Finite Group Databasebeta

← C43×#28902 #24948919

Subgroups — C43×#28902 #24948919

Order 11008.

850 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2512C211yesmaximal, characteristic, complemented
2C43×#2445C211yesmaximal, characteristic, complemented
3C43×#2084C211yesmaximal, characteristic, complemented
4C43×#2065C211yesmaximal, characteristic, complemented
5C43×#2054C211yesmaximal, characteristic, complemented
6C43×#2011C211yesmaximal, characteristic
7C43×#1972C211yesmaximal, characteristic, complemented
8C43×#1972C211yesmaximal, characteristic, complemented
9C43×#1957C211yesmaximal, characteristic, complemented
10C43×#1936C211yesmaximal, characteristic, complemented
11C43×#1934C211yesmaximal, characteristic, complemented
12C43×#1926C211yesmaximal, characteristic, complemented
13C43×#1879C211yesmaximal, characteristic, complemented
14C43×#1771C211yesmaximal, characteristic, complemented
15C43×#1762C211yesmaximal, characteristic, complemented
16C22×D8×C43C2211yescharacteristic
17C22×D8×C43C2211yescharacteristic
18C2×#127×C43C2211yescharacteristic
19C2×#126×C43—21no—
20C2×#123×C43—21no—
21C2×C4×D4×C43C2211yescharacteristic
22C2×#106×C43C2211yescharacteristic
23C2×#106×C43C2211yescharacteristic
24C2×C4⋊C8×C43C2211yescharacteristic
25C2×#102×C43C2211yescharacteristic
26C2×#102×C43C2211yescharacteristic
27C2×#102×C43C2211yescharacteristic
28C2×#102×C43C2211yescharacteristic
29C2×#102×C43C2211yescharacteristic
30C2×#102×C43C2211yescharacteristic
31C2×#102×C43C2211yescharacteristic
32C2×#102×C43C2211yescharacteristic
33C2×#97×C43C2211yescharacteristic
34C2×#97×C43C2211yescharacteristic
35C2×C4×C8×C43C2211yescharacteristic
36C43×#397—21no—
37C43×#396—21no—
38C43×#394—21no—
39C43×#394—21no—
40C43×#390C2211yescharacteristic
41C43×#390C2211yescharacteristic
42C43×#390C2211yescharacteristic
43C43×#390C2211yescharacteristic
44C43×#390C2211yescharacteristic
45C43×#390C2211yescharacteristic
46C43×#389C2211yescharacteristic
47C43×#389C2211yescharacteristic
48C43×#388—21no—
49C43×#386—21no—
50C43×#384C2211yescharacteristic
51C4×C4⋊C4×C43C2211yescharacteristic
52C4×C4⋊C4×C43C2211yescharacteristic
53C43×#340C2211yescharacteristic
54C43×#340C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×D4×C43—21no—
60C22×D4×C43—21no—
61C22×D4×C43C2311yescharacteristic
62C22×D4×C43C2311yescharacteristic
63C22×D4×C43C2311yescharacteristic
64C23×C4×C43—21no—
65C2×D8×C43—22no—
66C2×D8×C43—22no—
67C2×D8×C43—22no—
68C2×D8×C43—41no—
69C2×D8×C43—41no—
70C2×D8×C43—41no—
71C22×C8×C43C2311yescharacteristic
72C22×C8×C43C2311yescharacteristic
73C22×C8×C43C2311yescharacteristic
74C22×C8×C43C2311yescharacteristic
75#127×C43—22no—
76#127×C43—41no—
77#126×C43—44no—
78#123×C43—44no—
79C4×D4×C43—22no—
80C4×D4×C43—41no—
81C2×C4⋊C4×C43—21no—
82C2×C4⋊C4×C43—21no—
83C2×C4⋊C4×C43—21no—
84C2×C4⋊C4×C43—21no—
85C2×C4⋊C4×C43D411yescharacteristic
86C2×C4⋊C4×C43D411yescharacteristic
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×C43—21no—
101C2×C22⋊C4×C43—21no—
102C2×C22⋊C4×C43—21no—
103C2×C22⋊C4×C43—21no—
104C2×C22⋊C4×C43—21no—
105C2×C42×C43—21no—
106C2×C42×C43C2311yescharacteristic
107C2×C42×C43C2311yescharacteristic
108C2×C42×C43C2311yescharacteristic
109#106×C43—41no—
110#106×C43—41no—
111C4⋊C8×C43—22no—
112#102×C43—22no—
113#102×C43—22no—
114#102×C43—22no—
115#102×C43—22no—
116#102×C43—22no—
117#102×C43—41no—
118#102×C43—41no—
119#102×C43—41no—
120#97×C43—22no—
121#97×C43—41no—
122C4×C8×C43—41no—
123#95×C43—21no—
124#95×C43—21no—
125#95×C43—21no—
126#95×C43D411yescharacteristic
127#95×C43D411yescharacteristic
128C24×C43—21no—
129C24×C43—21no—
130C24×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—42no—
149C2×D4×C43—42no—
150C2×D4×C43—42no—
151C2×D4×C43—42no—
152C2×D4×C43—81no—
153C2×D4×C43—81no—
154C2×D4×C43#4112yes—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—42no—
161C22×C4×C43—42no—
162C22×C4×C43—81no—
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43C2×D411yescharacteristic
168C22×C4×C43C2×D411yescharacteristic
169C22×C4×C43C2411yescharacteristic
170D8×C43—44no—
171D8×C43—44no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
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#4112yes—
182C2×C8×C43#4112yes—
183C2×C8×C43#4112yes—
184C4⋊C4×C43—22no—
185C4⋊C4×C43—22no—
186C4⋊C4×C43—21no—
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—42no—
197C4⋊C4×C43—42no—
198C4⋊C4×C43—42no—
199C4⋊C4×C43—81no—
200C22⋊C4×C43—42no—
201C22⋊C4×C43—42no—
202C22⋊C4×C43—42no—
203C22⋊C4×C43—42no—
204C22⋊C4×C43—42no—
205C22⋊C4×C43—42no—
206C22⋊C4×C43—42no—
207C22⋊C4×C43—42no—
208C22⋊C4×C43—81no—
209C22⋊C4×C43—81no—
210C22⋊C4×C43—81no—
211C22⋊C4×C43—81no—
212C22⋊C4×C43—81no—
213C42×C43—21no—
214C42×C43—21no—
215C42×C43—21no—
216C42×C43—21no—
217C42×C43—21no—
218C42×C43—21no—
219C42×C43—42no—
220C23×C43—22no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43—41no—
229C23×C43—41no—
230C23×C43—41no—
231C23×C43—41no—
232C23×C43—41no—
233C23×C43—41no—
234C23×C43—41no—
235C23×C43—41no—
236C23×C43—41no—
237C23×C43—41no—
238C23×C43—41no—
239C23×C43—41no—
240C23×C43—41no—
241C23×C43C22×D411yescharacteristic
242D4×C43—22no—
243D4×C43—22no—
244D4×C43—41no—
245D4×C43—41no—
246D4×C43—41no—
247D4×C43—41no—
248D4×C43—41no—
249D4×C43—41no—
250D4×C43—41no—
251D4×C43—41no—
252D4×C43—41no—
253D4×C43—41no—
254D4×C43—84no—
255D4×C43—84no—
256C2×C4×C43—21no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—21no—
260C2×C4×C43—21no—
261C2×C4×C43—21no—
262C2×C4×C43—21no—
263C2×C4×C43—21no—
264C2×C4×C43—21no—
265C2×C4×C43—21no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
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×C43AGL(1,ℤ/8)12yes—
289C2×C4×C43AGL(1,ℤ/8)12yes—
290C2×C4×C43C2×#4111yescharacteristic
291C2×C4×C43C2×#4111yescharacteristic
292C2×C4×C43C2×#4111yescharacteristic
293C2×C4×C43C2×#4111yescharacteristic
294C2×C4×C43H(5,𝔽2)11yescharacteristic
295C2×C4×C43H(5,𝔽2)11yescharacteristic
296C8×C43—22no—
297C8×C43—22no—
298C8×C43—22no—
299C8×C43—41no—
300#28902C4311yesmaximal, characteristic, direct product factor, Sylow
301C22×C43—42no—
302C22×C43—42no—
303C22×C43—42no—
304C22×C43—81no—
305C22×C43—81no—
306C22×C43—81no—
307C22×C43—81no—
308C22×C43—81no—
309C22×C43—81no—
310C22×C43—81no—
311C22×C43—81no—
312C22×C43—81no—
313C22×C43—81no—
314C22×C43—81no—
315C22×C43—81no—
316C22×C43—81no—
317C22×C43—81no—
318C22×C43—81no—
319C22×C43—81no—
320C22×C43—81no—
321C22×C43—81no—
322C22×C43#53211yescharacteristic
323C22×C43#54611yescharacteristic
324C22×C43#55011yescharacteristic
325C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
326C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
327C22×C43#57611yescharacteristic
328C22×C43#57711yescharacteristic
329C4×C43—22no—
330C4×C43—22no—
331C4×C43—41no—
332C4×C43—41no—
333C4×C43—41no—
334C4×C43—41no—
335C4×C43—81no—
336C4×C43—81no—
337C4×C43—81no—
338C4×C43—81no—
339C4×C43—81no—
340C4×C43#52911yescharacteristic
341C4×C43#53811yescharacteristic
342C4×C43#55111yescharacteristic
343C4×C43#55311yescharacteristic
344#2512C2×C4311yescharacteristic, complemented
345#2445C2×C4311yescharacteristic, complemented
346#2084C2×C4311yescharacteristic, complemented
347#2065C2×C4311yescharacteristic, complemented
348#2054C2×C4311yescharacteristic, complemented
349#2011C2×C4311yescharacteristic
350#1972C2×C4311yescharacteristic, complemented
351#1972C2×C4311yescharacteristic, complemented
352#1957C2×C4311yescharacteristic, complemented
353#1936C2×C4311yescharacteristic, complemented
354#1934C2×C4311yescharacteristic, complemented
355#1926C2×C4311yescharacteristic, complemented
356#1879C2×C4311yescharacteristic, complemented
357#1771C2×C4311yescharacteristic, complemented
358#1762C2×C4311yescharacteristic, complemented
359C2×C43—82no—
360C2×C43—161no—
361C2×C43—161no—
362C2×C43#255411yescharacteristic
363C2×C43#317911yescharacteristic
364C2×C43#318411yescharacteristic
365C2×C43#330611yescharacteristic
366C2×C43#331811yescharacteristic
367C2×C43#339711yescharacteristic
368C2×C43#339911yescharacteristic
369C22×D8C22×C4311yescharacteristic
370C22×D8C22×C4311yescharacteristic
371C2×#127C22×C4311yescharacteristic
372C2×#126—21no—
373C2×#123—21no—
374C2×C4×D4C22×C4311yescharacteristic
375C2×#106C22×C4311yescharacteristic
376C2×#106C22×C4311yescharacteristic
377C2×C4⋊C8C22×C4311yescharacteristic
378C2×#102C22×C4311yescharacteristic
379C2×#102C22×C4311yescharacteristic
380C2×#102C22×C4311yescharacteristic
381C2×#102C22×C4311yescharacteristic
382C2×#102C22×C4311yescharacteristic
383C2×#102C22×C4311yescharacteristic
384C2×#102C22×C4311yescharacteristic
385C2×#102C22×C4311yescharacteristic
386C2×#97C22×C4311yescharacteristic
387C2×#97C22×C4311yescharacteristic
388C2×C4×C8C22×C4311yescharacteristic
389#397—21no—
390#396—21no—
391#394—21no—
392#394—21no—
393#390C22×C4311yescharacteristic
394#390C22×C4311yescharacteristic
395#390C22×C4311yescharacteristic
396#390C22×C4311yescharacteristic
397#390C22×C4311yescharacteristic
398#390C22×C4311yescharacteristic
399#389C22×C4311yescharacteristic
400#389C22×C4311yescharacteristic
401#388—21no—
402#386—21no—
403#384C22×C4311yescharacteristic
404C4×C4⋊C4C22×C4311yescharacteristic
405C4×C4⋊C4C22×C4311yescharacteristic
406#340C22×C4311yescharacteristic
407#340C22×C4311yescharacteristic
408#340C22×C4311yescharacteristic
409#340C22×C4311yescharacteristic
410#336C22×C4311yescharacteristic
411#336C22×C4311yescharacteristic
412C43#2890211yescharacteristic, direct product factor, Sylow
413C22×D4—21no—
414C22×D4—21no—
415C22×D4C23×C4311yescharacteristic
416C22×D4C23×C4311yescharacteristic
417C22×D4C23×C4311yescharacteristic
418C23×C4—21no—
419C2×D8—22no—
420C2×D8—22no—
421C2×D8—22no—
422C2×D8—41no—
423C2×D8—41no—
424C2×D8—41no—
425C22×C8C23×C4311yescharacteristic
426C22×C8C23×C4311yescharacteristic
427C22×C8C23×C4311yescharacteristic
428C22×C8C23×C4311yescharacteristic
429#127—22no—
430#127—41no—
431#126—44no—
432#123—44no—
433C4×D4—22no—
434C4×D4—41no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4D4×C4311yescharacteristic
440C2×C4⋊C4D4×C4311yescharacteristic
441C2×C4⋊C4C23×C4311yescharacteristic
442C2×C4⋊C4C23×C4311yescharacteristic
443C2×C4⋊C4C23×C4311yescharacteristic
444C2×C4⋊C4C23×C4311yescharacteristic
445C2×C4⋊C4C23×C4311yescharacteristic
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⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C42—21no—
460C2×C42C23×C4311yescharacteristic
461C2×C42C23×C4311yescharacteristic
462C2×C42C23×C4311yescharacteristic
463#106—41no—
464#106—41no—
465C4⋊C8—22no—
466#102—22no—
467#102—22no—
468#102—22no—
469#102—22no—
470#102—22no—
471#102—41no—
472#102—41no—
473#102—41no—
474#97—22no—
475#97—41no—
476C4×C8—41no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95D4×C4311yescharacteristic
481#95D4×C4311yescharacteristic
482C24—21no—
483C24—21no—
484C24—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—81no—
507C2×D4—81no—
508C2×D4#41×C4312yes—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—81no—
517C22×C4C2×D4×C4311yescharacteristic
518C22×C4C2×D4×C4311yescharacteristic
519C22×C4C2×D4×C4311yescharacteristic
520C22×C4C2×D4×C4311yescharacteristic
521C22×C4C2×D4×C4311yescharacteristic
522C22×C4C2×D4×C4311yescharacteristic
523C22×C4C24×C4311yescharacteristic
524D8—44no—
525D8—44no—
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#41×C4312yes—
536C2×C8#41×C4312yes—
537C2×C8#41×C4312yes—
538C4⋊C4—22no—
539C4⋊C4—22no—
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—42no—
551C4⋊C4—42no—
552C4⋊C4—42no—
553C4⋊C4—81no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—42no—
557C22⋊C4—42no—
558C22⋊C4—42no—
559C22⋊C4—42no—
560C22⋊C4—42no—
561C22⋊C4—42no—
562C22⋊C4—81no—
563C22⋊C4—81no—
564C22⋊C4—81no—
565C22⋊C4—81no—
566C22⋊C4—81no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—21no—
572C42—21no—
573C42—42no—
574C23—22no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23C22×D4×C4311yescharacteristic
596D4—22no—
597D4—22no—
598D4—41no—
599D4—41no—
600D4—41no—
601D4—41no—
602D4—41no—
603D4—41no—
604D4—41no—
605D4—41no—
606D4—41no—
607D4—41no—
608D4—84no—
609D4—84no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
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—84no—
642C2×C4AGL(1,ℤ/8)×C4312yes—
643C2×C4AGL(1,ℤ/8)×C4312yes—
644C2×C4C2×#41×C4311yescharacteristic
645C2×C4C2×#41×C4311yescharacteristic
646C2×C4C2×#41×C4311yescharacteristic
647C2×C4C2×#41×C4311yescharacteristic
648C2×C4H(5,𝔽2)×C4311yescharacteristic
649C2×C4H(5,𝔽2)×C4311yescharacteristic
650C8—22no—
651C8—22no—
652C8—22no—
653C8—41no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—81no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22—81no—
662C22—81no—
663C22—81no—
664C22—81no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22C43×#53211yescharacteristic
676C22C43×#54611yescharacteristic
677C22C43×#55011yescharacteristic
678C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
679C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
680C22C43×#57611yescharacteristic
681C22C43×#57711yescharacteristic
682C4—22no—
683C4—22no—
684C4—41no—
685C4—41no—
686C4—41no—
687C4—41no—
688C4—81no—
689C4—81no—
690C4—81no—
691C4—81no—
692C4—81no—
693C4C43×#52911yescharacteristic
694C4C43×#53811yescharacteristic
695C4C43×#55111yescharacteristic
696C4C43×#55311yescharacteristic
697C2—82no—
698C2—161no—
699C2—161no—
700C2C43×#255411yescharacteristic
701C2C43×#317911yescharacteristic
702C2C43×#318411yescharacteristic
703C2C43×#330611yescharacteristic
704C2C43×#331811yescharacteristic
705C2C43×#339711yescharacteristic
706C2C43×#339911yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC43×#2011C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C4×C4⋊C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#2512C2semidirect
2. C43×#2445C2semidirect
3. C43×#2084C2semidirect
4. C43×#2065C2semidirect
5. C43×#2054C2semidirect
7. C43×#1972C2semidirect
8. C43×#1972C2semidirect
9. C43×#1957C2semidirect
10. C43×#1936C2semidirect
11. C43×#1934C2semidirect
12. C43×#1926C2semidirect
13. C43×#1879C2semidirect
14. C43×#1771C2semidirect
15. C43×#1762C2semidirect
300. #28902C43direct (N × H)
344. #2512C2×C43semidirect
345. #2445C2×C43semidirect
346. #2084C2×C43semidirect
347. #2065C2×C43semidirect
348. #2054C2×C43semidirect
350. #1972C2×C43semidirect
351. #1972C2×C43semidirect
352. #1957C2×C43semidirect
353. #1936C2×C43semidirect
354. #1934C2×C43semidirect
355. #1926C2×C43semidirect
356. #1879C2×C43semidirect
357. #1771C2×C43semidirect
358. #1762C2×C43semidirect
412. C43#28902direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#25122
C43×#24452
C43×#20842
C43×#20652
C43×#20542
C43×#20112
C43×#19722
C43×#19572
C43×#19362
C43×#19342
C43×#19262
C43×#18792
C43×#17712
C43×#17622
#2890243