Finite Group Databasebeta

← #25148664

Subgroups — #25148664

Order 11008.

782 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583199C211yesmaximal, characteristic
2C2×#14583027C211yesmaximal, characteristic, complemented
3#19139978C211yesmaximal, characteristic, complemented
4#19139517C211yesmaximal, characteristic
5#19136099C211yesmaximal, characteristic, complemented
6#19136087C211yesmaximal, characteristic, complemented
7#19135965C211yesmaximal, characteristic
8#19135965C211yesmaximal, characteristic
9#19135564C211yesmaximal, characteristic, complemented
10#19135358C211yesmaximal, characteristic, complemented
11#19135337C211yesmaximal, characteristic, complemented
12#19135322C211yesmaximal, characteristic, complemented
13#19135294C211yesmaximal, characteristic
14#19135280C211yesmaximal, characteristic
15C43×#1762C211yesmaximal, characteristic
16C2×#13063317C2211yescharacteristic
17C2×#13063304—21no—
18C2×C4×Dic86C2211yescharacteristic
19#14583199—24no—
20#14583027—24no—
21C2×#13063258C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×Dic43⋊C8C2211yescharacteristic
27C2×Dic43⋊C8C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063235C2211yescharacteristic
31C2×C8×Dic43C2211yescharacteristic
32#14582831—21no—
33#14582822—21no—
34#14582822—21no—
35#14582820—21no—
36#14582802C2211yescharacteristic
37#14582802C2211yescharacteristic
38#14582798C2211yescharacteristic
39#14582798C2211yescharacteristic
40#14582798C2211yescharacteristic
41#14582798C2211yescharacteristic
42#14582797—21no—
43#14582797—21no—
44#14582795C2211yescharacteristic
45#14582795C2211yescharacteristic
46#14582769C2211yescharacteristic
47#14582759—21no—
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#97×C43C2211yescharacteristic
58C4×C4⋊C4×C43C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86D411yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64#13063317—22no—
65#13063317—22no—
66#13063304—44no—
67C4×Dic86—22no—
68C4×Dic86—22no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43D411yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4D411yescharacteristic
85C2×Dic43⋊C4D411yescharacteristic
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C4×Dic43C2311yescharacteristic
91C2×C4×Dic43C2311yescharacteristic
92#13063258—22no—
93#13063256—22no—
94#13063256—22no—
95#13063256—22no—
96C4⋊(C43⋊C8)D414yes—
97Dic43⋊C8—22no—
98Dic43⋊C8—22no—
99#13063246—22no—
100#13063246—22no—
101#13063235—22no—
102C8×Dic43—22no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C22×D4×C43C2311yescharacteristic
110C23×C4×C43—21no—
111C22×C8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C4×D4×C43—22no—
114C4×D4×C43—22no—
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C22⋊C4×C43—21no—
119C2×C42×C43—21no—
120C2×C42×C43C2311yescharacteristic
121#102×C43—22no—
122#102×C43Q814yescomplemented
123#97×C43—22no—
124#95×C43—21no—
125C24×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43C2×Q812yes—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—42no—
136C22×C4×C43—42no—
137C22×C4×C43—42no—
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2411yescharacteristic
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C22×Dic43C2×D411yescharacteristic
148C22×Dic43C2×D411yescharacteristic
149C2×Dic86—22no—
150C2×Dic86—22no—
151C2×Dic86—41no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43C2×Q812yes—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43C2×Q812yes—
163C4⋊C4×C43#4112yes—
164C22⋊C4×C43—42no—
165C42×C43—81no—
166C42×C43C2×D412yes—
167C42×C43#4112yes—
168C22⋊Dic43—42no—
169C22⋊Dic43—42no—
170C22⋊Dic43—81no—
171C22⋊Dic43—81no—
172C4⋊Dic43—22no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—42no—
182C4⋊Dic43—42no—
183C4⋊Dic43—42no—
184C4⋊Dic43—81no—
185C4⋊Dic43—81no—
186C4⋊Dic43—81no—
187Dic43⋊C4—22no—
188Dic43⋊C4—22no—
189Dic43⋊C4—42no—
190Dic43⋊C4—42no—
191Dic43⋊C4—42no—
192Dic43⋊C4—42no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8C2×D412yes—
202C2×C43⋊C8C2×D412yes—
203C23×C43—22no—
204C23×C43—41no—
205C23×C43—41no—
206C23×C43—41no—
207C23×C43—41no—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43C22×D411yescharacteristic
211D4×C43—22no—
212D4×C43—22no—
213D4×C43—41no—
214D4×C43—41no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—84no—
229C2×C4×C43#12112yes—
230C2×C4×C43#12112yes—
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43C22×Q811yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C432−1+411yescharacteristic
236C2×C4×C432−1+411yescharacteristic
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43AGL(1,ℤ/8)12yes—
261Dic86—44no—
262C8×C43—22no—
263C8×C43—41no—
264C43⋊C8—22no—
265C43⋊C8—22no—
266#25486—431nomaximal, Sylow
267C22×C43—42no—
268C22×C43—42no—
269C22×C43—42no—
270C22×C43—81no—
271C22×C43—81no—
272C22×C43—81no—
273C22×C43—81no—
274C22×C43C2×#12111yescharacteristic
275C22×C43#54811yescharacteristic
276C22×C43D4×Q811yescharacteristic
277C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
278C22×C43#57511yescharacteristic
279C22×C43#57711yescharacteristic
280C22×C43#57711yescharacteristic
281C4×C43—22no—
282C4×C43—22no—
283C4×C43—42no—
284C4×C43—42no—
285C4×C43—81no—
286C4×C43#53311yescharacteristic
287C4×C43#54111yescharacteristic
288C4×C43#54711yescharacteristic
289C4×C43D4×Q811yescharacteristic
290Dic43—22no—
291Dic43—41no—
292Dic43—41no—
293Dic43—41no—
294Dic43—81no—
295Dic43—81no—
296Dic43—81no—
297Dic43—81no—
298C2×#478—431no—
299C2×#446—431no—
300#2584—431no—
301#2538—431no—
302#2088—431no—
303#2086—431no—
304#2065—431no—
305#2065—431no—
306#1992—431no—
307#1948—431no—
308#1944—431no—
309#1941—431no—
310#1936—431no—
311#1934—431no—
312#1762D4311yescharacteristic
313C2×C43—82no—
314C2×C43#242911yescharacteristic
315C2×C43#305511yescharacteristic
316C2×C43#306011yescharacteristic
317C2×C43#336811yescharacteristic
318C2×C43#337611yescharacteristic
319C2×C43#338411yescharacteristic
320C2×C43#338811yescharacteristic
321C2×#125—431no—
322C2×C22⋊Q8—861no—
323C2×C4×Q8—431no—
324C2×C4×D4C2×D4311yescharacteristic
325#478—864no—
326#446—864no—
327C2×#107—431no—
328C2×#106—431no—
329C2×#106—431no—
330C2×#106—431no—
331C2×C4⋊C8—431no—
332C2×C4⋊C8—431no—
333C2×C4⋊C8—431no—
334C2×#102—431no—
335C2×#102—431no—
336C2×#102C2×D4311yescharacteristic
337C2×#102C2×D4311yescharacteristic
338C2×#97—431no—
339C2×#97C2×D4311yescharacteristic
340C2×C4×C8—431no—
341#398—861no—
342#396—861no—
343#396—861no—
344#395—861no—
345#390—431no—
346#390—431no—
347#389—431no—
348#389—431no—
349#389—431no—
350#389—431no—
351#389—431no—
352#389—431no—
353#389—861no—
354#389—861no—
355#384—431no—
356#380—861no—
357C4×C4⋊C4C2×D4311yescharacteristic
358#340—431no—
359#340—431no—
360#340—431no—
361#340—431no—
362#340—431no—
363#340—431no—
364#340C2×D4311yescharacteristic
365#340C2×D4311yescharacteristic
366C43#2548611yescharacteristic, complemented, Sylow
367C22×Q8—431no—
368C22×D4C22×D4311yescharacteristic
369C23×C4—21no—
370C22×C8—431no—
371C22×C8—431no—
372C22×C8C22×D4311yescharacteristic
373C22×C8C22×D4311yescharacteristic
374#125—862no—
375#125—862no—
376C22⋊Q8—1724no—
377C4×Q8—862no—
378C4×Q8—862no—
379C4×D4—22no—
380C4×D4—22no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—431no—
383C2×C4⋊C4—431no—
384C2×C4⋊C4—431no—
385C2×C4⋊C4—431no—
386C2×C4⋊C4—431no—
387C2×C4⋊C4—431no—
388C2×C4⋊C4—861no—
389C2×C4⋊C4—861no—
390C2×C4⋊C4—861no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4C22×D4311yescharacteristic
399C2×C4⋊C4C22×D4311yescharacteristic
400C2×C4⋊C4C22×D4311yescharacteristic
401C2×C22⋊C4—21no—
402C2×C22⋊C4—861no—
403C2×C22⋊C4—861no—
404C2×C22⋊C4—861no—
405C2×C22⋊C4—861no—
406C2×C42—21no—
407C2×C42—431no—
408C2×C42—431no—
409C2×C42C22×D4311yescharacteristic
410#107—862no—
411#106—862no—
412#106—862no—
413#106—862no—
414C4⋊C8—434no—
415C4⋊C8—862no—
416C4⋊C8—862no—
417#102—22no—
418#102—862no—
419#102—862no—
420#102Dic8614yescomplemented
421#97—22no—
422#97—862no—
423C4×C8—862no—
424#95—21no—
425#95—861no—
426#95—861no—
427#95—861no—
428#95—861no—
429#95—861no—
430#95—861no—
431C24—21no—
432C2×Q8—862no—
433C2×Q8—862no—
434C2×Q8—1721no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4C2×Dic8612yes—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—431no—
448C22×C4—431no—
449C22×C4—431no—
450C22×C4—431no—
451C22×C4—861no—
452C22×C4—861no—
453C22×C4—861no—
454C22×C4—861no—
455C22×C4D4×D4311yescharacteristic
456C22×C4D4×D4311yescharacteristic
457C22×C4C23×D4311yescharacteristic
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—432no—
464C2×C8—432no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—861no—
469C2×C8C2×Dic8612yes—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—862no—
475C4⋊C4—862no—
476C4⋊C4—862no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—3441no—
486C4⋊C4—3441no—
487C4⋊C4—3441no—
488C4⋊C4—1722no—
489C4⋊C4—1722no—
490C4⋊C4—1722no—
491C4⋊C4—1722no—
492C4⋊C4—1722no—
493C4⋊C4—1722no—
494C4⋊C4—1722no—
495C4⋊C4C2×Dic8612yes—
496C4⋊C4#1062189812yes—
497C22⋊C4—42no—
498C22⋊C4—3441no—
499C22⋊C4—3441no—
500C22⋊C4—1722no—
501C22⋊C4—1722no—
502C42—81no—
503C42—861no—
504C42—861no—
505C42—861no—
506C42—861no—
507C42#1062189812yes—
508C42D4×D4312yes—
509C23—22no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23C2×D4×D4311yescharacteristic
517Q8—1724no—
518D4—22no—
519D4—22no—
520D4—41no—
521D4—41no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—84no—
536C2×C4—432no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—861no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4#1306329812yes—
561C2×C4#1306329812yes—
562C2×C4C2×D4×D4311yescharacteristic
563C2×C4C22×Dic8611yescharacteristic
564C2×C4C2×#1062189811yescharacteristic
565C2×C4C2×#1062189811yescharacteristic
566C2×C4#1306337211yescharacteristic
567C2×C4#1306337211yescharacteristic
568C8—22no—
569C8—41no—
570C8—862no—
571C8—862no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22C2×#1306329811yescharacteristic
580C22#1458355811yescharacteristic
581C22D4×Dic8611yescharacteristic
582C22AGL(1,ℤ/8)×D4311yescharacteristic
583C22#1458369511yescharacteristic
584C22#1458370811yescharacteristic
585C22#1458370911yescharacteristic
586C4—22no—
587C4—22no—
588C4—42no—
589C4—42no—
590C4—81no—
591C4—862no—
592C4—3441no—
593C4—3441no—
594C4—3441no—
595C4—3441no—
596C4—1721no—
597C4—1721no—
598C4—1721no—
599C4#1458345611yescharacteristic
600C4#1458351111yescharacteristic
601C4#1458355411yescharacteristic
602C4D4×Dic8611yescharacteristic
603C2—82no—
604C2#1913819411yescharacteristic
605C2#1914421211yescharacteristic
606C2#1914425611yescharacteristic
607C2#1914732511yescharacteristic
608C2#1914742311yescharacteristic
609C2#1914749511yescharacteristic
610C2#1914754511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1762C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#1762D43
hypocenterC43#25486
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
2. C2×#14583027C2semidirect
3. #19139978C2semidirect
5. #19136099C2semidirect
6. #19136087C2semidirect
9. #19135564C2semidirect
10. #19135358C2semidirect
11. #19135337C2semidirect
12. #19135322C2semidirect
122. #102×C43Q8semidirect
366. C43#25486semidirect
420. #102Dic86semidirect

Maximal subgroups

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

subgroupindex
C2×#145831992
C2×#145830272
#191399782
#191395172
#191360992
#191360872
#191359652
#191355642
#191353582
#191353372
#191353222
#191352942
#191352802
C43×#17622
#2548643