Finite Group Databasebeta

← #25135304

Subgroups — #25135304

Order 11008.

1250 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582953C211yesmaximal, characteristic, complemented
2#19142921C211yesmaximal, characteristic, complemented
3C2×#14582802C211yesmaximal, characteristic, complemented
4#19135967C212yesmaximal, complemented
5#19135903C212yesmaximal, complemented
6#19135472C212yesmaximal, complemented
7#19135289C212yesmaximal, complemented
8#19134913C211yesmaximal, characteristic, complemented
9#19134790C211yesmaximal, characteristic, complemented
10#19134526C211yesmaximal, characteristic, complemented
11C2×C43×#447C211yesmaximal, characteristic
12C2×#13063306—21no—
13C22×C4⋊Dic43C2211yescharacteristic
14C22×C22⋊Dic43—21no—
15C22×C22⋊Dic43—21no—
16C22×C4×Dic43C2211yescharacteristic
17#14582953—24no—
18C2×#13063257C2212yescomplemented
19C2×Dic43⋊C8C2212yescomplemented
20C2×#13063246C2212yes—
21C2×#13063246C2212yes—
22C2×#13063246C2212yescomplemented
23C2×C22⋊(C43⋊C8)C2211yescharacteristic
24C2×#13063235C2212yescomplemented
25#14582802—21no—
26#14582802—21no—
27#14582802C2212yes—
28#14582802C2212yes—
29#14582802C2211yescharacteristic, complemented
30#14582802C2211yescharacteristic, complemented
31#14582795C2211yescharacteristic, complemented
32#14582795C2211yescharacteristic, complemented
33#14582787—21no—
34#14582787—21no—
35#14582779—21no—
36#14582759C2211yescharacteristic
37#14582662C2212yescomplemented
38#14582661C2212yescomplemented
39C23×D4×C43C2211yescharacteristic
40C22×D8×C43C2212yes—
41C2×#121×C43C2211yescharacteristic
42C43×#447—24no—
43C2×#102×C43C2212yes—
44C2×C22⋊C8×C43C2211yescharacteristic
45C23×Dic43—21no—
46C23×Dic43D411yescharacteristic
47C23×Dic43D411yescharacteristic
48C22×C43⋊C8C2312yes—
49#13063306—44no—
50C2×C4⋊Dic43—21no—
51C2×C4⋊Dic43—42no—
52C2×C4⋊Dic43C2311yescharacteristic
53C2×C4⋊Dic43C2311yescharacteristic
54C2×C4⋊Dic43C2312yes—
55C2×Dic43⋊C4—21no—
56C2×Dic43⋊C4—21no—
57C2×C22⋊Dic43—21no—
58C2×C22⋊Dic43—21no—
59C2×C22⋊Dic43—21no—
60C2×C22⋊Dic43—21no—
61C2×C22⋊Dic43—21no—
62C2×C22⋊Dic43—22no—
63C2×C22⋊Dic43—22no—
64C2×C22⋊Dic43—22no—
65C2×C22⋊Dic43—22no—
66C2×C22⋊Dic43—44no—
67C2×C22⋊Dic43—44no—
68C2×C4×Dic43—22no—
69C2×C4×Dic43—22no—
70C2×C4×Dic43D411yescharacteristic
71C2×C4×Dic43D411yescharacteristic
72C2×C4×Dic43C2311yescharacteristic
73C2×C4×Dic43C2311yescharacteristic
74#13063257—42no—
75Dic43⋊C8—24no—
76#13063246—24no—
77#13063246—42no—
78#13063246—42no—
79C22⋊(C43⋊C8)—22no—
80#13063235—24no—
81C43⋊#95—21no—
82C43⋊#95—21no—
83C43⋊#95—21no—
84C25×C43—21no—
85C22×D4×C43—24no—
86C22×D4×C43—21no—
87C22×D4×C43—21no—
88C22×D4×C43—22no—
89C22×D4×C43—22no—
90C22×D4×C43—42no—
91C22×D4×C43C2311yescharacteristic
92C22×D4×C43C2312yes—
93C23×C4×C43C2311yescharacteristic
94C2×D8×C43—24no—
95C2×D8×C43—24no—
96C2×D8×C43—42no—
97C22×C8×C43C2312yes—
98#121×C43—22no—
99#121×C43—22no—
100C2×C4⋊C4×C43C2311yescharacteristic
101C2×C22⋊C4×C43—21no—
102#102×C43—24no—
103C22⋊C8×C43D414yes—
104C24×C43—24no—
105C24×C43—22no—
106C24×C43—21no—
107C24×C43—42no—
108C24×C43—42no—
109C24×C43—42no—
110C24×C43—42no—
111C24×C43—42no—
112C24×C43—42no—
113C24×C43C2×D411yescharacteristic
114C2×D4×C43—24no—
115C2×D4×C43—22no—
116C2×D4×C43—22no—
117C2×D4×C43—21no—
118C2×D4×C43—22no—
119C2×D4×C43—21no—
120C2×D4×C43—22no—
121C2×D4×C43—22no—
122C2×D4×C43—22no—
123C2×D4×C43—22no—
124C2×D4×C43—48no—
125C2×D4×C43—48no—
126C2×D4×C43—42no—
127C2×D4×C43—42no—
128C2×D4×C43—42no—
129C2×D4×C43—42no—
130C2×D4×C43—42no—
131C2×D4×C43#4114yes—
132C22×C4×C43—22no—
133C22×C4×C43—22no—
134C22×C4×C43—21no—
135C22×C4×C43C2×D412yes—
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43#4112yes—
138C22×C4×C43C2411yescharacteristic
139C22×Dic43—22no—
140C22×Dic43—22no—
141C22×Dic43—22no—
142C22×Dic43—22no—
143C22×Dic43—22no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—22no—
147C22×Dic43—41no—
148C22×Dic43—42no—
149C22×Dic43—42no—
150C22×Dic43—42no—
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155D8×C43—48no—
156C2×C8×C43—22no—
157C2×C8×C43—22no—
158C2×C8×C43C2×D414yes—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C22⋊C4×C43—42no—
162C22⋊Dic43—42no—
163C22⋊Dic43—44no—
164C22⋊Dic43—44no—
165C22⋊Dic43—44no—
166C22⋊Dic43—42no—
167C22⋊Dic43—42no—
168C22⋊Dic43—42no—
169C22⋊Dic43—44no—
170C22⋊Dic43—42no—
171C4⋊Dic43—22no—
172C4⋊Dic43—22no—
173C4⋊Dic43—22no—
174C4⋊Dic43—22no—
175C4⋊Dic43—42no—
176Dic43⋊C4—42no—
177Dic43⋊C4—42no—
178C4×Dic43—22no—
179C4×Dic43—22no—
180C4×Dic43—21no—
181C4×Dic43—21no—
182C4×Dic43—21no—
183C4×Dic43—21no—
184C2×C43⋊C8—22no—
185C2×C43⋊C8—22no—
186C2×C43⋊C8—22no—
187C23×C43—21no—
188C23×C43—21no—
189C23×C43—21no—
190C23×C43—21no—
191C23×C43—24no—
192C23×C43—48no—
193C23×C43—48no—
194C23×C43—48no—
195C23×C43—42no—
196C23×C43—42no—
197C23×C43—42no—
198C23×C43—42no—
199C23×C43—42no—
200C23×C43—42no—
201C23×C43—41no—
202C23×C43—41no—
203C23×C43—41no—
204C23×C43—41no—
205C23×C43—41no—
206C23×C43—41no—
207C23×C43—41no—
208C23×C43—84no—
209C23×C43—84no—
210C23×C43—84no—
211C23×C43—84no—
212C23×C43#12112yes—
213C23×C43AGL(1,ℤ/8)12yes—
214C23×C43AGL(1,ℤ/8)12yes—
215C23×C43C22×D411yescharacteristic
216D4×C43—24no—
217D4×C43—24no—
218D4×C43—48no—
219D4×C43—42no—
220D4×C43—42no—
221D4×C43—42no—
222D4×C43—42no—
223D4×C43—84no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—24no—
227C2×C4×C43—24no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43#12112yes—
232C2×C4×C43C22×D411yescharacteristic
233C2×C4×C43C2×#4112yes—
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43H(5,𝔽2)12yes—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—44no—
248C2×Dic43—44no—
249C2×Dic43—41no—
250C2×Dic43—42no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—42no—
255C2×Dic43—42no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—84no—
259C2×Dic43AGL(1,ℤ/8)12yes—
260C8×C43—24no—
261C43⋊C8—42no—
262#24506—431nomaximal, Sylow
263C22×C43—22no—
264C22×C43—22no—
265C22×C43—22no—
266C22×C43—22no—
267C22×C43—22no—
268C22×C43—22no—
269C22×C43—44no—
270C22×C43—44no—
271C22×C43—44no—
272C22×C43—816no—
273C22×C43—82no—
274C22×C43—82no—
275C22×C43—82no—
276C22×C43—82no—
277C22×C43—81no—
278C22×C43—81no—
279C22×C43—81no—
280C22×C43—81no—
281C22×C43—81no—
282C22×C43—81no—
283C22×C43—81no—
284C22×C43#46914yes—
285C22×C43C2×#12111yescharacteristic
286C22×C43#52511yescharacteristic
287C22×C43#53511yescharacteristic
288C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
289C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
290C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
291C22×C43#57511yescharacteristic
292C4×C43—22no—
293C4×C43—81no—
294C4×C43#54612yes—
295C4×C43#55112yes—
296Dic43—22no—
297Dic43—41no—
298Dic43—41no—
299Dic43—41no—
300Dic43—81no—
301Dic43—81no—
302Dic43—82no—
303C2×#447D4311yescharacteristic
304C2×#432—431no—
305#2854—431no—
306C2×#390—431no—
307#2065—432no—
308#2054—432no—
309#1972—432no—
310#1936—432no—
311#1874—431no—
312#1853—431no—
313#1786—431no—
314C2×C43—24no—
315C2×C43—84no—
316C2×C43—161no—
317C2×C43#241111yescharacteristic
318C2×C43C2×#46911yescharacteristic
319C2×C43#305511yescharacteristic
320C2×C43#310911yescharacteristic
321C2×C43#311411yescharacteristic
322C2×C43#321311yescharacteristic
323C2×C43#321711yescharacteristic
324C23×D4C2×D4311yescharacteristic
325C22×D8C2×D4312yes—
326C2×#123—861no—
327C2×#121C2×D4311yescharacteristic
328C22×C4⋊C4—431no—
329C22×C22⋊C4—861no—
330C22×C22⋊C4—861no—
331C22×C42—431no—
332#447—24no—
333#432—864no—
334C2×#106—432no—
335C2×C4⋊C8—432no—
336C2×#102—432no—
337C2×#102—432no—
338C2×#102—432no—
339C2×#102C2×D4312yes—
340C2×C22⋊C8—431no—
341C2×C22⋊C8C2×D4311yescharacteristic
342C2×#97—432no—
343#390—431no—
344#390—432no—
345#390—432no—
346#390—431no—
347#390—861no—
348#390—861no—
349#389—431no—
350#389—431no—
351#388—861no—
352#388—861no—
353#386—861no—
354#380—431no—
355#340—432no—
356#340—432no—
357C43#2450611yescharacteristic, complemented, Sylow
358C25—21no—
359C22×D4—24no—
360C22×D4—21no—
361C22×D4—21no—
362C22×D4—22no—
363C22×D4—22no—
364C22×D4—42no—
365C22×D4C22×D4311yescharacteristic
366C22×D4C22×D4312yes—
367C23×C4—431no—
368C23×C4—431no—
369C23×C4—861no—
370C23×C4C22×D4311yescharacteristic
371C2×D8—24no—
372C2×D8—24no—
373C2×D8—42no—
374C22×C8—432no—
375C22×C8C22×D4312yes—
376#123—1724no—
377#121—22no—
378#121—22no—
379C2×C4⋊C4—432no—
380C2×C4⋊C4—431no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4—1722no—
386C2×C4⋊C4C22×D4311yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—862no—
389C2×C22⋊C4—862no—
390C2×C22⋊C4—862no—
391C2×C22⋊C4—862no—
392C2×C22⋊C4—861no—
393C2×C22⋊C4—861no—
394C2×C22⋊C4—861no—
395C2×C22⋊C4—861no—
396C2×C22⋊C4—861no—
397C2×C22⋊C4—1724no—
398C2×C22⋊C4—1724no—
399C2×C42—431no—
400C2×C42—431no—
401C2×C42—431no—
402C2×C42—431no—
403C2×C42—862no—
404C2×C42—862no—
405#106—1722no—
406C4⋊C8—864no—
407#102—24no—
408#102—864no—
409#102—1722no—
410#102—1722no—
411C22⋊C8—862no—
412C22⋊C8C22⋊D4314yes—
413#97—864no—
414#95—861no—
415#95—861no—
416#95—861no—
417C24—24no—
418C24—22no—
419C24—21no—
420C24—42no—
421C24—42no—
422C24—42no—
423C24—42no—
424C24—42no—
425C24—42no—
426C24D4×D4311yescharacteristic
427C2×D4—24no—
428C2×D4—22no—
429C2×D4—21no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—21no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—48no—
438C2×D4—48no—
439C2×D4—42no—
440C2×D4—42no—
441C2×D4—42no—
442C2×D4—42no—
443C2×D4—42no—
444C2×D4#1062190014yes—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—431no—
449C22×C4—431no—
450C22×C4—431no—
451C22×C4—431no—
452C22×C4—862no—
453C22×C4—862no—
454C22×C4—862no—
455C22×C4—862no—
456C22×C4—862no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—862no—
460C22×C4—1721no—
461C22×C4—1722no—
462C22×C4—1722no—
463C22×C4—1722no—
464C22×C4D4×D4311yescharacteristic
465C22×C4#1062190012yes—
466C22×C4C2×C22⋊D4312yes—
467C22×C4C23×D4311yescharacteristic
468D8—48no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—862no—
472C2×C8—862no—
473C2×C8—862no—
474C2×C8C2×C22⋊D4314yes—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—862no—
478C4⋊C4—862no—
479C4⋊C4—862no—
480C4⋊C4—862no—
481C4⋊C4—1722no—
482C4⋊C4—1722no—
483C4⋊C4—1722no—
484C22⋊C4—42no—
485C22⋊C4—1724no—
486C22⋊C4—1722no—
487C22⋊C4—1724no—
488C22⋊C4—1724no—
489C22⋊C4—1724no—
490C22⋊C4—1722no—
491C22⋊C4—1722no—
492C22⋊C4—1722no—
493C22⋊C4—1722no—
494C42—862no—
495C42—862no—
496C42—861no—
497C42—861no—
498C42—861no—
499C42—861no—
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23—24no—
505C23—48no—
506C23—48no—
507C23—48no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23—84no—
522C23—84no—
523C23—84no—
524C23—84no—
525C23#1306329612yes—
526C23#1306334912yes—
527C23#1306334912yes—
528C23C2×D4×D4311yescharacteristic
529D4—24no—
530D4—24no—
531D4—48no—
532D4—42no—
533D4—42no—
534D4—42no—
535D4—42no—
536D4—84no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—432no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—861no—
548C2×C4—861no—
549C2×C4—861no—
550C2×C4—861no—
551C2×C4—861no—
552C2×C4—861no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—861no—
556C2×C4—3444no—
557C2×C4—1724no—
558C2×C4—1721no—
559C2×C4—1722no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1722no—
564C2×C4—1721no—
565C2×C4—1722no—
566C2×C4—1721no—
567C2×C4—1724no—
568C2×C4#1306329612yes—
569C2×C4C22×C22⋊D4311yescharacteristic
570C2×C4C2×#1062190011yescharacteristic
571C2×C4C2×#1062190012yes—
572C2×C4#1306337012yes—
573C8—24no—
574C8—1722no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—22no—
580C22—22no—
581C22—44no—
582C22—44no—
583C22—44no—
584C22—816no—
585C22—82no—
586C22—82no—
587C22—82no—
588C22—82no—
589C22—81no—
590C22—81no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22—81no—
596C22#1458314914yes—
597C22C2×#1306329611yescharacteristic
598C22#1458340511yescharacteristic
599C22#1458346411yescharacteristic
600C22AGL(1,ℤ/8)×D4311yescharacteristic
601C22C2×#1306334911yescharacteristic
602C22C2×#1306334911yescharacteristic
603C22#1458369511yescharacteristic
604C4—22no—
605C4—81no—
606C4—862no—
607C4—3441no—
608C4—3442no—
609C4—3441no—
610C4—1721no—
611C4—1721no—
612C4—1721no—
613C4#1458354312yes—
614C4#1458358012yes—
615C2—24no—
616C2—84no—
617C2—161no—
618C2#1913797611yescharacteristic
619C2C2×#1458314911yescharacteristic
620C2#1914420811yescharacteristic
621C2#1914468111yescharacteristic
622C2#1914472811yescharacteristic
623C2#1914557911yescharacteristic
624C2#1914561111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#447C2
socleC23×C43C22×D4
hypercenterC2×#447D43
hypocenterC43#24506
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#447

Complements

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

NH ≅ G/Ntype
1. C2×#14582953C2semidirect
2. #19142921C2semidirect
3. C2×#14582802C2semidirect
4. #19135967C2semidirect
5. #19135903C2semidirect
6. #19135472C2semidirect
7. #19135289C2semidirect
8. #19134913C2semidirect
9. #19134790C2semidirect
10. #19134526C2semidirect
18. C2×#13063257C22semidirect
19. C2×Dic43⋊C8C22semidirect
22. C2×#13063246C22semidirect
24. C2×#13063235C22semidirect
29. #14582802C22semidirect
30. #14582802C22semidirect
31. #14582795C22semidirect
32. #14582795C22semidirect
37. #14582662C22semidirect
38. #14582661C22semidirect
357. C43#24506semidirect

Maximal subgroups

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

subgroupindex
C2×#145829532
#191429212
C2×#145828022
#191359672
#191359032
#191354722
#191352892
#191349132
#191347902
#191345262
C2×C43×#4472
#2450643