Finite Group Databasebeta

← #25003815

Subgroups — #25003815

Order 11008.

882 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143115C211yesmaximal, characteristic
2C2×#14582896C211yesmaximal, characteristic
3C2×#14582872C211yesmaximal, characteristic
4#19134327C211yesmaximal, characteristic, complemented
5#19134312C211yesmaximal, characteristic, complemented
6C2×#14582656C211yesmaximal, characteristic, complemented
7C2×C43×#424C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C2×#13063284C2211yescharacteristic
10C2×#13063284C2211yescharacteristic
11C2×#13063284C2211yescharacteristic
12#14582909—21no—
13#14582905—21no—
14#14582901—22no—
15#14582896—22no—
16#14582896—22no—
17#14582896—22no—
18C2×#13063250—21no—
19C2×#13063247—21no—
20#14582872—22no—
21#14582872C414yescomplemented
22C2×#13063239—22no—
23#14582665—22no—
24#14582662—22no—
25#14582656—22no—
26C22×M16×C43C2211yescharacteristic
27C23×C8×C43C2211yescharacteristic
28C2×#117×C43C2211yescharacteristic
29C43×#424—22no—
30C43×#424—22no—
31C2×C4⋊C8×C43—22no—
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×#10621898—21no—
41C2×#10621898—21no—
42C2×#10621898C2×C412yes—
43C2×#10621898Q812yes—
44C22×Dic86D411yescharacteristic
45C22×D172D411yescharacteristic
46C22×C22⋊D43—21no—
47C22×C4×D43—21no—
48#13063284—21no—
49#13063284—21no—
50#13063284—21no—
51#13063284—21no—
52#13063284—21no—
53#13063284—21no—
54#13063284—21no—
55#13063284—21no—
56#13063284—21no—
57#13063284—21no—
58#13063284C2×C412yes—
59#13063284D412yes—
60C2×C4⋊Dic43—21no—
61C2×C4⋊Dic43—21no—
62C2×C4⋊Dic43D412yes—
63C2×C22⋊Dic43—21no—
64C2×C22⋊Dic43—21no—
65C2×C22⋊Dic43—21no—
66C2×C4×Dic43—21no—
67C2×C4×Dic43—21no—
68C2×C4×Dic43—21no—
69#13063250—24no—
70#13063250—24no—
71#13063247—24no—
72#13063247—24no—
73#13063239—28no—
74C23×C4×C43C2311yescharacteristic
75C2×M16×C43—21no—
76C2×M16×C43—21no—
77C2×M16×C43—21no—
78C2×M16×C43—21no—
79C2×M16×C43—21no—
80C2×M16×C43—21no—
81C22×C8×C43—21no—
82C22×C8×C43—21no—
83C22×C8×C43—21no—
84C22×C8×C43—21no—
85C22×C8×C43—21no—
86C22×C8×C43—21no—
87C22×C8×C43D412yes—
88C22×C8×C43D412yes—
89#117×C43—21no—
90#117×C43—21no—
91#117×C43C2×C412yes—
92#117×C43D412yes—
93C2×C4⋊C4×C43—21no—
94C2×C22⋊C4×C43D412yes—
95C2×C42×C43—21no—
96C4⋊C8×C43—28no—
97C24×C43C2×D411yescharacteristic
98C23×D43—21no—
99C22×C4×C43—22no—
100C22×C4×C43C22×C411yescharacteristic
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43C2×D411yescharacteristic
105C22×C4×C43C2×D411yescharacteristic
106C22×C4×C43C2×D411yescharacteristic
107C22×C4×C43C2×Q811yescharacteristic
108C22×C4×C43#4111yescharacteristic
109C22×C4×C43#4111yescharacteristic
110C22×C4×C43#4111yescharacteristic
111C22×C4×C43#4111yescharacteristic
112C22×C4×C43#4111yescharacteristic
113C22×C4×C43#4111yescharacteristic
114C2×C22⋊D43—22no—
115C2×C22⋊D43—22no—
116C2×C22⋊D43—41no—
117C2×C22⋊D43—41no—
118C2×C22⋊D43—41no—
119C2×C22⋊D43—41no—
120C22×Dic43—21no—
121C22×Dic43—22no—
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⋊C412yes—
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⋊C412yes—
158M16×C43—41no—
159M16×C43—41no—
160M16×C43—41no—
161M16×C43—41no—
162C2×C8×C43—22no—
163C2×C8×C43—22no—
164C2×C8×C43—22no—
165C2×C8×C43—22no—
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—22no—
173C4⋊C4×C43—22no—
174C22⋊C4×C43—22no—
175C22⋊C4×C43C22⋊C414yes—
176C42×C43—22no—
177C42×C43—22no—
178C22⋊Dic43—22no—
179C22⋊Dic43—22no—
180C22⋊Dic43—41no—
181C22⋊Dic43—41no—
182C22⋊Dic43—41no—
183C22⋊Dic43—41no—
184C4⋊Dic43—22no—
185C4⋊Dic43—22no—
186C4⋊Dic43—22no—
187C4⋊Dic43—22no—
188C4⋊Dic43—41no—
189C4⋊Dic43—41no—
190C4×Dic43—22no—
191C4×Dic43—22no—
192C4×Dic43—41no—
193C4×Dic43—41no—
194C4×Dic43—41no—
195C4×Dic43—41no—
196C23×C43—42no—
197C23×C43C2×C22⋊C411yescharacteristic
198C23×C43#12111yescharacteristic
199C23×C43#12111yescharacteristic
200C23×C43#12111yescharacteristic
201C23×C43#12111yescharacteristic
202C23×C43#12111yescharacteristic
203C23×C43C22⋊Q811yescharacteristic
204C22×D43—22no—
205C22×D43—41no—
206C22×D43—41no—
207C22×D43—82no—
208C2×C4×C43—24no—
209C2×C4×C43—44no—
210C2×C4×C43C2×C4⋊C411yescharacteristic
211C2×C4×C43#11711yescharacteristic
212C2×C4×C43C4×D411yescharacteristic
213C2×C4×C43C4×D411yescharacteristic
214C2×C4×C43C4×D411yescharacteristic
215C2×C4×C43C4×D411yescharacteristic
216C2×C4×C43#12011yescharacteristic
217C2×C4×C43#12011yescharacteristic
218C2×C4×C43#12011yescharacteristic
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#12411yescharacteristic
235C2×C4×C43#12611yescharacteristic
236C2×C4×C43#12611yescharacteristic
237C2×C4×C43#12711yescharacteristic
238C22⋊D43—42no—
239C22⋊D43—42no—
240C22⋊D43—42no—
241C22⋊D43—42no—
242C2×Dic43—22no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—42no—
246C2×Dic43—42no—
247C2×Dic43—42no—
248C2×Dic43—82no—
249C2×Dic43—82no—
250C2×Dic43—82no—
251D172—22no—
252D172—22no—
253D172—41no—
254D172—41no—
255C4×D43—42no—
256C4×D43—42no—
257C4×D43—42no—
258C4×D43—42no—
259Dic86—22no—
260Dic86—22no—
261Dic86—41no—
262Dic86—41no—
263C8×C43—42no—
264C8×C43—42no—
265#11092—431nomaximal, Sylow
266C22×C43—22no—
267C22×C43—22no—
268C22×C43—22no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43#38011yescharacteristic
274C22×C43#38611yescharacteristic
275C22×C43#39011yescharacteristic
276C22×C43#39411yescharacteristic
277C22×C43#39411yescharacteristic
278C22×C43#39611yescharacteristic
279C22×C43#39611yescharacteristic
280C2×D43—42no—
281C2×D43—82no—
282C2×D43—82no—
283C2×D43—82no—
284C4×C43—44no—
285C4×C43#38511yescharacteristic
286C4×C43#38511yescharacteristic
287C4×C43#38811yescharacteristic
288C4×C43#38811yescharacteristic
289C4×C43#39211yescharacteristic
290C4×C43#39311yescharacteristic
291C4×C43#39711yescharacteristic
292C4×C43#39911yescharacteristic
293Dic43—42no—
294Dic43—82no—
295Dic43—82no—
296Dic43—82no—
297C2×#424D4311yescharacteristic, complemented
298#2896—431no—
299C2×#416—431no—
300C2×#410—431no—
301#1740—431no—
302#1735—431no—
303C2×H(3,ℤ/4)—431no—
304C2×C43—21no—
305C2×C43—21no—
306C2×C43—21no—
307C2×C43—21no—
308C2×C43—21no—
309C2×C43—21no—
310C2×C43#143911yescharacteristic
311C2×C43#205312yes—
312D43—82no—
313C22×#41—431no—
314C22×M16C2×D4311yescharacteristic
315C23×C8C2×D4311yescharacteristic
316C2×#117—431no—
317C2×#117—431no—
318C2×#117—431no—
319C2×#117C2×D4311yescharacteristic
320#424—22no—
321#424—22no—
322C2×C4⋊C8—22no—
323#419—861no—
324#418—861no—
325#417—862no—
326#416—862no—
327#416—862no—
328#416—862no—
329C2×#103—861no—
330C2×#102—861no—
331#410—434no—
332#410—862no—
333C2×#99—862no—
334#342—862no—
335#340—862no—
336H(3,ℤ/4)—862no—
337C43#1109211yescharacteristic, 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×C4C22×D4311yescharacteristic
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C22×C8—21no—
362C22×C8—21no—
363C22×C8—21no—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—21no—
367C22×C8C22⋊D4312yes—
368C22×C8C22⋊D4312yes—
369#117—21no—
370#117—21no—
371#117—432no—
372#117—432no—
373#117—861no—
374#117—861no—
375#117—861no—
376#117—861no—
377#117—861no—
378#117—861no—
379#117—861no—
380#117—861no—
381#117—861no—
382#117—861no—
383#117C4×D4312yes—
384#117C22⋊D4312yes—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—432no—
387C2×C4⋊C4—861no—
388C2×C4⋊C4—861no—
389C2×C22⋊C4—861no—
390C2×C22⋊C4—861no—
391C2×C22⋊C4—861no—
392C2×C22⋊C4D17212yes—
393C2×C42—21no—
394C2×C42—861no—
395C2×C42—861no—
396C2×C42—861no—
397C4⋊C8—28no—
398#103—864no—
399#103—864no—
400#102—864no—
401#102—864no—
402#99—868no—
403C24—861no—
404C24C2×D17211yescharacteristic
405#41—862no—
406#41—862no—
407#41—862no—
408#41—862no—
409#41—862no—
410#41—862no—
411#41—862no—
412#41—862no—
413#41—1721no—
414#41—1721no—
415#41—1721no—
416#41—1721no—
417#41—1721no—
418#41—1721no—
419#41—1721no—
420#41—1721no—
421C2×Q8—432no—
422C2×Q8—861no—
423C2×Q8—861no—
424C2×Q8—861no—
425C2×Q8—861no—
426C2×Q8—861no—
427C2×D4—432no—
428C2×D4—862no—
429C2×D4—862no—
430C2×D4—861no—
431C2×D4—861no—
432C2×D4—861no—
433C2×D4—861no—
434C2×D4—861no—
435C2×D4—1721no—
436C2×D4—1721no—
437C2×D4—1721no—
438C2×D4—1721no—
439C22×C4—22no—
440C22×C4—861no—
441C22×C4—862no—
442C22×C4—862no—
443C22×C4—862no—
444C22×C4—1721no—
445C22×C4—1721no—
446C22×C4—1721no—
447C22×C4—1721no—
448C22×C4—1721no—
449C22×C4—1721no—
450C22×C4C2×C4×D4311yescharacteristic
451C22×C4#1062189811yescharacteristic
452C22×C4#1062189811yescharacteristic
453C22×C4D4×D4311yescharacteristic
454C22×C4D4×D4311yescharacteristic
455C22×C4D4×D4311yescharacteristic
456C22×C4#1062190011yescharacteristic
457C22×C4Q8×D4311yescharacteristic
458C22×C4#1062190211yescharacteristic
459C22×C4#1062190211yescharacteristic
460C22×C4#1062190211yescharacteristic
461C22×C4C2×C22⋊D4311yescharacteristic
462C22×C4C2×C22⋊D4311yescharacteristic
463C22×C4C2×C22⋊D4311yescharacteristic
464M16—41no—
465M16—41no—
466M16—41no—
467M16—41no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—41no—
475C2×C8—41no—
476C2×C8—41no—
477C2×C8—41no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—862no—
481C4⋊C4—862no—
482C4⋊C4—862no—
483C4⋊C4—862no—
484C4⋊C4—1721no—
485C4⋊C4—1721no—
486C22⋊C4—22no—
487C22⋊C4—862no—
488C22⋊C4—862no—
489C22⋊C4—1721no—
490C22⋊C4—1721no—
491C22⋊C4—1721no—
492C22⋊C4—1721no—
493C22⋊C4(C2×D43)⋊C414yes—
494C42—22no—
495C42—22no—
496C42—862no—
497C42—862no—
498C42—1721no—
499C42—1721no—
500C42—1721no—
501C42—1721no—
502C23—42no—
503C23—862no—
504C23—3442no—
505C23—1721no—
506C23—1721no—
507C23C2×(C2×D43)⋊C411yescharacteristic
508C23#1306329911yescharacteristic
509C23#1306329911yescharacteristic
510C23#1306330011yescharacteristic
511C23#1306330011yescharacteristic
512C23#1306330011yescharacteristic
513C23#1306330511yescharacteristic
514Q8—862no—
515Q8—862no—
516Q8—1721no—
517Q8—1721no—
518D4—862no—
519D4—862no—
520D4—1722no—
521D4—1722no—
522D4—1722no—
523D4—1722no—
524D4—1721no—
525D4—1721no—
526C2×C4—24no—
527C2×C4—44no—
528C2×C4—862no—
529C2×C4—3442no—
530C2×C4—3442no—
531C2×C4—3442no—
532C2×C4—1722no—
533C2×C4—1722no—
534C2×C4—1722no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4—1722no—
538C2×C4—1722no—
539C2×C4—1722no—
540C2×C4—1722no—
541C2×C4C4⋊C4×D4311yescharacteristic
542C2×C4#1306328311yescharacteristic
543C2×C4C4×C22⋊D4311yescharacteristic
544C2×C4C4×C22⋊D4311yescharacteristic
545C2×C4#1306328711yescharacteristic
546C2×C4#1306328711yescharacteristic
547C2×C4#1306329311yescharacteristic
548C2×C4#1306329311yescharacteristic
549C2×C4#1306329411yescharacteristic
550C2×C4#1306329611yescharacteristic
551C2×C4#1306329711yescharacteristic
552C2×C4#1306329711yescharacteristic
553C2×C4#1306330111yescharacteristic
554C2×C4#1306330111yescharacteristic
555C2×C4#1306330111yescharacteristic
556C2×C4#1306330311yescharacteristic
557C2×C4#1306330311yescharacteristic
558C2×C4#1306330811yescharacteristic
559C2×C4#1306331011yescharacteristic
560C2×C4#1306331011yescharacteristic
561C2×C4#1306331011yescharacteristic
562C2×C4#1306331011yescharacteristic
563C2×C4#1306331411yescharacteristic
564C2×C4#1306331411yescharacteristic
565C2×C4#1306331411yescharacteristic
566C2×C4#1306332011yescharacteristic
567C2×C4#1306332011yescharacteristic
568C2×C4#1306332111yescharacteristic
569C8—42no—
570C8—42no—
571C22—22no—
572C22—22no—
573C22—22no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—3442no—
579C22—3442no—
580C22—3442no—
581C22—1722no—
582C22#1458275611yescharacteristic
583C22#1458277811yescharacteristic
584C22#1458280011yescharacteristic
585C22#1458281611yescharacteristic
586C22#1458281611yescharacteristic
587C22#1458282111yescharacteristic
588C22#1458282111yescharacteristic
589C4—44no—
590C4—3442no—
591C4—3442no—
592C4—3442no—
593C4—1722no—
594C4#1458277011yescharacteristic
595C4#1458277011yescharacteristic
596C4#1458278911yescharacteristic
597C4#1458278911yescharacteristic
598C4#1458280711yescharacteristic
599C4#1458281011yescharacteristic
600C4#1458282511yescharacteristic
601C4#1458283411yescharacteristic
602C2—21no—
603C2—21no—
604C2—21no—
605C2—21no—
606C2—21no—
607C2—21no—
608C2—3442no—
609C2#1913283711yescharacteristic
610C2#1913590112yes—
subgroupG/H
centerC2×C4#13063314
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#424C2
socleC22×C43#394
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenterC2×#424D43
hypocenterC43#11092
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
4. #19134327C2semidirect
5. #19134312C2semidirect
6. C2×#14582656C2semidirect
7. C2×C43×#424C2semidirect
21. #14582872C4semidirect
297. C2×#424D43semidirect
337. C43#11092semidirect

Maximal subgroups

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

subgroupindex
#191431152
C2×#145828962
C2×#145828722
#191343272
#191343122
C2×#145826562
C2×C43×#4242
#1109243