Finite Group Databasebeta

← #25159685

Subgroups — #25159685

Order 11008.

856 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583192C211yesmaximal, characteristic, complemented
2C2×C4×#10621884C211yesmaximal, characteristic
3#19138446C211yesmaximal, characteristic
4#19137513C211yesmaximal, characteristic, complemented
5#19136117C211yesmaximal, characteristic
6#19136082C211yesmaximal, characteristic, complemented
7#19135984C211yesmaximal, characteristic
8#19135926C211yesmaximal, characteristic, complemented
9#19135325C211yesmaximal, characteristic, complemented
10#19135150C211yesmaximal, characteristic, complemented
11#19134948C211yesmaximal, characteristic
12#19134948C211yesmaximal, characteristic
13#19134847C211yesmaximal, characteristic, complemented
14#19134845C211yesmaximal, characteristic
15C43×#1865C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C2×#13063324C2211yescharacteristic
18C2×#13063303—21no—
19C2×Q8×Dic43C2211yescharacteristic
20C2×Q8×Dic43C2211yescharacteristic
21C2×C4×D172C2211yescharacteristic
22#14583192—24no—
23C4×#10621884—24no—
24C2×#13063259C2211yescharacteristic
25C2×#13063258C2211yescharacteristic
26C2×#13063258C2211yescharacteristic
27C2×#13063256C2211yescharacteristic
28C2×Dic43⋊C8C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31C2×#13063247C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×C4×C43⋊C8C2211yescharacteristic
34#14582823—21no—
35#14582812—21no—
36#14582800C2211yescharacteristic
37#14582800C2211yescharacteristic
38#14582797—21no—
39#14582797C2211yescharacteristic
40#14582795—21no—
41#14582795C2211yescharacteristic
42#14582795C2211yescharacteristic
43#14582770—21no—
44#14582764—21no—
45#14582764C2211yescharacteristic
46C4×Dic43⋊C4—21no—
47C4×Dic43⋊C4C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×C4×Q8×C43C2211yescharacteristic
55C2×#106×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C43×#389C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×Dic86—21no—
62C22×D172C2311yescharacteristic
63C22×C4×D43—21no—
64C2×#10621884—22no—
65C2×#10621884—22no—
66C2×#10621884Q814yescomplemented
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69#13063324—22no—
70#13063324—41no—
71#13063303—44no—
72Q8×Dic43—22no—
73Q8×Dic43—22no—
74Q8×Dic43—22no—
75Q8×Dic43—41no—
76C4×D172—22no—
77C4×D172—41no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4D411yescharacteristic
88C2×Dic43⋊C4D411yescharacteristic
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43C2311yescharacteristic
97C2×C4×Dic43C2311yescharacteristic
98#13063259—22no—
99#13063258—22no—
100#13063258—22no—
101#13063256—22no—
102Dic43⋊C8—22no—
103#13063249D414yes—
104#13063247—22no—
105#13063247—41no—
106#13063245—22no—
107C4×C43⋊C8—22no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95D411yescharacteristic
114C43⋊#95D411yescharacteristic
115C22×Q8×C43C2311yescharacteristic
116C22×C8×C43C2311yescharacteristic
117C22×C8×C43C2311yescharacteristic
118C4×Q8×C43—22no—
119C4×Q8×C43—41no—
120C2×C4⋊C4×C43—21no—
121C2×C4⋊C4×C43—21no—
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C42×C43—21no—
126C2×C42×C43C2311yescharacteristic
127#106×C43—41no—
128#103×C43—22no—
129#103×C43—22no—
130#95×C43—21no—
131C23×D43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43C2×D412yes—
136C2×Q8×C43C2×Q812yes—
137C2×Q8×C43#4112yes—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2411yescharacteristic
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43C2×D411yescharacteristic
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172C2×Q812yes—
158C2×C4×D43—42no—
159C2×C4×D43—42no—
160C2×C4×D43—81no—
161C2×Dic86—42no—
162C2×Dic86—42no—
163C2×Dic86—81no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—42no—
177C4⋊C4×C43—42no—
178C42×C43—21no—
179C42×C43—21no—
180C42×C43—42no—
181#10621884—28no—
182(C2×D43)⋊C4—42no—
183(C2×D43)⋊C4—42no—
184(C2×D43)⋊C4—42no—
185(C2×D43)⋊C4—42no—
186(C2×D43)⋊C4—81no—
187C4⋊Dic43—24no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—42no—
193C4⋊Dic43C2×D412yes—
194C4⋊Dic43#4112yes—
195Dic43⋊C4—22no—
196Dic43⋊C4—22no—
197Dic43⋊C4—42no—
198Dic43⋊C4—42no—
199Dic43⋊C4—42no—
200Dic43⋊C4—42no—
201C4×Dic43—24no—
202C4×Dic43—21no—
203C4×Dic43—21no—
204C4×Dic43—21no—
205C4×Dic43—21no—
206C4×Dic43—42no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8C2×D412yes—
212C2×C43⋊C8C2×Q812yes—
213C23×C43C22×D411yescharacteristic
214C22×D43—22no—
215C22×D43—41no—
216C22×D43—41no—
217C22×D43—41no—
218C22×D43—41no—
219C22×D43—41no—
220C22×D43—41no—
221Q8×C43—22no—
222Q8×C43—22no—
223Q8×C43—22no—
224Q8×C43C22⋊Q814yescomplemented
225C2×C4×C43—22no—
226C2×C4×C43—22no—
227C2×C4×C43—21no—
228C2×C4×C43—22no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43AGL(1,ℤ/8)12yes—
243C2×C4×C43C22×D411yescharacteristic
244C2×C4×C43C22×Q811yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43H(5,𝔽2)11yescharacteristic
248C2×C4×C432−1+411yescharacteristic
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—22no—
254C2×Dic43—21no—
255C2×Dic43—22no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43#13512yes—
270D172—22no—
271D172—22no—
272D172—41no—
273D172—41no—
274C4×D43—84no—
275Dic86—84no—
276C8×C43—41no—
277C8×C43—41no—
278C43⋊C8—22no—
279C43⋊C8—22no—
280#26377—431nomaximal, Sylow
281C22×C43#52511yescharacteristic
282C22×C43D4211yescharacteristic
283C22×C43D4×Q811yescharacteristic
284C22×C43C2×#13511yescharacteristic
285C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
286C22×C43#57711yescharacteristic
287C22×C43#57811yescharacteristic
288C2×D43—42no—
289C2×D43—42no—
290C2×D43—42no—
291C2×D43—81no—
292C2×D43—81no—
293C2×D43—81no—
294C2×D43—81no—
295C4×C43—24no—
296C4×C43—22no—
297C4×C43—41no—
298C4×C43—81no—
299C4×C43—81no—
300C4×C43—81no—
301C4×C43C2×C22⋊Q811yescharacteristic
302C4×C43#53911yescharacteristic
303C4×C43#54711yescharacteristic
304C4×C43#55411yescharacteristic
305Dic43—22no—
306Dic43—41no—
307Dic43—42no—
308Dic43—41no—
309Dic43—41no—
310Dic43—42no—
311Dic43—81no—
312C2×#477—431no—
313C2×C4×SD16—431no—
314#2452—431no—
315#2351—431no—
316#2092—431no—
317#2085—431no—
318#2067—431no—
319#2058—431no—
320#1942—431no—
321#1916—431no—
322#1880—431no—
323#1880—431no—
324#1865D4311yescharacteristic, complemented
325#1863—431no—
326#1862—431no—
327C2×C43#244911yescharacteristic
328C2×C43#310611yescharacteristic
329C2×C43#312111yescharacteristic
330C2×C43#326511yescharacteristic
331C2×C43#328511yescharacteristic
332C2×C43#338111yescharacteristic
333C2×C43#338611yescharacteristic
334D43—82no—
335C22×SD16—431no—
336C2×C4⋊Q8—431no—
337C2×C22⋊Q8—861no—
338C2×C4×Q8—431no—
339C2×C4×Q8—431no—
340C2×C4×Q8C2×D4311yescharacteristic
341C2×C4×D4—431no—
342#477—864no—
343C4×SD16—864no—
344C2×#107—431no—
345C2×#107—431no—
346C2×#107—431no—
347C2×#106—431no—
348C2×#106C2×D4311yescharacteristic
349C2×C4⋊C8—431no—
350C2×#103—431no—
351C2×#103C2×D4311yescharacteristic
352C2×#103C2×D4311yescharacteristic
353C2×#102—431no—
354C2×#102—431no—
355C2×#102—431no—
356C2×C4×C8—431no—
357#396—861no—
358#393—861no—
359#390—431no—
360#390—431no—
361#389—431no—
362#389—431no—
363#389—431no—
364#389—861no—
365#389—861no—
366#389C2×D4311yescharacteristic
367#385—861no—
368#382—431no—
369#382—861no—
370C4×C4⋊C4—431no—
371C4×C4⋊C4—861no—
372#340—431no—
373#340—431no—
374#340—431no—
375#340C2×D4311yescharacteristic
376#336—431no—
377#336—431no—
378#336—431no—
379#336C2×D4311yescharacteristic
380C43#2637711yescharacteristic, complemented, Sylow
381C22×Q8—861no—
382C22×Q8C22×D4311yescharacteristic
383C22×D4—431no—
384C23×C4—861no—
385C2×SD16—434no—
386C2×SD16—862no—
387C2×SD16—862no—
388C22×C8—431no—
389C22×C8—431no—
390C22×C8C22×D4311yescharacteristic
391C22×C8C22×D4311yescharacteristic
392C4⋊Q8—862no—
393C4⋊Q8—1721no—
394C22⋊Q8—1724no—
395C4×Q8—22no—
396C4×Q8—41no—
397C4×Q8—862no—
398C4×Q8—862no—
399C4×Q8—862no—
400C4×Q8—1721no—
401C4×D4—862no—
402C4×D4—1721no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—431no—
406C2×C4⋊C4—431no—
407C2×C4⋊C4—431no—
408C2×C4⋊C4—431no—
409C2×C4⋊C4—431no—
410C2×C4⋊C4—861no—
411C2×C4⋊C4—861no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4C22×D4311yescharacteristic
417C2×C4⋊C4C22×D4311yescharacteristic
418C2×C4⋊C4C22×D4311yescharacteristic
419C2×C22⋊C4—861no—
420C2×C22⋊C4—861no—
421C2×C22⋊C4—861no—
422C2×C22⋊C4—861no—
423C2×C22⋊C4—861no—
424C2×C42—21no—
425C2×C42—431no—
426C2×C42—431no—
427C2×C42—861no—
428C2×C42—861no—
429C2×C42C22×D4311yescharacteristic
430#107—862no—
431#107—862no—
432#107—862no—
433#106—41no—
434#106—862no—
435C4⋊C8—862no—
436#103—22no—
437#103—22no—
438#103—434no—
439#102—862no—
440#102—862no—
441#102—1721no—
442C4×C8—862no—
443#95—21no—
444#95—431no—
445#95—431no—
446#95—861no—
447#95—861no—
448#95—861no—
449#95—861no—
450#95—861no—
451C24—861no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—3441no—
456C2×Q8—1722no—
457C2×Q8—1722no—
458C2×Q8#1062189812yes—
459C2×Q8D4×D4312yes—
460C2×Q8Q8×D4312yes—
461C2×D4—432no—
462C2×D4—861no—
463C2×D4—861no—
464C2×D4—861no—
465C2×D4—861no—
466C2×D4—861no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—431no—
472C22×C4—431no—
473C22×C4—431no—
474C22×C4—431no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4—861no—
478C22×C4—3441no—
479C22×C4—1722no—
480C22×C4—1722no—
481C22×C4D4×D4311yescharacteristic
482C22×C4D4×D4311yescharacteristic
483C22×C4C23×D4311yescharacteristic
484SD16—868no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—432no—
492C2×C8—432no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8—861no—
496C2×C8—861no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—42no—
504C4⋊C4—42no—
505C4⋊C4—432no—
506C4⋊C4—432no—
507C4⋊C4—862no—
508C4⋊C4—864no—
509C4⋊C4—862no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—1722no—
515C4⋊C4—1722no—
516C4⋊C4—1722no—
517C4⋊C4—1722no—
518C4⋊C4—1722no—
519C22⋊C4—3441no—
520C22⋊C4—1722no—
521C22⋊C4—1722no—
522C22⋊C4—1722no—
523C22⋊C4—1722no—
524C42—21no—
525C42—21no—
526C42—42no—
527C42—864no—
528C42—861no—
529C42—861no—
530C42—861no—
531C42—861no—
532C42—1722no—
533C23—862no—
534C23—1721no—
535C23—1721no—
536C23—1721no—
537C23—1721no—
538C23—1721no—
539C23—1721no—
540C23C2×D4×D4311yescharacteristic
541Q8—22no—
542Q8—22no—
543Q8—22no—
544Q8—3444no—
545Q8#1306330314yescomplemented
546D4—862no—
547D4—862no—
548D4—1721no—
549D4—1721no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—432no—
568C2×C4—861no—
569C2×C4—861no—
570C2×C4—861no—
571C2×C4—862no—
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—862no—
581C2×C4—3444no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4#1306335212yes—
590C2×C4C2×D4×D4311yescharacteristic
591C2×C4C2×Q8×D4311yescharacteristic
592C2×C4#41×D4311yescharacteristic
593C2×C4C2×#1062189811yescharacteristic
594C2×C4#1306337011yescharacteristic
595C2×C4#1306337211yescharacteristic
596C8—41no—
597C8—41no—
598C8—862no—
599C8—862no—
600C22—3441no—
601C22—3441no—
602C22—3441no—
603C22—3441no—
604C22—1722no—
605C22—1722no—
606C22—1722no—
607C22#1458340811yescharacteristic
608C22#1458353111yescharacteristic
609C22#1458356211yescharacteristic
610C22#135×D4311yescharacteristic
611C22C2×#1306335211yescharacteristic
612C22#1458370811yescharacteristic
613C22#1458371511yescharacteristic
614C4—22no—
615C4—24no—
616C4—41no—
617C4—81no—
618C4—81no—
619C4—81no—
620C4—862no—
621C4—3441no—
622C4—1721no—
623C4—1722no—
624C4—1721no—
625C4—1721no—
626C4—1722no—
627C4C2×#1306330311yescharacteristic
628C4#1458349111yescharacteristic
629C4#1458354711yescharacteristic
630C4#1458360311yescharacteristic
631C2—3442no—
632C2#1913840611yescharacteristic
633C2#1914465311yescharacteristic
634C2#1914482811yescharacteristic
635C2#1914608311yescharacteristic
636C2#1914633411yescharacteristic
637C2#1914747311yescharacteristic
638C2#1914751511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1865C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1865D43
hypocenterC43#26377
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1865

Complements

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

NH ≅ G/Ntype
1. C2×#14583192C2semidirect
4. #19137513C2semidirect
6. #19136082C2semidirect
8. #19135926C2semidirect
9. #19135325C2semidirect
10. #19135150C2semidirect
13. #19134847C2semidirect
15. C43×#1865C2semidirect
66. C2×#10621884Q8semidirect
224. Q8×C43C22⋊Q8semidirect
324. #1865D43semidirect
380. C43#26377semidirect
545. Q8#13063303semidirect

Maximal subgroups

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

subgroupindex
C2×#145831922
C2×C4×#106218842
#191384462
#191375132
#191361172
#191360822
#191359842
#191359262
#191353252
#191351502
#191349482
#191348472
#191348452
C43×#18652
#2637743