Finite Group Databasebeta

← #24995595

Subgroups — #24995595

Order 11008.

770 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142938C211yesmaximal, characteristic
2#19134359C211yesmaximal, characteristic, complemented
3C2×#14582634C211yesmaximal, characteristic, complemented
4C2×#14582633C211yesmaximal, characteristic, complemented
5C2×#14582632C211yesmaximal, characteristic, complemented
6#19132821C211yesmaximal, characteristic, complemented
7C2×C43×#327C211yesmaximal, characteristic, complemented
8C2×#13063321C411yescharacteristic, complemented
9C2×#13063299C2211yescharacteristic
10C2×#13063297—21no—
11C2×#13063297—21no—
12C22×C4×Dic43C2211yescharacteristic
13C2×C22⋊(C43⋊C8)C2211yescharacteristic
14C2×#13063235—21no—
15#14582802C411yescharacteristic, complemented
16#14582800C411yescharacteristic, complemented
17#14582799—21no—
18#14582799—21no—
19#14582768C411yescharacteristic, complemented
20C2×C43⋊#95—21no—
21C2×C43⋊#95—21no—
22C2×C43⋊#95C2211yescharacteristic
23#14582653—21no—
24#14582634—22no—
25#14582633—22no—
26#14582632—22no—
27C2×#121×C43C2211yescharacteristic
28C2×C22⋊C8×C43C2211yescharacteristic
29C2×#95×C43C2211yescharacteristic
30C43×#327—22no—
31C22×D172C2×C411yescharacteristic
32C22×C22⋊D43—21no—
33C22×C22⋊D43—21no—
34C22×C22⋊D43—21no—
35C23×Dic43—21no—
36C23×Dic43D411yescharacteristic
37C23×Dic43D411yescharacteristic
38C22×C43⋊C8—21no—
39#13063321—42no—
40#13063299—21no—
41#13063299—21no—
42#13063299—21no—
43#13063299—21no—
44#13063297—42no—
45#13063297—42no—
46#13063297—42no—
47#13063297—42no—
48C2×C4⋊Dic43C2×C411yescharacteristic
49C2×Dic43⋊C4—21no—
50C2×Dic43⋊C4—21no—
51C2×C22⋊Dic43—21no—
52C2×C22⋊Dic43—21no—
53C2×(C2×D43)⋊C4—21no—
54C2×(C2×D43)⋊C4—21no—
55C2×(C2×D43)⋊C4—21no—
56C2×C4×Dic43—42no—
57C2×C4×Dic43C2×C411yescharacteristic
58C2×C4×Dic43C2×C411yescharacteristic
59C2×C4×Dic43D411yescharacteristic
60C2×C4×Dic43D411yescharacteristic
61C22⋊(C43⋊C8)—21no—
62C22⋊(C43⋊C8)D412yescomplemented
63#13063235—42no—
64C43⋊#95—24no—
65C43⋊#95—21no—
66C43⋊#95—21no—
67C43⋊#95—42no—
68C22×D4×C43—21no—
69C22×D4×C43C2×C411yescharacteristic
70C23×C4×C43—21no—
71C23×C4×C43C2311yescharacteristic
72C22×C8×C43—21no—
73#121×C43—21no—
74#121×C43—21no—
75#121×C43—21no—
76#121×C43—21no—
77C2×C4⋊C4×C43C2×C411yescharacteristic
78C2×C22⋊C4×C43—21no—
79C22⋊C8×C43—21no—
80C22⋊C8×C43D412yescomplemented
81#95×C43—21no—
82#95×C43—21no—
83C24×C43—21no—
84C24×C43C2×D411yescharacteristic
85C23×D43—21no—
86C2×D4×C43—21no—
87C2×D4×C43—21no—
88C2×D4×C43—41no—
89C2×D4×C43—41no—
90C2×D4×C43—41no—
91C2×D4×C43—41no—
92C2×D4×C43—41no—
93C2×D4×C43—41no—
94C2×D4×C43—41no—
95C2×D4×C43—41no—
96C22×C4×C43—22no—
97C22×C4×C43—21no—
98C22×C4×C43—41no—
99C22×C4×C43—41no—
100C22×C4×C43—41no—
101C22×C4×C43—41no—
102C22×C4×C43—41no—
103C22×C4×C43—41no—
104C22×C4×C43—41no—
105C22×C4×C43—41no—
106C22×C4×C43C22×C411yescharacteristic
107C22×C4×C43C2×D411yescharacteristic
108C22×C4×C43C2×D411yescharacteristic
109C22×C4×C43C2×D411yescharacteristic
110C22×C4×C43#4111yescharacteristic
111C22×C4×C43#4111yescharacteristic
112C2×C22⋊D43—42no—
113C2×C22⋊D43—42no—
114C2×C22⋊D43—42no—
115C2×C22⋊D43—42no—
116C2×C22⋊D43—42no—
117C2×C22⋊D43—42no—
118C2×C22⋊D43—41no—
119C2×C22⋊D43—41no—
120C2×C22⋊D43—41no—
121C2×C22⋊D43—41no—
122C2×C22⋊D43—41no—
123C2×C22⋊D43—41no—
124C22×Dic43—22no—
125C22×Dic43—22no—
126C22×Dic43—22no—
127C22×Dic43—21no—
128C22×Dic43—21no—
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43—21no—
132C22×Dic43—41no—
133C22×Dic43—41no—
134C22×Dic43—41no—
135C22×Dic43—41no—
136C22×Dic43—41no—
137C22×Dic43—41no—
138C22×Dic43—41no—
139C22×Dic43—41no—
140C22×Dic43C22⋊C411yescharacteristic
141C22×Dic43C22⋊C411yescharacteristic
142C22×Dic43C22⋊C411yescharacteristic
143C22×Dic43C22⋊C411yescharacteristic
144C2×D172—21no—
145C2×D172—21no—
146C2×D172—41no—
147C2×D172—41no—
148C2×C8×C43—22no—
149C2×C8×C43—41no—
150C2×C8×C43—41no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—21no—
153C22⋊C4×C43—41no—
154C22⋊C4×C43—41no—
155C22⋊Dic43—42no—
156C22⋊Dic43—42no—
157(C2×D43)⋊C4—42no—
158(C2×D43)⋊C4—42no—
159(C2×D43)⋊C4—41no—
160(C2×D43)⋊C4—41no—
161C4⋊Dic43—21no—
162C4⋊Dic43—21no—
163Dic43⋊C4—42no—
164Dic43⋊C4—42no—
165C4×Dic43—22no—
166C4×Dic43—22no—
167C4×Dic43—41no—
168C4×Dic43—41no—
169C2×C43⋊C8—22no—
170C2×C43⋊C8—41no—
171C2×C43⋊C8—41no—
172C23×C43—21no—
173C23×C43—21no—
174C23×C43—21no—
175C23×C43—21no—
176C23×C43—41no—
177C23×C43—41no—
178C23×C43—41no—
179C23×C43—41no—
180C23×C43—41no—
181C23×C43—41no—
182C23×C43—41no—
183C23×C43C2×C22⋊C411yescharacteristic
184C23×C43#12411yescharacteristic
185C23×C43#12711yescharacteristic
186C23×C43AGL(1,ℤ/8)11yescharacteristic
187C23×C43AGL(1,ℤ/8)11yescharacteristic
188C23×C43AGL(1,ℤ/8)11yescharacteristic
189C23×C43AGL(1,ℤ/8)11yescharacteristic
190C22×D43—41no—
191C22×D43—41no—
192C22×D43—41no—
193C22×D43—41no—
194C22×D43—41no—
195C22×D43—41no—
196C22×D43—41no—
197D4×C43—81no—
198D4×C43—81no—
199D4×C43—81no—
200D4×C43—81no—
201D4×C43—81no—
202D4×C43—81no—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
211C2×C4×C43—42no—
212C2×C4×C43—42no—
213C2×C4×C43—42no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—81no—
218C2×C4×C43—81no—
219C2×C4×C43—81no—
220C2×C4×C43—81no—
221C2×C4×C43C4×D411yescharacteristic
222C2×C4×C43C4×D411yescharacteristic
223C2×C4×C43#12111yescharacteristic
224C2×C4×C43#12111yescharacteristic
225C22⋊D43—84no—
226C22⋊D43—84no—
227C22⋊D43—81no—
228C22⋊D43—81no—
229C22⋊D43—81no—
230C22⋊D43—81no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—42no—
242C2×Dic43—42no—
243C2×Dic43—42no—
244C2×Dic43—42no—
245C2×Dic43—42no—
246C2×Dic43—42no—
247C2×Dic43—42no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—81no—
252C2×Dic43—81no—
253C2×Dic43—81no—
254C2×Dic43—81no—
255C2×Dic43#9912yes—
256C2×Dic43#10412yes—
257D172—81no—
258D172—81no—
259C8×C43—42no—
260C43⋊C8—42no—
261#9684—431nomaximal, Sylow
262C22×C43—21no—
263C22×C43—21no—
264C22×C43—21no—
265C22×C43—21no—
266C22×C43—21no—
267C22×C43—21no—
268C22×C43—21no—
269C22×C43—21no—
270C22×C43—21no—
271C22×C43—21no—
272C22×C43—21no—
273C22×C43—21no—
274C22×C43—81no—
275C22×C43—81no—
276C22×C43—81no—
277C22×C43—81no—
278C22×C43—81no—
279C22×C43—81no—
280C22×C43—81no—
281C22×C43#39011yescharacteristic
282C22×C43C2×#9911yescharacteristic
283C22×C43#41011yescharacteristic
284C22×C43#41811yescharacteristic
285C22×C43#41811yescharacteristic
286C22×C43C2×#10411yescharacteristic
287C22×C43#42111yescharacteristic
288C22×C43#49011yescharacteristic
289C22×C43#49011yescharacteristic
290C22×C43#49611yescharacteristic
291C22×C43#49611yescharacteristic
292C2×D43—81no—
293C2×D43—81no—
294C2×D43—81no—
295C2×D43—81no—
296C2×D43—81no—
297C2×D43—81no—
298C2×D43—81no—
299C4×C43—21no—
300C4×C43—21no—
301C4×C43—21no—
302C4×C43—21no—
303C4×C43—82no—
304C4×C43—81no—
305Dic43—22no—
306Dic43—22no—
307Dic43—41no—
308Dic43—41no—
309Dic43—82no—
310Dic43—81no—
311#2856—431no—
312#1749—431no—
313C2×#327—431no—
314C2×#327—431no—
315C2×#327—431no—
316C2×#327D4311yescharacteristic, complemented
317#1434—431no—
318C2×C43—21no—
319C2×C43—21no—
320C2×C43—21no—
321C2×C43—21no—
322C2×C43—161no—
323C2×C43#150511yescharacteristic
324C2×C43#150711yescharacteristic
325C2×C43#151011yescharacteristic
326C2×C43#151411yescharacteristic
327C2×C43#196111yescharacteristic
328C2×C43#196411yescharacteristic
329C2×C43#198011yescharacteristic
330D43—161no—
331C2×#127—431no—
332C2×#121—431no—
333C2×#121—861no—
334C2×#121—861no—
335C2×#121C2×D4311yescharacteristic
336C22×C42—431no—
337C2×C22⋊C8—431no—
338C2×C22⋊C8C2×D4311yescharacteristic
339C2×#97—861no—
340#390—431no—
341#390—431no—
342#390—861no—
343#390—861no—
344#384—431no—
345C2×#95—431no—
346C2×#95—861no—
347C2×#95—861no—
348C2×#95C2×D4311yescharacteristic
349#336—861no—
350#327—22no—
351#327—862no—
352#327—862no—
353#327—862no—
354C43#968411yescharacteristic, complemented, Sylow
355C22×D4—21no—
356C22×D4—431no—
357C22×D4—861no—
358C22×D4—861no—
359C22×D4—861no—
360C22×D4C4×D4311yescharacteristic
361C23×C4—21no—
362C23×C4—431no—
363C23×C4—431no—
364C23×C4—861no—
365C23×C4C22×D4311yescharacteristic
366C22×C8—21no—
367C22×C8—861no—
368#127—1722no—
369#121—21no—
370#121—21no—
371#121—21no—
372#121—21no—
373#121—861no—
374#121—861no—
375#121—861no—
376#121—861no—
377#121—1722no—
378#121—1722no—
379#121—1722no—
380#121—1722no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4C4×D4311yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—861no—
387C2×C22⋊C4—861no—
388C2×C22⋊C4—861no—
389C2×C22⋊C4—861no—
390C2×C22⋊C4—861no—
391C2×C42—431no—
392C2×C42—431no—
393C2×C42—431no—
394C2×C42—431no—
395C2×C42—1722no—
396C22⋊C8—21no—
397C22⋊C8—432no—
398C22⋊C8—861no—
399C22⋊C8C22⋊D4312yescomplemented
400#97—1722no—
401#95—21no—
402#95—21no—
403#95—864no—
404#95—861no—
405#95—861no—
406#95—1722no—
407C24—21no—
408C24—861no—
409C24D4×D4311yescharacteristic
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—41no—
413C2×D4—41no—
414C2×D4—41no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4—41no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—861no—
421C2×D4—861no—
422C2×D4—1721no—
423C2×D4—1721no—
424C2×D4—1722no—
425C2×D4—1722no—
426C2×D4—1722no—
427C2×D4—1722no—
428C2×D4—1722no—
429C2×D4—1722no—
430C2×D4—1721no—
431C2×D4—1721no—
432C2×D4—1721no—
433C2×D4—1721no—
434C2×D4—1721no—
435C2×D4—1721no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—431no—
447C22×C4—431no—
448C22×C4—431no—
449C22×C4—431no—
450C22×C4—862no—
451C22×C4—862no—
452C22×C4—861no—
453C22×C4—861no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4—862no—
457C22×C4—861no—
458C22×C4—1721no—
459C22×C4—1721no—
460C22×C4—1721no—
461C22×C4—1721no—
462C22×C4—1721no—
463C22×C4—1721no—
464C22×C4—1721no—
465C22×C4—1721no—
466C22×C4C2×C4×D4311yescharacteristic
467C22×C4#1062189811yescharacteristic
468C22×C4D4×D4311yescharacteristic
469C22×C4D4×D4311yescharacteristic
470C22×C4#1062190011yescharacteristic
471C22×C4C2×C22⋊D4311yescharacteristic
472C2×C8—22no—
473C2×C8—41no—
474C2×C8—41no—
475C2×C8—862no—
476C2×C8—1721no—
477C2×C8—1721no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—1722no—
483C4⋊C4—1722no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—1722no—
487C22⋊C4—1722no—
488C22⋊C4—1722no—
489C22⋊C4—1722no—
490C22⋊C4—1721no—
491C22⋊C4—1721no—
492C42—862no—
493C42—862no—
494C42—1721no—
495C42—1721no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—1721no—
508C23—1721no—
509C23—1721no—
510C23—1721no—
511C23—1721no—
512C23—1721no—
513C23—1721no—
514C23C22⋊C4×D4311yescharacteristic
515C23#1306331111yescharacteristic
516C23#1306332111yescharacteristic
517C23#1306334911yescharacteristic
518C23#1306334911yescharacteristic
519C23#1306335211yescharacteristic
520C23#1306335211yescharacteristic
521D4—81no—
522D4—81no—
523D4—81no—
524D4—81no—
525D4—81no—
526D4—81no—
527D4—3441no—
528D4—3441no—
529D4—3444no—
530D4—3444no—
531D4—3441no—
532D4—3441no—
533D4—3441no—
534D4—3441no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—81no—
550C2×C4—81no—
551C2×C4—81no—
552C2×C4—81no—
553C2×C4—432no—
554C2×C4—432no—
555C2×C4—861no—
556C2×C4—861no—
557C2×C4—861no—
558C2×C4—861no—
559C2×C4—861no—
560C2×C4—861no—
561C2×C4—861no—
562C2×C4—861no—
563C2×C4—861no—
564C2×C4—861no—
565C2×C4—3441no—
566C2×C4—3441no—
567C2×C4—3441no—
568C2×C4—3441no—
569C2×C4—1722no—
570C2×C4—1722no—
571C2×C4—1722no—
572C2×C4—1722no—
573C2×C4—1722no—
574C2×C4—1722no—
575C2×C4—1722no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4—1721no—
579C2×C4(C22⋊D43)⋊C411yescharacteristic
580C2×C4C4×C22⋊D4311yescharacteristic
581C2×C4#1306329711yescharacteristic
582C2×C4#1306329811yescharacteristic
583C8—42no—
584C8—1722no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—21no—
589C22—21no—
590C22—21no—
591C22—21no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22—81no—
604C22—3441no—
605C22—3441no—
606C22—3441no—
607C22—3441no—
608C22—3441no—
609C22—3441no—
610C22—3441no—
611C22#1458279911yescharacteristic
612C22#99×D4311yescharacteristic
613C22#1458287111yescharacteristic
614C22#1458290211yescharacteristic
615C22#1458290211yescharacteristic
616C22#104×D4311yescharacteristic
617C22#1458291411yescharacteristic
618C22#1458326211yescharacteristic
619C22#1458326211yescharacteristic
620C22#1458328511yescharacteristic
621C22#1458328711yescharacteristic
622C4—21no—
623C4—21no—
624C4—21no—
625C4—21no—
626C4—82no—
627C4—81no—
628C4—862no—
629C4—862no—
630C4—3442no—
631C4—3441no—
632C4—1721no—
633C4—1721no—
634C2—21no—
635C2—21no—
636C2—21no—
637C2—21no—
638C2—161no—
639C2—6881no—
640C2#1913310111yescharacteristic
641C2#1913310911yescharacteristic
642C2#1913312211yescharacteristic
643C2#1913314011yescharacteristic
644C2#1913541711yescharacteristic
645C2#1913542911yescharacteristic
646C2#1913551211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#327C2
socleC23×C43C2×C22⋊C4
prime radical#19142938C2
cosocleC23×C4×C43C23
hypercenterC2×#327D43
hypocenterC43#9684
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. #19134359C2semidirect
3. C2×#14582634C2semidirect
4. C2×#14582633C2semidirect
5. C2×#14582632C2semidirect
6. #19132821C2semidirect
7. C2×C43×#327C2semidirect
8. C2×#13063321C4semidirect
15. #14582802C4semidirect
16. #14582800C4semidirect
19. #14582768C4semidirect
62. C22⋊(C43⋊C8)D4semidirect
80. C22⋊C8×C43D4semidirect
316. C2×#327D43semidirect
354. C43#9684semidirect
399. C22⋊C8C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
#191429382
#191343592
C2×#145826342
C2×#145826332
C2×#145826322
#191328212
C2×C43×#3272
#968443