22C43×#52511yescharacteristic
732C22D42×C4311yescharacteristic
733C22C43×#54611yescharacteristic
734C22C2×#135×C4311yescharacteristic
735C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
736C22C43×#57611yescharacteristic
737C22C43×#57811yescharacteristic
738C4—22no—
739C4—22no—
740C4—41no—
741C4—42no—
742C4—41no—
743C4—41no—
744C4—81no—
745C4—81no—
746C4—81no—
747C4—81no—
748C4—81no—
749C4C2×#123×C4311yescharacteristic
750C4C43×#53811yescharacteristic
751C4C43×#54611yescharacteristic
752C4C43×#55111yescharacteristic
753C2—44no—
754C2—81no—
755C2—82no—
756C2C43×#241811yescharacteristic
757C2C43×#310611yescharacteristic
758C2C43×#312411yescharacteristic
759C2C43×#326411yescharacteristic
760C2C43×#328311yescharacteristic
761C2C43×#329711yescharacteristic
762C2C43×#333011yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC2×C43×#449C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C4×C22⋊C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×D8×C43C2semidirect
3. C43×#2422C2semidirect
4. C43×#2339C2semidirect
5. C43×#2095C2semidirect
6. C43×#2076C2semidirect
7. C43×#2055C2semidirect
8. C43×#2033C2semidirect
9. C43×#1933C2semidirect
10. C43×#1923C2semidirect
11. C43×#1879C2semidirect
12. C43×#1877C2semidirect
13. C43×#1862C2semidirect
14. C43×#1802C2semidirect
15. C43×#1788C2semidirect
276. D4×C43#123semidirect
328. #24899C43direct (N × H)
373. C2×C4×D8C2×C43semidirect
374. #2422C2×C43semidirect
375. #2339C2×C43semidirect
376. #2095C2×C43semidirect
377. #2076C2×C43semidirect
378. #2055C2×C43semidirect
379. #2033C2×C43semidirect
380. #1933C2×C43semidirect
381. #1923C2×C43semidirect
382. #1879C2×C43semidirect
383. #1877C2×C43semidirect
384. #1862C2×C43semidirect
385. #1802C2×C43semidirect
386. #1788C2×C43semidirect
442. C43#24899direct (N × H)
658. D4#123×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4492
C2×C4×D8×C432
C43×#24222
C43×#23392
C43×#20952
C43×#20762
C43×#20552
C43×#20332
C43×#19332
C43×#19232
C43×#18792
C43×#18772
C43×#18622
C43×#18022
C43×#17882
#2489943