Finite Group Databasebeta

← C43×#24136 #24944153

Subgroups — C43×#24136 #24944153

Order 11008.

1238 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#553C211yesmaximal, characteristic, complemented
2C2×C43×#478C211yesmaximal, characteristic, complemented
3C2×C43×#442C211yesmaximal, characteristic, complemented
4C43×#2537C211yesmaximal, characteristic, complemented
5C43×#2034C211yesmaximal, characteristic, complemented
6C43×#2033C211yesmaximal, characteristic, complemented
7C43×#1999C211yesmaximal, characteristic, complemented
8C43×#1999C211yesmaximal, characteristic, complemented
9C43×#1992C211yesmaximal, characteristic, complemented
10C43×#1955C211yesmaximal, characteristic, complemented
11C43×#1875C211yesmaximal, characteristic, complemented
12C43×#1874C211yesmaximal, characteristic, complemented
13C43×#1854C211yesmaximal, characteristic, complemented
14C43×#1853C211yesmaximal, characteristic, complemented
15C43×#1802C211yesmaximal, characteristic, complemented
16C22×D8×C43C2211yescharacteristic
17C43×#553—24no—
18C43×#553—24no—
19C2×#126×C43—21no—
20C2×#125×C43C2211yescharacteristic
21C2×#123×C43—21no—
22C2×#121×C43—21no—
23C2×#121×C43—21no—
24C2×#121×C43C2211yescharacteristic
25C2×#121×C43C2211yescharacteristic
26C2×#121×C43C2211yescharacteristic
27C2×#121×C43C2211yescharacteristic
28C2×C4×D4×C43—21no—
29C2×C4×D4×C43C2211yescharacteristic
30C2×C4×D4×C43C2211yescharacteristic
31C2×C4×D4×C43C2211yescharacteristic
32C2×#117×C43C2211yescharacteristic
33C22×C4⋊C4×C43C2211yescharacteristic
34C43×#478—24no—
35C43×#442—24no—
36C2×#107×C43C2211yescharacteristic
37C2×#106×C43C2211yescharacteristic
38C2×#106×C43C2211yescharacteristic
39C2×C4⋊C8×C43C2211yescharacteristic
40C2×#102×C43C2211yescharacteristic
41C2×#102×C43C2211yescharacteristic
42C2×#102×C43C2211yescharacteristic
43C2×#102×C43C2211yescharacteristic
44C2×#102×C43C2211yescharacteristic
45C2×#102×C43C2211yescharacteristic
46C2×C22⋊C8×C43C2211yescharacteristic
47C2×C22⋊C8×C43C2211yescharacteristic
48C2×C22⋊C8×C43C2211yescharacteristic
49C2×C22⋊C8×C43C2211yescharacteristic
50C2×#97×C43C2211yescharacteristic
51C43×#394—21no—
52C43×#394—21no—
53C43×#384C2211yescharacteristic
54C43×#380—21no—
55C43×#380C2211yescharacteristic
56C43×#380C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C22×D4×C43—21no—
64C22×D4×C43—21no—
65C22×D4×C43—21no—
66C22×D4×C43—21no—
67C22×D4×C43D411yescharacteristic
68C22×D4×C43C2311yescharacteristic
69C22×D4×C43C2311yescharacteristic
70C23×C4×C43—21no—
71C23×C4×C43—21no—
72C23×C4×C43—21no—
73C23×C4×C43C2311yescharacteristic
74C23×C4×C43C2311yescharacteristic
75C2×D8×C43—22no—
76C2×D8×C43—22no—
77C2×D8×C43—22no—
78C22×C8×C43C2311yescharacteristic
79C22×C8×C43C2311yescharacteristic
80C22×C8×C43C2311yescharacteristic
81C22×C8×C43C2311yescharacteristic
82#126×C43—28no—
83#125×C43—22no—
84#125×C43D414yescomplemented
85#123×C43—28no—
86#121×C43—28no—
87#121×C43—22no—
88#121×C43—22no—
89#121×C43—22no—
90#121×C43—22no—
91#121×C43—22no—
92#121×C43—22no—
93#121×C43—41no—
94#121×C43—41no—
95#121×C43—44no—
96C4×D4×C43—28no—
97C4×D4×C43—22no—
98C4×D4×C43—22no—
99C4×D4×C43—22no—
100C4×D4×C43—22no—
101C4×D4×C43—22no—
102C4×D4×C43D414yescomplemented
103#117×C43—22no—
104#117×C43—22no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43—22no—
109C2×C4⋊C4×C43—22no—
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43D411yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
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×C43D411yescharacteristic
129C2×C22⋊C4×C43D411yescharacteristic
130C2×C42×C43—21no—
131C2×C42×C43C2311yescharacteristic
132#107×C43—22no—
133#106×C43—22no—
134#106×C43—22no—
135C4⋊C8×C43—22no—
136#102×C43—22no—
137#102×C43—22no—
138#102×C43—22no—
139#102×C43—22no—
140#102×C43—41no—
141#102×C43—41no—
142C22⋊C8×C43—22no—
143C22⋊C8×C43—22no—
144C22⋊C8×C43—41no—
145C22⋊C8×C43—41no—
146#97×C43—22no—
147#95×C43—21no—
148#95×C43—21no—
149C24×C43—21no—
150C24×C43—21no—
151C24×C43C2×D411yescharacteristic
152C24×C43C2×D411yescharacteristic
153C2×D4×C43—24no—
154C2×D4×C43—24no—
155C2×D4×C43—22no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—22no—
159C2×D4×C43—21no—
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—21no—
167C2×D4×C43—41no—
168C2×D4×C43—42no—
169C2×D4×C43—42no—
170C2×D4×C43—42no—
171C2×D4×C43—42no—
172C2×D4×C43—42no—
173C2×D4×C43—42no—
174C2×D4×C43—81no—
175C2×D4×C43—81no—
176C2×D4×C43—81no—
177C2×D4×C43—81no—
178C2×D4×C43C2×D412yes—
179C2×D4×C43#4112yes—
180C22×C4×C43—24no—
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—24no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—42no—
201C22×C4×C43—42no—
202C22×C4×C43—42no—
203C22×C4×C43—81no—
204C22×C4×C43—81no—
205C22×C4×C43—81no—
206C22×C4×C43—81no—
207C22×C4×C43C2×D411yescharacteristic
208C22×C4×C43C2×D411yescharacteristic
209C22×C4×C43C2×D411yescharacteristic
210C22×C4×C43C2×D411yescharacteristic
211C22×C4×C43C2411yescharacteristic
212D8×C43—28no—
213C2×C8×C43—21no—
214C2×C8×C43—21no—
215C2×C8×C43—21no—
216C2×C8×C43—21no—
217C2×C8×C43—21no—
218C2×C8×C43—21no—
219C2×C8×C43—21no—
220C2×C8×C43—21no—
221C2×C8×C43—21no—
222C2×C8×C43—21no—
223C2×C8×C43—21no—
224C2×C8×C43#4112yes—
225C4⋊C4×C43—24no—
226C4⋊C4×C43—24no—
227C4⋊C4×C43—24no—
228C4⋊C4×C43—22no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43—21no—
238C4⋊C4×C43—42no—
239C4⋊C4×C43—81no—
240C4⋊C4×C43C2×D412yes—
241C4⋊C4×C43C2×D412yes—
242C4⋊C4×C43C2×D412yes—
243C22⋊C4×C43—24no—
244C22⋊C4×C43—24no—
245C22⋊C4×C43—24no—
246C22⋊C4×C43—24no—
247C22⋊C4×C43—22no—
248C22⋊C4×C43—22no—
249C22⋊C4×C43—42no—
250C22⋊C4×C43—42no—
251C22⋊C4×C43—42no—
252C22⋊C4×C43—42no—
253C22⋊C4×C43—42no—
254C42×C43—24no—
255C42×C43C2×D412yes—
256C42×C43C2×D412yes—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—22no—
265C23×C43—22no—
266C23×C43—21no—
267C23×C43—21no—
268C23×C43—21no—
269C23×C43—21no—
270C23×C43—21no—
271C23×C43—21no—
272C23×C43—41no—
273C23×C43—41no—
274C23×C43—41no—
275C23×C43—41no—
276C23×C43—41no—
277C23×C43—41no—
278C23×C43—41no—
279C23×C43—41no—
280C23×C43—41no—
281C23×C43—41no—
282C23×C43—41no—
283C23×C43—41no—
284C23×C43AGL(1,ℤ/8)12yes—
285C23×C43C22×D411yescharacteristic
286D4×C43—22no—
287D4×C43—22no—
288D4×C43—22no—
289D4×C43—22no—
290D4×C43—44no—
291D4×C43—48no—
292D4×C43—41no—
293D4×C43—41no—
294D4×C43—41no—
295D4×C43—41no—
296D4×C43—84no—
297D4×C43—84no—
298D4×C43—84no—
299C2×C4×C43—21no—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
306C2×C4×C43—21no—
307C2×C4×C43—22no—
308C2×C4×C43—21no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
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—41no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43—84no—
336C2×C4×C43—84no—
337C2×C4×C43—84no—
338C2×C4×C43#12012yes—
339C2×C4×C43#12012yes—
340C2×C4×C43C22×D411yescharacteristic
341C2×C4×C43C22×D411yescharacteristic
342C2×C4×C43C2×#4111yescharacteristic
343C2×C4×C43C2×#4111yescharacteristic
344C2×C4×C43H(5,𝔽2)11yescharacteristic
345C2×C4×C432−1+411yescharacteristic
346C8×C43—22no—
347C8×C43—41no—
348C8×C43—41no—
349C8×C43—41no—
350#24136C4311yesmaximal, characteristic, direct product factor, Sylow
351C22×C43—22no—
352C22×C43—22no—
353C22×C43—22no—
354C22×C43—41no—
355C22×C43—41no—
356C22×C43—41no—
357C22×C43—41no—
358C22×C43—41no—
359C22×C43—41no—
360C22×C43—41no—
361C22×C43—42no—
362C22×C43—42no—
363C22×C43—41no—
364C22×C43—42no—
365C22×C43—41no—
366C22×C43—42no—
367C22×C43—41no—
368C22×C43—42no—
369C22×C43—41no—
370C22×C43—42no—
371C22×C43—81no—
372C22×C43—81no—
373C22×C43—81no—
374C22×C43—81no—
375C22×C43—81no—
376C22×C43—81no—
377C22×C43—81no—
378C22×C43—81no—
379C22×C43C2×#12011yescharacteristic
380C22×C43#54611yescharacteristic
381C22×C43#54711yescharacteristic
382C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
383C22×C43#57511yescharacteristic
384C22×C43#57611yescharacteristic
385C22×C43#57711yescharacteristic
386C4×C43—22no—
387C4×C43—22no—
388C4×C43—41no—
389C4×C43—41no—
390C4×C43—42no—
391C4×C43—42no—
392C4×C43—42no—
393C4×C43—81no—
394C4×C43—81no—
395C4×C43—81no—
396C4×C43#52511yescharacteristic
397C4×C43#53711yescharacteristic
398C4×C43#54811yescharacteristic
399C4×C43#55011yescharacteristic
400C2×#553C2×C4311yescharacteristic, complemented
401C2×#478C2×C4311yescharacteristic, complemented
402C2×#442C2×C4311yescharacteristic, complemented
403#2537C2×C4311yescharacteristic, complemented
404#2034C2×C4311yescharacteristic, complemented
405#2033C2×C4311yescharacteristic, complemented
406#1999C2×C4311yescharacteristic, complemented
407#1999C2×C4311yescharacteristic, complemented
408#1992C2×C4311yescharacteristic, complemented
409#1955C2×C4311yescharacteristic, complemented
410#1875C2×C4311yescharacteristic, complemented
411#1874C2×C4311yescharacteristic, complemented
412#1854C2×C4311yescharacteristic, complemented
413#1853C2×C4311yescharacteristic, complemented
414#1802C2×C4311yescharacteristic, complemented
415C2×C43—42no—
416C2×C43—81no—
417C2×C43—82no—
418C2×C43—82no—
419C2×C43#240711yescharacteristic
420C2×C43#300611yescharacteristic
421C2×C43#301211yescharacteristic
422C2×C43#330711yescharacteristic
423C2×C43#331811yescharacteristic
424C2×C43#334511yescharacteristic
425C2×C43#334711yescharacteristic
426C22×D8C22×C4311yescharacteristic
427#553—24no—
428#553—24no—
429C2×#126—21no—
430C2×#125C22×C4311yescharacteristic
431C2×#123—21no—
432C2×#121—21no—
433C2×#121—21no—
434C2×#121C22×C4311yescharacteristic
435C2×#121C22×C4311yescharacteristic
436C2×#121C22×C4311yescharacteristic
437C2×#121C22×C4311yescharacteristic
438C2×C4×D4—21no—
439C2×C4×D4C22×C4311yescharacteristic
440C2×C4×D4C22×C4311yescharacteristic
441C2×C4×D4C22×C4311yescharacteristic
442C2×#117C22×C4311yescharacteristic
443C22×C4⋊C4C22×C4311yescharacteristic
444#478—24no—
445#442—24no—
446C2×#107C22×C4311yescharacteristic
447C2×#106C22×C4311yescharacteristic
448C2×#106C22×C4311yescharacteristic
449C2×C4⋊C8C22×C4311yescharacteristic
450C2×#102C22×C4311yescharacteristic
451C2×#102C22×C4311yescharacteristic
452C2×#102C22×C4311yescharacteristic
453C2×#102C22×C4311yescharacteristic
454C2×#102C22×C4311yescharacteristic
455C2×#102C22×C4311yescharacteristic
456C2×C22⋊C8C22×C4311yescharacteristic
457C2×C22⋊C8C22×C4311yescharacteristic
458C2×C22⋊C8C22×C4311yescharacteristic
459C2×C22⋊C8C22×C4311yescharacteristic
460C2×#97C22×C4311yescharacteristic
461#394—21no—
462#394—21no—
463#384C22×C4311yescharacteristic
464#380—21no—
465#380C22×C4311yescharacteristic
466#380C22×C4311yescharacteristic
467#340C22×C4311yescharacteristic
468#340C22×C4311yescharacteristic
469#340C22×C4311yescharacteristic
470#340C22×C4311yescharacteristic
471#340C22×C4311yescharacteristic
472#340C22×C4311yescharacteristic
473C43#2413611yescharacteristic, direct product factor, Sylow
474C22×D4—21no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4D4×C4311yescharacteristic
479C22×D4C23×C4311yescharacteristic
480C22×D4C23×C4311yescharacteristic
481C23×C4—21no—
482C23×C4—21no—
483C23×C4—21no—
484C23×C4C23×C4311yescharacteristic
485C23×C4C23×C4311yescharacteristic
486C2×D8—22no—
487C2×D8—22no—
488C2×D8—22no—
489C22×C8C23×C4311yescharacteristic
490C22×C8C23×C4311yescharacteristic
491C22×C8C23×C4311yescharacteristic
492C22×C8C23×C4311yescharacteristic
493#126—28no—
494#125—22no—
495#125D4×C4314yescomplemented
496#123—28no—
497#121—28no—
498#121—22no—
499#121—22no—
500#121—22no—
501#121—22no—
502#121—22no—
503#121—22no—
504#121—41no—
505#121—41no—
506#121—44no—
507C4×D4—28no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4D4×C4314yescomplemented
514#117—22no—
515#117—22no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4D4×C4311yescharacteristic
524C2×C4⋊C4C23×C4311yescharacteristic
525C2×C4⋊C4C23×C4311yescharacteristic
526C2×C4⋊C4C23×C4311yescharacteristic
527C2×C4⋊C4C23×C4311yescharacteristic
528C2×C4⋊C4C23×C4311yescharacteristic
529C2×C4⋊C4C23×C4311yescharacteristic
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4D4×C4311yescharacteristic
540C2×C22⋊C4D4×C4311yescharacteristic
541C2×C42—21no—
542C2×C42C23×C4311yescharacteristic
543#107—22no—
544#106—22no—
545#106—22no—
546C4⋊C8—22no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—22no—
551#102—41no—
552#102—41no—
553C22⋊C8—22no—
554C22⋊C8—22no—
555C22⋊C8—41no—
556C22⋊C8—41no—
557#97—22no—
558#95—21no—
559#95—21no—
560C24—21no—
561C24—21no—
562C24C2×D4×C4311yescharacteristic
563C24C2×D4×C4311yescharacteristic
564C2×D4—24no—
565C2×D4—22no—
566C2×D4—24no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—41no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—81no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4—81no—
589C2×D4C2×D4×C4312yes—
590C2×D4#41×C4312yes—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—24no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—24no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—81no—
615C22×C4—81no—
616C22×C4—81no—
617C22×C4—81no—
618C22×C4C2×D4×C4311yescharacteristic
619C22×C4C2×D4×C4311yescharacteristic
620C22×C4C2×D4×C4311yescharacteristic
621C22×C4C2×D4×C4311yescharacteristic
622C22×C4C24×C4311yescharacteristic
623D8—28no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8#41×C4312yes—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—24no—
639C4⋊C4—22no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—42no—
650C4⋊C4—81no—
651C4⋊C4C2×D4×C4312yes—
652C4⋊C4C2×D4×C4312yes—
653C4⋊C4C2×D4×C4312yes—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C42—24no—
666C42C2×D4×C4312yes—
667C42C2×D4×C4312yes—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—22no—
676C23—22no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23AGL(1,ℤ/8)×C4312yes—
696C23C22×D4×C4311yescharacteristic
697D4—22no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—44no—
702D4—48no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—84no—
708D4—84no—
709D4—84no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
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—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—84no—
747C2×C4—84no—
748C2×C4—84no—
749C2×C4#120×C4312yes—
750C2×C4#120×C4312yes—
751C2×C4C22×D4×C4311yescharacteristic
752C2×C4C22×D4×C4311yescharacteristic
753C2×C4C2×#41×C4311yescharacteristic
754C2×C4C2×#41×C4311yescharacteristic
755C2×C4H(5,𝔽2)×C4311yescharacteristic
756C2×C42−1+4×C4311yescharacteristic
757C8—22no—
758C8—41no—
759C8—41no—
760C8—41no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—42no—
772C22—42no—
773C22—41no—
774C22—42no—
775C22—42no—
776C22—41no—
777C22—41no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22C2×#120×C4311yescharacteristic
790C22C43×#54611yescharacteristic
791C22C43×#54711yescharacteristic
792C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
793C22C43×#57511yescharacteristic
794C22C43×#57611yescharacteristic
795C22C43×#57711yescharacteristic
796C4—22no—
797C4—22no—
798C4—41no—
799C4—41no—
800C4—42no—
801C4—42no—
802C4—42no—
803C4—81no—
804C4—81no—
805C4—81no—
806C4C43×#52511yescharacteristic
807C4C43×#53711yescharacteristic
808C4C43×#54811yescharacteristic
809C4C43×#55011yescharacteristic
810C2—42no—
811C2—81no—
812C2—82no—
813C2—82no—
814C2C43×#240711yescharacteristic
815C2C43×#300611yescharacteristic
816C2C43×#301211yescharacteristic
817C2C43×#330711yescharacteristic
818C2C43×#331811yescharacteristic
819C2C43×#334511yescharacteristic
820C2C43×#334711yescharacteristic
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×#553C2semidirect
2. C2×C43×#478C2semidirect
3. C2×C43×#442C2semidirect
4. C43×#2537C2semidirect
5. C43×#2034C2semidirect
6. C43×#2033C2semidirect
7. C43×#1999C2semidirect
8. C43×#1999C2semidirect
9. C43×#1992C2semidirect
10. C43×#1955C2semidirect
11. C43×#1875C2semidirect
12. C43×#1874C2semidirect
13. C43×#1854C2semidirect
14. C43×#1853C2semidirect
15. C43×#1802C2semidirect
84. #125×C43D4semidirect
102. C4×D4×C43D4semidirect
350. #24136C43direct (N × H)
400. C2×#553C2×C43semidirect
401. C2×#478C2×C43semidirect
402. C2×#442C2×C43semidirect
403. #2537C2×C43semidirect
404. #2034C2×C43semidirect
405. #2033C2×C43semidirect
406. #1999C2×C43semidirect
407. #1999C2×C43semidirect
408. #1992C2×C43semidirect
409. #1955C2×C43semidirect
410. #1875C2×C43semidirect
411. #1874C2×C43semidirect
412. #1854C2×C43semidirect
413. #1853C2×C43semidirect
414. #1802C2×C43semidirect
473. C43#24136direct (N × H)
495. #125D4×C43semidirect
513. C4×D4D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#5532
C2×C43×#4782
C2×C43×#4422
C43×#25372
C43×#20342
C43×#20332
C43×#19992
C43×#19922
C43×#19552
C43×#18752
C43×#18742
C43×#18542
C43×#18532
C43×#18022
#2413643