Finite Group Databasebeta

← #25196733

Subgroups — #25196733

Order 11008.

776 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140425C211yesmaximal, characteristic, complemented
2#19137288C211yesmaximal, characteristic
3#19136159C211yesmaximal, characteristic, complemented
4#19136122C211yesmaximal, characteristic, complemented
5#19135934C211yesmaximal, characteristic, complemented
6#19135742C211yesmaximal, characteristic, complemented
7#19135188C211yesmaximal, characteristic, complemented
8#19135167C211yesmaximal, characteristic, complemented
9#19135033C211yesmaximal, characteristic
10#19135023C211yesmaximal, characteristic
11#19134859C211yesmaximal, characteristic, complemented
12#19134845C211yesmaximal, characteristic, complemented
13#19134628C211yesmaximal, characteristic, complemented
14#19134624C211yesmaximal, characteristic, complemented
15C43×#1729C211yesmaximal, characteristic, complemented
16C2×#13063317C2211yescharacteristic
17C2×#13063299C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19C2×#13063259C2211yescharacteristic
20C2×#13063259C2211yescharacteristic
21C2×#13063259C2211yescharacteristic
22C2×#13063257C2211yescharacteristic
23C2×#13063247C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27#14582832—21no—
28#14582832—21no—
29#14582822—21no—
30#14582822—21no—
31#14582801C2211yescharacteristic
32#14582799—21no—
33#14582797C2211yescharacteristic
34#14582797C2211yescharacteristic
35#14582797C2211yescharacteristic
36#14582789—21no—
37#14582775—21no—
38#14582770—21no—
39#14582769C2211yescharacteristic
40#14582759C2211yescharacteristic
41#14582759C2211yescharacteristic
42#14582759C2211yescharacteristic
43C4×C4⋊Dic43C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52C22×M16×C43C2211yescharacteristic
53C23×C8×C43C2211yescharacteristic
54C2×#117×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—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×C4×Dic43—21no—
90#13063259—22no—
91#13063259—22no—
92#13063259—41no—
93#13063257—41no—
94#13063247—22no—
95#13063247—22no—
96#13063247—41no—
97#13063247—41no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C23×C4×C43C2311yescharacteristic
106C2×M16×C43—22no—
107C2×M16×C43—22no—
108C2×M16×C43—41no—
109C22×C8×C43—22no—
110C22×C8×C43—22no—
111C22×C8×C43—41no—
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116#117×C43—41no—
117#117×C43—41no—
118C2×C4⋊C4×C43D411yescharacteristic
119C2×C4⋊C4×C43D411yescharacteristic
120C2×C22⋊C4×C43D411yescharacteristic
121C2×C22⋊C4×C43D411yescharacteristic
122C2×C42×C43C2311yescharacteristic
123C2×C42×C43C2311yescharacteristic
124C24×C43C2×D411yescharacteristic
125C23×D43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×Q812yes—
136C22×C4×C43#4112yes—
137C22×C4×C43C2411yescharacteristic
138C2×C22⋊D43—24no—
139C2×C22⋊D43—81no—
140C2×C22⋊D43—81no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C2×D172—21no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172C2×Q812yes—
154C2×C4×D43—42no—
155C2×C4×D43—81no—
156C2×C4×D43—81no—
157M16×C43—44no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—44no—
169C2×C8×C43#4112yes—
170C2×C8×C43#4112yes—
171C4⋊C4×C43—41no—
172C4⋊C4×C43—41no—
173C22⋊C4×C43—41no—
174C22⋊C4×C43—41no—
175C42×C43—21no—
176C42×C43—21no—
177C42×C43—21no—
178C42×C43—21no—
179C22⋊Dic43—81no—
180C22⋊Dic43—81no—
181C22⋊Dic43—81no—
182(C2×D43)⋊C4—24no—
183(C2×D43)⋊C4—42no—
184(C2×D43)⋊C4—81no—
185(C2×D43)⋊C4—81no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
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—81no—
200C4⋊Dic43—81no—
201C4⋊Dic43C2×Q812yes—
202Dic43⋊C4—42no—
203Dic43⋊C4—42no—
204Dic43⋊C4—81no—
205Dic43⋊C4—81no—
206Dic43⋊C4—81no—
207C4×Dic43—81no—
208C23×C43—21no—
209C23×C43—21no—
210C23×C43—21no—
211C23×C43—21no—
212C23×C43—21no—
213C23×C43—21no—
214C23×C43C22⋊Q812yes—
215C23×C43C22×D411yescharacteristic
216C22×D43—22no—
217C22×D43—41no—
218C22×D43—41no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—41no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—22no—
226C2×C4×C43—22no—
227C2×C4×C43—22no—
228C2×C4×C43—22no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
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×C43C22⋊Q812yes—
242C2×C4×C43C22×Q811yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43H(5,𝔽2)11yescharacteristic
247C2×C4×C43H(5,𝔽2)11yescharacteristic
248C22⋊D43—84no—
249C2×Dic43—22no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
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—
270D172—22no—
271D172—22no—
272D172—41no—
273D172—41no—
274C4×D43—84no—
275C8×C43—22no—
276C8×C43—22no—
277C8×C43—41no—
278C8×C43—41no—
279#29169—431nomaximal, Sylow
280C22×C43—22no—
281C22×C43—22no—
282C22×C43—22no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43—41no—
286C22×C43—41no—
287C22×C43C2×C22⋊Q811yescharacteristic
288C22×C43#53211yescharacteristic
289C22×C43#53411yescharacteristic
290C22×C43#57611yescharacteristic
291C22×C43#57611yescharacteristic
292C22×C43#57711yescharacteristic
293C22×C43#57811yescharacteristic
294C2×D43—42no—
295C2×D43—42no—
296C2×D43—42no—
297C2×D43—81no—
298C2×D43—81no—
299C2×D43—81no—
300C2×D43—81no—
301C4×C43—22no—
302C4×C43—41no—
303C4×C43—41no—
304C4×C43—41no—
305C4×C43—41no—
306C4×C43#55111yescharacteristic
307C4×C43#55111yescharacteristic
308C4×C43#55411yescharacteristic
309C4×C43#55411yescharacteristic
310Dic43—42no—
311Dic43—81no—
312Dic43—81no—
313Dic43—81no—
314Dic43—81no—
315Dic43—81no—
316Dic43—81no—
317#2629—431no—
318#2324—431no—
319#2100—431no—
320#2093—431no—
321#2059—431no—
322#2025—431no—
323#1921—431no—
324#1918—431no—
325#1895—431no—
326#1893—431no—
327#1864—431no—
328#1862—431no—
329#1809—431no—
330#1808—431no—
331#1729D4311yescharacteristic, complemented
332C2×C43—42no—
333C2×C43#256411yescharacteristic
334C2×C43#308111yescharacteristic
335C2×C43#308311yescharacteristic
336C2×C43#317611yescharacteristic
337C2×C43#317811yescharacteristic
338C2×C43#319811yescharacteristic
339C2×C43#320311yescharacteristic
340D43—82no—
341C22×M16C2×D4311yescharacteristic
342C23×C8C2×D4311yescharacteristic
343C2×#125—431no—
344C2×#121—431no—
345C2×C4×D4—431no—
346C2×#117C2×D4311yescharacteristic
347C2×#107—431no—
348C2×#107—431no—
349C2×#107—431no—
350C2×#106—431no—
351C2×#102—431no—
352C2×#102—431no—
353C2×#102—431no—
354C2×#102—431no—
355#398—861no—
356#398—861no—
357#396—861no—
358#396—861no—
359#390—431no—
360#390—861no—
361#389—431no—
362#389—431no—
363#389—431no—
364#388—861no—
365#386—861no—
366#385—861no—
367#384—431no—
368#380—431no—
369#380—431no—
370#380—431no—
371C4×C4⋊C4—431no—
372#340—431no—
373#340—431no—
374#340—431no—
375#340—431no—
376#340—431no—
377#340—431no—
378#340—431no—
379#340—431no—
380#336C2×D4311yescharacteristic
381#336C2×D4311yescharacteristic
382#336C2×D4311yescharacteristic
383#336C2×D4311yescharacteristic
384C43#2916911yescharacteristic, complemented, Sylow
385C22×D4—431no—
386C22×D4—861no—
387C23×C4—861no—
388C23×C4C22×D4311yescharacteristic
389C2×M16—22no—
390C2×M16—22no—
391C2×M16—41no—
392C22×C8—22no—
393C22×C8—22no—
394C22×C8—41no—
395C22×C8C22×D4311yescharacteristic
396C22×C8C22×D4311yescharacteristic
397C22×C8C22×D4311yescharacteristic
398C22×C8C22×D4311yescharacteristic
399#125—1721no—
400#125—1721no—
401#121—434no—
402#121—862no—
403C4×D4—1721no—
404C4×D4—1721no—
405#117—41no—
406#117—41no—
407C2×C4⋊C4—431no—
408C2×C4⋊C4—431no—
409C2×C4⋊C4—431no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4D17211yescharacteristic
422C2×C4⋊C4D17211yescharacteristic
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4—861no—
426C2×C22⋊C4—861no—
427C2×C22⋊C4—861no—
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C22⋊C4D17211yescharacteristic
431C2×C22⋊C4D17211yescharacteristic
432C2×C42—861no—
433C2×C42C22×D4311yescharacteristic
434C2×C42C22×D4311yescharacteristic
435#107—862no—
436#107—862no—
437#107—1721no—
438#106—1721no—
439#102—862no—
440#102—862no—
441#102—1721no—
442#102—1721no—
443#95—861no—
444#95—861no—
445#95—861no—
446#95—861no—
447#95—861no—
448#95—861no—
449#95—861no—
450C24—861no—
451C24C2×D17211yescharacteristic
452C2×D4—432no—
453C2×D4—864no—
454C2×D4—861no—
455C2×D4—861no—
456C2×D4—861no—
457C2×D4—861no—
458C2×D4—861no—
459C2×D4—3441no—
460C2×D4—3441no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4—3441no—
473C22×C4—3441no—
474C22×C4—1722no—
475C22×C4C2×D17211yescharacteristic
476C22×C4C2×D17211yescharacteristic
477C22×C4C2×D17211yescharacteristic
478C22×C4C2×D17211yescharacteristic
479C22×C4C2×D17211yescharacteristic
480C22×C4#1062190012yes—
481C22×C4Q8×D4312yes—
482C22×C4C23×D4311yescharacteristic
483M16—44no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—44no—
495C2×C8#1062189812yes—
496C2×C8#1062189812yes—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—432no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—3441no—
514C4⋊C4—3441no—
515C4⋊C4—3441no—
516C4⋊C4—3441no—
517C4⋊C4—3441no—
518C4⋊C4—1722no—
519C4⋊C4—1722no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C22⋊C4—864no—
523C22⋊C4—3441no—
524C22⋊C4—3441no—
525C22⋊C4—3441no—
526C22⋊C4—3441no—
527C22⋊C4—3441no—
528C22⋊C4—1722no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—3441no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—862no—
541C23—1721no—
542C23—1721no—
543C23—1721no—
544C23—1721no—
545C23—1721no—
546C23—1721no—
547C23#1306330512yes—
548C23C22×D17211yescharacteristic
549D4—862no—
550D4—862no—
551D4—3444no—
552D4—1721no—
553D4—1721no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—862no—
573C2×C4—3444no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4—1721no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1721no—
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#1306330512yes—
595C2×C4C2×Q8×D4311yescharacteristic
596C2×C4C2×#1062190011yescharacteristic
597C2×C4C2×#1062189811yescharacteristic
598C2×C4C2×#1062189811yescharacteristic
599C2×C4#1306337011yescharacteristic
600C2×C4#1306337011yescharacteristic
601C8—22no—
602C8—22no—
603C8—41no—
604C8—41no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—3441no—
613C22—3441no—
614C22—3441no—
615C22—3441no—
616C22—1722no—
617C22—1722no—
618C22—1722no—
619C22C2×#1306330511yescharacteristic
620C22#1458344911yescharacteristic
621C22#1458346111yescharacteristic
622C22#1458370411yescharacteristic
623C22#1458370411yescharacteristic
624C22#1458371111yescharacteristic
625C22#1458371611yescharacteristic
626C4—22no—
627C4—41no—
628C4—41no—
629C4—41no—
630C4—41no—
631C4—3441no—
632C4—3441no—
633C4—3441no—
634C4—3441no—
635C4—3441no—
636C4—3441no—
637C4—1722no—
638C4#1458357511yescharacteristic
639C4#1458357511yescharacteristic
640C4#1458360411yescharacteristic
641C4#1458360411yescharacteristic
642C2—42no—
643C2—3442no—
644C2#1913977511yescharacteristic
645C2#1914442711yescharacteristic
646C2#1914444811yescharacteristic
647C2#1914524511yescharacteristic
648C2#1914526311yescharacteristic
649C2#1914544911yescharacteristic
650C2#1914549711yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1729C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
hypercenter#1729D43
hypocenterC43#29169
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #1729

Complements

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

NH ≅ G/Ntype
1. #19140425C2semidirect
3. #19136159C2semidirect
4. #19136122C2semidirect
5. #19135934C2semidirect
6. #19135742C2semidirect
7. #19135188C2semidirect
8. #19135167C2semidirect
11. #19134859C2semidirect
12. #19134845C2semidirect
13. #19134628C2semidirect
14. #19134624C2semidirect
15. C43×#1729C2semidirect
331. #1729D43semidirect
384. C43#29169semidirect

Maximal subgroups

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

subgroupindex
#191404252
#191372882
#191361592
#191361222
#191359342
#191357422
#191351882
#191351672
#191350332
#191350232
#191348592
#191348452
#191346282
#191346242
C43×#17292
#2916943