Finite Group Databasebeta

← #25116025

Subgroups — #25116025

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×#14583008C211yesmaximal, characteristic
2#19137543C211yesmaximal, characteristic, complemented
3#19137504C211yesmaximal, characteristic, complemented
4#19135280C211yesmaximal, characteristic, complemented
5#19135183C211yesmaximal, characteristic, complemented
6#19135170C211yesmaximal, characteristic, complemented
7#19134946C211yesmaximal, characteristic
8#19134940C211yesmaximal, characteristic
9#19134727C211yesmaximal, characteristic, complemented
10#19134603C211yesmaximal, characteristic, complemented
11#19134594C211yesmaximal, characteristic, complemented
12#19134471C211yesmaximal, characteristic, complemented
13#19134421C211yesmaximal, characteristic, complemented
14#19134409C211yesmaximal, characteristic, complemented
15C43×#1936C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C2×C4×D172C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19C2×#13063287C2211yescharacteristic
20C2×#13063287C2211yescharacteristic
21C2×#13063281—21no—
22#14583008C418yescomplemented
23C2×#13063256C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063235C2211yescharacteristic
30C2×C8×Dic43C2211yescharacteristic
31#14582802C2211yescharacteristic
32#14582798C2211yescharacteristic
33#14582793—21no—
34#14582787—21no—
35#14582773—21no—
36#14582770—21no—
37#14582768C2211yescharacteristic
38#14582764C2211yescharacteristic
39#14582757—21no—
40#14582756—21no—
41C4⋊C4×Dic43C2211yescharacteristic
42C4×Dic43⋊C4C2211yescharacteristic
43C4×C4⋊Dic43C2211yescharacteristic
44#95×D43—21no—
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582654C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×#102×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#97×C43C2211yescharacteristic
56C43×#390C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C22×D172C2311yescharacteristic
61C23×Dic43—21no—
62C22×C4×D43—21no—
63C22×C4×D43—21no—
64C22×C4×D43—21no—
65C2×#10621882—22no—
66C2×#10621882—22no—
67C2×#10621882C2×C414yes—
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70C4×D172—22no—
71C4×D172—41no—
72D4×Dic43—22no—
73D4×Dic43C2×C414yescomplemented
74#13063287—22no—
75#13063287—22no—
76#13063287—41no—
77#13063287C2×C414yes—
78#13063281—44no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4D411yescharacteristic
86C2×Dic43⋊C4D411yescharacteristic
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43C2311yescharacteristic
96C2×C4×Dic43C2311yescharacteristic
97#13063256C2×C414yescomplemented
98Dic43⋊C8—22no—
99#13063247—22no—
100#13063247C2×C414yes—
101#13063246—41no—
102#13063245—22no—
103#13063235C2×C414yescomplemented
104C8×Dic43—41no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95D411yescharacteristic
111C43⋊#95D411yescharacteristic
112C22×D4×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C22⋊C4×C43—21no—
120C2×C22⋊C4×C43—21no—
121C2×C42×C43C2311yescharacteristic
122#102×C43—41no—
123#102×C43C2×C414yescomplemented
124#97×C43—41no—
125#95×C43—21no—
126C24×C43—21no—
127C23×D43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43C22×C412yes—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2411yescharacteristic
140C22×Dic43—24no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—42no—
145C22×Dic43—42no—
146C22×Dic43C2×D411yescharacteristic
147C22×Dic43C2×D411yescharacteristic
148C22×Dic43C2×D411yescharacteristic
149C22×Dic43C2×D411yescharacteristic
150C2×D172—21no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172C22×C412yes—
154C2×D172#4112yes—
155C2×D172#4112yes—
156C2×C4×D43—24no—
157C2×C4×D43—42no—
158C2×C4×D43—42no—
159C2×C4×D43—42no—
160C2×C4×D43—42no—
161C2×C4×D43—81no—
162C2×C4×D43—81no—
163C2×C4×D43—81no—
164C2×C4×D43—81no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43C22×C412yes—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—81no—
177C4⋊C4×C43C22×C412yes—
178C22⋊C4×C43—42no—
179C22⋊C4×C43—81no—
180C42×C43—21no—
181C42×C43—21no—
182C22⋊Dic43—24no—
183C22⋊Dic43—42no—
184C22⋊Dic43—81no—
185#10621882—28no—
186(C2×D43)⋊C4—24no—
187(C2×D43)⋊C4—42no—
188(C2×D43)⋊C4—42no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—81no—
195C4⋊Dic43C22×C412yes—
196Dic43⋊C4—22no—
197Dic43⋊C4—41no—
198Dic43⋊C4—42no—
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—41no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43C22×D411yescharacteristic
220C22×D43—22no—
221C22×D43—22no—
222C22×D43—22no—
223C22×D43—41no—
224C22×D43—41no—
225C22×D43—41no—
226C22×D43—41no—
227D4×C43—22no—
228D4×C43—22no—
229D4×C43—41no—
230D4×C43—41no—
231C2×C4×C43—22no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
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×C43C23×C411yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43H(5,𝔽2)11yescharacteristic
251C2×C4×C432−1+411yescharacteristic
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—22no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—48no—
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×Dic43C4×D412yes—
272C2×Dic43C4×D412yes—
273C2×Dic43AGL(1,ℤ/8)12yes—
274D172—22no—
275D172—22no—
276D172—22no—
277D172#11714yescomplemented
278C4×D43—84no—
279C4×D43—84no—
280C4×D43—84no—
281C8×C43—22no—
282C8×C43—41no—
283C43⋊C8—22no—
284C43⋊C8—41no—
285#22780—431nomaximal, Sylow
286C22×C43—42no—
287C22×C43—42no—
288C22×C43—42no—
289C22×C43—81no—
290C22×C43—81no—
291C22×C43—81no—
292C22×C43—81no—
293C22×C43C2×C4×D411yescharacteristic
294C22×C43#54611yescharacteristic
295C22×C43#54811yescharacteristic
296C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
297C22×C43#57511yescharacteristic
298C22×C43#57611yescharacteristic
299C22×C43#57711yescharacteristic
300C2×D43—24no—
301C2×D43—42no—
302C2×D43—42no—
303C2×D43—42no—
304C2×D43—42no—
305C2×D43—42no—
306C2×D43—42no—
307C4×C43—42no—
308C4×C43—41no—
309C4×C43—41no—
310C4×C43—81no—
311C4×C43—81no—
312C4×C43C2×#11711yescharacteristic
313C4×C43#52011yescharacteristic
314C4×C43#55211yescharacteristic
315C4×C43#55311yescharacteristic
316Dic43—22no—
317Dic43—22no—
318Dic43—22no—
319Dic43—42no—
320Dic43—41no—
321Dic43—81no—
322Dic43—81no—
323C2×#442—431no—
324#2354—431no—
325#2349—431no—
326#1936D4311yescharacteristic, complemented
327#1934—431no—
328#1920—431no—
329#1919—431no—
330#1879—431no—
331#1879—431no—
332#1836—431no—
333#1804—431no—
334#1802—431no—
335#1771—431no—
336#1762—431no—
337C4×#102—431no—
338C2×C43—82no—
339C2×C43#235211yescharacteristic
340C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
341C2×C43#294611yescharacteristic
342C2×C43#330611yescharacteristic
343C2×C43#331911yescharacteristic
344C2×C43#336611yescharacteristic
345C2×C43#337611yescharacteristic
346D43—44no—
347C22×D8—431no—
348C2×C4×D4—431no—
349C2×C4×D4—431no—
350C2×C4×D4—431no—
351C2×C4×D4—431no—
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×#97C2×D4311yescharacteristic
364C2×C4×C8—431no—
365#390—431no—
366#390C2×D4311yescharacteristic
367#389—431no—
368#389C2×D4311yescharacteristic
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#340C2×D4311yescharacteristic
388#340C2×D4311yescharacteristic
389#336—431no—
390#336—431no—
391C43#2278011yescharacteristic, complemented, Sylow
392C22×D4—431no—
393C22×D4C22×D4311yescharacteristic
394C23×C4—861no—
395C23×C4—861no—
396C23×C4—861no—
397C23×C4—861no—
398C2×D8—434no—
399C2×D8—862no—
400C2×D8—862no—
401C22×C8—431no—
402C22×C8—431no—
403C22×C8C22×D4311yescharacteristic
404C22×C8C22×D4311yescharacteristic
405C4×D4—434no—
406C4×D4—434no—
407C4×D4—862no—
408C4×D4—862no—
409C4×D4—862no—
410C4×D4—862no—
411C4×D4—1721no—
412C4×D4—1721no—
413#117—1724no—
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—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×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—41no—
442#102—434no—
443#102—862no—
444#102—862no—
445#102—1721no—
446#102C4×D4314yescomplemented
447#97—41no—
448#97—434no—
449C4×C8—1721no—
450#95—21no—
451#95—431no—
452#95—431no—
453#95—861no—
454#95—861no—
455#95—861no—
456#95—861no—
457#95—861no—
458C24—21no—
459C24—861no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—432no—
466C2×D4—432no—
467C2×D4—432no—
468C2×D4—861no—
469C2×D4—861no—
470C2×D4—861no—
471C2×D4C2×C4×D4312yes—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—431no—
476C22×C4—431no—
477C22×C4—431no—
478C22×C4—431no—
479C22×C4—864no—
480C22×C4—864no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—3441no—
485C22×C4—3441no—
486C22×C4—3441no—
487C22×C4—3441no—
488C22×C4—1722no—
489C22×C4—1722no—
490C22×C4—1722no—
491C22×C4—1722no—
492C22×C4—1722no—
493C22×C4—1722no—
494C22×C4D4×D4311yescharacteristic
495C22×C4D4×D4311yescharacteristic
496C22×C4C23×D4311yescharacteristic
497D8—868no—
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—21no—
515C4⋊C4—81no—
516C4⋊C4—432no—
517C4⋊C4—862no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—3441no—
524C4⋊C4—3441no—
525C4⋊C4—1721no—
526C4⋊C4—1722no—
527C4⋊C4C2×C4×D4312yes—
528C22⋊C4—42no—
529C22⋊C4—81no—
530C22⋊C4—864no—
531C22⋊C4—864no—
532C22⋊C4—3441no—
533C22⋊C4—1722no—
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—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—862no—
552C23—862no—
553C23—862no—
554C23—1721no—
555C23—1721no—
556C23—1721no—
557C23—1721no—
558C23C2×D4×D4311yescharacteristic
559D4—22no—
560D4—22no—
561D4—41no—
562D4—41no—
563D4—434no—
564D4—862no—
565D4—862no—
566D4—862no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—432no—
583C2×C4—432no—
584C2×C4—432no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—862no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—3444no—
596C2×C4—3444no—
597C2×C4—3444no—
598C2×C4—1728no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4C22×C4×D4311yescharacteristic
608C2×C4#41×D4311yescharacteristic
609C2×C4#41×D4311yescharacteristic
610C2×C4#41×D4311yescharacteristic
611C2×C4#1306337011yescharacteristic
612C2×C4#1306337211yescharacteristic
613C8—22no—
614C8—41no—
615C8—862no—
616C8—1721no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—81no—
621C22—81no—
622C22—81no—
623C22—81no—
624C22—864no—
625C22—1722no—
626C22—1722no—
627C22—1722no—
628C22—1722no—
629C22—1722no—
630C22—1722no—
631C22C4×D4×D4311yescharacteristic
632C22#1458353811yescharacteristic
633C22#1458355711yescharacteristic
634C22AGL(1,ℤ/8)×D4311yescharacteristic
635C22#1458369811yescharacteristic
636C22#1458370311yescharacteristic
637C22#1458370911yescharacteristic
638C4—42no—
639C4—41no—
640C4—41no—
641C4—81no—
642C4—81no—
643C4—862no—
644C4—862no—
645C4—862no—
646C4—3441no—
647C4—3441no—
648C4—1722no—
649C4—1721no—
650C4#117×D4311yescharacteristic
651C4#1458337811yescharacteristic
652C4#1458358511yescharacteristic
653C4#1458359411yescharacteristic
654C2—82no—
655C2—1724no—
656C2#1913752311yescharacteristic
657C2#1914340011yescharacteristic
658C2#1914342411yescharacteristic
659C2#1914655111yescharacteristic
660C2#1914674611yescharacteristic
661C2#1914729911yescharacteristic
662C2#1914742111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1936C2
socleC23×C43C22×D4
prime radicalC22×#10621882C22
cosocleC22×C4×C43C24
hypercenter#1936D43
hypocenterC43#22780
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
2. #19137543C2semidirect
3. #19137504C2semidirect
4. #19135280C2semidirect
5. #19135183C2semidirect
6. #19135170C2semidirect
9. #19134727C2semidirect
10. #19134603C2semidirect
11. #19134594C2semidirect
12. #19134471C2semidirect
13. #19134421C2semidirect
14. #19134409C2semidirect
15. C43×#1936C2semidirect
22. #14583008C4semidirect
73. D4×Dic43C2×C4semidirect
97. #13063256C2×C4semidirect
103. #13063235C2×C4semidirect
123. #102×C43C2×C4semidirect
277. D172#117semidirect
326. #1936D43semidirect
391. C43#22780semidirect
446. #102C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830082
#191375432
#191375042
#191352802
#191351832
#191351702
#191349462
#191349402
#191347272
#191346032
#191345942
#191344712
#191344212
#191344092
C43×#19362
#2278043