Finite Group Databasebeta

← C43×#24873 #24944890

Subgroups — C43×#24873 #24944890

Order 11008.

1180 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#482C211yesmaximal, characteristic, complemented
2C22×#102×C43C211yesmaximal, characteristic, complemented
3C43×#2408C211yesmaximal, characteristic
4C43×#2352C211yesmaximal, characteristic, complemented
5C43×#2092C211yesmaximal, characteristic, complemented
6C43×#2073C211yesmaximal, characteristic, complemented
7C43×#2034C211yesmaximal, characteristic, complemented
8C43×#2033C211yesmaximal, characteristic, complemented
9C43×#1926C211yesmaximal, characteristic, complemented
10C43×#1925C211yesmaximal, characteristic, complemented
11C43×#1875C211yesmaximal, characteristic, complemented
12C43×#1869C211yesmaximal, characteristic, complemented
13C43×#1852C211yesmaximal, characteristic, complemented
14C43×#1807C211yesmaximal, characteristic, complemented
15C43×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C43C2211yescharacteristic
17C23×C8×C43C2211yescharacteristic
18C2×#121×C43C2211yescharacteristic
19C2×#121×C43C2211yescharacteristic
20C2×#120×C43—21no—
21C2×C4×D4×C43C2211yescharacteristic
22C2×#117×C43C2211yescharacteristic, complemented
23C22×C4⋊C4×C43C2211yescharacteristic
24C43×#482—24no—
25C2×#107×C43C2211yescharacteristic, complemented
26C2×#107×C43C2211yescharacteristic, complemented
27C2×#106×C43C2211yescharacteristic, complemented
28C2×#106×C43C2211yescharacteristic, complemented
29C2×#102×C43—24no—
30C2×#102×C43C2211yescharacteristic
31C2×#102×C43C2211yescharacteristic
32C2×#102×C43C2211yescharacteristic
33C2×#102×C43C2211yescharacteristic
34C2×#102×C43C2211yescharacteristic
35C2×#102×C43C2211yescharacteristic
36C2×#102×C43C2211yescharacteristic
37C2×#102×C43C2211yescharacteristic
38C2×C22⋊C8×C43C2211yescharacteristic
39C2×C22⋊C8×C43C2211yescharacteristic, complemented
40C2×C22⋊C8×C43C2211yescharacteristic, complemented
41C43×#394—21no—
42C43×#392—21no—
43C43×#390C2211yescharacteristic
44C43×#390C2211yescharacteristic
45C43×#388—21no—
46C43×#387—21no—
47C43×#386—21no—
48C43×#382C2211yescharacteristic, complemented
49C43×#380C2211yescharacteristic
50C43×#380C2211yescharacteristic
51C43×#380C2211yescharacteristic, complemented
52C43×#379—21no—
53C4×C4⋊C4×C43C2211yescharacteristic, complemented
54C4×C22⋊C4×C43—21no—
55C43×#340C2211yescharacteristic, complemented
56C43×#340C2211yescharacteristic, complemented
57C43×#340C2211yescharacteristic, complemented
58C43×#340C2211yescharacteristic, complemented
59C43×#336C2211yescharacteristic, complemented
60C43×#336C2211yescharacteristic, complemented
61C25×C43—21no—
62C22×D4×C43—22no—
63C22×D4×C43—22no—
64C22×D4×C43—21no—
65C22×D4×C43—21no—
66C22×D4×C43—21no—
67C22×D4×C43—22no—
68C22×D4×C43—22no—
69C22×D4×C43—41no—
70C22×D4×C43—41no—
71C22×D4×C43D411yescharacteristic
72C22×D4×C43C2311yescharacteristic
73C22×D4×C43C2311yescharacteristic
74C23×C4×C43—21no—
75C23×C4×C43C2311yescharacteristic
76C23×C4×C43C2311yescharacteristic
77C22×C8×C43—22no—
78C22×C8×C43—22no—
79C22×C8×C43—41no—
80C22×C8×C43C2311yescharacteristic
81C22×C8×C43C2311yescharacteristic
82C22×C8×C43C2311yescharacteristic
83C22×C8×C43C2311yescharacteristic
84#121×C43—22no—
85#121×C43—22no—
86#121×C43—41no—
87#121×C43—41no—
88#120×C43—44no—
89C4×D4×C43—22no—
90C4×D4×C43—22no—
91#117×C43—22no—
92#117×C43—41no—
93C2×C4⋊C4×C43—22no—
94C2×C4⋊C4×C43—21no—
95C2×C4⋊C4×C43—41no—
96C2×C4⋊C4×C43D411yescharacteristic
97C2×C4⋊C4×C43C2311yescharacteristic
98C2×C4⋊C4×C43C2311yescharacteristic
99C2×C4⋊C4×C43C2311yescharacteristic
100C2×C4⋊C4×C43C2311yescharacteristic
101C2×C4⋊C4×C43C2311yescharacteristic
102C2×C4⋊C4×C43C2311yescharacteristic
103C2×C22⋊C4×C43—21no—
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×C43D411yescharacteristic
114C2×C22⋊C4×C43D411yescharacteristic
115C2×C42×C43—21no—
116C2×C42×C43—21no—
117C2×C42×C43C2311yescharacteristic
118#107×C43—22no—
119#107×C43—41no—
120#106×C43—22no—
121#106×C43—41no—
122#102×C43—22no—
123#102×C43—22no—
124#102×C43—22no—
125#102×C43—22no—
126#102×C43—22no—
127#102×C43—41no—
128#102×C43—41no—
129#102×C43D414yescomplemented
130C22⋊C8×C43—22no—
131C22⋊C8×C43—22no—
132C22⋊C8×C43—41no—
133#95×C43—21no—
134#95×C43—21no—
135#95×C43—21no—
136#95×C43—21no—
137#95×C43—21no—
138#95×C43—21no—
139C24×C43—21no—
140C24×C43—21no—
141C24×C43—42no—
142C24×C43—42no—
143C24×C43—42no—
144C24×C43—42no—
145C24×C43—42no—
146C24×C43—81no—
147C24×C43—81no—
148C24×C43C2×D411yescharacteristic
149C24×C43C2×D411yescharacteristic
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—22no—
153C2×D4×C43—22no—
154C2×D4×C43—22no—
155C2×D4×C43—28no—
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—21no—
164C2×D4×C43—42no—
165C2×D4×C43—42no—
166C2×D4×C43—42no—
167C2×D4×C43—42no—
168C2×D4×C43—42no—
169C2×D4×C43—42no—
170C2×D4×C43—44no—
171C2×D4×C43—44no—
172C2×D4×C43—44no—
173C2×D4×C43—42no—
174C2×D4×C43—81no—
175C2×D4×C43—81no—
176C2×D4×C43C2×D412yes—
177C2×D4×C43#4112yes—
178C22×C4×C43—21no—
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—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—42no—
195C22×C4×C43—42no—
196C22×C4×C43—81no—
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43#4112yes—
202C22×C4×C43#4112yes—
203C22×C4×C43C2411yescharacteristic
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×C43—21no—
214C2×C8×C43—21no—
215C2×C8×C43—44no—
216C2×C8×C43C2×D412yes—
217C4⋊C4×C43—22no—
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—21no—
225C4⋊C4×C43—21no—
226C4⋊C4×C43—21no—
227C4⋊C4×C43—21no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—42no—
230C4⋊C4×C43C2×D412yes—
231C22⋊C4×C43—22no—
232C22⋊C4×C43—22no—
233C22⋊C4×C43—42no—
234C22⋊C4×C43—42no—
235C22⋊C4×C43—42no—
236C22⋊C4×C43—42no—
237C22⋊C4×C43—42no—
238C22⋊C4×C43—42no—
239C22⋊C4×C43—42no—
240C22⋊C4×C43—81no—
241C22⋊C4×C43—81no—
242C22⋊C4×C43—81no—
243C42×C43—21no—
244C42×C43—21no—
245C42×C43—42no—
246C42×C43—81no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—22no—
254C23×C43—22no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—48no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43—84no—
274C23×C43—84no—
275C23×C43—84no—
276C23×C43—84no—
277C23×C43—84no—
278C23×C43—84no—
279C23×C43#12312yes—
280C23×C43#13512yes—
281C23×C43AGL(1,ℤ/8)12yes—
282C23×C43C22×D411yescharacteristic
283D4×C43—22no—
284D4×C43—22no—
285D4×C43—22no—
286D4×C43—22no—
287D4×C43—48no—
288D4×C43—44no—
289D4×C43—41no—
290D4×C43—41no—
291D4×C43—41no—
292D4×C43—41no—
293D4×C43—84no—
294D4×C43—84no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—22no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—21no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—41no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43—41no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43—41no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43—41no—
327C2×C4×C43—41no—
328C2×C4×C43—41no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43—84no—
333C2×C4×C43#12312yes—
334C2×C4×C43C22×D411yescharacteristic
335C2×C4×C43C2×#4111yescharacteristic
336C2×C4×C43C2×#4111yescharacteristic
337C2×C4×C43C2×#4111yescharacteristic
338C2×C4×C43H(5,𝔽2)11yescharacteristic
339C2×C4×C43H(5,𝔽2)11yescharacteristic
340C8×C43—22no—
341C8×C43—41no—
342C8×C43—41no—
343C8×C43—41no—
344#24873C4311yesmaximal, characteristic, direct product factor, Sylow
345C22×C43—22no—
346C22×C43—22no—
347C22×C43—22no—
348C22×C43—22no—
349C22×C43—22no—
350C22×C43—22no—
351C22×C43—41no—
352C22×C43—41no—
353C22×C43—41no—
354C22×C43—42no—
355C22×C43—42no—
356C22×C43—41no—
357C22×C43—42no—
358C22×C43—41no—
359C22×C43—42no—
360C22×C43—41no—
361C22×C43—42no—
362C22×C43—41no—
363C22×C43—42no—
364C22×C43—816no—
365C22×C43—81no—
366C22×C43—81no—
367C22×C43—81no—
368C22×C43—81no—
369C22×C43—81no—
370C22×C43—81no—
371C22×C43—81no—
372C22×C43—81no—
373C22×C43#48214yescomplemented
374C22×C43C2×#12311yescharacteristic
375C22×C43D4211yescharacteristic
376C22×C43#54611yescharacteristic
377C22×C43C2×#13511yescharacteristic
378C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
379C22×C43#57611yescharacteristic
380C22×C43#57711yescharacteristic
381C4×C43—22no—
382C4×C43—41no—
383C4×C43—41no—
384C4×C43—41no—
385C4×C43—42no—
386C4×C43—81no—
387C4×C43—81no—
388C4×C43—81no—
389C4×C43—81no—
390C4×C43—81no—
391C4×C43#52511yescharacteristic
392C4×C43#53811yescharacteristic
393C4×C43#54611yescharacteristic
394C4×C43#55111yescharacteristic
395C2×#482C2×C4311yescharacteristic, complemented
396C22×#102C2×C4311yescharacteristic, complemented
397#2408C2×C4311yescharacteristic
398#2352C2×C4311yescharacteristic, complemented
399#2092C2×C4311yescharacteristic, complemented
400#2073C2×C4311yescharacteristic, complemented
401#2034C2×C4311yescharacteristic, complemented
402#2033C2×C4311yescharacteristic, complemented
403#1926C2×C4311yescharacteristic, complemented
404#1925C2×C4311yescharacteristic, complemented
405#1875C2×C4311yescharacteristic, complemented
406#1869C2×C4311yescharacteristic, complemented
407#1852C2×C4311yescharacteristic, complemented
408#1807C2×C4311yescharacteristic, complemented
409#1786C2×C4311yescharacteristic, complemented
410C2×C43—24no—
411C2×C43—81no—
412C2×C43—82no—
413C2×C43—82no—
414C2×C43#241811yescharacteristic
415C2×C43C2×#48211yescharacteristic
416C2×C43#309611yescharacteristic
417C2×C43#326411yescharacteristic
418C2×C43#328211yescharacteristic
419C2×C43#329711yescharacteristic
420C2×C43#331011yescharacteristic
421C23×D4C22×C4311yescharacteristic
422C23×C8C22×C4311yescharacteristic
423C2×#121C22×C4311yescharacteristic
424C2×#121C22×C4311yescharacteristic
425C2×#120—21no—
426C2×C4×D4C22×C4311yescharacteristic
427C2×#117C22×C4311yescharacteristic, complemented
428C22×C4⋊C4C22×C4311yescharacteristic
429#482—24no—
430C2×#107C22×C4311yescharacteristic, complemented
431C2×#107C22×C4311yescharacteristic, complemented
432C2×#106C22×C4311yescharacteristic, complemented
433C2×#106C22×C4311yescharacteristic, complemented
434C2×#102—24no—
435C2×#102C22×C4311yescharacteristic
436C2×#102C22×C4311yescharacteristic
437C2×#102C22×C4311yescharacteristic
438C2×#102C22×C4311yescharacteristic
439C2×#102C22×C4311yescharacteristic
440C2×#102C22×C4311yescharacteristic
441C2×#102C22×C4311yescharacteristic
442C2×#102C22×C4311yescharacteristic
443C2×C22⋊C8C22×C4311yescharacteristic
444C2×C22⋊C8C22×C4311yescharacteristic, complemented
445C2×C22⋊C8C22×C4311yescharacteristic, complemented
446#394—21no—
447#392—21no—
448#390C22×C4311yescharacteristic
449#390C22×C4311yescharacteristic
450#388—21no—
451#387—21no—
452#386—21no—
453#382C22×C4311yescharacteristic, complemented
454#380C22×C4311yescharacteristic
455#380C22×C4311yescharacteristic
456#380C22×C4311yescharacteristic, complemented
457#379—21no—
458C4×C4⋊C4C22×C4311yescharacteristic, complemented
459C4×C22⋊C4—21no—
460#340C22×C4311yescharacteristic, complemented
461#340C22×C4311yescharacteristic, complemented
462#340C22×C4311yescharacteristic, complemented
463#340C22×C4311yescharacteristic, complemented
464#336C22×C4311yescharacteristic, complemented
465#336C22×C4311yescharacteristic, complemented
466C43#2487311yescharacteristic, direct product factor, Sylow
467C25—21no—
468C22×D4—22no—
469C22×D4—22no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—22no—
474C22×D4—22no—
475C22×D4—41no—
476C22×D4—41no—
477C22×D4D4×C4311yescharacteristic
478C22×D4C23×C4311yescharacteristic
479C22×D4C23×C4311yescharacteristic
480C23×C4—21no—
481C23×C4C23×C4311yescharacteristic
482C23×C4C23×C4311yescharacteristic
483C22×C8—22no—
484C22×C8—22no—
485C22×C8—41no—
486C22×C8C23×C4311yescharacteristic
487C22×C8C23×C4311yescharacteristic
488C22×C8C23×C4311yescharacteristic
489C22×C8C23×C4311yescharacteristic
490#121—22no—
491#121—22no—
492#121—41no—
493#121—41no—
494#120—44no—
495C4×D4—22no—
496C4×D4—22no—
497#117—22no—
498#117—41no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—41no—
502C2×C4⋊C4D4×C4311yescharacteristic
503C2×C4⋊C4C23×C4311yescharacteristic
504C2×C4⋊C4C23×C4311yescharacteristic
505C2×C4⋊C4C23×C4311yescharacteristic
506C2×C4⋊C4C23×C4311yescharacteristic
507C2×C4⋊C4C23×C4311yescharacteristic
508C2×C4⋊C4C23×C4311yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4D4×C4311yescharacteristic
520C2×C22⋊C4D4×C4311yescharacteristic
521C2×C42—21no—
522C2×C42—21no—
523C2×C42C23×C4311yescharacteristic
524#107—22no—
525#107—41no—
526#106—22no—
527#106—41no—
528#102—22no—
529#102—22no—
530#102—22no—
531#102—22no—
532#102—22no—
533#102—41no—
534#102—41no—
535#102D4×C4314yescomplemented
536C22⋊C8—22no—
537C22⋊C8—22no—
538C22⋊C8—41no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—21no—
544#95—21no—
545C24—21no—
546C24—21no—
547C24—42no—
548C24—42no—
549C24—42no—
550C24—42no—
551C24—42no—
552C24—81no—
553C24—81no—
554C24C2×D4×C4311yescharacteristic
555C24C2×D4×C4311yescharacteristic
556C2×D4—28no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—44no—
571C2×D4—44no—
572C2×D4—42no—
573C2×D4—42no—
574C2×D4—44no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—81no—
581C2×D4—81no—
582C2×D4C2×D4×C4312yes—
583C2×D4#41×C4312yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—81no—
603C22×C4C2×D4×C4311yescharacteristic
604C22×C4C2×D4×C4311yescharacteristic
605C22×C4C2×D4×C4311yescharacteristic
606C22×C4C2×D4×C4311yescharacteristic
607C22×C4#41×C4312yes—
608C22×C4#41×C4312yes—
609C22×C4C24×C4311yescharacteristic
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—44no—
622C2×C8C2×D4×C4312yes—
623C4⋊C4—22no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—42no—
636C4⋊C4C2×D4×C4312yes—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—81no—
647C22⋊C4—81no—
648C22⋊C4—81no—
649C42—21no—
650C42—21no—
651C42—42no—
652C42—81no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—22no—
660C23—22no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—48no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—84no—
680C23—84no—
681C23—84no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23#123×C4312yes—
686C23#135×C4312yes—
687C23AGL(1,ℤ/8)×C4312yes—
688C23C22×D4×C4311yescharacteristic
689D4—22no—
690D4—22no—
691D4—22no—
692D4—22no—
693D4—48no—
694D4—44no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—84no—
700D4—84no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—84no—
739C2×C4#123×C4312yes—
740C2×C4C22×D4×C4311yescharacteristic
741C2×C4C2×#41×C4311yescharacteristic
742C2×C4C2×#41×C4311yescharacteristic
743C2×C4C2×#41×C4311yescharacteristic
744C2×C4H(5,𝔽2)×C4311yescharacteristic
745C2×C4H(5,𝔽2)×C4311yescharacteristic
746C8—22no—
747C8—41no—
748C8—41no—
749C8—41no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—42no—
760C22—42no—
761C22—41no—
762C22—42no—
763C22—41no—
764C22—42no—
765C22—41no—
766C22—42no—
767C22—41no—
768C22—42no—
769C22—816no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22C43×#48214yescomplemented
779C22C2×#123×C4311yescharacteristic
780C22D42×C4311yescharacteristic
781C22C43×#54611yescharacteristic
782C22C2×#135×C4311yescharacteristic
783C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
784C22C43×#57611yescharacteristic
785C22C43×#57711yescharacteristic
786C4—22no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—42no—
791C4—81no—
792C4—81no—
793C4—81no—
794C4—81no—
795C4—81no—
796C4C43×#52511yescharacteristic
797C4C43×#53811yescharacteristic
798C4C43×#54611yescharacteristic
799C4C43×#55111yescharacteristic
800C2—24no—
801C2—81no—
802C2—82no—
803C2—82no—
804C2C43×#241811yescharacteristic
805C2C2×C43×#48211yescharacteristic
806C2C43×#309611yescharacteristic
807C2C43×#326411yescharacteristic
808C2C43×#328211yescharacteristic
809C2C43×#329711yescharacteristic
810C2C43×#331011yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC43×#2408C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C2×C4×D4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#482C2semidirect
2. C22×#102×C43C2semidirect
4. C43×#2352C2semidirect
5. C43×#2092C2semidirect
6. C43×#2073C2semidirect
7. C43×#2034C2semidirect
8. C43×#2033C2semidirect
9. C43×#1926C2semidirect
10. C43×#1925C2semidirect
11. C43×#1875C2semidirect
12. C43×#1869C2semidirect
13. C43×#1852C2semidirect
14. C43×#1807C2semidirect
15. C43×#1786C2semidirect
22. C2×#117×C43C22semidirect
25. C2×#107×C43C22semidirect
26. C2×#107×C43C22semidirect
27. C2×#106×C43C22semidirect
28. C2×#106×C43C22semidirect
39. C2×C22⋊C8×C43C22semidirect
40. C2×C22⋊C8×C43C22semidirect
48. C43×#382C22semidirect
51. C43×#380C22semidirect
53. C4×C4⋊C4×C43C22semidirect
55. C43×#340C22semidirect
56. C43×#340C22semidirect
57. C43×#340C22semidirect
58. C43×#340C22semidirect
59. C43×#336C22semidirect
60. C43×#336C22semidirect
129. #102×C43D4semidirect
344. #24873C43direct (N × H)
373. C22×C43#482semidirect
395. C2×#482C2×C43semidirect
396. C22×#102C2×C43semidirect
398. #2352C2×C43semidirect
399. #2092C2×C43semidirect
400. #2073C2×C43semidirect
401. #2034C2×C43semidirect
402. #2033C2×C43semidirect
403. #1926C2×C43semidirect
404. #1925C2×C43semidirect
405. #1875C2×C43semidirect
406. #1869C2×C43semidirect
407. #1852C2×C43semidirect
408. #1807C2×C43semidirect
409. #1786C2×C43semidirect
427. C2×#117C22×C43semidirect
430. C2×#107C22×C43semidirect
431. C2×#107C22×C43semidirect
432. C2×#106C22×C43semidirect
433. C2×#106C22×C43semidirect
444. C2×C22⋊C8C22×C43semidirect
445. C2×C22⋊C8C22×C43semidirect
453. #382C22×C43semidirect
456. #380C22×C43semidirect
458. C4×C4⋊C4C22×C43semidirect
460. #340C22×C43semidirect
461. #340C22×C43semidirect
462. #340C22×C43semidirect
463. #340C22×C43semidirect
464. #336C22×C43semidirect
465. #336C22×C43semidirect
466. C43#24873direct (N × H)
535. #102D4×C43semidirect
778. C22C43×#482semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4822
C22×#102×C432
C43×#24082
C43×#23522
C43×#20922
C43×#20732
C43×#20342
C43×#20332
C43×#19262
C43×#19252
C43×#18752
C43×#18692
C43×#18522
C43×#18072
C43×#17862
#2487343