Finite Group Databasebeta

← #25157028

Subgroups — #25157028

Order 11008.

924 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583114C211yesmaximal, characteristic
2C2×#14582996C211yesmaximal, characteristic, complemented
3#19138395C211yesmaximal, characteristic, complemented
4D4×Dic43⋊C4C211yesmaximal, characteristic, complemented
5#19136120C211yesmaximal, characteristic, complemented
6#19136091C211yesmaximal, characteristic, complemented
7#19136007C211yesmaximal, characteristic, complemented
8#19135837C211yesmaximal, characteristic, complemented
9#19135290C211yesmaximal, characteristic, complemented
10#19135162C211yesmaximal, characteristic, complemented
11#19134941C211yesmaximal, characteristic
12#19134941C211yesmaximal, characteristic
13#19134927C211yesmaximal, characteristic, complemented
14#19134846C211yesmaximal, characteristic, complemented
15C43×#1862C211yesmaximal, characteristic, complemented
16C22×#10621883C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C2×#13063313C2211yescharacteristic
19C2×#13063290C2211yescharacteristic
20C2×D4×Dic43C2211yescharacteristic
21C2×D4×Dic43C2211yescharacteristic
22C22×Dic43⋊C4—21no—
23#14583114—24no—
24#14582996—24no—
25C2×#13063258C2211yescharacteristic
26C2×C4⋊(C43⋊C8)C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063250C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31C2×#13063247C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063235C2211yescharacteristic
34#14582834—21no—
35#14582828—21no—
36#14582804C2211yescharacteristic
37#14582800C2211yescharacteristic
38#14582800C2211yescharacteristic
39#14582797C2211yescharacteristic
40#14582795C2211yescharacteristic
41#14582789—21no—
42#14582788—21no—
43#14582772—21no—
44#14582771—21no—
45#14582768C2211yescharacteristic
46#14582757—21no—
47C4×Dic43⋊C4C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic
55C2×#107×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C43×#389C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×Dic86C2311yescharacteristic
62C22×D172C2311yescharacteristic
63C23×Dic43—21no—
64C23×Dic43—21no—
65C2×#10621883—22no—
66C2×#10621883—22no—
67C2×#10621883D414yes—
68C2×#10621882—22no—
69C2×#10621882—22no—
70C2×#10621882—22no—
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73#13063313—22no—
74#13063313—41no—
75#13063290—22no—
76#13063290—41no—
77D4×Dic43—22no—
78D4×Dic43—22no—
79D4×Dic43—22no—
80D4×Dic43—41no—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—44no—
89C2×Dic43⋊C4D411yescharacteristic
90C2×Dic43⋊C4D411yescharacteristic
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43C2311yescharacteristic
101C2×C4×Dic43C2311yescharacteristic
102#13063258—22no—
103C4⋊(C43⋊C8)—22no—
104#13063250—22no—
105#13063250—22no—
106#13063248—22no—
107#13063247—22no—
108#13063247—41no—
109#13063245—22no—
110#13063235—22no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95D411yescharacteristic
116C43⋊#95D411yescharacteristic
117C22×D4×C43C2311yescharacteristic
118C23×C4×C43—21no—
119C22×C8×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C4×D4×C43—22no—
122C4×D4×C43—41no—
123C2×C4⋊C4×C43—21no—
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C22⋊C4×C43—21no—
128C2×C42×C43C2311yescharacteristic
129#107×C43—41no—
130#102×C43—22no—
131#102×C43—22no—
132#95×C43—21no—
133C24×C43—21no—
134C23×D43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43C2×D412yes—
139C2×D4×C43#4112yes—
140C2×D4×C43#4112yes—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—42no—
145C22×C4×C43—42no—
146C22×C4×C43—81no—
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2411yescharacteristic
150C22×Dic43—24no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—42no—
155C22×Dic43—42no—
156C22×Dic43—42no—
157C22×Dic43—42no—
158C22×Dic43—81no—
159C22×Dic43C2×D411yescharacteristic
160C22×Dic43C2×D411yescharacteristic
161C22×Dic43C2×D411yescharacteristic
162C22×Dic43C2×D411yescharacteristic
163C2×D172—21no—
164C2×D172—21no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86—21no—
173C2×Dic86—21no—
174C2×Dic86C2×D412yes—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—81no—
188C22⋊C4×C43—42no—
189C42×C43—21no—
190C42×C43—21no—
191C22⋊Dic43—24no—
192C22⋊Dic43—42no—
193#10621883—28no—
194#10621882—44no—
195(C2×D43)⋊C4—42no—
196(C2×D43)⋊C4—42no—
197(C2×D43)⋊C4—42no—
198(C2×D43)⋊C4—42no—
199(C2×D43)⋊C4—81no—
200(C2×D43)⋊C4—81no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43#4112yes—
205Dic43⋊C4—22no—
206Dic43⋊C4—41no—
207Dic43⋊C4—42no—
208Dic43⋊C4—42no—
209Dic43⋊C4—42no—
210Dic43⋊C4—42no—
211Dic43⋊C4—81no—
212C4×Dic43—21no—
213C4×Dic43—21no—
214C4×Dic43—21no—
215C4×Dic43—21no—
216C4×Dic43—42no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8C2×D412yes—
223C23×C43—22no—
224C23×C43—22no—
225C23×C43—22no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43—41no—
229C23×C43—41no—
230C23×C43C22×D411yescharacteristic
231C22×D43—41no—
232C22×D43—41no—
233C22×D43—41no—
234C22×D43—41no—
235C22×D43—41no—
236C22×D43—41no—
237C22×D43—41no—
238D4×C43—22no—
239D4×C43—22no—
240D4×C43—22no—
241D4×C43#12314yes—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—84no—
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C43H(5,𝔽2)11yescharacteristic
263C2×C4×C432−1+411yescharacteristic
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—22no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—22no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—21no—
277C2×Dic43—48no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—84no—
286C2×Dic43AGL(1,ℤ/8)12yes—
287D172—41no—
288D172—41no—
289D172—41no—
290D172—41no—
291Dic86—22no—
292Dic86—22no—
293Dic86—41no—
294Dic86—41no—
295C8×C43—41no—
296C8×C43—41no—
297C43⋊C8—22no—
298C43⋊C8—41no—
299#26188—431nomaximal, Sylow
300C22×C43—24no—
301C22×C43—42no—
302C22×C43—42no—
303C22×C43—42no—
304C22×C43—42no—
305C22×C43—42no—
306C22×C43—42no—
307C22×C43#52511yescharacteristic
308C22×C43D4211yescharacteristic
309C22×C43#54811yescharacteristic
310C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
311C22×C43#57511yescharacteristic
312C22×C43#57611yescharacteristic
313C22×C43#57811yescharacteristic
314C2×D43—81no—
315C2×D43—81no—
316C2×D43—81no—
317C2×D43—81no—
318C2×D43—81no—
319C2×D43—81no—
320C2×D43—81no—
321C4×C43—41no—
322C4×C43—41no—
323C4×C43—81no—
324C4×C43—81no—
325C4×C43—81no—
326C4×C43C2×#12311yescharacteristic
327C4×C43#53911yescharacteristic
328C4×C43#54711yescharacteristic
329C4×C43#55311yescharacteristic
330Dic43—22no—
331Dic43—42no—
332Dic43—41no—
333Dic43—42no—
334Dic43—41no—
335Dic43—41no—
336Dic43—81no—
337C2×#463—431no—
338C2×#440—431no—
339#2448—431no—
340D4×C4⋊C4—431no—
341#2093—431no—
342#2087—431no—
343#2072—431no—
344#2042—431no—
345#1936—431no—
346#1917—431no—
347#1879—431no—
348#1879—431no—
349#1877—431no—
350#1863—431no—
351#1862D4311yescharacteristic, complemented
352C2×C43—44no—
353C2×C43#244311yescharacteristic
354C2×C43#311411yescharacteristic
355C2×C43#312411yescharacteristic
356C2×C43#326911yescharacteristic
357C2×C43#327411yescharacteristic
358C2×C43#336711yescharacteristic
359C2×C43#337011yescharacteristic
360D43—161no—
361C22×SD16—431no—
362C22×D8—431no—
363C2×#124—431no—
364C2×C4×Q8—431no—
365C2×C4×D4—431no—
366C2×C4×D4—431no—
367C2×C4×D4C2×D4311yescharacteristic
368C22×C4⋊C4—861no—
369#463—864no—
370#440—864no—
371C2×#107—431no—
372C2×#107C2×D4311yescharacteristic
373C2×C4⋊C8—431no—
374C2×#103—431no—
375C2×#103—431no—
376C2×#103—431no—
377C2×#102—431no—
378C2×#102—431no—
379C2×#102—431no—
380C2×#102C2×D4311yescharacteristic
381C2×#102C2×D4311yescharacteristic
382C2×#97—431no—
383#399—861no—
384#397—861no—
385#391—431no—
386#390—431no—
387#390—431no—
388#389—431no—
389#389—431no—
390#389C2×D4311yescharacteristic
391#388—861no—
392#388—861no—
393#385—861no—
394#385—861no—
395#384—431no—
396#380—861no—
397C4×C4⋊C4—431no—
398#340—431no—
399#340—431no—
400#340—431no—
401#340C2×D4311yescharacteristic
402#336—431no—
403#336—431no—
404#336—431no—
405#336C2×D4311yescharacteristic
406C43#2618811yescharacteristic, complemented, Sylow
407C22×Q8—431no—
408C22×D4—431no—
409C22×D4C22×D4311yescharacteristic
410C23×C4—21no—
411C23×C4—861no—
412C23×C4—861no—
413C2×SD16—434no—
414C2×SD16—862no—
415C2×SD16—862no—
416C2×D8—862no—
417C2×D8—862no—
418C2×D8—862no—
419C22×C8—431no—
420C22×C8—431no—
421C22×C8C22×D4311yescharacteristic
422C22×C8C22×D4311yescharacteristic
423#124—862no—
424#124—1721no—
425C4×Q8—862no—
426C4×Q8—1721no—
427C4×D4—22no—
428C4×D4—41no—
429C4×D4—862no—
430C4×D4—862no—
431C4×D4—862no—
432C4×D4—1721no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—431no—
435C2×C4⋊C4—431no—
436C2×C4⋊C4—431no—
437C2×C4⋊C4—431no—
438C2×C4⋊C4—861no—
439C2×C4⋊C4—861no—
440C2×C4⋊C4—861no—
441C2×C4⋊C4—861no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4—1724no—
444C2×C4⋊C4C22×D4311yescharacteristic
445C2×C4⋊C4C22×D4311yescharacteristic
446C2×C4⋊C4C22×D4311yescharacteristic
447C2×C22⋊C4—21no—
448C2×C22⋊C4—861no—
449C2×C22⋊C4—861no—
450C2×C22⋊C4—861no—
451C2×C22⋊C4—861no—
452C2×C22⋊C4—861no—
453C2×C22⋊C4—861no—
454C2×C22⋊C4—861no—
455C2×C22⋊C4—861no—
456C2×C42—431no—
457C2×C42—431no—
458C2×C42—861no—
459C2×C42C22×D4311yescharacteristic
460#107—41no—
461#107—862no—
462C4⋊C8—862no—
463#103—862no—
464#103—862no—
465#103—862no—
466#102—22no—
467#102—22no—
468#102—862no—
469#102—862no—
470#102—1721no—
471#97—862no—
472#95—21no—
473#95—431no—
474#95—431no—
475#95—861no—
476#95—861no—
477#95—861no—
478#95—861no—
479C24—21no—
480C24—861no—
481C2×Q8—432no—
482C2×Q8—861no—
483C2×Q8—861no—
484C2×Q8—861no—
485C2×Q8—861no—
486C2×Q8—861no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—861no—
491C2×D4—861no—
492C2×D4—861no—
493C2×D4—861no—
494C2×D4—861no—
495C2×D4—861no—
496C2×D4#1062189812yes—
497C2×D4D4×D4312yes—
498C2×D4#1062190212yes—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—81no—
505C22×C4—431no—
506C22×C4—431no—
507C22×C4—431no—
508C22×C4—431no—
509C22×C4—864no—
510C22×C4—861no—
511C22×C4—861no—
512C22×C4—861no—
513C22×C4—3441no—
514C22×C4—1722no—
515C22×C4—1722no—
516C22×C4—1722no—
517C22×C4—1722no—
518C22×C4D4×D4311yescharacteristic
519C22×C4D4×D4311yescharacteristic
520C22×C4C23×D4311yescharacteristic
521SD16—868no—
522D8—1724no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—432no—
530C2×C8—861no—
531C2×C8—861no—
532C2×C8—861no—
533C2×C8—861no—
534C2×C8—861no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—81no—
542C4⋊C4—432no—
543C4⋊C4—862no—
544C4⋊C4—861no—
545C4⋊C4—861no—
546C4⋊C4—861no—
547C4⋊C4—3441no—
548C4⋊C4—1721no—
549C4⋊C4—1722no—
550C4⋊C4—1722no—
551C4⋊C4—1722no—
552C4⋊C4—1722no—
553C22⋊C4—42no—
554C22⋊C4—864no—
555C22⋊C4—3441no—
556C22⋊C4—3441no—
557C22⋊C4—1722no—
558C22⋊C4—1722no—
559C22⋊C4—1722no—
560C22⋊C4—1722no—
561C22⋊C4—1722no—
562C42—21no—
563C42—21no—
564C42—861no—
565C42—861no—
566C42—861no—
567C42—861no—
568C42—1722no—
569C23—22no—
570C23—22no—
571C23—22no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—1721no—
577C23—1721no—
578C23—1721no—
579C23—1721no—
580C23—1721no—
581C23—1721no—
582C23—1721no—
583C23C2×D4×D4311yescharacteristic
584Q8—862no—
585Q8—862no—
586Q8—1721no—
587Q8—1721no—
588D4—22no—
589D4—22no—
590D4—22no—
591D4—1721no—
592D4—1721no—
593D4—1721no—
594D4—1721no—
595D4#1306331014yes—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—84no—
612C2×C4—432no—
613C2×C4—861no—
614C2×C4—861no—
615C2×C4—861no—
616C2×C4—862no—
617C2×C4—861no—
618C2×C4—861no—
619C2×C4—861no—
620C2×C4—861no—
621C2×C4—861no—
622C2×C4—861no—
623C2×C4—861no—
624C2×C4—861no—
625C2×C4—862no—
626C2×C4—3444no—
627C2×C4—1728no—
628C2×C4—1721no—
629C2×C4—1721no—
630C2×C4—1721no—
631C2×C4—1721no—
632C2×C4—1721no—
633C2×C4—1721no—
634C2×C4—1721no—
635C2×C4C2×D4×D4311yescharacteristic
636C2×C4#41×D4311yescharacteristic
637C2×C4C2×#1062189811yescharacteristic
638C2×C4C2×#1062190211yescharacteristic
639C2×C4#1306337011yescharacteristic
640C2×C4#1306337211yescharacteristic
641C8—41no—
642C8—41no—
643C8—862no—
644C8—1721no—
645C22—24no—
646C22—42no—
647C22—42no—
648C22—42no—
649C22—42no—
650C22—42no—
651C22—42no—
652C22—3441no—
653C22—3441no—
654C22—3441no—
655C22—3441no—
656C22—3441no—
657C22—3441no—
658C22—3441no—
659C22#1458341211yescharacteristic
660C22#1458353111yescharacteristic
661C22#1458355811yescharacteristic
662C22AGL(1,ℤ/8)×D4311yescharacteristic
663C22#1458369611yescharacteristic
664C22#1458370011yescharacteristic
665C22#1458371511yescharacteristic
666C4—41no—
667C4—41no—
668C4—81no—
669C4—81no—
670C4—81no—
671C4—862no—
672C4—3441no—
673C4—1722no—
674C4—1722no—
675C4—1721no—
676C4—1721no—
677C4—1721no—
678C4C2×#1306331011yescharacteristic
679C4#1458349811yescharacteristic
680C4#1458354711yescharacteristic
681C4#1458359811yescharacteristic
682C2—44no—
683C2—6881no—
684C2#1913833411yescharacteristic
685C2#1914473811yescharacteristic
686C2#1914486211yescharacteristic
687C2#1914615411yescharacteristic
688C2#1914621311yescharacteristic
689C2#1914731411yescharacteristic
690C2#1914734411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1862C2
socleC23×C43C22×D4
prime radicalC22×#10621882C22
hypercenter#1862D43
hypocenterC43#26188
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1862

Complements

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

NH ≅ G/Ntype
2. C2×#14582996C2semidirect
3. #19138395C2semidirect
4. D4×Dic43⋊C4C2semidirect
5. #19136120C2semidirect
6. #19136091C2semidirect
7. #19136007C2semidirect
8. #19135837C2semidirect
9. #19135290C2semidirect
10. #19135162C2semidirect
13. #19134927C2semidirect
14. #19134846C2semidirect
15. C43×#1862C2semidirect
351. #1862D43semidirect
406. C43#26188semidirect

Maximal subgroups

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

subgroupindex
C2×#145831142
C2×#145829962
#191383952
D4×Dic43⋊C42
#191361202
#191360912
#191360072
#191358372
#191352902
#191351622
#191349412
#191349272
#191348462
C43×#18622
#2618843