Finite Group Databasebeta

← #25062842

Subgroups — #25062842

Order 11008.

1002 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583612C211yesmaximal, characteristic
2#19143254C212yesmaximal, complemented
3#19132953C212yesmaximal, complemented
4#19132948C212yesmaximal, complemented
5#19132945C212yesmaximal, complemented
6#19132932C211yesmaximal, characteristic, complemented
7#19132928C211yesmaximal, characteristic, complemented
8#19132912C211yesmaximal, characteristic, complemented
9#19132909C211yesmaximal, characteristic, complemented
10#19132908C211yesmaximal, characteristic, complemented
11C43×#1464C211yesmaximal, characteristic, complemented
12#14583612—22no—
13#14583612—22no—
14#14583612—22no—
15#14583612—22no—
16C2×#13063324C411yescharacteristic
17C2×#13063313C411yescharacteristic
18C2×#13063313C2211yescharacteristic
19C2×#13063311C411yescharacteristic
20C2×#13063311C2211yescharacteristic
21C2×#13063300C411yescharacteristic
22C2×#13063299C411yescharacteristic
23C2×#13063298C411yescharacteristic
24C2×#13063298C2211yescharacteristic
25C2×#13063287C2211yescharacteristic
26C2×C4×C22⋊D43C411yescharacteristic
27C2×#13063283C2211yescharacteristic
28C2×#13063282C411yescharacteristic
29C2×#13063282C2211yescharacteristic
30#14582961—22no—
31#14582959—22no—
32#14582953C2212yes—
33#14582952C2212yes—
34#14582949C2212yes—
35#14582924—22no—
36#14582861C2212yes—
37C22⋊C8×D43C2212yes—
38#14582856—22no—
39#14582625C2211yescharacteristic
40#14582625C2211yescharacteristic
41#14582623C2212yes—
42#14582622C2212yes—
43#14582622C2212yes—
44#14582622C2212yes—
45#14582622C2212yes—
46C2×#117×C43C2211yescharacteristic
47C43×#432C2212yes—
48C43×#324C2211yescharacteristic
49C43×#324C2211yescharacteristic
50C43×#323C2212yes—
51C22×Dic86C2×C411yescharacteristic
52C22×Dic86C2×C411yescharacteristic
53C22×D172C2×C411yescharacteristic
54C22×D172C2×C411yescharacteristic
55C22×D172C2×C411yescharacteristic
56C22×C22⋊D43C2×C411yescharacteristic
57C22×C22⋊D43C2×C411yescharacteristic
58C22×C22⋊D43C2×C411yescharacteristic
59C22×C4×D43C2×C411yescharacteristic
60C22×C4×D43C2×C411yescharacteristic
61C22×C4×D43C2311yescharacteristic
62C2×#10621872—22no—
63C2×C8×D43—22no—
64#13063324—22no—
65#13063324—22no—
66#13063313—22no—
67#13063313—22no—
68#13063313—22no—
69#13063313—22no—
70#13063311—22no—
71#13063311—22no—
72#13063311—22no—
73#13063311—22no—
74#13063300—22no—
75#13063300—22no—
76#13063299—22no—
77#13063299—22no—
78#13063298—22no—
79#13063298—22no—
80#13063298—22no—
81#13063298—22no—
82#13063287—22no—
83#13063287—22no—
84C4×C22⋊D43—21no—
85C4×C22⋊D43—21no—
86C4×C22⋊D43—21no—
87C4×C22⋊D43—21no—
88#13063283—22no—
89#13063283—22no—
90#13063282—21no—
91#13063282—21no—
92#13063282—21no—
93#13063282—21no—
94#13063282D412yes—
95#13063282D412yes—
96#13063282D412yes—
97#13063282D412yes—
98C2×C4⋊Dic43C2×C411yescharacteristic
99C2×Dic43⋊C4C2×C411yescharacteristic
100C2×Dic43⋊C4C2×C411yescharacteristic
101C2×Dic43⋊C4C2×C411yescharacteristic
102C2×C22⋊Dic43C2×C411yescharacteristic
103C2×(C2×D43)⋊C4C2×C411yescharacteristic
104C2×(C2×D43)⋊C4C2×C411yescharacteristic
105C2×(C2×D43)⋊C4C2×C411yescharacteristic
106C2×(C2×D43)⋊C4C2×C411yescharacteristic
107C2×(C2×D43)⋊C4C2×C411yescharacteristic
108C2×(C2×D43)⋊C4C2×C411yescharacteristic
109C2×(C2×D43)⋊C4C2×C411yescharacteristic
110C2×(C2×D43)⋊C4C2311yescharacteristic
111C2×(C2×D43)⋊C4C2311yescharacteristic
112C2×C4×Dic43C2×C411yescharacteristic
113C2×C4×Dic43C2×C411yescharacteristic
114C2×C4×Dic43C2311yescharacteristic
115C4⋊(C43⋊C8)—22no—
116Dic43⋊C8—22no—
117Dic43⋊C8—22no—
118C22⋊(C43⋊C8)C2312yes—
119C22⋊(C43⋊C8)C2312yes—
120(C2×D43)⋊C8—22no—
121(C2×D43)⋊C8—22no—
122#13063235—22no—
123C4×C43⋊C8—22no—
124C8×Dic43—22no—
125C23×C4×C43C2×C411yescharacteristic
126#117×C43—22no—
127#117×C43—22no—
128C2×C4⋊C4×C43C2×C411yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C22⋊C4×C43C2×C411yescharacteristic
131C2×C22⋊C4×C43C2311yescharacteristic
132C2×C42×C43C2×C411yescharacteristic
133C2×C42×C43C2311yescharacteristic
134C4⋊C8×C43—22no—
135C22⋊C8×C43C2312yes—
136C22⋊C8×C43C2312yes—
137#97×C43—22no—
138C24×C43C22×C411yescharacteristic
139C23×D43C22×C411yescharacteristic
140C23×D43C22×C411yescharacteristic
141C23×D43C22×C411yescharacteristic
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—22no—
145C22×C4×C43—41no—
146C22×C4×C43C22×C411yescharacteristic
147C22×C4×C43C22×C411yescharacteristic
148C22×C4×C43C22×C411yescharacteristic
149C22×C4×C43C22×C411yescharacteristic
150C22×C4×C43C22×C411yescharacteristic
151C22×C4×C43C2411yescharacteristic
152C2×C22⋊D43—21no—
153C2×C22⋊D43—21no—
154C2×C22⋊D43—22no—
155C2×C22⋊D43—22no—
156C2×C22⋊D43—42no—
157C2×C22⋊D43—81no—
158C2×C22⋊D43—81no—
159C22×Dic43C22×C411yescharacteristic
160C22×Dic43C22×C411yescharacteristic
161C22×Dic43C22×C411yescharacteristic
162C22×Dic43C22×C411yescharacteristic
163C22×Dic43C22×C411yescharacteristic
164C2×D172—22no—
165C2×D172—22no—
166C2×D172—22no—
167C2×D172—22no—
168C2×D172—41no—
169C2×D172—81no—
170C2×D172—81no—
171C2×C4×D43—22no—
172C2×C4×D43—21no—
173C2×C4×D43—21no—
174C2×C4×D43—21no—
175C2×C4×D43—21no—
176C2×C4×D43—41no—
177C2×C4×D43—42no—
178C2×C4×D43—42no—
179C2×C4×D43C2×D412yes—
180C2×C4×D43C2×D412yes—
181C2×Dic86—22no—
182C2×Dic86—22no—
183C2×Dic86—81no—
184C2×Dic86—81no—
185C2×C8×C43—22no—
186C2×C8×C43—22no—
187C4⋊C4×C43—22no—
188C4⋊C4×C43—22no—
189C22⋊C4×C43—22no—
190C22⋊C4×C43—22no—
191C42×C43—21no—
192C42×C43—21no—
193C42×C43C2×D412yes—
194C42×C43C2×D412yes—
195C22⋊Dic43—21no—
196C22⋊Dic43—21no—
197(C2×D43)⋊C4—21no—
198(C2×D43)⋊C4—21no—
199(C2×D43)⋊C4—21no—
200(C2×D43)⋊C4—21no—
201(C2×D43)⋊C4—22no—
202(C2×D43)⋊C4—22no—
203(C2×D43)⋊C4—21no—
204(C2×D43)⋊C4—21no—
205(C2×D43)⋊C4—22no—
206(C2×D43)⋊C4—22no—
207(C2×D43)⋊C4C22⋊C412yes—
208(C2×D43)⋊C4C22⋊C412yes—
209(C2×D43)⋊C4C22⋊C412yes—
210(C2×D43)⋊C4C22⋊C412yes—
211C4⋊Dic43—22no—
212Dic43⋊C4—21no—
213Dic43⋊C4—21no—
214Dic43⋊C4C22⋊C411yescharacteristic
215Dic43⋊C4C22⋊C411yescharacteristic
216Dic43⋊C4C22⋊C411yescharacteristic
217Dic43⋊C4C22⋊C411yescharacteristic
218Dic43⋊C4C22⋊C412yes—
219Dic43⋊C4C22⋊C412yes—
220C4×Dic43—21no—
221C4×Dic43—21no—
222C4×Dic43—21no—
223C4×Dic43—21no—
224C4×Dic43C2×D412yes—
225C4×Dic43C2×D412yes—
226C2×C43⋊C8—22no—
227C2×C43⋊C8—22no—
228#10621872—44no—
229C8×D43—44no—
230C23×C43—21no—
231C23×C43—21no—
232C23×C43—21no—
233C23×C43—41no—
234C23×C43—41no—
235C23×C43C23×C411yescharacteristic
236C22×D43—21no—
237C22×D43—21no—
238C22×D43—21no—
239C22×D43—21no—
240C22×D43—21no—
241C22×D43—21no—
242C22×D43—21no—
243C22×D43—21no—
244C22×D43—41no—
245C22×D43—41no—
246C22×D43—41no—
247C22×D43—41no—
248C22×D43—41no—
249C22×D43—41no—
250C22×D43C2×C22⋊C412yes—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—21no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—42no—
260C2×C4×C43—42no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43C2×C22⋊C411yescharacteristic
264C2×C4×C43C2×C22⋊C411yescharacteristic
265C2×C4×C43C2×C22⋊C412yes—
266C2×C4×C43#13112yes—
267C2×C4×C43C22×D412yes—
268C22⋊D43—42no—
269C22⋊D43—42no—
270C22⋊D43—82no—
271C22⋊D43—82no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—22no—
275C2×Dic43—21no—
276C2×Dic43—21no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43C2×C22⋊C411yescharacteristic
281C2×Dic43C2×C22⋊C411yescharacteristic
282C2×Dic43C2×C22⋊C411yescharacteristic
283C2×Dic43C2×C22⋊C412yes—
284C2×Dic43C2×C22⋊C411yescharacteristic
285D172—44no—
286D172—82no—
287D172—82no—
288C4×D43—24no—
289C4×D43—42no—
290C4×D43—42no—
291C4×D43—42no—
292C4×D43—42no—
293C4×D43—42no—
294Dic86—82no—
295Dic86—82no—
296C8×C43—42no—
297C8×C43—42no—
298C43⋊C8—42no—
299C43⋊C8—42no—
300#17418—431nomaximal, Sylow
301C22×C43—21no—
302C22×C43—21no—
303C22×C43—41no—
304C22×C43—41no—
305C22×C43—41no—
306C22×C43—81no—
307C22×C43—81no—
308C22×C43C22×C22⋊C411yescharacteristic
309C22×C43C2×#13111yescharacteristic
310C22×C43#56811yescharacteristic
311C2×D43—22no—
312C2×D43—22no—
313C2×D43—22no—
314C2×D43—41no—
315C2×D43—41no—
316C2×D43—41no—
317C2×D43—41no—
318C2×D43—41no—
319C2×D43—41no—
320C2×D43—81no—
321C2×D43—81no—
322C2×D43—81no—
323C2×D43—81no—
324C2×D43—81no—
325C2×D43—81no—
326C4×C43—22no—
327C4×C43—21no—
328C4×C43—21no—
329C4×C43—22no—
330C4×C43—22no—
331C4×C43—41no—
332C4×C43—41no—
333Dic43—21no—
334Dic43—21no—
335Dic43—21no—
336Dic43—22no—
337Dic43—41no—
338Dic43—41no—
339Dic43#41012yes—
340C2×#555—431no—
341#2924—432no—
342#1471—432no—
343#1469—432no—
344#1469—432no—
345#1465—431no—
346#1464—431no—
347#1464D4311yescharacteristic, complemented
348#1459—431no—
349#1458—431no—
350#1458—431no—
351C2×C43—21no—
352C2×C43—21no—
353C2×C43—81no—
354C2×C43#288011yescharacteristic
355C2×C43C2×#41011yescharacteristic
356C2×C43#288811yescharacteristic
357D43—42no—
358D43—81no—
359D43—81no—
360#555—862no—
361#555—862no—
362#555—862no—
363#555—862no—
364C2×C4⋊Q8—431no—
365C2×#124—431no—
366C2×#124—431no—
367C2×#124—431no—
368C2×#124—431no—
369C2×#121—431no—
370C2×#121—431no—
371C2×#121—431no—
372C2×#121—431no—
373C2×C4×D4—431no—
374C2×C4×D4—431no—
375C2×#117—431no—
376C2×#117—431no—
377C2×#117—431no—
378C2×#117C2×D4311yescharacteristic
379#433—862no—
380#433—862no—
381#432—432no—
382#432C2×D4312yes—
383#431—432no—
384#431—432no—
385#424—862no—
386#407—432no—
387C2×C22⋊C8—432no—
388#405—862no—
389#324—431no—
390#324—431no—
391#324C2×D4311yescharacteristic
392#324C2×D4311yescharacteristic
393#323—432no—
394#323—432no—
395#323—432no—
396#323—432no—
397#323—432no—
398#323C2×D4312yes—
399C43#1741811yescharacteristic, complemented, Sylow
400C22×Q8—431no—
401C22×Q8—431no—
402C22×D4—431no—
403C22×D4—431no—
404C22×D4—431no—
405C22×D4—431no—
406C22×D4—431no—
407C22×D4—431no—
408C23×C4—431no—
409C23×C4—431no—
410C23×C4—431no—
411C23×C4C4×D4311yescharacteristic
412C2×M16—862no—
413C22×C8—862no—
414C4⋊Q8—862no—
415C4⋊Q8—862no—
416#124—862no—
417#124—862no—
418#124—862no—
419#124—862no—
420#124—862no—
421#124—862no—
422#124—862no—
423#124—862no—
424#121—862no—
425#121—862no—
426#121—862no—
427#121—862no—
428#121—862no—
429#121—862no—
430#121—862no—
431#121—862no—
432C4×D4—862no—
433C4×D4—862no—
434C4×D4—861no—
435C4×D4—861no—
436C4×D4—861no—
437C4×D4—861no—
438#117—22no—
439#117—22no—
440#117—432no—
441#117—432no—
442#117—432no—
443#117—432no—
444#117—861no—
445#117—861no—
446#117—861no—
447#117—861no—
448#117—862no—
449#117—862no—
450C2×C4⋊C4—431no—
451C2×C4⋊C4—431no—
452C2×C4⋊C4—431no—
453C2×C4⋊C4—431no—
454C2×C4⋊C4C4×D4311yescharacteristic
455C2×C4⋊C4C22×D4311yescharacteristic
456C2×C22⋊C4—431no—
457C2×C22⋊C4—431no—
458C2×C22⋊C4—431no—
459C2×C22⋊C4—431no—
460C2×C22⋊C4—431no—
461C2×C22⋊C4—431no—
462C2×C22⋊C4—431no—
463C2×C22⋊C4—431no—
464C2×C22⋊C4—431no—
465C2×C22⋊C4—431no—
466C2×C22⋊C4C4×D4311yescharacteristic
467C2×C22⋊C4C22×D4311yescharacteristic
468C2×C42—431no—
469C2×C42—431no—
470C2×C42—431no—
471C2×C42C4×D4311yescharacteristic
472C2×C42C22×D4311yescharacteristic
473C4⋊C8—22no—
474C4⋊C8—862no—
475C4⋊C8—862no—
476C4⋊C8—862no—
477C22⋊C8—432no—
478C22⋊C8—432no—
479C22⋊C8—862no—
480C22⋊C8—862no—
481C22⋊C8C22×D4312yes—
482C22⋊C8C22×D4312yes—
483#97—22no—
484#97—862no—
485C4×C8—862no—
486C4×C8—862no—
487C24—431no—
488C24—431no—
489C24—431no—
490C24C2×C4×D4311yescharacteristic
491C2×Q8—862no—
492C2×Q8—862no—
493C2×Q8—3441no—
494C2×Q8—3441no—
495C2×D4—862no—
496C2×D4—862no—
497C2×D4—862no—
498C2×D4—861no—
499C2×D4—861no—
500C2×D4—862no—
501C2×D4—862no—
502C2×D4—862no—
503C2×D4—3441no—
504C2×D4—3441no—
505C2×D4—3441no—
506C2×D4—3441no—
507C2×D4—1721no—
508C2×D4—1722no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—41no—
513C22×C4—431no—
514C22×C4—431no—
515C22×C4—431no—
516C22×C4—432no—
517C22×C4—432no—
518C22×C4—431no—
519C22×C4—431no—
520C22×C4—861no—
521C22×C4—861no—
522C22×C4—861no—
523C22×C4—861no—
524C22×C4—862no—
525C22×C4—1721no—
526C22×C4—1722no—
527C22×C4—1722no—
528C22×C4C2×C4×D4311yescharacteristic
529C22×C4C2×C4×D4311yescharacteristic
530C22×C4C2×C4×D4311yescharacteristic
531C22×C4C2×C4×D4311yescharacteristic
532C22×C4C2×C4×D4311yescharacteristic
533C22×C4C23×D4311yescharacteristic
534M16—1724no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8—862no—
538C2×C8—862no—
539C2×C8—1724no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—431no—
543C4⋊C4—431no—
544C4⋊C4—431no—
545C4⋊C4—431no—
546C4⋊C4—432no—
547C4⋊C4—432no—
548C4⋊C4—861no—
549C4⋊C4—861no—
550C4⋊C4—862no—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—432no—
554C22⋊C4—432no—
555C22⋊C4—432no—
556C22⋊C4—432no—
557C22⋊C4—862no—
558C22⋊C4—861no—
559C22⋊C4—861no—
560C22⋊C4—862no—
561C22⋊C4—861no—
562C22⋊C4—861no—
563C22⋊C4—861no—
564C22⋊C4—861no—
565C22⋊C4—861no—
566C22⋊C4—861no—
567C22⋊C4—862no—
568C22⋊C4—862no—
569C42—21no—
570C42—21no—
571C42—432no—
572C42—432no—
573C42—861no—
574C42—861no—
575C42—861no—
576C42—861no—
577C42D4×D4312yes—
578C42D4×D4312yes—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—41no—
583C23—41no—
584C23—432no—
585C23—861no—
586C23—861no—
587C23—861no—
588C23—861no—
589C23—861no—
590C23—861no—
591C23—861no—
592C23—861no—
593C23—1721no—
594C23—1721no—
595C23—1721no—
596C23—1721no—
597C23—1721no—
598C23—1721no—
599C23C22×C4×D4311yescharacteristic
600Q8—3442no—
601Q8—3442no—
602D4—3442no—
603D4—3442no—
604D4—3442no—
605D4—3442no—
606D4—1724no—
607D4—1722no—
608D4—1722no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—431no—
622C2×C4—431no—
623C2×C4—431no—
624C2×C4—432no—
625C2×C4—431no—
626C2×C4—864no—
627C2×C4—862no—
628C2×C4—861no—
629C2×C4—861no—
630C2×C4—861no—
631C2×C4—861no—
632C2×C4—1722no—
633C2×C4—1722no—
634C2×C4—1722no—
635C2×C4—1722no—
636C2×C4—1722no—
637C2×C4—1721no—
638C2×C4—1721no—
639C2×C4—1721no—
640C2×C4C22⋊C4×D4311yescharacteristic
641C2×C4C22⋊C4×D4311yescharacteristic
642C2×C4C22⋊C4×D4312yes—
643C2×C4#1306333312yes—
644C2×C4C2×D4×D4312yes—
645C8—42no—
646C8—42no—
647C8—1722no—
648C8—1722no—
649C22—21no—
650C22—21no—
651C22—41no—
652C22—41no—
653C22—41no—
654C22—81no—
655C22—81no—
656C22—862no—
657C22—862no—
658C22—862no—
659C22—3441no—
660C22—3441no—
661C22—3441no—
662C22—3441no—
663C22—3441no—
664C22—3441no—
665C22—1721no—
666C22—1721no—
667C22—1721no—
668C22—1721no—
669C22—1721no—
670C22—1721no—
671C22C2×C22⋊C4×D4311yescharacteristic
672C22C2×#1306333311yescharacteristic
673C22#1458366511yescharacteristic
674C4—22no—
675C4—21no—
676C4—21no—
677C4—22no—
678C4—22no—
679C4—41no—
680C4—41no—
681C4—432no—
682C4—861no—
683C4—861no—
684C4—861no—
685C4—862no—
686C4—1721no—
687C4—1721no—
688C2—21no—
689C2—21no—
690C2—81no—
691C2—3441no—
692C2—3441no—
693C2—1722no—
694C2#1914304511yescharacteristic
695C2#410×D4311yescharacteristic
696C2#1914307211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1464C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583612C2
cosocleC22×C4×C43C24
hypercenter#1464D43
hypocenterC43#17418
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1464

Complements

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

NH ≅ G/Ntype
2. #19143254C2semidirect
3. #19132953C2semidirect
4. #19132948C2semidirect
5. #19132945C2semidirect
6. #19132932C2semidirect
7. #19132928C2semidirect
8. #19132912C2semidirect
9. #19132909C2semidirect
10. #19132908C2semidirect
11. C43×#1464C2semidirect
347. #1464D43semidirect
399. C43#17418semidirect

Maximal subgroups

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

subgroupindex
C2×#145836122
#191432542
#191329532
#191329482
#191329452
#191329322
#191329282
#191329122
#191329092
#191329082
C43×#14642
#1741843