Finite Group Databasebeta

← C43×#25097 #24945114

Subgroups — C43×#25097 #24945114

Order 11008.

1378 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#469C211yesmaximal, characteristic, complemented
2C2×C43×#459C211yesmaximal, characteristic, complemented
3C2×C43×#447C211yesmaximal, characteristic, complemented
4C2×C43×#418C211yesmaximal, characteristic, complemented
5C43×#2433C211yesmaximal, characteristic, complemented
6C43×#2363C211yesmaximal, characteristic, complemented
7C43×#2065C211yesmaximal, characteristic, complemented
8C43×#2054C211yesmaximal, characteristic, complemented
9C43×#2041C211yesmaximal, characteristic, complemented
10C43×#2011C211yesmaximal, characteristic, complemented
11C43×#1982C211yesmaximal, characteristic, complemented
12C43×#1926C211yesmaximal, characteristic, complemented
13C43×#1879C211yesmaximal, characteristic, complemented
14C43×#1875C211yesmaximal, characteristic, complemented
15C43×#1851C211yesmaximal, characteristic, complemented
16C23×D4×C43C2211yescharacteristic
17C22×D8×C43C2211yescharacteristic
18C22×D8×C43C2211yescharacteristic
19C22×D8×C43C2211yescharacteristic, complemented
20C22×M16×C43C2211yescharacteristic
21C2×#127×C43C2211yescharacteristic
22C2×#127×C43C2211yescharacteristic
23C2×#121×C43C2211yescharacteristic
24C2×#121×C43C2211yescharacteristic
25C2×#120×C43—21no—
26C2×#120×C43—21no—
27C2×C4×D4×C43C2211yescharacteristic, complemented
28C2×#117×C43C2211yescharacteristic
29C43×#469—24no—
30C43×#459—24no—
31C43×#447—24no—
32C2×#106×C43C2211yescharacteristic, complemented
33C2×C4⋊C8×C43C2211yescharacteristic, complemented
34C2×C4⋊C8×C43C2211yescharacteristic, complemented
35C43×#418—24no—
36C2×#102×C43C2211yescharacteristic
37C2×#102×C43C2211yescharacteristic
38C2×#102×C43C2211yescharacteristic
39C2×#102×C43C2211yescharacteristic
40C2×#102×C43C2211yescharacteristic
41C2×#102×C43C2211yescharacteristic
42C2×#102×C43C2211yescharacteristic, complemented
43C2×#102×C43C2211yescharacteristic, complemented
44C2×#102×C43C2211yescharacteristic, complemented
45C2×#102×C43C2211yescharacteristic, complemented
46C2×C22⋊C8×C43C2211yescharacteristic
47C43×#392—21no—
48C43×#392—21no—
49C43×#390—21no—
50C43×#390C2211yescharacteristic
51C43×#390C2211yescharacteristic
52C43×#390C2211yescharacteristic, complemented
53C43×#389C2211yescharacteristic, complemented
54C43×#388—21no—
55C43×#386—21no—
56C4×C4⋊C4×C43C2211yescharacteristic, complemented
57C4×C22⋊C4×C43—21no—
58C4×C22⋊C4×C43C2211yescharacteristic
59C43×#340C2211yescharacteristic, complemented
60C43×#340C2211yescharacteristic, complemented
61C43×#336C2211yescharacteristic, complemented
62C43×#336C2211yescharacteristic, complemented
63C25×C43—21no—
64C22×D4×C43—22no—
65C22×D4×C43—22no—
66C22×D4×C43—21no—
67C22×D4×C43—21no—
68C22×D4×C43—22no—
69C22×D4×C43—21no—
70C22×D4×C43—21no—
71C22×D4×C43—21no—
72C22×D4×C43—21no—
73C22×D4×C43—21no—
74C22×D4×C43—22no—
75C22×D4×C43—41no—
76C22×D4×C43—41no—
77C22×D4×C43C2311yescharacteristic
78C22×D4×C43C2311yescharacteristic
79C22×D4×C43C2311yescharacteristic
80C22×D4×C43C2311yescharacteristic
81C23×C4×C43—21no—
82C23×C4×C43C2311yescharacteristic
83C2×D8×C43—22no—
84C2×D8×C43—22no—
85C2×D8×C43—22no—
86C2×D8×C43—22no—
87C2×D8×C43—22no—
88C2×D8×C43—22no—
89C2×D8×C43—41no—
90C2×D8×C43—41no—
91C2×D8×C43—41no—
92C2×M16×C43—22no—
93C2×M16×C43—22no—
94C2×M16×C43—41no—
95C22×C8×C43C2311yescharacteristic
96C22×C8×C43C2311yescharacteristic
97C22×C8×C43C2311yescharacteristic
98C22×C8×C43C2311yescharacteristic
99#127×C43—22no—
100#127×C43—22no—
101#127×C43—41no—
102#127×C43—41no—
103#121×C43—22no—
104#121×C43—22no—
105#121×C43—22no—
106#121×C43D414yescomplemented
107#120×C43—44no—
108#120×C43—44no—
109C4×D4×C43—22no—
110C4×D4×C43—41no—
111#117×C43—22no—
112#117×C43—41no—
113C2×C4⋊C4×C43—21no—
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C22⋊C4×C43—21no—
119C2×C22⋊C4×C43—21no—
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122C2×C22⋊C4×C43—21no—
123C2×C22⋊C4×C43—21no—
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43D411yescharacteristic
129C2×C22⋊C4×C43D411yescharacteristic
130C2×C42×C43—21no—
131C2×C42×C43—21no—
132C2×C42×C43C2311yescharacteristic
133C2×C42×C43C2311yescharacteristic
134#106×C43—22no—
135C4⋊C8×C43—22no—
136C4⋊C8×C43—41no—
137#102×C43—22no—
138#102×C43—22no—
139#102×C43—22no—
140#102×C43—22no—
141#102×C43—22no—
142#102×C43—22no—
143#102×C43—22no—
144#102×C43—22no—
145#102×C43—41no—
146#102×C43D414yescomplemented
147C22⋊C8×C43—22no—
148#95×C43—21no—
149#95×C43—21no—
150#95×C43D411yescharacteristic
151#95×C43D411yescharacteristic
152C24×C43—21no—
153C24×C43—21no—
154C24×C43—21no—
155C24×C43—21no—
156C24×C43—42no—
157C24×C43—42no—
158C24×C43—42no—
159C24×C43—42no—
160C24×C43—42no—
161C24×C43—81no—
162C24×C43—81no—
163C24×C43C2×D411yescharacteristic
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—24no—
168C2×D4×C43—28no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43—21no—
174C2×D4×C43—21no—
175C2×D4×C43—21no—
176C2×D4×C43—21no—
177C2×D4×C43—21no—
178C2×D4×C43—21no—
179C2×D4×C43—21no—
180C2×D4×C43—21no—
181C2×D4×C43—21no—
182C2×D4×C43—21no—
183C2×D4×C43—21no—
184C2×D4×C43—21no—
185C2×D4×C43—21no—
186C2×D4×C43—21no—
187C2×D4×C43—42no—
188C2×D4×C43—42no—
189C2×D4×C43—42no—
190C2×D4×C43—42no—
191C2×D4×C43—42no—
192C2×D4×C43—42no—
193C2×D4×C43—42no—
194C2×D4×C43—42no—
195C2×D4×C43—44no—
196C2×D4×C43—44no—
197C2×D4×C43—44no—
198C2×D4×C43—42no—
199C2×D4×C43—42no—
200C2×D4×C43—42no—
201C2×D4×C43—42no—
202C2×D4×C43—42no—
203C2×D4×C43—42no—
204C2×D4×C43—81no—
205C2×D4×C43—81no—
206C2×D4×C43—81no—
207C2×D4×C43—81no—
208C2×D4×C43—81no—
209C2×D4×C43—81no—
210C2×D4×C43C2×D412yes—
211C2×D4×C43C2×D412yes—
212C2×D4×C43#4112yes—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—42no—
222C22×C4×C43—42no—
223C22×C4×C43—81no—
224C22×C4×C43C2×D412yes—
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43C2×D411yescharacteristic
228C22×C4×C43C2×D411yescharacteristic
229C22×C4×C43C2×D411yescharacteristic
230C22×C4×C43#4112yes—
231C22×C4×C43C2411yescharacteristic
232D8×C43—44no—
233D8×C43—44no—
234D8×C43—44no—
235M16×C43—44no—
236C2×C8×C43—21no—
237C2×C8×C43—21no—
238C2×C8×C43—21no—
239C2×C8×C43—21no—
240C2×C8×C43—21no—
241C2×C8×C43—21no—
242C2×C8×C43—21no—
243C2×C8×C43—21no—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C2×C8×C43C2×D412yes—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43—21no—
251C4⋊C4×C43—21no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43—21no—
254C4⋊C4×C43—81no—
255C4⋊C4×C43C2×D412yes—
256C4⋊C4×C43C2×D412yes—
257C22⋊C4×C43—24no—
258C22⋊C4×C43—22no—
259C22⋊C4×C43—22no—
260C22⋊C4×C43—42no—
261C22⋊C4×C43—42no—
262C22⋊C4×C43—42no—
263C22⋊C4×C43—42no—
264C22⋊C4×C43—42no—
265C22⋊C4×C43—42no—
266C22⋊C4×C43—42no—
267C22⋊C4×C43—42no—
268C22⋊C4×C43—81no—
269C42×C43—21no—
270C42×C43—21no—
271C42×C43—21no—
272C42×C43—21no—
273C42×C43—42no—
274C42×C43—81no—
275C23×C43—21no—
276C23×C43—21no—
277C23×C43—21no—
278C23×C43—21no—
279C23×C43—21no—
280C23×C43—21no—
281C23×C43—22no—
282C23×C43—22no—
283C23×C43—22no—
284C23×C43—48no—
285C23×C43—41no—
286C23×C43—41no—
287C23×C43—41no—
288C23×C43—41no—
289C23×C43—41no—
290C23×C43—41no—
291C23×C43—41no—
292C23×C43—41no—
293C23×C43—41no—
294C23×C43—41no—
295C23×C43—41no—
296C23×C43—41no—
297C23×C43—41no—
298C23×C43—41no—
299C23×C43—41no—
300C23×C43—41no—
301C23×C43—41no—
302C23×C43—41no—
303C23×C43—41no—
304C23×C43—41no—
305C23×C43—41no—
306C23×C43—41no—
307C23×C43—41no—
308C23×C43—41no—
309C23×C43—41no—
310C23×C43—84no—
311C23×C43—84no—
312C23×C43—84no—
313C23×C43—84no—
314C23×C43—84no—
315C23×C43—84no—
316C23×C43#12112yes—
317C23×C43C22×D411yescharacteristic
318D4×C43—22no—
319D4×C43—22no—
320D4×C43—22no—
321D4×C43—22no—
322D4×C43—22no—
323D4×C43—22no—
324D4×C43—48no—
325D4×C43—41no—
326D4×C43—41no—
327D4×C43—41no—
328D4×C43—41no—
329D4×C43—41no—
330D4×C43—41no—
331D4×C43—41no—
332D4×C43—41no—
333D4×C43—41no—
334D4×C43—41no—
335D4×C43—84no—
336D4×C43—84no—
337D4×C43—84no—
338D4×C43—84no—
339D4×C43—84no—
340D4×C43—84no—
341C2×C4×C43—21no—
342C2×C4×C43—21no—
343C2×C4×C43—21no—
344C2×C4×C43—21no—
345C2×C4×C43—21no—
346C2×C4×C43—21no—
347C2×C4×C43—22no—
348C2×C4×C43—22no—
349C2×C4×C43—22no—
350C2×C4×C43—22no—
351C2×C4×C43—22no—
352C2×C4×C43—21no—
353C2×C4×C43—22no—
354C2×C4×C43—21no—
355C2×C4×C43—21no—
356C2×C4×C43—21no—
357C2×C4×C43—21no—
358C2×C4×C43—21no—
359C2×C4×C43—41no—
360C2×C4×C43—41no—
361C2×C4×C43—41no—
362C2×C4×C43—41no—
363C2×C4×C43—41no—
364C2×C4×C43—41no—
365C2×C4×C43—41no—
366C2×C4×C43—41no—
367C2×C4×C43—41no—
368C2×C4×C43—41no—
369C2×C4×C43—84no—
370C2×C4×C43#12112yes—
371C2×C4×C43AGL(1,ℤ/8)12yes—
372C2×C4×C43AGL(1,ℤ/8)12yes—
373C2×C4×C43C22×D411yescharacteristic
374C2×C4×C43C22×D411yescharacteristic
375C2×C4×C43C2×#4111yescharacteristic
376C2×C4×C43C2×#4111yescharacteristic
377C2×C4×C43H(5,𝔽2)11yescharacteristic
378C2×C4×C43H(5,𝔽2)11yescharacteristic
379C8×C43—22no—
380C8×C43—41no—
381C8×C43—41no—
382C8×C43—41no—
383#25097C4311yesmaximal, characteristic, direct product factor, Sylow
384C22×C43—22no—
385C22×C43—22no—
386C22×C43—22no—
387C22×C43—41no—
388C22×C43—41no—
389C22×C43—41no—
390C22×C43—41no—
391C22×C43—42no—
392C22×C43—42no—
393C22×C43—42no—
394C22×C43—42no—
395C22×C43—42no—
396C22×C43—42no—
397C22×C43—42no—
398C22×C43—42no—
399C22×C43—42no—
400C22×C43—816no—
401C22×C43—81no—
402C22×C43—81no—
403C22×C43—81no—
404C22×C43—81no—
405C22×C43—81no—
406C22×C43—81no—
407C22×C43—81no—
408C22×C43—81no—
409C22×C43—81no—
410C22×C43—81no—
411C22×C43—81no—
412C22×C43—81no—
413C22×C43—81no—
414C22×C43—81no—
415C22×C43—81no—
416C22×C43—81no—
417C22×C43—81no—
418C22×C43—81no—
419C22×C43—81no—
420C22×C43C2×#12111yescharacteristic
421C22×C43D4211yescharacteristic
422C22×C43#54611yescharacteristic
423C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
424C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
425C22×C43#57611yescharacteristic
426C22×C43#57611yescharacteristic
427C4×C43—22no—
428C4×C43—22no—
429C4×C43—22no—
430C4×C43—42no—
431C4×C43—41no—
432C4×C43—42no—
433C4×C43—41no—
434C4×C43—81no—
435C4×C43—81no—
436C4×C43#52511yescharacteristic
437C4×C43#53811yescharacteristic
438C4×C43D4211yescharacteristic
439C4×C43#54611yescharacteristic
440C2×#469C2×C4311yescharacteristic, complemented
441C2×#459C2×C4311yescharacteristic, complemented
442C2×#447C2×C4311yescharacteristic, complemented
443C2×#418C2×C4311yescharacteristic, complemented
444#2433C2×C4311yescharacteristic, complemented
445#2363C2×C4311yescharacteristic, complemented
446#2065C2×C4311yescharacteristic, complemented
447#2054C2×C4311yescharacteristic, complemented
448#2041C2×C4311yescharacteristic, complemented
449#2011C2×C4311yescharacteristic, complemented
450#1982C2×C4311yescharacteristic, complemented
451#1926C2×C4311yescharacteristic, complemented
452#1879C2×C4311yescharacteristic, complemented
453#1875C2×C4311yescharacteristic, complemented
454#1851C2×C4311yescharacteristic, complemented
455C2×C43—42no—
456C2×C43—82no—
457C2×C43—82no—
458C2×C43—82no—
459C2×C43—161no—
460C2×C43#242411yescharacteristic
461C2×C43#303811yescharacteristic
462C2×C43#304111yescharacteristic
463C2×C43#326411yescharacteristic
464C2×C43#327411yescharacteristic
465C2×C43#331811yescharacteristic
466C2×C43#332511yescharacteristic
467C23×D4C22×C4311yescharacteristic
468C22×D8C22×C4311yescharacteristic
469C22×D8C22×C4311yescharacteristic
470C22×D8C22×C4311yescharacteristic, complemented
471C22×M16C22×C4311yescharacteristic
472C2×#127C22×C4311yescharacteristic
473C2×#127C22×C4311yescharacteristic
474C2×#121C22×C4311yescharacteristic
475C2×#121C22×C4311yescharacteristic
476C2×#120—21no—
477C2×#120—21no—
478C2×C4×D4C22×C4311yescharacteristic, complemented
479C2×#117C22×C4311yescharacteristic
480#469—24no—
481#459—24no—
482#447—24no—
483C2×#106C22×C4311yescharacteristic, complemented
484C2×C4⋊C8C22×C4311yescharacteristic, complemented
485C2×C4⋊C8C22×C4311yescharacteristic, complemented
486#418—24no—
487C2×#102C22×C4311yescharacteristic
488C2×#102C22×C4311yescharacteristic
489C2×#102C22×C4311yescharacteristic
490C2×#102C22×C4311yescharacteristic
491C2×#102C22×C4311yescharacteristic
492C2×#102C22×C4311yescharacteristic
493C2×#102C22×C4311yescharacteristic, complemented
494C2×#102C22×C4311yescharacteristic, complemented
495C2×#102C22×C4311yescharacteristic, complemented
496C2×#102C22×C4311yescharacteristic, complemented
497C2×C22⋊C8C22×C4311yescharacteristic
498#392—21no—
499#392—21no—
500#390—21no—
501#390C22×C4311yescharacteristic
502#390C22×C4311yescharacteristic
503#390C22×C4311yescharacteristic, complemented
504#389C22×C4311yescharacteristic, complemented
505#388—21no—
506#386—21no—
507C4×C4⋊C4C22×C4311yescharacteristic, complemented
508C4×C22⋊C4—21no—
509C4×C22⋊C4C22×C4311yescharacteristic
510#340C22×C4311yescharacteristic, complemented
511#340C22×C4311yescharacteristic, complemented
512#336C22×C4311yescharacteristic, complemented
513#336C22×C4311yescharacteristic, complemented
514C43#2509711yescharacteristic, direct product factor, Sylow
515C25—21no—
516C22×D4—22no—
517C22×D4—22no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—22no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—22no—
527C22×D4—41no—
528C22×D4—41no—
529C22×D4C23×C4311yescharacteristic
530C22×D4C23×C4311yescharacteristic
531C22×D4C23×C4311yescharacteristic
532C22×D4C23×C4311yescharacteristic
533C23×C4—21no—
534C23×C4C23×C4311yescharacteristic
535C2×D8—22no—
536C2×D8—22no—
537C2×D8—22no—
538C2×D8—22no—
539C2×D8—22no—
540C2×D8—22no—
541C2×D8—41no—
542C2×D8—41no—
543C2×D8—41no—
544C2×M16—22no—
545C2×M16—22no—
546C2×M16—41no—
547C22×C8C23×C4311yescharacteristic
548C22×C8C23×C4311yescharacteristic
549C22×C8C23×C4311yescharacteristic
550C22×C8C23×C4311yescharacteristic
551#127—22no—
552#127—22no—
553#127—41no—
554#127—41no—
555#121—22no—
556#121—22no—
557#121—22no—
558#121D4×C4314yescomplemented
559#120—44no—
560#120—44no—
561C4×D4—22no—
562C4×D4—41no—
563#117—22no—
564#117—41no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4C23×C4311yescharacteristic
567C2×C4⋊C4C23×C4311yescharacteristic
568C2×C4⋊C4C23×C4311yescharacteristic
569C2×C4⋊C4C23×C4311yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4D4×C4311yescharacteristic
581C2×C22⋊C4D4×C4311yescharacteristic
582C2×C42—21no—
583C2×C42—21no—
584C2×C42C23×C4311yescharacteristic
585C2×C42C23×C4311yescharacteristic
586#106—22no—
587C4⋊C8—22no—
588C4⋊C8—41no—
589#102—22no—
590#102—22no—
591#102—22no—
592#102—22no—
593#102—22no—
594#102—22no—
595#102—22no—
596#102—22no—
597#102—41no—
598#102D4×C4314yescomplemented
599C22⋊C8—22no—
600#95—21no—
601#95—21no—
602#95D4×C4311yescharacteristic
603#95D4×C4311yescharacteristic
604C24—21no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—42no—
612C24—42no—
613C24—81no—
614C24—81no—
615C24C2×D4×C4311yescharacteristic
616C2×D4—28no—
617C2×D4—24no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—44no—
640C2×D4—44no—
641C2×D4—42no—
642C2×D4—42no—
643C2×D4—44no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—42no—
649C2×D4—42no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—81no—
657C2×D4—81no—
658C2×D4—81no—
659C2×D4—81no—
660C2×D4—81no—
661C2×D4—81no—
662C2×D4C2×D4×C4312yes—
663C2×D4C2×D4×C4312yes—
664C2×D4#41×C4312yes—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—42no—
674C22×C4—42no—
675C22×C4—81no—
676C22×C4C2×D4×C4311yescharacteristic
677C22×C4C2×D4×C4311yescharacteristic
678C22×C4C2×D4×C4311yescharacteristic
679C22×C4C2×D4×C4312yes—
680C22×C4C2×D4×C4311yescharacteristic
681C22×C4C2×D4×C4311yescharacteristic
682C22×C4#41×C4312yes—
683C22×C4C24×C4311yescharacteristic
684D8—44no—
685D8—44no—
686D8—44no—
687M16—44no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8C2×D4×C4312yes—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—81no—
707C4⋊C4C2×D4×C4312yes—
708C4⋊C4C2×D4×C4312yes—
709C22⋊C4—24no—
710C22⋊C4—22no—
711C22⋊C4—22no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—42no—
716C22⋊C4—42no—
717C22⋊C4—42no—
718C22⋊C4—42no—
719C22⋊C4—42no—
720C22⋊C4—81no—
721C42—21no—
722C42—21no—
723C42—21no—
724C42—21no—
725C42—42no—
726C42—81no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—48no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—84no—
763C23—84no—
764C23—84no—
765C23—84no—
766C23—84no—
767C23—84no—
768C23#121×C4312yes—
769C23C22×D4×C4311yescharacteristic
770D4—22no—
771D4—22no—
772D4—22no—
773D4—22no—
774D4—22no—
775D4—22no—
776D4—48no—
777D4—41no—
778D4—41no—
779D4—41no—
780D4—41no—
781D4—41no—
782D4—41no—
783D4—41no—
784D4—41no—
785D4—41no—
786D4—41no—
787D4—84no—
788D4—84no—
789D4—84no—
790D4—84no—
791D4—84no—
792D4—84no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—21no—
805C2×C4—22no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—84no—
822C2×C4#121×C4312yes—
823C2×C4AGL(1,ℤ/8)×C4312yes—
824C2×C4AGL(1,ℤ/8)×C4312yes—
825C2×C4C22×D4×C4311yescharacteristic
826C2×C4C22×D4×C4311yescharacteristic
827C2×C4C2×#41×C4311yescharacteristic
828C2×C4C2×#41×C4311yescharacteristic
829C2×C4H(5,𝔽2)×C4311yescharacteristic
830C2×C4H(5,𝔽2)×C4311yescharacteristic
831C8—22no—
832C8—41no—
833C8—41no—
834C8—41no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—816no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22C2×#121×C4311yescharacteristic
872C22D42×C4311yescharacteristic
873C22C43×#54611yescharacteristic
874C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
875C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
876C22C43×#57611yescharacteristic
877C22C43×#57611yescharacteristic
878C4—22no—
879C4—22no—
880C4—22no—
881C4—42no—
882C4—41no—
883C4—42no—
884C4—41no—
885C4—81no—
886C4—81no—
887C4C43×#52511yescharacteristic
888C4C43×#53811yescharacteristic
889C4D42×C4311yescharacteristic
890C4C43×#54611yescharacteristic
891C2—42no—
892C2—82no—
893C2—82no—
894C2—82no—
895C2—161no—
896C2C43×#242411yescharacteristic
897C2C43×#303811yescharacteristic
898C2C43×#304111yescharacteristic
899C2C43×#326411yescharacteristic
900C2C43×#327411yescharacteristic
901C2C43×#331811yescharacteristic
902C2C43×#332511yescharacteristic
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×#459C2semidirect
3. C2×C43×#447C2semidirect
4. C2×C43×#418C2semidirect
5. C43×#2433C2semidirect
6. C43×#2363C2semidirect
7. C43×#2065C2semidirect
8. C43×#2054C2semidirect
9. C43×#2041C2semidirect
10. C43×#2011C2semidirect
11. C43×#1982C2semidirect
12. C43×#1926C2semidirect
13. C43×#1879C2semidirect
14. C43×#1875C2semidirect
15. C43×#1851C2semidirect
19. C22×D8×C43C22semidirect
27. C2×C4×D4×C43C22semidirect
32. C2×#106×C43C22semidirect
33. C2×C4⋊C8×C43C22semidirect
34. C2×C4⋊C8×C43C22semidirect
42. C2×#102×C43C22semidirect
43. C2×#102×C43C22semidirect
44. C2×#102×C43C22semidirect
45. C2×#102×C43C22semidirect
52. C43×#390C22semidirect
53. C43×#389C22semidirect
56. C4×C4⋊C4×C43C22semidirect
59. C43×#340C22semidirect
60. C43×#340C22semidirect
61. C43×#336C22semidirect
62. C43×#336C22semidirect
106. #121×C43D4semidirect
146. #102×C43D4semidirect
383. #25097C43direct (N × H)
440. C2×#469C2×C43semidirect
441. C2×#459C2×C43semidirect
442. C2×#447C2×C43semidirect
443. C2×#418C2×C43semidirect
444. #2433C2×C43semidirect
445. #2363C2×C43semidirect
446. #2065C2×C43semidirect
447. #2054C2×C43semidirect
448. #2041C2×C43semidirect
449. #2011C2×C43semidirect
450. #1982C2×C43semidirect
451. #1926C2×C43semidirect
452. #1879C2×C43semidirect
453. #1875C2×C43semidirect
454. #1851C2×C43semidirect
470. C22×D8C22×C43semidirect
478. C2×C4×D4C22×C43semidirect
483. C2×#106C22×C43semidirect
484. C2×C4⋊C8C22×C43semidirect
485. C2×C4⋊C8C22×C43semidirect
493. C2×#102C22×C43semidirect
494. C2×#102C22×C43semidirect
495. C2×#102C22×C43semidirect
496. C2×#102C22×C43semidirect
503. #390C22×C43semidirect
504. #389C22×C43semidirect
507. C4×C4⋊C4C22×C43semidirect
510. #340C22×C43semidirect
511. #340C22×C43semidirect
512. #336C22×C43semidirect
513. #336C22×C43semidirect
514. C43#25097direct (N × H)
558. #121D4×C43semidirect
598. #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×#4592
C2×C43×#4472
C2×C43×#4182
C43×#24332
C43×#23632
C43×#20652
C43×#20542
C43×#20412
C43×#20112
C43×#19822
C43×#19262
C43×#18792
C43×#18752
C43×#18512
#2509743