Finite Group Databasebeta

← #25169775

Subgroups — #25169775

Order 11008.

874 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137659C211yesmaximal, characteristic, complemented
2#19136119C211yesmaximal, characteristic, complemented
3#19135905C211yesmaximal, characteristic, complemented
4#19135829C211yesmaximal, characteristic, complemented
5#19135665C211yesmaximal, characteristic
6#19135460C211yesmaximal, characteristic, complemented
7#19135222C211yesmaximal, characteristic, complemented
8#19135219C211yesmaximal, characteristic, complemented
9#19135184C211yesmaximal, characteristic, complemented
10#19135154C211yesmaximal, characteristic, complemented
11#19134946C211yesmaximal, characteristic, complemented
12#19134946C211yesmaximal, characteristic, complemented
13#19134602C211yesmaximal, characteristic, complemented
14C4×#13063245C211yesmaximal, characteristic, complemented
15C43×#2513C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C2×#13063322C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×#13063287—21no—
22C2×#13063258C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×C4⋊(C43⋊C8)C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×C4×C43⋊C8C2211yescharacteristic
34#14582801C2211yescharacteristic
35#14582801C2211yescharacteristic
36#14582800—21no—
37#14582777—21no—
38#14582777—21no—
39C4×C4⋊Dic43C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582654C2211yescharacteristic
45#14582654C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C43×#397—21no—
49C43×#397—21no—
50C43×#390C2211yescharacteristic
51C43×#390C2211yescharacteristic
52C43×#390C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C43×#388—21no—
55C43×#388—21no—
56C43×#382C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C4×C4⋊C4×C43C2211yescharacteristic
59C22×D172—21no—
60C22×D172—21no—
61C22×D172C2311yescharacteristic
62C22×D172C2311yescharacteristic
63C22×C4×D43—21no—
64C22×C4×D43—21no—
65C2×#10621882—22no—
66C2×#10621882—22no—
67C2×#10621882—22no—
68C2×#10621882—41no—
69C2×#10621882—41no—
70C2×#10621882—41no—
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75#13063322—22no—
76#13063322—22no—
77C4×D172—22no—
78C4×D172—22no—
79C4×D172—41no—
80C4×D172—41no—
81#13063287—44no—
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×C4×Dic43—21no—
91#13063258—22no—
92#13063256—41no—
93C4⋊(C43⋊C8)—41no—
94#13063246—22no—
95#13063246—41no—
96#13063245—22no—
97#13063245—22no—
98#13063245—22no—
99#13063245—41no—
100#13063245—41no—
101#13063245—41no—
102C4×C43⋊C8—41no—
103C43⋊#95—21no—
104C22×D4×C43C2311yescharacteristic
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×C43—21no—
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43—21no—
116C2×C22⋊C4×C43—21no—
117C2×C42×C43—21no—
118C2×C42×C43C2311yescharacteristic
119C2×C42×C43C2311yescharacteristic
120C2×C42×C43C2311yescharacteristic
121#95×C43—21no—
122#95×C43—21no—
123#95×C43—21no—
124#95×C43—21no—
125#95×C43D411yescharacteristic
126#95×C43D411yescharacteristic
127C24×C43—21no—
128C23×D43—21no—
129C23×D43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×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×D411yescharacteristic
145C22×C4×C43C2411yescharacteristic
146C22×Dic43—21no—
147C22×Dic43—21no—
148C2×D172—24no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172—24no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—42no—
161C2×D172—42no—
162C2×D172—81no—
163C2×D172—81no—
164C2×D172#4112yes—
165C2×D172#4112yes—
166C2×C4×D43—42no—
167C2×C4×D43—42no—
168C2×C4×D43—42no—
169C2×C4×D43—42no—
170C2×C4×D43—81no—
171C2×C4×D43—81no—
172C4⋊C4×C43—22no—
173C4⋊C4×C43—22no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—81no—
181C22⋊C4×C43—42no—
182C22⋊C4×C43—42no—
183C22⋊C4×C43—81no—
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—21no—
192C42×C43—21no—
193C42×C43—81no—
194#10621882—44no—
195#10621882—44no—
196(C2×D43)⋊C4—42no—
197(C2×D43)⋊C4—42no—
198(C2×D43)⋊C4—42no—
199(C2×D43)⋊C4—42no—
200(C2×D43)⋊C4—81no—
201(C2×D43)⋊C4—81no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43#4112yes—
206C4×Dic43—42no—
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—
218C2×C43⋊C8#4112yes—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43C22×D411yescharacteristic
227C22×D43—22no—
228C22×D43—22no—
229C22×D43—41no—
230C22×D43—41no—
231C22×D43—41no—
232C22×D43—41no—
233C22×D43—41no—
234C22×D43—41no—
235C22×D43—41no—
236C22×D43—41no—
237C22×D43—41no—
238C22×D43—41no—
239C22×D43—41no—
240C22×D43—41no—
241D4×C43—41no—
242D4×C43—41no—
243D4×C43—41no—
244D4×C43—41no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
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#13512yes—
271C2×C4×C43AGL(1,ℤ/8)12yes—
272C2×C4×C43C2×#4111yescharacteristic
273C2×C4×C43C2×#4111yescharacteristic
274C2×C4×C43C2×#4111yescharacteristic
275C2×C4×C43C2×#4111yescharacteristic
276C2×C4×C43H(5,𝔽2)11yescharacteristic
277C2×C4×C43H(5,𝔽2)11yescharacteristic
278C2×Dic43—22no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284D172—22no—
285D172—22no—
286D172—22no—
287D172—22no—
288D172—48no—
289D172—41no—
290D172—41no—
291D172—41no—
292D172—41no—
293D172—84no—
294C4×D43—84no—
295C4×D43—84no—
296C43⋊C8—22no—
297C43⋊C8—41no—
298C43⋊C8—41no—
299C43⋊C8—41no—
300#27065—431nomaximal, Sylow
301C22×C43—81no—
302C22×C43—81no—
303C22×C43—81no—
304C22×C43—81no—
305C22×C43—81no—
306C22×C43—81no—
307C22×C43—81no—
308C22×C43#52511yescharacteristic
309C22×C43#54611yescharacteristic
310C22×C43#55011yescharacteristic
311C22×C43C2×#13511yescharacteristic
312C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
313C22×C43#57611yescharacteristic
314C22×C43#57611yescharacteristic
315C2×D43—42no—
316C2×D43—42no—
317C2×D43—42no—
318C2×D43—42no—
319C2×D43—42no—
320C2×D43—42no—
321C2×D43—81no—
322C2×D43—81no—
323C2×D43—81no—
324C2×D43—81no—
325C2×D43—81no—
326C2×D43—81no—
327C2×D43—81no—
328C2×D43—81no—
329C4×C43—22no—
330C4×C43—22no—
331C4×C43—41no—
332C4×C43—41no—
333C4×C43—41no—
334C4×C43—41no—
335C4×C43—81no—
336C4×C43—81no—
337C4×C43—81no—
338C4×C43#52911yescharacteristic
339C4×C43#53811yescharacteristic
340C4×C43#55111yescharacteristic
341C4×C43#55311yescharacteristic
342Dic43—42no—
343Dic43—81no—
344#2513D4311yescharacteristic, complemented
345#2366—431no—
346#2092—431no—
347#2054—431no—
348#2041—431no—
349#2011—431no—
350#1970—431no—
351#1926—431no—
352#1926—431no—
353#1921—431no—
354#1916—431no—
355#1879—431no—
356#1879—431no—
357#1804—431no—
358C4×#102—431no—
359C2×C43—161no—
360C2×C43#246711yescharacteristic
361C2×C43#310511yescharacteristic
362C2×C43#312211yescharacteristic
363C2×C43#330511yescharacteristic
364C2×C43#331811yescharacteristic
365C2×C43#339611yescharacteristic
366C2×C43#339911yescharacteristic
367D43—82no—
368D43—82no—
369C22×D8—431no—
370C22×D8—431no—
371C2×#127—431no—
372C2×C4×D4—431no—
373C2×C4×D4—431no—
374C2×C4×D4—861no—
375C2×#107—431no—
376C2×#106—431no—
377C2×C4⋊C8—431no—
378C2×#102—431no—
379C2×#102—431no—
380C2×#102—431no—
381C2×#102—431no—
382C2×#102—431no—
383C2×#102—431no—
384C2×#102—431no—
385C2×#102—431no—
386C2×C4×C8—431no—
387#397—21no—
388#397—21no—
389#390—431no—
390#390—431no—
391#390—861no—
392#390C2×D4311yescharacteristic
393#390C2×D4311yescharacteristic
394#390C2×D4311yescharacteristic
395#389C2×D4311yescharacteristic
396#388—21no—
397#388—21no—
398#386—861no—
399#386—861no—
400#382C2×D4311yescharacteristic
401C4×C4⋊C4—431no—
402C4×C4⋊C4C2×D4311yescharacteristic
403C4×C4⋊C4C2×D4311yescharacteristic
404#340—431no—
405#340—431no—
406#340—431no—
407#340—431no—
408#336—431no—
409#336—431no—
410#336—431no—
411#336—431no—
412C43#2706511yescharacteristic, complemented, Sylow
413C22×D4—431no—
414C22×D4—431no—
415C22×D4—861no—
416C22×D4—861no—
417C22×D4C22×D4311yescharacteristic
418C23×C4—861no—
419C23×C4—861no—
420C2×D8—862no—
421C2×D8—862no—
422C2×D8—862no—
423C2×D8—1721no—
424C2×D8—1721no—
425C2×D8—1721no—
426C22×C8—431no—
427C22×C8—431no—
428C22×C8—431no—
429C22×C8—431no—
430#127—862no—
431#127—862no—
432C4×D4—862no—
433C4×D4—862no—
434C4×D4—1721no—
435C4×D4—1721no—
436C4×D4—1724no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—431no—
439C2×C4⋊C4—431no—
440C2×C4⋊C4C22⋊D4311yescharacteristic
441C2×C4⋊C4C22⋊D4311yescharacteristic
442C2×C4⋊C4C22×D4311yescharacteristic
443C2×C4⋊C4C22×D4311yescharacteristic
444C2×C4⋊C4C22×D4311yescharacteristic
445C2×C22⋊C4—21no—
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⋊C4—861no—
457C2×C42—21no—
458C2×C42—861no—
459C2×C42C22×D4311yescharacteristic
460C2×C42C22×D4311yescharacteristic
461C2×C42C22×D4311yescharacteristic
462#107—862no—
463#106—1721no—
464C4⋊C8—1721no—
465#102—862no—
466#102—862no—
467#102—862no—
468#102—862no—
469#102—1721no—
470#102—1721no—
471#102—1721no—
472#102—1721no—
473C4×C8—1721no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—861no—
479#95C22⋊D4311yescharacteristic
480#95C22⋊D4311yescharacteristic
481C24—21no—
482C24—861no—
483C24—861no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—432no—
491C2×D4—432no—
492C2×D4—864no—
493C2×D4—864no—
494C2×D4—861no—
495C2×D4—861no—
496C2×D4—861no—
497C2×D4—861no—
498C2×D4—861no—
499C2×D4—861no—
500C2×D4—861no—
501C2×D4—861no—
502C2×D4—861no—
503C2×D4—861no—
504C2×D4—3441no—
505C2×D4—3441no—
506C2×D4—1722no—
507C2×D4—1722no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—861no—
512C22×C4—861no—
513C22×C4—3441no—
514C22×C4—3441no—
515C22×C4—1722no—
516C22×C4—1722no—
517C22×C4—1722no—
518C22×C4—1722no—
519C22×C4C2×C22⋊D4311yescharacteristic
520C22×C4C2×C22⋊D4311yescharacteristic
521C22×C4C2×C22⋊D4311yescharacteristic
522C22×C4C2×C22⋊D4311yescharacteristic
523C22×C4C2×C22⋊D4311yescharacteristic
524C22×C4C2×C22⋊D4311yescharacteristic
525C22×C4C23×D4311yescharacteristic
526D8—1724no—
527D8—1724no—
528C2×C8—432no—
529C2×C8—861no—
530C2×C8—861no—
531C2×C8—861no—
532C2×C8—861no—
533C2×C8—861no—
534C2×C8—861no—
535C2×C8—861no—
536C2×C8—861no—
537C2×C8—861no—
538C2×C8—861no—
539C2×C8—861no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—81no—
549C4⋊C4—432no—
550C4⋊C4—861no—
551C4⋊C4—861no—
552C4⋊C4—861no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—81no—
556C22⋊C4—81no—
557C22⋊C4—81no—
558C22⋊C4—81no—
559C22⋊C4—3441no—
560C22⋊C4—3441no—
561C22⋊C4—1722no—
562C22⋊C4—1722no—
563C22⋊C4—1722no—
564C22⋊C4—1722no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—81no—
572C42—1722no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—862no—
581C23—862no—
582C23—1721no—
583C23—1721no—
584C23—1721no—
585C23—1721no—
586C23—1721no—
587C23—1721no—
588C23—1721no—
589C23—1721no—
590C23—1721no—
591C23—1721no—
592C23—1721no—
593C23—1721no—
594C23C22×C22⋊D4311yescharacteristic
595D4—41no—
596D4—41no—
597D4—41no—
598D4—41no—
599D4—862no—
600D4—862no—
601D4—862no—
602D4—862no—
603D4—3444no—
604D4—1728no—
605D4—1721no—
606D4—1721no—
607D4—1721no—
608D4—1721no—
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—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—862no—
635C2×C4—3444no—
636C2×C4—3444no—
637C2×C4—1721no—
638C2×C4—1721no—
639C2×C4—1721no—
640C2×C4—1721no—
641C2×C4—1721no—
642C2×C4#1306334512yes—
643C2×C4#1306335012yes—
644C2×C4#41×D4311yescharacteristic
645C2×C4#41×D4311yescharacteristic
646C2×C4#41×D4311yescharacteristic
647C2×C4#41×D4311yescharacteristic
648C2×C4#1306337111yescharacteristic
649C2×C4#1306337111yescharacteristic
650C8—862no—
651C8—1721no—
652C8—1721no—
653C8—1721no—
654C22—81no—
655C22—81no—
656C22—81no—
657C22—81no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22—3441no—
662C22—3441no—
663C22—3441no—
664C22—3441no—
665C22—3441no—
666C22—3441no—
667C22—3441no—
668C22—3441no—
669C22—1722no—
670C22—1722no—
671C22—1722no—
672C22—1722no—
673C22—1722no—
674C22—1722no—
675C22#1458340611yescharacteristic
676C22#1458353711yescharacteristic
677C22#1458356811yescharacteristic
678C22C2×#1306334511yescharacteristic
679C22C2×#1306335011yescharacteristic
680C22#1458370211yescharacteristic
681C22#1458370211yescharacteristic
682C4—22no—
683C4—22no—
684C4—41no—
685C4—41no—
686C4—41no—
687C4—41no—
688C4—81no—
689C4—81no—
690C4—81no—
691C4—3441no—
692C4—1722no—
693C4#1458343211yescharacteristic
694C4#1458348811yescharacteristic
695C4#1458357411yescharacteristic
696C4#1458360011yescharacteristic
697C2—161no—
698C2—3442no—
699C2—3442no—
700C2#1913864211yescharacteristic
701C2#1914463811yescharacteristic
702C2#1914483311yescharacteristic
703C2#1914653911yescharacteristic
704C2#1914673011yescharacteristic
705C2#1914760311yescharacteristic
706C2#1914763311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2513C2
socleC23×C43C22×D4
prime radical#19135665C2
hypercenter#2513D43
hypocenterC43#27065
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2513

Complements

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

NH ≅ G/Ntype
1. #19137659C2semidirect
2. #19136119C2semidirect
3. #19135905C2semidirect
4. #19135829C2semidirect
6. #19135460C2semidirect
7. #19135222C2semidirect
8. #19135219C2semidirect
9. #19135184C2semidirect
10. #19135154C2semidirect
11. #19134946C2semidirect
12. #19134946C2semidirect
13. #19134602C2semidirect
14. C4×#13063245C2semidirect
15. C43×#2513C2semidirect
344. #2513D43semidirect
412. C43#27065semidirect

Maximal subgroups

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

subgroupindex
#191376592
#191361192
#191359052
#191358292
#191356652
#191354602
#191352222
#191352192
#191351842
#191351542
#191349462
#191346022
C4×#130632452
C43×#25132
#2706543