Finite Group Databasebeta

← #25116469

Subgroups — #25116469

Order 11008.

838 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582997C211yesmaximal, characteristic
2#19137560C211yesmaximal, characteristic, complemented
3#19137546C211yesmaximal, characteristic
4#19135473C211yesmaximal, characteristic
5#19135446C211yesmaximal, characteristic
6#19135239C211yesmaximal, characteristic, complemented
7#19135232C211yesmaximal, characteristic, complemented
8#19135220C211yesmaximal, characteristic
9#19135213C211yesmaximal, characteristic
10#19134761C211yesmaximal, characteristic, complemented
11#19134606C211yesmaximal, characteristic
12#19134491C211yesmaximal, characteristic, complemented
13#19134487C211yesmaximal, characteristic, complemented
14#19134472C211yesmaximal, characteristic, complemented
15C43×#1803C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C2×C4×D172C2211yescharacteristic
18C2×#13063283—21no—
19#14582997C418yescomplemented
20C2×#13063258C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063236C2211yescharacteristic
30C2×#13063235C2211yescharacteristic
31C2×C8×Dic43C2211yescharacteristic
32#14582806C2211yescharacteristic
33#14582806C2211yescharacteristic
34#14582800C2211yescharacteristic
35#14582800C2211yescharacteristic
36#14582789—21no—
37#14582789—21no—
38#14582785—21no—
39#14582785—21no—
40#14582767—21no—
41#14582765C2211yescharacteristic
42#14582756—21no—
43C4⋊C4×Dic43C2211yescharacteristic
44C4⋊C4×Dic43C2211yescharacteristic
45C4⋊C4×Dic43C2211yescharacteristic
46C4⋊C4×Dic43C2211yescharacteristic
47C4×C4⋊Dic43C2211yescharacteristic
48#14582745—21no—
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×C4×Q8×C43C2211yescharacteristic
54C2×C4⋊C8×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C43×#384C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C22×D172C2311yescharacteristic
61C22×C4×D43—21no—
62C2×#10621884—22no—
63C2×#10621884—22no—
64C2×#10621884C2×C414yes—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C4×D172—22no—
68C4×D172C2×C414yes—
69#13063283—44no—
70C2×C4⋊Dic43D411yescharacteristic
71C2×C4⋊Dic43D411yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×(C2×D43)⋊C4—21no—
76C2×(C2×D43)⋊C4—21no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×C4×Dic43—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43C2311yescharacteristic
85C2×C4×Dic43C2311yescharacteristic
86#13063258—22no—
87#13063258—41no—
88#13063258C2×C414yes—
89#13063256—22no—
90#13063256—41no—
91#13063249C2×C414yes—
92#13063247—41no—
93#13063247—41no—
94#13063245C2×C414yes—
95#13063236C2×C414yes—
96#13063235—22no—
97C8×Dic43—22no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95D411yescharacteristic
109C43⋊#95D411yescharacteristic
110C22×Q8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C4×Q8×C43—22no—
114C4×Q8×C43C2×C414yes—
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C42×C43—21no—
122C2×C42×C43C2311yescharacteristic
123C4⋊C8×C43—22no—
124#103×C43—41no—
125#103×C43—41no—
126C23×D43—21no—
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43C22×C412yes—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2411yescharacteristic
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43C2×D411yescharacteristic
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C2×D172—21no—
148C2×D172—21no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172C22×C412yes—
153C2×C4×D43—24no—
154C2×C4×D43—42no—
155C2×C4×D43—42no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C4⋊C4×C43—24no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—42no—
169C4⋊C4×C43—81no—
170C4⋊C4×C43C22×C412yes—
171C42×C43—24no—
172C42×C43C22×C412yes—
173C42×C43#4112yes—
174#10621884—28no—
175(C2×D43)⋊C4—24no—
176(C2×D43)⋊C4—42no—
177(C2×D43)⋊C4—42no—
178(C2×D43)⋊C4—81no—
179(C2×D43)⋊C4—81no—
180C4⋊Dic43—21no—
181C4⋊Dic43—22no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—41no—
187C4⋊Dic43C22×C412yes—
188C4×Dic43—21no—
189C4×Dic43—21no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192C4×Dic43—42no—
193C4×Dic43—42no—
194C4×Dic43—42no—
195C4×Dic43—42no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8C22×C412yes—
199C2×C43⋊C8C22×C412yes—
200C2×C43⋊C8#4112yes—
201C2×C43⋊C8#4112yes—
202C23×C43C22×D411yescharacteristic
203C22×D43—22no—
204C22×D43—41no—
205C22×D43—41no—
206C22×D43—41no—
207C22×D43—41no—
208C22×D43—41no—
209C22×D43—41no—
210Q8×C43—22no—
211Q8×C43—22no—
212Q8×C43—41no—
213Q8×C43—41no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—41no—
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—41no—
229C2×C4×C43—41no—
230C2×C4×C43C4×D412yes—
231C2×C4×C43C4×D412yes—
232C2×C4×C43C23×C411yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43H(5,𝔽2)11yescharacteristic
237C2×C4×C432−1+411yescharacteristic
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—22no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
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×Dic43AGL(1,ℤ/8)12yes—
259D172—22no—
260D172—22no—
261D172—41no—
262D172—41no—
263C4×D43—48no—
264C8×C43—41no—
265C8×C43—41no—
266C43⋊C8—22no—
267C43⋊C8#11714yescomplemented
268#22820—431nomaximal, Sylow
269C22×C43C2×C4×D411yescharacteristic
270C22×C43#54711yescharacteristic
271C22×C43#55011yescharacteristic
272C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
273C22×C43#57511yescharacteristic
274C22×C43#57711yescharacteristic
275C22×C43#57811yescharacteristic
276C2×D43—42no—
277C2×D43—42no—
278C2×D43—42no—
279C2×D43—81no—
280C2×D43—81no—
281C2×D43—81no—
282C2×D43—81no—
283C4×C43—22no—
284C4×C43—22no—
285C4×C43—42no—
286C4×C43—42no—
287C4×C43—81no—
288C4×C43—81no—
289C4×C43C2×#11711yescharacteristic
290C4×C43#52011yescharacteristic
291C4×C43#55511yescharacteristic
292C4×C43#55611yescharacteristic
293Dic43—22no—
294Dic43—41no—
295Dic43—41no—
296Dic43—41no—
297Dic43—42no—
298Dic43—81no—
299Dic43—81no—
300C2×#440—431no—
301#2356—431no—
302#2354—431no—
303#1973—431no—
304#1968—431no—
305#1928—431no—
306#1927—431no—
307#1926—431no—
308#1925—431no—
309#1847—431no—
310#1804—431no—
311#1803D4311yescharacteristic, complemented
312#1776—431no—
313C4×#107—431no—
314#1771—431no—
315C2×C43#235411yescharacteristic
316C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
317C2×C43#294711yescharacteristic
318C2×C43#334311yescharacteristic
319C2×C43#334811yescharacteristic
320C2×C43#339711yescharacteristic
321C2×C43#340211yescharacteristic
322D43—82no—
323C22×SD16—431no—
324C2×C4×Q8C2×D4311yescharacteristic
325C2×C4×D4—431no—
326C2×#117—861no—
327#440—438no—
328C2×#107—431no—
329C2×#107—431no—
330C2×#107—431no—
331C2×#106—431no—
332C2×#106—431no—
333C2×C4⋊C8C2×D4311yescharacteristic
334C2×#103—431no—
335C2×#103C2×D4311yescharacteristic
336C2×#103C2×D4311yescharacteristic
337C2×#102—431no—
338C2×#102—431no—
339C2×#102—431no—
340C2×#97—431no—
341C2×#97—431no—
342C2×C4×C8—431no—
343#391—431no—
344#391—431no—
345#390—431no—
346#390—431no—
347#388—861no—
348#388—861no—
349#387—861no—
350#387—861no—
351#384C2×D4311yescharacteristic
352#383—861no—
353#382—431no—
354#380—861no—
355C4×C4⋊C4—431no—
356C4×C4⋊C4—431no—
357C4×C4⋊C4—431no—
358C4×C4⋊C4—431no—
359C4×C4⋊C4—431no—
360#376—861no—
361#340—431no—
362#340—431no—
363#340C2×D4311yescharacteristic
364#340C2×D4311yescharacteristic
365#336—431no—
366#336—431no—
367C43#2282011yescharacteristic, complemented, Sylow
368C22×Q8C22×D4311yescharacteristic
369C22×D4—431no—
370C23×C4—861no—
371C2×SD16—434no—
372C2×SD16—862no—
373C2×SD16—862no—
374C22×C8—431no—
375C22×C8—431no—
376C22×C8C22×D4311yescharacteristic
377C22×C8C22×D4311yescharacteristic
378C4×Q8—22no—
379C4×Q8C4×D4314yes—
380C4×D4—434no—
381C4×D4—862no—
382#117—1724no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—431no—
387C2×C4⋊C4—431no—
388C2×C4⋊C4—431no—
389C2×C4⋊C4—431no—
390C2×C4⋊C4—431no—
391C2×C4⋊C4C22×D4311yescharacteristic
392C2×C4⋊C4C22×D4311yescharacteristic
393C2×C4⋊C4C22×D4311yescharacteristic
394C2×C22⋊C4—861no—
395C2×C22⋊C4—861no—
396C2×C22⋊C4—861no—
397C2×C22⋊C4—861no—
398C2×C22⋊C4—861no—
399C2×C42—21no—
400C2×C42—431no—
401C2×C42—431no—
402C2×C42—861no—
403C2×C42—861no—
404C2×C42—861no—
405C2×C42—861no—
406C2×C42C22×D4311yescharacteristic
407#107—434no—
408#107—862no—
409#107—1721no—
410#106—862no—
411#106—1721no—
412C4⋊C8—22no—
413#103—41no—
414#103—41no—
415#103—434no—
416#102—434no—
417#102—1721no—
418#102—1721no—
419#97—434no—
420#97—862no—
421C4×C8—862no—
422#95—431no—
423#95—431no—
424#95—861no—
425#95—861no—
426#95—861no—
427#95—861no—
428#95—861no—
429#95—861no—
430#95—861no—
431#95—861no—
432#95—861no—
433#95—861no—
434C24—861no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8C2×C4×D4312yes—
441C2×D4—432no—
442C2×D4—861no—
443C2×D4—861no—
444C2×D4—861no—
445C2×D4—861no—
446C2×D4—861no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—431no—
452C22×C4—431no—
453C22×C4—431no—
454C22×C4—431no—
455C22×C4—861no—
456C22×C4—864no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—1722no—
460C22×C4—1722no—
461C22×C4D4×D4311yescharacteristic
462C22×C4D4×D4311yescharacteristic
463C22×C4C23×D4311yescharacteristic
464SD16—868no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—432no—
472C2×C8—432no—
473C2×C8—432no—
474C2×C8—432no—
475C2×C8—861no—
476C2×C8—861no—
477C4⋊C4—24no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—42no—
484C4⋊C4—81no—
485C4⋊C4—432no—
486C4⋊C4—862no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—1721no—
493C4⋊C4C2×C4×D4312yes—
494C22⋊C4—864no—
495C22⋊C4—3441no—
496C22⋊C4—3441no—
497C22⋊C4—1722no—
498C22⋊C4—1722no—
499C42—24no—
500C42—861no—
501C42—861no—
502C42—861no—
503C42—861no—
504C42—1722no—
505C42—1722no—
506C42—1722no—
507C42—1722no—
508C42C2×C4×D4312yes—
509C42#1062190012yes—
510C23—862no—
511C23—1721no—
512C23—1721no—
513C23—1721no—
514C23—1721no—
515C23—1721no—
516C23—1721no—
517C23C2×D4×D4311yescharacteristic
518Q8—22no—
519Q8—22no—
520Q8—41no—
521Q8—41no—
522D4—862no—
523D4—862no—
524D4—1721no—
525D4—1721no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—432no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—862no—
546C2×C4—861no—
547C2×C4—861no—
548C2×C4—861no—
549C2×C4—861no—
550C2×C4—861no—
551C2×C4—861no—
552C2×C4—861no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—1728no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4(C22⋊D43)⋊C412yes—
565C2×C4(C22⋊D43)⋊C412yes—
566C2×C4C22×C4×D4311yescharacteristic
567C2×C4#41×D4311yescharacteristic
568C2×C4#41×D4311yescharacteristic
569C2×C4C2×#1062190011yescharacteristic
570C2×C4#1306337011yescharacteristic
571C2×C4#1306337311yescharacteristic
572C8—41no—
573C8—41no—
574C8—434no—
575C8—862no—
576C22—3441no—
577C22—3441no—
578C22—3441no—
579C22—3441no—
580C22—1722no—
581C22—1722no—
582C22—1722no—
583C22C2×(C22⋊D43)⋊C411yescharacteristic
584C22#1458355111yescharacteristic
585C22#1458356711yescharacteristic
586C22AGL(1,ℤ/8)×D4311yescharacteristic
587C22#1458369811yescharacteristic
588C22#1458370511yescharacteristic
589C22#1458371211yescharacteristic
590C4—22no—
591C4—22no—
592C4—42no—
593C4—42no—
594C4—81no—
595C4—81no—
596C4—862no—
597C4—3441no—
598C4—3441no—
599C4—1721no—
600C4—1721no—
601C4—1721no—
602C4—1722no—
603C4#117×D4311yescharacteristic
604C4#1458338011yescharacteristic
605C4#1458361311yescharacteristic
606C4#1458362011yescharacteristic
607C2—3442no—
608C2#1913753911yescharacteristic
609C2#1914340811yescharacteristic
610C2#1914343211yescharacteristic
611C2#1914703211yescharacteristic
612C2#1914711711yescharacteristic
613C2#1914761011yescharacteristic
614C2#1914766911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1803C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenter#1803D43
hypocenterC43#22820
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
2. #19137560C2semidirect
6. #19135239C2semidirect
7. #19135232C2semidirect
10. #19134761C2semidirect
12. #19134491C2semidirect
13. #19134487C2semidirect
14. #19134472C2semidirect
15. C43×#1803C2semidirect
19. #14582997C4semidirect
267. C43⋊C8#117semidirect
311. #1803D43semidirect
367. C43#22820semidirect

Maximal subgroups

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

subgroupindex
C2×#145829972
#191375602
#191375462
#191354732
#191354462
#191352392
#191352322
#191352202
#191352132
#191347612
#191346062
#191344912
#191344872
#191344722
C43×#18032
#2282043