Finite Group Databasebeta

← #25132994

Subgroups — #25132994

Order 11008.

1102 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583629C211yesmaximal, characteristic, complemented
2C2×#14583187C211yesmaximal, characteristic
3C2×#14582990C211yesmaximal, characteristic
4#19139515C211yesmaximal, characteristic
5#19135927C211yesmaximal, characteristic, complemented
6#19135925C211yesmaximal, characteristic, complemented
7#19135729C211yesmaximal, characteristic
8#19135554C211yesmaximal, characteristic, complemented
9#19135529C211yesmaximal, characteristic, complemented
10#19134953C211yesmaximal, characteristic
11#19134947C211yesmaximal, characteristic
12#19134866C211yesmaximal, characteristic, complemented
13#19134864C211yesmaximal, characteristic, complemented
14#19134599C211yesmaximal, characteristic, complemented
15C43×#2023C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17#14583629—24no—
18#14583629—24no—
19C2×#13063324—21no—
20C2×#13063324C2211yescharacteristic
21C2×#13063324C2211yescharacteristic
22C2×#13063323—21no—
23C2×#13063323—21no—
24C2×#13063302—21no—
25C2×C4×Dic86C2211yescharacteristic
26C2×C4×Dic86C2211yescharacteristic
27C2×#13063290—21no—
28C2×#13063290C2211yescharacteristic
29C2×#13063290C2211yescharacteristic
30C2×D4×Dic43C2211yescharacteristic
31#14583187—24no—
32#14582990—24no—
33C2×#13063257C2211yescharacteristic
34C2×#13063256C2211yescharacteristic
35C2×#13063256C2211yescharacteristic
36C2×Dic43⋊C8C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063250C2211yescharacteristic
39C2×#13063248C2211yescharacteristic
40C2×#13063246C2211yescharacteristic
41C2×C8×Dic43C2211yescharacteristic
42#14582822—21no—
43#14582822—21no—
44#14582802C2211yescharacteristic
45#14582798C2211yescharacteristic
46#14582797C2211yescharacteristic
47#14582768C2211yescharacteristic
48#14582757—21no—
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582654C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C2×C4⋊Q8×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C43×#390C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86—21no—
65C22×Dic86D411yescharacteristic
66C22×Dic86C2311yescharacteristic
67C23×Dic43—21no—
68C2×#10621883—22no—
69C2×#10621883—22no—
70C2×#10621883Q814yescomplemented
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73#13063324—28no—
74#13063324—22no—
75#13063324—22no—
76#13063324—22no—
77#13063324D414yes—
78#13063323—28no—
79#13063323—28no—
80#13063302—44no—
81C4×Dic86—22no—
82C4×Dic86—22no—
83C4×Dic86—22no—
84C4×Dic86—22no—
85#13063290—28no—
86#13063290—22no—
87#13063290—22no—
88#13063290—22no—
89#13063290D414yes—
90D4×Dic43—22no—
91D4×Dic43—22no—
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43D411yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4—21no—
105C2×Dic43⋊C4D411yescharacteristic
106C2×Dic43⋊C4D411yescharacteristic
107C2×C22⋊Dic43—21no—
108C2×C22⋊Dic43—21no—
109C2×C22⋊Dic43—21no—
110C2×C4×Dic43—21no—
111C2×C4×Dic43—21no—
112C2×C4×Dic43—21no—
113C2×C4×Dic43C2311yescharacteristic
114C2×C4×Dic43C2311yescharacteristic
115#13063257—22no—
116#13063256—22no—
117#13063256—22no—
118Dic43⋊C8—22no—
119#13063250—22no—
120#13063250—22no—
121#13063248—22no—
122#13063246—22no—
123C8×Dic43—22no—
124C43⋊#95—21no—
125C43⋊#95—21no—
126C22×Q8×C43—21no—
127C22×D4×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129C22×C8×C43C2311yescharacteristic
130C4⋊Q8×C43—22no—
131C4⋊Q8×C43—22no—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C22⋊C4×C43—21no—
137C2×C22⋊C4×C43—21no—
138C2×C42×C43C2311yescharacteristic
139#102×C43—22no—
140#102×C43—22no—
141C24×C43—21no—
142C2×Q8×C43—24no—
143C2×Q8×C43—81no—
144C2×Q8×C43—81no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43C2×Q812yes—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2411yescharacteristic
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—42no—
162C22×Dic43—42no—
163C22×Dic43—42no—
164C22×Dic43C2×D411yescharacteristic
165C22×Dic43C2×D411yescharacteristic
166C22×Dic43C2×D411yescharacteristic
167C22×Dic43C2×D411yescharacteristic
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—22no—
172C2×Dic86—22no—
173C2×Dic86—24no—
174C2×Dic86—24no—
175C2×Dic86—81no—
176C2×Dic86—81no—
177C2×Dic86—81no—
178C2×Dic86—81no—
179C2×Dic86SD1614yescomplemented
180C2×Dic86C2×D412yes—
181C2×Dic86C2×Q812yes—
182C2×Dic86#4112yes—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C4⋊C4×C43—24no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43C2×D412yes—
195C4⋊C4×C43C2×D412yes—
196C22⋊C4×C43—42no—
197C22⋊C4×C43—81no—
198C42×C43—21no—
199C42×C43—21no—
200C22⋊Dic43—42no—
201C22⋊Dic43—42no—
202C22⋊Dic43—81no—
203#10621883—28no—
204C4⋊Dic43—21no—
205C4⋊Dic43—22no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—42no—
211C4⋊Dic43C2×D412yes—
212Dic43⋊C4—24no—
213Dic43⋊C4—24no—
214Dic43⋊C4—24no—
215Dic43⋊C4—24no—
216Dic43⋊C4—24no—
217Dic43⋊C4—22no—
218Dic43⋊C4—22no—
219Dic43⋊C4—42no—
220Dic43⋊C4—42no—
221Dic43⋊C4—81no—
222C4×Dic43—24no—
223C4×Dic43—24no—
224C4×Dic43—21no—
225C4×Dic43—21no—
226C4×Dic43—24no—
227C4×Dic43C2×D412yes—
228C4×Dic43C2×D412yes—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8C2×Q812yes—
235C23×C43—22no—
236C23×C43—41no—
237C23×C43—41no—
238C23×C43—41no—
239C23×C43—41no—
240C23×C43—41no—
241C23×C43—41no—
242C23×C43C22×D411yescharacteristic
243Q8×C43—84no—
244D4×C43—22no—
245D4×C43—22no—
246D4×C43—41no—
247D4×C43—41no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—22no—
251C2×C4×C43—22no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—41no—
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×C43C2×SD1612yes—
263C2×C4×C43C22×D411yescharacteristic
264C2×C4×C43C22×D411yescharacteristic
265C2×C4×C43C22×Q811yescharacteristic
266C2×C4×C43C2×#4111yescharacteristic
267C2×C4×C432−1+411yescharacteristic
268C2×C4×C432−1+411yescharacteristic
269C2×Dic43—21no—
270C2×Dic43—22no—
271C2×Dic43—22no—
272C2×Dic43—22no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—21no—
277C2×Dic43—22no—
278C2×Dic43—21no—
279C2×Dic43—21no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43—84no—
289C2×Dic43#12012yes—
290C2×Dic43#12012yes—
291C2×Dic43C2×SD1612yes—
292C2×Dic43C2×SD1612yes—
293C2×Dic43#13712yes—
294Dic86—22no—
295Dic86—22no—
296Dic86—22no—
297Dic86—28no—
298Dic86—84no—
299Dic86—84no—
300Dic86C22⋊Q814yescomplemented
301C8×C43—41no—
302C8×C43—41no—
303C43⋊C8—22no—
304C43⋊C8—41no—
305#24329—431nomaximal, Sylow
306C22×C43—42no—
307C22×C43—42no—
308C22×C43—42no—
309C22×C43—81no—
310C22×C43—81no—
311C22×C43—81no—
312C22×C43—81no—
313C22×C43C2×#12011yescharacteristic
314C22×C43#54811yescharacteristic
315C22×C43D4×Q811yescharacteristic
316C22×C43C22×SD1611yescharacteristic
317C22×C43C2×#13711yescharacteristic
318C22×C43#57611yescharacteristic
319C22×C43#57711yescharacteristic
320C4×C43—22no—
321C4×C43—42no—
322C4×C43—42no—
323C4×C43—41no—
324C4×C43—81no—
325C4×C43C2×C22⋊Q811yescharacteristic
326C4×C43#53611yescharacteristic
327C4×C43#54811yescharacteristic
328C4×C43D4×Q811yescharacteristic
329Dic43—24no—
330Dic43—22no—
331Dic43—22no—
332Dic43—41no—
333Dic43—42no—
334Dic43—81no—
335Dic43—81no—
336Dic43#44814yes—
337C2×Q82—431no—
338C2×#476—431no—
339C2×C4×SD16—431no—
340#2538—431no—
341#2058—431no—
342#2058—431no—
343#2023—431no—
344#2023D4311yescharacteristic
345#1990—431no—
346#1984—431no—
347#1880—431no—
348#1880—431no—
349#1865—431no—
350#1865—431no—
351#1803—431no—
352C2×C43—82no—
353C2×C43#240911yescharacteristic
354C2×C43C2×#44811yescharacteristic
355C2×C43#301211yescharacteristic
356C2×C43#336211yescharacteristic
357C2×C43#336911yescharacteristic
358C2×C43Q8×SD1611yescharacteristic
359C2×C43#338511yescharacteristic
360C22×SD16—431no—
361Q82—864no—
362Q82—864no—
363C2×C4⋊Q8—431no—
364C2×C4⋊Q8—431no—
365C2×C4⋊Q8—861no—
366C2×C4⋊Q8—861no—
367C2×C4⋊Q8—861no—
368C2×C4⋊Q8C2×D4311yescharacteristic
369C2×C22⋊Q8—861no—
370C2×C4×Q8—431no—
371C2×C4×Q8—431no—
372C2×C4×Q8—431no—
373C2×C4×Q8—431no—
374C2×C4×Q8—861no—
375C2×C4×D4—431no—
376#476—864no—
377C4×SD16—864no—
378C2×#106—431no—
379C2×#106—431no—
380C2×#106—431no—
381C2×C4⋊C8—431no—
382C2×#103—431no—
383C2×#103—431no—
384C2×#103—431no—
385C2×#102—431no—
386C2×#102C2×D4311yescharacteristic
387C2×#102C2×D4311yescharacteristic
388C2×C4×C8—431no—
389#396—861no—
390#396—861no—
391#390—431no—
392#390C2×D4311yescharacteristic
393#389—431no—
394#389—431no—
395#384—431no—
396#380—861no—
397#340—431no—
398#340—431no—
399#340—431no—
400#340—431no—
401#340C2×D4311yescharacteristic
402#340C2×D4311yescharacteristic
403#336—431no—
404#336—431no—
405#336—431no—
406#336C2×D4311yescharacteristic
407C43#2432911yescharacteristic, complemented, Sylow
408C22×Q8—21no—
409C22×Q8—431no—
410C22×Q8—431no—
411C22×Q8—861no—
412C22×Q8—861no—
413C22×D4C22×D4311yescharacteristic
414C23×C4—861no—
415C2×SD16—434no—
416C2×SD16—862no—
417C2×SD16—862no—
418C22×C8—431no—
419C22×C8—431no—
420C22×C8C22×D4311yescharacteristic
421C22×C8C22×D4311yescharacteristic
422C4⋊Q8—22no—
423C4⋊Q8—22no—
424C4⋊Q8—434no—
425C4⋊Q8—862no—
426C4⋊Q8—862no—
427C4⋊Q8—868no—
428C4⋊Q8—868no—
429C4⋊Q8—868no—
430C4⋊Q8—862no—
431C22⋊Q8—1724no—
432C4×Q8—434no—
433C4×Q8—862no—
434C4×Q8—862no—
435C4×Q8—862no—
436C4×Q8—862no—
437C4×Q8—862no—
438C4×Q8—862no—
439C4×Q8—868no—
440C4×Q8—862no—
441C4×D4—862no—
442C4×D4—862no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—431no—
445C2×C4⋊C4—431no—
446C2×C4⋊C4—431no—
447C2×C4⋊C4—431no—
448C2×C4⋊C4—431no—
449C2×C4⋊C4—431no—
450C2×C4⋊C4—861no—
451C2×C4⋊C4—861no—
452C2×C4⋊C4—861no—
453C2×C4⋊C4—861no—
454C2×C4⋊C4—861no—
455C2×C4⋊C4—861no—
456C2×C4⋊C4—861no—
457C2×C4⋊C4—861no—
458C2×C4⋊C4—861no—
459C2×C4⋊C4C22×D4311yescharacteristic
460C2×C4⋊C4C22×D4311yescharacteristic
461C2×C4⋊C4C22×D4311yescharacteristic
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—861no—
465C2×C22⋊C4—861no—
466C2×C22⋊C4—861no—
467C2×C42—431no—
468C2×C42—431no—
469C2×C42—861no—
470C2×C42—861no—
471C2×C42—861no—
472C2×C42C22×D4311yescharacteristic
473#106—862no—
474#106—862no—
475#106—862no—
476C4⋊C8—862no—
477#103—862no—
478#103—862no—
479#103—862no—
480#102—22no—
481#102—22no—
482#102—862no—
483C4×C8—862no—
484#95—861no—
485#95—861no—
486C24—21no—
487C2×Q8—24no—
488C2×Q8—81no—
489C2×Q8—81no—
490C2×Q8—434no—
491C2×Q8—432no—
492C2×Q8—432no—
493C2×Q8—432no—
494C2×Q8—862no—
495C2×Q8—862no—
496C2×Q8—864no—
497C2×Q8—864no—
498C2×Q8—861no—
499C2×Q8—861no—
500C2×Q8—861no—
501C2×Q8—3441no—
502C2×Q8—3441no—
503C2×Q8—3441no—
504C2×Q8—3441no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4Q8×D4312yes—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—431no—
515C22×C4—431no—
516C22×C4—431no—
517C22×C4—431no—
518C22×C4—861no—
519C22×C4—861no—
520C22×C4—861no—
521C22×C4—861no—
522C22×C4—1722no—
523C22×C4—1722no—
524C22×C4—1722no—
525C22×C4D4×D4311yescharacteristic
526C22×C4D4×D4311yescharacteristic
527C22×C4C23×D4311yescharacteristic
528SD16—868no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—432no—
536C2×C8—861no—
537C2×C8—861no—
538C2×C8—861no—
539C2×C8—861no—
540C2×C8—861no—
541C4⋊C4—24no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—432no—
547C4⋊C4—862no—
548C4⋊C4—862no—
549C4⋊C4—862no—
550C4⋊C4—864no—
551C4⋊C4—864no—
552C4⋊C4—864no—
553C4⋊C4—864no—
554C4⋊C4—864no—
555C4⋊C4—861no—
556C4⋊C4—861no—
557C4⋊C4—861no—
558C4⋊C4—861no—
559C4⋊C4—861no—
560C4⋊C4—3441no—
561C4⋊C4—1722no—
562C4⋊C4—1722no—
563C4⋊C4—1722no—
564C4⋊C4D4×D4312yes—
565C4⋊C4D4×D4312yes—
566C22⋊C4—42no—
567C22⋊C4—81no—
568C22⋊C4—3441no—
569C22⋊C4—1722no—
570C22⋊C4—1722no—
571C42—21no—
572C42—21no—
573C42—432no—
574C42—432no—
575C42—864no—
576C42—864no—
577C42—864no—
578C42—861no—
579C42—861no—
580C23—22no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23C2×D4×D4311yescharacteristic
588Q8—84no—
589Q8—434no—
590Q8—868no—
591Q8—862no—
592Q8—862no—
593Q8—862no—
594Q8—3444no—
595Q8—3444no—
596D4—22no—
597D4—22no—
598D4—41no—
599D4—41no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—432no—
615C2×C4—432no—
616C2×C4—432no—
617C2×C4—432no—
618C2×C4—432no—
619C2×C4—862no—
620C2×C4—862no—
621C2×C4—861no—
622C2×C4—862no—
623C2×C4—861no—
624C2×C4—861no—
625C2×C4—861no—
626C2×C4—862no—
627C2×C4—861no—
628C2×C4—861no—
629C2×C4—861no—
630C2×C4—3444no—
631C2×C4—1721no—
632C2×C4—1721no—
633C2×C4—1721no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4—1721no—
637C2×C4—1721no—
638C2×C4—1721no—
639C2×C4SD16×D4312yes—
640C2×C4C2×D4×D4311yescharacteristic
641C2×C4C2×D4×D4311yescharacteristic
642C2×C4C2×Q8×D4311yescharacteristic
643C2×C4#41×D4311yescharacteristic
644C2×C4#1306337211yescharacteristic
645C2×C4#1306337211yescharacteristic
646C8—41no—
647C8—41no—
648C8—862no—
649C8—1721no—
650C22—42no—
651C22—42no—
652C22—42no—
653C22—81no—
654C22—81no—
655C22—81no—
656C22—81no—
657C22#120×D4311yescharacteristic
658C22#1458355711yescharacteristic
659C22#1458356211yescharacteristic
660C22C2×SD16×D4311yescharacteristic
661C22#137×D4311yescharacteristic
662C22#1458370011yescharacteristic
663C22#1458370911yescharacteristic
664C4—22no—
665C4—41no—
666C4—42no—
667C4—42no—
668C4—81no—
669C4—434no—
670C4—862no—
671C4—864no—
672C4—862no—
673C4—3441no—
674C4—3441no—
675C4—1721no—
676C4—1722no—
677C4C22⋊Q8×D4311yescharacteristic
678C4#1458346911yescharacteristic
679C4#1458355711yescharacteristic
680C4#1458356211yescharacteristic
681C2—82no—
682C2#1913795311yescharacteristic
683C2#448×D4311yescharacteristic
684C2#1914389411yescharacteristic
685C2#1914726311yescharacteristic
686C2#1914733211yescharacteristic
687C2#1914745011yescharacteristic
688C2#1914750011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2023C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#2023D43
hypocenterC43#24329
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2023

Complements

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

NH ≅ G/Ntype
1. C2×#14583629C2semidirect
5. #19135927C2semidirect
6. #19135925C2semidirect
8. #19135554C2semidirect
9. #19135529C2semidirect
12. #19134866C2semidirect
13. #19134864C2semidirect
14. #19134599C2semidirect
70. C2×#10621883Q8semidirect
179. C2×Dic86SD16semidirect
300. Dic86C22⋊Q8semidirect
407. C43#24329semidirect

Maximal subgroups

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

subgroupindex
C2×#145836292
C2×#145831872
C2×#145829902
#191395152
#191359272
#191359252
#191357292
#191355542
#191355292
#191349532
#191349472
#191348662
#191348642
#191345992
C43×#20232
#2432943