Finite Group Databasebeta

← C43×#24194 #24944211

Subgroups — C43×#24194 #24944211

Order 11008.

1138 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#559C211yesmaximal, characteristic
2C2×C43×#464C211yesmaximal, characteristic, complemented
3C2×C4×SD16×C43C211yesmaximal, characteristic, complemented
4C43×#2581C211yesmaximal, characteristic, complemented
5C43×#2042C211yesmaximal, characteristic, complemented
6C43×#2041C211yesmaximal, characteristic
7C43×#2015C211yesmaximal, characteristic, complemented
8C43×#2014C211yesmaximal, characteristic
9C43×#1984C211yesmaximal, characteristic, complemented
10C43×#1958C211yesmaximal, characteristic, complemented
11C43×#1878C211yesmaximal, characteristic, complemented
12C43×#1877C211yesmaximal, characteristic, complemented
13C43×#1865C211yesmaximal, characteristic, complemented
14C43×#1864C211yesmaximal, characteristic, complemented
15C43×#1804C211yesmaximal, characteristic, complemented
16C22×Q16×C43C2211yescharacteristic
17C22×SD16×C43C2211yescharacteristic
18C22×SD16×C43C2211yescharacteristic
19C43×#559—24no—
20C43×#559—24no—
21C2×#127×C43C2211yescharacteristic
22C2×#124×C43—21no—
23C2×#124×C43C2211yescharacteristic
24C2×#124×C43C2211yescharacteristic
25C2×#123×C43—21no—
26C2×#123×C43—21no—
27C2×C4×Q8×C43C2211yescharacteristic
28C2×C4×Q8×C43C2211yescharacteristic
29C2×C4×Q8×C43C2211yescharacteristic
30C2×C4×D4×C43—21no—
31C2×C4×D4×C43C2211yescharacteristic
32C2×C4×D4×C43C2211yescharacteristic
33C43×#464—24no—
34C4×SD16×C43—24no—
35C2×#106×C43C2211yescharacteristic
36C2×C4⋊C8×C43C2211yescharacteristic
37C2×#103×C43C2211yescharacteristic
38C2×#103×C43C2211yescharacteristic
39C2×#103×C43C2211yescharacteristic
40C2×#103×C43C2211yescharacteristic
41C2×#102×C43C2211yescharacteristic
42C2×#102×C43C2211yescharacteristic
43C2×#102×C43C2211yescharacteristic
44C2×#102×C43C2211yescharacteristic
45C2×#102×C43C2211yescharacteristic
46C2×#102×C43C2211yescharacteristic
47C2×C4×C8×C43C2211yescharacteristic
48C43×#400—21no—
49C43×#395—21no—
50C43×#391C2211yescharacteristic
51C43×#391C2211yescharacteristic
52C43×#389C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C43×#387—21no—
55C43×#387—21no—
56C43×#382C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×Q8×C43D411yescharacteristic
64C22×Q8×C43C2311yescharacteristic
65C22×Q8×C43C2311yescharacteristic
66C22×D4×C43—21no—
67C22×D4×C43—21no—
68C22×D4×C43C2311yescharacteristic
69C22×D4×C43C2311yescharacteristic
70C23×C4×C43—21no—
71C23×C4×C43—21no—
72C2×Q16×C43—22no—
73C2×Q16×C43—22no—
74C2×Q16×C43—41no—
75C2×SD16×C43—22no—
76C2×SD16×C43—22no—
77C2×SD16×C43—22no—
78C2×SD16×C43—22no—
79C2×SD16×C43—22no—
80C2×SD16×C43—41no—
81C22×C8×C43C2311yescharacteristic
82C22×C8×C43C2311yescharacteristic
83C22×C8×C43C2311yescharacteristic
84C22×C8×C43C2311yescharacteristic
85#127×C43—22no—
86#127×C43—22no—
87#124×C43—28no—
88#124×C43—22no—
89#124×C43—22no—
90#124×C43—22no—
91#124×C43D414yes—
92#123×C43—28no—
93#123×C43—28no—
94C4×Q8×C43—22no—
95C4×Q8×C43—22no—
96C4×Q8×C43—22no—
97C4×Q8×C43—22no—
98C4×Q8×C43—22no—
99C4×Q8×C43—22no—
100C4×D4×C43—28no—
101C4×D4×C43—22no—
102C4×D4×C43—22no—
103C4×D4×C43—22no—
104C4×D4×C43D414yes—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43D411yescharacteristic
110C2×C4⋊C4×C43D411yescharacteristic
111C2×C4⋊C4×C43D411yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C22⋊C4×C43—21no—
117C2×C22⋊C4×C43—21no—
118C2×C22⋊C4×C43—21no—
119C2×C22⋊C4×C43—21no—
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122C2×C42×C43—21no—
123C2×C42×C43—21no—
124C2×C42×C43C2311yescharacteristic
125C2×C42×C43C2311yescharacteristic
126C2×C42×C43C2311yescharacteristic
127#106×C43—22no—
128C4⋊C8×C43—22no—
129#103×C43—22no—
130#103×C43—22no—
131#103×C43—22no—
132#103×C43—41no—
133#102×C43—22no—
134#102×C43—22no—
135#102×C43—22no—
136#102×C43—41no—
137#102×C43—41no—
138#102×C43—41no—
139C4×C8×C43—22no—
140#95×C43—21no—
141#95×C43—21no—
142#95×C43—21no—
143#95×C43—21no—
144#95×C43—21no—
145#95×C43—21no—
146#95×C43—21no—
147#95×C43—21no—
148C24×C43—21no—
149C24×C43—21no—
150C2×Q8×C43—22no—
151C2×Q8×C43—22no—
152C2×Q8×C43—21no—
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—41no—
163C2×Q8×C43C2×D412yes—
164C2×Q8×C43#4112yes—
165C2×D4×C43—24no—
166C2×D4×C43—24no—
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×C43—21no—
177C2×D4×C43—42no—
178C2×D4×C43—42no—
179C2×D4×C43—81no—
180C2×D4×C43—81no—
181C2×D4×C43C2×D412yes—
182C2×D4×C43C2×D412yes—
183C22×C4×C43—24no—
184C22×C4×C43—24no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—81no—
192C22×C4×C43—81no—
193C22×C4×C43—81no—
194C22×C4×C43—81no—
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2411yescharacteristic
202Q16×C43—44no—
203SD16×C43—28no—
204SD16×C43—44no—
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×C43—21no—
214C2×C8×C43—21no—
215C2×C8×C43—21no—
216C2×C8×C43#4112yes—
217C4⋊C4×C43—24no—
218C4⋊C4×C43—22no—
219C4⋊C4×C43—22no—
220C4⋊C4×C43—22no—
221C4⋊C4×C43—21no—
222C4⋊C4×C43—21no—
223C4⋊C4×C43—21no—
224C4⋊C4×C43—21no—
225C4⋊C4×C43—21no—
226C4⋊C4×C43—21no—
227C4⋊C4×C43—21no—
228C4⋊C4×C43—42no—
229C4⋊C4×C43—42no—
230C4⋊C4×C43—42no—
231C4⋊C4×C43C2×D412yes—
232C22⋊C4×C43—24no—
233C22⋊C4×C43—24no—
234C22⋊C4×C43—24no—
235C22⋊C4×C43—24no—
236C22⋊C4×C43—24no—
237C22⋊C4×C43—24no—
238C42×C43—24no—
239C42×C43—21no—
240C42×C43—21no—
241C42×C43—21no—
242C42×C43—21no—
243C42×C43—42no—
244C42×C43C2×D412yes—
245C42×C43C2×D412yes—
246C23×C43—22no—
247C23×C43—22no—
248C23×C43—41no—
249C23×C43—41no—
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×C43C22×D411yescharacteristic
261Q8×C43—22no—
262Q8×C43—22no—
263Q8×C43—22no—
264Q8×C43—22no—
265Q8×C43—44no—
266Q8×C43—41no—
267Q8×C43—41no—
268Q8×C43—41no—
269Q8×C43—41no—
270D4×C43—22no—
271D4×C43—22no—
272D4×C43—22no—
273D4×C43—22no—
274D4×C43—48no—
275D4×C43—41no—
276D4×C43—41no—
277D4×C43—41no—
278D4×C43—41no—
279D4×C43—84no—
280C2×C4×C43—21no—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—22no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—22no—
290C2×C4×C43—21no—
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—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#12012yes—
316C2×C4×C43#12012yes—
317C2×C4×C43#13512yes—
318C2×C4×C43C22×D411yescharacteristic
319C2×C4×C43C22×D411yescharacteristic
320C2×C4×C43C2×#4111yescharacteristic
321C2×C4×C43C2×#4111yescharacteristic
322C2×C4×C43H(5,𝔽2)11yescharacteristic
323C2×C4×C432−1+411yescharacteristic
324C8×C43—22no—
325C8×C43—41no—
326C8×C43—41no—
327C8×C43—41no—
328#24194C4311yesmaximal, characteristic, direct product factor, Sylow
329C22×C43—42no—
330C22×C43—42no—
331C22×C43—42no—
332C22×C43—42no—
333C22×C43—42no—
334C22×C43—42no—
335C22×C43—81no—
336C22×C43—81no—
337C22×C43—81no—
338C22×C43—81no—
339C22×C43—81no—
340C22×C43—81no—
341C22×C43—81no—
342C22×C43—81no—
343C22×C43C2×#12011yescharacteristic
344C22×C43#54811yescharacteristic
345C22×C43#55011yescharacteristic
346C22×C43C2×#13511yescharacteristic
347C22×C43#57511yescharacteristic
348C22×C43#57711yescharacteristic
349C22×C43#57711yescharacteristic
350C4×C43—22no—
351C4×C43—22no—
352C4×C43—22no—
353C4×C43—42no—
354C4×C43—42no—
355C4×C43—41no—
356C4×C43—41no—
357C4×C43—41no—
358C4×C43—42no—
359C4×C43—81no—
360C4×C43—81no—
361C4×C43—81no—
362C4×C43#52511yescharacteristic
363C4×C43#53711yescharacteristic
364C4×C43#54611yescharacteristic
365C4×C43#54711yescharacteristic
366C2×#559C2×C4311yescharacteristic
367C2×#464C2×C4311yescharacteristic, complemented
368C2×C4×SD16C2×C4311yescharacteristic, complemented
369#2581C2×C4311yescharacteristic, complemented
370#2042C2×C4311yescharacteristic, complemented
371#2041C2×C4311yescharacteristic
372#2015C2×C4311yescharacteristic, complemented
373#2014C2×C4311yescharacteristic
374#1984C2×C4311yescharacteristic, complemented
375#1958C2×C4311yescharacteristic, complemented
376#1878C2×C4311yescharacteristic, complemented
377#1877C2×C4311yescharacteristic, complemented
378#1865C2×C4311yescharacteristic, complemented
379#1864C2×C4311yescharacteristic, complemented
380#1804C2×C4311yescharacteristic, complemented
381C2×C43—82no—
382C2×C43—82no—
383C2×C43#240711yescharacteristic
384C2×C43#300211yescharacteristic
385C2×C43#300911yescharacteristic
386C2×C43#336511yescharacteristic
387C2×C43#337111yescharacteristic
388C2×C43#339411yescharacteristic
389C2×C43#340111yescharacteristic
390C22×Q16C22×C4311yescharacteristic
391C22×SD16C22×C4311yescharacteristic
392C22×SD16C22×C4311yescharacteristic
393#559—24no—
394#559—24no—
395C2×#127C22×C4311yescharacteristic
396C2×#124—21no—
397C2×#124C22×C4311yescharacteristic
398C2×#124C22×C4311yescharacteristic
399C2×#123—21no—
400C2×#123—21no—
401C2×C4×Q8C22×C4311yescharacteristic
402C2×C4×Q8C22×C4311yescharacteristic
403C2×C4×Q8C22×C4311yescharacteristic
404C2×C4×D4—21no—
405C2×C4×D4C22×C4311yescharacteristic
406C2×C4×D4C22×C4311yescharacteristic
407#464—24no—
408C4×SD16—24no—
409C2×#106C22×C4311yescharacteristic
410C2×C4⋊C8C22×C4311yescharacteristic
411C2×#103C22×C4311yescharacteristic
412C2×#103C22×C4311yescharacteristic
413C2×#103C22×C4311yescharacteristic
414C2×#103C22×C4311yescharacteristic
415C2×#102C22×C4311yescharacteristic
416C2×#102C22×C4311yescharacteristic
417C2×#102C22×C4311yescharacteristic
418C2×#102C22×C4311yescharacteristic
419C2×#102C22×C4311yescharacteristic
420C2×#102C22×C4311yescharacteristic
421C2×C4×C8C22×C4311yescharacteristic
422#400—21no—
423#395—21no—
424#391C22×C4311yescharacteristic
425#391C22×C4311yescharacteristic
426#389C22×C4311yescharacteristic
427#389C22×C4311yescharacteristic
428#387—21no—
429#387—21no—
430#382C22×C4311yescharacteristic
431#340C22×C4311yescharacteristic
432#340C22×C4311yescharacteristic
433#336C22×C4311yescharacteristic
434#336C22×C4311yescharacteristic
435#336C22×C4311yescharacteristic
436#336C22×C4311yescharacteristic
437C43#2419411yescharacteristic, direct product factor, Sylow
438C22×Q8D4×C4311yescharacteristic
439C22×Q8C23×C4311yescharacteristic
440C22×Q8C23×C4311yescharacteristic
441C22×D4—21no—
442C22×D4—21no—
443C22×D4C23×C4311yescharacteristic
444C22×D4C23×C4311yescharacteristic
445C23×C4—21no—
446C23×C4—21no—
447C2×Q16—22no—
448C2×Q16—22no—
449C2×Q16—41no—
450C2×SD16—22no—
451C2×SD16—22no—
452C2×SD16—22no—
453C2×SD16—22no—
454C2×SD16—22no—
455C2×SD16—41no—
456C22×C8C23×C4311yescharacteristic
457C22×C8C23×C4311yescharacteristic
458C22×C8C23×C4311yescharacteristic
459C22×C8C23×C4311yescharacteristic
460#127—22no—
461#127—22no—
462#124—28no—
463#124—22no—
464#124—22no—
465#124—22no—
466#124D4×C4314yes—
467#123—28no—
468#123—28no—
469C4×Q8—22no—
470C4×Q8—22no—
471C4×Q8—22no—
472C4×Q8—22no—
473C4×Q8—22no—
474C4×Q8—22no—
475C4×D4—28no—
476C4×D4—22no—
477C4×D4—22no—
478C4×D4—22no—
479C4×D4D4×C4314yes—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4D4×C4311yescharacteristic
485C2×C4⋊C4D4×C4311yescharacteristic
486C2×C4⋊C4D4×C4311yescharacteristic
487C2×C4⋊C4C23×C4311yescharacteristic
488C2×C4⋊C4C23×C4311yescharacteristic
489C2×C4⋊C4C23×C4311yescharacteristic
490C2×C4⋊C4C23×C4311yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C42—21no—
498C2×C42—21no—
499C2×C42C23×C4311yescharacteristic
500C2×C42C23×C4311yescharacteristic
501C2×C42C23×C4311yescharacteristic
502#106—22no—
503C4⋊C8—22no—
504#103—22no—
505#103—22no—
506#103—22no—
507#103—41no—
508#102—22no—
509#102—22no—
510#102—22no—
511#102—41no—
512#102—41no—
513#102—41no—
514C4×C8—22no—
515#95—21no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—21no—
521#95—21no—
522#95—21no—
523C24—21no—
524C24—21no—
525C2×Q8—22no—
526C2×Q8—22no—
527C2×Q8—21no—
528C2×Q8—21no—
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—41no—
538C2×Q8C2×D4×C4312yes—
539C2×Q8#41×C4312yes—
540C2×D4—24no—
541C2×D4—24no—
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×D4—42no—
553C2×D4—42no—
554C2×D4—81no—
555C2×D4—81no—
556C2×D4C2×D4×C4312yes—
557C2×D4C2×D4×C4312yes—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—81no—
567C22×C4—81no—
568C22×C4—81no—
569C22×C4—81no—
570C22×C4C2×D4×C4311yescharacteristic
571C22×C4C2×D4×C4311yescharacteristic
572C22×C4C2×D4×C4311yescharacteristic
573C22×C4C2×D4×C4311yescharacteristic
574C22×C4C2×D4×C4311yescharacteristic
575C22×C4C2×D4×C4311yescharacteristic
576C22×C4C24×C4311yescharacteristic
577Q16—44no—
578SD16—28no—
579SD16—44no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8#41×C4312yes—
592C4⋊C4—24no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4C2×D4×C4312yes—
607C22⋊C4—24no—
608C22⋊C4—24no—
609C22⋊C4—24no—
610C22⋊C4—24no—
611C22⋊C4—24no—
612C22⋊C4—24no—
613C42—24no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—42no—
619C42C2×D4×C4312yes—
620C42C2×D4×C4312yes—
621C23—22no—
622C23—22no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23C22×D4×C4311yescharacteristic
636Q8—22no—
637Q8—22no—
638Q8—22no—
639Q8—22no—
640Q8—44no—
641Q8—41no—
642Q8—41no—
643Q8—41no—
644Q8—41no—
645D4—22no—
646D4—22no—
647D4—22no—
648D4—22no—
649D4—48no—
650D4—41no—
651D4—41no—
652D4—41no—
653D4—41no—
654D4—84no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—22no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—41no—
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—84no—
689C2×C4—84no—
690C2×C4#120×C4312yes—
691C2×C4#120×C4312yes—
692C2×C4#135×C4312yes—
693C2×C4C22×D4×C4311yescharacteristic
694C2×C4C22×D4×C4311yescharacteristic
695C2×C4C2×#41×C4311yescharacteristic
696C2×C4C2×#41×C4311yescharacteristic
697C2×C4H(5,𝔽2)×C4311yescharacteristic
698C2×C42−1+4×C4311yescharacteristic
699C8—22no—
700C8—41no—
701C8—41no—
702C8—41no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22C2×#120×C4311yescharacteristic
718C22C43×#54811yescharacteristic
719C22C43×#55011yescharacteristic
720C22C2×#135×C4311yescharacteristic
721C22C43×#57511yescharacteristic
722C22C43×#57711yescharacteristic
723C22C43×#57711yescharacteristic
724C4—22no—
725C4—22no—
726C4—22no—
727C4—42no—
728C4—42no—
729C4—41no—
730C4—41no—
731C4—41no—
732C4—42no—
733C4—81no—
734C4—81no—
735C4—81no—
736C4C43×#52511yescharacteristic
737C4C43×#53711yescharacteristic
738C4C43×#54611yescharacteristic
739C4C43×#54711yescharacteristic
740C2—82no—
741C2—82no—
742C2C43×#240711yescharacteristic
743C2C43×#300211yescharacteristic
744C2C43×#300911yescharacteristic
745C2C43×#336511yescharacteristic
746C2C43×#337111yescharacteristic
747C2C43×#339411yescharacteristic
748C2C43×#340111yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC2×#127×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
2. C2×C43×#464C2semidirect
3. C2×C4×SD16×C43C2semidirect
4. C43×#2581C2semidirect
5. C43×#2042C2semidirect
7. C43×#2015C2semidirect
9. C43×#1984C2semidirect
10. C43×#1958C2semidirect
11. C43×#1878C2semidirect
12. C43×#1877C2semidirect
13. C43×#1865C2semidirect
14. C43×#1864C2semidirect
15. C43×#1804C2semidirect
328. #24194C43direct (N × H)
367. C2×#464C2×C43semidirect
368. C2×C4×SD16C2×C43semidirect
369. #2581C2×C43semidirect
370. #2042C2×C43semidirect
372. #2015C2×C43semidirect
374. #1984C2×C43semidirect
375. #1958C2×C43semidirect
376. #1878C2×C43semidirect
377. #1877C2×C43semidirect
378. #1865C2×C43semidirect
379. #1864C2×C43semidirect
380. #1804C2×C43semidirect
437. C43#24194direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#5592
C2×C43×#4642
C2×C4×SD16×C432
C43×#25812
C43×#20422
C43×#20412
C43×#20152
C43×#20142
C43×#19842
C43×#19582
C43×#18782
C43×#18772
C43×#18652
C43×#18642
C43×#18042
#2419443