Finite Group Databasebeta

← #25199441

Subgroups — #25199441

Order 11008.

868 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13063301C211yesmaximal, characteristic, complemented
2#19137103C211yesmaximal, characteristic
3#19136024C211yesmaximal, characteristic, complemented
4#19135797C211yesmaximal, characteristic, complemented
5#19135787C211yesmaximal, characteristic
6#19135597C211yesmaximal, characteristic
7#19135232C211yesmaximal, characteristic, complemented
8#19135216C211yesmaximal, characteristic, complemented
9#19135177C211yesmaximal, characteristic, complemented
10#19135165C211yesmaximal, characteristic, complemented
11#19134950C211yesmaximal, characteristic, complemented
12#19134926C211yesmaximal, characteristic, complemented
13#19134839C211yesmaximal, characteristic, complemented
14#19134662C211yesmaximal, characteristic, complemented
15C43×#1863C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C2×#13063301C2211yescharacteristic
18C2×#13063300C2211yescharacteristic
19C2×#13063287—21no—
20C2×#13063287C2211yescharacteristic
21C2×C42×D43C2211yescharacteristic
22C2×#13063259C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×(C2×D43)⋊C8C2211yescharacteristic
29C2×(C2×D43)⋊C8C2211yescharacteristic
30#14582806C2211yescharacteristic
31#14582801C2211yescharacteristic
32#14582795C2211yescharacteristic
33#14582789—21no—
34#14582780—21no—
35#14582777—21no—
36#14582770—21no—
37#14582756C2211yescharacteristic
38#14582756C2211yescharacteristic
39C4⋊C4×Dic43C2211yescharacteristic
40C4×Dic43⋊C4—21no—
41C4×C4⋊Dic43C2211yescharacteristic
42C4×(C2×D43)⋊C4—21no—
43#14582746—21no—
44#14582662C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×C4×Q8×C43C2211yescharacteristic
53C2×#107×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C43×#389C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×D172—21no—
60C22×D172C2311yescharacteristic
61C22×C4×D43—21no—
62C22×C4×D43D411yescharacteristic
63C22×C4×D43D411yescharacteristic
64C22×C4×D43C2311yescharacteristic
65C2×#10621884—22no—
66C2×#10621884—22no—
67C2×#10621884—41no—
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70#13063301—22no—
71#13063301—22no—
72#13063300—22no—
73#13063300—22no—
74#13063287—41no—
75#13063287—41no—
76#13063287—44no—
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43D411yescharacteristic
92C2×C4×Dic43D411yescharacteristic
93C2×C4×Dic43C2311yescharacteristic
94C42×D43—41no—
95C42×D43—41no—
96#13063259—22no—
97#13063256—22no—
98#13063249—22no—
99#13063247—22no—
100#13063247—22no—
101#13063245—41no—
102(C2×D43)⋊C8—41no—
103(C2×D43)⋊C8—41no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C22×Q8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C4×Q8×C43—41no—
115C4×Q8×C43—41no—
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
123#107×C43—41no—
124#103×C43—22no—
125#103×C43—41no—
126#95×C43—21no—
127C23×D43—21no—
128C23×D43C2×D411yescharacteristic
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43#4112yes—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2411yescharacteristic
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C22×Dic43C2×D411yescharacteristic
148C2×D172—24no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—42no—
155C2×D172—42no—
156C2×D172#4112yes—
157C2×C4×D43—22no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×C4×D43—22no—
165C2×C4×D43—22no—
166C2×C4×D43—41no—
167C2×C4×D43—41no—
168C2×C4×D43—41no—
169C2×C4×D43—42no—
170C2×C4×D43—42no—
171C2×C4×D43—42no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—42no—
184C4⋊C4×C43—42no—
185C4⋊C4×C43#4112yes—
186C42×C43—21no—
187C42×C43—21no—
188C42×C43—42no—
189#10621884—44no—
190(C2×D43)⋊C4—24no—
191(C2×D43)⋊C4—24no—
192(C2×D43)⋊C4—42no—
193(C2×D43)⋊C4—42no—
194(C2×D43)⋊C4—42no—
195(C2×D43)⋊C4—42no—
196(C2×D43)⋊C4—42no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43#4112yes—
203Dic43⋊C4—24no—
204Dic43⋊C4—42no—
205C4×Dic43—21no—
206C4×Dic43—21no—
207C4×Dic43—41no—
208C4×Dic43—41no—
209C4×Dic43—42no—
210C4×Dic43—42no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C23×C43C22×D411yescharacteristic
218C22×D43—21no—
219C22×D43—21no—
220C22×D43—21no—
221C22×D43—21no—
222C22×D43—21no—
223C22×D43—21no—
224C22×D43—22no—
225C22×D43—41no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43—41no—
229C22×D43—41no—
230C22×D43—41no—
231C22×D43#13712yes—
232Q8×C43—22no—
233Q8×C43—22no—
234Q8×C43—41no—
235Q8×C43—41no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43#13512yes—
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43H(5,𝔽2)11yescharacteristic
259C2×C4×C43H(5,𝔽2)11yescharacteristic
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—22no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43AGL(1,ℤ/8)12yes—
278D172—22no—
279D172—22no—
280D172—48no—
281D172—41no—
282D172—41no—
283C4×D43—44no—
284C4×D43—44no—
285C4×D43—41no—
286C4×D43—41no—
287C4×D43—41no—
288C4×D43—41no—
289C4×D43—84no—
290C8×C43—41no—
291C8×C43—41no—
292C43⋊C8—41no—
293C43⋊C8—41no—
294#29414—431nomaximal, Sylow
295C22×C43#52511yescharacteristic
296C22×C43#52511yescharacteristic
297C22×C43#53411yescharacteristic
298C22×C43C2×#13511yescharacteristic
299C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
300C22×C43C2×#13711yescharacteristic
301C22×C43#57511yescharacteristic
302C2×D43—22no—
303C2×D43—22no—
304C2×D43—22no—
305C2×D43—41no—
306C2×D43—41no—
307C2×D43—41no—
308C2×D43—41no—
309C2×D43—42no—
310C2×D43—42no—
311C2×D43—42no—
312C2×D43—81no—
313C2×D43—81no—
314C2×D43—81no—
315C2×D43—81no—
316C4×C43—22no—
317C4×C43—42no—
318C4×C43—42no—
319C4×C43—41no—
320C4×C43—81no—
321C4×C43—81no—
322C4×C43#55111yescharacteristic
323C4×C43#55311yescharacteristic
324C4×C43#55311yescharacteristic
325C4×C43#55911yescharacteristic
326Dic43—22no—
327Dic43—42no—
328Dic43—41no—
329Dic43—41no—
330Dic43—81no—
331Dic43—81no—
332C4×C22⋊Q8—431no—
333C4×#121—431no—
334#2076—431no—
335#2036—431no—
336#2034—431no—
337#2000—431no—
338#1927—431no—
339#1925—431no—
340#1920—431no—
341#1918—431no—
342#1880—431no—
343#1877—431no—
344#1863D4311yescharacteristic, complemented
345#1862—431no—
346#1817—431no—
347C2×C43#260011yescharacteristic
348C2×C43#310211yescharacteristic
349C2×C43#310611yescharacteristic
350C2×C43#311011yescharacteristic
351C2×C43#311711yescharacteristic
352C2×C43#319011yescharacteristic
353C2×C43#319411yescharacteristic
354D43—42no—
355D43—82no—
356C22×SD16—431no—
357C2×C22⋊Q8—431no—
358C2×#121—431no—
359C2×C4×Q8C2×D4311yescharacteristic
360C2×C4×D4—431no—
361C2×C4×D4—861no—
362C22×C42—431no—
363C2×#107—431no—
364C2×#107C2×D4311yescharacteristic
365C2×#106—431no—
366C2×#103—431no—
367C2×#103C2×D4311yescharacteristic
368C2×#103C2×D4311yescharacteristic
369C2×#102—431no—
370C2×#102—431no—
371C2×#102—431no—
372C2×C22⋊C8—431no—
373C2×C22⋊C8—431no—
374#391—431no—
375#390—431no—
376#389—431no—
377#389C2×D4311yescharacteristic
378#388—861no—
379#387—861no—
380#386—861no—
381#385—861no—
382#380—431no—
383#380—431no—
384C4×C4⋊C4—431no—
385C4×C4⋊C4—431no—
386C4×C4⋊C4—861no—
387C4×C22⋊C4—861no—
388C4×C22⋊C4—861no—
389#340—431no—
390#340—431no—
391#340—431no—
392#340—431no—
393#340—431no—
394#340C2×D4311yescharacteristic
395#336—431no—
396#336—431no—
397#336—431no—
398#336C2×D4311yescharacteristic
399C43#2941411yescharacteristic, complemented, Sylow
400C22×Q8C22×D4311yescharacteristic
401C22×D4—431no—
402C22×D4—861no—
403C23×C4—431no—
404C23×C4—431no—
405C23×C4—431no—
406C23×C4—861no—
407C2×SD16—862no—
408C2×SD16—862no—
409C2×SD16—1721no—
410C22×C8—431no—
411C22×C8—431no—
412C22×C8C22×D4311yescharacteristic
413C22×C8C22×D4311yescharacteristic
414C22⋊Q8—862no—
415C22⋊Q8—862no—
416#121—862no—
417#121—862no—
418C4×Q8—41no—
419C4×Q8—41no—
420C4×D4—1721no—
421C4×D4—1721no—
422C4×D4—1724no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—431no—
426C2×C4⋊C4—431no—
427C2×C4⋊C4—431no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4C22×D4311yescharacteristic
431C2×C4⋊C4C22×D4311yescharacteristic
432C2×C4⋊C4C22×D4311yescharacteristic
433C2×C22⋊C4—861no—
434C2×C22⋊C4—861no—
435C2×C22⋊C4—861no—
436C2×C22⋊C4—861no—
437C2×C22⋊C4—861no—
438C2×C22⋊C4—861no—
439C2×C22⋊C4—861no—
440C2×C42—21no—
441C2×C42—431no—
442C2×C42—431no—
443C2×C42—431no—
444C2×C42—861no—
445C2×C42—861no—
446C2×C42—1721no—
447C2×C42—1721no—
448C2×C42C22×D4311yescharacteristic
449#107—41no—
450#107—862no—
451#106—862no—
452#103—22no—
453#103—41no—
454#103—862no—
455#102—862no—
456#102—862no—
457#102—1721no—
458C22⋊C8—1721no—
459C22⋊C8—1721no—
460#95—21no—
461#95—861no—
462#95—861no—
463#95—861no—
464#95—861no—
465#95—861no—
466#95—861no—
467#95—861no—
468C24—431no—
469C24—861no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8#1062190212yes—
476C2×D4—432no—
477C2×D4—864no—
478C2×D4—861no—
479C2×D4—861no—
480C2×D4—861no—
481C2×D4—861no—
482C2×D4—861no—
483C2×D4—1722no—
484C2×D4—1722no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—431no—
490C22×C4—431no—
491C22×C4—431no—
492C22×C4—862no—
493C22×C4—862no—
494C22×C4—861no—
495C22×C4—862no—
496C22×C4—861no—
497C22×C4—861no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4—861no—
504C22×C4—1721no—
505C22×C4—1721no—
506C22×C4—1721no—
507C22×C4—1722no—
508C22×C4—1722no—
509C22×C4—1722no—
510C22×C4D4×D4311yescharacteristic
511C22×C4D4×D4311yescharacteristic
512C22×C4C23×D4311yescharacteristic
513SD16—1724no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—861no—
523C2×C8—861no—
524C2×C8—861no—
525C2×C8—861no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—42no—
532C4⋊C4—42no—
533C4⋊C4—432no—
534C4⋊C4—864no—
535C4⋊C4—861no—
536C4⋊C4—861no—
537C4⋊C4—861no—
538C4⋊C4—861no—
539C4⋊C4—861no—
540C4⋊C4—1722no—
541C4⋊C4#1062189812yes—
542C22⋊C4—864no—
543C22⋊C4—864no—
544C22⋊C4—1722no—
545C22⋊C4—1722no—
546C22⋊C4—1722no—
547C22⋊C4—1722no—
548C22⋊C4—1722no—
549C42—21no—
550C42—21no—
551C42—42no—
552C42—861no—
553C42—861no—
554C42—1721no—
555C42—1721no—
556C42—1722no—
557C42—1722no—
558C23—432no—
559C23—861no—
560C23—861no—
561C23—861no—
562C23—861no—
563C23—861no—
564C23—861no—
565C23—862no—
566C23—1721no—
567C23—1721no—
568C23—1721no—
569C23—1721no—
570C23—1721no—
571C23—1721no—
572C23C2×D4×D4311yescharacteristic
573Q8—22no—
574Q8—22no—
575Q8—41no—
576Q8—41no—
577D4—862no—
578D4—862no—
579D4—1728no—
580D4—1721no—
581D4—1721no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—432no—
600C2×C4—861no—
601C2×C4—861no—
602C2×C4—861no—
603C2×C4—862no—
604C2×C4—861no—
605C2×C4—861no—
606C2×C4—861no—
607C2×C4—861no—
608C2×C4—861no—
609C2×C4—3444no—
610C2×C4—1724no—
611C2×C4—1724no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4—1721no—
620C2×C4—1721no—
621C2×C4—1721no—
622C2×C4—1721no—
623C2×C4—1721no—
624C2×C4#1306334812yes—
625C2×C4#41×D4311yescharacteristic
626C2×C4#41×D4311yescharacteristic
627C2×C4C2×#1062189811yescharacteristic
628C2×C4C2×#1062190211yescharacteristic
629C2×C4#1306337011yescharacteristic
630C2×C4#1306337011yescharacteristic
631C8—41no—
632C8—41no—
633C8—1721no—
634C8—1721no—
635C22—862no—
636C22—862no—
637C22—862no—
638C22—3441no—
639C22—3441no—
640C22—3441no—
641C22—3441no—
642C22—1722no—
643C22—1722no—
644C22—1722no—
645C22—1721no—
646C22—1721no—
647C22—1721no—
648C22—1721no—
649C22#1458340811yescharacteristic
650C22#1458341211yescharacteristic
651C22#1458345911yescharacteristic
652C22C2×#1306334811yescharacteristic
653C22AGL(1,ℤ/8)×D4311yescharacteristic
654C22#137×D4311yescharacteristic
655C22#1458369611yescharacteristic
656C4—22no—
657C4—42no—
658C4—41no—
659C4—42no—
660C4—81no—
661C4—81no—
662C4—862no—
663C4—3441no—
664C4—3441no—
665C4—1721no—
666C4—1721no—
667C4—1722no—
668C4#1458357611yescharacteristic
669C4#1458359411yescharacteristic
670C4#1458359711yescharacteristic
671C4#1458363211yescharacteristic
672C2—3442no—
673C2—1722no—
674C2#1914018111yescharacteristic
675C2#1914461911yescharacteristic
676C2#1914465811yescharacteristic
677C2#1914469211yescharacteristic
678C2#1914477111yescharacteristic
679C2#1914537911yescharacteristic
680C2#1914540711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1863C2
socleC23×C43C22×D4
prime radicalC2×#13063300C22
hypercenter#1863D43
hypocenterC43#29414
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1863

Complements

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

NH ≅ G/Ntype
1. C4×#13063301C2semidirect
3. #19136024C2semidirect
4. #19135797C2semidirect
7. #19135232C2semidirect
8. #19135216C2semidirect
9. #19135177C2semidirect
10. #19135165C2semidirect
11. #19134950C2semidirect
12. #19134926C2semidirect
13. #19134839C2semidirect
14. #19134662C2semidirect
15. C43×#1863C2semidirect
344. #1863D43semidirect
399. C43#29414semidirect

Maximal subgroups

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

subgroupindex
C4×#130633012
#191371032
#191360242
#191357972
#191357872
#191355972
#191352322
#191352162
#191351772
#191351652
#191349502
#191349262
#191348392
#191346622
C43×#18632
#2941443