Finite Group Databasebeta

← #25099065

Subgroups — #25099065

Order 11008.

1078 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582934C211yesmaximal, characteristic
2C2×#14582906C211yesmaximal, characteristic
3C2×#103×D43C211yesmaximal, characteristic
4#19137178C211yesmaximal, characteristic
5#19136949C211yesmaximal, characteristic
6#19135239C211yesmaximal, characteristic, complemented
7#19135236C211yesmaximal, characteristic, complemented
8#19135234C211yesmaximal, characteristic, complemented
9#19135233C211yesmaximal, characteristic, complemented
10#19135231C211yesmaximal, characteristic, complemented
11#19135230C211yesmaximal, characteristic, complemented
12#19135228C211yesmaximal, characteristic, complemented
13#19134313C211yesmaximal, characteristic
14#19134290C211yesmaximal, characteristic
15C43×#1927C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19C2×#13063283C2211yescharacteristic
20C2×#13063283C2211yescharacteristic
21C2×#13063282C2211yescharacteristic
22C2×C4⋊C4×D43C2211yescharacteristic
23#14582934—24no—
24C2×#13063258C2211yescharacteristic
25C2×#13063258C2211yescharacteristic
26C2×#13063257C2211yescharacteristic
27#14582906—24no—
28C2×#13063250C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063248C2211yescharacteristic
33C2×#13063248C2211yescharacteristic
34#103×D43C418yescomplemented
35#14582806C2211yescharacteristic
36#14582805C2211yescharacteristic
37#14582804C2211yescharacteristic
38#14582803—21no—
39#14582803—21no—
40#14582761—21no—
41#14582761—21no—
42C4⋊C4×Dic43C2211yescharacteristic
43C4⋊C4×Dic43C2211yescharacteristic
44C4×Dic43⋊C4—21no—
45C4×C4⋊Dic43C2211yescharacteristic
46#14582750—21no—
47C4×(C2×D43)⋊C4—21no—
48#14582746—21no—
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582654C2211yescharacteristic
53#14582653C2211yescharacteristic
54#14582653C2211yescharacteristic
55C2×#106×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C43×#391C2211yescharacteristic
59C4×C4⋊C4×C43C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C22×Dic86—21no—
63C22×Dic86C2311yescharacteristic
64C2×Q8×D43—22no—
65C2×Q8×D43—22no—
66C2×Q8×D43—22no—
67C2×Q8×D43—22no—
68C2×Q8×D43—22no—
69C2×Q8×D43C2×C414yes—
70C22×C4×D43—21no—
71C22×C4×D43—21no—
72C22×C4×D43C2311yescharacteristic
73C2×#10621872—22no—
74C2×#10621872—22no—
75C2×#10621872—22no—
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C2×C8×D43—22no—
79C2×C8×D43—22no—
80C2×C8×D43C2×C414yes—
81#13063283—22no—
82#13063283—22no—
83#13063283—22no—
84#13063283D414yes—
85#13063282—22no—
86#13063282—22no—
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4D411yescharacteristic
92C2×Dic43⋊C4D411yescharacteristic
93C4⋊C4×D43—22no—
94C4⋊C4×D43C2×C414yes—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4D411yescharacteristic
98C2×(C2×D43)⋊C4D411yescharacteristic
99C2×C4×Dic43—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43—21no—
102C2×C4×Dic43—21no—
103C2×C4×Dic43—21no—
104C2×C4×Dic43C2311yescharacteristic
105#13063258—22no—
106#13063258—22no—
107#13063257—22no—
108#13063250—22no—
109#13063250C2×C414yes—
110#13063249—22no—
111#13063249C2×C414yes—
112#13063248—22no—
113#13063248C2×C414yes—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C22×Q8×C43C2311yescharacteristic
124C22×C8×C43C2311yescharacteristic
125C22×C8×C43C2311yescharacteristic
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C42×C43—21no—
130C2×C42×C43C2311yescharacteristic
131#106×C43—22no—
132#103×C43—22no—
133#103×C43C2×C414yes—
134#95×C43—21no—
135#95×C43—21no—
136#95×C43—21no—
137C23×D43C2×D411yescharacteristic
138C2×Q8×C43—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43C22×C412yes—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2411yescharacteristic
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43C2×D411yescharacteristic
156C22×Dic43C2×D411yescharacteristic
157C22×Dic43C2×D411yescharacteristic
158Q8×D43—28no—
159Q8×D43—28no—
160Q8×D43—44no—
161Q8×D43—44no—
162C2×C4×D43—24no—
163C2×C4×D43—24no—
164C2×C4×D43—42no—
165C2×C4×D43—42no—
166C2×C4×D43—81no—
167C2×C4×D43—81no—
168C2×C4×D43C22×C412yes—
169C2×C4×D43C2×D412yes—
170C2×C4×D43#4112yes—
171C2×C4×D43#4112yes—
172C2×C4×D43#4112yes—
173C2×C4×D43#4112yes—
174C2×Dic86—21no—
175C2×Dic86—21no—
176C2×Dic86—21no—
177C2×Dic86—21no—
178C2×Dic86—21no—
179C2×Dic86—24no—
180C2×Dic86—42no—
181C2×Dic86—42no—
182C2×Dic86C22×C412yes—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43C22×C412yes—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43C22×C412yes—
194C4⋊C4×C43C2×D412yes—
195C42×C43—21no—
196C42×C43—21no—
197C42×C43—81no—
198(C2×D43)⋊C4—24no—
199(C2×D43)⋊C4—22no—
200(C2×D43)⋊C4—22no—
201(C2×D43)⋊C4—42no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43C22×C412yes—
207C4⋊Dic43C2×D412yes—
208Dic43⋊C4—24no—
209Dic43⋊C4—22no—
210Dic43⋊C4—22no—
211C4×Dic43—21no—
212C4×Dic43—21no—
213C4×Dic43—24no—
214C4×Dic43—42no—
215C4×Dic43—81no—
216C4×Dic43—81no—
217C4×Dic43—81no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8C22×C412yes—
224#10621872—44no—
225C8×D43—28no—
226C23×C43C22×D411yescharacteristic
227C22×D43—21no—
228C22×D43—21no—
229C22×D43—21no—
230C22×D43—21no—
231C22×D43C4×D412yes—
232C22×D43#12112yes—
233C22×D43#12312yes—
234Q8×C43—22no—
235Q8×C43—22no—
236Q8×C43—41no—
237Q8×C43—41no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43C23×C411yescharacteristic
257C2×C4×C43C22×D411yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×Dic43—22no—
263C2×Dic43—22no—
264C2×Dic43—22no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43C4×D412yes—
281C2×Dic43#12112yes—
282C2×Dic43#12312yes—
283C4×D43—48no—
284C4×D43—84no—
285C4×D43#11714yes—
286C4×D43C4×D414yes—
287C4×D43#12414yes—
288C4×D43#12614yes—
289Dic86—22no—
290Dic86—22no—
291Dic86—41no—
292Dic86—41no—
293Dic86—48no—
294C8×C43—22no—
295C8×C43—41no—
296C43⋊C8—22no—
297C43⋊C8—41no—
298#21066—431nomaximal, Sylow
299C22×C43C2×C4×D411yescharacteristic
300C22×C43C2×#12111yescharacteristic
301C22×C43C2×#12311yescharacteristic
302C22×C43#57711yescharacteristic
303C22×C43#57711yescharacteristic
304C22×C43#57811yescharacteristic
305C22×C43#57811yescharacteristic
306C2×D43—22no—
307C2×D43—22no—
308C2×D43—22no—
309C2×D43—22no—
310C2×D43—22no—
311C2×D43—22no—
312C2×D43#38814yes—
313C4×C43—41no—
314C4×C43—41no—
315C4×C43—42no—
316C4×C43—42no—
317C4×C43—42no—
318C4×C43—81no—
319C4×C43C2×#11711yescharacteristic
320C4×C43C2×C4×D411yescharacteristic
321C4×C43C2×#12411yescharacteristic
322C4×C43C2×#12611yescharacteristic
323Dic43—41no—
324Dic43—41no—
325Dic43—42no—
326Dic43—42no—
327Dic43—42no—
328Dic43—81no—
329Dic43#38814yes—
330C2×#427—431no—
331C2×#419—431no—
332C22×#103—431no—
333#2310—431no—
334#2274—431no—
335#1928—431no—
336#1928—431no—
337#1928—431no—
338#1928—431no—
339#1927—431no—
340#1927—431no—
341#1927—431no—
342#1927D4311yescharacteristic, complemented
343#1736—431no—
344#1729—431no—
345C2×C43C2×#38811yescharacteristic
346C2×C43#294911yescharacteristic
347C2×C43#295011yescharacteristic
348C2×C43#304611yescharacteristic
349C2×C43#304611yescharacteristic
350C2×C43#309711yescharacteristic
351C2×C43#309711yescharacteristic
352D43—24no—
353C23×Q8—431no—
354C22×M16—431no—
355C23×C8—431no—
356C2×#117—431no—
357C2×#117—431no—
358C2×#117—431no—
359C22×C4⋊C4—431no—
360#427—864no—
361C2×#107—431no—
362C2×#107—431no—
363C2×#106—431no—
364C2×#106C2×D4311yescharacteristic
365#419—864no—
366C2×#103—431no—
367C2×#103—431no—
368C2×#103—431no—
369C2×#103—438no—
370C2×#103—431no—
371C2×#103—431no—
372C2×#103—431no—
373C2×#103C2×D4311yescharacteristic
374C2×#103C2×D4311yescharacteristic
375#391—431no—
376#391—431no—
377#391—431no—
378#391—861no—
379#391—861no—
380#391C2×D4311yescharacteristic
381#381—861no—
382#381—861no—
383C4×C4⋊C4—431no—
384C4×C4⋊C4—431no—
385C4×C4⋊C4—431no—
386C4×C4⋊C4—861no—
387C4×C4⋊C4—861no—
388C4×C4⋊C4C2×D4311yescharacteristic
389C4×C22⋊C4—861no—
390C4×C22⋊C4—861no—
391#340—431no—
392#340—431no—
393#340—431no—
394#340C2×D4311yescharacteristic
395#336—431no—
396#336—431no—
397#336—431no—
398#336C2×D4311yescharacteristic
399C43#2106611yescharacteristic, complemented, Sylow
400C22×Q8—434no—
401C22×Q8—431no—
402C22×Q8—861no—
403C22×Q8—862no—
404C22×Q8—862no—
405C22×Q8—862no—
406C22×Q8—862no—
407C22×Q8—862no—
408C22×Q8C22×D4311yescharacteristic
409C23×C4—431no—
410C23×C4—861no—
411C23×C4—861no—
412C2×M16—862no—
413C2×M16—862no—
414C2×M16—862no—
415C22×C8—431no—
416C22×C8—434no—
417C22×C8—431no—
418C22×C8—862no—
419C22×C8—862no—
420C22×C8C22×D4311yescharacteristic
421C22×C8C22×D4311yescharacteristic
422#117—434no—
423#117—862no—
424#117—862no—
425#117—862no—
426#117—862no—
427#117—862no—
428C2×C4⋊C4—431no—
429C2×C4⋊C4—431no—
430C2×C4⋊C4—434no—
431C2×C4⋊C4—431no—
432C2×C4⋊C4—431no—
433C2×C4⋊C4—431no—
434C2×C4⋊C4—862no—
435C2×C4⋊C4—861no—
436C2×C4⋊C4C22×D4311yescharacteristic
437C2×C4⋊C4C22×D4311yescharacteristic
438C2×C4⋊C4C22×D4311yescharacteristic
439C2×C22⋊C4—431no—
440C2×C22⋊C4—431no—
441C2×C22⋊C4—861no—
442C2×C22⋊C4—861no—
443C2×C42—21no—
444C2×C42—431no—
445C2×C42—861no—
446C2×C42—861no—
447C2×C42—861no—
448C2×C42—861no—
449C2×C42—861no—
450C2×C42C22×D4311yescharacteristic
451#107—862no—
452#107—862no—
453#106—22no—
454#106—862no—
455#103—22no—
456#103—434no—
457#103—434no—
458#103—434no—
459#103—862no—
460#103—862no—
461#103—862no—
462#103C4×D4314yes—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—861no—
467#95—861no—
468#95—861no—
469#95—861no—
470#95—861no—
471#95—861no—
472#95—861no—
473#95—861no—
474#95—861no—
475C24—431no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—432no—
482C2×Q8—864no—
483C2×Q8—868no—
484C2×Q8—868no—
485C2×Q8—861no—
486C2×Q8—861no—
487C2×Q8—861no—
488C2×Q8—861no—
489C2×Q8—861no—
490C2×Q8—1722no—
491C2×Q8—1722no—
492C2×Q8—1724no—
493C2×Q8—1724no—
494C2×Q8C2×C4×D4312yes—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—431no—
500C22×C4—432no—
501C22×C4—432no—
502C22×C4—432no—
503C22×C4—432no—
504C22×C4—432no—
505C22×C4—432no—
506C22×C4—431no—
507C22×C4—431no—
508C22×C4—864no—
509C22×C4—864no—
510C22×C4—861no—
511C22×C4—861no—
512C22×C4—861no—
513C22×C4—861no—
514C22×C4—3441no—
515C22×C4—3441no—
516C22×C4—1722no—
517C22×C4—1722no—
518C22×C4D4×D4311yescharacteristic
519C22×C4D4×D4311yescharacteristic
520C22×C4C23×D4311yescharacteristic
521M16—1724no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—432no—
528C2×C8—868no—
529C2×C8—861no—
530C2×C8—861no—
531C2×C8—861no—
532C2×C8—861no—
533C2×C8—861no—
534C2×C8C2×C4×D4312yes—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—432no—
540C4⋊C4—432no—
541C4⋊C4—864no—
542C4⋊C4—862no—
543C4⋊C4—862no—
544C4⋊C4—861no—
545C4⋊C4—861no—
546C4⋊C4—861no—
547C4⋊C4—861no—
548C4⋊C4C2×C4×D4312yes—
549C4⋊C4D4×D4312yes—
550C22⋊C4—862no—
551C22⋊C4—862no—
552C22⋊C4—864no—
553C22⋊C4—1722no—
554C42—21no—
555C42—21no—
556C42—81no—
557C42—864no—
558C42—861no—
559C42—861no—
560C42—3441no—
561C42—3441no—
562C42—3441no—
563C42—1722no—
564C23—432no—
565C23—432no—
566C23—432no—
567C23—861no—
568C23—861no—
569C23—861no—
570C23—861no—
571C23C2×D4×D4311yescharacteristic
572Q8—22no—
573Q8—22no—
574Q8—41no—
575Q8—41no—
576Q8—862no—
577Q8—862no—
578Q8—1728no—
579Q8—1721no—
580Q8—1721no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—432no—
600C2×C4—432no—
601C2×C4—432no—
602C2×C4—434no—
603C2×C4—434no—
604C2×C4—434no—
605C2×C4—434no—
606C2×C4—862no—
607C2×C4—862no—
608C2×C4—862no—
609C2×C4—861no—
610C2×C4—861no—
611C2×C4—861no—
612C2×C4—861no—
613C2×C4—861no—
614C2×C4—861no—
615C2×C4—3444no—
616C2×C4—1728no—
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×C4C22×C4×D4311yescharacteristic
627C2×C4C2×D4×D4311yescharacteristic
628C2×C4#41×D4311yescharacteristic
629C2×C4#41×D4311yescharacteristic
630C2×C4#41×D4311yescharacteristic
631C2×C4#41×D4311yescharacteristic
632C8—22no—
633C8—41no—
634C8—862no—
635C8—1721no—
636C22—434no—
637C22—862no—
638C22—862no—
639C22—862no—
640C22—862no—
641C22—862no—
642C22—862no—
643C22C4×D4×D4311yescharacteristic
644C22#121×D4311yescharacteristic
645C22#123×D4311yescharacteristic
646C22#1458370511yescharacteristic
647C22#1458370611yescharacteristic
648C22#1458371511yescharacteristic
649C22#1458371511yescharacteristic
650C4—42no—
651C4—41no—
652C4—41no—
653C4—42no—
654C4—42no—
655C4—81no—
656C4—434no—
657C4—3441no—
658C4—1722no—
659C4—1721no—
660C4—1721no—
661C4—1722no—
662C4—1722no—
663C4#117×D4311yescharacteristic
664C4C4×D4×D4311yescharacteristic
665C4#124×D4311yescharacteristic
666C4#126×D4311yescharacteristic
667C2—864no—
668C2#388×D4311yescharacteristic
669C2#1914344911yescharacteristic
670C2#1914346011yescharacteristic
671C2#1914414011yescharacteristic
672C2#1914414811yescharacteristic
673C2#1914455711yescharacteristic
674C2#1914456111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1927C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenter#1927D43
hypocenterC43#21066
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1927

Complements

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

NH ≅ G/Ntype
6. #19135239C2semidirect
7. #19135236C2semidirect
8. #19135234C2semidirect
9. #19135233C2semidirect
10. #19135231C2semidirect
11. #19135230C2semidirect
12. #19135228C2semidirect
15. C43×#1927C2semidirect
34. #103×D43C4semidirect
342. #1927D43semidirect
399. C43#21066semidirect

Maximal subgroups

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

subgroupindex
C2×#145829342
C2×#145829062
C2×#103×D432
#191371782
#191369492
#191352392
#191352362
#191352342
#191352332
#191352312
#191352302
#191352282
#191343132
#191342902
C43×#19272
#2106643