Finite Group Databasebeta

← #25118402

Subgroups — #25118402

Order 11008.

898 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583187C211yesmaximal, characteristic
2#19137681C211yesmaximal, characteristic, complemented
3D4×Dic43⋊C4C211yesmaximal, characteristic
4#19135554C211yesmaximal, characteristic, complemented
5#19135355C211yesmaximal, characteristic, complemented
6#19135321C211yesmaximal, characteristic, complemented
7#19135320C211yesmaximal, characteristic, complemented
8#19135174C211yesmaximal, characteristic, complemented
9#19135171C211yesmaximal, characteristic, complemented
10#19134854C211yesmaximal, characteristic
11#19134456C211yesmaximal, characteristic, complemented
12#102×Dic43C211yesmaximal, characteristic
13#102×Dic43C211yesmaximal, characteristic
14C4×#13063246C211yesmaximal, characteristic
15C43×#1864C211yesmaximal, characteristic
16C2×#13063324C2211yescharacteristic
17C2×D4×Dic43C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19C22×Dic43⋊C4—21no—
20#14583187C418yescomplemented
21C2×#13063257C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×C4×C43⋊C8C2211yescharacteristic
28C2×C8×Dic43C2211yescharacteristic
29C2×C8×Dic43C2211yescharacteristic
30#14582804—21no—
31#14582803—21no—
32#14582797C2211yescharacteristic
33#14582795C2211yescharacteristic
34#14582795C2211yescharacteristic
35#14582794—21no—
36#14582772—21no—
37#14582771—21no—
38#14582768C2211yescharacteristic
39#14582757—21no—
40C4⋊C4×Dic43C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42C4×Dic43⋊C4C2211yescharacteristic
43C4×C4⋊Dic43C2211yescharacteristic
44#14582750—21no—
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×C4×D4×C43C2211yescharacteristic
54C2×#106×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C22×Dic86—21no—
61C23×Dic43—21no—
62C23×Dic43—21no—
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65#13063324—22no—
66#13063324C2×C414yescomplemented
67D4×Dic43—22no—
68D4×Dic43—22no—
69D4×Dic43—41no—
70D4×Dic43C2×C414yes—
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—44no—
82C2×Dic43⋊C4D411yescharacteristic
83C2×Dic43⋊C4D411yescharacteristic
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43C2311yescharacteristic
90C2×C4×Dic43C2311yescharacteristic
91#13063257C2×C414yescomplemented
92#13063256—41no—
93#13063256C2×C414yescomplemented
94Dic43⋊C8C2×C414yescomplemented
95#13063246C2×C414yes—
96#13063246Q814yescomplemented
97C4×C43⋊C8—41no—
98C8×Dic43—22no—
99C8×Dic43—41no—
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
109C23×C4×C43—21no—
110C22×C8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C4×D4×C43—22no—
113C4×D4×C43—41no—
114C2×C4⋊C4×C43—21no—
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C22⋊C4×C43—21no—
119C2×C42×C43C2311yescharacteristic
120#106×C43—41no—
121#102×C43—22no—
122#102×C43C2×C414yes—
123#95×C43—21no—
124C24×C43—21no—
125C2×D4×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43C22×C412yes—
129C2×D4×C43C2×Q812yes—
130C2×D4×C43#4112yes—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—42no—
135C22×C4×C43—42no—
136C22×C4×C43—81no—
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2411yescharacteristic
140C22×Dic43—24no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—42no—
146C22×Dic43—42no—
147C22×Dic43—42no—
148C22×Dic43—42no—
149C22×Dic43—81no—
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C22×Dic43C2×D411yescharacteristic
154C2×Dic86—24no—
155C2×Dic86—81no—
156C2×Dic86—81no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43C22×C412yes—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—81no—
169C4⋊C4×C43C22×C412yes—
170C22⋊C4×C43—42no—
171C42×C43—21no—
172C42×C43—21no—
173C22⋊Dic43—24no—
174C22⋊Dic43—42no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43C22×C412yes—
181C4⋊Dic43C22×C412yes—
182C4⋊Dic43C2×Q812yes—
183Dic43⋊C4—24no—
184Dic43⋊C4—22no—
185Dic43⋊C4—42no—
186Dic43⋊C4—42no—
187Dic43⋊C4—42no—
188Dic43⋊C4—81no—
189Dic43⋊C4—81no—
190Dic43⋊C4SD1614yes—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—42no—
194C4×Dic43—81no—
195C4×Dic43—81no—
196C4×Dic43C22×C412yes—
197C4×Dic43#4112yes—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8C22×C412yes—
203C2×C43⋊C8C2×Q812yes—
204C23×C43—22no—
205C23×C43—22no—
206C23×C43—22no—
207C23×C43—41no—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43C22×D411yescharacteristic
212D4×C43—22no—
213D4×C43—22no—
214D4×C43—22no—
215D4×C43C4×Q814yes—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—22no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—84no—
231C2×C4×C43C2×SD1612yes—
232C2×C4×C43C23×C411yescharacteristic
233C2×C4×C43C22×Q811yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43H(5,𝔽2)11yescharacteristic
237C2×C4×C432−1+411yescharacteristic
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—22no—
243C2×Dic43—22no—
244C2×Dic43—21no—
245C2×Dic43—22no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—48no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—84no—
259C2×Dic43C4×D412yes—
260C2×Dic43C4×D412yes—
261C2×Dic43C2×SD1612yes—
262C2×Dic43C2×SD1612yes—
263C2×Dic43#13512yes—
264Dic86—84no—
265C8×C43—22no—
266C8×C43—41no—
267C43⋊C8—22no—
268C43⋊C8—22no—
269#22963—431nomaximal, Sylow
270C22×C43—24no—
271C22×C43—42no—
272C22×C43—42no—
273C22×C43—42no—
274C22×C43—42no—
275C22×C43—42no—
276C22×C43—42no—
277C22×C43C2×C4×D411yescharacteristic
278C22×C43#54611yescharacteristic
279C22×C43D4×Q811yescharacteristic
280C22×C43C22×SD1611yescharacteristic
281C22×C43C2×#13511yescharacteristic
282C22×C43#57611yescharacteristic
283C22×C43#57711yescharacteristic
284C4×C43—22no—
285C4×C43—42no—
286C4×C43—41no—
287C4×C43—81no—
288C4×C43—81no—
289C4×C43C2×C4×Q811yescharacteristic
290C4×C43#52011yescharacteristic
291C4×C43#55211yescharacteristic
292C4×C43#55411yescharacteristic
293Dic43—22no—
294Dic43—22no—
295Dic43—42no—
296Dic43—42no—
297Dic43—42no—
298Dic43—41no—
299Dic43—81no—
300Dic43C4×SD1614yes—
301C2×#476—431no—
302#2369—431no—
303D4×C4⋊C4—431no—
304#1990—431no—
305#1948—431no—
306#1941—431no—
307#1941—431no—
308#1919—431no—
309#1919—431no—
310#1864—431no—
311#1864D4311yescharacteristic
312C8×C4⋊C4—431no—
313C4×#102—431no—
314C4×#102—431no—
315C4×#102—431no—
316C2×C43—44no—
317C2×C43#236011yescharacteristic
318C2×C43C2×C4×SD1611yescharacteristic
319C2×C43#294611yescharacteristic
320C2×C43#329511yescharacteristic
321C2×C43#330311yescharacteristic
322C2×C43Q8×SD1611yescharacteristic
323C2×C43#338011yescharacteristic
324C2×C4⋊Q8—431no—
325C2×C4×D4—431no—
326C2×C4×D4—431no—
327C2×C4×D4C2×D4311yescharacteristic
328C22×C4⋊C4—861no—
329#476—438no—
330C2×#106—431no—
331C2×#106—431no—
332C2×#106—431no—
333C2×#106C2×D4311yescharacteristic
334C2×C4⋊C8—431no—
335C2×#102—431no—
336C2×#102—431no—
337C2×#102C2×D4311yescharacteristic
338C2×#102C2×D4311yescharacteristic
339C2×C4×C8—431no—
340C2×C4×C8—431no—
341C2×C4×C8—431no—
342#391—861no—
343#391—861no—
344#389—431no—
345#389—431no—
346#389—431no—
347#389—861no—
348#389C2×D4311yescharacteristic
349#385—861no—
350#385—861no—
351#384—431no—
352#380—861no—
353C4×C4⋊C4—431no—
354C4×C4⋊C4—431no—
355C4×C4⋊C4—431no—
356C4×C4⋊C4—431no—
357C4×C4⋊C4—861no—
358#340—431no—
359#340—431no—
360#340—431no—
361#340—431no—
362#340—431no—
363#340—431no—
364#340—431no—
365#340C2×D4311yescharacteristic
366#336—431no—
367#336C2×D4311yescharacteristic
368C43#2296311yescharacteristic, complemented, Sylow
369C22×Q8—861no—
370C22×D4C22×D4311yescharacteristic
371C23×C4—21no—
372C23×C4—861no—
373C23×C4—861no—
374C22×C8—431no—
375C22×C8—431no—
376C22×C8C22×D4311yescharacteristic
377C22×C8C22×D4311yescharacteristic
378C4⋊Q8—434no—
379C4⋊Q8—862no—
380C4×D4—22no—
381C4×D4—41no—
382C4×D4—434no—
383C4×D4—862no—
384C4×D4—862no—
385C4×D4—1721no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—431no—
388C2×C4⋊C4—431no—
389C2×C4⋊C4—431no—
390C2×C4⋊C4—431no—
391C2×C4⋊C4—431no—
392C2×C4⋊C4—431no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—1724no—
400C2×C4⋊C4C22×D4311yescharacteristic
401C2×C4⋊C4C22×D4311yescharacteristic
402C2×C4⋊C4C22×D4311yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—861no—
405C2×C22⋊C4—861no—
406C2×C42—431no—
407C2×C42—431no—
408C2×C42—861no—
409C2×C42—861no—
410C2×C42—861no—
411C2×C42C22×D4311yescharacteristic
412#106—41no—
413#106—434no—
414#106—434no—
415#106—1721no—
416C4⋊C8—434no—
417#102—22no—
418#102—434no—
419#102—434no—
420#102C4×D4314yes—
421C4×C8—862no—
422C4×C8—1721no—
423C4×C8—1721no—
424#95—21no—
425#95—431no—
426#95—431no—
427#95—861no—
428#95—861no—
429#95—861no—
430#95—861no—
431#95—861no—
432#95—861no—
433C24—21no—
434C2×Q8—864no—
435C2×Q8—3441no—
436C2×Q8—3441no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4C2×C4×D4312yes—
441C2×D4#1062190012yes—
442C2×D4Q8×D4312yes—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—81no—
449C22×C4—431no—
450C22×C4—431no—
451C22×C4—431no—
452C22×C4—431no—
453C22×C4—864no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—3441no—
459C22×C4—1722no—
460C22×C4—1722no—
461C22×C4—1722no—
462C22×C4—1722no—
463C22×C4D4×D4311yescharacteristic
464C22×C4D4×D4311yescharacteristic
465C22×C4C23×D4311yescharacteristic
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—432no—
472C2×C8—432no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—861no—
476C2×C8—861no—
477C2×C8C2×C4×D4312yes—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—81no—
484C4⋊C4—434no—
485C4⋊C4—432no—
486C4⋊C4—432no—
487C4⋊C4—432no—
488C4⋊C4—862no—
489C4⋊C4—864no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—3441no—
496C4⋊C4—3441no—
497C4⋊C4—1722no—
498C4⋊C4—1722no—
499C4⋊C4—1722no—
500C4⋊C4C2×C4×D4312yes—
501C22⋊C4—42no—
502C22⋊C4—864no—
503C22⋊C4—1722no—
504C42—21no—
505C42—21no—
506C42—432no—
507C42—432no—
508C42—861no—
509C42—861no—
510C42—3441no—
511C42—3441no—
512C42—1722no—
513C23—22no—
514C23—22no—
515C23—22no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23C2×D4×D4311yescharacteristic
521Q8—3444no—
522D4—22no—
523D4—22no—
524D4—22no—
525D4#1306329014yes—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
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—84no—
541C2×C4—432no—
542C2×C4—432no—
543C2×C4—432no—
544C2×C4—432no—
545C2×C4—432no—
546C2×C4—861no—
547C2×C4—861no—
548C2×C4—861no—
549C2×C4—861no—
550C2×C4—862no—
551C2×C4—862no—
552C2×C4—862no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—861no—
556C2×C4—3444no—
557C2×C4—1728no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4SD16×D4312yes—
568C2×C4C22×C4×D4311yescharacteristic
569C2×C4C2×Q8×D4311yescharacteristic
570C2×C4#41×D4311yescharacteristic
571C2×C4C2×#1062190011yescharacteristic
572C2×C4#1306337011yescharacteristic
573C2×C4#1306337211yescharacteristic
574C8—22no—
575C8—41no—
576C8—862no—
577C8—862no—
578C22—24no—
579C22—42no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22C4×D4×D4311yescharacteristic
586C22#1458353611yescharacteristic
587C22#1458356211yescharacteristic
588C22C2×SD16×D4311yescharacteristic
589C22#135×D4311yescharacteristic
590C22#1458370311yescharacteristic
591C22#1458370911yescharacteristic
592C4—22no—
593C4—42no—
594C4—41no—
595C4—81no—
596C4—81no—
597C4—434no—
598C4—862no—
599C4—862no—
600C4—3441no—
601C4—1722no—
602C4—1721no—
603C4—1722no—
604C4—1722no—
605C4C2×#1306329011yescharacteristic
606C4#1458337811yescharacteristic
607C4#1458358611yescharacteristic
608C4#1458360311yescharacteristic
609C2—44no—
610C2#1913759511yescharacteristic
611C2C4×SD16×D4311yescharacteristic
612C2#1914342411yescharacteristic
613C2#1914641211yescharacteristic
614C2#1914651611yescharacteristic
615C2#1914745011yescharacteristic
616C2#1914745711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1864C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
cosocleC22×C4×C43C24
hypercenter#1864D43
hypocenterC43#22963
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1864

Complements

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

NH ≅ G/Ntype
2. #19137681C2semidirect
4. #19135554C2semidirect
5. #19135355C2semidirect
6. #19135321C2semidirect
7. #19135320C2semidirect
8. #19135174C2semidirect
9. #19135171C2semidirect
11. #19134456C2semidirect
20. #14583187C4semidirect
66. #13063324C2×C4semidirect
91. #13063257C2×C4semidirect
93. #13063256C2×C4semidirect
94. Dic43⋊C8C2×C4semidirect
96. #13063246Q8semidirect
368. C43#22963semidirect

Maximal subgroups

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

subgroupindex
C2×#145831872
#191376812
D4×Dic43⋊C42
#191355542
#191353552
#191353212
#191353202
#191351742
#191351712
#191348542
#191344562
#102×Dic432
C4×#130632462
C43×#18642
#2296343