Finite Group Databasebeta

← #25116024

Subgroups — #25116024

Order 11008.

942 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583011C211yesmaximal, characteristic
2#19137543C211yesmaximal, characteristic, complemented
3#19137500C211yesmaximal, characteristic, complemented
4#19135289C211yesmaximal, characteristic, complemented
5#19135281C211yesmaximal, characteristic, complemented
6#19135181C211yesmaximal, characteristic, complemented
7#19135172C211yesmaximal, characteristic, complemented
8#19134945C211yesmaximal, characteristic
9#19134727C211yesmaximal, characteristic, complemented
10#19134603C211yesmaximal, characteristic, complemented
11#19134593C211yesmaximal, characteristic, complemented
12#19134466C211yesmaximal, characteristic, complemented
13#19134422C211yesmaximal, characteristic, complemented
14C4×#13063246C211yesmaximal, characteristic, complemented
15C43×#1879C211yesmaximal, characteristic
16C2×D4×Dic43C2211yescharacteristic
17C2×D4×Dic43C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19C2×#13063281—21no—
20#14583011C418yescomplemented
21C2×#13063257C2211yescharacteristic
22C2×Dic43⋊C8C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063235C2211yescharacteristic
28C2×#13063235C2211yescharacteristic
29C2×C4×C43⋊C8C2211yescharacteristic
30#14582802C2211yescharacteristic
31#14582797C2211yescharacteristic
32#14582795C2211yescharacteristic
33#14582793—21no—
34#14582787—21no—
35#14582772—21no—
36#14582771—21no—
37#14582768C2211yescharacteristic
38#14582764C2211yescharacteristic
39#14582757—21no—
40#14582757—21no—
41C4⋊C4×Dic43C2211yescharacteristic
42C4×Dic43⋊C4C2211yescharacteristic
43C4×C4⋊Dic43C2211yescharacteristic
44C2×C43⋊#95—21no—
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582653C2211yescharacteristic
53C22×D8×C43C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C43×#390C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C23×Dic43—21no—
61C23×Dic43—21no—
62C23×Dic43—21no—
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65D4×Dic43—22no—
66D4×Dic43—22no—
67D4×Dic43—22no—
68D4×Dic43—41no—
69D4×Dic43C2×C414yes—
70D4×Dic43C2×C414yescomplemented
71#13063281—44no—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4D411yescharacteristic
81C2×Dic43⋊C4D411yescharacteristic
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43C2311yescharacteristic
90C2×C4×Dic43C2311yescharacteristic
91#13063257C2×C414yescomplemented
92Dic43⋊C8—22no—
93#13063246—22no—
94#13063246—41no—
95#13063246C2×C414yes—
96#13063246C2×C414yescomplemented
97#13063235—41no—
98#13063235C2×C414yescomplemented
99C4×C43⋊C8—41no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95D411yescharacteristic
107C43⋊#95D411yescharacteristic
108C22×D4×C43C2311yescharacteristic
109C22×D4×C43C2311yescharacteristic
110C23×C4×C43—21no—
111C2×D8×C43—22no—
112C2×D8×C43—22no—
113C2×D8×C43C2×C414yes—
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C4×D4×C43—22no—
117C4×D4×C43—41no—
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122C2×C22⋊C4×C43—21no—
123C2×C42×C43C2311yescharacteristic
124#102×C43—22no—
125#102×C43—41no—
126C24×C43—21no—
127C24×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43C22×C412yes—
137C2×D4×C43C22×C412yes—
138C2×D4×C43#4112yes—
139C2×D4×C43#4112yes—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—42no—
143C22×C4×C43—42no—
144C22×C4×C43—81no—
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2411yescharacteristic
148C22×Dic43—24no—
149C22×Dic43—24no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—42no—
155C22×Dic43—42no—
156C22×Dic43—42no—
157C22×Dic43—42no—
158C22×Dic43—81no—
159C22×Dic43—81no—
160C22×Dic43—81no—
161C22×Dic43C2×D411yescharacteristic
162C22×Dic43C2×D411yescharacteristic
163C22×Dic43C2×D411yescharacteristic
164C22×Dic43C2×D411yescharacteristic
165D8×C43—28no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43C22×C412yes—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C22⋊C4×C43—42no—
177C22⋊C4×C43—42no—
178C22⋊C4×C43—81no—
179C42×C43—21no—
180C42×C43—21no—
181C22⋊Dic43—24no—
182C22⋊Dic43—24no—
183C22⋊Dic43—42no—
184C22⋊Dic43—42no—
185C22⋊Dic43—81no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43C22×C412yes—
193C4⋊Dic43C22×C412yes—
194Dic43⋊C4—22no—
195Dic43⋊C4—41no—
196Dic43⋊C4—42no—
197Dic43⋊C4—81no—
198Dic43⋊C4—81no—
199Dic43⋊C4—81no—
200C4×Dic43—21no—
201C4×Dic43—21no—
202C4×Dic43—42no—
203C4×Dic43—42no—
204C4×Dic43C22×C412yes—
205C4×Dic43#4112yes—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8C22×C412yes—
212C23×C43—22no—
213C23×C43—22no—
214C23×C43—22no—
215C23×C43—22no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43C22×D411yescharacteristic
227D4×C43—22no—
228D4×C43—22no—
229D4×C43—22no—
230D4×C43—22no—
231D4×C43—22no—
232D4×C43—41no—
233D4×C43—41no—
234D4×C43#11714yescomplemented
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—84no—
247C2×C4×C43AGL(1,ℤ/8)12yes—
248C2×C4×C43C23×C411yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43H(5,𝔽2)11yescharacteristic
253C2×C4×C432−1+411yescharacteristic
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—22no—
259C2×Dic43—22no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—48no—
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×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—84no—
278C2×Dic43—84no—
279C2×Dic43C4×D412yes—
280C2×Dic43C4×D412yes—
281C8×C43—22no—
282C8×C43—41no—
283C43⋊C8—22no—
284C43⋊C8—41no—
285#22780—431nomaximal, Sylow
286C22×C43—24no—
287C22×C43—42no—
288C22×C43—42no—
289C22×C43—42no—
290C22×C43—42no—
291C22×C43—42no—
292C22×C43—42no—
293C22×C43—42no—
294C22×C43—42no—
295C22×C43—42no—
296C22×C43—81no—
297C22×C43—81no—
298C22×C43—81no—
299C22×C43—81no—
300C22×C43C2×C4×D411yescharacteristic
301C22×C43#54611yescharacteristic
302C22×C43#54811yescharacteristic
303C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
304C22×C43#57511yescharacteristic
305C22×C43#57611yescharacteristic
306C22×C43#57711yescharacteristic
307C4×C43—22no—
308C4×C43—41no—
309C4×C43—81no—
310C4×C43—81no—
311C4×C43C2×#11711yescharacteristic
312C4×C43#52011yescharacteristic
313C4×C43#55211yescharacteristic
314C4×C43#55311yescharacteristic
315Dic43—22no—
316Dic43—22no—
317Dic43—42no—
318Dic43—42no—
319Dic43—41no—
320Dic43—41no—
321Dic43—81no—
322Dic43—81no—
323C2×#442—431no—
324#2354—431no—
325#2349—431no—
326#1936—431no—
327#1934—431no—
328#1920—431no—
329#1919—431no—
330#1879—431no—
331#1879D4311yescharacteristic
332#1836—431no—
333#1804—431no—
334#1802—431no—
335#1771—431no—
336#1762—431no—
337C4×#102—431no—
338C2×C43—44no—
339C2×C43—82no—
340C2×C43#235211yescharacteristic
341C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
342C2×C43#294611yescharacteristic
343C2×C43#330611yescharacteristic
344C2×C43#331911yescharacteristic
345C2×C43#336611yescharacteristic
346C2×C43#337611yescharacteristic
347C22×D8C2×D4311yescharacteristic
348C2×C4×D4—431no—
349C2×C4×D4—431no—
350C2×C4×D4—431no—
351C2×C4×D4C2×D4311yescharacteristic
352C2×#117—861no—
353#442—438no—
354C2×#106—431no—
355C2×C4⋊C8—431no—
356C2×#102—431no—
357C2×#102—431no—
358C2×#102—431no—
359C2×#102—431no—
360C2×#102C2×D4311yescharacteristic
361C2×#102C2×D4311yescharacteristic
362C2×#97—431no—
363C2×#97—431no—
364C2×C4×C8—431no—
365#390—431no—
366#390C2×D4311yescharacteristic
367#389—431no—
368#389—431no—
369#388—861no—
370#388—861no—
371#385—861no—
372#385—861no—
373#384—431no—
374#382—431no—
375#380—861no—
376#380—861no—
377C4×C4⋊C4—431no—
378C4×C4⋊C4—431no—
379C4×C4⋊C4—431no—
380C2×#95—861no—
381#340—431no—
382#340—431no—
383#340—431no—
384#340—431no—
385#340—431no—
386#340—431no—
387#340—431no—
388#340C2×D4311yescharacteristic
389#336—431no—
390#336C2×D4311yescharacteristic
391C43#2278011yescharacteristic, complemented, Sylow
392C22×D4C22×D4311yescharacteristic
393C22×D4C22×D4311yescharacteristic
394C23×C4—21no—
395C23×C4—861no—
396C23×C4—861no—
397C23×C4—861no—
398C2×D8—22no—
399C2×D8—22no—
400C2×D8C4×D4314yes—
401C22×C8—431no—
402C22×C8—431no—
403C22×C8C22×D4311yescharacteristic
404C22×C8C22×D4311yescharacteristic
405C4×D4—22no—
406C4×D4—41no—
407C4×D4—434no—
408C4×D4—434no—
409C4×D4—862no—
410C4×D4—862no—
411C4×D4—862no—
412C4×D4—1721no—
413#117—1724no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—431no—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4C22×D4311yescharacteristic
425C2×C4⋊C4C22×D4311yescharacteristic
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—861no—
430C2×C22⋊C4—861no—
431C2×C22⋊C4—861no—
432C2×C22⋊C4—861no—
433C2×C22⋊C4—861no—
434C2×C42—431no—
435C2×C42—431no—
436C2×C42—861no—
437C2×C42—861no—
438C2×C42C22×D4311yescharacteristic
439#106—434no—
440C4⋊C8—862no—
441#102—22no—
442#102—41no—
443#102—434no—
444#102—434no—
445#102—862no—
446#102—1721no—
447#97—434no—
448#97—1721no—
449C4×C8—1721no—
450#95—431no—
451#95—431no—
452#95—861no—
453#95—861no—
454#95—861no—
455#95—861no—
456#95—861no—
457#95—861no—
458C24—21no—
459C24—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4C2×C4×D4312yes—
469C2×D4C2×C4×D4312yes—
470C2×D4#1062190012yes—
471C2×D4#1062190012yes—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—81no—
477C22×C4—431no—
478C22×C4—431no—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—864no—
482C22×C4—864no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—3441no—
488C22×C4—3441no—
489C22×C4—3441no—
490C22×C4—1722no—
491C22×C4—1722no—
492C22×C4—1722no—
493C22×C4—1722no—
494C22×C4D4×D4311yescharacteristic
495C22×C4D4×D4311yescharacteristic
496C22×C4C23×D4311yescharacteristic
497D8—28no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—432no—
504C2×C8—861no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8C2×C4×D4312yes—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—432no—
515C4⋊C4—432no—
516C4⋊C4—862no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—3441no—
524C4⋊C4—3441no—
525C4⋊C4—3441no—
526C4⋊C4—1721no—
527C4⋊C4—1722no—
528C22⋊C4—42no—
529C22⋊C4—42no—
530C22⋊C4—81no—
531C22⋊C4—864no—
532C22⋊C4—864no—
533C22⋊C4—3441no—
534C22⋊C4—1722no—
535C22⋊C4—1722no—
536C42—21no—
537C42—21no—
538C42—432no—
539C42—432no—
540C42—861no—
541C42—861no—
542C42—1722no—
543C42—1722no—
544C23—22no—
545C23—22no—
546C23—22no—
547C23—22no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23C2×D4×D4311yescharacteristic
559D4—22no—
560D4—22no—
561D4—22no—
562D4—22no—
563D4—22no—
564D4—41no—
565D4—41no—
566D4#1306328114yescomplemented
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—84no—
579C2×C4—432no—
580C2×C4—432no—
581C2×C4—861no—
582C2×C4—861no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—862no—
586C2×C4—862no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—861no—
592C2×C4—861no—
593C2×C4—3444no—
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×C4#1306334912yes—
607C2×C4C22×C4×D4311yescharacteristic
608C2×C4#41×D4311yescharacteristic
609C2×C4C2×#1062190011yescharacteristic
610C2×C4C2×#1062190011yescharacteristic
611C2×C4#1306337011yescharacteristic
612C2×C4#1306337211yescharacteristic
613C8—22no—
614C8—41no—
615C8—862no—
616C8—1721no—
617C22—24no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22—42no—
625C22—42no—
626C22—42no—
627C22—81no—
628C22—81no—
629C22—81no—
630C22—81no—
631C22C4×D4×D4311yescharacteristic
632C22#1458353611yescharacteristic
633C22#1458355511yescharacteristic
634C22C2×#1306334911yescharacteristic
635C22#1458369611yescharacteristic
636C22#1458370311yescharacteristic
637C22#1458370911yescharacteristic
638C4—22no—
639C4—41no—
640C4—81no—
641C4—81no—
642C4—862no—
643C4—862no—
644C4—3441no—
645C4—3441no—
646C4—1722no—
647C4—1721no—
648C4—1721no—
649C4—1722no—
650C4C2×#1306328111yescharacteristic
651C4#1458337811yescharacteristic
652C4#1458358611yescharacteristic
653C4#1458359211yescharacteristic
654C2—44no—
655C2—82no—
656C2#1913752211yescharacteristic
657C2C4×#1306334911yescharacteristic
658C2#1914342411yescharacteristic
659C2#1914656011yescharacteristic
660C2#1914675511yescharacteristic
661C2#1914730611yescharacteristic
662C2#1914742611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1879C2
socleC23×C43C22×D4
prime radicalC22×D8×C43C22
cosocleC22×C4×C43C24
hypercenter#1879D43
hypocenterC43#22780
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
2. #19137543C2semidirect
3. #19137500C2semidirect
4. #19135289C2semidirect
5. #19135281C2semidirect
6. #19135181C2semidirect
7. #19135172C2semidirect
9. #19134727C2semidirect
10. #19134603C2semidirect
11. #19134593C2semidirect
12. #19134466C2semidirect
13. #19134422C2semidirect
14. C4×#13063246C2semidirect
20. #14583011C4semidirect
70. D4×Dic43C2×C4semidirect
91. #13063257C2×C4semidirect
96. #13063246C2×C4semidirect
98. #13063235C2×C4semidirect
234. D4×C43#117semidirect
391. C43#22780semidirect
566. D4#13063281semidirect

Maximal subgroups

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

subgroupindex
C2×#145830112
#191375432
#191375002
#191352892
#191352812
#191351812
#191351722
#191349452
#191347272
#191346032
#191345932
#191344662
#191344222
C4×#130632462
C43×#18792
#2278043