Finite Group Databasebeta

← #25108673

Subgroups — #25108673

Order 11008.

796 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583197C211yesmaximal, characteristic
2#19137154C211yesmaximal, characteristic, complemented
3#19137057C211yesmaximal, characteristic
4#19135551C211yesmaximal, characteristic, complemented
5#19135366C211yesmaximal, characteristic, complemented
6#19135328C211yesmaximal, characteristic, complemented
7#19135320C211yesmaximal, characteristic, complemented
8#19135281C211yesmaximal, characteristic
9#19135225C211yesmaximal, characteristic
10#19135217C211yesmaximal, characteristic
11#19135186C211yesmaximal, characteristic, complemented
12#19135178C211yesmaximal, characteristic, complemented
13#19134603C211yesmaximal, characteristic
14C4×Dic43⋊C8C211yesmaximal, characteristic, complemented
15C43×#1934C211yesmaximal, characteristic
16C2×#13063316C2211yescharacteristic
17C2×D4×Dic43C2211yescharacteristic
18C2×#13063281—21no—
19#14583197C418yescomplemented
20C2×#13063259C2211yescharacteristic
21C2×#13063259C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×C4×C43⋊C8C2211yescharacteristic
29#14582802C2211yescharacteristic
30#14582797C2211yescharacteristic
31#14582797C2211yescharacteristic
32#14582795C2211yescharacteristic
33#14582793—21no—
34#14582787—21no—
35#14582784—21no—
36#14582780—21no—
37#14582764C2211yescharacteristic
38C4⋊C4×Dic43—21no—
39C4⋊C4×Dic43C2211yescharacteristic
40C4⋊C4×Dic43C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42#14582750—21no—
43C22⋊C4×Dic43—21no—
44C42×Dic43C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×#102×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×C4×C8×C43C2211yescharacteristic
56C43×#390C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C23×Dic43—21no—
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63#13063316—22no—
64#13063316C2×C414yes—
65D4×Dic43—22no—
66D4×Dic43C2×C414yes—
67#13063281—44no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C4×Dic43—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43D411yescharacteristic
84C2×C4×Dic43D411yescharacteristic
85C2×C4×Dic43D411yescharacteristic
86C2×C4×Dic43D411yescharacteristic
87C2×C4×Dic43C2311yescharacteristic
88C2×C4×Dic43C2311yescharacteristic
89#13063259—41no—
90#13063259C2×C414yes—
91#13063256—41no—
92#13063256C2×C414yes—
93Dic43⋊C8—22no—
94Dic43⋊C8C2×C414yes—
95#13063246—41no—
96#13063246C2×C414yes—
97C4×C43⋊C8—41no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C22×D4×C43C2311yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115C2×C42×C43C2311yescharacteristic
116#102×C43—41no—
117#102×C43C2×C414yes—
118C4×C8×C43—41no—
119#95×C43—21no—
120C24×C43—21no—
121C2×D4×C43—21no—
122C2×D4×C43—21no—
123C2×D4×C43—21no—
124C2×D4×C43—21no—
125C2×D4×C43—21no—
126C2×D4×C43C22×C412yes—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2411yescharacteristic
133C22×Dic43—24no—
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—42no—
139C22×Dic43—42no—
140C22×Dic43C2×D411yescharacteristic
141C22×Dic43C2×D411yescharacteristic
142C22×Dic43C2×D411yescharacteristic
143C22×Dic43C2×D411yescharacteristic
144C2×C8×C43—21no—
145C2×C8×C43—21no—
146C2×C8×C43—21no—
147C2×C8×C43—21no—
148C2×C8×C43—21no—
149C2×C8×C43C22×C412yes—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—42no—
156C4⋊C4×C43C22×C412yes—
157C22⋊C4×C43—42no—
158C22⋊C4×C43—42no—
159C42×C43—21no—
160C42×C43—21no—
161C22⋊Dic43—24no—
162C22⋊Dic43—42no—
163C22⋊Dic43—42no—
164C4⋊Dic43—21no—
165C4⋊Dic43—21no—
166C4⋊Dic43—24no—
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43C22×C412yes—
172C4⋊Dic43C22×C412yes—
173Dic43⋊C4—24no—
174Dic43⋊C4—42no—
175Dic43⋊C4—42no—
176Dic43⋊C4—42no—
177C4×Dic43—22no—
178C4×Dic43—22no—
179C4×Dic43—21no—
180C4×Dic43—21no—
181C4×Dic43—22no—
182C4×Dic43—41no—
183C4×Dic43—42no—
184C4×Dic43—42no—
185C4×Dic43—42no—
186C4×Dic43C22×C412yes—
187C4×Dic43#4112yes—
188C2×C43⋊C8—21no—
189C2×C43⋊C8—21no—
190C2×C43⋊C8—21no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8C22×C412yes—
194C23×C43—22no—
195C23×C43—41no—
196C23×C43—41no—
197C23×C43—41no—
198C23×C43—41no—
199C23×C43—41no—
200C23×C43—41no—
201C23×C43C22×D411yescharacteristic
202D4×C43—22no—
203D4×C43—22no—
204D4×C43—41no—
205D4×C43—41no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—22no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43#13512yes—
220C2×C4×C43AGL(1,ℤ/8)12yes—
221C2×C4×C43C23×C411yescharacteristic
222C2×C4×C43C2×#4111yescharacteristic
223C2×C4×C43H(5,𝔽2)11yescharacteristic
224C2×C4×C432−1+411yescharacteristic
225C2×C4×C432−1+411yescharacteristic
226C2×C4×C432−1+411yescharacteristic
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—22no—
234C2×Dic43—22no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—48no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43C4×D412yes—
250C2×Dic43C4×D412yes—
251C2×Dic43#13512yes—
252C8×C43—22no—
253C8×C43—41no—
254C43⋊C8—22no—
255C43⋊C8—41no—
256#22114—431nomaximal, Sylow
257C22×C43—42no—
258C22×C43—42no—
259C22×C43—42no—
260C22×C43—81no—
261C22×C43—81no—
262C22×C43—81no—
263C22×C43—81no—
264C22×C43C2×C4×D411yescharacteristic
265C22×C43#53611yescharacteristic
266C22×C43#53711yescharacteristic
267C22×C43C2×#13511yescharacteristic
268C22×C43C2×#13511yescharacteristic
269C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
270C22×C43#57511yescharacteristic
271C4×C43—22no—
272C4×C43—22no—
273C4×C43—42no—
274C4×C43—81no—
275C4×C43—81no—
276C4×C43#51911yescharacteristic
277C4×C43#52011yescharacteristic
278C4×C43#54111yescharacteristic
279C4×C43#54211yescharacteristic
280Dic43—22no—
281Dic43—22no—
282Dic43—22no—
283Dic43—42no—
284Dic43—42no—
285Dic43—41no—
286Dic43—81no—
287Dic43—81no—
288C2×#478—431no—
289C4×#125—431no—
290#2293—431no—
291#1989—431no—
292#1949—431no—
293#1942—431no—
294#1941—431no—
295#1934—431no—
296#1934D4311yescharacteristic
297#1926—431no—
298#1925—431no—
299#1921—431no—
300#1920—431no—
301#1804—431no—
302C4×C4⋊C8—431no—
303C2×C43—82no—
304C2×C43#232311yescharacteristic
305C2×C43C4×#13511yescharacteristic
306C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
307C2×C43#322811yescharacteristic
308C2×C43#323211yescharacteristic
309C2×C43#324711yescharacteristic
310C2×C43#325011yescharacteristic
311C2×#125—431no—
312C2×C4×D4—431no—
313C2×#117—861no—
314#478—438no—
315C2×#107—431no—
316C2×#107—431no—
317C2×#106—431no—
318C2×#106—431no—
319C2×C4⋊C8—431no—
320C2×C4⋊C8—431no—
321C2×#102—431no—
322C2×#102—431no—
323C2×#102C2×D4311yescharacteristic
324C2×#102C2×D4311yescharacteristic
325C2×C4×C8—431no—
326C2×C4×C8C2×D4311yescharacteristic
327#390—431no—
328#390C2×D4311yescharacteristic
329#389—431no—
330#389—431no—
331#389—431no—
332#389C2×D4311yescharacteristic
333#388—861no—
334#388—861no—
335#387—861no—
336#387—861no—
337#382—431no—
338C4×C4⋊C4—431no—
339C4×C4⋊C4—431no—
340C4×C4⋊C4—431no—
341C4×C4⋊C4—861no—
342C4×C4⋊C4—861no—
343C4×C22⋊C4—861no—
344C43—431no—
345#340—431no—
346#340—431no—
347#340—431no—
348#340—431no—
349#340—431no—
350#340—431no—
351#340C2×D4311yescharacteristic
352#340C2×D4311yescharacteristic
353#336—431no—
354#336—431no—
355C43#2211411yescharacteristic, complemented, Sylow
356C22×D4C22×D4311yescharacteristic
357C23×C4—861no—
358C22×C8—431no—
359C22×C8—431no—
360C22×C8C22×D4311yescharacteristic
361C22×C8C22×D4311yescharacteristic
362#125—434no—
363#125—862no—
364C4×D4—434no—
365C4×D4—862no—
366#117—1724no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—431no—
369C2×C4⋊C4—431no—
370C2×C4⋊C4—431no—
371C2×C4⋊C4—431no—
372C2×C4⋊C4—861no—
373C2×C4⋊C4—861no—
374C2×C4⋊C4—861no—
375C2×C4⋊C4—861no—
376C2×C4⋊C4—861no—
377C2×C4⋊C4C22×D4311yescharacteristic
378C2×C4⋊C4C22×D4311yescharacteristic
379C2×C4⋊C4C22×D4311yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—861no—
383C2×C22⋊C4—861no—
384C2×C22⋊C4—861no—
385C2×C42—431no—
386C2×C42—431no—
387C2×C42—431no—
388C2×C42—431no—
389C2×C42—431no—
390C2×C42—431no—
391C2×C42—861no—
392C2×C42—861no—
393C2×C42—861no—
394C2×C42C22×D4311yescharacteristic
395#107—434no—
396#107—1721no—
397#106—434no—
398#106—1721no—
399C4⋊C8—434no—
400C4⋊C8—862no—
401#102—41no—
402#102—434no—
403#102—1721no—
404#102C4×D4314yes—
405C4×C8—41no—
406C4×C8—1721no—
407#95—21no—
408#95—861no—
409#95—861no—
410#95—861no—
411#95—861no—
412#95—861no—
413#95—861no—
414#95—861no—
415#95—861no—
416C24—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4C2×C4×D4312yes—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—431no—
427C22×C4—431no—
428C22×C4—431no—
429C22×C4—431no—
430C22×C4—864no—
431C22×C4—861no—
432C22×C4—861no—
433C22×C4—861no—
434C22×C4—861no—
435C22×C4—1722no—
436C22×C4—1722no—
437C22×C4D4×D4311yescharacteristic
438C22×C4D4×D4311yescharacteristic
439C22×C4C23×D4311yescharacteristic
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—432no—
446C2×C8—861no—
447C2×C8—861no—
448C2×C8—861no—
449C2×C8—861no—
450C2×C8—861no—
451C2×C8C2×C4×D4312yes—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—42no—
458C4⋊C4—432no—
459C4⋊C4—432no—
460C4⋊C4—864no—
461C4⋊C4—864no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—1722no—
469C4⋊C4—1722no—
470C4⋊C4—1722no—
471C4⋊C4C2×C4×D4312yes—
472C22⋊C4—42no—
473C22⋊C4—42no—
474C22⋊C4—864no—
475C22⋊C4—1722no—
476C22⋊C4—1722no—
477C42—21no—
478C42—21no—
479C42—432no—
480C42—432no—
481C42—862no—
482C42—862no—
483C42—862no—
484C42—861no—
485C42—861no—
486C42—1721no—
487C42—1722no—
488C42—1722no—
489C42—1722no—
490C23—22no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23C2×D4×D4311yescharacteristic
498D4—22no—
499D4—22no—
500D4—41no—
501D4—41no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—22no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—432no—
516C2×C4—432no—
517C2×C4—432no—
518C2×C4—861no—
519C2×C4—861no—
520C2×C4—861no—
521C2×C4—861no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—862no—
525C2×C4—862no—
526C2×C4—861no—
527C2×C4—861no—
528C2×C4—861no—
529C2×C4—1728no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4—1721no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4#1306334412yes—
541C2×C4#1306335212yes—
542C2×C4C22×C4×D4311yescharacteristic
543C2×C4#41×D4311yescharacteristic
544C2×C4#1306337011yescharacteristic
545C2×C4#1306337211yescharacteristic
546C2×C4#1306337211yescharacteristic
547C2×C4#1306337211yescharacteristic
548C8—22no—
549C8—41no—
550C8—862no—
551C8—1721no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22C4×D4×D4311yescharacteristic
560C22#1458346911yescharacteristic
561C22#1458347611yescharacteristic
562C22#135×D4311yescharacteristic
563C22C2×#1306334411yescharacteristic
564C22C2×#1306335211yescharacteristic
565C22#1458369611yescharacteristic
566C4—22no—
567C4—22no—
568C4—42no—
569C4—81no—
570C4—81no—
571C4—862no—
572C4—862no—
573C4—862no—
574C4—3441no—
575C4—3441no—
576C4—1722no—
577C4—1722no—
578C4—1721no—
579C4#1458337611yescharacteristic
580C4#1458337811yescharacteristic
581C4#1458350611yescharacteristic
582C4#1458351711yescharacteristic
583C2—82no—
584C2#1913727011yescharacteristic
585C2C4×#1306334411yescharacteristic
586C2C4×#1306335211yescharacteristic
587C2#1914572611yescharacteristic
588C2#1914575811yescharacteristic
589C2#1914591611yescharacteristic
590C2#1914594111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1934C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
cosocleC22×C4×C43C24
hypercenter#1934D43
hypocenterC43#22114
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1934

Complements

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

NH ≅ G/Ntype
2. #19137154C2semidirect
4. #19135551C2semidirect
5. #19135366C2semidirect
6. #19135328C2semidirect
7. #19135320C2semidirect
11. #19135186C2semidirect
12. #19135178C2semidirect
14. C4×Dic43⋊C8C2semidirect
19. #14583197C4semidirect
355. C43#22114semidirect

Maximal subgroups

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

subgroupindex
C2×#145831972
#191371542
#191370572
#191355512
#191353662
#191353282
#191353202
#191352812
#191352252
#191352172
#191351862
#191351782
#191346032
C4×Dic43⋊C82
C43×#19342
#2211443