Finite Group Databasebeta

← C43×#28567 #24948584

Subgroups — C43×#28567 #24948584

Order 11008.

1012 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#469C211yesmaximal, characteristic, complemented
2C2×C43×#436C211yesmaximal, characteristic, complemented
3C43×#2416C211yesmaximal, characteristic, complemented
4C43×#2414C211yesmaximal, characteristic, complemented
5C43×#2088C211yesmaximal, characteristic, complemented
6C43×#2077C211yesmaximal, characteristic, complemented
7C43×#2054C211yesmaximal, characteristic, complemented
8C43×#1999C211yesmaximal, characteristic, complemented
9C43×#1934C211yesmaximal, characteristic, complemented
10C43×#1934C211yesmaximal, characteristic, complemented
11C43×#1895C211yesmaximal, characteristic, complemented
12C43×#1895C211yesmaximal, characteristic, complemented
13C43×#1875C211yesmaximal, characteristic, complemented
14C43×#1874C211yesmaximal, characteristic, complemented
15C43×#1736C211yesmaximal, characteristic, complemented
16C22×D8×C43C2211yescharacteristic
17C22×M16×C43C2211yescharacteristic
18C22×M16×C43C2211yescharacteristic
19C2×#121×C43—21no—
20C2×#121×C43C2211yescharacteristic
21C2×#121×C43C2211yescharacteristic
22C2×#121×C43C2211yescharacteristic
23C2×#121×C43C2211yescharacteristic
24C2×C4×D4×C43C2211yescharacteristic
25C2×#117×C43C2211yescharacteristic
26C22×C4⋊C4×C43C2211yescharacteristic
27C43×#469—24no—
28C43×#436—24no—
29C2×#106×C43C2211yescharacteristic
30C2×C4⋊C8×C43C2211yescharacteristic
31C2×#102×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×#396—21no—
41C43×#394—21no—
42C43×#394—21no—
43C43×#392—21no—
44C43×#390—21no—
45C43×#390C2211yescharacteristic
46C43×#390C2211yescharacteristic
47C43×#389C2211yescharacteristic
48C43×#389C2211yescharacteristic
49C43×#388—21no—
50C43×#386—21no—
51C43×#380C2211yescharacteristic
52C43×#380C2211yescharacteristic
53C43×#340C2211yescharacteristic
54C43×#340C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×D4×C43—21no—
62C22×D4×C43—21no—
63C22×D4×C43—21no—
64C22×D4×C43—21no—
65C22×D4×C43D411yescharacteristic
66C22×D4×C43C2311yescharacteristic
67C22×D4×C43C2311yescharacteristic
68C23×C4×C43—21no—
69C23×C4×C43C2311yescharacteristic
70C23×C4×C43C2311yescharacteristic
71C2×D8×C43—22no—
72C2×D8×C43—41no—
73C2×D8×C43—41no—
74C2×M16×C43—22no—
75C2×M16×C43—41no—
76C2×M16×C43—41no—
77C2×M16×C43—41no—
78C2×M16×C43—41no—
79C2×M16×C43D414yescomplemented
80C22×C8×C43C2311yescharacteristic
81C22×C8×C43C2311yescharacteristic
82C22×C8×C43C2311yescharacteristic
83C22×C8×C43C2311yescharacteristic
84#121×C43—22no—
85#121×C43—22no—
86#121×C43—22no—
87#121×C43—22no—
88#121×C43—22no—
89#121×C43—22no—
90#121×C43—41no—
91#121×C43—41no—
92#121×C43—44no—
93C4×D4×C43—22no—
94C4×D4×C43—22no—
95#117×C43—22no—
96#117×C43—41no—
97C2×C4⋊C4×C43—22no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—41no—
102C2×C4⋊C4×C43D411yescharacteristic
103C2×C4⋊C4×C43C2311yescharacteristic
104C2×C4⋊C4×C43C2311yescharacteristic
105C2×C4⋊C4×C43C2311yescharacteristic
106C2×C4⋊C4×C43C2311yescharacteristic
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C4⋊C4×C43C2311yescharacteristic
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×C43—21no—
115C2×C22⋊C4×C43—21no—
116C2×C22⋊C4×C43—21no—
117C2×C22⋊C4×C43—21no—
118C2×C22⋊C4×C43—21no—
119C2×C22⋊C4×C43—21no—
120C2×C22⋊C4×C43D411yescharacteristic
121C2×C22⋊C4×C43D411yescharacteristic
122C2×C42×C43—21no—
123C2×C42×C43C2311yescharacteristic
124#106×C43—22no—
125C4⋊C8×C43—22no—
126#102×C43—22no—
127#102×C43—22no—
128#102×C43—22no—
129#102×C43—22no—
130#102×C43—41no—
131#102×C43—41no—
132C22⋊C8×C43—22no—
133C22⋊C8×C43—22no—
134C4×C8×C43—22no—
135#95×C43—21no—
136#95×C43—21no—
137#95×C43—21no—
138#95×C43—21no—
139C24×C43—21no—
140C24×C43—21no—
141C24×C43C2×D411yescharacteristic
142C24×C43C2×D411yescharacteristic
143C2×D4×C43—22no—
144C2×D4×C43—22no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—41no—
158C2×D4×C43—42no—
159C2×D4×C43—42no—
160C2×D4×C43—42no—
161C2×D4×C43—42no—
162C2×D4×C43—42no—
163C2×D4×C43—42no—
164C2×D4×C43—42no—
165C2×D4×C43—42no—
166C2×D4×C43—81no—
167C2×D4×C43—81no—
168C2×D4×C43—81no—
169C2×D4×C43—81no—
170C22×C4×C43—21no—
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—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—42no—
187C22×C4×C43—42no—
188C22×C4×C43—81no—
189C22×C4×C43C2×D412yes—
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43#4112yes—
195C22×C4×C43C2411yescharacteristic
196D8×C43—44no—
197M16×C43—44no—
198M16×C43—44no—
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×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43C2×D412yes—
210C2×C8×C43C2×D412yes—
211C4⋊C4×C43—22no—
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—21no—
219C4⋊C4×C43—21no—
220C4⋊C4×C43—21no—
221C4⋊C4×C43—21no—
222C4⋊C4×C43—42no—
223C4⋊C4×C43—42no—
224C4⋊C4×C43—81no—
225C4⋊C4×C43#4112yes—
226C4⋊C4×C43#4112yes—
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—42no—
237C22⋊C4×C43—81no—
238C22⋊C4×C43—81no—
239C22⋊C4×C43—81no—
240C42×C43—21no—
241C42×C43—21no—
242C42×C43—42no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
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#12112yes—
271C23×C43C22×D411yescharacteristic
272D4×C43—44no—
273D4×C43—41no—
274D4×C43—41no—
275D4×C43—41no—
276D4×C43—41no—
277D4×C43—41no—
278D4×C43—41no—
279D4×C43—41no—
280D4×C43—41no—
281D4×C43—84no—
282D4×C43—84no—
283D4×C43—84no—
284D4×C43—84no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—22no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—22no—
299C2×C4×C43—21no—
300C2×C4×C43—21no—
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—41no—
316C2×C4×C43—41no—
317C2×C4×C43—41no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43—84no—
322C2×C4×C43#12112yes—
323C2×C4×C43AGL(1,ℤ/8)12yes—
324C2×C4×C43C22×D411yescharacteristic
325C2×C4×C43C2×#4111yescharacteristic
326C2×C4×C43C2×#4111yescharacteristic
327C2×C4×C43C2×#4111yescharacteristic
328C2×C4×C43H(5,𝔽2)11yescharacteristic
329C2×C4×C43H(5,𝔽2)11yescharacteristic
330C8×C43—22no—
331C8×C43—22no—
332C8×C43—41no—
333C8×C43—41no—
334#28567C4311yesmaximal, characteristic, direct product factor, Sylow
335C22×C43—22no—
336C22×C43—22no—
337C22×C43—22no—
338C22×C43—41no—
339C22×C43—41no—
340C22×C43—41no—
341C22×C43—41no—
342C22×C43—41no—
343C22×C43—41no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43—41no—
347C22×C43—41no—
348C22×C43—41no—
349C22×C43—81no—
350C22×C43—81no—
351C22×C43—81no—
352C22×C43—81no—
353C22×C43—81no—
354C22×C43—81no—
355C22×C43—81no—
356C22×C43—81no—
357C22×C43—81no—
358C22×C43—81no—
359C22×C43—81no—
360C22×C43—81no—
361C22×C43—81no—
362C22×C43—81no—
363C22×C43C2×#12111yescharacteristic
364C22×C43#54611yescharacteristic
365C22×C43#54611yescharacteristic
366C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
367C22×C43#57511yescharacteristic
368C22×C43#57611yescharacteristic
369C22×C43#57711yescharacteristic
370C4×C43—22no—
371C4×C43—22no—
372C4×C43—41no—
373C4×C43—41no—
374C4×C43—42no—
375C4×C43—42no—
376C4×C43—81no—
377C4×C43—81no—
378C4×C43—81no—
379C4×C43—81no—
380C4×C43#53211yescharacteristic
381C4×C43#53411yescharacteristic
382C4×C43#55311yescharacteristic
383C4×C43#55311yescharacteristic
384C2×#469C2×C4311yescharacteristic, complemented
385C2×#436C2×C4311yescharacteristic, complemented
386#2416C2×C4311yescharacteristic, complemented
387#2414C2×C4311yescharacteristic, complemented
388#2088C2×C4311yescharacteristic, complemented
389#2077C2×C4311yescharacteristic, complemented
390#2054C2×C4311yescharacteristic, complemented
391#1999C2×C4311yescharacteristic, complemented
392#1934C2×C4311yescharacteristic, complemented
393#1934C2×C4311yescharacteristic, complemented
394#1895C2×C4311yescharacteristic, complemented
395#1895C2×C4311yescharacteristic, complemented
396#1875C2×C4311yescharacteristic, complemented
397#1874C2×C4311yescharacteristic, complemented
398#1736C2×C4311yescharacteristic, complemented
399C2×C43—42no—
400C2×C43—81no—
401C2×C43—161no—
402C2×C43—161no—
403C2×C43#254311yescharacteristic
404C2×C43#305511yescharacteristic
405C2×C43#306211yescharacteristic
406C2×C43#332211yescharacteristic
407C2×C43#332511yescharacteristic
408C2×C43#332611yescharacteristic
409C2×C43#333211yescharacteristic
410C22×D8C22×C4311yescharacteristic
411C22×M16C22×C4311yescharacteristic
412C22×M16C22×C4311yescharacteristic
413C2×#121—21no—
414C2×#121C22×C4311yescharacteristic
415C2×#121C22×C4311yescharacteristic
416C2×#121C22×C4311yescharacteristic
417C2×#121C22×C4311yescharacteristic
418C2×C4×D4C22×C4311yescharacteristic
419C2×#117C22×C4311yescharacteristic
420C22×C4⋊C4C22×C4311yescharacteristic
421#469—24no—
422#436—24no—
423C2×#106C22×C4311yescharacteristic
424C2×C4⋊C8C22×C4311yescharacteristic
425C2×#102C22×C4311yescharacteristic
426C2×#102C22×C4311yescharacteristic
427C2×#102C22×C4311yescharacteristic
428C2×#102C22×C4311yescharacteristic
429C2×#102C22×C4311yescharacteristic
430C2×#102C22×C4311yescharacteristic
431C2×C22⋊C8C22×C4311yescharacteristic
432C2×C22⋊C8C22×C4311yescharacteristic
433C2×C4×C8C22×C4311yescharacteristic
434#396—21no—
435#394—21no—
436#394—21no—
437#392—21no—
438#390—21no—
439#390C22×C4311yescharacteristic
440#390C22×C4311yescharacteristic
441#389C22×C4311yescharacteristic
442#389C22×C4311yescharacteristic
443#388—21no—
444#386—21no—
445#380C22×C4311yescharacteristic
446#380C22×C4311yescharacteristic
447#340C22×C4311yescharacteristic
448#340C22×C4311yescharacteristic
449#340C22×C4311yescharacteristic
450#340C22×C4311yescharacteristic
451#340C22×C4311yescharacteristic
452#340C22×C4311yescharacteristic
453#340C22×C4311yescharacteristic
454#340C22×C4311yescharacteristic
455C43#2856711yescharacteristic, direct product factor, Sylow
456C22×D4—21no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4D4×C4311yescharacteristic
461C22×D4C23×C4311yescharacteristic
462C22×D4C23×C4311yescharacteristic
463C23×C4—21no—
464C23×C4C23×C4311yescharacteristic
465C23×C4C23×C4311yescharacteristic
466C2×D8—22no—
467C2×D8—41no—
468C2×D8—41no—
469C2×M16—22no—
470C2×M16—41no—
471C2×M16—41no—
472C2×M16—41no—
473C2×M16—41no—
474C2×M16D4×C4314yescomplemented
475C22×C8C23×C4311yescharacteristic
476C22×C8C23×C4311yescharacteristic
477C22×C8C23×C4311yescharacteristic
478C22×C8C23×C4311yescharacteristic
479#121—22no—
480#121—22no—
481#121—22no—
482#121—22no—
483#121—22no—
484#121—22no—
485#121—41no—
486#121—41no—
487#121—44no—
488C4×D4—22no—
489C4×D4—22no—
490#117—22no—
491#117—41no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—41no—
497C2×C4⋊C4D4×C4311yescharacteristic
498C2×C4⋊C4C23×C4311yescharacteristic
499C2×C4⋊C4C23×C4311yescharacteristic
500C2×C4⋊C4C23×C4311yescharacteristic
501C2×C4⋊C4C23×C4311yescharacteristic
502C2×C4⋊C4C23×C4311yescharacteristic
503C2×C4⋊C4C23×C4311yescharacteristic
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
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⋊C4D4×C4311yescharacteristic
516C2×C22⋊C4D4×C4311yescharacteristic
517C2×C42—21no—
518C2×C42C23×C4311yescharacteristic
519#106—22no—
520C4⋊C8—22no—
521#102—22no—
522#102—22no—
523#102—22no—
524#102—22no—
525#102—41no—
526#102—41no—
527C22⋊C8—22no—
528C22⋊C8—22no—
529C4×C8—22no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95—21no—
534C24—21no—
535C24—21no—
536C24C2×D4×C4311yescharacteristic
537C24C2×D4×C4311yescharacteristic
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—21no—
541C2×D4—21no—
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—41no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—81no—
562C2×D4—81no—
563C2×D4—81no—
564C2×D4—81no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—81no—
584C22×C4C2×D4×C4311yescharacteristic
585C22×C4C2×D4×C4311yescharacteristic
586C22×C4C2×D4×C4311yescharacteristic
587C22×C4C2×D4×C4312yes—
588C22×C4C2×D4×C4311yescharacteristic
589C22×C4#41×C4312yes—
590C22×C4C24×C4311yescharacteristic
591D8—44no—
592M16—44no—
593M16—44no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8C2×D4×C4312yes—
605C2×C8C2×D4×C4312yes—
606C4⋊C4—22no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—42no—
618C4⋊C4—42no—
619C4⋊C4—81no—
620C4⋊C4#41×C4312yes—
621C4⋊C4#41×C4312yes—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—81no—
633C22⋊C4—81no—
634C22⋊C4—81no—
635C42—21no—
636C42—21no—
637C42—42no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23#121×C4312yes—
666C23C22×D4×C4311yescharacteristic
667D4—44no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—84no—
677D4—84no—
678D4—84no—
679D4—84no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—84no—
717C2×C4#121×C4312yes—
718C2×C4AGL(1,ℤ/8)×C4312yes—
719C2×C4C22×D4×C4311yescharacteristic
720C2×C4C2×#41×C4311yescharacteristic
721C2×C4C2×#41×C4311yescharacteristic
722C2×C4C2×#41×C4311yescharacteristic
723C2×C4H(5,𝔽2)×C4311yescharacteristic
724C2×C4H(5,𝔽2)×C4311yescharacteristic
725C8—22no—
726C8—22no—
727C8—41no—
728C8—41no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22C2×#121×C4311yescharacteristic
758C22C43×#54611yescharacteristic
759C22C43×#54611yescharacteristic
760C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
761C22C43×#57511yescharacteristic
762C22C43×#57611yescharacteristic
763C22C43×#57711yescharacteristic
764C4—22no—
765C4—22no—
766C4—41no—
767C4—41no—
768C4—42no—
769C4—42no—
770C4—81no—
771C4—81no—
772C4—81no—
773C4—81no—
774C4C43×#53211yescharacteristic
775C4C43×#53411yescharacteristic
776C4C43×#55311yescharacteristic
777C4C43×#55311yescharacteristic
778C2—42no—
779C2—81no—
780C2—161no—
781C2—161no—
782C2C43×#254311yescharacteristic
783C2C43×#305511yescharacteristic
784C2C43×#306211yescharacteristic
785C2C43×#332211yescharacteristic
786C2C43×#332511yescharacteristic
787C2C43×#332611yescharacteristic
788C2C43×#333211yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
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×#469C2semidirect
2. C2×C43×#436C2semidirect
3. C43×#2416C2semidirect
4. C43×#2414C2semidirect
5. C43×#2088C2semidirect
6. C43×#2077C2semidirect
7. C43×#2054C2semidirect
8. C43×#1999C2semidirect
9. C43×#1934C2semidirect
10. C43×#1934C2semidirect
11. C43×#1895C2semidirect
12. C43×#1895C2semidirect
13. C43×#1875C2semidirect
14. C43×#1874C2semidirect
15. C43×#1736C2semidirect
79. C2×M16×C43D4semidirect
334. #28567C43direct (N × H)
384. C2×#469C2×C43semidirect
385. C2×#436C2×C43semidirect
386. #2416C2×C43semidirect
387. #2414C2×C43semidirect
388. #2088C2×C43semidirect
389. #2077C2×C43semidirect
390. #2054C2×C43semidirect
391. #1999C2×C43semidirect
392. #1934C2×C43semidirect
393. #1934C2×C43semidirect
394. #1895C2×C43semidirect
395. #1895C2×C43semidirect
396. #1875C2×C43semidirect
397. #1874C2×C43semidirect
398. #1736C2×C43semidirect
455. C43#28567direct (N × H)
474. C2×M16D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4692
C2×C43×#4362
C43×#24162
C43×#24142
C43×#20882
C43×#20772
C43×#20542
C43×#19992
C43×#19342
C43×#18952
C43×#18752
C43×#18742
C43×#17362
#2856743