Finite Group Databasebeta

← #25199538

Subgroups — #25199538

Order 11008.

836 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137288C211yesmaximal, characteristic, complemented
2#19136026C211yesmaximal, characteristic, complemented
3#19135777C211yesmaximal, characteristic, complemented
4#19135774C211yesmaximal, characteristic, complemented
5#19135591C211yesmaximal, characteristic
6#19135215C211yesmaximal, characteristic, complemented
7#19135212C211yesmaximal, characteristic, complemented
8#19135187C211yesmaximal, characteristic, complemented
9#19135184C211yesmaximal, characteristic, complemented
10#19134946C211yesmaximal, characteristic, complemented
11#19134943C211yesmaximal, characteristic, complemented
12#19134842C211yesmaximal, characteristic, complemented
13#19134841C211yesmaximal, characteristic, complemented
14#19134666C211yesmaximal, characteristic, complemented
15C43×#2324C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C2×#13063299C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×#13063258C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063246C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063245C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×C22⋊(C43⋊C8)C2211yescharacteristic
29C2×C22⋊(C43⋊C8)C2211yescharacteristic
30#14582801C2211yescharacteristic
31#14582799—21no—
32#14582797C2211yescharacteristic
33#14582789—21no—
34#14582775—21no—
35#14582770—21no—
36#14582759C2211yescharacteristic
37C4×C4⋊Dic43C2211yescharacteristic
38#14582661C2211yescharacteristic
39#14582661C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582654C2211yescharacteristic
45#14582654C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C2×#121×C43C2211yescharacteristic
49C2×C4×D4×C43C2211yescharacteristic
50C2×#117×C43C2211yescharacteristic
51C43×#390—21no—
52C43×#390C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C43×#388—21no—
55C43×#386—21no—
56C43×#385—21no—
57C43×#380C2211yescharacteristic
58C4×C4⋊C4×C43C2211yescharacteristic
59C22×D172C2311yescharacteristic
60C22×C22⋊D43—21no—
61C22×C4×D43—21no—
62C2×#10621882—22no—
63C2×#10621882—22no—
64C2×#10621882—41no—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69#13063299—22no—
70#13063299—22no—
71C4×D172—41no—
72C4×D172—41no—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×C22⋊Dic43—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×C4×Dic43—21no—
83#13063258—22no—
84#13063258—22no—
85#13063258—41no—
86#13063246—22no—
87#13063246—22no—
88#13063246—41no—
89#13063245—22no—
90#13063245—22no—
91#13063245—41no—
92C22⋊(C43⋊C8)—41no—
93C22⋊(C43⋊C8)—41no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C22×D4×C43—21no—
98C22×D4×C43C2311yescharacteristic
99C23×C4×C43—21no—
100C23×C4×C43C2311yescharacteristic
101#121×C43—22no—
102#121×C43—22no—
103C4×D4×C43—41no—
104C4×D4×C43—41no—
105#117×C43—41no—
106#117×C43—41no—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43D411yescharacteristic
109C2×C4⋊C4×C43D411yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43—21no—
116C2×C22⋊C4×C43—21no—
117C2×C22⋊C4×C43—21no—
118C2×C22⋊C4×C43D411yescharacteristic
119C2×C22⋊C4×C43D411yescharacteristic
120C2×C42×C43—21no—
121C2×C42×C43C2311yescharacteristic
122C2×C42×C43C2311yescharacteristic
123#95×C43—21no—
124#95×C43—21no—
125#95×C43—21no—
126C24×C43—21no—
127C24×C43C2×D411yescharacteristic
128C23×D43—21no—
129C2×D4×C43—24no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—81no—
136C2×D4×C43—81no—
137C2×D4×C43#4112yes—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—42no—
148C22×C4×C43—81no—
149C22×C4×C43—81no—
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2411yescharacteristic
156C2×C22⋊D43—24no—
157C2×C22⋊D43—81no—
158C2×C22⋊D43—81no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172—21no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172#4112yes—
168C2×C4×D43—42no—
169C2×C4×D43—81no—
170C2×C4×D43—81no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—41no—
177C4⋊C4×C43—41no—
178C4⋊C4×C43—81no—
179C4⋊C4×C43#4112yes—
180C22⋊C4×C43—24no—
181C22⋊C4×C43—41no—
182C22⋊C4×C43—41no—
183C22⋊C4×C43—42no—
184C22⋊C4×C43—81no—
185C22⋊C4×C43—81no—
186C22⋊C4×C43—81no—
187C42×C43—21no—
188C42×C43—21no—
189C42×C43—21no—
190C42×C43—21no—
191C42×C43—81no—
192C22⋊Dic43—81no—
193#10621882—44no—
194(C2×D43)⋊C4—24no—
195(C2×D43)⋊C4—42no—
196(C2×D43)⋊C4—81no—
197(C2×D43)⋊C4—81no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43#4112yes—
204Dic43⋊C4—81no—
205C4×Dic43—81no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C23×C43—22no—
219C23×C43—21no—
220C23×C43—21no—
221C23×C43—21no—
222C23×C43—21no—
223C23×C43—21no—
224C23×C43—21no—
225C23×C43—21no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43—41no—
229C23×C43—41no—
230C23×C43—41no—
231C23×C43—41no—
232C23×C43C22×D411yescharacteristic
233C22×D43—22no—
234C22×D43—41no—
235C22×D43—41no—
236C22×D43—41no—
237C22×D43—41no—
238C22×D43—41no—
239C22×D43—41no—
240D4×C43—22no—
241D4×C43—22no—
242D4×C43—41no—
243D4×C43—41no—
244D4×C43—84no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—22no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—21no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—21no—
260C2×C4×C43—21no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43—41no—
268C2×C4×C43—41no—
269C2×C4×C43—41no—
270C2×C4×C43—41no—
271C2×C4×C43—41no—
272C2×C4×C43—41no—
273C2×C4×C43—84no—
274C2×C4×C43C2×#4111yescharacteristic
275C2×C4×C43C2×#4111yescharacteristic
276C2×C4×C43C2×#4111yescharacteristic
277C2×C4×C43C2×#4111yescharacteristic
278C2×C4×C43H(5,𝔽2)11yescharacteristic
279C2×C4×C43H(5,𝔽2)11yescharacteristic
280C22⋊D43—84no—
281C2×Dic43—22no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289C2×Dic43—41no—
290D172—22no—
291D172—22no—
292D172—41no—
293D172—41no—
294C4×D43—84no—
295C43⋊C8—41no—
296C43⋊C8—41no—
297C43⋊C8—41no—
298C43⋊C8—41no—
299#29422—431nomaximal, Sylow
300C22×C43—41no—
301C22×C43—42no—
302C22×C43—41no—
303C22×C43—41no—
304C22×C43—42no—
305C22×C43—41no—
306C22×C43—41no—
307C22×C43—42no—
308C22×C43—41no—
309C22×C43—41no—
310C22×C43—81no—
311C22×C43—81no—
312C22×C43—81no—
313C22×C43—81no—
314C22×C43#52511yescharacteristic
315C22×C43#52511yescharacteristic
316C22×C43#53411yescharacteristic
317C22×C43#57611yescharacteristic
318C22×C43#57611yescharacteristic
319C22×C43#57611yescharacteristic
320C22×C43#57811yescharacteristic
321C2×D43—42no—
322C2×D43—42no—
323C2×D43—42no—
324C2×D43—81no—
325C2×D43—81no—
326C2×D43—81no—
327C2×D43—81no—
328C4×C43—41no—
329C4×C43—42no—
330C4×C43—41no—
331C4×C43—41no—
332C4×C43—41no—
333C4×C43—41no—
334C4×C43—81no—
335C4×C43—81no—
336C4×C43#55111yescharacteristic
337C4×C43#55311yescharacteristic
338C4×C43#55311yescharacteristic
339C4×C43#55911yescharacteristic
340Dic43—42no—
341Dic43—81no—
342Dic43—81no—
343#2324—431no—
344#2324D4311yescharacteristic, complemented
345#2076—431no—
346#2033—431no—
347#2033—431no—
348#1999—431no—
349#1925—431no—
350#1925—431no—
351#1921—431no—
352#1921—431no—
353#1879—431no—
354#1879—431no—
355#1862—431no—
356#1862—431no—
357#1818—431no—
358C2×C43—81no—
359C2×C43—82no—
360C2×C43#260011yescharacteristic
361C2×C43#312211yescharacteristic
362C2×C43#312211yescharacteristic
363C2×C43#312411yescharacteristic
364C2×C43#312411yescharacteristic
365C2×C43#319911yescharacteristic
366C2×C43#320311yescharacteristic
367D43—82no—
368C22×D8—431no—
369C2×#121—431no—
370C2×#121C2×D4311yescharacteristic
371C2×C4×D4—431no—
372C2×C4×D4C2×D4311yescharacteristic
373C2×#117C2×D4311yescharacteristic
374C2×#107—431no—
375C2×#107—431no—
376C2×#107—431no—
377C2×#102—431no—
378C2×#102—431no—
379C2×#102—431no—
380C2×#102—431no—
381C2×#102—431no—
382C2×#102—431no—
383C2×C22⋊C8—431no—
384C2×C22⋊C8—431no—
385#390—21no—
386#390—431no—
387#390—861no—
388#390C2×D4311yescharacteristic
389#389—431no—
390#389C2×D4311yescharacteristic
391#388—21no—
392#388—861no—
393#386—21no—
394#386—861no—
395#385—21no—
396#385—861no—
397#380—431no—
398#380C2×D4311yescharacteristic
399C4×C4⋊C4—431no—
400C4×C4⋊C4C2×D4311yescharacteristic
401#340—431no—
402#340—431no—
403#340—431no—
404#340—431no—
405#340—431no—
406#340—431no—
407#336—431no—
408#336—431no—
409#336—431no—
410#336—431no—
411C43#2942211yescharacteristic, complemented, Sylow
412C22×D4—21no—
413C22×D4—431no—
414C22×D4—861no—
415C22×D4C22×D4311yescharacteristic
416C23×C4—21no—
417C23×C4—861no—
418C23×C4C22×D4311yescharacteristic
419C2×D8—862no—
420C2×D8—862no—
421C2×D8—1721no—
422C22×C8—431no—
423C22×C8—431no—
424C22×C8—431no—
425C22×C8—431no—
426#121—22no—
427#121—22no—
428#121—862no—
429#121—862no—
430C4×D4—41no—
431C4×D4—41no—
432C4×D4—1721no—
433C4×D4—1721no—
434#117—41no—
435#117—41no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—431no—
438C2×C4⋊C4—431no—
439C2×C4⋊C4—431no—
440C2×C4⋊C4—861no—
441C2×C4⋊C4C22⋊D4311yescharacteristic
442C2×C4⋊C4C22⋊D4311yescharacteristic
443C2×C4⋊C4C22×D4311yescharacteristic
444C2×C4⋊C4C22×D4311yescharacteristic
445C2×C4⋊C4C22×D4311yescharacteristic
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—861no—
452C2×C22⋊C4—861no—
453C2×C22⋊C4—861no—
454C2×C22⋊C4—861no—
455C2×C22⋊C4—861no—
456C2×C22⋊C4C22⋊D4311yescharacteristic
457C2×C22⋊C4C22⋊D4311yescharacteristic
458C2×C42—21no—
459C2×C42—861no—
460C2×C42C22×D4311yescharacteristic
461C2×C42C22×D4311yescharacteristic
462#107—862no—
463#107—862no—
464#107—1721no—
465#102—862no—
466#102—862no—
467#102—862no—
468#102—862no—
469#102—1721no—
470#102—1721no—
471C22⋊C8—1721no—
472C22⋊C8—1721no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—861no—
477#95—861no—
478#95—861no—
479C24—21no—
480C24—861no—
481C24C2×C22⋊D4311yescharacteristic
482C2×D4—24no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—81no—
489C2×D4—81no—
490C2×D4—432no—
491C2×D4—864no—
492C2×D4—861no—
493C2×D4—861no—
494C2×D4—861no—
495C2×D4—861no—
496C2×D4—861no—
497C2×D4—3441no—
498C2×D4—3441no—
499C2×D4#1062189812yes—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—42no—
510C22×C4—81no—
511C22×C4—81no—
512C22×C4—861no—
513C22×C4—861no—
514C22×C4—861no—
515C22×C4—3441no—
516C22×C4—3441no—
517C22×C4—1722no—
518C22×C4C2×C22⋊D4311yescharacteristic
519C22×C4C2×C22⋊D4311yescharacteristic
520C22×C4C2×C22⋊D4311yescharacteristic
521C22×C4C2×C22⋊D4311yescharacteristic
522C22×C4C2×C22⋊D4311yescharacteristic
523C22×C4C23×D4311yescharacteristic
524D8—1724no—
525C2×C8—861no—
526C2×C8—861no—
527C2×C8—861no—
528C2×C8—861no—
529C2×C8—861no—
530C2×C8—861no—
531C2×C8—861no—
532C2×C8—861no—
533C2×C8—861no—
534C2×C8—861no—
535C2×C8—861no—
536C2×C8—861no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—41no—
543C4⋊C4—41no—
544C4⋊C4—81no—
545C4⋊C4—432no—
546C4⋊C4—861no—
547C4⋊C4—861no—
548C4⋊C4—861no—
549C4⋊C4—861no—
550C4⋊C4—861no—
551C4⋊C4—3441no—
552C4⋊C4#1062189812yes—
553C22⋊C4—24no—
554C22⋊C4—41no—
555C22⋊C4—41no—
556C22⋊C4—42no—
557C22⋊C4—81no—
558C22⋊C4—81no—
559C22⋊C4—81no—
560C22⋊C4—864no—
561C22⋊C4—3441no—
562C22⋊C4—3441no—
563C22⋊C4—3441no—
564C22⋊C4—1722no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—81no—
570C42—3441no—
571C23—21no—
572C23—22no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—862no—
586C23—1721no—
587C23—1721no—
588C23—1721no—
589C23—1721no—
590C23—1721no—
591C23—1721no—
592C23C22×C22⋊D4311yescharacteristic
593D4—22no—
594D4—22no—
595D4—41no—
596D4—41no—
597D4—84no—
598D4—862no—
599D4—862no—
600D4—3444no—
601D4—1721no—
602D4—1721no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—22no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—84no—
632C2×C4—862no—
633C2×C4—3444no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4—1721no—
637C2×C4—1721no—
638C2×C4—1721no—
639C2×C4—1721no—
640C2×C4—1721no—
641C2×C4—1721no—
642C2×C4#41×D4311yescharacteristic
643C2×C4#41×D4311yescharacteristic
644C2×C4C2×#1062189811yescharacteristic
645C2×C4C2×#1062189811yescharacteristic
646C2×C4#1306337011yescharacteristic
647C2×C4#1306337011yescharacteristic
648C8—1721no—
649C8—1721no—
650C8—1721no—
651C8—1721no—
652C22—41no—
653C22—41no—
654C22—42no—
655C22—41no—
656C22—41no—
657C22—42no—
658C22—41no—
659C22—41no—
660C22—42no—
661C22—41no—
662C22—81no—
663C22—81no—
664C22—81no—
665C22—81no—
666C22—3441no—
667C22—3441no—
668C22—3441no—
669C22—3441no—
670C22—1722no—
671C22—1722no—
672C22—1722no—
673C22#1458340611yescharacteristic
674C22#1458341011yescharacteristic
675C22#1458345811yescharacteristic
676C22#1458370211yescharacteristic
677C22#1458370211yescharacteristic
678C22#1458370211yescharacteristic
679C22#1458371411yescharacteristic
680C4—41no—
681C4—41no—
682C4—41no—
683C4—42no—
684C4—41no—
685C4—41no—
686C4—81no—
687C4—81no—
688C4—3441no—
689C4—3441no—
690C4—1722no—
691C4#1458357811yescharacteristic
692C4#1458359811yescharacteristic
693C4#1458359911yescharacteristic
694C4#1458363211yescharacteristic
695C2—81no—
696C2—82no—
697C2—3442no—
698C2#1914017711yescharacteristic
699C2#1914483311yescharacteristic
700C2#1914483811yescharacteristic
701C2#1914485111yescharacteristic
702C2#1914485711yescharacteristic
703C2#1914545611yescharacteristic
704C2#1914549211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2324C2
socleC23×C43C22×D4
prime radical#19135591C2
hypercenter#2324D43
hypocenterC43#29422
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2324

Complements

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

NH ≅ G/Ntype
1. #19137288C2semidirect
2. #19136026C2semidirect
3. #19135777C2semidirect
4. #19135774C2semidirect
6. #19135215C2semidirect
7. #19135212C2semidirect
8. #19135187C2semidirect
9. #19135184C2semidirect
10. #19134946C2semidirect
11. #19134943C2semidirect
12. #19134842C2semidirect
13. #19134841C2semidirect
14. #19134666C2semidirect
15. C43×#2324C2semidirect
344. #2324D43semidirect
411. C43#29422semidirect

Maximal subgroups

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

subgroupindex
#191372882
#191360262
#191357772
#191357742
#191355912
#191352152
#191352122
#191351872
#191351842
#191349462
#191349432
#191348422
#191348412
#191346662
C43×#23242
#2942243