Finite Group Databasebeta

← #25196787

Subgroups — #25196787

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#19140425C211yesmaximal, characteristic
2#19136153C211yesmaximal, characteristic, complemented
3#19136133C211yesmaximal, characteristic, complemented
4#19135933C211yesmaximal, characteristic, complemented
5#19135746C211yesmaximal, characteristic, complemented
6#19135187C211yesmaximal, characteristic, complemented
7#19135166C211yesmaximal, characteristic, complemented
8#19135029C211yesmaximal, characteristic
9#19135019C211yesmaximal, characteristic
10#19134863C211yesmaximal, characteristic, complemented
11#19134849C211yesmaximal, characteristic, complemented
12#19134626C211yesmaximal, characteristic
13#19134622C211yesmaximal, characteristic
14#19134292C211yesmaximal, characteristic
15C43×#2323C211yesmaximal, characteristic
16C22×#10621877C2211yescharacteristic
17C23×C43⋊C8C2211yescharacteristic
18C2×#13063317C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×#13063258C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27#14582832—21no—
28#14582832—21no—
29#14582822—21no—
30#14582822—21no—
31#14582797C2211yescharacteristic
32#14582797C2211yescharacteristic
33#14582769C2211yescharacteristic
34#14582759C2211yescharacteristic
35#14582759C2211yescharacteristic
36#14582661C2211yescharacteristic
37#14582661C2211yescharacteristic
38#14582661C2211yescharacteristic
39#14582661C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582654C2211yescharacteristic
45#14582654C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C2×C22⋊Q8×C43C2211yescharacteristic
49C2×C4×Q8×C43C2211yescharacteristic
50C2×#117×C43C2211yescharacteristic
51C43×#391C2211yescharacteristic
52C43×#389—21no—
53C43×#389C2211yescharacteristic
54C43×#388—21no—
55C43×#388—21no—
56C43×#387—21no—
57C43×#380C2211yescharacteristic
58C4×C4⋊C4×C43C2211yescharacteristic
59C2×#10621877—22no—
60C2×#10621877—22no—
61C2×#10621877—41no—
62C22×C43⋊C8—22no—
63C22×C43⋊C8—22no—
64C22×C43⋊C8—41no—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69#13063317—41no—
70#13063317—41no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83#13063258—22no—
84#13063258—22no—
85#13063258—41no—
86#13063256—41no—
87#13063249—22no—
88#13063249—22no—
89#13063249—41no—
90#13063249—41no—
91C43⋊#95—21no—
92C43⋊#95—21no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C22×Q8×C43C2311yescharacteristic
96C23×C4×C43C2311yescharacteristic
97C22⋊Q8×C43—22no—
98C22⋊Q8×C43Q814yes—
99C4×Q8×C43—41no—
100C4×Q8×C43—41no—
101#117×C43—41no—
102#117×C43—41no—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43D411yescharacteristic
107C2×C4⋊C4×C43D411yescharacteristic
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43D411yescharacteristic
114C2×C22⋊C4×C43D411yescharacteristic
115C2×C42×C43—21no—
116C2×C42×C43—21no—
117C2×C42×C43C2311yescharacteristic
118C2×C42×C43C2311yescharacteristic
119#95×C43—21no—
120#95×C43—21no—
121#95×C43—21no—
122#95×C43—21no—
123#95×C43—21no—
124C24×C43C2×D411yescharacteristic
125C2×Q8×C43—21no—
126C2×Q8×C43—21no—
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43C2×Q812yes—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×Q812yes—
145C22×C4×C43#4112yes—
146C22×C4×C43C2411yescharacteristic
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C4⋊C4×C43—24no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—41no—
158C4⋊C4×C43—41no—
159C4⋊C4×C43—42no—
160C4⋊C4×C43—81no—
161C4⋊C4×C43C2×Q812yes—
162C22⋊C4×C43—24no—
163C22⋊C4×C43—41no—
164C22⋊C4×C43—41no—
165C22⋊C4×C43—81no—
166C42×C43—21no—
167C42×C43—21no—
168C42×C43—21no—
169C42×C43—21no—
170C42×C43—42no—
171C42×C43—81no—
172C22⋊Dic43—81no—
173C22⋊Dic43—81no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—81no—
183C4⋊Dic43—81no—
184Dic43⋊C4—42no—
185Dic43⋊C4—42no—
186Dic43⋊C4—81no—
187Dic43⋊C4—81no—
188#10621877—44no—
189C2×C43⋊C8—21no—
190C2×C43⋊C8—21no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—44no—
200C2×C43⋊C8#4112yes—
201C2×C43⋊C8#4112yes—
202C23×C43—21no—
203C23×C43—21no—
204C23×C43—21no—
205C23×C43—21no—
206C23×C43—21no—
207C23×C43—21no—
208C23×C43C22⋊Q812yes—
209C23×C43C22×D411yescharacteristic
210Q8×C43—22no—
211Q8×C43—22no—
212Q8×C43—41no—
213Q8×C43—41no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—22no—
217C2×C4×C43—22no—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43C22⋊Q812yes—
245C2×C4×C43C22×Q811yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43H(5,𝔽2)11yescharacteristic
250C2×C4×C43H(5,𝔽2)11yescharacteristic
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C43⋊C8—22no—
264C43⋊C8—22no—
265C43⋊C8—41no—
266C43⋊C8—41no—
267#29173—431nomaximal, Sylow
268C22×C43—22no—
269C22×C43—22no—
270C22×C43—22no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43C2×C22⋊Q811yescharacteristic
276C22×C43#53211yescharacteristic
277C22×C43#53411yescharacteristic
278C22×C43#57611yescharacteristic
279C22×C43#57711yescharacteristic
280C22×C43#57811yescharacteristic
281C22×C43#57811yescharacteristic
282C4×C43—22no—
283C4×C43—42no—
284C4×C43—42no—
285C4×C43—41no—
286C4×C43—41no—
287C4×C43—41no—
288C4×C43—41no—
289C4×C43—81no—
290C4×C43—81no—
291C4×C43#55111yescharacteristic
292C4×C43#55111yescharacteristic
293C4×C43#55411yescharacteristic
294C4×C43#55411yescharacteristic
295Dic43—81no—
296Dic43—81no—
297Dic43—81no—
298Dic43—81no—
299#2629—431no—
300#2323D4311yescharacteristic
301#2099—431no—
302#2095—431no—
303#2059—431no—
304#2026—431no—
305#1921—431no—
306#1918—431no—
307#1894—431no—
308#1892—431no—
309#1865—431no—
310#1863—431no—
311#1809—431no—
312#1808—431no—
313#1729—431no—
314C2×C43—42no—
315C2×C43#256411yescharacteristic
316C2×C43#308211yescharacteristic
317C2×C43#308311yescharacteristic
318C2×C43#317711yescharacteristic
319C2×C43#317911yescharacteristic
320C2×C43#320111yescharacteristic
321C2×C43#320311yescharacteristic
322C22×M16—431no—
323C23×C8—431no—
324C2×#125—431no—
325C2×C22⋊Q8C2×D4311yescharacteristic
326C2×C4×Q8C2×D4311yescharacteristic
327C2×#117C2×D4311yescharacteristic
328C2×#107—431no—
329C2×#107—431no—
330C2×#107—431no—
331C2×#106—431no—
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#391C2×D4311yescharacteristic
341#389—21no—
342#389—431no—
343#389—431no—
344#389C2×D4311yescharacteristic
345#388—21no—
346#388—21no—
347#387—21no—
348#384—431no—
349#380—431no—
350#380—431no—
351#380C2×D4311yescharacteristic
352C4×C4⋊C4C2×D4311yescharacteristic
353#340—431no—
354#340—431no—
355#340—431no—
356#340—431no—
357#340—431no—
358#340—431no—
359#340—431no—
360#340—431no—
361#336—431no—
362#336—431no—
363#336—431no—
364#336—431no—
365C43#2917311yescharacteristic, complemented, Sylow
366C22×Q8C22×D4311yescharacteristic
367C23×C4C22×D4311yescharacteristic
368C2×M16—862no—
369C2×M16—862no—
370C2×M16—1721no—
371C22×C8—431no—
372C22×C8—431no—
373C22×C8—431no—
374C22×C8—431no—
375C22×C8—862no—
376C22×C8—862no—
377C22×C8—1721no—
378#125—1721no—
379#125—1721no—
380C22⋊Q8—22no—
381C22⋊Q8Dic8614yes—
382C4×Q8—41no—
383C4×Q8—41no—
384#117—41no—
385#117—41no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—431no—
390C2×C4⋊C4—431no—
391C2×C4⋊C4—431no—
392C2×C4⋊C4—431no—
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⋊C4C22⋊D4311yescharacteristic
400C2×C4⋊C4C22⋊D4311yescharacteristic
401C2×C4⋊C4C22×D4311yescharacteristic
402C2×C4⋊C4C22×D4311yescharacteristic
403C2×C4⋊C4C22×D4311yescharacteristic
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C22⋊C4C22⋊D4311yescharacteristic
409C2×C22⋊C4C22⋊D4311yescharacteristic
410C2×C42—21no—
411C2×C42—21no—
412C2×C42C22×D4311yescharacteristic
413C2×C42C22×D4311yescharacteristic
414#107—862no—
415#107—862no—
416#107—1721no—
417#106—1721no—
418#103—862no—
419#103—862no—
420#103—1721no—
421#103—1721no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—861no—
428#95—861no—
429#95—861no—
430#95—861no—
431C24C2×C22⋊D4311yescharacteristic
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8C2×Dic8612yes—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4—861no—
449C22×C4—861no—
450C22×C4C2×Dic8612yes—
451C22×C4#1062189812yes—
452C22×C4C2×C22⋊D4311yescharacteristic
453C22×C4C2×C22⋊D4311yescharacteristic
454C22×C4C2×C22⋊D4311yescharacteristic
455C22×C4C2×C22⋊D4311yescharacteristic
456C22×C4C2×C22⋊D4311yescharacteristic
457C22×C4C23×D4311yescharacteristic
458M16—1724no—
459C2×C8—432no—
460C2×C8—432no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—861no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—1724no—
472C4⋊C4—24no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4—42no—
481C4⋊C4—81no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—3441no—
491C4⋊C4—3441no—
492C4⋊C4—3441no—
493C4⋊C4—3441no—
494C4⋊C4—1722no—
495C4⋊C4—1722no—
496C4⋊C4C2×Dic8612yes—
497C22⋊C4—24no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—81no—
501C22⋊C4—3441no—
502C22⋊C4—3441no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—42no—
508C42—81no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23#1306330412yes—
516C23C22×C22⋊D4311yescharacteristic
517Q8—22no—
518Q8—22no—
519Q8—41no—
520Q8—41no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—1721no—
552C2×C4—1721no—
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#1306330412yes—
564C2×C4C22×Dic8611yescharacteristic
565C2×C4#41×D4311yescharacteristic
566C2×C4#41×D4311yescharacteristic
567C2×C4C2×#1062189811yescharacteristic
568C2×C4#1306337011yescharacteristic
569C2×C4#1306337011yescharacteristic
570C8—862no—
571C8—862no—
572C8—1721no—
573C8—1721no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22C2×#1306330411yescharacteristic
582C22#1458344511yescharacteristic
583C22#1458345811yescharacteristic
584C22#1458370211yescharacteristic
585C22#1458370711yescharacteristic
586C22#1458371411yescharacteristic
587C22#1458371411yescharacteristic
588C4—22no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—41no—
593C4—42no—
594C4—42no—
595C4—81no—
596C4—81no—
597C4—3441no—
598C4—3441no—
599C4—3441no—
600C4—3441no—
601C4#1458357811yescharacteristic
602C4#1458357811yescharacteristic
603C4#1458360811yescharacteristic
604C4#1458360811yescharacteristic
605C2—42no—
606C2#1913977111yescharacteristic
607C2#1914443711yescharacteristic
608C2#1914444611yescharacteristic
609C2#1914524811yescharacteristic
610C2#1914527211yescharacteristic
611C2#1914547711yescharacteristic
612C2#1914549211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2323C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#2323D43
hypocenterC43#29173
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2323

Complements

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

NH ≅ G/Ntype
2. #19136153C2semidirect
3. #19136133C2semidirect
4. #19135933C2semidirect
5. #19135746C2semidirect
6. #19135187C2semidirect
7. #19135166C2semidirect
10. #19134863C2semidirect
11. #19134849C2semidirect
365. C43#29173semidirect

Maximal subgroups

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

subgroupindex
#191404252
#191361532
#191361332
#191359332
#191357462
#191351872
#191351662
#191350292
#191350192
#191348632
#191348492
#191346262
#191346222
#191342922
C43×#23232
#2917343