Finite Group Databasebeta

← C43×#14725 #24934742

Subgroups — C43×#14725 #24934742

Order 11008.

4034 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C43C211yesmaximal, characteristic
2C23×C22⋊C4×C43C211yesmaximal, characteristic, complemented
3C2×C43×#394C212yesmaximal, complemented
4C2×C43×#386C211yesmaximal, characteristic, complemented
5C2×C43×#386C211yesmaximal, characteristic, complemented
6C2×C43×#380C211yesmaximal, characteristic, complemented
7C2×C43×#379C211yesmaximal, characteristic, complemented
8C43×#1440C212yesmaximal, complemented
9C43×#1439C212yesmaximal, complemented
10C43×#1438C212yesmaximal, complemented
11C43×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C43C2211yescharacteristic
13C23×D4×C43C2211yescharacteristic
14C23×D4×C43C2212yes—
15C24×C4×C43C2211yescharacteristic
16C24×C4×C43C2211yescharacteristic
17C2×#120×C43—24no—
18C2×#120×C43—24no—
19C2×#120×C43—24no—
20C22×C4⋊C4×C43C2212yescomplemented
21C22×C22⋊C4×C43—24no—
22C22×C22⋊C4×C43—28no—
23C22×C22⋊C4×C43C2212yes—
24C22×C22⋊C4×C43C2212yes—
25C22×C22⋊C4×C43C2212yes—
26C22×C22⋊C4×C43C2211yescharacteristic
27C22×C22⋊C4×C43C2211yescharacteristic
28C22×C22⋊C4×C43C2211yescharacteristic
29C22×C22⋊C4×C43C2212yes—
30C22×C22⋊C4×C43C2212yes—
31C22×C22⋊C4×C43C2211yescharacteristic, complemented
32C22×C22⋊C4×C43C2212yescomplemented
33C22×C22⋊C4×C43C2211yescharacteristic, complemented
34C43×#394—28no—
35C43×#386—24no—
36C43×#386—24no—
37C43×#380—24no—
38C43×#379—24no—
39C2×#95×C43C2212yescomplemented
40C2×#95×C43C2212yescomplemented
41C2×#95×C43C2211yescharacteristic, complemented
42C2×#95×C43C2212yescomplemented
43C2×#95×C43C2211yescharacteristic, complemented
44C2×#95×C43C2212yescomplemented
45C25×C43—24no—
46C25×C43—22no—
47C25×C43—24no—
48C25×C43—22no—
49C25×C43—22no—
50C25×C43—22no—
51C25×C43—22no—
52C25×C43—22no—
53C25×C43—42no—
54C25×C43—42no—
55C25×C43D414yes—
56C25×C43C2311yescharacteristic
57C25×C43C2312yes—
58C25×C43C2311yescharacteristic
59C22×D4×C43—24no—
60C22×D4×C43—24no—
61C22×D4×C43—22no—
62C22×D4×C43—22no—
63C22×D4×C43—22no—
64C22×D4×C43—22no—
65C22×D4×C43—22no—
66C22×D4×C43—22no—
67C22×D4×C43—24no—
68C22×D4×C43—24no—
69C22×D4×C43—24no—
70C22×D4×C43—42no—
71C22×D4×C43—42no—
72C22×D4×C43D414yes—
73C23×C4×C43—22no—
74C23×C4×C43—22no—
75C23×C4×C43—22no—
76C23×C4×C43—24no—
77C23×C4×C43—24no—
78C23×C4×C43—22no—
79C23×C4×C43—22no—
80C23×C4×C43—42no—
81C23×C4×C43—42no—
82C23×C4×C43D414yescomplemented
83C23×C4×C43C2312yes—
84C23×C4×C43C2311yescharacteristic
85C23×C4×C43C2311yescharacteristic
86C23×C4×C43C2311yescharacteristic
87C23×C4×C43C2312yes—
88C23×C4×C43C2312yes—
89C23×C4×C43C2311yescharacteristic
90C23×C4×C43C2311yescharacteristic
91#120×C43—232no—
92C2×C4⋊C4×C43—24no—
93C2×C4⋊C4×C43—24no—
94C2×C4⋊C4×C43—42no—
95C2×C22⋊C4×C43—232no—
96C2×C22⋊C4×C43—24no—
97C2×C22⋊C4×C43—24no—
98C2×C22⋊C4×C43—22no—
99C2×C22⋊C4×C43—22no—
100C2×C22⋊C4×C43—24no—
101C2×C22⋊C4×C43—24no—
102C2×C22⋊C4×C43—24no—
103C2×C22⋊C4×C43—24no—
104C2×C22⋊C4×C43—24no—
105C2×C22⋊C4×C43—24no—
106C2×C22⋊C4×C43—24no—
107C2×C22⋊C4×C43—22no—
108C2×C22⋊C4×C43—24no—
109C2×C22⋊C4×C43—22no—
110C2×C22⋊C4×C43—22no—
111C2×C22⋊C4×C43—22no—
112C2×C22⋊C4×C43—22no—
113C2×C22⋊C4×C43—24no—
114C2×C22⋊C4×C43—24no—
115C2×C22⋊C4×C43—24no—
116C2×C22⋊C4×C43—22no—
117C2×C22⋊C4×C43—22no—
118C2×C22⋊C4×C43—22no—
119C2×C22⋊C4×C43—24no—
120C2×C22⋊C4×C43—24no—
121C2×C22⋊C4×C43—42no—
122C2×C22⋊C4×C43—42no—
123C2×C22⋊C4×C43—42no—
124C2×C22⋊C4×C43—42no—
125C2×C22⋊C4×C43D414yes—
126C2×C22⋊C4×C43D418yescomplemented
127#95×C43—24no—
128#95×C43—22no—
129#95×C43—22no—
130#95×C43—24no—
131#95×C43—24no—
132#95×C43—42no—
133C24×C43—22no—
134C24×C43—22no—
135C24×C43—22no—
136C24×C43—22no—
137C24×C43—28no—
138C24×C43—28no—
139C24×C43—216no—
140C24×C43—216no—
141C24×C43—28no—
142C24×C43—22no—
143C24×C43—22no—
144C24×C43—22no—
145C24×C43—22no—
146C24×C43—22no—
147C24×C43—22no—
148C24×C43—22no—
149C24×C43—22no—
150C24×C43—22no—
151C24×C43—22no—
152C24×C43—22no—
153C24×C43—22no—
154C24×C43—28no—
155C24×C43—28no—
156C24×C43—21no—
157C24×C43—22no—
158C24×C43—21no—
159C24×C43—21no—
160C24×C43—21no—
161C24×C43—21no—
162C24×C43—21no—
163C24×C43—22no—
164C24×C43—22no—
165C24×C43—22no—
166C24×C43—48no—
167C24×C43—48no—
168C24×C43—48no—
169C24×C43—48no—
170C24×C43—48no—
171C24×C43—48no—
172C24×C43—48no—
173C24×C43—48no—
174C24×C43—48no—
175C24×C43—44no—
176C24×C43—44no—
177C24×C43—48no—
178C24×C43—44no—
179C24×C43—44no—
180C24×C43—44no—
181C24×C43—44no—
182C24×C43C2×D412yes—
183C24×C43C2×D414yes—
184C24×C43C2×D414yes—
185C24×C43C2×D412yes—
186C24×C43C2×D412yes—
187C24×C43C2×D412yes—
188C24×C43C2×D412yes—
189C24×C43#4114yes—
190C24×C43#4112yes—
191C24×C43#4112yes—
192C24×C43#4112yes—
193C24×C43C2411yescharacteristic
194C2×D4×C43—216no—
195C2×D4×C43—28no—
196C2×D4×C43—28no—
197C2×D4×C43—28no—
198C2×D4×C43—48no—
199C2×D4×C43—48no—
200C2×D4×C43—48no—
201C2×D4×C43—48no—
202C2×D4×C43—48no—
203C2×D4×C43—48no—
204C2×D4×C43—44no—
205C2×D4×C43—44no—
206C2×D4×C43—44no—
207C2×D4×C43—44no—
208C22×C4×C43—28no—
209C22×C4×C43—28no—
210C22×C4×C43—28no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—22no—
215C22×C4×C43—22no—
216C22×C4×C43—22no—
217C22×C4×C43—22no—
218C22×C4×C43—22no—
219C22×C4×C43—21no—
220C22×C4×C43—22no—
221C22×C4×C43—22no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43—22no—
226C22×C4×C43—22no—
227C22×C4×C43—22no—
228C22×C4×C43—22no—
229C22×C4×C43—21no—
230C22×C4×C43—21no—
231C22×C4×C43—22no—
232C22×C4×C43—21no—
233C22×C4×C43—21no—
234C22×C4×C43—22no—
235C22×C4×C43—21no—
236C22×C4×C43—21no—
237C22×C4×C43—21no—
238C22×C4×C43—22no—
239C22×C4×C43—21no—
240C22×C4×C43—21no—
241C22×C4×C43—22no—
242C22×C4×C43—22no—
243C22×C4×C43—22no—
244C22×C4×C43—22no—
245C22×C4×C43—22no—
246C22×C4×C43—22no—
247C22×C4×C43—22no—
248C22×C4×C43—22no—
249C22×C4×C43—22no—
250C22×C4×C43—22no—
251C22×C4×C43—22no—
252C22×C4×C43—22no—
253C22×C4×C43—44no—
254C22×C4×C43—48no—
255C22×C4×C43—48no—
256C22×C4×C43—48no—
257C22×C4×C43—48no—
258C22×C4×C43—44no—
259C22×C4×C43—44no—
260C22×C4×C43C2×D412yes—
261C22×C4×C43C2×D412yes—
262C22×C4×C43C2×D414yes—
263C22×C4×C43C2×D414yes—
264C22×C4×C43C2×D412yes—
265C22×C4×C43C2×D414yes—
266C4⋊C4×C43—48no—
267C22⋊C4×C43—216no—
268C22⋊C4×C43—216no—
269C22⋊C4×C43—216no—
270C22⋊C4×C43—28no—
271C22⋊C4×C43—48no—
272C22⋊C4×C43—48no—
273C22⋊C4×C43—44no—
274C22⋊C4×C43—44no—
275C22⋊C4×C43—44no—
276C22⋊C4×C43—48no—
277C22⋊C4×C43—44no—
278C23×C43—22no—
279C23×C43—24no—
280C23×C43—22no—
281C23×C43—24no—
282C23×C43—22no—
283C23×C43—24no—
284C23×C43—22no—
285C23×C43—24no—
286C23×C43—24no—
287C23×C43—24no—
288C23×C43—24no—
289C23×C43—24no—
290C23×C43—24no—
291C23×C43—24no—
292C23×C43—24no—
293C23×C43—24no—
294C23×C43—232no—
295C23×C43—24no—
296C23×C43—24no—
297C23×C43—24no—
298C23×C43—24no—
299C23×C43—24no—
300C23×C43—24no—
301C23×C43—24no—
302C23×C43—24no—
303C23×C43—24no—
304C23×C43—24no—
305C23×C43—24no—
306C23×C43—24no—
307C23×C43—24no—
308C23×C43—24no—
309C23×C43—24no—
310C23×C43—24no—
311C23×C43—24no—
312C23×C43—24no—
313C23×C43—22no—
314C23×C43—22no—
315C23×C43—22no—
316C23×C43—24no—
317C23×C43—24no—
318C23×C43—432no—
319C23×C43—432no—
320C23×C43—416no—
321C23×C43—416no—
322C23×C43—416no—
323C23×C43—416no—
324C23×C43—432no—
325C23×C43—432no—
326C23×C43—416no—
327C23×C43—42no—
328C23×C43—42no—
329C23×C43—42no—
330C23×C43—42no—
331C23×C43—42no—
332C23×C43—42no—
333C23×C43—42no—
334C23×C43—42no—
335C23×C43—42no—
336C23×C43—42no—
337C23×C43—42no—
338C23×C43—42no—
339C23×C43—42no—
340C23×C43—42no—
341C23×C43—42no—
342C23×C43—42no—
343C23×C43—416no—
344C23×C43—41no—
345C23×C43—41no—
346C23×C43—41no—
347C23×C43—42no—
348C23×C43—41no—
349C23×C43—42no—
350C23×C43—41no—
351C23×C43—41no—
352C23×C43—41no—
353C23×C43—42no—
354C23×C43—41no—
355C23×C43—42no—
356C23×C43—42no—
357C23×C43—42no—
358C23×C43—42no—
359C23×C43—42no—
360C23×C43—42no—
361C23×C43—42no—
362C23×C43#12014yes—
363C23×C43#12118yes—
364C23×C43#12114yes—
365C23×C43#12114yes—
366C23×C43#12114yes—
367C23×C43#12314yes—
368C23×C43#12314yes—
369C23×C43#12414yes—
370C23×C43C22×D411yescharacteristic
371C23×C43C22×D411yescharacteristic
372C23×C43C22×D411yescharacteristic
373C23×C43C22×D412yes—
374C23×C43C22×D411yescharacteristic
375C23×C43C2×#4111yescharacteristic
376C23×C43C2×#4111yescharacteristic
377C23×C43C2×#4111yescharacteristic
378C23×C43C2×#4112yes—
379C23×C43H(5,𝔽2)12yes—
380C23×C43H(5,𝔽2)12yes—
381D4×C43—432no—
382D4×C43—416no—
383C2×C4×C43—22no—
384C2×C4×C43—22no—
385C2×C4×C43—24no—
386C2×C4×C43—24no—
387C2×C4×C43—24no—
388C2×C4×C43—22no—
389C2×C4×C43—22no—
390C2×C4×C43—24no—
391C2×C4×C43—22no—
392C2×C4×C43—22no—
393C2×C4×C43—22no—
394C2×C4×C43—22no—
395C2×C4×C43—24no—
396C2×C4×C43—24no—
397C2×C4×C43—24no—
398C2×C4×C43—24no—
399C2×C4×C43—416no—
400C2×C4×C43—416no—
401C2×C4×C43—42no—
402C2×C4×C43—41no—
403C2×C4×C43—41no—
404C2×C4×C43—42no—
405C2×C4×C43—41no—
406C2×C4×C43—41no—
407C2×C4×C43—42no—
408C2×C4×C43—42no—
409C2×C4×C43—42no—
410C2×C4×C43—42no—
411C2×C4×C43—42no—
412C2×C4×C43—42no—
413C2×C4×C43—42no—
414C2×C4×C43—42no—
415C2×C4×C43—41no—
416C2×C4×C43—42no—
417C2×C4×C43—41no—
418C2×C4×C43—42no—
419C2×C4×C43—41no—
420C2×C4×C43—42no—
421C2×C4×C43—41no—
422C2×C4×C43—42no—
423C2×C4×C43—42no—
424C2×C4×C43—41no—
425C2×C4×C43—42no—
426C2×C4×C43—41no—
427C2×C4×C43—42no—
428C2×C4×C43—42no—
429C2×C4×C43—42no—
430C2×C4×C43—42no—
431C2×C4×C43—42no—
432C2×C4×C43#12014yescomplemented
433#14725C4311yesmaximal, characteristic, direct product factor, Sylow
434C22×C43—24no—
435C22×C43—24no—
436C22×C43—24no—
437C22×C43—28no—
438C22×C43—24no—
439C22×C43—24no—
440C22×C43—28no—
441C22×C43—28no—
442C22×C43—28no—
443C22×C43—24no—
444C22×C43—28no—
445C22×C43—28no—
446C22×C43—28no—
447C22×C43—464no—
448C22×C43—44no—
449C22×C43—44no—
450C22×C43—44no—
451C22×C43—44no—
452C22×C43—44no—
453C22×C43—44no—
454C22×C43—44no—
455C22×C43—44no—
456C22×C43—44no—
457C22×C43—44no—
458C22×C43—44no—
459C22×C43—44no—
460C22×C43—42no—
461C22×C43—42no—
462C22×C43—44no—
463C22×C43—44no—
464C22×C43—42no—
465C22×C43—81no—
466C22×C43—81no—
467C22×C43—81no—
468C22×C43—81no—
469C22×C43—82no—
470C22×C43—82no—
471C22×C43#39418yescomplemented
472C22×C43C2×#12011yescharacteristic
473C22×C43C2×#12011yescharacteristic
474C22×C43C2×#12111yescharacteristic
475C22×C43C2×#12112yes—
476C22×C43C2×#12111yescharacteristic
477C22×C43C2×#12111yescharacteristic
478C22×C43C2×#12311yescharacteristic
479C22×C43C2×#12311yescharacteristic
480C22×C43#52511yescharacteristic
481C22×C43#52512yes—
482C22×C43C2×#12411yescharacteristic
483C22×C43#53412yes—
484C22×C43#53411yescharacteristic
485C22×C43#53511yescharacteristic
486C22×C43#53812yes—
487C22×C43D4212yes—
488C22×C43D4212yes—
489C22×C43#54612yes—
490C22×C43#54612yes—
491C22×C43#54612yes—
492C22×C43#54612yes—
493C22×C43#55112yes—
494C22×C43#55112yes—
495C4×C43—24no—
496C4×C43—42no—
497C4×C43—44no—
498C4×C43—42no—
499C4×C43—44no—
500C4×C43—81no—
501C4×C43—81no—
502C4×C43—82no—
503C22×#120C2×C4311yescharacteristic
504C23×C22⋊C4C2×C4311yescharacteristic, complemented
505C2×#394C2×C4312yescomplemented
506C2×#386C2×C4311yescharacteristic, complemented
507C2×#386C2×C4311yescharacteristic, complemented
508C2×#380C2×C4311yescharacteristic, complemented
509C2×#379C2×C4311yescharacteristic, complemented
510#1440C2×C4312yescomplemented
511#1439C2×C4312yescomplemented
512#1438C2×C4312yescomplemented
513C22⋊#95C2×C4311yescharacteristic, complemented
514C2×C43—28no—
515C2×C43—48no—
516C2×C43—82no—
517C2×C43C2×#39411yescharacteristic
518C2×C43#240811yescharacteristic
519C2×C43#241011yescharacteristic
520C2×C43#241012yes—
521C2×C43#241111yescharacteristic
522C2×C43#241212yes—
523C2×C43#241812yes—
524C2×C43#247212yes—
525C2×C43#253411yescharacteristic
526C2×C43#261711yescharacteristic
527C2×C43#284711yescharacteristic
528C26C22×C4311yescharacteristic
529C23×D4C22×C4311yescharacteristic
530C23×D4C22×C4312yes—
531C24×C4C22×C4311yescharacteristic
532C24×C4C22×C4311yescharacteristic
533C2×#120—24no—
534C2×#120—24no—
535C2×#120—24no—
536C22×C4⋊C4C22×C4312yescomplemented
537C22×C22⋊C4—24no—
538C22×C22⋊C4—28no—
539C22×C22⋊C4C22×C4312yes—
540C22×C22⋊C4C22×C4312yes—
541C22×C22⋊C4C22×C4312yes—
542C22×C22⋊C4C22×C4311yescharacteristic
543C22×C22⋊C4C22×C4311yescharacteristic
544C22×C22⋊C4C22×C4311yescharacteristic
545C22×C22⋊C4C22×C4312yes—
546C22×C22⋊C4C22×C4312yes—
547C22×C22⋊C4C22×C4311yescharacteristic, complemented
548C22×C22⋊C4C22×C4312yescomplemented
549C22×C22⋊C4C22×C4311yescharacteristic, complemented
550#394—28no—
551#386—24no—
552#386—24no—
553#380—24no—
554#379—24no—
555C2×#95C22×C4312yescomplemented
556C2×#95C22×C4312yescomplemented
557C2×#95C22×C4311yescharacteristic, complemented
558C2×#95C22×C4312yescomplemented
559C2×#95C22×C4311yescharacteristic, complemented
560C2×#95C22×C4312yescomplemented
561C43#1472511yescharacteristic, direct product factor, Sylow
562C25—24no—
563C25—22no—
564C25—24no—
565C25—22no—
566C25—22no—
567C25—22no—
568C25—22no—
569C25—22no—
570C25—42no—
571C25—42no—
572C25D4×C4314yes—
573C25C23×C4311yescharacteristic
574C25C23×C4312yes—
575C25C23×C4311yescharacteristic
576C22×D4—24no—
577C22×D4—24no—
578C22×D4—22no—
579C22×D4—22no—
580C22×D4—22no—
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—22no—
584C22×D4—24no—
585C22×D4—24no—
586C22×D4—24no—
587C22×D4—42no—
588C22×D4—42no—
589C22×D4D4×C4314yes—
590C23×C4—22no—
591C23×C4—22no—
592C23×C4—22no—
593C23×C4—24no—
594C23×C4—24no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—42no—
598C23×C4—42no—
599C23×C4D4×C4314yescomplemented
600C23×C4C23×C4312yes—
601C23×C4C23×C4311yescharacteristic
602C23×C4C23×C4311yescharacteristic
603C23×C4C23×C4311yescharacteristic
604C23×C4C23×C4312yes—
605C23×C4C23×C4312yes—
606C23×C4C23×C4311yescharacteristic
607C23×C4C23×C4311yescharacteristic
608#120—232no—
609C2×C4⋊C4—24no—
610C2×C4⋊C4—24no—
611C2×C4⋊C4—42no—
612C2×C22⋊C4—232no—
613C2×C22⋊C4—24no—
614C2×C22⋊C4—24no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—24no—
618C2×C22⋊C4—24no—
619C2×C22⋊C4—24no—
620C2×C22⋊C4—24no—
621C2×C22⋊C4—24no—
622C2×C22⋊C4—24no—
623C2×C22⋊C4—24no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—24no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—24no—
631C2×C22⋊C4—24no—
632C2×C22⋊C4—24no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—24no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—42no—
639C2×C22⋊C4—42no—
640C2×C22⋊C4—42no—
641C2×C22⋊C4—42no—
642C2×C22⋊C4D4×C4314yes—
643C2×C22⋊C4D4×C4318yescomplemented
644#95—24no—
645#95—22no—
646#95—22no—
647#95—24no—
648#95—24no—
649#95—42no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—28no—
655C24—28no—
656C24—216no—
657C24—216no—
658C24—28no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—28no—
672C24—28no—
673C24—21no—
674C24—22no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—48no—
684C24—48no—
685C24—48no—
686C24—48no—
687C24—48no—
688C24—48no—
689C24—48no—
690C24—48no—
691C24—48no—
692C24—44no—
693C24—44no—
694C24—48no—
695C24—44no—
696C24—44no—
697C24—44no—
698C24—44no—
699C24C2×D4×C4312yes—
700C24C2×D4×C4314yes—
701C24C2×D4×C4314yes—
702C24C2×D4×C4312yes—
703C24C2×D4×C4312yes—
704C24C2×D4×C4312yes—
705C24C2×D4×C4312yes—
706C24#41×C4314yes—
707C24#41×C4312yes—
708C24#41×C4312yes—
709C24#41×C4312yes—
710C24C24×C4311yescharacteristic
711C2×D4—216no—
712C2×D4—28no—
713C2×D4—28no—
714C2×D4—28no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—44no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—22no—
728C22×C4—28no—
729C22×C4—28no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—21no—
742C22×C4—22no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—28no—
753C22×C4—21no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—21no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—22no—
762C22×C4—21no—
763C22×C4—22no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—44no—
771C22×C4—48no—
772C22×C4—48no—
773C22×C4—48no—
774C22×C4—48no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4C2×D4×C4312yes—
778C22×C4C2×D4×C4312yes—
779C22×C4C2×D4×C4314yes—
780C22×C4C2×D4×C4314yes—
781C22×C4C2×D4×C4312yes—
782C22×C4C2×D4×C4314yes—
783C4⋊C4—48no—
784C22⋊C4—216no—
785C22⋊C4—216no—
786C22⋊C4—28no—
787C22⋊C4—216no—
788C22⋊C4—48no—
789C22⋊C4—44no—
790C22⋊C4—48no—
791C22⋊C4—44no—
792C22⋊C4—48no—
793C22⋊C4—44no—
794C22⋊C4—44no—
795C23—22no—
796C23—24no—
797C23—22no—
798C23—24no—
799C23—22no—
800C23—24no—
801C23—22no—
802C23—24no—
803C23—24no—
804C23—24no—
805C23—24no—
806C23—24no—
807C23—24no—
808C23—24no—
809C23—24no—
810C23—24no—
811C23—232no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—24no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—24no—
834C23—24no—
835C23—432no—
836C23—432no—
837C23—416no—
838C23—416no—
839C23—416no—
840C23—416no—
841C23—432no—
842C23—432no—
843C23—416no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—416no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—42no—
865C23—41no—
866C23—42no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—42no—
871C23—41no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—42no—
876C23—42no—
877C23—42no—
878C23—42no—
879C23#120×C4314yes—
880C23#121×C4318yes—
881C23#121×C4314yes—
882C23#121×C4314yes—
883C23#121×C4314yes—
884C23#123×C4314yes—
885C23#123×C4314yes—
886C23#124×C4314yes—
887C23C22×D4×C4311yescharacteristic
888C23C22×D4×C4311yescharacteristic
889C23C22×D4×C4311yescharacteristic
890C23C22×D4×C4312yes—
891C23C22×D4×C4311yescharacteristic
892C23C2×#41×C4311yescharacteristic
893C23C2×#41×C4311yescharacteristic
894C23C2×#41×C4311yescharacteristic
895C23C2×#41×C4312yes—
896C23H(5,𝔽2)×C4312yes—
897C23H(5,𝔽2)×C4312yes—
898D4—432no—
899D4—416no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—24no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—416no—
917C2×C4—416no—
918C2×C4—42no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—42no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—42no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—41no—
933C2×C4—42no—
934C2×C4—41no—
935C2×C4—42no—
936C2×C4—41no—
937C2×C4—42no—
938C2×C4—41no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—41no—
942C2×C4—42no—
943C2×C4—41no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4#120×C4314yescomplemented
950C22—24no—
951C22—24no—
952C22—24no—
953C22—24no—
954C22—28no—
955C22—24no—
956C22—28no—
957C22—28no—
958C22—28no—
959C22—24no—
960C22—28no—
961C22—28no—
962C22—28no—
963C22—464no—
964C22—44no—
965C22—44no—
966C22—44no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—44no—
974C22—44no—
975C22—44no—
976C22—42no—
977C22—42no—
978C22—44no—
979C22—44no—
980C22—42no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—82no—
986C22—82no—
987C22C43×#39418yescomplemented
988C22C2×#120×C4311yescharacteristic
989C22C2×#120×C4311yescharacteristic
990C22C2×#121×C4311yescharacteristic
991C22C2×#121×C4312yes—
992C22C2×#121×C4311yescharacteristic
993C22C2×#121×C4311yescharacteristic
994C22C2×#123×C4311yescharacteristic
995C22C2×#123×C4311yescharacteristic
996C22C43×#52511yescharacteristic
997C22C43×#52512yes—
998C22C2×#124×C4311yescharacteristic
999C22C43×#53412yes—
1000C22C43×#53411yescharacteristic
1001C22C43×#53511yescharacteristic
1002C22C43×#53812yes—
1003C22D42×C4312yes—
1004C22D42×C4312yes—
1005C22C43×#54612yes—
1006C22C43×#54612yes—
1007C22C43×#54612yes—
1008C22C43×#54612yes—
1009C22C43×#55112yes—
1010C22C43×#55112yes—
1011C4—24no—
1012C4—42no—
1013C4—44no—
1014C4—42no—
1015C4—44no—
1016C4—81no—
1017C4—81no—
1018C4—82no—
1019C2—28no—
1020C2—48no—
1021C2—82no—
1022C2C2×C43×#39411yescharacteristic
1023C2C43×#240811yescharacteristic
1024C2C43×#241011yescharacteristic
1025C2C43×#241012yes—
1026C2C43×#241111yescharacteristic
1027C2C43×#241212yes—
1028C2C43×#241812yes—
1029C2C43×#247212yes—
1030C2C43×#253411yescharacteristic
1031C2C43×#261711yescharacteristic
1032C2C43×#284711yescharacteristic
subgroupG/H
center, socleC24×C43C24
commutator, Frattini, cosocleC24C24×C43
prime radicalC22×#120×C43C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C22⋊C4×C43C2semidirect
3. C2×C43×#394C2semidirect
4. C2×C43×#386C2semidirect
5. C2×C43×#386C2semidirect
6. C2×C43×#380C2semidirect
7. C2×C43×#379C2semidirect
8. C43×#1440C2semidirect
9. C43×#1439C2semidirect
10. C43×#1438C2semidirect
11. C43×C22⋊#95C2semidirect
20. C22×C4⋊C4×C43C22semidirect
31. C22×C22⋊C4×C43C22semidirect
32. C22×C22⋊C4×C43C22semidirect
33. C22×C22⋊C4×C43C22semidirect
39. C2×#95×C43C22semidirect
40. C2×#95×C43C22semidirect
41. C2×#95×C43C22semidirect
42. C2×#95×C43C22semidirect
43. C2×#95×C43C22semidirect
44. C2×#95×C43C22semidirect
82. C23×C4×C43D4semidirect
126. C2×C22⋊C4×C43D4semidirect
432. C2×C4×C43#120semidirect
433. #14725C43direct (N × H)
471. C22×C43#394semidirect
504. C23×C22⋊C4C2×C43semidirect
505. C2×#394C2×C43semidirect
506. C2×#386C2×C43semidirect
507. C2×#386C2×C43semidirect
508. C2×#380C2×C43semidirect
509. C2×#379C2×C43semidirect
510. #1440C2×C43semidirect
511. #1439C2×C43semidirect
512. #1438C2×C43semidirect
513. C22⋊#95C2×C43semidirect
536. C22×C4⋊C4C22×C43semidirect
547. C22×C22⋊C4C22×C43semidirect
548. C22×C22⋊C4C22×C43semidirect
549. C22×C22⋊C4C22×C43semidirect
555. C2×#95C22×C43semidirect
556. C2×#95C22×C43semidirect
557. C2×#95C22×C43semidirect
558. C2×#95C22×C43semidirect
559. C2×#95C22×C43semidirect
560. C2×#95C22×C43semidirect
561. C43#14725direct (N × H)
599. C23×C4D4×C43semidirect
643. C2×C22⋊C4D4×C43semidirect
949. C2×C4#120×C43semidirect
987. C22C43×#394semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C432
C23×C22⋊C4×C432
C2×C43×#3942
C2×C43×#3862
C2×C43×#3802
C2×C43×#3792
C43×#14402
C43×#14392
C43×#14382
C43×C22⋊#952
#1472543