Finite Group Databasebeta

← #25114211

Subgroups — #25114211

Order 11008.

686 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143252C211yesmaximal, characteristic
2#19143250C211yesmaximal, characteristic
3#19143183C211yesmaximal, characteristic
4#19135347C211yesmaximal, characteristic, complemented
5#19135340C211yesmaximal, characteristic, complemented
6#19135196C211yesmaximal, characteristic, complemented
7#19135195C211yesmaximal, characteristic, complemented
8#19135193C211yesmaximal, characteristic, complemented
9#19134693C211yesmaximal, characteristic
10#19134693C211yesmaximal, characteristic
11#19134636C211yesmaximal, characteristic
12#19134478C211yesmaximal, characteristic, complemented
13#19134475C211yesmaximal, characteristic, complemented
14#19134377C211yesmaximal, characteristic
15C43×#1922C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17#117×D43C2211yescharacteristic
18#117×D43C2211yescharacteristic
19#14582961—21no—
20#14582959—21no—
21#14582959—21no—
22#14582958—21no—
23#14582955—21no—
24#14582954—21no—
25#14582951—21no—
26#14582950—21no—
27C2×#13063260C2211yescharacteristic
28C2×#13063260C2211yescharacteristic
29#14582940C411yescharacteristic, complemented
30#14582940C411yescharacteristic, complemented
31#14582940C411yescharacteristic, complemented
32#14582940C411yescharacteristic, complemented
33#14582938C411yescharacteristic, complemented
34#14582938C411yescharacteristic, complemented
35#14582938C411yescharacteristic, complemented
36#14582938C411yescharacteristic, complemented
37#14582937C2211yescharacteristic
38#14582935C2211yescharacteristic
39#14582935C2211yescharacteristic
40#14582927C2211yescharacteristic
41#14582926C2211yescharacteristic
42#14582925C2211yescharacteristic
43#14582862C2211yescharacteristic
44#14582862C2211yescharacteristic
45C2×(C2×D43)⋊C8C2211yescharacteristic
46#14582857C2211yescharacteristic
47#14582855C2211yescharacteristic
48#14582854C2211yescharacteristic
49C2×#13063236C2211yescharacteristic
50C2×C8×Dic43C2211yescharacteristic
51C4×(C2×D43)⋊C4C2211yescharacteristic
52#14582664C2211yescharacteristic
53#14582660C2211yescharacteristic
54#14582660C2211yescharacteristic
55#14582659C2211yescharacteristic
56#14582659C2211yescharacteristic
57#14582658C2211yescharacteristic
58#14582658C2211yescharacteristic
59#14582653C2211yescharacteristic
60C43×#427C2211yescharacteristic
61C43×#424C2211yescharacteristic
62C43×#405C2211yescharacteristic
63C43×#341C2211yescharacteristic
64C43×#339C2211yescharacteristic
65C43×#339C2211yescharacteristic
66C43×#336C2211yescharacteristic
67C22×C4×D43C2311yescharacteristic
68C2×#10621877C2311yescharacteristic
69C2×#10621877C2311yescharacteristic
70C2×#10621872—22no—
71C2×#10621872—22no—
72C2×#10621872C2×C411yescharacteristic
73C2×#10621872C2×C411yescharacteristic
74C2×#10621872C2×C411yescharacteristic
75C2×#10621872C2×C411yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78#13063284C2311yescharacteristic
79#13063284C2311yescharacteristic
80#13063283C2×C411yescharacteristic
81#13063283C2×C411yescharacteristic
82#13063283C2×C411yescharacteristic
83#13063283C2×C411yescharacteristic
84#13063282—21no—
85#13063282—21no—
86#13063281—21no—
87#13063281—21no—
88C4⋊C4×D43C2×C411yescharacteristic
89C4⋊C4×D43C2×C411yescharacteristic
90C4⋊C4×D43C2×C411yescharacteristic
91C4⋊C4×D43C2×C411yescharacteristic
92C2×(C2×D43)⋊C4—21no—
93C22⋊C4×D43—21no—
94C22⋊C4×D43—21no—
95C2×C4×Dic43C2311yescharacteristic
96C42×D43—21no—
97C42×D43—21no—
98#13063260—22no—
99#13063260—22no—
100#13063259C2×C411yescharacteristic
101#13063259C2×C411yescharacteristic
102#13063258C2×C411yescharacteristic
103#13063258C2×C411yescharacteristic
104#13063258C2×C411yescharacteristic
105#13063258C2×C411yescharacteristic
106#13063257C2×C411yescharacteristic
107#13063257C2×C411yescharacteristic
108#13063256C2×C411yescharacteristic
109#13063256C2×C411yescharacteristic
110#13063256C2×C411yescharacteristic
111#13063256C2×C411yescharacteristic
112C4⋊(C43⋊C8)—21no—
113C4⋊(C43⋊C8)—21no—
114Dic43⋊C8—21no—
115Dic43⋊C8—21no—
116Dic43⋊C8—21no—
117Dic43⋊C8—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121(C2×D43)⋊C8—21no—
122(C2×D43)⋊C8D411yescharacteristic
123(C2×D43)⋊C8D411yescharacteristic
124(C2×D43)⋊C8D411yescharacteristic
125(C2×D43)⋊C8D411yescharacteristic
126#13063236—21no—
127#13063236—22no—
128#13063235—21no—
129#13063235—21no—
130C4×C43⋊C8—21no—
131C8×Dic43—21no—
132C8×Dic43—21no—
133C8×Dic43—22no—
134C43⋊#95—21no—
135C2×M16×C43C2311yescharacteristic
136C2×M16×C43C2311yescharacteristic
137C22×C8×C43C2311yescharacteristic
138C22×C8×C43C2311yescharacteristic
139#117×C43C2311yescharacteristic
140#117×C43C2311yescharacteristic
141C2×C42×C43C2311yescharacteristic
142#107×C43C2×C411yescharacteristic
143#107×C43C2×C411yescharacteristic
144#106×C43C2×C411yescharacteristic
145#106×C43C2×C411yescharacteristic
146C4⋊C8×C43—21no—
147C4⋊C8×C43—21no—
148#97×C43—21no—
149C4×C8×C43—21no—
150C23×D43#4111yescharacteristic
151C22×C4×C43—21no—
152C22×C4×C43C2411yescharacteristic
153C22×Dic43—21no—
154C22×Dic43#4111yescharacteristic
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×C4×D43—21no—
163C2×C4×D43C22×C411yescharacteristic
164C2×C4×D43C22×C411yescharacteristic
165C2×C4×D43C2×D411yescharacteristic
166C2×C4×D43C2×D411yescharacteristic
167M16×C43—21no—
168M16×C43—21no—
169M16×C43—21no—
170M16×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43C22×C411yescharacteristic
178C2×C8×C43C22×C411yescharacteristic
179C2×C8×C43C2×D411yescharacteristic
180C2×C8×C43C2×D411yescharacteristic
181C4⋊C4×C43C22×C411yescharacteristic
182C4⋊C4×C43C22×C411yescharacteristic
183C4⋊C4×C43C22×C411yescharacteristic
184C4⋊C4×C43C22×C411yescharacteristic
185C22⋊C4×C43—21no—
186C22⋊C4×C43—21no—
187C42×C43—21no—
188C42×C43—21no—
189C42×C43—21no—
190C42×C43—21no—
191C22⋊Dic43—21no—
192C22⋊Dic43—21no—
193(C2×D43)⋊C4—21no—
194(C2×D43)⋊C4—21no—
195(C2×D43)⋊C4—21no—
196(C2×D43)⋊C4—21no—
197(C2×D43)⋊C4—42no—
198C4⋊Dic43C22×C411yescharacteristic
199C4⋊Dic43C22×C411yescharacteristic
200C4⋊Dic43C22×C411yescharacteristic
201C4⋊Dic43C22×C411yescharacteristic
202Dic43⋊C4—21no—
203Dic43⋊C4—21no—
204Dic43⋊C4—21no—
205Dic43⋊C4—21no—
206C4×Dic43—21no—
207C4×Dic43—21no—
208C4×Dic43—21no—
209C4×Dic43—21no—
210C4×Dic43—21no—
211C4×Dic43—21no—
212C4×Dic43—21no—
213C4×Dic43—21no—
214#10621877—21no—
215#10621877—21no—
216#10621877—21no—
217#10621877—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8C22×C411yescharacteristic
223C2×C43⋊C8C22×C411yescharacteristic
224C2×C43⋊C8C2×D411yescharacteristic
225C2×C43⋊C8C2×D411yescharacteristic
226C2×C43⋊C8#4112yes—
227C2×C43⋊C8#4112yes—
228#10621872—22no—
229#10621872—22no—
230#10621872—22no—
231#10621872—22no—
232C23×C43C2×#4111yescharacteristic
233C22×D43—21no—
234C22×D43—21no—
235C22×D43—41no—
236C22×D43—41no—
237C22×D43C4×D411yescharacteristic
238C22×D43C4×D411yescharacteristic
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43C23×C411yescharacteristic
247C2×C4×C43C22×D411yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C432−1+411yescharacteristic
251C2×C4×C432−1+411yescharacteristic
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—22no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43C4×D411yescharacteristic
262C2×Dic43C4×D411yescharacteristic
263C4×D43—21no—
264C4×D43—21no—
265C4×D43—21no—
266C4×D43—21no—
267C4×D43—21no—
268C4×D43—21no—
269C4×D43—21no—
270C4×D43—21no—
271C4×D43—42no—
272C4×D43—42no—
273C4×D43—81no—
274C4×D43—81no—
275C8×C43—21no—
276C8×C43—21no—
277C8×C43—21no—
278C8×C43—21no—
279C8×C43—41no—
280C8×C43—41no—
281C43⋊C8—21no—
282C43⋊C8—21no—
283C43⋊C8—41no—
284C43⋊C8—41no—
285C43⋊C8#11712yes—
286C43⋊C8#11712yes—
287#22608—431nomaximal, Sylow
288C22×C43—21no—
289C22×C43—21no—
290C22×C43C2×C4×D411yescharacteristic
291C22×C43#55211yescharacteristic
292C22×C43#55211yescharacteristic
293C2×D43—21no—
294C2×D43—21no—
295C2×D43—21no—
296C2×D43—21no—
297C2×D43—21no—
298C2×D43—21no—
299C2×D43—81no—
300C2×D43—81no—
301C4×C43—41no—
302C4×C43—41no—
303C4×C43—41no—
304C4×C43—41no—
305C4×C43—81no—
306C4×C43C2×#11711yescharacteristic
307C4×C43#51911yescharacteristic
308C4×C43#54711yescharacteristic
309C4×C43#54711yescharacteristic
310Dic43—21no—
311Dic43—21no—
312Dic43—42no—
313Dic43—41no—
314Dic43—41no—
315Dic43—41no—
316Dic43—41no—
317#2924—431no—
318#2924—431no—
319#2911—431no—
320#1946—431no—
321#1945—431no—
322#1922—431no—
323#1922—431no—
324#1922—431no—
325#1922D4311yescharacteristic, complemented
326#1826—431no—
327#1826—431no—
328#1811—431no—
329#1773—431no—
330#1772—431no—
331#1753—431no—
332C2×C43—21no—
333C2×C43—21no—
334C2×C43#234411yescharacteristic
335C2×C43#295511yescharacteristic
336C2×C43#295611yescharacteristic
337D43—41no—
338D43—41no—
339C22×M16—431no—
340C2×#117—431no—
341C2×#117—431no—
342#433—861no—
343#433—861no—
344#433—861no—
345#433—861no—
346#432—861no—
347#432—861no—
348#431—861no—
349#431—861no—
350C2×#108—431no—
351C2×#108—431no—
352#428—431no—
353#428—431no—
354#428—431no—
355#428—431no—
356#428—431no—
357#428—431no—
358#428—431no—
359#428—431no—
360#427—431no—
361#427—431no—
362#427—431no—
363#427C2×D4311yescharacteristic
364#424—431no—
365#424—431no—
366#424—431no—
367#424C2×D4311yescharacteristic
368#407—431no—
369#407—431no—
370C2×C22⋊C8—431no—
371#405—431no—
372#405—431no—
373#405—431no—
374#405C2×D4311yescharacteristic
375C2×#97—431no—
376C2×C4×C8—431no—
377C4×C22⋊C4—431no—
378#341—431no—
379#341C2×D4311yescharacteristic
380#339—431no—
381#339—431no—
382#339—431no—
383#339—431no—
384#339—431no—
385#339—431no—
386#339C2×D4311yescharacteristic
387#339C2×D4311yescharacteristic
388#336—431no—
389#336C2×D4311yescharacteristic
390C43#2260811yescharacteristic, complemented, Sylow
391C23×C4—431no—
392C2×M16—431no—
393C2×M16—431no—
394C2×M16—431no—
395C2×M16—431no—
396C2×M16—431no—
397C2×M16—431no—
398C2×M16—862no—
399C2×M16—862no—
400C2×M16C22×D4311yescharacteristic
401C2×M16C22×D4311yescharacteristic
402C22×C8—431no—
403C22×C8—431no—
404C22×C8C22×D4311yescharacteristic
405C22×C8C22×D4311yescharacteristic
406#117—431no—
407#117—431no—
408#117—431no—
409#117—431no—
410#117—431no—
411#117—431no—
412#117—861no—
413#117—861no—
414#117—861no—
415#117—861no—
416#117C22×D4311yescharacteristic
417#117C22×D4311yescharacteristic
418C2×C4⋊C4—431no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—431no—
422C2×C22⋊C4—861no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C42—431no—
426C2×C42—861no—
427C2×C42—861no—
428C2×C42C22×D4311yescharacteristic
429#108—862no—
430#108—862no—
431#107—431no—
432#107—431no—
433#107—431no—
434#107—431no—
435#107—431no—
436#107—431no—
437#107C4×D4311yescharacteristic
438#107C4×D4311yescharacteristic
439#106—431no—
440#106—431no—
441#106—431no—
442#106—431no—
443#106—431no—
444#106—431no—
445#106C4×D4311yescharacteristic
446#106C4×D4311yescharacteristic
447C4⋊C8—21no—
448C4⋊C8—21no—
449C4⋊C8—861no—
450C4⋊C8—861no—
451C4⋊C8—861no—
452C4⋊C8—861no—
453C4⋊C8—861no—
454C4⋊C8—861no—
455C22⋊C8—431no—
456C22⋊C8—431no—
457C22⋊C8—431no—
458C22⋊C8—431no—
459C22⋊C8—861no—
460C22⋊C8—861no—
461C22⋊C8—861no—
462C22⋊C8—861no—
463#97—21no—
464#97—862no—
465#97—861no—
466#97—861no—
467#97—861no—
468C4×C8—21no—
469C4×C8—861no—
470C4×C8—862no—
471C4×C8—861no—
472C4×C8—861no—
473#95—861no—
474C24—431no—
475C22×C4—21no—
476C22×C4—431no—
477C22×C4—431no—
478C22×C4—431no—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4C23×D4311yescharacteristic
491M16—21no—
492M16—21no—
493M16—21no—
494M16—21no—
495M16—862no—
496M16—862no—
497M16—862no—
498M16—862no—
499M16—861no—
500M16—861no—
501M16—861no—
502M16—861no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—431no—
510C2×C8—431no—
511C2×C8—432no—
512C2×C8—432no—
513C2×C8—431no—
514C2×C8—431no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8C2×C4×D4311yescharacteristic
520C2×C8C2×C4×D4311yescharacteristic
521C2×C8D4×D4311yescharacteristic
522C2×C8D4×D4311yescharacteristic
523C4⋊C4—431no—
524C4⋊C4—431no—
525C4⋊C4—431no—
526C4⋊C4—431no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4C2×C4×D4311yescharacteristic
532C4⋊C4C2×C4×D4311yescharacteristic
533C4⋊C4C2×C4×D4311yescharacteristic
534C4⋊C4C2×C4×D4311yescharacteristic
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—861no—
538C22⋊C4—861no—
539C22⋊C4—861no—
540C22⋊C4—861no—
541C22⋊C4—861no—
542C22⋊C4—861no—
543C22⋊C4—1722no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—861no—
549C42—861no—
550C42—861no—
551C42—861no—
552C42—861no—
553C42—861no—
554C42—861no—
555C42—861no—
556C23—431no—
557C23—431no—
558C23—861no—
559C23—861no—
560C23—1721no—
561C23—1721no—
562C23#41×D4311yescharacteristic
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—431no—
571C2×C4—431no—
572C2×C4—861no—
573C2×C4—861no—
574C2×C4—861no—
575C2×C4—861no—
576C2×C4—861no—
577C2×C4—861no—
578C2×C4—861no—
579C2×C4—861no—
580C2×C4—861no—
581C2×C4—861no—
582C2×C4—862no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—3441no—
588C2×C4—3441no—
589C2×C4—1722no—
590C2×C4—1722no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4C22×C4×D4311yescharacteristic
594C2×C4C2×D4×D4311yescharacteristic
595C2×C4#41×D4311yescharacteristic
596C2×C4#41×D4311yescharacteristic
597C2×C4#1306337211yescharacteristic
598C2×C4#1306337311yescharacteristic
599C8—21no—
600C8—21no—
601C8—21no—
602C8—21no—
603C8—41no—
604C8—41no—
605C8—432no—
606C8—432no—
607C8—861no—
608C8—861no—
609C8—1721no—
610C8—1721no—
611C22—21no—
612C22—21no—
613C22—861no—
614C22—861no—
615C22—861no—
616C22—861no—
617C22—861no—
618C22—861no—
619C22—3441no—
620C22—3441no—
621C22C4×D4×D4311yescharacteristic
622C22#1458358111yescharacteristic
623C22#1458358511yescharacteristic
624C4—41no—
625C4—41no—
626C4—41no—
627C4—41no—
628C4—81no—
629C4—861no—
630C4—861no—
631C4—1722no—
632C4—1721no—
633C4—1721no—
634C4—1721no—
635C4—1721no—
636C4#117×D4311yescharacteristic
637C4#1458337511yescharacteristic
638C4#1458354711yescharacteristic
639C4#1458355111yescharacteristic
640C2—21no—
641C2—21no—
642C2—1721no—
643C2—1721no—
644C2#1913746111yescharacteristic
645C2#1914349311yescharacteristic
646C2#1914350311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1922C2
socleC22×C43C2×C4×D4
prime radicalC23×D43#41
cosocleC22×C4×C43C24
hypercenter#1922D43
hypocenterC43#22608
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1922

Complements

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

NH ≅ G/Ntype
4. #19135347C2semidirect
5. #19135340C2semidirect
6. #19135196C2semidirect
7. #19135195C2semidirect
8. #19135193C2semidirect
12. #19134478C2semidirect
13. #19134475C2semidirect
15. C43×#1922C2semidirect
29. #14582940C4semidirect
30. #14582940C4semidirect
31. #14582940C4semidirect
32. #14582940C4semidirect
33. #14582938C4semidirect
34. #14582938C4semidirect
35. #14582938C4semidirect
36. #14582938C4semidirect
325. #1922D43semidirect
390. C43#22608semidirect

Maximal subgroups

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

subgroupindex
#191432522
#191432502
#191431832
#191353472
#191353402
#191351962
#191351952
#191351932
#191346932
#191346362
#191344782
#191344752
#191343772
C43×#19222
#2260843