Finite Group Databasebeta

← #25106159

Subgroups — #25106159

Order 11008.

1100 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D43C211yesmaximal, characteristic
2#19143226C211yesmaximal, characteristic
3C4×#13063283C211yesmaximal, characteristic
4#19135570C214yesmaximal, complemented
5#19135540C211yesmaximal, characteristic, complemented
6#19135539C211yesmaximal, characteristic, complemented
7#19135538C211yesmaximal, characteristic, complemented
8#19134693C214yesmaximal
9C43×#1986C211yesmaximal, characteristic, complemented
10#14583456C2211yescharacteristic
11#14583455C412yescomplemented
12#14583454C411yescharacteristic, complemented
13#14583454C411yescharacteristic, complemented
14#14583453—21no—
15#14583453—21no—
16#14583452C2212yes—
17#14583451—21no—
18#14583451—21no—
19C4⋊Q8×D43C411yescharacteristic, complemented
20C4⋊Q8×D43C411yescharacteristic, complemented
21#125×D43C412yescomplemented
22C22⋊Q8×D43—21no—
23C22⋊Q8×D43—21no—
24C4×Q8×D43—21no—
25C4×Q8×D43—21no—
26C2×#13063283—21no—
27#117×D43C2212yes—
28C2×C42×D43C2211yescharacteristic
29#14582954—21no—
30#14582954—21no—
31#14582950—21no—
32#14582950—21no—
33#14582922C2212yes—
34#14582862C2212yes—
35C4×#10621877C2211yescharacteristic
36C4⋊C4×Dic43—21no—
37C4×C4⋊Dic43C2211yescharacteristic
38C4×(C2×D43)⋊C4C2212yes—
39#14582746—21no—
40#14582744—21no—
41C42×Dic43C2212yes—
42#14582660C2214yes—
43#14582659C2214yes—
44#14582658C2214yes—
45C43×#533C2211yescharacteristic
46C4×M16×C43C2211yescharacteristic
47C4×C4⋊C4×C43C2211yescharacteristic
48C43×#339C2214yes—
49C2×Q8×D43—21no—
50C2×Q8×D43—21no—
51C22×C4×D43D411yescharacteristic
52C22×C4×D43D411yescharacteristic
53C22×C4×D43C2311yescharacteristic
54C2×#10621877C2312yes—
55#13063325C2×C411yescharacteristic
56#13063325C2×C411yescharacteristic
57#13063324—21no—
58#13063324—21no—
59#13063324C2×C412yes—
60#13063324C2×C412yes—
61#13063323—21no—
62#13063323—21no—
63#13063317C2×C412yes—
64#13063316C2×C412yes—
65#13063316C2×C412yes—
66#13063315—22no—
67#13063315—22no—
68#13063305—21no—
69#13063305—21no—
70#13063304—21no—
71#13063304—21no—
72#13063303—22no—
73#13063303—22no—
74#13063302—22no—
75#13063302—22no—
76#13063301—21no—
77#13063301—21no—
78Q8×Dic43—21no—
79Q8×Dic43—21no—
80C4×Dic86—21no—
81C4×Dic86—21no—
82C4×Dic86—22no—
83C4×Dic86—22no—
84#13063290—21no—
85#13063290—21no—
86#13063290—22no—
87#13063290—22no—
88#13063284C2312yes—
89#13063283—28no—
90#13063283C2×C412yes—
91#13063283C2×C412yes—
92#13063282—22no—
93#13063281—22no—
94C2×C4⋊Dic43—21no—
95C4⋊C4×D43—22no—
96C4⋊C4×D43—22no—
97C4⋊C4×D43—21no—
98C4⋊C4×D43—21no—
99C4⋊C4×D43C2×C412yes—
100C4⋊C4×D43C2×C412yes—
101C2×(C2×D43)⋊C4—22no—
102C22⋊C4×D43—22no—
103C2×C4×Dic43—22no—
104C2×C4×Dic43—22no—
105C2×C4×Dic43D411yescharacteristic
106C2×C4×Dic43D411yescharacteristic
107C2×C4×Dic43C2312yes—
108C2×C4×Dic43C2311yescharacteristic
109C42×D43—22no—
110C42×D43C2×C411yescharacteristic
111C42×D43C2×C411yescharacteristic
112C42×D43C2×C411yescharacteristic
113C42×D43C2×C411yescharacteristic
114C42×D43D411yescharacteristic
115C42×D43D411yescharacteristic
116C42×D43D411yescharacteristic
117C42×D43D411yescharacteristic
118Dic43⋊C8—22no—
119Dic43⋊C8—22no—
120(C2×D43)⋊C8—22no—
121(C2×D43)⋊C8—22no—
122#13063236—21no—
123C4×C43⋊C8—21no—
124C43⋊#95—21no—
125C43⋊#95—22no—
126C2×M16×C43C2312yes—
127C4⋊Q8×C43C2×C411yescharacteristic
128C4⋊Q8×C43C2×C411yescharacteristic
129#125×C43C2×C412yes—
130C22⋊Q8×C43—21no—
131C22⋊Q8×C43—21no—
132C4×Q8×C43—21no—
133C4×Q8×C43—21no—
134#117×C43C2312yes—
135C2×C4⋊C4×C43—21no—
136C2×C42×C43C2312yes—
137C2×C42×C43C2311yescharacteristic
138#97×C43—21no—
139C4×C8×C43—21no—
140#95×C43—21no—
141C23×D43C2×D411yescharacteristic
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C22×C4×C43—22no—
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2411yescharacteristic
148C22×Dic43—22no—
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152Q8×D43—44no—
153Q8×D43—44no—
154C2×C4×D43—22no—
155C2×C4×D43—22no—
156C2×C4×D43—24no—
157C2×C4×D43—22no—
158C2×C4×D43—22no—
159C2×C4×D43—42no—
160C2×C4×D43C22⋊C411yescharacteristic
161C2×C4×D43C22⋊C411yescharacteristic
162C2×C4×D43C22⋊C411yescharacteristic
163C2×C4×D43C22⋊C411yescharacteristic
164C2×C4×D43C22⋊C411yescharacteristic
165C2×C4×D43C22⋊C411yescharacteristic
166C2×C4×D43C22⋊C411yescharacteristic
167C2×C4×D43C22⋊C411yescharacteristic
168C2×C4×D43C22×C411yescharacteristic
169C2×C4×D43C22×C411yescharacteristic
170C2×C4×D43C2×D411yescharacteristic
171C2×C4×D43C2×D411yescharacteristic
172C2×Dic86—21no—
173C2×Dic86—21no—
174C2×Dic86—22no—
175C2×Dic86—22no—
176M16×C43—22no—
177M16×C43—22no—
178C2×C8×C43—22no—
179C4⋊C4×C43—24no—
180C4⋊C4×C43—22no—
181C4⋊C4×C43—22no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43C22×C412yes—
185C4⋊C4×C43C22×C412yes—
186C22⋊C4×C43—22no—
187C42×C43—22no—
188C42×C43—24no—
189C42×C43C22×C411yescharacteristic
190C42×C43C22×C411yescharacteristic
191C42×C43C2×D411yescharacteristic
192C42×C43C2×D411yescharacteristic
193C22⋊Dic43—22no—
194(C2×D43)⋊C4—28no—
195(C2×D43)⋊C4—22no—
196(C2×D43)⋊C4—22no—
197C4⋊Dic43—24no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—22no—
201C4⋊Dic43—22no—
202C4⋊Dic43C22×C412yes—
203C4⋊Dic43C22×C412yes—
204Dic43⋊C4—22no—
205Dic43⋊C4—22no—
206Dic43⋊C4—22no—
207Dic43⋊C4—22no—
208Dic43⋊C4—22no—
209Dic43⋊C4—22no—
210Dic43⋊C4—22no—
211Dic43⋊C4—22no—
212C4×Dic43—28no—
213C4×Dic43—22no—
214C4×Dic43—22no—
215C4×Dic43—22no—
216C4×Dic43—24no—
217C4×Dic43—44no—
218C4×Dic43C22⋊C411yescharacteristic
219C4×Dic43C22⋊C411yescharacteristic
220C4×Dic43C22⋊C411yescharacteristic
221C4×Dic43C22⋊C411yescharacteristic
222C4×Dic43C22⋊C411yescharacteristic
223C4×Dic43C22⋊C411yescharacteristic
224C4×Dic43C22⋊C411yescharacteristic
225C4×Dic43C22⋊C411yescharacteristic
226C4×Dic43C22×C411yescharacteristic
227C4×Dic43C22×C411yescharacteristic
228C4×Dic43C2×D411yescharacteristic
229C4×Dic43C2×D411yescharacteristic
230#10621877—22no—
231#10621877—22no—
232C2×C43⋊C8—22no—
233C23×C43C22×D411yescharacteristic
234C22×D43—21no—
235C22×D43—21no—
236C22×D43—22no—
237C22×D43—41no—
238C22×D43C2×C22⋊C411yescharacteristic
239C22×D43C2×C22⋊C411yescharacteristic
240Q8×C43—42no—
241Q8×C43—42no—
242C2×C4×C43—22no—
243C2×C4×C43—24no—
244C2×C4×C43—22no—
245C2×C4×C43—22no—
246C2×C4×C43—41no—
247C2×C4×C43—42no—
248C2×C4×C43—42no—
249C2×C4×C43C2×C22⋊C411yescharacteristic
250C2×C4×C43C2×C22⋊C411yescharacteristic
251C2×C4×C43C2×C22⋊C411yescharacteristic
252C2×C4×C43C2×C22⋊C411yescharacteristic
253C2×C4×C43C23×C411yescharacteristic
254C2×C4×C43C22×D411yescharacteristic
255C2×C4×C432−1+412yes—
256C2×C4×C432−1+412yes—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—22no—
260C2×Dic43—22no—
261C2×Dic43—24no—
262C2×Dic43—22no—
263C2×Dic43—22no—
264C2×Dic43—42no—
265C2×Dic43—42no—
266C2×Dic43C2×C22⋊C411yescharacteristic
267C2×Dic43C2×C22⋊C411yescharacteristic
268C2×Dic43C2×C22⋊C411yescharacteristic
269C2×Dic43C2×C22⋊C411yescharacteristic
270C2×Dic43C2×C22⋊C411yescharacteristic
271C2×Dic43C2×C22⋊C411yescharacteristic
272C4×D43—22no—
273C4×D43—22no—
274C4×D43—22no—
275C4×D43—22no—
276C4×D43—22no—
277C4×D43—22no—
278C4×D43—22no—
279C4×D43—22no—
280C4×D43—22no—
281C4×D43—41no—
282C4×D43—41no—
283C4×D43—44no—
284C4×D43—44no—
285C4×D43#10414yes—
286Dic86—42no—
287Dic86—42no—
288Dic86—44no—
289Dic86—44no—
290C8×C43—42no—
291C43⋊C8—42no—
292#21844—431nomaximal, Sylow
293C22×C43—21no—
294C22×C43—21no—
295C22×C43C22×C22⋊C411yescharacteristic
296C22×C43#53611yescharacteristic
297C22×C43#53611yescharacteristic
298C2×D43—21no—
299C2×D43—21no—
300C2×D43—21no—
301C2×D43—21no—
302C2×D43—21no—
303C2×D43—42no—
304C2×D43—42no—
305C2×D43C2×#10412yes—
306C4×C43—21no—
307C4×C43—21no—
308C4×C43—21no—
309C4×C43—44no—
310C4×C43—42no—
311C4×C43—42no—
312C4×C43C2×#10412yes—
313C4×C43#51912yes—
314C4×C43#53612yes—
315Dic43—21no—
316Dic43—21no—
317Dic43—21no—
318Dic43—21no—
319Dic43—44no—
320Dic43—42no—
321Dic43—42no—
322Dic43C2×#10412yes—
323Dic43#42112yes—
324C2×#533—431no—
325#2920—431no—
326C4×#117—431no—
327#1994—434no—
328#1986—431no—
329#1986—431no—
330#1986—431no—
331#1986D4311yescharacteristic, complemented
332#1826—434no—
333C2×C43—21no—
334C2×C43—21no—
335C2×C43#231011yescharacteristic
336C2×C43C22×#10411yescharacteristic
337C2×C43C2×#42111yescharacteristic
338D43—22no—
339D43—41no—
340#533—431no—
341#533—431no—
342#533—432no—
343#533—432no—
344#533—431no—
345#533—861no—
346#533—861no—
347#533—861no—
348#533—861no—
349#533C2×D4311yescharacteristic
350C2×C4⋊Q8—431no—
351C2×C4⋊Q8—431no—
352C2×#125—432no—
353C2×C22⋊Q8—861no—
354C2×C22⋊Q8—861no—
355C2×C4×Q8—861no—
356C2×C4×Q8—861no—
357C2×#117—432no—
358C2×#117—861no—
359C22×C42—431no—
360#432—861no—
361#432—861no—
362#431—861no—
363#431—861no—
364#423—432no—
365#407—432no—
366C4×M16—431no—
367C4×M16C2×D4311yescharacteristic
368C4×C4⋊C4—431no—
369C4×C4⋊C4—861no—
370C4×C4⋊C4C2×D4311yescharacteristic
371C4×C22⋊C4—432no—
372C4×C22⋊C4—861no—
373#376—861no—
374C43—432no—
375#339—434no—
376#339—434no—
377#339—434no—
378#339C2×D4314yes—
379C43#2184411yescharacteristic, complemented, Sylow
380C22×Q8—861no—
381C22×Q8—861no—
382C23×C4—431no—
383C23×C4—431no—
384C23×C4—431no—
385C2×M16—432no—
386C2×M16C22×D4312yes—
387C4⋊Q8—432no—
388C4⋊Q8—432no—
389C4⋊Q8—431no—
390C4⋊Q8—431no—
391C4⋊Q8—861no—
392C4⋊Q8—861no—
393C4⋊Q8—861no—
394C4⋊Q8—861no—
395C4⋊Q8C4×D4311yescharacteristic
396C4⋊Q8C4×D4311yescharacteristic
397#125—432no—
398#125—432no—
399#125—432no—
400#125—862no—
401#125—862no—
402#125C4×D4312yes—
403C22⋊Q8—21no—
404C22⋊Q8—21no—
405C22⋊Q8—862no—
406C22⋊Q8—862no—
407C22⋊Q8—862no—
408C22⋊Q8—862no—
409C22⋊Q8—861no—
410C22⋊Q8—861no—
411C22⋊Q8—861no—
412C22⋊Q8—861no—
413C22⋊Q8—861no—
414C22⋊Q8—861no—
415C4×Q8—21no—
416C4×Q8—21no—
417C4×Q8—862no—
418C4×Q8—862no—
419C4×Q8—862no—
420C4×Q8—862no—
421C4×Q8—861no—
422C4×Q8—861no—
423C4×Q8—861no—
424C4×Q8—861no—
425C4×Q8—861no—
426C4×Q8—861no—
427#117—432no—
428#117—432no—
429#117—432no—
430#117—862no—
431#117—862no—
432#117—868no—
433#117C22×D4312yes—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—432no—
436C2×C4⋊C4—432no—
437C2×C4⋊C4—862no—
438C2×C4⋊C4—862no—
439C2×C4⋊C4—861no—
440C2×C4⋊C4—861no—
441C2×C4⋊C4—861no—
442C2×C22⋊C4—862no—
443C2×C22⋊C4—862no—
444C2×C42—431no—
445C2×C42—431no—
446C2×C42—431no—
447C2×C42—431no—
448C2×C42—431no—
449C2×C42—431no—
450C2×C42—431no—
451C2×C42—431no—
452C2×C42—431no—
453C2×C42—431no—
454C2×C42—431no—
455C2×C42—432no—
456C2×C42—862no—
457C2×C42—862no—
458C2×C42—862no—
459C2×C42C22×D4312yes—
460C2×C42C22×D4311yescharacteristic
461C4⋊C8—862no—
462C4⋊C8—862no—
463C22⋊C8—862no—
464C22⋊C8—862no—
465#97—21no—
466#97—861no—
467C4×C8—21no—
468C4×C8—861no—
469#95—21no—
470#95—862no—
471#95—861no—
472C24—431no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—862no—
476C2×Q8—862no—
477C2×Q8—861no—
478C2×Q8—861no—
479C2×Q8—1724no—
480C2×Q8—1724no—
481C22×C4—22no—
482C22×C4—431no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—431no—
487C22×C4—431no—
488C22×C4—431no—
489C22×C4—431no—
490C22×C4—431no—
491C22×C4—431no—
492C22×C4—431no—
493C22×C4—431no—
494C22×C4—431no—
495C22×C4—431no—
496C22×C4—431no—
497C22×C4—864no—
498C22×C4—862no—
499C22×C4—862no—
500C22×C4—862no—
501C22×C4—862no—
502C22×C4—862no—
503C22×C4—1722no—
504C22×C4D4×D4311yescharacteristic
505C22×C4D4×D4311yescharacteristic
506C22×C4C23×D4311yescharacteristic
507M16—22no—
508M16—22no—
509M16—862no—
510M16—862no—
511C2×C8—22no—
512C2×C8—862no—
513C4⋊C4—24no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—432no—
519C4⋊C4—432no—
520C4⋊C4—862no—
521C4⋊C4—862no—
522C4⋊C4—862no—
523C4⋊C4—862no—
524C4⋊C4—862no—
525C4⋊C4—862no—
526C4⋊C4—862no—
527C4⋊C4—862no—
528C4⋊C4—864no—
529C4⋊C4—862no—
530C4⋊C4—862no—
531C4⋊C4—861no—
532C4⋊C4—861no—
533C4⋊C4C2×C4×D4312yes—
534C4⋊C4C2×C4×D4312yes—
535C22⋊C4—22no—
536C22⋊C4—862no—
537C22⋊C4—862no—
538C22⋊C4—868no—
539C22⋊C4—862no—
540C42—22no—
541C42—24no—
542C42—431no—
543C42—431no—
544C42—431no—
545C42—431no—
546C42—431no—
547C42—431no—
548C42—431no—
549C42—431no—
550C42—431no—
551C42—431no—
552C42—431no—
553C42—431no—
554C42—862no—
555C42—862no—
556C42—868no—
557C42—862no—
558C42—864no—
559C42—1724no—
560C42C2×C4×D4311yescharacteristic
561C42C2×C4×D4311yescharacteristic
562C42D4×D4311yescharacteristic
563C42D4×D4311yescharacteristic
564C23—431no—
565C23—431no—
566C23—862no—
567C23—861no—
568C23—861no—
569C23—1721no—
570C23C2×D4×D4311yescharacteristic
571Q8—42no—
572Q8—42no—
573Q8—1722no—
574Q8—1724no—
575Q8—1724no—
576Q8—1722no—
577C2×C4—22no—
578C2×C4—24no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—41no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—431no—
585C2×C4—431no—
586C2×C4—434no—
587C2×C4—431no—
588C2×C4—431no—
589C2×C4—431no—
590C2×C4—431no—
591C2×C4—862no—
592C2×C4—862no—
593C2×C4—862no—
594C2×C4—862no—
595C2×C4—862no—
596C2×C4—862no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—862no—
600C2×C4—862no—
601C2×C4—862no—
602C2×C4—862no—
603C2×C4—862no—
604C2×C4—864no—
605C2×C4—862no—
606C2×C4—862no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1724no—
610C2×C4—1724no—
611C2×C4—1722no—
612C2×C4—1722no—
613C2×C4C22⋊C4×D4311yescharacteristic
614C2×C4C22⋊C4×D4311yescharacteristic
615C2×C4C22⋊C4×D4311yescharacteristic
616C2×C4C22⋊C4×D4311yescharacteristic
617C2×C4C22×C4×D4311yescharacteristic
618C2×C4C2×D4×D4311yescharacteristic
619C2×C4#1306337212yes—
620C2×C4#1306337312yes—
621C8—42no—
622C8—1722no—
623C22—21no—
624C22—21no—
625C22—432no—
626C22—861no—
627C22—861no—
628C22—861no—
629C22—861no—
630C22—861no—
631C22—1722no—
632C22—1722no—
633C22C2×C22⋊C4×D4311yescharacteristic
634C22#1458346911yescharacteristic
635C22#1458347411yescharacteristic
636C4—21no—
637C4—21no—
638C4—21no—
639C4—44no—
640C4—42no—
641C4—42no—
642C4—432no—
643C4—432no—
644C4—861no—
645C4—861no—
646C4—861no—
647C4—861no—
648C4—1724no—
649C4—1722no—
650C4—1722no—
651C4#104×D4312yes—
652C4#1458337512yes—
653C4#1458347212yes—
654C2—21no—
655C2—21no—
656C2—862no—
657C2—1721no—
658C2#1913717811yescharacteristic
659C2C2×#104×D4311yescharacteristic
660C2#421×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1986C2
socleC22×C43C22×C22⋊C4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenter#1986D43
hypocenterC43#21844
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1986

Complements

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

NH ≅ G/Ntype
4. #19135570C2semidirect
5. #19135540C2semidirect
6. #19135539C2semidirect
7. #19135538C2semidirect
9. C43×#1986C2semidirect
11. #14583455C4semidirect
12. #14583454C4semidirect
13. #14583454C4semidirect
19. C4⋊Q8×D43C4semidirect
20. C4⋊Q8×D43C4semidirect
21. #125×D43C4semidirect
331. #1986D43semidirect
379. C43#21844semidirect

Maximal subgroups

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

subgroupindex
#533×D432
#191432262
C4×#130632832
#191355702
#191355402
#191355392
#191355382
#191346932
C43×#19862
#2184443