Finite Group Databasebeta

← #25106164

Subgroups — #25106164

Order 11008.

1008 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
1C2×#14583452C211yesmaximal, characteristic
2#19143224C211yesmaximal, characteristic
3#19136989C211yesmaximal, characteristic
4#19135574C214yesmaximal, complemented
5#19135537C214yesmaximal, complemented
6#19134695C211yesmaximal, characteristic
7#19134694C211yesmaximal, characteristic
8#19134692C211yesmaximal, characteristic
9C43×#1826C211yesmaximal, characteristic
10#14583452—21no—
11#14583452—21no—
12#14583452—21no—
13#14583452—21no—
14#14583452C412yescomplemented
15#14583452C412yescomplemented
16#14583452C2212yes—
17#14583452C2212yes—
18C2×#13063324C411yescharacteristic, complemented
19C2×#13063324C411yescharacteristic, complemented
20C2×#13063316C411yescharacteristic, complemented
21C2×#13063316C411yescharacteristic, complemented
22C2×#13063302—21no—
23C2×#13063302—21no—
24C2×C4×Dic86—21no—
25C2×C4×Dic86—21no—
26C2×#13063284C2211yescharacteristic
27C22×C4×Dic43C2211yescharacteristic
28#14582953—21no—
29#14582953—21no—
30#14582949—21no—
31#14582949—21no—
32#14582922C2212yes—
33#14582863C2211yescharacteristic
34M16×Dic43C2212yes—
35#14582766—21no—
36#14582763—21no—
37#14582760—21no—
38#14582757—21no—
39C4×Dic43⋊C4C2212yes—
40C4×C22⋊Dic43C2211yescharacteristic
41#14582745C2212yes—
42#14582660C2214yes—
43#14582659C2214yes—
44#14582658C2214yes—
45C2×#117×C43C2211yescharacteristic
46C43×#407C2211yescharacteristic
47C4×C22⋊C4×C43C2211yescharacteristic
48C43×#339C2214yes—
49C22×Dic86—21no—
50C22×Dic86—21no—
51C23×Dic43D411yescharacteristic
52C23×Dic43D411yescharacteristic
53C2×#10621877C2312yes—
54#13063324—21no—
55#13063324—21no—
56#13063324—21no—
57#13063324—21no—
58#13063324C2×C412yes—
59#13063324C2×C412yes—
60#13063324C2×C412yes—
61#13063324C2×C412yes—
62#13063316—21no—
63#13063316—21no—
64#13063316—21no—
65#13063316—21no—
66#13063316C2×C412yes—
67#13063316C2×C412yes—
68#13063316C2×C412yes—
69#13063316C2×C412yes—
70#13063302—22no—
71#13063302—22no—
72#13063302—22no—
73#13063302—22no—
74#13063302—22no—
75#13063302—22no—
76#13063302—22no—
77#13063302—22no—
78C4×Dic86—22no—
79C4×Dic86—22no—
80C4×Dic86—22no—
81C4×Dic86—22no—
82C4×Dic86—22no—
83C4×Dic86—22no—
84C4×Dic86—22no—
85C4×Dic86—22no—
86#13063284—21no—
87#13063284—21no—
88#13063284C2×C412yes—
89#13063284C2312yes—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43C2×C411yescharacteristic
93C2×C4⋊Dic43C2×C411yescharacteristic
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—22no—
99C2×C22⋊Dic43—21no—
100C2×C22⋊Dic43—21no—
101C2×C4×Dic43—21no—
102C2×C4×Dic43C2×C411yescharacteristic
103C2×C4×Dic43C2×C411yescharacteristic
104C2×C4×Dic43C2×C411yescharacteristic
105C2×C4×Dic43C2×C411yescharacteristic
106C2×C4×Dic43D411yescharacteristic
107C2×C4×Dic43D411yescharacteristic
108C2×C4×Dic43D411yescharacteristic
109C2×C4×Dic43D411yescharacteristic
110C2×C4×Dic43D411yescharacteristic
111C2×C4×Dic43D411yescharacteristic
112C2×C4×Dic43C2312yes—
113C2×C4×Dic43C2311yescharacteristic
114C2×C4×Dic43C2311yescharacteristic
115Dic43⋊C8—22no—
116Dic43⋊C8—22no—
117C22⋊(C43⋊C8)—21no—
118C22⋊(C43⋊C8)—21no—
119#13063235—22no—
120C8×Dic43—22no—
121C43⋊#95—21no—
122C43⋊#95—22no—
123C43⋊#95—22no—
124C43⋊#95—22no—
125C23×C4×C43C2311yescharacteristic
126C2×M16×C43C2312yes—
127#117×C43—21no—
128#117×C43—21no—
129#117×C43C2×C412yes—
130#117×C43C2312yes—
131C2×C4⋊C4×C43C2×C411yescharacteristic
132C2×C4⋊C4×C43C2×C411yescharacteristic
133C2×C22⋊C4×C43—21no—
134C2×C22⋊C4×C43—21no—
135C2×C42×C43—21no—
136C2×C42×C43C2312yes—
137C22⋊C8×C43—21no—
138C22⋊C8×C43—21no—
139#95×C43—21no—
140C24×C43C2×D411yescharacteristic
141C22×C4×C43—24no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—22no—
145C22×C4×C43C22×C411yescharacteristic
146C22×C4×C43C22×C411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2411yescharacteristic
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—22no—
154C22×Dic43—42no—
155C22×Dic43—42no—
156C22×Dic43C22⋊C411yescharacteristic
157C22×Dic43C22⋊C411yescharacteristic
158C22×Dic43C22⋊C411yescharacteristic
159C22×Dic43C22⋊C411yescharacteristic
160C22×Dic43C22⋊C411yescharacteristic
161C22×Dic43C22⋊C411yescharacteristic
162C22×Dic43C22⋊C411yescharacteristic
163C22×Dic43C22⋊C411yescharacteristic
164C22×Dic43C2×D411yescharacteristic
165C22×Dic43C2×D411yescharacteristic
166C22×Dic43C2×D411yescharacteristic
167C22×Dic43C2×D411yescharacteristic
168C2×Dic86—22no—
169C2×Dic86—22no—
170C2×Dic86—22no—
171C2×Dic86—22no—
172C2×Dic86—44no—
173C2×Dic86—44no—
174M16×C43—24no—
175C2×C8×C43—22no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43C22×C412yes—
179C4⋊C4×C43C22×C412yes—
180C22⋊C4×C43—22no—
181C22⋊C4×C43—22no—
182C22⋊C4×C43—42no—
183C42×C43—22no—
184C42×C43—22no—
185C42×C43—24no—
186C22⋊Dic43—22no—
187C22⋊Dic43—22no—
188C22⋊Dic43—42no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—22no—
192C4⋊Dic43—22no—
193C4⋊Dic43—22no—
194C4⋊Dic43—22no—
195C4⋊Dic43C22×C412yes—
196C4⋊Dic43C22×C412yes—
197Dic43⋊C4—22no—
198Dic43⋊C4—22no—
199Dic43⋊C4—22no—
200Dic43⋊C4—22no—
201Dic43⋊C4—22no—
202Dic43⋊C4—22no—
203Dic43⋊C4—22no—
204Dic43⋊C4—22no—
205Dic43⋊C4—44no—
206C4×Dic43—22no—
207C4×Dic43—22no—
208C4×Dic43—24no—
209C4×Dic43C22⋊C411yescharacteristic
210C4×Dic43C22⋊C411yescharacteristic
211C4×Dic43C22⋊C411yescharacteristic
212C4×Dic43C22⋊C411yescharacteristic
213C4×Dic43C22⋊C411yescharacteristic
214C4×Dic43C22⋊C411yescharacteristic
215C4×Dic43C22⋊C411yescharacteristic
216C4×Dic43C22⋊C411yescharacteristic
217C4×Dic43C22×C411yescharacteristic
218C4×Dic43C22×C411yescharacteristic
219C4×Dic43C22×C411yescharacteristic
220C4×Dic43C22×C411yescharacteristic
221C4×Dic43C2×D411yescharacteristic
222C4×Dic43C2×D411yescharacteristic
223C4×Dic43C2×D411yescharacteristic
224C4×Dic43C2×D411yescharacteristic
225#10621877—24no—
226C2×C43⋊C8—22no—
227C23×C43—22no—
228C23×C43—22no—
229C23×C43—41no—
230C23×C43C2×C22⋊C411yescharacteristic
231C23×C43C2×C22⋊C411yescharacteristic
232C23×C43C22×D411yescharacteristic
233C2×C4×C43—22no—
234C2×C4×C43—22no—
235C2×C4×C43—22no—
236C2×C4×C43—22no—
237C2×C4×C43—22no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—42no—
241C2×C4×C43—42no—
242C2×C4×C43—42no—
243C2×C4×C43—42no—
244C2×C4×C43—42no—
245C2×C4×C43C2×C22⋊C411yescharacteristic
246C2×C4×C43C2×C22⋊C411yescharacteristic
247C2×C4×C43C23×C411yescharacteristic
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C432−1+414yes—
250C2×Dic43—22no—
251C2×Dic43—22no—
252C2×Dic43—22no—
253C2×Dic43—22no—
254C2×Dic43—22no—
255C2×Dic43—22no—
256C2×Dic43—22no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—42no—
265C2×Dic43—42no—
266C2×Dic43—42no—
267C2×Dic43—42no—
268C2×Dic43—42no—
269C2×Dic43C2×C22⋊C411yescharacteristic
270C2×Dic43C2×C22⋊C411yescharacteristic
271C2×Dic43C2×C22⋊C411yescharacteristic
272C2×Dic43C2×C22⋊C411yescharacteristic
273C2×Dic43C2×C22⋊C411yescharacteristic
274C2×Dic43C2×C22⋊C411yescharacteristic
275C2×Dic43C2×C22⋊C411yescharacteristic
276C2×Dic43C2×C22⋊C411yescharacteristic
277Dic86—44no—
278Dic86—44no—
279Dic86—44no—
280Dic86—44no—
281C8×C43—42no—
282C43⋊C8—42no—
283#21845—431nomaximal, Sylow
284C22×C43—21no—
285C22×C43—21no—
286C22×C43—21no—
287C22×C43—21no—
288C22×C43—21no—
289C22×C43—21no—
290C22×C43—21no—
291C22×C43—44no—
292C22×C43#42112yes—
293C22×C43C22×C22⋊C411yescharacteristic
294C22×C43#53612yes—
295C4×C43—21no—
296C4×C43—21no—
297C4×C43—42no—
298C4×C43—42no—
299C4×C43—82no—
300C4×C43#51912yes—
301C4×C43#53612yes—
302Dic43—21no—
303Dic43—21no—
304Dic43—21no—
305Dic43—21no—
306Dic43—21no—
307Dic43—21no—
308Dic43—21no—
309Dic43—42no—
310Dic43—42no—
311Dic43—82no—
312Dic43#42112yes—
313C2×#533—431no—
314#2920—431no—
315#2283—431no—
316#1995—434no—
317#1986—434no—
318#1826—431no—
319#1826—431no—
320#1826—431no—
321#1826D4311yescharacteristic
322C2×C43—22no—
323C2×C43—22no—
324C2×C43—41no—
325C2×C43#231011yescharacteristic
326C2×C43C2×#42111yescharacteristic
327C2×C43C2×#42111yescharacteristic
328#533—432no—
329#533—432no—
330#533—432no—
331#533—432no—
332#533—861no—
333#533—861no—
334#533—861no—
335#533—861no—
336C2×C4⋊Q8—431no—
337C2×C4⋊Q8—431no—
338C2×#125—431no—
339C2×#125—431no—
340C2×C22⋊Q8—861no—
341C2×C22⋊Q8—861no—
342C2×C4×Q8—861no—
343C2×C4×Q8—861no—
344C2×#117—431no—
345C2×#117C2×D4311yescharacteristic
346C22×C42—431no—
347#432—861no—
348#432—861no—
349#431—861no—
350#431—861no—
351#423—432no—
352#407—431no—
353#407C2×D4311yescharacteristic
354C4×M16—432no—
355#383—861no—
356#382—861no—
357#381—861no—
358#380—861no—
359C4×C4⋊C4—432no—
360C4×C22⋊C4—431no—
361C4×C22⋊C4C2×D4311yescharacteristic
362#376—432no—
363#339—434no—
364#339—434no—
365#339—434no—
366#339C2×D4314yes—
367C43#2184511yescharacteristic, complemented, Sylow
368C22×Q8—861no—
369C22×Q8—861no—
370C23×C4—431no—
371C23×C4—431no—
372C23×C4C22×D4311yescharacteristic
373C2×M16—432no—
374C2×M16C22×D4312yes—
375C4⋊Q8—432no—
376C4⋊Q8—432no—
377C4⋊Q8—432no—
378C4⋊Q8—432no—
379C4⋊Q8—861no—
380C4⋊Q8—861no—
381C4⋊Q8—861no—
382C4⋊Q8—861no—
383#125—432no—
384#125—432no—
385#125—432no—
386#125—432no—
387#125—861no—
388#125—861no—
389#125—861no—
390#125—861no—
391C22⋊Q8—862no—
392C22⋊Q8—862no—
393C22⋊Q8—862no—
394C22⋊Q8—862no—
395C22⋊Q8—862no—
396C22⋊Q8—862no—
397C22⋊Q8—862no—
398C22⋊Q8—862no—
399C4×Q8—862no—
400C4×Q8—862no—
401C4×Q8—862no—
402C4×Q8—862no—
403C4×Q8—862no—
404C4×Q8—862no—
405C4×Q8—862no—
406C4×Q8—862no—
407#117—21no—
408#117—21no—
409#117—432no—
410#117—432no—
411#117—861no—
412#117—861no—
413#117C4×D4312yes—
414#117C22×D4312yes—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—431no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—862no—
424C2×C4⋊C4C4×D4311yescharacteristic
425C2×C4⋊C4C4×D4311yescharacteristic
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C42—21no—
431C2×C42—431no—
432C2×C42—431no—
433C2×C42—431no—
434C2×C42—431no—
435C2×C42—431no—
436C2×C42—431no—
437C2×C42—431no—
438C2×C42—431no—
439C2×C42—431no—
440C2×C42—431no—
441C2×C42—431no—
442C2×C42—431no—
443C2×C42—432no—
444C2×C42—861no—
445C2×C42C22×D4312yes—
446C4⋊C8—862no—
447C4⋊C8—862no—
448C22⋊C8—21no—
449C22⋊C8—21no—
450C22⋊C8—861no—
451C22⋊C8—861no—
452#97—862no—
453C4×C8—862no—
454#95—21no—
455#95—862no—
456#95—862no—
457#95—862no—
458#95—861no—
459C24D4×D4311yescharacteristic
460C2×Q8—862no—
461C2×Q8—862no—
462C2×Q8—862no—
463C2×Q8—862no—
464C2×Q8—1724no—
465C2×Q8—1724no—
466C22×C4—24no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—431no—
471C22×C4—431no—
472C22×C4—431no—
473C22×C4—431no—
474C22×C4—431no—
475C22×C4—431no—
476C22×C4—431no—
477C22×C4—431no—
478C22×C4—431no—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—431no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—862no—
485C22×C4—1722no—
486C22×C4—1722no—
487C22×C4C2×C4×D4311yescharacteristic
488C22×C4C2×C4×D4311yescharacteristic
489C22×C4D4×D4311yescharacteristic
490C22×C4D4×D4311yescharacteristic
491C22×C4D4×D4311yescharacteristic
492C22×C4C23×D4311yescharacteristic
493M16—24no—
494M16—864no—
495C2×C8—22no—
496C2×C8—862no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—432no—
500C4⋊C4—432no—
501C4⋊C4—862no—
502C4⋊C4—862no—
503C4⋊C4—862no—
504C4⋊C4—862no—
505C4⋊C4—862no—
506C4⋊C4—862no—
507C4⋊C4—862no—
508C4⋊C4—862no—
509C4⋊C4—862no—
510C4⋊C4—862no—
511C4⋊C4—862no—
512C4⋊C4—862no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—1724no—
516C4⋊C4C2×C4×D4312yes—
517C4⋊C4C2×C4×D4312yes—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—42no—
521C22⋊C4—862no—
522C22⋊C4—862no—
523C22⋊C4—1722no—
524C42—22no—
525C42—22no—
526C42—24no—
527C42—431no—
528C42—431no—
529C42—431no—
530C42—431no—
531C42—431no—
532C42—431no—
533C42—431no—
534C42—431no—
535C42—431no—
536C42—431no—
537C42—431no—
538C42—431no—
539C42—431no—
540C42—431no—
541C42—431no—
542C42—431no—
543C42—862no—
544C42—862no—
545C42—864no—
546C23—22no—
547C23—22no—
548C23—41no—
549C23C22⋊C4×D4311yescharacteristic
550C23C22⋊C4×D4311yescharacteristic
551C23C2×D4×D4311yescharacteristic
552Q8—1724no—
553Q8—1724no—
554Q8—1724no—
555Q8—1724no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—431no—
569C2×C4—431no—
570C2×C4—431no—
571C2×C4—431no—
572C2×C4—431no—
573C2×C4—431no—
574C2×C4—431no—
575C2×C4—431no—
576C2×C4—862no—
577C2×C4—862no—
578C2×C4—862no—
579C2×C4—862no—
580C2×C4—862no—
581C2×C4—862no—
582C2×C4—862no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1722no—
591C2×C4—1722no—
592C2×C4—1722no—
593C2×C4—1722no—
594C2×C4—1722no—
595C2×C4C22⋊C4×D4311yescharacteristic
596C2×C4C22⋊C4×D4311yescharacteristic
597C2×C4C22×C4×D4311yescharacteristic
598C2×C4C2×D4×D4311yescharacteristic
599C2×C4#1306337214yes—
600C8—42no—
601C8—1722no—
602C22—21no—
603C22—21no—
604C22—21no—
605C22—21no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—44no—
610C22#1458291412yes—
611C22C2×C22⋊C4×D4311yescharacteristic
612C22#1458347112yes—
613C4—21no—
614C4—21no—
615C4—42no—
616C4—42no—
617C4—82no—
618C4—432no—
619C4—861no—
620C4—861no—
621C4—861no—
622C4—861no—
623C4—861no—
624C4—861no—
625C4—861no—
626C4—3442no—
627C4—1722no—
628C4—1722no—
629C4#1458337612yes—
630C4#1458347112yes—
631C2—22no—
632C2—22no—
633C2—41no—
634C2#1913718011yescharacteristic
635C2#421×D4311yescharacteristic
636C2C2×#1458291411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1826C2
socleC22×C43C22×C22⋊C4
prime radicalC24×C43C2×D4
cosocleC22×C4×C43C24
hypercenter#1826D43
hypocenterC43#21845
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
4. #19135574C2semidirect
5. #19135537C2semidirect
14. #14583452C4semidirect
15. #14583452C4semidirect
18. C2×#13063324C4semidirect
19. C2×#13063324C4semidirect
20. C2×#13063316C4semidirect
21. C2×#13063316C4semidirect
367. C43#21845semidirect

Maximal subgroups

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

subgroupindex
C2×#145834522
#191432242
#191369892
#191355742
#191355372
#191346952
#191346942
#191346922
C43×#18262
#2184543