Finite Group Databasebeta

← C43×#26984 #24947001

Subgroups — C43×#26984 #24947001

Order 11008.

1050 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#469C211yesmaximal, characteristic, complemented
2C2×C43×#442C211yesmaximal, characteristic, complemented
3C43×#2428C211yesmaximal, characteristic, complemented
4C43×#2422C211yesmaximal, characteristic, complemented
5C43×#2084C211yesmaximal, characteristic, complemented
6C43×#2034C211yesmaximal, characteristic, complemented
7C43×#2011C211yesmaximal, characteristic, complemented
8C43×#1999C211yesmaximal, characteristic, complemented
9C43×#1957C211yesmaximal, characteristic, complemented
10C43×#1936C211yesmaximal, characteristic, complemented
11C43×#1934C211yesmaximal, characteristic, complemented
12C43×#1895C211yesmaximal, characteristic, complemented
13C43×#1879C211yesmaximal, characteristic, complemented
14C43×#1864C211yesmaximal, characteristic, complemented
15C43×#1753C211yesmaximal, characteristic, complemented
16C22×D8×C43C2211yescharacteristic
17C22×D8×C43C2211yescharacteristic
18C22×M16×C43C2211yescharacteristic
19C2×#127×C43C2211yescharacteristic
20C2×#123×C43—21no—
21C2×#121×C43—21no—
22C2×#121×C43C2211yescharacteristic
23C2×#121×C43C2211yescharacteristic
24C2×#121×C43C2211yescharacteristic
25C2×C4×D4×C43C2211yescharacteristic
26C2×C4×D4×C43C2211yescharacteristic
27C43×#469—24no—
28C43×#442—24no—
29C2×#106×C43C2211yescharacteristic
30C2×#106×C43C2211yescharacteristic
31C2×#102×C43C2211yescharacteristic
32C2×#102×C43C2211yescharacteristic
33C2×#102×C43C2211yescharacteristic
34C2×#102×C43C2211yescharacteristic
35C2×#102×C43C2211yescharacteristic
36C2×#102×C43C2211yescharacteristic
37C2×#102×C43C2211yescharacteristic
38C2×#102×C43C2211yescharacteristic
39C2×C22⋊C8×C43C2211yescharacteristic
40C2×#97×C43C2211yescharacteristic
41C2×C4×C8×C43C2211yescharacteristic
42C43×#397—21no—
43C43×#394—21no—
44C43×#394—21no—
45C43×#392—21no—
46C43×#390C2211yescharacteristic
47C43×#390C2211yescharacteristic
48C43×#389C2211yescharacteristic
49C43×#389C2211yescharacteristic
50C43×#386—21no—
51C43×#385—21no—
52C43×#384C2211yescharacteristic
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—
78C2×M16×C43—22no—
79C2×M16×C43—22no—
80C2×M16×C43—41no—
81C22×C8×C43C2311yescharacteristic
82C22×C8×C43C2311yescharacteristic
83C22×C8×C43C2311yescharacteristic
84C22×C8×C43C2311yescharacteristic
85#127×C43—22no—
86#127×C43—41no—
87#123×C43—44no—
88#121×C43—22no—
89#121×C43—22no—
90#121×C43—22no—
91#121×C43—44no—
92#121×C43—41no—
93#121×C43—41no—
94#121×C43—41no—
95C4×D4×C43—22no—
96C4×D4×C43—22no—
97C4×D4×C43—41no—
98C4×D4×C43—41no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43C2311yescharacteristic
104C2×C4⋊C4×C43C2311yescharacteristic
105C2×C4⋊C4×C43C2311yescharacteristic
106C2×C4⋊C4×C43C2311yescharacteristic
107C2×C4⋊C4×C43C2311yescharacteristic
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×C43—21no—
116C2×C22⋊C4×C43—21no—
117C2×C22⋊C4×C43—21no—
118C2×C22⋊C4×C43D411yescharacteristic
119C2×C22⋊C4×C43D411yescharacteristic
120C2×C42×C43C2311yescharacteristic
121C2×C42×C43C2311yescharacteristic
122#106×C43—22no—
123#106×C43—22no—
124#102×C43—22no—
125#102×C43—22no—
126#102×C43—22no—
127#102×C43—22no—
128#102×C43—41no—
129#102×C43—41no—
130#102×C43—41no—
131#102×C43D414yescomplemented
132C22⋊C8×C43—22no—
133#97×C43—22no—
134C4×C8×C43—41no—
135#95×C43—21no—
136#95×C43—21no—
137#95×C43—21no—
138#95×C43D411yescharacteristic
139#95×C43D411yescharacteristic
140C24×C43—21no—
141C24×C43—21no—
142C24×C43—21no—
143C24×C43C2×D411yescharacteristic
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—21no—
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—42no—
170C2×D4×C43—81no—
171C2×D4×C43—81no—
172C2×D4×C43—81no—
173C2×D4×C43—81no—
174C2×D4×C43—81no—
175C2×D4×C43C2×D412yes—
176C2×D4×C43#4112yes—
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—21no—
188C22×C4×C43—42no—
189C22×C4×C43—42no—
190C22×C4×C43—42no—
191C22×C4×C43—42no—
192C22×C4×C43—81no—
193C22×C4×C43—81no—
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2411yescharacteristic
200D8×C43—28no—
201D8×C43—44no—
202M16×C43—44no—
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—21no—
211C2×C8×C43—21no—
212C2×C8×C43C2×D412yes—
213C2×C8×C43#4112yes—
214C2×C8×C43#4112yes—
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—21no—
224C4⋊C4×C43—42no—
225C4⋊C4×C43—42no—
226C4⋊C4×C43—42no—
227C4⋊C4×C43—81no—
228C4⋊C4×C43C2×D412yes—
229C22⋊C4×C43—22no—
230C22⋊C4×C43—22no—
231C22⋊C4×C43—42no—
232C22⋊C4×C43—42no—
233C22⋊C4×C43—42no—
234C22⋊C4×C43—42no—
235C22⋊C4×C43—42no—
236C22⋊C4×C43—42no—
237C22⋊C4×C43—42no—
238C22⋊C4×C43—42no—
239C22⋊C4×C43—42no—
240C22⋊C4×C43—81no—
241C42×C43—21no—
242C42×C43—21no—
243C42×C43—21no—
244C42×C43—21no—
245C23×C43—21no—
246C23×C43—22no—
247C23×C43—21no—
248C23×C43—22no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
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×C43—41no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43C22×D411yescharacteristic
274D4×C43—22no—
275D4×C43—22no—
276D4×C43—22no—
277D4×C43—22no—
278D4×C43—41no—
279D4×C43—41no—
280D4×C43—41no—
281D4×C43—41no—
282D4×C43—41no—
283D4×C43—41no—
284D4×C43—41no—
285D4×C43—41no—
286D4×C43—84no—
287D4×C43—84no—
288D4×C43—84no—
289D4×C43—84no—
290D4×C43—84no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
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—22no—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
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—41no—
323C2×C4×C43—84no—
324C2×C4×C43—84no—
325C2×C4×C43AGL(1,ℤ/8)12yes—
326C2×C4×C43AGL(1,ℤ/8)12yes—
327C2×C4×C43C22×D411yescharacteristic
328C2×C4×C43C2×#4111yescharacteristic
329C2×C4×C43C2×#4111yescharacteristic
330C2×C4×C43C2×#4111yescharacteristic
331C2×C4×C43H(5,𝔽2)11yescharacteristic
332C2×C4×C43H(5,𝔽2)11yescharacteristic
333C8×C43—22no—
334C8×C43—22no—
335C8×C43—22no—
336C8×C43—41no—
337#26984C4311yesmaximal, characteristic, direct product factor, Sylow
338C22×C43—41no—
339C22×C43—41no—
340C22×C43—41no—
341C22×C43—42no—
342C22×C43—42no—
343C22×C43—41no—
344C22×C43—42no—
345C22×C43—41no—
346C22×C43—42no—
347C22×C43—41no—
348C22×C43—42no—
349C22×C43—41no—
350C22×C43—42no—
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—81no—
364C22×C43—81no—
365C22×C43—81no—
366C22×C43#53211yescharacteristic
367C22×C43D4211yescharacteristic
368C22×C43#54611yescharacteristic
369C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
370C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
371C22×C43#57611yescharacteristic
372C22×C43#57711yescharacteristic
373C4×C43—22no—
374C4×C43—22no—
375C4×C43—41no—
376C4×C43—41no—
377C4×C43—42no—
378C4×C43—41no—
379C4×C43—81no—
380C4×C43—81no—
381C4×C43—81no—
382C4×C43—81no—
383C4×C43#52511yescharacteristic
384C4×C43#54011yescharacteristic
385C4×C43#54611yescharacteristic
386C4×C43#55311yescharacteristic
387C2×#469C2×C4311yescharacteristic, complemented
388C2×#442C2×C4311yescharacteristic, complemented
389#2428C2×C4311yescharacteristic, complemented
390#2422C2×C4311yescharacteristic, complemented
391#2084C2×C4311yescharacteristic, complemented
392#2034C2×C4311yescharacteristic, complemented
393#2011C2×C4311yescharacteristic, complemented
394#1999C2×C4311yescharacteristic, complemented
395#1957C2×C4311yescharacteristic, complemented
396#1936C2×C4311yescharacteristic, complemented
397#1934C2×C4311yescharacteristic, complemented
398#1895C2×C4311yescharacteristic, complemented
399#1879C2×C4311yescharacteristic, complemented
400#1864C2×C4311yescharacteristic, complemented
401#1753C2×C4311yescharacteristic, complemented
402C2×C43—81no—
403C2×C43—82no—
404C2×C43—82no—
405C2×C43—161no—
406C2×C43#246411yescharacteristic
407C2×C43#317911yescharacteristic
408C2×C43#318411yescharacteristic
409C2×C43#327211yescharacteristic
410C2×C43#327411yescharacteristic
411C2×C43#330611yescharacteristic
412C2×C43#331811yescharacteristic
413C22×D8C22×C4311yescharacteristic
414C22×D8C22×C4311yescharacteristic
415C22×M16C22×C4311yescharacteristic
416C2×#127C22×C4311yescharacteristic
417C2×#123—21no—
418C2×#121—21no—
419C2×#121C22×C4311yescharacteristic
420C2×#121C22×C4311yescharacteristic
421C2×#121C22×C4311yescharacteristic
422C2×C4×D4C22×C4311yescharacteristic
423C2×C4×D4C22×C4311yescharacteristic
424#469—24no—
425#442—24no—
426C2×#106C22×C4311yescharacteristic
427C2×#106C22×C4311yescharacteristic
428C2×#102C22×C4311yescharacteristic
429C2×#102C22×C4311yescharacteristic
430C2×#102C22×C4311yescharacteristic
431C2×#102C22×C4311yescharacteristic
432C2×#102C22×C4311yescharacteristic
433C2×#102C22×C4311yescharacteristic
434C2×#102C22×C4311yescharacteristic
435C2×#102C22×C4311yescharacteristic
436C2×C22⋊C8C22×C4311yescharacteristic
437C2×#97C22×C4311yescharacteristic
438C2×C4×C8C22×C4311yescharacteristic
439#397—21no—
440#394—21no—
441#394—21no—
442#392—21no—
443#390C22×C4311yescharacteristic
444#390C22×C4311yescharacteristic
445#389C22×C4311yescharacteristic
446#389C22×C4311yescharacteristic
447#386—21no—
448#385—21no—
449#384C22×C4311yescharacteristic
450#380C22×C4311yescharacteristic
451C4×C22⋊C4C22×C4311yescharacteristic
452#340C22×C4311yescharacteristic
453#340C22×C4311yescharacteristic
454#340C22×C4311yescharacteristic
455#340C22×C4311yescharacteristic
456#336C22×C4311yescharacteristic
457#336C22×C4311yescharacteristic
458C43#2698411yescharacteristic, direct product factor, Sylow
459C22×D4—21no—
460C22×D4—21no—
461C22×D4—21no—
462C22×D4—21no—
463C22×D4—21no—
464C22×D4C23×C4311yescharacteristic
465C22×D4C23×C4311yescharacteristic
466C22×D4C23×C4311yescharacteristic
467C23×C4—21no—
468C23×C4—21no—
469C23×C4C23×C4311yescharacteristic
470C2×D8—22no—
471C2×D8—22no—
472C2×D8—22no—
473C2×D8—22no—
474C2×D8—22no—
475C2×D8—41no—
476C2×M16—22no—
477C2×M16—22no—
478C2×M16—41no—
479C22×C8C23×C4311yescharacteristic
480C22×C8C23×C4311yescharacteristic
481C22×C8C23×C4311yescharacteristic
482C22×C8C23×C4311yescharacteristic
483#127—22no—
484#127—41no—
485#123—44no—
486#121—22no—
487#121—22no—
488#121—22no—
489#121—44no—
490#121—41no—
491#121—41no—
492#121—41no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—41no—
496C4×D4—41no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4C23×C4311yescharacteristic
502C2×C4⋊C4C23×C4311yescharacteristic
503C2×C4⋊C4C23×C4311yescharacteristic
504C2×C4⋊C4C23×C4311yescharacteristic
505C2×C4⋊C4C23×C4311yescharacteristic
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4D4×C4311yescharacteristic
517C2×C22⋊C4D4×C4311yescharacteristic
518C2×C42C23×C4311yescharacteristic
519C2×C42C23×C4311yescharacteristic
520#106—22no—
521#106—22no—
522#102—22no—
523#102—22no—
524#102—22no—
525#102—22no—
526#102—41no—
527#102—41no—
528#102—41no—
529#102D4×C4314yescomplemented
530C22⋊C8—22no—
531#97—22no—
532C4×C8—41no—
533#95—21no—
534#95—21no—
535#95—21no—
536#95D4×C4311yescharacteristic
537#95D4×C4311yescharacteristic
538C24—21no—
539C24—21no—
540C24—21no—
541C24C2×D4×C4311yescharacteristic
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—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—81no—
569C2×D4—81no—
570C2×D4—81no—
571C2×D4—81no—
572C2×D4—81no—
573C2×D4C2×D4×C4312yes—
574C2×D4#41×C4312yes—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—81no—
591C22×C4—81no—
592C22×C4C2×D4×C4311yescharacteristic
593C22×C4C2×D4×C4311yescharacteristic
594C22×C4C2×D4×C4311yescharacteristic
595C22×C4C2×D4×C4311yescharacteristic
596C22×C4C2×D4×C4311yescharacteristic
597C22×C4C24×C4311yescharacteristic
598D8—28no—
599D8—44no—
600M16—44no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8C2×D4×C4312yes—
611C2×C8#41×C4312yes—
612C2×C8#41×C4312yes—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—81no—
626C4⋊C4C2×D4×C4312yes—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—81no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—21no—
643C23—21no—
644C23—22no—
645C23—21no—
646C23—22no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23C22×D4×C4311yescharacteristic
672D4—22no—
673D4—22no—
674D4—22no—
675D4—22no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—84no—
685D4—84no—
686D4—84no—
687D4—84no—
688D4—84no—
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—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
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—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—84no—
722C2×C4—84no—
723C2×C4AGL(1,ℤ/8)×C4312yes—
724C2×C4AGL(1,ℤ/8)×C4312yes—
725C2×C4C22×D4×C4311yescharacteristic
726C2×C4C2×#41×C4311yescharacteristic
727C2×C4C2×#41×C4311yescharacteristic
728C2×C4C2×#41×C4311yescharacteristic
729C2×C4H(5,𝔽2)×C4311yescharacteristic
730C2×C4H(5,𝔽2)×C4311yescharacteristic
731C8—22no—
732C8—22no—
733C8—22no—
734C8—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—42no—
739C22—42no—
740C22—41no—
741C22—42no—
742C22—42no—
743C22—41no—
744C22—42no—
745C22—41no—
746C22—41no—
747C22—42no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22C43×#53211yescharacteristic
764C22D42×C4311yescharacteristic
765C22C43×#54611yescharacteristic
766C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
767C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
768C22C43×#57611yescharacteristic
769C22C43×#57711yescharacteristic
770C4—22no—
771C4—22no—
772C4—41no—
773C4—41no—
774C4—42no—
775C4—41no—
776C4—81no—
777C4—81no—
778C4—81no—
779C4—81no—
780C4C43×#52511yescharacteristic
781C4C43×#54011yescharacteristic
782C4C43×#54611yescharacteristic
783C4C43×#55311yescharacteristic
784C2—81no—
785C2—82no—
786C2—82no—
787C2—161no—
788C2C43×#246411yescharacteristic
789C2C43×#317911yescharacteristic
790C2C43×#318411yescharacteristic
791C2C43×#327211yescharacteristic
792C2C43×#327411yescharacteristic
793C2C43×#330611yescharacteristic
794C2C43×#331811yescharacteristic
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×#469C2semidirect
2. C2×C43×#442C2semidirect
3. C43×#2428C2semidirect
4. C43×#2422C2semidirect
5. C43×#2084C2semidirect
6. C43×#2034C2semidirect
7. C43×#2011C2semidirect
8. C43×#1999C2semidirect
9. C43×#1957C2semidirect
10. C43×#1936C2semidirect
11. C43×#1934C2semidirect
12. C43×#1895C2semidirect
13. C43×#1879C2semidirect
14. C43×#1864C2semidirect
15. C43×#1753C2semidirect
131. #102×C43D4semidirect
337. #26984C43direct (N × H)
387. C2×#469C2×C43semidirect
388. C2×#442C2×C43semidirect
389. #2428C2×C43semidirect
390. #2422C2×C43semidirect
391. #2084C2×C43semidirect
392. #2034C2×C43semidirect
393. #2011C2×C43semidirect
394. #1999C2×C43semidirect
395. #1957C2×C43semidirect
396. #1936C2×C43semidirect
397. #1934C2×C43semidirect
398. #1895C2×C43semidirect
399. #1879C2×C43semidirect
400. #1864C2×C43semidirect
401. #1753C2×C43semidirect
458. C43#26984direct (N × H)
529. #102D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4692
C2×C43×#4422
C43×#24282
C43×#24222
C43×#20842
C43×#20342
C43×#20112
C43×#19992
C43×#19572
C43×#19362
C43×#19342
C43×#18952
C43×#18792
C43×#18642
C43×#17532
#2698443