Finite Group Databasebeta

← #25169774

Subgroups — #25169774

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#19139190C211yesmaximal, characteristic, complemented
2#19137660C211yesmaximal, characteristic, complemented
3#19136114C211yesmaximal, characteristic, complemented
4#19135903C211yesmaximal, characteristic, complemented
5#19135826C211yesmaximal, characteristic, complemented
6#19135462C211yesmaximal, characteristic, complemented
7#19135225C211yesmaximal, characteristic, complemented
8#19135219C211yesmaximal, characteristic, complemented
9#19135188C211yesmaximal, characteristic, complemented
10#19135151C211yesmaximal, characteristic, complemented
11#19134945C211yesmaximal, characteristic, complemented
12#19134945C211yesmaximal, characteristic, complemented
13#19134603C211yesmaximal, characteristic, complemented
14#102×Dic43C211yesmaximal, characteristic, complemented
15C43×#2011C211yesmaximal, characteristic
16C2×D4×Dic43—21no—
17C2×D4×Dic43C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19C2×#13063259C2211yescharacteristic
20C2×#13063256C2211yescharacteristic
21C2×Dic43⋊C8C2211yescharacteristic
22C2×#13063246C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×C8×Dic43C2211yescharacteristic
29#14582827—21no—
30#14582824—21no—
31#14582802—21no—
32#14582802C2211yescharacteristic
33#14582802C2211yescharacteristic
34#14582802C2211yescharacteristic
35#14582802C2211yescharacteristic
36#14582797C2211yescharacteristic
37#14582792—21no—
38#14582787—21no—
39#14582779—21no—
40#14582779—21no—
41#14582764C2211yescharacteristic
42C4⋊C4×Dic43C2211yescharacteristic
43C4×C4⋊Dic43C2211yescharacteristic
44C4×C4⋊Dic43C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C22×D8×C43C2211yescharacteristic
53C22×D8×C43C2211yescharacteristic
54C2×#127×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C43×#390C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C23×Dic43—21no—
60C23×Dic43—21no—
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63D4×Dic43—22no—
64D4×Dic43—22no—
65D4×Dic43—41no—
66D4×Dic43—41no—
67D4×Dic43—44no—
68C2×C4⋊Dic43D411yescharacteristic
69C2×C4⋊Dic43D411yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×Dic43⋊C4—21no—
75C2×C22⋊Dic43—21no—
76C2×C22⋊Dic43—21no—
77C2×C22⋊Dic43—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×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43C2311yescharacteristic
88C2×C4×Dic43C2311yescharacteristic
89#13063259—22no—
90#13063256—41no—
91Dic43⋊C8—41no—
92#13063246—22no—
93#13063246—22no—
94#13063246—22no—
95#13063246—41no—
96#13063246—41no—
97#13063246—41no—
98C8×Dic43—41no—
99C43⋊#95—21no—
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
110C22×D4×C43C2311yescharacteristic
111C2×D8×C43—22no—
112C2×D8×C43—22no—
113C2×D8×C43—22no—
114C2×D8×C43—41no—
115C2×D8×C43—41no—
116C2×D8×C43—41no—
117C22×C8×C43C2311yescharacteristic
118C22×C8×C43C2311yescharacteristic
119#127×C43—22no—
120#127×C43—22no—
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C22⋊C4×C43—21no—
123C2×C22⋊C4×C43—21no—
124C2×C42×C43C2311yescharacteristic
125#102×C43—22no—
126#102×C43—41no—
127C24×C43—21no—
128C24×C43—21no—
129C24×C43—21no—
130C2×D4×C43—24no—
131C2×D4×C43—24no—
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—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—42no—
149C2×D4×C43—42no—
150C2×D4×C43—81no—
151C2×D4×C43—81no—
152C2×D4×C43#4112yes—
153C2×D4×C43#4112yes—
154C22×C4×C43—21no—
155C22×C4×C43C2×D411yescharacteristic
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—
173D8×C43—44no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43#4112yes—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C22⋊C4×C43—42no—
183C22⋊C4×C43—81no—
184C42×C43—21no—
185C42×C43—21no—
186C22⋊Dic43—42no—
187C22⋊Dic43—42no—
188C22⋊Dic43—42no—
189C22⋊Dic43—42no—
190C22⋊Dic43—42no—
191C22⋊Dic43—81no—
192C22⋊Dic43—81no—
193C22⋊Dic43—81no—
194C22⋊Dic43—81no—
195C22⋊Dic43—81no—
196C4⋊Dic43—22no—
197C4⋊Dic43—21no—
198C4⋊Dic43—22no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43#4112yes—
206Dic43⋊C4—81no—
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—22no—
220C23×C43—22no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—41no—
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—41no—
240C23×C43C22×D411yescharacteristic
241D4×C43—22no—
242D4×C43—22no—
243D4×C43—22no—
244D4×C43—22no—
245D4×C43—48no—
246D4×C43—41no—
247D4×C43—41no—
248D4×C43—41no—
249D4×C43—41no—
250D4×C43—41no—
251D4×C43—41no—
252D4×C43—41no—
253D4×C43—41no—
254D4×C43—84no—
255C2×C4×C43—21no—
256C2×C4×C43—21no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—21no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43#13512yes—
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—22no—
297C8×C43—41no—
298C43⋊C8—41no—
299C43⋊C8—41no—
300#27065—431nomaximal, Sylow
301C22×C43—42no—
302C22×C43—42no—
303C22×C43—42no—
304C22×C43—42no—
305C22×C43—42no—
306C22×C43—42no—
307C22×C43—81no—
308C22×C43—81no—
309C22×C43—81no—
310C22×C43—81no—
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#55011yescharacteristic
325C22×C43C2×#13511yescharacteristic
326C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
327C22×C43#57611yescharacteristic
328C22×C43#57611yescharacteristic
329C4×C43—22no—
330C4×C43—41no—
331C4×C43—81no—
332C4×C43#52911yescharacteristic
333C4×C43#53811yescharacteristic
334C4×C43#55111yescharacteristic
335C4×C43#55311yescharacteristic
336Dic43—22no—
337Dic43—41no—
338Dic43—41no—
339Dic43—41no—
340Dic43—42no—
341Dic43—81no—
342Dic43—81no—
343Dic43—81no—
344#2513—431no—
345#2366—431no—
346#2092—431no—
347#2054—431no—
348#2041—431no—
349#2011D4311yescharacteristic
350#1970—431no—
351#1926—431no—
352#1926—431no—
353#1921—431no—
354#1916—431no—
355#1879—431no—
356#1879—431no—
357#1804—431no—
358C4×#102—431no—
359C2×C43—82no—
360C2×C43—82no—
361C2×C43—161no—
362C2×C43#246711yescharacteristic
363C2×C43#310511yescharacteristic
364C2×C43#312211yescharacteristic
365C2×C43#330511yescharacteristic
366C2×C43#331811yescharacteristic
367C2×C43#339611yescharacteristic
368C2×C43#339911yescharacteristic
369C22×D8C2×D4311yescharacteristic
370C22×D8C2×D4311yescharacteristic
371C2×#127C2×D4311yescharacteristic
372C2×C4×D4—431no—
373C2×C4×D4—431no—
374C2×C4×D4—861no—
375C2×#107—431no—
376C2×#106—431no—
377C2×C4⋊C8—431no—
378C2×#102—431no—
379C2×#102—431no—
380C2×#102—431no—
381C2×#102—431no—
382C2×#102—431no—
383C2×#102—431no—
384C2×#102C2×D4311yescharacteristic
385C2×#102C2×D4311yescharacteristic
386C2×C4×C8—431no—
387#397—861no—
388#397—861no—
389#390—431no—
390#390—431no—
391#390—431no—
392#390—431no—
393#390—861no—
394#390C2×D4311yescharacteristic
395#389—431no—
396#388—861no—
397#388—861no—
398#386—861no—
399#386—861no—
400#382—431no—
401C4×C4⋊C4—431no—
402C4×C4⋊C4—431no—
403C4×C4⋊C4—431no—
404#340—431no—
405#340—431no—
406#340—431no—
407#340—431no—
408#336—431no—
409#336—431no—
410#336—431no—
411#336C2×D4311yescharacteristic
412C43#2706511yescharacteristic, complemented, Sylow
413C22×D4—21no—
414C22×D4—21no—
415C22×D4C22×D4311yescharacteristic
416C22×D4C22×D4311yescharacteristic
417C22×D4C22×D4311yescharacteristic
418C23×C4—861no—
419C23×C4—861no—
420C2×D8—22no—
421C2×D8—22no—
422C2×D8—22no—
423C2×D8—41no—
424C2×D8—41no—
425C2×D8—41no—
426C22×C8—431no—
427C22×C8—431no—
428C22×C8C22×D4311yescharacteristic
429C22×C8C22×D4311yescharacteristic
430#127—22no—
431#127—22no—
432C4×D4—862no—
433C4×D4—862no—
434C4×D4—1721no—
435C4×D4—1721no—
436C4×D4—1724no—
437C2×C4⋊C4—431no—
438C2×C4⋊C4—431no—
439C2×C4⋊C4—431no—
440C2×C4⋊C4—431no—
441C2×C4⋊C4—431no—
442C2×C4⋊C4—431no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4C22×D4311yescharacteristic
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—861no—
448C2×C22⋊C4—861no—
449C2×C22⋊C4—861no—
450C2×C22⋊C4—861no—
451C2×C22⋊C4—861no—
452C2×C22⋊C4—861no—
453C2×C22⋊C4—861no—
454C2×C22⋊C4—861no—
455C2×C22⋊C4—861no—
456C2×C22⋊C4—861no—
457C2×C42—431no—
458C2×C42—431no—
459C2×C42—861no—
460C2×C42—861no—
461C2×C42C22×D4311yescharacteristic
462#107—862no—
463#106—1721no—
464C4⋊C8—1721no—
465#102—22no—
466#102—41no—
467#102—862no—
468#102—862no—
469#102—862no—
470#102—1721no—
471#102—1721no—
472#102—1721no—
473C4×C8—1721no—
474#95—431no—
475#95—431no—
476#95—861no—
477#95—861no—
478#95—861no—
479#95—861no—
480#95—861no—
481C24—21no—
482C24—21no—
483C24—21no—
484C2×D4—24no—
485C2×D4—24no—
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—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—81no—
505C2×D4—81no—
506C2×D4#1062190012yes—
507C2×D4#1062190012yes—
508C22×C4—21no—
509C22×C4—431no—
510C22×C4—431no—
511C22×C4—431no—
512C22×C4—431no—
513C22×C4—861no—
514C22×C4—861no—
515C22×C4—861no—
516C22×C4—861no—
517C22×C4—3441no—
518C22×C4—3441no—
519C22×C4—1722no—
520C22×C4—1722no—
521C22×C4—1722no—
522C22×C4—1722no—
523C22×C4D4×D4311yescharacteristic
524C22×C4D4×D4311yescharacteristic
525C22×C4C23×D4311yescharacteristic
526D8—44no—
527D8—44no—
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—
539C2×C8#1062190012yes—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—432no—
543C4⋊C4—862no—
544C4⋊C4—862no—
545C4⋊C4—861no—
546C4⋊C4—861no—
547C4⋊C4—861no—
548C4⋊C4—861no—
549C4⋊C4—861no—
550C4⋊C4—861no—
551C4⋊C4—861no—
552C4⋊C4—3441no—
553C22⋊C4—42no—
554C22⋊C4—81no—
555C22⋊C4—3441no—
556C22⋊C4—3441no—
557C22⋊C4—3441no—
558C22⋊C4—3441no—
559C22⋊C4—3441no—
560C22⋊C4—1722no—
561C22⋊C4—1722no—
562C22⋊C4—1722no—
563C22⋊C4—1722no—
564C22⋊C4—1722no—
565C42—21no—
566C42—21no—
567C42—861no—
568C42—861no—
569C42—861no—
570C42—861no—
571C42—3441no—
572C42—1722no—
573C23—22no—
574C23—22no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
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—41no—
594C23C2×D4×D4311yescharacteristic
595D4—22no—
596D4—22no—
597D4—22no—
598D4—22no—
599D4—48no—
600D4—41no—
601D4—41no—
602D4—41no—
603D4—41no—
604D4—41no—
605D4—41no—
606D4—41no—
607D4—41no—
608D4—84no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—432no—
618C2×C4—861no—
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—862no—
630C2×C4—3444no—
631C2×C4—3444no—
632C2×C4—1721no—
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#1306334412yes—
644C2×C4#41×D4311yescharacteristic
645C2×C4C2×#1062190011yescharacteristic
646C2×C4C2×#1062190011yescharacteristic
647C2×C4C2×#1062190011yescharacteristic
648C2×C4#1306337011yescharacteristic
649C2×C4#1306337011yescharacteristic
650C8—22no—
651C8—41no—
652C8—1721no—
653C8—1721no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—42no—
658C22—42no—
659C22—42no—
660C22—81no—
661C22—81no—
662C22—81no—
663C22—81no—
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#1458354611yescharacteristic
677C22#1458356911yescharacteristic
678C22C2×#1306334411yescharacteristic
679C22AGL(1,ℤ/8)×D4311yescharacteristic
680C22#1458370011yescharacteristic
681C22#1458370311yescharacteristic
682C4—22no—
683C4—41no—
684C4—81no—
685C4—862no—
686C4—3441no—
687C4—3441no—
688C4—3441no—
689C4—1721no—
690C4—1721no—
691C4—1721no—
692C4—1722no—
693C4#1458343011yescharacteristic
694C4#1458348411yescharacteristic
695C4#1458358011yescharacteristic
696C4#1458359211yescharacteristic
697C2—82no—
698C2—82no—
699C2—161no—
700C2#1913864111yescharacteristic
701C2#1914463711yescharacteristic
702C2#1914483211yescharacteristic
703C2#1914654811yescharacteristic
704C2#1914674311yescharacteristic
705C2#1914760911yescharacteristic
706C2#1914763411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC43×#2011C2
socleC23×C43C22×D4
hypercenter#2011D43
hypocenterC43#27065
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2011

Complements

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

NH ≅ G/Ntype
1. #19139190C2semidirect
2. #19137660C2semidirect
3. #19136114C2semidirect
4. #19135903C2semidirect
5. #19135826C2semidirect
6. #19135462C2semidirect
7. #19135225C2semidirect
8. #19135219C2semidirect
9. #19135188C2semidirect
10. #19135151C2semidirect
11. #19134945C2semidirect
12. #19134945C2semidirect
13. #19134603C2semidirect
14. #102×Dic43C2semidirect
412. C43#27065semidirect

Maximal subgroups

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

subgroupindex
#191391902
#191376602
#191361142
#191359032
#191358262
#191354622
#191352252
#191352192
#191351882
#191351512
#191349452
#191346032
#102×Dic432
C43×#20112
#2706543