Finite Group Databasebeta

← #25140946

Subgroups — #25140946

Order 11008.

754 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138892C211yesmaximal, characteristic
2#19136162C211yesmaximal, characteristic, complemented
3#19136077C211yesmaximal, characteristic, complemented
4#19136031C211yesmaximal, characteristic, complemented
5#19136021C211yesmaximal, characteristic, complemented
6#19135187C211yesmaximal, characteristic, complemented
7#19135166C211yesmaximal, characteristic, complemented
8#19134888C211yesmaximal, characteristic
9#19134794C211yesmaximal, characteristic, complemented
10#19134783C211yesmaximal, characteristic, complemented
11#19134687C211yesmaximal, characteristic, complemented
12#19134685C211yesmaximal, characteristic, complemented
13#19134622C211yesmaximal, characteristic, complemented
14#19134311C211yesmaximal, characteristic, complemented
15C43×#2352C211yesmaximal, characteristic
16C23×C43⋊C8C2211yescharacteristic
17C2×#13063284C2211yescharacteristic
18C2×#13063258C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×#13063258C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×C22⋊(C43⋊C8)C2211yescharacteristic
23C2×C22⋊(C43⋊C8)C2211yescharacteristic
24C2×C22⋊(C43⋊C8)C2211yescharacteristic
25#14582827—21no—
26#14582813—21no—
27#14582797C2211yescharacteristic
28#14582797C2211yescharacteristic
29#14582787—21no—
30#14582780—21no—
31#14582759C2211yescharacteristic
32#14582759C2211yescharacteristic
33#14582759C2211yescharacteristic
34#14582661C2211yescharacteristic
35#14582661C2211yescharacteristic
36#14582661C2211yescharacteristic
37#14582661C2211yescharacteristic
38#14582661C2211yescharacteristic
39#14582661C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C2×C4×D4×C43C2211yescharacteristic
49C2×#117×C43C2211yescharacteristic
50C22×C4⋊C4×C43C2211yescharacteristic
51C43×#388—21no—
52C43×#387—21no—
53C43×#386—21no—
54C43×#382C2211yescharacteristic
55C43×#380C2211yescharacteristic
56C43×#380C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C4×C22⋊C4×C43—21no—
59C22×C43⋊C8—22no—
60C22×C43⋊C8—22no—
61C22×C43⋊C8—41no—
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66#13063284—22no—
67#13063284—22no—
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×C22⋊Dic43—21no—
75C2×C22⋊Dic43—21no—
76C2×C22⋊Dic43—21no—
77C2×C22⋊Dic43—21no—
78C2×C4×Dic43—21no—
79#13063258—22no—
80#13063258—22no—
81#13063258—41no—
82#13063256—41no—
83C22⋊(C43⋊C8)—22no—
84C22⋊(C43⋊C8)—22no—
85C22⋊(C43⋊C8)—41no—
86C43⋊#95—21no—
87C43⋊#95—21no—
88C43⋊#95—21no—
89C43⋊#95—21no—
90C43⋊#95—21no—
91C22×D4×C43D411yescharacteristic
92C23×C4×C43—21no—
93C23×C4×C43C2311yescharacteristic
94C23×C4×C43C2311yescharacteristic
95C4×D4×C43—22no—
96C4×D4×C43—22no—
97#117×C43—22no—
98#117×C43—41no—
99C2×C4⋊C4×C43—22no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—41no—
102C2×C4⋊C4×C43D411yescharacteristic
103C2×C4⋊C4×C43C2311yescharacteristic
104C2×C4⋊C4×C43C2311yescharacteristic
105C2×C4⋊C4×C43C2311yescharacteristic
106C2×C4⋊C4×C43C2311yescharacteristic
107C2×C22⋊C4×C43—21no—
108C2×C22⋊C4×C43—21no—
109C2×C22⋊C4×C43—21no—
110C2×C22⋊C4×C43D411yescharacteristic
111C2×C22⋊C4×C43D411yescharacteristic
112C2×C42×C43—21no—
113C2×C42×C43—21no—
114C2×C42×C43C2311yescharacteristic
115#95×C43—21no—
116#95×C43—21no—
117#95×C43—21no—
118#95×C43—21no—
119#95×C43—21no—
120C24×C43C2×D411yescharacteristic
121C24×C43C2×D411yescharacteristic
122C2×D4×C43—22no—
123C2×D4×C43—22no—
124C2×D4×C43—41no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—42no—
140C22×C4×C43—42no—
141C22×C4×C43—81no—
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43#4112yes—
147C22×C4×C43#4112yes—
148C22×C4×C43C2411yescharacteristic
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C4⋊C4×C43—22no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—42no—
162C4⋊C4×C43#4112yes—
163C22⋊C4×C43—22no—
164C22⋊C4×C43—22no—
165C22⋊C4×C43—42no—
166C22⋊C4×C43—42no—
167C22⋊C4×C43—81no—
168C42×C43—21no—
169C42×C43—21no—
170C42×C43—42no—
171C42×C43—81no—
172C22⋊Dic43—42no—
173C22⋊Dic43—42no—
174C22⋊Dic43—81no—
175C22⋊Dic43—81no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184Dic43⋊C4—42no—
185Dic43⋊C4—81no—
186C4×Dic43—42no—
187C2×C43⋊C8—21no—
188C2×C43⋊C8—21no—
189C2×C43⋊C8—21no—
190C2×C43⋊C8—21no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—44no—
199C2×C43⋊C8#4112yes—
200C23×C43—21no—
201C23×C43—21no—
202C23×C43—21no—
203C23×C43—21no—
204C23×C43—21no—
205C23×C43—21no—
206C23×C43—21no—
207C23×C43—21no—
208C23×C43—21no—
209C23×C43—21no—
210C23×C43—21no—
211C23×C43—21no—
212C23×C43#12312yes—
213C23×C43#13512yes—
214C23×C43C22×D411yescharacteristic
215D4×C43—44no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—22no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
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×C43—41no—
247C2×C4×C43—84no—
248C2×C4×C43#12312yes—
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43H(5,𝔽2)11yescharacteristic
254C2×C4×C432−1+411yescharacteristic
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C43⋊C8—22no—
268C43⋊C8—41no—
269C43⋊C8—41no—
270C43⋊C8—41no—
271#24934—431nomaximal, Sylow
272C22×C43—22no—
273C22×C43—22no—
274C22×C43—22no—
275C22×C43—22no—
276C22×C43—22no—
277C22×C43—22no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43—41no—
286C22×C43C2×#12311yescharacteristic
287C22×C43#54611yescharacteristic
288C22×C43#54711yescharacteristic
289C22×C43C2×#13511yescharacteristic
290C22×C43#57511yescharacteristic
291C22×C43#57611yescharacteristic
292C22×C43#57811yescharacteristic
293C4×C43—22no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43—41no—
297C4×C43—42no—
298C4×C43—81no—
299C4×C43—81no—
300C4×C43—81no—
301C4×C43#52911yescharacteristic
302C4×C43#53911yescharacteristic
303C4×C43#55111yescharacteristic
304C4×C43#55211yescharacteristic
305Dic43—81no—
306Dic43—81no—
307Dic43—81no—
308Dic43—81no—
309#2485—431no—
310#2352D4311yescharacteristic
311#2101—431no—
312#2085—431no—
313#2077—431no—
314#2075—431no—
315#1921—431no—
316#1918—431no—
317#1869—431no—
318#1854—431no—
319#1852—431no—
320#1825—431no—
321#1824—431no—
322#1808—431no—
323#1735—431no—
324C2×C43—42no—
325C2×C43—42no—
326C2×C43#241911yescharacteristic
327C2×C43#309111yescharacteristic
328C2×C43#309811yescharacteristic
329C2×C43#330011yescharacteristic
330C2×C43#331911yescharacteristic
331C2×C43#333911yescharacteristic
332C2×C43#334911yescharacteristic
333C23×C8—431no—
334C2×C4×D4C2×D4311yescharacteristic
335C2×#117—431no—
336C2×#117C2×D4311yescharacteristic
337C22×C4⋊C4C2×D4311yescharacteristic
338C2×#107—431no—
339C2×#107—431no—
340C2×#107—431no—
341C2×#106—431no—
342C2×C22⋊C8—431no—
343C2×C22⋊C8—431no—
344C2×C22⋊C8—431no—
345#397—861no—
346#394—861no—
347#389—431no—
348#389—431no—
349#388—21no—
350#388—861no—
351#387—21no—
352#387—861no—
353#386—21no—
354#382C2×D4311yescharacteristic
355#380—431no—
356#380—431no—
357#380—431no—
358#380C2×D4311yescharacteristic
359#380C2×D4311yescharacteristic
360C4×C4⋊C4C2×D4311yescharacteristic
361C4×C22⋊C4—21no—
362#340—431no—
363#340—431no—
364#340—431no—
365#340—431no—
366#340—431no—
367#340—431no—
368#340—431no—
369#340—431no—
370#340—431no—
371#340—431no—
372#340—431no—
373#340—431no—
374#336—431no—
375#336—431no—
376C43#2493411yescharacteristic, complemented, Sylow
377C22×D4C22⋊D4311yescharacteristic
378C23×C4—21no—
379C23×C4C22×D4311yescharacteristic
380C23×C4C22×D4311yescharacteristic
381C22×C8—431no—
382C22×C8—431no—
383C22×C8—431no—
384C22×C8—431no—
385C22×C8—862no—
386C22×C8—862no—
387C22×C8—1721no—
388C4×D4—22no—
389C4×D4—22no—
390#117—22no—
391#117—41no—
392#117—862no—
393#117—862no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—41no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—431no—
399C2×C4⋊C4—431no—
400C2×C4⋊C4—431no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4C22⋊D4311yescharacteristic
404C2×C4⋊C4C22×D4311yescharacteristic
405C2×C4⋊C4C22×D4311yescharacteristic
406C2×C4⋊C4C22×D4311yescharacteristic
407C2×C4⋊C4C22×D4311yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—861no—
412C2×C22⋊C4—861no—
413C2×C22⋊C4—861no—
414C2×C22⋊C4—861no—
415C2×C22⋊C4C22⋊D4311yescharacteristic
416C2×C22⋊C4C22⋊D4311yescharacteristic
417C2×C42—21no—
418C2×C42—21no—
419C2×C42—861no—
420C2×C42C22×D4311yescharacteristic
421#107—862no—
422#107—862no—
423#107—1721no—
424#106—1721no—
425C22⋊C8—862no—
426C22⋊C8—862no—
427C22⋊C8—1721no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—861no—
434#95—861no—
435#95—861no—
436#95—861no—
437#95—861no—
438C24C2×C22⋊D4311yescharacteristic
439C24C2×C22⋊D4311yescharacteristic
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—41no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—42no—
458C22×C4—42no—
459C22×C4—81no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4#1062189812yes—
465C22×C4#1062189812yes—
466C22×C4C2×C22⋊D4311yescharacteristic
467C22×C4C2×C22⋊D4311yescharacteristic
468C22×C4C2×C22⋊D4311yescharacteristic
469C22×C4C2×C22⋊D4311yescharacteristic
470C22×C4C23×D4311yescharacteristic
471C2×C8—432no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—861no—
476C2×C8—861no—
477C2×C8—861no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8—861no—
482C2×C8—861no—
483C2×C8—1724no—
484C4⋊C4—22no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—42no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—3441no—
502C4⋊C4—1722no—
503C4⋊C4#1062190012yes—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—42no—
507C22⋊C4—42no—
508C22⋊C4—81no—
509C22⋊C4—3441no—
510C22⋊C4—3441no—
511C22⋊C4—1722no—
512C22⋊C4—1722no—
513C42—21no—
514C42—21no—
515C42—42no—
516C42—81no—
517C42—1722no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23#1306330812yes—
531C23#1306334512yes—
532C23C22×C22⋊D4311yescharacteristic
533D4—44no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—22no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—84no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4#1306330812yes—
579C2×C4#41×D4311yescharacteristic
580C2×C4C2×#1062190011yescharacteristic
581C2×C4C2×#1062189811yescharacteristic
582C2×C4C2×#1062189811yescharacteristic
583C2×C4#1306337011yescharacteristic
584C2×C4#1306337211yescharacteristic
585C8—862no—
586C8—1721no—
587C8—1721no—
588C8—1721no—
589C22—22no—
590C22—22no—
591C22—22no—
592C22—22no—
593C22—22no—
594C22—22no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22C2×#1306330811yescharacteristic
604C22#1458354311yescharacteristic
605C22#1458354811yescharacteristic
606C22C2×#1306334511yescharacteristic
607C22#1458369711yescharacteristic
608C22#1458370211yescharacteristic
609C22#1458371411yescharacteristic
610C4—22no—
611C4—41no—
612C4—41no—
613C4—41no—
614C4—42no—
615C4—81no—
616C4—81no—
617C4—81no—
618C4—3441no—
619C4—3441no—
620C4—3441no—
621C4—3441no—
622C4#1458342911yescharacteristic
623C4#1458349111yescharacteristic
624C4#1458357811yescharacteristic
625C4#1458358911yescharacteristic
626C2—42no—
627C2—42no—
628C2#1913806611yescharacteristic
629C2#1914450811yescharacteristic
630C2#1914457311yescharacteristic
631C2#1914648211yescharacteristic
632C2#1914675111yescharacteristic
633C2#1914699111yescharacteristic
634C2#1914712511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2352C2
socleC23×C43C22×D4
prime radicalC22×D4×C43D4
hypercenter#2352D43
hypocenterC43#24934
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. #19136162C2semidirect
3. #19136077C2semidirect
4. #19136031C2semidirect
5. #19136021C2semidirect
6. #19135187C2semidirect
7. #19135166C2semidirect
9. #19134794C2semidirect
10. #19134783C2semidirect
11. #19134687C2semidirect
12. #19134685C2semidirect
13. #19134622C2semidirect
14. #19134311C2semidirect
376. C43#24934semidirect

Maximal subgroups

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

subgroupindex
#191388922
#191361622
#191360772
#191360312
#191360212
#191351872
#191351662
#191348882
#191347942
#191347832
#191346872
#191346852
#191346222
#191343112
C43×#23522
#2493443