Finite Group Databasebeta

← #25200291

Subgroups — #25200291

Order 11008.

756 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
1#19140392C211yesmaximal, characteristic, complemented
2#19136031C211yesmaximal, characteristic, complemented
3#19135798C211yesmaximal, characteristic, complemented
4#19135774C211yesmaximal, characteristic
5#19135598C211yesmaximal, characteristic
6#19135448C211yesmaximal, characteristic, complemented
7#19135325C211yesmaximal, characteristic, complemented
8#19135295C211yesmaximal, characteristic, complemented
9#19135284C211yesmaximal, characteristic, complemented
10#19135236C211yesmaximal, characteristic, complemented
11#19135180C211yesmaximal, characteristic, complemented
12#19134929C211yesmaximal, characteristic, complemented
13#19134842C211yesmaximal, characteristic, complemented
14#19134361C211yesmaximal, characteristic, complemented
15C43×#2324C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C2×#13063304C2211yescharacteristic
18C2×#13063258C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×#13063256C2211yescharacteristic
21C2×#13063248C2211yescharacteristic
22C2×#13063248C2211yescharacteristic
23C2×#13063248C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×C22⋊(C43⋊C8)C2211yescharacteristic
28C2×C22⋊(C43⋊C8)C2211yescharacteristic
29C2×#13063236C2211yescharacteristic
30C2×C4×C43⋊C8C2211yescharacteristic
31#14582837—21no—
32#14582830—21no—
33#14582827—21no—
34#14582827—21no—
35#14582805C2211yescharacteristic
36#14582805C2211yescharacteristic
37#14582797C2211yescharacteristic
38#14582797C2211yescharacteristic
39#14582759C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C2×#121×C43C2211yescharacteristic
49C2×C4×D4×C43C2211yescharacteristic
50C2×#117×C43C2211yescharacteristic
51C43×#390—21no—
52C43×#390C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C43×#388—21no—
55C43×#386—21no—
56C43×#385—21no—
57C43×#380C2211yescharacteristic
58C4×C4⋊C4×C43C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C2×#10621883—22no—
61C2×#10621883—22no—
62C2×#10621883—41no—
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063304—41no—
68#13063304—41no—
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×C22⋊Dic43—21no—
76C2×C22⋊Dic43—21no—
77#13063258—22no—
78#13063258—41no—
79#13063256—22no—
80#13063248—22no—
81#13063248—22no—
82#13063248—41no—
83#13063246—22no—
84#13063246—22no—
85#13063246—41no—
86C22⋊(C43⋊C8)—22no—
87C22⋊(C43⋊C8)—22no—
88#13063236—41no—
89C4×C43⋊C8—41no—
90C43⋊#95—21no—
91C43⋊#95—21no—
92C43⋊#95—21no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C22×D4×C43—21no—
98C22×D4×C43C2311yescharacteristic
99C23×C4×C43—21no—
100C23×C4×C43C2311yescharacteristic
101#121×C43—22no—
102#121×C43—22no—
103C4×D4×C43—41no—
104C4×D4×C43—41no—
105#117×C43—41no—
106#117×C43—41no—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43D411yescharacteristic
109C2×C4⋊C4×C43D411yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43—21no—
116C2×C22⋊C4×C43—21no—
117C2×C22⋊C4×C43—21no—
118C2×C22⋊C4×C43D411yescharacteristic
119C2×C22⋊C4×C43D411yescharacteristic
120C2×C42×C43—21no—
121C2×C42×C43C2311yescharacteristic
122C2×C42×C43C2311yescharacteristic
123#95×C43—21no—
124#95×C43—21no—
125#95×C43—21no—
126C24×C43—21no—
127C24×C43C2×D411yescharacteristic
128C2×D4×C43—24no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—81no—
135C2×D4×C43—81no—
136C2×D4×C43#4112yes—
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×C43—42no—
147C22×C4×C43—81no—
148C22×C4×C43—81no—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2411yescharacteristic
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—41no—
171C4⋊C4×C43—41no—
172C4⋊C4×C43—81no—
173C4⋊C4×C43#4112yes—
174C22⋊C4×C43—24no—
175C22⋊C4×C43—41no—
176C22⋊C4×C43—41no—
177C22⋊C4×C43—42no—
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—42no—
187C22⋊Dic43—81no—
188#10621883—44no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195Dic43⋊C4—42no—
196Dic43⋊C4—81no—
197Dic43⋊C4—81no—
198C2×C43⋊C8—21no—
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#4112yes—
209C2×C43⋊C8#4112yes—
210C23×C43—22no—
211C23×C43—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×C43C22×D411yescharacteristic
225D4×C43—22no—
226D4×C43—22no—
227D4×C43—41no—
228D4×C43—41no—
229D4×C43—84no—
230C2×C4×C43—21no—
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—21no—
239C2×C4×C43—21no—
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—41no—
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—84no—
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C43C2×#4111yescharacteristic
263C2×C4×C43H(5,𝔽2)11yescharacteristic
264C2×C4×C43H(5,𝔽2)11yescharacteristic
265C2×Dic43—41no—
266C2×Dic43—41no—
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—
277Dic86—41no—
278Dic86—41no—
279Dic86—41no—
280Dic86—41no—
281C43⋊C8—22no—
282C43⋊C8—22no—
283C43⋊C8—41no—
284C43⋊C8—41no—
285#29473—431nomaximal, Sylow
286C22×C43—41no—
287C22×C43—42no—
288C22×C43—41no—
289C22×C43—42no—
290C22×C43—41no—
291C22×C43—42no—
292C22×C43—41no—
293C22×C43—41no—
294C22×C43—41no—
295C22×C43—41no—
296C22×C43—81no—
297C22×C43—81no—
298C22×C43—81no—
299C22×C43—81no—
300C22×C43#52511yescharacteristic
301C22×C43#53211yescharacteristic
302C22×C43#53411yescharacteristic
303C22×C43#57611yescharacteristic
304C22×C43#57711yescharacteristic
305C22×C43#57711yescharacteristic
306C22×C43#57811yescharacteristic
307C4×C43—41no—
308C4×C43—42no—
309C4×C43—41no—
310C4×C43—41no—
311C4×C43—41no—
312C4×C43—41no—
313C4×C43—81no—
314C4×C43—81no—
315C4×C43#55111yescharacteristic
316C4×C43#55311yescharacteristic
317C4×C43#55311yescharacteristic
318C4×C43#55911yescharacteristic
319Dic43—81no—
320Dic43—81no—
321Dic43—81no—
322Dic43—81no—
323#2625—431no—
324#2324D4311yescharacteristic
325#2077—431no—
326#2036—431no—
327#2033—431no—
328#2000—431no—
329#1968—431no—
330#1942—431no—
331#1936—431no—
332#1935—431no—
333#1928—431no—
334#1920—431no—
335#1877—431no—
336#1862—431no—
337#1750—431no—
338C2×C43—81no—
339C2×C43—82no—
340C2×C43#260211yescharacteristic
341C2×C43#311811yescharacteristic
342C2×C43#312011yescharacteristic
343C2×C43#317411yescharacteristic
344C2×C43#317511yescharacteristic
345C2×C43#319811yescharacteristic
346C2×C43#320111yescharacteristic
347C22×SD16—431no—
348C2×C22⋊Q8—431no—
349C2×#121C2×D4311yescharacteristic
350C2×C4×D4C2×D4311yescharacteristic
351C2×#117C2×D4311yescharacteristic
352C2×#107—431no—
353C2×#107—431no—
354C2×#106—431no—
355C2×#103—431no—
356C2×#103—431no—
357C2×#103—431no—
358C2×#102—431no—
359C2×#102—431no—
360C2×#102—431no—
361C2×C22⋊C8—431no—
362C2×C22⋊C8—431no—
363C2×#97—431no—
364C2×C4×C8—431no—
365#400—861no—
366#398—861no—
367#397—861no—
368#397—861no—
369#391—431no—
370#391—431no—
371#390—21no—
372#390C2×D4311yescharacteristic
373#389—431no—
374#389—431no—
375#389C2×D4311yescharacteristic
376#388—21no—
377#386—21no—
378#385—21no—
379#380—431no—
380#380C2×D4311yescharacteristic
381C4×C4⋊C4C2×D4311yescharacteristic
382#340—431no—
383#340—431no—
384#340—431no—
385#340—431no—
386#340—431no—
387#340—431no—
388#336—431no—
389#336—431no—
390C43#2947311yescharacteristic, complemented, Sylow
391C22×Q8—431no—
392C22×D4—21no—
393C22×D4C22×D4311yescharacteristic
394C23×C4—21no—
395C23×C4C22×D4311yescharacteristic
396C2×SD16—862no—
397C2×SD16—862no—
398C2×SD16—1721no—
399C22×C8—431no—
400C22×C8—431no—
401C22×C8—431no—
402C22×C8—431no—
403C22⋊Q8—1721no—
404C22⋊Q8—1721no—
405#121—22no—
406#121—22no—
407C4×D4—41no—
408C4×D4—41no—
409#117—41no—
410#117—41no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4C22⋊D4311yescharacteristic
419C2×C4⋊C4C22⋊D4311yescharacteristic
420C2×C4⋊C4C22×D4311yescharacteristic
421C2×C4⋊C4C22×D4311yescharacteristic
422C2×C4⋊C4C22×D4311yescharacteristic
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C22⋊C4C22⋊D4311yescharacteristic
431C2×C22⋊C4C22⋊D4311yescharacteristic
432C2×C42—21no—
433C2×C42C22×D4311yescharacteristic
434C2×C42C22×D4311yescharacteristic
435#107—862no—
436#107—1721no—
437#106—862no—
438#103—862no—
439#103—862no—
440#103—1721no—
441#102—862no—
442#102—862no—
443#102—1721no—
444C22⋊C8—862no—
445C22⋊C8—862no—
446#97—1721no—
447C4×C8—1721no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—861no—
452#95—861no—
453#95—861no—
454#95—861no—
455#95—861no—
456#95—861no—
457#95—861no—
458C24—21no—
459C24C2×C22⋊D4311yescharacteristic
460C2×Q8—861no—
461C2×Q8—861no—
462C2×Q8—861no—
463C2×Q8—861no—
464C2×Q8—861no—
465C2×Q8—861no—
466C2×D4—24no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—81no—
473C2×D4—81no—
474C2×D4#1062189812yes—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—42no—
485C22×C4—81no—
486C22×C4—81no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4C2×C22⋊D4311yescharacteristic
492C22×C4C2×C22⋊D4311yescharacteristic
493C22×C4C2×C22⋊D4311yescharacteristic
494C22×C4C2×C22⋊D4311yescharacteristic
495C22×C4C2×C22⋊D4311yescharacteristic
496C22×C4C23×D4311yescharacteristic
497SD16—1724no—
498C2×C8—432no—
499C2×C8—432no—
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—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—41no—
516C4⋊C4—41no—
517C4⋊C4—81no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—3441no—
525C4⋊C4—3441no—
526C4⋊C4—1722no—
527C4⋊C4#1062189812yes—
528C22⋊C4—24no—
529C22⋊C4—41no—
530C22⋊C4—41no—
531C22⋊C4—42no—
532C22⋊C4—81no—
533C22⋊C4—81no—
534C22⋊C4—81no—
535C22⋊C4—3441no—
536C22⋊C4—1722no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—81no—
542C23—22no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23C22×C22⋊D4311yescharacteristic
557Q8—1721no—
558Q8—1721no—
559Q8—1721no—
560Q8—1721no—
561D4—22no—
562D4—22no—
563D4—41no—
564D4—41no—
565D4—84no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—21no—
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—41no—
583C2×C4—41no—
584C2×C4—41no—
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—84no—
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—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4#41×D4311yescharacteristic
608C2×C4#41×D4311yescharacteristic
609C2×C4C2×#1062189811yescharacteristic
610C2×C4C2×#1062189811yescharacteristic
611C2×C4#1306337011yescharacteristic
612C2×C4#1306337011yescharacteristic
613C8—862no—
614C8—862no—
615C8—1721no—
616C8—1721no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—42no—
621C22—41no—
622C22—42no—
623C22—41no—
624C22—42no—
625C22—41no—
626C22—41no—
627C22—81no—
628C22—81no—
629C22—81no—
630C22—81no—
631C22#1458341011yescharacteristic
632C22#1458344511yescharacteristic
633C22#1458345811yescharacteristic
634C22#1458370211yescharacteristic
635C22#1458371011yescharacteristic
636C22#1458371011yescharacteristic
637C22#1458371411yescharacteristic
638C4—42no—
639C4—41no—
640C4—41no—
641C4—41no—
642C4—41no—
643C4—41no—
644C4—81no—
645C4—81no—
646C4—3441no—
647C4—3441no—
648C4—3441no—
649C4—3441no—
650C4#1458357811yescharacteristic
651C4#1458359811yescharacteristic
652C4#1458359911yescharacteristic
653C4#1458363211yescharacteristic
654C2—81no—
655C2—82no—
656C2#1914020711yescharacteristic
657C2#1914477911yescharacteristic
658C2#1914480911yescharacteristic
659C2#1914521711yescharacteristic
660C2#1914522811yescharacteristic
661C2#1914544711yescharacteristic
662C2#1914547111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2324C2
socleC23×C43C22×D4
prime radicalC2×#121×C43C22
hypercenter#2324D43
hypocenterC43#29473
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2324

Complements

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

NH ≅ G/Ntype
1. #19140392C2semidirect
2. #19136031C2semidirect
3. #19135798C2semidirect
6. #19135448C2semidirect
7. #19135325C2semidirect
8. #19135295C2semidirect
9. #19135284C2semidirect
10. #19135236C2semidirect
11. #19135180C2semidirect
12. #19134929C2semidirect
13. #19134842C2semidirect
14. #19134361C2semidirect
390. C43#29473semidirect

Maximal subgroups

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

subgroupindex
#191403922
#191360312
#191357982
#191357742
#191355982
#191354482
#191353252
#191352952
#191352842
#191352362
#191351802
#191349292
#191348422
#191343612
C43×#23242
#2947343