Finite Group Databasebeta

← #25169249

Subgroups — #25169249

Order 11008.

812 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139013C211yesmaximal, characteristic, complemented
2#19137615C211yesmaximal, characteristic
3#19136001C211yesmaximal, characteristic, complemented
4#19135981C211yesmaximal, characteristic, complemented
5#19135774C211yesmaximal, characteristic
6#19135350C211yesmaximal, characteristic, complemented
7#19135329C211yesmaximal, characteristic, complemented
8#19135204C211yesmaximal, characteristic, complemented
9#19135169C211yesmaximal, characteristic, complemented
10#19135165C211yesmaximal, characteristic, complemented
11#19134844C211yesmaximal, characteristic, complemented
12#19134785C211yesmaximal, characteristic, complemented
13#19134679C211yesmaximal, characteristic, complemented
14#102×Dic43C211yesmaximal, characteristic, complemented
15C43×#2033C211yesmaximal, characteristic
16C2×#13063318—21no—
17C2×D4×Dic43—21no—
18C2×D4×Dic43C2211yescharacteristic
19C22×C4⋊Dic43C2211yescharacteristic
20C2×#13063259C2211yescharacteristic
21C2×#13063259C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×Dic43⋊C8C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×C22⋊(C43⋊C8)C2211yescharacteristic
27C2×C8×Dic43C2211yescharacteristic
28#14582840—21no—
29#14582827—21no—
30#14582802C2211yescharacteristic
31#14582798C2211yescharacteristic
32#14582798C2211yescharacteristic
33#14582795C2211yescharacteristic
34#14582792—21no—
35#14582786—21no—
36#14582779—21no—
37#14582774—21no—
38#14582768C2211yescharacteristic
39#14582759C2211yescharacteristic
40C4⋊C4×Dic43C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42C4×C22⋊Dic43C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#121×C43C2211yescharacteristic
53C2×#107×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C23×Dic43—21no—
60C23×Dic43—21no—
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63#13063318—44no—
64D4×Dic43—22no—
65D4×Dic43—41no—
66D4×Dic43—44no—
67C2×C4⋊Dic43—22no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—41no—
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×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43D411yescharacteristic
84C2×C22⋊Dic43D411yescharacteristic
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43C2311yescharacteristic
88C2×C4×Dic43C2311yescharacteristic
89#13063259—22no—
90#13063259—41no—
91#13063258—22no—
92Dic43⋊C8—22no—
93#13063246—22no—
94#13063246—41no—
95C22⋊(C43⋊C8)—41no—
96C8×Dic43—41no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95D411yescharacteristic
104C43⋊#95D411yescharacteristic
105C22×D4×C43—21no—
106C22×D4×C43C2311yescharacteristic
107C23×C4×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110#121×C43—22no—
111#121×C43—22no—
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C22⋊C4×C43—21no—
116C2×C22⋊C4×C43—21no—
117#107×C43—22no—
118#102×C43—22no—
119#102×C43—22no—
120C22⋊C8×C43—22no—
121#95×C43—21no—
122C24×C43—21no—
123C24×C43C2×D411yescharacteristic
124C2×D4×C43—24no—
125C2×D4×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—42no—
131C2×D4×C43—42no—
132C2×D4×C43#4112yes—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2411yescharacteristic
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—42no—
149C22×Dic43—42no—
150C22×Dic43—42no—
151C22×Dic43—42no—
152C22×Dic43—81no—
153C22×Dic43—81no—
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156C22×Dic43C2×D411yescharacteristic
157C22×Dic43C2×D411yescharacteristic
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43#4112yes—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43#4112yes—
170C22⋊C4×C43—24no—
171C22⋊C4×C43—42no—
172C22⋊Dic43—41no—
173C22⋊Dic43—42no—
174C22⋊Dic43—42no—
175C22⋊Dic43—42no—
176C22⋊Dic43—81no—
177C22⋊Dic43D814yes—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—42no—
186C4⋊Dic43—42no—
187C4⋊Dic43—42no—
188C4⋊Dic43#4112yes—
189Dic43⋊C4—42no—
190Dic43⋊C4—42no—
191Dic43⋊C4—42no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—42no—
197C4×Dic43—42no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C23×C43—21no—
205C23×C43—21no—
206C23×C43—21no—
207C23×C43—21no—
208C23×C43—21no—
209C23×C43—21no—
210C23×C43—22no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43C2×D812yes—
218C23×C43C22×D411yescharacteristic
219D4×C43—22no—
220D4×C43—22no—
221D4×C43—48no—
222D4×C43—41no—
223D4×C43—41no—
224C2×C4×C43—21no—
225C2×C4×C43—22no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43C2×#4111yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43H(5,𝔽2)11yescharacteristic
245C2×C4×C432−1+411yescharacteristic
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—22no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
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—84no—
269C2×Dic43—84no—
270C2×Dic43C2×D812yes—
271C2×Dic43C2×D812yes—
272C8×C43—22no—
273C8×C43—41no—
274C43⋊C8—41no—
275C43⋊C8—41no—
276#27030—431nomaximal, Sylow
277C22×C43—22no—
278C22×C43—22no—
279C22×C43—22no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43—42no—
285C22×C43—42no—
286C22×C43—42no—
287C22×C43—81no—
288C22×C43—81no—
289C22×C43—81no—
290C22×C43—81no—
291C22×C43#52511yescharacteristic
292C22×C43#54611yescharacteristic
293C22×C43#54711yescharacteristic
294C22×C43C22×D811yescharacteristic
295C22×C43#57511yescharacteristic
296C22×C43#57711yescharacteristic
297C22×C43#57811yescharacteristic
298C4×C43—42no—
299C4×C43—41no—
300C4×C43—81no—
301C4×C43—81no—
302C4×C43#52911yescharacteristic
303C4×C43#53911yescharacteristic
304C4×C43#55311yescharacteristic
305C4×C43#55611yescharacteristic
306Dic43—22no—
307Dic43—22no—
308Dic43—41no—
309Dic43—42no—
310Dic43—41no—
311Dic43—81no—
312Dic43—81no—
313Dic43—81no—
314#2496—431no—
315#2361—431no—
316#2071—431no—
317#2067—431no—
318#2033—431no—
319#2033D4311yescharacteristic
320#1947—431no—
321#1942—431no—
322#1923—431no—
323#1918—431no—
324#1918—431no—
325#1862—431no—
326#1852—431no—
327#1823—431no—
328C4×#102—431no—
329C2×C43—42no—
330C2×C43—82no—
331C2×C43#246611yescharacteristic
332C2×C43#310011yescharacteristic
333C2×C43#312011yescharacteristic
334C2×C43#329411yescharacteristic
335C2×C43#331311yescharacteristic
336C2×C43#333411yescharacteristic
337C2×C43#335111yescharacteristic
338C2×#126—861no—
339C2×#121C2×D4311yescharacteristic
340C2×C4×D4—431no—
341C2×C4×D4—861no—
342C22×C4⋊C4—431no—
343C2×#107—431no—
344C2×#107—431no—
345C2×#107—431no—
346C2×#107C2×D4311yescharacteristic
347C2×C4⋊C8—431no—
348C2×#102—431no—
349C2×#102—431no—
350C2×#102C2×D4311yescharacteristic
351C2×#102C2×D4311yescharacteristic
352C2×C22⋊C8—431no—
353C2×C22⋊C8C2×D4311yescharacteristic
354C2×C4×C8—431no—
355#400—861no—
356#397—861no—
357#390—431no—
358#389—431no—
359#389—431no—
360#389—431no—
361#388—861no—
362#387—861no—
363#386—861no—
364#385—861no—
365#384—431no—
366#380—431no—
367#380C2×D4311yescharacteristic
368C4×C4⋊C4—431no—
369C4×C4⋊C4—431no—
370C4×C22⋊C4—431no—
371#340—431no—
372#340—431no—
373#340—431no—
374#340—431no—
375#340—431no—
376#340—431no—
377#340—431no—
378#340C2×D4311yescharacteristic
379#336—431no—
380#336—431no—
381C43#2703011yescharacteristic, complemented, Sylow
382C22×D4—21no—
383C22×D4C22×D4311yescharacteristic
384C23×C4—861no—
385C23×C4—861no—
386C23×C4C22×D4311yescharacteristic
387C22×C8—431no—
388C22×C8—431no—
389C22×C8C22×D4311yescharacteristic
390C22×C8C22×D4311yescharacteristic
391#126—1724no—
392#121—22no—
393#121—22no—
394C4×D4—862no—
395C4×D4—1721no—
396C4×D4—1724no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—431no—
399C2×C4⋊C4—431no—
400C2×C4⋊C4—431no—
401C2×C4⋊C4—862no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4—861no—
406C2×C4⋊C4—861no—
407C2×C4⋊C4—861no—
408C2×C4⋊C4—1721no—
409C2×C4⋊C4C22×D4311yescharacteristic
410C2×C4⋊C4C22×D4311yescharacteristic
411C2×C4⋊C4C22×D4311yescharacteristic
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—431no—
415C2×C22⋊C4—431no—
416C2×C22⋊C4—861no—
417C2×C22⋊C4—861no—
418C2×C22⋊C4—861no—
419C2×C22⋊C4—861no—
420C2×C42—431no—
421C2×C42—431no—
422C2×C42—861no—
423C2×C42—861no—
424#107—22no—
425#107—862no—
426#107—862no—
427#107—1721no—
428C4⋊C8—862no—
429#102—22no—
430#102—22no—
431#102—862no—
432#102—1721no—
433C22⋊C8—22no—
434C22⋊C8—1721no—
435C4×C8—1721no—
436#95—21no—
437#95—431no—
438#95—431no—
439#95—861no—
440#95—861no—
441#95—861no—
442#95—861no—
443#95—861no—
444#95—861no—
445C24—21no—
446C24D4×D4311yescharacteristic
447C2×D4—24no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—42no—
454C2×D4—42no—
455C2×D4#1062190012yes—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—431no—
466C22×C4—431no—
467C22×C4—431no—
468C22×C4—431no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—3441no—
474C22×C4—3441no—
475C22×C4—1722no—
476C22×C4—1722no—
477C22×C4—1722no—
478C22×C4—1722no—
479C22×C4D4×D4311yescharacteristic
480C22×C4C23×D4311yescharacteristic
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8—861no—
492C2×C8#1062190012yes—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—432no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4—1722no—
507C4⋊C4—1722no—
508C4⋊C4—1722no—
509C4⋊C4—1722no—
510C4⋊C4—1722no—
511C4⋊C4—1722no—
512C4⋊C4#1062190012yes—
513C22⋊C4—24no—
514C22⋊C4—42no—
515C22⋊C4—434no—
516C22⋊C4—3441no—
517C22⋊C4—1722no—
518C22⋊C4—1721no—
519C22⋊C4—1722no—
520C22⋊C4—1722no—
521C42—861no—
522C42—861no—
523C42—861no—
524C42—861no—
525C42—1722no—
526C42—1722no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—22no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23D8×D4312yes—
541C23C2×D4×D4311yescharacteristic
542D4—22no—
543D4—22no—
544D4—48no—
545D4—41no—
546D4—41no—
547C2×C4—21no—
548C2×C4—22no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—432no—
564C2×C4—432no—
565C2×C4—861no—
566C2×C4—861no—
567C2×C4—861no—
568C2×C4—861no—
569C2×C4—861no—
570C2×C4—861no—
571C2×C4—861no—
572C2×C4—861no—
573C2×C4—861no—
574C2×C4—862no—
575C2×C4—861no—
576C2×C4—3444no—
577C2×C4—3444no—
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#41×D4311yescharacteristic
590C2×C4C2×#1062190011yescharacteristic
591C2×C4C2×#1062190011yescharacteristic
592C2×C4C2×#1062190011yescharacteristic
593C2×C4#1306337111yescharacteristic
594C2×C4#1306337211yescharacteristic
595C8—22no—
596C8—41no—
597C8—1721no—
598C8—1721no—
599C22—22no—
600C22—22no—
601C22—22no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—42no—
607C22—42no—
608C22—42no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22#1458340511yescharacteristic
614C22#1458354111yescharacteristic
615C22#1458354911yescharacteristic
616C22C2×D8×D4311yescharacteristic
617C22#1458369511yescharacteristic
618C22#1458370811yescharacteristic
619C22#1458371311yescharacteristic
620C4—41no—
621C4—42no—
622C4—81no—
623C4—81no—
624C4—862no—
625C4—862no—
626C4—3441no—
627C4—3441no—
628C4—3441no—
629C4—1721no—
630C4—1722no—
631C4—1721no—
632C4#1458343011yescharacteristic
633C4#1458349311yescharacteristic
634C4#1458360111yescharacteristic
635C4#1458361811yescharacteristic
636C2—42no—
637C2—82no—
638C2#1913862611yescharacteristic
639C2#1914459011yescharacteristic
640C2#1914481011yescharacteristic
641C2#1914640611yescharacteristic
642C2#1914666411yescharacteristic
643C2#1914693911yescharacteristic
644C2#1914715011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2033C2
socleC23×C43C22×D4
prime radicalC2×#121×C43C22
hypercenter#2033D43
hypocenterC43#27030
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2033

Complements

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

NH ≅ G/Ntype
1. #19139013C2semidirect
3. #19136001C2semidirect
4. #19135981C2semidirect
6. #19135350C2semidirect
7. #19135329C2semidirect
8. #19135204C2semidirect
9. #19135169C2semidirect
10. #19135165C2semidirect
11. #19134844C2semidirect
12. #19134785C2semidirect
13. #19134679C2semidirect
14. #102×Dic43C2semidirect
381. C43#27030semidirect

Maximal subgroups

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

subgroupindex
#191390132
#191376152
#191360012
#191359812
#191357742
#191353502
#191353292
#191352042
#191351692
#191351652
#191348442
#191347852
#191346792
#102×Dic432
C43×#20332
#2703043