Finite Group Databasebeta

← #25106162

Subgroups — #25106162

Order 11008.

1008 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D43C211yesmaximal, characteristic
2#19143227C211yesmaximal, characteristic
3#19136987C211yesmaximal, characteristic
4#19135577C211yesmaximal, characteristic, complemented
5#19135576C211yesmaximal, characteristic, complemented
6#19135575C211yesmaximal, characteristic, complemented
7#19135537C214yesmaximal, complemented
8#19134693C214yesmaximal
9C43×#1995C211yesmaximal, 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—
26#117×D43C2212yes—
27C2×C42×D43C2211yescharacteristic
28#14582955—21no—
29#14582955—21no—
30#14582951—21no—
31#14582951—21no—
32#14582923C2211yescharacteristic
33#14582862C2212yes—
34M16×Dic43C2212yes—
35#14582766—21no—
36#14582763—21no—
37#14582761—21no—
38#14582758—21no—
39C4×Dic43⋊C4C2212yes—
40C4×(C2×D43)⋊C4C2212yes—
41#14582745C2211yescharacteristic
42#14582660C2214yes—
43#14582659C2214yes—
44#14582658C2214yes—
45C43×#533C2211yescharacteristic
46C43×#423C2211yescharacteristic
47C43×#376C2211yescharacteristic
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#13063283C2×C412yes—
90#13063283C2×C412yes—
91#13063282—22no—
92#13063281—22no—
93C2×Dic43⋊C4—22no—
94C4⋊C4×D43—22no—
95C4⋊C4×D43—22no—
96C4⋊C4×D43—21no—
97C4⋊C4×D43—21no—
98C4⋊C4×D43C2×C412yes—
99C4⋊C4×D43C2×C412yes—
100C2×(C2×D43)⋊C4—22no—
101C22⋊C4×D43—22no—
102C2×C4×Dic43D411yescharacteristic
103C2×C4×Dic43D411yescharacteristic
104C2×C4×Dic43C2312yes—
105C2×C4×Dic43C2311yescharacteristic
106C42×D43—22no—
107C42×D43C2×C411yescharacteristic
108C42×D43C2×C411yescharacteristic
109C42×D43C2×C411yescharacteristic
110C42×D43C2×C411yescharacteristic
111C42×D43D411yescharacteristic
112C42×D43D411yescharacteristic
113C42×D43D411yescharacteristic
114C42×D43D411yescharacteristic
115C4⋊(C43⋊C8)—21no—
116C4⋊(C43⋊C8)—21no—
117(C2×D43)⋊C8—22no—
118(C2×D43)⋊C8—22no—
119#13063235—22no—
120C8×Dic43—22no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95—22no—
124C43⋊#95—22no—
125C2×M16×C43C2312yes—
126C4⋊Q8×C43C2×C411yescharacteristic
127C4⋊Q8×C43C2×C411yescharacteristic
128#125×C43C2×C412yes—
129C22⋊Q8×C43—21no—
130C22⋊Q8×C43—21no—
131C4×Q8×C43—21no—
132C4×Q8×C43—21no—
133#117×C43C2312yes—
134C2×C42×C43C2312yes—
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43—21no—
137C4⋊C8×C43—21no—
138#95×C43—21no—
139#95×C43—21no—
140C23×D43C2×D411yescharacteristic
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C22×C4×C43—22no—
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2411yescharacteristic
147C22×Dic43—22no—
148C22×Dic43C2×D411yescharacteristic
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151Q8×D43—44no—
152Q8×D43—44no—
153C2×C4×D43—22no—
154C2×C4×D43—22no—
155C2×C4×D43—22no—
156C2×C4×D43—22no—
157C2×C4×D43—42no—
158C2×C4×D43—42no—
159C2×C4×D43C22⋊C411yescharacteristic
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×D43C2×D411yescharacteristic
170C2×C4×D43C2×D411yescharacteristic
171C2×Dic86—21no—
172C2×Dic86—21no—
173C2×Dic86—22no—
174C2×Dic86—22no—
175M16×C43—24no—
176C2×C8×C43—22no—
177C4⋊C4×C43—22no—
178C4⋊C4×C43—22no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43C22×C412yes—
182C4⋊C4×C43C22×C412yes—
183C22⋊C4×C43—22no—
184C42×C43—22no—
185C42×C43—22no—
186C42×C43—22no—
187C42×C43C22×C411yescharacteristic
188C42×C43C22×C411yescharacteristic
189C42×C43C2×D411yescharacteristic
190C42×C43C2×D411yescharacteristic
191C22⋊Dic43—22no—
192(C2×D43)⋊C4—22no—
193(C2×D43)⋊C4—22no—
194(C2×D43)⋊C4—44no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—22no—
198C4⋊Dic43—22no—
199C4⋊Dic43C22×C412yes—
200C4⋊Dic43C22×C412yes—
201Dic43⋊C4—22no—
202Dic43⋊C4—22no—
203Dic43⋊C4—22no—
204Dic43⋊C4—22no—
205Dic43⋊C4—22no—
206Dic43⋊C4—22no—
207Dic43⋊C4—22no—
208Dic43⋊C4—22no—
209Dic43⋊C4—44no—
210C4×Dic43—22no—
211C4×Dic43—22no—
212C4×Dic43—22no—
213C4×Dic43—22no—
214C4×Dic43—22no—
215C4×Dic43C22⋊C411yescharacteristic
216C4×Dic43C22⋊C411yescharacteristic
217C4×Dic43C22⋊C411yescharacteristic
218C4×Dic43C22⋊C411yescharacteristic
219C4×Dic43C22⋊C411yescharacteristic
220C4×Dic43C22⋊C411yescharacteristic
221C4×Dic43C22⋊C411yescharacteristic
222C4×Dic43C22⋊C411yescharacteristic
223C4×Dic43C22×C411yescharacteristic
224C4×Dic43C22×C411yescharacteristic
225C4×Dic43C2×D411yescharacteristic
226C4×Dic43C2×D411yescharacteristic
227#10621877—24no—
228C2×C43⋊C8—22no—
229C23×C43C22×D411yescharacteristic
230C22×D43—22no—
231C22×D43—22no—
232C22×D43—41no—
233C22×D43C2×C22⋊C411yescharacteristic
234C22×D43C2×C22⋊C411yescharacteristic
235Q8×C43—42no—
236Q8×C43—42no—
237C2×C4×C43—22no—
238C2×C4×C43—22no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—42no—
242C2×C4×C43—42no—
243C2×C4×C43—42no—
244C2×C4×C43C2×C22⋊C411yescharacteristic
245C2×C4×C43C2×C22⋊C411yescharacteristic
246C2×C4×C43C2×C22⋊C411yescharacteristic
247C2×C4×C43C2×C22⋊C411yescharacteristic
248C2×C4×C43C23×C411yescharacteristic
249C2×C4×C43C22×D411yescharacteristic
250C2×C4×C432−1+412yes—
251C2×C4×C432−1+412yes—
252C2×Dic43—22no—
253C2×Dic43—22no—
254C2×Dic43—22no—
255C2×Dic43—22no—
256C2×Dic43—41no—
257C2×Dic43—42no—
258C2×Dic43—42no—
259C2×Dic43—42no—
260C2×Dic43C2×C22⋊C411yescharacteristic
261C2×Dic43C2×C22⋊C411yescharacteristic
262C2×Dic43C2×C22⋊C411yescharacteristic
263C2×Dic43C2×C22⋊C411yescharacteristic
264C2×Dic43C2×C22⋊C411yescharacteristic
265C2×Dic43C2×C22⋊C411yescharacteristic
266C4×D43—22no—
267C4×D43—22no—
268C4×D43—22no—
269C4×D43—22no—
270C4×D43—21no—
271C4×D43—21no—
272C4×D43—21no—
273C4×D43—21no—
274C4×D43—22no—
275C4×D43—22no—
276C4×D43—41no—
277C4×D43—41no—
278C4×D43—41no—
279C4×D43—41no—
280C4×D43—44no—
281C4×D43—44no—
282Dic86—44no—
283Dic86—42no—
284Dic86—42no—
285Dic86—44no—
286C8×C43—42no—
287C43⋊C8—42no—
288#21845—431nomaximal, Sylow
289C22×C43—21no—
290C22×C43—21no—
291C22×C43C22×C22⋊C411yescharacteristic
292C22×C43#53612yes—
293C2×D43—21no—
294C2×D43—21no—
295C2×D43—21no—
296C2×D43—21no—
297C2×D43—21no—
298C2×D43—44no—
299C2×D43#42112yes—
300C4×C43—21no—
301C4×C43—21no—
302C4×C43—21no—
303C4×C43—21no—
304C4×C43—42no—
305C4×C43—42no—
306C4×C43—82no—
307C4×C43#51912yes—
308C4×C43#53611yescharacteristic
309C4×C43#53611yescharacteristic
310Dic43—21no—
311Dic43—21no—
312Dic43—21no—
313Dic43—21no—
314Dic43—21no—
315Dic43—42no—
316Dic43—42no—
317Dic43—82no—
318Dic43#42112yes—
319C2×#533—431no—
320#2920—431no—
321#2283—431no—
322#1995—431no—
323#1995—431no—
324#1995—431no—
325#1995D4311yescharacteristic, complemented
326#1986—434no—
327#1826—434no—
328C2×C43—22no—
329C2×C43#231011yescharacteristic
330C2×C43C2×#42111yescharacteristic
331C2×C43C2×#42111yescharacteristic
332D43—22no—
333D43—41no—
334#533—431no—
335#533—431no—
336#533—432no—
337#533—432no—
338#533—431no—
339#533—861no—
340#533—861no—
341#533—861no—
342#533—861no—
343#533C2×D4311yescharacteristic
344C2×C4⋊Q8—431no—
345C2×C4⋊Q8—431no—
346C2×#125—432no—
347C2×C22⋊Q8—861no—
348C2×C22⋊Q8—861no—
349C2×C4×Q8—861no—
350C2×C4×Q8—861no—
351C2×#117—432no—
352C22×C42—431no—
353#432—861no—
354#432—861no—
355#431—861no—
356#431—861no—
357#423—431no—
358#423C2×D4311yescharacteristic
359#407—432no—
360C4×M16—432no—
361#383—861no—
362#382—861no—
363#381—861no—
364#380—861no—
365C4×C4⋊C4—432no—
366C4×C22⋊C4—432no—
367#376—431no—
368#376C2×D4311yescharacteristic
369#339—434no—
370#339—434no—
371#339—434no—
372#339C2×D4314yes—
373C43#2184511yescharacteristic, complemented, Sylow
374C22×Q8—861no—
375C22×Q8—861no—
376C23×C4—431no—
377C23×C4—431no—
378C23×C4—431no—
379C2×M16—432no—
380C2×M16C22×D4312yes—
381C4⋊Q8—432no—
382C4⋊Q8—432no—
383C4⋊Q8—431no—
384C4⋊Q8—431no—
385C4⋊Q8—861no—
386C4⋊Q8—861no—
387C4⋊Q8—861no—
388C4⋊Q8—861no—
389C4⋊Q8C4×D4311yescharacteristic
390C4⋊Q8C4×D4311yescharacteristic
391#125—432no—
392#125—432no—
393#125—432no—
394#125—862no—
395#125—862no—
396#125C4×D4312yes—
397C22⋊Q8—21no—
398C22⋊Q8—21no—
399C22⋊Q8—862no—
400C22⋊Q8—862no—
401C22⋊Q8—862no—
402C22⋊Q8—862no—
403C22⋊Q8—861no—
404C22⋊Q8—861no—
405C22⋊Q8—861no—
406C22⋊Q8—861no—
407C22⋊Q8—861no—
408C22⋊Q8—861no—
409C4×Q8—21no—
410C4×Q8—21no—
411C4×Q8—862no—
412C4×Q8—862no—
413C4×Q8—862no—
414C4×Q8—862no—
415C4×Q8—861no—
416C4×Q8—861no—
417C4×Q8—861no—
418C4×Q8—861no—
419C4×Q8—861no—
420C4×Q8—861no—
421#117—432no—
422#117—432no—
423#117—432no—
424#117—862no—
425#117—862no—
426#117C22×D4312yes—
427C2×C4⋊C4—432no—
428C2×C4⋊C4—432no—
429C2×C4⋊C4—862no—
430C2×C4⋊C4—862no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4—861no—
433C2×C4⋊C4—862no—
434C2×C22⋊C4—862no—
435C2×C22⋊C4—862no—
436C2×C42—431no—
437C2×C42—431no—
438C2×C42—431no—
439C2×C42—431no—
440C2×C42—431no—
441C2×C42—431no—
442C2×C42—431no—
443C2×C42—431no—
444C2×C42—431no—
445C2×C42—431no—
446C2×C42—431no—
447C2×C42—432no—
448C2×C42—862no—
449C2×C42C22×D4312yes—
450C2×C42C22×D4311yescharacteristic
451C4⋊C8—21no—
452C4⋊C8—21no—
453C4⋊C8—861no—
454C4⋊C8—861no—
455C22⋊C8—862no—
456C22⋊C8—862no—
457#97—862no—
458C4×C8—862no—
459#95—21no—
460#95—21no—
461#95—862no—
462#95—862no—
463#95—861no—
464#95—861no—
465C24—431no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—862no—
469C2×Q8—862no—
470C2×Q8—861no—
471C2×Q8—861no—
472C2×Q8—1724no—
473C2×Q8—1724no—
474C22×C4—22no—
475C22×C4—431no—
476C22×C4—431no—
477C22×C4—431no—
478C22×C4—431no—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—431no—
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—862no—
491C22×C4—862no—
492C22×C4—862no—
493C22×C4—862no—
494C22×C4—862no—
495C22×C4—1722no—
496C22×C4—1722no—
497C22×C4D4×D4311yescharacteristic
498C22×C4D4×D4311yescharacteristic
499C22×C4C23×D4311yescharacteristic
500M16—24no—
501M16—864no—
502C2×C8—22no—
503C2×C8—862no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—432no—
509C4⋊C4—432no—
510C4⋊C4—862no—
511C4⋊C4—862no—
512C4⋊C4—862no—
513C4⋊C4—862no—
514C4⋊C4—862no—
515C4⋊C4—862no—
516C4⋊C4—862no—
517C4⋊C4—862no—
518C4⋊C4—862no—
519C4⋊C4—862no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—1724no—
523C4⋊C4C2×C4×D4312yes—
524C4⋊C4C2×C4×D4312yes—
525C22⋊C4—22no—
526C22⋊C4—862no—
527C22⋊C4—862no—
528C22⋊C4—862no—
529C22⋊C4—1724no—
530C42—22no—
531C42—22no—
532C42—22no—
533C42—431no—
534C42—431no—
535C42—431no—
536C42—431no—
537C42—431no—
538C42—431no—
539C42—431no—
540C42—431no—
541C42—431no—
542C42—431no—
543C42—431no—
544C42—431no—
545C42—862no—
546C42—862no—
547C42—862no—
548C42—862no—
549C42—862no—
550C42C2×C4×D4311yescharacteristic
551C42C2×C4×D4311yescharacteristic
552C42D4×D4311yescharacteristic
553C42D4×D4311yescharacteristic
554C23—431no—
555C23—431no—
556C23—862no—
557C23—862no—
558C23—1721no—
559C23C2×D4×D4311yescharacteristic
560Q8—42no—
561Q8—42no—
562Q8—1722no—
563Q8—1722no—
564Q8—1724no—
565Q8—1724no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—431no—
574C2×C4—431no—
575C2×C4—431no—
576C2×C4—431no—
577C2×C4—431no—
578C2×C4—431no—
579C2×C4—862no—
580C2×C4—862no—
581C2×C4—862no—
582C2×C4—862no—
583C2×C4—862no—
584C2×C4—862no—
585C2×C4—862no—
586C2×C4—862no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—862no—
592C2×C4—862no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1724no—
598C2×C4—1724no—
599C2×C4—1721no—
600C2×C4—1722no—
601C2×C4—1722no—
602C2×C4—1722no—
603C2×C4C22⋊C4×D4311yescharacteristic
604C2×C4C22⋊C4×D4311yescharacteristic
605C2×C4C22⋊C4×D4311yescharacteristic
606C2×C4C22⋊C4×D4311yescharacteristic
607C2×C4C22×C4×D4311yescharacteristic
608C2×C4C2×D4×D4311yescharacteristic
609C2×C4#1306337212yes—
610C2×C4#1306337312yes—
611C8—42no—
612C8—1722no—
613C22—21no—
614C22—21no—
615C22—432no—
616C22—861no—
617C22—861no—
618C22—861no—
619C22—861no—
620C22—861no—
621C22—1724no—
622C22C2×C22⋊C4×D4311yescharacteristic
623C22#1458347212yes—
624C4—21no—
625C4—21no—
626C4—21no—
627C4—21no—
628C4—42no—
629C4—42no—
630C4—82no—
631C4—432no—
632C4—861no—
633C4—861no—
634C4—861no—
635C4—861no—
636C4—861no—
637C4—3442no—
638C4—1722no—
639C4—1722no—
640C4#1458337512yes—
641C4#1458346911yescharacteristic
642C4#1458347411yescharacteristic
643C2—22no—
644C2—862no—
645C2—1721no—
646C2#1913717811yescharacteristic
647C2#421×D4311yescharacteristic
648C2#421×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1995C2
socleC22×C43C22×C22⋊C4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenter#1995D43
hypocenterC43#21845
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1995

Complements

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

NH ≅ G/Ntype
4. #19135577C2semidirect
5. #19135576C2semidirect
6. #19135575C2semidirect
7. #19135537C2semidirect
9. C43×#1995C2semidirect
11. #14583455C4semidirect
12. #14583454C4semidirect
13. #14583454C4semidirect
19. C4⋊Q8×D43C4semidirect
20. C4⋊Q8×D43C4semidirect
21. #125×D43C4semidirect
325. #1995D43semidirect
373. C43#21845semidirect

Maximal subgroups

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

subgroupindex
#533×D432
#191432272
#191369872
#191355772
#191355762
#191355752
#191355372
#191346932
C43×#19952
#2184543