Finite Group Databasebeta

← C43×#24981 #24944998

Subgroups — C43×#24981 #24944998

Order 11008.

862 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2537C211yesmaximal, characteristic
2C43×#2352C211yesmaximal, characteristic, complemented
3C43×#2076C211yesmaximal, characteristic, complemented
4C43×#2075C211yesmaximal, characteristic, complemented
5C43×#2033C211yesmaximal, characteristic, complemented
6C43×#2033C211yesmaximal, characteristic, complemented
7C43×#1955C211yesmaximal, characteristic, complemented
8C43×#1947C211yesmaximal, characteristic, complemented
9C43×#1875C211yesmaximal, characteristic, complemented
10C43×#1874C211yesmaximal, characteristic, complemented
11C43×#1836C211yesmaximal, characteristic, complemented
12C43×#1825C211yesmaximal, characteristic, complemented
13C43×#1824C211yesmaximal, characteristic, complemented
14C43×#1804C211yesmaximal, characteristic, complemented
15C43×#1762C211yesmaximal, characteristic, complemented
16C2×#121×C43—21no—
17C2×#121×C43C2211yescharacteristic
18C2×#121×C43C2211yescharacteristic
19C2×C4×D4×C43C2211yescharacteristic
20C2×C4×D4×C43C2211yescharacteristic
21C2×#117×C43C2211yescharacteristic
22C22×C4⋊C4×C43C2211yescharacteristic
23C2×#107×C43C2211yescharacteristic
24C2×#107×C43C2211yescharacteristic
25C2×C4⋊C8×C43C2211yescharacteristic
26C2×#102×C43C2211yescharacteristic
27C2×#102×C43C2211yescharacteristic
28C2×#102×C43C2211yescharacteristic
29C2×#102×C43C2211yescharacteristic
30C2×C22⋊C8×C43C2211yescharacteristic
31C2×C22⋊C8×C43C2211yescharacteristic
32C2×C22⋊C8×C43C2211yescharacteristic
33C2×C22⋊C8×C43C2211yescharacteristic
34C2×#97×C43C2211yescharacteristic
35C43×#394—21no—
36C43×#394—21no—
37C43×#388—21no—
38C43×#387—21no—
39C43×#386—21no—
40C43×#384C2211yescharacteristic
41C43×#382C2211yescharacteristic
42C43×#380—21no—
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—
75#121×C43—44no—
76C4×D4×C43—22no—
77C4×D4×C43—22no—
78C4×D4×C43—22no—
79C4×D4×C43—22no—
80#117×C43—22no—
81#117×C43—41no—
82C2×C4⋊C4×C43—22no—
83C2×C4⋊C4×C43—21no—
84C2×C4⋊C4×C43—21no—
85C2×C4⋊C4×C43—21no—
86C2×C4⋊C4×C43—41no—
87C2×C4⋊C4×C43D411yescharacteristic
88C2×C4⋊C4×C43C2311yescharacteristic
89C2×C4⋊C4×C43C2311yescharacteristic
90C2×C4⋊C4×C43C2311yescharacteristic
91C2×C4⋊C4×C43C2311yescharacteristic
92C2×C4⋊C4×C43C2311yescharacteristic
93C2×C4⋊C4×C43C2311yescharacteristic
94C2×C4⋊C4×C43C2311yescharacteristic
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×C43—21no—
101C2×C22⋊C4×C43—21no—
102C2×C22⋊C4×C43—21no—
103C2×C22⋊C4×C43D411yescharacteristic
104C2×C22⋊C4×C43D411yescharacteristic
105C2×C42×C43—21no—
106C2×C42×C43—21no—
107C2×C42×C43C2311yescharacteristic
108#107×C43—41no—
109#107×C43—41no—
110C4⋊C8×C43—22no—
111#102×C43—22no—
112#102×C43—22no—
113#102×C43—41no—
114#102×C43—41no—
115C22⋊C8×C43—41no—
116C22⋊C8×C43—41no—
117C22⋊C8×C43—41no—
118C22⋊C8×C43—41no—
119#97×C43—22no—
120#95×C43—21no—
121#95×C43—21no—
122#95×C43—21no—
123#95×C43—21no—
124#95×C43—21no—
125#95×C43—21no—
126#95×C43—21no—
127C24×C43—21no—
128C24×C43C2×D411yescharacteristic
129C24×C43C2×D411yescharacteristic
130C2×D4×C43—22no—
131C2×D4×C43—21no—
132C2×D4×C43—22no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—41no—
138C2×D4×C43—42no—
139C2×D4×C43—42no—
140C2×D4×C43—42no—
141C2×D4×C43—42no—
142C2×D4×C43—81no—
143C2×D4×C43—81no—
144C2×D4×C43#4112yes—
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—21no—
164C22×C4×C43—42no—
165C22×C4×C43—42no—
166C22×C4×C43—42no—
167C22×C4×C43—42no—
168C22×C4×C43—42no—
169C22×C4×C43—81no—
170C22×C4×C43C2×D411yescharacteristic
171C22×C4×C43C2×D411yescharacteristic
172C22×C4×C43C2×D411yescharacteristic
173C22×C4×C43C2×D411yescharacteristic
174C22×C4×C43C2411yescharacteristic
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—
186C2×C8×C43—21no—
187C4⋊C4×C43—22no—
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—21no—
201C4⋊C4×C43—42no—
202C4⋊C4×C43—42no—
203C4⋊C4×C43—81no—
204C4⋊C4×C43#4112yes—
205C22⋊C4×C43—22no—
206C22⋊C4×C43—22no—
207C22⋊C4×C43—42no—
208C22⋊C4×C43—42no—
209C22⋊C4×C43—42no—
210C22⋊C4×C43—42no—
211C22⋊C4×C43—42no—
212C22⋊C4×C43—42no—
213C22⋊C4×C43—42no—
214C22⋊C4×C43—81no—
215C42×C43—42no—
216C42×C43—81no—
217C42×C43#4112yes—
218C42×C43#4112yes—
219C23×C43—21no—
220C23×C43—21no—
221C23×C43—21no—
222C23×C43—21no—
223C23×C43—21no—
224C23×C43—21no—
225C23×C43—21no—
226C23×C43—21no—
227C23×C43—22no—
228C23×C43—21no—
229C23×C43—21no—
230C23×C43—21no—
231C23×C43—21no—
232C23×C43—21no—
233C23×C43—41no—
234C23×C43—41no—
235C23×C43—41no—
236C23×C43—41no—
237C23×C43—41no—
238C23×C43—41no—
239C23×C43AGL(1,ℤ/8)12yes—
240C23×C43C22×D411yescharacteristic
241D4×C43—22no—
242D4×C43—22no—
243D4×C43—44no—
244D4×C43—41no—
245D4×C43—41no—
246D4×C43—84no—
247D4×C43—84no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—22no—
256C2×C4×C43—21no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
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—41no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—84no—
288C2×C4×C43—84no—
289C2×C4×C43#12312yes—
290C2×C4×C43#12312yes—
291C2×C4×C43C2×#4111yescharacteristic
292C2×C4×C43C2×#4111yescharacteristic
293C2×C4×C43C2×#4111yescharacteristic
294C2×C4×C43C2×#4111yescharacteristic
295C2×C4×C43H(5,𝔽2)11yescharacteristic
296C2×C4×C43H(5,𝔽2)11yescharacteristic
297C8×C43—41no—
298C8×C43—41no—
299C8×C43—41no—
300C8×C43—41no—
301#24981C4311yesmaximal, characteristic, direct product factor, Sylow
302C22×C43—22no—
303C22×C43—22no—
304C22×C43—22no—
305C22×C43—41no—
306C22×C43—41no—
307C22×C43—41no—
308C22×C43—41no—
309C22×C43—41no—
310C22×C43—41no—
311C22×C43—41no—
312C22×C43—42no—
313C22×C43—41no—
314C22×C43—41no—
315C22×C43—42no—
316C22×C43—41no—
317C22×C43—42no—
318C22×C43—41no—
319C22×C43—81no—
320C22×C43—81no—
321C22×C43—81no—
322C22×C43—81no—
323C22×C43C2×#12311yescharacteristic
324C22×C43#54611yescharacteristic
325C22×C43#54611yescharacteristic
326C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
327C22×C43#57511yescharacteristic
328C22×C43#57611yescharacteristic
329C22×C43#57811yescharacteristic
330C4×C43—22no—
331C4×C43—22no—
332C4×C43—41no—
333C4×C43—41no—
334C4×C43—42no—
335C4×C43—81no—
336C4×C43—81no—
337C4×C43—81no—
338C4×C43—81no—
339C4×C43—81no—
340C4×C43—81no—
341C4×C43#52911yescharacteristic
342C4×C43#54011yescharacteristic
343C4×C43#55311yescharacteristic
344C4×C43#55511yescharacteristic
345#2537C2×C4311yescharacteristic
346#2352C2×C4311yescharacteristic, complemented
347#2076C2×C4311yescharacteristic, complemented
348#2075C2×C4311yescharacteristic, complemented
349#2033C2×C4311yescharacteristic, complemented
350#2033C2×C4311yescharacteristic, complemented
351#1955C2×C4311yescharacteristic, complemented
352#1947C2×C4311yescharacteristic, complemented
353#1875C2×C4311yescharacteristic, complemented
354#1874C2×C4311yescharacteristic, complemented
355#1836C2×C4311yescharacteristic, complemented
356#1825C2×C4311yescharacteristic, complemented
357#1824C2×C4311yescharacteristic, complemented
358#1804C2×C4311yescharacteristic, complemented
359#1762C2×C4311yescharacteristic, complemented
360C2×C43—42no—
361C2×C43—81no—
362C2×C43—82no—
363C2×C43#242011yescharacteristic
364C2×C43#309411yescharacteristic
365C2×C43#309811yescharacteristic
366C2×C43#330811yescharacteristic
367C2×C43#331511yescharacteristic
368C2×C43#331811yescharacteristic
369C2×C43#331911yescharacteristic
370C2×#121—21no—
371C2×#121C22×C4311yescharacteristic
372C2×#121C22×C4311yescharacteristic
373C2×C4×D4C22×C4311yescharacteristic
374C2×C4×D4C22×C4311yescharacteristic
375C2×#117C22×C4311yescharacteristic
376C22×C4⋊C4C22×C4311yescharacteristic
377C2×#107C22×C4311yescharacteristic
378C2×#107C22×C4311yescharacteristic
379C2×C4⋊C8C22×C4311yescharacteristic
380C2×#102C22×C4311yescharacteristic
381C2×#102C22×C4311yescharacteristic
382C2×#102C22×C4311yescharacteristic
383C2×#102C22×C4311yescharacteristic
384C2×C22⋊C8C22×C4311yescharacteristic
385C2×C22⋊C8C22×C4311yescharacteristic
386C2×C22⋊C8C22×C4311yescharacteristic
387C2×C22⋊C8C22×C4311yescharacteristic
388C2×#97C22×C4311yescharacteristic
389#394—21no—
390#394—21no—
391#388—21no—
392#387—21no—
393#386—21no—
394#384C22×C4311yescharacteristic
395#382C22×C4311yescharacteristic
396#380—21no—
397#380C22×C4311yescharacteristic
398#380C22×C4311yescharacteristic
399#380C22×C4311yescharacteristic
400#380C22×C4311yescharacteristic
401C4×C4⋊C4C22×C4311yescharacteristic
402C4×C22⋊C4—21no—
403#340C22×C4311yescharacteristic
404#340C22×C4311yescharacteristic
405#340C22×C4311yescharacteristic
406#340C22×C4311yescharacteristic
407#340C22×C4311yescharacteristic
408#340C22×C4311yescharacteristic
409#340C22×C4311yescharacteristic
410#340C22×C4311yescharacteristic
411#340C22×C4311yescharacteristic
412#340C22×C4311yescharacteristic
413C43#2498111yescharacteristic, direct product factor, Sylow
414C22×D4—21no—
415C22×D4—21no—
416C22×D4D4×C4311yescharacteristic
417C22×D4C23×C4311yescharacteristic
418C23×C4—21no—
419C23×C4—21no—
420C23×C4C23×C4311yescharacteristic
421C23×C4C23×C4311yescharacteristic
422C22×C8C23×C4311yescharacteristic
423C22×C8C23×C4311yescharacteristic
424C22×C8C23×C4311yescharacteristic
425C22×C8C23×C4311yescharacteristic
426#121—22no—
427#121—22no—
428#121—41no—
429#121—41no—
430#121—44no—
431C4×D4—22no—
432C4×D4—22no—
433C4×D4—22no—
434C4×D4—22no—
435#117—22no—
436#117—41no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—41no—
442C2×C4⋊C4D4×C4311yescharacteristic
443C2×C4⋊C4C23×C4311yescharacteristic
444C2×C4⋊C4C23×C4311yescharacteristic
445C2×C4⋊C4C23×C4311yescharacteristic
446C2×C4⋊C4C23×C4311yescharacteristic
447C2×C4⋊C4C23×C4311yescharacteristic
448C2×C4⋊C4C23×C4311yescharacteristic
449C2×C4⋊C4C23×C4311yescharacteristic
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4D4×C4311yescharacteristic
459C2×C22⋊C4D4×C4311yescharacteristic
460C2×C42—21no—
461C2×C42—21no—
462C2×C42C23×C4311yescharacteristic
463#107—41no—
464#107—41no—
465C4⋊C8—22no—
466#102—22no—
467#102—22no—
468#102—41no—
469#102—41no—
470C22⋊C8—41no—
471C22⋊C8—41no—
472C22⋊C8—41no—
473C22⋊C8—41no—
474#97—22no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482C24—21no—
483C24C2×D4×C4311yescharacteristic
484C24C2×D4×C4311yescharacteristic
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—41no—
493C2×D4—42no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4—81no—
498C2×D4—81no—
499C2×D4#41×C4312yes—
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—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—81no—
525C22×C4C2×D4×C4311yescharacteristic
526C22×C4C2×D4×C4311yescharacteristic
527C22×C4C2×D4×C4311yescharacteristic
528C22×C4C2×D4×C4311yescharacteristic
529C22×C4C24×C4311yescharacteristic
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C4⋊C4—22no—
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—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—42no—
557C4⋊C4—42no—
558C4⋊C4—81no—
559C4⋊C4#41×C4312yes—
560C22⋊C4—22no—
561C22⋊C4—22no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—81no—
570C42—42no—
571C42—81no—
572C42#41×C4312yes—
573C42#41×C4312yes—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—22no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23AGL(1,ℤ/8)×C4312yes—
595C23C22×D4×C4311yescharacteristic
596D4—22no—
597D4—22no—
598D4—44no—
599D4—41no—
600D4—41no—
601D4—84no—
602D4—84no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—22no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
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—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—84no—
643C2×C4—84no—
644C2×C4#123×C4312yes—
645C2×C4#123×C4312yes—
646C2×C4C2×#41×C4311yescharacteristic
647C2×C4C2×#41×C4311yescharacteristic
648C2×C4C2×#41×C4311yescharacteristic
649C2×C4C2×#41×C4311yescharacteristic
650C2×C4H(5,𝔽2)×C4311yescharacteristic
651C2×C4H(5,𝔽2)×C4311yescharacteristic
652C8—41no—
653C8—41no—
654C8—41no—
655C8—41no—
656C22—22no—
657C22—22no—
658C22—22no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—42no—
667C22—41no—
668C22—41no—
669C22—42no—
670C22—41no—
671C22—42no—
672C22—41no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22C2×#123×C4311yescharacteristic
678C22C43×#54611yescharacteristic
679C22C43×#54611yescharacteristic
680C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
681C22C43×#57511yescharacteristic
682C22C43×#57611yescharacteristic
683C22C43×#57811yescharacteristic
684C4—22no—
685C4—22no—
686C4—41no—
687C4—41no—
688C4—42no—
689C4—81no—
690C4—81no—
691C4—81no—
692C4—81no—
693C4—81no—
694C4—81no—
695C4C43×#52911yescharacteristic
696C4C43×#54011yescharacteristic
697C4C43×#55311yescharacteristic
698C4C43×#55511yescharacteristic
699C2—42no—
700C2—81no—
701C2—82no—
702C2C43×#242011yescharacteristic
703C2C43×#309411yescharacteristic
704C2C43×#309811yescharacteristic
705C2C43×#330811yescharacteristic
706C2C43×#331511yescharacteristic
707C2C43×#331811yescharacteristic
708C2C43×#331911yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC43×#2537C2
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×#2076C2semidirect
4. C43×#2075C2semidirect
5. C43×#2033C2semidirect
6. C43×#2033C2semidirect
7. C43×#1955C2semidirect
8. C43×#1947C2semidirect
9. C43×#1875C2semidirect
10. C43×#1874C2semidirect
11. C43×#1836C2semidirect
12. C43×#1825C2semidirect
13. C43×#1824C2semidirect
14. C43×#1804C2semidirect
15. C43×#1762C2semidirect
301. #24981C43direct (N × H)
346. #2352C2×C43semidirect
347. #2076C2×C43semidirect
348. #2075C2×C43semidirect
349. #2033C2×C43semidirect
350. #2033C2×C43semidirect
351. #1955C2×C43semidirect
352. #1947C2×C43semidirect
353. #1875C2×C43semidirect
354. #1874C2×C43semidirect
355. #1836C2×C43semidirect
356. #1825C2×C43semidirect
357. #1824C2×C43semidirect
358. #1804C2×C43semidirect
359. #1762C2×C43semidirect
413. C43#24981direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#25372
C43×#23522
C43×#20762
C43×#20752
C43×#20332
C43×#19552
C43×#19472
C43×#18752
C43×#18742
C43×#18362
C43×#18252
C43×#18242
C43×#18042
C43×#17622
#2498143