Finite Group Databasebeta

← #25164729

Subgroups — #25164729

Order 11008.

790 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
1#19137598C211yesmaximal, characteristic, complemented
2#19135912C211yesmaximal, characteristic, complemented
3#19135798C211yesmaximal, characteristic, complemented
4#19135743C211yesmaximal, characteristic, complemented
5#19135598C211yesmaximal, characteristic
6#19135553C211yesmaximal, characteristic, complemented
7#19135281C211yesmaximal, characteristic, complemented
8#19135212C211yesmaximal, characteristic, complemented
9#19135203C211yesmaximal, characteristic, complemented
10#19135187C211yesmaximal, characteristic, complemented
11#19134953C211yesmaximal, characteristic, complemented
12#19134913C211yesmaximal, characteristic
13#19134679C211yesmaximal, characteristic, complemented
14C4×#13063248C211yesmaximal, characteristic, complemented
15C43×#2490C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C2×#13063304C2211yescharacteristic
18C2×C4×Dic86C2211yescharacteristic
19C22×C4⋊Dic43C2211yescharacteristic
20C2×#13063258C2211yescharacteristic
21C2×C4⋊(C43⋊C8)C2211yescharacteristic
22C2×#13063248C2211yescharacteristic
23C2×#13063248C2211yescharacteristic
24C2×#13063248C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×C22⋊(C43⋊C8)C2211yescharacteristic
29C2×C22⋊(C43⋊C8)C2211yescharacteristic
30C2×C4×C43⋊C8C2211yescharacteristic
31#14582805C2211yescharacteristic
32#14582797C2211yescharacteristic
33#14582796—21no—
34#14582786—21no—
35#14582771—21no—
36C4×C4⋊Dic43C2211yescharacteristic
37C22⋊C4×Dic43—21no—
38#14582661C2211yescharacteristic
39#14582661C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C2×#125×C43C2211yescharacteristic
49C2×#121×C43C2211yescharacteristic
50C43×#397—21no—
51C43×#394—21no—
52C43×#390—21no—
53C43×#390C2211yescharacteristic
54C43×#390C2211yescharacteristic
55C43×#388—21no—
56C43×#380C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C4×C22⋊C4×C43C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C23×Dic43—21no—
61C2×#10621883—22no—
62C2×#10621883—41no—
63C2×#10621883—41no—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68#13063304—22no—
69#13063304—22no—
70C4×Dic86—22no—
71C4×Dic86—41no—
72C2×C4⋊Dic43—22no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43—41no—
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×C22⋊Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84#13063258—22no—
85C4⋊(C43⋊C8)—41no—
86#13063248—22no—
87#13063248—22no—
88#13063248—41no—
89#13063246—22no—
90#13063246—22no—
91#13063246—41no—
92C22⋊(C43⋊C8)—41no—
93C22⋊(C43⋊C8)—41no—
94C4×C43⋊C8—41no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C22×D4×C43—21no—
100C22×D4×C43C2311yescharacteristic
101C23×C4×C43C2311yescharacteristic
102#125×C43—22no—
103#125×C43—41no—
104#121×C43—22no—
105#121×C43—41no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43—21no—
116C2×C22⋊C4×C43—21no—
117C2×C22⋊C4×C43D411yescharacteristic
118C2×C22⋊C4×C43D411yescharacteristic
119C2×C42×C43—21no—
120C2×C42×C43C2311yescharacteristic
121C2×C42×C43C2311yescharacteristic
122#95×C43—21no—
123#95×C43—21no—
124#95×C43D411yescharacteristic
125#95×C43D411yescharacteristic
126C24×C43—21no—
127C24×C43C2×D411yescharacteristic
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—42no—
135C2×D4×C43—42no—
136C2×D4×C43—81no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2411yescharacteristic
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—42no—
157C22×Dic43—42no—
158C22×Dic43—81no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86#4112yes—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—42no—
171C4⋊C4×C43—42no—
172C4⋊C4×C43#4112yes—
173C22⋊C4×C43—22no—
174C22⋊C4×C43—22no—
175C22⋊C4×C43—42no—
176C22⋊C4×C43—42no—
177C22⋊C4×C43—81no—
178C22⋊C4×C43—81no—
179C22⋊C4×C43—81no—
180C22⋊C4×C43—81no—
181C42×C43—21no—
182C42×C43—21no—
183C42×C43—21no—
184C42×C43—21no—
185C42×C43—81no—
186C22⋊Dic43—24no—
187#10621883—44no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—42no—
193C4⋊Dic43#4112yes—
194C4⋊Dic43#4112yes—
195Dic43⋊C4—24no—
196Dic43⋊C4—42no—
197Dic43⋊C4—81no—
198C4×Dic43—42no—
199C4×Dic43—81no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C23×C43—21no—
213C23×C43—21no—
214C23×C43—21no—
215C23×C43—21no—
216C23×C43—21no—
217C23×C43—21no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43#13512yes—
226C23×C43C22×D411yescharacteristic
227D4×C43—41no—
228D4×C43—41no—
229D4×C43—41no—
230D4×C43—41no—
231D4×C43—84no—
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—21no—
239C2×C4×C43—21no—
240C2×C4×C43—22no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43#13712yes—
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C43C2×#4111yescharacteristic
263C2×C4×C43C2×#4111yescharacteristic
264C2×C4×C43H(5,𝔽2)11yescharacteristic
265C2×C4×C43H(5,𝔽2)11yescharacteristic
266C2×Dic43—22no—
267C2×Dic43—22no—
268C2×Dic43—22no—
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—41no—
278C2×Dic43—84no—
279Dic86—22no—
280Dic86—22no—
281Dic86—41no—
282Dic86—41no—
283C43⋊C8—41no—
284C43⋊C8—41no—
285C43⋊C8—41no—
286C43⋊C8—41no—
287#26727—431nomaximal, Sylow
288C22×C43—22no—
289C22×C43—22no—
290C22×C43—22no—
291C22×C43—41no—
292C22×C43—41no—
293C22×C43—41no—
294C22×C43—41no—
295C22×C43—81no—
296C22×C43—81no—
297C22×C43—81no—
298C22×C43—81no—
299C22×C43—81no—
300C22×C43—81no—
301C22×C43—81no—
302C22×C43#52511yescharacteristic
303C22×C43#54611yescharacteristic
304C22×C43#54611yescharacteristic
305C22×C43C2×#13511yescharacteristic
306C22×C43C2×#13711yescharacteristic
307C22×C43#57611yescharacteristic
308C22×C43#57711yescharacteristic
309C4×C43—22no—
310C4×C43—41no—
311C4×C43—41no—
312C4×C43—41no—
313C4×C43—42no—
314C4×C43—41no—
315C4×C43—81no—
316C4×C43—81no—
317C4×C43#52911yescharacteristic
318C4×C43#53811yescharacteristic
319C4×C43#55511yescharacteristic
320C4×C43#55911yescharacteristic
321Dic43—42no—
322Dic43—42no—
323Dic43—42no—
324Dic43—81no—
325#2490D4311yescharacteristic
326#2360—431no—
327#2055—431no—
328#2036—431no—
329#2026—431no—
330#2000—431no—
331#1989—431no—
332#1934—431no—
333#1925—431no—
334#1923—431no—
335#1921—431no—
336#1880—431no—
337#1874—431no—
338#1823—431no—
339C4×#103—431no—
340C2×C43—42no—
341C2×C43—161no—
342C2×C43#245911yescharacteristic
343C2×C43#310811yescharacteristic
344C2×C43#311911yescharacteristic
345C2×C43#329611yescharacteristic
346C2×C43#329711yescharacteristic
347C2×C43#332011yescharacteristic
348C2×C43#333311yescharacteristic
349C22×SD16—431no—
350C2×#125C2×D4311yescharacteristic
351C2×C22⋊Q8—431no—
352C2×#121C2×D4311yescharacteristic
353C2×C4×Q8—431no—
354C22×C4⋊C4—431no—
355C2×#107—431no—
356C2×C4⋊C8—431no—
357C2×#103—431no—
358C2×#103—431no—
359C2×#103—431no—
360C2×#102—431no—
361C2×#102—431no—
362C2×#102—431no—
363C2×C22⋊C8—431no—
364C2×C22⋊C8—431no—
365C2×C4×C8—431no—
366#397—21no—
367#394—21no—
368#391—431no—
369#390—21no—
370#390C2×D4311yescharacteristic
371#390C2×D4311yescharacteristic
372#389—431no—
373#389—861no—
374#388—21no—
375#387—861no—
376#385—861no—
377#380C2×D4311yescharacteristic
378C4×C4⋊C4—431no—
379C4×C4⋊C4C2×D4311yescharacteristic
380C4×C22⋊C4—861no—
381C4×C22⋊C4C2×D4311yescharacteristic
382#340—431no—
383#340—431no—
384#340—431no—
385#340—431no—
386#340—431no—
387#340—431no—
388#340—431no—
389#340—431no—
390#336—431no—
391#336—431no—
392C43#2672711yescharacteristic, complemented, Sylow
393C22×Q8—431no—
394C22×D4—21no—
395C22×D4C22×D4311yescharacteristic
396C23×C4—861no—
397C23×C4C22×D4311yescharacteristic
398C2×SD16—862no—
399C2×SD16—1721no—
400C2×SD16—1721no—
401C22×C8—431no—
402C22×C8—431no—
403C22×C8—431no—
404C22×C8—431no—
405#125—22no—
406#125—41no—
407C22⋊Q8—862no—
408C22⋊Q8—862no—
409#121—22no—
410#121—41no—
411C4×Q8—862no—
412C4×Q8—1721no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—431no—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—862no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—1721no—
424C2×C4⋊C4C22×D4311yescharacteristic
425C2×C4⋊C4C22×D4311yescharacteristic
426C2×C4⋊C4C22×D4311yescharacteristic
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—861no—
434C2×C22⋊C4C22⋊D4311yescharacteristic
435C2×C22⋊C4C22⋊D4311yescharacteristic
436C2×C42—21no—
437C2×C42—861no—
438C2×C42—861no—
439C2×C42C22×D4311yescharacteristic
440C2×C42C22×D4311yescharacteristic
441#107—862no—
442C4⋊C8—1721no—
443#103—862no—
444#103—862no—
445#103—1721no—
446#102—862no—
447#102—862no—
448#102—1721no—
449C22⋊C8—1721no—
450C22⋊C8—1721no—
451C4×C8—1721no—
452#95—21no—
453#95—21no—
454#95—861no—
455#95—861no—
456#95—861no—
457#95—861no—
458#95C22⋊D4311yescharacteristic
459#95C22⋊D4311yescharacteristic
460C24—21no—
461C24C2×C22⋊D4311yescharacteristic
462C2×Q8—432no—
463C2×Q8—861no—
464C2×Q8—861no—
465C2×Q8—861no—
466C2×Q8—861no—
467C2×Q8—861no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—42no—
475C2×D4—42no—
476C2×D4—81no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4—3441no—
491C22×C4—1722no—
492C22×C4—1722no—
493C22×C4C2×C22⋊D4311yescharacteristic
494C22×C4C2×C22⋊D4311yescharacteristic
495C22×C4C2×C22⋊D4311yescharacteristic
496C22×C4C2×C22⋊D4311yescharacteristic
497C22×C4C2×C22⋊D4311yescharacteristic
498C22×C4C23×D4311yescharacteristic
499SD16—1724no—
500C2×C8—861no—
501C2×C8—861no—
502C2×C8—861no—
503C2×C8—861no—
504C2×C8—861no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8—861no—
510C2×C8—861no—
511C2×C8—861no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—42no—
518C4⋊C4—42no—
519C4⋊C4—432no—
520C4⋊C4—432no—
521C4⋊C4—864no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—3441no—
527C4⋊C4—1722no—
528C4⋊C4—1722no—
529C4⋊C4#1062190012yes—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—42no—
533C22⋊C4—42no—
534C22⋊C4—81no—
535C22⋊C4—81no—
536C22⋊C4—81no—
537C22⋊C4—81no—
538C22⋊C4—864no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—81no—
544C42—3441no—
545C42—1722no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23#1306334512yes—
560C23C22×C22⋊D4311yescharacteristic
561Q8—862no—
562Q8—862no—
563Q8—1721no—
564Q8—1721no—
565D4—41no—
566D4—41no—
567D4—41no—
568D4—41no—
569D4—84no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—862no—
598C2×C4—862no—
599C2×C4—862no—
600C2×C4—3444no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4#1306335512yes—
611C2×C4#41×D4311yescharacteristic
612C2×C4#41×D4311yescharacteristic
613C2×C4#41×D4311yescharacteristic
614C2×C4C2×#1062190011yescharacteristic
615C2×C4#1306337011yescharacteristic
616C2×C4#1306337111yescharacteristic
617C8—1721no—
618C8—1721no—
619C8—1721no—
620C8—1721no—
621C22—22no—
622C22—22no—
623C22—22no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—81no—
629C22—81no—
630C22—81no—
631C22—81no—
632C22—81no—
633C22—81no—
634C22—81no—
635C22#1458340611yescharacteristic
636C22#1458353711yescharacteristic
637C22#1458354311yescharacteristic
638C22C2×#1306334511yescharacteristic
639C22C2×#1306335511yescharacteristic
640C22#1458370211yescharacteristic
641C22#1458371011yescharacteristic
642C4—22no—
643C4—41no—
644C4—41no—
645C4—42no—
646C4—41no—
647C4—41no—
648C4—81no—
649C4—81no—
650C4—3441no—
651C4—1722no—
652C4—1722no—
653C4—1722no—
654C4#1458342811yescharacteristic
655C4#1458348311yescharacteristic
656C4#1458361111yescharacteristic
657C4#1458363111yescharacteristic
658C2—42no—
659C2—161no—
660C2#1913852811yescharacteristic
661C2#1914467111yescharacteristic
662C2#1914478811yescharacteristic
663C2#1914643011yescharacteristic
664C2#1914643911yescharacteristic
665C2#1914676011yescharacteristic
666C2#1914693311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2490C2
socleC23×C43C22×D4
prime radicalC2×#121×C43C22
hypercenter#2490D43
hypocenterC43#26727
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2490

Complements

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

NH ≅ G/Ntype
1. #19137598C2semidirect
2. #19135912C2semidirect
3. #19135798C2semidirect
4. #19135743C2semidirect
6. #19135553C2semidirect
7. #19135281C2semidirect
8. #19135212C2semidirect
9. #19135203C2semidirect
10. #19135187C2semidirect
11. #19134953C2semidirect
13. #19134679C2semidirect
14. C4×#13063248C2semidirect
392. C43#26727semidirect

Maximal subgroups

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

subgroupindex
#191375982
#191359122
#191357982
#191357432
#191355982
#191355532
#191352812
#191352122
#191352032
#191351872
#191349532
#191349132
#191346792
C4×#130632482
C43×#24902
#2672743