Finite Group Databasebeta

← C43×#24974 #24944991

Subgroups — C43×#24974 #24944991

Order 11008.

840 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2535C211yesmaximal, characteristic
2C43×#2352C211yesmaximal, characteristic, complemented
3C43×#2077C211yesmaximal, characteristic, complemented
4C43×#2076C211yesmaximal, characteristic, complemented
5C43×#2034C211yesmaximal, characteristic, complemented
6C43×#2033C211yesmaximal, characteristic, complemented
7C43×#1954C211yesmaximal, characteristic, complemented
8C43×#1949C211yesmaximal, characteristic, complemented
9C43×#1875C211yesmaximal, characteristic, complemented
10C43×#1874C211yesmaximal, characteristic, complemented
11C43×#1835C211yesmaximal, characteristic, complemented
12C43×#1825C211yesmaximal, characteristic, complemented
13C43×#1823C211yesmaximal, characteristic, complemented
14C43×#1804C211yesmaximal, characteristic, complemented
15C4×#102×C43C211yesmaximal, characteristic, complemented
16C2×#121×C43C2211yescharacteristic
17C2×#121×C43C2211yescharacteristic
18C2×C4×D4×C43C2211yescharacteristic
19C2×C4×D4×C43C2211yescharacteristic
20C2×#117×C43C2211yescharacteristic
21C22×C4⋊C4×C43C2211yescharacteristic
22C2×#107×C43C2211yescharacteristic
23C2×#106×C43C2211yescharacteristic
24C2×C4⋊C8×C43C2211yescharacteristic
25C2×#102×C43C2211yescharacteristic
26C2×#102×C43C2211yescharacteristic
27C2×#102×C43C2211yescharacteristic
28C2×#102×C43C2211yescharacteristic
29C2×C22⋊C8×C43C2211yescharacteristic
30C2×C22⋊C8×C43C2211yescharacteristic
31C2×C22⋊C8×C43C2211yescharacteristic
32C2×C22⋊C8×C43C2211yescharacteristic
33C2×C4×C8×C43C2211yescharacteristic
34C43×#397—21no—
35C43×#392—21no—
36C43×#388—21no—
37C43×#387—21no—
38C43×#386—21no—
39C43×#386—21no—
40C43×#386—21no—
41C43×#382C2211yescharacteristic
42C43×#382C2211yescharacteristic
43C43×#380C2211yescharacteristic
44C43×#380C2211yescharacteristic
45C43×#380C2211yescharacteristic
46C43×#380C2211yescharacteristic
47C4×C4⋊C4×C43C2211yescharacteristic
48C4×C22⋊C4×C43—21no—
49C43×#340C2211yescharacteristic
50C43×#340C2211yescharacteristic
51C43×#340C2211yescharacteristic
52C43×#340C2211yescharacteristic
53C43×#340C2211yescharacteristic
54C43×#340C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×D4×C43—21no—
60C22×D4×C43—21no—
61C22×D4×C43D411yescharacteristic
62C22×D4×C43C2311yescharacteristic
63C23×C4×C43—21no—
64C23×C4×C43—21no—
65C23×C4×C43C2311yescharacteristic
66C23×C4×C43C2311yescharacteristic
67C22×C8×C43C2311yescharacteristic
68C22×C8×C43C2311yescharacteristic
69C22×C8×C43C2311yescharacteristic
70C22×C8×C43C2311yescharacteristic
71#121×C43—22no—
72#121×C43—22no—
73#121×C43—41no—
74#121×C43—41no—
75C4×D4×C43—22no—
76C4×D4×C43—22no—
77C4×D4×C43—22no—
78C4×D4×C43—22no—
79#117×C43—22no—
80#117×C43—41no—
81C2×C4⋊C4×C43—22no—
82C2×C4⋊C4×C43—21no—
83C2×C4⋊C4×C43—41no—
84C2×C4⋊C4×C43D411yescharacteristic
85C2×C4⋊C4×C43C2311yescharacteristic
86C2×C4⋊C4×C43C2311yescharacteristic
87C2×C4⋊C4×C43C2311yescharacteristic
88C2×C4⋊C4×C43C2311yescharacteristic
89C2×C4⋊C4×C43C2311yescharacteristic
90C2×C4⋊C4×C43C2311yescharacteristic
91C2×C4⋊C4×C43C2311yescharacteristic
92C2×C22⋊C4×C43—21no—
93C2×C22⋊C4×C43—21no—
94C2×C22⋊C4×C43—21no—
95C2×C22⋊C4×C43—21no—
96C2×C22⋊C4×C43—21no—
97C2×C22⋊C4×C43—21no—
98C2×C22⋊C4×C43—21no—
99C2×C22⋊C4×C43—21no—
100C2×C22⋊C4×C43D411yescharacteristic
101C2×C22⋊C4×C43D411yescharacteristic
102C2×C42×C43—21no—
103C2×C42×C43—21no—
104C2×C42×C43C2311yescharacteristic
105#107×C43—41no—
106#106×C43—41no—
107C4⋊C8×C43—22no—
108#102×C43—22no—
109#102×C43—22no—
110#102×C43—41no—
111#102×C43—41no—
112C22⋊C8×C43—41no—
113C22⋊C8×C43—41no—
114C22⋊C8×C43—41no—
115C22⋊C8×C43—41no—
116C4×C8×C43—22no—
117#95×C43—21no—
118#95×C43—21no—
119#95×C43—21no—
120#95×C43—21no—
121#95×C43—21no—
122#95×C43—21no—
123#95×C43—21no—
124#95×C43—21no—
125#95×C43—21no—
126C24×C43—21no—
127C24×C43C2×D411yescharacteristic
128C24×C43C2×D411yescharacteristic
129C2×D4×C43—22no—
130C2×D4×C43—21no—
131C2×D4×C43—22no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—41no—
137C2×D4×C43—42no—
138C2×D4×C43—42no—
139C2×D4×C43—42no—
140C2×D4×C43—42no—
141C2×D4×C43—81no—
142C2×D4×C43—81no—
143C2×D4×C43#4112yes—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—42no—
164C22×C4×C43—42no—
165C22×C4×C43—42no—
166C22×C4×C43—81no—
167C22×C4×C43—81no—
168C22×C4×C43—81no—
169C22×C4×C43C2×D411yescharacteristic
170C22×C4×C43C2×D411yescharacteristic
171C22×C4×C43C2×D411yescharacteristic
172C22×C4×C43C2×D411yescharacteristic
173C22×C4×C43C2411yescharacteristic
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C4⋊C4×C43—22no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—42no—
201C4⋊C4×C43#4112yes—
202C22⋊C4×C43—22no—
203C22⋊C4×C43—22no—
204C22⋊C4×C43—42no—
205C22⋊C4×C43—42no—
206C22⋊C4×C43—42no—
207C22⋊C4×C43—42no—
208C22⋊C4×C43—42no—
209C22⋊C4×C43—81no—
210C22⋊C4×C43—81no—
211C22⋊C4×C43—81no—
212C42×C43—42no—
213C42×C43—81no—
214C42×C43#4112yes—
215C42×C43#4112yes—
216C23×C43—21no—
217C23×C43—21no—
218C23×C43—21no—
219C23×C43—21no—
220C23×C43—21no—
221C23×C43—21no—
222C23×C43—21no—
223C23×C43—21no—
224C23×C43—22no—
225C23×C43—21no—
226C23×C43—21no—
227C23×C43—21no—
228C23×C43—21no—
229C23×C43—21no—
230C23×C43—41no—
231C23×C43—41no—
232C23×C43—41no—
233C23×C43—41no—
234C23×C43—41no—
235C23×C43—41no—
236C23×C43#13512yes—
237C23×C43C22×D411yescharacteristic
238D4×C43—22no—
239D4×C43—22no—
240D4×C43—44no—
241D4×C43—41no—
242D4×C43—41no—
243D4×C43—84no—
244D4×C43—84no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—22no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43—41no—
268C2×C4×C43—41no—
269C2×C4×C43—41no—
270C2×C4×C43—41no—
271C2×C4×C43—41no—
272C2×C4×C43—41no—
273C2×C4×C43—41no—
274C2×C4×C43—41no—
275C2×C4×C43—41no—
276C2×C4×C43—41no—
277C2×C4×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—84no—
285C2×C4×C43—84no—
286C2×C4×C43#12312yes—
287C2×C4×C43#12312yes—
288C2×C4×C43C2×#4111yescharacteristic
289C2×C4×C43C2×#4111yescharacteristic
290C2×C4×C43C2×#4111yescharacteristic
291C2×C4×C43C2×#4111yescharacteristic
292C2×C4×C43H(5,𝔽2)11yescharacteristic
293C2×C4×C43H(5,𝔽2)11yescharacteristic
294C8×C43—41no—
295C8×C43—41no—
296C8×C43—41no—
297C8×C43—41no—
298#24974C4311yesmaximal, characteristic, direct product factor, Sylow
299C22×C43—22no—
300C22×C43—22no—
301C22×C43—22no—
302C22×C43—41no—
303C22×C43—41no—
304C22×C43—41no—
305C22×C43—41no—
306C22×C43—41no—
307C22×C43—41no—
308C22×C43—41no—
309C22×C43—42no—
310C22×C43—41no—
311C22×C43—42no—
312C22×C43—41no—
313C22×C43—41no—
314C22×C43—42no—
315C22×C43—41no—
316C22×C43—81no—
317C22×C43—81no—
318C22×C43—81no—
319C22×C43—81no—
320C22×C43C2×#12311yescharacteristic
321C22×C43#54611yescharacteristic
322C22×C43#54611yescharacteristic
323C22×C43C2×#13511yescharacteristic
324C22×C43#57511yescharacteristic
325C22×C43#57611yescharacteristic
326C22×C43#57711yescharacteristic
327C4×C43—22no—
328C4×C43—22no—
329C4×C43—41no—
330C4×C43—41no—
331C4×C43—42no—
332C4×C43—81no—
333C4×C43—81no—
334C4×C43—81no—
335C4×C43—81no—
336C4×C43—81no—
337C4×C43—81no—
338C4×C43#52911yescharacteristic
339C4×C43#54011yescharacteristic
340C4×C43#55311yescharacteristic
341C4×C43#55511yescharacteristic
342#2535C2×C4311yescharacteristic
343#2352C2×C4311yescharacteristic, complemented
344#2077C2×C4311yescharacteristic, complemented
345#2076C2×C4311yescharacteristic, complemented
346#2034C2×C4311yescharacteristic, complemented
347#2033C2×C4311yescharacteristic, complemented
348#1954C2×C4311yescharacteristic, complemented
349#1949C2×C4311yescharacteristic, complemented
350#1875C2×C4311yescharacteristic, complemented
351#1874C2×C4311yescharacteristic, complemented
352#1835C2×C4311yescharacteristic, complemented
353#1825C2×C4311yescharacteristic, complemented
354#1823C2×C4311yescharacteristic, complemented
355#1804C2×C4311yescharacteristic, complemented
356C4×#102C2×C4311yescharacteristic, complemented
357C2×C43—42no—
358C2×C43—81no—
359C2×C43—82no—
360C2×C43#242011yescharacteristic
361C2×C43#309111yescharacteristic
362C2×C43#309611yescharacteristic
363C2×C43#329611yescharacteristic
364C2×C43#329711yescharacteristic
365C2×C43#332211yescharacteristic
366C2×C43#332611yescharacteristic
367C2×#121C22×C4311yescharacteristic
368C2×#121C22×C4311yescharacteristic
369C2×C4×D4C22×C4311yescharacteristic
370C2×C4×D4C22×C4311yescharacteristic
371C2×#117C22×C4311yescharacteristic
372C22×C4⋊C4C22×C4311yescharacteristic
373C2×#107C22×C4311yescharacteristic
374C2×#106C22×C4311yescharacteristic
375C2×C4⋊C8C22×C4311yescharacteristic
376C2×#102C22×C4311yescharacteristic
377C2×#102C22×C4311yescharacteristic
378C2×#102C22×C4311yescharacteristic
379C2×#102C22×C4311yescharacteristic
380C2×C22⋊C8C22×C4311yescharacteristic
381C2×C22⋊C8C22×C4311yescharacteristic
382C2×C22⋊C8C22×C4311yescharacteristic
383C2×C22⋊C8C22×C4311yescharacteristic
384C2×C4×C8C22×C4311yescharacteristic
385#397—21no—
386#392—21no—
387#388—21no—
388#387—21no—
389#386—21no—
390#386—21no—
391#386—21no—
392#382C22×C4311yescharacteristic
393#382C22×C4311yescharacteristic
394#380C22×C4311yescharacteristic
395#380C22×C4311yescharacteristic
396#380C22×C4311yescharacteristic
397#380C22×C4311yescharacteristic
398C4×C4⋊C4C22×C4311yescharacteristic
399C4×C22⋊C4—21no—
400#340C22×C4311yescharacteristic
401#340C22×C4311yescharacteristic
402#340C22×C4311yescharacteristic
403#340C22×C4311yescharacteristic
404#340C22×C4311yescharacteristic
405#340C22×C4311yescharacteristic
406#340C22×C4311yescharacteristic
407#340C22×C4311yescharacteristic
408#340C22×C4311yescharacteristic
409#340C22×C4311yescharacteristic
410C43#2497411yescharacteristic, direct product factor, Sylow
411C22×D4—21no—
412C22×D4—21no—
413C22×D4D4×C4311yescharacteristic
414C22×D4C23×C4311yescharacteristic
415C23×C4—21no—
416C23×C4—21no—
417C23×C4C23×C4311yescharacteristic
418C23×C4C23×C4311yescharacteristic
419C22×C8C23×C4311yescharacteristic
420C22×C8C23×C4311yescharacteristic
421C22×C8C23×C4311yescharacteristic
422C22×C8C23×C4311yescharacteristic
423#121—22no—
424#121—22no—
425#121—41no—
426#121—41no—
427C4×D4—22no—
428C4×D4—22no—
429C4×D4—22no—
430C4×D4—22no—
431#117—22no—
432#117—41no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—41no—
436C2×C4⋊C4D4×C4311yescharacteristic
437C2×C4⋊C4C23×C4311yescharacteristic
438C2×C4⋊C4C23×C4311yescharacteristic
439C2×C4⋊C4C23×C4311yescharacteristic
440C2×C4⋊C4C23×C4311yescharacteristic
441C2×C4⋊C4C23×C4311yescharacteristic
442C2×C4⋊C4C23×C4311yescharacteristic
443C2×C4⋊C4C23×C4311yescharacteristic
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4D4×C4311yescharacteristic
453C2×C22⋊C4D4×C4311yescharacteristic
454C2×C42—21no—
455C2×C42—21no—
456C2×C42C23×C4311yescharacteristic
457#107—41no—
458#106—41no—
459C4⋊C8—22no—
460#102—22no—
461#102—22no—
462#102—41no—
463#102—41no—
464C22⋊C8—41no—
465C22⋊C8—41no—
466C22⋊C8—41no—
467C22⋊C8—41no—
468C4×C8—22no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478C24—21no—
479C24C2×D4×C4311yescharacteristic
480C24C2×D4×C4311yescharacteristic
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—41no—
489C2×D4—42no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4—42no—
493C2×D4—81no—
494C2×D4—81no—
495C2×D4#41×C4312yes—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—81no—
519C22×C4—81no—
520C22×C4—81no—
521C22×C4C2×D4×C4311yescharacteristic
522C22×C4C2×D4×C4311yescharacteristic
523C22×C4C2×D4×C4311yescharacteristic
524C22×C4C2×D4×C4311yescharacteristic
525C22×C4C24×C4311yescharacteristic
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C4⋊C4—22no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—42no—
553C4⋊C4#41×C4312yes—
554C22⋊C4—22no—
555C22⋊C4—22no—
556C22⋊C4—42no—
557C22⋊C4—42no—
558C22⋊C4—42no—
559C22⋊C4—42no—
560C22⋊C4—42no—
561C22⋊C4—81no—
562C22⋊C4—81no—
563C22⋊C4—81no—
564C42—42no—
565C42—81no—
566C42#41×C4312yes—
567C42#41×C4312yes—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—22no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23#135×C4312yes—
589C23C22×D4×C4311yescharacteristic
590D4—22no—
591D4—22no—
592D4—44no—
593D4—41no—
594D4—41no—
595D4—84no—
596D4—84no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—84no—
637C2×C4—84no—
638C2×C4#123×C4312yes—
639C2×C4#123×C4312yes—
640C2×C4C2×#41×C4311yescharacteristic
641C2×C4C2×#41×C4311yescharacteristic
642C2×C4C2×#41×C4311yescharacteristic
643C2×C4C2×#41×C4311yescharacteristic
644C2×C4H(5,𝔽2)×C4311yescharacteristic
645C2×C4H(5,𝔽2)×C4311yescharacteristic
646C8—41no—
647C8—41no—
648C8—41no—
649C8—41no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—41no—
654C22—41no—
655C22—41no—
656C22—41no—
657C22—41no—
658C22—41no—
659C22—41no—
660C22—42no—
661C22—42no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—42no—
666C22—41no—
667C22—81no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22C2×#123×C4311yescharacteristic
672C22C43×#54611yescharacteristic
673C22C43×#54611yescharacteristic
674C22C2×#135×C4311yescharacteristic
675C22C43×#57511yescharacteristic
676C22C43×#57611yescharacteristic
677C22C43×#57711yescharacteristic
678C4—22no—
679C4—22no—
680C4—41no—
681C4—41no—
682C4—42no—
683C4—81no—
684C4—81no—
685C4—81no—
686C4—81no—
687C4—81no—
688C4—81no—
689C4C43×#52911yescharacteristic
690C4C43×#54011yescharacteristic
691C4C43×#55311yescharacteristic
692C4C43×#55511yescharacteristic
693C2—42no—
694C2—81no—
695C2—82no—
696C2C43×#242011yescharacteristic
697C2C43×#309111yescharacteristic
698C2C43×#309611yescharacteristic
699C2C43×#329611yescharacteristic
700C2C43×#329711yescharacteristic
701C2C43×#332211yescharacteristic
702C2C43×#332611yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC43×#2535C2
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
2. C43×#2352C2semidirect
3. C43×#2077C2semidirect
4. C43×#2076C2semidirect
5. C43×#2034C2semidirect
6. C43×#2033C2semidirect
7. C43×#1954C2semidirect
8. C43×#1949C2semidirect
9. C43×#1875C2semidirect
10. C43×#1874C2semidirect
11. C43×#1835C2semidirect
12. C43×#1825C2semidirect
13. C43×#1823C2semidirect
14. C43×#1804C2semidirect
15. C4×#102×C43C2semidirect
298. #24974C43direct (N × H)
343. #2352C2×C43semidirect
344. #2077C2×C43semidirect
345. #2076C2×C43semidirect
346. #2034C2×C43semidirect
347. #2033C2×C43semidirect
348. #1954C2×C43semidirect
349. #1949C2×C43semidirect
350. #1875C2×C43semidirect
351. #1874C2×C43semidirect
352. #1835C2×C43semidirect
353. #1825C2×C43semidirect
354. #1823C2×C43semidirect
355. #1804C2×C43semidirect
356. C4×#102C2×C43semidirect
410. C43#24974direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#25352
C43×#23522
C43×#20772
C43×#20762
C43×#20342
C43×#20332
C43×#19542
C43×#19492
C43×#18752
C43×#18742
C43×#18352
C43×#18252
C43×#18232
C43×#18042
C4×#102×C432
#2497443