Finite Group Databasebeta

← #25003819

Subgroups — #25003819

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
1C2×#14582926C211yesmaximal, characteristic, complemented
2#19143112C211yesmaximal, characteristic
3C2×#14582893C211yesmaximal, characteristic
4C2×#14582872C211yesmaximal, characteristic
5#19134311C211yesmaximal, characteristic, complemented
6C2×#14582655C211yesmaximal, characteristic, complemented
7C43×#1740C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10C23×C43⋊C8C2211yescharacteristic
11C2×#13063284C2211yescharacteristic
12#14582926—22no—
13#14582926—22no—
14C2×C4⋊(C43⋊C8)—22no—
15#14582907—21no—
16#14582903—21no—
17#14582898—22no—
18#14582893—22no—
19#14582893—22no—
20#14582893—22no—
21C2×#13063248—21no—
22C2×#13063245—21no—
23#14582872—22no—
24#14582872C414yescomplemented
25C2×#13063239—22no—
26#14582661—22no—
27#14582655—22no—
28C2×#117×C43C2211yescharacteristic
29C2×#117×C43C2211yescharacteristic
30C2×#117×C43C2211yescharacteristic
31C43×#342—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—
48C2×#10621877—21no—
49C2×#10621877—21no—
50C2×#10621877—21no—
51C2×#10621877—21no—
52C2×#10621877—21no—
53C2×#10621877—21no—
54C22×C43⋊C8—21no—
55C22×C43⋊C8—21no—
56C22×C43⋊C8—21no—
57C22×C43⋊C8—21no—
58C22×C43⋊C8—21no—
59C22×C43⋊C8—21no—
60C22×C43⋊C8D412yes—
61C22×C43⋊C8D412yes—
62#13063284—21no—
63#13063284—21no—
64#13063284—21no—
65#13063284C2×C412yes—
66C2×C4⋊Dic43—21no—
67C2×C22⋊Dic43—21no—
68C2×C4×Dic43—21no—
69C4⋊(C43⋊C8)—28no—
70#13063248—24no—
71#13063248—24no—
72#13063245—24no—
73#13063245—24no—
74#13063239—28no—
75C23×C4×C43C2311yescharacteristic
76#117×C43—21no—
77#117×C43—21no—
78#117×C43—21no—
79#117×C43—21no—
80#117×C43—21no—
81#117×C43—21no—
82#117×C43—21no—
83#117×C43—21no—
84#117×C43—21no—
85#117×C43C2×C412yes—
86#117×C43D412yes—
87#117×C43D412yes—
88C2×C4⋊C4×C43—21no—
89C2×C4⋊C4×C43—21no—
90C2×C4⋊C4×C43D412yes—
91C2×C22⋊C4×C43—21no—
92C2×C22⋊C4×C43—21no—
93C2×C22⋊C4×C43D412yes—
94C2×C42×C43—21no—
95C2×C42×C43—21no—
96C2×C42×C43—21no—
97C24×C43C2×D411yescharacteristic
98C23×D43—21no—
99C22×C4×C43—22no—
100C22×C4×C43—22no—
101C22×C4×C43—41no—
102C22×C4×C43C22×C411yescharacteristic
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43C2×D411yescharacteristic
105C22×C4×C43C2×D411yescharacteristic
106C22×C4×C43C2×D411yescharacteristic
107C22×C4×C43C2×D411yescharacteristic
108C22×C4×C43C2×D411yescharacteristic
109C22×C4×C43C2×Q811yescharacteristic
110C22×C4×C43#4111yescharacteristic
111C22×C4×C43#4111yescharacteristic
112C22×C4×C43#4111yescharacteristic
113C22×C4×C43#4111yescharacteristic
114C22×C4×C43#4111yescharacteristic
115C22×C4×C43#4111yescharacteristic
116C2×C22⋊D43—22no—
117C2×C22⋊D43—22no—
118C2×C22⋊D43—41no—
119C2×C22⋊D43—41no—
120C2×C22⋊D43—41no—
121C2×C22⋊D43—41no—
122C22×Dic43—21no—
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—
158C4⋊C4×C43—22no—
159C4⋊C4×C43—22no—
160C4⋊C4×C43—22no—
161C4⋊C4×C43—22no—
162C4⋊C4×C43—22no—
163C4⋊C4×C43—41no—
164C22⋊C4×C43—22no—
165C22⋊C4×C43—22no—
166C22⋊C4×C43—41no—
167C22⋊C4×C43—41no—
168C22⋊C4×C43—41no—
169C22⋊C4×C43C22⋊C414yes—
170C42×C43—22no—
171C42×C43—22no—
172C42×C43—22no—
173C42×C43—41no—
174C42×C43—41no—
175C42×C43—41no—
176C22⋊Dic43—22no—
177C22⋊Dic43—41no—
178C4⋊Dic43—22no—
179C4⋊Dic43—41no—
180C4×Dic43—22no—
181C4×Dic43—41no—
182#10621877—41no—
183#10621877—41no—
184#10621877—41no—
185#10621877—41no—
186C2×C43⋊C8—22no—
187C2×C43⋊C8—22no—
188C2×C43⋊C8—22no—
189C2×C43⋊C8—22no—
190C2×C43⋊C8—22no—
191C2×C43⋊C8—22no—
192C2×C43⋊C8—41no—
193C2×C43⋊C8—41no—
194C2×C43⋊C8—41no—
195C2×C43⋊C8—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×C43—42no—
211C2×C4×C43—42no—
212C2×C4×C43—82no—
213C2×C4×C43—82no—
214C2×C4×C43C2×C4⋊C411yescharacteristic
215C2×C4×C43#11711yescharacteristic
216C2×C4×C43C4×D411yescharacteristic
217C2×C4×C43C4×D411yescharacteristic
218C2×C4×C43C4×D411yescharacteristic
219C2×C4×C43C4×D411yescharacteristic
220C2×C4×C43#12011yescharacteristic
221C2×C4×C43#12011yescharacteristic
222C2×C4×C43#12011yescharacteristic
223C2×C4×C43#12111yescharacteristic
224C2×C4×C43#12111yescharacteristic
225C2×C4×C43#12111yescharacteristic
226C2×C4×C43C22⋊Q811yescharacteristic
227C2×C4×C43C22⋊Q811yescharacteristic
228C2×C4×C43C22⋊Q811yescharacteristic
229C2×C4×C43C22⋊Q811yescharacteristic
230C2×C4×C43C22⋊Q811yescharacteristic
231C2×C4×C43#12311yescharacteristic
232C2×C4×C43#12311yescharacteristic
233C2×C4×C43#12311yescharacteristic
234C2×C4×C43#12311yescharacteristic
235C2×C4×C43#12311yescharacteristic
236C2×C4×C43#12411yescharacteristic
237C2×C4×C43#12411yescharacteristic
238C2×C4×C43#12411yescharacteristic
239C2×C4×C43#12611yescharacteristic
240C2×C4×C43#12611yescharacteristic
241C2×C4×C43#12711yescharacteristic
242C22⋊D43—42no—
243C22⋊D43—42no—
244C22⋊D43—42no—
245C22⋊D43—42no—
246C2×Dic43—22no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—42no—
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—
263C43⋊C8—42no—
264C43⋊C8—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—82no—
286C4×C43—82no—
287C4×C43#38511yescharacteristic
288C4×C43#38511yescharacteristic
289C4×C43#38811yescharacteristic
290C4×C43#38811yescharacteristic
291C4×C43#39211yescharacteristic
292C4×C43#39311yescharacteristic
293C4×C43#39711yescharacteristic
294C4×C43#39911yescharacteristic
295Dic43—42no—
296Dic43—82no—
297C2×#424—431no—
298#2896—431no—
299C2×#416—431no—
300C2×#410—431no—
301#1740D4311yescharacteristic, complemented
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×M16—431no—
315C23×C8—431no—
316C2×#117—431no—
317C2×#117C2×D4311yescharacteristic
318C2×#117C2×D4311yescharacteristic
319C2×#117C2×D4311yescharacteristic
320#424—862no—
321#424—862no—
322C2×C4⋊C8—862no—
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—22no—
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—861no—
356C2×M16—861no—
357C2×M16—861no—
358C2×M16—861no—
359C2×M16—861no—
360C2×M16—861no—
361C22×C8—432no—
362C22×C8—432no—
363C22×C8—861no—
364C22×C8—861no—
365C22×C8—861no—
366C22×C8—861no—
367C22×C8—861no—
368C22×C8—861no—
369#117—21no—
370#117—21no—
371#117—21no—
372#117—21no—
373#117—21no—
374#117—21no—
375#117—21no—
376#117—21no—
377#117—21no—
378#117—432no—
379#117—861no—
380#117—861no—
381#117—861no—
382#117C4×D4312yes—
383#117D17212yes—
384#117D17212yes—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—861no—
388C2×C4⋊C4D17212yes—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—861no—
392C2×C22⋊C4C22⋊D4312yes—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—861no—
397C4⋊C8—868no—
398#103—864no—
399#103—864no—
400#102—864no—
401#102—864no—
402#99—868no—
403C24—861no—
404C24C2×C22⋊D4311yescharacteristic
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—22no—
441C22×C4—41no—
442C22×C4—861no—
443C22×C4—862no—
444C22×C4—862no—
445C22×C4—1721no—
446C22×C4—1721no—
447C22×C4—1721no—
448C22×C4—1721no—
449C22×C4—1721no—
450C22×C4C2×C4×D4311yescharacteristic
451C22×C4C2×D17211yescharacteristic
452C22×C4C2×D17211yescharacteristic
453C22×C4C2×D17211yescharacteristic
454C22×C4#1062189811yescharacteristic
455C22×C4#1062189811yescharacteristic
456C22×C4D4×D4311yescharacteristic
457C22×C4D4×D4311yescharacteristic
458C22×C4D4×D4311yescharacteristic
459C22×C4#1062190011yescharacteristic
460C22×C4#1062190011yescharacteristic
461C22×C4#1062190011yescharacteristic
462C22×C4Q8×D4311yescharacteristic
463C22×C4#1062190211yescharacteristic
464M16—1721no—
465M16—1721no—
466M16—1721no—
467M16—1721no—
468C2×C8—862no—
469C2×C8—862no—
470C2×C8—862no—
471C2×C8—862no—
472C2×C8—862no—
473C2×C8—862no—
474C2×C8—1721no—
475C2×C8—1721no—
476C2×C8—1721no—
477C2×C8—1721no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—41no—
484C4⋊C4—862no—
485C4⋊C4—1721no—
486C22⋊C4—22no—
487C22⋊C4—22no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C22⋊C4—862no—
492C22⋊C4—1721no—
493C22⋊C4(C2×D43)⋊C414yes—
494C42—22no—
495C42—22no—
496C42—22no—
497C42—41no—
498C42—41no—
499C42—41no—
500C42—862no—
501C42—1721no—
502C23—42no—
503C23—862no—
504C23—3442no—
505C23—1721no—
506C23—1721no—
507C23C2×(C2×D43)⋊C411yescharacteristic
508C23#1306329611yescharacteristic
509C23#1306329711yescharacteristic
510C23#1306329711yescharacteristic
511C23#1306329911yescharacteristic
512C23#1306329911yescharacteristic
513C23#1306330111yescharacteristic
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—42no—
529C2×C4—42no—
530C2×C4—82no—
531C2×C4—82no—
532C2×C4—862no—
533C2×C4—3442no—
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×C4(C22⋊D43)⋊C411yescharacteristic
544C2×C4(C22⋊D43)⋊C411yescharacteristic
545C2×C4C4×D17211yescharacteristic
546C2×C4C4×D17211yescharacteristic
547C2×C4#1306329511yescharacteristic
548C2×C4#1306329511yescharacteristic
549C2×C4#1306329511yescharacteristic
550C2×C4#1306330011yescharacteristic
551C2×C4#1306330011yescharacteristic
552C2×C4#1306330011yescharacteristic
553C2×C4#1306330311yescharacteristic
554C2×C4#1306330311yescharacteristic
555C2×C4#1306330511yescharacteristic
556C2×C4#1306330511yescharacteristic
557C2×C4#1306330511yescharacteristic
558C2×C4#1306330711yescharacteristic
559C2×C4#1306330711yescharacteristic
560C2×C4#1306330911yescharacteristic
561C2×C4#1306330911yescharacteristic
562C2×C4#1306330911yescharacteristic
563C2×C4#1306331111yescharacteristic
564C2×C4#1306331111yescharacteristic
565C2×C4#1306331311yescharacteristic
566C2×C4#1306332011yescharacteristic
567C2×C4#1306332011yescharacteristic
568C2×C4#1306332211yescharacteristic
569C8—1722no—
570C8—1722no—
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#1458277611yescharacteristic
584C22#1458280111yescharacteristic
585C22#1458281511yescharacteristic
586C22#1458281511yescharacteristic
587C22#1458282111yescharacteristic
588C22#1458282111yescharacteristic
589C4—44no—
590C4—82no—
591C4—82no—
592C4—3442no—
593C4—1722no—
594C4#1458277311yescharacteristic
595C4#1458277311yescharacteristic
596C4#1458279111yescharacteristic
597C4#1458279111yescharacteristic
598C4#1458280911yescharacteristic
599C4#1458281211yescharacteristic
600C4#1458282611yescharacteristic
601C4#1458283611yescharacteristic
602C2—21no—
603C2—21no—
604C2—21no—
605C2—21no—
606C2—21no—
607C2—21no—
608C2—3442no—
609C2#1913284111yescharacteristic
610C2#1913590012yes—
subgroupG/H
centerC2×C4#13063311
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1740C2
socleC22×C43#394
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenter#1740D43
hypocenterC43#11092
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1740

Complements

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

NH ≅ G/Ntype
1. C2×#14582926C2semidirect
5. #19134311C2semidirect
6. C2×#14582655C2semidirect
7. C43×#1740C2semidirect
24. #14582872C4semidirect
301. #1740D43semidirect
337. C43#11092semidirect

Maximal subgroups

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

subgroupindex
C2×#145829262
#191431122
C2×#145828932
C2×#145828722
#191343112
C2×#145826552
C43×#17402
#1109243