Finite Group Databasebeta

← #25164668

Subgroups — #25164668

Order 11008.

874 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138949C211yesmaximal, characteristic, complemented
2#19137615C211yesmaximal, characteristic, complemented
3#19135903C211yesmaximal, characteristic, complemented
4#19135781C211yesmaximal, characteristic, complemented
5#19135739C211yesmaximal, characteristic, complemented
6#19135551C211yesmaximal, characteristic, complemented
7#19135280C211yesmaximal, characteristic, complemented
8#19135225C211yesmaximal, characteristic, complemented
9#19135198C211yesmaximal, characteristic, complemented
10#19135176C211yesmaximal, characteristic, complemented
11#19134945C211yesmaximal, characteristic, complemented
12#19134913C211yesmaximal, characteristic, complemented
13#19134686C211yesmaximal, characteristic, complemented
14#102×Dic43C211yesmaximal, characteristic, complemented
15C43×#1999C211yesmaximal, characteristic
16C2×#13063316C2211yescharacteristic
17C2×D4×Dic43—21no—
18C2×D4×Dic43C2211yescharacteristic
19C22×C4⋊Dic43C2211yescharacteristic
20C2×#13063256C2211yescharacteristic
21C2×Dic43⋊C8C2211yescharacteristic
22C2×#13063246C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×C22⋊(C43⋊C8)C2211yescharacteristic
27C2×C8×Dic43C2211yescharacteristic
28#14582824—21no—
29#14582813—21no—
30#14582802—21no—
31#14582802C2211yescharacteristic
32#14582802C2211yescharacteristic
33#14582802C2211yescharacteristic
34#14582798C2211yescharacteristic
35#14582793—21no—
36#14582792—21no—
37#14582779—21no—
38#14582774—21no—
39#14582759C2211yescharacteristic
40C4⋊C4×Dic43C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42C4×C22⋊Dic43C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C22×D8×C43C2211yescharacteristic
53C2×#121×C43C2211yescharacteristic
54C2×#121×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×C22⋊C8×C43C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C23×Dic43—21no—
60C23×Dic43—21no—
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63#13063316—22no—
64#13063316—41no—
65D4×Dic43—22no—
66D4×Dic43—41no—
67D4×Dic43—44no—
68C2×C4⋊Dic43—22no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43—41no—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43D411yescharacteristic
87C2×C22⋊Dic43D411yescharacteristic
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43C2311yescharacteristic
91C2×C4×Dic43C2311yescharacteristic
92#13063256—22no—
93Dic43⋊C8—41no—
94#13063246—22no—
95#13063246—22no—
96#13063246—41no—
97#13063246—41no—
98C22⋊(C43⋊C8)—41no—
99C8×Dic43—41no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95D411yescharacteristic
105C43⋊#95D411yescharacteristic
106C22×D4×C43—21no—
107C22×D4×C43—21no—
108C22×D4×C43C2311yescharacteristic
109C22×D4×C43C2311yescharacteristic
110C23×C4×C43C2311yescharacteristic
111C2×D8×C43—22no—
112C2×D8×C43—41no—
113C2×D8×C43—41no—
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116#121×C43—22no—
117#121×C43—22no—
118#121×C43—22no—
119#121×C43—41no—
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C22⋊C4×C43—21no—
123C2×C22⋊C4×C43—21no—
124#102×C43—22no—
125#102×C43—22no—
126C22⋊C8×C43—41no—
127C24×C43—21no—
128C24×C43—21no—
129C24×C43C2×D411yescharacteristic
130C2×D4×C43—24no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—42no—
143C2×D4×C43—42no—
144C2×D4×C43—42no—
145C2×D4×C43—42no—
146C2×D4×C43—81no—
147C2×D4×C43#4112yes—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2411yescharacteristic
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—42no—
163C22×Dic43—42no—
164C22×Dic43—42no—
165C22×Dic43—42no—
166C22×Dic43—81no—
167C22×Dic43—81no—
168C22×Dic43C2×D411yescharacteristic
169C22×Dic43C2×D411yescharacteristic
170C22×Dic43C2×D411yescharacteristic
171C22×Dic43C2×D411yescharacteristic
172D8×C43—44no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43#4112yes—
182C4⋊C4×C43#4112yes—
183C22⋊C4×C43—24no—
184C22⋊C4×C43—42no—
185C22⋊Dic43—22no—
186C22⋊Dic43—22no—
187C22⋊Dic43—42no—
188C22⋊Dic43—42no—
189C22⋊Dic43—42no—
190C22⋊Dic43—81no—
191C22⋊Dic43—81no—
192C22⋊Dic43—81no—
193C22⋊Dic43—81no—
194C22⋊Dic43—81no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—42no—
203C4⋊Dic43—42no—
204C4⋊Dic43—42no—
205C4⋊Dic43#4112yes—
206Dic43⋊C4—42no—
207C4×Dic43—21no—
208C4×Dic43—21no—
209C4×Dic43—21no—
210C4×Dic43—21no—
211C4×Dic43—42no—
212C4×Dic43—81no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C23×C43—21no—
220C23×C43—21no—
221C23×C43—21no—
222C23×C43—21no—
223C23×C43—21no—
224C23×C43—21no—
225C23×C43—22no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43—41no—
229C23×C43—41no—
230C23×C43—41no—
231C23×C43—41no—
232C23×C43—41no—
233C23×C43—41no—
234C23×C43—41no—
235C23×C43—41no—
236C23×C43—41no—
237C23×C43—41no—
238C23×C43—41no—
239C23×C43#13512yes—
240C23×C43C22×D411yescharacteristic
241D4×C43—22no—
242D4×C43—22no—
243D4×C43—48no—
244D4×C43—41no—
245D4×C43—41no—
246D4×C43—41no—
247D4×C43—41no—
248D4×C43—41no—
249D4×C43—41no—
250D4×C43—84no—
251C2×C4×C43—21no—
252C2×C4×C43—22no—
253C2×C4×C43—22no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43C2×#4111yescharacteristic
265C2×C4×C43C2×#4111yescharacteristic
266C2×C4×C43C2×#4111yescharacteristic
267C2×C4×C43C2×#4111yescharacteristic
268C2×C4×C43H(5,𝔽2)11yescharacteristic
269C2×C4×C43H(5,𝔽2)11yescharacteristic
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—22no—
276C2×Dic43—21no—
277C2×Dic43—21no—
278C2×Dic43—21no—
279C2×Dic43—21no—
280C2×Dic43—21no—
281C2×Dic43—21no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289C2×Dic43—41no—
290C2×Dic43—41no—
291C2×Dic43—41no—
292C2×Dic43—41no—
293C2×Dic43—84no—
294C2×Dic43—84no—
295C2×Dic43AGL(1,ℤ/8)12yes—
296C8×C43—41no—
297C8×C43—41no—
298C43⋊C8—41no—
299C43⋊C8—41no—
300#26723—431nomaximal, Sylow
301C22×C43—22no—
302C22×C43—22no—
303C22×C43—22no—
304C22×C43—41no—
305C22×C43—41no—
306C22×C43—41no—
307C22×C43—41no—
308C22×C43—42no—
309C22×C43—42no—
310C22×C43—42no—
311C22×C43—81no—
312C22×C43—81no—
313C22×C43—81no—
314C22×C43—81no—
315C22×C43—81no—
316C22×C43—81no—
317C22×C43—81no—
318C22×C43—81no—
319C22×C43—81no—
320C22×C43—81no—
321C22×C43—81no—
322C22×C43#52511yescharacteristic
323C22×C43#54611yescharacteristic
324C22×C43#54611yescharacteristic
325C22×C43C2×#13511yescharacteristic
326C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
327C22×C43#57611yescharacteristic
328C22×C43#57711yescharacteristic
329C4×C43—42no—
330C4×C43—41no—
331C4×C43—42no—
332C4×C43#52911yescharacteristic
333C4×C43#53811yescharacteristic
334C4×C43#55511yescharacteristic
335C4×C43#55911yescharacteristic
336Dic43—22no—
337Dic43—41no—
338Dic43—41no—
339Dic43—41no—
340Dic43—42no—
341Dic43—81no—
342Dic43—81no—
343Dic43—81no—
344#2490—431no—
345#2361—431no—
346#2054—431no—
347#2034—431no—
348#2025—431no—
349#1999D4311yescharacteristic
350#1989—431no—
351#1934—431no—
352#1926—431no—
353#1923—431no—
354#1919—431no—
355#1879—431no—
356#1874—431no—
357#1824—431no—
358C4×#102—431no—
359C2×C43—42no—
360C2×C43—82no—
361C2×C43—161no—
362C2×C43#245911yescharacteristic
363C2×C43#310511yescharacteristic
364C2×C43#311911yescharacteristic
365C2×C43#329711yescharacteristic
366C2×C43#330111yescharacteristic
367C2×C43#331811yescharacteristic
368C2×C43#333211yescharacteristic
369C22×D8C2×D4311yescharacteristic
370C2×#125—431no—
371C2×#121C2×D4311yescharacteristic
372C2×#121C2×D4311yescharacteristic
373C2×C4×D4—431no—
374C2×C4×D4—861no—
375C22×C4⋊C4—431no—
376C2×#106—431no—
377C2×C4⋊C8—431no—
378C2×#102—431no—
379C2×#102—431no—
380C2×#102—431no—
381C2×#102—431no—
382C2×#102C2×D4311yescharacteristic
383C2×#102C2×D4311yescharacteristic
384C2×C22⋊C8—431no—
385C2×C22⋊C8C2×D4311yescharacteristic
386C2×C4×C8—431no—
387#397—861no—
388#394—861no—
389#390—431no—
390#390—431no—
391#390—431no—
392#390—861no—
393#389—431no—
394#388—861no—
395#388—861no—
396#386—861no—
397#385—861no—
398#380—431no—
399C4×C4⋊C4—431no—
400C4×C4⋊C4—431no—
401C4×C22⋊C4—431no—
402#340—431no—
403#340—431no—
404#340—431no—
405#340—431no—
406#340—431no—
407#340—431no—
408#340—431no—
409#340C2×D4311yescharacteristic
410#336—431no—
411#336—431no—
412C43#2672311yescharacteristic, complemented, Sylow
413C22×D4—21no—
414C22×D4—21no—
415C22×D4C22×D4311yescharacteristic
416C22×D4C22×D4311yescharacteristic
417C23×C4—861no—
418C23×C4—861no—
419C23×C4C22×D4311yescharacteristic
420C2×D8—22no—
421C2×D8—41no—
422C2×D8—41no—
423C22×C8—431no—
424C22×C8—431no—
425C22×C8C22×D4311yescharacteristic
426C22×C8C22×D4311yescharacteristic
427#125—862no—
428#125—1721no—
429#121—22no—
430#121—22no—
431#121—22no—
432#121—41no—
433C4×D4—862no—
434C4×D4—1721no—
435C4×D4—1724no—
436C2×C4⋊C4—431no—
437C2×C4⋊C4—431no—
438C2×C4⋊C4—431no—
439C2×C4⋊C4—431no—
440C2×C4⋊C4—862no—
441C2×C4⋊C4—861no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4—861no—
445C2×C4⋊C4—1721no—
446C2×C4⋊C4C22×D4311yescharacteristic
447C2×C4⋊C4C22×D4311yescharacteristic
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—431no—
451C2×C22⋊C4—431no—
452C2×C22⋊C4—861no—
453C2×C22⋊C4—861no—
454C2×C22⋊C4—861no—
455C2×C22⋊C4—861no—
456C2×C22⋊C4—861no—
457C2×C22⋊C4—861no—
458C2×C22⋊C4—861no—
459C2×C22⋊C4—861no—
460C2×C42—431no—
461C2×C42—431no—
462C2×C42—861no—
463C2×C42—861no—
464#106—862no—
465C4⋊C8—1721no—
466#102—22no—
467#102—22no—
468#102—862no—
469#102—862no—
470#102—1721no—
471#102—1721no—
472C22⋊C8—41no—
473C22⋊C8—1721no—
474C4×C8—1721no—
475#95—431no—
476#95—431no—
477#95—861no—
478#95—861no—
479#95—861no—
480#95—861no—
481C24—21no—
482C24—21no—
483C24D4×D4311yescharacteristic
484C2×D4—24no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4—81no—
501C2×D4#1062190012yes—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—431no—
511C22×C4—431no—
512C22×C4—431no—
513C22×C4—431no—
514C22×C4—861no—
515C22×C4—861no—
516C22×C4—861no—
517C22×C4—861no—
518C22×C4—3441no—
519C22×C4—3441no—
520C22×C4—1722no—
521C22×C4—1722no—
522C22×C4—1722no—
523C22×C4—1722no—
524C22×C4D4×D4311yescharacteristic
525C22×C4C23×D4311yescharacteristic
526D8—44no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—861no—
534C2×C8—861no—
535C2×C8—861no—
536C2×C8—861no—
537C2×C8—861no—
538C2×C8—861no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—432no—
542C4⋊C4—861no—
543C4⋊C4—861no—
544C4⋊C4—861no—
545C4⋊C4—861no—
546C4⋊C4—861no—
547C4⋊C4—861no—
548C4⋊C4—861no—
549C4⋊C4—1722no—
550C4⋊C4—1722no—
551C4⋊C4—1722no—
552C4⋊C4—1722no—
553C4⋊C4#1062190012yes—
554C4⋊C4#1062190012yes—
555C22⋊C4—24no—
556C22⋊C4—42no—
557C22⋊C4—862no—
558C22⋊C4—862no—
559C22⋊C4—3441no—
560C22⋊C4—3441no—
561C22⋊C4—3441no—
562C22⋊C4—3441no—
563C22⋊C4—3441no—
564C22⋊C4—1722no—
565C22⋊C4—1722no—
566C22⋊C4—1722no—
567C42—861no—
568C42—861no—
569C42—861no—
570C42—861no—
571C42—3441no—
572C42—1722no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—22no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23#1306334412yes—
594C23C2×D4×D4311yescharacteristic
595D4—22no—
596D4—22no—
597D4—48no—
598D4—41no—
599D4—41no—
600D4—41no—
601D4—41no—
602D4—41no—
603D4—41no—
604D4—84no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—22no—
609C2×C4—21no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—432no—
619C2×C4—861no—
620C2×C4—861no—
621C2×C4—861no—
622C2×C4—861no—
623C2×C4—861no—
624C2×C4—861no—
625C2×C4—861no—
626C2×C4—861no—
627C2×C4—861no—
628C2×C4—861no—
629C2×C4—861no—
630C2×C4—862no—
631C2×C4—3444no—
632C2×C4—3444no—
633C2×C4—1721no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4—1721no—
637C2×C4—1721no—
638C2×C4—1721no—
639C2×C4—1721no—
640C2×C4—1721no—
641C2×C4—1721no—
642C2×C4—1721no—
643C2×C4—1721no—
644C2×C4#41×D4311yescharacteristic
645C2×C4C2×#1062190011yescharacteristic
646C2×C4C2×#1062190011yescharacteristic
647C2×C4C2×#1062190011yescharacteristic
648C2×C4#1306337011yescharacteristic
649C2×C4#1306337011yescharacteristic
650C8—41no—
651C8—41no—
652C8—1721no—
653C8—1721no—
654C22—22no—
655C22—22no—
656C22—22no—
657C22—41no—
658C22—41no—
659C22—41no—
660C22—41no—
661C22—42no—
662C22—42no—
663C22—42no—
664C22—81no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22#1458340511yescharacteristic
676C22#1458353611yescharacteristic
677C22#1458353811yescharacteristic
678C22C2×#1306334411yescharacteristic
679C22AGL(1,ℤ/8)×D4311yescharacteristic
680C22#1458370311yescharacteristic
681C22#1458370611yescharacteristic
682C4—42no—
683C4—42no—
684C4—41no—
685C4—862no—
686C4—3441no—
687C4—3441no—
688C4—3441no—
689C4—1721no—
690C4—1721no—
691C4—1721no—
692C4—1722no—
693C4#1458343011yescharacteristic
694C4#1458348411yescharacteristic
695C4#1458361311yescharacteristic
696C4#1458363511yescharacteristic
697C2—42no—
698C2—82no—
699C2—161no—
700C2#1913852711yescharacteristic
701C2#1914463711yescharacteristic
702C2#1914479511yescharacteristic
703C2#1914644911yescharacteristic
704C2#1914650311yescharacteristic
705C2#1914673111yescharacteristic
706C2#1914691511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC43×#1999C2
socleC23×C43C22×D4
hypercenter#1999D43
hypocenterC43#26723
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1999

Complements

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

NH ≅ G/Ntype
1. #19138949C2semidirect
2. #19137615C2semidirect
3. #19135903C2semidirect
4. #19135781C2semidirect
5. #19135739C2semidirect
6. #19135551C2semidirect
7. #19135280C2semidirect
8. #19135225C2semidirect
9. #19135198C2semidirect
10. #19135176C2semidirect
11. #19134945C2semidirect
12. #19134913C2semidirect
13. #19134686C2semidirect
14. #102×Dic43C2semidirect
412. C43#26723semidirect

Maximal subgroups

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

subgroupindex
#191389492
#191376152
#191359032
#191357812
#191357392
#191355512
#191352802
#191352252
#191351982
#191351762
#191349452
#191349132
#191346862
#102×Dic432
C43×#19992
#2672343