Finite Group Databasebeta

← #25114942

Subgroups — #25114942

Order 11008.

1010 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583002C211yesmaximal, characteristic
2C2×#14583002C211yesmaximal, characteristic
3C2×C4×#10621884C211yesmaximal, characteristic
4#19137513C211yesmaximal, characteristic, complemented
5#19137496C211yesmaximal, characteristic
6#19135332C211yesmaximal, characteristic, complemented
7#19135325C211yesmaximal, characteristic, complemented
8#19134853C211yesmaximal, characteristic
9#19134851C211yesmaximal, characteristic, complemented
10#19134845C211yesmaximal, characteristic
11#19134760C211yesmaximal, characteristic, complemented
12#19134604C211yesmaximal, characteristic
13#19134598C211yesmaximal, characteristic, complemented
14#19134466C211yesmaximal, characteristic, complemented
15C43×#1865C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C2×Q8×Dic43C2211yescharacteristic
18C2×Q8×Dic43C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic
20C2×#13063287C2211yescharacteristic
21C2×#13063287C2211yescharacteristic
22C2×C4⋊C4×D43—21no—
23#14583002—24no—
24#14583002C418yescomplemented
25C4×#10621884—24no—
26C2×#13063259C2211yescharacteristic
27C2×#13063258C2211yescharacteristic
28C2×#13063258C2211yescharacteristic
29C2×#13063256C2211yescharacteristic
30C2×Dic43⋊C8C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×#13063235C2211yescharacteristic
36C2×#13063235C2211yescharacteristic
37C2×C4×C43⋊C8C2211yescharacteristic
38#14582798C2211yescharacteristic
39#14582797—21no—
40#14582797C2211yescharacteristic
41#14582795—21no—
42#14582795C2211yescharacteristic
43#14582773—21no—
44#14582770—21no—
45#14582768C2211yescharacteristic
46#14582764—21no—
47#14582764C2211yescharacteristic
48#14582758—21no—
49C4×Dic43⋊C4—21no—
50C4×Dic43⋊C4C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582653C2211yescharacteristic
55C2×C4×Q8×C43C2211yescharacteristic
56C2×#106×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C43×#389C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C22×D172C2311yescharacteristic
63C22×C4×D43—21no—
64C22×C4×D43—21no—
65C22×C4×D43—21no—
66C2×#10621884C2×C414yes—
67C2×#10621884D414yes—
68C2×#10621884Q814yes—
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71Q8×Dic43—22no—
72Q8×Dic43—22no—
73Q8×Dic43—41no—
74Q8×Dic43C2×C414yescomplemented
75C4×D172—22no—
76C4×D172—41no—
77#13063287—22no—
78#13063287—22no—
79#13063287—41no—
80#13063287C2×C414yes—
81C2×C4⋊Dic43—21no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43—21no—
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4D411yescharacteristic
92C2×Dic43⋊C4D411yescharacteristic
93C4⋊C4×D43—44no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43—21no—
99C2×C4×Dic43C2311yescharacteristic
100C2×C4×Dic43C2311yescharacteristic
101#13063259—41no—
102#13063258—22no—
103#13063258C2×C414yescomplemented
104#13063256—22no—
105Dic43⋊C8—22no—
106#13063249—22no—
107#13063247—22no—
108#13063247C2×C414yes—
109#13063245—22no—
110#13063235—22no—
111#13063235C2×C414yescomplemented
112C4×C43⋊C8—22no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95D411yescharacteristic
119C43⋊#95D411yescharacteristic
120C22×Q8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C22×C8×C43C2311yescharacteristic
123C4×Q8×C43—22no—
124C4×Q8×C43—41no—
125C2×C4⋊C4×C43—21no—
126C2×C4⋊C4×C43—21no—
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C42×C43—21no—
131C2×C42×C43C2311yescharacteristic
132#106×C43—41no—
133#103×C43—22no—
134#103×C43C2×C414yescomplemented
135#95×C43—21no—
136C23×D43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43C22×C412yes—
141C2×Q8×C43C2×D412yes—
142C2×Q8×C43C2×Q812yes—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2411yescharacteristic
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156C22×Dic43C2×D411yescharacteristic
157C2×D172—21no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172C22×C412yes—
161C2×D172C2×D412yes—
162C2×D172C2×Q812yes—
163C2×C4×D43—24no—
164C2×C4×D43—42no—
165C2×C4×D43—42no—
166C2×C4×D43—42no—
167C2×C4×D43—42no—
168C2×C4×D43—42no—
169C2×C4×D43—42no—
170C2×C4×D43—81no—
171C2×C4×D43—81no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43C22×C412yes—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—42no—
184C4⋊C4×C43—42no—
185C4⋊C4×C43C22×C412yes—
186C42×C43—21no—
187C42×C43—21no—
188C42×C43—42no—
189#10621884C4⋊C4116yescomplemented
190(C2×D43)⋊C4—24no—
191(C2×D43)⋊C4—42no—
192(C2×D43)⋊C4—42no—
193C4⋊Dic43—21no—
194C4⋊Dic43—24no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—42no—
200C4⋊Dic43—42no—
201C4⋊Dic43C22×C412yes—
202Dic43⋊C4—22no—
203Dic43⋊C4—41no—
204Dic43⋊C4—42no—
205Dic43⋊C4—42no—
206Dic43⋊C4—42no—
207Dic43⋊C4—81no—
208C4×Dic43—21no—
209C4×Dic43—21no—
210C4×Dic43—24no—
211C4×Dic43—42no—
212C4×Dic43C22×C412yes—
213C4×Dic43#4112yes—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8C22×C412yes—
218C2×C43⋊C8C2×D412yes—
219C2×C43⋊C8C2×Q812yes—
220C23×C43C22×D411yescharacteristic
221C22×D43—22no—
222C22×D43—22no—
223C22×D43—22no—
224C22×D43—41no—
225C22×D43—41no—
226C22×D43—41no—
227C22×D43—41no—
228Q8×C43—22no—
229Q8×C43—22no—
230Q8×C43—22no—
231Q8×C43C2×C4⋊C414yescomplemented
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43—21no—
235C2×C4×C43—22no—
236C2×C4×C43—21no—
237C2×C4×C43—22no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43AGL(1,ℤ/8)12yes—
250C2×C4×C43C23×C411yescharacteristic
251C2×C4×C43C22×D411yescharacteristic
252C2×C4×C43C22×Q811yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43H(5,𝔽2)11yescharacteristic
255C2×C4×C432−1+411yescharacteristic
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—22no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43C4×D412yes—
276C2×Dic43C4×D412yes—
277D172—22no—
278D172—22no—
279D172—22no—
280D172C2×C4⋊C414yes—
281C4×D43—48no—
282C4×D43—84no—
283C4×D43—84no—
284C8×C43—22no—
285C8×C43—41no—
286C43⋊C8—41no—
287C43⋊C8C2×C4⋊C414yescomplemented
288#22677—431nomaximal, Sylow
289C22×C43C2×C4×D411yescharacteristic
290C22×C43D4211yescharacteristic
291C22×C43D4×Q811yescharacteristic
292C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
293C22×C43#57511yescharacteristic
294C22×C43#57711yescharacteristic
295C22×C43#57811yescharacteristic
296C2×D43—24no—
297C2×D43—42no—
298C2×D43—42no—
299C2×D43—42no—
300C2×D43—42no—
301C2×D43—42no—
302C2×D43—42no—
303C4×C43—24no—
304C4×C43—22no—
305C4×C43—42no—
306C4×C43—41no—
307C4×C43—81no—
308C4×C43—81no—
309C4×C43C22×C4⋊C411yescharacteristic
310C4×C43#52011yescharacteristic
311C4×C43#54711yescharacteristic
312C4×C43#55411yescharacteristic
313Dic43—22no—
314Dic43—22no—
315Dic43—42no—
316Dic43—41no—
317Dic43—41no—
318Dic43—81no—
319Dic43—81no—
320C2×#440—431no—
321C2×#440—431no—
322C2×C4×SD16—431no—
323#2351—431no—
324D4×C4⋊C4—431no—
325#1943—431no—
326#1942—431no—
327#1865D4311yescharacteristic, complemented
328#1864—431no—
329#1863—431no—
330#1862—431no—
331#1847—431no—
332#1804—431no—
333#1803—431no—
334#1771—431no—
335C2×C43D4×C4⋊C411yescharacteristic
336C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
337C2×C43#294711yescharacteristic
338C2×C43#326511yescharacteristic
339C2×C43#326911yescharacteristic
340C2×C43#338611yescharacteristic
341C2×C43#338811yescharacteristic
342D43—44no—
343C22×SD16—431no—
344C2×C4×Q8—431no—
345C2×C4×Q8—431no—
346C2×C4×Q8C2×D4311yescharacteristic
347C2×C4×D4—431no—
348C2×C4×D4—431no—
349C2×C4×D4—431no—
350C22×C4⋊C4—861no—
351#440—438no—
352#440—864no—
353C4×SD16—864no—
354C2×#107—431no—
355C2×#107—431no—
356C2×#107—431no—
357C2×#106—431no—
358C2×#106C2×D4311yescharacteristic
359C2×C4⋊C8—431no—
360C2×#103—431no—
361C2×#103C2×D4311yescharacteristic
362C2×#103C2×D4311yescharacteristic
363C2×#102—431no—
364C2×#102—431no—
365C2×#102—431no—
366C2×#97—431no—
367C2×#97—431no—
368C2×C4×C8—431no—
369#389—431no—
370#389—431no—
371#389—431no—
372#389—861no—
373#389—861no—
374#389C2×D4311yescharacteristic
375#385—861no—
376#385—861no—
377#384—431no—
378#382—431no—
379#382—861no—
380#380—861no—
381C4×C4⋊C4—431no—
382C4×C4⋊C4—861no—
383#340—431no—
384#340—431no—
385#340—431no—
386#340C2×D4311yescharacteristic
387#336—431no—
388#336C2×D4311yescharacteristic
389C43#2267711yescharacteristic, complemented, Sylow
390C22×Q8C22×D4311yescharacteristic
391C22×D4—431no—
392C23×C4—861no—
393C23×C4—861no—
394C23×C4—861no—
395C2×SD16—434no—
396C2×SD16—434no—
397C2×SD16—434no—
398C22×C8—431no—
399C22×C8—431no—
400C22×C8C22×D4311yescharacteristic
401C22×C8C22×D4311yescharacteristic
402C4×Q8—22no—
403C4×Q8—41no—
404C4×Q8—434no—
405C4×Q8—862no—
406C4×Q8—862no—
407C4×Q8—1721no—
408C4×D4—434no—
409C4×D4—862no—
410C4×D4—862no—
411C4×D4—862no—
412C4×D4—1721no—
413C4×D4—1721no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—431no—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—1724no—
429C2×C4⋊C4C22×D4311yescharacteristic
430C2×C4⋊C4C22×D4311yescharacteristic
431C2×C4⋊C4C22×D4311yescharacteristic
432C2×C22⋊C4—861no—
433C2×C22⋊C4—861no—
434C2×C22⋊C4—861no—
435C2×C42—21no—
436C2×C42—431no—
437C2×C42—431no—
438C2×C42—861no—
439C2×C42—861no—
440C2×C42C22×D4311yescharacteristic
441#107—434no—
442#107—862no—
443#107—1721no—
444#106—41no—
445#106—862no—
446C4⋊C8—862no—
447#103—22no—
448#103—862no—
449#103C4×D4314yescomplemented
450#102—434no—
451#102—862no—
452#102—862no—
453#97—434no—
454#97—862no—
455C4×C8—862no—
456#95—21no—
457#95—431no—
458#95—431no—
459#95—861no—
460#95—861no—
461#95—861no—
462#95—861no—
463#95—861no—
464C24—861no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8C2×C4×D4312yes—
469C2×Q8D4×D4312yes—
470C2×Q8Q8×D4312yes—
471C2×D4—432no—
472C2×D4—432no—
473C2×D4—432no—
474C2×D4—861no—
475C2×D4—861no—
476C2×D4—861no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—431no—
482C22×C4—431no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—864no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—3441no—
490C22×C4—3441no—
491C22×C4—1722no—
492C22×C4—1722no—
493C22×C4—1722no—
494C22×C4—1722no—
495C22×C4—1722no—
496C22×C4—1722no—
497C22×C4D4×D4311yescharacteristic
498C22×C4D4×D4311yescharacteristic
499C22×C4C23×D4311yescharacteristic
500SD16—4316no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—432no—
507C2×C8—432no—
508C2×C8—432no—
509C2×C8—861no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8C2×C4×D4312yes—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—42no—
519C4⋊C4—42no—
520C4⋊C4—432no—
521C4⋊C4—864no—
522C4⋊C4—862no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—3441no—
529C4⋊C4—1721no—
530C4⋊C4—1722no—
531C4⋊C4—1722no—
532C4⋊C4—1722no—
533C4⋊C4—1722no—
534C4⋊C4—1722no—
535C4⋊C4C2×C4×D4312yes—
536C22⋊C4—864no—
537C22⋊C4—1722no—
538C22⋊C4—1722no—
539C42—21no—
540C42—21no—
541C42—42no—
542C42—432no—
543C42—432no—
544C42—864no—
545C42—861no—
546C42—861no—
547C42—1722no—
548C23—862no—
549C23—862no—
550C23—862no—
551C23—1721no—
552C23—1721no—
553C23—1721no—
554C23—1721no—
555C23C2×D4×D4311yescharacteristic
556Q8—22no—
557Q8—22no—
558Q8—22no—
559Q8C4⋊C4×D4314yescomplemented
560D4—434no—
561D4—862no—
562D4—862no—
563D4—862no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—432no—
582C2×C4—432no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—862no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—861no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—3444no—
595C2×C4—3444no—
596C2×C4—1728no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4#1306335212yes—
606C2×C4C22×C4×D4311yescharacteristic
607C2×C4C2×D4×D4311yescharacteristic
608C2×C4C2×Q8×D4311yescharacteristic
609C2×C4#41×D4311yescharacteristic
610C2×C4#1306337011yescharacteristic
611C2×C4#1306337211yescharacteristic
612C8—22no—
613C8—41no—
614C8—434no—
615C8—1721no—
616C22—864no—
617C22—1722no—
618C22—1722no—
619C22—1722no—
620C22—1722no—
621C22—1722no—
622C22—1722no—
623C22C4×D4×D4311yescharacteristic
624C22#1458353111yescharacteristic
625C22#1458356211yescharacteristic
626C22C2×#1306335211yescharacteristic
627C22#1458369611yescharacteristic
628C22#1458370811yescharacteristic
629C22#1458371511yescharacteristic
630C4—22no—
631C4—24no—
632C4—41no—
633C4—42no—
634C4—81no—
635C4—81no—
636C4—862no—
637C4—862no—
638C4—3441no—
639C4—3441no—
640C4—1721no—
641C4—1721no—
642C4—1722no—
643C4C2×C4⋊C4×D4311yescharacteristic
644C4#1458337811yescharacteristic
645C4#1458354711yescharacteristic
646C4#1458360311yescharacteristic
647C2—1724no—
648C2#1913749311yescharacteristic
649C2C4×#1306335211yescharacteristic
650C2#1914343711yescharacteristic
651C2#1914608311yescharacteristic
652C2#1914614311yescharacteristic
653C2#1914751511yescharacteristic
654C2#1914753811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1865C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenter#1865D43
hypocenterC43#22677
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1865

Complements

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

NH ≅ G/Ntype
4. #19137513C2semidirect
6. #19135332C2semidirect
7. #19135325C2semidirect
9. #19134851C2semidirect
11. #19134760C2semidirect
13. #19134598C2semidirect
14. #19134466C2semidirect
15. C43×#1865C2semidirect
24. #14583002C4semidirect
74. Q8×Dic43C2×C4semidirect
103. #13063258C2×C4semidirect
111. #13063235C2×C4semidirect
134. #103×C43C2×C4semidirect
189. #10621884C4⋊C4semidirect
231. Q8×C43C2×C4⋊C4semidirect
287. C43⋊C8C2×C4⋊C4semidirect
327. #1865D43semidirect
389. C43#22677semidirect
449. #103C4×D43semidirect
559. Q8C4⋊C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830022
C2×C4×#106218842
#191375132
#191374962
#191353322
#191353252
#191348532
#191348512
#191348452
#191347602
#191346042
#191345982
#191344662
C43×#18652
#2267743