Finite Group Databasebeta

← #25062809

Subgroups — #25062809

Order 11008.

1008 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583598C211yesmaximal, characteristic
2#19143248C212yesmaximal, complemented
3#19132962C212yesmaximal, complemented
4#19132961C212yesmaximal, complemented
5#19132953C212yesmaximal, complemented
6#19132936C211yesmaximal, characteristic, complemented
7#19132934C211yesmaximal, characteristic, complemented
8#19132930C211yesmaximal, characteristic, complemented
9#19132914C211yesmaximal, characteristic, complemented
10#19132910C211yesmaximal, characteristic, complemented
11C43×#1460C211yesmaximal, characteristic, complemented
12#14583598—22no—
13#14583598—22no—
14#14583598—22no—
15#14583598—22no—
16C2×#13063319C2211yescharacteristic
17C2×#13063318C2211yescharacteristic
18C2×#13063315C411yescharacteristic
19C2×#13063310C411yescharacteristic
20C2×#13063308C411yescharacteristic
21C2×#13063299C411yescharacteristic
22C2×#13063298C2211yescharacteristic
23C2×#13063297C411yescharacteristic
24C2×#13063297C411yescharacteristic
25C2×C4×C22⋊D43C411yescharacteristic
26C2×(C22⋊D43)⋊C4C2211yescharacteristic
27C2×(C22⋊D43)⋊C4C2211yescharacteristic
28C2×#13063282C2211yescharacteristic
29C22×Dic43⋊C4C411yescharacteristic
30#14582959—22no—
31#14582958—22no—
32#14582956C2212yes—
33#14582953C2212yes—
34#14582949C2212yes—
35#14582924—22no—
36#14582861C2212yes—
37C22⋊C8×D43C2212yes—
38#14582853—22no—
39#14582624C2212yes—
40#14582624C2212yes—
41#14582623C2211yescharacteristic
42#14582623C2211yescharacteristic
43#14582623C2212yes—
44#14582622C2212yes—
45#14582622C2212yes—
46C2×C4×D4×C43C2211yescharacteristic
47C43×#431C2212yes—
48C43×#323C2211yescharacteristic
49C43×#323C2212yes—
50C43×#323C2211yescharacteristic
51C22×D172C2×C411yescharacteristic
52C22×C22⋊D43C2×C411yescharacteristic
53C22×C22⋊D43C2×C411yescharacteristic
54C22×C22⋊D43C2×C411yescharacteristic
55C22×C22⋊D43C2×C411yescharacteristic
56C23×Dic43C2×C411yescharacteristic
57C23×Dic43C2×C411yescharacteristic
58C22×C4×D43C2×C411yescharacteristic
59C22×C4×D43C2311yescharacteristic
60C2×#10621872—22no—
61C2×C8×D43—22no—
62#13063319—22no—
63#13063319—22no—
64#13063318—22no—
65#13063318—22no—
66#13063315—22no—
67#13063315—22no—
68#13063310—22no—
69#13063310—22no—
70#13063308—22no—
71#13063308—22no—
72#13063299—22no—
73#13063299—22no—
74#13063298—22no—
75#13063298—22no—
76#13063297—22no—
77#13063297—22no—
78#13063297—22no—
79#13063297—22no—
80C4×C22⋊D43—21no—
81C4×C22⋊D43—21no—
82C4×C22⋊D43—21no—
83C4×C22⋊D43—21no—
84(C22⋊D43)⋊C4—22no—
85(C22⋊D43)⋊C4—22no—
86(C22⋊D43)⋊C4—22no—
87(C22⋊D43)⋊C4—22no—
88#13063282D412yes—
89#13063282D412yes—
90#13063282D412yes—
91#13063282D412yes—
92C2×C4⋊Dic43C2×C411yescharacteristic
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4C2×C411yescharacteristic
98C2×Dic43⋊C4C2×C411yescharacteristic
99C2×Dic43⋊C4C2×C411yescharacteristic
100C2×Dic43⋊C4C2×C411yescharacteristic
101C2×Dic43⋊C4C2×C411yescharacteristic
102C2×Dic43⋊C4C2×C411yescharacteristic
103C2×Dic43⋊C4C2×C411yescharacteristic
104C2×Dic43⋊C4C2311yescharacteristic
105C2×C22⋊Dic43C2×C411yescharacteristic
106C2×C22⋊Dic43C2×C411yescharacteristic
107C2×(C2×D43)⋊C4C2×C411yescharacteristic
108C2×(C2×D43)⋊C4C2×C411yescharacteristic
109C2×(C2×D43)⋊C4C2×C411yescharacteristic
110C2×(C2×D43)⋊C4C2×C411yescharacteristic
111C2×(C2×D43)⋊C4C2×C411yescharacteristic
112C2×(C2×D43)⋊C4C2311yescharacteristic
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#13063236—22no—
123#13063235—22no—
124C8×Dic43—22no—
125C22×D4×C43C2×C411yescharacteristic
126C23×C4×C43C2×C411yescharacteristic
127C23×C4×C43C2×C411yescharacteristic
128C4×D4×C43—22no—
129C4×D4×C43—22no—
130C2×C4⋊C4×C43C2×C411yescharacteristic
131C2×C22⋊C4×C43C2311yescharacteristic
132C2×C22⋊C4×C43C2311yescharacteristic
133C2×C42×C43C2311yescharacteristic
134C4⋊C8×C43—22no—
135C22⋊C8×C43C2312yes—
136C22⋊C8×C43C2312yes—
137C4×C8×C43—22no—
138C24×C43C22×C411yescharacteristic
139C24×C43C22×C411yescharacteristic
140C23×D43C22×C411yescharacteristic
141C23×D43C22×C411yescharacteristic
142C2×D4×C43—22no—
143C2×D4×C43—22no—
144C2×D4×C43—41no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—81no—
150C22×C4×C43—81no—
151C22×C4×C43C22×C411yescharacteristic
152C22×C4×C43C22×C411yescharacteristic
153C22×C4×C43C22×C411yescharacteristic
154C22×C4×C43C22×C411yescharacteristic
155C22×C4×C43C2411yescharacteristic
156C2×C22⋊D43—22no—
157C2×C22⋊D43—21no—
158C2×C22⋊D43—21no—
159C2×C22⋊D43—22no—
160C2×C22⋊D43—22no—
161C2×C22⋊D43—22no—
162C2×C22⋊D43—22no—
163C2×C22⋊D43—41no—
164C2×C22⋊D43—41no—
165C2×C22⋊D43—42no—
166C2×C22⋊D43—81no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43—42no—
172C22×Dic43—81no—
173C22×Dic43C22×C411yescharacteristic
174C22×Dic43C22×C411yescharacteristic
175C22×Dic43C22×C411yescharacteristic
176C22×Dic43C22×C411yescharacteristic
177C22×Dic43C22×C411yescharacteristic
178C22×Dic43C22×C411yescharacteristic
179C2×D172—22no—
180C2×D172—81no—
181C2×C4×D43—21no—
182C2×C4×D43—21no—
183C2×C4×D43—42no—
184C2×C4×D43—81no—
185C2×C4×D43C2×D412yes—
186C2×C4×D43C2×D412yes—
187C2×C8×C43—22no—
188C2×C8×C43—22no—
189C4⋊C4×C43—22no—
190C22⋊C4×C43—22no—
191C22⋊C4×C43—22no—
192C42×C43C2×D412yes—
193C42×C43C2×D412yes—
194C22⋊Dic43—21no—
195C22⋊Dic43—21no—
196C22⋊Dic43—22no—
197(C2×D43)⋊C4—21no—
198(C2×D43)⋊C4—21no—
199(C2×D43)⋊C4—22no—
200(C2×D43)⋊C4—22no—
201(C2×D43)⋊C4—22no—
202(C2×D43)⋊C4C22⋊C412yes—
203(C2×D43)⋊C4C22⋊C412yes—
204(C2×D43)⋊C4C22⋊C412yes—
205(C2×D43)⋊C4C22⋊C412yes—
206C4⋊Dic43—22no—
207Dic43⋊C4—21no—
208Dic43⋊C4—21no—
209Dic43⋊C4—22no—
210Dic43⋊C4—22no—
211Dic43⋊C4—21no—
212Dic43⋊C4—21no—
213Dic43⋊C4—21no—
214Dic43⋊C4—21no—
215Dic43⋊C4—22no—
216Dic43⋊C4C22⋊C411yescharacteristic
217Dic43⋊C4C22⋊C411yescharacteristic
218Dic43⋊C4C22⋊C411yescharacteristic
219Dic43⋊C4C22⋊C411yescharacteristic
220Dic43⋊C4C22⋊C412yes—
221Dic43⋊C4C22⋊C412yes—
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—21no—
234C23×C43—21no—
235C23×C43—41no—
236C23×C43—41no—
237C23×C43—41no—
238C23×C43—41no—
239C23×C43#13112yes—
240C23×C43C23×C411yescharacteristic
241C22×D43—21no—
242C22×D43—21no—
243C22×D43—21no—
244C22×D43—21no—
245C22×D43—21no—
246C22×D43—41no—
247C22×D43—41no—
248C22×D43—41no—
249C22×D43—41no—
250C22×D43C2×C22⋊C412yes—
251D4×C43—44no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—81no—
261C2×C4×C43—81no—
262C2×C4×C43—81no—
263C2×C4×C43—81no—
264C2×C4×C43C2×C22⋊C412yes—
265C2×C4×C43C2×C22⋊C411yescharacteristic
266C2×C4×C43C2×C22⋊C411yescharacteristic
267C2×C4×C43C22×D412yes—
268C22⋊D43—44no—
269C22⋊D43—42no—
270C22⋊D43—44no—
271C22⋊D43—42no—
272C22⋊D43—82no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—22no—
276C2×Dic43—21no—
277C2×Dic43—21no—
278C2×Dic43—21no—
279C2×Dic43—21no—
280C2×Dic43—21no—
281C2×Dic43—41no—
282C2×Dic43—42no—
283C2×Dic43—42no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—81no—
287C2×Dic43—81no—
288C2×Dic43C2×C22⋊C411yescharacteristic
289C2×Dic43C2×C22⋊C412yes—
290C2×Dic43C2×C22⋊C411yescharacteristic
291C2×Dic43C2×C22⋊C411yescharacteristic
292C2×Dic43C2×C22⋊C411yescharacteristic
293D172—82no—
294C4×D43—24no—
295C4×D43—42no—
296C4×D43—81no—
297C4×D43—81no—
298C8×C43—42no—
299C8×C43—42no—
300C43⋊C8—42no—
301C43⋊C8—42no—
302#17415—431nomaximal, Sylow
303C22×C43—21no—
304C22×C43—21no—
305C22×C43—22no—
306C22×C43—42no—
307C22×C43—42no—
308C22×C43—41no—
309C22×C43—41no—
310C22×C43—41no—
311C22×C43—41no—
312C22×C43—41no—
313C22×C43—81no—
314C22×C43—81no—
315C22×C43C22×C22⋊C411yescharacteristic
316C22×C43C2×#13111yescharacteristic
317C22×C43#56811yescharacteristic
318C2×D43—22no—
319C2×D43—22no—
320C2×D43—22no—
321C2×D43—41no—
322C2×D43—41no—
323C2×D43—41no—
324C2×D43—81no—
325C2×D43—81no—
326C2×D43—81no—
327C2×D43—81no—
328C4×C43—22no—
329C4×C43—22no—
330C4×C43—21no—
331C4×C43—21no—
332C4×C43—41no—
333C4×C43—41no—
334Dic43—22no—
335Dic43—21no—
336Dic43—21no—
337Dic43—21no—
338Dic43—41no—
339Dic43—41no—
340Dic43—41no—
341Dic43#41012yes—
342C2×#553—431no—
343#2924—432no—
344#1473—432no—
345#1473—432no—
346#1471—432no—
347#1466—431no—
348#1466—431no—
349#1465—431no—
350#1460—431no—
351#1460D4311yescharacteristic, complemented
352#1459—431no—
353C2×C43—21no—
354C2×C43—21no—
355C2×C43—42no—
356C2×C43—81no—
357C2×C43#288011yescharacteristic
358C2×C43C2×#41011yescharacteristic
359C2×C43#288811yescharacteristic
360D43—42no—
361D43—81no—
362#553—862no—
363#553—862no—
364#553—862no—
365#553—862no—
366C2×#126—431no—
367C2×#126—431no—
368C2×#125—431no—
369C2×#123—431no—
370C2×#123—431no—
371C2×#121—431no—
372C2×#121—431no—
373C2×#121—431no—
374C2×#121—431no—
375C2×C4×D4—431no—
376C2×C4×D4—431no—
377C2×C4×D4—431no—
378C2×C4×D4C2×D4311yescharacteristic
379C2×#117—431no—
380C22×C4⋊C4—431no—
381#433—862no—
382#433—862no—
383#432—432no—
384#432—432no—
385#431—432no—
386#431C2×D4312yes—
387#424—862no—
388#407—432no—
389C2×C22⋊C8—432no—
390#405—862no—
391#324—432no—
392#324—432no—
393#323—431no—
394#323—431no—
395#323—432no—
396#323—432no—
397#323—432no—
398#323C2×D4311yescharacteristic
399#323C2×D4311yescharacteristic
400#323C2×D4312yes—
401C43#1741511yescharacteristic, complemented, Sylow
402C22×D4—431no—
403C22×D4—431no—
404C22×D4—431no—
405C22×D4—431no—
406C22×D4—431no—
407C22×D4C4×D4311yescharacteristic
408C23×C4—431no—
409C23×C4—431no—
410C23×C4—431no—
411C23×C4—431no—
412C23×C4C4×D4311yescharacteristic
413C23×C4C4×D4311yescharacteristic
414C2×M16—862no—
415C22×C8—862no—
416#126—862no—
417#126—862no—
418#126—862no—
419#126—862no—
420#125—862no—
421#125—862no—
422#123—862no—
423#123—862no—
424#123—862no—
425#123—862no—
426#121—862no—
427#121—862no—
428#121—862no—
429#121—862no—
430#121—862no—
431#121—862no—
432#121—862no—
433#121—862no—
434C4×D4—22no—
435C4×D4—22no—
436C4×D4—862no—
437C4×D4—862no—
438C4×D4—862no—
439C4×D4—862no—
440C4×D4—861no—
441C4×D4—861no—
442C4×D4—861no—
443C4×D4—861no—
444#117—432no—
445#117—432no—
446#117—432no—
447#117—432no—
448C2×C4⋊C4—431no—
449C2×C4⋊C4—431no—
450C2×C4⋊C4—431no—
451C2×C4⋊C4—431no—
452C2×C4⋊C4—431no—
453C2×C4⋊C4—431no—
454C2×C4⋊C4—431no—
455C2×C4⋊C4—431no—
456C2×C4⋊C4—431no—
457C2×C4⋊C4—861no—
458C2×C4⋊C4—861no—
459C2×C4⋊C4—861no—
460C2×C4⋊C4—861no—
461C2×C4⋊C4C4×D4311yescharacteristic
462C2×C22⋊C4—431no—
463C2×C22⋊C4—431no—
464C2×C22⋊C4—431no—
465C2×C22⋊C4—431no—
466C2×C22⋊C4—431no—
467C2×C22⋊C4—431no—
468C2×C22⋊C4—431no—
469C2×C22⋊C4—431no—
470C2×C22⋊C4C22×D4311yescharacteristic
471C2×C22⋊C4C22×D4311yescharacteristic
472C2×C42—431no—
473C2×C42—431no—
474C2×C42C22×D4311yescharacteristic
475C4⋊C8—22no—
476C4⋊C8—862no—
477C4⋊C8—862no—
478C4⋊C8—862no—
479C22⋊C8—432no—
480C22⋊C8—432no—
481C22⋊C8—862no—
482C22⋊C8—862no—
483C22⋊C8C22×D4312yes—
484C22⋊C8C22×D4312yes—
485#97—862no—
486#97—862no—
487C4×C8—22no—
488C4×C8—862no—
489C24—431no—
490C24—431no—
491C24C2×C4×D4311yescharacteristic
492C24C2×C4×D4311yescharacteristic
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—41no—
496C2×D4—862no—
497C2×D4—861no—
498C2×D4—862no—
499C2×D4—861no—
500C2×D4—862no—
501C2×D4—862no—
502C2×D4—862no—
503C2×D4—862no—
504C2×D4—3441no—
505C2×D4—3441no—
506C2×D4—1721no—
507C2×D4—1721no—
508C2×D4—1722no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—81no—
514C22×C4—81no—
515C22×C4—431no—
516C22×C4—431no—
517C22×C4—431no—
518C22×C4—432no—
519C22×C4—432no—
520C22×C4—431no—
521C22×C4—431no—
522C22×C4—431no—
523C22×C4—861no—
524C22×C4—861no—
525C22×C4—861no—
526C22×C4—861no—
527C22×C4—861no—
528C22×C4—861no—
529C22×C4—3441no—
530C22×C4—3441no—
531C22×C4—1722no—
532C22×C4—1722no—
533C22×C4C2×C4×D4311yescharacteristic
534C22×C4C2×C4×D4311yescharacteristic
535C22×C4C2×C4×D4311yescharacteristic
536C22×C4C2×C4×D4311yescharacteristic
537C22×C4C23×D4311yescharacteristic
538M16—1724no—
539C2×C8—22no—
540C2×C8—22no—
541C2×C8—862no—
542C2×C8—862no—
543C2×C8—1724no—
544C4⋊C4—22no—
545C4⋊C4—431no—
546C4⋊C4—431no—
547C4⋊C4—431no—
548C4⋊C4—431no—
549C4⋊C4—432no—
550C4⋊C4—432no—
551C4⋊C4—861no—
552C4⋊C4—861no—
553C4⋊C4—861no—
554C4⋊C4—861no—
555C4⋊C4—862no—
556C4⋊C4—862no—
557C4⋊C4—861no—
558C4⋊C4—861no—
559C4⋊C4—862no—
560C4⋊C4—862no—
561C22⋊C4—22no—
562C22⋊C4—22no—
563C22⋊C4—432no—
564C22⋊C4—432no—
565C22⋊C4—432no—
566C22⋊C4—432no—
567C22⋊C4—862no—
568C22⋊C4—861no—
569C22⋊C4—861no—
570C22⋊C4—862no—
571C22⋊C4—861no—
572C22⋊C4—861no—
573C22⋊C4—862no—
574C22⋊C4—862no—
575C42—432no—
576C42—432no—
577C42—861no—
578C42—861no—
579C42D4×D4312yes—
580C42D4×D4312yes—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—432no—
591C23—861no—
592C23—861no—
593C23—861no—
594C23—861no—
595C23—861no—
596C23—1721no—
597C23—1721no—
598C23—1721no—
599C23—1721no—
600C23#1306333112yes—
601C23C22×C4×D4311yescharacteristic
602D4—44no—
603D4—3442no—
604D4—3442no—
605D4—1722no—
606D4—1724no—
607D4—1722no—
608D4—1724no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—81no—
618C2×C4—81no—
619C2×C4—81no—
620C2×C4—81no—
621C2×C4—431no—
622C2×C4—432no—
623C2×C4—431no—
624C2×C4—431no—
625C2×C4—431no—
626C2×C4—864no—
627C2×C4—862no—
628C2×C4—861no—
629C2×C4—861no—
630C2×C4—861no—
631C2×C4—861no—
632C2×C4—861no—
633C2×C4—861no—
634C2×C4—861no—
635C2×C4—3441no—
636C2×C4—3441no—
637C2×C4—3441no—
638C2×C4—3441no—
639C2×C4—1722no—
640C2×C4—1722no—
641C2×C4—1721no—
642C2×C4—1722no—
643C2×C4—1721no—
644C2×C4—1721no—
645C2×C4C22⋊C4×D4312yes—
646C2×C4C22⋊C4×D4311yescharacteristic
647C2×C4C22⋊C4×D4311yescharacteristic
648C2×C4C2×D4×D4312yes—
649C8—42no—
650C8—42no—
651C8—1722no—
652C8—1722no—
653C22—21no—
654C22—21no—
655C22—22no—
656C22—42no—
657C22—42no—
658C22—41no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—81no—
664C22—81no—
665C22—862no—
666C22—862no—
667C22—862no—
668C22—3441no—
669C22—3441no—
670C22—3441no—
671C22—3441no—
672C22—1721no—
673C22—1721no—
674C22—1721no—
675C22C2×C22⋊C4×D4311yescharacteristic
676C22C2×#1306333111yescharacteristic
677C22#1458366511yescharacteristic
678C4—22no—
679C4—22no—
680C4—21no—
681C4—21no—
682C4—41no—
683C4—41no—
684C4—432no—
685C4—862no—
686C4—861no—
687C4—861no—
688C4—861no—
689C4—1721no—
690C4—1721no—
691C4—1721no—
692C2—21no—
693C2—21no—
694C2—42no—
695C2—81no—
696C2—3441no—
697C2—1722no—
698C2#1914304111yescharacteristic
699C2#410×D4311yescharacteristic
700C2#1914307111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1460C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583598C2
cosocleC22×C4×C43C24
hypercenter#1460D43
hypocenterC43#17415
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1460

Complements

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

NH ≅ G/Ntype
2. #19143248C2semidirect
3. #19132962C2semidirect
4. #19132961C2semidirect
5. #19132953C2semidirect
6. #19132936C2semidirect
7. #19132934C2semidirect
8. #19132930C2semidirect
9. #19132914C2semidirect
10. #19132910C2semidirect
11. C43×#1460C2semidirect
351. #1460D43semidirect
401. C43#17415semidirect

Maximal subgroups

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

subgroupindex
C2×#145835982
#191432482
#191329622
#191329612
#191329532
#191329362
#191329342
#191329302
#191329142
#191329102
C43×#14602
#1741543