Finite Group Databasebeta

← #25196703

Subgroups — #25196703

Order 11008.

844 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142905C211yesmaximal, characteristic, complemented
2C4×#13063299C211yesmaximal, characteristic
3#19136164C211yesmaximal, characteristic, complemented
4#19136115C211yesmaximal, characteristic, complemented
5#19135934C211yesmaximal, characteristic, complemented
6#19135742C211yesmaximal, characteristic, complemented
7#19135181C211yesmaximal, characteristic, complemented
8#19135167C211yesmaximal, characteristic, complemented
9#19135033C211yesmaximal, characteristic
10#19135033C211yesmaximal, characteristic
11#19134859C211yesmaximal, characteristic, complemented
12#19134845C211yesmaximal, characteristic, complemented
13#19134628C211yesmaximal, characteristic, complemented
14#19134628C211yesmaximal, characteristic, complemented
15C43×#1728C211yesmaximal, characteristic, complemented
16C2×#13063317C2211yescharacteristic
17C2×#13063299C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19C2×C4×C22⋊D43—21no—
20C2×#13063259C2211yescharacteristic
21C2×#13063259C2211yescharacteristic
22C2×#13063257C2211yescharacteristic
23C2×#13063257C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28#14582801C2211yescharacteristic
29#14582797C2211yescharacteristic
30#14582797C2211yescharacteristic
31#14582797C2211yescharacteristic
32#14582790—21no—
33#14582783—21no—
34#14582783—21no—
35#14582778—21no—
36#14582772—21no—
37#14582772—21no—
38#14582765C2211yescharacteristic
39#14582759C2211yescharacteristic
40#14582759C2211yescharacteristic
41#14582759C2211yescharacteristic
42C4×C4⋊Dic43C2211yescharacteristic
43C4×(C2×D43)⋊C4—21no—
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52C22×M16×C43C2211yescharacteristic
53C22×M16×C43C2211yescharacteristic
54C22×C42×C43C2211yescharacteristic
55C43×#336C2211yescharacteristic
56C43×#336C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×D172C2311yescharacteristic
60C22×C22⋊D43—21no—
61C22×C4×D43—21no—
62#13063317—41no—
63#13063317—41no—
64#13063299—22no—
65#13063299Q814yes—
66C4×D172—41no—
67C4×D172—41no—
68C4×C22⋊D43—44no—
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×C4×Dic43—21no—
89#13063259—22no—
90#13063259—41no—
91#13063257—22no—
92#13063257—41no—
93#13063247—22no—
94#13063247—22no—
95#13063247—41no—
96#13063247—41no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C23×C4×C43D411yescharacteristic
107C23×C4×C43D411yescharacteristic
108C23×C4×C43C2311yescharacteristic
109C2×M16×C43—22no—
110C2×M16×C43—22no—
111C2×M16×C43—22no—
112C2×M16×C43—22no—
113C2×M16×C43—41no—
114C2×M16×C43—41no—
115C22×C8×C43C2311yescharacteristic
116C22×C8×C43C2311yescharacteristic
117C22×C8×C43C2311yescharacteristic
118C22×C8×C43C2311yescharacteristic
119C2×C42×C43—41no—
120C2×C42×C43—41no—
121C2×C42×C43D411yescharacteristic
122C2×C42×C43D411yescharacteristic
123C2×C42×C43C2311yescharacteristic
124C2×C42×C43C2311yescharacteristic
125C24×C43C2×D411yescharacteristic
126C23×D43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—22no—
132C22×C4×C43—41no—
133C22×C4×C43—41no—
134C22×C4×C43—41no—
135C22×C4×C43—41no—
136C22×C4×C43—41no—
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×Q812yes—
143C22×C4×C43#4112yes—
144C22×C4×C43C2411yescharacteristic
145C2×C22⋊D43—24no—
146C2×C22⋊D43—42no—
147C2×C22⋊D43—42no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172C2×Q812yes—
161C2×C4×D43—42no—
162C2×C4×D43—42no—
163C2×C4×D43—42no—
164M16×C43—44no—
165M16×C43—44no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43#4112yes—
177C2×C8×C43#4112yes—
178C42×C43—21no—
179C42×C43—21no—
180C42×C43—21no—
181C42×C43—21no—
182C42×C43—41no—
183C42×C43—41no—
184C22⋊Dic43—42no—
185C22⋊Dic43—42no—
186C22⋊Dic43—42no—
187(C2×D43)⋊C4—24no—
188(C2×D43)⋊C4—42no—
189(C2×D43)⋊C4—42no—
190(C2×D43)⋊C4—42no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43C2×Q812yes—
205Dic43⋊C4—42no—
206Dic43⋊C4—42no—
207Dic43⋊C4—42no—
208Dic43⋊C4—42no—
209Dic43⋊C4—42no—
210C4×Dic43—42no—
211C23×C43—21no—
212C23×C43—21no—
213C23×C43—21no—
214C23×C43—21no—
215C23×C43—21no—
216C23×C43—21no—
217C23×C43C22⋊Q812yes—
218C23×C43C22×D411yescharacteristic
219C22×D43—22no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—41no—
223C22×D43—41no—
224C22×D43—41no—
225C22×D43—41no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—22no—
231C2×C4×C43—22no—
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—44no—
244C2×C4×C43—44no—
245C2×C4×C43C22⋊Q812yes—
246C2×C4×C43AGL(1,ℤ/8)12yes—
247C2×C4×C43C22×Q811yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43H(5,𝔽2)11yescharacteristic
252C2×C4×C43H(5,𝔽2)11yescharacteristic
253C22⋊D43—48no—
254C2×Dic43—22no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275D172—22no—
276D172—22no—
277D172—41no—
278D172—41no—
279C4×D43—84no—
280C8×C43—22no—
281C8×C43—22no—
282C8×C43—41no—
283C8×C43—41no—
284#29167—431nomaximal, Sylow
285C22×C43—22no—
286C22×C43—22no—
287C22×C43—22no—
288C22×C43—41no—
289C22×C43—41no—
290C22×C43—41no—
291C22×C43—41no—
292C22×C43C2×C22⋊Q811yescharacteristic
293C22×C43#53211yescharacteristic
294C22×C43#53411yescharacteristic
295C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
296C22×C43#57511yescharacteristic
297C22×C43#57511yescharacteristic
298C22×C43#57511yescharacteristic
299C2×D43—42no—
300C2×D43—42no—
301C2×D43—42no—
302C2×D43—81no—
303C2×D43—81no—
304C2×D43—81no—
305C2×D43—81no—
306C4×C43—22no—
307C4×C43—22no—
308C4×C43—41no—
309C4×C43—41no—
310C4×C43—41no—
311C4×C43#55111yescharacteristic
312C4×C43#55111yescharacteristic
313C4×C43#55411yescharacteristic
314C4×C43#55411yescharacteristic
315Dic43—42no—
316Dic43—81no—
317Dic43—81no—
318Dic43—81no—
319Dic43—81no—
320Dic43—81no—
321Dic43—81no—
322#2851—431no—
323C4×#121—431no—
324#2101—431no—
325#2092—431no—
326#2059—431no—
327#2025—431no—
328#1920—431no—
329#1918—431no—
330#1895—431no—
331#1895—431no—
332#1864—431no—
333#1862—431no—
334#1809—431no—
335#1809—431no—
336#1728D4311yescharacteristic, complemented
337C2×C43—42no—
338C2×C43#256411yescharacteristic
339C2×C43#307711yescharacteristic
340C2×C43#308011yescharacteristic
341C2×C43#317111yescharacteristic
342C2×C43#318311yescharacteristic
343C2×C43#319411yescharacteristic
344C2×C43#319711yescharacteristic
345D43—82no—
346C22×M16C2×D4311yescharacteristic
347C22×M16C2×D4311yescharacteristic
348C2×#125—431no—
349C2×#121—431no—
350C2×C4×D4—431no—
351C2×C4×D4—861no—
352C22×C42C2×D4311yescharacteristic
353C2×#107—431no—
354C2×#107—431no—
355C2×#106—431no—
356C2×#106—431no—
357C2×#102—431no—
358C2×#102—431no—
359C2×#102—431no—
360C2×#102—431no—
361#390—431no—
362#389—431no—
363#389—431no—
364#389—431no—
365#388—861no—
366#387—861no—
367#387—861no—
368#386—861no—
369#385—861no—
370#385—861no—
371#382—431no—
372#380—431no—
373#380—431no—
374#380—431no—
375C4×C4⋊C4—431no—
376C4×C22⋊C4—861no—
377#340—431no—
378#340—431no—
379#340—431no—
380#340—431no—
381#340—431no—
382#340—431no—
383#340—431no—
384#340—431no—
385#336C2×D4311yescharacteristic
386#336C2×D4311yescharacteristic
387#336C2×D4311yescharacteristic
388#336C2×D4311yescharacteristic
389C43#2916711yescharacteristic, complemented, Sylow
390C22×D4—431no—
391C22×D4—861no—
392C23×C4—861no—
393C23×C4D17211yescharacteristic
394C23×C4D17211yescharacteristic
395C23×C4C22×D4311yescharacteristic
396C2×M16—22no—
397C2×M16—22no—
398C2×M16—22no—
399C2×M16—22no—
400C2×M16—41no—
401C2×M16—41no—
402C22×C8C22×D4311yescharacteristic
403C22×C8C22×D4311yescharacteristic
404C22×C8C22×D4311yescharacteristic
405C22×C8C22×D4311yescharacteristic
406#125—1721no—
407#125—1721no—
408#121—434no—
409#121—862no—
410C4×D4—1721no—
411C4×D4—1721no—
412C4×D4—1724no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—431no—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—861no—
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×C42—41no—
433C2×C42—41no—
434C2×C42—861no—
435C2×C42D17211yescharacteristic
436C2×C42D17211yescharacteristic
437C2×C42C22×D4311yescharacteristic
438C2×C42C22×D4311yescharacteristic
439#107—862no—
440#107—1721no—
441#106—862no—
442#106—1721no—
443#102—862no—
444#102—862no—
445#102—1721no—
446#102—1721no—
447#95—861no—
448#95—861no—
449#95—861no—
450#95—861no—
451#95—861no—
452#95—861no—
453#95—861no—
454#95—861no—
455#95—861no—
456C24—861no—
457C24C2×D17211yescharacteristic
458C2×D4—432no—
459C2×D4—864no—
460C2×D4—861no—
461C2×D4—861no—
462C2×D4—861no—
463C2×D4—861no—
464C2×D4—861no—
465C2×D4—1722no—
466C2×D4—1722no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—861no—
478C22×C4—861no—
479C22×C4—861no—
480C22×C4—861no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—1722no—
485C22×C4—1722no—
486C22×C4—1722no—
487C22×C4C2×D17211yescharacteristic
488C22×C4C2×D17211yescharacteristic
489C22×C4C2×D17211yescharacteristic
490C22×C4C2×D17211yescharacteristic
491C22×C4C2×D17211yescharacteristic
492C22×C4#1062190012yes—
493C22×C4Q8×D4312yes—
494C22×C4C23×D4311yescharacteristic
495M16—44no—
496M16—44no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8#1062189812yes—
508C2×C8#1062189812yes—
509C4⋊C4—432no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—1722no—
524C4⋊C4—1722no—
525C4⋊C4—1722no—
526C4⋊C4—1722no—
527C4⋊C4—1722no—
528C22⋊C4—864no—
529C22⋊C4—1722no—
530C22⋊C4—1722no—
531C22⋊C4—1722no—
532C22⋊C4—1722no—
533C22⋊C4—1722no—
534C22⋊C4—1722no—
535C42—21no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—41no—
540C42—41no—
541C42—1722no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—862no—
549C23—1721no—
550C23—1721no—
551C23—1721no—
552C23—1721no—
553C23—1721no—
554C23—1721no—
555C23#1306330512yes—
556C23C22×D17211yescharacteristic
557D4—862no—
558D4—862no—
559D4—1728no—
560D4—1721no—
561D4—1721no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—44no—
580C2×C4—44no—
581C2×C4—862no—
582C2×C4—3444no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4#1306330512yes—
604C2×C4#1306335312yes—
605C2×C4C2×Q8×D4311yescharacteristic
606C2×C4C2×#1062190011yescharacteristic
607C2×C4C2×#1062189811yescharacteristic
608C2×C4C2×#1062189811yescharacteristic
609C2×C4#1306337011yescharacteristic
610C2×C4#1306337011yescharacteristic
611C8—22no—
612C8—22no—
613C8—41no—
614C8—41no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—3441no—
623C22—3441no—
624C22—3441no—
625C22—3441no—
626C22—1722no—
627C22—1722no—
628C22—1722no—
629C22C2×#1306330511yescharacteristic
630C22#1458344911yescharacteristic
631C22#1458346111yescharacteristic
632C22C2×#1306335311yescharacteristic
633C22#1458369911yescharacteristic
634C22#1458369911yescharacteristic
635C22#1458369911yescharacteristic
636C4—22no—
637C4—22no—
638C4—41no—
639C4—41no—
640C4—41no—
641C4—3441no—
642C4—3441no—
643C4—3441no—
644C4—3441no—
645C4—3441no—
646C4—3441no—
647C4—1722no—
648C4#1458357511yescharacteristic
649C4#1458357511yescharacteristic
650C4#1458360411yescharacteristic
651C4#1458360411yescharacteristic
652C2—42no—
653C2—3442no—
654C2#1913977511yescharacteristic
655C2#1914439411yescharacteristic
656C2#1914441811yescharacteristic
657C2#1914519011yescharacteristic
658C2#1914532411yescharacteristic
659C2#1914541111yescharacteristic
660C2#1914543711yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1728C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
hypercenter#1728D43
hypocenterC43#29167
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1728

Complements

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

NH ≅ G/Ntype
1. #19142905C2semidirect
3. #19136164C2semidirect
4. #19136115C2semidirect
5. #19135934C2semidirect
6. #19135742C2semidirect
7. #19135181C2semidirect
8. #19135167C2semidirect
11. #19134859C2semidirect
12. #19134845C2semidirect
13. #19134628C2semidirect
14. #19134628C2semidirect
15. C43×#1728C2semidirect
336. #1728D43semidirect
389. C43#29167semidirect

Maximal subgroups

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

subgroupindex
#191429052
C4×#130632992
#191361642
#191361152
#191359342
#191357422
#191351812
#191351672
#191350332
#191348592
#191348452
#191346282
C43×#17282
#2916743