Finite Group Databasebeta

← C43×#24896 #24944913

Subgroups — C43×#24896 #24944913

Order 11008.

1042 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#449C211yesmaximal, characteristic
2C2×C4×SD16×C43C211yesmaximal, characteristic, complemented
3C43×#2422C211yesmaximal, characteristic, complemented
4C43×#2341C211yesmaximal, characteristic, complemented
5C43×#2094C211yesmaximal, characteristic, complemented
6C43×#2077C211yesmaximal, characteristic, complemented
7C43×#2054C211yesmaximal, characteristic, complemented
8C43×#2034C211yesmaximal, characteristic, complemented
9C43×#1934C211yesmaximal, characteristic, complemented
10C43×#1923C211yesmaximal, characteristic, complemented
11C43×#1880C211yesmaximal, characteristic, complemented
12C43×#1879C211yesmaximal, characteristic, complemented
13C43×#1865C211yesmaximal, characteristic, complemented
14C43×#1803C211yesmaximal, characteristic, complemented
15C43×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C43C2211yescharacteristic
17C22×SD16×C43C2211yescharacteristic
18C22×D8×C43C2211yescharacteristic
19C2×#123×C43—21no—
20C2×#121×C43C2211yescharacteristic
21C2×C4×Q8×C43C2211yescharacteristic
22C2×C4×Q8×C43C2211yescharacteristic
23C2×C4×D4×C43C2211yescharacteristic
24C43×#449—24no—
25C4×SD16×C43—24no—
26C2×#106×C43C2211yescharacteristic
27C2×#106×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×#390—21no—
43C43×#390—21no—
44C43×#390C2211yescharacteristic
45C43×#390C2211yescharacteristic
46C43×#390C2211yescharacteristic
47C43×#389C2211yescharacteristic
48C43×#385—21no—
49C43×#384C2211yescharacteristic
50C43×#380—21no—
51C43×#380C2211yescharacteristic
52C43×#380C2211yescharacteristic
53C4×C22⋊C4×C43—21no—
54C4×C22⋊C4×C43C2211yescharacteristic
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×C43C2311yescharacteristic
75C2×SD16×C43—22no—
76C2×SD16×C43—22no—
77C2×SD16×C43D414yes—
78C2×D8×C43—22no—
79C2×D8×C43—22no—
80C2×D8×C43—41no—
81C22×C8×C43C2311yescharacteristic
82C22×C8×C43C2311yescharacteristic
83C22×C8×C43C2311yescharacteristic
84C22×C8×C43C2311yescharacteristic
85#123×C43—44no—
86#121×C43—22no—
87#121×C43—41no—
88C4×Q8×C43—22no—
89C4×Q8×C43—22no—
90C4×Q8×C43—41no—
91C4×Q8×C43—41no—
92C4×D4×C43—22no—
93C4×D4×C43—41no—
94C2×C4⋊C4×C43—21no—
95C2×C4⋊C4×C43—21no—
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×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43D411yescharacteristic
115C2×C22⋊C4×C43D411yescharacteristic
116C2×C42×C43—21no—
117C2×C42×C43—21no—
118C2×C42×C43C2311yescharacteristic
119C2×C42×C43C2311yescharacteristic
120#106×C43—22no—
121#106×C43—41no—
122C4⋊C8×C43—41no—
123#103×C43—22no—
124#103×C43—22no—
125#103×C43—22no—
126#102×C43—22no—
127#102×C43—22no—
128#102×C43—22no—
129#102×C43—41no—
130#102×C43—41no—
131C22⋊C8×C43—22no—
132C22⋊C8×C43—41no—
133C4×C8×C43—22no—
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×C43C2×D412yes—
150C2×Q8×C43#4112yes—
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—21no—
162C2×D4×C43—21no—
163C2×D4×C43—42no—
164C2×D4×C43—42no—
165C2×D4×C43—42no—
166C2×D4×C43—42no—
167C2×D4×C43—81no—
168C2×D4×C43C2×D412yes—
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—81no—
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2411yescharacteristic
194SD16×C43—28no—
195D8×C43—44no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43C2×D412yes—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43—21no—
215C4⋊C4×C43—21no—
216C4⋊C4×C43—21no—
217C4⋊C4×C43—21no—
218C4⋊C4×C43—42no—
219C4⋊C4×C43—42no—
220C4⋊C4×C43—42no—
221C4⋊C4×C43—42no—
222C4⋊C4×C43—81no—
223C22⋊C4×C43—22no—
224C22⋊C4×C43—22no—
225C22⋊C4×C43—42no—
226C22⋊C4×C43—42no—
227C22⋊C4×C43—42no—
228C22⋊C4×C43—42no—
229C22⋊C4×C43—42no—
230C22⋊C4×C43—42no—
231C22⋊C4×C43—42no—
232C22⋊C4×C43—81no—
233C22⋊C4×C43—81no—
234C22⋊C4×C43—81no—
235C42×C43—21no—
236C42×C43—21no—
237C42×C43—21no—
238C42×C43—21no—
239C42×C43—42no—
240C42×C43—42no—
241C23×C43—21no—
242C23×C43—22no—
243C23×C43—22no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—41no—
251C23×C43—41no—
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—22no—
266Q8×C43#12314yescomplemented
267D4×C43—22no—
268D4×C43—22no—
269D4×C43—22no—
270D4×C43—22no—
271D4×C43—48no—
272D4×C43—41no—
273D4×C43—41no—
274D4×C43—41no—
275D4×C43—41no—
276D4×C43—84no—
277C2×C4×C43—22no—
278C2×C4×C43—21no—
279C2×C4×C43—22no—
280C2×C4×C43—21no—
281C2×C4×C43—22no—
282C2×C4×C43—21no—
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—21no—
292C2×C4×C43—21no—
293C2×C4×C43—48no—
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#13512yes—
315C2×C4×C43AGL(1,ℤ/8)12yes—
316C2×C4×C43C22×D411yescharacteristic
317C2×C4×C43C2×#4111yescharacteristic
318C2×C4×C43C2×#4111yescharacteristic
319C2×C4×C43C2×#4111yescharacteristic
320C2×C4×C43H(5,𝔽2)11yescharacteristic
321C2×C4×C43H(5,𝔽2)11yescharacteristic
322C8×C43—22no—
323C8×C43—41no—
324C8×C43—41no—
325C8×C43—41no—
326#24896C4311yesmaximal, characteristic, direct product factor, Sylow
327C22×C43—41no—
328C22×C43—41no—
329C22×C43—42no—
330C22×C43—41no—
331C22×C43—42no—
332C22×C43—41no—
333C22×C43—42no—
334C22×C43—42no—
335C22×C43—41no—
336C22×C43—42no—
337C22×C43—41no—
338C22×C43—42no—
339C22×C43—41no—
340C22×C43—81no—
341C22×C43—81no—
342C22×C43—81no—
343C22×C43—81no—
344C22×C43—81no—
345C22×C43—81no—
346C22×C43—81no—
347C22×C43—81no—
348C22×C43#52511yescharacteristic
349C22×C43D4211yescharacteristic
350C22×C43#54611yescharacteristic
351C22×C43C2×#13511yescharacteristic
352C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
353C22×C43#57711yescharacteristic
354C22×C43#57711yescharacteristic
355C4×C43—24no—
356C4×C43—22no—
357C4×C43—22no—
358C4×C43—41no—
359C4×C43—41no—
360C4×C43—41no—
361C4×C43—81no—
362C4×C43—81no—
363C4×C43—81no—
364C4×C43—81no—
365C4×C43—81no—
366C4×C43C2×#12311yescharacteristic
367C4×C43#53811yescharacteristic
368C4×C43#54611yescharacteristic
369C4×C43#55111yescharacteristic
370C2×#449C2×C4311yescharacteristic
371C2×C4×SD16C2×C4311yescharacteristic, complemented
372#2422C2×C4311yescharacteristic, complemented
373#2341C2×C4311yescharacteristic, complemented
374#2094C2×C4311yescharacteristic, complemented
375#2077C2×C4311yescharacteristic, complemented
376#2054C2×C4311yescharacteristic, complemented
377#2034C2×C4311yescharacteristic, complemented
378#1934C2×C4311yescharacteristic, complemented
379#1923C2×C4311yescharacteristic, complemented
380#1880C2×C4311yescharacteristic, complemented
381#1879C2×C4311yescharacteristic, complemented
382#1865C2×C4311yescharacteristic, complemented
383#1803C2×C4311yescharacteristic, complemented
384#1788C2×C4311yescharacteristic, complemented
385C2×C43—81no—
386C2×C43—82no—
387C2×C43—82no—
388C2×C43#241811yescharacteristic
389C2×C43#310611yescharacteristic
390C2×C43#312511yescharacteristic
391C2×C43#326511yescharacteristic
392C2×C43#328411yescharacteristic
393C2×C43#330111yescharacteristic
394C2×C43#333211yescharacteristic
395C22×#41C22×C4311yescharacteristic
396C22×SD16C22×C4311yescharacteristic
397C22×D8C22×C4311yescharacteristic
398C2×#123—21no—
399C2×#121C22×C4311yescharacteristic
400C2×C4×Q8C22×C4311yescharacteristic
401C2×C4×Q8C22×C4311yescharacteristic
402C2×C4×D4C22×C4311yescharacteristic
403#449—24no—
404C4×SD16—24no—
405C2×#106C22×C4311yescharacteristic
406C2×#106C22×C4311yescharacteristic
407C2×C4⋊C8C22×C4311yescharacteristic
408C2×#103C22×C4311yescharacteristic
409C2×#103C22×C4311yescharacteristic
410C2×#103C22×C4311yescharacteristic
411C2×#102C22×C4311yescharacteristic
412C2×#102C22×C4311yescharacteristic
413C2×#102C22×C4311yescharacteristic
414C2×#102C22×C4311yescharacteristic
415C2×#102C22×C4311yescharacteristic
416C2×C22⋊C8C22×C4311yescharacteristic
417C2×C22⋊C8C22×C4311yescharacteristic
418C2×C4×C8C22×C4311yescharacteristic
419#397—21no—
420#394—21no—
421#390—21no—
422#390—21no—
423#390C22×C4311yescharacteristic
424#390C22×C4311yescharacteristic
425#390C22×C4311yescharacteristic
426#389C22×C4311yescharacteristic
427#385—21no—
428#384C22×C4311yescharacteristic
429#380—21no—
430#380C22×C4311yescharacteristic
431#380C22×C4311yescharacteristic
432C4×C22⋊C4—21no—
433C4×C22⋊C4C22×C4311yescharacteristic
434#340C22×C4311yescharacteristic
435#340C22×C4311yescharacteristic
436#340C22×C4311yescharacteristic
437#340C22×C4311yescharacteristic
438#336C22×C4311yescharacteristic
439#336C22×C4311yescharacteristic
440C43#2489611yescharacteristic, direct product factor, Sylow
441C2×#41—22no—
442C2×#41—22no—
443C2×#41—22no—
444C2×#41—22no—
445C2×#41—41no—
446C2×#41—41no—
447C22×Q8C23×C4311yescharacteristic
448C22×D4—21no—
449C22×D4—21no—
450C22×D4C23×C4311yescharacteristic
451C22×D4C23×C4311yescharacteristic
452C23×C4—21no—
453C23×C4—21no—
454C23×C4C23×C4311yescharacteristic
455C2×SD16—22no—
456C2×SD16—22no—
457C2×SD16D4×C4314yes—
458C2×D8—22no—
459C2×D8—22no—
460C2×D8—41no—
461C22×C8C23×C4311yescharacteristic
462C22×C8C23×C4311yescharacteristic
463C22×C8C23×C4311yescharacteristic
464C22×C8C23×C4311yescharacteristic
465#123—44no—
466#121—22no—
467#121—41no—
468C4×Q8—22no—
469C4×Q8—22no—
470C4×Q8—41no—
471C4×Q8—41no—
472C4×D4—22no—
473C4×D4—41no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4C23×C4311yescharacteristic
480C2×C4⋊C4C23×C4311yescharacteristic
481C2×C4⋊C4C23×C4311yescharacteristic
482C2×C4⋊C4C23×C4311yescharacteristic
483C2×C4⋊C4C23×C4311yescharacteristic
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
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×C42—21no—
497C2×C42—21no—
498C2×C42C23×C4311yescharacteristic
499C2×C42C23×C4311yescharacteristic
500#106—22no—
501#106—41no—
502C4⋊C8—41no—
503#103—22no—
504#103—22no—
505#103—22no—
506#102—22no—
507#102—22no—
508#102—22no—
509#102—41no—
510#102—41no—
511C22⋊C8—22no—
512C22⋊C8—41no—
513C4×C8—22no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95D4×C4311yescharacteristic
518#95D4×C4311yescharacteristic
519C24—21no—
520C24—21no—
521C24C2×D4×C4311yescharacteristic
522#41—44no—
523#41—44no—
524#41—44no—
525#41—44no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8C2×D4×C4312yes—
530C2×Q8#41×C4312yes—
531C2×Q8#41×C4312yes—
532C2×D4—24no—
533C2×D4—21no—
534C2×D4—21no—
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×D4#41×C4312yes—
550C22×C4—21no—
551C22×C4—24no—
552C22×C4—21no—
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—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—81no—
568C22×C4C2×D4×C4311yescharacteristic
569C22×C4C2×D4×C4311yescharacteristic
570C22×C4C2×D4×C4311yescharacteristic
571C22×C4C2×D4×C4311yescharacteristic
572C22×C4C2×D4×C4311yescharacteristic
573C22×C4C24×C4311yescharacteristic
574SD16—28no—
575D8—44no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8C2×D4×C4312yes—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—42no—
602C4⋊C4—81no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—42no—
612C22⋊C4—81no—
613C22⋊C4—81no—
614C22⋊C4—81no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—42no—
620C42—42no—
621C23—21no—
622C23—22no—
623C23—22no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23C22×D4×C4311yescharacteristic
643Q8—22no—
644Q8—22no—
645Q8—22no—
646Q8#123×C4314yescomplemented
647D4—22no—
648D4—22no—
649D4—22no—
650D4—22no—
651D4—48no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—84no—
657C2×C4—22no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
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—84no—
694C2×C4#135×C4312yes—
695C2×C4AGL(1,ℤ/8)×C4312yes—
696C2×C4C22×D4×C4311yescharacteristic
697C2×C4C2×#41×C4311yescharacteristic
698C2×C4C2×#41×C4311yescharacteristic
699C2×C4C2×#41×C4311yescharacteristic
700C2×C4H(5,𝔽2)×C4311yescharacteristic
701C2×C4H(5,𝔽2)×C4311yescharacteristic
702C8—22no—
703C8—41no—
704C8—41no—
705C8—41no—
706C22—41no—
707C22—42no—
708C22—41no—
709C22—42no—
710C22—42no—
711C22—41no—
712C22—42no—
713C22—42no—
714C22—41no—
715C22—41no—
716C22—42no—
717C22—41no—
718C22—41no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22C43×#52511yescharacteristic
728C22D42×C4311yescharacteristic
729C22C43×#54611yescharacteristic
730C22C2×#135×C4311yescharacteristic
731C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
732C22C43×#57711yescharacteristic
733C22C43×#57711yescharacteristic
734C4—24no—
735C4—22no—
736C4—22no—
737C4—41no—
738C4—41no—
739C4—41no—
740C4—81no—
741C4—81no—
742C4—81no—
743C4—81no—
744C4—81no—
745C4C2×#123×C4311yescharacteristic
746C4C43×#53811yescharacteristic
747C4C43×#54611yescharacteristic
748C4C43×#55111yescharacteristic
749C2—81no—
750C2—82no—
751C2—82no—
752C2C43×#241811yescharacteristic
753C2C43×#310611yescharacteristic
754C2C43×#312511yescharacteristic
755C2C43×#326511yescharacteristic
756C2C43×#328411yescharacteristic
757C2C43×#330111yescharacteristic
758C2C43×#333211yescharacteristic
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×SD16×C43C2semidirect
3. C43×#2422C2semidirect
4. C43×#2341C2semidirect
5. C43×#2094C2semidirect
6. C43×#2077C2semidirect
7. C43×#2054C2semidirect
8. C43×#2034C2semidirect
9. C43×#1934C2semidirect
10. C43×#1923C2semidirect
11. C43×#1880C2semidirect
12. C43×#1879C2semidirect
13. C43×#1865C2semidirect
14. C43×#1803C2semidirect
15. C43×#1788C2semidirect
266. Q8×C43#123semidirect
326. #24896C43direct (N × H)
371. C2×C4×SD16C2×C43semidirect
372. #2422C2×C43semidirect
373. #2341C2×C43semidirect
374. #2094C2×C43semidirect
375. #2077C2×C43semidirect
376. #2054C2×C43semidirect
377. #2034C2×C43semidirect
378. #1934C2×C43semidirect
379. #1923C2×C43semidirect
380. #1880C2×C43semidirect
381. #1879C2×C43semidirect
382. #1865C2×C43semidirect
383. #1803C2×C43semidirect
384. #1788C2×C43semidirect
440. C43#24896direct (N × H)
646. Q8#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×SD16×C432
C43×#24222
C43×#23412
C43×#20942
C43×#20772
C43×#20542
C43×#20342
C43×#19342
C43×#19232
C43×#18802
C43×#18792
C43×#18652
C43×#18032
C43×#17882
#2489643