Finite Group Databasebeta

← #25196697

Subgroups — #25196697

Order 11008.

844 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142905C211yesmaximal, characteristic, complemented
2#19136163C211yesmaximal, characteristic, complemented
3#19136116C211yesmaximal, characteristic, complemented
4#19135933C211yesmaximal, characteristic, complemented
5#19135741C211yesmaximal, characteristic, complemented
6#19135180C211yesmaximal, characteristic, complemented
7#19135166C211yesmaximal, characteristic, complemented
8#19135034C211yesmaximal, characteristic
9#19135034C211yesmaximal, characteristic
10#19134856C211yesmaximal, characteristic, complemented
11#19134842C211yesmaximal, characteristic, complemented
12#19134626C211yesmaximal, characteristic, complemented
13#19134626C211yesmaximal, characteristic, complemented
14#19134289C211yesmaximal, characteristic, complemented
15C4×#121×C43C211yesmaximal, characteristic
16C22×#10621877C2211yescharacteristic
17C22×#10621877C2211yescharacteristic
18C2×#13063317C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×#13063258C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27#14582797C2211yescharacteristic
28#14582797C2211yescharacteristic
29#14582783—21no—
30#14582783—21no—
31#14582772—21no—
32#14582772—21no—
33#14582765C2211yescharacteristic
34#14582759C2211yescharacteristic
35#14582759C2211yescharacteristic
36#14582661C2211yescharacteristic
37#14582661C2211yescharacteristic
38#14582661C2211yescharacteristic
39#14582661C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582654C2211yescharacteristic
45#14582654C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C2×#121×C43C2211yescharacteristic
49C2×C4×D4×C43—21no—
50C2×C4×D4×C43C2211yescharacteristic
51C22×C42×C43C2211yescharacteristic
52C43×#390C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C43×#388—21no—
55C43×#386—21no—
56C43×#380C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C4×C22⋊C4×C43—21no—
59C2×#10621877—22no—
60C2×#10621877—22no—
61C2×#10621877—22no—
62C2×#10621877—22no—
63C2×#10621877—41no—
64C2×#10621877—41no—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69#13063317—41no—
70#13063317—41no—
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81#13063258—22no—
82#13063258—41no—
83#13063256—22no—
84#13063256—41no—
85#13063246—22no—
86#13063246—22no—
87#13063246—41no—
88#13063246—41no—
89C43⋊#95—21no—
90C43⋊#95—21no—
91C43⋊#95—21no—
92C43⋊#95—21no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C22×D4×C43—21no—
96C22×D4×C43C2311yescharacteristic
97C23×C4×C43—21no—
98C23×C4×C43D411yescharacteristic
99C23×C4×C43D411yescharacteristic
100C23×C4×C43C2311yescharacteristic
101#121×C43—22no—
102#121×C43Q814yes—
103C4×D4×C43—41no—
104C4×D4×C43—41no—
105C4×D4×C43—44no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C22⋊C4×C43—21no—
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115C2×C42×C43—21no—
116C2×C42×C43—41no—
117C2×C42×C43—41no—
118C2×C42×C43D411yescharacteristic
119C2×C42×C43D411yescharacteristic
120C2×C42×C43C2311yescharacteristic
121C2×C42×C43C2311yescharacteristic
122#95×C43—21no—
123#95×C43—21no—
124#95×C43—21no—
125C24×C43—21no—
126C24×C43C2×D411yescharacteristic
127C2×D4×C43—21no—
128C2×D4×C43—24no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—42no—
134C2×D4×C43—42no—
135C2×D4×C43C2×Q812yes—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—22no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—41no—
145C22×C4×C43—41no—
146C22×C4×C43—41no—
147C22×C4×C43—41no—
148C22×C4×C43—41no—
149C22×C4×C43—42no—
150C22×C4×C43—42no—
151C22×C4×C43—42no—
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×Q812yes—
158C22×C4×C43#4112yes—
159C22×C4×C43C2411yescharacteristic
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—42no—
170C4⋊C4×C43C2×Q812yes—
171C22⋊C4×C43—24no—
172C22⋊C4×C43—42no—
173C22⋊C4×C43—42no—
174C22⋊C4×C43—42no—
175C22⋊C4×C43—42no—
176C42×C43—21no—
177C42×C43—21no—
178C42×C43—21no—
179C42×C43—21no—
180C42×C43—41no—
181C42×C43—41no—
182C42×C43—42no—
183C22⋊Dic43—42no—
184C22⋊Dic43—42no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193Dic43⋊C4—42no—
194Dic43⋊C4—42no—
195Dic43⋊C4—42no—
196Dic43⋊C4—42no—
197#10621877—44no—
198#10621877—44no—
199C2×C43⋊C8—21no—
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#4112yes—
210C2×C43⋊C8#4112yes—
211C23×C43—21no—
212C23×C43—21no—
213C23×C43—21no—
214C23×C43—21no—
215C23×C43—21no—
216C23×C43—21no—
217C23×C43—22no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43C22⋊Q812yes—
225C23×C43C22×D411yescharacteristic
226D4×C43—22no—
227D4×C43—22no—
228D4×C43—48no—
229D4×C43—41no—
230D4×C43—41no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—22no—
236C2×C4×C43—22no—
237C2×C4×C43—22no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—21no—
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—21no—
248C2×C4×C43—21no—
249C2×C4×C43—44no—
250C2×C4×C43—44no—
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—84no—
260C2×C4×C43C22⋊Q812yes—
261C2×C4×C43AGL(1,ℤ/8)12yes—
262C2×C4×C43C22×Q811yescharacteristic
263C2×C4×C43C2×#4111yescharacteristic
264C2×C4×C43C2×#4111yescharacteristic
265C2×C4×C43C2×#4111yescharacteristic
266C2×C4×C43H(5,𝔽2)11yescharacteristic
267C2×C4×C43H(5,𝔽2)11yescharacteristic
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—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C43⋊C8—22no—
281C43⋊C8—22no—
282C43⋊C8—41no—
283C43⋊C8—41no—
284#29167—431nomaximal, Sylow
285C22×C43—22no—
286C22×C43—22no—
287C22×C43—22no—
288C22×C43—41no—
289C22×C43—41no—
290C22×C43—41no—
291C22×C43—41no—
292C22×C43—42no—
293C22×C43—42no—
294C22×C43—42no—
295C22×C43—81no—
296C22×C43—81no—
297C22×C43—81no—
298C22×C43—81no—
299C22×C43C2×C22⋊Q811yescharacteristic
300C22×C43#53211yescharacteristic
301C22×C43#53411yescharacteristic
302C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
303C22×C43#57511yescharacteristic
304C22×C43#57511yescharacteristic
305C22×C43#57511yescharacteristic
306C4×C43—22no—
307C4×C43—22no—
308C4×C43—42no—
309C4×C43—41no—
310C4×C43—41no—
311C4×C43—41no—
312C4×C43—81no—
313C4×C43—81no—
314C4×C43#55111yescharacteristic
315C4×C43#55111yescharacteristic
316C4×C43#55411yescharacteristic
317C4×C43#55411yescharacteristic
318Dic43—81no—
319Dic43—81no—
320Dic43—81no—
321Dic43—81no—
322#2851—431no—
323C4×#121D4311yescharacteristic
324#2101—431no—
325#2092—431no—
326#2059—431no—
327#2025—431no—
328#1920—431no—
329#1918—431no—
330#1895—431no—
331#1895—431no—
332#1864—431no—
333#1862—431no—
334#1809—431no—
335#1809—431no—
336#1728—431no—
337C2×C43—42no—
338C2×C43—82no—
339C2×C43#256411yescharacteristic
340C2×C43#307711yescharacteristic
341C2×C43#308011yescharacteristic
342C2×C43#317111yescharacteristic
343C2×C43#318311yescharacteristic
344C2×C43#319411yescharacteristic
345C2×C43#319711yescharacteristic
346C22×M16—431no—
347C22×M16—431no—
348C2×#125—431no—
349C2×#121C2×D4311yescharacteristic
350C2×C4×D4—21no—
351C2×C4×D4C2×D4311yescharacteristic
352C22×C42C2×D4311yescharacteristic
353C2×#107—431no—
354C2×#107—431no—
355C2×#106—431no—
356C2×#106—431no—
357C2×#102—431no—
358C2×#102—431no—
359C2×#102—431no—
360C2×#102—431no—
361#390C2×D4311yescharacteristic
362#389—431no—
363#389—431no—
364#389C2×D4311yescharacteristic
365#388—21no—
366#387—861no—
367#387—861no—
368#386—21no—
369#385—861no—
370#385—861no—
371#382—431no—
372#380—431no—
373#380—431no—
374#380C2×D4311yescharacteristic
375C4×C4⋊C4C2×D4311yescharacteristic
376C4×C22⋊C4—21no—
377#340—431no—
378#340—431no—
379#340—431no—
380#340—431no—
381#340—431no—
382#340—431no—
383#340—431no—
384#340—431no—
385#336—431no—
386#336—431no—
387#336—431no—
388#336—431no—
389C43#2916711yescharacteristic, complemented, Sylow
390C22×D4—21no—
391C22×D4C22×D4311yescharacteristic
392C23×C4—21no—
393C23×C4C22⋊D4311yescharacteristic
394C23×C4C22⋊D4311yescharacteristic
395C23×C4C22×D4311yescharacteristic
396C2×M16—862no—
397C2×M16—862no—
398C2×M16—862no—
399C2×M16—862no—
400C2×M16—1721no—
401C2×M16—1721no—
402C22×C8—431no—
403C22×C8—431no—
404C22×C8—431no—
405C22×C8—431no—
406#125—1721no—
407#125—1721no—
408#121—22no—
409#121Dic8614yes—
410C4×D4—41no—
411C4×D4—41no—
412C4×D4—44no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—431no—
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⋊C4C22×D4311yescharacteristic
423C2×C4⋊C4C22×D4311yescharacteristic
424C2×C4⋊C4C22×D4311yescharacteristic
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—861no—
431C2×C22⋊C4—861no—
432C2×C42—21no—
433C2×C42—41no—
434C2×C42—41no—
435C2×C42C22⋊D4311yescharacteristic
436C2×C42C22⋊D4311yescharacteristic
437C2×C42C22×D4311yescharacteristic
438C2×C42C22×D4311yescharacteristic
439#107—862no—
440#107—1721no—
441#106—862no—
442#106—1721no—
443#102—862no—
444#102—862no—
445#102—1721no—
446#102—1721no—
447#95—21no—
448#95—21no—
449#95—21no—
450#95—861no—
451#95—861no—
452#95—861no—
453#95—861no—
454#95—861no—
455#95—861no—
456C24—21no—
457C24C2×C22⋊D4311yescharacteristic
458C2×D4—24no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—42no—
465C2×D4—42no—
466C2×D4C2×Dic8612yes—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4C2×Dic8612yes—
488C22×C4#1062189812yes—
489C22×C4C2×C22⋊D4311yescharacteristic
490C22×C4C2×C22⋊D4311yescharacteristic
491C22×C4C2×C22⋊D4311yescharacteristic
492C22×C4C2×C22⋊D4311yescharacteristic
493C22×C4C2×C22⋊D4311yescharacteristic
494C22×C4C23×D4311yescharacteristic
495M16—1724no—
496M16—1724no—
497C2×C8—432no—
498C2×C8—432no—
499C2×C8—861no—
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—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—42no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—1722no—
524C4⋊C4—1722no—
525C4⋊C4—1722no—
526C4⋊C4—1722no—
527C4⋊C4C2×Dic8612yes—
528C22⋊C4—24no—
529C22⋊C4—42no—
530C22⋊C4—42no—
531C22⋊C4—42no—
532C22⋊C4—42no—
533C22⋊C4—1722no—
534C22⋊C4—1722no—
535C42—21no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—41no—
540C42—41no—
541C42—42no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—22no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23#1306330412yes—
556C23C22×C22⋊D4311yescharacteristic
557D4—22no—
558D4—22no—
559D4—48no—
560D4—41no—
561D4—41no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
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—44no—
581C2×C4—44no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—84no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4#1306330412yes—
604C2×C4#1306335112yes—
605C2×C4C22×Dic8611yescharacteristic
606C2×C4#41×D4311yescharacteristic
607C2×C4#41×D4311yescharacteristic
608C2×C4C2×#1062189811yescharacteristic
609C2×C4#1306337011yescharacteristic
610C2×C4#1306337011yescharacteristic
611C8—862no—
612C8—862no—
613C8—1721no—
614C8—1721no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—42no—
623C22—42no—
624C22—42no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22—81no—
629C22C2×#1306330411yescharacteristic
630C22#1458344511yescharacteristic
631C22#1458345811yescharacteristic
632C22C2×#1306335111yescharacteristic
633C22#1458369711yescharacteristic
634C22#1458369711yescharacteristic
635C22#1458369711yescharacteristic
636C4—22no—
637C4—22no—
638C4—41no—
639C4—42no—
640C4—41no—
641C4—41no—
642C4—81no—
643C4—81no—
644C4—3441no—
645C4—3441no—
646C4—3441no—
647C4—3441no—
648C4#1458357811yescharacteristic
649C4#1458357811yescharacteristic
650C4#1458360811yescharacteristic
651C4#1458360811yescharacteristic
652C2—42no—
653C2—82no—
654C2#1913977111yescharacteristic
655C2#1914439211yescharacteristic
656C2#1914441711yescharacteristic
657C2#1914518411yescharacteristic
658C2#1914531811yescharacteristic
659C2#1914540911yescharacteristic
660C2#1914543211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC4×#121×C43C2
socleC23×C43C22×D4
prime radicalC2×#121×C43C22
hypercenterC4×#121D43
hypocenterC43#29167
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. #19142905C2semidirect
2. #19136163C2semidirect
3. #19136116C2semidirect
4. #19135933C2semidirect
5. #19135741C2semidirect
6. #19135180C2semidirect
7. #19135166C2semidirect
10. #19134856C2semidirect
11. #19134842C2semidirect
12. #19134626C2semidirect
13. #19134626C2semidirect
14. #19134289C2semidirect
389. C43#29167semidirect

Maximal subgroups

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

subgroupindex
#191429052
#191361632
#191361162
#191359332
#191357412
#191351802
#191351662
#191350342
#191348562
#191348422
#191346262
#191342892
C4×#121×C432
#2916743