Finite Group Databasebeta

← C43×#24205 #24944222

Subgroups — C43×#24205 #24944222

Order 11008.

1144 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#556C211yesmaximal, characteristic, complemented
2C2×C43×#463C211yesmaximal, characteristic
3C2×C43×#440C211yesmaximal, characteristic, complemented
4C43×#2538C211yesmaximal, characteristic, complemented
5C43×#2043C211yesmaximal, characteristic, complemented
6C43×#2042C211yesmaximal, characteristic, complemented
7C43×#2013C211yesmaximal, characteristic, complemented
8C43×#2012C211yesmaximal, characteristic
9C43×#1985C211yesmaximal, characteristic, complemented
10C43×#1959C211yesmaximal, characteristic, complemented
11C43×#1880C211yesmaximal, characteristic, complemented
12C43×#1879C211yesmaximal, characteristic
13C43×#1863C211yesmaximal, characteristic, complemented
14C43×#1862C211yesmaximal, characteristic, complemented
15C43×#1803C211yesmaximal, characteristic, complemented
16C22×SD16×C43C2211yescharacteristic
17C22×SD16×C43C2211yescharacteristic
18C22×D8×C43C2211yescharacteristic
19C43×#556—24no—
20C43×#556—24no—
21C2×C4⋊Q8×C43C2211yescharacteristic
22C2×#126×C43—21no—
23C2×#126×C43—21no—
24C2×#124×C43C2211yescharacteristic
25C2×#124×C43C2211yescharacteristic
26C2×C22⋊Q8×C43—21no—
27C2×C22⋊Q8×C43—21no—
28C2×C4×Q8×C43C2211yescharacteristic
29C2×C4×Q8×C43C2211yescharacteristic
30C2×C4×Q8×C43C2211yescharacteristic
31C2×C4×D4×C43C2211yescharacteristic
32C2×C4×D4×C43C2211yescharacteristic
33C2×#117×C43—21no—
34C43×#463—24no—
35C43×#440—24no—
36C2×#107×C43C2211yescharacteristic
37C2×C4⋊C8×C43C2211yescharacteristic
38C2×#103×C43C2211yescharacteristic
39C2×#103×C43C2211yescharacteristic
40C2×#103×C43C2211yescharacteristic
41C2×#103×C43C2211yescharacteristic
42C2×#103×C43C2211yescharacteristic
43C2×#103×C43C2211yescharacteristic
44C2×#102×C43C2211yescharacteristic
45C2×#102×C43C2211yescharacteristic
46C2×#102×C43C2211yescharacteristic
47C2×#102×C43C2211yescharacteristic
48C2×#97×C43C2211yescharacteristic
49C43×#396—21no—
50C43×#396—21no—
51C43×#390C2211yescharacteristic
52C43×#390C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C43×#389C2211yescharacteristic
55C43×#384C2211yescharacteristic
56C43×#380—21no—
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×Q8×C43D411yescharacteristic
64C22×Q8×C43C2311yescharacteristic
65C22×Q8×C43C2311yescharacteristic
66C22×D4×C43C2311yescharacteristic
67C22×D4×C43C2311yescharacteristic
68C23×C4×C43—21no—
69C23×C4×C43—21no—
70C2×SD16×C43—22no—
71C2×SD16×C43—22no—
72C2×SD16×C43—22no—
73C2×SD16×C43—22no—
74C2×SD16×C43—22no—
75C2×SD16×C43—41no—
76C2×D8×C43—22no—
77C2×D8×C43—22no—
78C2×D8×C43—41no—
79C22×C8×C43C2311yescharacteristic
80C22×C8×C43C2311yescharacteristic
81C22×C8×C43C2311yescharacteristic
82C22×C8×C43C2311yescharacteristic
83C4⋊Q8×C43—22no—
84C4⋊Q8×C43—22no—
85#126×C43—28no—
86#126×C43—28no—
87#124×C43—22no—
88#124×C43—22no—
89#124×C43—22no—
90#124×C43D414yes—
91C22⋊Q8×C43—28no—
92C22⋊Q8×C43—44no—
93C4×Q8×C43—22no—
94C4×Q8×C43—22no—
95C4×Q8×C43—22no—
96C4×Q8×C43—22no—
97C4×Q8×C43—22no—
98C4×Q8×C43D414yes—
99C4×D4×C43—22no—
100C4×D4×C43—22no—
101C4×D4×C43—22no—
102C4×D4×C43—22no—
103#117×C43—28no—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43D411yescharacteristic
113C2×C4⋊C4×C43D411yescharacteristic
114C2×C4⋊C4×C43D411yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C22⋊C4×C43—21no—
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122C2×C22⋊C4×C43—21no—
123C2×C22⋊C4×C43—21no—
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C42×C43—21no—
130C2×C42×C43—21no—
131C2×C42×C43C2311yescharacteristic
132C2×C42×C43C2311yescharacteristic
133C2×C42×C43C2311yescharacteristic
134#107×C43—22no—
135C4⋊C8×C43—22no—
136#103×C43—22no—
137#103×C43—22no—
138#103×C43—22no—
139#103×C43—41no—
140#103×C43—41no—
141#103×C43—41no—
142#102×C43—22no—
143#102×C43—22no—
144#102×C43—22no—
145#102×C43—41no—
146#97×C43—22no—
147#95×C43—21no—
148#95×C43—21no—
149C24×C43—21no—
150C24×C43—21no—
151C2×Q8×C43—22no—
152C2×Q8×C43—22no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43—41no—
164C2×Q8×C43C2×D412yes—
165C2×Q8×C43C2×D412yes—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43—21no—
174C2×D4×C43—21no—
175C2×D4×C43—21no—
176C2×D4×C43C2×D412yes—
177C2×D4×C43#4112yes—
178C22×C4×C43—24no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—42no—
186C22×C4×C43—42no—
187C22×C4×C43—42no—
188C22×C4×C43—42no—
189C22×C4×C43—42no—
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2411yescharacteristic
197SD16×C43—28no—
198SD16×C43—44no—
199D8×C43—44no—
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×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43#4112yes—
212C4⋊C4×C43—24no—
213C4⋊C4×C43—24no—
214C4⋊C4×C43—24no—
215C4⋊C4×C43—24no—
216C4⋊C4×C43—22no—
217C4⋊C4×C43—22no—
218C4⋊C4×C43—22no—
219C4⋊C4×C43—21no—
220C4⋊C4×C43—21no—
221C4⋊C4×C43—21no—
222C4⋊C4×C43—21no—
223C4⋊C4×C43—21no—
224C4⋊C4×C43—21no—
225C4⋊C4×C43—21no—
226C4⋊C4×C43—42no—
227C4⋊C4×C43—42no—
228C4⋊C4×C43—42no—
229C4⋊C4×C43—81no—
230C4⋊C4×C43C2×D412yes—
231C22⋊C4×C43—24no—
232C22⋊C4×C43—24no—
233C22⋊C4×C43—24no—
234C22⋊C4×C43—24no—
235C22⋊C4×C43—24no—
236C22⋊C4×C43—42no—
237C22⋊C4×C43—42no—
238C22⋊C4×C43—42no—
239C22⋊C4×C43—81no—
240C22⋊C4×C43—81no—
241C42×C43—24no—
242C42×C43—24no—
243C42×C43—21no—
244C42×C43—21no—
245C42×C43—21no—
246C42×C43—21no—
247C42×C43C2×D412yes—
248C42×C43C2×D412yes—
249C23×C43—22no—
250C23×C43—22no—
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×C43—41no—
263C23×C43C22×D411yescharacteristic
264Q8×C43—22no—
265Q8×C43—22no—
266Q8×C43—22no—
267Q8×C43—22no—
268Q8×C43—44no—
269Q8×C43—41no—
270Q8×C43—41no—
271Q8×C43—41no—
272Q8×C43—41no—
273D4×C43—22no—
274D4×C43—22no—
275D4×C43—22no—
276D4×C43—22no—
277D4×C43—41no—
278D4×C43—41no—
279D4×C43—41no—
280D4×C43—41no—
281C2×C4×C43—21no—
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—22no—
289C2×C4×C43—21no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—48no—
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—41no—
314C2×C4×C43—41no—
315C2×C4×C43—84no—
316C2×C4×C43#12012yes—
317C2×C4×C43#12012yes—
318C2×C4×C43AGL(1,ℤ/8)12yes—
319C2×C4×C43C22×D411yescharacteristic
320C2×C4×C43C22×D411yescharacteristic
321C2×C4×C43C2×#4111yescharacteristic
322C2×C4×C43C2×#4111yescharacteristic
323C2×C4×C43H(5,𝔽2)11yescharacteristic
324C2×C4×C432−1+411yescharacteristic
325C8×C43—22no—
326C8×C43—41no—
327C8×C43—41no—
328C8×C43—41no—
329#24205C4311yesmaximal, characteristic, direct product factor, Sylow
330C22×C43—42no—
331C22×C43—42no—
332C22×C43—42no—
333C22×C43—42no—
334C22×C43—42no—
335C22×C43—42no—
336C22×C43—81no—
337C22×C43—81no—
338C22×C43—81no—
339C22×C43—81no—
340C22×C43—81no—
341C22×C43—81no—
342C22×C43—81no—
343C22×C43—81no—
344C22×C43C2×#12011yescharacteristic
345C22×C43#54811yescharacteristic
346C22×C43#55011yescharacteristic
347C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
348C22×C43#57511yescharacteristic
349C22×C43#57711yescharacteristic
350C22×C43#57811yescharacteristic
351C4×C43—22no—
352C4×C43—22no—
353C4×C43—22no—
354C4×C43—42no—
355C4×C43—42no—
356C4×C43—41no—
357C4×C43—42no—
358C4×C43—41no—
359C4×C43—41no—
360C4×C43—81no—
361C4×C43—81no—
362C4×C43—81no—
363C4×C43#52511yescharacteristic
364C4×C43#53711yescharacteristic
365C4×C43#54611yescharacteristic
366C4×C43#54711yescharacteristic
367C2×#556C2×C4311yescharacteristic, complemented
368C2×#463C2×C4311yescharacteristic
369C2×#440C2×C4311yescharacteristic, complemented
370#2538C2×C4311yescharacteristic, complemented
371#2043C2×C4311yescharacteristic, complemented
372#2042C2×C4311yescharacteristic, complemented
373#2013C2×C4311yescharacteristic, complemented
374#2012C2×C4311yescharacteristic
375#1985C2×C4311yescharacteristic, complemented
376#1959C2×C4311yescharacteristic, complemented
377#1880C2×C4311yescharacteristic, complemented
378#1879C2×C4311yescharacteristic
379#1863C2×C4311yescharacteristic, complemented
380#1862C2×C4311yescharacteristic, complemented
381#1803C2×C4311yescharacteristic, complemented
382C2×C43—82no—
383C2×C43—82no—
384C2×C43#240711yescharacteristic
385C2×C43#300611yescharacteristic
386C2×C43#301311yescharacteristic
387C2×C43#336711yescharacteristic
388C2×C43#337611yescharacteristic
389C2×C43#339711yescharacteristic
390C2×C43#340211yescharacteristic
391C22×SD16C22×C4311yescharacteristic
392C22×SD16C22×C4311yescharacteristic
393C22×D8C22×C4311yescharacteristic
394#556—24no—
395#556—24no—
396C2×C4⋊Q8C22×C4311yescharacteristic
397C2×#126—21no—
398C2×#126—21no—
399C2×#124C22×C4311yescharacteristic
400C2×#124C22×C4311yescharacteristic
401C2×C22⋊Q8—21no—
402C2×C22⋊Q8—21no—
403C2×C4×Q8C22×C4311yescharacteristic
404C2×C4×Q8C22×C4311yescharacteristic
405C2×C4×Q8C22×C4311yescharacteristic
406C2×C4×D4C22×C4311yescharacteristic
407C2×C4×D4C22×C4311yescharacteristic
408C2×#117—21no—
409#463—24no—
410#440—24no—
411C2×#107C22×C4311yescharacteristic
412C2×C4⋊C8C22×C4311yescharacteristic
413C2×#103C22×C4311yescharacteristic
414C2×#103C22×C4311yescharacteristic
415C2×#103C22×C4311yescharacteristic
416C2×#103C22×C4311yescharacteristic
417C2×#103C22×C4311yescharacteristic
418C2×#103C22×C4311yescharacteristic
419C2×#102C22×C4311yescharacteristic
420C2×#102C22×C4311yescharacteristic
421C2×#102C22×C4311yescharacteristic
422C2×#102C22×C4311yescharacteristic
423C2×#97C22×C4311yescharacteristic
424#396—21no—
425#396—21no—
426#390C22×C4311yescharacteristic
427#390C22×C4311yescharacteristic
428#389C22×C4311yescharacteristic
429#389C22×C4311yescharacteristic
430#384C22×C4311yescharacteristic
431#380—21no—
432#340C22×C4311yescharacteristic
433#340C22×C4311yescharacteristic
434#336C22×C4311yescharacteristic
435#336C22×C4311yescharacteristic
436#336C22×C4311yescharacteristic
437#336C22×C4311yescharacteristic
438C43#2420511yescharacteristic, direct product factor, Sylow
439C22×Q8D4×C4311yescharacteristic
440C22×Q8C23×C4311yescharacteristic
441C22×Q8C23×C4311yescharacteristic
442C22×D4C23×C4311yescharacteristic
443C22×D4C23×C4311yescharacteristic
444C23×C4—21no—
445C23×C4—21no—
446C2×SD16—22no—
447C2×SD16—22no—
448C2×SD16—22no—
449C2×SD16—22no—
450C2×SD16—22no—
451C2×SD16—41no—
452C2×D8—22no—
453C2×D8—22no—
454C2×D8—41no—
455C22×C8C23×C4311yescharacteristic
456C22×C8C23×C4311yescharacteristic
457C22×C8C23×C4311yescharacteristic
458C22×C8C23×C4311yescharacteristic
459C4⋊Q8—22no—
460C4⋊Q8—22no—
461#126—28no—
462#126—28no—
463#124—22no—
464#124—22no—
465#124—22no—
466#124D4×C4314yes—
467C22⋊Q8—28no—
468C22⋊Q8—44no—
469C4×Q8—22no—
470C4×Q8—22no—
471C4×Q8—22no—
472C4×Q8—22no—
473C4×Q8—22no—
474C4×Q8D4×C4314yes—
475C4×D4—22no—
476C4×D4—22no—
477C4×D4—22no—
478C4×D4—22no—
479#117—28no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4D4×C4311yescharacteristic
489C2×C4⋊C4D4×C4311yescharacteristic
490C2×C4⋊C4D4×C4311yescharacteristic
491C2×C4⋊C4C23×C4311yescharacteristic
492C2×C4⋊C4C23×C4311yescharacteristic
493C2×C4⋊C4C23×C4311yescharacteristic
494C2×C4⋊C4C23×C4311yescharacteristic
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C42—21no—
506C2×C42—21no—
507C2×C42C23×C4311yescharacteristic
508C2×C42C23×C4311yescharacteristic
509C2×C42C23×C4311yescharacteristic
510#107—22no—
511C4⋊C8—22no—
512#103—22no—
513#103—22no—
514#103—22no—
515#103—41no—
516#103—41no—
517#103—41no—
518#102—22no—
519#102—22no—
520#102—22no—
521#102—41no—
522#97—22no—
523#95—21no—
524#95—21no—
525C24—21no—
526C24—21no—
527C2×Q8—22no—
528C2×Q8—22no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—41no—
540C2×Q8C2×D4×C4312yes—
541C2×Q8C2×D4×C4312yes—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4C2×D4×C4312yes—
553C2×D4#41×C4312yes—
554C22×C4—24no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4C2×D4×C4311yescharacteristic
567C22×C4C2×D4×C4311yescharacteristic
568C22×C4C2×D4×C4311yescharacteristic
569C22×C4C2×D4×C4311yescharacteristic
570C22×C4C2×D4×C4311yescharacteristic
571C22×C4C2×D4×C4311yescharacteristic
572C22×C4C24×C4311yescharacteristic
573SD16—28no—
574SD16—44no—
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×C8#41×C4312yes—
588C4⋊C4—24no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—42no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—81no—
606C4⋊C4C2×D4×C4312yes—
607C22⋊C4—24no—
608C22⋊C4—24no—
609C22⋊C4—24no—
610C22⋊C4—24no—
611C22⋊C4—24no—
612C22⋊C4—42no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—81no—
616C22⋊C4—81no—
617C42—24no—
618C42—24no—
619C42—21no—
620C42—21no—
621C42—21no—
622C42—21no—
623C42C2×D4×C4312yes—
624C42C2×D4×C4312yes—
625C23—22no—
626C23—22no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23C22×D4×C4311yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—22no—
643Q8—22no—
644Q8—44no—
645Q8—41no—
646Q8—41no—
647Q8—41no—
648Q8—41no—
649D4—22no—
650D4—22no—
651D4—22no—
652D4—22no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—41no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—48no—
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—84no—
692C2×C4#120×C4312yes—
693C2×C4#120×C4312yes—
694C2×C4AGL(1,ℤ/8)×C4312yes—
695C2×C4C22×D4×C4311yescharacteristic
696C2×C4C22×D4×C4311yescharacteristic
697C2×C4C2×#41×C4311yescharacteristic
698C2×C4C2×#41×C4311yescharacteristic
699C2×C4H(5,𝔽2)×C4311yescharacteristic
700C2×C42−1+4×C4311yescharacteristic
701C8—22no—
702C8—41no—
703C8—41no—
704C8—41no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22C2×#120×C4311yescharacteristic
720C22C43×#54811yescharacteristic
721C22C43×#55011yescharacteristic
722C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
723C22C43×#57511yescharacteristic
724C22C43×#57711yescharacteristic
725C22C43×#57811yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—42no—
730C4—42no—
731C4—41no—
732C4—42no—
733C4—41no—
734C4—41no—
735C4—81no—
736C4—81no—
737C4—81no—
738C4C43×#52511yescharacteristic
739C4C43×#53711yescharacteristic
740C4C43×#54611yescharacteristic
741C4C43×#54711yescharacteristic
742C2—82no—
743C2—82no—
744C2C43×#240711yescharacteristic
745C2C43×#300611yescharacteristic
746C2C43×#301311yescharacteristic
747C2C43×#336711yescharacteristic
748C2C43×#337611yescharacteristic
749C2C43×#339711yescharacteristic
750C2C43×#340211yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC22×D8×C43C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C2×C4×Q8×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#556C2semidirect
3. C2×C43×#440C2semidirect
4. C43×#2538C2semidirect
5. C43×#2043C2semidirect
6. C43×#2042C2semidirect
7. C43×#2013C2semidirect
9. C43×#1985C2semidirect
10. C43×#1959C2semidirect
11. C43×#1880C2semidirect
13. C43×#1863C2semidirect
14. C43×#1862C2semidirect
15. C43×#1803C2semidirect
329. #24205C43direct (N × H)
367. C2×#556C2×C43semidirect
369. C2×#440C2×C43semidirect
370. #2538C2×C43semidirect
371. #2043C2×C43semidirect
372. #2042C2×C43semidirect
373. #2013C2×C43semidirect
375. #1985C2×C43semidirect
376. #1959C2×C43semidirect
377. #1880C2×C43semidirect
379. #1863C2×C43semidirect
380. #1862C2×C43semidirect
381. #1803C2×C43semidirect
438. C43#24205direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#5562
C2×C43×#4632
C2×C43×#4402
C43×#25382
C43×#20432
C43×#20422
C43×#20132
C43×#20122
C43×#19852
C43×#19592
C43×#18802
C43×#18792
C43×#18632
C43×#18622
C43×#18032
#2420543