Finite Group Databasebeta

← #25196775

Subgroups — #25196775

Order 11008.

720 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#19140430C211yesmaximal, characteristic
2#19137278C211yesmaximal, characteristic
3#19136161C211yesmaximal, characteristic, complemented
4#19136135C211yesmaximal, characteristic, complemented
5#19135932C211yesmaximal, characteristic, complemented
6#19135745C211yesmaximal, characteristic, complemented
7#19135180C211yesmaximal, characteristic, complemented
8#19135027C211yesmaximal, characteristic
9#19135017C211yesmaximal, characteristic
10#19134866C211yesmaximal, characteristic, complemented
11#19134848C211yesmaximal, characteristic, complemented
12#19134627C211yesmaximal, characteristic
13#19134617C211yesmaximal, characteristic
14#19134290C211yesmaximal, characteristic
15C43×#1919C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C2×#13063316C2211yescharacteristic
19C2×#13063305C2211yescharacteristic
20C2×C4×Dic86C2211yescharacteristic
21C2×#13063282C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063257C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29#14582833—21no—
30#14582830—21no—
31#14582823—21no—
32#14582821—21no—
33#14582804C2211yescharacteristic
34#14582798C2211yescharacteristic
35#14582797—21no—
36#14582797C2211yescharacteristic
37#14582791—21no—
38#14582790—21no—
39#14582784—21no—
40#14582768C2211yescharacteristic
41#14582756C2211yescharacteristic
42#14582756C2211yescharacteristic
43#14582756C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#106×C43C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C4×C4⋊C4×C43C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×C4×D43C2311yescharacteristic
61C2×#10621872—22no—
62C2×#10621872—22no—
63C2×#10621872—41no—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C2×C8×D43—22no—
67C2×C8×D43—22no—
68C2×C8×D43—41no—
69#13063316—41no—
70#13063316—41no—
71#13063305—22no—
72#13063305Q814yes—
73C4×Dic86—41no—
74C4×Dic86—41no—
75#13063282—41no—
76#13063282—41no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4D411yescharacteristic
89C2×Dic43⋊C4D411yescharacteristic
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4D411yescharacteristic
95C2×(C2×D43)⋊C4D411yescharacteristic
96C2×C4×Dic43—21no—
97C2×C4×Dic43C2311yescharacteristic
98#13063258—41no—
99#13063257—41no—
100#13063256—22no—
101#13063250—22no—
102#13063250—41no—
103#13063248—22no—
104#13063248—41no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C2×C4⋊C4×C43—21no—
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C42×C43—21no—
120C2×C42×C43C2311yescharacteristic
121#106×C43—22no—
122#95×C43—21no—
123#95×C43—21no—
124C23×D43C2×D411yescharacteristic
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2411yescharacteristic
132C22×Dic43—21no—
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43C2×D411yescharacteristic
137C22×Dic43C2×D411yescharacteristic
138C22×Dic43C2×D411yescharacteristic
139C2×C4×D43—21no—
140C2×C4×D43—21no—
141C2×C4×D43—21no—
142C2×C4×D43—21no—
143C2×C4×D43C2×Q812yes—
144C2×C4×D43#4112yes—
145C2×Dic86—21no—
146C2×Dic86—21no—
147C2×Dic86—21no—
148C2×Dic86—21no—
149C2×Dic86—21no—
150C2×Dic86C2×Q812yes—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43#4112yes—
157C4⋊C4×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—81no—
165C4⋊C4×C43C2×Q812yes—
166C42×C43—21no—
167C42×C43—21no—
168C42×C43—81no—
169(C2×D43)⋊C4—24no—
170(C2×D43)⋊C4—41no—
171(C2×D43)⋊C4—41no—
172(C2×D43)⋊C4—81no—
173(C2×D43)⋊C4—81no—
174(C2×D43)⋊C4—81no—
175C4⋊Dic43—24no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—42no—
183C4⋊Dic43—81no—
184Dic43⋊C4—41no—
185Dic43⋊C4—41no—
186Dic43⋊C4—42no—
187Dic43⋊C4—42no—
188Dic43⋊C4—81no—
189Dic43⋊C4—81no—
190Dic43⋊C4—81no—
191C4×Dic43—21no—
192C4×Dic43—21no—
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#4112yes—
200#10621872—44no—
201C8×D43—44no—
202C23×C43C22×D411yescharacteristic
203C22×D43—21no—
204C22×D43—21no—
205C22×D43—21no—
206C22×D43—21no—
207C22×D43—21no—
208C22×D43—21no—
209C22×D43C22⋊Q812yes—
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×C43H(5,𝔽2)11yescharacteristic
233C2×C4×C43H(5,𝔽2)11yescharacteristic
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—22no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43C22⋊Q812yes—
255C4×D43—22no—
256C4×D43—22no—
257C4×D43—22no—
258C4×D43—22no—
259Dic86—22no—
260Dic86—22no—
261Dic86—41no—
262Dic86—41no—
263C8×C43—22no—
264C8×C43—41no—
265C43⋊C8—22no—
266C43⋊C8—41no—
267#29172—431nomaximal, Sylow
268C22×C43C2×C22⋊Q811yescharacteristic
269C22×C43#53211yescharacteristic
270C22×C43#53411yescharacteristic
271C22×C43#57711yescharacteristic
272C22×C43#57711yescharacteristic
273C22×C43#57711yescharacteristic
274C22×C43#57811yescharacteristic
275C2×D43—22no—
276C2×D43—22no—
277C2×D43—22no—
278C2×D43—41no—
279C2×D43—41no—
280C2×D43—41no—
281C2×D43—41no—
282C4×C43—42no—
283C4×C43—41no—
284C4×C43—41no—
285C4×C43—81no—
286C4×C43—81no—
287C4×C43—81no—
288C4×C43#55111yescharacteristic
289C4×C43#55111yescharacteristic
290C4×C43#55411yescharacteristic
291C4×C43#55411yescharacteristic
292Dic43—22no—
293Dic43—42no—
294Dic43—41no—
295Dic43—41no—
296Dic43—81no—
297Dic43—81no—
298Dic43—81no—
299#2629—431no—
300#2323—431no—
301#2100—431no—
302#2096—431no—
303#2059—431no—
304#2026—431no—
305#1920—431no—
306#1919D4311yescharacteristic, complemented
307#1894—431no—
308#1892—431no—
309#1865—431no—
310#1863—431no—
311#1809—431no—
312#1807—431no—
313#1729—431no—
314C2×C43#256411yescharacteristic
315C2×C43#308211yescharacteristic
316C2×C43#308411yescharacteristic
317C2×C43#317411yescharacteristic
318C2×C43#317811yescharacteristic
319C2×C43#320111yescharacteristic
320C2×C43#320411yescharacteristic
321D43—42no—
322C22×M16—431no—
323C23×C8—431no—
324C2×#125—431no—
325C2×C22⋊Q8—431no—
326C2×C4×Q8—431no—
327C2×#117—431no—
328C2×#107—431no—
329C2×#106—431no—
330C2×#106—431no—
331C2×#106C2×D4311yescharacteristic
332C2×#103—431no—
333C2×#103—431no—
334C2×#103—431no—
335C2×#103—431no—
336#398—861no—
337#398—861no—
338#396—861no—
339#396—861no—
340#391—431no—
341#389—431no—
342#389—431no—
343#389—861no—
344#389C2×D4311yescharacteristic
345#388—861no—
346#388—861no—
347#387—861no—
348#384—431no—
349#380—431no—
350#380—431no—
351#380—431no—
352C4×C4⋊C4C2×D4311yescharacteristic
353#340—431no—
354#340—431no—
355#340—431no—
356#340—431no—
357#340—431no—
358#340C2×D4311yescharacteristic
359#340C2×D4311yescharacteristic
360#340C2×D4311yescharacteristic
361#336—431no—
362#336—431no—
363#336—431no—
364#336C2×D4311yescharacteristic
365C43#2917211yescharacteristic, complemented, Sylow
366C22×Q8—431no—
367C23×C4—431no—
368C2×M16—862no—
369C2×M16—862no—
370C2×M16—1721no—
371C22×C8—431no—
372C22×C8—431no—
373C22×C8—862no—
374C22×C8—862no—
375C22×C8—1721no—
376C22×C8C22×D4311yescharacteristic
377C22×C8C22×D4311yescharacteristic
378#125—1721no—
379#125—1721no—
380C22⋊Q8—434no—
381C22⋊Q8—862no—
382C4×Q8—1721no—
383C4×Q8—1721no—
384#117—1721no—
385#117—1721no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—431no—
388C2×C4⋊C4—431no—
389C2×C4⋊C4—431no—
390C2×C4⋊C4—431no—
391C2×C4⋊C4—431no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4—861no—
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⋊C4C22×D4311yescharacteristic
401C2×C4⋊C4C22×D4311yescharacteristic
402C2×C4⋊C4C22×D4311yescharacteristic
403C2×C4⋊C4C22×D4311yescharacteristic
404C2×C22⋊C4—431no—
405C2×C22⋊C4—431no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C22⋊C4—861no—
409C2×C22⋊C4—861no—
410C2×C42—21no—
411C2×C42—431no—
412C2×C42—861no—
413C2×C42C22×D4311yescharacteristic
414#107—1721no—
415#106—22no—
416#106—862no—
417#106—1721no—
418#103—862no—
419#103—862no—
420#103—1721no—
421#103—1721no—
422#95—21no—
423#95—21no—
424#95—861no—
425#95—861no—
426#95—861no—
427#95—861no—
428#95—861no—
429#95—861no—
430#95—861no—
431C24—431no—
432C2×Q8—432no—
433C2×Q8—861no—
434C2×Q8—861no—
435C2×Q8—861no—
436C2×Q8—861no—
437C2×Q8—861no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—431no—
443C22×C4—432no—
444C22×C4—432no—
445C22×C4—431no—
446C22×C4—431no—
447C22×C4—861no—
448C22×C4—861no—
449C22×C4—861no—
450C22×C4—861no—
451C22×C4—861no—
452C22×C4—861no—
453C22×C4—861no—
454C22×C4—861no—
455C22×C4D4×D4311yescharacteristic
456C22×C4D4×D4311yescharacteristic
457C22×C4C23×D4311yescharacteristic
458M16—1724no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—432no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—861no—
469C2×C8—861no—
470C2×C8—1724no—
471C2×C8#1062189812yes—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—81no—
480C4⋊C4—864no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—3441no—
488C4⋊C4—3441no—
489C4⋊C4—3441no—
490C4⋊C4—3441no—
491C4⋊C4—1721no—
492C4⋊C4—1721no—
493C4⋊C4—1722no—
494C4⋊C4—1722no—
495C4⋊C4—1722no—
496C4⋊C4Q8×D4312yes—
497C22⋊C4—864no—
498C22⋊C4—3441no—
499C22⋊C4—3441no—
500C22⋊C4—3441no—
501C22⋊C4—1721no—
502C22⋊C4—1721no—
503C42—21no—
504C42—21no—
505C42—81no—
506C42—861no—
507C42—861no—
508C42—1722no—
509C23—432no—
510C23—861no—
511C23—861no—
512C23—861no—
513C23—861no—
514C23—861no—
515C23—861no—
516C23C2×D4×D4311yescharacteristic
517Q8—862no—
518Q8—862no—
519Q8—1721no—
520Q8—1721no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—432no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—862no—
543C2×C4—862no—
544C2×C4—862no—
545C2×C4—862no—
546C2×C4—862no—
547C2×C4—861no—
548C2×C4—861no—
549C2×C4—861no—
550C2×C4—861no—
551C2×C4—861no—
552C2×C4—861no—
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×C4C2×#1062189811yescharacteristic
568C2×C4#1306337111yescharacteristic
569C2×C4#1306337111yescharacteristic
570C8—22no—
571C8—41no—
572C8—862no—
573C8—1721no—
574C22—862no—
575C22—862no—
576C22—862no—
577C22—1721no—
578C22—1721no—
579C22—1721no—
580C22—1721no—
581C22C22⋊Q8×D4311yescharacteristic
582C22#1458344611yescharacteristic
583C22#1458346011yescharacteristic
584C22#1458370511yescharacteristic
585C22#1458370611yescharacteristic
586C22#1458370911yescharacteristic
587C22#1458371511yescharacteristic
588C4—42no—
589C4—41no—
590C4—41no—
591C4—81no—
592C4—81no—
593C4—81no—
594C4—862no—
595C4—3441no—
596C4—3441no—
597C4—3441no—
598C4—1721no—
599C4—1721no—
600C4—1722no—
601C4#1458357311yescharacteristic
602C4#1458357411yescharacteristic
603C4#1458360511yescharacteristic
604C4#1458360911yescharacteristic
605C2—1722no—
606C2#1913977411yescharacteristic
607C2#1914443011yescharacteristic
608C2#1914445811yescharacteristic
609C2#1914521911yescharacteristic
610C2#1914526111yescharacteristic
611C2#1914548311yescharacteristic
612C2#1914550811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1919C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#1919D43
hypocenterC43#29172
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1919

Complements

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

NH ≅ G/Ntype
3. #19136161C2semidirect
4. #19136135C2semidirect
5. #19135932C2semidirect
6. #19135745C2semidirect
7. #19135180C2semidirect
10. #19134866C2semidirect
11. #19134848C2semidirect
15. C43×#1919C2semidirect
306. #1919D43semidirect
365. C43#29172semidirect

Maximal subgroups

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

subgroupindex
#191404302
#191372782
#191361612
#191361352
#191359322
#191357452
#191351802
#191350272
#191350172
#191348662
#191348482
#191346272
#191346172
#191342902
C43×#19192
#2917243