Finite Group Databasebeta

← C41×#10991 #23787192

Subgroups — C41×#10991 #23787192

Order 10496.

3122 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C41C211yesmaximal, characteristic
2C22×#99×C41C211yesmaximal, characteristic, complemented
3C41×#2308C211yesmaximal, characteristic, complemented
4C2×C41×#379C212yesmaximal, complemented
5C2×C41×#342C212yesmaximal, complemented
6C26×C41C2211yescharacteristic
7C23×D4×C41—21no—
8C23×D4×C41C2211yescharacteristic
9C2×#120×C41—24no—
10C2×#120×C41—22no—
11C2×#120×C41—24no—
12C2×#120×C41C414yescomplemented
13C22×C22⋊C4×C41—21no—
14C22×C22⋊C4×C41—24no—
15C22×C22⋊C4×C41C2212yes—
16C22×C22⋊C4×C41C2212yes—
17C22×C22⋊C4×C41C2211yescharacteristic
18C2×#99×C41—22no—
19C2×#99×C41—24no—
20C41×#386—24no—
21C41×#381—21no—
22C41×#379—24no—
23C41×#379—21no—
24C41×#379—24no—
25C41×#342—24no—
26C25×C41—22no—
27C25×C41—21no—
28C25×C41—21no—
29C25×C41—22no—
30C25×C41—22no—
31C25×C41—22no—
32C25×C41—22no—
33C25×C41—48no—
34C25×C41C2×C412yes—
35C25×C41D414yes—
36C25×C41D411yescharacteristic
37C25×C41C2311yescharacteristic
38C22×D4×C41—28no—
39C22×D4×C41—24no—
40C22×D4×C41—22no—
41C22×D4×C41—22no—
42C22×D4×C41—22no—
43C22×D4×C41—22no—
44C22×D4×C41—22no—
45C22×D4×C41—22no—
46C22×D4×C41—48no—
47C22×D4×C41C2×C412yes—
48C22×D4×C41D412yes—
49C23×C4×C41—21no—
50C23×C4×C41—22no—
51C23×C4×C41D411yescharacteristic
52C23×C4×C41D414yescomplemented
53#120×C41—216no—
54#120×C41—28no—
55#120×C41—28no—
56C2×C22⋊C4×C41—28no—
57C2×C22⋊C4×C41—22no—
58C2×C22⋊C4×C41—21no—
59C2×C22⋊C4×C41—24no—
60C2×C22⋊C4×C41—22no—
61C2×C22⋊C4×C41—22no—
62C2×C22⋊C4×C41—22no—
63C2×C22⋊C4×C41—22no—
64C2×C22⋊C4×C41—216no—
65C2×C22⋊C4×C41—22no—
66C2×C22⋊C4×C41—22no—
67C2×C22⋊C4×C41—22no—
68C2×C22⋊C4×C41—22no—
69C2×C22⋊C4×C41—22no—
70C2×C22⋊C4×C41—22no—
71C2×C22⋊C4×C41—22no—
72C2×C22⋊C4×C41—24no—
73C2×C22⋊C4×C41—416no—
74C2×C22⋊C4×C41C2×C412yes—
75C2×C22⋊C4×C41D414yes—
76C2×C22⋊C4×C41D414yescomplemented
77#99×C41—28no—
78#95×C41—24no—
79C24×C41—216no—
80C24×C41—28no—
81C24×C41—22no—
82C24×C41—24no—
83C24×C41—24no—
84C24×C41—24no—
85C24×C41—24no—
86C24×C41—22no—
87C24×C41—24no—
88C24×C41—24no—
89C24×C41—22no—
90C24×C41—21no—
91C24×C41—24no—
92C24×C41—24no—
93C24×C41—22no—
94C24×C41—21no—
95C24×C41—48no—
96C24×C41—416no—
97C24×C41—44no—
98C24×C41—48no—
99C24×C41—44no—
100C24×C41—416no—
101C24×C41—48no—
102C24×C41—416no—
103C24×C41—416no—
104C24×C41—416no—
105C24×C41—44no—
106C24×C41—41no—
107C24×C41—41no—
108C24×C41—42no—
109C24×C41—42no—
110C24×C41—42no—
111C24×C41—42no—
112C24×C41—41no—
113C24×C41—41no—
114C24×C41—42no—
115C24×C41—42no—
116C24×C41C22⋊C414yescomplemented
117C24×C41C22⋊C412yescomplemented
118C24×C41C22×C411yescharacteristic
119C24×C41C2×D411yescharacteristic
120C24×C41C2×D412yes—
121C24×C41C2×D412yes—
122C24×C41C2×D411yescharacteristic
123C24×C41C2×D412yes—
124C24×C41C2×D412yes—
125C24×C41#4112yes—
126C24×C41#4112yes—
127C2×D4×C41—216no—
128C2×D4×C41—22no—
129C2×D4×C41—22no—
130C2×D4×C41—24no—
131C2×D4×C41—24no—
132C2×D4×C41—22no—
133C2×D4×C41—24no—
134C2×D4×C41—24no—
135C2×D4×C41—22no—
136C2×D4×C41—416no—
137C2×D4×C41—432no—
138C2×D4×C41—42no—
139C2×D4×C41—42no—
140C2×D4×C41—42no—
141C2×D4×C41—42no—
142C2×D4×C41—42no—
143C2×D4×C41—42no—
144C2×D4×C41—42no—
145C2×D4×C41—42no—
146C22×C4×C41—22no—
147C22×C4×C41—22no—
148C22×C4×C41—24no—
149C22×C4×C41—21no—
150C22×C4×C41—22no—
151C22×C4×C41—21no—
152C22×C4×C41—24no—
153C22×C4×C41—24no—
154C22×C4×C41—24no—
155C22×C4×C41—24no—
156C22×C4×C41—44no—
157C22×C4×C41—48no—
158C22×C4×C41—48no—
159C22×C4×C41—42no—
160C22×C4×C41—42no—
161C22×C4×C41C22⋊C412yescomplemented
162C22⋊C4×C41—216no—
163C22⋊C4×C41—22no—
164C22⋊C4×C41—24no—
165C22⋊C4×C41—24no—
166C22⋊C4×C41—24no—
167C22⋊C4×C41—432no—
168C22⋊C4×C41—42no—
169C22⋊C4×C41—42no—
170C22⋊C4×C41—42no—
171C22⋊C4×C41—42no—
172C22⋊C4×C41—42no—
173C22⋊C4×C41—42no—
174C22⋊C4×C41—84no—
175C22⋊C4×C41C22⋊C414yescomplemented
176C23×C41—28no—
177C23×C41—24no—
178C23×C41—216no—
179C23×C41—28no—
180C23×C41—216no—
181C23×C41—216no—
182C23×C41—216no—
183C23×C41—24no—
184C23×C41—28no—
185C23×C41—22no—
186C23×C41—22no—
187C23×C41—22no—
188C23×C41—48no—
189C23×C41—42no—
190C23×C41—42no—
191C23×C41—44no—
192C23×C41—44no—
193C23×C41—44no—
194C23×C41—44no—
195C23×C41—44no—
196C23×C41—44no—
197C23×C41—416no—
198C23×C41—48no—
199C23×C41—48no—
200C23×C41—48no—
201C23×C41—48no—
202C23×C41—416no—
203C23×C41—416no—
204C23×C41—48no—
205C23×C41—416no—
206C23×C41—48no—
207C23×C41—416no—
208C23×C41—416no—
209C23×C41—416no—
210C23×C41—416no—
211C23×C41—44no—
212C23×C41—48no—
213C23×C41—48no—
214C23×C41—416no—
215C23×C41—48no—
216C23×C41—416no—
217C23×C41—42no—
218C23×C41—42no—
219C23×C41—44no—
220C23×C41—44no—
221C23×C41—44no—
222C23×C41—44no—
223C23×C41—44no—
224C23×C41—48no—
225C23×C41—42no—
226C23×C41—42no—
227C23×C41—44no—
228C23×C41—82no—
229C23×C41—84no—
230C23×C41C2×C22⋊C411yescharacteristic
231C23×C41C2×C22⋊C411yescharacteristic
232C23×C41C2×C22⋊C411yescharacteristic
233C23×C41C4×D412yes—
234C23×C41C4×D412yes—
235C23×C41#12012yes—
236C23×C41#12012yes—
237C23×C41#12012yes—
238C23×C41#12011yescharacteristic
239C23×C41#12011yescharacteristic
240C23×C41#12112yes—
241C23×C41#12112yes—
242C23×C41#12112yes—
243C23×C41#12112yes—
244C23×C41#12112yes—
245C23×C41#12112yes—
246C23×C41#12311yescharacteristic
247C23×C41#12311yescharacteristic
248C23×C41#12312yes—
249C23×C41#12412yes—
250C23×C41#12712yes—
251D4×C41—432no—
252D4×C41—44no—
253D4×C41—44no—
254D4×C41—44no—
255D4×C41—44no—
256C2×C4×C41—22no—
257C2×C4×C41—24no—
258C2×C4×C41—22no—
259C2×C4×C41—22no—
260C2×C4×C41—44no—
261C2×C4×C41—48no—
262C2×C4×C41—42no—
263C2×C4×C41—42no—
264C2×C4×C41—48no—
265C2×C4×C41—48no—
266C2×C4×C41—44no—
267C2×C4×C41—44no—
268C2×C4×C41—48no—
269C2×C4×C41—84no—
270C2×C4×C41—84no—
271C2×C4×C41—84no—
272#10991C4111yesmaximal, characteristic, direct product factor, Sylow
273C22×C41—22no—
274C22×C41—24no—
275C22×C41—24no—
276C22×C41—22no—
277C22×C41—24no—
278C22×C41—24no—
279C22×C41—24no—
280C22×C41—24no—
281C22×C41—24no—
282C22×C41—24no—
283C22×C41—28no—
284C22×C41—216no—
285C22×C41—41no—
286C22×C41—41no—
287C22×C41—42no—
288C22×C41—42no—
289C22×C41—41no—
290C22×C41—42no—
291C22×C41—42no—
292C22×C41—42no—
293C22×C41—41no—
294C22×C41—42no—
295C22×C41—44no—
296C22×C41—416no—
297C22×C41—48no—
298C22×C41—48no—
299C22×C41—416no—
300C22×C41—416no—
301C22×C41—416no—
302C22×C41—44no—
303C22×C41—48no—
304C22×C41—44no—
305C22×C41—416no—
306C22×C41—44no—
307C22×C41—42no—
308C22×C41—82no—
309C22×C41—84no—
310C22×C41—84no—
311C22×C41#37911yescharacteristic
312C22×C41#38611yescharacteristic
313C22×C41#38612yes—
314C22×C41#38611yescharacteristic
315C22×C41#39012yes—
316C22×C41#39212yes—
317C22×C41#39212yes—
318C22×C41#39412yes—
319C22×C41#39412yes—
320C22×C41B(4,𝔽2)14yes—
321C4×C41—44no—
322C4×C41—42no—
323C4×C41—84no—
324C4×C41—84no—
325C22×#120C2×C4111yescharacteristic
326C22×#99C2×C4111yescharacteristic, complemented
327#2308C2×C4111yescharacteristic, complemented
328C2×#379C2×C4112yescomplemented
329C2×#342C2×C4112yescomplemented
330C2×C41—21no—
331C2×C41—22no—
332C2×C41—22no—
333C2×C41—21no—
334C2×C41—22no—
335C2×C41—22no—
336C2×C41—22no—
337C2×C41—48no—
338C2×C41—82no—
339C2×C41#143811yescharacteristic
340C2×C41#188912yes—
341C2×C41#202114yes—
342C26C22×C4111yescharacteristic
343C23×D4—21no—
344C23×D4C22×C4111yescharacteristic
345C2×#120—24no—
346C2×#120—22no—
347C2×#120—24no—
348C2×#120C4×C4114yescomplemented
349C22×C22⋊C4—21no—
350C22×C22⋊C4—24no—
351C22×C22⋊C4C22×C4112yes—
352C22×C22⋊C4C22×C4112yes—
353C22×C22⋊C4C22×C4111yescharacteristic
354C2×#99—22no—
355C2×#99—24no—
356#386—24no—
357#381—21no—
358#379—21no—
359#379—24no—
360#379—24no—
361#342—24no—
362C41#1099111yescharacteristic, direct product factor, Sylow
363C25—22no—
364C25—21no—
365C25—21no—
366C25—22no—
367C25—22no—
368C25—22no—
369C25—22no—
370C25—48no—
371C25C2×C4×C4112yes—
372C25D4×C4114yes—
373C25D4×C4111yescharacteristic
374C25C23×C4111yescharacteristic
375C22×D4—28no—
376C22×D4—24no—
377C22×D4—22no—
378C22×D4—22no—
379C22×D4—22no—
380C22×D4—22no—
381C22×D4—22no—
382C22×D4—22no—
383C22×D4—48no—
384C22×D4C2×C4×C4112yes—
385C22×D4D4×C4112yes—
386C23×C4—21no—
387C23×C4—22no—
388C23×C4D4×C4111yescharacteristic
389C23×C4D4×C4114yescomplemented
390#120—216no—
391#120—28no—
392#120—28no—
393C2×C22⋊C4—28no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—216no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—416no—
411C2×C22⋊C4C2×C4×C4112yes—
412C2×C22⋊C4D4×C4114yes—
413C2×C22⋊C4D4×C4114yescomplemented
414#99—28no—
415#95—24no—
416C24—216no—
417C24—28no—
418C24—22no—
419C24—24no—
420C24—24no—
421C24—24no—
422C24—24no—
423C24—22no—
424C24—24no—
425C24—21no—
426C24—24no—
427C24—22no—
428C24—24no—
429C24—24no—
430C24—22no—
431C24—21no—
432C24—48no—
433C24—416no—
434C24—44no—
435C24—48no—
436C24—44no—
437C24—416no—
438C24—416no—
439C24—48no—
440C24—416no—
441C24—416no—
442C24—44no—
443C24—41no—
444C24—41no—
445C24—42no—
446C24—42no—
447C24—42no—
448C24—42no—
449C24—41no—
450C24—41no—
451C24—42no—
452C24—42no—
453C24C22⋊C4×C4114yescomplemented
454C24C22⋊C4×C4112yescomplemented
455C24C22×C4×C4111yescharacteristic
456C24C2×D4×C4111yescharacteristic
457C24C2×D4×C4112yes—
458C24C2×D4×C4112yes—
459C24C2×D4×C4111yescharacteristic
460C24C2×D4×C4112yes—
461C24C2×D4×C4112yes—
462C24#41×C4112yes—
463C24#41×C4112yes—
464C2×D4—216no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—24no—
468C2×D4—24no—
469C2×D4—22no—
470C2×D4—24no—
471C2×D4—24no—
472C2×D4—22no—
473C2×D4—416no—
474C2×D4—432no—
475C2×D4—42no—
476C2×D4—42no—
477C2×D4—42no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4—42no—
481C2×D4—42no—
482C2×D4—42no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—44no—
494C22×C4—48no—
495C22×C4—48no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4C22⋊C4×C4112yescomplemented
499C22⋊C4—216no—
500C22⋊C4—22no—
501C22⋊C4—24no—
502C22⋊C4—24no—
503C22⋊C4—24no—
504C22⋊C4—432no—
505C22⋊C4—42no—
506C22⋊C4—42no—
507C22⋊C4—42no—
508C22⋊C4—42no—
509C22⋊C4—42no—
510C22⋊C4—42no—
511C22⋊C4—84no—
512C22⋊C4C22⋊C4×C4114yescomplemented
513C23—28no—
514C23—24no—
515C23—216no—
516C23—216no—
517C23—28no—
518C23—216no—
519C23—216no—
520C23—24no—
521C23—28no—
522C23—22no—
523C23—22no—
524C23—22no—
525C23—48no—
526C23—42no—
527C23—44no—
528C23—44no—
529C23—44no—
530C23—42no—
531C23—44no—
532C23—44no—
533C23—48no—
534C23—48no—
535C23—416no—
536C23—416no—
537C23—48no—
538C23—416no—
539C23—44no—
540C23—416no—
541C23—48no—
542C23—48no—
543C23—48no—
544C23—416no—
545C23—416no—
546C23—416no—
547C23—416no—
548C23—44no—
549C23—48no—
550C23—48no—
551C23—416no—
552C23—48no—
553C23—416no—
554C23—42no—
555C23—42no—
556C23—44no—
557C23—44no—
558C23—44no—
559C23—44no—
560C23—44no—
561C23—48no—
562C23—42no—
563C23—42no—
564C23—44no—
565C23—82no—
566C23—84no—
567C23C2×C22⋊C4×C4111yescharacteristic
568C23C2×C22⋊C4×C4111yescharacteristic
569C23C2×C22⋊C4×C4111yescharacteristic
570C23C4×D4×C4112yes—
571C23C4×D4×C4112yes—
572C23#120×C4112yes—
573C23#120×C4112yes—
574C23#120×C4112yes—
575C23#120×C4111yescharacteristic
576C23#120×C4111yescharacteristic
577C23#121×C4112yes—
578C23#121×C4112yes—
579C23#121×C4112yes—
580C23#121×C4112yes—
581C23#121×C4112yes—
582C23#121×C4112yes—
583C23#123×C4111yescharacteristic
584C23#123×C4111yescharacteristic
585C23#123×C4112yes—
586C23#124×C4112yes—
587C23#127×C4112yes—
588D4—432no—
589D4—44no—
590D4—44no—
591D4—44no—
592D4—44no—
593C2×C4—22no—
594C2×C4—24no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—48no—
598C2×C4—44no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—48no—
602C2×C4—48no—
603C2×C4—44no—
604C2×C4—44no—
605C2×C4—48no—
606C2×C4—84no—
607C2×C4—84no—
608C2×C4—84no—
609C22—24no—
610C22—24no—
611C22—24no—
612C22—24no—
613C22—24no—
614C22—24no—
615C22—22no—
616C22—24no—
617C22—24no—
618C22—22no—
619C22—28no—
620C22—216no—
621C22—41no—
622C22—41no—
623C22—42no—
624C22—42no—
625C22—41no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22—41no—
630C22—42no—
631C22—44no—
632C22—416no—
633C22—48no—
634C22—48no—
635C22—416no—
636C22—416no—
637C22—416no—
638C22—44no—
639C22—416no—
640C22—48no—
641C22—44no—
642C22—44no—
643C22—42no—
644C22—82no—
645C22—84no—
646C22—84no—
647C22C41×#37911yescharacteristic
648C22C41×#38611yescharacteristic
649C22C41×#38612yes—
650C22C41×#38611yescharacteristic
651C22C41×#39012yes—
652C22C41×#39212yes—
653C22C41×#39212yes—
654C22C41×#39412yes—
655C22C41×#39412yes—
656C22C41×B(4,𝔽2)14yes—
657C4—44no—
658C4—42no—
659C4—84no—
660C4—84no—
661C2—21no—
662C2—22no—
663C2—22no—
664C2—21no—
665C2—22no—
666C2—22no—
667C2—22no—
668C2—48no—
669C2—82no—
670C2C41×#143811yescharacteristic
671C2C41×#188912yes—
672C2C41×#202114yes—
subgroupG/H
center, socleC23×C41#120
commutatorC24C22×C4×C41
Frattini, cosocleC25C23×C41
prime radicalC22×#120×C41C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C41 ◁ C25×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#99×C41C2semidirect
3. C41×#2308C2semidirect
4. C2×C41×#379C2semidirect
5. C2×C41×#342C2semidirect
12. C2×#120×C41C4semidirect
52. C23×C4×C41D4semidirect
76. C2×C22⋊C4×C41D4semidirect
116. C24×C41C22⋊C4semidirect
117. C24×C41C22⋊C4semidirect
161. C22×C4×C41C22⋊C4semidirect
175. C22⋊C4×C41C22⋊C4semidirect
272. #10991C41direct (N × H)
326. C22×#99C2×C41semidirect
327. #2308C2×C41semidirect
328. C2×#379C2×C41semidirect
329. C2×#342C2×C41semidirect
348. C2×#120C4×C41semidirect
362. C41#10991direct (N × H)
389. C23×C4D4×C41semidirect
413. C2×C22⋊C4D4×C41semidirect
453. C24C22⋊C4×C41semidirect
454. C24C22⋊C4×C41semidirect
498. C22×C4C22⋊C4×C41semidirect
512. C22⋊C4C22⋊C4×C41semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C412
C22×#99×C412
C41×#23082
C2×C41×#3792
C2×C41×#3422
#1099141