Finite Group Databasebeta

← #25114941

Subgroups — #25114941

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×#14583000C211yesmaximal, characteristic
2C2×SD16×Dic43C211yesmaximal, characteristic
3#19137513C211yesmaximal, characteristic, complemented
4D4×Dic43⋊C4C211yesmaximal, characteristic
5#19135333C211yesmaximal, characteristic, complemented
6#19135326C211yesmaximal, characteristic, complemented
7#19134861C211yesmaximal, characteristic, complemented
8#19134856C211yesmaximal, characteristic
9#19134849C211yesmaximal, characteristic, complemented
10#19134840C211yesmaximal, characteristic
11#19134762C211yesmaximal, characteristic, complemented
12#19134603C211yesmaximal, characteristic
13#19134598C211yesmaximal, characteristic, complemented
14#19134471C211yesmaximal, characteristic, complemented
15C2×C43×#440C211yesmaximal, characteristic
16C2×Q8×Dic43C2211yescharacteristic
17C2×Q8×Dic43C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19C2×D4×Dic43C2211yescharacteristic
20C22×Dic43⋊C4—21no—
21#14583000C418yescomplemented
22SD16×Dic43—24no—
23C2×#13063259C2211yescharacteristic
24C2×#13063258C2211yescharacteristic
25C2×#13063257C2211yescharacteristic
26C2×#13063256C2211yescharacteristic
27C2×Dic43⋊C8C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063235C2211yescharacteristic
33C2×C8×Dic43C2211yescharacteristic
34#14582797—21no—
35#14582797C2211yescharacteristic
36#14582797C2211yescharacteristic
37#14582795—21no—
38#14582795C2211yescharacteristic
39#14582795C2211yescharacteristic
40#14582772—21no—
41#14582771—21no—
42#14582768C2211yescharacteristic
43#14582764—21no—
44#14582764C2211yescharacteristic
45#14582757—21no—
46C4×Dic43⋊C4—21no—
47C4×Dic43⋊C4C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582654C2211yescharacteristic
53#14582653C2211yescharacteristic
54C22×SD16×C43C2211yescharacteristic
55C2×C4×Q8×C43C2211yescharacteristic
56C2×C4×D4×C43C2211yescharacteristic
57C43×#440—24no—
58C2×#107×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C2×#97×C43C2211yescharacteristic
62C23×Dic43—21no—
63C23×Dic43—21no—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66Q8×Dic43—22no—
67Q8×Dic43—22no—
68Q8×Dic43—41no—
69Q8×Dic43C2×C414yescomplemented
70D4×Dic43—22no—
71D4×Dic43—22no—
72D4×Dic43—41no—
73D4×Dic43C2×C414yes—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—44no—
87C2×Dic43⋊C4D411yescharacteristic
88C2×Dic43⋊C4D411yescharacteristic
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43C2311yescharacteristic
94C2×C4×Dic43C2311yescharacteristic
95#13063259C2×C414yescomplemented
96#13063258—41no—
97#13063257—22no—
98#13063256—41no—
99Dic43⋊C8—22no—
100#13063249—22no—
101#13063249C2×C414yescomplemented
102#13063246—22no—
103#13063246C2×C414yes—
104#13063235C2×C414yescomplemented
105C8×Dic43—22no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95D411yescharacteristic
113C43⋊#95D411yescharacteristic
114C22×Q8×C43C2311yescharacteristic
115C22×D4×C43C2311yescharacteristic
116C23×C4×C43—21no—
117C2×SD16×C43C2×C414yes—
118C2×SD16×C43D414yes—
119C2×SD16×C43Q814yes—
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C4×Q8×C43—22no—
123C4×Q8×C43—41no—
124C4×D4×C43—22no—
125C4×D4×C43—41no—
126C2×C4⋊C4×C43—21no—
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C22⋊C4×C43—21no—
130C2×C42×C43—21no—
131C2×C42×C43C2311yescharacteristic
132#107×C43—22no—
133#103×C43—22no—
134#102×C43—22no—
135#97×C43—22no—
136C24×C43—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—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43C22×C412yes—
147C2×D4×C43C2×D412yes—
148C2×D4×C43C2×Q812yes—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—42no—
153C22×C4×C43—42no—
154C22×C4×C43—81no—
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2411yescharacteristic
158C22×Dic43—24no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—42no—
164C22×Dic43—42no—
165C22×Dic43—42no—
166C22×Dic43—42no—
167C22×Dic43—81no—
168C22×Dic43C2×D411yescharacteristic
169C22×Dic43C2×D411yescharacteristic
170C22×Dic43C2×D411yescharacteristic
171C22×Dic43C2×D411yescharacteristic
172SD16×C43C4⋊C4116yescomplemented
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43C22×C412yes—
177C2×C8×C43C2×D412yes—
178C2×C8×C43C2×Q812yes—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—42no—
184C22⋊C4×C43—42no—
185C42×C43—21no—
186C42×C43—21no—
187C42×C43—42no—
188C22⋊Dic43—24no—
189C22⋊Dic43—42no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—24no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—42no—
198C4⋊Dic43C22×C412yes—
199C4⋊Dic43C22×C412yes—
200Dic43⋊C4—22no—
201Dic43⋊C4—41no—
202Dic43⋊C4—42no—
203Dic43⋊C4—42no—
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⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8C22×C412yes—
220C23×C43—22no—
221C23×C43—22no—
222C23×C43—22no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43C22×D411yescharacteristic
228Q8×C43—22no—
229Q8×C43—22no—
230Q8×C43—22no—
231Q8×C43C2×C4⋊C414yescomplemented
232D4×C43—22no—
233D4×C43—22no—
234D4×C43—22no—
235D4×C43C2×C4⋊C414yes—
236C2×C4×C43—22no—
237C2×C4×C43—22no—
238C2×C4×C43—22no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—84no—
252C2×C4×C43C23×C411yescharacteristic
253C2×C4×C43C22×D411yescharacteristic
254C2×C4×C43C22×Q811yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43H(5,𝔽2)11yescharacteristic
257C2×C4×C432−1+411yescharacteristic
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—22no—
265C2×Dic43—22no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—48no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—84no—
281C2×Dic43C4×D412yes—
282C2×Dic43C4×D412yes—
283C2×Dic43AGL(1,ℤ/8)12yes—
284C8×C43—41no—
285C8×C43C2×C4⋊C414yescomplemented
286C43⋊C8—22no—
287C43⋊C8—41no—
288#22677—431nomaximal, Sylow
289C22×C43—24no—
290C22×C43—42no—
291C22×C43—42no—
292C22×C43—42no—
293C22×C43—42no—
294C22×C43—42no—
295C22×C43—42no—
296C22×C43C2×C4×D411yescharacteristic
297C22×C43D4211yescharacteristic
298C22×C43D4×Q811yescharacteristic
299C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
300C22×C43#57511yescharacteristic
301C22×C43#57711yescharacteristic
302C22×C43#57811yescharacteristic
303C4×C43—24no—
304C4×C43—41no—
305C4×C43—41no—
306C4×C43—81no—
307C4×C43—81no—
308C4×C43C22×C4⋊C411yescharacteristic
309C4×C43#52011yescharacteristic
310C4×C43#54711yescharacteristic
311C4×C43#55411yescharacteristic
312Dic43—22no—
313Dic43—22no—
314Dic43—22no—
315Dic43—42no—
316Dic43—42no—
317Dic43—41no—
318Dic43—81no—
319Dic43—81no—
320C2×#440—431no—
321C2×#440D4311yescharacteristic
322C2×C4×SD16—431no—
323#2351—431no—
324D4×C4⋊C4—431no—
325#1943—431no—
326#1942—431no—
327#1865—431no—
328#1864—431no—
329#1863—431no—
330#1862—431no—
331#1847—431no—
332#1804—431no—
333#1803—431no—
334#1771—431no—
335C2×C43—44no—
336C2×C43D4×C4⋊C411yescharacteristic
337C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
338C2×C43#294711yescharacteristic
339C2×C43#326511yescharacteristic
340C2×C43#326911yescharacteristic
341C2×C43#338611yescharacteristic
342C2×C43#338811yescharacteristic
343C22×SD16C2×D4311yescharacteristic
344C2×C4×Q8—431no—
345C2×C4×Q8—431no—
346C2×C4×Q8C2×D4311yescharacteristic
347C2×C4×D4—431no—
348C2×C4×D4—431no—
349C2×C4×D4C2×D4311yescharacteristic
350C22×C4⋊C4—861no—
351#440—24no—
352#440—438no—
353C4×SD16—864no—
354C2×#107—431no—
355C2×#107—431no—
356C2×#107C2×D4311yescharacteristic
357C2×#106—431no—
358C2×#106—431no—
359C2×C4⋊C8—431no—
360C2×#103—431no—
361C2×#103—431no—
362C2×#103C2×D4311yescharacteristic
363C2×#102—431no—
364C2×#102—431no—
365C2×#102C2×D4311yescharacteristic
366C2×#97—431no—
367C2×#97C2×D4311yescharacteristic
368C2×C4×C8—431no—
369#389—431no—
370#389—431no—
371#389—431no—
372#389—431no—
373#389—861no—
374#389—861no—
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#340—431no—
387#336—431no—
388#336—431no—
389C43#2267711yescharacteristic, complemented, Sylow
390C22×Q8C22×D4311yescharacteristic
391C22×D4C22×D4311yescharacteristic
392C23×C4—21no—
393C23×C4—861no—
394C23×C4—861no—
395C2×SD16Dic8614yes—
396C2×SD16C4×D4314yes—
397C2×SD16C22⋊D4314yes—
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—22no—
409C4×D4—41no—
410C4×D4—434no—
411C4×D4—862no—
412C4×D4—862no—
413C4×D4—1721no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—431no—
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—861no—
429C2×C4⋊C4—1724no—
430C2×C4⋊C4C22×D4311yescharacteristic
431C2×C4⋊C4C22×D4311yescharacteristic
432C2×C22⋊C4—21no—
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—22no—
442#107—434no—
443#107—1721no—
444#106—862no—
445#106—1721no—
446C4⋊C8—862no—
447#103—22no—
448#103—434no—
449#103—862no—
450#102—22no—
451#102—434no—
452#102—862no—
453#97—22no—
454#97—434no—
455C4×C8—862no—
456#95—431no—
457#95—431no—
458#95—861no—
459#95—861no—
460#95—861no—
461#95—861no—
462#95—861no—
463#95—861no—
464C24—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8C2×Dic8612yes—
469C2×Q8C2×C4×D4312yes—
470C2×Q8C2×C22⋊D4312yes—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4C2×Dic8612yes—
475C2×D4C2×C4×D4312yes—
476C2×D4C2×C22⋊D4312yes—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—81no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—431no—
487C22×C4—864no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4—3441no—
493C22×C4—1722no—
494C22×C4—1722no—
495C22×C4—1722no—
496C22×C4—1722no—
497C22×C4D4×D4311yescharacteristic
498C22×C4D4×D4311yescharacteristic
499C22×C4C23×D4311yescharacteristic
500SD16Dic43⋊C4116yescomplemented
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—432no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8—861no—
510C2×C8C2×Dic8612yes—
511C2×C8C2×C4×D4312yes—
512C2×C8C2×C22⋊D4312yes—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—42no—
518C4⋊C4—432no—
519C4⋊C4—432no—
520C4⋊C4—862no—
521C4⋊C4—864no—
522C4⋊C4—861no—
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⋊C4—1722no—
536C22⋊C4—42no—
537C22⋊C4—864no—
538C22⋊C4—1722no—
539C42—21no—
540C42—21no—
541C42—42no—
542C42—432no—
543C42—432no—
544C42—864no—
545C42—861no—
546C42—861no—
547C42—1722no—
548C23—22no—
549C23—22no—
550C23—22no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23C2×D4×D4311yescharacteristic
556Q8—22no—
557Q8—22no—
558Q8—22no—
559Q8C2×Dic43⋊C414yescomplemented
560D4—22no—
561D4—22no—
562D4—22no—
563D4C2×Dic43⋊C414yes—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
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—84no—
580C2×C4—432no—
581C2×C4—432no—
582C2×C4—432no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—862no—
590C2×C4—862no—
591C2×C4—861no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—3444no—
595C2×C4—1728no—
596C2×C4—1721no—
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—1721no—
606C2×C4C22×C4×D4311yescharacteristic
607C2×C4C22×C22⋊D4311yescharacteristic
608C2×C4C22×Dic8611yescharacteristic
609C2×C4#41×D4311yescharacteristic
610C2×C4#1306337011yescharacteristic
611C2×C4#1306337211yescharacteristic
612C8—41no—
613C8—862no—
614C8—1721no—
615C8C2×Dic43⋊C414yescomplemented
616C22—24no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—42no—
622C22—42no—
623C22C4×D4×D4311yescharacteristic
624C22D4×C22⋊D4311yescharacteristic
625C22D4×Dic8611yescharacteristic
626C22AGL(1,ℤ/8)×D4311yescharacteristic
627C22#1458369811yescharacteristic
628C22#1458370911yescharacteristic
629C22#1458371511yescharacteristic
630C4—24no—
631C4—41no—
632C4—41no—
633C4—81no—
634C4—81no—
635C4—862no—
636C4—862no—
637C4—862no—
638C4—3441no—
639C4—3441no—
640C4—1721no—
641C4—1722no—
642C4—1722no—
643C4C22×Dic43⋊C411yescharacteristic
644C4#1458337811yescharacteristic
645C4#1458354811yescharacteristic
646C4#1458360811yescharacteristic
647C2—44no—
648C2D4×Dic43⋊C411yescharacteristic
649C2#1914340011yescharacteristic
650C2#1914343511yescharacteristic
651C2#1914608411yescharacteristic
652C2#1914614411yescharacteristic
653C2#1914751711yescharacteristic
654C2#1914754111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#440C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
cosocleC22×C4×C43C24
hypercenterC2×#440D43
hypocenterC43#22677
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
3. #19137513C2semidirect
5. #19135333C2semidirect
6. #19135326C2semidirect
7. #19134861C2semidirect
9. #19134849C2semidirect
11. #19134762C2semidirect
13. #19134598C2semidirect
14. #19134471C2semidirect
21. #14583000C4semidirect
69. Q8×Dic43C2×C4semidirect
95. #13063259C2×C4semidirect
101. #13063249C2×C4semidirect
104. #13063235C2×C4semidirect
172. SD16×C43C4⋊C4semidirect
231. Q8×C43C2×C4⋊C4semidirect
285. C8×C43C2×C4⋊C4semidirect
389. C43#22677semidirect
500. SD16Dic43⋊C4semidirect
559. Q8C2×Dic43⋊C4semidirect
615. C8C2×Dic43⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#145830002
C2×SD16×Dic432
#191375132
D4×Dic43⋊C42
#191353332
#191353262
#191348612
#191348562
#191348492
#191348402
#191347622
#191346032
#191345982
#191344712
C2×C43×#4402
#2267743