Finite Group Databasebeta

← #25126536

Subgroups — #25126536

Order 11008.

858 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#389×D43C211yesmaximal, characteristic
2#19137001C211yesmaximal, characteristic
3#19136164C211yesmaximal, characteristic, complemented
4#19136163C211yesmaximal, characteristic, complemented
5#19136162C211yesmaximal, characteristic, complemented
6#19136161C211yesmaximal, characteristic, complemented
7#19136160C211yesmaximal, characteristic, complemented
8#19136156C211yesmaximal, characteristic, complemented
9#19136155C211yesmaximal, characteristic, complemented
10#19134313C211yesmaximal, characteristic
11#19134313C211yesmaximal, characteristic
12#19134313C211yesmaximal, characteristic
13#19134313C211yesmaximal, characteristic
14#19134287C211yesmaximal, characteristic
15C43×#2101C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C2×#13063283C2211yescharacteristic
19C2×#13063283C2211yescharacteristic
20C2×C4⋊C4×D43—21no—
21C2×C4⋊C4×D43C2211yescharacteristic
22C2×C4⋊C4×D43C2211yescharacteristic
23C2×C42×D43C2211yescharacteristic
24#14582798C2211yescharacteristic
25#14582797C2211yescharacteristic
26#14582796—21no—
27#14582795C2211yescharacteristic
28#14582794—21no—
29#14582768C2211yescharacteristic
30#14582768C2211yescharacteristic
31#14582765C2211yescharacteristic
32#14582758—21no—
33#14582758—21no—
34#14582750—21no—
35#14582750—21no—
36#95×D43—21no—
37#14582662C2211yescharacteristic
38#14582662C2211yescharacteristic
39#14582662C2211yescharacteristic
40#14582662C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C43×#389C2211yescharacteristic
53C43×#382C2211yescharacteristic
54C43×#340C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×C4×D43—21no—
60C22×C4×D43—21no—
61C22×C4×D43D411yescharacteristic
62C22×C4×D43D411yescharacteristic
63C22×C4×D43C2311yescharacteristic
64C2×#10621872—22no—
65C2×#10621872—22no—
66C2×#10621872—22no—
67C2×#10621872—22no—
68C2×#10621872—22no—
69C2×#10621872—22no—
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72#13063283—22no—
73#13063283—22no—
74#13063283—22no—
75#13063283—22no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C4⋊C4×D43—22no—
90C4⋊C4×D43—22no—
91C4⋊C4×D43—22no—
92C4⋊C4×D43—44no—
93C4⋊C4×D43Q814yes—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×C4×Dic43—21no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43D411yescharacteristic
99C2×C4×Dic43D411yescharacteristic
100C2×C4×Dic43C2311yescharacteristic
101C42×D43—22no—
102C42×D43—22no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C22×C8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C42×C43C2311yescharacteristic
116#95×C43—21no—
117#95×C43—21no—
118#95×C43—21no—
119C23×D43C2×D411yescharacteristic
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2411yescharacteristic
127C22×Dic43—21no—
128C22×Dic43—21no—
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43C2×D411yescharacteristic
132C22×Dic43C2×D411yescharacteristic
133C22×Dic43C2×D411yescharacteristic
134C2×C4×D43—22no—
135C2×C4×D43—22no—
136C2×C4×D43—24no—
137C2×C4×D43—22no—
138C2×C4×D43—22no—
139C2×C4×D43—41no—
140C2×C4×D43—41no—
141C2×C4×D43—42no—
142C2×C4×D43—42no—
143C2×C4×D43—42no—
144C2×C4×D43—42no—
145C2×C4×D43—42no—
146C2×C4×D43C2×Q812yes—
147C2×C4×D43#4112yes—
148C2×C4×D43#4112yes—
149C2×C4×D43#4112yes—
150C2×C4×D43#4112yes—
151C2×C4×D43#4112yes—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—42no—
166C4⋊C4×C43C2×Q812yes—
167C42×C43—21no—
168C42×C43—21no—
169(C2×D43)⋊C4—42no—
170(C2×D43)⋊C4—42no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—42no—
179C4⋊Dic43C2×Q812yes—
180Dic43⋊C4—24no—
181Dic43⋊C4—42no—
182Dic43⋊C4—42no—
183Dic43⋊C4—42no—
184Dic43⋊C4—42no—
185Dic43⋊C4—42no—
186Dic43⋊C4—42no—
187Dic43⋊C4—42no—
188C4×Dic43—21no—
189C4×Dic43—21no—
190C4×Dic43—22no—
191C4×Dic43—22no—
192C4×Dic43—42no—
193C4×Dic43—42no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200#10621872—44no—
201#10621872—44no—
202C23×C43C22×D411yescharacteristic
203C22×D43—21no—
204C22×D43—21no—
205C22×D43—21no—
206C22×D43—21no—
207C22×D43C22⋊Q812yes—
208C22×D43#12312yes—
209C22×D43#12412yes—
210C2×C4×C43—22no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43C22×Q811yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—22no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43C22⋊Q812yes—
251C2×Dic43#12312yes—
252C2×Dic43#12412yes—
253C2×Dic43AGL(1,ℤ/8)12yes—
254C2×Dic43#13712yes—
255C4×D43—44no—
256C4×D43—44no—
257C4×D43—48no—
258C4×D43—84no—
259C4×D43#12514yes—
260C4×D43#12514yes—
261C4×D43#12614yes—
262C4×D43#12614yes—
263C8×C43—41no—
264C8×C43—41no—
265C43⋊C8—41no—
266C43⋊C8—41no—
267#23747—431nomaximal, Sylow
268C22×C43C2×C22⋊Q811yescharacteristic
269C22×C43C2×#12311yescharacteristic
270C22×C43C2×#12411yescharacteristic
271C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
272C22×C43C2×#13711yescharacteristic
273C22×C43#57511yescharacteristic
274C22×C43#57511yescharacteristic
275C2×D43—22no—
276C2×D43—22no—
277C2×D43—22no—
278C2×D43—22no—
279C2×D43—22no—
280C2×D43—22no—
281C2×D43#40014yes—
282C4×C43—42no—
283C4×C43—41no—
284C4×C43—41no—
285C4×C43—81no—
286C4×C43—81no—
287C4×C43—81no—
288C4×C43C2×#12511yescharacteristic
289C4×C43C2×#12511yescharacteristic
290C4×C43C2×#12611yescharacteristic
291C4×C43C2×#12611yescharacteristic
292Dic43—22no—
293Dic43—22no—
294Dic43—42no—
295Dic43—81no—
296Dic43—81no—
297Dic43—81no—
298Dic43#40014yes—
299C2×#389—431no—
300#2285—431no—
301#2101—431no—
302#2101—431no—
303#2101—431no—
304#2101D4311yescharacteristic, complemented
305#2100—431no—
306#2100—431no—
307#2099—431no—
308#2099—431no—
309#1736—431no—
310#1736—431no—
311#1736—431no—
312#1736—431no—
313#1728—431no—
314C2×C43C2×#40011yescharacteristic
315C2×C43#307711yescharacteristic
316C2×C43#307811yescharacteristic
317C2×C43#309411yescharacteristic
318C2×C43#309511yescharacteristic
319C2×C43#314111yescharacteristic
320C2×C43#314211yescharacteristic
321D43—24no—
322C22×M16—431no—
323C22×M16—431no—
324C2×#117—431no—
325C2×#117—431no—
326C22×C4⋊C4—431no—
327C22×C4⋊C4—431no—
328C22×C4⋊C4—861no—
329C22×C42—431no—
330#389—431no—
331#389—431no—
332#389—431no—
333#389—861no—
334#389—861no—
335#389C2×D4311yescharacteristic
336#384—431no—
337#384—431no—
338#382—431no—
339#382C2×D4311yescharacteristic
340#380—861no—
341#380—861no—
342C4×C4⋊C4—861no—
343C4×C4⋊C4—861no—
344C2×#95—861no—
345#340—431no—
346#340—431no—
347#340—431no—
348#340—431no—
349#340—431no—
350#340—431no—
351#340—431no—
352#340—431no—
353#340—431no—
354#340—431no—
355#340—431no—
356#340—431no—
357#340C2×D4311yescharacteristic
358#340C2×D4311yescharacteristic
359#340C2×D4311yescharacteristic
360#340C2×D4311yescharacteristic
361#336—431no—
362#336—431no—
363#336—431no—
364#336C2×D4311yescharacteristic
365C43#2374711yescharacteristic, complemented, Sylow
366C23×C4—431no—
367C23×C4—431no—
368C23×C4—431no—
369C23×C4—861no—
370C23×C4—861no—
371C2×M16—862no—
372C2×M16—862no—
373C2×M16—862no—
374C2×M16—862no—
375C2×M16—862no—
376C2×M16—862no—
377C22×C8—431no—
378C22×C8—431no—
379C22×C8C22×D4311yescharacteristic
380C22×C8C22×D4311yescharacteristic
381#117—862no—
382#117—862no—
383#117—862no—
384#117—862no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—431no—
387C2×C4⋊C4—434no—
388C2×C4⋊C4—431no—
389C2×C4⋊C4—431no—
390C2×C4⋊C4—431no—
391C2×C4⋊C4—862no—
392C2×C4⋊C4—862no—
393C2×C4⋊C4—862no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4—1724no—
404C2×C4⋊C4C22×D4311yescharacteristic
405C2×C4⋊C4C22×D4311yescharacteristic
406C2×C4⋊C4C22×D4311yescharacteristic
407C2×C4⋊C4C22×D4311yescharacteristic
408C2×C22⋊C4—861no—
409C2×C22⋊C4—861no—
410C2×C42—431no—
411C2×C42—431no—
412C2×C42—431no—
413C2×C42—862no—
414C2×C42—862no—
415C2×C42—861no—
416C2×C42—861no—
417C2×C42C22×D4311yescharacteristic
418#95—21no—
419#95—21no—
420#95—21no—
421#95—861no—
422#95—861no—
423#95—861no—
424#95—861no—
425#95—861no—
426C24—431no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—431no—
432C22×C4—432no—
433C22×C4—432no—
434C22×C4—432no—
435C22×C4—432no—
436C22×C4—432no—
437C22×C4—432no—
438C22×C4—431no—
439C22×C4—431no—
440C22×C4—862no—
441C22×C4—862no—
442C22×C4—862no—
443C22×C4—862no—
444C22×C4—864no—
445C22×C4—861no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4—861no—
449C22×C4—1721no—
450C22×C4—1721no—
451C22×C4—1722no—
452C22×C4—1722no—
453C22×C4—1722no—
454C22×C4—1722no—
455C22×C4—1722no—
456C22×C4D4×D4311yescharacteristic
457C22×C4D4×D4311yescharacteristic
458C22×C4C23×D4311yescharacteristic
459M16—1724no—
460M16—1724no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—861no—
468C2×C8—861no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8—861no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—42no—
481C4⋊C4—432no—
482C4⋊C4—864no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—1722no—
491C4⋊C4—1722no—
492C4⋊C4—1722no—
493C4⋊C4—1722no—
494C4⋊C4—1722no—
495C4⋊C4—1722no—
496C4⋊C4—1722no—
497C4⋊C4—1722no—
498C4⋊C4Q8×D4312yes—
499C22⋊C4—1722no—
500C22⋊C4—1722no—
501C42—21no—
502C42—21no—
503C42—862no—
504C42—862no—
505C42—861no—
506C42—861no—
507C42—1722no—
508C42—1722no—
509C23—432no—
510C23—432no—
511C23—432no—
512C23—861no—
513C23—861no—
514C23—861no—
515C23—861no—
516C23C2×D4×D4311yescharacteristic
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—432no—
536C2×C4—432no—
537C2×C4—432no—
538C2×C4—434no—
539C2×C4—434no—
540C2×C4—434no—
541C2×C4—434no—
542C2×C4—432no—
543C2×C4—432no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—861no—
548C2×C4—862no—
549C2×C4—3444no—
550C2×C4—1724no—
551C2×C4—1724no—
552C2×C4—1728no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4C2×Q8×D4311yescharacteristic
565C2×C4#41×D4311yescharacteristic
566C2×C4#41×D4311yescharacteristic
567C2×C4#41×D4311yescharacteristic
568C2×C4#41×D4311yescharacteristic
569C2×C4#41×D4311yescharacteristic
570C8—41no—
571C8—41no—
572C8—1721no—
573C8—1721no—
574C22—434no—
575C22—862no—
576C22—862no—
577C22—862no—
578C22—862no—
579C22—862no—
580C22—862no—
581C22C22⋊Q8×D4311yescharacteristic
582C22#123×D4311yescharacteristic
583C22#124×D4311yescharacteristic
584C22AGL(1,ℤ/8)×D4311yescharacteristic
585C22#137×D4311yescharacteristic
586C22#1458369611yescharacteristic
587C22#1458369611yescharacteristic
588C4—41no—
589C4—41no—
590C4—42no—
591C4—81no—
592C4—81no—
593C4—81no—
594C4—434no—
595C4—862no—
596C4—862no—
597C4—3441no—
598C4—3441no—
599C4—3441no—
600C4—1722no—
601C4#125×D4311yescharacteristic
602C4#125×D4311yescharacteristic
603C4#126×D4311yescharacteristic
604C4#126×D4311yescharacteristic
605C2—864no—
606C2#400×D4311yescharacteristic
607C2#1914439011yescharacteristic
608C2#1914439811yescharacteristic
609C2#1914453411yescharacteristic
610C2#1914454211yescharacteristic
611C2#1914498711yescharacteristic
612C2#1914499211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2101C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#2101D43
hypocenterC43#23747
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2101

Complements

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

NH ≅ G/Ntype
3. #19136164C2semidirect
4. #19136163C2semidirect
5. #19136162C2semidirect
6. #19136161C2semidirect
7. #19136160C2semidirect
8. #19136156C2semidirect
9. #19136155C2semidirect
15. C43×#2101C2semidirect
304. #2101D43semidirect
365. C43#23747semidirect

Maximal subgroups

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

subgroupindex
#389×D432
#191370012
#191361642
#191361632
#191361622
#191361612
#191361602
#191361562
#191361552
#191343132
#191342872
C43×#21012
#2374743