Finite Group Databasebeta

← C43×#25560 #24945577

Subgroups — C43×#25560 #24945577

Order 11008.

1178 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#552C211yesmaximal, characteristic, complemented
2C2×C43×#482C211yesmaximal, characteristic, complemented
3C2×C43×#468C211yesmaximal, characteristic, complemented
4C43×#2416C211yesmaximal, characteristic
5C43×#2059C211yesmaximal, characteristic, complemented
6C43×#2035C211yesmaximal, characteristic, complemented
7C43×#2025C211yesmaximal, characteristic, complemented
8C43×#2000C211yesmaximal, characteristic, complemented
9C43×#1880C211yesmaximal, characteristic, complemented
10C43×#1874C211yesmaximal, characteristic, complemented
11C43×#1872C211yesmaximal, characteristic, complemented
12C43×#1870C211yesmaximal, characteristic, complemented
13C43×#1863C211yesmaximal, characteristic, complemented
14C43×#1852C211yesmaximal, characteristic, complemented
15C43×#1736C211yesmaximal, characteristic, complemented
16C22×SD16×C43C2211yescharacteristic
17C22×M16×C43C2211yescharacteristic
18C43×#552—24no—
19C43×#552—24no—
20C2×#126×C43—21no—
21C2×#125×C43—21no—
22C2×#125×C43C2211yescharacteristic
23C2×#123×C43—21no—
24C2×C22⋊Q8×C43C2211yescharacteristic
25C2×C22⋊Q8×C43C2211yescharacteristic
26C2×#121×C43—21no—
27C2×#121×C43C2211yescharacteristic
28C2×#121×C43C2211yescharacteristic
29C2×C4×Q8×C43C2211yescharacteristic
30C2×C4×D4×C43C2211yescharacteristic
31C2×#117×C43—21no—
32C2×#117×C43C2211yescharacteristic
33C22×C4⋊C4×C43C2211yescharacteristic
34C22×C4⋊C4×C43C2211yescharacteristic
35C43×#482—24no—
36C43×#468—24no—
37C2×#107×C43C2211yescharacteristic
38C2×#107×C43C2211yescharacteristic
39C2×#106×C43C2211yescharacteristic
40C2×#103×C43C2211yescharacteristic
41C2×#103×C43C2211yescharacteristic
42C2×#103×C43C2211yescharacteristic
43C2×#102×C43C2211yescharacteristic
44C2×#102×C43C2211yescharacteristic
45C2×#102×C43C2211yescharacteristic
46C2×C22⋊C8×C43C2211yescharacteristic
47C2×C22⋊C8×C43C2211yescharacteristic
48C2×C22⋊C8×C43C2211yescharacteristic
49C43×#396—21no—
50C43×#394—21no—
51C43×#390C2211yescharacteristic
52C43×#389C2211yescharacteristic
53C43×#386—21no—
54C43×#380C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×Q8×C43C2311yescharacteristic
64C22×D4×C43—21no—
65C22×D4×C43—21no—
66C22×D4×C43D411yescharacteristic
67C22×D4×C43C2311yescharacteristic
68C23×C4×C43—21no—
69C23×C4×C43—21no—
70C23×C4×C43C2311yescharacteristic
71C23×C4×C43C2311yescharacteristic
72C2×SD16×C43—22no—
73C2×SD16×C43—22no—
74C2×SD16×C43—41no—
75C2×M16×C43—22no—
76C2×M16×C43—22no—
77C2×M16×C43—41no—
78C22×C8×C43C2311yescharacteristic
79C22×C8×C43C2311yescharacteristic
80C22×C8×C43C2311yescharacteristic
81C22×C8×C43C2311yescharacteristic
82#126×C43—28no—
83#125×C43—28no—
84#125×C43—22no—
85#125×C43—22no—
86#123×C43—28no—
87C22⋊Q8×C43—22no—
88C22⋊Q8×C43—22no—
89C22⋊Q8×C43—22no—
90C22⋊Q8×C43D414yescomplemented
91#121×C43—22no—
92#121×C43—22no—
93#121×C43—22no—
94#121×C43—41no—
95#121×C43—44no—
96C4×Q8×C43—22no—
97C4×Q8×C43—22no—
98C4×D4×C43—22no—
99C4×D4×C43—22no—
100#117×C43—28no—
101#117×C43—22no—
102#117×C43D414yescomplemented
103C2×C4⋊C4×C43—21no—
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—22no—
110C2×C4⋊C4×C43—22no—
111C2×C4⋊C4×C43—22no—
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43—21no—
114C2×C4⋊C4×C43—41no—
115C2×C4⋊C4×C43D411yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
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×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43D411yescharacteristic
131C2×C22⋊C4×C43D411yescharacteristic
132C2×C42×C43—21no—
133C2×C42×C43—21no—
134C2×C42×C43C2311yescharacteristic
135#107×C43—22no—
136#107×C43—22no—
137#106×C43—22no—
138#103×C43—22no—
139#103×C43—22no—
140#103×C43—41no—
141#102×C43—22no—
142#102×C43—22no—
143#102×C43—22no—
144C22⋊C8×C43—22no—
145C22⋊C8×C43—22no—
146C22⋊C8×C43—41no—
147#95×C43—21no—
148#95×C43—21no—
149C24×C43—21no—
150C24×C43C2×D411yescharacteristic
151C24×C43C2×D411yescharacteristic
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43C2×D412yes—
158C2×D4×C43—22no—
159C2×D4×C43—22no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—41no—
167C2×D4×C43—42no—
168C2×D4×C43—42no—
169C2×D4×C43—42no—
170C2×D4×C43—42no—
171C2×D4×C43—42no—
172C2×D4×C43—81no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—24no—
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—42no—
192C22×C4×C43—42no—
193C22×C4×C43—42no—
194C22×C4×C43—42no—
195C22×C4×C43—81no—
196C22×C4×C43C2×D412yes—
197C22×C4×C43C2×D412yes—
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2411yescharacteristic
203SD16×C43—44no—
204M16×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—24no—
219C4⋊C4×C43—24no—
220C4⋊C4×C43—24no—
221C4⋊C4×C43—24no—
222C4⋊C4×C43—24no—
223C4⋊C4×C43—22no—
224C4⋊C4×C43—21no—
225C4⋊C4×C43—21no—
226C4⋊C4×C43—21no—
227C4⋊C4×C43—21no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—42no—
233C4⋊C4×C43—42no—
234C4⋊C4×C43C2×D412yes—
235C4⋊C4×C43C2×D412yes—
236C4⋊C4×C43C2×D412yes—
237C4⋊C4×C43#4112yes—
238C22⋊C4×C43—24no—
239C22⋊C4×C43—22no—
240C22⋊C4×C43—24no—
241C22⋊C4×C43—24no—
242C22⋊C4×C43—22no—
243C22⋊C4×C43—42no—
244C22⋊C4×C43—42no—
245C22⋊C4×C43—42no—
246C22⋊C4×C43—42no—
247C22⋊C4×C43—81no—
248C42×C43—24no—
249C42×C43—24no—
250C42×C43—21no—
251C42×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43—41no—
271C23×C43#12012yes—
272C23×C43AGL(1,ℤ/8)12yes—
273C23×C43C22×D411yescharacteristic
274Q8×C43—22no—
275Q8×C43—22no—
276Q8×C43—41no—
277Q8×C43—41no—
278D4×C43—44no—
279D4×C43—41no—
280D4×C43—41no—
281D4×C43—41no—
282D4×C43—41no—
283D4×C43—84no—
284D4×C43—84no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—21no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—22no—
298C2×C4×C43—21no—
299C2×C4×C43—22no—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—48no—
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—41no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43—84no—
327C2×C4×C43#12012yes—
328C2×C4×C43C22×D411yescharacteristic
329C2×C4×C43C22×D411yescharacteristic
330C2×C4×C43C2×#4111yescharacteristic
331C2×C4×C43C2×#4111yescharacteristic
332C2×C4×C43H(5,𝔽2)11yescharacteristic
333C2×C4×C432−1+411yescharacteristic
334C8×C43—22no—
335C8×C43—41no—
336C8×C43—41no—
337C8×C43—41no—
338#25560C4311yesmaximal, characteristic, direct product factor, Sylow
339C22×C43—22no—
340C22×C43—22no—
341C22×C43—22no—
342C22×C43—22no—
343C22×C43—22no—
344C22×C43—22no—
345C22×C43—41no—
346C22×C43—41no—
347C22×C43—41no—
348C22×C43—41no—
349C22×C43—41no—
350C22×C43—41no—
351C22×C43—41no—
352C22×C43—41no—
353C22×C43—81no—
354C22×C43—81no—
355C22×C43—81no—
356C22×C43—81no—
357C22×C43—81no—
358C22×C43—81no—
359C22×C43—81no—
360C22×C43C2×#12011yescharacteristic
361C22×C43#54611yescharacteristic
362C22×C43#54711yescharacteristic
363C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
364C22×C43#57511yescharacteristic
365C22×C43#57711yescharacteristic
366C22×C43#57811yescharacteristic
367C4×C43—22no—
368C4×C43—41no—
369C4×C43—42no—
370C4×C43—41no—
371C4×C43—42no—
372C4×C43—42no—
373C4×C43—41no—
374C4×C43—42no—
375C4×C43—42no—
376C4×C43—81no—
377C4×C43—81no—
378C4×C43#53211yescharacteristic
379C4×C43#53711yescharacteristic
380C4×C43#54611yescharacteristic
381C4×C43#54711yescharacteristic
382C2×#552C2×C4311yescharacteristic, complemented
383C2×#482C2×C4311yescharacteristic, complemented
384C2×#468C2×C4311yescharacteristic, complemented
385#2416C2×C4311yescharacteristic
386#2059C2×C4311yescharacteristic, complemented
387#2035C2×C4311yescharacteristic, complemented
388#2025C2×C4311yescharacteristic, complemented
389#2000C2×C4311yescharacteristic, complemented
390#1880C2×C4311yescharacteristic, complemented
391#1874C2×C4311yescharacteristic, complemented
392#1872C2×C4311yescharacteristic, complemented
393#1870C2×C4311yescharacteristic, complemented
394#1863C2×C4311yescharacteristic, complemented
395#1852C2×C4311yescharacteristic, complemented
396#1736C2×C4311yescharacteristic, complemented
397C2×C43—42no—
398C2×C43—42no—
399C2×C43—161no—
400C2×C43#243011yescharacteristic
401C2×C43#300611yescharacteristic
402C2×C43#301311yescharacteristic
403C2×C43#331011yescharacteristic
404C2×C43#332711yescharacteristic
405C2×C43#334311yescharacteristic
406C2×C43#335111yescharacteristic
407C22×SD16C22×C4311yescharacteristic
408C22×M16C22×C4311yescharacteristic
409#552—24no—
410#552—24no—
411C2×#126—21no—
412C2×#125—21no—
413C2×#125C22×C4311yescharacteristic
414C2×#123—21no—
415C2×C22⋊Q8C22×C4311yescharacteristic
416C2×C22⋊Q8C22×C4311yescharacteristic
417C2×#121—21no—
418C2×#121C22×C4311yescharacteristic
419C2×#121C22×C4311yescharacteristic
420C2×C4×Q8C22×C4311yescharacteristic
421C2×C4×D4C22×C4311yescharacteristic
422C2×#117—21no—
423C2×#117C22×C4311yescharacteristic
424C22×C4⋊C4C22×C4311yescharacteristic
425C22×C4⋊C4C22×C4311yescharacteristic
426#482—24no—
427#468—24no—
428C2×#107C22×C4311yescharacteristic
429C2×#107C22×C4311yescharacteristic
430C2×#106C22×C4311yescharacteristic
431C2×#103C22×C4311yescharacteristic
432C2×#103C22×C4311yescharacteristic
433C2×#103C22×C4311yescharacteristic
434C2×#102C22×C4311yescharacteristic
435C2×#102C22×C4311yescharacteristic
436C2×#102C22×C4311yescharacteristic
437C2×C22⋊C8C22×C4311yescharacteristic
438C2×C22⋊C8C22×C4311yescharacteristic
439C2×C22⋊C8C22×C4311yescharacteristic
440#396—21no—
441#394—21no—
442#390C22×C4311yescharacteristic
443#389C22×C4311yescharacteristic
444#386—21no—
445#380C22×C4311yescharacteristic
446#340C22×C4311yescharacteristic
447#340C22×C4311yescharacteristic
448#340C22×C4311yescharacteristic
449#340C22×C4311yescharacteristic
450#340C22×C4311yescharacteristic
451#340C22×C4311yescharacteristic
452#336C22×C4311yescharacteristic
453#336C22×C4311yescharacteristic
454C43#2556011yescharacteristic, direct product factor, Sylow
455C22×Q8C23×C4311yescharacteristic
456C22×D4—21no—
457C22×D4—21no—
458C22×D4D4×C4311yescharacteristic
459C22×D4C23×C4311yescharacteristic
460C23×C4—21no—
461C23×C4—21no—
462C23×C4C23×C4311yescharacteristic
463C23×C4C23×C4311yescharacteristic
464C2×SD16—22no—
465C2×SD16—22no—
466C2×SD16—41no—
467C2×M16—22no—
468C2×M16—22no—
469C2×M16—41no—
470C22×C8C23×C4311yescharacteristic
471C22×C8C23×C4311yescharacteristic
472C22×C8C23×C4311yescharacteristic
473C22×C8C23×C4311yescharacteristic
474#126—28no—
475#125—28no—
476#125—22no—
477#125—22no—
478#123—28no—
479C22⋊Q8—22no—
480C22⋊Q8—22no—
481C22⋊Q8—22no—
482C22⋊Q8D4×C4314yescomplemented
483#121—22no—
484#121—22no—
485#121—22no—
486#121—41no—
487#121—44no—
488C4×Q8—22no—
489C4×Q8—22no—
490C4×D4—22no—
491C4×D4—22no—
492#117—28no—
493#117—22no—
494#117D4×C4314yescomplemented
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—41no—
507C2×C4⋊C4D4×C4311yescharacteristic
508C2×C4⋊C4C23×C4311yescharacteristic
509C2×C4⋊C4C23×C4311yescharacteristic
510C2×C4⋊C4C23×C4311yescharacteristic
511C2×C4⋊C4C23×C4311yescharacteristic
512C2×C4⋊C4C23×C4311yescharacteristic
513C2×C4⋊C4C23×C4311yescharacteristic
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4D4×C4311yescharacteristic
523C2×C22⋊C4D4×C4311yescharacteristic
524C2×C42—21no—
525C2×C42—21no—
526C2×C42C23×C4311yescharacteristic
527#107—22no—
528#107—22no—
529#106—22no—
530#103—22no—
531#103—22no—
532#103—41no—
533#102—22no—
534#102—22no—
535#102—22no—
536C22⋊C8—22no—
537C22⋊C8—22no—
538C22⋊C8—41no—
539#95—21no—
540#95—21no—
541C24—21no—
542C24C2×D4×C4311yescharacteristic
543C24C2×D4×C4311yescharacteristic
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8C2×D4×C4312yes—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—41no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—81no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—24no—
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—21no—
582C22×C4—21no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—81no—
588C22×C4C2×D4×C4311yescharacteristic
589C22×C4C2×D4×C4311yescharacteristic
590C22×C4C2×D4×C4311yescharacteristic
591C22×C4C2×D4×C4311yescharacteristic
592C22×C4C2×D4×C4312yes—
593C22×C4C2×D4×C4312yes—
594C22×C4C24×C4311yescharacteristic
595SD16—44no—
596M16—44no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8#41×C4312yes—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—22no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4C2×D4×C4312yes—
627C4⋊C4C2×D4×C4312yes—
628C4⋊C4C2×D4×C4312yes—
629C4⋊C4#41×C4312yes—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—81no—
640C42—24no—
641C42—24no—
642C42—21no—
643C42—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23#120×C4312yes—
664C23AGL(1,ℤ/8)×C4312yes—
665C23C22×D4×C4311yescharacteristic
666Q8—22no—
667Q8—22no—
668Q8—41no—
669Q8—41no—
670D4—44no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—84no—
676D4—84no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—48no—
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—41no—
717C2×C4—41no—
718C2×C4—84no—
719C2×C4#120×C4312yes—
720C2×C4C22×D4×C4311yescharacteristic
721C2×C4C22×D4×C4311yescharacteristic
722C2×C4C2×#41×C4311yescharacteristic
723C2×C4C2×#41×C4311yescharacteristic
724C2×C4H(5,𝔽2)×C4311yescharacteristic
725C2×C42−1+4×C4311yescharacteristic
726C8—22no—
727C8—41no—
728C8—41no—
729C8—41no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22C2×#120×C4311yescharacteristic
752C22C43×#54611yescharacteristic
753C22C43×#54711yescharacteristic
754C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
755C22C43×#57511yescharacteristic
756C22C43×#57711yescharacteristic
757C22C43×#57811yescharacteristic
758C4—22no—
759C4—41no—
760C4—42no—
761C4—41no—
762C4—42no—
763C4—42no—
764C4—41no—
765C4—42no—
766C4—42no—
767C4—81no—
768C4—81no—
769C4C43×#53211yescharacteristic
770C4C43×#53711yescharacteristic
771C4C43×#54611yescharacteristic
772C4C43×#54711yescharacteristic
773C2—42no—
774C2—42no—
775C2—161no—
776C2C43×#243011yescharacteristic
777C2C43×#300611yescharacteristic
778C2C43×#301311yescharacteristic
779C2C43×#331011yescharacteristic
780C2C43×#332711yescharacteristic
781C2C43×#334311yescharacteristic
782C2C43×#335111yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC43×#2416C2
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×#552C2semidirect
2. C2×C43×#482C2semidirect
3. C2×C43×#468C2semidirect
5. C43×#2059C2semidirect
6. C43×#2035C2semidirect
7. C43×#2025C2semidirect
8. C43×#2000C2semidirect
9. C43×#1880C2semidirect
10. C43×#1874C2semidirect
11. C43×#1872C2semidirect
12. C43×#1870C2semidirect
13. C43×#1863C2semidirect
14. C43×#1852C2semidirect
15. C43×#1736C2semidirect
90. C22⋊Q8×C43D4semidirect
102. #117×C43D4semidirect
338. #25560C43direct (N × H)
382. C2×#552C2×C43semidirect
383. C2×#482C2×C43semidirect
384. C2×#468C2×C43semidirect
386. #2059C2×C43semidirect
387. #2035C2×C43semidirect
388. #2025C2×C43semidirect
389. #2000C2×C43semidirect
390. #1880C2×C43semidirect
391. #1874C2×C43semidirect
392. #1872C2×C43semidirect
393. #1870C2×C43semidirect
394. #1863C2×C43semidirect
395. #1852C2×C43semidirect
396. #1736C2×C43semidirect
454. C43#25560direct (N × H)
482. C22⋊Q8D4×C43semidirect
494. #117D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#5522
C2×C43×#4822
C2×C43×#4682
C43×#24162
C43×#20592
C43×#20352
C43×#20252
C43×#20002
C43×#18802
C43×#18742
C43×#18722
C43×#18702
C43×#18632
C43×#18522
C43×#17362
#2556043