Finite Group Databasebeta

← #25200126

Subgroups — #25200126

Order 11008.

766 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142934C211yesmaximal, characteristic
2#19136026C211yesmaximal, characteristic
3#19135798C211yesmaximal, characteristic
4#19135795C211yesmaximal, characteristic
5#19135603C211yesmaximal, characteristic
6#19135455C211yesmaximal, characteristic, complemented
7#19135325C211yesmaximal, characteristic, complemented
8#19135274C211yesmaximal, characteristic, complemented
9#19135270C211yesmaximal, characteristic, complemented
10#19135236C211yesmaximal, characteristic, complemented
11#19135187C211yesmaximal, characteristic, complemented
12#19134936C211yesmaximal, characteristic, complemented
13#19134849C211yesmaximal, characteristic, complemented
14C4×C22⋊(C43⋊C8)C211yesmaximal, characteristic
15C4×C22⋊Q8×C43C211yesmaximal, characteristic
16C22×#10621885C2211yescharacteristic
17C2×#13063304C2211yescharacteristic
18C2×#13063258C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×#13063258C2211yescharacteristic
21C2×#13063249C2211yescharacteristic
22C2×#13063249C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063248C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063248C2211yescharacteristic
27C2×C22⋊(C43⋊C8)C2211yescharacteristic
28C2×C22⋊(C43⋊C8)C2211yescharacteristic
29C2×C4×C43⋊C8C2211yescharacteristic
30C2×C4×C43⋊C8C2211yescharacteristic
31#14582805C2211yescharacteristic
32#14582805C2211yescharacteristic
33#14582797C2211yescharacteristic
34#14582797C2211yescharacteristic
35#14582783—21no—
36#14582783—21no—
37#14582772—21no—
38#14582762—21no—
39#14582759C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C2×C22⋊Q8×C43C2211yescharacteristic
49C2×C4×Q8×C43C2211yescharacteristic
50C22×C42×C43C2211yescharacteristic
51C43×#391C2211yescharacteristic
52C43×#389C2211yescharacteristic
53C43×#387—21no—
54C43×#385—21no—
55C43×#380C2211yescharacteristic
56C4×C4⋊C4×C43—21no—
57C4×C4⋊C4×C43C2211yescharacteristic
58C4×C22⋊C4×C43—21no—
59C22×Dic86C2311yescharacteristic
60C2×#10621885—22no—
61C2×#10621885—22no—
62C2×#10621885—41no—
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063304—41no—
68#13063304—41no—
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×C22⋊Dic43—21no—
76C2×C22⋊Dic43—21no—
77#13063258—22no—
78#13063258—22no—
79#13063258—41no—
80#13063249—22no—
81#13063249—22no—
82#13063249—41no—
83#13063248—22no—
84#13063248—22no—
85#13063248—41no—
86C22⋊(C43⋊C8)—22no—
87C22⋊(C43⋊C8)—22no—
88C4×C43⋊C8—41no—
89C4×C43⋊C8—41no—
90C43⋊#95—21no—
91C43⋊#95—21no—
92C43⋊#95—21no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C22×Q8×C43C2311yescharacteristic
98C23×C4×C43D411yescharacteristic
99C23×C4×C43D411yescharacteristic
100C23×C4×C43C2311yescharacteristic
101C22⋊Q8×C43—22no—
102C22⋊Q8×C43—22no—
103C4×Q8×C43—41no—
104C4×Q8×C43—41no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43—21no—
113C2×C42×C43—21no—
114C2×C42×C43—21no—
115C2×C42×C43—41no—
116C2×C42×C43—41no—
117C2×C42×C43D411yescharacteristic
118C2×C42×C43D411yescharacteristic
119C2×C42×C43C2311yescharacteristic
120C2×C42×C43C2311yescharacteristic
121#95×C43—21no—
122#95×C43—21no—
123#95×C43—21no—
124#95×C43—21no—
125#95×C43—21no—
126C24×C43C2×D411yescharacteristic
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43#4112yes—
133C22×C4×C43—22no—
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×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—41no—
145C22×C4×C43—41no—
146C22×C4×C43—41no—
147C22×C4×C43—41no—
148C22×C4×C43Q1614yescomplemented
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2411yescharacteristic
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C4⋊C4×C43—24no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—42no—
172C4⋊C4×C43—42no—
173C4⋊C4×C43#4112yes—
174C22⋊C4×C43—24no—
175C22⋊C4×C43—42no—
176C42×C43—21no—
177C42×C43—21no—
178C42×C43—21no—
179C42×C43—21no—
180C42×C43—41no—
181C42×C43—41no—
182C42×C43—42no—
183C42×C43—42no—
184C22⋊Dic43—42no—
185C22⋊Dic43—42no—
186#10621885—44no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193Dic43⋊C4—42no—
194Dic43⋊C4—42no—
195Dic43⋊C4—42no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8#4112yes—
207C2×C43⋊C8#4112yes—
208C23×C43—21no—
209C23×C43—21no—
210C23×C43—21no—
211C23×C43—21no—
212C23×C43—21no—
213C23×C43—21no—
214C23×C43C2×Q1612yes—
215C23×C43C22×D411yescharacteristic
216Q8×C43—22no—
217Q8×C43—22no—
218Q8×C43—41no—
219Q8×C43—41no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—22no—
227C2×C4×C43—22no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—44no—
235C2×C4×C43—44no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
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×C43C2×Q1612yes—
251C2×C4×C43C2×Q1612yes—
252C2×C4×C43#13512yes—
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43H(5,𝔽2)11yescharacteristic
258C2×C4×C43H(5,𝔽2)11yescharacteristic
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—
271Dic86—41no—
272Dic86—41no—
273Dic86—41no—
274Dic86—41no—
275C43⋊C8—22no—
276C43⋊C8—22no—
277C43⋊C8—41no—
278C43⋊C8—41no—
279#29462—431nomaximal, Sylow
280C22×C43—22no—
281C22×C43—22no—
282C22×C43—22no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43—41no—
286C22×C43—41no—
287C22×C43#52511yescharacteristic
288C22×C43#53211yescharacteristic
289C22×C43#53411yescharacteristic
290C22×C43C22×Q1611yescharacteristic
291C22×C43C2×#13511yescharacteristic
292C22×C43#57511yescharacteristic
293C22×C43#57511yescharacteristic
294C4×C43—22no—
295C4×C43—22no—
296C4×C43—22no—
297C4×C43—42no—
298C4×C43—41no—
299C4×C43—42no—
300C4×C43—41no—
301C4×C43—81no—
302C4×C43—81no—
303C4×C43#55111yescharacteristic
304C4×C43#55311yescharacteristic
305C4×C43#55311yescharacteristic
306C4×C43#55911yescharacteristic
307Dic43—81no—
308Dic43—81no—
309Dic43—81no—
310Dic43—81no—
311#2855—431no—
312C4×C22⋊Q8D4311yescharacteristic
313#2076—431no—
314#2036—431no—
315#2036—431no—
316#2001—431no—
317#1969—431no—
318#1942—431no—
319#1933—431no—
320#1933—431no—
321#1928—431no—
322#1921—431no—
323#1878—431no—
324#1863—431no—
325C4×C22⋊C8—431no—
326C2×C43—42no—
327C2×C43#260211yescharacteristic
328C2×C43#310211yescharacteristic
329C2×C43#310411yescharacteristic
330C2×C43#317011yescharacteristic
331C2×C43#318311yescharacteristic
332C2×C43#318911yescharacteristic
333C2×C43#319111yescharacteristic
334C22×Q16—431no—
335C2×C22⋊Q8—431no—
336C2×C22⋊Q8C2×D4311yescharacteristic
337C2×C4×Q8C2×D4311yescharacteristic
338C22×C42C2×D4311yescharacteristic
339C2×#107—431no—
340C2×#107—431no—
341C2×#107—431no—
342C2×#103—431no—
343C2×#103—431no—
344C2×#103—431no—
345C2×#103—431no—
346C2×#103—431no—
347C2×#103—431no—
348C2×C22⋊C8—431no—
349C2×C22⋊C8—431no—
350C2×C4×C8—431no—
351C2×C4×C8—431no—
352#391—431no—
353#391—431no—
354#391C2×D4311yescharacteristic
355#389—431no—
356#389—431no—
357#389C2×D4311yescharacteristic
358#387—21no—
359#387—861no—
360#387—861no—
361#385—21no—
362#385—861no—
363#381—861no—
364#380—431no—
365#380C2×D4311yescharacteristic
366C4×C4⋊C4—21no—
367C4×C4⋊C4C2×D4311yescharacteristic
368C4×C22⋊C4—21no—
369#340—431no—
370#340—431no—
371#340—431no—
372#340—431no—
373#340—431no—
374#340—431no—
375#336—431no—
376#336—431no—
377C43#2946211yescharacteristic, complemented, Sylow
378C22×Q8—431no—
379C22×Q8C22×D4311yescharacteristic
380C23×C4C22⋊D4311yescharacteristic
381C23×C4C22⋊D4311yescharacteristic
382C23×C4C22×D4311yescharacteristic
383C2×Q16—862no—
384C2×Q16—862no—
385C2×Q16—1721no—
386C22×C8—431no—
387C22×C8—431no—
388C22×C8—431no—
389C22×C8—431no—
390C22⋊Q8—22no—
391C22⋊Q8—22no—
392C22⋊Q8—1721no—
393C22⋊Q8—1721no—
394C4×Q8—41no—
395C4×Q8—41no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—431no—
400C2×C4⋊C4—431no—
401C2×C4⋊C4—431no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4C22×D4311yescharacteristic
406C2×C4⋊C4C22×D4311yescharacteristic
407C2×C4⋊C4C22×D4311yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—861no—
411C2×C22⋊C4—861no—
412C2×C42—21no—
413C2×C42—21no—
414C2×C42—41no—
415C2×C42—41no—
416C2×C42C22⋊D4311yescharacteristic
417C2×C42C22⋊D4311yescharacteristic
418C2×C42C22×D4311yescharacteristic
419C2×C42C22×D4311yescharacteristic
420#107—862no—
421#107—862no—
422#107—1721no—
423#103—862no—
424#103—862no—
425#103—862no—
426#103—862no—
427#103—1721no—
428#103—1721no—
429C22⋊C8—862no—
430C22⋊C8—862no—
431C4×C8—1721no—
432C4×C8—1721no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—861no—
439#95—861no—
440#95—861no—
441#95—861no—
442#95—861no—
443#95—861no—
444#95—861no—
445C24C2×C22⋊D4311yescharacteristic
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—861no—
452C2×Q8—861no—
453C2×Q8—861no—
454C2×Q8—861no—
455C2×Q8—861no—
456C2×Q8—861no—
457C2×Q8#1062189812yes—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4#1062188514yescomplemented
478C22×C4C2×C22⋊D4311yescharacteristic
479C22×C4C2×C22⋊D4311yescharacteristic
480C22×C4C2×C22⋊D4311yescharacteristic
481C22×C4C2×C22⋊D4311yescharacteristic
482C22×C4C2×C22⋊D4311yescharacteristic
483C22×C4C23×D4311yescharacteristic
484Q16—1724no—
485C2×C8—432no—
486C2×C8—432no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8—861no—
492C2×C8—861no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8—861no—
496C2×C8—861no—
497C4⋊C4—24no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—42no—
504C4⋊C4—42no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—1722no—
512C4⋊C4—1722no—
513C4⋊C4—1722no—
514C4⋊C4#1062189812yes—
515C22⋊C4—24no—
516C22⋊C4—42no—
517C22⋊C4—1722no—
518C22⋊C4—1722no—
519C42—21no—
520C42—21no—
521C42—21no—
522C42—21no—
523C42—41no—
524C42—41no—
525C42—42no—
526C42—42no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23C2×#1062188512yes—
534C23C22×C22⋊D4311yescharacteristic
535Q8—22no—
536Q8—22no—
537Q8—41no—
538Q8—41no—
539Q8—1721no—
540Q8—1721no—
541Q8—1721no—
542Q8—1721no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—44no—
558C2×C4—44no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
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×C4C2×#1062188512yes—
586C2×C4C2×#1062188512yes—
587C2×C4#1306334512yes—
588C2×C4#41×D4311yescharacteristic
589C2×C4#41×D4311yescharacteristic
590C2×C4C2×#1062189811yescharacteristic
591C2×C4C2×#1062189811yescharacteristic
592C2×C4#1306337011yescharacteristic
593C2×C4#1306337011yescharacteristic
594C8—862no—
595C8—862no—
596C8—1721no—
597C8—1721no—
598C22—22no—
599C22—22no—
600C22—22no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22#1458341011yescharacteristic
606C22#1458344511yescharacteristic
607C22#1458345811yescharacteristic
608C22C22×#1062188511yescharacteristic
609C22C2×#1306334511yescharacteristic
610C22#1458369711yescharacteristic
611C22#1458369711yescharacteristic
612C4—22no—
613C4—22no—
614C4—22no—
615C4—41no—
616C4—42no—
617C4—42no—
618C4—41no—
619C4—81no—
620C4—81no—
621C4—3441no—
622C4—3441no—
623C4—3441no—
624C4—3441no—
625C4#1458357811yescharacteristic
626C4#1458359811yescharacteristic
627C4#1458359911yescharacteristic
628C4#1458363211yescharacteristic
629C2—42no—
630C2#1914020711yescharacteristic
631C2#1914461311yescharacteristic
632C2#1914463411yescharacteristic
633C2#1914517711yescharacteristic
634C2#1914531811yescharacteristic
635C2#1914536711yescharacteristic
636C2#1914538311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC4×C22⋊Q8×C43C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenterC4×C22⋊Q8D43
hypocenterC43#29462
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
6. #19135455C2semidirect
7. #19135325C2semidirect
8. #19135274C2semidirect
9. #19135270C2semidirect
10. #19135236C2semidirect
11. #19135187C2semidirect
12. #19134936C2semidirect
13. #19134849C2semidirect
148. C22×C4×C43Q16semidirect
377. C43#29462semidirect
477. C22×C4#10621885semidirect

Maximal subgroups

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

subgroupindex
#191429342
#191360262
#191357982
#191357952
#191356032
#191354552
#191353252
#191352742
#191352702
#191352362
#191351872
#191349362
#191348492
C4×C22⋊(C43⋊C8)2
C4×C22⋊Q8×C432
#2946243