Finite Group Databasebeta

← #25104667

Subgroups — #25104667

Order 11008.

970 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583262C211yesmaximal, characteristic
2#19137159C211yesmaximal, characteristic
3#19137154C211yesmaximal, characteristic, complemented
4#19135562C211yesmaximal, characteristic, complemented
5#19135417C211yesmaximal, characteristic
6#19135295C211yesmaximal, characteristic, complemented
7#19135292C211yesmaximal, characteristic, complemented
8#19135291C211yesmaximal, characteristic, complemented
9#19134727C211yesmaximal, characteristic, complemented
10#102×Dic43C211yesmaximal, characteristic, complemented
11#102×Dic43C211yesmaximal, characteristic, complemented
12#19134409C211yesmaximal, characteristic, complemented
13#19134409C211yesmaximal, characteristic, complemented
14#97×Dic43C211yesmaximal, characteristic, complemented
15C43×#1936C211yesmaximal, characteristic, complemented
16C2×#13063321C2211yescharacteristic
17C2×#13063316C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19C2×#13063287C2211yescharacteristic
20C2×(C22⋊D43)⋊C4—21no—
21C2×(C22⋊D43)⋊C4—21no—
22#14583262C418yescomplemented
23C2×#13063247C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063236C2211yescharacteristic
30C2×#13063235C2211yescharacteristic
31C2×#13063235C2211yescharacteristic
32C2×C8×Dic43C2211yescharacteristic
33C2×C8×Dic43C2211yescharacteristic
34#14582801C2211yescharacteristic
35#14582799—21no—
36#14582799—21no—
37#14582797C2211yescharacteristic
38#14582784—21no—
39#14582780—21no—
40#14582768C2211yescharacteristic
41#14582764C2211yescharacteristic
42C4⋊C4×Dic43—21no—
43C4⋊C4×Dic43C2211yescharacteristic
44C4⋊C4×Dic43C2211yescharacteristic
45#14582750—21no—
46C42×Dic43C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53C2×#102×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#97×C43C2211yescharacteristic
56C43×#390C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C22×D172C2311yescharacteristic
61C22×C22⋊D43—21no—
62C22×C22⋊D43—21no—
63C23×Dic43—21no—
64C22×C4×D43—21no—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063321—22no—
68#13063321C2×C414yes—
69#13063316—22no—
70#13063316C2×C414yescomplemented
71D4×Dic43—22no—
72D4×Dic43—22no—
73#13063287—22no—
74#13063287—22no—
75(C22⋊D43)⋊C4—44no—
76(C22⋊D43)⋊C4—44no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×C22⋊Dic43—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43D411yescharacteristic
92C2×C4×Dic43D411yescharacteristic
93C2×C4×Dic43D411yescharacteristic
94C2×C4×Dic43D411yescharacteristic
95C2×C4×Dic43C2311yescharacteristic
96C2×C4×Dic43C2311yescharacteristic
97#13063247—22no—
98#13063247C2×C414yescomplemented
99#13063246—22no—
100#13063246C2×C414yescomplemented
101#13063245—22no—
102#13063245C2×C414yescomplemented
103#13063236—22no—
104#13063235—22no—
105#13063235C2×C414yescomplemented
106C8×Dic43—22no—
107C8×Dic43—22no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C22×D4×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122C2×C42×C43C2311yescharacteristic
123#102×C43—22no—
124#102×C43C2×C414yescomplemented
125#97×C43—22no—
126#95×C43—21no—
127C24×C43—21no—
128C23×D43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43C22×C412yes—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2411yescharacteristic
141C2×C22⋊D43—24no—
142C2×C22⋊D43—24no—
143C2×C22⋊D43—42no—
144C2×C22⋊D43—42no—
145C2×C22⋊D43—42no—
146C2×C22⋊D43—42no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—42no—
151C22×Dic43—42no—
152C22×Dic43—42no—
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156C22×Dic43C2×D411yescharacteristic
157C2×D172—21no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172C22×C412yes—
163C2×C4×D43—42no—
164C2×C4×D43—42no—
165C2×C4×D43—42no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43C22×C412yes—
171C2×C8×C43#4112yes—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—42no—
178C4⋊C4×C43C22×C412yes—
179C22⋊C4×C43—42no—
180C22⋊C4×C43—42no—
181C42×C43—21no—
182C42×C43—21no—
183C22⋊Dic43—42no—
184(C2×D43)⋊C4—42no—
185(C2×D43)⋊C4—42no—
186(C2×D43)⋊C4—42no—
187C4⋊Dic43—21no—
188C4⋊Dic43—24no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43C22×C412yes—
194Dic43⋊C4—24no—
195Dic43⋊C4—42no—
196Dic43⋊C4—42no—
197Dic43⋊C4—42no—
198C4×Dic43—22no—
199C4×Dic43—22no—
200C4×Dic43—41no—
201C4×Dic43—41no—
202C4×Dic43—42no—
203C4×Dic43—42no—
204C4×Dic43C22×C412yes—
205C4×Dic43#4112yes—
206C4×Dic43#4112yes—
207C4×Dic43#4112yes—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8C22×C412yes—
213C2×C43⋊C8#4112yes—
214C23×C43—22no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43C22×D411yescharacteristic
222C22×D43—22no—
223C22×D43—41no—
224C22×D43—41no—
225C22×D43—41no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43—41no—
229D4×C43—22no—
230D4×C43—22no—
231D4×C43—41no—
232D4×C43—41no—
233C2×C4×C43—22no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—41no—
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×C43C23×C411yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C22⋊D43—48no—
255C22⋊D43—48no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—22no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—84no—
272C2×Dic43C4×D412yes—
273C2×Dic43C4×D412yes—
274C2×Dic43#12412yes—
275C2×Dic43#12412yes—
276C2×Dic43AGL(1,ℤ/8)12yes—
277C2×Dic43AGL(1,ℤ/8)12yes—
278D172—22no—
279D172—22no—
280D172—41no—
281D172—41no—
282C4×D43—84no—
283C8×C43—22no—
284C8×C43—22no—
285C43⋊C8—22no—
286C43⋊C8—22no—
287C4×#490—431nomaximal, Sylow
288C22×C43—42no—
289C22×C43—42no—
290C22×C43—42no—
291C22×C43—81no—
292C22×C43—81no—
293C22×C43—81no—
294C22×C43—81no—
295C22×C43C2×C4×D411yescharacteristic
296C22×C43C2×#12411yescharacteristic
297C22×C43#53211yescharacteristic
298C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
299C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
300C22×C43#57511yescharacteristic
301C22×C43#57511yescharacteristic
302C2×D43—42no—
303C2×D43—42no—
304C2×D43—42no—
305C2×D43—81no—
306C2×D43—81no—
307C2×D43—81no—
308C2×D43—81no—
309C4×C43—41no—
310C4×C43—41no—
311C4×C43—42no—
312C4×C43—81no—
313C4×C43—81no—
314C4×C43C4×#4111yescharacteristic
315C4×C43C4×#4111yescharacteristic
316C4×C43#52911yescharacteristic
317C4×C43#52911yescharacteristic
318Dic43—22no—
319Dic43—22no—
320Dic43—22no—
321Dic43—42no—
322Dic43—81no—
323Dic43—81no—
324Dic43#49014yescomplemented
325C2×#490—431no—
326C4×#127—431no—
327C4×#125—431no—
328#1992—431no—
329#1961—431no—
330#1936—431no—
331#1936—431no—
332#1936—431no—
333#1936D4311yescharacteristic, complemented
334#1836—431no—
335C4×#102—431no—
336C4×#102—431no—
337C4×#102—431no—
338C4×#102—431no—
339C4×#97—431no—
340C2×C43—82no—
341C2×C43C4×#12411yescharacteristic
342C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
343C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
344C2×C43C2×#49011yescharacteristic
345C2×C43#313511yescharacteristic
346C2×C43#317111yescharacteristic
347C2×C43#317111yescharacteristic
348D43—82no—
349C2×#127—431no—
350C2×#125—431no—
351C2×C4×D4—431no—
352C2×C4×D4—431no—
353C2×C4×D4—861no—
354C2×C4×D4—861no—
355#490—438no—
356C2×#102—431no—
357C2×#102—431no—
358C2×#102—431no—
359C2×#102—431no—
360C2×#102—431no—
361C2×#102—431no—
362C2×#102C2×D4311yescharacteristic
363C2×#102C2×D4311yescharacteristic
364C2×#97—431no—
365C2×#97—431no—
366C2×#97—431no—
367C2×#97C2×D4311yescharacteristic
368C2×C4×C8—431no—
369C2×C4×C8—431no—
370#390—431no—
371#390—861no—
372#390—861no—
373#390C2×D4311yescharacteristic
374#389—431no—
375#389C2×D4311yescharacteristic
376#387—861no—
377#387—861no—
378#384—431no—
379#382—431no—
380C4×C4⋊C4—431no—
381C4×C4⋊C4—431no—
382C4×C4⋊C4—861no—
383C4×C4⋊C4—861no—
384C43—431no—
385#340—431no—
386#340—431no—
387#340—431no—
388#340—431no—
389#340—431no—
390#340—431no—
391#340C2×D4311yescharacteristic
392#340C2×D4311yescharacteristic
393C43C4×#49011yescharacteristic, complemented, Sylow
394C22×D4—431no—
395C22×D4—861no—
396C22×D4—861no—
397C22×D4C22×D4311yescharacteristic
398C23×C4—861no—
399C23×C4—861no—
400C22×C8—431no—
401C22×C8—431no—
402C22×C8C22×D4311yescharacteristic
403C22×C8C22×D4311yescharacteristic
404#127—434no—
405#127—862no—
406#125—434no—
407#125—862no—
408C4×D4—862no—
409C4×D4—862no—
410C4×D4—862no—
411C4×D4—862no—
412C4×D4—1724no—
413C4×D4—1724no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—431no—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4C22×D4311yescharacteristic
424C2×C4⋊C4C22×D4311yescharacteristic
425C2×C4⋊C4C22×D4311yescharacteristic
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C22⋊C4—861no—
431C2×C22⋊C4—861no—
432C2×C42—431no—
433C2×C42—431no—
434C2×C42—431no—
435C2×C42—431no—
436C2×C42—431no—
437C2×C42—431no—
438C2×C42—861no—
439C2×C42—861no—
440C2×C42C22×D4311yescharacteristic
441#102—22no—
442#102—434no—
443#102—434no—
444#102—434no—
445#102—862no—
446#102—862no—
447#102—862no—
448#102C4×D4314yescomplemented
449#97—22no—
450#97—434no—
451#97—862no—
452#97—862no—
453C4×C8—862no—
454C4×C8—862no—
455#95—21no—
456#95—861no—
457#95—861no—
458#95—861no—
459#95—861no—
460#95—861no—
461C24—21no—
462C24—861no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—432no—
469C2×D4—864no—
470C2×D4—864no—
471C2×D4—861no—
472C2×D4—861no—
473C2×D4—861no—
474C2×D4—861no—
475C2×D4—861no—
476C2×D4—1722no—
477C2×D4—1722no—
478C2×D4—1722no—
479C2×D4—1722no—
480C2×D4C2×C4×D4312yes—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—431no—
487C22×C4—431no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4—861no—
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
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—432no—
505C2×C8—432no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8—861no—
510C2×C8C2×C4×D4312yes—
511C2×C8#1062190012yes—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—42no—
518C4⋊C4—432no—
519C4⋊C4—864no—
520C4⋊C4—864no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—1722no—
527C4⋊C4—1722no—
528C4⋊C4—1722no—
529C4⋊C4C2×C4×D4312yes—
530C22⋊C4—42no—
531C22⋊C4—42no—
532C22⋊C4—1722no—
533C22⋊C4—1722no—
534C22⋊C4—1722no—
535C22⋊C4—1722no—
536C42—21no—
537C42—21no—
538C42—432no—
539C42—432no—
540C42—432no—
541C42—432no—
542C42—862no—
543C42—862no—
544C42—1721no—
545C42—1721no—
546C42—1722no—
547C42—1722no—
548C23—22no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—862no—
556C23—1721no—
557C23—1721no—
558C23—1721no—
559C23—1721no—
560C23—1721no—
561C23—1721no—
562C23C2×D4×D4311yescharacteristic
563D4—22no—
564D4—22no—
565D4—41no—
566D4—41no—
567D4—862no—
568D4—862no—
569D4—1728no—
570D4—1728no—
571D4—1721no—
572D4—1721no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—432no—
589C2×C4—432no—
590C2×C4—432no—
591C2×C4—432no—
592C2×C4—432no—
593C2×C4—432no—
594C2×C4—861no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—862no—
601C2×C4—3444no—
602C2×C4—3444no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4C22×C4×D4311yescharacteristic
612C2×C4#41×D4311yescharacteristic
613C2×C4#41×D4311yescharacteristic
614C2×C4#41×D4311yescharacteristic
615C2×C4#41×D4311yescharacteristic
616C2×C4C2×#1062190011yescharacteristic
617C8—22no—
618C8—22no—
619C8—862no—
620C8—862no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22—3441no—
629C22—3441no—
630C22—3441no—
631C22—3441no—
632C22—1722no—
633C22—1722no—
634C22—1722no—
635C22C4×D4×D4311yescharacteristic
636C22#124×D4311yescharacteristic
637C22#1458344411yescharacteristic
638C22AGL(1,ℤ/8)×D4311yescharacteristic
639C22AGL(1,ℤ/8)×D4311yescharacteristic
640C22#1458369511yescharacteristic
641C22#1458369811yescharacteristic
642C4—41no—
643C4—41no—
644C4—42no—
645C4—81no—
646C4—81no—
647C4—434no—
648C4—862no—
649C4—862no—
650C4—862no—
651C4—3441no—
652C4—3441no—
653C4—1722no—
654C4C4×#1062190011yescharacteristic
655C4#1458336711yescharacteristic
656C4#1458342611yescharacteristic
657C4#1458343211yescharacteristic
658C2—82no—
659C2—3442no—
660C2#1913713611yescharacteristic
661C2#1914340011yescharacteristic
662C2#1914340611yescharacteristic
663C2#490×D4311yescharacteristic
664C2#1914493711yescharacteristic
665C2#1914518311yescharacteristic
666C2#1914518511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1936C2
socleC23×C43C22×D4
prime radicalC2×#13063321C22
cosocleC22×C4×C43C24
hypercenter#1936D43
hypocenterC43C4×#490
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1936

Complements

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

NH ≅ G/Ntype
3. #19137154C2semidirect
4. #19135562C2semidirect
6. #19135295C2semidirect
7. #19135292C2semidirect
8. #19135291C2semidirect
9. #19134727C2semidirect
10. #102×Dic43C2semidirect
11. #102×Dic43C2semidirect
12. #19134409C2semidirect
13. #19134409C2semidirect
14. #97×Dic43C2semidirect
15. C43×#1936C2semidirect
22. #14583262C4semidirect
70. #13063316C2×C4semidirect
98. #13063247C2×C4semidirect
100. #13063246C2×C4semidirect
102. #13063245C2×C4semidirect
105. #13063235C2×C4semidirect
124. #102×C43C2×C4semidirect
324. Dic43#490semidirect
333. #1936D43semidirect
393. C43C4×#490semidirect
448. #102C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145832622
#191371592
#191371542
#191355622
#191354172
#191352952
#191352922
#191352912
#191347272
#102×Dic432
#191344092
#97×Dic432
C43×#19362
C4×#49043