Finite Group Databasebeta

← #25159751

Subgroups — #25159751

Order 11008.

932 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583196C211yesmaximal, characteristic, complemented
2C2×#14582981C211yesmaximal, characteristic
3#19138463C211yesmaximal, characteristic, complemented
4#19137496C211yesmaximal, characteristic, complemented
5#19136125C211yesmaximal, characteristic, complemented
6#19136069C211yesmaximal, characteristic, complemented
7#19135966C211yesmaximal, characteristic, complemented
8#19135322C211yesmaximal, characteristic, complemented
9#19135155C211yesmaximal, characteristic, complemented
10#19134944C211yesmaximal, characteristic
11#19134942C211yesmaximal, characteristic
12#19134857C211yesmaximal, characteristic, complemented
13#19134853C211yesmaximal, characteristic, complemented
14#19134843C211yesmaximal, characteristic, complemented
15C43×#2059C211yesmaximal, characteristic, complemented
16C22×D344C2211yescharacteristic
17C2×C4×D172C2211yescharacteristic
18C2×#13063287C2211yescharacteristic
19C2×#13063287C2211yescharacteristic
20C2×#13063287C2211yescharacteristic
21C2×C4⋊C4×D43—21no—
22#14583196—24no—
23#14582981—24no—
24C2×#13063258C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×#13063256C2211yescharacteristic
27C2×C4⋊(C43⋊C8)C2211yescharacteristic
28C2×#13063247C2211yescharacteristic
29C2×#13063247C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×C8×Dic43C2211yescharacteristic
35#14582834—21no—
36#14582821—21no—
37#14582801C2211yescharacteristic
38#14582800C2211yescharacteristic
39#14582798C2211yescharacteristic
40#14582798C2211yescharacteristic
41#14582795C2211yescharacteristic
42#14582773—21no—
43#14582770—21no—
44#14582770—21no—
45#14582768C2211yescharacteristic
46#14582758—21no—
47#14582756—21no—
48C4×Dic43⋊C4C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×#125×C43C2211yescharacteristic
55C2×#107×C43C2211yescharacteristic
56C2×#106×C43C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×D172C2311yescharacteristic
62C22×D172C2311yescharacteristic
63C22×C4×D43—21no—
64C22×C4×D43—21no—
65C22×C4×D43—21no—
66C22×C4×D43—21no—
67C2×D344—22no—
68C2×D344—22no—
69C2×D344Q814yes—
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72C4×D172—22no—
73C4×D172—41no—
74#13063287—22no—
75#13063287—22no—
76#13063287—22no—
77#13063287—22no—
78#13063287—41no—
79#13063287—41no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43—21no—
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4D411yescharacteristic
88C2×Dic43⋊C4D411yescharacteristic
89C4⋊C4×D43—44no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×C4×Dic43C2311yescharacteristic
99C2×C4×Dic43C2311yescharacteristic
100#13063258—22no—
101#13063256—22no—
102#13063256—22no—
103C4⋊(C43⋊C8)—22no—
104#13063247—22no—
105#13063247—41no—
106#13063245—22no—
107#13063245—22no—
108#13063245—22no—
109#13063245D414yes—
110C8×Dic43—22no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95D411yescharacteristic
115C43⋊#95D411yescharacteristic
116C22×C8×C43C2311yescharacteristic
117C22×C8×C43C2311yescharacteristic
118#125×C43—22no—
119#125×C43—41no—
120C2×C4⋊C4×C43—21no—
121C2×C4⋊C4×C43—21no—
122C2×C4⋊C4×C43—21no—
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C42×C43C2311yescharacteristic
128#107×C43—22no—
129#106×C43—41no—
130#95×C43—21no—
131C23×D43—21no—
132C23×D43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2411yescharacteristic
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43C2×D411yescharacteristic
143C22×Dic43C2×D411yescharacteristic
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C2×D172—21no—
147C2×D172—21no—
148C2×D172—21no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172C2×D412yes—
155C2×D172C2×Q812yes—
156C2×D172C2×Q812yes—
157C2×D172#4112yes—
158C2×C4×D43—24no—
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×C4×D43—42no—
167C2×C4×D43—81no—
168C2×C4×D43—81no—
169C2×C4×D43—81no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43C2×Q812yes—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—42no—
183C4⋊C4×C43—42no—
184C4⋊C4×C43—42no—
185C4⋊C4×C43C2×D412yes—
186C4⋊C4×C43#4112yes—
187C42×C43—21no—
188C42×C43—21no—
189(C2×D43)⋊C4—24no—
190(C2×D43)⋊C4—42no—
191(C2×D43)⋊C4—42no—
192(C2×D43)⋊C4—42no—
193(C2×D43)⋊C4—42no—
194(C2×D43)⋊C4—81no—
195(C2×D43)⋊C4—81no—
196(C2×D43)⋊C4—81no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—42no—
202C4⋊Dic43—81no—
203Dic43⋊C4—22no—
204Dic43⋊C4—22no—
205Dic43⋊C4—42no—
206Dic43⋊C4—81no—
207Dic43⋊C4—81no—
208C4×Dic43—21no—
209C4×Dic43—21no—
210C4×Dic43—21no—
211C4×Dic43—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8C2×D412yes—
218D344—28no—
219C23×C43C22×D411yescharacteristic
220C22×D43—22no—
221C22×D43—22no—
222C22×D43—22no—
223C22×D43—22no—
224C22×D43—41no—
225C22×D43—41no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43—41no—
229C22×D43—41no—
230C22×D43—41no—
231C22×D43—41no—
232C22×D43—41no—
233C22×D43—41no—
234C2×C4×C43—22no—
235C2×C4×C43—21no—
236C2×C4×C43—22no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43C22×D411yescharacteristic
253C2×C4×C43C22×Q811yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43H(5,𝔽2)11yescharacteristic
257C2×C4×C432−1+411yescharacteristic
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43#13512yes—
275C2×Dic43AGL(1,ℤ/8)12yes—
276D172—22no—
277D172—22no—
278D172—22no—
279D172—22no—
280D172—22no—
281D172—41no—
282D172—41no—
283D172C22⋊Q814yes—
284C4×D43—48no—
285C4×D43—84no—
286C4×D43—84no—
287C4×D43—84no—
288C8×C43—22no—
289C8×C43—41no—
290C43⋊C8—22no—
291C43⋊C8—41no—
292#26382—431nomaximal, Sylow
293C22×C43#52511yescharacteristic
294C22×C43D4211yescharacteristic
295C22×C43D4×Q811yescharacteristic
296C22×C43C2×#13511yescharacteristic
297C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
298C22×C43#57611yescharacteristic
299C22×C43#57711yescharacteristic
300C2×D43—24no—
301C2×D43—42no—
302C2×D43—42no—
303C2×D43—42no—
304C2×D43—42no—
305C2×D43—42no—
306C2×D43—42no—
307C2×D43—42no—
308C2×D43—42no—
309C2×D43—42no—
310C2×D43—81no—
311C2×D43—81no—
312C2×D43—81no—
313C2×D43—81no—
314C4×C43—42no—
315C4×C43—41no—
316C4×C43—42no—
317C4×C43—41no—
318C4×C43—81no—
319C4×C43—81no—
320C4×C43C2×C22⋊Q811yescharacteristic
321C4×C43#53911yescharacteristic
322C4×C43#54711yescharacteristic
323C4×C43#55411yescharacteristic
324Dic43—22no—
325Dic43—22no—
326Dic43—41no—
327Dic43—41no—
328Dic43—81no—
329Dic43—81no—
330C2×#478—431no—
331C2×C4×D8—431no—
332#2454—431no—
333D4×C4⋊C4—431no—
334#2094—431no—
335#2083—431no—
336#2065—431no—
337#2059D4311yescharacteristic, complemented
338#1941—431no—
339#1916—431no—
340#1879—431no—
341#1879—431no—
342#1864—431no—
343#1864—431no—
344#1862—431no—
345C2×C43#244911yescharacteristic
346C2×C43#310511yescharacteristic
347C2×C43#311911yescharacteristic
348C2×C43#326411yescharacteristic
349C2×C43#328411yescharacteristic
350C2×C43#338011yescharacteristic
351C2×C43#338411yescharacteristic
352D43—44no—
353D43—82no—
354C22×D8—431no—
355C2×#125C2×D4311yescharacteristic
356C2×C4×D4—431no—
357C2×C4×D4—431no—
358C2×C4×D4—431no—
359C2×C4×D4—431no—
360C22×C4⋊C4—861no—
361#478—864no—
362C4×D8—864no—
363C2×#107—431no—
364C2×#107C2×D4311yescharacteristic
365C2×#106—431no—
366C2×#106—431no—
367C2×#106C2×D4311yescharacteristic
368C2×C4⋊C8—431no—
369C2×#102—431no—
370C2×#102—431no—
371C2×#102—431no—
372C2×#102—431no—
373C2×#102—431no—
374C2×#102—431no—
375C2×C4×C8—431no—
376#399—861no—
377#396—861no—
378#390—431no—
379#390—431no—
380#389—431no—
381#389—431no—
382#389—431no—
383#389C2×D4311yescharacteristic
384#385—861no—
385#385—861no—
386#385—861no—
387#384—431no—
388#380—861no—
389#380—861no—
390C4×C4⋊C4—431no—
391#340—431no—
392#340—431no—
393#340C2×D4311yescharacteristic
394#340C2×D4311yescharacteristic
395#336—431no—
396#336—431no—
397#336—431no—
398#336C2×D4311yescharacteristic
399C43#2638211yescharacteristic, complemented, Sylow
400C22×D4—431no—
401C22×D4—431no—
402C23×C4—861no—
403C23×C4—861no—
404C23×C4—861no—
405C23×C4—861no—
406C2×D8—434no—
407C2×D8—862no—
408C2×D8—862no—
409C22×C8—431no—
410C22×C8—431no—
411C22×C8C22×D4311yescharacteristic
412C22×C8C22×D4311yescharacteristic
413#125—22no—
414#125—41no—
415C4×D4—862no—
416C4×D4—862no—
417C4×D4—862no—
418C4×D4—862no—
419C4×D4—862no—
420C4×D4—1721no—
421C4×D4—1721no—
422C4×D4—1721no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—431no—
427C2×C4⋊C4—431no—
428C2×C4⋊C4—431no—
429C2×C4⋊C4—431no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4—861no—
433C2×C4⋊C4—861no—
434C2×C4⋊C4—861no—
435C2×C4⋊C4—1724no—
436C2×C4⋊C4C22×D4311yescharacteristic
437C2×C4⋊C4C22×D4311yescharacteristic
438C2×C4⋊C4C22×D4311yescharacteristic
439C2×C4⋊C4C22×D4311yescharacteristic
440C2×C22⋊C4—861no—
441C2×C22⋊C4—861no—
442C2×C22⋊C4—861no—
443C2×C22⋊C4—861no—
444C2×C22⋊C4—861no—
445C2×C22⋊C4—861no—
446C2×C22⋊C4—861no—
447C2×C22⋊C4—861no—
448C2×C42—431no—
449C2×C42—431no—
450C2×C42C22×D4311yescharacteristic
451#107—22no—
452#107—862no—
453#106—41no—
454#106—862no—
455#106—862no—
456C4⋊C8—862no—
457#102—434no—
458#102—862no—
459#102—862no—
460#102—862no—
461#102—862no—
462#102—1721no—
463C4×C8—862no—
464#95—21no—
465#95—431no—
466#95—431no—
467#95—861no—
468#95—861no—
469#95—861no—
470C24—861no—
471C24—861no—
472C2×D4—432no—
473C2×D4—432no—
474C2×D4—432no—
475C2×D4—432no—
476C2×D4—861no—
477C2×D4—861no—
478C2×D4—861no—
479C2×D4—861no—
480C2×D4—861no—
481C2×D4—861no—
482C2×D4—861no—
483C2×D4—861no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—431no—
489C22×C4—431no—
490C22×C4—431no—
491C22×C4—431no—
492C22×C4—864no—
493C22×C4—861no—
494C22×C4—861no—
495C22×C4—3441no—
496C22×C4—3441no—
497C22×C4—3441no—
498C22×C4—1722no—
499C22×C4—1722no—
500C22×C4—1722no—
501C22×C4—1722no—
502C22×C4—1722no—
503C22×C4—1722no—
504C22×C4—1722no—
505C22×C4—1722no—
506C22×C4D4×D4311yescharacteristic
507C22×C4D4×D4311yescharacteristic
508C22×C4C23×D4311yescharacteristic
509D8—868no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—432no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8Q8×D4312yes—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—42no—
529C4⋊C4—42no—
530C4⋊C4—42no—
531C4⋊C4—862no—
532C4⋊C4—862no—
533C4⋊C4—861no—
534C4⋊C4—861no—
535C4⋊C4—861no—
536C4⋊C4—861no—
537C4⋊C4—3441no—
538C4⋊C4—3441no—
539C4⋊C4—3441no—
540C4⋊C4—1722no—
541C4⋊C4—1722no—
542C4⋊C4D4×D4312yes—
543C4⋊C4#1062190212yes—
544C22⋊C4—864no—
545C22⋊C4—3441no—
546C22⋊C4—3441no—
547C22⋊C4—3441no—
548C22⋊C4—1722no—
549C22⋊C4—1722no—
550C22⋊C4—1722no—
551C22⋊C4—1722no—
552C42—21no—
553C42—21no—
554C42—861no—
555C42—861no—
556C42—861no—
557C42—861no—
558C23—862no—
559C23—862no—
560C23—862no—
561C23—862no—
562C23—1721no—
563C23—1721no—
564C23—1721no—
565C23—1721no—
566C23—1721no—
567C23—1721no—
568C23—1721no—
569C23—1721no—
570C23—1721no—
571C23—1721no—
572C23C2×D4×D4311yescharacteristic
573D4—434no—
574D4—862no—
575D4—862no—
576D4—862no—
577D4—862no—
578D4—862no—
579D4—1721no—
580D4—1721no—
581C2×C4—22no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—22no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—432no—
600C2×C4—432no—
601C2×C4—861no—
602C2×C4—861no—
603C2×C4—861no—
604C2×C4—861no—
605C2×C4—861no—
606C2×C4—861no—
607C2×C4—861no—
608C2×C4—861no—
609C2×C4—861no—
610C2×C4—861no—
611C2×C4—3444no—
612C2×C4—3444no—
613C2×C4—3444no—
614C2×C4—1728no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4—1721no—
620C2×C4—1721no—
621C2×C4C2×D4×D4311yescharacteristic
622C2×C4C2×Q8×D4311yescharacteristic
623C2×C4#41×D4311yescharacteristic
624C2×C4C2×#1062190211yescharacteristic
625C2×C4#1306337011yescharacteristic
626C2×C4#1306337311yescharacteristic
627C8—22no—
628C8—41no—
629C8—862no—
630C8—1721no—
631C22—864no—
632C22—3441no—
633C22—3441no—
634C22—3441no—
635C22—3441no—
636C22—1722no—
637C22—1722no—
638C22—1722no—
639C22—1722no—
640C22—1722no—
641C22—1722no—
642C22—1722no—
643C22—1722no—
644C22—1722no—
645C22#1458341211yescharacteristic
646C22#1458353111yescharacteristic
647C22#1458356411yescharacteristic
648C22#135×D4311yescharacteristic
649C22AGL(1,ℤ/8)×D4311yescharacteristic
650C22#1458370111yescharacteristic
651C22#1458370811yescharacteristic
652C4—41no—
653C4—41no—
654C4—42no—
655C4—42no—
656C4—81no—
657C4—81no—
658C4—862no—
659C4—862no—
660C4—3441no—
661C4—3441no—
662C4—1721no—
663C4—1721no—
664C4C22⋊Q8×D4311yescharacteristic
665C4#1458349511yescharacteristic
666C4#1458355211yescharacteristic
667C4#1458361011yescharacteristic
668C2—3442no—
669C2—1724no—
670C2#1913839711yescharacteristic
671C2#1914464711yescharacteristic
672C2#1914480111yescharacteristic
673C2#1914607811yescharacteristic
674C2#1914631811yescharacteristic
675C2#1914745911yescharacteristic
676C2#1914749111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2059C2
socleC23×C43C22×D4
prime radicalC22×D344C22
hypercenter#2059D43
hypocenterC43#26382
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2059

Complements

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

NH ≅ G/Ntype
1. C2×#14583196C2semidirect
3. #19138463C2semidirect
4. #19137496C2semidirect
5. #19136125C2semidirect
6. #19136069C2semidirect
7. #19135966C2semidirect
8. #19135322C2semidirect
9. #19135155C2semidirect
12. #19134857C2semidirect
13. #19134853C2semidirect
14. #19134843C2semidirect
15. C43×#2059C2semidirect
337. #2059D43semidirect
399. C43#26382semidirect

Maximal subgroups

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

subgroupindex
C2×#145831962
C2×#145829812
#191384632
#191374962
#191361252
#191360692
#191359662
#191353222
#191351552
#191349442
#191349422
#191348572
#191348532
#191348432
C43×#20592
#2638243