Finite Group Databasebeta

← #25200152

Subgroups — #25200152

Order 11008.

850 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142936C211yesmaximal, characteristic, complemented
2C4×#13063296C211yesmaximal, characteristic
3#19136030C211yesmaximal, characteristic, complemented
4#19135789C211yesmaximal, characteristic, complemented
5#19135782C211yesmaximal, characteristic
6#19135595C211yesmaximal, characteristic
7#19135451C211yesmaximal, characteristic, complemented
8#19135322C211yesmaximal, characteristic, complemented
9#19135280C211yesmaximal, characteristic, complemented
10#19135268C211yesmaximal, characteristic, complemented
11#19135226C211yesmaximal, characteristic, complemented
12#19135181C211yesmaximal, characteristic, complemented
13#19134856C211yesmaximal, characteristic, complemented
14#19134352C211yesmaximal, characteristic, complemented
15C43×#1877C211yesmaximal, characteristic, complemented
16C2×#13063301C2211yescharacteristic
17C2×#13063296C2211yescharacteristic
18C2×C4×C22⋊D43—21no—
19C2×C42×D43C2211yescharacteristic
20C2×#13063257C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×(C2×D43)⋊C8C2211yescharacteristic
28C2×(C2×D43)⋊C8C2211yescharacteristic
29C2×C8×Dic43C2211yescharacteristic
30C2×C8×Dic43C2211yescharacteristic
31#14582806C2211yescharacteristic
32#14582802C2211yescharacteristic
33#14582798C2211yescharacteristic
34#14582797C2211yescharacteristic
35#14582795C2211yescharacteristic
36#14582787—21no—
37#14582782—21no—
38#14582781—21no—
39#14582775—21no—
40#14582773—21no—
41#14582761—21no—
42#14582756C2211yescharacteristic
43#14582756C2211yescharacteristic
44C4×C4⋊Dic43C2211yescharacteristic
45C4×C22⋊Dic43—21no—
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582654C2211yescharacteristic
52C22×SD16×C43C2211yescharacteristic
53C2×C4×D4×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C43×#391C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×C22⋊D43—21no—
60C22×C4×D43D411yescharacteristic
61C22×C4×D43D411yescharacteristic
62C22×C4×D43C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65#13063301—41no—
66#13063301—41no—
67#13063296—22no—
68#13063296—22no—
69C4×C22⋊D43—44no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43D411yescharacteristic
86C2×C4×Dic43D411yescharacteristic
87C2×C4×Dic43C2311yescharacteristic
88C42×D43—41no—
89C42×D43—41no—
90#13063257—22no—
91#13063256—22no—
92#13063256—41no—
93#13063249—22no—
94#13063249—22no—
95#13063246—22no—
96#13063246—41no—
97(C2×D43)⋊C8—22no—
98(C2×D43)⋊C8—22no—
99C8×Dic43—41no—
100C8×Dic43—41no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C22×Q8×C43C2311yescharacteristic
110C22×D4×C43C2311yescharacteristic
111C23×C4×C43—21no—
112C2×SD16×C43—22no—
113C2×SD16×C43—22no—
114C2×SD16×C43—41no—
115C22×C8×C43C2311yescharacteristic
116C22×C8×C43C2311yescharacteristic
117C4×D4×C43—41no—
118C4×D4×C43—41no—
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C22⋊C4×C43—21no—
122C2×C42×C43C2311yescharacteristic
123#103×C43—41no—
124#102×C43—22no—
125#95×C43—21no—
126#95×C43—21no—
127C24×C43—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—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
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—42no—
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2411yescharacteristic
150C2×C22⋊D43—24no—
151C2×C22⋊D43—42no—
152C2×C22⋊D43—42no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43C2×D411yescharacteristic
158C22×Dic43C2×D411yescharacteristic
159C22×Dic43C2×D411yescharacteristic
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165C2×C4×D43—21no—
166C2×C4×D43—22no—
167C2×C4×D43—41no—
168C2×C4×D43—41no—
169C2×C4×D43—41no—
170C2×C4×D43—41no—
171C2×C4×D43SD1614yescomplemented
172SD16×C43—44no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43#4112yes—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C22⋊C4×C43—42no—
184C42×C43—21no—
185C42×C43—21no—
186C22⋊Dic43—24no—
187C22⋊Dic43—42no—
188C22⋊Dic43—42no—
189(C2×D43)⋊C4—42no—
190(C2×D43)⋊C4—42no—
191(C2×D43)⋊C4—42no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—42no—
200C4⋊Dic43#4112yes—
201Dic43⋊C4—42no—
202Dic43⋊C4—42no—
203Dic43⋊C4—42no—
204C4×Dic43—21no—
205C4×Dic43—21no—
206C4×Dic43—41no—
207C4×Dic43—41no—
208C4×Dic43—42no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8#4112yes—
215C23×C43—22no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43C22×D411yescharacteristic
223C22×D43—21no—
224C22×D43—21no—
225C22×D43—21no—
226C22×D43—21no—
227C22×D43—21no—
228C22×D43—21no—
229C22×D43C2×SD1612yes—
230Q8×C43—41no—
231Q8×C43—41no—
232Q8×C43—41no—
233Q8×C43—41no—
234D4×C43—22no—
235D4×C43—22no—
236D4×C43—41no—
237D4×C43—41no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
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—84no—
253C2×C4×C43C2×SD1612yes—
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
260C22⋊D43—48no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—22no—
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×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43C2×SD1612yes—
281C2×Dic43#13512yes—
282C4×D43—44no—
283C4×D43—44no—
284C4×D43—41no—
285C4×D43—41no—
286C4×D43—41no—
287C4×D43—41no—
288C8×C43—22no—
289C8×C43—41no—
290C43⋊C8—22no—
291C43⋊C8—41no—
292#29464—431nomaximal, Sylow
293C22×C43—42no—
294C22×C43—42no—
295C22×C43—42no—
296C22×C43—81no—
297C22×C43—81no—
298C22×C43—81no—
299C22×C43—81no—
300C22×C43#52511yescharacteristic
301C22×C43#53211yescharacteristic
302C22×C43#53411yescharacteristic
303C22×C43C22×SD1611yescharacteristic
304C22×C43C2×#13511yescharacteristic
305C22×C43#57511yescharacteristic
306C22×C43#57511yescharacteristic
307C2×D43—22no—
308C2×D43—22no—
309C2×D43—22no—
310C2×D43—41no—
311C2×D43—41no—
312C2×D43—41no—
313C2×D43—41no—
314C4×C43—22no—
315C4×C43—41no—
316C4×C43—81no—
317C4×C43—81no—
318C4×C43—81no—
319C4×C43#55111yescharacteristic
320C4×C43#55311yescharacteristic
321C4×C43#55311yescharacteristic
322C4×C43#55911yescharacteristic
323Dic43—22no—
324Dic43—22no—
325Dic43—42no—
326Dic43—41no—
327Dic43—81no—
328Dic43—81no—
329Dic43—81no—
330#2855—431no—
331C4×#121—431no—
332#2077—431no—
333#2035—431no—
334#2034—431no—
335#2000—431no—
336#1968—431no—
337#1941—431no—
338#1934—431no—
339#1933—431no—
340#1927—431no—
341#1920—431no—
342#1877D4311yescharacteristic, complemented
343#1864—431no—
344C4×C22⋊C8—431no—
345C2×C43—82no—
346C2×C43#260211yescharacteristic
347C2×C43#310111yescharacteristic
348C2×C43#310211yescharacteristic
349C2×C43#316711yescharacteristic
350C2×C43#318311yescharacteristic
351C2×C43#318711yescharacteristic
352C2×C43#319111yescharacteristic
353D43—42no—
354C22×SD16C2×D4311yescharacteristic
355C2×C22⋊Q8—431no—
356C2×#121—431no—
357C2×C4×D4—861no—
358C2×C4×D4C2×D4311yescharacteristic
359C22×C42—431no—
360C2×#106—431no—
361C2×#106—431no—
362C2×#106—431no—
363C2×#103—431no—
364C2×#103—431no—
365C2×#103C2×D4311yescharacteristic
366C2×#102—431no—
367C2×#102—431no—
368C2×#102C2×D4311yescharacteristic
369C2×C22⋊C8—431no—
370C2×C22⋊C8—431no—
371C2×C4×C8—431no—
372C2×C4×C8—431no—
373#391—431no—
374#391C2×D4311yescharacteristic
375#390—431no—
376#389—431no—
377#389—431no—
378#389—431no—
379#388—861no—
380#387—861no—
381#387—861no—
382#386—861no—
383#385—861no—
384#381—861no—
385#380—431no—
386#380—431no—
387C4×C4⋊C4—431no—
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#336C2×D4311yescharacteristic
397C43#2946411yescharacteristic, complemented, Sylow
398C22×Q8C22×D4311yescharacteristic
399C22×D4—861no—
400C22×D4C22×D4311yescharacteristic
401C23×C4—21no—
402C23×C4—431no—
403C23×C4—431no—
404C23×C4—431no—
405C2×SD16—22no—
406C2×SD16—22no—
407C2×SD16—41no—
408C22×C8—431no—
409C22×C8—431no—
410C22×C8C22×D4311yescharacteristic
411C22×C8C22×D4311yescharacteristic
412C22⋊Q8—1721no—
413C22⋊Q8—1721no—
414#121—862no—
415#121—862no—
416C4×D4—41no—
417C4×D4—41no—
418C4×D4—1724no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4C22×D4311yescharacteristic
428C2×C4⋊C4C22×D4311yescharacteristic
429C2×C22⋊C4—21no—
430C2×C22⋊C4—861no—
431C2×C22⋊C4—861no—
432C2×C22⋊C4—861no—
433C2×C22⋊C4—861no—
434C2×C22⋊C4—861no—
435C2×C22⋊C4—861no—
436C2×C42—431no—
437C2×C42—431no—
438C2×C42—431no—
439C2×C42—861no—
440C2×C42—1721no—
441C2×C42—1721no—
442C2×C42C22×D4311yescharacteristic
443#106—862no—
444#106—862no—
445#106—1721no—
446#103—41no—
447#103—862no—
448#103—862no—
449#102—22no—
450#102—862no—
451#102—1721no—
452C22⋊C8—862no—
453C22⋊C8—862no—
454C4×C8—1721no—
455C4×C8—1721no—
456#95—21no—
457#95—21no—
458#95—861no—
459#95—861no—
460#95—861no—
461#95—861no—
462#95—861no—
463#95—861no—
464#95—861no—
465#95—861no—
466C24—21no—
467C24—431no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—864no—
480C2×D4—1722no—
481C2×D4—1722no—
482C2×D4#1062190012yes—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—431no—
490C22×C4—431no—
491C22×C4—434no—
492C22×C4—431no—
493C22×C4—862no—
494C22×C4—861no—
495C22×C4—861no—
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—1721no—
508C22×C4D4×D4311yescharacteristic
509C22×C4D4×D4311yescharacteristic
510C22×C4C23×D4311yescharacteristic
511SD16—44no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—432no—
518C2×C8—861no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—861no—
523C2×C8#1062189812yes—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—432no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—861no—
533C4⋊C4—861no—
534C4⋊C4—861no—
535C4⋊C4—861no—
536C4⋊C4—1722no—
537C4⋊C4—1722no—
538C4⋊C4—1722no—
539C4⋊C4—1722no—
540C22⋊C4—42no—
541C22⋊C4—864no—
542C22⋊C4—1722no—
543C22⋊C4—1722no—
544C22⋊C4—1722no—
545C22⋊C4—1722no—
546C22⋊C4—1722no—
547C42—21no—
548C42—21no—
549C42—861no—
550C42—861no—
551C42—1721no—
552C42—1721no—
553C42—1722no—
554C23—22no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—432no—
562C23—861no—
563C23—861no—
564C23—861no—
565C23—861no—
566C23—861no—
567C23—861no—
568C23C2×D4×D4311yescharacteristic
569Q8—41no—
570Q8—41no—
571Q8—41no—
572Q8—41no—
573D4—22no—
574D4—22no—
575D4—41no—
576D4—41no—
577D4—1728no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—84no—
593C2×C4—432no—
594C2×C4—432no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—862no—
601C2×C4—861no—
602C2×C4—861no—
603C2×C4—1724no—
604C2×C4—1724no—
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—1721no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4—1721no—
620C2×C4SD16×D4312yes—
621C2×C4#41×D4311yescharacteristic
622C2×C4#41×D4311yescharacteristic
623C2×C4C2×#1062190011yescharacteristic
624C2×C4C2×#1062189811yescharacteristic
625C2×C4#1306337011yescharacteristic
626C2×C4#1306337011yescharacteristic
627C8—22no—
628C8—41no—
629C8—862no—
630C8—1721no—
631C22—42no—
632C22—42no—
633C22—42no—
634C22—81no—
635C22—81no—
636C22—81no—
637C22—81no—
638C22—862no—
639C22—862no—
640C22—862no—
641C22—1721no—
642C22—1721no—
643C22—1721no—
644C22—1721no—
645C22#1458340911yescharacteristic
646C22#1458344611yescharacteristic
647C22#1458345911yescharacteristic
648C22C2×SD16×D4311yescharacteristic
649C22#135×D4311yescharacteristic
650C22#1458369511yescharacteristic
651C22#1458369811yescharacteristic
652C4—22no—
653C4—41no—
654C4—81no—
655C4—81no—
656C4—81no—
657C4—862no—
658C4—862no—
659C4—3441no—
660C4—3441no—
661C4—3441no—
662C4—1721no—
663C4—1722no—
664C4#1458357511yescharacteristic
665C4#1458359211yescharacteristic
666C4#1458359411yescharacteristic
667C4#1458363211yescharacteristic
668C2—82no—
669C2—1722no—
670C2#1914020311yescharacteristic
671C2#1914460211yescharacteristic
672C2#1914461011yescharacteristic
673C2#1914515111yescharacteristic
674C2#1914532011yescharacteristic
675C2#1914534911yescharacteristic
676C2#1914538711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1877C2
socleC23×C43C22×D4
prime radicalC2×#13063296C22
hypercenter#1877D43
hypocenterC43#29464
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1877

Complements

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

NH ≅ G/Ntype
1. #19142936C2semidirect
3. #19136030C2semidirect
4. #19135789C2semidirect
7. #19135451C2semidirect
8. #19135322C2semidirect
9. #19135280C2semidirect
10. #19135268C2semidirect
11. #19135226C2semidirect
12. #19135181C2semidirect
13. #19134856C2semidirect
14. #19134352C2semidirect
15. C43×#1877C2semidirect
171. C2×C4×D43SD16semidirect
342. #1877D43semidirect
397. C43#29464semidirect

Maximal subgroups

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

subgroupindex
#191429362
C4×#130632962
#191360302
#191357892
#191357822
#191355952
#191354512
#191353222
#191352802
#191352682
#191352262
#191351812
#191348562
#191343522
C43×#18772
#2946443