Finite Group Databasebeta

← #25200733

Subgroups — #25200733

Order 11008.

822 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140555C211yesmaximal, characteristic, complemented
2#19136077C211yesmaximal, characteristic, complemented
3#19136009C211yesmaximal, characteristic, complemented
4#19135826C211yesmaximal, characteristic, complemented
5#19135666C211yesmaximal, characteristic
6#19135470C211yesmaximal, characteristic, complemented
7#19135460C211yesmaximal, characteristic, complemented
8#19135295C211yesmaximal, characteristic, complemented
9#19135281C211yesmaximal, characteristic, complemented
10#19134943C211yesmaximal, characteristic, complemented
11#19134943C211yesmaximal, characteristic, complemented
12#19134856C211yesmaximal, characteristic, complemented
13#19134842C211yesmaximal, characteristic, complemented
14#19134347C211yesmaximal, characteristic, complemented
15C43×#2328C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C2×#13063258C2211yescharacteristic
19C2×#13063256C2211yescharacteristic
20C2×#13063246C2211yescharacteristic
21C2×#13063246C2211yescharacteristic
22C2×#13063246C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063236C2211yescharacteristic
29C2×C4×C43⋊C8C2211yescharacteristic
30#14582828—21no—
31#14582828—21no—
32#14582828—21no—
33#14582823—21no—
34#14582801C2211yescharacteristic
35#14582801C2211yescharacteristic
36#14582801C2211yescharacteristic
37#14582797C2211yescharacteristic
38#14582797C2211yescharacteristic
39#14582797C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582654C2211yescharacteristic
45#14582654C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C2×#127×C43C2211yescharacteristic
49C2×C4×D4×C43C2211yescharacteristic
50C2×C4×D4×C43C2211yescharacteristic
51C43×#390C2211yescharacteristic
52C43×#390C2211yescharacteristic
53C43×#386—21no—
54C43×#386—21no—
55C43×#386—21no—
56C43×#386—21no—
57C43×#382C2211yescharacteristic
58C43×#376C2211yescharacteristic
59C22×D172C2311yescharacteristic
60C2×#10621882—22no—
61C2×#10621882—22no—
62C2×#10621882—22no—
63C2×#10621882—22no—
64C2×#10621882—41no—
65C2×#10621882—41no—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×(C2×D43)⋊C4—21no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82#13063258—41no—
83#13063256—41no—
84#13063246—22no—
85#13063246—22no—
86#13063246—22no—
87#13063246—22no—
88#13063246—41no—
89#13063246—41no—
90#13063245—41no—
91#13063245—41no—
92#13063236—22no—
93C4×C43⋊C8—22no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C22×D4×C43—21no—
98C22×D4×C43—21no—
99C22×D4×C43C2311yescharacteristic
100C22×D4×C43C2311yescharacteristic
101C23×C4×C43—21no—
102C23×C4×C43—21no—
103#127×C43—22no—
104#127×C43—22no—
105C4×D4×C43—41no—
106C4×D4×C43—41no—
107C4×D4×C43—41no—
108C4×D4×C43—41no—
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43—21no—
116C2×C22⋊C4×C43—21no—
117C2×C42×C43C2311yescharacteristic
118C2×C42×C43C2311yescharacteristic
119C2×C42×C43C2311yescharacteristic
120#95×C43—21no—
121#95×C43—21no—
122#95×C43D411yescharacteristic
123#95×C43D411yescharacteristic
124#95×C43D411yescharacteristic
125#95×C43D411yescharacteristic
126C24×C43—21no—
127C24×C43—21no—
128C23×D43—21no—
129C2×D4×C43—24no—
130C2×D4×C43—24no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43—21no—
141C2×D4×C43—81no—
142C2×D4×C43—81no—
143C2×D4×C43—81no—
144C2×D4×C43—81no—
145C2×D4×C43#4112yes—
146C2×D4×C43#4112yes—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—42no—
150C22×C4×C43—42no—
151C22×C4×C43—81no—
152C22×C4×C43—81no—
153C22×C4×C43—81no—
154C22×C4×C43—81no—
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2411yescharacteristic
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—21no—
169C2×D172—21no—
170C2×D172—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C22⋊C4×C43—42no—
176C22⋊C4×C43—42no—
177C22⋊C4×C43—81no—
178C22⋊C4×C43—81no—
179C22⋊C4×C43—81no—
180C22⋊C4×C43—81no—
181C42×C43—21no—
182C42×C43—21no—
183C42×C43—21no—
184C42×C43—21no—
185C42×C43—21no—
186C42×C43—21no—
187#10621882—44no—
188#10621882—44no—
189(C2×D43)⋊C4—81no—
190(C2×D43)⋊C4—81no—
191(C2×D43)⋊C4—81no—
192(C2×D43)⋊C4—81no—
193(C2×D43)⋊C4—81no—
194(C2×D43)⋊C4—81no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201Dic43⋊C4—81no—
202Dic43⋊C4—81no—
203Dic43⋊C4—81no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
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#4112yes—
215C2×C43⋊C8#4112yes—
216C23×C43—22no—
217C23×C43—22no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43—41no—
229C23×C43—41no—
230C23×C43C22×D411yescharacteristic
231C22×D43—41no—
232C22×D43—41no—
233C22×D43—41no—
234C22×D43—41no—
235C22×D43—41no—
236C22×D43—41no—
237C22×D43—41no—
238D4×C43—22no—
239D4×C43—22no—
240D4×C43—22no—
241D4×C43—22no—
242D4×C43—41no—
243D4×C43—41no—
244D4×C43—41no—
245D4×C43—41no—
246D4×C43—84no—
247D4×C43—84no—
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—21no—
262C2×C4×C43—21no—
263C2×C4×C43—21no—
264C2×C4×C43—21no—
265C2×C4×C43—21no—
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—84no—
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
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289D172—41no—
290D172—41no—
291D172—41no—
292D172—41no—
293C43⋊C8—22no—
294C43⋊C8—22no—
295C43⋊C8—41no—
296C43⋊C8—41no—
297#29505—431nomaximal, Sylow
298C22×C43—42no—
299C22×C43—42no—
300C22×C43—42no—
301C22×C43—42no—
302C22×C43—42no—
303C22×C43—42no—
304C22×C43—81no—
305C22×C43—81no—
306C22×C43—81no—
307C22×C43—81no—
308C22×C43—81no—
309C22×C43—81no—
310C22×C43—81no—
311C22×C43—81no—
312C22×C43#52511yescharacteristic
313C22×C43#53211yescharacteristic
314C22×C43#53511yescharacteristic
315C22×C43#57611yescharacteristic
316C22×C43#57611yescharacteristic
317C22×C43#57611yescharacteristic
318C22×C43#57711yescharacteristic
319C2×D43—81no—
320C2×D43—81no—
321C2×D43—81no—
322C2×D43—81no—
323C2×D43—81no—
324C2×D43—81no—
325C2×D43—81no—
326C4×C43—41no—
327C4×C43—41no—
328C4×C43—41no—
329C4×C43—41no—
330C4×C43—41no—
331C4×C43—41no—
332C4×C43—81no—
333C4×C43—81no—
334C4×C43#55111yescharacteristic
335C4×C43#55111yescharacteristic
336C4×C43#55311yescharacteristic
337C4×C43#55311yescharacteristic
338Dic43—81no—
339Dic43—81no—
340Dic43—81no—
341#2644—431no—
342#2328D4311yescharacteristic, complemented
343#2085—431no—
344#2073—431no—
345#2041—431no—
346#2011—431no—
347#1972—431no—
348#1970—431no—
349#1936—431no—
350#1934—431no—
351#1879—431no—
352#1879—431no—
353#1864—431no—
354#1862—431no—
355#1746—431no—
356C2×C43—82no—
357C2×C43—82no—
358C2×C43#260311yescharacteristic
359C2×C43#311811yescharacteristic
360C2×C43#312211yescharacteristic
361C2×C43#317611yescharacteristic
362C2×C43#317911yescharacteristic
363C2×C43#322011yescharacteristic
364C2×C43#322411yescharacteristic
365D43—161no—
366C22×D8—431no—
367C22×D8—431no—
368C2×#127C2×D4311yescharacteristic
369C2×C4×D4C2×D4311yescharacteristic
370C2×C4×D4C2×D4311yescharacteristic
371C2×#107—431no—
372C2×#106—431no—
373C2×#102—431no—
374C2×#102—431no—
375C2×#102—431no—
376C2×#102—431no—
377C2×#102—431no—
378C2×#102—431no—
379C2×#102—431no—
380C2×#102—431no—
381C2×#97—431no—
382C2×C4×C8—431no—
383#397—861no—
384#397—861no—
385#397—861no—
386#396—861no—
387#390—431no—
388#390—431no—
389#390—431no—
390#390C2×D4311yescharacteristic
391#390C2×D4311yescharacteristic
392#389—431no—
393#389—431no—
394#389—431no—
395#386—21no—
396#386—21no—
397#386—21no—
398#386—21no—
399#382C2×D4311yescharacteristic
400#376C2×D4311yescharacteristic
401#340—431no—
402#340—431no—
403#340—431no—
404#340—431no—
405#336—431no—
406#336—431no—
407#336—431no—
408#336—431no—
409C43#2950511yescharacteristic, complemented, Sylow
410C22×D4—21no—
411C22×D4—21no—
412C22×D4—431no—
413C22×D4C22×D4311yescharacteristic
414C22×D4C22×D4311yescharacteristic
415C23×C4—21no—
416C23×C4—21no—
417C2×D8—862no—
418C2×D8—862no—
419C2×D8—862no—
420C2×D8—862no—
421C2×D8—1721no—
422C2×D8—1721no—
423C22×C8—431no—
424C22×C8—431no—
425C22×C8—431no—
426C22×C8—431no—
427#127—22no—
428#127—22no—
429C4×D4—41no—
430C4×D4—41no—
431C4×D4—41no—
432C4×D4—41no—
433C2×C4⋊C4—431no—
434C2×C4⋊C4—431no—
435C2×C4⋊C4—431no—
436C2×C4⋊C4—861no—
437C2×C4⋊C4—861no—
438C2×C4⋊C4—861no—
439C2×C4⋊C4C22×D4311yescharacteristic
440C2×C4⋊C4C22×D4311yescharacteristic
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—861no—
448C2×C22⋊C4—861no—
449C2×C22⋊C4—861no—
450C2×C22⋊C4—861no—
451C2×C22⋊C4—861no—
452C2×C22⋊C4—861no—
453C2×C42C22×D4311yescharacteristic
454C2×C42C22×D4311yescharacteristic
455C2×C42C22×D4311yescharacteristic
456#107—1721no—
457#106—1721no—
458#102—862no—
459#102—862no—
460#102—862no—
461#102—862no—
462#102—1721no—
463#102—1721no—
464#102—1721no—
465#102—1721no—
466#97—862no—
467C4×C8—862no—
468#95—21no—
469#95—21no—
470#95—861no—
471#95—861no—
472#95—861no—
473#95C22⋊D4311yescharacteristic
474#95C22⋊D4311yescharacteristic
475#95C22⋊D4311yescharacteristic
476#95C22⋊D4311yescharacteristic
477C24—21no—
478C24—21no—
479C24—861no—
480C2×D4—24no—
481C2×D4—24no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—81no—
493C2×D4—81no—
494C2×D4—81no—
495C2×D4—81no—
496C2×D4—861no—
497C2×D4—861no—
498C2×D4—861no—
499C2×D4—861no—
500C2×D4—861no—
501C2×D4—861no—
502C2×D4#1062189812yes—
503C2×D4#1062189812yes—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—81no—
509C22×C4—81no—
510C22×C4—81no—
511C22×C4—81no—
512C22×C4—861no—
513C22×C4—861no—
514C22×C4—861no—
515C22×C4C2×C22⋊D4311yescharacteristic
516C22×C4C2×C22⋊D4311yescharacteristic
517C22×C4C2×C22⋊D4311yescharacteristic
518C22×C4C2×C22⋊D4311yescharacteristic
519C22×C4C2×C22⋊D4311yescharacteristic
520C22×C4C2×C22⋊D4311yescharacteristic
521C22×C4C23×D4311yescharacteristic
522D8—1724no—
523D8—1724no—
524C2×C8—432no—
525C2×C8—432no—
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—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—861no—
541C4⋊C4—861no—
542C4⋊C4—861no—
543C4⋊C4—861no—
544C4⋊C4—861no—
545C4⋊C4—861no—
546C4⋊C4—3441no—
547C4⋊C4—3441no—
548C4⋊C4—3441no—
549C22⋊C4—42no—
550C22⋊C4—42no—
551C22⋊C4—81no—
552C22⋊C4—81no—
553C22⋊C4—81no—
554C22⋊C4—81no—
555C22⋊C4—3441no—
556C22⋊C4—3441no—
557C22⋊C4—3441no—
558C22⋊C4—3441no—
559C22⋊C4—3441no—
560C22⋊C4—3441no—
561C42—21no—
562C42—21no—
563C42—21no—
564C42—21no—
565C42—21no—
566C42—21no—
567C23—22no—
568C23—22no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—1721no—
582C23—1721no—
583C23—1721no—
584C23—1721no—
585C23—1721no—
586C23—1721no—
587C23—1721no—
588C23C22×C22⋊D4311yescharacteristic
589D4—22no—
590D4—22no—
591D4—22no—
592D4—22no—
593D4—41no—
594D4—41no—
595D4—41no—
596D4—41no—
597D4—84no—
598D4—84no—
599D4—1721no—
600D4—1721no—
601D4—1721no—
602D4—1721no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
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—21no—
620C2×C4—21no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—84no—
628C2×C4—84no—
629C2×C4—1721no—
630C2×C4—1721no—
631C2×C4—1721no—
632C2×C4—1721no—
633C2×C4—1721no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4—1721no—
637C2×C4—1721no—
638C2×C4#41×D4311yescharacteristic
639C2×C4#41×D4311yescharacteristic
640C2×C4C2×#1062189811yescharacteristic
641C2×C4C2×#1062189811yescharacteristic
642C2×C4#1306337011yescharacteristic
643C2×C4#1306337011yescharacteristic
644C8—862no—
645C8—862no—
646C8—1721no—
647C8—1721no—
648C22—42no—
649C22—42no—
650C22—42no—
651C22—42no—
652C22—42no—
653C22—42no—
654C22—81no—
655C22—81no—
656C22—81no—
657C22—81no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22—81no—
662C22—3441no—
663C22—3441no—
664C22—3441no—
665C22—3441no—
666C22—3441no—
667C22—3441no—
668C22—3441no—
669C22#1458341011yescharacteristic
670C22#1458344511yescharacteristic
671C22#1458346611yescharacteristic
672C22#1458370211yescharacteristic
673C22#1458370211yescharacteristic
674C22#1458370211yescharacteristic
675C22#1458371011yescharacteristic
676C4—41no—
677C4—41no—
678C4—41no—
679C4—41no—
680C4—41no—
681C4—41no—
682C4—81no—
683C4—81no—
684C4—3441no—
685C4—3441no—
686C4—3441no—
687C4#1458357811yescharacteristic
688C4#1458357811yescharacteristic
689C4#1458359811yescharacteristic
690C4#1458359811yescharacteristic
691C2—82no—
692C2—82no—
693C2—6881no—
694C2#1914021611yescharacteristic
695C2#1914477911yescharacteristic
696C2#1914483811yescharacteristic
697C2#1914523911yescharacteristic
698C2#1914528011yescharacteristic
699C2#1914564511yescharacteristic
700C2#1914568911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2328C2
socleC23×C43C22×D4
prime radical#19135666C2
hypercenter#2328D43
hypocenterC43#29505
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ #376 ◁ #2328

Complements

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

NH ≅ G/Ntype
1. #19140555C2semidirect
2. #19136077C2semidirect
3. #19136009C2semidirect
4. #19135826C2semidirect
6. #19135470C2semidirect
7. #19135460C2semidirect
8. #19135295C2semidirect
9. #19135281C2semidirect
10. #19134943C2semidirect
11. #19134943C2semidirect
12. #19134856C2semidirect
13. #19134842C2semidirect
14. #19134347C2semidirect
15. C43×#2328C2semidirect
342. #2328D43semidirect
409. C43#29505semidirect

Maximal subgroups

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

subgroupindex
#191405552
#191360772
#191360092
#191358262
#191356662
#191354702
#191354602
#191352952
#191352812
#191349432
#191348562
#191348422
#191343472
C43×#23282
#2950543