Finite Group Databasebeta

← #25004107

Subgroups — #25004107

Order 11008.

864 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143184C211yesmaximal, characteristic, complemented
2C2×#14582881C211yesmaximal, characteristic
3C2×#14582872C211yesmaximal, characteristic
4C2×#14582872C211yesmaximal, characteristic
5#19134306C211yesmaximal, characteristic, complemented
6#19134304C211yesmaximal, characteristic, complemented
7C2×C43×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10C2×#13063284C2211yescharacteristic
11C2×#13063284C2211yescharacteristic
12#14582942—22no—
13#14582939—22no—
14#14582935—22no—
15#14582881—22no—
16#14582881—22no—
17C2×#13063243C412yescomplemented
18C2×#13063241C412yescomplemented
19#14582872—22no—
20#14582872—22no—
21#14582872—22no—
22#14582872—22no—
23C2×#13063239—22no—
24C2×#13063239—22no—
25#14582660—22no—
26#14582658—22no—
27C22×M16×C43C2211yescharacteristic
28C2×#117×C43C2211yescharacteristic
29C2×#117×C43C2211yescharacteristic
30C43×H(3,ℤ/4)—22no—
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×#10621898—21no—
41C2×#10621898—21no—
42C2×#10621898—21no—
43C22×Dic86C2×C411yescharacteristic
44C22×D172C2×C411yescharacteristic
45C22×C22⋊D43D412yes—
46C22×C4×D43Q812yes—
47C2×#10621877—21no—
48C2×#10621877—21no—
49C2×#10621877—21no—
50C2×#10621877C2×C412yes—
51C2×#10621877D412yes—
52C2×#10621877D412yes—
53C22×C43⋊C8—21no—
54#13063284—21no—
55#13063284—21no—
56#13063284—21no—
57#13063284—21no—
58#13063284—21no—
59#13063284—21no—
60#13063284D412yes—
61#13063284D412yes—
62C2×C4⋊Dic43—21no—
63C2×C4⋊Dic43—21no—
64C2×C22⋊Dic43—21no—
65C2×C22⋊Dic43—21no—
66C2×C4×Dic43—21no—
67C2×C4×Dic43—21no—
68#13063258—24no—
69#13063256—24no—
70#13063243—24no—
71#13063241—24no—
72#13063239—28no—
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×C43C2×C412yes—
81C22×C8×C43—21no—
82#117×C43—21no—
83#117×C43—21no—
84#117×C43—21no—
85#117×C43—21no—
86#117×C43—21no—
87#117×C43—21no—
88#117×C43D412yes—
89#117×C43D412yes—
90C2×C4⋊C4×C43—21no—
91C2×C4⋊C4×C43—21no—
92C2×C22⋊C4×C43—21no—
93C2×C22⋊C4×C43—21no—
94C2×C42×C43—21no—
95C2×C42×C43—21no—
96C24×C43C2×D411yescharacteristic
97C23×D43C4⋊C412yes—
98C22×C4×C43—41no—
99C22×C4×C43—41no—
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—22no—
117C2×C22⋊D43—22no—
118C2×C22⋊D43—22no—
119C2×C22⋊D43—22no—
120C22×Dic43—41no—
121C22×Dic43—41no—
122C22×Dic43C4⋊C412yes—
123#10621898—41no—
124#10621898—41no—
125#10621898—41no—
126#10621898—41no—
127#10621898—41no—
128#10621898—41no—
129#10621898—41no—
130#10621898—41no—
131#10621898—41no—
132#10621898—41no—
133#10621898—41no—
134#10621898—41no—
135#10621898—41no—
136#10621898—41no—
137#10621898—41no—
138#10621898—41no—
139C2×D172—21no—
140C2×D172—21no—
141C2×D172—21no—
142C2×D172—21no—
143C2×D172—21no—
144C2×D172—21no—
145C2×C4×D43—22no—
146C2×C4×D43—22no—
147C2×C4×D43—22no—
148C2×C4×D43—22no—
149C2×C4×D43—22no—
150C2×C4×D43—22no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157M16×C43—22no—
158M16×C43—22no—
159M16×C43—41no—
160M16×C43—41no—
161C2×C8×C43—22no—
162C2×C8×C43—41no—
163C2×C8×C43—41no—
164C4⋊C4×C43—22no—
165C4⋊C4×C43—22no—
166C4⋊C4×C43—41no—
167C4⋊C4×C43—41no—
168C22⋊C4×C43—22no—
169C22⋊C4×C43—22no—
170C22⋊C4×C43—41no—
171C22⋊C4×C43—41no—
172C42×C43—22no—
173C42×C43—22no—
174C42×C43—41no—
175C42×C43—41no—
176C22⋊Dic43—22no—
177C22⋊Dic43—22no—
178C22⋊Dic43—41no—
179C22⋊Dic43—41no—
180C4⋊Dic43—22no—
181C4⋊Dic43—22no—
182C4⋊Dic43—41no—
183C4⋊Dic43—41no—
184C4×Dic43—22no—
185C4×Dic43—22no—
186C4×Dic43—41no—
187C4×Dic43—41no—
188#10621877—22no—
189#10621877—22no—
190#10621877—22no—
191#10621877C22⋊C414yes—
192C2×C43⋊C8—22no—
193C2×C43⋊C8—22no—
194C2×C43⋊C8—22no—
195C23×C43—81no—
196C23×C43C2×C4⋊C411yescharacteristic
197C23×C43#12011yescharacteristic
198C23×C43#12011yescharacteristic
199C23×C43#12111yescharacteristic
200C23×C43#12111yescharacteristic
201C23×C43#12311yescharacteristic
202C23×C43#12311yescharacteristic
203C22×D43—22no—
204C22×D43—22no—
205C22×D43—22no—
206C22×D43—82no—
207C2×C4×C43—42no—
208C2×C4×C43—42no—
209C2×C4×C43—82no—
210C2×C4×C43—82no—
211C2×C4×C43C2×C22⋊C411yescharacteristic
212C2×C4×C43#11711yescharacteristic
213C2×C4×C43C4×D411yescharacteristic
214C2×C4×C43C4×D411yescharacteristic
215C2×C4×C43C4×D411yescharacteristic
216C2×C4×C43C4×D411yescharacteristic
217C2×C4×C43#12011yescharacteristic
218C2×C4×C43#12111yescharacteristic
219C2×C4×C43#12111yescharacteristic
220C2×C4×C43#12111yescharacteristic
221C2×C4×C43#12111yescharacteristic
222C2×C4×C43#12111yescharacteristic
223C2×C4×C43#12111yescharacteristic
224C2×C4×C43C22⋊Q811yescharacteristic
225C2×C4×C43C22⋊Q811yescharacteristic
226C2×C4×C43C22⋊Q811yescharacteristic
227C2×C4×C43C22⋊Q811yescharacteristic
228C2×C4×C43C22⋊Q811yescharacteristic
229C2×C4×C43C22⋊Q811yescharacteristic
230C2×C4×C43#12311yescharacteristic
231C2×C4×C43#12311yescharacteristic
232C2×C4×C43#12311yescharacteristic
233C2×C4×C43#12411yescharacteristic
234C2×C4×C43#12411yescharacteristic
235C2×C4×C43#12411yescharacteristic
236C2×C4×C43#12611yescharacteristic
237C2×C4×C43#12611yescharacteristic
238C2×C4×C43#12711yescharacteristic
239C22⋊D43—42no—
240C22⋊D43—42no—
241C22⋊D43—42no—
242C22⋊D43—42no—
243C2×Dic43—22no—
244C2×Dic43—22no—
245C2×Dic43—22no—
246C2×Dic43—42no—
247C2×Dic43—42no—
248C2×Dic43—82no—
249C2×Dic43—82no—
250D172—41no—
251D172—41no—
252D172—41no—
253D172—41no—
254C4×D43—42no—
255C4×D43—42no—
256C4×D43—42no—
257C4×D43—42no—
258Dic86—41no—
259Dic86—41no—
260Dic86—41no—
261Dic86—41no—
262C8×C43—42no—
263C43⋊C8—24no—
264#11138—431nomaximal, Sylow
265C22×C43—41no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43—41no—
272C22×C43#38011yescharacteristic
273C22×C43#38511yescharacteristic
274C22×C43#38511yescharacteristic
275C22×C43#39211yescharacteristic
276C22×C43#39411yescharacteristic
277C22×C43#39411yescharacteristic
278C22×C43#39711yescharacteristic
279C2×D43—42no—
280C2×D43—82no—
281C2×D43—82no—
282C2×D43—82no—
283C4×C43—82no—
284C4×C43—82no—
285C4×C43#38611yescharacteristic
286C4×C43#38811yescharacteristic
287C4×C43#38811yescharacteristic
288C4×C43#39011yescharacteristic
289C4×C43#39311yescharacteristic
290C4×C43#39611yescharacteristic
291C4×C43#39611yescharacteristic
292C4×C43#39911yescharacteristic
293Dic43—42no—
294Dic43—82no—
295Dic43—82no—
296#2911—431no—
297C2×#413—431no—
298C2×#410—431no—
299C2×#410—431no—
300#1733—431no—
301#1733—431no—
302C2×H(3,ℤ/4)D4311yescharacteristic, complemented
303C2×C43—21no—
304C2×C43—21no—
305C2×C43—21no—
306C2×C43—21no—
307C2×C43—21no—
308C2×C43—21no—
309C2×C43—21no—
310C2×C43#143911yescharacteristic
311D43—82no—
312C22×#41—431no—
313C22×M16—431no—
314C22×M16C2×D4311yescharacteristic
315C2×#117—431no—
316C2×#117—431no—
317C2×#117C2×D4311yescharacteristic
318C2×#117C2×D4311yescharacteristic
319#428—862no—
320#428—862no—
321#427—862no—
322#413—862no—
323#413—862no—
324C2×#101—432no—
325C2×#100—432no—
326#410—862no—
327#410—862no—
328#410—862no—
329#410—862no—
330C2×#99—862no—
331C2×#99—862no—
332#339—862no—
333#339—862no—
334H(3,ℤ/4)—22no—
335C43#1113811yescharacteristic, complemented, Sylow
336C2×#41—861no—
337C2×#41—861no—
338C2×#41—861no—
339C2×#41—861no—
340C2×#41—861no—
341C2×#41—861no—
342C2×#41—861no—
343C2×#41—861no—
344C2×#41—861no—
345C2×#41—861no—
346C2×#41—861no—
347C2×#41—861no—
348C22×Q8—431no—
349C22×D4—432no—
350C22×D4—431no—
351C23×C4—432no—
352C23×C4C22×D4311yescharacteristic
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—432no—
359C2×M16—432no—
360C2×M16—432no—
361C2×M16—861no—
362C2×M16—861no—
363C2×M16—861no—
364C2×M16C4×D4312yes—
365C22×C8—21no—
366C22×C8—861no—
367#117—21no—
368#117—21no—
369#117—21no—
370#117—21no—
371#117—21no—
372#117—21no—
373#117—432no—
374#117—432no—
375#117—861no—
376#117—861no—
377#117—861no—
378#117—861no—
379#117—861no—
380#117—861no—
381#117D17212yes—
382#117C22⋊D4312yes—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—861no—
386C2×C4⋊C4—861no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—861no—
390C2×C22⋊C4—861no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—861no—
394C2×C42—861no—
395#107—864no—
396#106—864no—
397#101—864no—
398#100—864no—
399#99—868no—
400#99—868no—
401C24—432no—
402C24D4×D4311yescharacteristic
403#41—1721no—
404#41—1721no—
405#41—1721no—
406#41—1721no—
407#41—1721no—
408#41—1721no—
409#41—1721no—
410#41—1721no—
411#41—1721no—
412#41—1721no—
413#41—1721no—
414#41—1721no—
415#41—1721no—
416#41—1721no—
417#41—1721no—
418#41—1721no—
419C2×Q8—861no—
420C2×Q8—861no—
421C2×Q8—861no—
422C2×Q8—861no—
423C2×Q8—861no—
424C2×Q8—861no—
425C2×D4—862no—
426C2×D4—862no—
427C2×D4—862no—
428C2×D4—862no—
429C2×D4—862no—
430C2×D4—862no—
431C2×D4—861no—
432C2×D4—861no—
433C2×D4—861no—
434C2×D4—861no—
435C2×D4—861no—
436C2×D4—861no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—432no—
440C22×C4—862no—
441C22×C4—862no—
442C22×C4—862no—
443C22×C4—862no—
444C22×C4—862no—
445C22×C4—862no—
446C22×C4—1721no—
447C22×C4—1721no—
448C22×C4C2×C4×D4311yescharacteristic
449C22×C4C2×D17211yescharacteristic
450C22×C4#1062189811yescharacteristic
451C22×C4#1062189811yescharacteristic
452C22×C4#1062189811yescharacteristic
453C22×C4#1062189811yescharacteristic
454C22×C4D4×D4311yescharacteristic
455C22×C4D4×D4311yescharacteristic
456C22×C4D4×D4311yescharacteristic
457C22×C4D4×D4311yescharacteristic
458C22×C4#1062190011yescharacteristic
459C22×C4Q8×D4311yescharacteristic
460C22×C4#1062190211yescharacteristic
461C22×C4C2×C22⋊D4311yescharacteristic
462M16—22no—
463M16—22no—
464M16—41no—
465M16—41no—
466M16—434no—
467M16—862no—
468M16—862no—
469M16—862no—
470C2×C8—22no—
471C2×C8—41no—
472C2×C8—41no—
473C2×C8—862no—
474C2×C8—862no—
475C2×C8—862no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4—862no—
481C4⋊C4—862no—
482C4⋊C4—1721no—
483C4⋊C4—1721no—
484C22⋊C4—22no—
485C22⋊C4—22no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C22⋊C4—862no—
489C22⋊C4—862no—
490C22⋊C4—1721no—
491C22⋊C4—1721no—
492C42—22no—
493C42—22no—
494C42—41no—
495C42—41no—
496C42—862no—
497C42—862no—
498C42—1721no—
499C42—1721no—
500C23—81no—
501C23—862no—
502C23—862no—
503C23—862no—
504C23—3442no—
505C23C4⋊C4×D4311yescharacteristic
506C23#1306329311yescharacteristic
507C23#1306329511yescharacteristic
508C23#1306329811yescharacteristic
509C23#1306329811yescharacteristic
510C23#1306330711yescharacteristic
511C23#1306331011yescharacteristic
512Q8—1721no—
513Q8—1721no—
514Q8—1721no—
515Q8—1721no—
516D4—1722no—
517D4—1722no—
518D4—1722no—
519D4—1722no—
520D4—1721no—
521D4—1721no—
522D4—1721no—
523D4—1721no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—82no—
527C2×C4—82no—
528C2×C4—862no—
529C2×C4—862no—
530C2×C4—862no—
531C2×C4—3442no—
532C2×C4—3442no—
533C2×C4—1722no—
534C2×C4—1722no—
535C2×C4—1722no—
536C2×C4—1722no—
537C2×C4—1722no—
538C2×C4—1722no—
539C2×C4C22⋊C4×D4311yescharacteristic
540C2×C4#1306328211yescharacteristic
541C2×C4(C22⋊D43)⋊C411yescharacteristic
542C2×C4C4×C22⋊D4311yescharacteristic
543C2×C4#1306328711yescharacteristic
544C2×C4C4×D17211yescharacteristic
545C2×C4#1306329511yescharacteristic
546C2×C4#1306329711yescharacteristic
547C2×C4#1306329811yescharacteristic
548C2×C4#1306329811yescharacteristic
549C2×C4#1306329811yescharacteristic
550C2×C4#1306329911yescharacteristic
551C2×C4#1306330011yescharacteristic
552C2×C4#1306330111yescharacteristic
553C2×C4#1306330311yescharacteristic
554C2×C4#1306330311yescharacteristic
555C2×C4#1306330311yescharacteristic
556C2×C4#1306330311yescharacteristic
557C2×C4#1306330511yescharacteristic
558C2×C4#1306330811yescharacteristic
559C2×C4#1306331011yescharacteristic
560C2×C4#1306331011yescharacteristic
561C2×C4#1306331111yescharacteristic
562C2×C4#1306331111yescharacteristic
563C2×C4#1306331311yescharacteristic
564C2×C4#1306331911yescharacteristic
565C2×C4#1306332011yescharacteristic
566C2×C4#1306332111yescharacteristic
567C8—42no—
568C8—864no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—3442no—
577C22—3442no—
578C22—3442no—
579C22—1722no—
580C22#1458275811yescharacteristic
581C22#1458277011yescharacteristic
582C22#1458277311yescharacteristic
583C22#1458280811yescharacteristic
584C22#1458281411yescharacteristic
585C22#1458281711yescharacteristic
586C22#1458282811yescharacteristic
587C4—82no—
588C4—82no—
589C4—3442no—
590C4—3442no—
591C4—1722no—
592C4#1458277711yescharacteristic
593C4#1458278811yescharacteristic
594C4#1458279011yescharacteristic
595C4#1458279911yescharacteristic
596C4#1458281211yescharacteristic
597C4#1458282111yescharacteristic
598C4#1458282311yescharacteristic
599C4#1458283411yescharacteristic
600C2—21no—
601C2—21no—
602C2—21no—
603C2—21no—
604C2—21no—
605C2—21no—
606C2—21no—
607C2—3442no—
608C2#1913283911yescharacteristic
subgroupG/H
centerC4#14582823
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×H(3,ℤ/4)C2
socleC2×C43#1439
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenterC2×H(3,ℤ/4)D43
hypocenterC43#11138
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
1. #19143184C2semidirect
5. #19134306C2semidirect
6. #19134304C2semidirect
7. C2×C43×H(3,ℤ/4)C2semidirect
17. C2×#13063243C4semidirect
18. C2×#13063241C4semidirect
302. C2×H(3,ℤ/4)D43semidirect
335. C43#11138semidirect

Maximal subgroups

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

subgroupindex
#191431842
C2×#145828812
C2×#145828722
#191343062
#191343042
C2×C43×H(3,ℤ/4)2
#1113843