Finite Group Databasebeta

← #25200182

Subgroups — #25200182

Order 11008.

828 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142925C211yesmaximal, characteristic
2C4×#13063301C211yesmaximal, characteristic, complemented
3#19136030C211yesmaximal, characteristic, complemented
4#19135789C211yesmaximal, characteristic, complemented
5#19135782C211yesmaximal, characteristic
6#19135595C211yesmaximal, characteristic
7#19135451C211yesmaximal, characteristic, complemented
8#19135322C211yesmaximal, characteristic, complemented
9#19135275C211yesmaximal, characteristic, complemented
10#19135273C211yesmaximal, characteristic, complemented
11#19135219C211yesmaximal, characteristic, complemented
12#19135174C211yesmaximal, characteristic, complemented
13#19134863C211yesmaximal, characteristic, complemented
14#19134352C211yesmaximal, characteristic, complemented
15C43×#1880C211yesmaximal, characteristic, complemented
16C2×#13063307—21no—
17C2×#13063301C2211yescharacteristic
18C2×#13063296C2211yescharacteristic
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#14582793—21no—
37#14582792—21no—
38#14582780—21no—
39#14582775—21no—
40#14582770—21no—
41#14582756C2211yescharacteristic
42#14582756C2211yescharacteristic
43C4×Dic43⋊C4—21no—
44C4×C4⋊Dic43C2211yescharacteristic
45C4×(C2×D43)⋊C4—21no—
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582654C2211yescharacteristic
52C22×SD16×C43C2211yescharacteristic
53C2×C4×Q8×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C43×#390C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×C22⋊D43—21no—
60C22×C4×D43D411yescharacteristic
61C22×C4×D43D411yescharacteristic
62C22×C4×D43C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65#13063307—44no—
66#13063301—22no—
67#13063301—22no—
68#13063296—41no—
69#13063296—41no—
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—41no—
95#13063246—22no—
96#13063246—22no—
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
111C2×SD16×C43—22no—
112C2×SD16×C43—22no—
113C2×SD16×C43—41no—
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C4×Q8×C43—41no—
117C4×Q8×C43—41no—
118C2×C4⋊C4×C43—21no—
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C22⋊C4×C43—21no—
122C2×C22⋊C4×C43—21no—
123C2×C42×C43—21no—
124C2×C42×C43C2311yescharacteristic
125#103×C43—22no—
126#102×C43—41no—
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#4112yes—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2411yescharacteristic
147C2×C22⋊D43—42no—
148C2×C22⋊D43—42no—
149C2×C22⋊D43—42no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156C22×Dic43C2×D411yescharacteristic
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×C4×D43—21no—
163C2×C4×D43—22no—
164C2×C4×D43—41no—
165C2×C4×D43—41no—
166C2×C4×D43—41no—
167C2×C4×D43—41no—
168C2×C4×D43SD1614yescomplemented
169SD16×C43—44no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43#4112yes—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—42no—
181C22⋊C4×C43—42no—
182C22⋊C4×C43—42no—
183C42×C43—21no—
184C42×C43—21no—
185C42×C43—42no—
186C22⋊Dic43—42no—
187C22⋊Dic43—42no—
188C22⋊Dic43—42no—
189(C2×D43)⋊C4—24no—
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—24no—
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—41no—
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—22no—
231Q8×C43—22no—
232Q8×C43—41no—
233Q8×C43—41no—
234D4×C43—41no—
235D4×C43—41no—
236D4×C43—41no—
237D4×C43—41no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—22no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
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×C43C2×SD1612yes—
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43H(5,𝔽2)11yescharacteristic
258C2×C4×C43H(5,𝔽2)11yescharacteristic
259C22⋊D43—84no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—22no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—41no—
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×Dic43C2×SD1612yes—
280C2×Dic43#13512yes—
281C4×D43—44no—
282C4×D43—44no—
283C4×D43—41no—
284C4×D43—41no—
285C4×D43—41no—
286C4×D43—41no—
287C8×C43—22no—
288C8×C43—41no—
289C43⋊C8—22no—
290C43⋊C8—41no—
291#29466—431nomaximal, Sylow
292C22×C43—81no—
293C22×C43—81no—
294C22×C43—81no—
295C22×C43—81no—
296C22×C43—81no—
297C22×C43—81no—
298C22×C43—81no—
299C22×C43#52511yescharacteristic
300C22×C43#53211yescharacteristic
301C22×C43#53411yescharacteristic
302C22×C43C22×SD1611yescharacteristic
303C22×C43C2×#13511yescharacteristic
304C22×C43#57511yescharacteristic
305C22×C43#57511yescharacteristic
306C2×D43—22no—
307C2×D43—22no—
308C2×D43—22no—
309C2×D43—41no—
310C2×D43—41no—
311C2×D43—41no—
312C2×D43—41no—
313C4×C43—22no—
314C4×C43—42no—
315C4×C43—41no—
316C4×C43—81no—
317C4×C43—81no—
318C4×C43#55111yescharacteristic
319C4×C43#55311yescharacteristic
320C4×C43#55311yescharacteristic
321C4×C43#55911yescharacteristic
322Dic43—22no—
323Dic43—22no—
324Dic43—42no—
325Dic43—41no—
326Dic43—81no—
327Dic43—81no—
328Dic43—81no—
329#2854—431no—
330C4×C22⋊Q8—431no—
331#2077—431no—
332#2035—431no—
333#2034—431no—
334#2000—431no—
335#1968—431no—
336#1941—431no—
337#1934—431no—
338#1933—431no—
339#1926—431no—
340#1919—431no—
341#1880D4311yescharacteristic, complemented
342#1865—431no—
343C4×C22⋊C8—431no—
344C2×C43—161no—
345C2×C43#260211yescharacteristic
346C2×C43#310211yescharacteristic
347C2×C43#310311yescharacteristic
348C2×C43#316711yescharacteristic
349C2×C43#318311yescharacteristic
350C2×C43#318711yescharacteristic
351C2×C43#319111yescharacteristic
352D43—42no—
353C22×SD16C2×D4311yescharacteristic
354C2×#123—861no—
355C2×C22⋊Q8—431no—
356C2×#121—431no—
357C2×C4×Q8C2×D4311yescharacteristic
358C22×C42—431no—
359C2×#106—431no—
360C2×#106—431no—
361C2×#106—431no—
362C2×#103—431no—
363C2×#103—431no—
364C2×#103C2×D4311yescharacteristic
365C2×#102—431no—
366C2×#102—431no—
367C2×#102C2×D4311yescharacteristic
368C2×C22⋊C8—431no—
369C2×C22⋊C8—431no—
370C2×C4×C8—431no—
371C2×C4×C8—431no—
372#391—431no—
373#390—431no—
374#390C2×D4311yescharacteristic
375#389—431no—
376#389—431no—
377#389—431no—
378#388—861no—
379#388—861no—
380#387—861no—
381#386—861no—
382#385—861no—
383#380—431no—
384#380—431no—
385C4×C4⋊C4—431no—
386C4×C4⋊C4—861no—
387C4×C22⋊C4—861no—
388#340—431no—
389#340—431no—
390#340—431no—
391#340—431no—
392#340—431no—
393#340C2×D4311yescharacteristic
394#336—431no—
395#336C2×D4311yescharacteristic
396C43#2946611yescharacteristic, complemented, Sylow
397C22×Q8C22×D4311yescharacteristic
398C22×D4—861no—
399C22×D4C22×D4311yescharacteristic
400C23×C4—431no—
401C23×C4—431no—
402C23×C4—431no—
403C2×SD16—22no—
404C2×SD16—22no—
405C2×SD16—41no—
406C22×C8—431no—
407C22×C8—431no—
408C22×C8C22×D4311yescharacteristic
409C22×C8C22×D4311yescharacteristic
410#123—1724no—
411C22⋊Q8—862no—
412C22⋊Q8—862no—
413#121—1721no—
414#121—1721no—
415C4×Q8—41no—
416C4×Q8—41no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4C22×D4311yescharacteristic
427C2×C4⋊C4C22×D4311yescharacteristic
428C2×C22⋊C4—21no—
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—21no—
437C2×C42—431no—
438C2×C42—431no—
439C2×C42—431no—
440C2×C42—861no—
441C2×C42—1721no—
442C2×C42—1721no—
443C2×C42C22×D4311yescharacteristic
444#106—862no—
445#106—862no—
446#106—1721no—
447#103—22no—
448#103—862no—
449#103—1721no—
450#102—41no—
451#102—862no—
452#102—862no—
453C22⋊C8—862no—
454C22⋊C8—862no—
455C4×C8—1721no—
456C4×C8—1721no—
457#95—861no—
458#95—861no—
459#95—861no—
460#95—861no—
461#95—861no—
462#95—861no—
463#95—861no—
464#95—861no—
465C24—21no—
466C24—431no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8#1062190012yes—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—1722no—
480C2×D4—1722no—
481C2×D4—1722no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—431no—
486C22×C4—431no—
487C22×C4—434no—
488C22×C4—431no—
489C22×C4—862no—
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—861no—
500C22×C4—1721no—
501C22×C4—1721no—
502C22×C4—1721no—
503C22×C4—1721no—
504C22×C4D4×D4311yescharacteristic
505C22×C4D4×D4311yescharacteristic
506C22×C4C23×D4311yescharacteristic
507SD16—44no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—432no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8#1062189812yes—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—42no—
525C4⋊C4—432no—
526C4⋊C4—864no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—861no—
533C4⋊C4—861no—
534C4⋊C4—1722no—
535C4⋊C4—1722no—
536C4⋊C4—1722no—
537C22⋊C4—42no—
538C22⋊C4—42no—
539C22⋊C4—864no—
540C22⋊C4—1722no—
541C22⋊C4—1722no—
542C22⋊C4—1722no—
543C22⋊C4—1722no—
544C22⋊C4—1722no—
545C42—21no—
546C42—21no—
547C42—42no—
548C42—861no—
549C42—861no—
550C42—1721no—
551C42—1721no—
552C42—1722no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—432no—
561C23—861no—
562C23—861no—
563C23—861no—
564C23—861no—
565C23—861no—
566C23—861no—
567C23C2×D4×D4311yescharacteristic
568Q8—22no—
569Q8—22no—
570Q8—41no—
571Q8—41no—
572D4—41no—
573D4—41no—
574D4—41no—
575D4—41no—
576D4—3444no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
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—432no—
592C2×C4—432no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—862no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—1724no—
602C2×C4—1724no—
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—1721no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4SD16×D4312yes—
619C2×C4#41×D4311yescharacteristic
620C2×C4#41×D4311yescharacteristic
621C2×C4C2×#1062190011yescharacteristic
622C2×C4C2×#1062189811yescharacteristic
623C2×C4#1306337011yescharacteristic
624C2×C4#1306337011yescharacteristic
625C8—22no—
626C8—41no—
627C8—862no—
628C8—1721no—
629C22—81no—
630C22—81no—
631C22—81no—
632C22—81no—
633C22—81no—
634C22—81no—
635C22—81no—
636C22—862no—
637C22—862no—
638C22—862no—
639C22—1721no—
640C22—1721no—
641C22—1721no—
642C22—1721no—
643C22#1458340911yescharacteristic
644C22#1458344611yescharacteristic
645C22#1458345911yescharacteristic
646C22C2×SD16×D4311yescharacteristic
647C22#135×D4311yescharacteristic
648C22#1458369511yescharacteristic
649C22#1458369811yescharacteristic
650C4—22no—
651C4—42no—
652C4—41no—
653C4—81no—
654C4—81no—
655C4—862no—
656C4—862no—
657C4—3441no—
658C4—3441no—
659C4—3441no—
660C4—1721no—
661C4—1722no—
662C4#1458357511yescharacteristic
663C4#1458359211yescharacteristic
664C4#1458359411yescharacteristic
665C4#1458363211yescharacteristic
666C2—161no—
667C2—1722no—
668C2#1914020311yescharacteristic
669C2#1914461211yescharacteristic
670C2#1914462511yescharacteristic
671C2#1914515111yescharacteristic
672C2#1914532011yescharacteristic
673C2#1914535011yescharacteristic
674C2#1914538511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1880C2
socleC23×C43C22×D4
prime radicalC2×#13063296C22
hypercenter#1880D43
hypocenterC43#29466
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. C4×#13063301C2semidirect
3. #19136030C2semidirect
4. #19135789C2semidirect
7. #19135451C2semidirect
8. #19135322C2semidirect
9. #19135275C2semidirect
10. #19135273C2semidirect
11. #19135219C2semidirect
12. #19135174C2semidirect
13. #19134863C2semidirect
14. #19134352C2semidirect
15. C43×#1880C2semidirect
168. C2×C4×D43SD16semidirect
341. #1880D43semidirect
396. C43#29466semidirect

Maximal subgroups

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

subgroupindex
#191429252
C4×#130633012
#191360302
#191357892
#191357822
#191355952
#191354512
#191353222
#191352752
#191352732
#191352192
#191351742
#191348632
#191343522
C43×#18802
#2946643