Finite Group Databasebeta

← C43×#26977 #24946994

Subgroups — C43×#26977 #24946994

Order 11008.

1028 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#466C211yesmaximal, characteristic, complemented
2C2×C43×#442C211yesmaximal, characteristic, complemented
3C43×#2428C211yesmaximal, characteristic, complemented
4C43×#2420C211yesmaximal, characteristic, complemented
5C43×#2085C211yesmaximal, characteristic, complemented
6C43×#2034C211yesmaximal, characteristic, complemented
7C43×#2011C211yesmaximal, characteristic, complemented
8C43×#1999C211yesmaximal, characteristic, complemented
9C43×#1961C211yesmaximal, characteristic, complemented
10C43×#1936C211yesmaximal, characteristic, complemented
11C43×#1936C211yesmaximal, characteristic, complemented
12C43×#1893C211yesmaximal, characteristic, complemented
13C43×#1879C211yesmaximal, characteristic, complemented
14C43×#1862C211yesmaximal, characteristic, complemented
15C43×#1752C211yesmaximal, characteristic, complemented
16C22×D8×C43C2211yescharacteristic
17C22×D8×C43C2211yescharacteristic
18C23×C8×C43C2211yescharacteristic
19C2×#127×C43C2211yescharacteristic
20C2×#121×C43—21no—
21C2×#121×C43C2211yescharacteristic
22C2×#121×C43C2211yescharacteristic
23C2×#121×C43C2211yescharacteristic
24C2×C4×D4×C43C2211yescharacteristic
25C2×C4×D4×C43C2211yescharacteristic
26C43×#466—24no—
27C43×#442—24no—
28C2×#107×C43C2211yescharacteristic
29C2×#106×C43C2211yescharacteristic
30C2×#102×C43C2211yescharacteristic
31C2×#102×C43C2211yescharacteristic
32C2×#102×C43C2211yescharacteristic
33C2×#102×C43C2211yescharacteristic
34C2×#102×C43C2211yescharacteristic
35C2×#102×C43C2211yescharacteristic
36C2×#102×C43C2211yescharacteristic
37C2×#102×C43C2211yescharacteristic
38C2×C22⋊C8×C43C2211yescharacteristic
39C2×#97×C43C2211yescharacteristic
40C2×#97×C43C2211yescharacteristic
41C43×#397—21no—
42C43×#394—21no—
43C43×#394—21no—
44C43×#392—21no—
45C43×#390C2211yescharacteristic
46C43×#390C2211yescharacteristic
47C43×#389C2211yescharacteristic
48C43×#389C2211yescharacteristic
49C43×#386—21no—
50C43×#386—21no—
51C43×#382C2211yescharacteristic
52C43×#381—21no—
53C43×#380C2211yescharacteristic
54C4×C22⋊C4×C43C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×D4×C43—21no—
62C22×D4×C43—21no—
63C22×D4×C43—21no—
64C22×D4×C43—21no—
65C22×D4×C43—21no—
66C22×D4×C43C2311yescharacteristic
67C22×D4×C43C2311yescharacteristic
68C22×D4×C43C2311yescharacteristic
69C23×C4×C43—21no—
70C23×C4×C43—21no—
71C23×C4×C43C2311yescharacteristic
72C2×D8×C43—22no—
73C2×D8×C43—22no—
74C2×D8×C43—22no—
75C2×D8×C43—22no—
76C2×D8×C43—22no—
77C2×D8×C43—41no—
78C22×C8×C43—22no—
79C22×C8×C43—22no—
80C22×C8×C43—41no—
81C22×C8×C43C2311yescharacteristic
82C22×C8×C43C2311yescharacteristic
83C22×C8×C43C2311yescharacteristic
84C22×C8×C43C2311yescharacteristic
85#127×C43—22no—
86#127×C43—41no—
87#121×C43—22no—
88#121×C43—22no—
89#121×C43—22no—
90#121×C43—44no—
91#121×C43—41no—
92#121×C43—41no—
93#121×C43—41no—
94C4×D4×C43—22no—
95C4×D4×C43—22no—
96C4×D4×C43—41no—
97C4×D4×C43—41no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43C2311yescharacteristic
101C2×C4⋊C4×C43C2311yescharacteristic
102C2×C4⋊C4×C43C2311yescharacteristic
103C2×C4⋊C4×C43C2311yescharacteristic
104C2×C4⋊C4×C43C2311yescharacteristic
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×C43—21no—
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43D411yescharacteristic
116C2×C22⋊C4×C43D411yescharacteristic
117C2×C42×C43C2311yescharacteristic
118C2×C42×C43C2311yescharacteristic
119#107×C43—22no—
120#106×C43—22no—
121#102×C43—22no—
122#102×C43—22no—
123#102×C43—22no—
124#102×C43—22no—
125#102×C43—41no—
126#102×C43—41no—
127#102×C43—41no—
128#102×C43D414yescomplemented
129C22⋊C8×C43—22no—
130#97×C43—22no—
131#97×C43—41no—
132#95×C43—21no—
133#95×C43—21no—
134#95×C43—21no—
135#95×C43—21no—
136#95×C43—21no—
137#95×C43D411yescharacteristic
138#95×C43D411yescharacteristic
139C24×C43—21no—
140C24×C43—21no—
141C24×C43—21no—
142C24×C43C2×D411yescharacteristic
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—42no—
160C2×D4×C43—42no—
161C2×D4×C43—42no—
162C2×D4×C43—42no—
163C2×D4×C43—42no—
164C2×D4×C43—42no—
165C2×D4×C43—42no—
166C2×D4×C43—42no—
167C2×D4×C43—42no—
168C2×D4×C43—42no—
169C2×D4×C43—81no—
170C2×D4×C43—81no—
171C2×D4×C43—81no—
172C2×D4×C43—81no—
173C2×D4×C43—81no—
174C2×D4×C43C2×D412yes—
175C2×D4×C43#4112yes—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
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—42no—
188C22×C4×C43—42no—
189C22×C4×C43—42no—
190C22×C4×C43—42no—
191C22×C4×C43—81no—
192C22×C4×C43—81no—
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2411yescharacteristic
199D8×C43—28no—
200D8×C43—44no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—44no—
211C2×C8×C43C2×D412yes—
212C2×C8×C43#4112yes—
213C2×C8×C43#4112yes—
214C4⋊C4×C43—21no—
215C4⋊C4×C43—21no—
216C4⋊C4×C43—21no—
217C4⋊C4×C43—21no—
218C4⋊C4×C43—21no—
219C4⋊C4×C43—21no—
220C4⋊C4×C43—21no—
221C4⋊C4×C43—21no—
222C4⋊C4×C43—21no—
223C4⋊C4×C43—42no—
224C4⋊C4×C43—81no—
225C4⋊C4×C43C2×D412yes—
226C22⋊C4×C43—22no—
227C22⋊C4×C43—41no—
228C22⋊C4×C43—42no—
229C22⋊C4×C43—42no—
230C22⋊C4×C43—42no—
231C22⋊C4×C43—42no—
232C22⋊C4×C43—42no—
233C22⋊C4×C43—42no—
234C22⋊C4×C43—81no—
235C22⋊C4×C43—81no—
236C22⋊C4×C43—81no—
237C22⋊C4×C43—81no—
238C42×C43—21no—
239C42×C43—21no—
240C42×C43—21no—
241C42×C43—21no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—22no—
249C23×C43—22no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43AGL(1,ℤ/8)12yes—
270C23×C43C22×D411yescharacteristic
271D4×C43—22no—
272D4×C43—22no—
273D4×C43—22no—
274D4×C43—22no—
275D4×C43—41no—
276D4×C43—41no—
277D4×C43—41no—
278D4×C43—41no—
279D4×C43—41no—
280D4×C43—41no—
281D4×C43—41no—
282D4×C43—41no—
283D4×C43—84no—
284D4×C43—84no—
285D4×C43—84no—
286D4×C43—84no—
287D4×C43—84no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—22no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43—41no—
307C2×C4×C43—41no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
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—84no—
323C2×C4×C43—84no—
324C2×C4×C43C22×D411yescharacteristic
325C2×C4×C43C2×#4111yescharacteristic
326C2×C4×C43C2×#4111yescharacteristic
327C2×C4×C43C2×#4111yescharacteristic
328C2×C4×C43H(5,𝔽2)11yescharacteristic
329C2×C4×C43H(5,𝔽2)11yescharacteristic
330C8×C43—22no—
331C8×C43—22no—
332C8×C43—22no—
333C8×C43—41no—
334#26977C4311yesmaximal, characteristic, direct product factor, Sylow
335C22×C43—22no—
336C22×C43—22no—
337C22×C43—22no—
338C22×C43—41no—
339C22×C43—41no—
340C22×C43—41no—
341C22×C43—41no—
342C22×C43—42no—
343C22×C43—42no—
344C22×C43—42no—
345C22×C43—42no—
346C22×C43—42no—
347C22×C43—42no—
348C22×C43—81no—
349C22×C43—81no—
350C22×C43—81no—
351C22×C43—81no—
352C22×C43—81no—
353C22×C43—81no—
354C22×C43—81no—
355C22×C43—81no—
356C22×C43—81no—
357C22×C43—81no—
358C22×C43—81no—
359C22×C43—81no—
360C22×C43—81no—
361C22×C43—81no—
362C22×C43—81no—
363C22×C43#53211yescharacteristic
364C22×C43D4211yescharacteristic
365C22×C43#54611yescharacteristic
366C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
367C22×C43#57511yescharacteristic
368C22×C43#57611yescharacteristic
369C22×C43#57611yescharacteristic
370C4×C43—41no—
371C4×C43—41no—
372C4×C43—42no—
373C4×C43—41no—
374C4×C43—41no—
375C4×C43—41no—
376C4×C43—81no—
377C4×C43—81no—
378C4×C43—81no—
379C4×C43—81no—
380C4×C43#52511yescharacteristic
381C4×C43#54011yescharacteristic
382C4×C43#54611yescharacteristic
383C4×C43#55311yescharacteristic
384C2×#466C2×C4311yescharacteristic, complemented
385C2×#442C2×C4311yescharacteristic, complemented
386#2428C2×C4311yescharacteristic, complemented
387#2420C2×C4311yescharacteristic, complemented
388#2085C2×C4311yescharacteristic, complemented
389#2034C2×C4311yescharacteristic, complemented
390#2011C2×C4311yescharacteristic, complemented
391#1999C2×C4311yescharacteristic, complemented
392#1961C2×C4311yescharacteristic, complemented
393#1936C2×C4311yescharacteristic, complemented
394#1936C2×C4311yescharacteristic, complemented
395#1893C2×C4311yescharacteristic, complemented
396#1879C2×C4311yescharacteristic, complemented
397#1862C2×C4311yescharacteristic, complemented
398#1752C2×C4311yescharacteristic, complemented
399C2×C43—42no—
400C2×C43—82no—
401C2×C43—82no—
402C2×C43—161no—
403C2×C43#246411yescharacteristic
404C2×C43#317611yescharacteristic
405C2×C43#318011yescharacteristic
406C2×C43#326411yescharacteristic
407C2×C43#326811yescharacteristic
408C2×C43#331811yescharacteristic
409C2×C43#331911yescharacteristic
410C22×D8C22×C4311yescharacteristic
411C22×D8C22×C4311yescharacteristic
412C23×C8C22×C4311yescharacteristic
413C2×#127C22×C4311yescharacteristic
414C2×#121—21no—
415C2×#121C22×C4311yescharacteristic
416C2×#121C22×C4311yescharacteristic
417C2×#121C22×C4311yescharacteristic
418C2×C4×D4C22×C4311yescharacteristic
419C2×C4×D4C22×C4311yescharacteristic
420#466—24no—
421#442—24no—
422C2×#107C22×C4311yescharacteristic
423C2×#106C22×C4311yescharacteristic
424C2×#102C22×C4311yescharacteristic
425C2×#102C22×C4311yescharacteristic
426C2×#102C22×C4311yescharacteristic
427C2×#102C22×C4311yescharacteristic
428C2×#102C22×C4311yescharacteristic
429C2×#102C22×C4311yescharacteristic
430C2×#102C22×C4311yescharacteristic
431C2×#102C22×C4311yescharacteristic
432C2×C22⋊C8C22×C4311yescharacteristic
433C2×#97C22×C4311yescharacteristic
434C2×#97C22×C4311yescharacteristic
435#397—21no—
436#394—21no—
437#394—21no—
438#392—21no—
439#390C22×C4311yescharacteristic
440#390C22×C4311yescharacteristic
441#389C22×C4311yescharacteristic
442#389C22×C4311yescharacteristic
443#386—21no—
444#386—21no—
445#382C22×C4311yescharacteristic
446#381—21no—
447#380C22×C4311yescharacteristic
448C4×C22⋊C4C22×C4311yescharacteristic
449#340C22×C4311yescharacteristic
450#340C22×C4311yescharacteristic
451#340C22×C4311yescharacteristic
452#340C22×C4311yescharacteristic
453#336C22×C4311yescharacteristic
454#336C22×C4311yescharacteristic
455C43#2697711yescharacteristic, direct product factor, Sylow
456C22×D4—21no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—21no—
461C22×D4C23×C4311yescharacteristic
462C22×D4C23×C4311yescharacteristic
463C22×D4C23×C4311yescharacteristic
464C23×C4—21no—
465C23×C4—21no—
466C23×C4C23×C4311yescharacteristic
467C2×D8—22no—
468C2×D8—22no—
469C2×D8—22no—
470C2×D8—22no—
471C2×D8—22no—
472C2×D8—41no—
473C22×C8—22no—
474C22×C8—22no—
475C22×C8—41no—
476C22×C8C23×C4311yescharacteristic
477C22×C8C23×C4311yescharacteristic
478C22×C8C23×C4311yescharacteristic
479C22×C8C23×C4311yescharacteristic
480#127—22no—
481#127—41no—
482#121—22no—
483#121—22no—
484#121—22no—
485#121—44no—
486#121—41no—
487#121—41no—
488#121—41no—
489C4×D4—22no—
490C4×D4—22no—
491C4×D4—41no—
492C4×D4—41no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4C23×C4311yescharacteristic
496C2×C4⋊C4C23×C4311yescharacteristic
497C2×C4⋊C4C23×C4311yescharacteristic
498C2×C4⋊C4C23×C4311yescharacteristic
499C2×C4⋊C4C23×C4311yescharacteristic
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4D4×C4311yescharacteristic
511C2×C22⋊C4D4×C4311yescharacteristic
512C2×C42C23×C4311yescharacteristic
513C2×C42C23×C4311yescharacteristic
514#107—22no—
515#106—22no—
516#102—22no—
517#102—22no—
518#102—22no—
519#102—22no—
520#102—41no—
521#102—41no—
522#102—41no—
523#102D4×C4314yescomplemented
524C22⋊C8—22no—
525#97—22no—
526#97—41no—
527#95—21no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95—21no—
532#95D4×C4311yescharacteristic
533#95D4×C4311yescharacteristic
534C24—21no—
535C24—21no—
536C24—21no—
537C24C2×D4×C4311yescharacteristic
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—81no—
565C2×D4—81no—
566C2×D4—81no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4C2×D4×C4312yes—
570C2×D4#41×C4312yes—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—81no—
587C22×C4—81no—
588C22×C4C2×D4×C4311yescharacteristic
589C22×C4C2×D4×C4311yescharacteristic
590C22×C4C2×D4×C4311yescharacteristic
591C22×C4C2×D4×C4311yescharacteristic
592C22×C4C2×D4×C4311yescharacteristic
593C22×C4C24×C4311yescharacteristic
594D8—28no—
595D8—44no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—44no—
606C2×C8C2×D4×C4312yes—
607C2×C8#41×C4312yes—
608C2×C8#41×C4312yes—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—42no—
619C4⋊C4—81no—
620C4⋊C4C2×D4×C4312yes—
621C22⋊C4—22no—
622C22⋊C4—41no—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—81no—
630C22⋊C4—81no—
631C22⋊C4—81no—
632C22⋊C4—81no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—22no—
644C23—22no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23AGL(1,ℤ/8)×C4312yes—
665C23C22×D4×C4311yescharacteristic
666D4—22no—
667D4—22no—
668D4—22no—
669D4—22no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—41no—
678D4—84no—
679D4—84no—
680D4—84no—
681D4—84no—
682D4—84no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—84no—
718C2×C4—84no—
719C2×C4C22×D4×C4311yescharacteristic
720C2×C4C2×#41×C4311yescharacteristic
721C2×C4C2×#41×C4311yescharacteristic
722C2×C4C2×#41×C4311yescharacteristic
723C2×C4H(5,𝔽2)×C4311yescharacteristic
724C2×C4H(5,𝔽2)×C4311yescharacteristic
725C8—22no—
726C8—22no—
727C8—22no—
728C8—41no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22C43×#53211yescharacteristic
758C22D42×C4311yescharacteristic
759C22C43×#54611yescharacteristic
760C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
761C22C43×#57511yescharacteristic
762C22C43×#57611yescharacteristic
763C22C43×#57611yescharacteristic
764C4—41no—
765C4—41no—
766C4—42no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—81no—
771C4—81no—
772C4—81no—
773C4—81no—
774C4C43×#52511yescharacteristic
775C4C43×#54011yescharacteristic
776C4C43×#54611yescharacteristic
777C4C43×#55311yescharacteristic
778C2—42no—
779C2—82no—
780C2—82no—
781C2—161no—
782C2C43×#246411yescharacteristic
783C2C43×#317611yescharacteristic
784C2C43×#318011yescharacteristic
785C2C43×#326411yescharacteristic
786C2C43×#326811yescharacteristic
787C2C43×#331811yescharacteristic
788C2C43×#331911yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
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×#466C2semidirect
2. C2×C43×#442C2semidirect
3. C43×#2428C2semidirect
4. C43×#2420C2semidirect
5. C43×#2085C2semidirect
6. C43×#2034C2semidirect
7. C43×#2011C2semidirect
8. C43×#1999C2semidirect
9. C43×#1961C2semidirect
10. C43×#1936C2semidirect
11. C43×#1936C2semidirect
12. C43×#1893C2semidirect
13. C43×#1879C2semidirect
14. C43×#1862C2semidirect
15. C43×#1752C2semidirect
128. #102×C43D4semidirect
334. #26977C43direct (N × H)
384. C2×#466C2×C43semidirect
385. C2×#442C2×C43semidirect
386. #2428C2×C43semidirect
387. #2420C2×C43semidirect
388. #2085C2×C43semidirect
389. #2034C2×C43semidirect
390. #2011C2×C43semidirect
391. #1999C2×C43semidirect
392. #1961C2×C43semidirect
393. #1936C2×C43semidirect
394. #1936C2×C43semidirect
395. #1893C2×C43semidirect
396. #1879C2×C43semidirect
397. #1862C2×C43semidirect
398. #1752C2×C43semidirect
455. C43#26977direct (N × H)
523. #102D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4662
C2×C43×#4422
C43×#24282
C43×#24202
C43×#20852
C43×#20342
C43×#20112
C43×#19992
C43×#19612
C43×#19362
C43×#18932
C43×#18792
C43×#18622
C43×#17522
#2697743