Finite Group Databasebeta

← #25099626

Subgroups — #25099626

Order 11008.

1042 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583012C211yesmaximal, characteristic
2#19137056C211yesmaximal, characteristic, complemented
3C4×#13063287C211yesmaximal, characteristic, complemented
4#19135221C211yesmaximal, characteristic, complemented
5#19135214C211yesmaximal, characteristic, complemented
6#19135179C211yesmaximal, characteristic, complemented
7#19135172C211yesmaximal, characteristic, complemented
8#19134944C211yesmaximal, characteristic
9#19134944C211yesmaximal, characteristic
10#19134853C211yesmaximal, characteristic, complemented
11#19134839C211yesmaximal, characteristic, complemented
12#19134423C211yesmaximal, characteristic, complemented
13#19134423C211yesmaximal, characteristic, complemented
14#19134343C211yesmaximal, characteristic, complemented
15C43×#1776C211yesmaximal, characteristic, complemented
16C22×D344C2211yescharacteristic
17C2×C4×D172C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19C2×#13063287C2211yescharacteristic
20C2×#13063287C2211yescharacteristic
21C2×#13063282—21no—
22C2×C42×D43—21no—
23#14583012C418yescomplemented
24C2×#13063257C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×#13063236C2211yescharacteristic
32#14582800C2211yescharacteristic
33#14582800C2211yescharacteristic
34#14582795C2211yescharacteristic
35#14582795C2211yescharacteristic
36#14582788—21no—
37#14582788—21no—
38C4⋊C4×Dic43C2211yescharacteristic
39C4⋊C4×Dic43C2211yescharacteristic
40C4×(C2×D43)⋊C4—21no—
41C4×(C2×D43)⋊C4—21no—
42#14582746—21no—
43#14582746—21no—
44C42×Dic43C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×#107×C43C2211yescharacteristic
54C2×#106×C43C2211yescharacteristic
55C2×#97×C43C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C22×D172C2311yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C4×D43—21no—
63C22×C4×D43—21no—
64C22×C4×D43—21no—
65C22×C4×D43—21no—
66C2×D344—22no—
67C2×D344—22no—
68C2×D344C2×C414yes—
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71C4×D172—22no—
72C4×D172—22no—
73C4×D172C2×C414yes—
74C4×D172C2×C414yescomplemented
75#13063287—22no—
76#13063287—22no—
77#13063287—22no—
78#13063287—22no—
79#13063282—44no—
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
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×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43D411yescharacteristic
95C2×C4×Dic43D411yescharacteristic
96C2×C4×Dic43D411yescharacteristic
97C2×C4×Dic43D411yescharacteristic
98C2×C4×Dic43C2311yescharacteristic
99C2×C4×Dic43C2311yescharacteristic
100C42×D43—44no—
101#13063257C2×C414yescomplemented
102#13063247C2×C414yes—
103#13063247C2×C414yescomplemented
104#13063245—22no—
105#13063245—22no—
106#13063245—22no—
107#13063245—22no—
108#13063236—22no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C42×C43—21no—
120C2×C42×C43—21no—
121C2×C42×C43C2311yescharacteristic
122#107×C43—22no—
123#106×C43—22no—
124#97×C43C2×C414yescomplemented
125#95×C43—21no—
126#95×C43—21no—
127C23×D43—21no—
128C23×D43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2411yescharacteristic
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43C2×D411yescharacteristic
139C22×Dic43C2×D411yescharacteristic
140C22×Dic43C2×D411yescharacteristic
141C22×Dic43C2×D411yescharacteristic
142C2×D172—21no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172—21no—
146C2×D172—21no—
147C2×D172—21no—
148C2×D172—21no—
149C2×D172—21no—
150C2×D172C22×C412yes—
151C2×D172C22×C412yes—
152C2×D172#4112yes—
153C2×D172#4112yes—
154C2×C4×D43—24no—
155C2×C4×D43—24no—
156C2×C4×D43—24no—
157C2×C4×D43—24no—
158C2×C4×D43—42no—
159C2×C4×D43—42no—
160C2×C4×D43—42no—
161C2×C4×D43—42no—
162C2×C4×D43—42no—
163C2×C4×D43—42no—
164C2×C4×D43—42no—
165C2×C4×D43—42no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43C22×C412yes—
171C2×C8×C43C22×C412yes—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43#4112yes—
179C4⋊C4×C43#4112yes—
180C42×C43—42no—
181C42×C43—42no—
182C42×C43C22×C412yes—
183C42×C43#4112yes—
184(C2×D43)⋊C4—24no—
185(C2×D43)⋊C4—24no—
186(C2×D43)⋊C4—24no—
187(C2×D43)⋊C4—24no—
188(C2×D43)⋊C4—42no—
189(C2×D43)⋊C4—42no—
190(C2×D43)⋊C4—42no—
191(C2×D43)⋊C4—42no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43C22×C412yes—
195C4⋊Dic43C22×C412yes—
196Dic43⋊C4—42no—
197Dic43⋊C4—42no—
198C4×Dic43—21no—
199C4×Dic43—21no—
200C4×Dic43—21no—
201C4×Dic43—21no—
202C4×Dic43—22no—
203C4×Dic43—22no—
204C4×Dic43—41no—
205C4×Dic43—41no—
206C4×Dic43—42no—
207C4×Dic43—42no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214D344—28no—
215C23×C43C22×D411yescharacteristic
216C22×D43—22no—
217C22×D43—22no—
218C22×D43—22no—
219C22×D43—22no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—41no—
223C22×D43—41no—
224C22×D43—41no—
225C22×D43—41no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43—41no—
229C22×D43—41no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—22no—
235C2×C4×C43—22no—
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×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43C4×D412yes—
247C2×C4×C43C4×D412yes—
248C2×C4×C43C23×C411yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—22no—
259C2×Dic43—22no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43AGL(1,ℤ/8)12yes—
271C2×Dic43AGL(1,ℤ/8)12yes—
272D172—22no—
273D172—22no—
274D172—22no—
275D172—22no—
276D172—22no—
277D172—41no—
278D172—41no—
279D172#11714yescomplemented
280C4×D43—48no—
281C4×D43—48no—
282C4×D43—48no—
283C4×D43—48no—
284C8×C43—22no—
285C8×C43—22no—
286C43⋊C8—41no—
287C43⋊C8—41no—
288#21122—431nomaximal, Sylow
289C22×C43C2×C4×D411yescharacteristic
290C22×C43#52511yescharacteristic
291C22×C43#52511yescharacteristic
292C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
293C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
294C22×C43#57511yescharacteristic
295C22×C43#57511yescharacteristic
296C2×D43—24no—
297C2×D43—42no—
298C2×D43—42no—
299C2×D43—42no—
300C2×D43—42no—
301C2×D43—42no—
302C2×D43—42no—
303C2×D43—42no—
304C2×D43—42no—
305C2×D43—42no—
306C2×D43—81no—
307C2×D43—81no—
308C2×D43—81no—
309C2×D43—81no—
310C4×C43—22no—
311C4×C43—22no—
312C4×C43—42no—
313C4×C43—42no—
314C4×C43—81no—
315C4×C43—81no—
316C4×C43C2×#11711yescharacteristic
317C4×C43C4×#4111yescharacteristic
318C4×C43#52911yescharacteristic
319C4×C43#52911yescharacteristic
320Dic43—22no—
321Dic43—22no—
322Dic43—41no—
323Dic43—41no—
324Dic43—42no—
325Dic43—42no—
326C2×#442—431no—
327#2293—431no—
328C42×D4—431no—
329#1926—431no—
330#1925—431no—
331#1920—431no—
332#1919—431no—
333#1879—431no—
334#1879—431no—
335#1864—431no—
336#1862—431no—
337#1776D4311yescharacteristic, complemented
338#1762—431no—
339#1762—431no—
340#1745—431no—
341C2×C43#229011yescharacteristic
342C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
343C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
344C2×C43#310911yescharacteristic
345C2×C43#311111yescharacteristic
346C2×C43#311411yescharacteristic
347C2×C43#311511yescharacteristic
348D43—44no—
349D43—82no—
350C22×D8—431no—
351C2×C4×D4—431no—
352C2×C4×D4—431no—
353C2×C4×D4—431no—
354C2×C4×D4—431no—
355C2×#117—861no—
356C22×C42—861no—
357#442—438no—
358C2×#107C2×D4311yescharacteristic
359C2×#106—431no—
360C2×#106C2×D4311yescharacteristic
361C2×#102—431no—
362C2×#102—431no—
363C2×#102—431no—
364C2×#102—431no—
365C2×#102—431no—
366C2×#102—431no—
367C2×#97—431no—
368C2×#97C2×D4311yescharacteristic
369#390—431no—
370#390—431no—
371#389—431no—
372#389—431no—
373#388—861no—
374#388—861no—
375C4×C4⋊C4—431no—
376C4×C4⋊C4—431no—
377C4×C4⋊C4C2×D4311yescharacteristic
378C4×C4⋊C4C2×D4311yescharacteristic
379C4×C22⋊C4—861no—
380C4×C22⋊C4—861no—
381C4×C22⋊C4—861no—
382C4×C22⋊C4—861no—
383C43—431no—
384#340—431no—
385#340—431no—
386#340—431no—
387#340—431no—
388#340C2×D4311yescharacteristic
389#340C2×D4311yescharacteristic
390#336—431no—
391#336—431no—
392#336—431no—
393#336—431no—
394C43#2112211yescharacteristic, complemented, Sylow
395C22×D4—431no—
396C22×D4—431no—
397C23×C4—861no—
398C23×C4—861no—
399C23×C4—861no—
400C23×C4—861no—
401C2×D8—434no—
402C2×D8—862no—
403C2×D8—862no—
404C22×C8—431no—
405C22×C8—431no—
406C22×C8C22×D4311yescharacteristic
407C22×C8C22×D4311yescharacteristic
408C4×D4—434no—
409C4×D4—434no—
410C4×D4—862no—
411C4×D4—862no—
412C4×D4—862no—
413C4×D4—862no—
414C4×D4—862no—
415C4×D4—862no—
416#117—1724no—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4C22×D4311yescharacteristic
422C2×C4⋊C4C22×D4311yescharacteristic
423C2×C4⋊C4C22×D4311yescharacteristic
424C2×C4⋊C4C22×D4311yescharacteristic
425C2×C22⋊C4—861no—
426C2×C22⋊C4—861no—
427C2×C22⋊C4—861no—
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C22⋊C4—861no—
431C2×C22⋊C4—861no—
432C2×C22⋊C4—861no—
433C2×C42—21no—
434C2×C42—21no—
435C2×C42—431no—
436C2×C42—431no—
437C2×C42—431no—
438C2×C42—431no—
439C2×C42—431no—
440C2×C42—431no—
441C2×C42—861no—
442C2×C42—861no—
443C2×C42—1724no—
444C2×C42C22×D4311yescharacteristic
445#107—22no—
446#106—22no—
447#106—434no—
448#102—434no—
449#102—434no—
450#102—862no—
451#102—862no—
452#102—862no—
453#102—862no—
454#97—862no—
455#97C4×D4314yescomplemented
456#95—21no—
457#95—21no—
458#95—861no—
459#95—861no—
460#95—861no—
461#95—861no—
462C24—861no—
463C24—861no—
464C2×D4—432no—
465C2×D4—432no—
466C2×D4—432no—
467C2×D4—432no—
468C2×D4—861no—
469C2×D4—861no—
470C2×D4—861no—
471C2×D4—861no—
472C2×D4—861no—
473C2×D4—861no—
474C2×D4—861no—
475C2×D4—861no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—431no—
481C22×C4—431no—
482C22×C4—431no—
483C22×C4—431no—
484C22×C4—864no—
485C22×C4—864no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—864no—
489C22×C4—864no—
490C22×C4—1722no—
491C22×C4—1722no—
492C22×C4—1722no—
493C22×C4—1722no—
494C22×C4—1722no—
495C22×C4—1722no—
496C22×C4—1722no—
497C22×C4—1722no—
498C22×C4D4×D4311yescharacteristic
499C22×C4D4×D4311yescharacteristic
500C22×C4C23×D4311yescharacteristic
501D8—868no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8—861no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8C2×C4×D4312yes—
513C2×C8C2×C4×D4312yes—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—432no—
521C4⋊C4—432no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—1722no—
525C4⋊C4—1722no—
526C4⋊C4#1062189812yes—
527C4⋊C4#1062189812yes—
528C22⋊C4—864no—
529C22⋊C4—864no—
530C22⋊C4—864no—
531C22⋊C4—864no—
532C22⋊C4—1722no—
533C22⋊C4—1722no—
534C22⋊C4—1722no—
535C22⋊C4—1722no—
536C42—42no—
537C42—42no—
538C42—862no—
539C42—862no—
540C42—861no—
541C42—861no—
542C42—861no—
543C42—861no—
544C42—1721no—
545C42—1721no—
546C42—1722no—
547C42—1722no—
548C42C2×C4×D4312yes—
549C42#1062190212yes—
550C23—862no—
551C23—862no—
552C23—862no—
553C23—862no—
554C23—1721no—
555C23—1721no—
556C23—1721no—
557C23—1721no—
558C23—1721no—
559C23—1721no—
560C23—1721no—
561C23—1721no—
562C23—1721no—
563C23—1721no—
564C23C2×D4×D4311yescharacteristic
565D4—434no—
566D4—862no—
567D4—862no—
568D4—862no—
569D4—862no—
570D4—862no—
571D4—1721no—
572D4—1721no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—432no—
590C2×C4—432no—
591C2×C4—861no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—862no—
596C2×C4—862no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—861no—
602C2×C4—861no—
603C2×C4—1728no—
604C2×C4—1728no—
605C2×C4—1728no—
606C2×C4—1728no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4#1306328712yes—
612C2×C4#1306328712yes—
613C2×C4C22×C4×D4311yescharacteristic
614C2×C4#41×D4311yescharacteristic
615C2×C4#41×D4311yescharacteristic
616C2×C4C2×#1062189811yescharacteristic
617C2×C4C2×#1062189811yescharacteristic
618C2×C4C2×#1062190211yescharacteristic
619C8—22no—
620C8—22no—
621C8—1721no—
622C8—1721no—
623C22—864no—
624C22—3441no—
625C22—3441no—
626C22—3441no—
627C22—3441no—
628C22—1722no—
629C22—1722no—
630C22—1722no—
631C22—1722no—
632C22—1722no—
633C22—1722no—
634C22—1722no—
635C22—1722no—
636C22—1722no—
637C22C2×#1306328711yescharacteristic
638C22#1458340811yescharacteristic
639C22#1458340811yescharacteristic
640C22AGL(1,ℤ/8)×D4311yescharacteristic
641C22AGL(1,ℤ/8)×D4311yescharacteristic
642C22#1458369811yescharacteristic
643C22#1458369811yescharacteristic
644C4—22no—
645C4—22no—
646C4—42no—
647C4—42no—
648C4—81no—
649C4—81no—
650C4—862no—
651C4—862no—
652C4—1721no—
653C4—1721no—
654C4—1722no—
655C4—1722no—
656C4#117×D4311yescharacteristic
657C4C4×#1062189811yescharacteristic
658C4#1458343611yescharacteristic
659C4#1458343611yescharacteristic
660C2—3442no—
661C2—1724no—
662C2#1913703611yescharacteristic
663C2#1914340211yescharacteristic
664C2#1914340211yescharacteristic
665C2#1914468411yescharacteristic
666C2#1914471011yescharacteristic
667C2#1914473711yescharacteristic
668C2#1914474411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1776C2
socleC23×C43C22×D4
prime radicalC22×D344C22
cosocleC22×C4×C43C24
hypercenter#1776D43
hypocenterC43#21122
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1776

Complements

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

NH ≅ G/Ntype
2. #19137056C2semidirect
3. C4×#13063287C2semidirect
4. #19135221C2semidirect
5. #19135214C2semidirect
6. #19135179C2semidirect
7. #19135172C2semidirect
10. #19134853C2semidirect
11. #19134839C2semidirect
12. #19134423C2semidirect
13. #19134423C2semidirect
14. #19134343C2semidirect
15. C43×#1776C2semidirect
23. #14583012C4semidirect
74. C4×D172C2×C4semidirect
101. #13063257C2×C4semidirect
103. #13063247C2×C4semidirect
124. #97×C43C2×C4semidirect
279. D172#117semidirect
337. #1776D43semidirect
394. C43#21122semidirect
455. #97C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830122
#191370562
C4×#130632872
#191352212
#191352142
#191351792
#191351722
#191349442
#191348532
#191348392
#191344232
#191343432
C43×#17762
#2112243