Finite Group Databasebeta

← #25146317

Subgroups — #25146317

Order 11008.

856 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×#14583028C211yesmaximal, characteristic, complemented
2#19140084C211yesmaximal, characteristic, complemented
3#19139517C211yesmaximal, characteristic, complemented
4#19135974C211yesmaximal, characteristic, complemented
5#19135967C211yesmaximal, characteristic, complemented
6#19135908C211yesmaximal, characteristic, complemented
7#19135903C211yesmaximal, characteristic
8#19135472C211yesmaximal, characteristic
9#19135451C211yesmaximal, characteristic, complemented
10#19135412C211yesmaximal, characteristic, complemented
11#19135359C211yesmaximal, characteristic, complemented
12#19135282C211yesmaximal, characteristic, complemented
13#19135275C211yesmaximal, characteristic, complemented
14#19134420C211yesmaximal, characteristic, complemented
15C2×C43×#463C211yesmaximal, characteristic
16C2×#13063304—21no—
17C2×C4×Dic86C2211yescharacteristic
18#14583028—24no—
19C2×#13063257C2211yescharacteristic
20C2×#13063257C2211yescharacteristic
21C2×Dic43⋊C8C2211yescharacteristic
22C2×Dic43⋊C8C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063236C2211yescharacteristic
30C2×#13063235C2211yescharacteristic
31C2×C8×Dic43C2211yescharacteristic
32#14582824—21no—
33#14582822—21no—
34#14582822—21no—
35#14582811—21no—
36#14582806C2211yescharacteristic
37#14582806C2211yescharacteristic
38#14582802C2211yescharacteristic
39#14582802C2211yescharacteristic
40#14582802C2211yescharacteristic
41#14582802C2211yescharacteristic
42#14582795C2211yescharacteristic
43#14582795C2211yescharacteristic
44#14582793—21no—
45#14582793—21no—
46#14582769C2211yescharacteristic
47#14582759—21no—
48C4×C4⋊Dic43C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53C22×SD16×C43C2211yescharacteristic
54C22×D8×C43C2211yescharacteristic
55C2×#124×C43C2211yescharacteristic
56C2×C4×D4×C43C2211yescharacteristic
57C43×#463—24no—
58C2×C4⋊C8×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C22×Dic86D411yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64#13063304—44no—
65C4×Dic86—22no—
66C4×Dic86—22no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43D411yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4D411yescharacteristic
77C2×Dic43⋊C4D411yescharacteristic
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×C22⋊Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43C2311yescharacteristic
88C2×C4×Dic43C2311yescharacteristic
89#13063257—41no—
90#13063257—41no—
91Dic43⋊C8—22no—
92Dic43⋊C8—22no—
93#13063249—22no—
94#13063249—41no—
95#13063246—22no—
96#13063246—22no—
97#13063246—22no—
98#13063246—41no—
99#13063236—22no—
100#13063235—22no—
101C8×Dic43—22no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C22×Q8×C43C2311yescharacteristic
110C22×D4×C43C2311yescharacteristic
111C22×D4×C43C2311yescharacteristic
112C23×C4×C43—21no—
113C2×SD16×C43—22no—
114C2×SD16×C43—22no—
115C2×SD16×C43—41no—
116C2×D8×C43—22no—
117C2×D8×C43—22no—
118C2×D8×C43—41no—
119C22×C8×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121#124×C43—22no—
122#124×C43—22no—
123C4×D4×C43—22no—
124C4×D4×C43—22no—
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C42×C43C2311yescharacteristic
130C4⋊C8×C43D414yes—
131#103×C43—22no—
132#102×C43—22no—
133C24×C43—21no—
134C24×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43—21no—
140C2×Q8×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—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43#4112yes—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—42no—
156C22×C4×C43—42no—
157C22×C4×C43—42no—
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2411yescharacteristic
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43C2×D411yescharacteristic
166C22×Dic43C2×D411yescharacteristic
167C22×Dic43C2×D411yescharacteristic
168C22×Dic43C2×D411yescharacteristic
169C2×Dic86—22no—
170C2×Dic86—22no—
171C2×Dic86—41no—
172SD16×C43—44no—
173D8×C43—44no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43C2×D412yes—
179C2×C8×C43C2×D412yes—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C22⋊C4×C43—42no—
183C22⋊C4×C43—42no—
184C22⋊C4×C43—42no—
185C42×C43C2×D412yes—
186C42×C43#4112yes—
187C22⋊Dic43—42no—
188C22⋊Dic43—42no—
189C22⋊Dic43—42no—
190C22⋊Dic43—42no—
191C22⋊Dic43—81no—
192C22⋊Dic43—81no—
193C22⋊Dic43—81no—
194C22⋊Dic43—81no—
195C4⋊Dic43—22no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—42no—
205C4⋊Dic43—81no—
206Dic43⋊C4—22no—
207Dic43⋊C4—22no—
208Dic43⋊C4—42no—
209Dic43⋊C4—42no—
210C4×Dic43—21no—
211C4×Dic43—21no—
212C4×Dic43—21no—
213C4×Dic43—21no—
214C4×Dic43—81no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8#4112yes—
221C23×C43—22no—
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×C43C22×D411yescharacteristic
236Q8×C43—41no—
237Q8×C43—41no—
238Q8×C43—41no—
239Q8×C43—41no—
240D4×C43—22no—
241D4×C43—22no—
242D4×C43—41no—
243D4×C43—41no—
244D4×C43—41no—
245D4×C43—41no—
246D4×C43—41no—
247D4×C43—41no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—84no—
259C2×C4×C43#12112yes—
260C2×C4×C43#12112yes—
261C2×C4×C43C22×D411yescharacteristic
262C2×C4×C43C2×#4111yescharacteristic
263C2×C4×C43C2×#4111yescharacteristic
264C2×C4×C43C2×#4111yescharacteristic
265C2×C4×C43H(5,𝔽2)11yescharacteristic
266C2×C4×C432−1+411yescharacteristic
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—21no—
277C2×Dic43—21no—
278C2×Dic43—41no—
279C2×Dic43—41no—
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—41no—
289C2×Dic43—41no—
290C2×Dic43AGL(1,ℤ/8)12yes—
291Dic86—44no—
292C8×C43—22no—
293C8×C43—22no—
294C43⋊C8—22no—
295C43⋊C8—41no—
296#25309—431nomaximal, Sylow
297C22×C43—42no—
298C22×C43—42no—
299C22×C43—42no—
300C22×C43—81no—
301C22×C43—81no—
302C22×C43—81no—
303C22×C43—81no—
304C22×C43—81no—
305C22×C43—81no—
306C22×C43—81no—
307C22×C43—81no—
308C22×C43—81no—
309C22×C43—81no—
310C22×C43—81no—
311C22×C43C2×#12111yescharacteristic
312C22×C43#54811yescharacteristic
313C22×C43#55011yescharacteristic
314C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
315C22×C43#57511yescharacteristic
316C22×C43#57711yescharacteristic
317C22×C43#57711yescharacteristic
318C4×C43—22no—
319C4×C43—22no—
320C4×C43—81no—
321C4×C43—81no—
322C4×C43#52911yescharacteristic
323C4×C43#54211yescharacteristic
324C4×C43#54611yescharacteristic
325C4×C43#54811yescharacteristic
326Dic43—22no—
327Dic43—41no—
328Dic43—41no—
329Dic43—41no—
330Dic43—81no—
331Dic43—81no—
332Dic43—81no—
333Dic43—81no—
334C2×#463D4311yescharacteristic
335C2×#446—431no—
336#2592—431no—
337#2538—431no—
338#2066—431no—
339#2065—431no—
340#2055—431no—
341#2054—431no—
342#1972—431no—
343#1968—431no—
344#1959—431no—
345#1948—431no—
346#1935—431no—
347#1934—431no—
348#1762—431no—
349C2×C43—82no—
350C2×C43—161no—
351C2×C43#242611yescharacteristic
352C2×C43#305511yescharacteristic
353C2×C43#306011yescharacteristic
354C2×C43#337311yescharacteristic
355C2×C43#337611yescharacteristic
356C2×C43#339711yescharacteristic
357C2×C43#340111yescharacteristic
358C22×SD16C2×D4311yescharacteristic
359C22×D8C2×D4311yescharacteristic
360C2×#124C2×D4311yescharacteristic
361C2×C22⋊Q8—861no—
362C2×C4×Q8—431no—
363C2×C4×D4C2×D4311yescharacteristic
364#463—24no—
365#446—864no—
366C2×#106—431no—
367C2×#106—431no—
368C2×C4⋊C8—431no—
369C2×C4⋊C8—431no—
370C2×C4⋊C8C2×D4311yescharacteristic
371C2×#103—431no—
372C2×#103—431no—
373C2×#103C2×D4311yescharacteristic
374C2×#102—431no—
375C2×#102—431no—
376C2×#102—431no—
377C2×#102—431no—
378C2×#102C2×D4311yescharacteristic
379C2×#97—431no—
380C2×#97—431no—
381C2×C4×C8—431no—
382#397—861no—
383#396—861no—
384#396—861no—
385#393—861no—
386#391—431no—
387#391—431no—
388#390—431no—
389#390—431no—
390#390—431no—
391#390—431no—
392#389—431no—
393#389—431no—
394#388—861no—
395#388—861no—
396#384—431no—
397#380—861no—
398C4×C4⋊C4—431no—
399#340—431no—
400#340—431no—
401#340—431no—
402#340—431no—
403C43#2530911yescharacteristic, complemented, Sylow
404C22×Q8—431no—
405C22×Q8C22×D4311yescharacteristic
406C22×D4C22×D4311yescharacteristic
407C22×D4C22×D4311yescharacteristic
408C23×C4—21no—
409C2×SD16—22no—
410C2×SD16—22no—
411C2×SD16—41no—
412C2×D8—22no—
413C2×D8—22no—
414C2×D8—41no—
415C22×C8—431no—
416C22×C8—431no—
417C22×C8C22×D4311yescharacteristic
418C22×C8C22×D4311yescharacteristic
419#124—22no—
420#124—22no—
421C22⋊Q8—1724no—
422C4×Q8—862no—
423C4×Q8—862no—
424C4×D4—22no—
425C4×D4—22no—
426C2×C4⋊C4—431no—
427C2×C4⋊C4—431no—
428C2×C4⋊C4—431no—
429C2×C4⋊C4—431no—
430C2×C4⋊C4—431no—
431C2×C4⋊C4—431no—
432C2×C4⋊C4—431no—
433C2×C4⋊C4—861no—
434C2×C4⋊C4—861no—
435C2×C4⋊C4—861no—
436C2×C4⋊C4—861no—
437C2×C4⋊C4C22×D4311yescharacteristic
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—861no—
442C2×C22⋊C4—861no—
443C2×C22⋊C4—861no—
444C2×C22⋊C4—861no—
445C2×C22⋊C4—861no—
446C2×C22⋊C4—861no—
447C2×C22⋊C4—861no—
448C2×C22⋊C4—861no—
449C2×C42—431no—
450C2×C42—431no—
451C2×C42—861no—
452C2×C42C22×D4311yescharacteristic
453#106—1721no—
454#106—1721no—
455C4⋊C8—862no—
456C4⋊C8—862no—
457C4⋊C8C22⋊D4314yes—
458#103—22no—
459#103—862no—
460#103—1721no—
461#102—22no—
462#102—862no—
463#102—862no—
464#102—862no—
465#102—1721no—
466#97—862no—
467#97—862no—
468C4×C8—862no—
469#95—861no—
470#95—861no—
471#95—861no—
472#95—861no—
473#95—861no—
474#95—861no—
475#95—861no—
476C24—21no—
477C24—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—862no—
485C2×Q8—862no—
486C2×Q8—1721no—
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#1062190012yes—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—431no—
505C22×C4—431no—
506C22×C4—431no—
507C22×C4—431no—
508C22×C4—861no—
509C22×C4—861no—
510C22×C4—861no—
511C22×C4—861no—
512C22×C4D4×D4311yescharacteristic
513C22×C4D4×D4311yescharacteristic
514C22×C4C23×D4311yescharacteristic
515SD16—44no—
516D8—44no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—432no—
522C2×C8—861no—
523C2×C8—861no—
524C2×C8—861no—
525C2×C8—861no—
526C2×C8—861no—
527C2×C8C2×C22⋊D4312yes—
528C2×C8C2×C22⋊D4312yes—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—862no—
532C4⋊C4—862no—
533C4⋊C4—862no—
534C4⋊C4—861no—
535C4⋊C4—861no—
536C4⋊C4—861no—
537C4⋊C4—861no—
538C4⋊C4—861no—
539C4⋊C4—861no—
540C4⋊C4—861no—
541C4⋊C4—861no—
542C4⋊C4—3441no—
543C4⋊C4—1722no—
544C4⋊C4—1722no—
545C4⋊C4—1722no—
546C22⋊C4—42no—
547C22⋊C4—42no—
548C22⋊C4—42no—
549C22⋊C4—3441no—
550C22⋊C4—3441no—
551C22⋊C4—3441no—
552C22⋊C4—3441no—
553C22⋊C4—1722no—
554C22⋊C4—1722no—
555C22⋊C4—1722no—
556C22⋊C4—1722no—
557C42—861no—
558C42—861no—
559C42—861no—
560C42—861no—
561C42—3441no—
562C42#1062190012yes—
563C42C2×C22⋊D4312yes—
564C23—22no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23C2×D4×D4311yescharacteristic
579Q8—41no—
580Q8—41no—
581Q8—41no—
582Q8—41no—
583Q8—1724no—
584D4—22no—
585D4—22no—
586D4—41no—
587D4—41no—
588D4—41no—
589D4—41no—
590D4—41no—
591D4—41no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—84no—
603C2×C4—432no—
604C2×C4—861no—
605C2×C4—861no—
606C2×C4—861no—
607C2×C4—861no—
608C2×C4—861no—
609C2×C4—861no—
610C2×C4—861no—
611C2×C4—861no—
612C2×C4—861no—
613C2×C4—861no—
614C2×C4—861no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4—1721no—
620C2×C4—1721no—
621C2×C4—1721no—
622C2×C4—1721no—
623C2×C4—1721no—
624C2×C4—1721no—
625C2×C4—1721no—
626C2×C4—1721no—
627C2×C4#1306329612yes—
628C2×C4#1306329612yes—
629C2×C4C22×C22⋊D4311yescharacteristic
630C2×C4#41×D4311yescharacteristic
631C2×C4C2×#1062190011yescharacteristic
632C2×C4C2×#1062190011yescharacteristic
633C2×C4#1306337011yescharacteristic
634C2×C4#1306337211yescharacteristic
635C8—22no—
636C8—22no—
637C8—862no—
638C8—1721no—
639C22—42no—
640C22—42no—
641C22—42no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22—81no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22C2×#1306329611yescharacteristic
654C22#1458355511yescharacteristic
655C22#1458356711yescharacteristic
656C22AGL(1,ℤ/8)×D4311yescharacteristic
657C22#1458369511yescharacteristic
658C22#1458370611yescharacteristic
659C22#1458370611yescharacteristic
660C4—22no—
661C4—22no—
662C4—81no—
663C4—81no—
664C4—862no—
665C4—3441no—
666C4—3441no—
667C4—3441no—
668C4—3441no—
669C4—1721no—
670C4—1721no—
671C4—1721no—
672C4#1458343011yescharacteristic
673C4#1458351611yescharacteristic
674C4#1458354311yescharacteristic
675C4#1458355611yescharacteristic
676C2—82no—
677C2—161no—
678C2#1913815711yescharacteristic
679C2#1914420811yescharacteristic
680C2#1914425311yescharacteristic
681C2#1914738211yescharacteristic
682C2#1914741911yescharacteristic
683C2#1914761811yescharacteristic
684C2#1914765811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#463C2
socleC23×C43C22×D4
prime radicalC22×D8×C43C22
hypercenterC2×#463D43
hypocenterC43#25309
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#14583028C2semidirect
2. #19140084C2semidirect
3. #19139517C2semidirect
4. #19135974C2semidirect
5. #19135967C2semidirect
6. #19135908C2semidirect
9. #19135451C2semidirect
10. #19135412C2semidirect
11. #19135359C2semidirect
12. #19135282C2semidirect
13. #19135275C2semidirect
14. #19134420C2semidirect
403. C43#25309semidirect

Maximal subgroups

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

subgroupindex
C2×#145830282
#191400842
#191395172
#191359742
#191359672
#191359082
#191359032
#191354722
#191354512
#191354122
#191353592
#191352822
#191352752
#191344202
C2×C43×#4632
#2530943