Finite Group Databasebeta

← #25140468

Subgroups — #25140468

Order 11008.

932 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q16×Dic43C211yesmaximal, characteristic, complemented
2#19138094C211yesmaximal, characteristic
3Q8×C22⋊Dic43C211yesmaximal, characteristic
4#19136141C211yesmaximal, characteristic, complemented
5#19136018C211yesmaximal, characteristic
6#19135915C211yesmaximal, characteristic, complemented
7#19135788C211yesmaximal, characteristic
8#19135268C211yesmaximal, characteristic, complemented
9#19135198C211yesmaximal, characteristic
10#19134938C211yesmaximal, characteristic, complemented
11#19134938C211yesmaximal, characteristic, complemented
12#19134861C211yesmaximal, characteristic, complemented
13#19134608C211yesmaximal, characteristic, complemented
14#19134530C211yesmaximal, characteristic
15C2×C43×#451C211yesmaximal, characteristic
16C2×Q8×Dic43C2211yescharacteristic
17C2×Q8×Dic43C2211yescharacteristic
18C2×Q8×Dic43C2211yescharacteristic
19Q16×Dic43—24no—
20C2×#13063259C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×Dic43⋊C8C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×C22⋊(C43⋊C8)C2211yescharacteristic
30C2×C8×Dic43C2211yescharacteristic
31#14582838—21no—
32#14582824—21no—
33#14582806—21no—
34#14582806—21no—
35#14582806C2211yescharacteristic
36#14582806C2211yescharacteristic
37#14582806C2211yescharacteristic
38#14582795C2211yescharacteristic
39#14582787—21no—
40#14582780—21no—
41#14582764C2211yescharacteristic
42#14582759—21no—
43#14582759C2211yescharacteristic
44#14582759C2211yescharacteristic
45C4×C22⋊Dic43—21no—
46C4×C22⋊Dic43C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C23×Q8×C43C2211yescharacteristic
54C22×Q16×C43C2211yescharacteristic
55C22×Q16×C43C2211yescharacteristic
56C2×C22⋊Q8×C43C2211yescharacteristic
57C43×#451—24no—
58C2×#103×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63Q8×Dic43—22no—
64Q8×Dic43—22no—
65Q8×Dic43—22no—
66Q8×Dic43—41no—
67Q8×Dic43—41no—
68Q8×Dic43—41no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43D411yescharacteristic
80C2×C22⋊Dic43D411yescharacteristic
81C2×C4×Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43C2311yescharacteristic
85C2×C4×Dic43C2311yescharacteristic
86#13063259—22no—
87#13063256—41no—
88Dic43⋊C8—41no—
89#13063249—22no—
90#13063249—22no—
91#13063249—22no—
92#13063249—22no—
93#13063249—41no—
94#13063249—41no—
95C22⋊(C43⋊C8)—41no—
96C8×Dic43—22no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95D411yescharacteristic
109C43⋊#95D411yescharacteristic
110C22×Q8×C43—22no—
111C22×Q8×C43—22no—
112C22×Q8×C43—21no—
113C22×Q8×C43—22no—
114C22×Q8×C43—22no—
115C22×Q8×C43—41no—
116C22×Q8×C43—41no—
117C22×Q8×C43C2311yescharacteristic
118C22×Q8×C43C2311yescharacteristic
119C22×Q8×C43C2311yescharacteristic
120C23×C4×C43—21no—
121C23×C4×C43C2311yescharacteristic
122C2×Q16×C43—22no—
123C2×Q16×C43—22no—
124C2×Q16×C43—22no—
125C2×Q16×C43—22no—
126C2×Q16×C43—41no—
127C2×Q16×C43D414yes—
128C22×C8×C43C2311yescharacteristic
129C22×C8×C43C2311yescharacteristic
130C22⋊Q8×C43—22no—
131C22⋊Q8×C43—41no—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C22⋊C4×C43—21no—
135#103×C43—22no—
136#103×C43—22no—
137C22⋊C8×C43—22no—
138C24×C43C2×D411yescharacteristic
139C2×Q8×C43—24no—
140C2×Q8×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—42no—
154C2×Q8×C43—42no—
155C2×Q8×C43—44no—
156C2×Q8×C43—44no—
157C2×Q8×C43—44no—
158C2×Q8×C43—44no—
159C2×Q8×C43C2×D412yes—
160C2×Q8×C43C2×D412yes—
161C2×Q8×C43#4112yes—
162C2×Q8×C43#4112yes—
163C2×Q8×C43#4112yes—
164C22×C4×C43—24no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—42no—
176C22×C4×C43—42no—
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2411yescharacteristic
179C22×Dic43—21no—
180C22×Dic43—21no—
181C22×Dic43—21no—
182C22×Dic43—21no—
183C22×Dic43C2×D411yescharacteristic
184C22×Dic43C2×D411yescharacteristic
185C22×Dic43C2×D411yescharacteristic
186C22×Dic43C2×D411yescharacteristic
187Q16×C43—28no—
188Q16×C43—44no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43C2×D412yes—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—42no—
198C22⋊C4×C43—42no—
199C22⋊Dic43—22no—
200C22⋊Dic43—22no—
201C22⋊Dic43—42no—
202C22⋊Dic43—42no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—42no—
212C4⋊Dic43—42no—
213C4⋊Dic43—42no—
214Dic43⋊C4—42no—
215C4×Dic43—21no—
216C4×Dic43—21no—
217C4×Dic43—21no—
218C4×Dic43—21no—
219C4×Dic43—42no—
220C4×Dic43—42no—
221C4×Dic43—42no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C23×C43—21no—
229C23×C43—21no—
230C23×C43—21no—
231C23×C43—21no—
232C23×C43—21no—
233C23×C43—21no—
234C23×C43#13512yes—
235C23×C43C22×D411yescharacteristic
236Q8×C43—22no—
237Q8×C43—22no—
238Q8×C43—22no—
239Q8×C43—22no—
240Q8×C43—22no—
241Q8×C43—22no—
242Q8×C43—22no—
243Q8×C43—48no—
244Q8×C43—41no—
245Q8×C43—41no—
246Q8×C43—41no—
247Q8×C43—41no—
248Q8×C43#12314yes—
249C2×C4×C43—22no—
250C2×C4×C43—22no—
251C2×C4×C43—22no—
252C2×C4×C43—22no—
253C2×C4×C43—21no—
254C2×C4×C43—22no—
255C2×C4×C43—21no—
256C2×C4×C43—21no—
257C2×C4×C43—48no—
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×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43—41no—
268C2×C4×C43—41no—
269C2×C4×C43C22×D411yescharacteristic
270C2×C4×C43C2×#4111yescharacteristic
271C2×C4×C43C2×#4111yescharacteristic
272C2×C4×C43C2×#4111yescharacteristic
273C2×C4×C43H(5,𝔽2)11yescharacteristic
274C2×C4×C43H(5,𝔽2)11yescharacteristic
275C2×Dic43—21no—
276C2×Dic43—21no—
277C2×Dic43—21no—
278C2×Dic43—21no—
279C2×Dic43—21no—
280C2×Dic43—21no—
281C2×Dic43—21no—
282C2×Dic43—21no—
283C2×Dic43—21no—
284C2×Dic43—21no—
285C2×Dic43—21no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289C2×Dic43—41no—
290C2×Dic43—41no—
291C2×Dic43—41no—
292C2×Dic43—41no—
293C2×Dic43—41no—
294C2×Dic43—41no—
295C2×Dic43—41no—
296C2×Dic43—41no—
297C2×Dic43—41no—
298C2×Dic43#13712yes—
299C8×C43—22no—
300C8×C43—41no—
301C43⋊C8—41no—
302C43⋊C8—41no—
303#24902—431nomaximal, Sylow
304C22×C43—22no—
305C22×C43—22no—
306C22×C43—22no—
307C22×C43—41no—
308C22×C43—41no—
309C22×C43—41no—
310C22×C43—41no—
311C22×C43#52511yescharacteristic
312C22×C43D4211yescharacteristic
313C22×C43#54611yescharacteristic
314C22×C43C2×#13511yescharacteristic
315C22×C43C2×#13711yescharacteristic
316C22×C43#57811yescharacteristic
317C22×C43#57811yescharacteristic
318C4×C43—24no—
319C4×C43—41no—
320C4×C43—42no—
321C4×C43—42no—
322C4×C43—81no—
323C4×C43C2×#12311yescharacteristic
324C4×C43#53811yescharacteristic
325C4×C43#54611yescharacteristic
326C4×C43#55111yescharacteristic
327Dic43—22no—
328Dic43—41no—
329Dic43—41no—
330Dic43—41no—
331Dic43—81no—
332Dic43—81no—
333Dic43—81no—
334Dic43—81no—
335C2×#451D4311yescharacteristic
336C2×C4×Q16—431no—
337#2421—431no—
338Q8×C22⋊C4—431no—
339#2097—431no—
340#2075—431no—
341#2056—431no—
342#2035—431no—
343#1933—431no—
344#1923—431no—
345#1878—431no—
346#1878—431no—
347#1865—431no—
348#1805—431no—
349#1787—431no—
350C2×C43—42no—
351C2×C43#241811yescharacteristic
352C2×C43#310811yescharacteristic
353C2×C43#312711yescharacteristic
354C2×C43#327011yescharacteristic
355C2×C43#328511yescharacteristic
356C2×C43#330011yescharacteristic
357C2×C43#332811yescharacteristic
358C23×Q8C2×D4311yescharacteristic
359C22×Q16C2×D4311yescharacteristic
360C22×Q16C2×D4311yescharacteristic
361C2×C22⋊Q8C2×D4311yescharacteristic
362C2×C4×Q8—431no—
363C2×C4×Q8—431no—
364C2×C4×Q8—431no—
365#451—24no—
366C4×Q16—864no—
367C2×#107—431no—
368C2×#106—431no—
369C2×C4⋊C8—431no—
370C2×#103—431no—
371C2×#103—431no—
372C2×#103—431no—
373C2×#103—431no—
374C2×#103—431no—
375C2×#103—431no—
376C2×#103C2×D4311yescharacteristic
377C2×#103C2×D4311yescharacteristic
378C2×C22⋊C8—431no—
379C2×C22⋊C8C2×D4311yescharacteristic
380C2×C4×C8—431no—
381#400—861no—
382#397—861no—
383#391—431no—
384#391—431no—
385#391—431no—
386#391—861no—
387#391—861no—
388#389—431no—
389#388—861no—
390#387—861no—
391#382—431no—
392#380—431no—
393#380—431no—
394#380—861no—
395C4×C22⋊C4—431no—
396C4×C22⋊C4—861no—
397#340—431no—
398#340—431no—
399#340—431no—
400#340—431no—
401#336—431no—
402#336—431no—
403C43#2490211yescharacteristic, complemented, Sylow
404C22×Q8—22no—
405C22×Q8—22no—
406C22×Q8—21no—
407C22×Q8—22no—
408C22×Q8—22no—
409C22×Q8—41no—
410C22×Q8—41no—
411C22×Q8C22×D4311yescharacteristic
412C22×Q8C22×D4311yescharacteristic
413C22×Q8C22×D4311yescharacteristic
414C23×C4—21no—
415C23×C4C22×D4311yescharacteristic
416C2×Q16—22no—
417C2×Q16—22no—
418C2×Q16—22no—
419C2×Q16—22no—
420C2×Q16—41no—
421C2×Q16C22⋊D4314yes—
422C22×C8—431no—
423C22×C8—431no—
424C22×C8C22×D4311yescharacteristic
425C22×C8C22×D4311yescharacteristic
426C22⋊Q8—22no—
427C22⋊Q8—41no—
428C4×Q8—862no—
429C4×Q8—862no—
430C4×Q8—862no—
431C4×Q8—1721no—
432C4×Q8—1721no—
433C4×Q8—1721no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—431no—
436C2×C4⋊C4—431no—
437C2×C4⋊C4—431no—
438C2×C4⋊C4—431no—
439C2×C4⋊C4—861no—
440C2×C4⋊C4—861no—
441C2×C4⋊C4—861no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4C22×D4311yescharacteristic
444C2×C22⋊C4—21no—
445C2×C22⋊C4—431no—
446C2×C22⋊C4—431no—
447C2×C22⋊C4—861no—
448C2×C22⋊C4—861no—
449C2×C42—431no—
450C2×C42—431no—
451C2×C42—861no—
452C2×C42—861no—
453C2×C42—861no—
454#107—862no—
455#106—1721no—
456C4⋊C8—1721no—
457#103—22no—
458#103—22no—
459#103—862no—
460#103—862no—
461#103—862no—
462#103—862no—
463#103—1721no—
464#103—1721no—
465C22⋊C8—22no—
466C22⋊C8—1721no—
467C4×C8—862no—
468#95—431no—
469#95—431no—
470#95—861no—
471#95—861no—
472#95—861no—
473#95—861no—
474#95—861no—
475#95—861no—
476#95—861no—
477#95—861no—
478#95—861no—
479#95—861no—
480#95—861no—
481C24D4×D4311yescharacteristic
482C2×Q8—24no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—42no—
497C2×Q8—42no—
498C2×Q8—44no—
499C2×Q8—44no—
500C2×Q8—44no—
501C2×Q8—44no—
502C2×Q8#1062190012yes—
503C2×Q8#1062190012yes—
504C2×Q8#1062190012yes—
505C2×Q8C2×C22⋊D4312yes—
506C2×Q8C2×C22⋊D4312yes—
507C22×C4—21no—
508C22×C4—24no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—431no—
521C22×C4—431no—
522C22×C4—431no—
523C22×C4—431no—
524C22×C4—861no—
525C22×C4—861no—
526C22×C4—861no—
527C22×C4—861no—
528C22×C4D4×D4311yescharacteristic
529C22×C4C23×D4311yescharacteristic
530Q16—28no—
531Q16—44no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—861no—
538C2×C8—861no—
539C2×C8—861no—
540C2×C8—861no—
541C2×C8—861no—
542C2×C8—861no—
543C2×C8C2×C22⋊D4312yes—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—42no—
547C4⋊C4—861no—
548C4⋊C4—861no—
549C4⋊C4—861no—
550C4⋊C4—861no—
551C4⋊C4—861no—
552C4⋊C4—861no—
553C4⋊C4—861no—
554C4⋊C4—861no—
555C4⋊C4—1722no—
556C4⋊C4—1722no—
557C4⋊C4—1722no—
558C4⋊C4—1722no—
559C22⋊C4—42no—
560C22⋊C4—862no—
561C22⋊C4—862no—
562C22⋊C4—1722no—
563C22⋊C4—1722no—
564C42—861no—
565C42—861no—
566C42—861no—
567C42—861no—
568C42—1722no—
569C42—1722no—
570C42—1722no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23#1306334812yes—
578C23C2×D4×D4311yescharacteristic
579Q8—22no—
580Q8—22no—
581Q8—22no—
582Q8—22no—
583Q8—22no—
584Q8—22no—
585Q8—22no—
586Q8—48no—
587Q8—41no—
588Q8—41no—
589Q8—41no—
590Q8—41no—
591Q8#1306330614yes—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—48no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—432no—
613C2×C4—861no—
614C2×C4—861no—
615C2×C4—861no—
616C2×C4—861no—
617C2×C4—861no—
618C2×C4—861no—
619C2×C4—861no—
620C2×C4—861no—
621C2×C4—861no—
622C2×C4—861no—
623C2×C4—861no—
624C2×C4—1721no—
625C2×C4—1721no—
626C2×C4—1721no—
627C2×C4—1721no—
628C2×C4—1721no—
629C2×C4—1721no—
630C2×C4—1721no—
631C2×C4—1721no—
632C2×C4—1721no—
633C2×C4—1721no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4C22×C22⋊D4311yescharacteristic
637C2×C4C2×#1062190011yescharacteristic
638C2×C4C2×#1062190011yescharacteristic
639C2×C4C2×#1062190011yescharacteristic
640C2×C4#1306337011yescharacteristic
641C2×C4#1306337011yescharacteristic
642C8—22no—
643C8—41no—
644C8—1721no—
645C8—1721no—
646C22—22no—
647C22—22no—
648C22—22no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22#1458340511yescharacteristic
654C22D4×C22⋊D4311yescharacteristic
655C22#1458353611yescharacteristic
656C22C2×#1306334811yescharacteristic
657C22#137×D4311yescharacteristic
658C22#1458371211yescharacteristic
659C22#1458371511yescharacteristic
660C4—24no—
661C4—41no—
662C4—42no—
663C4—42no—
664C4—81no—
665C4—862no—
666C4—3441no—
667C4—3441no—
668C4—3441no—
669C4—3441no—
670C4—1721no—
671C4—1721no—
672C4—1721no—
673C4C2×#1306330611yescharacteristic
674C4#1458348411yescharacteristic
675C4#1458354311yescharacteristic
676C4#1458358011yescharacteristic
677C2—42no—
678C2#1913805311yescharacteristic
679C2#1914467611yescharacteristic
680C2#1914488911yescharacteristic
681C2#1914615911yescharacteristic
682C2#1914633611yescharacteristic
683C2#1914648611yescharacteristic
684C2#1914687111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#451C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenterC2×#451D43
hypocenterC43#24902
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
1. C2×Q16×Dic43C2semidirect
4. #19136141C2semidirect
6. #19135915C2semidirect
8. #19135268C2semidirect
10. #19134938C2semidirect
11. #19134938C2semidirect
12. #19134861C2semidirect
13. #19134608C2semidirect
403. C43#24902semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×Dic432
#191380942
Q8×C22⋊Dic432
#191361412
#191360182
#191359152
#191357882
#191352682
#191351982
#191349382
#191348612
#191346082
#191345302
C2×C43×#4512
#2490243