Finite Group Databasebeta

← #25063777

Subgroups — #25063777

Order 11008.

1084 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D43C211yesmaximal, characteristic
2#19143223C211yesmaximal, characteristic
3C4×#13063283C211yesmaximal, characteristic
4#19133113C214yesmaximal
5#19133105C214yesmaximal, complemented
6#19133095C211yesmaximal, characteristic, complemented
7#19133094C211yesmaximal, characteristic, complemented
8#19133093C211yesmaximal, characteristic, complemented
9C43×#1503C211yesmaximal, 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
26C2×#13063283—21no—
27#117×D43—21no—
28C2×C42×D43C2211yescharacteristic
29#14582955—21no—
30#14582953C2212yes—
31#14582952C2211yescharacteristic
32#14582950—21no—
33#14582921—21no—
34#14582861C2212yes—
35C4×#10621872—21no—
36C4⋊C4×Dic43—21no—
37C4×C4⋊Dic43C2211yescharacteristic
38C4×(C2×D43)⋊C4—21no—
39#14582746C2212yes—
40#14582744C2212yes—
41C42×Dic43—21no—
42#14582637C2214yes—
43#14582636C2214yes—
44#14582635C2214yes—
45C43×#533C2211yescharacteristic
46C43×#431C2211yescharacteristic
47C4×C4⋊C4×C43C2211yescharacteristic
48C43×#328C2214yes—
49C2×Q8×D43—21no—
50C2×Q8×D43C2×C412yes—
51C22×C4×D43D411yescharacteristic
52C22×C4×D43D411yescharacteristic
53C22×C4×D43C2311yescharacteristic
54C2×#10621872—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—28no—
90#13063283—21no—
91#13063283—21no—
92#13063282—22no—
93#13063281—22no—
94C2×C4⋊Dic43—21no—
95C4⋊C4×D43—21no—
96C4⋊C4×D43—21no—
97C4⋊C4×D43—21no—
98C4⋊C4×D43—22no—
99C4⋊C4×D43—22no—
100C4⋊C4×D43C2×C412yes—
101C2×(C2×D43)⋊C4—22no—
102C22⋊C4×D43—22no—
103C2×C4×Dic43—22no—
104C2×C4×Dic43—21no—
105C2×C4×Dic43—22no—
106C2×C4×Dic43D411yescharacteristic
107C2×C4×Dic43D411yescharacteristic
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
118C4⋊(C43⋊C8)—21no—
119Dic43⋊C8—22no—
120C22⋊(C43⋊C8)C2312yes—
121(C2×D43)⋊C8—22no—
122#13063235—22no—
123C4×C43⋊C8—21no—
124C43⋊#95—22no—
125C43⋊#95C2312yes—
126C4⋊Q8×C43C2×C411yescharacteristic
127C4⋊Q8×C43C2×C411yescharacteristic
128#125×C43—21no—
129C22⋊Q8×C43—21no—
130C22⋊Q8×C43C2312yes—
131C4×Q8×C43—21no—
132C4×Q8×C43C2×C412yes—
133#117×C43—21no—
134C2×C4⋊C4×C43—21no—
135C2×C42×C43—21no—
136C2×C42×C43C2311yescharacteristic
137C4⋊C8×C43—21no—
138C22⋊C8×C43C2312yes—
139C4×C8×C43—21no—
140#95×C43C2312yes—
141C23×D43C2×D411yescharacteristic
142C2×Q8×C43—21no—
143C2×Q8×C43C22×C412yes—
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—22no—
174C2×Dic86—22no—
175C2×Dic86C22×C412yes—
176C2×C8×C43—22no—
177C4⋊C4×C43—24no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—22no—
182C4⋊C4×C43—22no—
183C4⋊C4×C43C22×C412yes—
184C22⋊C4×C43—22no—
185C42×C43—22no—
186C42×C43—42no—
187C42×C43C22×C411yescharacteristic
188C42×C43C22×C411yescharacteristic
189C42×C43C2×D411yescharacteristic
190C42×C43C2×D411yescharacteristic
191C22⋊Dic43—22no—
192(C2×D43)⋊C4—28no—
193(C2×D43)⋊C4—22no—
194(C2×D43)⋊C4—22no—
195C4⋊Dic43—24no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—22no—
200C4⋊Dic43—22no—
201C4⋊Dic43C22×C412yes—
202Dic43⋊C4—22no—
203Dic43⋊C4—22no—
204Dic43⋊C4—22no—
205Dic43⋊C4—22no—
206Dic43⋊C4—22no—
207Dic43⋊C4—22no—
208Dic43⋊C4—22no—
209Dic43⋊C4—22no—
210C4×Dic43—28no—
211C4×Dic43—22no—
212C4×Dic43—22no—
213C4×Dic43—22no—
214C4×Dic43—44no—
215C4×Dic43—42no—
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×Dic43C22×C411yescharacteristic
226C4×Dic43C2×D411yescharacteristic
227C4×Dic43C2×D411yescharacteristic
228C2×C43⋊C8—22no—
229#10621872—44no—
230C23×C43C22×D411yescharacteristic
231C22×D43—21no—
232C22×D43—21no—
233C22×D43—22no—
234C22×D43—41no—
235C22×D43C2×C22⋊C411yescharacteristic
236C22×D43C2×C22⋊C411yescharacteristic
237Q8×C43—42no—
238Q8×C43—42no—
239C2×C4×C43—22no—
240C2×C4×C43—24no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
243C2×C4×C43—41no—
244C2×C4×C43—42no—
245C2×C4×C43—42no—
246C2×C4×C43C2×C22⋊C411yescharacteristic
247C2×C4×C43C2×C22⋊C411yescharacteristic
248C2×C4×C43C2×C22⋊C411yescharacteristic
249C2×C4×C43C2×C22⋊C411yescharacteristic
250C2×C4×C43#13712yes—
251C2×C4×C43#13712yes—
252C2×C4×C43C23×C411yescharacteristic
253C2×C4×C43C22×D411yescharacteristic
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—22no—
257C2×Dic43—22no—
258C2×Dic43—24no—
259C2×Dic43—22no—
260C2×Dic43—22no—
261C2×Dic43—42no—
262C2×Dic43—42no—
263C2×Dic43C2×C22⋊C411yescharacteristic
264C2×Dic43C2×C22⋊C411yescharacteristic
265C2×Dic43C2×C22⋊C411yescharacteristic
266C2×Dic43C2×C22⋊C411yescharacteristic
267C2×Dic43C2×C22⋊C411yescharacteristic
268C2×Dic43C2×C22⋊C411yescharacteristic
269C4×D43—22no—
270C4×D43—22no—
271C4×D43—22no—
272C4×D43—22no—
273C4×D43—22no—
274C4×D43—22no—
275C4×D43—22no—
276C4×D43—22no—
277C4×D43—22no—
278C4×D43—41no—
279C4×D43—41no—
280C4×D43—44no—
281C4×D43—44no—
282C4×D43#10414yes—
283Dic86—42no—
284Dic86—44no—
285Dic86—44no—
286Dic86—42no—
287C8×C43—42no—
288C43⋊C8—42no—
289#17545—431nomaximal, Sylow
290C22×C43—21no—
291C22×C43—21no—
292C22×C43C22×C22⋊C411yescharacteristic
293C22×C43C2×#13711yescharacteristic
294C22×C43C2×#13711yescharacteristic
295C2×D43—21no—
296C2×D43—21no—
297C2×D43—21no—
298C2×D43—21no—
299C2×D43—21no—
300C2×D43—42no—
301C2×D43—42no—
302C2×D43C2×#10412yes—
303C4×C43—21no—
304C4×C43—21no—
305C4×C43—21no—
306C4×C43—44no—
307C4×C43—42no—
308C4×C43—42no—
309C4×C43#41912yes—
310C4×C43#41912yes—
311C4×C43C2×#10412yes—
312Dic43—21no—
313Dic43—21no—
314Dic43—21no—
315Dic43—21no—
316Dic43—44no—
317Dic43—42no—
318Dic43—42no—
319Dic43#41012yes—
320Dic43C2×#10412yes—
321C2×#533—431no—
322#2920—431no—
323C4×#117—431no—
324#1508—434no—
325#1506—434no—
326#1503—431no—
327#1503—431no—
328#1503—431no—
329#1503D4311yescharacteristic, complemented
330C2×C43—21no—
331C2×C43—21no—
332C2×C43C2×#41011yescharacteristic
333C2×C43C2×#41911yescharacteristic
334C2×C43C22×#10411yescharacteristic
335D43—22no—
336D43—41no—
337#533—431no—
338#533—431no—
339#533—432no—
340#533—432no—
341#533—431no—
342#533—861no—
343#533—861no—
344#533—861no—
345#533—861no—
346#533C2×D4311yescharacteristic
347C2×C4⋊Q8—431no—
348C2×C4⋊Q8—431no—
349C2×#125—861no—
350C2×C22⋊Q8—432no—
351C2×C22⋊Q8—861no—
352C2×C4×Q8—432no—
353C2×C4×Q8—861no—
354C2×#117—861no—
355C2×#117—861no—
356C22×C42—431no—
357#432—432no—
358#432—861no—
359#431—431no—
360#431—861no—
361#431C2×D4311yescharacteristic
362#423—861no—
363#407—432no—
364C4×M16—861no—
365C4×C4⋊C4—431no—
366C4×C4⋊C4—861no—
367C4×C4⋊C4C2×D4311yescharacteristic
368C4×C22⋊C4—432no—
369C4×C22⋊C4—861no—
370#376—432no—
371C43—861no—
372#328—434no—
373#328—434no—
374#328—434no—
375#328C2×D4314yes—
376C43#1754511yescharacteristic, complemented, Sylow
377C22×Q8—432no—
378C22×Q8—861no—
379C23×C4—431no—
380C23×C4—431no—
381C23×C4—431no—
382C2×M16—862no—
383C4⋊Q8—432no—
384C4⋊Q8—432no—
385C4⋊Q8—431no—
386C4⋊Q8—431no—
387C4⋊Q8—861no—
388C4⋊Q8—861no—
389C4⋊Q8—861no—
390C4⋊Q8—861no—
391C4⋊Q8C4×D4311yescharacteristic
392C4⋊Q8C4×D4311yescharacteristic
393#125—21no—
394#125—862no—
395#125—862no—
396#125—861no—
397#125—861no—
398#125—861no—
399C22⋊Q8—21no—
400C22⋊Q8—432no—
401C22⋊Q8—432no—
402C22⋊Q8—432no—
403C22⋊Q8—862no—
404C22⋊Q8—862no—
405C22⋊Q8—862no—
406C22⋊Q8—862no—
407C22⋊Q8—861no—
408C22⋊Q8—861no—
409C22⋊Q8—861no—
410C22⋊Q8C22×D4312yes—
411C4×Q8—21no—
412C4×Q8—432no—
413C4×Q8—432no—
414C4×Q8—432no—
415C4×Q8—862no—
416C4×Q8—862no—
417C4×Q8—862no—
418C4×Q8—861no—
419C4×Q8—862no—
420C4×Q8—861no—
421C4×Q8—861no—
422C4×Q8C4×D4312yes—
423#117—21no—
424#117—862no—
425#117—862no—
426#117—861no—
427#117—861no—
428#117—868no—
429#117—861no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—432no—
432C2×C4⋊C4—861no—
433C2×C4⋊C4—861no—
434C2×C4⋊C4—862no—
435C2×C4⋊C4—862no—
436C2×C4⋊C4—861no—
437C2×C4⋊C4—861no—
438C2×C22⋊C4—862no—
439C2×C22⋊C4—862no—
440C2×C42—21no—
441C2×C42—431no—
442C2×C42—431no—
443C2×C42—431no—
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—862no—
453C2×C42—862no—
454C2×C42—862no—
455C2×C42—861no—
456C2×C42C22×D4311yescharacteristic
457C4⋊C8—21no—
458C4⋊C8—862no—
459C4⋊C8—861no—
460C22⋊C8—432no—
461C22⋊C8—862no—
462C22⋊C8C22×D4312yes—
463#97—862no—
464C4×C8—21no—
465C4×C8—861no—
466#95—432no—
467#95—862no—
468#95C22×D4312yes—
469C24—431no—
470C2×Q8—21no—
471C2×Q8—432no—
472C2×Q8—862no—
473C2×Q8—862no—
474C2×Q8—861no—
475C2×Q8—1724no—
476C2×Q8—1724no—
477C2×Q8C2×C4×D4312yes—
478C22×C4—22no—
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—431no—
491C22×C4—431no—
492C22×C4—431no—
493C22×C4—431no—
494C22×C4—864no—
495C22×C4—862no—
496C22×C4—862no—
497C22×C4—862no—
498C22×C4—862no—
499C22×C4—862no—
500C22×C4—1722no—
501C22×C4D4×D4311yescharacteristic
502C22×C4D4×D4311yescharacteristic
503C22×C4C23×D4311yescharacteristic
504M16—1724no—
505C2×C8—22no—
506C2×C8—862no—
507C4⋊C4—24no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—432no—
514C4⋊C4—862no—
515C4⋊C4—862no—
516C4⋊C4—862no—
517C4⋊C4—862no—
518C4⋊C4—862no—
519C4⋊C4—862no—
520C4⋊C4—862no—
521C4⋊C4—862no—
522C4⋊C4—864no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—862no—
526C4⋊C4—861no—
527C4⋊C4—862no—
528C4⋊C4C2×C4×D4312yes—
529C22⋊C4—22no—
530C22⋊C4—862no—
531C22⋊C4—862no—
532C22⋊C4—868no—
533C22⋊C4—862no—
534C42—22no—
535C42—42no—
536C42—431no—
537C42—431no—
538C42—431no—
539C42—431no—
540C42—431no—
541C42—431no—
542C42—431no—
543C42—431no—
544C42—431no—
545C42—431no—
546C42—431no—
547C42—431no—
548C42—862no—
549C42—862no—
550C42—868no—
551C42—862no—
552C42—1724no—
553C42—1722no—
554C42C2×C4×D4311yescharacteristic
555C42C2×C4×D4311yescharacteristic
556C42D4×D4311yescharacteristic
557C42D4×D4311yescharacteristic
558C23—431no—
559C23—431no—
560C23—862no—
561C23—861no—
562C23—861no—
563C23—1721no—
564C23C2×D4×D4311yescharacteristic
565Q8—42no—
566Q8—42no—
567Q8—1722no—
568Q8—1724no—
569Q8—1724no—
570Q8—1722no—
571C2×C4—22no—
572C2×C4—24no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—41no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—431no—
579C2×C4—431no—
580C2×C4—434no—
581C2×C4—431no—
582C2×C4—431no—
583C2×C4—431no—
584C2×C4—431no—
585C2×C4—862no—
586C2×C4—862no—
587C2×C4—862no—
588C2×C4—862no—
589C2×C4—862no—
590C2×C4—862no—
591C2×C4—861no—
592C2×C4—861no—
593C2×C4—862no—
594C2×C4—862no—
595C2×C4—862no—
596C2×C4—862no—
597C2×C4—862no—
598C2×C4—864no—
599C2×C4—862no—
600C2×C4—862no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1724no—
604C2×C4—1724no—
605C2×C4—1722no—
606C2×C4—1722no—
607C2×C4C22⋊C4×D4311yescharacteristic
608C2×C4C22⋊C4×D4311yescharacteristic
609C2×C4C22⋊C4×D4311yescharacteristic
610C2×C4C22⋊C4×D4311yescharacteristic
611C2×C4#1306335412yes—
612C2×C4#1306335712yes—
613C2×C4C22×C4×D4311yescharacteristic
614C2×C4C2×D4×D4311yescharacteristic
615C8—42no—
616C8—1722no—
617C22—21no—
618C22—21no—
619C22—432no—
620C22—861no—
621C22—861no—
622C22—861no—
623C22—861no—
624C22—861no—
625C22—1722no—
626C22—1722no—
627C22C2×C22⋊C4×D4311yescharacteristic
628C22C2×#1306335411yescharacteristic
629C22C2×#1306335711yescharacteristic
630C4—21no—
631C4—21no—
632C4—21no—
633C4—44no—
634C4—42no—
635C4—42no—
636C4—432no—
637C4—432no—
638C4—861no—
639C4—861no—
640C4—861no—
641C4—861no—
642C4—1724no—
643C4—1722no—
644C4—1722no—
645C4#1458290612yes—
646C4#1458290612yes—
647C4#104×D4312yes—
648C2—21no—
649C2—21no—
650C2—862no—
651C2—1721no—
652C2#410×D4311yescharacteristic
653C2C2×#1458290611yescharacteristic
654C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1503C2
socleC22×C43C22×C22⋊C4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenter#1503D43
hypocenterC43#17545
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1503

Complements

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

NH ≅ G/Ntype
5. #19133105C2semidirect
6. #19133095C2semidirect
7. #19133094C2semidirect
8. #19133093C2semidirect
9. C43×#1503C2semidirect
12. #14583454C4semidirect
13. #14583454C4semidirect
15. #14583453C4semidirect
19. C4⋊Q8×D43C4semidirect
20. C4⋊Q8×D43C4semidirect
25. C4×Q8×D43C4semidirect
329. #1503D43semidirect
376. C43#17545semidirect

Maximal subgroups

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

subgroupindex
#533×D432
#191432232
C4×#130632832
#191331132
#191331052
#191330952
#191330942
#191330932
C43×#15032
#1754543