Finite Group Databasebeta

← #25064109

Subgroups — #25064109

Order 11008.

994 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D43C211yesmaximal, characteristic
2#432×D43C211yesmaximal, characteristic
3#19136992C211yesmaximal, characteristic
4#19133165C214yesmaximal
5#19133147C211yesmaximal, characteristic, complemented
6#19133146C211yesmaximal, characteristic, complemented
7#19133145C211yesmaximal, characteristic, complemented
8#19133105C214yesmaximal, complemented
9C43×#1515C211yesmaximal, characteristic, complemented
10#14583456C2211yescharacteristic
11#14583455—21no—
12#14583454C411yescharacteristic, complemented
13#14583454C411yescharacteristic, complemented
14#14583453—21no—
15#14583453C412yescomplemented
16#14583452—21no—
17#14583451—21no—
18#14583451C2212yes—
19C4⋊Q8×D43C411yescharacteristic, complemented
20C4⋊Q8×D43C411yescharacteristic, complemented
21#125×D43—21no—
22C22⋊Q8×D43—21no—
23C22⋊Q8×D43C2212yes—
24C4×Q8×D43—21no—
25C4×Q8×D43C412yescomplemented
26#117×D43—21no—
27C2×C42×D43C2211yescharacteristic
28#14582956C2211yescharacteristic
29#14582955—21no—
30#14582954—21no—
31#14582953C2212yes—
32C4⋊C8×D43—21no—
33C22⋊C8×D43C2212yes—
34#97×D43—21no—
35#14582767C2211yescharacteristic
36#14582763—21no—
37#14582761—21no—
38#14582758C2212yes—
39#14582750—21no—
40#14582746—21no—
41#14582744C2212yes—
42#14582637C2214yes—
43#14582636C2214yes—
44#14582635C2214yes—
45C43×#533C2211yescharacteristic
46C43×#432C2211yescharacteristic
47C43×#383C2211yescharacteristic
48C43×#328C2214yes—
49C2×Q8×D43—21no—
50C2×Q8×D43C2×C412yes—
51C22×C4×D43D411yescharacteristic
52C22×C4×D43D411yescharacteristic
53C22×C4×D43C2311yescharacteristic
54C2×C8×D43—22no—
55#13063325C2×C411yescharacteristic
56#13063325C2×C411yescharacteristic
57#13063324—21no—
58#13063324—21no—
59#13063324—21no—
60#13063324C2×C412yes—
61#13063323—21no—
62#13063323C2×C412yes—
63#13063317—21no—
64#13063316—21no—
65#13063316—21no—
66#13063315—22no—
67#13063315—22no—
68#13063305—21no—
69#13063305C2×C412yes—
70#13063304—21no—
71#13063304C2312yes—
72#13063303—22no—
73#13063303—22no—
74#13063302—22no—
75#13063302—22no—
76#13063301—21no—
77#13063301C2×C412yes—
78Q8×Dic43—21no—
79Q8×Dic43C2×C412yes—
80C4×Dic86—21no—
81C4×Dic86—22no—
82C4×Dic86—22no—
83C4×Dic86C2×C412yes—
84#13063290—21no—
85#13063290—22no—
86#13063290—22no—
87#13063290C2×C412yes—
88#13063284—21no—
89#13063283—21no—
90#13063283—21no—
91#13063282—22no—
92#13063281—22no—
93C2×Dic43⋊C4—22no—
94C4⋊C4×D43—21no—
95C4⋊C4×D43—21no—
96C4⋊C4×D43—21no—
97C4⋊C4×D43—22no—
98C4⋊C4×D43—22no—
99C4⋊C4×D43C2×C412yes—
100C2×(C2×D43)⋊C4—22no—
101C22⋊C4×D43—22no—
102C2×C4×Dic43—22no—
103C2×C4×Dic43D411yescharacteristic
104C2×C4×Dic43D411yescharacteristic
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—
116Dic43⋊C8—22no—
117C22⋊(C43⋊C8)C2312yes—
118(C2×D43)⋊C8—22no—
119#13063236—21no—
120#13063235—22no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95—22no—
124C43⋊#95C2312yes—
125C4⋊Q8×C43C2×C411yescharacteristic
126C4⋊Q8×C43C2×C411yescharacteristic
127#125×C43—21no—
128C22⋊Q8×C43—21no—
129C22⋊Q8×C43C2312yes—
130C4×Q8×C43—21no—
131C4×Q8×C43C2×C412yes—
132#117×C43—21no—
133C2×C42×C43C2311yescharacteristic
134C4⋊C8×C43—21no—
135C22⋊C8×C43C2312yes—
136#97×C43—21no—
137#95×C43—21no—
138#95×C43—21no—
139#95×C43C2312yes—
140C23×D43C2×D411yescharacteristic
141C2×Q8×C43—21no—
142C2×Q8×C43C22×C412yes—
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—24no—
156C2×C4×D43—42no—
157C2×C4×D43—42no—
158C2×C4×D43C22⋊C411yescharacteristic
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×D43C2×D411yescharacteristic
169C2×C4×D43C2×D411yescharacteristic
170C2×Dic86—21no—
171C2×Dic86—22no—
172C2×Dic86—22no—
173C2×Dic86C22×C412yes—
174C2×C8×C43—22no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—22no—
179C4⋊C4×C43—22no—
180C4⋊C4×C43C22×C412yes—
181C22⋊C4×C43—22no—
182C42×C43—22no—
183C42×C43C22×C411yescharacteristic
184C42×C43C22×C411yescharacteristic
185C42×C43C2×D411yescharacteristic
186C42×C43C2×D411yescharacteristic
187C22⋊Dic43—22no—
188(C2×D43)⋊C4—22no—
189(C2×D43)⋊C4—22no—
190(C2×D43)⋊C4—44no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—22no—
195C4⋊Dic43—22no—
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—22no—
209C4×Dic43—44no—
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×Dic43C2×D411yescharacteristic
221C4×Dic43C2×D411yescharacteristic
222C2×C43⋊C8—22no—
223C8×D43—44no—
224C23×C43C22×D411yescharacteristic
225C22×D43—41no—
226C22×D43—41no—
227C22×D43C2×C22⋊C411yescharacteristic
228C22×D43C2×C22⋊C411yescharacteristic
229C22×D43#13714yes—
230Q8×C43—42no—
231Q8×C43—42no—
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43—22no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—42no—
238C2×C4×C43—42no—
239C2×C4×C43—42no—
240C2×C4×C43C2×C22⋊C411yescharacteristic
241C2×C4×C43C2×C22⋊C411yescharacteristic
242C2×C4×C43C2×C22⋊C411yescharacteristic
243C2×C4×C43C2×C22⋊C411yescharacteristic
244C2×C4×C43C23×C411yescharacteristic
245C2×C4×C43C22×D411yescharacteristic
246C2×Dic43—22no—
247C2×Dic43—22no—
248C2×Dic43—22no—
249C2×Dic43—22no—
250C2×Dic43—22no—
251C2×Dic43—42no—
252C2×Dic43—42no—
253C2×Dic43—42no—
254C2×Dic43C2×C22⋊C411yescharacteristic
255C2×Dic43C2×C22⋊C411yescharacteristic
256C2×Dic43C2×C22⋊C411yescharacteristic
257C2×Dic43C2×C22⋊C411yescharacteristic
258C2×Dic43C2×C22⋊C411yescharacteristic
259C2×Dic43C2×C22⋊C411yescharacteristic
260C4×D43—22no—
261C4×D43—22no—
262C4×D43—22no—
263C4×D43—22no—
264C4×D43—22no—
265C4×D43—22no—
266C4×D43—22no—
267C4×D43—22no—
268C4×D43—41no—
269C4×D43—41no—
270C4×D43—41no—
271C4×D43—41no—
272C4×D43—44no—
273C4×D43—44no—
274Dic86—42no—
275Dic86—44no—
276Dic86—44no—
277Dic86—42no—
278C8×C43—42no—
279C43⋊C8—42no—
280#17596—431nomaximal, Sylow
281C22×C43—21no—
282C22×C43—21no—
283C22×C43C22×C22⋊C411yescharacteristic
284C22×C43C2×#13712yes—
285C2×D43—21no—
286C2×D43—21no—
287C2×D43—21no—
288C2×D43—21no—
289C2×D43—44no—
290C2×D43#41912yes—
291C2×D43#41912yes—
292C4×C43—21no—
293C4×C43—21no—
294C4×C43—21no—
295C4×C43—21no—
296C4×C43—21no—
297C4×C43—21no—
298C4×C43—42no—
299C4×C43—42no—
300C4×C43—82no—
301Dic43—21no—
302Dic43—21no—
303Dic43—21no—
304Dic43—21no—
305Dic43—42no—
306Dic43—42no—
307Dic43—82no—
308Dic43#41012yes—
309Dic43#42112yes—
310C2×#533—431no—
311C2×#432—431no—
312#2283—431no—
313#1520—434no—
314#1515—431no—
315#1515—431no—
316#1515—431no—
317#1515D4311yescharacteristic, complemented
318#1506—434no—
319C2×C43—22no—
320C2×C43C2×#41011yescharacteristic
321C2×C43C2×#41911yescharacteristic
322C2×C43C2×#42111yescharacteristic
323D43—22no—
324D43—22no—
325#533—431no—
326#533—431no—
327#533—432no—
328#533—432no—
329#533—431no—
330#533—861no—
331#533—861no—
332#533—861no—
333#533—861no—
334#533C2×D4311yescharacteristic
335C2×C4⋊Q8—431no—
336C2×C4⋊Q8—431no—
337C2×#125—861no—
338C2×C22⋊Q8—432no—
339C2×C22⋊Q8—861no—
340C2×C4×Q8—432no—
341C2×C4×Q8—861no—
342C2×#117—861no—
343C22×C42—431no—
344#432—431no—
345#432—432no—
346#432—861no—
347#432—861no—
348#432C2×D4311yescharacteristic
349C2×C4⋊C8—861no—
350C2×C22⋊C8—432no—
351C2×#97—861no—
352#383—431no—
353#383C2×D4311yescharacteristic
354#382—861no—
355#381—861no—
356#380—432no—
357C4×C4⋊C4—861no—
358C4×C22⋊C4—861no—
359#376—432no—
360#328—434no—
361#328—434no—
362#328—434no—
363#328C2×D4314yes—
364C43#1759611yescharacteristic, complemented, Sylow
365C22×Q8—432no—
366C22×Q8—861no—
367C23×C4—431no—
368C23×C4—431no—
369C23×C4—431no—
370C22×C8—862no—
371C4⋊Q8—432no—
372C4⋊Q8—432no—
373C4⋊Q8—431no—
374C4⋊Q8—431no—
375C4⋊Q8—861no—
376C4⋊Q8—861no—
377C4⋊Q8—861no—
378C4⋊Q8—861no—
379C4⋊Q8C4×D4311yescharacteristic
380C4⋊Q8C4×D4311yescharacteristic
381#125—21no—
382#125—862no—
383#125—862no—
384#125—861no—
385#125—861no—
386#125—861no—
387C22⋊Q8—21no—
388C22⋊Q8—432no—
389C22⋊Q8—432no—
390C22⋊Q8—432no—
391C22⋊Q8—862no—
392C22⋊Q8—862no—
393C22⋊Q8—862no—
394C22⋊Q8—862no—
395C22⋊Q8—861no—
396C22⋊Q8—861no—
397C22⋊Q8—861no—
398C22⋊Q8C22×D4312yes—
399C4×Q8—21no—
400C4×Q8—432no—
401C4×Q8—432no—
402C4×Q8—432no—
403C4×Q8—862no—
404C4×Q8—862no—
405C4×Q8—862no—
406C4×Q8—861no—
407C4×Q8—862no—
408C4×Q8—861no—
409C4×Q8—861no—
410C4×Q8C4×D4312yes—
411#117—21no—
412#117—862no—
413#117—862no—
414#117—861no—
415#117—861no—
416#117—861no—
417C2×C4⋊C4—432no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4—862no—
421C2×C4⋊C4—862no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—862no—
424C2×C22⋊C4—862no—
425C2×C22⋊C4—862no—
426C2×C42—431no—
427C2×C42—431no—
428C2×C42—431no—
429C2×C42—431no—
430C2×C42—431no—
431C2×C42—431no—
432C2×C42—431no—
433C2×C42—431no—
434C2×C42—431no—
435C2×C42—431no—
436C2×C42—431no—
437C2×C42—862no—
438C2×C42—862no—
439C2×C42C22×D4311yescharacteristic
440C4⋊C8—21no—
441C4⋊C8—862no—
442C4⋊C8—861no—
443C22⋊C8—432no—
444C22⋊C8—862no—
445C22⋊C8C22×D4312yes—
446#97—21no—
447#97—862no—
448#97—861no—
449#95—21no—
450#95—21no—
451#95—432no—
452#95—862no—
453#95—861no—
454#95—861no—
455#95C22×D4312yes—
456C24—431no—
457C2×Q8—21no—
458C2×Q8—432no—
459C2×Q8—862no—
460C2×Q8—862no—
461C2×Q8—861no—
462C2×Q8—1724no—
463C2×Q8—1724no—
464C2×Q8C2×C4×D4312yes—
465C22×C4—22no—
466C22×C4—431no—
467C22×C4—431no—
468C22×C4—431no—
469C22×C4—431no—
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—864no—
482C22×C4—862no—
483C22×C4—862no—
484C22×C4—862no—
485C22×C4—1722no—
486C22×C4—1722no—
487C22×C4D4×D4311yescharacteristic
488C22×C4D4×D4311yescharacteristic
489C22×C4C23×D4311yescharacteristic
490C2×C8—22no—
491C2×C8—862no—
492C2×C8—1724no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—432no—
499C4⋊C4—862no—
500C4⋊C4—862no—
501C4⋊C4—862no—
502C4⋊C4—862no—
503C4⋊C4—862no—
504C4⋊C4—862no—
505C4⋊C4—862no—
506C4⋊C4—862no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—862no—
510C4⋊C4—861no—
511C4⋊C4—862no—
512C4⋊C4—1724no—
513C4⋊C4C2×C4×D4312yes—
514C22⋊C4—22no—
515C22⋊C4—862no—
516C22⋊C4—862no—
517C22⋊C4—862no—
518C22⋊C4—1724no—
519C42—22no—
520C42—431no—
521C42—431no—
522C42—431no—
523C42—431no—
524C42—431no—
525C42—431no—
526C42—431no—
527C42—431no—
528C42—431no—
529C42—431no—
530C42—431no—
531C42—431no—
532C42—862no—
533C42—862no—
534C42—862no—
535C42—1724no—
536C42C2×C4×D4311yescharacteristic
537C42C2×C4×D4311yescharacteristic
538C42D4×D4311yescharacteristic
539C42D4×D4311yescharacteristic
540C23—431no—
541C23—431no—
542C23—434no—
543C23—1721no—
544C23—1721no—
545C23C2×D4×D4311yescharacteristic
546Q8—42no—
547Q8—42no—
548Q8—1722no—
549Q8—1722no—
550Q8—1724no—
551Q8—1724no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—431no—
561C2×C4—431no—
562C2×C4—431no—
563C2×C4—431no—
564C2×C4—431no—
565C2×C4—431no—
566C2×C4—862no—
567C2×C4—862no—
568C2×C4—862no—
569C2×C4—862no—
570C2×C4—862no—
571C2×C4—862no—
572C2×C4—862no—
573C2×C4—862no—
574C2×C4—862no—
575C2×C4—862no—
576C2×C4—862no—
577C2×C4—862no—
578C2×C4—862no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4—1724no—
584C2×C4—1724no—
585C2×C4—1722no—
586C2×C4—1722no—
587C2×C4—1722no—
588C2×C4C22⋊C4×D4311yescharacteristic
589C2×C4C22⋊C4×D4311yescharacteristic
590C2×C4C22⋊C4×D4311yescharacteristic
591C2×C4C22⋊C4×D4311yescharacteristic
592C2×C4C22×C4×D4311yescharacteristic
593C2×C4C2×D4×D4311yescharacteristic
594C8—42no—
595C8—1722no—
596C22—21no—
597C22—21no—
598C22—432no—
599C22—432no—
600C22—861no—
601C22—861no—
602C22—861no—
603C22—861no—
604C22—1724no—
605C22C2×C22⋊C4×D4311yescharacteristic
606C22#137×D4312yes—
607C4—21no—
608C4—21no—
609C4—21no—
610C4—21no—
611C4—21no—
612C4—21no—
613C4—42no—
614C4—42no—
615C4—82no—
616C4—432no—
617C4—432no—
618C4—861no—
619C4—861no—
620C4—861no—
621C4—861no—
622C4—3442no—
623C4—1722no—
624C4—1722no—
625C2—22no—
626C2—862no—
627C2—862no—
628C2#410×D4311yescharacteristic
629C2#419×D4311yescharacteristic
630C2#421×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1515C2
socleC22×C43C22×C22⋊C4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenter#1515D43
hypocenterC43#17596
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1515

Complements

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

NH ≅ G/Ntype
5. #19133147C2semidirect
6. #19133146C2semidirect
7. #19133145C2semidirect
8. #19133105C2semidirect
9. C43×#1515C2semidirect
12. #14583454C4semidirect
13. #14583454C4semidirect
15. #14583453C4semidirect
19. C4⋊Q8×D43C4semidirect
20. C4⋊Q8×D43C4semidirect
25. C4×Q8×D43C4semidirect
317. #1515D43semidirect
364. C43#17596semidirect

Maximal subgroups

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

subgroupindex
#533×D432
#432×D432
#191369922
#191331652
#191331472
#191331462
#191331452
#191331052
C43×#15152
#1759643