Finite Group Databasebeta

← #25063845

Subgroups — #25063845

Order 11008.

1024 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583435C211yesmaximal, characteristic
2#19143224C211yesmaximal, characteristic, complemented
3#19136986C211yesmaximal, characteristic, complemented
4#19133132C214yesmaximal, complemented
5#19133128C211yesmaximal, characteristic, complemented
6#19133125C211yesmaximal, characteristic
7#19133123C211yesmaximal, characteristic
8#19133080C214yesmaximal, complemented
9C43×#1511C211yesmaximal, characteristic, complemented
10#14583435—21no—
11#14583435—21no—
12#14583435—21no—
13#14583435—21no—
14#14583435C412yescomplemented
15#14583435C412yescomplemented
16#14583435C2212yes—
17#14583435C2212yes—
18C2×#13063320—21no—
19C2×#13063316C411yescharacteristic, complemented
20C2×#13063314C411yescharacteristic, complemented
21C2×#13063309—21no—
22C2×#13063299C2211yescharacteristic
23C2×Q8×Dic43C411yescharacteristic, complemented
24C2×#13063287C411yescharacteristic, complemented
25C2×(C22⋊D43)⋊C4—21no—
26C2×#13063283—21no—
27C22×C4×Dic43C2211yescharacteristic
28#14582953—21no—
29#14582953C2212yescomplemented
30#14582949—21no—
31#14582949C2212yescomplemented
32#14582922—21no—
33#14582863C2211yescharacteristic
34M16×Dic43—21no—
35#14582766—21no—
36#14582763C2212yescomplemented
37#14582762C2211yescharacteristic
38#14582757—21no—
39#14582750—21no—
40C22⋊C4×Dic43—21no—
41#14582744C2212yescomplemented
42#14582636C2214yescomplemented
43#14582634C2214yes—
44#14582632C2214yes—
45C2×C22⋊Q8×C43C2211yescharacteristic
46C43×#407C2211yescharacteristic
47C43×#381C2211yescharacteristic
48C43×#328C2214yescomplemented
49C22×D172C2×C411yescharacteristic
50C22×C22⋊D43—21no—
51C23×Dic43D411yescharacteristic
52C23×Dic43D411yescharacteristic
53C22×C4×D43—21no—
54C2×#10621877—21no—
55#13063320—22no—
56#13063320—22no—
57#13063320—22no—
58#13063320—22no—
59#13063316—21no—
60#13063316—21no—
61#13063316C2×C412yes—
62#13063316C2×C412yes—
63#13063314—21no—
64#13063314—21no—
65#13063314C2×C412yes—
66#13063314C2×C412yes—
67#13063309—22no—
68#13063309—22no—
69#13063309—22no—
70#13063309—22no—
71#13063299—21no—
72#13063299—21no—
73#13063299C2×C412yes—
74#13063299C2312yes—
75Q8×Dic43—21no—
76Q8×Dic43—21no—
77Q8×Dic43C2×C412yes—
78Q8×Dic43C2×C412yes—
79#13063287—21no—
80#13063287—21no—
81#13063287C2×C412yes—
82#13063287C2×C412yes—
83(C22⋊D43)⋊C4—22no—
84(C22⋊D43)⋊C4—22no—
85(C22⋊D43)⋊C4—22no—
86(C22⋊D43)⋊C4—22no—
87#13063283—22no—
88#13063283—22no—
89#13063283—22no—
90#13063283—22no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43C2×C411yescharacteristic
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—22no—
96C2×C22⋊Dic43—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×C4×Dic43—21no—
102C2×C4×Dic43—22no—
103C2×C4×Dic43C2×C411yescharacteristic
104C2×C4×Dic43C2×C411yescharacteristic
105C2×C4×Dic43C2×C411yescharacteristic
106C2×C4×Dic43C2×C411yescharacteristic
107C2×C4×Dic43D411yescharacteristic
108C2×C4×Dic43D411yescharacteristic
109C2×C4×Dic43D411yescharacteristic
110C2×C4×Dic43D411yescharacteristic
111C2×C4×Dic43D411yescharacteristic
112C2×C4×Dic43D411yescharacteristic
113C2×C4×Dic43C2311yescharacteristic
114C2×C4×Dic43C2311yescharacteristic
115Dic43⋊C8—22no—
116Dic43⋊C8—22no—
117C22⋊(C43⋊C8)—21no—
118C22⋊(C43⋊C8)C2312yes—
119#13063235—22no—
120C8×Dic43—22no—
121C43⋊#95—21no—
122C43⋊#95—22no—
123C43⋊#95—22no—
124C43⋊#95C2312yes—
125C22×Q8×C43C2×C411yescharacteristic
126C23×C4×C43C2311yescharacteristic
127C2×M16×C43—21no—
128C22⋊Q8×C43—21no—
129C22⋊Q8×C43—21no—
130C22⋊Q8×C43C2×C412yes—
131C22⋊Q8×C43C2312yes—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43C2×C411yescharacteristic
134C2×C22⋊C4×C43—21no—
135C2×C22⋊C4×C43—21no—
136C22⋊C8×C43—21no—
137C22⋊C8×C43C2312yes—
138#95×C43—21no—
139#95×C43C2312yes—
140C24×C43C2×D411yescharacteristic
141C23×D43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43—42no—
144C2×Q8×C43C22×C412yes—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—22no—
148C22×C4×C43—42no—
149C22×C4×C43C22×C411yescharacteristic
150C22×C4×C43C22×C411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2411yescharacteristic
155C2×C22⋊D43—22no—
156C2×C22⋊D43—22no—
157C2×C22⋊D43—44no—
158C22×Dic43—21no—
159C22×Dic43—22no—
160C22×Dic43—42no—
161C22×Dic43—42no—
162C22×Dic43C22⋊C411yescharacteristic
163C22×Dic43C22⋊C411yescharacteristic
164C22×Dic43C22⋊C411yescharacteristic
165C22×Dic43C22⋊C411yescharacteristic
166C22×Dic43C22⋊C411yescharacteristic
167C22×Dic43C22⋊C411yescharacteristic
168C22×Dic43C22⋊C411yescharacteristic
169C22×Dic43C22⋊C411yescharacteristic
170C22×Dic43C2×D411yescharacteristic
171C22×Dic43C2×D411yescharacteristic
172C22×Dic43C2×D411yescharacteristic
173C22×Dic43C2×D411yescharacteristic
174C2×D172—21no—
175C2×D172—42no—
176C2×D172C22×C412yes—
177C2×C4×D43—22no—
178C2×C4×D43—22no—
179C2×C4×D43—44no—
180M16×C43—42no—
181C2×C8×C43—22no—
182C4⋊C4×C43—22no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—22no—
185C4⋊C4×C43C22×C412yes—
186C22⋊C4×C43—22no—
187C22⋊C4×C43—22no—
188C22⋊C4×C43—42no—
189C22⋊Dic43—42no—
190(C2×D43)⋊C4—22no—
191(C2×D43)⋊C4—22no—
192(C2×D43)⋊C4—22no—
193(C2×D43)⋊C4—22no—
194(C2×D43)⋊C4—22no—
195(C2×D43)⋊C4—22no—
196(C2×D43)⋊C4—22no—
197(C2×D43)⋊C4—22no—
198C4⋊Dic43—21no—
199C4⋊Dic43—22no—
200C4⋊Dic43—22no—
201C4⋊Dic43—22no—
202C4⋊Dic43—22no—
203C4⋊Dic43C22×C412yes—
204Dic43⋊C4—22no—
205Dic43⋊C4—22no—
206Dic43⋊C4—44no—
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×Dic43C22×C411yescharacteristic
221C4×Dic43C22×C411yescharacteristic
222C4×Dic43C2×D411yescharacteristic
223C4×Dic43C2×D411yescharacteristic
224C4×Dic43C2×D411yescharacteristic
225C4×Dic43C2×D411yescharacteristic
226#10621877—42no—
227C2×C43⋊C8—22no—
228C23×C43—22no—
229C23×C43—22no—
230C23×C43—41no—
231C23×C43C2×C22⋊C411yescharacteristic
232C23×C43C2×C22⋊C411yescharacteristic
233C23×C43C22×D411yescharacteristic
234C22×D43—22no—
235C22×D43—42no—
236C22×D43—42no—
237C22×D43—42no—
238Q8×C43—42no—
239Q8×C43—42no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
243C2×C4×C43—22no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—42no—
249C2×C4×C43—42no—
250C2×C4×C43—42no—
251C2×C4×C43—42no—
252C2×C4×C43—42no—
253C2×C4×C43C2×C22⋊C411yescharacteristic
254C2×C4×C43C2×C22⋊C411yescharacteristic
255C2×C4×C43C23×C411yescharacteristic
256C2×C4×C43C22×D411yescharacteristic
257C22⋊D43—44no—
258C22⋊D43—44no—
259C2×Dic43—22no—
260C2×Dic43—22no—
261C2×Dic43—22no—
262C2×Dic43—22no—
263C2×Dic43—22no—
264C2×Dic43—22no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—42no—
273C2×Dic43—42no—
274C2×Dic43—42no—
275C2×Dic43—42no—
276C2×Dic43C2×C22⋊C411yescharacteristic
277C2×Dic43C2×C22⋊C411yescharacteristic
278C2×Dic43C2×C22⋊C411yescharacteristic
279C2×Dic43C2×C22⋊C411yescharacteristic
280C2×Dic43C2×C22⋊C411yescharacteristic
281C2×Dic43C2×C22⋊C411yescharacteristic
282C2×Dic43C2×C22⋊C411yescharacteristic
283C2×Dic43C2×C22⋊C411yescharacteristic
284D172—42no—
285D172—42no—
286C4×D43—44no—
287C4×D43—44no—
288C8×C43—42no—
289C43⋊C8—42no—
290#17554—431nomaximal, Sylow
291C22×C43—21no—
292C22×C43—21no—
293C22×C43—21no—
294C22×C43—21no—
295C22×C43—21no—
296C22×C43—21no—
297C22×C43—21no—
298C22×C43—44no—
299C22×C43#41012yes—
300C22×C43C22×C22⋊C411yescharacteristic
301C22×C43#57512yes—
302C2×D43—42no—
303C2×D43—42no—
304C2×D43—42no—
305C2×D43—84no—
306C4×C43—21no—
307C4×C43—21no—
308C4×C43—21no—
309C4×C43—21no—
310C4×C43—42no—
311C4×C43—42no—
312C4×C43—82no—
313Dic43—21no—
314Dic43—21no—
315Dic43—21no—
316Dic43—21no—
317Dic43—21no—
318Dic43—21no—
319Dic43—21no—
320Dic43—42no—
321Dic43—82no—
322Dic43#42112yes—
323C2×#529—431no—
324#2920—431no—
325#2283—431no—
326#1512—434no—
327#1511—431no—
328#1511D4311yescharacteristic, complemented
329#1510—431no—
330#1510—431no—
331#1500—434no—
332C2×C43—22no—
333C2×C43—22no—
334C2×C43—41no—
335C2×C43C2×#41011yescharacteristic
336C2×C43#289611yescharacteristic
337C2×C43C2×#42111yescharacteristic
338D43—82no—
339#529—432no—
340#529—432no—
341#529—432no—
342#529—432no—
343#529—861no—
344#529—861no—
345#529—861no—
346#529—861no—
347C2×#126—861no—
348C2×#125—431no—
349C2×#124—431no—
350C2×#123—861no—
351C2×C22⋊Q8C2×D4311yescharacteristic
352C2×#121—431no—
353C2×C4×Q8—431no—
354C2×C4×D4—431no—
355C2×C4×D4—861no—
356C2×#117—861no—
357C22×C42—431no—
358#432—432no—
359#432—861no—
360#431—432no—
361#431—861no—
362#423—861no—
363#407—431no—
364#407C2×D4311yescharacteristic
365C4×M16—861no—
366#383—861no—
367#382—432no—
368#381—431no—
369#381C2×D4311yescharacteristic
370#380—861no—
371C4×C4⋊C4—861no—
372C4×C22⋊C4—861no—
373#376—432no—
374#328—434no—
375#328C2×D4314yescomplemented
376#327—434no—
377#327—434no—
378C43#1755411yescharacteristic, complemented, Sylow
379C22×Q8C4×D4311yescharacteristic
380C22×D4—431no—
381C22×D4—861no—
382C23×C4—431no—
383C23×C4—431no—
384C23×C4—861no—
385C23×C4C22×D4311yescharacteristic
386C2×M16—21no—
387C2×M16—861no—
388#126—862no—
389#126—862no—
390#126—862no—
391#126—862no—
392#125—432no—
393#125—432no—
394#125—861no—
395#125—861no—
396#124—432no—
397#124—432no—
398#124—861no—
399#124—861no—
400#123—862no—
401#123—862no—
402#123—862no—
403#123—862no—
404C22⋊Q8—21no—
405C22⋊Q8—21no—
406C22⋊Q8C4×D4312yes—
407C22⋊Q8C22×D4312yes—
408#121—432no—
409#121—432no—
410#121—861no—
411#121—861no—
412C4×Q8—432no—
413C4×Q8—432no—
414C4×Q8—861no—
415C4×Q8—861no—
416C4×D4—432no—
417C4×D4—432no—
418C4×D4—861no—
419C4×D4—861no—
420C4×D4—862no—
421C4×D4—862no—
422C4×D4—862no—
423C4×D4—862no—
424#117—862no—
425#117—862no—
426#117—862no—
427#117—862no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—431no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4—861no—
433C2×C4⋊C4—862no—
434C2×C4⋊C4C4×D4311yescharacteristic
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—861no—
438C2×C22⋊C4—861no—
439C2×C22⋊C4—861no—
440C2×C22⋊C4—861no—
441C2×C22⋊C4—861no—
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—431no—
453C2×C42—431no—
454C2×C42—861no—
455C2×C42—862no—
456C4⋊C8—862no—
457C4⋊C8—862no—
458C22⋊C8—21no—
459C22⋊C8—432no—
460C22⋊C8—861no—
461C22⋊C8C22×D4312yes—
462#97—862no—
463C4×C8—862no—
464#95—21no—
465#95—432no—
466#95—862no—
467#95—862no—
468#95—861no—
469#95C22×D4312yes—
470C24—861no—
471C24D4×D4311yescharacteristic
472C2×Q8—21no—
473C2×Q8—42no—
474C2×Q8C2×C4×D4312yes—
475C2×D4—432no—
476C2×D4—862no—
477C2×D4—862no—
478C2×D4—861no—
479C2×D4—1722no—
480C2×D4—1724no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—42no—
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—862no—
498C22×C4—862no—
499C22×C4—861no—
500C22×C4—862no—
501C22×C4—1724no—
502C22×C4—1722no—
503C22×C4—1722no—
504C22×C4C2×C4×D4311yescharacteristic
505C22×C4C2×C4×D4311yescharacteristic
506C22×C4D4×D4311yescharacteristic
507C22×C4D4×D4311yescharacteristic
508C22×C4D4×D4311yescharacteristic
509C22×C4C23×D4311yescharacteristic
510M16—42no—
511M16—1722no—
512C2×C8—22no—
513C2×C8—862no—
514C4⋊C4—22no—
515C4⋊C4—21no—
516C4⋊C4—22no—
517C4⋊C4—432no—
518C4⋊C4—862no—
519C4⋊C4—862no—
520C4⋊C4—862no—
521C4⋊C4—862no—
522C4⋊C4—862no—
523C4⋊C4—862no—
524C4⋊C4—861no—
525C4⋊C4—1724no—
526C4⋊C4C2×C4×D4312yes—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—42no—
530C22⋊C4—862no—
531C22⋊C4—862no—
532C22⋊C4—862no—
533C22⋊C4—862no—
534C22⋊C4—862no—
535C22⋊C4—862no—
536C22⋊C4—862no—
537C22⋊C4—862no—
538C22⋊C4—1722no—
539C42—431no—
540C42—431no—
541C42—431no—
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—431no—
555C42—862no—
556C42—862no—
557C42—1724no—
558C23—22no—
559C23—22no—
560C23—41no—
561C23—862no—
562C23—1722no—
563C23—1722no—
564C23—1722no—
565C23C22⋊C4×D4311yescharacteristic
566C23C22⋊C4×D4311yescharacteristic
567C23C2×D4×D4311yescharacteristic
568Q8—42no—
569Q8—42no—
570D4—1722no—
571D4—1722no—
572D4—1724no—
573D4—1724no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—431no—
588C2×C4—431no—
589C2×C4—431no—
590C2×C4—431no—
591C2×C4—431no—
592C2×C4—431no—
593C2×C4—431no—
594C2×C4—431no—
595C2×C4—862no—
596C2×C4—862no—
597C2×C4—862no—
598C2×C4—862no—
599C2×C4—862no—
600C2×C4—862no—
601C2×C4—1724no—
602C2×C4—1724no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1722no—
611C2×C4—1722no—
612C2×C4—1722no—
613C2×C4—1722no—
614C2×C4C22⋊C4×D4311yescharacteristic
615C2×C4C22⋊C4×D4311yescharacteristic
616C2×C4C22×C4×D4311yescharacteristic
617C2×C4C2×D4×D4311yescharacteristic
618C8—42no—
619C8—1722no—
620C22—21no—
621C22—21no—
622C22—21no—
623C22—21no—
624C22—21no—
625C22—21no—
626C22—21no—
627C22—44no—
628C22—3444no—
629C22—1722no—
630C22—1722no—
631C22—1722no—
632C22#1458287112yes—
633C22C2×C22⋊C4×D4311yescharacteristic
634C22#1458369812yes—
635C4—21no—
636C4—21no—
637C4—21no—
638C4—21no—
639C4—42no—
640C4—42no—
641C4—82no—
642C4—432no—
643C4—861no—
644C4—861no—
645C4—861no—
646C4—861no—
647C4—861no—
648C4—861no—
649C4—861no—
650C4—3442no—
651C4—1722no—
652C2—22no—
653C2—22no—
654C2—41no—
655C2—3442no—
656C2C2×#1458287111yescharacteristic
657C2#1914311311yescharacteristic
658C2#421×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1511C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#13063299C22
cosocleC22×C4×C43C24
hypercenter#1511D43
hypocenterC43#17554
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1511

Complements

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

NH ≅ G/Ntype
2. #19143224C2semidirect
3. #19136986C2semidirect
4. #19133132C2semidirect
5. #19133128C2semidirect
8. #19133080C2semidirect
9. C43×#1511C2semidirect
14. #14583435C4semidirect
15. #14583435C4semidirect
19. C2×#13063316C4semidirect
20. C2×#13063314C4semidirect
23. C2×Q8×Dic43C4semidirect
24. C2×#13063287C4semidirect
29. #14582953C22semidirect
31. #14582949C22semidirect
36. #14582763C22semidirect
41. #14582744C22semidirect
42. #14582636C22semidirect
48. C43×#328C22semidirect
328. #1511D43semidirect
375. #328C2×D43semidirect
378. C43#17554semidirect

Maximal subgroups

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

subgroupindex
C2×#145834352
#191432242
#191369862
#191331322
#191331282
#191331252
#191331232
#191330802
C43×#15112
#1755443