Finite Group Databasebeta

← #25164643

Subgroups — #25164643

Order 11008.

832 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138930C211yesmaximal, characteristic, complemented
2#19137607C211yesmaximal, characteristic
3#19135911C211yesmaximal, characteristic, complemented
4#19135775C211yesmaximal, characteristic
5#19135739C211yesmaximal, characteristic, complemented
6#19135599C211yesmaximal, characteristic
7#19135549C211yesmaximal, characteristic, complemented
8#19135271C211yesmaximal, characteristic, complemented
9#19135234C211yesmaximal, characteristic, complemented
10#19135201C211yesmaximal, characteristic, complemented
11#19135166C211yesmaximal, characteristic, complemented
12#19134929C211yesmaximal, characteristic, complemented
13#19134901C211yesmaximal, characteristic, complemented
14#19134684C211yesmaximal, characteristic, complemented
15C4×#102×C43C211yesmaximal, characteristic, complemented
16C22×#10621883C2211yescharacteristic
17C2×#13063316C2211yescharacteristic
18C2×#13063305C2211yescharacteristic
19C2×#13063296C2211yescharacteristic
20C2×C4×C22⋊D43—21no—
21C2×C4⋊C4×D43C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×Dic43⋊C8C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063248C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×(C2×D43)⋊C8C2211yescharacteristic
29C2×(C2×D43)⋊C8C2211yescharacteristic
30#14582839—21no—
31#14582826—21no—
32#14582805C2211yescharacteristic
33#14582804C2211yescharacteristic
34#14582802C2211yescharacteristic
35#14582797C2211yescharacteristic
36#14582793—21no—
37#14582790—21no—
38#14582775—21no—
39#14582772—21no—
40#14582765—21no—
41#14582756C2211yescharacteristic
42C4⋊C4×Dic43C2211yescharacteristic
43C4×(C2×D43)⋊C4C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×C4×D4×C43C2211yescharacteristic
53C2×#102×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×C4×C8×C43C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×C22⋊D43—21no—
61C22×C4×D43—21no—
62C22×C4×D43C2311yescharacteristic
63C2×#10621883—22no—
64C2×#10621883—41no—
65C2×#10621883—41no—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68#13063316—22no—
69#13063316—41no—
70#13063305—22no—
71#13063305—41no—
72#13063296—22no—
73#13063296—22no—
74C4×C22⋊D43—44no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C4⋊C4×D43—22no—
84C4⋊C4×D43—41no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4D411yescharacteristic
91C2×(C2×D43)⋊C4D411yescharacteristic
92C2×C4×Dic43—21no—
93C2×C4×Dic43C2311yescharacteristic
94#13063258—22no—
95Dic43⋊C8—41no—
96#13063250—22no—
97#13063250—41no—
98#13063248—22no—
99#13063246—41no—
100(C2×D43)⋊C8—41no—
101(C2×D43)⋊C8—41no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95D411yescharacteristic
110C43⋊#95D411yescharacteristic
111C22×D4×C43C2311yescharacteristic
112C23×C4×C43—21no—
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C4×D4×C43—22no—
116C4×D4×C43—41no—
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C22⋊C4×C43—21no—
121C2×C42×C43—21no—
122C2×C42×C43C2311yescharacteristic
123#102×C43—22no—
124#102×C43—22no—
125C4×C8×C43—41no—
126#95×C43—21no—
127C24×C43—21no—
128C23×D43C2×D411yescharacteristic
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43#4112yes—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—42no—
139C22×C4×C43—42no—
140C22×C4×C43—81no—
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2411yescharacteristic
144C2×C22⋊D43—24no—
145C2×C22⋊D43—42no—
146C2×C22⋊D43—42no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C22×Dic43C2×D411yescharacteristic
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—42no—
161C2×C4×D43—42no—
162C2×C4×D43—81no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43#4112yes—
180C4⋊C4×C43#4112yes—
181C22⋊C4×C43—42no—
182C42×C43—21no—
183C42×C43—21no—
184C42×C43—42no—
185C22⋊Dic43—24no—
186C22⋊Dic43—42no—
187C22⋊Dic43—81no—
188#10621883—44no—
189(C2×D43)⋊C4—22no—
190(C2×D43)⋊C4—22no—
191(C2×D43)⋊C4—42no—
192(C2×D43)⋊C4—42no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—42no—
199C4⋊Dic43—42no—
200C4⋊Dic43#4112yes—
201Dic43⋊C4—42no—
202Dic43⋊C4—42no—
203Dic43⋊C4—42no—
204C4×Dic43—21no—
205C4×Dic43—21no—
206C4×Dic43—42no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C23×C43—22no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43C22×D411yescharacteristic
221C22×D43—21no—
222C22×D43—21no—
223C22×D43—21no—
224C22×D43—21no—
225C22×D43—21no—
226C22×D43—21no—
227C22×D43#13512yes—
228D4×C43—22no—
229D4×C43—22no—
230D4×C43—41no—
231D4×C43—41no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—22no—
235C2×C4×C43—22no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—84no—
247C2×C4×C43AGL(1,ℤ/8)12yes—
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43H(5,𝔽2)11yescharacteristic
253C2×C4×C43H(5,𝔽2)11yescharacteristic
254C22⋊D43—48no—
255C2×Dic43—22no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C4×D43—41no—
277C4×D43—41no—
278C4×D43—41no—
279C4×D43—41no—
280C4×D43—84no—
281Dic86—41no—
282Dic86—41no—
283Dic86—41no—
284Dic86—41no—
285C8×C43—41no—
286C8×C43—41no—
287C43⋊C8—41no—
288C43⋊C8—41no—
289#26721—431nomaximal, Sylow
290C22×C43—42no—
291C22×C43—42no—
292C22×C43—42no—
293C22×C43—81no—
294C22×C43—81no—
295C22×C43—81no—
296C22×C43—81no—
297C22×C43#52511yescharacteristic
298C22×C43#54611yescharacteristic
299C22×C43#54611yescharacteristic
300C22×C43C2×#13511yescharacteristic
301C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
302C22×C43#57711yescharacteristic
303C22×C43#57811yescharacteristic
304C2×D43—22no—
305C2×D43—22no—
306C2×D43—22no—
307C2×D43—41no—
308C2×D43—41no—
309C2×D43—41no—
310C2×D43—41no—
311C4×C43—22no—
312C4×C43—42no—
313C4×C43—41no—
314C4×C43—42no—
315C4×C43—81no—
316C4×C43#52911yescharacteristic
317C4×C43#53811yescharacteristic
318C4×C43#55511yescharacteristic
319C4×C43#55911yescharacteristic
320Dic43—41no—
321Dic43—42no—
322Dic43—41no—
323Dic43—41no—
324Dic43—81no—
325Dic43—81no—
326Dic43—81no—
327#2489—431no—
328#2361—431no—
329#2055—431no—
330#2033—431no—
331#2025—431no—
332#2000—431no—
333#1989—431no—
334#1933—431no—
335#1928—431no—
336#1923—431no—
337#1918—431no—
338#1877—431no—
339#1872—431no—
340#1824—431no—
341C4×#102D4311yescharacteristic, complemented
342C2×C43—82no—
343C2×C43#245911yescharacteristic
344C2×C43#310511yescharacteristic
345C2×C43#312011yescharacteristic
346C2×C43#330011yescharacteristic
347C2×C43#330111yescharacteristic
348C2×C43#331011yescharacteristic
349C2×C43#333011yescharacteristic
350D43—42no—
351C22×SD16—431no—
352C2×#125—431no—
353C2×C22⋊Q8—431no—
354C2×#121—431no—
355C2×C4×D4—861no—
356C2×C4×D4C2×D4311yescharacteristic
357C22×C4⋊C4—431no—
358C2×#107—431no—
359C2×C4⋊C8—431no—
360C2×#103—431no—
361C2×#103—431no—
362C2×#103—431no—
363C2×#102—431no—
364C2×#102C2×D4311yescharacteristic
365C2×#102C2×D4311yescharacteristic
366C2×C22⋊C8—431no—
367C2×C22⋊C8—431no—
368C2×C4×C8C2×D4311yescharacteristic
369#400—861no—
370#397—861no—
371#391—431no—
372#391—431no—
373#390—431no—
374#389—431no—
375#388—861no—
376#388—861no—
377#386—861no—
378#385—861no—
379#382—861no—
380#380—431no—
381C4×C4⋊C4—431no—
382C4×C4⋊C4C2×D4311yescharacteristic
383C4×C22⋊C4—431no—
384#340—431no—
385#340—431no—
386#340—431no—
387#340—431no—
388#340—431no—
389#340—431no—
390#340C2×D4311yescharacteristic
391#340C2×D4311yescharacteristic
392#336—431no—
393#336—431no—
394C43#2672111yescharacteristic, complemented, Sylow
395C22×Q8—431no—
396C22×D4—861no—
397C22×D4C22×D4311yescharacteristic
398C23×C4—21no—
399C23×C4—431no—
400C23×C4—861no—
401C2×SD16—862no—
402C2×SD16—1721no—
403C2×SD16—1721no—
404C22×C8—431no—
405C22×C8—431no—
406C22×C8C22×D4311yescharacteristic
407C22×C8C22×D4311yescharacteristic
408#125—862no—
409#125—1721no—
410C22⋊Q8—862no—
411C22⋊Q8—1721no—
412#121—862no—
413#121—862no—
414C4×D4—22no—
415C4×D4—41no—
416C4×D4—1724no—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—862no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4—1721no—
427C2×C4⋊C4C22×D4311yescharacteristic
428C2×C4⋊C4C22×D4311yescharacteristic
429C2×C4⋊C4C22×D4311yescharacteristic
430C2×C22⋊C4—21no—
431C2×C22⋊C4—431no—
432C2×C22⋊C4—431no—
433C2×C22⋊C4—861no—
434C2×C22⋊C4—861no—
435C2×C22⋊C4—861no—
436C2×C22⋊C4—861no—
437C2×C22⋊C4—861no—
438C2×C42—21no—
439C2×C42—431no—
440C2×C42—861no—
441C2×C42C22×D4311yescharacteristic
442#107—862no—
443C4⋊C8—1721no—
444#103—862no—
445#103—862no—
446#103—1721no—
447#102—22no—
448#102—22no—
449#102—1721no—
450C22⋊C8—1721no—
451C22⋊C8—1721no—
452C4×C8—41no—
453#95—21no—
454#95—431no—
455#95—431no—
456#95—861no—
457#95—861no—
458#95—861no—
459#95—861no—
460#95—861no—
461#95—861no—
462#95—861no—
463C24—21no—
464C24—431no—
465C2×Q8—861no—
466C2×Q8—861no—
467C2×Q8—861no—
468C2×Q8—861no—
469C2×Q8—861no—
470C2×Q8—861no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—864no—
477C2×D4—1722no—
478C2×D4—1722no—
479C2×D4#1062189812yes—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—81no—
486C22×C4—431no—
487C22×C4—431no—
488C22×C4—431no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4—861no—
493C22×C4—861no—
494C22×C4—861no—
495C22×C4—861no—
496C22×C4—861no—
497C22×C4—861no—
498C22×C4—861no—
499C22×C4—3441no—
500C22×C4—1722no—
501C22×C4—1722no—
502C22×C4D4×D4311yescharacteristic
503C22×C4D4×D4311yescharacteristic
504C22×C4C23×D4311yescharacteristic
505SD16—1724no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—432no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—1722no—
529C4⋊C4—1722no—
530C4⋊C4—1722no—
531C4⋊C4—1722no—
532C4⋊C4—1722no—
533C4⋊C4#1062189812yes—
534C4⋊C4#1062189812yes—
535C22⋊C4—42no—
536C22⋊C4—862no—
537C22⋊C4—864no—
538C22⋊C4—862no—
539C22⋊C4—3441no—
540C22⋊C4—1722no—
541C22⋊C4—1722no—
542C22⋊C4—1722no—
543C42—21no—
544C42—21no—
545C42—42no—
546C42—861no—
547C42—861no—
548C42—1722no—
549C23—22no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—432no—
557C23—861no—
558C23—861no—
559C23—861no—
560C23—861no—
561C23—861no—
562C23—861no—
563C23C2×D4×D4311yescharacteristic
564Q8—1721no—
565Q8—1721no—
566Q8—1721no—
567Q8—1721no—
568D4—22no—
569D4—22no—
570D4—41no—
571D4—41no—
572D4—1728no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—84no—
588C2×C4—861no—
589C2×C4—862no—
590C2×C4—861no—
591C2×C4—861no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—3444no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4#1306334912yes—
615C2×C4#41×D4311yescharacteristic
616C2×C4C2×#1062189811yescharacteristic
617C2×C4C2×#1062189811yescharacteristic
618C2×C4C2×#1062189811yescharacteristic
619C2×C4#1306337011yescharacteristic
620C2×C4#1306337111yescharacteristic
621C8—41no—
622C8—41no—
623C8—1721no—
624C8—1721no—
625C22—42no—
626C22—42no—
627C22—42no—
628C22—81no—
629C22—81no—
630C22—81no—
631C22—81no—
632C22—862no—
633C22—862no—
634C22—862no—
635C22—1721no—
636C22—1721no—
637C22—1721no—
638C22—1721no—
639C22#1458340811yescharacteristic
640C22#1458353911yescharacteristic
641C22#1458354511yescharacteristic
642C22#135×D4311yescharacteristic
643C22C2×#1306334911yescharacteristic
644C22#1458370511yescharacteristic
645C22#1458371311yescharacteristic
646C4—22no—
647C4—42no—
648C4—42no—
649C4—41no—
650C4—81no—
651C4—3441no—
652C4—3441no—
653C4—3441no—
654C4—1721no—
655C4—1721no—
656C4—1722no—
657C4—1721no—
658C4#1458343311yescharacteristic
659C4#1458348211yescharacteristic
660C4#1458361211yescharacteristic
661C4#1458363211yescharacteristic
662C2—82no—
663C2—1722no—
664C2#1913853211yescharacteristic
665C2#1914464011yescharacteristic
666C2#1914480511yescharacteristic
667C2#1914648311yescharacteristic
668C2#1914650211yescharacteristic
669C2#1914661211yescharacteristic
670C2#1914690211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC4×#102×C43C2
socleC23×C43C22×D4
prime radicalC2×#13063296C22
hypercenterC4×#102D43
hypocenterC43#26721
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
1. #19138930C2semidirect
3. #19135911C2semidirect
5. #19135739C2semidirect
7. #19135549C2semidirect
8. #19135271C2semidirect
9. #19135234C2semidirect
10. #19135201C2semidirect
11. #19135166C2semidirect
12. #19134929C2semidirect
13. #19134901C2semidirect
14. #19134684C2semidirect
15. C4×#102×C43C2semidirect
341. C4×#102D43semidirect
394. C43#26721semidirect

Maximal subgroups

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

subgroupindex
#191389302
#191376072
#191359112
#191357752
#191357392
#191355992
#191355492
#191352712
#191352342
#191352012
#191351662
#191349292
#191349012
#191346842
C4×#102×C432
#2672143