Finite Group Databasebeta

← #25096724

Subgroups — #25096724

Order 11008.

1336 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583367C211yesmaximal, characteristic
2#19143224C211yesmaximal, characteristic, complemented
3#19136989C211yesmaximal, characteristic, complemented
4#19134694C211yesmaximal, characteristic, complemented
5#19134614C214yesmaximal, complemented
6#19134540C211yesmaximal, characteristic
7#19134538C211yesmaximal, characteristic
8#19134404C214yesmaximal, complemented
9C43×#1826C211yesmaximal, characteristic, complemented
10C22×#10621898C2211yescharacteristic
11#14583367—21no—
12#14583367—21no—
13#14583367—21no—
14#14583367—21no—
15#14583367C412yescomplemented
16#14583367C412yescomplemented
17#14583367C2212yes—
18#14583367C2212yes—
19C2×#13063290C411yescharacteristic, complemented
20C2×#13063290C411yescharacteristic, complemented
21C2×#13063287C411yescharacteristic, complemented
22C2×#13063287C411yescharacteristic, complemented
23C2×(C22⋊D43)⋊C4—21no—
24C2×(C22⋊D43)⋊C4—21no—
25C2×#13063282—21no—
26C22×C4×Dic43C2211yescharacteristic
27C2×C42×D43—21no—
28#14582953—21no—
29#14582953—21no—
30#14582949—21no—
31#14582949—21no—
32#14582922C2212yescomplemented
33C2×#13063253C2214yes—
34C2×#13063251C2214yes—
35#14582863C2211yescharacteristic
36M16×Dic43C2212yescomplemented
37#14582766—21no—
38#14582763—21no—
39#14582760—21no—
40#14582757—21no—
41C4×Dic43⋊C4C2212yescomplemented
42C4×C22⋊Dic43C2211yescharacteristic
43#14582745C2212yescomplemented
44#14582658C2214yescomplemented
45C2×#117×C43C2211yescharacteristic
46C43×#407C2211yescharacteristic
47C4×C22⋊C4×C43C2211yescharacteristic
48C43×#339C2214yescomplemented
49C2×#10621898—21no—
50C2×#10621898—21no—
51C2×#10621898—28no—
52C2×#10621898C2×C412yes—
53C2×#10621898C2312yes—
54C22×Dic86C2×C411yescharacteristic
55C22×D172C2×C411yescharacteristic
56C22×C22⋊D43—21no—
57C23×Dic43D411yescharacteristic
58C23×Dic43D411yescharacteristic
59C22×C4×D43—21no—
60C22×C4×D43—21no—
61C22×C4×D43—21no—
62C2×#10621877C2312yes—
63#13063290—21no—
64#13063290—21no—
65#13063290—21no—
66#13063290—21no—
67#13063290C2×C412yes—
68#13063290C2×C412yes—
69#13063290C2×C412yes—
70#13063290C2×C412yes—
71#13063287—21no—
72#13063287—21no—
73#13063287—21no—
74#13063287—21no—
75#13063287C2×C412yes—
76#13063287C2×C412yes—
77#13063287C2×C412yes—
78#13063287C2×C412yes—
79(C22⋊D43)⋊C4—22no—
80(C22⋊D43)⋊C4—22no—
81(C22⋊D43)⋊C4—22no—
82(C22⋊D43)⋊C4—22no—
83(C22⋊D43)⋊C4—22no—
84(C22⋊D43)⋊C4—22no—
85(C22⋊D43)⋊C4—22no—
86(C22⋊D43)⋊C4—22no—
87#13063282—22no—
88#13063282—22no—
89#13063282—22no—
90#13063282—22no—
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—22no—
94C2×C22⋊Dic43—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43—21no—
99C2×C4×Dic43C2×C411yescharacteristic
100C2×C4×Dic43C2×C411yescharacteristic
101C2×C4×Dic43C2×C411yescharacteristic
102C2×C4×Dic43C2×C411yescharacteristic
103C2×C4×Dic43D411yescharacteristic
104C2×C4×Dic43D411yescharacteristic
105C2×C4×Dic43D411yescharacteristic
106C2×C4×Dic43D411yescharacteristic
107C2×C4×Dic43D411yescharacteristic
108C2×C4×Dic43D411yescharacteristic
109C2×C4×Dic43C2312yes—
110C2×C4×Dic43C2311yescharacteristic
111C2×C4×Dic43C2311yescharacteristic
112C42×D43—22no—
113C42×D43—22no—
114C42×D43—22no—
115C42×D43—22no—
116Dic43⋊C8—22no—
117Dic43⋊C8—22no—
118#13063253—28no—
119#13063251—28no—
120C22⋊(C43⋊C8)—21no—
121C22⋊(C43⋊C8)—21no—
122#13063235—22no—
123C8×Dic43—22no—
124C43⋊#95—21no—
125C43⋊#95—22no—
126C43⋊#95—22no—
127C43⋊#95—22no—
128C23×C4×C43C2311yescharacteristic
129C2×M16×C43C2312yes—
130#117×C43—21no—
131#117×C43—21no—
132#117×C43C2×C412yes—
133#117×C43C2312yes—
134C2×C4⋊C4×C43C2×C411yescharacteristic
135C2×C4⋊C4×C43C2×C411yescharacteristic
136C2×C22⋊C4×C43—21no—
137C2×C22⋊C4×C43—21no—
138C2×C42×C43—21no—
139C2×C42×C43C2312yes—
140C22⋊C8×C43—21no—
141C22⋊C8×C43—21no—
142#95×C43—21no—
143C24×C43C2×D411yescharacteristic
144C23×D43—21no—
145C22×C4×C43—24no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—22no—
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—28no—
156C2×C22⋊D43—22no—
157C2×C22⋊D43—22no—
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
174#10621898—28no—
175#10621898—28no—
176#10621898—24no—
177#10621898—24no—
178#10621898—24no—
179#10621898#4118yes—
180C2×D172—21no—
181C2×D172—24no—
182C2×D172C22×C412yes—
183C2×C4×D43—28no—
184C2×C4×D43—22no—
185C2×C4×D43—22no—
186C2×C4×D43—22no—
187C2×C4×D43—22no—
188C2×C4×D43—22no—
189C2×C4×D43—22no—
190C2×C4×D43—44no—
191C2×C4×D43—44no—
192C2×Dic86—21no—
193C2×Dic86—24no—
194C2×Dic86C22×C412yes—
195M16×C43—24no—
196C2×C8×C43—22no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43C22×C412yes—
200C4⋊C4×C43C22×C412yes—
201C22⋊C4×C43—22no—
202C22⋊C4×C43—22no—
203C22⋊C4×C43—42no—
204C42×C43—22no—
205C42×C43—22no—
206C42×C43—24no—
207C22⋊Dic43—42no—
208(C2×D43)⋊C4—22no—
209(C2×D43)⋊C4—22no—
210(C2×D43)⋊C4—22no—
211(C2×D43)⋊C4—22no—
212Dic43⋊C4—22no—
213Dic43⋊C4—22no—
214Dic43⋊C4—22no—
215Dic43⋊C4—22no—
216Dic43⋊C4—44no—
217C4×Dic43—22no—
218C4×Dic43—22no—
219C4×Dic43—22no—
220C4×Dic43—22no—
221C4×Dic43—24no—
222C4×Dic43C22⋊C411yescharacteristic
223C4×Dic43C22⋊C411yescharacteristic
224C4×Dic43C22⋊C411yescharacteristic
225C4×Dic43C22⋊C411yescharacteristic
226C4×Dic43C22⋊C411yescharacteristic
227C4×Dic43C22⋊C411yescharacteristic
228C4×Dic43C22⋊C411yescharacteristic
229C4×Dic43C22⋊C411yescharacteristic
230C4×Dic43C22×C411yescharacteristic
231C4×Dic43C22×C411yescharacteristic
232C4×Dic43C22×C411yescharacteristic
233C4×Dic43C22×C411yescharacteristic
234C4×Dic43C2×D411yescharacteristic
235C4×Dic43C2×D411yescharacteristic
236C4×Dic43C2×D411yescharacteristic
237C4×Dic43C2×D411yescharacteristic
238#10621877—24no—
239C2×C43⋊C8—22no—
240C23×C43—22no—
241C23×C43—22no—
242C23×C43—41no—
243C23×C43C2×C22⋊C411yescharacteristic
244C23×C43C2×C22⋊C411yescharacteristic
245C23×C43C22×D411yescharacteristic
246C22×D43—24no—
247C22×D43—22no—
248C22×D43—42no—
249C22×D43—42no—
250C2×C4×C43—22no—
251C2×C4×C43—22no—
252C2×C4×C43—22no—
253C2×C4×C43—22no—
254C2×C4×C43—22no—
255C2×C4×C43—22no—
256C2×C4×C43—22no—
257C2×C4×C43—42no—
258C2×C4×C43—42no—
259C2×C4×C43—42no—
260C2×C4×C43—42no—
261C2×C4×C43—42no—
262C2×C4×C43C2×C22⋊C411yescharacteristic
263C2×C4×C43C2×C22⋊C411yescharacteristic
264C2×C4×C43C23×C411yescharacteristic
265C2×C4×C43C22×D411yescharacteristic
266C2×C4×C43C2×#4114yes—
267C22⋊D43—28no—
268C22⋊D43—28no—
269C2×Dic43—24no—
270C2×Dic43—22no—
271C2×Dic43—22no—
272C2×Dic43—22no—
273C2×Dic43—22no—
274C2×Dic43—22no—
275C2×Dic43—22no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—42no—
284C2×Dic43—42no—
285C2×Dic43—42no—
286C2×Dic43C2×C22⋊C411yescharacteristic
287C2×Dic43C2×C22⋊C411yescharacteristic
288C2×Dic43C2×C22⋊C411yescharacteristic
289C2×Dic43C2×C22⋊C411yescharacteristic
290C2×Dic43C2×C22⋊C411yescharacteristic
291C2×Dic43C2×C22⋊C411yescharacteristic
292C2×Dic43C2×C22⋊C411yescharacteristic
293C2×Dic43C2×C22⋊C411yescharacteristic
294D172—24no—
295D172—22no—
296D172#11714yes—
297C4×D43—28no—
298C4×D43—28no—
299C4×D43—44no—
300C4×D43—44no—
301C4×D43—44no—
302C4×D43—44no—
303Dic86—24no—
304Dic86—22no—
305Dic86#11714yes—
306C8×C43—42no—
307C43⋊C8—42no—
308#20748—431nomaximal, Sylow
309C22×C43—21no—
310C22×C43—21no—
311C22×C43—21no—
312C22×C43—21no—
313C22×C43—21no—
314C22×C43—21no—
315C22×C43—21no—
316C22×C43—44no—
317C22×C43#42112yes—
318C22×C43C22×C22⋊C411yescharacteristic
319C22×C43#52512yes—
320C2×D43—24no—
321C2×D43—48no—
322C2×D43—42no—
323C2×D43—42no—
324C4×C43—21no—
325C4×C43—21no—
326C4×C43—42no—
327C4×C43—42no—
328C4×C43—82no—
329C4×C43C2×#11712yes—
330C4×C43#52512yes—
331Dic43—21no—
332Dic43—21no—
333Dic43—21no—
334Dic43—21no—
335Dic43—21no—
336Dic43—21no—
337Dic43—21no—
338Dic43—24no—
339Dic43—82no—
340Dic43#42112yes—
341C2×C4×#41—431no—
342#2920—431no—
343#2283—431no—
344#1826—431no—
345#1826D4311yescharacteristic, complemented
346#1806—434no—
347#1789—431no—
348#1789—431no—
349#1759—434no—
350C2×C43—22no—
351C2×C43—22no—
352C2×C43—41no—
353C2×C43#228011yescharacteristic
354C2×C43C2×#42111yescharacteristic
355C2×C43C2×#42111yescharacteristic
356D43—44no—
357C22×#41—431no—
358C4×#41—432no—
359C4×#41—432no—
360C4×#41—432no—
361C4×#41—432no—
362C4×#41—861no—
363C4×#41—861no—
364C4×#41—861no—
365C4×#41—861no—
366C2×C4×Q8—431no—
367C2×C4×Q8—431no—
368C2×C4×D4—431no—
369C2×C4×D4—431no—
370C2×C4×D4—861no—
371C2×C4×D4—861no—
372C2×#117—861no—
373C2×#117C2×D4311yescharacteristic
374C22×C42—431no—
375C22×C42—861no—
376#432—861no—
377#432—861no—
378#431—861no—
379#431—861no—
380#423—432no—
381C2×#104—434no—
382C2×#104—434no—
383#407—431no—
384#407C2×D4311yescharacteristic
385C4×M16—432no—
386#383—861no—
387#382—861no—
388#381—861no—
389#380—861no—
390C4×C4⋊C4—432no—
391C4×C22⋊C4—431no—
392C4×C22⋊C4C2×D4311yescharacteristic
393#376—432no—
394#339—434no—
395#339C2×D4314yescomplemented
396C43#2074811yescharacteristic, complemented, Sylow
397C2×#41—432no—
398C2×#41—432no—
399C2×#41—868no—
400C2×#41—861no—
401C2×#41—861no—
402C22×Q8—431no—
403C22×D4—431no—
404C22×D4—861no—
405C23×C4—431no—
406C23×C4—431no—
407C23×C4—861no—
408C23×C4—861no—
409C23×C4—861no—
410C23×C4C22×D4311yescharacteristic
411C2×M16—432no—
412C2×M16C22×D4312yes—
413C4×Q8—432no—
414C4×Q8—432no—
415C4×Q8—432no—
416C4×Q8—432no—
417C4×Q8—861no—
418C4×Q8—861no—
419C4×Q8—861no—
420C4×Q8—861no—
421C4×D4—432no—
422C4×D4—432no—
423C4×D4—432no—
424C4×D4—432no—
425C4×D4—861no—
426C4×D4—861no—
427C4×D4—861no—
428C4×D4—861no—
429C4×D4—862no—
430C4×D4—862no—
431C4×D4—862no—
432C4×D4—862no—
433C4×D4—862no—
434C4×D4—862no—
435C4×D4—862no—
436C4×D4—862no—
437#117—21no—
438#117—21no—
439#117—862no—
440#117—862no—
441#117—862no—
442#117—862no—
443#117C4×D4312yes—
444#117C22×D4312yes—
445C2×C4⋊C4—861no—
446C2×C4⋊C4—861no—
447C2×C4⋊C4—862no—
448C2×C4⋊C4C4×D4311yescharacteristic
449C2×C4⋊C4C4×D4311yescharacteristic
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—861no—
453C2×C22⋊C4—861no—
454C2×C22⋊C4—861no—
455C2×C42—21no—
456C2×C42—431no—
457C2×C42—431no—
458C2×C42—431no—
459C2×C42—431no—
460C2×C42—431no—
461C2×C42—431no—
462C2×C42—431no—
463C2×C42—431no—
464C2×C42—431no—
465C2×C42—431no—
466C2×C42—431no—
467C2×C42—431no—
468C2×C42—432no—
469C2×C42—862no—
470C2×C42—862no—
471C2×C42—862no—
472C2×C42—862no—
473C2×C42—861no—
474C2×C42—861no—
475C2×C42C22×D4312yes—
476C4⋊C8—862no—
477C4⋊C8—862no—
478#104—868no—
479#104—868no—
480C22⋊C8—21no—
481C22⋊C8—21no—
482C22⋊C8—861no—
483C22⋊C8—861no—
484#97—862no—
485C4×C8—862no—
486#95—21no—
487#95—862no—
488#95—862no—
489#95—862no—
490#95—861no—
491C24—861no—
492C24D4×D4311yescharacteristic
493#41—438no—
494#41—864no—
495#41—864no—
496#41—868no—
497#41—868no—
498#41—864no—
499C2×Q8—432no—
500C2×Q8—864no—
501C2×Q8—861no—
502C2×D4—432no—
503C2×D4—864no—
504C2×D4—868no—
505C2×D4—862no—
506C2×D4—862no—
507C2×D4—861no—
508C22×C4—24no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—431no—
513C22×C4—431no—
514C22×C4—431no—
515C22×C4—431no—
516C22×C4—431no—
517C22×C4—431no—
518C22×C4—431no—
519C22×C4—431no—
520C22×C4—431no—
521C22×C4—431no—
522C22×C4—431no—
523C22×C4—431no—
524C22×C4—862no—
525C22×C4—862no—
526C22×C4—862no—
527C22×C4—862no—
528C22×C4—868no—
529C22×C4—861no—
530C22×C4—862no—
531C22×C4—862no—
532C22×C4—862no—
533C22×C4—1724no—
534C22×C4—1724no—
535C22×C4—1722no—
536C22×C4—1722no—
537C22×C4C2×C4×D4311yescharacteristic
538C22×C4C2×C4×D4311yescharacteristic
539C22×C4D4×D4311yescharacteristic
540C22×C4D4×D4311yescharacteristic
541C22×C4D4×D4311yescharacteristic
542C22×C4C23×D4311yescharacteristic
543M16—24no—
544M16—864no—
545C2×C8—22no—
546C2×C8—862no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—862no—
550C4⋊C4—862no—
551C4⋊C4—862no—
552C4⋊C4—862no—
553C4⋊C4—1724no—
554C4⋊C4C2×C4×D4312yes—
555C4⋊C4C2×C4×D4312yes—
556C22⋊C4—22no—
557C22⋊C4—22no—
558C22⋊C4—42no—
559C22⋊C4—862no—
560C22⋊C4—862no—
561C22⋊C4—862no—
562C22⋊C4—862no—
563C22⋊C4—1722no—
564C42—22no—
565C42—22no—
566C42—24no—
567C42—431no—
568C42—431no—
569C42—431no—
570C42—431no—
571C42—431no—
572C42—431no—
573C42—431no—
574C42—431no—
575C42—431no—
576C42—431no—
577C42—431no—
578C42—431no—
579C42—431no—
580C42—431no—
581C42—431no—
582C42—431no—
583C42—862no—
584C42—862no—
585C42—862no—
586C42—862no—
587C42—864no—
588C23—22no—
589C23—22no—
590C23—41no—
591C23—864no—
592C23—862no—
593C23—1722no—
594C23—1722no—
595C23C22⋊C4×D4311yescharacteristic
596C23C22⋊C4×D4311yescharacteristic
597C23C2×D4×D4311yescharacteristic
598Q8—434no—
599Q8—864no—
600Q8—862no—
601D4—434no—
602D4—864no—
603D4—868no—
604D4—868no—
605D4—862no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—431no—
619C2×C4—431no—
620C2×C4—431no—
621C2×C4—431no—
622C2×C4—431no—
623C2×C4—431no—
624C2×C4—431no—
625C2×C4—431no—
626C2×C4—868no—
627C2×C4—862no—
628C2×C4—862no—
629C2×C4—862no—
630C2×C4—864no—
631C2×C4—862no—
632C2×C4—862no—
633C2×C4—862no—
634C2×C4—868no—
635C2×C4—1724no—
636C2×C4—1724no—
637C2×C4—1724no—
638C2×C4—1724no—
639C2×C4—1721no—
640C2×C4—1721no—
641C2×C4—1721no—
642C2×C4—1721no—
643C2×C4—1721no—
644C2×C4—1721no—
645C2×C4—1721no—
646C2×C4—1722no—
647C2×C4—1722no—
648C2×C4—1722no—
649C2×C4C22⋊C4×D4311yescharacteristic
650C2×C4C22⋊C4×D4311yescharacteristic
651C2×C4C22×C4×D4311yescharacteristic
652C2×C4C2×D4×D4311yescharacteristic
653C2×C4#41×D4314yes—
654C8—42no—
655C8—1722no—
656C22—21no—
657C22—21no—
658C22—21no—
659C22—21no—
660C22—21no—
661C22—21no—
662C22—21no—
663C22—44no—
664C22—864no—
665C22—1728no—
666C22—1722no—
667C22—1722no—
668C22#1458291412yes—
669C22C2×C22⋊C4×D4311yescharacteristic
670C22#1458340712yes—
671C4—21no—
672C4—21no—
673C4—42no—
674C4—42no—
675C4—82no—
676C4—432no—
677C4—864no—
678C4—861no—
679C4—861no—
680C4—861no—
681C4—861no—
682C4—861no—
683C4—861no—
684C4—861no—
685C4—3442no—
686C4#117×D4312yes—
687C4#1458340712yes—
688C2—22no—
689C2—22no—
690C2—41no—
691C2—1724no—
692C2#1913697511yescharacteristic
693C2#421×D4311yescharacteristic
694C2C2×#1458291411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1826C2
socleC22×C43C22×C22⋊C4
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenter#1826D43
hypocenterC43#20748
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
2. #19143224C2semidirect
3. #19136989C2semidirect
4. #19134694C2semidirect
5. #19134614C2semidirect
8. #19134404C2semidirect
9. C43×#1826C2semidirect
15. #14583367C4semidirect
16. #14583367C4semidirect
19. C2×#13063290C4semidirect
20. C2×#13063290C4semidirect
21. C2×#13063287C4semidirect
22. C2×#13063287C4semidirect
32. #14582922C22semidirect
36. M16×Dic43C22semidirect
41. C4×Dic43⋊C4C22semidirect
43. #14582745C22semidirect
44. #14582658C22semidirect
48. C43×#339C22semidirect
345. #1826D43semidirect
395. #339C2×D43semidirect
396. C43#20748semidirect

Maximal subgroups

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

subgroupindex
C2×#145833672
#191432242
#191369892
#191346942
#191346142
#191345402
#191345382
#191344042
C43×#18262
#2074843