Finite Group Databasebeta

← #25064097

Subgroups — #25064097

Order 11008.

1014 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147890C211yesmaximal, characteristic
2#19143225C211yesmaximal, characteristic, complemented
3#19136987C211yesmaximal, characteristic, complemented
4#19133169C214yesmaximal, complemented
5#19133135C214yesmaximal, complemented
6#19133108C211yesmaximal, characteristic, complemented
7#19133106C211yesmaximal, characteristic, complemented
8#19133103C211yesmaximal, characteristic, complemented
9C43×#1505C211yesmaximal, characteristic, complemented
10#14583456C2211yescharacteristic
11#14583454C411yescharacteristic, complemented
12#14583454C411yescharacteristic, complemented
13#14583447C411yescharacteristic, complemented
14#14583447C411yescharacteristic, complemented
15#14583431—21no—
16#14583431C412yescomplemented
17#14583430—21no—
18#14583430C2212yes—
19#14583428—21no—
20#14583428—21no—
21#14583409—21no—
22#14583409C2212yes—
23#14583406—21no—
24#41×Dic43—21no—
25C4×#10621900—21no—
26C4×#10621900C412yescomplemented
27C2×C42×D43C2211yescharacteristic
28#14582956C2211yescharacteristic
29#14582954—21no—
30#14582951—21no—
31#14582949C2212yes—
32#14582921—21no—
33#14582861C2212yes—
34#14582851—21no—
35#14582766C2212yes—
36#14582763—21no—
37#14582761—21no—
38#14582758C2212yes—
39C4×Dic43⋊C4—21no—
40C4×(C2×D43)⋊C4—21no—
41#14582745C2211yescharacteristic
42#14582637C2214yes—
43#14582635C2214yes—
44#14582633C2214yes—
45C43×#532C2211yescharacteristic
46C43×#432C2211yescharacteristic
47C43×#376C2211yescharacteristic
48C43×#327C2214yes—
49C2×#10621900—21no—
50C2×#10621900C2×C412yes—
51C22×C4×D43D411yescharacteristic
52C22×C4×D43D411yescharacteristic
53C22×C4×D43C2311yescharacteristic
54C2×#10621872—22no—
55#13063325C2×C411yescharacteristic
56#13063325C2×C411yescharacteristic
57#13063318—22no—
58#13063318—22no—
59#13063317—21no—
60#13063316—21no—
61#13063316C2×C412yes—
62#13063312—21no—
63#13063312C2×C412yes—
64#13063307—22no—
65#13063307—22no—
66#13063306—22no—
67#13063305—21no—
68#13063305C2×C412yes—
69#13063304—21no—
70#13063304C2312yes—
71#13063301—21no—
72#13063301—21no—
73#13063296—21no—
74#13063296—21no—
75#13063296—21no—
76#13063296C2×C412yes—
77#13063293—22no—
78Q8×Dic43—21no—
79Q8×Dic43—21no—
80C4×Dic86—21no—
81C4×Dic86C2×C412yes—
82#13063290—21no—
83#13063290C2×C412yes—
84D4×Dic43—22no—
85D4×Dic43—22no—
86D4×Dic43—21no—
87D4×Dic43—21no—
88D4×Dic43—21no—
89D4×Dic43C2×C412yes—
90C4×C22⋊D43—22no—
91C4×C22⋊D43—22no—
92(C22⋊D43)⋊C4—22no—
93(C22⋊D43)⋊C4—22no—
94#13063284—21no—
95#13063284—22no—
96#13063283—21no—
97#13063283C2×C412yes—
98#13063281—22no—
99#13063281—22no—
100C2×Dic43⋊C4—22no—
101C2×(C2×D43)⋊C4—22no—
102C2×C4×Dic43—22no—
103C2×C4×Dic43—21no—
104C2×C4×Dic43D411yescharacteristic
105C2×C4×Dic43D411yescharacteristic
106C2×C4×Dic43C2311yescharacteristic
107C42×D43C2×C411yescharacteristic
108C42×D43C2×C411yescharacteristic
109C42×D43C2×C411yescharacteristic
110C42×D43C2×C411yescharacteristic
111C42×D43D411yescharacteristic
112C42×D43D411yescharacteristic
113C42×D43D411yescharacteristic
114C42×D43D411yescharacteristic
115C4⋊(C43⋊C8)—21no—
116Dic43⋊C8—22no—
117C22⋊(C43⋊C8)C2312yes—
118(C2×D43)⋊C8—22no—
119#13063236—21no—
120C8×Dic43—22no—
121C43⋊#95—21no—
122C43⋊#95—22no—
123C43⋊#95—22no—
124C43⋊#95C2312yes—
125C2×#41×C43—21no—
126C4⋊Q8×C43C2×C411yescharacteristic
127#127×C43C2×C411yescharacteristic
128#124×C43—21no—
129#121×C43—21no—
130#121×C43C2312yes—
131C4×D4×C43—21no—
132C4×D4×C43C2×C412yes—
133C2×C42×C43—21no—
134C2×C42×C43C2311yescharacteristic
135C4⋊C8×C43—21no—
136C22⋊C8×C43C2312yes—
137#97×C43—21no—
138#95×C43—21no—
139#95×C43C2312yes—
140C23×D43C2×D411yescharacteristic
141#41×C43—44no—
142C2×Q8×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—22no—
146C2×D4×C43C22×C412yes—
147C22×C4×C43—22no—
148C22×C4×C43—22no—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2411yescharacteristic
152C2×C22⋊D43—22no—
153C2×C22⋊D43—22no—
154C22×Dic43—22no—
155C22×Dic43—22no—
156C22×Dic43—22no—
157C22×Dic43C2×D411yescharacteristic
158C22×Dic43C2×D411yescharacteristic
159C22×Dic43C2×D411yescharacteristic
160#10621900—44no—
161#10621900—44no—
162C2×C4×D43—42no—
163C2×C4×D43—42no—
164C2×C4×D43—42no—
165C2×C4×D43C22⋊C411yescharacteristic
166C2×C4×D43C22⋊C411yescharacteristic
167C2×C4×D43C22⋊C411yescharacteristic
168C2×C4×D43C22⋊C411yescharacteristic
169C2×C4×D43C22⋊C411yescharacteristic
170C2×C4×D43C22⋊C411yescharacteristic
171C2×C4×D43C22⋊C411yescharacteristic
172C2×C4×D43C22⋊C411yescharacteristic
173C2×C4×D43C22×C411yescharacteristic
174C2×C4×D43C22×C411yescharacteristic
175C2×C4×D43C2×D411yescharacteristic
176C2×C4×D43C2×D411yescharacteristic
177C2×Dic86—21no—
178C2×Dic86C22×C412yes—
179C2×C8×C43—22no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43C22×C412yes—
182C22⋊C4×C43—22no—
183C22⋊C4×C43—22no—
184C42×C43—42no—
185C42×C43C22×C411yescharacteristic
186C42×C43C22×C411yescharacteristic
187C42×C43C2×D411yescharacteristic
188C42×C43C2×D411yescharacteristic
189C22⋊Dic43—22no—
190C22⋊Dic43—22no—
191C22⋊Dic43—22no—
192C22⋊Dic43—22no—
193C22⋊Dic43—22no—
194(C2×D43)⋊C4—22no—
195(C2×D43)⋊C4—22no—
196(C2×D43)⋊C4—44no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—22no—
201C4⋊Dic43—22no—
202C4⋊Dic43C22×C412yes—
203Dic43⋊C4—22no—
204Dic43⋊C4—22no—
205Dic43⋊C4—22no—
206Dic43⋊C4—22no—
207Dic43⋊C4—44no—
208C4×Dic43—22no—
209C4×Dic43—22no—
210C4×Dic43—22no—
211C4×Dic43—42no—
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
224C2×C43⋊C8—22no—
225#10621872—44no—
226C23×C43—22no—
227C23×C43C22×D411yescharacteristic
228C22×D43—22no—
229C22×D43—41no—
230C22×D43—41no—
231C22×D43C2×C22⋊C411yescharacteristic
232C22×D43C2×C22⋊C411yescharacteristic
233Q8×C43—42no—
234D4×C43—42no—
235D4×C43—42no—
236D4×C43—44no—
237D4×C43—42no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—41no—
242C2×C4×C43—44no—
243C2×C4×C43—42no—
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×C43C23×C411yescharacteristic
251C2×C4×C43C22×D411yescharacteristic
252C22⋊D43—44no—
253C22⋊D43—44no—
254C2×Dic43—22no—
255C2×Dic43—22no—
256C2×Dic43—22no—
257C2×Dic43—22no—
258C2×Dic43—41no—
259C2×Dic43—44no—
260C2×Dic43—44no—
261C2×Dic43—42no—
262C2×Dic43—42no—
263C2×Dic43—42no—
264C2×Dic43C2×C22⋊C411yescharacteristic
265C2×Dic43C2×C22⋊C411yescharacteristic
266C2×Dic43C2×C22⋊C411yescharacteristic
267C2×Dic43C2×C22⋊C411yescharacteristic
268C2×Dic43C2×C22⋊C411yescharacteristic
269C2×Dic43C2×C22⋊C411yescharacteristic
270C4×D43—22no—
271C4×D43—22no—
272C4×D43—22no—
273C4×D43—22no—
274C4×D43—41no—
275C4×D43—41no—
276C4×D43—41no—
277C4×D43—41no—
278C4×D43—41no—
279C4×D43—41no—
280C4×D43—41no—
281C4×D43—41no—
282Dic86—42no—
283Dic86—42no—
284C8×C43—42no—
285C43⋊C8—42no—
286#17594—431nomaximal, Sylow
287C22×C43—21no—
288C22×C43—21no—
289C22×C43—42no—
290C22×C43—42no—
291C22×C43—42no—
292C22×C43C22×C22⋊C411yescharacteristic
293C22×C43#57512yes—
294C2×D43—21no—
295C2×D43—21no—
296C2×D43—21no—
297C2×D43—21no—
298C2×D43—21no—
299C2×D43—21no—
300C2×D43—44no—
301C4×C43—21no—
302C4×C43—21no—
303C4×C43—21no—
304C4×C43—21no—
305C4×C43—21no—
306C4×C43—42no—
307C4×C43—82no—
308C4×C43#42112yes—
309Dic43—21no—
310Dic43—21no—
311Dic43—21no—
312Dic43—21no—
313Dic43—21no—
314Dic43—42no—
315Dic43—42no—
316Dic43—82no—
317Dic43#41012yes—
318#3444—431no—
319#2920—431no—
320#2283—431no—
321#1521—434no—
322#1513—434no—
323#1506—431no—
324#1506—431no—
325#1505—431no—
326#1505D4311yescharacteristic, complemented
327C2×C43—22no—
328C2×C43—82no—
329C2×C43C2×#41011yescharacteristic
330C2×C43#289611yescharacteristic
331C2×C43C2×#42111yescharacteristic
332D43—41no—
333D43—41no—
334#533—431no—
335#533—431no—
336#533—431no—
337#532—431no—
338#532—431no—
339#532C2×D4311yescharacteristic
340#529—432no—
341#529—432no—
342#529—861no—
343#529—861no—
344#529—861no—
345#529—861no—
346#525—432no—
347#525—861no—
348#525—861no—
349C4×#41—432no—
350C4×#41—861no—
351C4×#41—861no—
352C22×C42—431no—
353#432—431no—
354#432—861no—
355#432C2×D4311yescharacteristic
356#431—432no—
357#431—861no—
358#423—861no—
359#407—432no—
360C4×M16—861no—
361#383—432no—
362#382—861no—
363#381—861no—
364#380—432no—
365C4×C4⋊C4—861no—
366C4×C22⋊C4—861no—
367#376—431no—
368#376C2×D4311yescharacteristic
369#328—434no—
370#328—434no—
371#327—434no—
372#327C2×D4314yes—
373C43#1759411yescharacteristic, complemented, Sylow
374C2×#41—21no—
375C2×#41—432no—
376C2×#41—861no—
377C23×C4—431no—
378C23×C4—431no—
379C23×C4—431no—
380C2×M16—862no—
381C4⋊Q8—431no—
382C4⋊Q8—431no—
383C4⋊Q8C4×D4311yescharacteristic
384#127C4×D4311yescharacteristic
385#126—862no—
386#126—862no—
387#125—432no—
388#125—861no—
389#125—861no—
390#124—21no—
391#124—432no—
392#124—861no—
393#123—862no—
394#123—862no—
395#123—862no—
396C22⋊Q8—432no—
397C22⋊Q8—432no—
398C22⋊Q8—861no—
399C22⋊Q8—861no—
400C22⋊Q8—861no—
401C22⋊Q8—861no—
402#121—21no—
403#121—432no—
404#121—861no—
405#121—861no—
406#121—861no—
407#121C22×D4312yes—
408#120—862no—
409C4×Q8—432no—
410C4×Q8—432no—
411C4×Q8—861no—
412C4×Q8—861no—
413C4×Q8—861no—
414C4×Q8—861no—
415C4×D4—21no—
416C4×D4—432no—
417C4×D4—861no—
418C4×D4—861no—
419C4×D4—861no—
420C4×D4—862no—
421C4×D4—862no—
422C4×D4—862no—
423C4×D4—862no—
424C4×D4—862no—
425C4×D4—862no—
426C4×D4C4×D4312yes—
427#117—432no—
428#117—862no—
429#117—862no—
430#117—862no—
431#117—861no—
432#117—861no—
433C2×C4⋊C4—862no—
434C2×C22⋊C4—862no—
435C2×C42—21no—
436C2×C42—431no—
437C2×C42—431no—
438C2×C42—431no—
439C2×C42—431no—
440C2×C42—431no—
441C2×C42—431no—
442C2×C42—431no—
443C2×C42—431no—
444C2×C42—431no—
445C2×C42—431no—
446C2×C42—431no—
447C2×C42—862no—
448C2×C42—861no—
449C2×C42C22×D4311yescharacteristic
450C4⋊C8—21no—
451C4⋊C8—862no—
452C4⋊C8—861no—
453C22⋊C8—432no—
454C22⋊C8—862no—
455C22⋊C8C22×D4312yes—
456#97—21no—
457#97—861no—
458C4×C8—862no—
459#95—21no—
460#95—432no—
461#95—862no—
462#95—862no—
463#95—861no—
464#95C22×D4312yes—
465C24—431no—
466#41—44no—
467#41—1724no—
468#41—1724no—
469C2×Q8—21no—
470C2×Q8—432no—
471C2×Q8—861no—
472C2×D4—22no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—862no—
476C2×D4—862no—
477C2×D4C2×C4×D4312yes—
478C22×C4—22no—
479C22×C4—22no—
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—431no—
495C22×C4—862no—
496C22×C4—862no—
497C22×C4—862no—
498C22×C4—1722no—
499C22×C4—1722no—
500C22×C4—1722no—
501C22×C4D4×D4311yescharacteristic
502C22×C4D4×D4311yescharacteristic
503C22×C4C23×D4311yescharacteristic
504M16—1724no—
505C2×C8—22no—
506C2×C8—862no—
507C4⋊C4—21no—
508C4⋊C4—432no—
509C4⋊C4—862no—
510C4⋊C4—862no—
511C4⋊C4—862no—
512C4⋊C4—862no—
513C4⋊C4—862no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—862no—
518C4⋊C4—1724no—
519C4⋊C4C2×C4×D4312yes—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—862no—
523C22⋊C4—862no—
524C22⋊C4—862no—
525C22⋊C4—862no—
526C22⋊C4—862no—
527C22⋊C4—862no—
528C22⋊C4—862no—
529C22⋊C4—1724no—
530C42—42no—
531C42—431no—
532C42—431no—
533C42—431no—
534C42—431no—
535C42—431no—
536C42—431no—
537C42—431no—
538C42—431no—
539C42—431no—
540C42—431no—
541C42—431no—
542C42—431no—
543C42—862no—
544C42—862no—
545C42—862no—
546C42—1722no—
547C42C2×C4×D4311yescharacteristic
548C42C2×C4×D4311yescharacteristic
549C42D4×D4311yescharacteristic
550C42D4×D4311yescharacteristic
551C23—22no—
552C23—431no—
553C23—431no—
554C23—862no—
555C23—1721no—
556C23—1721no—
557C23C2×D4×D4311yescharacteristic
558Q8—42no—
559Q8—1722no—
560Q8—1722no—
561D4—42no—
562D4—42no—
563D4—44no—
564D4—42no—
565D4—1724no—
566D4—1724no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—41no—
571C2×C4—44no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—431no—
576C2×C4—431no—
577C2×C4—431no—
578C2×C4—431no—
579C2×C4—431no—
580C2×C4—431no—
581C2×C4—862no—
582C2×C4—862no—
583C2×C4—862no—
584C2×C4—862no—
585C2×C4—862no—
586C2×C4—862no—
587C2×C4—862no—
588C2×C4—862no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1724no—
598C2×C4—1721no—
599C2×C4—1724no—
600C2×C4—1722no—
601C2×C4—1722no—
602C2×C4—1722no—
603C2×C4C22⋊C4×D4311yescharacteristic
604C2×C4C22⋊C4×D4311yescharacteristic
605C2×C4C22⋊C4×D4311yescharacteristic
606C2×C4C22⋊C4×D4311yescharacteristic
607C2×C4C22×C4×D4311yescharacteristic
608C2×C4C2×D4×D4311yescharacteristic
609C8—42no—
610C8—1722no—
611C22—21no—
612C22—21no—
613C22—42no—
614C22—42no—
615C22—42no—
616C22—861no—
617C22—861no—
618C22—861no—
619C22—861no—
620C22—861no—
621C22—861no—
622C22—1724no—
623C22C2×C22⋊C4×D4311yescharacteristic
624C22#1458369512yes—
625C4—21no—
626C4—21no—
627C4—21no—
628C4—21no—
629C4—21no—
630C4—42no—
631C4—82no—
632C4—432no—
633C4—861no—
634C4—861no—
635C4—861no—
636C4—861no—
637C4—861no—
638C4—3442no—
639C4—1722no—
640C4—1722no—
641C4#1458291412yes—
642C2—22no—
643C2—82no—
644C2—1721no—
645C2—1721no—
646C2#410×D4311yescharacteristic
647C2#1914310911yescharacteristic
648C2C2×#1458291411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1505C2
socleC22×C43C22×C22⋊C4
prime radical#19147890C2
cosocleC22×C4×C43C24
hypercenter#1505D43
hypocenterC43#17594
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1505

Complements

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

NH ≅ G/Ntype
2. #19143225C2semidirect
3. #19136987C2semidirect
4. #19133169C2semidirect
5. #19133135C2semidirect
6. #19133108C2semidirect
7. #19133106C2semidirect
8. #19133103C2semidirect
9. C43×#1505C2semidirect
11. #14583454C4semidirect
12. #14583454C4semidirect
13. #14583447C4semidirect
14. #14583447C4semidirect
16. #14583431C4semidirect
26. C4×#10621900C4semidirect
326. #1505D43semidirect
373. C43#17594semidirect

Maximal subgroups

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

subgroupindex
#191478902
#191432252
#191369872
#191331692
#191331352
#191331082
#191331062
#191331032
C43×#15052
#1759443