Finite Group Databasebeta

← #25156595

Subgroups — #25156595

Order 11008.

910 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×#14583097C211yesmaximal, characteristic
2C2×#14582984C211yesmaximal, characteristic, complemented
3#19138363C211yesmaximal, characteristic
4#19137516C211yesmaximal, characteristic, complemented
5#19136116C211yesmaximal, characteristic, complemented
6#19136099C211yesmaximal, characteristic, complemented
7#19136010C211yesmaximal, characteristic, complemented
8#19135828C211yesmaximal, characteristic
9#19135280C211yesmaximal, characteristic, complemented
10#19135151C211yesmaximal, characteristic, complemented
11#19134952C211yesmaximal, characteristic, complemented
12#19134950C211yesmaximal, characteristic, complemented
13#19134847C211yesmaximal, characteristic, complemented
14#19134843C211yesmaximal, characteristic, complemented
15C43×#1880C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C2×#13063321C2211yescharacteristic
18C2×#13063307—21no—
19C2×Q8×Dic43C2211yescharacteristic
20C2×Q8×Dic43C2211yescharacteristic
21C2×#13063287C2211yescharacteristic
22#14583097—24no—
23#14582984—24no—
24C2×#13063258C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×Dic43⋊C8C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063247C2211yescharacteristic
29C2×#13063247C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×C8×Dic43C2211yescharacteristic
34#14582815—21no—
35#14582814—21no—
36#14582802C2211yescharacteristic
37#14582801C2211yescharacteristic
38#14582798—21no—
39#14582798—21no—
40#14582798C2211yescharacteristic
41#14582798C2211yescharacteristic
42#14582795C2211yescharacteristic
43#14582775—21no—
44#14582765—21no—
45#14582765C2211yescharacteristic
46C4×C4⋊Dic43—21no—
47C4×C4⋊Dic43C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582654C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C22×SD16×C43C2211yescharacteristic
55C2×C4×Q8×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C43×#390C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C22⋊D43—21no—
63C22×C22⋊D43—21no—
64C22×C4×D43—21no—
65C2×#10621884—22no—
66C2×#10621884—22no—
67C2×#10621884D414yes—
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70#13063321—22no—
71#13063321—41no—
72#13063307—44no—
73Q8×Dic43—22no—
74Q8×Dic43—22no—
75Q8×Dic43—41no—
76Q8×Dic43—41no—
77#13063287—22no—
78#13063287—41no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43—21no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43D411yescharacteristic
84C2×C4⋊Dic43D411yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×Dic43⋊C4—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43C2311yescharacteristic
97C2×C4×Dic43C2311yescharacteristic
98#13063258—41no—
99#13063256—22no—
100Dic43⋊C8—22no—
101#13063249—22no—
102#13063247—22no—
103#13063247—22no—
104#13063246—22no—
105#13063246—41no—
106#13063245—22no—
107C8×Dic43—22no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95D411yescharacteristic
114C43⋊#95D411yescharacteristic
115C22×Q8×C43C2311yescharacteristic
116C22×D4×C43C2311yescharacteristic
117C2×SD16×C43—22no—
118C2×SD16×C43—22no—
119C2×SD16×C43—22no—
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C4×Q8×C43—22no—
123C4×Q8×C43—22no—
124C2×C4⋊C4×C43—21no—
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C42×C43—21no—
130C2×C42×C43C2311yescharacteristic
131#103×C43—22no—
132#102×C43—22no—
133C24×C43—21no—
134C23×D43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43C2×D412yes—
139C2×Q8×C43#4112yes—
140C2×Q8×C43#4112yes—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2411yescharacteristic
153C2×C22⋊D43—42no—
154C2×C22⋊D43—42no—
155C2×C22⋊D43—42no—
156C2×C22⋊D43—42no—
157C2×C22⋊D43—81no—
158C2×C22⋊D43—81no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43C2×D411yescharacteristic
163C22×Dic43C2×D411yescharacteristic
164C22×Dic43C2×D411yescharacteristic
165C22×Dic43C2×D411yescharacteristic
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—21no—
169C2×D172—21no—
170C2×D172—21no—
171C2×D172C2×D412yes—
172C2×C4×D43—42no—
173C2×C4×D43—42no—
174C2×C4×D43—81no—
175SD16×C43—44no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C4⋊C4×C43—24no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43#4112yes—
187C22⋊C4×C43—42no—
188C22⋊C4×C43—81no—
189C42×C43—24no—
190C42×C43—21no—
191C42×C43—21no—
192C22⋊Dic43—42no—
193C22⋊Dic43—81no—
194#10621884—28no—
195(C2×D43)⋊C4—42no—
196(C2×D43)⋊C4—42no—
197(C2×D43)⋊C4—81no—
198C4⋊Dic43—22no—
199C4⋊Dic43—22no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—42no—
207C4⋊Dic43—42no—
208C4⋊Dic43—42no—
209C4⋊Dic43—42no—
210Dic43⋊C4—42no—
211C4×Dic43—21no—
212C4×Dic43—21no—
213C4×Dic43—21no—
214C4×Dic43—21no—
215C4×Dic43—42no—
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—41no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43—41no—
229C23×C43—41no—
230C23×C43C22×D411yescharacteristic
231C22×D43—22no—
232C22×D43—41no—
233C22×D43—41no—
234C22×D43—41no—
235C22×D43—41no—
236C22×D43—41no—
237C22×D43—41no—
238Q8×C43—22no—
239Q8×C43—22no—
240Q8×C43—22no—
241Q8×C43#12314yescomplemented
242D4×C43—41no—
243D4×C43—41no—
244D4×C43—41no—
245D4×C43—41no—
246C2×C4×C43—22no—
247C2×C4×C43—22no—
248C2×C4×C43—22no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—22no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43C22×D411yescharacteristic
262C2×C4×C43C2×#4111yescharacteristic
263C2×C4×C43C2×#4111yescharacteristic
264C2×C4×C43C2×#4111yescharacteristic
265C2×C4×C43H(5,𝔽2)11yescharacteristic
266C2×C4×C432−1+411yescharacteristic
267C22⋊D43—84no—
268C22⋊D43—84no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—21no—
277C2×Dic43—21no—
278C2×Dic43—21no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43#13512yes—
289C2×Dic43AGL(1,ℤ/8)12yes—
290D172—22no—
291D172—22no—
292D172—41no—
293D172—41no—
294C4×D43—84no—
295C8×C43—41no—
296C8×C43—41no—
297C43⋊C8—22no—
298C43⋊C8—41no—
299#26159—431nomaximal, Sylow
300C22×C43—81no—
301C22×C43—81no—
302C22×C43—81no—
303C22×C43—81no—
304C22×C43—81no—
305C22×C43—81no—
306C22×C43—81no—
307C22×C43#52511yescharacteristic
308C22×C43D4211yescharacteristic
309C22×C43#54811yescharacteristic
310C22×C43C2×#13511yescharacteristic
311C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
312C22×C43#57711yescharacteristic
313C22×C43#57711yescharacteristic
314C2×D43—42no—
315C2×D43—42no—
316C2×D43—42no—
317C2×D43—81no—
318C2×D43—81no—
319C2×D43—81no—
320C2×D43—81no—
321C4×C43—24no—
322C4×C43—41no—
323C4×C43—42no—
324C4×C43—41no—
325C4×C43—81no—
326C4×C43C2×#12311yescharacteristic
327C4×C43#53911yescharacteristic
328C4×C43#54711yescharacteristic
329C4×C43#55311yescharacteristic
330Dic43—22no—
331Dic43—22no—
332Dic43—41no—
333Dic43—41no—
334Dic43—81no—
335Dic43—81no—
336Dic43—81no—
337C2×#460—431no—
338C2×C4×SD16—431no—
339#2445—431no—
340#2351—431no—
341#2092—431no—
342#2088—431no—
343#2073—431no—
344#2041—431no—
345#1934—431no—
346#1916—431no—
347#1880—431no—
348#1880—431no—
349#1880D4311yescharacteristic, complemented
350#1863—431no—
351#1862—431no—
352C2×C43—161no—
353C2×C43#244311yescharacteristic
354C2×C43#310611yescharacteristic
355C2×C43#312611yescharacteristic
356C2×C43#326511yescharacteristic
357C2×C43#328211yescharacteristic
358C2×C43#336511yescharacteristic
359C2×C43#336811yescharacteristic
360D43—82no—
361C22×SD16—431no—
362C22×SD16C2×D4311yescharacteristic
363C2×#127—431no—
364C2×#123—861no—
365C2×C4×Q8—431no—
366C2×C4×Q8—431no—
367C2×C4×Q8C2×D4311yescharacteristic
368C2×C4×D4—431no—
369#460—864no—
370C4×SD16—864no—
371C2×#107—431no—
372C2×#106—431no—
373C2×C4⋊C8—431no—
374C2×#103—431no—
375C2×#103C2×D4311yescharacteristic
376C2×#102—431no—
377C2×#102—431no—
378C2×#102—431no—
379C2×#102—431no—
380C2×#102—431no—
381C2×#102C2×D4311yescharacteristic
382C2×C4×C8—431no—
383#394—861no—
384#394—861no—
385#390—431no—
386#390—431no—
387#390C2×D4311yescharacteristic
388#389—431no—
389#389—431no—
390#389—431no—
391#389—861no—
392#389—861no—
393#386—861no—
394#382—431no—
395#382—861no—
396C4×C4⋊C4—431no—
397C4×C4⋊C4—861no—
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#2615911yescharacteristic, complemented, Sylow
407C22×Q8C22×D4311yescharacteristic
408C22×D4—431no—
409C22×D4—861no—
410C22×D4—861no—
411C22×D4C22×D4311yescharacteristic
412C23×C4—861no—
413C2×SD16—22no—
414C2×SD16—22no—
415C2×SD16—22no—
416C2×SD16—434no—
417C2×SD16—862no—
418C2×SD16—862no—
419C22×C8—431no—
420C22×C8—431no—
421C22×C8C22×D4311yescharacteristic
422C22×C8C22×D4311yescharacteristic
423#127—862no—
424#127—1721no—
425#123—1724no—
426C4×Q8—22no—
427C4×Q8—22no—
428C4×Q8—862no—
429C4×Q8—862no—
430C4×Q8—1721no—
431C4×Q8—1721no—
432C4×D4—862no—
433C4×D4—1721no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—431no—
436C2×C4⋊C4—431no—
437C2×C4⋊C4—431no—
438C2×C4⋊C4—431no—
439C2×C4⋊C4—431no—
440C2×C4⋊C4—861no—
441C2×C4⋊C4—861no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4—861no—
445C2×C4⋊C4C22×D4311yescharacteristic
446C2×C4⋊C4C22×D4311yescharacteristic
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—861no—
450C2×C22⋊C4—861no—
451C2×C22⋊C4—861no—
452C2×C22⋊C4—861no—
453C2×C22⋊C4—861no—
454C2×C42—21no—
455C2×C42—431no—
456C2×C42—431no—
457C2×C42—861no—
458C2×C42—861no—
459C2×C42C22×D4311yescharacteristic
460#107—1721no—
461#106—862no—
462C4⋊C8—862no—
463#103—22no—
464#103—862no—
465#102—22no—
466#102—862no—
467#102—862no—
468#102—862no—
469#102—862no—
470#102—1721no—
471C4×C8—862no—
472#95—431no—
473#95—431no—
474#95—861no—
475#95—861no—
476#95—861no—
477#95—861no—
478#95—861no—
479C24—21no—
480C24—861no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8#1062189812yes—
485C2×Q8D4×D4312yes—
486C2×Q8#1062190012yes—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—432no—
494C2×D4—861no—
495C2×D4—861no—
496C2×D4—861no—
497C2×D4—861no—
498C2×D4—861no—
499C2×D4—3441no—
500C2×D4—3441no—
501C2×D4—1722no—
502C2×D4—1722no—
503C2×D4—1722no—
504C2×D4—1722no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—431no—
509C22×C4—431no—
510C22×C4—431no—
511C22×C4—431no—
512C22×C4—861no—
513C22×C4—861no—
514C22×C4—861no—
515C22×C4—3441no—
516C22×C4—1722no—
517C22×C4—1722no—
518C22×C4D4×D4311yescharacteristic
519C22×C4D4×D4311yescharacteristic
520C22×C4C23×D4311yescharacteristic
521SD16—44no—
522SD16—868no—
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—24no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—862no—
540C4⋊C4—862no—
541C4⋊C4—861no—
542C4⋊C4—861no—
543C4⋊C4—861no—
544C4⋊C4—861no—
545C4⋊C4—861no—
546C4⋊C4—861no—
547C4⋊C4—1722no—
548C4⋊C4—1722no—
549C4⋊C4—1722no—
550C4⋊C4—1722no—
551C4⋊C4—1722no—
552C4⋊C4#1062190012yes—
553C22⋊C4—42no—
554C22⋊C4—81no—
555C22⋊C4—3441no—
556C22⋊C4—3441no—
557C22⋊C4—1722no—
558C22⋊C4—1722no—
559C22⋊C4—1722no—
560C42—24no—
561C42—21no—
562C42—21no—
563C42—861no—
564C42—861no—
565C42—861no—
566C42—861no—
567C42—1722no—
568C42—1722no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—862no—
577C23—1721no—
578C23—1721no—
579C23—1721no—
580C23—1721no—
581C23—1721no—
582C23—1721no—
583C23C2×D4×D4311yescharacteristic
584Q8—22no—
585Q8—22no—
586Q8—22no—
587Q8#1306330714yescomplemented
588D4—41no—
589D4—41no—
590D4—41no—
591D4—41no—
592D4—862no—
593D4—862no—
594D4—3444no—
595D4—3444no—
596D4—1721no—
597D4—1721no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—22no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—432no—
614C2×C4—432no—
615C2×C4—861no—
616C2×C4—861no—
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—3444no—
626C2×C4—1721no—
627C2×C4—1721no—
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×C4C2×#1062190011yescharacteristic
637C2×C4C2×#1062190011yescharacteristic
638C2×C4C2×#1062189811yescharacteristic
639C2×C4#1306337111yescharacteristic
640C2×C4#1306337211yescharacteristic
641C8—41no—
642C8—41no—
643C8—862no—
644C8—1721no—
645C22—81no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22—81no—
651C22—81no—
652C22—3441no—
653C22—3441no—
654C22—3441no—
655C22—3441no—
656C22—1722no—
657C22—1722no—
658C22—1722no—
659C22#1458340511yescharacteristic
660C22#1458353311yescharacteristic
661C22#1458355811yescharacteristic
662C22#135×D4311yescharacteristic
663C22AGL(1,ℤ/8)×D4311yescharacteristic
664C22#1458370511yescharacteristic
665C22#1458370811yescharacteristic
666C4—24no—
667C4—41no—
668C4—41no—
669C4—42no—
670C4—81no—
671C4—862no—
672C4—862no—
673C4—3441no—
674C4—3441no—
675C4—3441no—
676C4—1721no—
677C4—1721no—
678C4C2×#1306330711yescharacteristic
679C4#1458349311yescharacteristic
680C4#1458354911yescharacteristic
681C4#1458359511yescharacteristic
682C2—161no—
683C2—3442no—
684C2#1913833611yescharacteristic
685C2#1914464811yescharacteristic
686C2#1914488011yescharacteristic
687C2#1914608511yescharacteristic
688C2#1914629711yescharacteristic
689C2#1914729211yescharacteristic
690C2#1914732511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1880C2
socleC23×C43C22×D4
prime radicalC2×#13063321C22
hypercenter#1880D43
hypocenterC43#26159
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1880

Complements

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

NH ≅ G/Ntype
2. C2×#14582984C2semidirect
4. #19137516C2semidirect
5. #19136116C2semidirect
6. #19136099C2semidirect
7. #19136010C2semidirect
9. #19135280C2semidirect
10. #19135151C2semidirect
11. #19134952C2semidirect
12. #19134950C2semidirect
13. #19134847C2semidirect
14. #19134843C2semidirect
15. C43×#1880C2semidirect
241. Q8×C43#123semidirect
349. #1880D43semidirect
406. C43#26159semidirect
587. Q8#13063307semidirect

Maximal subgroups

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

subgroupindex
C2×#145830972
C2×#145829842
#191383632
#191375162
#191361162
#191360992
#191360102
#191358282
#191352802
#191351512
#191349522
#191349502
#191348472
#191348432
C43×#18802
#2615943