Finite Group Databasebeta

← #25169308

Subgroups — #25169308

Order 11008.

728 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139017C211yesmaximal, characteristic
2#19136003C211yesmaximal, characteristic, complemented
3#19135976C211yesmaximal, characteristic, complemented
4#19135788C211yesmaximal, characteristic
5#19135788C211yesmaximal, characteristic
6#19135358C211yesmaximal, characteristic, complemented
7#19135320C211yesmaximal, characteristic, complemented
8#19135203C211yesmaximal, characteristic
9#19135177C211yesmaximal, characteristic, complemented
10#19135173C211yesmaximal, characteristic, complemented
11#19134863C211yesmaximal, characteristic, complemented
12#19134788C211yesmaximal, characteristic
13#19134685C211yesmaximal, characteristic
14C4×#13063249C211yesmaximal, characteristic, complemented
15C43×#2360C211yesmaximal, characteristic
16C2×#13063318—21no—
17C2×#13063256C2211yescharacteristic
18C2×#13063256C2211yescharacteristic
19C2×#13063256C2211yescharacteristic
20C2×#13063256C2211yescharacteristic
21C2×C4⋊(C43⋊C8)C2211yescharacteristic
22C2×#13063249C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×C22⋊(C43⋊C8)C2211yescharacteristic
27C2×C22⋊(C43⋊C8)C2211yescharacteristic
28C2×C4×C43⋊C8C2211yescharacteristic
29#14582839—21no—
30#14582824—21no—
31#14582797C2211yescharacteristic
32#14582797C2211yescharacteristic
33#14582784—21no—
34#14582769C2211yescharacteristic
35#14582759C2211yescharacteristic
36#14582759C2211yescharacteristic
37C4×C4⋊Dic43C2211yescharacteristic
38#14582661C2211yescharacteristic
39#14582661C2211yescharacteristic
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×C4⋊C4×C43C2211yescharacteristic
51C43×#391C2211yescharacteristic
52C43×#389—21no—
53C43×#389C2211yescharacteristic
54C43×#387—21no—
55C43×#385—21no—
56C4×C4⋊C4×C43C2211yescharacteristic
57C4×C22⋊C4×C43—21no—
58C4×C22⋊C4×C43C2211yescharacteristic
59C22×C43⋊C8C2311yescharacteristic
60C22×C43⋊C8C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63#13063318—44no—
64C2×C4⋊Dic43—21no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43C2311yescharacteristic
67C2×C4⋊Dic43C2311yescharacteristic
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×Dic43⋊C4—21no—
71C2×Dic43⋊C4—21no—
72C2×C22⋊Dic43—21no—
73C2×C22⋊Dic43—21no—
74C2×C4×Dic43—21no—
75#13063256—22no—
76#13063256—22no—
77#13063256—22no—
78#13063256—41no—
79C4⋊(C43⋊C8)—22no—
80#13063249—22no—
81#13063249—22no—
82#13063249—22no—
83#13063249—41no—
84C22⋊(C43⋊C8)—22no—
85C22⋊(C43⋊C8)—41no—
86C4×C43⋊C8—41no—
87C43⋊#95—21no—
88C43⋊#95—21no—
89C43⋊#95—21no—
90C43⋊#95—21no—
91C43⋊#95—21no—
92C22×Q8×C43C2311yescharacteristic
93C23×C4×C43—21no—
94C23×C4×C43C2311yescharacteristic
95C22⋊Q8×C43—22no—
96C22⋊Q8×C43—22no—
97C4×Q8×C43—22no—
98C4×Q8×C43—41no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43—22no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43—41no—
105C2×C4⋊C4×C43C2311yescharacteristic
106C2×C4⋊C4×C43C2311yescharacteristic
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C22⋊C4×C43—21no—
109C2×C22⋊C4×C43D411yescharacteristic
110C2×C22⋊C4×C43D411yescharacteristic
111C2×C42×C43—21no—
112C2×C42×C43—21no—
113C2×C42×C43C2311yescharacteristic
114C2×C42×C43C2311yescharacteristic
115#95×C43—21no—
116#95×C43—21no—
117#95×C43—21no—
118#95×C43—21no—
119#95×C43D411yescharacteristic
120#95×C43D411yescharacteristic
121C24×C43C2×D411yescharacteristic
122C2×Q8×C43—21no—
123C2×Q8×C43—21no—
124C2×Q8×C43—21no—
125C2×Q8×C43—21no—
126C2×Q8×C43—21no—
127C2×Q8×C43#4112yes—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—42no—
139C22×C4×C43—42no—
140C22×C4×C43—81no—
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2411yescharacteristic
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C4⋊C4×C43—24no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—42no—
157C4⋊C4×C43—42no—
158C4⋊C4×C43—81no—
159C4⋊C4×C43#4112yes—
160C4⋊C4×C43#4112yes—
161C22⋊C4×C43—24no—
162C22⋊C4×C43—41no—
163C22⋊C4×C43SD1614yes—
164C42×C43—21no—
165C42×C43—21no—
166C42×C43—21no—
167C42×C43—21no—
168C42×C43—42no—
169C42×C43—81no—
170C22⋊Dic43—42no—
171C22⋊Dic43—42no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—42no—
181C4⋊Dic43—42no—
182Dic43⋊C4—42no—
183Dic43⋊C4—42no—
184C4×Dic43—42no—
185C2×C43⋊C8—21no—
186C2×C43⋊C8—21no—
187C2×C43⋊C8—21no—
188C2×C43⋊C8—21no—
189C2×C43⋊C8—21no—
190C2×C43⋊C8—21no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8#4112yes—
197C23×C43—21no—
198C23×C43—21no—
199C23×C43—21no—
200C23×C43—21no—
201C23×C43—21no—
202C23×C43—21no—
203C23×C43C2×SD1612yes—
204C23×C43C22×D411yescharacteristic
205Q8×C43—22no—
206Q8×C43—22no—
207Q8×C43—41no—
208Q8×C43—41no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—22no—
214C2×C4×C43—22no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—22no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
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×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—84no—
239C2×C4×C43C2×SD1612yes—
240C2×C4×C43C2×SD1612yes—
241C2×C4×C43C2×#4111yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43H(5,𝔽2)11yescharacteristic
246C2×C4×C432−1+411yescharacteristic
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
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—
259C43⋊C8—22no—
260C43⋊C8—41no—
261C43⋊C8—41no—
262C43⋊C8—41no—
263#27034—431nomaximal, Sylow
264C22×C43—22no—
265C22×C43—22no—
266C22×C43—22no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43#52511yescharacteristic
272C22×C43#54611yescharacteristic
273C22×C43#54711yescharacteristic
274C22×C43C22×SD1611yescharacteristic
275C22×C43#57511yescharacteristic
276C22×C43#57711yescharacteristic
277C22×C43#57811yescharacteristic
278C4×C43—22no—
279C4×C43—22no—
280C4×C43—41no—
281C4×C43—42no—
282C4×C43—41no—
283C4×C43—42no—
284C4×C43—41no—
285C4×C43—42no—
286C4×C43—81no—
287C4×C43#52911yescharacteristic
288C4×C43#53911yescharacteristic
289C4×C43#55311yescharacteristic
290C4×C43#55611yescharacteristic
291Dic43—81no—
292Dic43—81no—
293Dic43—81no—
294Dic43—81no—
295#2496—431no—
296#2360D4311yescharacteristic
297#2072—431no—
298#2066—431no—
299#2035—431no—
300#2035—431no—
301#1948—431no—
302#1941—431no—
303#1923—431no—
304#1920—431no—
305#1919—431no—
306#1865—431no—
307#1853—431no—
308#1824—431no—
309C4×#103—431no—
310C2×C43—42no—
311C2×C43#246611yescharacteristic
312C2×C43#310311yescharacteristic
313C2×C43#312011yescharacteristic
314C2×C43#329811yescharacteristic
315C2×C43#331111yescharacteristic
316C2×C43#333511yescharacteristic
317C2×C43#335211yescharacteristic
318C2×#126—861no—
319C2×C22⋊Q8C2×D4311yescharacteristic
320C2×C4×Q8C2×D4311yescharacteristic
321C22×C4⋊C4C2×D4311yescharacteristic
322C2×#106—431no—
323C2×#106—431no—
324C2×#106—431no—
325C2×#106—431no—
326C2×C4⋊C8—431no—
327C2×#103—431no—
328C2×#103—431no—
329C2×#103—431no—
330C2×#103—431no—
331C2×C22⋊C8—431no—
332C2×C22⋊C8—431no—
333C2×C4×C8—431no—
334#400—861no—
335#397—861no—
336#391C2×D4311yescharacteristic
337#389—21no—
338#389—431no—
339#389—431no—
340#389C2×D4311yescharacteristic
341#387—21no—
342#387—861no—
343#385—21no—
344#384—431no—
345#380—431no—
346#380—431no—
347C4×C4⋊C4—431no—
348C4×C4⋊C4C2×D4311yescharacteristic
349C4×C22⋊C4—21no—
350C4×C22⋊C4C2×D4311yescharacteristic
351#340—431no—
352#340—431no—
353#340—431no—
354#340—431no—
355#340—431no—
356#340—431no—
357#340—431no—
358#340—431no—
359#336—431no—
360#336—431no—
361C43#2703411yescharacteristic, complemented, Sylow
362C22×Q8C22×D4311yescharacteristic
363C23×C4—21no—
364C23×C4C22×D4311yescharacteristic
365C22×C8—431no—
366C22×C8—431no—
367C22×C8—431no—
368C22×C8—431no—
369#126—1724no—
370C22⋊Q8—22no—
371C22⋊Q8—22no—
372C4×Q8—22no—
373C4×Q8—41no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—41no—
380C2×C4⋊C4—431no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—431no—
383C2×C4⋊C4—431no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4—861no—
386C2×C4⋊C4—861no—
387C2×C4⋊C4—861no—
388C2×C4⋊C4C22×D4311yescharacteristic
389C2×C4⋊C4C22×D4311yescharacteristic
390C2×C4⋊C4C22×D4311yescharacteristic
391C2×C22⋊C4—21no—
392C2×C22⋊C4—861no—
393C2×C22⋊C4—861no—
394C2×C22⋊C4C22⋊D4311yescharacteristic
395C2×C22⋊C4C22⋊D4311yescharacteristic
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—861no—
399C2×C42C22×D4311yescharacteristic
400C2×C42C22×D4311yescharacteristic
401#106—862no—
402#106—862no—
403#106—862no—
404#106—1721no—
405C4⋊C8—862no—
406#103—862no—
407#103—862no—
408#103—862no—
409#103—1721no—
410C22⋊C8—862no—
411C22⋊C8—1721no—
412C4×C8—1721no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—861no—
418#95—861no—
419#95—861no—
420#95—861no—
421#95—861no—
422#95C22⋊D4311yescharacteristic
423#95C22⋊D4311yescharacteristic
424C24C2×C22⋊D4311yescharacteristic
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8#1062189812yes—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—81no—
444C22×C4—861no—
445C22×C4—861no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4C2×C22⋊D4311yescharacteristic
449C22×C4C2×C22⋊D4311yescharacteristic
450C22×C4C2×C22⋊D4311yescharacteristic
451C22×C4C2×C22⋊D4311yescharacteristic
452C22×C4C2×C22⋊D4311yescharacteristic
453C22×C4C23×D4311yescharacteristic
454C2×C8—432no—
455C2×C8—861no—
456C2×C8—861no—
457C2×C8—861no—
458C2×C8—861no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—861no—
466C4⋊C4—24no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—42no—
472C4⋊C4—42no—
473C4⋊C4—81no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—1722no—
483C4⋊C4—1722no—
484C4⋊C4—1722no—
485C4⋊C4—1722no—
486C4⋊C4#1062189812yes—
487C4⋊C4#1062190012yes—
488C22⋊C4—24no—
489C22⋊C4—41no—
490C22⋊C4—1722no—
491C22⋊C4—1722no—
492C22⋊C4#1062188414yes—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—42no—
498C42—81no—
499C42—1722no—
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23C2×#1062188412yes—
507C23C22×C22⋊D4311yescharacteristic
508Q8—22no—
509Q8—22no—
510Q8—41no—
511Q8—41no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—84no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4C2×#1062188412yes—
555C2×C4C2×#1062188412yes—
556C2×C4#41×D4311yescharacteristic
557C2×C4C2×#1062190011yescharacteristic
558C2×C4C2×#1062189811yescharacteristic
559C2×C4C2×#1062189811yescharacteristic
560C2×C4#1306337011yescharacteristic
561C2×C4#1306337211yescharacteristic
562C8—862no—
563C8—1721no—
564C8—1721no—
565C8—1721no—
566C22—22no—
567C22—22no—
568C22—22no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22#1458341011yescharacteristic
574C22#1458354311yescharacteristic
575C22#1458354811yescharacteristic
576C22C22×#1062188411yescharacteristic
577C22#1458369711yescharacteristic
578C22#1458371011yescharacteristic
579C22#1458371411yescharacteristic
580C4—22no—
581C4—22no—
582C4—41no—
583C4—42no—
584C4—42no—
585C4—41no—
586C4—42no—
587C4—41no—
588C4—81no—
589C4—3441no—
590C4—3441no—
591C4—3441no—
592C4—3441no—
593C4#1458342911yescharacteristic
594C4#1458349111yescharacteristic
595C4#1458359911yescharacteristic
596C4#1458361911yescharacteristic
597C2—42no—
598C2#1913862511yescharacteristic
599C2#1914462611yescharacteristic
600C2#1914480911yescharacteristic
601C2#1914646011yescharacteristic
602C2#1914663111yescharacteristic
603C2#1914694611yescharacteristic
604C2#1914716411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2360C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#2360D43
hypocenterC43#27034
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2360

Complements

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

NH ≅ G/Ntype
2. #19136003C2semidirect
3. #19135976C2semidirect
6. #19135358C2semidirect
7. #19135320C2semidirect
9. #19135177C2semidirect
10. #19135173C2semidirect
11. #19134863C2semidirect
14. C4×#13063249C2semidirect
361. C43#27034semidirect

Maximal subgroups

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

subgroupindex
#191390172
#191360032
#191359762
#191357882
#191353582
#191353202
#191352032
#191351772
#191351732
#191348632
#191347882
#191346852
C4×#130632492
C43×#23602
#2703443