Finite Group Databasebeta

← #25003768

Subgroups — #25003768

Order 11008.

938 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582915C211yesmaximal, characteristic
2C22×#13063251C211yesmaximal, characteristic
3C2×#14582872C211yesmaximal, characteristic
4#19137077C211yesmaximal, characteristic, complemented
5C2×#14582660C211yesmaximal, characteristic, complemented
6C2×#14582656C211yesmaximal, characteristic, complemented
7C2×C43×#344C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C2×#13063284C2211yescharacteristic
10C2×#13063284C2211yescharacteristic
11C22×C4×Dic43C2211yescharacteristic
12#14582915—22no—
13#14582915C414yescomplemented
14C2×#13063251—22no—
15C2×#13063251—22no—
16C2×#13063251—22no—
17C2×#13063251—22no—
18#14582872—22no—
19#14582872—22no—
20C2×#13063239—22no—
21#14582795—22no—
22#14582771—22no—
23C4×Dic43⋊C4—22no—
24#14582660—22no—
25#14582656—22no—
26C22×M16×C43C2211yescharacteristic
27C22×M16×C43C2211yescharacteristic
28C2×#117×C43C2211yescharacteristic
29C43×#344—22no—
30C2×#10621898—21no—
31C2×#10621898—21no—
32C2×#10621898—21no—
33C2×#10621898—21no—
34C2×#10621898—21no—
35C2×#10621898—21no—
36C2×#10621898—21no—
37C2×#10621898—21no—
38C2×#10621898—21no—
39C2×#10621898—21no—
40C2×#10621898C2×C412yes—
41C2×#10621898D412yes—
42C22×Dic86Q811yescharacteristic
43C22×D172Q811yescharacteristic
44C22×C22⋊D43—21no—
45C23×Dic43—21no—
46C22×C4×D43—21no—
47#13063284—21no—
48#13063284—21no—
49#13063284—21no—
50#13063284—21no—
51#13063284—21no—
52#13063284C2×C412yes—
53#13063284D412yes—
54#13063284D412yes—
55C2×C4⋊Dic43—21no—
56C2×C4⋊Dic43—21no—
57C2×Dic43⋊C4—24no—
58C2×C22⋊Dic43—21no—
59C2×C22⋊Dic43—21no—
60C2×C4×Dic43—21no—
61C2×C4×Dic43—21no—
62C2×C4×Dic43—21no—
63C2×C4×Dic43—21no—
64C2×C4×Dic43—21no—
65C2×C4×Dic43—21no—
66C2×C4×Dic43D412yes—
67C2×C4×Dic43D412yes—
68#13063251—28no—
69#13063251—28no—
70#13063239—28no—
71C43⋊#95—24no—
72C23×C4×C43C2311yescharacteristic
73C2×M16×C43—21no—
74C2×M16×C43—21no—
75C2×M16×C43—21no—
76C2×M16×C43—21no—
77C2×M16×C43—21no—
78C2×M16×C43—21no—
79C2×M16×C43—21no—
80C2×M16×C43—21no—
81C2×M16×C43—21no—
82C2×M16×C43—21no—
83C2×M16×C43C2×C412yes—
84C2×M16×C43D412yes—
85C22×C8×C43—21no—
86C22×C8×C43—21no—
87#117×C43—21no—
88#117×C43—21no—
89#117×C43—21no—
90#117×C43—21no—
91C2×C4⋊C4×C43—21no—
92C2×C22⋊C4×C43D412yes—
93C2×C42×C43—21no—
94C24×C43C2×D411yescharacteristic
95C23×D43—21no—
96C22×C4×C43—22no—
97C22×C4×C43C22×C411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43C2×D411yescharacteristic
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43C2×Q811yescharacteristic
105C22×C4×C43#4111yescharacteristic
106C22×C4×C43#4111yescharacteristic
107C22×C4×C43#4111yescharacteristic
108C22×C4×C43#4111yescharacteristic
109C22×C4×C43#4111yescharacteristic
110C22×C4×C43#4111yescharacteristic
111C2×C22⋊D43—22no—
112C2×C22⋊D43—22no—
113C2×C22⋊D43—41no—
114C2×C22⋊D43—41no—
115C2×C22⋊D43—41no—
116C2×C22⋊D43—41no—
117C22×Dic43—22no—
118C22×Dic43—22no—
119C22×Dic43—21no—
120C22×Dic43—44no—
121C22×Dic43—41no—
122C22×Dic43—41no—
123C22×Dic43—41no—
124#10621898—22no—
125#10621898—22no—
126#10621898—22no—
127#10621898—22no—
128#10621898—22no—
129#10621898—22no—
130#10621898—22no—
131#10621898—22no—
132#10621898—41no—
133#10621898—41no—
134#10621898—41no—
135#10621898—41no—
136#10621898—41no—
137#10621898—41no—
138#10621898—41no—
139#10621898—41no—
140C2×D172—21no—
141C2×D172—21no—
142C2×D172—21no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172C4⋊C412yescomplemented
146C2×C4×D43—22no—
147C2×C4×D43—22no—
148C2×C4×D43—41no—
149C2×C4×D43—41no—
150C2×C4×D43—41no—
151C2×C4×D43—41no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86C4⋊C412yescomplemented
158M16×C43—22no—
159M16×C43—22no—
160M16×C43—22no—
161M16×C43—22no—
162M16×C43—41no—
163M16×C43—41no—
164M16×C43—41no—
165M16×C43—41no—
166C2×C8×C43—22no—
167C2×C8×C43—22no—
168C2×C8×C43—41no—
169C2×C8×C43—41no—
170C2×C8×C43—41no—
171C2×C8×C43—41no—
172C4⋊C4×C43—41no—
173C4⋊C4×C43—41no—
174C22⋊C4×C43—22no—
175C22⋊C4×C43—22no—
176C42×C43—41no—
177C42×C43—41no—
178C22⋊Dic43—22no—
179C22⋊Dic43—22no—
180C22⋊Dic43—22no—
181C22⋊Dic43—41no—
182C4⋊Dic43—22no—
183C4⋊Dic43—22no—
184C4⋊Dic43—22no—
185C4⋊Dic43—41no—
186Dic43⋊C4—48no—
187C4×Dic43—22no—
188C4×Dic43—22no—
189C4×Dic43—22no—
190C4×Dic43—22no—
191C4×Dic43—41no—
192C4×Dic43—41no—
193C4×Dic43—41no—
194C4×Dic43C22⋊C414yes—
195C23×C43—42no—
196C23×C43C4×D411yescharacteristic
197C23×C43#12011yescharacteristic
198C23×C43#12011yescharacteristic
199C23×C43#12111yescharacteristic
200C23×C43#12111yescharacteristic
201C23×C43C22⋊Q811yescharacteristic
202C23×C43#12411yescharacteristic
203C22×D43—22no—
204C22×D43—41no—
205C22×D43—41no—
206C22×D43—82no—
207C2×C4×C43—44no—
208C2×C4×C43—42no—
209C2×C4×C43C2×C22⋊C411yescharacteristic
210C2×C4×C43C2×C4⋊C411yescharacteristic
211C2×C4×C43#11711yescharacteristic
212C2×C4×C43C4×D411yescharacteristic
213C2×C4×C43C4×D411yescharacteristic
214C2×C4×C43C4×D411yescharacteristic
215C2×C4×C43#12011yescharacteristic
216C2×C4×C43#12111yescharacteristic
217C2×C4×C43#12111yescharacteristic
218C2×C4×C43#12111yescharacteristic
219C2×C4×C43#12111yescharacteristic
220C2×C4×C43#12111yescharacteristic
221C2×C4×C43#12111yescharacteristic
222C2×C4×C43C22⋊Q811yescharacteristic
223C2×C4×C43C22⋊Q811yescharacteristic
224C2×C4×C43C22⋊Q811yescharacteristic
225C2×C4×C43C22⋊Q811yescharacteristic
226C2×C4×C43C22⋊Q811yescharacteristic
227C2×C4×C43#12311yescharacteristic
228C2×C4×C43#12311yescharacteristic
229C2×C4×C43#12311yescharacteristic
230C2×C4×C43#12311yescharacteristic
231C2×C4×C43#12311yescharacteristic
232C2×C4×C43#12411yescharacteristic
233C2×C4×C43#12411yescharacteristic
234C2×C4×C43#12611yescharacteristic
235C2×C4×C43#12611yescharacteristic
236C2×C4×C43#12711yescharacteristic
237C22⋊D43—42no—
238C22⋊D43—42no—
239C22⋊D43—42no—
240C22⋊D43—42no—
241C2×Dic43—24no—
242C2×Dic43—22no—
243C2×Dic43—24no—
244C2×Dic43—44no—
245C2×Dic43—42no—
246C2×Dic43—44no—
247C2×Dic43—44no—
248C2×Dic43—42no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—42no—
252C2×Dic43—82no—
253D172—22no—
254D172—22no—
255D172—41no—
256D172—41no—
257C4×D43—42no—
258C4×D43—42no—
259C4×D43—42no—
260C4×D43—42no—
261Dic86—22no—
262Dic86—22no—
263Dic86—41no—
264Dic86—41no—
265C8×C43—42no—
266C8×C43—42no—
267#11085—431nomaximal, Sylow
268C22×C43—22no—
269C22×C43—22no—
270C22×C43—22no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43#38511yescharacteristic
276C22×C43#38611yescharacteristic
277C22×C43#38811yescharacteristic
278C22×C43#39211yescharacteristic
279C22×C43#39311yescharacteristic
280C22×C43#39411yescharacteristic
281C22×C43#39611yescharacteristic
282C2×D43—42no—
283C2×D43—82no—
284C2×D43—82no—
285C2×D43—82no—
286C4×C43—82no—
287C4×C43#38011yescharacteristic
288C4×C43#38511yescharacteristic
289C4×C43#38811yescharacteristic
290C4×C43#39011yescharacteristic
291C4×C43#39411yescharacteristic
292C4×C43#39611yescharacteristic
293C4×C43#39711yescharacteristic
294C4×C43#39911yescharacteristic
295Dic43—44no—
296Dic43—44no—
297Dic43—42no—
298Dic43—82no—
299C2×#421—431no—
300C22×#104—431no—
301C2×#410—431no—
302#2296—431no—
303C2×#344D4311yescharacteristic, complemented
304C2×#339—431no—
305C2×H(3,ℤ/4)—431no—
306C2×C43—21no—
307C2×C43—21no—
308C2×C43—21no—
309C2×C43—21no—
310C2×C43—21no—
311C2×C43—21no—
312C2×C43#143911yescharacteristic
313C2×C43#203112yes—
314D43—82no—
315C22×#41—431no—
316C22×M16C2×D4311yescharacteristic
317C22×M16C2×D4311yescharacteristic
318C2×#117—431no—
319C2×#117—431no—
320C2×#117C2×D4311yescharacteristic
321C22×C42—431no—
322#421—434no—
323#421—862no—
324C2×#104—862no—
325C2×#104—862no—
326C2×#104—862no—
327C2×#104—862no—
328#410—862no—
329#410—862no—
330C2×#99—862no—
331#389—862no—
332#385—862no—
333C4×C4⋊C4—862no—
334#344—22no—
335#339—862no—
336H(3,ℤ/4)—862no—
337C43#1108511yescharacteristic, complemented, Sylow
338C2×#41—432no—
339C2×#41—432no—
340C2×#41—861no—
341C2×#41—861no—
342C2×#41—861no—
343C2×#41—861no—
344C2×#41—861no—
345C2×#41—861no—
346C2×#41—861no—
347C2×#41—861no—
348C2×#41—861no—
349C2×#41—861no—
350C22×Q8—431no—
351C22×D4—431no—
352C22×D4—861no—
353C23×C4—861no—
354C23×C4—861no—
355C23×C4C22×D4311yescharacteristic
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16C4×D4312yes—
367C2×M16C22⋊D4312yes—
368C22×C8—21no—
369C22×C8—21no—
370#117—21no—
371#117—21no—
372#117—21no—
373#117—21no—
374#117—432no—
375#117—432no—
376#117—432no—
377#117—861no—
378#117—861no—
379#117—861no—
380#117—861no—
381#117—861no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4—864no—
386C2×C22⋊C4—861no—
387C2×C22⋊C4—861no—
388C2×C22⋊C4D17212yes—
389C2×C42—21no—
390C2×C42—432no—
391C2×C42—432no—
392C2×C42—861no—
393C2×C42—861no—
394C2×C42—861no—
395C2×C42—861no—
396C2×C42—861no—
397C2×C42—861no—
398#104—868no—
399#104—868no—
400#99—868no—
401#95—864no—
402C24—861no—
403C24C2×D17211yescharacteristic
404#41—862no—
405#41—862no—
406#41—862no—
407#41—862no—
408#41—862no—
409#41—862no—
410#41—862no—
411#41—862no—
412#41—1721no—
413#41—1721no—
414#41—1721no—
415#41—1721no—
416#41—1721no—
417#41—1721no—
418#41—1721no—
419#41—1721no—
420C2×Q8—432no—
421C2×Q8—861no—
422C2×Q8—861no—
423C2×Q8—861no—
424C2×Q8—861no—
425C2×Q8—861no—
426C2×D4—432no—
427C2×D4—862no—
428C2×D4—862no—
429C2×D4—861no—
430C2×D4—861no—
431C2×D4—861no—
432C2×D4—861no—
433C2×D4—861no—
434C2×D4—1721no—
435C2×D4—1721no—
436C2×D4—1721no—
437C2×D4—1721no—
438C22×C4—22no—
439C22×C4—862no—
440C22×C4—862no—
441C22×C4—861no—
442C22×C4—862no—
443C22×C4—862no—
444C22×C4—1724no—
445C22×C4—1721no—
446C22×C4—1721no—
447C22×C4—1721no—
448C22×C4—1721no—
449C22×C4—1721no—
450C22×C4—1721no—
451C22×C4—1721no—
452C22×C4C2×C4×D4311yescharacteristic
453C22×C4#1062189811yescharacteristic
454C22×C4#1062189811yescharacteristic
455C22×C4#1062189811yescharacteristic
456C22×C4#1062189811yescharacteristic
457C22×C4D4×D4311yescharacteristic
458C22×C4D4×D4311yescharacteristic
459C22×C4D4×D4311yescharacteristic
460C22×C4D4×D4311yescharacteristic
461C22×C4D4×D4311yescharacteristic
462C22×C4#1062190011yescharacteristic
463C22×C4Q8×D4311yescharacteristic
464C22×C4#1062190211yescharacteristic
465C22×C4C2×C22⋊D4311yescharacteristic
466M16—22no—
467M16—22no—
468M16—22no—
469M16—22no—
470M16—41no—
471M16—41no—
472M16—41no—
473M16—41no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—41no—
480C4⋊C4—41no—
481C4⋊C4—41no—
482C4⋊C4—862no—
483C4⋊C4—862no—
484C4⋊C4—862no—
485C4⋊C4—1728no—
486C4⋊C4—1721no—
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—862no—
490C22⋊C4—862no—
491C22⋊C4—862no—
492C22⋊C4—1721no—
493C42—41no—
494C42—41no—
495C42—434no—
496C42—862no—
497C42—862no—
498C42—862no—
499C42—862no—
500C42—1721no—
501C42—1721no—
502C42—1721no—
503C23—42no—
504C23—862no—
505C23—3442no—
506C23—1721no—
507C23—1721no—
508C23C4×D17211yescharacteristic
509C23#1306329511yescharacteristic
510C23#1306329511yescharacteristic
511C23#1306329911yescharacteristic
512C23#1306330011yescharacteristic
513C23#1306330511yescharacteristic
514C23#1306331311yescharacteristic
515Q8—862no—
516Q8—862no—
517Q8—1721no—
518Q8—1721no—
519D4—862no—
520D4—862no—
521D4—1722no—
522D4—1722no—
523D4—1722no—
524D4—1722no—
525D4—1721no—
526D4—1721no—
527C2×C4—44no—
528C2×C4—42no—
529C2×C4—864no—
530C2×C4—862no—
531C2×C4—864no—
532C2×C4—3442no—
533C2×C4—1722no—
534C2×C4—1724no—
535C2×C4—1722no—
536C2×C4—1724no—
537C2×C4—1724no—
538C2×C4—1722no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4—1722no—
542C2×C4—1722no—
543C2×C4—1722no—
544C2×C4—1722no—
545C2×C4C22⋊C4×D4311yescharacteristic
546C2×C4C4⋊C4×D4311yescharacteristic
547C2×C4#1306328211yescharacteristic
548C2×C4(C22⋊D43)⋊C411yescharacteristic
549C2×C4C4×C22⋊D4311yescharacteristic
550C2×C4#1306328711yescharacteristic
551C2×C4#1306329311yescharacteristic
552C2×C4#1306329711yescharacteristic
553C2×C4#1306329811yescharacteristic
554C2×C4#1306329811yescharacteristic
555C2×C4#1306329811yescharacteristic
556C2×C4#1306329811yescharacteristic
557C2×C4#1306329811yescharacteristic
558C2×C4#1306330111yescharacteristic
559C2×C4#1306330311yescharacteristic
560C2×C4#1306330311yescharacteristic
561C2×C4#1306330311yescharacteristic
562C2×C4#1306330311yescharacteristic
563C2×C4#1306330711yescharacteristic
564C2×C4#1306330811yescharacteristic
565C2×C4#1306331011yescharacteristic
566C2×C4#1306331011yescharacteristic
567C2×C4#1306331011yescharacteristic
568C2×C4#1306331111yescharacteristic
569C2×C4#1306331111yescharacteristic
570C2×C4#1306331911yescharacteristic
571C2×C4#1306332011yescharacteristic
572C2×C4#1306332111yescharacteristic
573C8—42no—
574C8—42no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—3442no—
583C22—3442no—
584C22—3442no—
585C22—1722no—
586C22#1458277311yescharacteristic
587C22#1458277711yescharacteristic
588C22#1458279011yescharacteristic
589C22#1458280811yescharacteristic
590C22#1458281211yescharacteristic
591C22#1458281711yescharacteristic
592C22#1458282111yescharacteristic
593C4—82no—
594C4—3442no—
595C4—1724no—
596C4—1724no—
597C4—1722no—
598C4#1458275811yescharacteristic
599C4#1458277011yescharacteristic
600C4#1458278811yescharacteristic
601C4#1458279911yescharacteristic
602C4#1458281411yescharacteristic
603C4#1458282311yescharacteristic
604C4#1458282811yescharacteristic
605C4#1458283411yescharacteristic
606C2—21no—
607C2—21no—
608C2—21no—
609C2—21no—
610C2—21no—
611C2—21no—
612C2—3442no—
613C2#1913283911yescharacteristic
614C2#1913577012yes—
subgroupG/H
centerC2×C4#13063311
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#344C2
socleC22×C43#393
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenterC2×#344D43
hypocenterC43#11085
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
4. #19137077C2semidirect
5. C2×#14582660C2semidirect
6. C2×#14582656C2semidirect
7. C2×C43×#344C2semidirect
13. #14582915C4semidirect
145. C2×D172C4⋊C4semidirect
157. C2×Dic86C4⋊C4semidirect
303. C2×#344D43semidirect
337. C43#11085semidirect

Maximal subgroups

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

subgroupindex
C2×#145829152
C22×#130632512
C2×#145828722
#191370772
C2×#145826602
C2×#145826562
C2×C43×#3442
#1108543