Finite Group Databasebeta

← C43×#25967 #24945984

Subgroups — C43×#25967 #24945984

Order 11008.

1004 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#475C211yesmaximal, characteristic, complemented
2C2×C43×#417C211yesmaximal, characteristic
3C43×#2440C211yesmaximal, characteristic, complemented
4C43×#2341C211yesmaximal, characteristic
5C43×#2094C211yesmaximal, characteristic, complemented
6C43×#2067C211yesmaximal, characteristic, complemented
7C43×#2065C211yesmaximal, characteristic, complemented
8C43×#2023C211yesmaximal, characteristic, complemented
9C43×#1865C211yesmaximal, characteristic, complemented
10C43×#1863C211yesmaximal, characteristic, complemented
11C43×#1853C211yesmaximal, characteristic, complemented
12C43×#1851C211yesmaximal, characteristic, complemented
13C43×#1809C211yesmaximal, characteristic, complemented
14C43×#1803C211yesmaximal, characteristic, complemented
15C43×#1788C211yesmaximal, characteristic
16C22×#41×C43C2211yescharacteristic
17C22×M16×C43C2211yescharacteristic
18C2×C4⋊Q8×C43C2211yescharacteristic
19C2×C22⋊Q8×C43—21no—
20C2×C4×Q8×C43C2211yescharacteristic
21C2×C4×Q8×C43C2211yescharacteristic
22C22×C4⋊C4×C43C2211yescharacteristic
23C43×#475—24no—
24C2×#107×C43C2211yescharacteristic
25C2×#106×C43C2211yescharacteristic
26C2×#106×C43C2211yescharacteristic
27C2×#106×C43C2211yescharacteristic
28C2×C4⋊C8×C43C2211yescharacteristic
29C2×C4⋊C8×C43C2211yescharacteristic
30C43×#417—24no—
31C2×#103×C43C2211yescharacteristic
32C2×#103×C43C2211yescharacteristic
33C2×#103×C43C2211yescharacteristic
34C2×#103×C43C2211yescharacteristic
35C2×#102×C43C2211yescharacteristic
36C2×#102×C43C2211yescharacteristic
37C2×#102×C43C2211yescharacteristic
38C2×#102×C43C2211yescharacteristic
39C2×C22⋊C8×C43C2211yescharacteristic
40C43×#398—21no—
41C43×#395—21no—
42C43×#390—21no—
43C43×#390—21no—
44C43×#390C2211yescharacteristic
45C43×#390C2211yescharacteristic
46C43×#389C2211yescharacteristic
47C43×#389C2211yescharacteristic
48C43×#385—21no—
49C43×#384C2211yescharacteristic
50C43×#380—21no—
51C43×#380C2211yescharacteristic
52C43×#380C2211yescharacteristic
53C4×C22⋊C4×C43—21no—
54C4×C22⋊C4×C43C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C2×#41×C43—22no—
62C2×#41×C43—22no—
63C2×#41×C43—22no—
64C2×#41×C43—41no—
65C2×#41×C43—41no—
66C2×#41×C43Q814yescomplemented
67C22×Q8×C43—21no—
68C22×Q8×C43C2311yescharacteristic
69C22×D4×C43—21no—
70C22×D4×C43C2311yescharacteristic
71C23×C4×C43—21no—
72C23×C4×C43—21no—
73C23×C4×C43C2311yescharacteristic
74C2×M16×C43—22no—
75C2×M16×C43—22no—
76C2×M16×C43—41no—
77C22×C8×C43C2311yescharacteristic
78C22×C8×C43C2311yescharacteristic
79C22×C8×C43C2311yescharacteristic
80C22×C8×C43C2311yescharacteristic
81C4⋊Q8×C43—22no—
82C4⋊Q8×C43—41no—
83C22⋊Q8×C43—44no—
84C4×Q8×C43—22no—
85C4×Q8×C43—22no—
86C4×Q8×C43—41no—
87C4×Q8×C43—41no—
88C2×C4⋊C4×C43—22no—
89C2×C4⋊C4×C43—21no—
90C2×C4⋊C4×C43—21no—
91C2×C4⋊C4×C43—21no—
92C2×C4⋊C4×C43—21no—
93C2×C4⋊C4×C43—21no—
94C2×C4⋊C4×C43—21no—
95C2×C4⋊C4×C43—21no—
96C2×C4⋊C4×C43—21no—
97C2×C4⋊C4×C43—41no—
98C2×C4⋊C4×C43C2311yescharacteristic
99C2×C4⋊C4×C43C2311yescharacteristic
100C2×C4⋊C4×C43C2311yescharacteristic
101C2×C4⋊C4×C43C2311yescharacteristic
102C2×C4⋊C4×C43C2311yescharacteristic
103C2×C4⋊C4×C43C2311yescharacteristic
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×C43D411yescharacteristic
111C2×C22⋊C4×C43D411yescharacteristic
112C2×C42×C43—21no—
113C2×C42×C43—21no—
114C2×C42×C43C2311yescharacteristic
115C2×C42×C43C2311yescharacteristic
116#107×C43—41no—
117#106×C43—22no—
118#106×C43—22no—
119#106×C43—41no—
120C4⋊C8×C43—22no—
121C4⋊C8×C43—41no—
122#103×C43—22no—
123#103×C43—22no—
124#103×C43—22no—
125#103×C43D414yes—
126#102×C43—22no—
127#102×C43—22no—
128#102×C43—41no—
129#102×C43—41no—
130C22⋊C8×C43—22no—
131#95×C43—21no—
132#95×C43—21no—
133#95×C43—21no—
134#95×C43—21no—
135#95×C43D411yescharacteristic
136#95×C43D411yescharacteristic
137C24×C43—21no—
138C24×C43C2×D411yescharacteristic
139#41×C43—28no—
140#41×C43—44no—
141#41×C43—44no—
142#41×C43—44no—
143C2×Q8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—42no—
147C2×Q8×C43—42no—
148C2×Q8×C43—81no—
149C2×Q8×C43C2×D412yes—
150C2×Q8×C43C2×Q812yes—
151C2×Q8×C43#4112yes—
152C2×D4×C43—21no—
153C2×D4×C43—24no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—42no—
159C2×D4×C43—42no—
160C2×D4×C43C2×Q812yes—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—24no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—42no—
174C22×C4×C43—42no—
175C22×C4×C43—42no—
176C22×C4×C43—42no—
177C22×C4×C43—81no—
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2×D411yescharacteristic
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2×Q812yes—
184C22×C4×C43#4112yes—
185C22×C4×C43C2411yescharacteristic
186M16×C43—44no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43C2×D412yes—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—42no—
211C4⋊C4×C43—42no—
212C4⋊C4×C43—42no—
213C4⋊C4×C43—42no—
214C4⋊C4×C43—42no—
215C4⋊C4×C43—42no—
216C4⋊C4×C43—42no—
217C4⋊C4×C43—81no—
218C4⋊C4×C43C2×D412yes—
219C22⋊C4×C43—22no—
220C22⋊C4×C43—22no—
221C22⋊C4×C43—42no—
222C22⋊C4×C43—42no—
223C22⋊C4×C43—42no—
224C22⋊C4×C43—81no—
225C22⋊C4×C43—81no—
226C22⋊C4×C43—81no—
227C42×C43—21no—
228C42×C43—21no—
229C42×C43—21no—
230C42×C43—21no—
231C42×C43—42no—
232C42×C43—42no—
233C23×C43—21no—
234C23×C43—21no—
235C23×C43—21no—
236C23×C43—21no—
237C23×C43—21no—
238C23×C43—21no—
239C23×C43—22no—
240C23×C43—41no—
241C23×C43—41no—
242C23×C43—41no—
243C23×C43—41no—
244C23×C43—41no—
245C23×C43—41no—
246C23×C43C22⋊Q812yes—
247C23×C43C22×D411yescharacteristic
248Q8×C43—22no—
249Q8×C43—22no—
250Q8×C43—22no—
251Q8×C43—84no—
252Q8×C43C22⋊Q814yescomplemented
253D4×C43—22no—
254D4×C43—22no—
255D4×C43—48no—
256D4×C43—41no—
257D4×C43—41no—
258C2×C4×C43—22no—
259C2×C4×C43—21no—
260C2×C4×C43—22no—
261C2×C4×C43—21no—
262C2×C4×C43—21no—
263C2×C4×C43—22no—
264C2×C4×C43—21no—
265C2×C4×C43—21no—
266C2×C4×C43—21no—
267C2×C4×C43—22no—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
270C2×C4×C43—22no—
271C2×C4×C43—21no—
272C2×C4×C43—22no—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
278C2×C4×C43—48no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—84no—
297C2×C4×C43C22⋊Q812yes—
298C2×C4×C43AGL(1,ℤ/8)12yes—
299C2×C4×C43#13712yes—
300C2×C4×C43C22×D411yescharacteristic
301C2×C4×C43C22×Q811yescharacteristic
302C2×C4×C43C2×#4111yescharacteristic
303C2×C4×C43C2×#4111yescharacteristic
304C2×C4×C43H(5,𝔽2)11yescharacteristic
305C2×C4×C43H(5,𝔽2)11yescharacteristic
306C8×C43—22no—
307C8×C43—41no—
308C8×C43—41no—
309C8×C43—41no—
310#25967C4311yesmaximal, characteristic, direct product factor, Sylow
311C22×C43—22no—
312C22×C43—22no—
313C22×C43—22no—
314C22×C43—41no—
315C22×C43—41no—
316C22×C43—41no—
317C22×C43—41no—
318C22×C43—42no—
319C22×C43—42no—
320C22×C43—42no—
321C22×C43—81no—
322C22×C43—81no—
323C22×C43—81no—
324C22×C43—81no—
325C22×C43C2×C22⋊Q811yescharacteristic
326C22×C43D4211yescharacteristic
327C22×C43#54611yescharacteristic
328C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
329C22×C43C2×#13711yescharacteristic
330C22×C43#57711yescharacteristic
331C22×C43#57711yescharacteristic
332C4×C43—22no—
333C4×C43—24no—
334C4×C43—22no—
335C4×C43—22no—
336C4×C43—41no—
337C4×C43—42no—
338C4×C43—41no—
339C4×C43—81no—
340C4×C43—81no—
341C4×C43—81no—
342C4×C43—81no—
343C4×C43—81no—
344C4×C43C2×C22⋊Q811yescharacteristic
345C4×C43#54311yescharacteristic
346C4×C43#54611yescharacteristic
347C4×C43#55111yescharacteristic
348C2×#475C2×C4311yescharacteristic, complemented
349C2×#417C2×C4311yescharacteristic
350#2440C2×C4311yescharacteristic, complemented
351#2341C2×C4311yescharacteristic
352#2094C2×C4311yescharacteristic, complemented
353#2067C2×C4311yescharacteristic, complemented
354#2065C2×C4311yescharacteristic, complemented
355#2023C2×C4311yescharacteristic, complemented
356#1865C2×C4311yescharacteristic, complemented
357#1863C2×C4311yescharacteristic, complemented
358#1853C2×C4311yescharacteristic, complemented
359#1851C2×C4311yescharacteristic, complemented
360#1809C2×C4311yescharacteristic, complemented
361#1803C2×C4311yescharacteristic, complemented
362#1788C2×C4311yescharacteristic
363C2×C43—42no—
364C2×C43—82no—
365C2×C43#243711yescharacteristic
366C2×C43#307911yescharacteristic
367C2×C43#308411yescharacteristic
368C2×C43#326511yescharacteristic
369C2×C43#327811yescharacteristic
370C2×C43#331611yescharacteristic
371C2×C43#333211yescharacteristic
372C22×#41C22×C4311yescharacteristic
373C22×M16C22×C4311yescharacteristic
374C2×C4⋊Q8C22×C4311yescharacteristic
375C2×C22⋊Q8—21no—
376C2×C4×Q8C22×C4311yescharacteristic
377C2×C4×Q8C22×C4311yescharacteristic
378C22×C4⋊C4C22×C4311yescharacteristic
379#475—24no—
380C2×#107C22×C4311yescharacteristic
381C2×#106C22×C4311yescharacteristic
382C2×#106C22×C4311yescharacteristic
383C2×#106C22×C4311yescharacteristic
384C2×C4⋊C8C22×C4311yescharacteristic
385C2×C4⋊C8C22×C4311yescharacteristic
386#417—24no—
387C2×#103C22×C4311yescharacteristic
388C2×#103C22×C4311yescharacteristic
389C2×#103C22×C4311yescharacteristic
390C2×#103C22×C4311yescharacteristic
391C2×#102C22×C4311yescharacteristic
392C2×#102C22×C4311yescharacteristic
393C2×#102C22×C4311yescharacteristic
394C2×#102C22×C4311yescharacteristic
395C2×C22⋊C8C22×C4311yescharacteristic
396#398—21no—
397#395—21no—
398#390—21no—
399#390—21no—
400#390C22×C4311yescharacteristic
401#390C22×C4311yescharacteristic
402#389C22×C4311yescharacteristic
403#389C22×C4311yescharacteristic
404#385—21no—
405#384C22×C4311yescharacteristic
406#380—21no—
407#380C22×C4311yescharacteristic
408#380C22×C4311yescharacteristic
409C4×C22⋊C4—21no—
410C4×C22⋊C4C22×C4311yescharacteristic
411#340C22×C4311yescharacteristic
412#340C22×C4311yescharacteristic
413#340C22×C4311yescharacteristic
414#340C22×C4311yescharacteristic
415#336C22×C4311yescharacteristic
416#336C22×C4311yescharacteristic
417C43#2596711yescharacteristic, direct product factor, Sylow
418C2×#41—22no—
419C2×#41—22no—
420C2×#41—22no—
421C2×#41—41no—
422C2×#41—41no—
423C2×#41Q8×C4314yescomplemented
424C22×Q8—21no—
425C22×Q8C23×C4311yescharacteristic
426C22×D4—21no—
427C22×D4C23×C4311yescharacteristic
428C23×C4—21no—
429C23×C4—21no—
430C23×C4C23×C4311yescharacteristic
431C2×M16—22no—
432C2×M16—22no—
433C2×M16—41no—
434C22×C8C23×C4311yescharacteristic
435C22×C8C23×C4311yescharacteristic
436C22×C8C23×C4311yescharacteristic
437C22×C8C23×C4311yescharacteristic
438C4⋊Q8—22no—
439C4⋊Q8—41no—
440C22⋊Q8—44no—
441C4×Q8—22no—
442C4×Q8—22no—
443C4×Q8—41no—
444C4×Q8—41no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—41no—
455C2×C4⋊C4C23×C4311yescharacteristic
456C2×C4⋊C4C23×C4311yescharacteristic
457C2×C4⋊C4C23×C4311yescharacteristic
458C2×C4⋊C4C23×C4311yescharacteristic
459C2×C4⋊C4C23×C4311yescharacteristic
460C2×C4⋊C4C23×C4311yescharacteristic
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4D4×C4311yescharacteristic
468C2×C22⋊C4D4×C4311yescharacteristic
469C2×C42—21no—
470C2×C42—21no—
471C2×C42C23×C4311yescharacteristic
472C2×C42C23×C4311yescharacteristic
473#107—41no—
474#106—22no—
475#106—22no—
476#106—41no—
477C4⋊C8—22no—
478C4⋊C8—41no—
479#103—22no—
480#103—22no—
481#103—22no—
482#103D4×C4314yes—
483#102—22no—
484#102—22no—
485#102—41no—
486#102—41no—
487C22⋊C8—22no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95D4×C4311yescharacteristic
493#95D4×C4311yescharacteristic
494C24—21no—
495C24C2×D4×C4311yescharacteristic
496#41—28no—
497#41—44no—
498#41—44no—
499#41—44no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—42no—
504C2×Q8—42no—
505C2×Q8—81no—
506C2×Q8C2×D4×C4312yes—
507C2×Q8C2×Q8×C4312yes—
508C2×Q8#41×C4312yes—
509C2×D4—24no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4C2×Q8×C4312yes—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—24no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—81no—
535C22×C4C2×D4×C4311yescharacteristic
536C22×C4C2×D4×C4311yescharacteristic
537C22×C4C2×D4×C4311yescharacteristic
538C22×C4C2×D4×C4311yescharacteristic
539C22×C4C2×D4×C4311yescharacteristic
540C22×C4C2×Q8×C4312yes—
541C22×C4#41×C4312yes—
542C22×C4C24×C4311yescharacteristic
543M16—44no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8C2×D4×C4312yes—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—42no—
568C4⋊C4—42no—
569C4⋊C4—42no—
570C4⋊C4—42no—
571C4⋊C4—42no—
572C4⋊C4—42no—
573C4⋊C4—42no—
574C4⋊C4—81no—
575C4⋊C4C2×D4×C4312yes—
576C22⋊C4—22no—
577C22⋊C4—22no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—81no—
582C22⋊C4—81no—
583C22⋊C4—81no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—42no—
589C42—42no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—22no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23C22⋊Q8×C4312yes—
604C23C22×D4×C4311yescharacteristic
605Q8—22no—
606Q8—22no—
607Q8—22no—
608Q8—84no—
609Q8C22⋊Q8×C4314yescomplemented
610D4—22no—
611D4—22no—
612D4—48no—
613D4—41no—
614D4—41no—
615C2×C4—22no—
616C2×C4—21no—
617C2×C4—22no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—22no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—48no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—84no—
654C2×C4C22⋊Q8×C4312yes—
655C2×C4AGL(1,ℤ/8)×C4312yes—
656C2×C4#137×C4312yes—
657C2×C4C22×D4×C4311yescharacteristic
658C2×C4C22×Q8×C4311yescharacteristic
659C2×C4C2×#41×C4311yescharacteristic
660C2×C4C2×#41×C4311yescharacteristic
661C2×C4H(5,𝔽2)×C4311yescharacteristic
662C2×C4H(5,𝔽2)×C4311yescharacteristic
663C8—22no—
664C8—41no—
665C8—41no—
666C8—41no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22C2×C22⋊Q8×C4311yescharacteristic
682C22D42×C4311yescharacteristic
683C22C43×#54611yescharacteristic
684C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
685C22C2×#137×C4311yescharacteristic
686C22C43×#57711yescharacteristic
687C22C43×#57711yescharacteristic
688C4—22no—
689C4—24no—
690C4—22no—
691C4—22no—
692C4—42no—
693C4—41no—
694C4—41no—
695C4—81no—
696C4—81no—
697C4—81no—
698C4—81no—
699C4—81no—
700C4C2×C22⋊Q8×C4311yescharacteristic
701C4C43×#54311yescharacteristic
702C4C43×#54611yescharacteristic
703C4C43×#55111yescharacteristic
704C2—42no—
705C2—82no—
706C2C43×#243711yescharacteristic
707C2C43×#307911yescharacteristic
708C2C43×#308411yescharacteristic
709C2C43×#326511yescharacteristic
710C2C43×#327811yescharacteristic
711C2C43×#331611yescharacteristic
712C2C43×#333211yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC22×#41×C43C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C4×C22⋊C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#475C2semidirect
3. C43×#2440C2semidirect
5. C43×#2094C2semidirect
6. C43×#2067C2semidirect
7. C43×#2065C2semidirect
8. C43×#2023C2semidirect
9. C43×#1865C2semidirect
10. C43×#1863C2semidirect
11. C43×#1853C2semidirect
12. C43×#1851C2semidirect
13. C43×#1809C2semidirect
14. C43×#1803C2semidirect
66. C2×#41×C43Q8semidirect
252. Q8×C43C22⋊Q8semidirect
310. #25967C43direct (N × H)
348. C2×#475C2×C43semidirect
350. #2440C2×C43semidirect
352. #2094C2×C43semidirect
353. #2067C2×C43semidirect
354. #2065C2×C43semidirect
355. #2023C2×C43semidirect
356. #1865C2×C43semidirect
357. #1863C2×C43semidirect
358. #1853C2×C43semidirect
359. #1851C2×C43semidirect
360. #1809C2×C43semidirect
361. #1803C2×C43semidirect
417. C43#25967direct (N × H)
423. C2×#41Q8×C43semidirect
609. Q8C22⋊Q8×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4752
C2×C43×#4172
C43×#24402
C43×#23412
C43×#20942
C43×#20672
C43×#20652
C43×#20232
C43×#18652
C43×#18632
C43×#18532
C43×#18512
C43×#18092
C43×#18032
C43×#17882
#2596743