Finite Group Databasebeta

← #25148192

Subgroups — #25148192

Order 11008.

834 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583296C211yesmaximal, characteristic, complemented
2C2×#14583187C211yesmaximal, characteristic
3#19139546C211yesmaximal, characteristic
4#19137682C211yesmaximal, characteristic, complemented
5#19136074C211yesmaximal, characteristic, complemented
6#19136073C211yesmaximal, characteristic, complemented
7#19135969C211yesmaximal, characteristic
8#19135965C211yesmaximal, characteristic
9#19135545C211yesmaximal, characteristic, complemented
10#19135358C211yesmaximal, characteristic, complemented
11#19135357C211yesmaximal, characteristic, complemented
12#19135312C211yesmaximal, characteristic, complemented
13#19135224C211yesmaximal, characteristic
14#102×Dic43C211yesmaximal, characteristic
15C43×#1926C211yesmaximal, characteristic
16C2×#13063324C2211yescharacteristic
17C2×#13063324C2211yescharacteristic
18C2×#13063302—21no—
19C2×#13063302—21no—
20C2×D4×Dic43C2211yescharacteristic
21#14583296—24no—
22#14583187—24no—
23C2×#13063257C2211yescharacteristic
24C2×#13063257C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×#13063256C2211yescharacteristic
27C2×#13063256C2211yescharacteristic
28C2×C4⋊(C43⋊C8)C2211yescharacteristic
29C2×Dic43⋊C8C2211yescharacteristic
30C2×Dic43⋊C8C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×C8×Dic43C2211yescharacteristic
34#14582835—21no—
35#14582835—21no—
36#14582805—21no—
37#14582803—21no—
38#14582802C2211yescharacteristic
39#14582798C2211yescharacteristic
40#14582797C2211yescharacteristic
41#14582796—21no—
42#14582769C2211yescharacteristic
43#14582768C2211yescharacteristic
44C4⋊C4×Dic43C2211yescharacteristic
45C4⋊C4×Dic43C2211yescharacteristic
46C4×Dic43⋊C4—21no—
47C4×Dic43⋊C4C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×#106×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C43×#390C2211yescharacteristic
58C4×C4⋊C4×C43C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×Dic86—21no—
62C22×Dic86—21no—
63C23×Dic43—21no—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66#13063324—22no—
67#13063324—22no—
68#13063324—22no—
69#13063324D414yes—
70#13063302—44no—
71#13063302—44no—
72D4×Dic43—22no—
73D4×Dic43—22no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4D411yescharacteristic
87C2×Dic43⋊C4D411yescharacteristic
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43C2311yescharacteristic
94C2×C4×Dic43C2311yescharacteristic
95#13063257—22no—
96#13063257—22no—
97#13063256—22no—
98#13063256—22no—
99#13063256—22no—
100C4⋊(C43⋊C8)—22no—
101Dic43⋊C8—22no—
102Dic43⋊C8—22no—
103#13063246—22no—
104#13063246—22no—
105C8×Dic43—22no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95D411yescharacteristic
111C43⋊#95D411yescharacteristic
112C22×D4×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C22⋊C4×C43—21no—
119C2×C22⋊C4×C43—21no—
120C2×C42×C43—21no—
121C2×C42×C43C2311yescharacteristic
122#106×C43—22no—
123#102×C43—22no—
124#102×C43Q814yescomplemented
125#95×C43—21no—
126C24×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43C2×Q812yes—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2411yescharacteristic
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—42no—
144C22×Dic43—42no—
145C22×Dic43—42no—
146C22×Dic43C2×D411yescharacteristic
147C22×Dic43C2×D411yescharacteristic
148C22×Dic43C2×D411yescharacteristic
149C22×Dic43C2×D411yescharacteristic
150C2×Dic86—24no—
151C2×Dic86—42no—
152C2×Dic86—42no—
153C2×Dic86—42no—
154C2×Dic86—81no—
155C2×Dic86—81no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43C2×Q812yes—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43C2×D412yes—
167C4⋊C4×C43C2×Q812yes—
168C22⋊C4×C43—42no—
169C22⋊C4×C43—42no—
170C42×C43—21no—
171C42×C43—21no—
172C42×C43—81no—
173C22⋊Dic43—42no—
174C22⋊Dic43—42no—
175C22⋊Dic43—42no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—42no—
184C4⋊Dic43—42no—
185C4⋊Dic43—81no—
186C4⋊Dic43C2×D412yes—
187Dic43⋊C4—24no—
188Dic43⋊C4—22no—
189Dic43⋊C4—42no—
190Dic43⋊C4—42no—
191Dic43⋊C4—42no—
192Dic43⋊C4—81no—
193Dic43⋊C4SD1614yes—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—42no—
197C4×Dic43—81no—
198C4×Dic43C2×D412yes—
199C4×Dic43#4112yes—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8#4112yes—
206C23×C43—22no—
207C23×C43—41no—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43C22×D411yescharacteristic
214D4×C43—22no—
215D4×C43—22no—
216D4×C43—41no—
217D4×C43—41no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—22no—
221C2×C4×C43—21no—
222C2×C4×C43—22no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43C2×SD1612yes—
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C22×Q811yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C432−1+411yescharacteristic
238C2×C4×C432−1+411yescharacteristic
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—22no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—41no—
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—84no—
259C2×Dic43#12112yes—
260C2×Dic43#12112yes—
261C2×Dic43C2×SD1612yes—
262C2×Dic43C2×SD1612yes—
263C2×Dic43AGL(1,ℤ/8)12yes—
264Dic86—84no—
265Dic86—84no—
266C8×C43—22no—
267C8×C43—41no—
268C43⋊C8—22no—
269C43⋊C8—41no—
270#25451—431nomaximal, Sylow
271C22×C43—42no—
272C22×C43—42no—
273C22×C43—42no—
274C22×C43—81no—
275C22×C43—81no—
276C22×C43—81no—
277C22×C43—81no—
278C22×C43C2×#12111yescharacteristic
279C22×C43#54711yescharacteristic
280C22×C43D4×Q811yescharacteristic
281C22×C43C22×SD1611yescharacteristic
282C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
283C22×C43#57711yescharacteristic
284C22×C43#57711yescharacteristic
285C4×C43—22no—
286C4×C43—41no—
287C4×C43—42no—
288C4×C43—42no—
289C4×C43—81no—
290C4×C43#53311yescharacteristic
291C4×C43#54111yescharacteristic
292C4×C43#54811yescharacteristic
293C4×C43D4×Q811yescharacteristic
294Dic43—22no—
295Dic43—22no—
296Dic43—41no—
297Dic43—42no—
298Dic43—81no—
299Dic43—81no—
300Dic43—81no—
301Dic43#46014yes—
302C2×#498—431no—
303C2×#476—431no—
304#2542—431no—
305#2369—431no—
306#2084—431no—
307#2084—431no—
308#2065—431no—
309#2065—431no—
310#1988—431no—
311#1948—431no—
312#1948—431no—
313#1939—431no—
314#1926—431no—
315#1926D4311yescharacteristic
316C4×#102—431no—
317C2×C43—82no—
318C2×C43#242911yescharacteristic
319C2×C43C2×#46011yescharacteristic
320C2×C43#304211yescharacteristic
321C2×C43#333511yescharacteristic
322C2×C43#335411yescharacteristic
323C2×C43Q8×SD1611yescharacteristic
324C2×C43#338411yescharacteristic
325C2×C4⋊Q8—431no—
326C2×C4⋊Q8—431no—
327C2×C22⋊Q8—861no—
328C2×C22⋊Q8—861no—
329C2×C4×D4—431no—
330#498—864no—
331#476—864no—
332C2×#106—431no—
333C2×#106—431no—
334C2×#106—431no—
335C2×#106—431no—
336C2×#106—431no—
337C2×#106C2×D4311yescharacteristic
338C2×C4⋊C8—431no—
339C2×C4⋊C8—431no—
340C2×C4⋊C8—431no—
341C2×#102—431no—
342C2×#102—431no—
343C2×#102C2×D4311yescharacteristic
344C2×#102C2×D4311yescharacteristic
345C2×C4×C8—431no—
346#399—861no—
347#399—861no—
348#391—861no—
349#391—861no—
350#390—431no—
351#390C2×D4311yescharacteristic
352#389—431no—
353#389—431no—
354#389—861no—
355#384—431no—
356#384—431no—
357C4×C4⋊C4—431no—
358C4×C4⋊C4—431no—
359C4×C4⋊C4—431no—
360C4×C4⋊C4—861no—
361C4×C4⋊C4C2×D4311yescharacteristic
362#340—431no—
363#340—431no—
364#340—431no—
365#340—431no—
366#340—431no—
367#340C2×D4311yescharacteristic
368#336—431no—
369#336C2×D4311yescharacteristic
370C43#2545111yescharacteristic, complemented, Sylow
371C22×Q8—861no—
372C22×Q8—861no—
373C22×D4C22×D4311yescharacteristic
374C23×C4—861no—
375C22×C8—431no—
376C22×C8—431no—
377C22×C8C22×D4311yescharacteristic
378C22×C8C22×D4311yescharacteristic
379C4⋊Q8—434no—
380C4⋊Q8—862no—
381C4⋊Q8—862no—
382C4⋊Q8—862no—
383C22⋊Q8—1724no—
384C22⋊Q8—1724no—
385C4×D4—862no—
386C4×D4—862no—
387C2×C4⋊C4—431no—
388C2×C4⋊C4—431no—
389C2×C4⋊C4—431no—
390C2×C4⋊C4—431no—
391C2×C4⋊C4—431no—
392C2×C4⋊C4—431no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4C22×D4311yescharacteristic
402C2×C4⋊C4C22×D4311yescharacteristic
403C2×C4⋊C4C22×D4311yescharacteristic
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C22⋊C4—861no—
409C2×C42—21no—
410C2×C42—431no—
411C2×C42—431no—
412C2×C42—861no—
413C2×C42—861no—
414C2×C42C22×D4311yescharacteristic
415#106—22no—
416#106—862no—
417#106—862no—
418#106—862no—
419#106—862no—
420#106—862no—
421C4⋊C8—862no—
422C4⋊C8—862no—
423C4⋊C8—862no—
424#102—22no—
425#102—862no—
426#102—862no—
427#102Dic8614yescomplemented
428C4×C8—862no—
429#95—21no—
430#95—431no—
431#95—431no—
432#95—861no—
433#95—861no—
434#95—861no—
435#95—861no—
436C24—21no—
437C2×Q8—864no—
438C2×Q8—3441no—
439C2×Q8—3441no—
440C2×Q8—1722no—
441C2×Q8—1722no—
442C2×Q8—1722no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4C2×Dic8612yes—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—431no—
453C22×C4—431no—
454C22×C4—431no—
455C22×C4—431no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4—1722no—
461C22×C4—1722no—
462C22×C4—1722no—
463C22×C4D4×D4311yescharacteristic
464C22×C4D4×D4311yescharacteristic
465C22×C4C23×D4311yescharacteristic
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—432no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—861no—
476C2×C8—861no—
477C2×C8C2×Dic8612yes—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—434no—
483C4⋊C4—432no—
484C4⋊C4—862no—
485C4⋊C4—864no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—3441no—
494C4⋊C4—3441no—
495C4⋊C4—1722no—
496C4⋊C4—1722no—
497C4⋊C4—1722no—
498C4⋊C4—1722no—
499C4⋊C4—1722no—
500C4⋊C4C2×Dic8612yes—
501C4⋊C4D4×D4312yes—
502C22⋊C4—42no—
503C22⋊C4—42no—
504C22⋊C4—1722no—
505C22⋊C4—1722no—
506C22⋊C4—1722no—
507C42—21no—
508C42—21no—
509C42—81no—
510C42—432no—
511C42—432no—
512C42—861no—
513C42—861no—
514C42—3441no—
515C42—1722no—
516C23—22no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23—41no—
522C23—41no—
523C23C2×D4×D4311yescharacteristic
524Q8—3444no—
525Q8—3444no—
526D4—22no—
527D4—22no—
528D4—41no—
529D4—41no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—432no—
545C2×C4—432no—
546C2×C4—432no—
547C2×C4—432no—
548C2×C4—432no—
549C2×C4—861no—
550C2×C4—861no—
551C2×C4—861no—
552C2×C4—861no—
553C2×C4—862no—
554C2×C4—861no—
555C2×C4—861no—
556C2×C4—861no—
557C2×C4—3444no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4SD16×D4312yes—
570C2×C4C2×D4×D4311yescharacteristic
571C2×C4C22×Dic8611yescharacteristic
572C2×C4#41×D4311yescharacteristic
573C2×C4#41×D4311yescharacteristic
574C2×C4#1306337211yescharacteristic
575C2×C4#1306337211yescharacteristic
576C8—22no—
577C8—41no—
578C8—862no—
579C8—1721no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22#121×D4311yescharacteristic
588C22#1458354711yescharacteristic
589C22D4×Dic8611yescharacteristic
590C22C2×SD16×D4311yescharacteristic
591C22AGL(1,ℤ/8)×D4311yescharacteristic
592C22#1458370611yescharacteristic
593C22#1458370911yescharacteristic
594C4—22no—
595C4—42no—
596C4—41no—
597C4—42no—
598C4—81no—
599C4—434no—
600C4—862no—
601C4—862no—
602C4—3441no—
603C4—3441no—
604C4—3441no—
605C4—1722no—
606C4—1721no—
607C4#1458345211yescharacteristic
608C4#1458350611yescharacteristic
609C4#1458355711yescharacteristic
610C4D4×Dic8611yescharacteristic
611C2—82no—
612C2#1913819111yescharacteristic
613C2#460×D4311yescharacteristic
614C2#1914410511yescharacteristic
615C2#1914695011yescharacteristic
616C2#1914718811yescharacteristic
617C2SD16×Dic8611yescharacteristic
618C2#1914749511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1926C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#1926D43
hypocenterC43#25451
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1926

Complements

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

NH ≅ G/Ntype
1. C2×#14583296C2semidirect
4. #19137682C2semidirect
5. #19136074C2semidirect
6. #19136073C2semidirect
9. #19135545C2semidirect
10. #19135358C2semidirect
11. #19135357C2semidirect
12. #19135312C2semidirect
124. #102×C43Q8semidirect
370. C43#25451semidirect
427. #102Dic86semidirect

Maximal subgroups

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

subgroupindex
C2×#145832962
C2×#145831872
#191395462
#191376822
#191360742
#191360732
#191359692
#191359652
#191355452
#191353582
#191353572
#191353122
#191352242
#102×Dic432
C43×#19262
#2545143