Finite Group Databasebeta

← C43×#18516 #24938533

Subgroups — C43×#18516 #24938533

Order 11008.

1258 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#41×C43C211yesmaximal, characteristic, complemented
2C43×#3169C211yesmaximal, characteristic, complemented
3C43×#3100C211yesmaximal, characteristic, complemented
4C43×#3035C211yesmaximal, characteristic, complemented
5C43×#1649C211yesmaximal, characteristic, complemented
6C43×#1647C211yesmaximal, characteristic, complemented
7C43×#1641C211yesmaximal, characteristic, complemented
8C43×#1639C211yesmaximal, characteristic, complemented
9C43×#1627C211yesmaximal, characteristic, complemented
10C43×#1625C211yesmaximal, characteristic, complemented
11C43×#1621C211yesmaximal, characteristic, complemented
12C43×#1619C211yesmaximal, characteristic, complemented
13C43×#1540C211yesmaximal, characteristic, complemented
14C43×#1476C211yesmaximal, characteristic, complemented
15C2×C43×D4⋊C8C211yesmaximal, characteristic, complemented
16C22×#41×C43—21no—
17C2×#135×C43—21no—
18C43×#550C2211yescharacteristic
19D4×Q8×C43C2211yescharacteristic
20C43×#548—21no—
21C43×#547—21no—
22C43×#547C2211yescharacteristic
23C43×#546—22no—
24C43×#546—21no—
25D42×C43—21no—
26D42×C43C2211yescharacteristic
27C43×#532—21no—
28C43×#532C2211yescharacteristic
29C43×#532C2211yescharacteristic, complemented
30C43×#525—22no—
31C43×#525—21no—
32C4×#41×C43C2211yescharacteristic
33C2×C4×D4×C43—21no—
34C2×C4×D4×C43C2211yescharacteristic
35C43×#500C2211yescharacteristic, complemented
36C43×#493C2211yescharacteristic, complemented
37C43×#486C2211yescharacteristic, complemented
38C43×#486C2211yescharacteristic, complemented
39C43×#480—21no—
40C43×#474C2211yescharacteristic
41C43×#474C2211yescharacteristic, complemented
42C43×#466—22no—
43C43×#464—21no—
44C43×#463—21no—
45C43×#462C2211yescharacteristic, complemented
46C43×#461C2211yescharacteristic, complemented
47C43×#460C2211yescharacteristic, complemented
48C43×#459C2211yescharacteristic
49C43×#459C2211yescharacteristic, complemented
50C43×#459C2211yescharacteristic, complemented
51C43×#447—21no—
52C4×D8×C43—21no—
53C4×D8×C43—21no—
54C4×D8×C43—22no—
55C43×#431C2211yescharacteristic, complemented
56C2×C4⋊C8×C43C2211yescharacteristic, complemented
57C43×#416—21no—
58C2×C4×C8×C43C2211yescharacteristic, complemented
59C43×#332C2211yescharacteristic, complemented
60C43×#332C2211yescharacteristic, complemented
61C43×#331C2211yescharacteristic, complemented
62C43×#331C2211yescharacteristic, complemented
63C43×Q8⋊C8C2211yescharacteristic, complemented
64C43×Q8⋊C8C2211yescharacteristic, complemented
65C43×D4⋊C8C2211yescharacteristic
66C43×D4⋊C8C2211yescharacteristic
67C43×D4⋊C8C2211yescharacteristic, complemented
68C43×D4⋊C8C2211yescharacteristic, complemented
69C43×D4⋊C8C2211yescharacteristic, complemented
70C43×D4⋊C8C2211yescharacteristic, complemented
71C2×#41×C43—22no—
72C2×#41×C43—22no—
73C2×#41×C43—21no—
74C2×#41×C43—21no—
75C2×#41×C43—21no—
76C2×#41×C43—21no—
77C2×#41×C43—44no—
78C2×#41×C43—44no—
79C2×#41×C43D411yescharacteristic
80C22×Q8×C43—21no—
81C22×D4×C43—22no—
82C22×D4×C43—21no—
83C22×D4×C43—21no—
84C22×D4×C43D411yescharacteristic
85C23×C4×C43—22no—
86C23×C4×C43—21no—
87#135×C43—44no—
88C2×Q16×C43—21no—
89C2×SD16×C43—21no—
90C2×SD16×C43—21no—
91C2×D8×C43—21no—
92C2×D8×C43—21no—
93C2×D8×C43—21no—
94C2×D8×C43—22no—
95C22×C8×C43—21no—
96C22×C8×C43—21no—
97C4⋊Q8×C43—21no—
98C4⋊Q8×C43C2311yescharacteristic
99C4⋊Q8×C43C2311yescharacteristic
100#127×C43—21no—
101#127×C43C2311yescharacteristic
102#127×C43C2311yescharacteristic
103#124×C43—22no—
104#124×C43—21no—
105#124×C43—21no—
106#123×C43—22no—
107#123×C43—22no—
108#123×C43—22no—
109C22⋊Q8×C43—22no—
110C22⋊Q8×C43—21no—
111C22⋊Q8×C43—22no—
112C22⋊Q8×C43—21no—
113#121×C43—22no—
114#121×C43—22no—
115#121×C43—22no—
116#121×C43—21no—
117#121×C43—21no—
118#121×C43—21no—
119#121×C43—21no—
120#121×C43—21no—
121#121×C43—21no—
122#121×C43—21no—
123#121×C43D412yes—
124#120×C43—22no—
125#120×C43—22no—
126#120×C43—22no—
127C4×Q8×C43D411yescharacteristic
128C4×Q8×C43C2311yescharacteristic
129C4×D4×C43—22no—
130C4×D4×C43—22no—
131C4×D4×C43—22no—
132C4×D4×C43—21no—
133C4×D4×C43—21no—
134C4×D4×C43—21no—
135C4×D4×C43—21no—
136C4×D4×C43—21no—
137C4×D4×C43—21no—
138C4×D4×C43—21no—
139C4×D4×C43—21no—
140C4×D4×C43—21no—
141C4×D4×C43D411yescharacteristic
142C4×D4×C43D411yescharacteristic
143C4×D4×C43D411yescharacteristic
144C4×D4×C43D412yes—
145C4×D4×C43C2311yescharacteristic
146C4×D4×C43C2311yescharacteristic
147C4×D4×C43C2311yescharacteristic
148#117×C43—21no—
149#117×C43D411yescharacteristic
150C2×C4⋊C4×C43—21no—
151C2×C4⋊C4×C43D411yescharacteristic
152C2×C22⋊C4×C43—22no—
153C2×C22⋊C4×C43—21no—
154C2×C42×C43—21no—
155C2×C42×C43C2311yescharacteristic
156#107×C43—22no—
157#107×C43—21no—
158#107×C43—21no—
159C4⋊C8×C43—21no—
160C4⋊C8×C43C2311yescharacteristic
161C4⋊C8×C43C2311yescharacteristic
162C4⋊C8×C43C2311yescharacteristic
163C4⋊C8×C43C2311yescharacteristic
164#103×C43—21no—
165#103×C43—21no—
166#102×C43—21no—
167#102×C43—21no—
168#102×C43—22no—
169#102×C43—21no—
170#102×C43—21no—
171#102×C43—21no—
172#102×C43—21no—
173#102×C43—22no—
174C22⋊C8×C43—21no—
175C4×C8×C43—21no—
176C4×C8×C43—21no—
177C4×C8×C43C2311yescharacteristic
178C4×C8×C43C2311yescharacteristic
179C24×C43—22no—
180C24×C43—21no—
181#41×C43—22no—
182#41×C43—48no—
183#41×C43—48no—
184#41×C43—42no—
185#41×C43—42no—
186#41×C43—42no—
187#41×C43—42no—
188#41×C43—42no—
189#41×C43—42no—
190#41×C43—42no—
191#41×C43—42no—
192#41×C43D814yescomplemented
193C2×Q8×C43—22no—
194C2×Q8×C43—21no—
195C2×Q8×C43—21no—
196C2×Q8×C43—42no—
197C2×Q8×C43—42no—
198C2×Q8×C43C2×D411yescharacteristic
199C2×D4×C43—22no—
200C2×D4×C43—22no—
201C2×D4×C43—22no—
202C2×D4×C43—22no—
203C2×D4×C43—22no—
204C2×D4×C43—21no—
205C2×D4×C43—21no—
206C2×D4×C43—21no—
207C2×D4×C43—21no—
208C2×D4×C43—22no—
209C2×D4×C43—22no—
210C2×D4×C43—21no—
211C2×D4×C43—21no—
212C2×D4×C43—21no—
213C2×D4×C43—41no—
214C2×D4×C43—42no—
215C2×D4×C43—42no—
216C2×D4×C43—48no—
217C2×D4×C43—42no—
218C2×D4×C43—42no—
219C2×D4×C43—41no—
220C2×D4×C43C2×D411yescharacteristic
221C2×D4×C43C2×D411yescharacteristic
222C2×D4×C43C2×D411yescharacteristic
223C2×D4×C43C2×D412yes—
224C22×C4×C43—21no—
225C22×C4×C43—22no—
226C22×C4×C43—22no—
227C22×C4×C43—22no—
228C22×C4×C43—21no—
229C22×C4×C43—22no—
230C22×C4×C43—21no—
231C22×C4×C43—21no—
232C22×C4×C43—21no—
233C22×C4×C43—21no—
234C22×C4×C43—21no—
235C22×C4×C43—21no—
236C22×C4×C43—48no—
237C22×C4×C43—42no—
238C22×C4×C43—42no—
239C22×C4×C43—41no—
240C22×C4×C43C2×D411yescharacteristic
241C22×C4×C43C2×D411yescharacteristic
242C22×C4×C43C2×D411yescharacteristic
243Q16×C43—42no—
244SD16×C43—42no—
245SD16×C43—42no—
246D8×C43—44no—
247D8×C43—42no—
248D8×C43—42no—
249D8×C43—42no—
250C2×C8×C43—21no—
251C2×C8×C43—21no—
252C2×C8×C43—21no—
253C2×C8×C43—21no—
254C2×C8×C43—21no—
255C2×C8×C43—21no—
256C2×C8×C43—42no—
257C2×C8×C43—42no—
258C4⋊C4×C43—22no—
259C4⋊C4×C43—22no—
260C4⋊C4×C43—21no—
261C4⋊C4×C43—21no—
262C4⋊C4×C43—21no—
263C4⋊C4×C43—21no—
264C4⋊C4×C43—21no—
265C4⋊C4×C43—21no—
266C4⋊C4×C43C2×D411yescharacteristic
267C4⋊C4×C43C2×D411yescharacteristic
268C4⋊C4×C43C2×D411yescharacteristic
269C4⋊C4×C43C2×D411yescharacteristic
270C4⋊C4×C43C2×D412yes—
271C22⋊C4×C43—22no—
272C22⋊C4×C43—22no—
273C22⋊C4×C43—22no—
274C22⋊C4×C43—22no—
275C22⋊C4×C43—21no—
276C22⋊C4×C43—22no—
277C22⋊C4×C43—21no—
278C22⋊C4×C43—21no—
279C22⋊C4×C43—22no—
280C22⋊C4×C43—21no—
281C22⋊C4×C43—21no—
282C22⋊C4×C43—21no—
283C22⋊C4×C43—21no—
284C22⋊C4×C43—41no—
285C22⋊C4×C43—41no—
286C42×C43—21no—
287C42×C43—21no—
288C42×C43—21no—
289C42×C43C2×D411yescharacteristic
290C42×C43C2×D411yescharacteristic
291C42×C43C2×D411yescharacteristic
292C42×C43C2411yescharacteristic
293C23×C43—21no—
294C23×C43—21no—
295C23×C43—21no—
296C23×C43—22no—
297C23×C43—42no—
298C23×C43—44no—
299C23×C43—44no—
300C23×C43—42no—
301C23×C43—41no—
302C23×C43—81no—
303C23×C43—82no—
304C23×C43#12011yescharacteristic
305Q8×C43—21no—
306Q8×C43—44no—
307Q8×C43—41no—
308Q8×C43—41no—
309Q8×C43—41no—
310Q8×C43—41no—
311Q8×C43C2×D812yes—
312D4×C43—24no—
313D4×C43—21no—
314D4×C43—21no—
315D4×C43—21no—
316D4×C43—21no—
317D4×C43—42no—
318D4×C43—42no—
319D4×C43—44no—
320D4×C43—42no—
321D4×C43—44no—
322D4×C43—44no—
323D4×C43—44no—
324D4×C43—44no—
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—82no—
334D4×C43—82no—
335D4×C43C2×D812yes—
336D4×C43#13512yescomplemented
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—24no—
341C2×C4×C43—21no—
342C2×C4×C43—21no—
343C2×C4×C43—21no—
344C2×C4×C43—22no—
345C2×C4×C43—21no—
346C2×C4×C43—41no—
347C2×C4×C43—44no—
348C2×C4×C43—44no—
349C2×C4×C43—44no—
350C2×C4×C43—42no—
351C2×C4×C43—41no—
352C2×C4×C43—41no—
353C2×C4×C43—41no—
354C2×C4×C43—41no—
355C2×C4×C43—41no—
356C2×C4×C43—41no—
357C2×C4×C43—42no—
358C2×C4×C43—44no—
359C2×C4×C43—42no—
360C2×C4×C43—41no—
361C2×C4×C43—81no—
362C2×C4×C43—82no—
363C2×C4×C43#12011yescharacteristic
364C2×C4×C43#12011yescharacteristic
365C2×C4×C43#12011yescharacteristic
366C2×C4×C43C2×D812yes—
367C2×C4×C43AGL(1,ℤ/8)12yes—
368C2×C4×C43C22×D411yescharacteristic
369C2×C4×C43C22×D411yescharacteristic
370C2×C4×C43C22×D411yescharacteristic
371C8×C43—22no—
372C8×C43—41no—
373C8×C43—41no—
374C8×C43—41no—
375C8×C43—41no—
376C8×C43—41no—
377#18516C4311yesmaximal, characteristic, direct product factor, Sylow
378C22×C43—21no—
379C22×C43—21no—
380C22×C43—22no—
381C22×C43—22no—
382C22×C43—41no—
383C22×C43—41no—
384C22×C43—41no—
385C22×C43—41no—
386C22×C43—42no—
387C22×C43—41no—
388C22×C43—41no—
389C22×C43—42no—
390C22×C43—42no—
391C22×C43—41no—
392C22×C43—84no—
393C22×C43—88no—
394C22×C43—81no—
395C22×C43—81no—
396C22×C43—81no—
397C22×C43#44712yes—
398C22×C43C2×#12011yescharacteristic
399C4×C43—22no—
400C4×C43—21no—
401C4×C43—21no—
402C4×C43—21no—
403C4×C43—41no—
404C4×C43—42no—
405C4×C43—41no—
406C4×C43—41no—
407C4×C43—41no—
408C4×C43—81no—
409C4×C43#44712yes—
410C4×C43C22×D811yescharacteristic
411C4×C43C2×#13511yescharacteristic
412C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
413C4×C43#57511yescharacteristic
414D4×#41C2×C4311yescharacteristic, complemented
415#3169C2×C4311yescharacteristic, complemented
416#3100C2×C4311yescharacteristic, complemented
417#3035C2×C4311yescharacteristic, complemented
418#1649C2×C4311yescharacteristic, complemented
419#1647C2×C4311yescharacteristic, complemented
420#1641C2×C4311yescharacteristic, complemented
421#1639C2×C4311yescharacteristic, complemented
422#1627C2×C4311yescharacteristic, complemented
423#1625C2×C4311yescharacteristic, complemented
424#1621C2×C4311yescharacteristic, complemented
425#1619C2×C4311yescharacteristic, complemented
426#1540C2×C4311yescharacteristic, complemented
427#1476C2×C4311yescharacteristic, complemented
428C2×D4⋊C8C2×C4311yescharacteristic, complemented
429C2×C43—22no—
430C2×C43—42no—
431C2×C43—42no—
432C2×C43—81no—
433C2×C43—82no—
434C2×C43—161no—
435C2×C43C2×#44711yescharacteristic
436C2×C43#300211yescharacteristic
437C2×C43#301811yescharacteristic
438C22×#41—21no—
439C2×#135—21no—
440#550C22×C4311yescharacteristic
441D4×Q8C22×C4311yescharacteristic
442#548—21no—
443#547—21no—
444#547C22×C4311yescharacteristic
445#546—22no—
446#546—21no—
447D42—21no—
448D42C22×C4311yescharacteristic
449#532—21no—
450#532C22×C4311yescharacteristic
451#532C22×C4311yescharacteristic, complemented
452#525—22no—
453#525—21no—
454C4×#41C22×C4311yescharacteristic
455C2×C4×D4—21no—
456C2×C4×D4C22×C4311yescharacteristic
457#500C22×C4311yescharacteristic, complemented
458#493C22×C4311yescharacteristic, complemented
459#486C22×C4311yescharacteristic, complemented
460#486C22×C4311yescharacteristic, complemented
461#480—21no—
462#474C22×C4311yescharacteristic
463#474C22×C4311yescharacteristic, complemented
464#466—22no—
465#464—21no—
466#463—21no—
467#462C22×C4311yescharacteristic, complemented
468#461C22×C4311yescharacteristic, complemented
469#460C22×C4311yescharacteristic, complemented
470#459C22×C4311yescharacteristic
471#459C22×C4311yescharacteristic, complemented
472#459C22×C4311yescharacteristic, complemented
473#447—21no—
474C4×D8—21no—
475C4×D8—21no—
476C4×D8—22no—
477#431C22×C4311yescharacteristic, complemented
478C2×C4⋊C8C22×C4311yescharacteristic, complemented
479#416—21no—
480C2×C4×C8C22×C4311yescharacteristic, complemented
481#332C22×C4311yescharacteristic, complemented
482#332C22×C4311yescharacteristic, complemented
483#331C22×C4311yescharacteristic, complemented
484#331C22×C4311yescharacteristic, complemented
485Q8⋊C8C22×C4311yescharacteristic, complemented
486Q8⋊C8C22×C4311yescharacteristic, complemented
487D4⋊C8C22×C4311yescharacteristic
488D4⋊C8C22×C4311yescharacteristic
489D4⋊C8C22×C4311yescharacteristic, complemented
490D4⋊C8C22×C4311yescharacteristic, complemented
491D4⋊C8C22×C4311yescharacteristic, complemented
492D4⋊C8C22×C4311yescharacteristic, complemented
493C43#1851611yescharacteristic, direct product factor, Sylow
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—21no—
497C2×#41—21no—
498C2×#41—21no—
499C2×#41—21no—
500C2×#41—44no—
501C2×#41—44no—
502C2×#41D4×C4311yescharacteristic
503C22×Q8—21no—
504C22×D4—22no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4D4×C4311yescharacteristic
508C23×C4—22no—
509C23×C4—21no—
510#135—44no—
511C2×Q16—21no—
512C2×SD16—21no—
513C2×SD16—21no—
514C2×D8—21no—
515C2×D8—21no—
516C2×D8—21no—
517C2×D8—22no—
518C22×C8—21no—
519C22×C8—21no—
520C4⋊Q8—21no—
521C4⋊Q8C23×C4311yescharacteristic
522C4⋊Q8C23×C4311yescharacteristic
523#127—21no—
524#127C23×C4311yescharacteristic
525#127C23×C4311yescharacteristic
526#124—22no—
527#124—21no—
528#124—21no—
529#123—22no—
530#123—22no—
531#123—22no—
532C22⋊Q8—22no—
533C22⋊Q8—21no—
534C22⋊Q8—22no—
535C22⋊Q8—21no—
536#121—22no—
537#121—22no—
538#121—22no—
539#121—21no—
540#121—21no—
541#121—21no—
542#121—21no—
543#121—21no—
544#121—21no—
545#121—21no—
546#121D4×C4312yes—
547#120—22no—
548#120—22no—
549#120—22no—
550C4×Q8D4×C4311yescharacteristic
551C4×Q8C23×C4311yescharacteristic
552C4×D4—22no—
553C4×D4—22no—
554C4×D4—22no—
555C4×D4—21no—
556C4×D4—21no—
557C4×D4—21no—
558C4×D4—21no—
559C4×D4—21no—
560C4×D4—21no—
561C4×D4—21no—
562C4×D4—21no—
563C4×D4—21no—
564C4×D4D4×C4311yescharacteristic
565C4×D4D4×C4311yescharacteristic
566C4×D4D4×C4311yescharacteristic
567C4×D4D4×C4312yes—
568C4×D4C23×C4311yescharacteristic
569C4×D4C23×C4311yescharacteristic
570C4×D4C23×C4311yescharacteristic
571#117—21no—
572#117D4×C4311yescharacteristic
573C2×C4⋊C4—21no—
574C2×C4⋊C4D4×C4311yescharacteristic
575C2×C22⋊C4—22no—
576C2×C22⋊C4—21no—
577C2×C42—21no—
578C2×C42C23×C4311yescharacteristic
579#107—22no—
580#107—21no—
581#107—21no—
582C4⋊C8—21no—
583C4⋊C8C23×C4311yescharacteristic
584C4⋊C8C23×C4311yescharacteristic
585C4⋊C8C23×C4311yescharacteristic
586C4⋊C8C23×C4311yescharacteristic
587#103—21no—
588#103—21no—
589#102—21no—
590#102—21no—
591#102—22no—
592#102—21no—
593#102—21no—
594#102—21no—
595#102—21no—
596#102—22no—
597C22⋊C8—21no—
598C4×C8—21no—
599C4×C8—21no—
600C4×C8C23×C4311yescharacteristic
601C4×C8C23×C4311yescharacteristic
602C24—22no—
603C24—21no—
604#41—22no—
605#41—48no—
606#41—48no—
607#41—42no—
608#41—42no—
609#41—42no—
610#41—42no—
611#41—42no—
612#41—42no—
613#41—42no—
614#41—42no—
615#41D8×C4314yescomplemented
616C2×Q8—22no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—42no—
620C2×Q8—42no—
621C2×Q8C2×D4×C4311yescharacteristic
622C2×D4—21no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—22no—
629C2×D4—22no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—41no—
637C2×D4—48no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—41no—
643C2×D4C2×D4×C4311yescharacteristic
644C2×D4C2×D4×C4311yescharacteristic
645C2×D4C2×D4×C4311yescharacteristic
646C2×D4C2×D4×C4312yes—
647C22×C4—21no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—22no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—48no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—41no—
663C22×C4C2×D4×C4311yescharacteristic
664C22×C4C2×D4×C4311yescharacteristic
665C22×C4C2×D4×C4311yescharacteristic
666Q16—42no—
667SD16—42no—
668SD16—42no—
669D8—44no—
670D8—42no—
671D8—42no—
672D8—42no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—42no—
680C2×C8—42no—
681C4⋊C4—22no—
682C4⋊C4—22no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4C2×D4×C4311yescharacteristic
690C4⋊C4C2×D4×C4311yescharacteristic
691C4⋊C4C2×D4×C4311yescharacteristic
692C4⋊C4C2×D4×C4311yescharacteristic
693C4⋊C4C2×D4×C4312yes—
694C22⋊C4—22no—
695C22⋊C4—22no—
696C22⋊C4—22no—
697C22⋊C4—22no—
698C22⋊C4—21no—
699C22⋊C4—21no—
700C22⋊C4—22no—
701C22⋊C4—21no—
702C22⋊C4—21no—
703C22⋊C4—22no—
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—41no—
708C22⋊C4—41no—
709C42—21no—
710C42—21no—
711C42—21no—
712C42C2×D4×C4311yescharacteristic
713C42C2×D4×C4311yescharacteristic
714C42C2×D4×C4311yescharacteristic
715C42C24×C4311yescharacteristic
716C23—21no—
717C23—21no—
718C23—21no—
719C23—22no—
720C23—42no—
721C23—44no—
722C23—44no—
723C23—42no—
724C23—41no—
725C23—81no—
726C23—82no—
727C23#120×C4311yescharacteristic
728Q8—21no—
729Q8—44no—
730Q8—41no—
731Q8—41no—
732Q8—41no—
733Q8—41no—
734Q8C2×D8×C4312yes—
735D4—24no—
736D4—21no—
737D4—21no—
738D4—21no—
739D4—21no—
740D4—42no—
741D4—42no—
742D4—44no—
743D4—42no—
744D4—44no—
745D4—44no—
746D4—44no—
747D4—44no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—41no—
756D4—82no—
757D4—82no—
758D4C2×D8×C4312yes—
759D4#135×C4312yescomplemented
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—24no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—41no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—42no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—44no—
782C2×C4—42no—
783C2×C4—41no—
784C2×C4—81no—
785C2×C4—82no—
786C2×C4#120×C4311yescharacteristic
787C2×C4#120×C4311yescharacteristic
788C2×C4#120×C4311yescharacteristic
789C2×C4C2×D8×C4312yes—
790C2×C4AGL(1,ℤ/8)×C4312yes—
791C2×C4C22×D4×C4311yescharacteristic
792C2×C4C22×D4×C4311yescharacteristic
793C2×C4C22×D4×C4311yescharacteristic
794C8—22no—
795C8—41no—
796C8—41no—
797C8—41no—
798C8—41no—
799C8—41no—
800C22—21no—
801C22—21no—
802C22—22no—
803C22—22no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—42no—
809C22—41no—
810C22—41no—
811C22—42no—
812C22—42no—
813C22—41no—
814C22—84no—
815C22—88no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22C43×#44712yes—
820C22C2×#120×C4311yescharacteristic
821C4—22no—
822C4—21no—
823C4—21no—
824C4—21no—
825C4—41no—
826C4—42no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—81no—
831C4C43×#44712yes—
832C4C22×D8×C4311yescharacteristic
833C4C2×#135×C4311yescharacteristic
834C4C2×AGL(1,ℤ/8)×C4311yescharacteristic
835C4C43×#57511yescharacteristic
836C2—22no—
837C2—42no—
838C2—42no—
839C2—81no—
840C2—82no—
841C2—161no—
842C2C2×C43×#44711yescharacteristic
843C2C43×#300211yescharacteristic
844C2C43×#301811yescharacteristic
subgroupG/H
centerC2×C4×C43#120
commutator, Frattini, cosocleC42C24×C43
socleC22×C43C2×#120
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. D4×#41×C43C2semidirect
2. C43×#3169C2semidirect
3. C43×#3100C2semidirect
4. C43×#3035C2semidirect
5. C43×#1649C2semidirect
6. C43×#1647C2semidirect
7. C43×#1641C2semidirect
8. C43×#1639C2semidirect
9. C43×#1627C2semidirect
10. C43×#1625C2semidirect
11. C43×#1621C2semidirect
12. C43×#1619C2semidirect
13. C43×#1540C2semidirect
14. C43×#1476C2semidirect
15. C2×C43×D4⋊C8C2semidirect
29. C43×#532C22semidirect
35. C43×#500C22semidirect
36. C43×#493C22semidirect
37. C43×#486C22semidirect
38. C43×#486C22semidirect
41. C43×#474C22semidirect
45. C43×#462C22semidirect
46. C43×#461C22semidirect
47. C43×#460C22semidirect
49. C43×#459C22semidirect
50. C43×#459C22semidirect
55. C43×#431C22semidirect
56. C2×C4⋊C8×C43C22semidirect
58. C2×C4×C8×C43C22semidirect
59. C43×#332C22semidirect
60. C43×#332C22semidirect
61. C43×#331C22semidirect
62. C43×#331C22semidirect
63. C43×Q8⋊C8C22semidirect
64. C43×Q8⋊C8C22semidirect
67. C43×D4⋊C8C22semidirect
68. C43×D4⋊C8C22semidirect
69. C43×D4⋊C8C22semidirect
70. C43×D4⋊C8C22semidirect
192. #41×C43D8semidirect
336. D4×C43#135semidirect
377. #18516C43direct (N × H)
414. D4×#41C2×C43semidirect
415. #3169C2×C43semidirect
416. #3100C2×C43semidirect
417. #3035C2×C43semidirect
418. #1649C2×C43semidirect
419. #1647C2×C43semidirect
420. #1641C2×C43semidirect
421. #1639C2×C43semidirect
422. #1627C2×C43semidirect
423. #1625C2×C43semidirect
424. #1621C2×C43semidirect
425. #1619C2×C43semidirect
426. #1540C2×C43semidirect
427. #1476C2×C43semidirect
428. C2×D4⋊C8C2×C43semidirect
451. #532C22×C43semidirect
457. #500C22×C43semidirect
458. #493C22×C43semidirect
459. #486C22×C43semidirect
460. #486C22×C43semidirect
463. #474C22×C43semidirect
467. #462C22×C43semidirect
468. #461C22×C43semidirect
469. #460C22×C43semidirect
471. #459C22×C43semidirect
472. #459C22×C43semidirect
477. #431C22×C43semidirect
478. C2×C4⋊C8C22×C43semidirect
480. C2×C4×C8C22×C43semidirect
481. #332C22×C43semidirect
482. #332C22×C43semidirect
483. #331C22×C43semidirect
484. #331C22×C43semidirect
485. Q8⋊C8C22×C43semidirect
486. Q8⋊C8C22×C43semidirect
489. D4⋊C8C22×C43semidirect
490. D4⋊C8C22×C43semidirect
491. D4⋊C8C22×C43semidirect
492. D4⋊C8C22×C43semidirect
493. C43#18516direct (N × H)
615. #41D8×C43semidirect
759. D4#135×C43semidirect

Maximal subgroups

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

subgroupindex
D4×#41×C432
C43×#31692
C43×#31002
C43×#30352
C43×#16492
C43×#16472
C43×#16412
C43×#16392
C43×#16272
C43×#16252
C43×#16212
C43×#16192
C43×#15402
C43×#14762
C2×C43×D4⋊C82
#1851643