Finite Group Databasebeta

← #25124140

Subgroups — #25124140

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×#14583480C211yesmaximal, characteristic
2C2×#14582901C211yesmaximal, characteristic, complemented
3C2×#14582893C211yesmaximal, characteristic, complemented
4C2×#14582867C211yesmaximal, characteristic, complemented
5#19137183C211yesmaximal, characteristic, complemented
6#19135800C212yesmaximal, complemented
7#19135793C212yesmaximal, complemented
8#19135786C212yesmaximal, complemented
9#19135779C212yesmaximal, complemented
10C2×#14582661C211yesmaximal, characteristic, complemented
11C2×C43×#428C211yesmaximal, characteristic, complemented
12C22×#10621898C2211yescharacteristic
13C22×#10621898C2211yescharacteristic
14C23×C43⋊C8C2211yescharacteristic
15#14583480—24no—
16#14583480—24no—
17C2×#13063305—21no—
18C2×#13063305C2212yes—
19C2×#13063300—21no—
20C2×#13063300C2212yes—
21C2×#13063299—22no—
22C22×C4⋊Dic43C2211yescharacteristic
23#14582901—24no—
24#14582893—24no—
25C2×#13063250C2212yes—
26C2×#13063248C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×#13063247C2212yes—
29C2×#13063245C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31#14582867—24no—
32C2×(C2×D43)⋊C8C2212yes—
33C2×(C2×D43)⋊C8C2212yes—
34#14582805—21no—
35#14582801—21no—
36#14582776—22no—
37#14582756C2212yes—
38#14582756C2212yes—
39#14582661C2212yes—
40#14582661C2212yes—
41C22×M16×C43C2211yescharacteristic
42C2×#117×C43C2211yescharacteristic
43C22×C4⋊C4×C43C2211yescharacteristic
44C43×#428—24no—
45C2×#107×C43C2212yes—
46C2×#106×C43C2212yes—
47C2×#10621898—22no—
48C2×#10621898—22no—
49C2×#10621898—22no—
50C2×#10621898—22no—
51C2×#10621898—22no—
52C2×#10621898—22no—
53C2×#10621898—22no—
54C2×#10621898—22no—
55C2×#10621898—22no—
56C2×#10621898—22no—
57C2×#10621898—22no—
58C2×#10621898D414yes—
59C22×Dic86D411yescharacteristic
60C22×Dic86C2311yescharacteristic
61C22×D172—22no—
62C22×D172D411yescharacteristic
63C22×D172C2311yescharacteristic
64C22×C22⋊D43—21no—
65C22×C22⋊D43D412yes—
66C23×Dic43—21no—
67C22×C4×D43—21no—
68C22×C4×D43C2312yes—
69C22×C43⋊C8—22no—
70C22×C43⋊C8—22no—
71C22×C43⋊C8—22no—
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74#13063305—28no—
75#13063305—24no—
76#13063305—24no—
77#13063300—28no—
78#13063300—24no—
79#13063300—24no—
80#13063299—216no—
81C2×C4⋊Dic43—22no—
82C2×C4⋊Dic43—22no—
83C2×C4⋊Dic43—22no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43C2312yes—
86C2×(C2×D43)⋊C4—22no—
87C2×(C2×D43)⋊C4—22no—
88C2×(C2×D43)⋊C4—22no—
89C2×(C2×D43)⋊C4—22no—
90#13063250—24no—
91#13063248—22no—
92#13063248—22no—
93#13063247—24no—
94#13063245—22no—
95#13063245—22no—
96(C2×D43)⋊C8—24no—
97(C2×D43)⋊C8—24no—
98C43⋊#95—22no—
99C43⋊#95—22no—
100C23×C4×C43—21no—
101C23×C4×C43C2311yescharacteristic
102C2×M16×C43—22no—
103C2×M16×C43—22no—
104C2×M16×C43D414yescomplemented
105C22×C8×C43C2312yes—
106#117×C43—22no—
107#117×C43—22no—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43—22no—
110C2×C4⋊C4×C43D414yes—
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2312yes—
114C2×C22⋊C4×C43—21no—
115C2×C42×C43—21no—
116#107×C43—24no—
117#106×C43—24no—
118C24×C43C2×D411yescharacteristic
119C23×D43—21no—
120C23×D43C2×D412yes—
121C22×C4×C43—24no—
122C22×C4×C43—22no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—81no—
126C22×C4×C43—81no—
127C22×C4×C43C2×D412yes—
128C22×C4×C43C2×D412yes—
129C22×C4×C43C2×D412yes—
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43#4112yes—
132C22×C4×C43#4112yes—
133C22×C4×C43#4112yes—
134C22×C4×C43C2411yescharacteristic
135C2×C22⋊D43—24no—
136C2×C22⋊D43—24no—
137C2×C22⋊D43—24no—
138C2×C22⋊D43—24no—
139C2×C22⋊D43—42no—
140C2×C22⋊D43—42no—
141C22×Dic43—21no—
142C22×Dic43—22no—
143C22×Dic43—42no—
144C22×Dic43—81no—
145C22×Dic43—81no—
146C22×Dic43C2×D412yes—
147#10621898—28no—
148#10621898—28no—
149#10621898—44no—
150#10621898—44no—
151#10621898—44no—
152#10621898—44no—
153#10621898—44no—
154#10621898—44no—
155C2×D172—22no—
156C2×D172—22no—
157C2×D172—22no—
158C2×D172—21no—
159C2×D172—28no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172—82no—
165C2×D172—82no—
166C2×D172C2×D412yes—
167C2×C4×D43—24no—
168C2×C4×D43—22no—
169C2×C4×D43—22no—
170C2×C4×D43—22no—
171C2×C4×D43—22no—
172C2×C4×D43—22no—
173C2×C4×D43—22no—
174C2×C4×D43—42no—
175C2×C4×D43—42no—
176C2×Dic86—21no—
177C2×Dic86—21no—
178C2×Dic86—21no—
179C2×Dic86—21no—
180C2×Dic86—22no—
181C2×Dic86—22no—
182C2×Dic86—22no—
183C2×Dic86—21no—
184C2×Dic86C2×D412yes—
185M16×C43—28no—
186C2×C8×C43—22no—
187C2×C8×C43—22no—
188C2×C8×C43C2×D414yes—
189C4⋊C4×C43—24no—
190C4⋊C4×C43—22no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43C2×D414yes—
196C22⋊C4×C43—42no—
197C42×C43—42no—
198(C2×D43)⋊C4—28no—
199(C2×D43)⋊C4—28no—
200(C2×D43)⋊C4—82no—
201(C2×D43)⋊C4—82no—
202C4⋊Dic43—28no—
203C4⋊Dic43—22no—
204C4⋊Dic43—22no—
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#12012yes—
218C23×C43#12112yes—
219C23×C43#12312yes—
220C23×C43C22×D411yescharacteristic
221C22×D43—22no—
222C22×D43—22no—
223C22×D43—22no—
224C22×D43—22no—
225C22×D43—22no—
226C22×D43—22no—
227C22×D43—22no—
228C22×D43—22no—
229C22×D43—41no—
230C22×D43—41no—
231C22×D43—41no—
232C22×D43—41no—
233C22×D43—41no—
234C22×D43—41no—
235C2×C4×C43—24no—
236C2×C4×C43—42no—
237C2×C4×C43—42no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—84no—
245C2×C4×C43#12012yes—
246C2×C4×C43#12114yes—
247C2×C4×C43#12114yes—
248C2×C4×C43#12112yes—
249C2×C4×C43#12314yes—
250C2×C4×C43#12312yes—
251C2×C4×C43#12414yes—
252C2×C4×C43C22×D411yescharacteristic
253C2×C4×C43C22×D411yescharacteristic
254C2×C4×C43C22×D411yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C22⋊D43—48no—
259C22⋊D43—48no—
260C2×Dic43—22no—
261C2×Dic43—22no—
262C2×Dic43—22no—
263C2×Dic43—22no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—42no—
267C2×Dic43—42no—
268C2×Dic43—42no—
269C2×Dic43—84no—
270D172—22no—
271D172—22no—
272D172—41no—
273D172—41no—
274D172—44no—
275D172—88no—
276C4×D43—42no—
277C4×D43—42no—
278C4×D43—42no—
279C4×D43—42no—
280C4×D43—48no—
281Dic86—22no—
282Dic86—22no—
283Dic86—41no—
284Dic86—41no—
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#39414yes—
297C22×C43C2×#12011yescharacteristic
298C22×C43C2×#12111yescharacteristic
299C22×C43C2×#12311yescharacteristic
300C22×C43#57611yescharacteristic
301C22×C43#57711yescharacteristic
302C22×C43#57711yescharacteristic
303C22×C43#57811yescharacteristic
304C2×D43—42no—
305C2×D43—42no—
306C2×D43—42no—
307C2×D43—42no—
308C2×D43—42no—
309C2×D43—42no—
310C2×D43—42no—
311C2×D43—42no—
312C2×D43—42no—
313C2×D43—42no—
314C2×D43—81no—
315C2×D43—81no—
316C2×D43—81no—
317C2×D43—81no—
318C4×C43—44no—
319C4×C43—81no—
320C4×C43—81no—
321C4×C43#39414yes—
322C4×C43C2×#12111yescharacteristic
323C4×C43C2×#12111yescharacteristic
324C4×C43C2×#12311yescharacteristic
325C4×C43C2×#12411yescharacteristic
326Dic43—42no—
327Dic43—42no—
328Dic43—82no—
329C2×#537—431no—
330C2×#428D4311yescharacteristic, complemented
331C2×#417—431no—
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×C43C2×#39411yescharacteristic
342C2×C43#301211yescharacteristic
343C2×C43#301311yescharacteristic
344C2×C43#306211yescharacteristic
345C2×C43#306311yescharacteristic
346C2×C43#309811yescharacteristic
347C2×C43#309911yescharacteristic
348D43—82no—
349D43—82no—
350C22×#41—431no—
351C22×#41—431no—
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×#117C2×D4311yescharacteristic
362C22×C4⋊C4—431no—
363C22×C4⋊C4C2×D4311yescharacteristic
364#428—24no—
365C2×#107C2×D4312yes—
366C2×#106C2×D4312yes—
367#417—864no—
368#416—864no—
369C2×#103—432no—
370C2×#103—431no—
371C2×#103—431no—
372C2×#102—432no—
373C2×#102—431no—
374C2×#102—431no—
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—434no—
387C2×#41—862no—
388C2×#41—862no—
389C2×#41—862no—
390C2×#41—862no—
391C2×#41—862no—
392C2×#41—862no—
393C2×#41—862no—
394C2×#41—862no—
395C2×#41—862no—
396C2×#41—862no—
397C2×#41—862no—
398C22×Q8—431no—
399C22×Q8—431no—
400C22×D4—432no—
401C22×D4—431no—
402C22×D4—431no—
403C22×D4—862no—
404C22×D4—861no—
405C23×C4—21no—
406C23×C4—432no—
407C23×C4—861no—
408C23×C4—861no—
409C23×C4C22×D4311yescharacteristic
410C2×M16—22no—
411C2×M16—22no—
412C2×M16D17214yescomplemented
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—22no—
427#117—22no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—432no—
431C2×C4⋊C4—862no—
432C2×C4⋊C4—862no—
433C2×C4⋊C4—862no—
434C2×C4⋊C4—861no—
435C2×C4⋊C4C22⋊D4314yes—
436C2×C4⋊C4C22×D4311yescharacteristic
437C2×C4⋊C4C22×D4311yescharacteristic
438C2×C4⋊C4C22×D4312yes—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—862no—
441C2×C22⋊C4—862no—
442C2×C22⋊C4—862no—
443C2×C22⋊C4—862no—
444C2×C42—21no—
445#107—24no—
446#106—24no—
447#103—862no—
448#103—862no—
449#103—864no—
450#102—862no—
451#102—862no—
452#102—864no—
453C22⋊C8—864no—
454C22⋊C8—864no—
455#95—862no—
456#95—862no—
457C24—432no—
458C24—861no—
459C24D4×D4311yescharacteristic
460#41—868no—
461#41—868no—
462#41—1724no—
463#41—1724no—
464#41—1724no—
465#41—1724no—
466#41—1724no—
467#41—1724no—
468C2×Q8—432no—
469C2×Q8—862no—
470C2×Q8—862no—
471C2×Q8—862no—
472C2×Q8—861no—
473C2×Q8—861no—
474C2×Q8—861no—
475C2×Q8—861no—
476C2×Q8—861no—
477C2×D4—432no—
478C2×D4—868no—
479C2×D4—864no—
480C2×D4—864no—
481C2×D4—864no—
482C2×D4—864no—
483C2×D4—862no—
484C2×D4—862no—
485C2×D4—862no—
486C2×D4—861no—
487C2×D4—861no—
488C2×D4—861no—
489C2×D4—861no—
490C2×D4—861no—
491C2×D4—3442no—
492C2×D4—3442no—
493C2×D4—1722no—
494C2×D4—1722no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—81no—
500C22×C4—81no—
501C22×C4—432no—
502C22×C4—861no—
503C22×C4—864no—
504C22×C4—862no—
505C22×C4—862no—
506C22×C4—862no—
507C22×C4—862no—
508C22×C4—862no—
509C22×C4—862no—
510C22×C4—862no—
511C22×C4—3441no—
512C22×C4—3441no—
513C22×C4—1722no—
514C22×C4—1722no—
515C22×C4—1722no—
516C22×C4C2×D17212yes—
517C22×C4#1062189812yes—
518C22×C4D4×D4311yescharacteristic
519C22×C4D4×D4312yes—
520C22×C4#1062190212yes—
521C22×C4#1062190212yes—
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×D17214yes—
535C4⋊C4—24no—
536C4⋊C4—22no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—868no—
542C4⋊C4—862no—
543C4⋊C4—862no—
544C4⋊C4—1722no—
545C4⋊C4C2×C22⋊D4314yes—
546C22⋊C4—42no—
547C22⋊C4—868no—
548C22⋊C4—868no—
549C22⋊C4—3442no—
550C22⋊C4—3442no—
551C42—42no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—862no—
557C23—862no—
558C23—862no—
559C23—862no—
560C23—862no—
561C23—862no—
562C23—862no—
563C23—862no—
564C23—1721no—
565C23—1721no—
566C23—1721no—
567C23—1721no—
568C23—1721no—
569C23—1721no—
570C23#1306329312yes—
571C23#1306330012yes—
572C23#1306331012yes—
573C23C2×D4×D4311yescharacteristic
574Q8—862no—
575Q8—862no—
576Q8—1724no—
577Q8—1721no—
578Q8—1721no—
579D4—862no—
580D4—862no—
581D4—3448no—
582D4—1728no—
583D4—1728no—
584D4—1724no—
585D4—1721no—
586D4—1721no—
587C2×C4—24no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—84no—
597C2×C4—862no—
598C2×C4—862no—
599C2×C4—862no—
600C2×C4—862no—
601C2×C4—3444no—
602C2×C4—1722no—
603C2×C4—1722no—
604C2×C4—1722no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1728no—
608C2×C4—1722no—
609C2×C4—1722no—
610C2×C4—1722no—
611C2×C4—1722no—
612C2×C4#1306329312yes—
613C2×C4#1306329914yes—
614C2×C4#1306330012yes—
615C2×C4#1306330014yes—
616C2×C4#1306331012yes—
617C2×C4#1306331014yes—
618C2×C4#1306331414yes—
619C2×C4C2×D4×D4311yescharacteristic
620C2×C4C22×C22⋊D4311yescharacteristic
621C2×C4C22×D17211yescharacteristic
622C2×C4C2×#1062189811yescharacteristic
623C2×C4C2×#1062190211yescharacteristic
624C2×C4C2×#1062190211yescharacteristic
625C8—24no—
626C8—1721no—
627C8—1721no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—22no—
633C22—22no—
634C22—3441no—
635C22—3441no—
636C22—3441no—
637C22—3441no—
638C22—1722no—
639C22—1722no—
640C22—1722no—
641C22—1722no—
642C22—1722no—
643C22—1722no—
644C22—1722no—
645C22—1722no—
646C22—1722no—
647C22—1722no—
648C22#1458281614yes—
649C22C2×#1306329311yescharacteristic
650C22C2×#1306330011yescharacteristic
651C22C2×#1306331011yescharacteristic
652C22#1458370311yescharacteristic
653C22#1458370811yescharacteristic
654C22#1458370911yescharacteristic
655C22#1458371511yescharacteristic
656C4—44no—
657C4—81no—
658C4—81no—
659C4—3442no—
660C4—1722no—
661C4—1722no—
662C4#1458281614yes—
663C4C2×#1306329911yescharacteristic
664C4C2×#1306330011yescharacteristic
665C4C2×#1306331011yescharacteristic
666C4C2×#1306331411yescharacteristic
667C2—24no—
668C2—3442no—
669C2—3442no—
670C2C2×#1458281611yescharacteristic
671C2#1914389811yescharacteristic
672C2#1914390911yescharacteristic
673C2#1914427611yescharacteristic
674C2#1914428711yescharacteristic
675C2#1914457711yescharacteristic
676C2#1914458811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#428C2
socleC23×C43C22×D4
prime radicalC2×#14583480C2
hypercenterC2×#428D43
hypocenterC43#23485
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
2. C2×#14582901C2semidirect
3. C2×#14582893C2semidirect
4. C2×#14582867C2semidirect
5. #19137183C2semidirect
6. #19135800C2semidirect
7. #19135793C2semidirect
8. #19135786C2semidirect
9. #19135779C2semidirect
10. C2×#14582661C2semidirect
11. C2×C43×#428C2semidirect
104. C2×M16×C43D4semidirect
330. C2×#428D43semidirect
385. C43#23485semidirect
412. C2×M16D172semidirect

Maximal subgroups

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

subgroupindex
C2×#145834802
C2×#145829012
C2×#145828932
C2×#145828672
#191371832
#191358002
#191357932
#191357862
#191357792
C2×#145826612
C2×C43×#4282
#2348543