Finite Group Databasebeta

← C43×#33347 #24953364

Subgroups — C43×#33347 #24953364

Order 11008.

1236 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3449C211yesmaximal, characteristic
2C2×C43×#413C211yesmaximal, characteristic, complemented
3C2×C43×#410C211yesmaximal, characteristic, complemented
4C43×#2123C212yesmaximal, complemented
5C43×#2122C212yesmaximal, complemented
6C43×#2121C214yesmaximal, complemented
7C43×#2120C214yesmaximal, complemented
8C22×#41×C43C411yescharacteristic, complemented
9C22×#41×C43C2211yescharacteristic
10C22×M16×C43—21no—
11C43×#537—21no—
12C43×#537—21no—
13C43×#536—21no—
14C43×#536C411yescharacteristic, complemented
15C43×#536C2211yescharacteristic
16C43×#535—21no—
17C43×#535C411yescharacteristic, complemented
18C43×#535C2211yescharacteristic
19C43×#534C412yescomplemented
20C43×#534C2212yes—
21C43×#532—21no—
22C43×#532—21no—
23C43×#525—21no—
24C43×#525—21no—
25C43×#525C412yescomplemented
26C43×#525C2212yes—
27C2×#117×C43—21no—
28C2×#117×C43C411yescharacteristic, complemented
29C43×#413—21no—
30C43×#413—21no—
31C43×#413C2212yes—
32C43×#413C2212yes—
33C2×#101×C43—21no—
34C2×#100×C43C2212yes—
35C43×#410—21no—
36C43×#410—21no—
37C43×#410C2212yes—
38C43×#410C2212yes—
39C2×#99×C43—21no—
40C2×#99×C43C2212yes—
41C43×#352C2218yescomplemented
42C43×AΣL(1,𝔽16)C2218yescomplemented
43C2×#41×C43—21no—
44C2×#41×C43—21no—
45C2×#41×C43—21no—
46C2×#41×C43—21no—
47C2×#41×C43—41no—
48C2×#41×C43—41no—
49C2×#41×C43—41no—
50C2×#41×C43—41no—
51C2×#41×C43—41no—
52C2×#41×C43—41no—
53C2×#41×C43—41no—
54C2×#41×C43—41no—
55C2×#41×C43C2×C411yescharacteristic
56C2×#41×C43C2×C411yescharacteristic
57C2×#41×C43D411yescharacteristic
58C2×#41×C43D411yescharacteristic
59C2×#41×C43D411yescharacteristic
60C2×#41×C43D411yescharacteristic
61C2×#41×C43C2311yescharacteristic
62C2×#41×C43C2311yescharacteristic
63C22×Q8×C43C2×C411yescharacteristic, complemented
64C22×Q8×C43D411yescharacteristic
65C22×D4×C43C2×C411yescharacteristic
66C22×D4×C43C2×C412yes—
67C22×D4×C43C2×C411yescharacteristic, complemented
68C22×D4×C43D411yescharacteristic
69C22×D4×C43C2311yescharacteristic
70C23×C4×C43C2×C411yescharacteristic
71C23×C4×C43C2×C412yescomplemented
72C23×C4×C43D411yescharacteristic
73C23×C4×C43D411yescharacteristic
74C2×M16×C43—22no—
75C2×M16×C43—22no—
76C2×M16×C43—22no—
77C2×M16×C43—41no—
78C2×M16×C43—41no—
79C2×M16×C43—41no—
80C22×C8×C43—41no—
81C4⋊Q8×C43—21no—
82C4⋊Q8×C43—21no—
83#127×C43—21no—
84#127×C43—21no—
85#124×C43—21no—
86#124×C43—21no—
87#124×C43—21no—
88#124×C43—21no—
89#123×C43—22no—
90#123×C43—22no—
91#123×C43C2×C412yes—
92#123×C43C2×C412yescomplemented
93#123×C43C2×C412yescomplemented
94#123×C43C2312yes—
95C22⋊Q8×C43—22no—
96C22⋊Q8×C43—22no—
97C22⋊Q8×C43—21no—
98C22⋊Q8×C43—21no—
99C22⋊Q8×C43—21no—
100C22⋊Q8×C43—21no—
101#121×C43—22no—
102#121×C43—22no—
103#121×C43—22no—
104#121×C43—22no—
105#121×C43—22no—
106#121×C43—22no—
107#121×C43—21no—
108#121×C43—21no—
109#121×C43—21no—
110#121×C43—21no—
111#120×C43—22no—
112#120×C43—22no—
113#120×C43C2×C412yes—
114#120×C43C2×C412yescomplemented
115#120×C43C2×C412yescomplemented
116#120×C43C2312yes—
117C4×D4×C43—22no—
118C4×D4×C43—22no—
119C4×D4×C43—22no—
120C4×D4×C43—22no—
121#117×C43—21no—
122#117×C43—21no—
123#117×C43—22no—
124#117×C43—22no—
125#117×C43—41no—
126#117×C43—41no—
127#117×C43C2×C412yescomplemented
128#117×C43C2×C411yescharacteristic, complemented
129#117×C43C2×C411yescharacteristic, complemented
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43—41no—
132C2×C22⋊C4×C43—22no—
133C2×C22⋊C4×C43C2×C412yes—
134C2×C42×C43—21no—
135C2×C42×C43—41no—
136#101×C43—22no—
137#101×C43—22no—
138#100×C43—22no—
139#100×C43C2314yes—
140#99×C43—22no—
141#99×C43—22no—
142#99×C43—22no—
143#99×C43C2314yes—
144C24×C43C22⋊C411yescharacteristic
145C24×C43C22×C411yescharacteristic
146C24×C43C22×C412yes—
147C24×C43C2×D411yescharacteristic
148#41×C43—41no—
149#41×C43—41no—
150#41×C43—41no—
151#41×C43—41no—
152#41×C43—41no—
153#41×C43—41no—
154#41×C43—41no—
155#41×C43—41no—
156#41×C43—41no—
157#41×C43—41no—
158#41×C43—41no—
159#41×C43—41no—
160#41×C43—41no—
161#41×C43—41no—
162#41×C43—41no—
163#41×C43—41no—
164#41×C43—42no—
165#41×C43—42no—
166#41×C43—42no—
167#41×C43—42no—
168#41×C43—42no—
169#41×C43—42no—
170#41×C43—41no—
171#41×C43—41no—
172#41×C43—41no—
173#41×C43—41no—
174C2×Q8×C43—21no—
175C2×Q8×C43—21no—
176C2×Q8×C43—41no—
177C2×Q8×C43—41no—
178C2×Q8×C43—41no—
179C2×Q8×C43—41no—
180C2×Q8×C43C22⋊C411yescharacteristic
181C2×Q8×C43C22⋊C411yescharacteristic
182C2×Q8×C43C2×D411yescharacteristic
183C2×Q8×C43C2×D411yescharacteristic
184C2×D4×C43—21no—
185C2×D4×C43—21no—
186C2×D4×C43—22no—
187C2×D4×C43—22no—
188C2×D4×C43—22no—
189C2×D4×C43—22no—
190C2×D4×C43—22no—
191C2×D4×C43—22no—
192C2×D4×C43—41no—
193C2×D4×C43—41no—
194C2×D4×C43—41no—
195C2×D4×C43—41no—
196C2×D4×C43—41no—
197C2×D4×C43—41no—
198C2×D4×C43—42no—
199C2×D4×C43—42no—
200C2×D4×C43—41no—
201C2×D4×C43—41no—
202C2×D4×C43C22⋊C411yescharacteristic
203C2×D4×C43C22⋊C411yescharacteristic
204C2×D4×C43C22⋊C411yescharacteristic
205C2×D4×C43C22⋊C411yescharacteristic
206C2×D4×C43C22×C411yescharacteristic
207C2×D4×C43C22×C411yescharacteristic
208C2×D4×C43C22×C411yescharacteristic
209C2×D4×C43C2×D411yescharacteristic
210C2×D4×C43C2×D411yescharacteristic
211C2×D4×C43C2×D411yescharacteristic
212C2×D4×C43C2×D411yescharacteristic
213C2×D4×C43C2411yescharacteristic
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—21no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43—21no—
226C22×C4×C43—22no—
227C22×C4×C43—22no—
228C22×C4×C43—22no—
229C22×C4×C43—42no—
230C22×C4×C43—42no—
231C22×C4×C43—42no—
232C22×C4×C43C22⋊C411yescharacteristic
233C22×C4×C43C22⋊C411yescharacteristic
234C22×C4×C43C22⋊C411yescharacteristic
235C22×C4×C43C22⋊C411yescharacteristic
236C22×C4×C43C22⋊C411yescharacteristic
237C22×C4×C43C22⋊C411yescharacteristic
238C22×C4×C43C22⋊C411yescharacteristic
239C22×C4×C43C22⋊C411yescharacteristic
240C22×C4×C43C22⋊C411yescharacteristic
241C22×C4×C43C22×C411yescharacteristic
242C22×C4×C43C22×C411yescharacteristic
243C22×C4×C43C22×C412yes—
244C22×C4×C43C2×D411yescharacteristic
245C22×C4×C43C2×D411yescharacteristic
246C22×C4×C43C2×D411yescharacteristic
247C22×C4×C43C2×D411yescharacteristic
248C22×C4×C43C2×D411yescharacteristic
249M16×C43—24no—
250M16×C43—42no—
251M16×C43—42no—
252M16×C43—42no—
253C2×C8×C43—42no—
254C2×C8×C43—42no—
255C2×C8×C43—42no—
256C4⋊C4×C43—22no—
257C4⋊C4×C43—21no—
258C4⋊C4×C43—21no—
259C4⋊C4×C43—22no—
260C4⋊C4×C43—22no—
261C4⋊C4×C43—22no—
262C4⋊C4×C43—22no—
263C4⋊C4×C43—42no—
264C4⋊C4×C43—42no—
265C22⋊C4×C43—22no—
266C22⋊C4×C43—22no—
267C22⋊C4×C43—22no—
268C22⋊C4×C43—22no—
269C22⋊C4×C43—22no—
270C22⋊C4×C43—22no—
271C22⋊C4×C43—22no—
272C22⋊C4×C43—22no—
273C22⋊C4×C43—22no—
274C22⋊C4×C43—24no—
275C22⋊C4×C43—42no—
276C22⋊C4×C43C22×C412yes—
277C22⋊C4×C43C22×C412yes—
278C42×C43—22no—
279C42×C43—21no—
280C42×C43—21no—
281C42×C43—42no—
282C42×C43—42no—
283C23×C43—21no—
284C23×C43—21no—
285C23×C43—21no—
286C23×C43—21no—
287C23×C43—21no—
288C23×C43—21no—
289C23×C43—22no—
290C23×C43—42no—
291C23×C43—81no—
292C23×C43—81no—
293C23×C43—81no—
294C23×C43—82no—
295C23×C43C2×C22⋊C411yescharacteristic
296C23×C43C2×C22⋊C411yescharacteristic
297C23×C43C2×C22⋊C411yescharacteristic
298C23×C43C2×C22⋊C411yescharacteristic
299C23×C43C2×C22⋊C411yescharacteristic
300C23×C43C23×C411yescharacteristic
301C23×C43C22×D411yescharacteristic
302Q8×C43—41no—
303Q8×C43—41no—
304Q8×C43—41no—
305Q8×C43—41no—
306Q8×C43—42no—
307Q8×C43—41no—
308Q8×C43—41no—
309D4×C43—41no—
310D4×C43—41no—
311D4×C43—41no—
312D4×C43—41no—
313D4×C43—41no—
314D4×C43—41no—
315D4×C43—41no—
316D4×C43—41no—
317D4×C43—41no—
318D4×C43—41no—
319D4×C43—41no—
320D4×C43—41no—
321D4×C43—42no—
322D4×C43—44no—
323D4×C43—42no—
324D4×C43—42no—
325D4×C43—41no—
326D4×C43—41no—
327D4×C43—82no—
328D4×C43—82no—
329D4×C43—82no—
330D4×C43—82no—
331C2×C4×C43—21no—
332C2×C4×C43—21no—
333C2×C4×C43—21no—
334C2×C4×C43—21no—
335C2×C4×C43—21no—
336C2×C4×C43—21no—
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—21no—
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—21no—
348C2×C4×C43—21no—
349C2×C4×C43—21no—
350C2×C4×C43—21no—
351C2×C4×C43—21no—
352C2×C4×C43—21no—
353C2×C4×C43—21no—
354C2×C4×C43—21no—
355C2×C4×C43—21no—
356C2×C4×C43—21no—
357C2×C4×C43—21no—
358C2×C4×C43—21no—
359C2×C4×C43—21no—
360C2×C4×C43—21no—
361C2×C4×C43—22no—
362C2×C4×C43—22no—
363C2×C4×C43—22no—
364C2×C4×C43—44no—
365C2×C4×C43—42no—
366C2×C4×C43—42no—
367C2×C4×C43—42no—
368C2×C4×C43—44no—
369C2×C4×C43—82no—
370C2×C4×C43—84no—
371C2×C4×C43#9911yescharacteristic
372C2×C4×C43#9911yescharacteristic
373C2×C4×C43#9911yescharacteristic
374C2×C4×C43#9911yescharacteristic
375C2×C4×C43C2×C22⋊C411yescharacteristic
376C2×C4×C43C2×C22⋊C411yescharacteristic
377C2×C4×C43C2×C22⋊C411yescharacteristic
378C2×C4×C43C2×C22⋊C411yescharacteristic
379C2×C4×C43C2×C22⋊C411yescharacteristic
380C2×C4×C43C2×C22⋊C411yescharacteristic
381C2×C4×C43C2×C22⋊C411yescharacteristic
382C2×C4×C43C22×D411yescharacteristic
383C8×C43—44no—
384#33347C4311yesmaximal, characteristic, direct product factor, Sylow
385C22×C43—21no—
386C22×C43—21no—
387C22×C43—21no—
388C22×C43—21no—
389C22×C43—21no—
390C22×C43—21no—
391C22×C43—41no—
392C22×C43—41no—
393C22×C43—41no—
394C22×C43—41no—
395C22×C43—41no—
396C22×C43—41no—
397C22×C43—41no—
398C22×C43—42no—
399C22×C43—42no—
400C22×C43—42no—
401C22×C43—42no—
402C22×C43—42no—
403C22×C43—81no—
404C22×C43—81no—
405C22×C43—81no—
406C22×C43—81no—
407C22×C43—84no—
408C22×C43C2×#9911yescharacteristic
409C22×C43C2×#9911yescharacteristic
410C22×C43C22×C22⋊C411yescharacteristic
411C4×C43—21no—
412C4×C43—21no—
413C4×C43—21no—
414C4×C43—21no—
415C4×C43—21no—
416C4×C43—21no—
417C4×C43—42no—
418C4×C43—42no—
419C4×C43—42no—
420C4×C43—84no—
421C4×C43C2×#9911yescharacteristic
422C4×C43C2×#9911yescharacteristic
423C4×C43C2×#9911yescharacteristic
424C4×C43C2×#9911yescharacteristic
425#3449C2×C4311yescharacteristic
426C2×#413C2×C4311yescharacteristic, complemented
427C2×#410C2×C4311yescharacteristic, complemented
428#2123C2×C4312yescomplemented
429#2122C2×C4312yescomplemented
430#2121C2×C4314yescomplemented
431#2120C2×C4314yescomplemented
432C2×C43—21no—
433C2×C43—21no—
434C2×C43—21no—
435C2×C43—41no—
436C2×C43—41no—
437C2×C43—41no—
438C2×C43—41no—
439C2×C43—41no—
440C2×C43—41no—
441C2×C43—82no—
442C2×C43C22×#9911yescharacteristic
443C22×#41C4×C4311yescharacteristic, complemented
444C22×#41C22×C4311yescharacteristic
445C22×M16—21no—
446#537—21no—
447#537—21no—
448#536—21no—
449#536C4×C4311yescharacteristic, complemented
450#536C22×C4311yescharacteristic
451#535—21no—
452#535C4×C4311yescharacteristic, complemented
453#535C22×C4311yescharacteristic
454#534C4×C4312yescomplemented
455#534C22×C4312yes—
456#532—21no—
457#532—21no—
458#525—21no—
459#525—21no—
460#525C4×C4312yescomplemented
461#525C22×C4312yes—
462C2×#117—21no—
463C2×#117C4×C4311yescharacteristic, complemented
464#413—21no—
465#413—21no—
466#413C22×C4312yes—
467#413C22×C4312yes—
468C2×#101—21no—
469C2×#100C22×C4312yes—
470#410—21no—
471#410—21no—
472#410C22×C4312yes—
473#410C22×C4312yes—
474C2×#99—21no—
475C2×#99C22×C4312yes—
476#352C22×C4318yescomplemented
477AΣL(1,𝔽16)C22×C4318yescomplemented
478C43#3334711yescharacteristic, direct product factor, Sylow
479C2×#41—21no—
480C2×#41—21no—
481C2×#41—21no—
482C2×#41—21no—
483C2×#41—41no—
484C2×#41—41no—
485C2×#41—41no—
486C2×#41—41no—
487C2×#41—41no—
488C2×#41—41no—
489C2×#41—41no—
490C2×#41—41no—
491C2×#41C2×C4×C4311yescharacteristic
492C2×#41C2×C4×C4311yescharacteristic
493C2×#41D4×C4311yescharacteristic
494C2×#41D4×C4311yescharacteristic
495C2×#41D4×C4311yescharacteristic
496C2×#41D4×C4311yescharacteristic
497C2×#41C23×C4311yescharacteristic
498C2×#41C23×C4311yescharacteristic
499C22×Q8C2×C4×C4311yescharacteristic, complemented
500C22×Q8D4×C4311yescharacteristic
501C22×D4C2×C4×C4311yescharacteristic
502C22×D4C2×C4×C4312yes—
503C22×D4C2×C4×C4311yescharacteristic, complemented
504C22×D4D4×C4311yescharacteristic
505C22×D4C23×C4311yescharacteristic
506C23×C4C2×C4×C4311yescharacteristic
507C23×C4C2×C4×C4312yescomplemented
508C23×C4D4×C4311yescharacteristic
509C23×C4D4×C4311yescharacteristic
510C2×M16—22no—
511C2×M16—22no—
512C2×M16—22no—
513C2×M16—41no—
514C2×M16—41no—
515C2×M16—41no—
516C22×C8—41no—
517C4⋊Q8—21no—
518C4⋊Q8—21no—
519#127—21no—
520#127—21no—
521#124—21no—
522#124—21no—
523#124—21no—
524#124—21no—
525#123—22no—
526#123—22no—
527#123C2×C4×C4312yes—
528#123C2×C4×C4312yescomplemented
529#123C2×C4×C4312yescomplemented
530#123C23×C4312yes—
531C22⋊Q8—22no—
532C22⋊Q8—22no—
533C22⋊Q8—21no—
534C22⋊Q8—21no—
535C22⋊Q8—21no—
536C22⋊Q8—21no—
537#121—22no—
538#121—22no—
539#121—22no—
540#121—22no—
541#121—22no—
542#121—22no—
543#121—21no—
544#121—21no—
545#121—21no—
546#121—21no—
547#120—22no—
548#120—22no—
549#120C2×C4×C4312yes—
550#120C2×C4×C4312yescomplemented
551#120C2×C4×C4312yescomplemented
552#120C23×C4312yes—
553C4×D4—22no—
554C4×D4—22no—
555C4×D4—22no—
556C4×D4—22no—
557#117—21no—
558#117—21no—
559#117—22no—
560#117—22no—
561#117—41no—
562#117—41no—
563#117C2×C4×C4312yescomplemented
564#117C2×C4×C4311yescharacteristic, complemented
565#117C2×C4×C4311yescharacteristic, complemented
566C2×C4⋊C4—21no—
567C2×C4⋊C4—41no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4C2×C4×C4312yes—
570C2×C42—21no—
571C2×C42—41no—
572#101—22no—
573#101—22no—
574#100—22no—
575#100C23×C4314yes—
576#99—22no—
577#99—22no—
578#99—22no—
579#99C23×C4314yes—
580C24C22⋊C4×C4311yescharacteristic
581C24C22×C4×C4311yescharacteristic
582C24C22×C4×C4312yes—
583C24C2×D4×C4311yescharacteristic
584#41—41no—
585#41—41no—
586#41—41no—
587#41—41no—
588#41—41no—
589#41—41no—
590#41—41no—
591#41—41no—
592#41—41no—
593#41—41no—
594#41—41no—
595#41—41no—
596#41—41no—
597#41—41no—
598#41—41no—
599#41—41no—
600#41—42no—
601#41—42no—
602#41—42no—
603#41—42no—
604#41—42no—
605#41—42no—
606#41—41no—
607#41—41no—
608#41—41no—
609#41—41no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—41no—
613C2×Q8—41no—
614C2×Q8—41no—
615C2×Q8—41no—
616C2×Q8C22⋊C4×C4311yescharacteristic
617C2×Q8C22⋊C4×C4311yescharacteristic
618C2×Q8C2×D4×C4311yescharacteristic
619C2×Q8C2×D4×C4311yescharacteristic
620C2×D4—22no—
621C2×D4—22no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—41no—
631C2×D4—41no—
632C2×D4—41no—
633C2×D4—41no—
634C2×D4—41no—
635C2×D4—41no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4C22⋊C4×C4311yescharacteristic
639C2×D4C22⋊C4×C4311yescharacteristic
640C2×D4C22⋊C4×C4311yescharacteristic
641C2×D4C22⋊C4×C4311yescharacteristic
642C2×D4C22×C4×C4311yescharacteristic
643C2×D4C22×C4×C4311yescharacteristic
644C2×D4C22×C4×C4311yescharacteristic
645C2×D4C2×D4×C4311yescharacteristic
646C2×D4C2×D4×C4311yescharacteristic
647C2×D4C2×D4×C4311yescharacteristic
648C2×D4C2×D4×C4311yescharacteristic
649C2×D4C24×C4311yescharacteristic
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4C22⋊C4×C4311yescharacteristic
669C22×C4C22⋊C4×C4311yescharacteristic
670C22×C4C22⋊C4×C4311yescharacteristic
671C22×C4C22⋊C4×C4311yescharacteristic
672C22×C4C22⋊C4×C4311yescharacteristic
673C22×C4C22⋊C4×C4311yescharacteristic
674C22×C4C22⋊C4×C4311yescharacteristic
675C22×C4C22⋊C4×C4311yescharacteristic
676C22×C4C22⋊C4×C4311yescharacteristic
677C22×C4C22×C4×C4311yescharacteristic
678C22×C4C22×C4×C4311yescharacteristic
679C22×C4C22×C4×C4312yes—
680C22×C4C2×D4×C4311yescharacteristic
681C22×C4C2×D4×C4311yescharacteristic
682C22×C4C2×D4×C4311yescharacteristic
683C22×C4C2×D4×C4311yescharacteristic
684C22×C4C2×D4×C4311yescharacteristic
685M16—24no—
686M16—42no—
687M16—42no—
688M16—42no—
689C2×C8—42no—
690C2×C8—42no—
691C2×C8—42no—
692C4⋊C4—22no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—22no—
696C4⋊C4—22no—
697C4⋊C4—22no—
698C4⋊C4—22no—
699C4⋊C4—42no—
700C4⋊C4—42no—
701C22⋊C4—22no—
702C22⋊C4—22no—
703C22⋊C4—22no—
704C22⋊C4—22no—
705C22⋊C4—22no—
706C22⋊C4—22no—
707C22⋊C4—22no—
708C22⋊C4—22no—
709C22⋊C4—22no—
710C22⋊C4—24no—
711C22⋊C4—42no—
712C22⋊C4C22×C4×C4312yes—
713C22⋊C4C22×C4×C4312yes—
714C42—22no—
715C42—21no—
716C42—21no—
717C42—42no—
718C42—42no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—22no—
726C23—42no—
727C23—81no—
728C23—81no—
729C23—81no—
730C23—82no—
731C23C2×C22⋊C4×C4311yescharacteristic
732C23C2×C22⋊C4×C4311yescharacteristic
733C23C2×C22⋊C4×C4311yescharacteristic
734C23C2×C22⋊C4×C4311yescharacteristic
735C23C2×C22⋊C4×C4311yescharacteristic
736C23C23×C4×C4311yescharacteristic
737C23C22×D4×C4311yescharacteristic
738Q8—41no—
739Q8—41no—
740Q8—41no—
741Q8—41no—
742Q8—42no—
743Q8—41no—
744Q8—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—41no—
756D4—41no—
757D4—42no—
758D4—44no—
759D4—42no—
760D4—42no—
761D4—41no—
762D4—41no—
763D4—82no—
764D4—82no—
765D4—82no—
766D4—82no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—44no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—44no—
805C2×C4—82no—
806C2×C4—84no—
807C2×C4#99×C4311yescharacteristic
808C2×C4#99×C4311yescharacteristic
809C2×C4#99×C4311yescharacteristic
810C2×C4#99×C4311yescharacteristic
811C2×C4C2×C22⋊C4×C4311yescharacteristic
812C2×C4C2×C22⋊C4×C4311yescharacteristic
813C2×C4C2×C22⋊C4×C4311yescharacteristic
814C2×C4C2×C22⋊C4×C4311yescharacteristic
815C2×C4C2×C22⋊C4×C4311yescharacteristic
816C2×C4C2×C22⋊C4×C4311yescharacteristic
817C2×C4C2×C22⋊C4×C4311yescharacteristic
818C2×C4C22×D4×C4311yescharacteristic
819C8—44no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—84no—
843C22C2×#99×C4311yescharacteristic
844C22C2×#99×C4311yescharacteristic
845C22C22×C22⋊C4×C4311yescharacteristic
846C4—21no—
847C4—21no—
848C4—21no—
849C4—21no—
850C4—21no—
851C4—21no—
852C4—42no—
853C4—42no—
854C4—42no—
855C4—84no—
856C4C2×#99×C4311yescharacteristic
857C4C2×#99×C4311yescharacteristic
858C4C2×#99×C4311yescharacteristic
859C4C2×#99×C4311yescharacteristic
860C2—21no—
861C2—21no—
862C2—21no—
863C2—41no—
864C2—41no—
865C2—41no—
866C2—41no—
867C2—41no—
868C2—41no—
869C2—82no—
870C2C22×#99×C4311yescharacteristic
subgroupG/H
centerC4×C43C2×#99
commutatorC23C23×C4×C43
Frattini, cosocleC2×D4C24×C43
socleC2×C43C22×#99
prime radicalC43×#3449C2
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C43 ◁ C22×C4×C43 ◁ C22×#41×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C43×#413C2semidirect
3. C2×C43×#410C2semidirect
4. C43×#2123C2semidirect
5. C43×#2122C2semidirect
6. C43×#2121C2semidirect
7. C43×#2120C2semidirect
8. C22×#41×C43C4semidirect
14. C43×#536C4semidirect
17. C43×#535C4semidirect
19. C43×#534C4semidirect
25. C43×#525C4semidirect
28. C2×#117×C43C4semidirect
41. C43×#352C22semidirect
42. C43×AΣL(1,𝔽16)C22semidirect
63. C22×Q8×C43C2×C4semidirect
67. C22×D4×C43C2×C4semidirect
71. C23×C4×C43C2×C4semidirect
92. #123×C43C2×C4semidirect
93. #123×C43C2×C4semidirect
114. #120×C43C2×C4semidirect
115. #120×C43C2×C4semidirect
127. #117×C43C2×C4semidirect
128. #117×C43C2×C4semidirect
129. #117×C43C2×C4semidirect
384. #33347C43direct (N × H)
426. C2×#413C2×C43semidirect
427. C2×#410C2×C43semidirect
428. #2123C2×C43semidirect
429. #2122C2×C43semidirect
430. #2121C2×C43semidirect
431. #2120C2×C43semidirect
443. C22×#41C4×C43semidirect
449. #536C4×C43semidirect
452. #535C4×C43semidirect
454. #534C4×C43semidirect
460. #525C4×C43semidirect
463. C2×#117C4×C43semidirect
476. #352C22×C43semidirect
477. AΣL(1,𝔽16)C22×C43semidirect
478. C43#33347direct (N × H)
499. C22×Q8C2×C4×C43semidirect
503. C22×D4C2×C4×C43semidirect
507. C23×C4C2×C4×C43semidirect
528. #123C2×C4×C43semidirect
529. #123C2×C4×C43semidirect
550. #120C2×C4×C43semidirect
551. #120C2×C4×C43semidirect
563. #117C2×C4×C43semidirect
564. #117C2×C4×C43semidirect
565. #117C2×C4×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#34492
C2×C43×#4132
C2×C43×#4102
C43×#21232
C43×#21222
C43×#21212
C43×#21202
#3334743