Finite Group Databasebeta

← #25169285

Subgroups — #25169285

Order 11008.

792 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139031C211yesmaximal, characteristic, complemented
2#19137616C211yesmaximal, characteristic
3#19135969C211yesmaximal, characteristic, complemented
4#19135782C211yesmaximal, characteristic
5#19135782C211yesmaximal, characteristic
6#19135356C211yesmaximal, characteristic, complemented
7#19135322C211yesmaximal, characteristic, complemented
8#19135202C211yesmaximal, characteristic, complemented
9#19135181C211yesmaximal, characteristic, complemented
10#19135171C211yesmaximal, characteristic, complemented
11#19134858C211yesmaximal, characteristic, complemented
12#19134789C211yesmaximal, characteristic, complemented
13#19134680C211yesmaximal, characteristic, complemented
14#102×Dic43C211yesmaximal, characteristic, complemented
15C43×#2071C211yesmaximal, characteristic, complemented
16C2×#13063296C2211yescharacteristic
17C2×D4×Dic43C2211yescharacteristic
18C2×(C22⋊D43)⋊C4—21no—
19C2×C4⋊C4×D43C2211yescharacteristic
20C2×#13063257C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×C4⋊(C43⋊C8)C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×(C2×D43)⋊C8C2211yescharacteristic
28C2×(C2×D43)⋊C8C2211yescharacteristic
29C2×C8×Dic43C2211yescharacteristic
30#14582838—21no—
31#14582821—21no—
32#14582798C2211yescharacteristic
33#14582797C2211yescharacteristic
34#14582795C2211yescharacteristic
35#14582789—21no—
36#14582787—21no—
37#14582780—21no—
38#14582775—21no—
39#14582771—21no—
40#14582756C2211yescharacteristic
41#14582756C2211yescharacteristic
42C4⋊C4×Dic43C2211yescharacteristic
43C4×C4⋊Dic43C2211yescharacteristic
44C4×(C2×D43)⋊C4C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#102×C43C2211yescharacteristic
53C2×#102×C43C2211yescharacteristic
54C43×#390C2211yescharacteristic
55C43×#384C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×C22⋊D43—21no—
60C23×Dic43—21no—
61C22×C4×D43—21no—
62C22×C4×D43C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65#13063296—22no—
66#13063296—22no—
67D4×Dic43—22no—
68D4×Dic43—41no—
69(C22⋊D43)⋊C4—44no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C4⋊C4×D43—22no—
79C4⋊C4×D43—41no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4D411yescharacteristic
85C2×(C2×D43)⋊C4D411yescharacteristic
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43C2311yescharacteristic
89#13063257—22no—
90#13063256—22no—
91#13063256—22no—
92#13063256—41no—
93C4⋊(C43⋊C8)—22no—
94#13063246—22no—
95#13063246—41no—
96(C2×D43)⋊C8—22no—
97(C2×D43)⋊C8—41no—
98C8×Dic43—41no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95D411yescharacteristic
107C43⋊#95D411yescharacteristic
108C22×D4×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C22×C8×C43C2311yescharacteristic
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C22⋊C4×C43—21no—
117C2×C22⋊C4×C43—21no—
118C2×C42×C43C2311yescharacteristic
119#102×C43—22no—
120#102×C43—22no—
121C24×C43—21no—
122C23×D43C2×D411yescharacteristic
123C2×D4×C43—21no—
124C2×D4×C43—21no—
125C2×D4×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43#4112yes—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2411yescharacteristic
135C2×C22⋊D43—24no—
136C2×C22⋊D43—42no—
137C2×C22⋊D43—42no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—42no—
143C22×Dic43—42no—
144C22×Dic43—81no—
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C22×Dic43C2×D411yescharacteristic
148C2×C4×D43—21no—
149C2×C4×D43—21no—
150C2×C4×D43—21no—
151C2×C4×D43—21no—
152C2×C4×D43—21no—
153C2×C4×D43—21no—
154C2×C4×D43—42no—
155C2×C4×D43—42no—
156C2×C4×D43—81no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—81no—
170C4⋊C4×C43—81no—
171C22⋊C4×C43—42no—
172C22⋊C4×C43—81no—
173C42×C43—21no—
174C42×C43—21no—
175C22⋊Dic43—24no—
176C22⋊Dic43—42no—
177(C2×D43)⋊C4—41no—
178(C2×D43)⋊C4—81no—
179(C2×D43)⋊C4—81no—
180(C2×D43)⋊C4SD1614yes—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—81no—
188C4⋊Dic43#4112yes—
189C4⋊Dic43#4112yes—
190Dic43⋊C4—42no—
191Dic43⋊C4—42no—
192Dic43⋊C4—42no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—42no—
196C4×Dic43—81no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8#4112yes—
203C23×C43—22no—
204C23×C43—41no—
205C23×C43—41no—
206C23×C43—41no—
207C23×C43—41no—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43C22×D411yescharacteristic
211C22×D43—21no—
212C22×D43—21no—
213C22×D43—21no—
214C22×D43—21no—
215C22×D43—21no—
216C22×D43—21no—
217C22×D43C2×SD1612yes—
218D4×C43—22no—
219D4×C43—22no—
220D4×C43—41no—
221D4×C43—41no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—41no—
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×C43C2×SD1612yes—
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×C4×C43H(5,𝔽2)11yescharacteristic
242C2×C4×C432−1+411yescharacteristic
243C22⋊D43—48no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—22no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—22no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
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—84no—
265C2×Dic43C2×SD1612yes—
266C4×D43—41no—
267C4×D43—41no—
268C4×D43—41no—
269C4×D43—41no—
270C4×D43—84no—
271C8×C43—41no—
272C8×C43—41no—
273C43⋊C8—22no—
274C43⋊C8—41no—
275#27032—431nomaximal, Sylow
276C22×C43—42no—
277C22×C43—42no—
278C22×C43—42no—
279C22×C43—81no—
280C22×C43—81no—
281C22×C43—81no—
282C22×C43—81no—
283C22×C43#52511yescharacteristic
284C22×C43#54611yescharacteristic
285C22×C43#54711yescharacteristic
286C22×C43C22×SD1611yescharacteristic
287C22×C43#57511yescharacteristic
288C22×C43#57611yescharacteristic
289C22×C43#57711yescharacteristic
290C2×D43—22no—
291C2×D43—22no—
292C2×D43—22no—
293C2×D43—41no—
294C2×D43—41no—
295C2×D43—41no—
296C2×D43—41no—
297C4×C43—22no—
298C4×C43—41no—
299C4×C43—81no—
300C4×C43—81no—
301C4×C43—81no—
302C4×C43#52911yescharacteristic
303C4×C43#53911yescharacteristic
304C4×C43#55311yescharacteristic
305C4×C43#55611yescharacteristic
306Dic43—22no—
307Dic43—42no—
308Dic43—41no—
309Dic43—42no—
310Dic43—41no—
311Dic43—81no—
312Dic43—81no—
313#2497—431no—
314#2361—431no—
315#2071D4311yescharacteristic, complemented
316#2065—431no—
317#2034—431no—
318#2034—431no—
319#1948—431no—
320#1941—431no—
321#1923—431no—
322#1920—431no—
323#1919—431no—
324#1864—431no—
325#1853—431no—
326#1823—431no—
327C4×#102—431no—
328C2×C43—82no—
329C2×C43#246611yescharacteristic
330C2×C43#310111yescharacteristic
331C2×C43#311911yescharacteristic
332C2×C43#329511yescharacteristic
333C2×C43#332111yescharacteristic
334C2×C43#333511yescharacteristic
335C2×C43#335511yescharacteristic
336D43—42no—
337C2×#121—431no—
338C2×C4×D4—431no—
339C2×C4×D4—861no—
340C22×C4⋊C4—431no—
341C2×#106—431no—
342C2×#106—431no—
343C2×#106—431no—
344C2×#106—431no—
345C2×C4⋊C8—431no—
346C2×#102—431no—
347C2×#102—431no—
348C2×#102C2×D4311yescharacteristic
349C2×#102C2×D4311yescharacteristic
350C2×C22⋊C8—431no—
351C2×C22⋊C8—431no—
352C2×C4×C8—431no—
353#400—861no—
354#396—861no—
355#390C2×D4311yescharacteristic
356#389—431no—
357#389—431no—
358#389—431no—
359#388—861no—
360#388—861no—
361#387—861no—
362#386—861no—
363#385—861no—
364#384C2×D4311yescharacteristic
365#380—431no—
366#380—431no—
367C4×C4⋊C4—431no—
368C4×C4⋊C4—431no—
369C4×C22⋊C4—431no—
370#340—431no—
371#340—431no—
372#340—431no—
373#340—431no—
374#340—431no—
375#340—431no—
376#340C2×D4311yescharacteristic
377#340C2×D4311yescharacteristic
378#336—431no—
379#336C2×D4311yescharacteristic
380C43#2703211yescharacteristic, complemented, Sylow
381C22×D4—861no—
382C22×D4C22×D4311yescharacteristic
383C23×C4—431no—
384C23×C4—861no—
385C23×C4—861no—
386C22×C8—431no—
387C22×C8—431no—
388C22×C8C22×D4311yescharacteristic
389C22×C8C22×D4311yescharacteristic
390#121—862no—
391#121—862no—
392C4×D4—862no—
393C4×D4—1721no—
394C4×D4—1724no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
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—1721no—
407C2×C4⋊C4C22×D4311yescharacteristic
408C2×C4⋊C4C22×D4311yescharacteristic
409C2×C4⋊C4C22×D4311yescharacteristic
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—431no—
413C2×C22⋊C4—431no—
414C2×C22⋊C4—861no—
415C2×C22⋊C4—861no—
416C2×C22⋊C4—861no—
417C2×C22⋊C4—861no—
418C2×C42—431no—
419C2×C42—861no—
420C2×C42—861no—
421C2×C42C22×D4311yescharacteristic
422#106—862no—
423#106—862no—
424#106—862no—
425#106—1721no—
426C4⋊C8—862no—
427#102—22no—
428#102—22no—
429#102—862no—
430#102—1721no—
431C22⋊C8—862no—
432C22⋊C8—1721no—
433C4×C8—1721no—
434#95—431no—
435#95—431no—
436#95—861no—
437#95—861no—
438#95—861no—
439#95—861no—
440#95—861no—
441#95—861no—
442#95—861no—
443C24—21no—
444C24—431no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—864no—
451C2×D4—1722no—
452C2×D4—1722no—
453C2×D4#1062190012yes—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—431no—
458C22×C4—431no—
459C22×C4—431no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—3441no—
471C22×C4—3441no—
472C22×C4—1722no—
473C22×C4—1722no—
474C22×C4—1722no—
475C22×C4—1722no—
476C22×C4D4×D4311yescharacteristic
477C22×C4D4×D4311yescharacteristic
478C22×C4C23×D4311yescharacteristic
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—432no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—861no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—81no—
498C4⋊C4—81no—
499C4⋊C4—432no—
500C4⋊C4—432no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4—3441no—
508C4⋊C4—1722no—
509C4⋊C4—1722no—
510C4⋊C4—1722no—
511C22⋊C4—42no—
512C22⋊C4—81no—
513C22⋊C4—434no—
514C22⋊C4—864no—
515C22⋊C4—3441no—
516C22⋊C4—3441no—
517C22⋊C4—1721no—
518C22⋊C4—1722no—
519C42—21no—
520C42—21no—
521C42—861no—
522C42—861no—
523C42—3441no—
524C42—1722no—
525C23—22no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—432no—
533C23—861no—
534C23—861no—
535C23—861no—
536C23—861no—
537C23—861no—
538C23—861no—
539C23C2×D4×D4311yescharacteristic
540D4—22no—
541D4—22no—
542D4—41no—
543D4—41no—
544D4—1728no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—41no—
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—432no—
560C2×C4—861no—
561C2×C4—861no—
562C2×C4—861no—
563C2×C4—862no—
564C2×C4—861no—
565C2×C4—861no—
566C2×C4—861no—
567C2×C4—862no—
568C2×C4—861no—
569C2×C4—861no—
570C2×C4—3444no—
571C2×C4—3444no—
572C2×C4—1721no—
573C2×C4—1721no—
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×C4SD16×D4312yes—
587C2×C4#41×D4311yescharacteristic
588C2×C4#41×D4311yescharacteristic
589C2×C4#41×D4311yescharacteristic
590C2×C4C2×#1062190011yescharacteristic
591C2×C4#1306337111yescharacteristic
592C2×C4#1306337211yescharacteristic
593C8—41no—
594C8—41no—
595C8—862no—
596C8—1721no—
597C22—42no—
598C22—42no—
599C22—42no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22—81no—
604C22—862no—
605C22—862no—
606C22—862no—
607C22—1721no—
608C22—1721no—
609C22—1721no—
610C22—1721no—
611C22#1458340911yescharacteristic
612C22#1458354211yescharacteristic
613C22#1458354711yescharacteristic
614C22C2×SD16×D4311yescharacteristic
615C22#1458369811yescharacteristic
616C22#1458370011yescharacteristic
617C22#1458370911yescharacteristic
618C4—22no—
619C4—41no—
620C4—81no—
621C4—81no—
622C4—81no—
623C4—862no—
624C4—3441no—
625C4—3441no—
626C4—1721no—
627C4—1721no—
628C4—1722no—
629C4—1722no—
630C4#1458342611yescharacteristic
631C4#1458349311yescharacteristic
632C4#1458360011yescharacteristic
633C4#1458361611yescharacteristic
634C2—82no—
635C2—1722no—
636C2#1913863211yescharacteristic
637C2#1914460211yescharacteristic
638C2#1914479111yescharacteristic
639C2#1914641811yescharacteristic
640C2#1914678011yescharacteristic
641C2#1914695011yescharacteristic
642C2#1914720111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2071C2
socleC23×C43C22×D4
prime radicalC2×#13063296C22
hypercenter#2071D43
hypocenterC43#27032
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2071

Complements

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

NH ≅ G/Ntype
1. #19139031C2semidirect
3. #19135969C2semidirect
6. #19135356C2semidirect
7. #19135322C2semidirect
8. #19135202C2semidirect
9. #19135181C2semidirect
10. #19135171C2semidirect
11. #19134858C2semidirect
12. #19134789C2semidirect
13. #19134680C2semidirect
14. #102×Dic43C2semidirect
15. C43×#2071C2semidirect
315. #2071D43semidirect
380. C43#27032semidirect

Maximal subgroups

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

subgroupindex
#191390312
#191376162
#191359692
#191357822
#191353562
#191353222
#191352022
#191351812
#191351712
#191348582
#191347892
#191346802
#102×Dic432
C43×#20712
#2703243