Finite Group Databasebeta

← #24988044

Subgroups — #24988044

Order 11008.

908 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583430C211yesmaximal, characteristic
2#19134661C211yesmaximal, characteristic, complemented
3C2×#14582637C211yesmaximal, characteristic, complemented
4C2×#14582635C211yesmaximal, characteristic, complemented
5C2×#14582633C211yesmaximal, characteristic
6#19132819C211yesmaximal, characteristic, complemented
7C2×C43×#327C211yesmaximal, characteristic
8#14583430—22no—
9#14583430—22no—
10#14583430—22no—
11#14583430—22no—
12C2×#13063318—21no—
13C2×#13063316C411yescharacteristic, complemented
14C2×#13063312C411yescharacteristic, complemented
15C2×#13063306—21no—
16C2×#13063304C2211yescharacteristic
17C2×#13063290C411yescharacteristic, complemented
18C2×D4×Dic43—21no—
19C2×D4×Dic43C411yescharacteristic, complemented
20C2×#13063281—21no—
21C22×C4×Dic43C2211yescharacteristic
22C2×C22⋊(C43⋊C8)C2211yescharacteristic
23C2×C43⋊#95—21no—
24C2×C43⋊#95—21no—
25C2×C43⋊#95C2211yescharacteristic
26#14582653—21no—
27#14582653—21no—
28#14582637—22no—
29#14582635—22no—
30#14582633—22no—
31C2×#121×C43C2211yescharacteristic
32C2×C22⋊C8×C43C2211yescharacteristic
33C2×#95×C43C2211yescharacteristic
34C43×#327—22no—
35C22×Dic86C2×C411yescharacteristic
36C23×Dic43—21no—
37C23×Dic43—21no—
38C23×Dic43D411yescharacteristic
39C23×Dic43D411yescharacteristic
40C22×C43⋊C8—21no—
41#13063318—24no—
42#13063318—24no—
43#13063316—22no—
44#13063316—22no—
45#13063312—22no—
46#13063312—22no—
47#13063306—24no—
48#13063306—24no—
49#13063304—21no—
50#13063304—21no—
51#13063304D412yes—
52#13063304D412yes—
53#13063290—22no—
54#13063290—22no—
55D4×Dic43—24no—
56D4×Dic43—24no—
57D4×Dic43—22no—
58D4×Dic43—22no—
59#13063281—24no—
60#13063281—24no—
61C2×C4⋊Dic43—21no—
62C2×C4⋊Dic43C2×C411yescharacteristic
63C2×Dic43⋊C4—21no—
64C2×Dic43⋊C4—21no—
65C2×Dic43⋊C4—21no—
66C2×C22⋊Dic43—21no—
67C2×C22⋊Dic43—21no—
68C2×C22⋊Dic43—21no—
69C2×C22⋊Dic43—21no—
70C2×C4×Dic43—21no—
71C2×C4×Dic43—21no—
72C2×C4×Dic43—21no—
73C2×C4×Dic43—21no—
74C2×C4×Dic43—21no—
75C2×C4×Dic43C2×C411yescharacteristic
76C2×C4×Dic43C2×C411yescharacteristic
77C2×C4×Dic43D411yescharacteristic
78C2×C4×Dic43D411yescharacteristic
79C22⋊(C43⋊C8)—21no—
80C22⋊(C43⋊C8)—21no—
81C43⋊#95—24no—
82C43⋊#95—21no—
83C43⋊#95—21no—
84C43⋊#95—42no—
85C22×D4×C43—21no—
86C22×D4×C43C2×C411yescharacteristic
87C23×C4×C43—21no—
88C23×C4×C43C2311yescharacteristic
89C22×C8×C43—21no—
90#121×C43—21no—
91#121×C43—21no—
92#121×C43D412yes—
93#121×C43D412yes—
94C2×C4⋊C4×C43C2×C411yescharacteristic
95C2×C22⋊C4×C43—21no—
96C22⋊C8×C43—21no—
97C22⋊C8×C43—21no—
98#95×C43—21no—
99#95×C43—21no—
100C24×C43—21no—
101C24×C43C2×D411yescharacteristic
102C2×D4×C43—21no—
103C2×D4×C43—22no—
104C2×D4×C43—22no—
105C2×D4×C43—41no—
106C2×D4×C43—41no—
107C2×D4×C43—41no—
108C2×D4×C43—41no—
109C2×D4×C43—41no—
110C2×D4×C43—41no—
111C2×D4×C43C22⋊C412yes—
112C22×C4×C43—22no—
113C22×C4×C43—21no—
114C22×C4×C43—41no—
115C22×C4×C43—41no—
116C22×C4×C43—41no—
117C22×C4×C43—41no—
118C22×C4×C43—41no—
119C22×C4×C43—41no—
120C22×C4×C43—41no—
121C22×C4×C43—41no—
122C22×C4×C43C22×C411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×Dic43—24no—
129C22×Dic43—22no—
130C22×Dic43—22no—
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—41no—
142C22×Dic43—41no—
143C22×Dic43—41no—
144C22×Dic43—41no—
145C22×Dic43—42no—
146C22×Dic43—42no—
147C22×Dic43—41no—
148C22×Dic43—41no—
149C22×Dic43—41no—
150C22×Dic43C22⋊C411yescharacteristic
151C22×Dic43C22⋊C411yescharacteristic
152C22×Dic43C22⋊C411yescharacteristic
153C22×Dic43C22⋊C411yescharacteristic
154C2×Dic86—21no—
155C2×Dic86—41no—
156C2×Dic86—41no—
157C2×Dic86C22⋊C412yes—
158C2×C8×C43—41no—
159C2×C8×C43—41no—
160C2×C8×C43—41no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43C22⋊C412yes—
163C22⋊C4×C43—22no—
164C22⋊C4×C43—22no—
165C22⋊Dic43—24no—
166C22⋊Dic43—24no—
167C22⋊Dic43—24no—
168C22⋊Dic43—22no—
169C22⋊Dic43—22no—
170C4⋊Dic43—24no—
171C4⋊Dic43—21no—
172C4⋊Dic43C22⋊C412yes—
173Dic43⋊C4—24no—
174Dic43⋊C4—24no—
175Dic43⋊C4—22no—
176Dic43⋊C4—22no—
177C4×Dic43—24no—
178C4×Dic43—21no—
179C4×Dic43—21no—
180C4×Dic43—21no—
181C4×Dic43—21no—
182C4×Dic43—21no—
183C4×Dic43—21no—
184C4×Dic43—21no—
185C4×Dic43—21no—
186C2×C43⋊C8—41no—
187C2×C43⋊C8—41no—
188C2×C43⋊C8—41no—
189C23×C43—21no—
190C23×C43—21no—
191C23×C43—21no—
192C23×C43—21no—
193C23×C43—22no—
194C23×C43—41no—
195C23×C43—41no—
196C23×C43—41no—
197C23×C43—41no—
198C23×C43—41no—
199C23×C43—41no—
200C23×C43C2×C22⋊C411yescharacteristic
201C23×C43#12011yescharacteristic
202C23×C43#12011yescharacteristic
203C23×C43#13511yescharacteristic
204C23×C43#13511yescharacteristic
205C23×C43AGL(1,ℤ/8)11yescharacteristic
206C23×C43#13711yescharacteristic
207D4×C43—42no—
208D4×C43—42no—
209D4×C43—42no—
210D4×C43—42no—
211D4×C43—42no—
212D4×C43—42no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—22no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—42no—
225C2×C4×C43—42no—
226C2×C4×C43—42no—
227C2×C4×C43—81no—
228C2×C4×C43—81no—
229C2×C4×C43—81no—
230C2×C4×C43—81no—
231C2×C4×C43C2×C22⋊C411yescharacteristic
232C2×C4×C43C2×C22⋊C411yescharacteristic
233C2×C4×C43#12011yescharacteristic
234C2×C4×C43#12011yescharacteristic
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—22no—
241C2×Dic43—22no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—42no—
249C2×Dic43—42no—
250C2×Dic43—48no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—42no—
260C2×Dic43—42no—
261C2×Dic43—42no—
262C2×Dic43—81no—
263C2×Dic43—81no—
264C2×Dic43—81no—
265C2×Dic43—81no—
266C2×Dic43#10412yes—
267Dic86—42no—
268Dic86—42no—
269C8×C43—81no—
270C43⋊C8—81no—
271#8330—431nomaximal, Sylow
272C22×C43—21no—
273C22×C43—21no—
274C22×C43—21no—
275C22×C43—21no—
276C22×C43—21no—
277C22×C43—21no—
278C22×C43—21no—
279C22×C43—21no—
280C22×C43—21no—
281C22×C43—21no—
282C22×C43—21no—
283C22×C43—21no—
284C22×C43—42no—
285C22×C43—42no—
286C22×C43—42no—
287C22×C43—81no—
288C22×C43—81no—
289C22×C43—81no—
290C22×C43—81no—
291C22×C43#37911yescharacteristic
292C22×C43#41011yescharacteristic
293C22×C43#41011yescharacteristic
294C22×C43#41611yescharacteristic
295C22×C43#41711yescharacteristic
296C22×C43C2×#10411yescharacteristic
297C22×C43#42111yescharacteristic
298C22×C43#44911yescharacteristic
299C22×C43#44911yescharacteristic
300C22×C43#45211yescharacteristic
301C22×C43#45211yescharacteristic
302C4×C43—21no—
303C4×C43—21no—
304C4×C43—21no—
305C4×C43—21no—
306C4×C43—42no—
307C4×C43—82no—
308Dic43—22no—
309Dic43—42no—
310Dic43—41no—
311Dic43—41no—
312Dic43—41no—
313Dic43—42no—
314Dic43—82no—
315C2×#529—431no—
316#1817—431no—
317C2×#328—431no—
318C2×#328—431no—
319C2×#327—431no—
320C2×#327D4311yescharacteristic
321#1434—431no—
322C2×C43—21no—
323C2×C43—21no—
324C2×C43—21no—
325C2×C43—21no—
326C2×C43—82no—
327C2×C43#150011yescharacteristic
328C2×C43#150911yescharacteristic
329C2×C43#151211yescharacteristic
330C2×C43#152111yescharacteristic
331C2×C43#178211yescharacteristic
332C2×C43#178811yescharacteristic
333C2×C43#178911yescharacteristic
334#529—862no—
335#529—862no—
336#529—862no—
337#529—862no—
338C2×#126—861no—
339C2×#125—431no—
340C2×#124—431no—
341C2×#123—861no—
342C2×C22⋊Q8—431no—
343C2×#121C2×D4311yescharacteristic
344C2×C4×Q8—431no—
345C2×C4×D4—431no—
346C2×C4×D4—861no—
347C2×#117—861no—
348C22×C42—431no—
349C2×C22⋊C8—431no—
350C2×C22⋊C8C2×D4311yescharacteristic
351C2×#95—431no—
352C2×#95—861no—
353C2×#95—861no—
354C2×#95C2×D4311yescharacteristic
355#336—861no—
356#336—861no—
357#328—862no—
358#328—862no—
359#327—22no—
360#327—862no—
361C43#833011yescharacteristic, complemented, Sylow
362C22×Q8—431no—
363C22×D4—21no—
364C22×D4C4×D4311yescharacteristic
365C23×C4—21no—
366C23×C4—431no—
367C23×C4—431no—
368C23×C4—861no—
369C23×C4—861no—
370C23×C4C22×D4311yescharacteristic
371C22×C8—21no—
372C22×C8—861no—
373#126—864no—
374#126—864no—
375#125—862no—
376#125—862no—
377#124—862no—
378#124—862no—
379#123—864no—
380#123—864no—
381C22⋊Q8—432no—
382C22⋊Q8—432no—
383C22⋊Q8—861no—
384C22⋊Q8—861no—
385#121—21no—
386#121—21no—
387#121D17212yes—
388#121C22⋊D4312yes—
389C4×Q8—862no—
390C4×Q8—862no—
391C4×D4—862no—
392C4×D4—864no—
393C4×D4—864no—
394C4×D4—862no—
395#117—864no—
396#117—864no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4C4×D4311yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—861no—
405C2×C22⋊C4—861no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C42—431no—
409C2×C42—431no—
410C2×C42—431no—
411C2×C42—431no—
412C2×C42—861no—
413C2×C42—861no—
414C2×C42—861no—
415C2×C42—861no—
416C2×C42—861no—
417C22⋊C8—21no—
418C22⋊C8—21no—
419C22⋊C8—861no—
420C22⋊C8—861no—
421#95—21no—
422#95—21no—
423#95—864no—
424#95—861no—
425#95—861no—
426#95—1722no—
427C24—21no—
428C24D4×D4311yescharacteristic
429C2×Q8—432no—
430C2×Q8—861no—
431C2×Q8—1721no—
432C2×Q8—1721no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—21no—
436C2×D4—41no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—41no—
442C2×D4(C2×D43)⋊C412yes—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—431no—
454C22×C4—431no—
455C22×C4—431no—
456C22×C4—431no—
457C22×C4—862no—
458C22×C4—864no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—862no—
470C22×C4—1722no—
471C22×C4—1721no—
472C22×C4—1722no—
473C22×C4—1721no—
474C22×C4—1721no—
475C22×C4—1721no—
476C22×C4—1721no—
477C22×C4—1721no—
478C22×C4—1721no—
479C22×C4C2×C4×D4311yescharacteristic
480C22×C4C2×D17211yescharacteristic
481C22×C4D4×D4311yescharacteristic
482C22×C4D4×D4311yescharacteristic
483C22×C4D4×D4311yescharacteristic
484C22×C4C2×C22⋊D4311yescharacteristic
485C2×C8—41no—
486C2×C8—41no—
487C2×C8—41no—
488C2×C8—1721no—
489C2×C8—1721no—
490C2×C8—1721no—
491C4⋊C4—21no—
492C4⋊C4—432no—
493C4⋊C4—864no—
494C4⋊C4—864no—
495C4⋊C4—864no—
496C4⋊C4—861no—
497C4⋊C4—862no—
498C4⋊C4—862no—
499C4⋊C4(C2×D43)⋊C412yes—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—864no—
503C22⋊C4—864no—
504C22⋊C4—864no—
505C22⋊C4—862no—
506C22⋊C4—862no—
507C42—864no—
508C42—861no—
509C42—861no—
510C42—861no—
511C42—861no—
512C42—861no—
513C42—861no—
514C42—861no—
515C42—861no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—22no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23C22⋊C4×D4311yescharacteristic
528C23#1306329311yescharacteristic
529C23#1306329511yescharacteristic
530C23#1306334411yescharacteristic
531C23#1306334611yescharacteristic
532C23#1306334911yescharacteristic
533C23#1306335411yescharacteristic
534Q8—1722no—
535Q8—1722no—
536D4—42no—
537D4—42no—
538D4—42no—
539D4—42no—
540D4—42no—
541D4—42no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—81no—
557C2×C4—81no—
558C2×C4—81no—
559C2×C4—81no—
560C2×C4—432no—
561C2×C4—861no—
562C2×C4—861no—
563C2×C4—861no—
564C2×C4—861no—
565C2×C4—861no—
566C2×C4—861no—
567C2×C4—861no—
568C2×C4—861no—
569C2×C4—861no—
570C2×C4—861no—
571C2×C4—861no—
572C2×C4—862no—
573C2×C4—862no—
574C2×C4—3441no—
575C2×C4—3441no—
576C2×C4—3441no—
577C2×C4—3441no—
578C2×C4—1722no—
579C2×C4—1722no—
580C2×C4—1728no—
581C2×C4—1722no—
582C2×C4—1722no—
583C2×C4—1722no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4C22⋊C4×D4311yescharacteristic
593C2×C4C2×(C2×D43)⋊C411yescharacteristic
594C2×C4#1306329311yescharacteristic
595C2×C4#1306329511yescharacteristic
596C8—81no—
597C8—3441no—
598C22—21no—
599C22—21no—
600C22—21no—
601C22—21no—
602C22—21no—
603C22—21no—
604C22—21no—
605C22—21no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22—81no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22#1458275411yescharacteristic
618C22#1458287111yescharacteristic
619C22#1458287111yescharacteristic
620C22#1458289211yescharacteristic
621C22#1458289711yescharacteristic
622C22#104×D4311yescharacteristic
623C22#1458291411yescharacteristic
624C22#1458304111yescharacteristic
625C22#1458304511yescharacteristic
626C22#1458305811yescharacteristic
627C22#1458306211yescharacteristic
628C4—21no—
629C4—21no—
630C4—21no—
631C4—21no—
632C4—42no—
633C4—82no—
634C4—862no—
635C4—3442no—
636C4—1722no—
637C4—1721no—
638C4—1721no—
639C4—1721no—
640C4—1722no—
641C2—21no—
642C2—21no—
643C2—21no—
644C2—21no—
645C2—82no—
646C2#1913307811yescharacteristic
647C2#1913311711yescharacteristic
648C2#1913313011yescharacteristic
649C2#1913316911yescharacteristic
650C2#1913451111yescharacteristic
651C2#1913453211yescharacteristic
652C2#1913453711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#327C2
socleC23×C43C2×C22⋊C4
prime radicalC2×#121×C43C22
cosocleC23×C4×C43C23
hypercenterC2×#327D43
hypocenterC43#8330
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. #19134661C2semidirect
3. C2×#14582637C2semidirect
4. C2×#14582635C2semidirect
6. #19132819C2semidirect
13. C2×#13063316C4semidirect
14. C2×#13063312C4semidirect
17. C2×#13063290C4semidirect
19. C2×D4×Dic43C4semidirect
361. C43#8330semidirect

Maximal subgroups

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

subgroupindex
C2×#145834302
#191346612
C2×#145826372
C2×#145826352
C2×#145826332
#191328192
C2×C43×#3272
#833043