Finite Group Databasebeta

← #25149946

Subgroups — #25149946

Order 11008.

1262 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583589C211yesmaximal, characteristic, complemented
2C2×#14583263C211yesmaximal, characteristic, complemented
3C2×#14583096C211yesmaximal, characteristic, complemented
4#19135598C212yesmaximal, complemented
5#19135598C212yesmaximal, complemented
6#19135552C211yesmaximal, characteristic, complemented
7#19135394C211yesmaximal, characteristic, complemented
8#19134918C212yesmaximal, complemented
9#19134913C212yesmaximal, complemented
10#19134428C211yesmaximal, characteristic, complemented
11C43×#2541C211yesmaximal, characteristic
12C22×#10621883C2212yes—
13#14583589—24no—
14#14583589—24no—
15C2×#13063318—21no—
16C2×#13063317C2211yescharacteristic
17C2×#13063315—21no—
18C2×#13063306—21no—
19C2×#13063304C2211yescharacteristic
20C2×#13063304C2211yescharacteristic
21C2×C4×Dic86C2211yescharacteristic
22C2×#13063284C2211yescharacteristic
23C2×#13063281—21no—
24C22×C4⋊Dic43C2211yescharacteristic
25#14583263—24no—
26#14583096—24no—
27C2×C4⋊(C43⋊C8)C2211yescharacteristic
28C2×#13063248C2212yes—
29C2×#13063246C2212yes—
30C2×#13063246C2212yes—
31C2×#13063246C2212yes—
32C2×C22⋊(C43⋊C8)C2212yes—
33C2×C22⋊(C43⋊C8)C2212yes—
34C2×#13063236C2211yescharacteristic
35#14582661C2212yes—
36#14582661C2212yes—
37#14582661C2212yes—
38C2×#127×C43—21no—
39C2×#127×C43C2211yescharacteristic
40C2×#121×C43C2212yes—
41C2×#121×C43C2212yes—
42C2×C4×D4×C43C2211yescharacteristic
43C43×#392—21no—
44C43×#392—21no—
45C43×#390—21no—
46C4×C4⋊C4×C43C2211yescharacteristic
47C22×Dic86C2311yescharacteristic
48C23×Dic43—21no—
49C2×#10621883—24no—
50C2×#10621883—42no—
51C2×#10621883—42no—
52C22×C43⋊C8C2312yes—
53C22×C43⋊C8C2312yes—
54#13063318—28no—
55#13063317—22no—
56#13063317D414yescomplemented
57#13063315—28no—
58#13063306—28no—
59#13063304—22no—
60#13063304—22no—
61#13063304—22no—
62#13063304—22no—
63C4×Dic86—22no—
64C4×Dic86D414yescomplemented
65#13063284—22no—
66#13063284—22no—
67#13063281—28no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—22no—
70C2×C4⋊Dic43—22no—
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C4⋊(C43⋊C8)—22no—
85#13063248—24no—
86#13063246—24no—
87#13063246—24no—
88#13063246—24no—
89C22⋊(C43⋊C8)—42no—
90C22⋊(C43⋊C8)—42no—
91#13063236—22no—
92C22×D4×C43—22no—
93C22×D4×C43—22no—
94C22×D4×C43—21no—
95C22×D4×C43—21no—
96C22×D4×C43D411yescharacteristic
97C22×D4×C43C2312yes—
98C23×C4×C43C2311yescharacteristic
99C23×C4×C43C2311yescharacteristic
100#127×C43—22no—
101#127×C43—22no—
102#127×C43—44no—
103#121×C43—24no—
104#121×C43—24no—
105#121×C43—42no—
106#121×C43—42no—
107C4×D4×C43—22no—
108C4×D4×C43—22no—
109C2×C4⋊C4×C43D411yescharacteristic
110C2×C4⋊C4×C43C2312yes—
111C2×C22⋊C4×C43—22no—
112C2×C22⋊C4×C43—22no—
113C2×C22⋊C4×C43D411yescharacteristic
114C2×C22⋊C4×C43D411yescharacteristic
115C2×C42×C43—21no—
116C2×C42×C43C2311yescharacteristic
117#95×C43—21no—
118C24×C43—22no—
119C24×C43C2×D411yescharacteristic
120C24×C43C2×D411yescharacteristic
121C2×D4×C43—22no—
122C2×D4×C43—22no—
123C2×D4×C43—22no—
124C2×D4×C43—22no—
125C2×D4×C43—22no—
126C2×D4×C43—22no—
127C2×D4×C43—22no—
128C2×D4×C43—22no—
129C2×D4×C43—41no—
130C2×D4×C43—44no—
131C2×D4×C43—44no—
132C2×D4×C43—44no—
133C2×D4×C43—42no—
134C2×D4×C43—42no—
135C2×D4×C43—42no—
136C2×D4×C43—42no—
137C2×D4×C43—44no—
138C2×D4×C43—82no—
139C2×D4×C43—82no—
140C2×D4×C43—82no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—22no—
146C22×C4×C43—22no—
147C22×C4×C43—22no—
148C22×C4×C43—22no—
149C22×C4×C43—22no—
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2411yescharacteristic
155C22×Dic43—24no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—42no—
161C22×Dic43—42no—
162C2×Dic86—22no—
163C2×Dic86—22no—
164C2×Dic86—21no—
165C2×Dic86C2×D412yes—
166C4⋊C4×C43—22no—
167C4⋊C4×C43—22no—
168C4⋊C4×C43#4114yes—
169C22⋊C4×C43—22no—
170C22⋊C4×C43—22no—
171C22⋊C4×C43—44no—
172C22⋊C4×C43—44no—
173C42×C43—42no—
174C42×C43C2×D412yes—
175C42×C43C2×D412yes—
176C22⋊Dic43—24no—
177C22⋊Dic43—24no—
178C22⋊Dic43—24no—
179#10621883—48no—
180C4⋊Dic43—24no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43C2×D412yes—
185C4⋊Dic43C2×D412yes—
186C4⋊Dic43C2×D412yes—
187Dic43⋊C4—24no—
188Dic43⋊C4—24no—
189Dic43⋊C4—24no—
190Dic43⋊C4—24no—
191Dic43⋊C4—24no—
192C4×Dic43—24no—
193C4×Dic43—24no—
194C2×C43⋊C8—22no—
195C2×C43⋊C8—22no—
196C2×C43⋊C8—22no—
197C2×C43⋊C8—22no—
198C2×C43⋊C8—22no—
199C2×C43⋊C8—22no—
200C23×C43—21no—
201C23×C43—22no—
202C23×C43—21no—
203C23×C43—22no—
204C23×C43—21no—
205C23×C43—22no—
206C23×C43—21no—
207C23×C43—21no—
208C23×C43—22no—
209C23×C43—42no—
210C23×C43—42no—
211C23×C43—42no—
212C23×C43—42no—
213C23×C43—42no—
214C23×C43—42no—
215C23×C43—42no—
216C23×C43AGL(1,ℤ/8)12yes—
217C23×C43C22×D411yescharacteristic
218D4×C43—44no—
219D4×C43—42no—
220D4×C43—42no—
221D4×C43—42no—
222D4×C43—42no—
223D4×C43—84no—
224D4×C43—84no—
225D4×C43—88no—
226D4×C43—88no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—22no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—24no—
233C2×C4×C43—22no—
234C2×C4×C43—22no—
235C2×C4×C43—42no—
236C2×C4×C43—42no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—42no—
242C2×C4×C43—42no—
243C2×C4×C43#12012yes—
244C2×C4×C43#12012yes—
245C2×C4×C43C22×D411yescharacteristic
246C2×C4×C43C22×D411yescharacteristic
247C2×C4×C43C2×#4112yes—
248C2×C4×C43H(5,𝔽2)12yes—
249C2×Dic43—22no—
250C2×Dic43—22no—
251C2×Dic43—22no—
252C2×Dic43—22no—
253C2×Dic43—48no—
254C2×Dic43—42no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—42no—
260Dic86—22no—
261Dic86—22no—
262Dic86—42no—
263C43⋊C8—42no—
264C43⋊C8—42no—
265#25583—431nomaximal, Sylow
266C22×C43—22no—
267C22×C43—24no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—42no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43—42no—
275C22×C43—42no—
276C22×C43—82no—
277C22×C43—82no—
278C22×C43—82no—
279C22×C43—82no—
280C22×C43—82no—
281C22×C43—82no—
282C22×C43—82no—
283C22×C43C2×#12011yescharacteristic
284C22×C43#54612yes—
285C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
286C22×C43#57511yescharacteristic
287C22×C43#57712yes—
288C4×C43—22no—
289C4×C43—22no—
290C4×C43—41no—
291C4×C43—41no—
292C4×C43—44no—
293C4×C43#53211yescharacteristic
294C4×C43#53511yescharacteristic
295C4×C43#55012yes—
296Dic43—42no—
297Dic43—42no—
298Dic43—42no—
299Dic43—42no—
300C2×#552—431no—
301C2×#490—431no—
302C2×#460—431no—
303#2541D4311yescharacteristic
304#2000—432no—
305#2000—432no—
306#1989—431no—
307#1955—431no—
308#1875—432no—
309#1874—432no—
310#1763—431no—
311C2×C43—42no—
312C2×C43—81no—
313C2×C43—162no—
314C2×C43#243111yescharacteristic
315C2×C43#300611yescharacteristic
316C2×C43#301011yescharacteristic
317C2×C43#331012yes—
318C2×C43#331712yes—
319C22×SD16—432no—
320#552—864no—
321#552—864no—
322C2×#127—21no—
323C2×#127C2×D4311yescharacteristic
324C2×#126—861no—
325C2×#125—431no—
326C2×#125—861no—
327C2×#123—861no—
328C2×C22⋊Q8—431no—
329C2×C22⋊Q8—431no—
330C2×#121C2×D4312yes—
331C2×#121C2×D4312yes—
332C2×C4×Q8—431no—
333C2×C4×D4C2×D4311yescharacteristic
334C2×#117—431no—
335C2×#117—861no—
336C22×C4⋊C4—431no—
337#490—864no—
338#460—864no—
339C2×C4⋊C8—431no—
340C2×#103—432no—
341C2×#102—432no—
342C2×#102—432no—
343C2×#102—432no—
344C2×C22⋊C8—432no—
345C2×C22⋊C8—432no—
346C2×#97—431no—
347#392—21no—
348#392—21no—
349#390—21no—
350C4×C4⋊C4C2×D4311yescharacteristic
351#340—432no—
352#340—432no—
353#340—432no—
354C43#2558311yescharacteristic, complemented, Sylow
355C22×Q8—431no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—21no—
359C22×D4—21no—
360C22×D4C22⋊D4311yescharacteristic
361C22×D4C22×D4312yes—
362C23×C4—861no—
363C23×C4C22×D4311yescharacteristic
364C23×C4C22×D4311yescharacteristic
365C2×SD16—864no—
366C2×SD16—1722no—
367C2×SD16—1722no—
368C22×C8—432no—
369C22×C8—432no—
370#127—22no—
371#127—22no—
372#127—44no—
373#126—868no—
374#125—434no—
375#125—868no—
376#125—862no—
377#123—868no—
378C22⋊Q8—862no—
379C22⋊Q8—862no—
380C22⋊Q8—862no—
381C22⋊Q8—862no—
382#121—24no—
383#121—24no—
384#121—42no—
385#121—42no—
386C4×Q8—434no—
387C4×Q8—862no—
388C4×D4—22no—
389C4×D4—22no—
390#117—868no—
391#117—862no—
392#117—862no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—862no—
397C2×C4⋊C4—862no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4C22⋊D4311yescharacteristic
405C2×C4⋊C4C22×D4312yes—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—861no—
409C2×C22⋊C4—861no—
410C2×C22⋊C4—861no—
411C2×C22⋊C4C22⋊D4311yescharacteristic
412C2×C22⋊C4C22⋊D4311yescharacteristic
413C2×C42—21no—
414C2×C42—861no—
415C2×C42—861no—
416C2×C42C22×D4311yescharacteristic
417C4⋊C8—862no—
418#103—864no—
419#102—864no—
420#102—864no—
421#102—864no—
422C22⋊C8—1722no—
423C22⋊C8—1722no—
424#97—862no—
425#95—21no—
426C24—22no—
427C24C2×C22⋊D4311yescharacteristic
428C24C2×C22⋊D4311yescharacteristic
429C2×Q8—432no—
430C2×Q8—861no—
431C2×Q8—862no—
432C2×Q8—862no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—41no—
442C2×D4—44no—
443C2×D4—44no—
444C2×D4—42no—
445C2×D4—42no—
446C2×D4—44no—
447C2×D4—44no—
448C2×D4—42no—
449C2×D4—42no—
450C2×D4—82no—
451C2×D4—82no—
452C2×D4—82no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—864no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4—1722no—
468C22×C4—1722no—
469C22×C4C2×C22⋊D4311yescharacteristic
470C22×C4C2×C22⋊D4311yescharacteristic
471C22×C4C2×C22⋊D4311yescharacteristic
472C22×C4C2×C22⋊D4311yescharacteristic
473C22×C4C23×D4311yescharacteristic
474SD16—1728no—
475C2×C8—862no—
476C2×C8—862no—
477C2×C8—862no—
478C2×C8—862no—
479C2×C8—862no—
480C2×C8—862no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—432no—
484C4⋊C4—432no—
485C4⋊C4—432no—
486C4⋊C4—864no—
487C4⋊C4—864no—
488C4⋊C4—864no—
489C4⋊C4—864no—
490C4⋊C4—864no—
491C4⋊C4—864no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4#1062190014yes—
496C22⋊C4—22no—
497C22⋊C4—22no—
498C22⋊C4—44no—
499C22⋊C4—44no—
500C22⋊C4—864no—
501C22⋊C4—864no—
502C22⋊C4—864no—
503C42—42no—
504C42—864no—
505C42—864no—
506C42D4×D4312yes—
507C42D4×D4312yes—
508C23—21no—
509C23—21no—
510C23—22no—
511C23—22no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—22no—
516C23—22no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23#1306335112yes—
525C23C22×C22⋊D4311yescharacteristic
526Q8—862no—
527Q8—862no—
528Q8—1722no—
529D4—44no—
530D4—42no—
531D4—42no—
532D4—42no—
533D4—42no—
534D4—84no—
535D4—84no—
536D4—88no—
537D4—88no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—862no—
555C2×C4—862no—
556C2×C4—862no—
557C2×C4—862no—
558C2×C4—1728no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1722no—
564C2×C4—1722no—
565C2×C4#1306329312yes—
566C2×C4#1306329312yes—
567C2×C4C2×D4×D4311yescharacteristic
568C2×C4C2×D4×D4311yescharacteristic
569C2×C4C2×#1062190012yes—
570C2×C4#1306337012yes—
571C8—1722no—
572C8—1722no—
573C22—24no—
574C22—22no—
575C22—41no—
576C22—41no—
577C22—42no—
578C22—42no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—42no—
583C22—82no—
584C22—82no—
585C22—82no—
586C22—82no—
587C22—82no—
588C22—82no—
589C22—82no—
590C22C2×#1306329311yescharacteristic
591C22#1458354312yes—
592C22C2×#1306335111yescharacteristic
593C22#1458369711yescharacteristic
594C22#1458371012yes—
595C4—22no—
596C4—22no—
597C4—44no—
598C4—41no—
599C4—41no—
600C4—1722no—
601C4—1722no—
602C4—1722no—
603C4—1722no—
604C4#1458344711yescharacteristic
605C4#1458346211yescharacteristic
606C4#1458356912yes—
607C2—42no—
608C2—81no—
609C2—162no—
610C2#1913821111yescharacteristic
611C2#1914384511yescharacteristic
612C2#1914387911yescharacteristic
613C2#1914661612yes—
614C2#1914672112yes—
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC43×#2541C2
socleC23×C43C22×D4
hypercenter#2541D43
hypocenterC43#25583
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2541

Complements

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

NH ≅ G/Ntype
1. C2×#14583589C2semidirect
2. C2×#14583263C2semidirect
3. C2×#14583096C2semidirect
4. #19135598C2semidirect
5. #19135598C2semidirect
6. #19135552C2semidirect
7. #19135394C2semidirect
8. #19134918C2semidirect
9. #19134913C2semidirect
10. #19134428C2semidirect
56. #13063317D4semidirect
64. C4×Dic86D4semidirect
354. C43#25583semidirect

Maximal subgroups

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

subgroupindex
C2×#145835892
C2×#145832632
C2×#145830962
#191355982
#191355522
#191353942
#191349182
#191349132
#191344282
C43×#25412
#2558343