Finite Group Databasebeta

← #25124135

Subgroups — #25124135

Order 11008.

1482 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583477C211yesmaximal, characteristic
2C2×#14582941C211yesmaximal, characteristic, complemented
3C2×#14582895C211yesmaximal, characteristic, complemented
4C2×#14582867C211yesmaximal, characteristic, complemented
5#19137188C211yesmaximal, characteristic, complemented
6#19135797C212yesmaximal, complemented
7#19135790C212yesmaximal, complemented
8#19135783C212yesmaximal, complemented
9#19135776C212yesmaximal, complemented
10C2×#14582661C211yesmaximal, characteristic, complemented
11C2×C43×#417C211yesmaximal, characteristic, complemented
12C22×#10621898C2211yescharacteristic
13C23×C43⋊C8C2211yescharacteristic
14#14583477—24no—
15#14583477—24no—
16C2×#13063304—21no—
17C2×#13063301C2212yes—
18C2×#13063299—21no—
19C2×#13063297—22no—
20C2×#13063296C2212yes—
21C2×#13063284C2211yescharacteristic
22C22×C4⋊Dic43C2211yescharacteristic
23#14582941—24no—
24C2×#13063259C2212yes—
25C2×#13063257C2212yes—
26#14582895—24no—
27C2×#13063249C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31#14582867—24no—
32C2×(C2×D43)⋊C8C2212yes—
33C2×(C2×D43)⋊C8C2212yes—
34#14582804—21no—
35#14582800—21no—
36#14582778—22no—
37#14582756C2212yes—
38#14582756C2212yes—
39#14582661C2212yes—
40#14582661C2212yes—
41C22×#41×C43C2211yescharacteristic
42C22×M16×C43C2211yescharacteristic
43C22×C4⋊C4×C43C2211yescharacteristic
44C43×#417—24no—
45C2×#103×C43C2212yes—
46C2×#102×C43C2212yes—
47C2×#10621898—22no—
48C2×#10621898—22no—
49C2×#10621898—22no—
50C2×#10621898—22no—
51C2×#10621898—22no—
52C2×#10621898—22no—
53C22×Dic86D411yescharacteristic
54C22×D172D411yescharacteristic
55C22×C22⋊D43—22no—
56C22×C22⋊D43D412yes—
57C23×Dic43—21no—
58C22×C4×D43C2312yes—
59C22×C43⋊C8—22no—
60C22×C43⋊C8—22no—
61C22×C43⋊C8—22no—
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64#13063304—28no—
65#13063301—24no—
66#13063301—24no—
67#13063299—28no—
68#13063297—216no—
69#13063296—24no—
70#13063296—24no—
71#13063284—22no—
72#13063284—22no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43—22no—
75C2×C4⋊Dic43D414yes—
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2312yes—
79C2×Dic43⋊C4—22no—
80C2×C22⋊Dic43—22no—
81C2×C22⋊Dic43—21no—
82C2×(C2×D43)⋊C4—22no—
83C2×(C2×D43)⋊C4—22no—
84C2×(C2×D43)⋊C4—22no—
85C2×C4×Dic43—21no—
86#13063259—24no—
87#13063257—24no—
88#13063249—22no—
89#13063249—22no—
90#13063246—22no—
91#13063246—22no—
92(C2×D43)⋊C8—24no—
93(C2×D43)⋊C8—24no—
94C43⋊#95—22no—
95C43⋊#95—22no—
96C2×#41×C43—22no—
97C2×#41×C43—22no—
98C2×#41×C43—22no—
99C2×#41×C43—22no—
100C2×#41×C43—22no—
101C2×#41×C43D414yes—
102C22×Q8×C43C2311yescharacteristic
103C22×D4×C43—21no—
104C22×D4×C43C2311yescharacteristic
105C23×C4×C43—21no—
106C23×C4×C43—21no—
107C23×C4×C43C2311yescharacteristic
108C2×M16×C43—22no—
109C2×M16×C43—22no—
110C2×M16×C43D414yescomplemented
111C22×C8×C43C2312yes—
112C2×C4⋊C4×C43—22no—
113C2×C4⋊C4×C43—22no—
114C2×C4⋊C4×C43—21no—
115C2×C4⋊C4×C43C2312yes—
116#103×C43—24no—
117#102×C43—24no—
118C24×C43—21no—
119C24×C43C2×D411yescharacteristic
120C23×D43C2×D412yes—
121#41×C43—28no—
122#41×C43—28no—
123#41×C43—44no—
124#41×C43—44no—
125C2×Q8×C43—21no—
126C2×Q8×C43—21no—
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43C2×D412yes—
131C2×D4×C43—21no—
132C2×D4×C43—24no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—42no—
138C2×D4×C43—42no—
139C2×D4×C43C2×D412yes—
140C22×C4×C43—24no—
141C22×C4×C43—21no—
142C22×C4×C43—22no—
143C22×C4×C43—42no—
144C22×C4×C43—42no—
145C22×C4×C43—42no—
146C22×C4×C43—81no—
147C22×C4×C43—81no—
148C22×C4×C43C2×D412yes—
149C22×C4×C43C2×D412yes—
150C22×C4×C43C2×D412yes—
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43#4112yes—
153C22×C4×C43#4112yes—
154C22×C4×C43#4112yes—
155C22×C4×C43C2411yescharacteristic
156C2×C22⋊D43—28no—
157C2×C22⋊D43—24no—
158C2×C22⋊D43—24no—
159C2×C22⋊D43—24no—
160C2×C22⋊D43—82no—
161C2×C22⋊D43—82no—
162C22×Dic43—24no—
163C22×Dic43—22no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—81no—
167C22×Dic43—81no—
168C22×Dic43C2×D412yes—
169#10621898—44no—
170#10621898—44no—
171#10621898—44no—
172#10621898—44no—
173C2×D172—22no—
174C2×D172—22no—
175C2×D172—22no—
176C2×C4×D43—22no—
177C2×C4×D43—22no—
178C2×C4×D43—22no—
179C2×C4×D43—22no—
180C2×C4×D43—22no—
181C2×C4×D43—22no—
182C2×Dic86—22no—
183C2×Dic86—22no—
184C2×Dic86—22no—
185M16×C43—28no—
186C2×C8×C43—22no—
187C2×C8×C43—22no—
188C2×C8×C43C2×D414yes—
189C4⋊C4×C43—22no—
190C4⋊C4×C43—22no—
191C4⋊C4×C43—42no—
192C22⋊Dic43—28no—
193C22⋊Dic43—42no—
194(C2×D43)⋊C4—28no—
195(C2×D43)⋊C4—82no—
196(C2×D43)⋊C4—82no—
197C4⋊Dic43—24no—
198C4⋊Dic43—22no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43C2×D414yes—
204Dic43⋊C4—28no—
205C4×Dic43—42no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—44no—
213C23×C43—21no—
214C23×C43—21no—
215C23×C43—21no—
216C23×C43—21no—
217C23×C43—22no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43#12012yes—
225C23×C43#12112yes—
226C23×C43#12312yes—
227C23×C43C22×D411yescharacteristic
228C22×D43—22no—
229C22×D43—22no—
230C22×D43—22no—
231C22×D43—22no—
232C22×D43—22no—
233C22×D43—22no—
234C22×D43—22no—
235Q8×C43—22no—
236Q8×C43—22no—
237Q8×C43—41no—
238Q8×C43—41no—
239D4×C43—22no—
240D4×C43—22no—
241D4×C43—48no—
242D4×C43—41no—
243D4×C43—41no—
244C2×C4×C43—22no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—48no—
248C2×C4×C43—42no—
249C2×C4×C43—42no—
250C2×C4×C43—42no—
251C2×C4×C43—84no—
252C2×C4×C43#12012yes—
253C2×C4×C43#12112yes—
254C2×C4×C43#12114yes—
255C2×C4×C43#12114yes—
256C2×C4×C43#12312yes—
257C2×C4×C43#12314yes—
258C2×C4×C43#12414yes—
259C2×C4×C43C22×D411yescharacteristic
260C2×C4×C43C22×D411yescharacteristic
261C2×C4×C43C22×D411yescharacteristic
262C2×C4×C43C2×#4111yescharacteristic
263C2×C4×C43C2×#4111yescharacteristic
264C2×C4×C43C2×#4111yescharacteristic
265C22⋊D43—48no—
266C22⋊D43—88no—
267C2×Dic43—22no—
268C2×Dic43—24no—
269C2×Dic43—22no—
270C2×Dic43—22no—
271C2×Dic43—42no—
272C2×Dic43—42no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—84no—
280D172—44no—
281C4×D43—42no—
282C4×D43—42no—
283C4×D43—42no—
284C4×D43—42no—
285Dic86—44no—
286C8×C43—24no—
287C43⋊C8—41no—
288C43⋊C8—41no—
289#23485—431nomaximal, Sylow
290C22×C43—22no—
291C22×C43—22no—
292C22×C43—22no—
293C22×C43—22no—
294C22×C43—22no—
295C22×C43—22no—
296C22×C43—42no—
297C22×C43—42no—
298C22×C43—42no—
299C22×C43—81no—
300C22×C43—81no—
301C22×C43—81no—
302C22×C43—81no—
303C22×C43#39414yes—
304C22×C43C2×#12011yescharacteristic
305C22×C43C2×#12111yescharacteristic
306C22×C43C2×#12311yescharacteristic
307C22×C43#57611yescharacteristic
308C22×C43#57711yescharacteristic
309C22×C43#57711yescharacteristic
310C22×C43#57811yescharacteristic
311C2×D43—42no—
312C2×D43—42no—
313C2×D43—42no—
314C2×D43—42no—
315C2×D43—42no—
316C2×D43—42no—
317C2×D43—42no—
318C4×C43—42no—
319C4×C43—82no—
320C4×C43#39414yes—
321C4×C43C2×#12111yescharacteristic
322C4×C43C2×#12111yescharacteristic
323C4×C43C2×#12311yescharacteristic
324C4×C43C2×#12411yescharacteristic
325Dic43—42no—
326Dic43—44no—
327Dic43—81no—
328Dic43—81no—
329C2×#537—431no—
330C2×#428—431no—
331C2×#417D4311yescharacteristic, complemented
332C2×#416—431no—
333C2×#408—431no—
334#2311—431no—
335#2036—432no—
336#2035—432no—
337#2034—432no—
338#2033—432no—
339C2×#340—431no—
340C2×C43—24no—
341C2×C43—82no—
342C2×C43C2×#39411yescharacteristic
343C2×C43#301211yescharacteristic
344C2×C43#301311yescharacteristic
345C2×C43#306211yescharacteristic
346C2×C43#306311yescharacteristic
347C2×C43#309811yescharacteristic
348C2×C43#309911yescharacteristic
349D43—82no—
350C22×#41—431no—
351C22×#41C2×D4311yescharacteristic
352C22×M16C2×D4311yescharacteristic
353C23×C8—431no—
354#537—864no—
355#537—864no—
356C2×C22⋊Q8—432no—
357C2×C22⋊Q8—861no—
358C2×#121—432no—
359C2×#121—861no—
360C2×#121—862no—
361C2×#117—431no—
362C22×C4⋊C4—431no—
363C22×C4⋊C4C2×D4311yescharacteristic
364#428—864no—
365C2×#107—432no—
366C2×#106—432no—
367#417—24no—
368#416—864no—
369C2×#103—431no—
370C2×#103—431no—
371C2×#103C2×D4312yes—
372C2×#102—431no—
373C2×#102—431no—
374C2×#102C2×D4312yes—
375#408—864no—
376C2×C22⋊C8—432no—
377C2×C22⋊C8—432no—
378#391—861no—
379#390—861no—
380#386—862no—
381#380—432no—
382#380—432no—
383#340—432no—
384#340—432no—
385C43#2348511yescharacteristic, complemented, Sylow
386C2×#41—22no—
387C2×#41—22no—
388C2×#41—22no—
389C2×#41—22no—
390C2×#41—22no—
391C2×#41—862no—
392C2×#41—862no—
393C2×#41—862no—
394C2×#41—862no—
395C2×#41—862no—
396C2×#41—862no—
397C2×#41D17214yes—
398C22×Q8—431no—
399C22×Q8C22×D4311yescharacteristic
400C22×D4—21no—
401C22×D4—432no—
402C22×D4—431no—
403C22×D4—862no—
404C22×D4C22×D4311yescharacteristic
405C23×C4—21no—
406C23×C4—21no—
407C23×C4—432no—
408C23×C4—861no—
409C23×C4C22×D4311yescharacteristic
410C2×M16—22no—
411C2×M16—22no—
412C2×M16C22⋊D4314yescomplemented
413C22×C8—431no—
414C22×C8—431no—
415C22×C8—862no—
416C22×C8—862no—
417C22×C8—862no—
418C22×C8C22×D4312yes—
419C22⋊Q8—864no—
420C22⋊Q8—868no—
421C22⋊Q8—864no—
422#121—864no—
423#121—868no—
424#121—8616no—
425#121—864no—
426#117—862no—
427#117—862no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—434no—
432C2×C4⋊C4—432no—
433C2×C4⋊C4—431no—
434C2×C4⋊C4—431no—
435C2×C4⋊C4—862no—
436C2×C4⋊C4—862no—
437C2×C4⋊C4—861no—
438C2×C4⋊C4C22×D4312yes—
439C2×C22⋊C4—862no—
440C2×C22⋊C4—862no—
441C2×C22⋊C4—862no—
442C2×C22⋊C4—862no—
443C2×C22⋊C4—861no—
444C2×C42—861no—
445#107—864no—
446#106—864no—
447#103—24no—
448#103—862no—
449#103—862no—
450#102—24no—
451#102—862no—
452#102—862no—
453C22⋊C8—864no—
454C22⋊C8—864no—
455#95—862no—
456#95—862no—
457C24—21no—
458C24—432no—
459C24D4×D4311yescharacteristic
460#41—28no—
461#41—28no—
462#41—44no—
463#41—44no—
464#41—1724no—
465#41—1724no—
466#41—1724no—
467#41—1724no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—862no—
474C2×Q8—862no—
475C2×Q8—862no—
476C2×Q8C2×D17212yes—
477C2×D4—24no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—42no—
484C2×D4—42no—
485C2×D4—868no—
486C2×D4—864no—
487C2×D4—864no—
488C2×D4—864no—
489C2×D4—862no—
490C2×D4—862no—
491C2×D4—862no—
492C2×D4—3442no—
493C2×D4—3442no—
494C2×D4C2×D17212yes—
495C22×C4—21no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—81no—
502C22×C4—81no—
503C22×C4—432no—
504C22×C4—864no—
505C22×C4—862no—
506C22×C4—862no—
507C22×C4—862no—
508C22×C4—862no—
509C22×C4—862no—
510C22×C4—862no—
511C22×C4—862no—
512C22×C4—861no—
513C22×C4—861no—
514C22×C4—3441no—
515C22×C4—3441no—
516C22×C4C2×D17212yes—
517C22×C4#1062189812yes—
518C22×C4D4×D4311yescharacteristic
519C22×C4D4×D4312yes—
520C22×C4#1062190012yes—
521C22×C4#1062190012yes—
522C22×C4C2×C22⋊D4312yes—
523C22×C4C23×D4311yescharacteristic
524M16—28no—
525C2×C8—22no—
526C2×C8—22no—
527C2×C8—861no—
528C2×C8—861no—
529C2×C8—861no—
530C2×C8—861no—
531C2×C8—861no—
532C2×C8—861no—
533C2×C8—1724no—
534C2×C8C2×C22⋊D4314yes—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—42no—
538C4⋊C4—434no—
539C4⋊C4—868no—
540C4⋊C4—864no—
541C4⋊C4—862no—
542C4⋊C4—861no—
543C4⋊C4—861no—
544C4⋊C4—861no—
545C4⋊C4—861no—
546C22⋊C4—868no—
547C22⋊C4—868no—
548C22⋊C4—3442no—
549C22⋊C4—3442no—
550C22⋊C4—1722no—
551C42—1722no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—22no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—862no—
564C23—862no—
565C23—862no—
566C23—862no—
567C23—862no—
568C23—862no—
569C23—862no—
570C23#1306329512yes—
571C23#1306329612yes—
572C23#1306330712yes—
573C23C2×D4×D4311yescharacteristic
574Q8—22no—
575Q8—22no—
576Q8—41no—
577Q8—41no—
578Q8—1724no—
579D4—22no—
580D4—22no—
581D4—48no—
582D4—41no—
583D4—41no—
584D4—3448no—
585D4—1728no—
586D4—1724no—
587C2×C4—22no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—48no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—84no—
595C2×C4—864no—
596C2×C4—862no—
597C2×C4—862no—
598C2×C4—862no—
599C2×C4—3444no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1722no—
607C2×C4—1722no—
608C2×C4—1722no—
609C2×C4—1722no—
610C2×C4—1722no—
611C2×C4—1722no—
612C2×C4#1306329512yes—
613C2×C4#1306329612yes—
614C2×C4#1306329714yes—
615C2×C4#1306329914yes—
616C2×C4#1306330712yes—
617C2×C4#1306330914yes—
618C2×C4#1306331114yes—
619C2×C4C2×D4×D4311yescharacteristic
620C2×C4C22×C22⋊D4311yescharacteristic
621C2×C4C22×D17211yescharacteristic
622C2×C4C2×#1062190011yescharacteristic
623C2×C4C2×#1062190011yescharacteristic
624C2×C4C2×#1062189811yescharacteristic
625C8—24no—
626C8—1721no—
627C8—1721no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—22no—
633C22—22no—
634C22—42no—
635C22—42no—
636C22—42no—
637C22—81no—
638C22—81no—
639C22—81no—
640C22—81no—
641C22—1722no—
642C22—1722no—
643C22—1722no—
644C22—1722no—
645C22—1722no—
646C22—1722no—
647C22—1722no—
648C22#1458281514yes—
649C22C2×#1306329511yescharacteristic
650C22C2×#1306329611yescharacteristic
651C22C2×#1306330711yescharacteristic
652C22#1458370311yescharacteristic
653C22#1458370811yescharacteristic
654C22#1458370911yescharacteristic
655C22#1458371511yescharacteristic
656C4—42no—
657C4—82no—
658C4—3441no—
659C4—3441no—
660C4—1722no—
661C4—1724no—
662C4#1458281514yes—
663C4C2×#1306329711yescharacteristic
664C4C2×#1306329911yescharacteristic
665C4C2×#1306330911yescharacteristic
666C4C2×#1306331111yescharacteristic
667C2—24no—
668C2—82no—
669C2—3442no—
670C2C2×#1458281511yescharacteristic
671C2#1914390111yescharacteristic
672C2#1914391211yescharacteristic
673C2#1914426911yescharacteristic
674C2#1914428011yescharacteristic
675C2#1914457211yescharacteristic
676C2#1914458311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#417C2
socleC23×C43C22×D4
prime radicalC2×#14583477C2
hypercenterC2×#417D43
hypocenterC43#23485
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C2×#14582941C2semidirect
3. C2×#14582895C2semidirect
4. C2×#14582867C2semidirect
5. #19137188C2semidirect
6. #19135797C2semidirect
7. #19135790C2semidirect
8. #19135783C2semidirect
9. #19135776C2semidirect
10. C2×#14582661C2semidirect
11. C2×C43×#417C2semidirect
110. C2×M16×C43D4semidirect
331. C2×#417D43semidirect
385. C43#23485semidirect
412. C2×M16C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834772
C2×#145829412
C2×#145828952
C2×#145828672
#191371882
#191357972
#191357902
#191357832
#191357762
C2×#145826612
C2×C43×#4172
#2348543