Finite Group Databasebeta

← C43×#20722 #24940739

Subgroups — C43×#20722 #24940739

Order 11008.

1866 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C43C211yesmaximal, characteristic
2C43×#2280C212yesmaximal, complemented
3C43×#1819C212yesmaximal, complemented
4C43×#1799C214yesmaximal, complemented
5C43×#1781C212yesmaximal
6C4×#99×C43C214yesmaximal, complemented
7C23×D4×C43C2211yescharacteristic
8C24×C4×C43C411yescharacteristic, complemented
9C24×C4×C43C2211yescharacteristic
10C2×C4×D4×C43—22no—
11C2×C4×D4×C43—22no—
12C2×C4×D4×C43—22no—
13C2×C4×D4×C43—22no—
14C2×C4×D4×C43C412yescomplemented
15C2×C4×D4×C43C412yescomplemented
16C2×C4×D4×C43C2212yes—
17C2×C4×D4×C43C2212yes—
18C2×#117×C43—22no—
19C22×C4⋊C4×C43C411yescharacteristic, complemented
20C22×C22⋊C4×C43C411yescharacteristic, complemented
21C22×C22⋊C4×C43C2211yescharacteristic
22C22×C42×C43C411yescharacteristic, complemented
23C2×#99×C43C2218yes—
24C43×#381—22no—
25C43×#380—22no—
26C43×#380C2214yescomplemented
27C43×#379C2214yes—
28C4×C22⋊C4×C43—22no—
29C4×C22⋊C4×C43C2214yescomplemented
30C43×#342C2218yescomplemented
31C25×C43C2×C411yescharacteristic
32C25×C43C2311yescharacteristic
33C22×D4×C43—22no—
34C22×D4×C43—22no—
35C22×D4×C43—28no—
36C22×D4×C43C2×C412yes—
37C22×D4×C43C2312yes—
38C23×C4×C43—21no—
39C23×C4×C43—21no—
40C23×C4×C43—21no—
41C23×C4×C43—21no—
42C23×C4×C43—44no—
43C23×C4×C43—44no—
44C23×C4×C43C2×C411yescharacteristic
45C23×C4×C43C2×C411yescharacteristic
46C23×C4×C43C2×C411yescharacteristic
47C23×C4×C43C2×C411yescharacteristic
48C23×C4×C43C2×C412yes—
49C23×C4×C43C2×C412yes—
50C23×C4×C43C2×C411yescharacteristic
51C23×C4×C43C2×C411yescharacteristic
52C23×C4×C43C2×C411yescharacteristic
53C23×C4×C43D412yes—
54C23×C4×C43D412yes—
55C23×C4×C43D412yes—
56C23×C4×C43D412yes—
57C23×C4×C43C2311yescharacteristic
58C23×C4×C43C2311yescharacteristic
59C4×D4×C43—24no—
60C4×D4×C43—24no—
61C4×D4×C43—24no—
62C4×D4×C43—24no—
63C4×D4×C43—24no—
64C4×D4×C43—24no—
65C4×D4×C43—24no—
66C4×D4×C43—24no—
67#117×C43—48no—
68C2×C4⋊C4×C43—22no—
69C2×C4⋊C4×C43—22no—
70C2×C4⋊C4×C43—24no—
71C2×C4⋊C4×C43C2×C412yes—
72C2×C4⋊C4×C43C2×C412yes—
73C2×C22⋊C4×C43—22no—
74C2×C22⋊C4×C43—22no—
75C2×C22⋊C4×C43—22no—
76C2×C22⋊C4×C43—22no—
77C2×C22⋊C4×C43—24no—
78C2×C22⋊C4×C43—24no—
79C2×C22⋊C4×C43C2×C412yes—
80C2×C22⋊C4×C43C2×C412yes—
81C2×C22⋊C4×C43C2×C412yes—
82C2×C22⋊C4×C43C2318yes—
83C2×C22⋊C4×C43C2312yes—
84C2×C42×C43—21no—
85C2×C42×C43—21no—
86C2×C42×C43—21no—
87C2×C42×C43—21no—
88C2×C42×C43—24no—
89C2×C42×C43C2×C412yes—
90C2×C42×C43C2×C412yes—
91#99×C43—216no—
92#95×C43—24no—
93#95×C43—24no—
94C24×C43—21no—
95C24×C43—21no—
96C24×C43—24no—
97C24×C43—24no—
98C24×C43—42no—
99C24×C43—42no—
100C24×C43—42no—
101C24×C43—42no—
102C24×C43C22×C411yescharacteristic
103C24×C43C22×C411yescharacteristic
104C24×C43C22×C412yes—
105C24×C43C2×D412yes—
106C24×C43C2×D412yes—
107C24×C43C2411yescharacteristic
108C2×D4×C43—216no—
109C2×D4×C43—216no—
110C2×D4×C43—24no—
111C2×D4×C43—24no—
112C2×D4×C43—24no—
113C2×D4×C43—24no—
114C2×D4×C43—24no—
115C2×D4×C43#4118yes—
116C22×C4×C43—28no—
117C22×C4×C43—24no—
118C22×C4×C43—24no—
119C22×C4×C43—22no—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—28no—
130C22×C4×C43—42no—
131C22×C4×C43—44no—
132C22×C4×C43—42no—
133C22×C4×C43—42no—
134C22×C4×C43—42no—
135C22×C4×C43—42no—
136C22×C4×C43—44no—
137C22×C4×C43—44no—
138C22×C4×C43—42no—
139C22×C4×C43—42no—
140C22×C4×C43—44no—
141C22×C4×C43—44no—
142C22×C4×C43—44no—
143C22×C4×C43—44no—
144C22×C4×C43—44no—
145C22×C4×C43—44no—
146C22×C4×C43C22⋊C411yescharacteristic
147C22×C4×C43C22⋊C411yescharacteristic
148C22×C4×C43C22⋊C412yes—
149C22×C4×C43C22⋊C412yes—
150C22×C4×C43C22⋊C411yescharacteristic
151C22×C4×C43C22⋊C412yes—
152C22×C4×C43C22⋊C412yes—
153C22×C4×C43C22⋊C412yes—
154C22×C4×C43C22⋊C412yes—
155C22×C4×C43C22⋊C411yescharacteristic
156C22×C4×C43C22×C411yescharacteristic
157C22×C4×C43C22×C411yescharacteristic
158C22×C4×C43C22×C412yes—
159C22×C4×C43C22×C412yes—
160C22×C4×C43C22×C412yes—
161C22×C4×C43C22×C411yescharacteristic
162C22×C4×C43C22×C411yescharacteristic
163C22×C4×C43C2×D412yes—
164C22×C4×C43C2×D412yes—
165C22×C4×C43C2×D412yes—
166C22×C4×C43C2×D412yes—
167C4⋊C4×C43—24no—
168C4⋊C4×C43—24no—
169C4⋊C4×C43—48no—
170C22⋊C4×C43—24no—
171C22⋊C4×C43—24no—
172C22⋊C4×C43—24no—
173C22⋊C4×C43—24no—
174C22⋊C4×C43—216no—
175C22⋊C4×C43—48no—
176C22⋊C4×C43—48no—
177C42×C43—22no—
178C42×C43—22no—
179C42×C43—22no—
180C42×C43—22no—
181C42×C43—48no—
182C23×C43—22no—
183C23×C43—22no—
184C23×C43—22no—
185C23×C43—24no—
186C23×C43—24no—
187C23×C43—22no—
188C23×C43—22no—
189C23×C43—22no—
190C23×C43—24no—
191C23×C43—24no—
192C23×C43—24no—
193C23×C43—24no—
194C23×C43—41no—
195C23×C43—42no—
196C23×C43—41no—
197C23×C43—41no—
198C23×C43—42no—
199C23×C43—41no—
200C23×C43—42no—
201C23×C43—42no—
202C23×C43—42no—
203C23×C43—416no—
204C23×C43—416no—
205C23×C43—42no—
206C23×C43—42no—
207C23×C43—42no—
208C23×C43C2×C22⋊C412yes—
209C23×C43C2×C22⋊C411yescharacteristic
210C23×C43C2×C22⋊C411yescharacteristic
211C23×C43#11714yescomplemented
212C23×C43C23×C411yescharacteristic
213C23×C43C22×D412yes—
214C23×C43C2×#4114yes—
215D4×C43—216no—
216D4×C43—216no—
217C2×C4×C43—24no—
218C2×C4×C43—24no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—24no—
223C2×C4×C43—24no—
224C2×C4×C43—24no—
225C2×C4×C43—22no—
226C2×C4×C43—22no—
227C2×C4×C43—22no—
228C2×C4×C43—22no—
229C2×C4×C43—24no—
230C2×C4×C43—24no—
231C2×C4×C43—22no—
232C2×C4×C43—22no—
233C2×C4×C43—42no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—42no—
239C2×C4×C43—42no—
240C2×C4×C43—44no—
241C2×C4×C43—44no—
242C2×C4×C43—42no—
243C2×C4×C43—42no—
244C2×C4×C43—42no—
245C2×C4×C43—42no—
246C2×C4×C43—44no—
247C2×C4×C43—44no—
248C2×C4×C43—42no—
249C2×C4×C43—42no—
250C2×C4×C43—48no—
251C2×C4×C43—48no—
252C2×C4×C43—48no—
253C2×C4×C43#9914yescomplemented
254C2×C4×C43C2×C22⋊C411yescharacteristic
255C2×C4×C43C2×C22⋊C411yescharacteristic
256C2×C4×C43C2×C22⋊C412yes—
257C2×C4×C43C2×C22⋊C412yes—
258C2×C4×C43C2×C22⋊C411yescharacteristic
259C2×C4×C43C2×C22⋊C411yescharacteristic
260C2×C4×C43#11714yescomplemented
261#20722C4311yesmaximal, characteristic, direct product factor, Sylow
262C22×C43—28no—
263C22×C43—21no—
264C22×C43—21no—
265C22×C43—22no—
266C22×C43—21no—
267C22×C43—21no—
268C22×C43—22no—
269C22×C43—21no—
270C22×C43—21no—
271C22×C43—22no—
272C22×C43—22no—
273C22×C43—22no—
274C22×C43—24no—
275C22×C43—44no—
276C22×C43—48no—
277C22×C43—48no—
278C22×C43—44no—
279C22×C43—44no—
280C22×C43—44no—
281C22×C43—48no—
282C22×C43—48no—
283C22×C43—42no—
284C22×C43—42no—
285C22×C43C2×#9912yes—
286C22×C43#41012yes—
287C22×C43C22×C22⋊C411yescharacteristic
288C22×C43C2×#11712yes—
289C22×C43#52514yes—
290C4×C43—21no—
291C4×C43—21no—
292C4×C43—22no—
293C4×C43—22no—
294C4×C43—24no—
295C4×C43—42no—
296C4×C43—42no—
297C4×C43—88no—
298C4×C43C2×#9912yes—
299C4×C43C2×#9912yes—
300C22×C4×D4C2×C4311yescharacteristic
301#2280C2×C4312yescomplemented
302#1819C2×C4312yescomplemented
303#1799C2×C4314yescomplemented
304#1781C2×C4312yes—
305C4×#99C2×C4314yescomplemented
306C2×C43—24no—
307C2×C43—22no—
308C2×C43—22no—
309C2×C43—22no—
310C2×C43—42no—
311C2×C43—44no—
312C2×C43#228011yescharacteristic
313C2×C43C22×#9911yescharacteristic
314C2×C43C2×#41011yescharacteristic
315C23×D4C22×C4311yescharacteristic
316C24×C4C4×C4311yescharacteristic, complemented
317C24×C4C22×C4311yescharacteristic
318C2×C4×D4—22no—
319C2×C4×D4—22no—
320C2×C4×D4—22no—
321C2×C4×D4—22no—
322C2×C4×D4C4×C4312yescomplemented
323C2×C4×D4C4×C4312yescomplemented
324C2×C4×D4C22×C4312yes—
325C2×C4×D4C22×C4312yes—
326C2×#117—22no—
327C22×C4⋊C4C4×C4311yescharacteristic, complemented
328C22×C22⋊C4C4×C4311yescharacteristic, complemented
329C22×C22⋊C4C22×C4311yescharacteristic
330C22×C42C4×C4311yescharacteristic, complemented
331C2×#99C22×C4318yes—
332#381—22no—
333#380—22no—
334#380C22×C4314yescomplemented
335#379C22×C4314yes—
336C4×C22⋊C4—22no—
337C4×C22⋊C4C22×C4314yescomplemented
338#342C22×C4318yescomplemented
339C43#2072211yescharacteristic, direct product factor, Sylow
340C25C2×C4×C4311yescharacteristic
341C25C23×C4311yescharacteristic
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—28no—
345C22×D4C2×C4×C4312yes—
346C22×D4C23×C4312yes—
347C23×C4—21no—
348C23×C4—21no—
349C23×C4—21no—
350C23×C4—21no—
351C23×C4—44no—
352C23×C4—44no—
353C23×C4C2×C4×C4311yescharacteristic
354C23×C4C2×C4×C4311yescharacteristic
355C23×C4C2×C4×C4311yescharacteristic
356C23×C4C2×C4×C4311yescharacteristic
357C23×C4C2×C4×C4312yes—
358C23×C4C2×C4×C4312yes—
359C23×C4C2×C4×C4311yescharacteristic
360C23×C4C2×C4×C4311yescharacteristic
361C23×C4C2×C4×C4311yescharacteristic
362C23×C4D4×C4312yes—
363C23×C4D4×C4312yes—
364C23×C4D4×C4312yes—
365C23×C4D4×C4312yes—
366C23×C4C23×C4311yescharacteristic
367C23×C4C23×C4311yescharacteristic
368C4×D4—24no—
369C4×D4—24no—
370C4×D4—24no—
371C4×D4—24no—
372C4×D4—24no—
373C4×D4—24no—
374C4×D4—24no—
375C4×D4—24no—
376#117—48no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—24no—
380C2×C4⋊C4C2×C4×C4312yes—
381C2×C4⋊C4C2×C4×C4312yes—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4C2×C4×C4312yes—
389C2×C22⋊C4C2×C4×C4312yes—
390C2×C22⋊C4C2×C4×C4312yes—
391C2×C22⋊C4C23×C4318yes—
392C2×C22⋊C4C23×C4312yes—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—24no—
398C2×C42C2×C4×C4312yes—
399C2×C42C2×C4×C4312yes—
400#99—216no—
401#95—24no—
402#95—24no—
403C24—21no—
404C24—21no—
405C24—24no—
406C24—24no—
407C24—42no—
408C24—42no—
409C24—42no—
410C24—42no—
411C24C22×C4×C4311yescharacteristic
412C24C22×C4×C4311yescharacteristic
413C24C22×C4×C4312yes—
414C24C2×D4×C4312yes—
415C24C2×D4×C4312yes—
416C24C24×C4311yescharacteristic
417C2×D4—216no—
418C2×D4—216no—
419C2×D4—24no—
420C2×D4—24no—
421C2×D4—24no—
422C2×D4—24no—
423C2×D4—24no—
424C2×D4#41×C4318yes—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—28no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—28no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—44no—
444C22×C4—44no—
445C22×C4—42no—
446C22×C4—44no—
447C22×C4—44no—
448C22×C4—44no—
449C22×C4—44no—
450C22×C4—44no—
451C22×C4—44no—
452C22×C4—44no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4C22⋊C4×C4311yescharacteristic
456C22×C4C22⋊C4×C4311yescharacteristic
457C22×C4C22⋊C4×C4311yescharacteristic
458C22×C4C22⋊C4×C4312yes—
459C22×C4C22⋊C4×C4312yes—
460C22×C4C22⋊C4×C4312yes—
461C22×C4C22⋊C4×C4312yes—
462C22×C4C22⋊C4×C4312yes—
463C22×C4C22⋊C4×C4312yes—
464C22×C4C22⋊C4×C4311yescharacteristic
465C22×C4C22×C4×C4311yescharacteristic
466C22×C4C22×C4×C4311yescharacteristic
467C22×C4C22×C4×C4312yes—
468C22×C4C22×C4×C4312yes—
469C22×C4C22×C4×C4312yes—
470C22×C4C22×C4×C4311yescharacteristic
471C22×C4C22×C4×C4311yescharacteristic
472C22×C4C2×D4×C4312yes—
473C22×C4C2×D4×C4312yes—
474C22×C4C2×D4×C4312yes—
475C22×C4C2×D4×C4312yes—
476C4⋊C4—24no—
477C4⋊C4—24no—
478C4⋊C4—48no—
479C22⋊C4—24no—
480C22⋊C4—24no—
481C22⋊C4—24no—
482C22⋊C4—24no—
483C22⋊C4—216no—
484C22⋊C4—48no—
485C22⋊C4—48no—
486C42—22no—
487C42—22no—
488C42—22no—
489C42—22no—
490C42—48no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—24no—
495C23—24no—
496C23—22no—
497C23—22no—
498C23—22no—
499C23—24no—
500C23—24no—
501C23—24no—
502C23—24no—
503C23—41no—
504C23—42no—
505C23—41no—
506C23—41no—
507C23—42no—
508C23—41no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—416no—
513C23—416no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23C2×C22⋊C4×C4312yes—
518C23C2×C22⋊C4×C4311yescharacteristic
519C23C2×C22⋊C4×C4311yescharacteristic
520C23#117×C4314yescomplemented
521C23C23×C4×C4311yescharacteristic
522C23C22×D4×C4312yes—
523C23C2×#41×C4314yes—
524D4—216no—
525D4—216no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—44no—
550C2×C4—44no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—44no—
556C2×C4—44no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—48no—
560C2×C4—48no—
561C2×C4—48no—
562C2×C4#99×C4314yescomplemented
563C2×C4C2×C22⋊C4×C4311yescharacteristic
564C2×C4C2×C22⋊C4×C4311yescharacteristic
565C2×C4C2×C22⋊C4×C4312yes—
566C2×C4C2×C22⋊C4×C4312yes—
567C2×C4C2×C22⋊C4×C4311yescharacteristic
568C2×C4C2×C22⋊C4×C4311yescharacteristic
569C2×C4#117×C4314yescomplemented
570C22—28no—
571C22—22no—
572C22—21no—
573C22—21no—
574C22—22no—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—22no—
580C22—22no—
581C22—22no—
582C22—24no—
583C22—44no—
584C22—48no—
585C22—48no—
586C22—44no—
587C22—44no—
588C22—44no—
589C22—48no—
590C22—48no—
591C22—42no—
592C22—42no—
593C22C2×#99×C4312yes—
594C22C43×#41012yes—
595C22C22×C22⋊C4×C4311yescharacteristic
596C22C2×#117×C4312yes—
597C22C43×#52514yes—
598C4—21no—
599C4—21no—
600C4—22no—
601C4—22no—
602C4—24no—
603C4—42no—
604C4—42no—
605C4—88no—
606C4C2×#99×C4312yes—
607C4C2×#99×C4312yes—
608C2—24no—
609C2—22no—
610C2—22no—
611C2—22no—
612C2—42no—
613C2—44no—
614C2C43×#228011yescharacteristic
615C2C22×#99×C4311yescharacteristic
616C2C2×C43×#41011yescharacteristic
subgroupG/H
centerC2×C4×C43C2×C22⋊C4
commutatorC23C23×C4×C43
Frattini, cosocleC24C24×C43
socleC22×C43C22×C22⋊C4
prime radicalC23×D4×C43C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C43 ◁ C24×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2280C2semidirect
3. C43×#1819C2semidirect
4. C43×#1799C2semidirect
6. C4×#99×C43C2semidirect
8. C24×C4×C43C4semidirect
14. C2×C4×D4×C43C4semidirect
15. C2×C4×D4×C43C4semidirect
19. C22×C4⋊C4×C43C4semidirect
20. C22×C22⋊C4×C43C4semidirect
22. C22×C42×C43C4semidirect
26. C43×#380C22semidirect
29. C4×C22⋊C4×C43C22semidirect
30. C43×#342C22semidirect
211. C23×C43#117semidirect
253. C2×C4×C43#99semidirect
260. C2×C4×C43#117semidirect
261. #20722C43direct (N × H)
301. #2280C2×C43semidirect
302. #1819C2×C43semidirect
303. #1799C2×C43semidirect
305. C4×#99C2×C43semidirect
316. C24×C4C4×C43semidirect
322. C2×C4×D4C4×C43semidirect
323. C2×C4×D4C4×C43semidirect
327. C22×C4⋊C4C4×C43semidirect
328. C22×C22⋊C4C4×C43semidirect
330. C22×C42C4×C43semidirect
334. #380C22×C43semidirect
337. C4×C22⋊C4C22×C43semidirect
338. #342C22×C43semidirect
339. C43#20722direct (N × H)
520. C23#117×C43semidirect
562. C2×C4#99×C43semidirect
569. C2×C4#117×C43semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D4×C432
C43×#22802
C43×#18192
C43×#17992
C43×#17812
C4×#99×C432
#2072243