Finite Group Databasebeta

← #25063767

Subgroups — #25063767

Order 11008.

1108 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147892C211yesmaximal, characteristic
2#432×D43C211yesmaximal, characteristic, complemented
3#19136934C211yesmaximal, characteristic, complemented
4#19133119C214yesmaximal, complemented
5#19133107C211yesmaximal, characteristic, complemented
6#19133104C211yesmaximal, characteristic, complemented
7#19133102C211yesmaximal, characteristic, complemented
8#19133085C214yesmaximal, complemented
9C43×#1506C211yesmaximal, characteristic, complemented
10#14583454C411yescharacteristic, complemented
11#14583454C411yescharacteristic, complemented
12#14583450C411yescharacteristic, complemented
13#14583450C411yescharacteristic, complemented
14#14583449C2211yescharacteristic
15#14583436—21no—
16#14583436C412yescomplemented
17#14583435—21no—
18#14583435C2212yes—
19#14583434—21no—
20#14583434—21no—
21#14583412—21no—
22#14583412C2212yes—
23#14583411—21no—
24C4×#10621902—21no—
25C4×#10621902C412yescomplemented
26#14583367—21no—
27C2×#13063282—21no—
28C2×C42×D43C2211yescharacteristic
29#14582956C2211yescharacteristic
30#14582955—21no—
31#14582954—21no—
32#14582953C2212yes—
33C4⋊C8×D43—21no—
34C22⋊C8×D43C2212yes—
35#97×D43—21no—
36#14582750—21no—
37#14582750C2212yes—
38#14582746—21no—
39#14582746C2212yes—
40#14582745C2211yescharacteristic
41C42×Dic43—21no—
42#14582636C2214yes—
43#14582634C2214yes—
44#14582632C2214yes—
45C43×#533C2211yescharacteristic
46C43×#432C2211yescharacteristic
47C43×#376C2211yescharacteristic
48C43×#328C2214yes—
49C2×#10621902—21no—
50C2×#10621902C2×C412yes—
51C2×#10621898—21no—
52C22×C4×D43D411yescharacteristic
53C22×C4×D43D411yescharacteristic
54C22×C4×D43C2311yescharacteristic
55C2×C8×D43—22no—
56#13063325C2×C411yescharacteristic
57#13063322C2×C411yescharacteristic
58#13063320—22no—
59#13063320—22no—
60#13063316—21no—
61#13063316C2×C412yes—
62#13063314—21no—
63#13063314C2×C412yes—
64#13063313—21no—
65#13063310—22no—
66#13063310—22no—
67#13063309—22no—
68#13063305—21no—
69#13063305—21no—
70#13063301—21no—
71#13063301C2×C412yes—
72#13063300—21no—
73#13063300—21no—
74#13063300—21no—
75#13063300C2×C412yes—
76#13063299—21no—
77#13063299C2312yes—
78#13063295—22no—
79Q8×Dic43—21no—
80Q8×Dic43C2×C412yes—
81#13063290—21no—
82#13063290—21no—
83C4×D172—22no—
84C4×D172—22no—
85C4×D172—21no—
86C4×D172C2×C412yes—
87#13063287—22no—
88#13063287—22no—
89#13063287—21no—
90#13063287—21no—
91#13063287—21no—
92#13063287C2×C412yes—
93(C22⋊D43)⋊C4—22no—
94(C22⋊D43)⋊C4—22no—
95#13063283—21no—
96#13063283—22no—
97#13063283—22no—
98#13063283C2×C412yes—
99#13063282—28no—
100#13063282—22no—
101C2×Dic43⋊C4—22no—
102C2×(C2×D43)⋊C4—22no—
103C2×C4×Dic43—21no—
104C2×C4×Dic43—22no—
105C2×C4×Dic43—22no—
106C2×C4×Dic43D411yescharacteristic
107C2×C4×Dic43D411yescharacteristic
108C2×C4×Dic43C2311yescharacteristic
109C42×D43—22no—
110C42×D43C2×C411yescharacteristic
111C42×D43C2×C411yescharacteristic
112C42×D43C2×C411yescharacteristic
113C42×D43C2×C411yescharacteristic
114C42×D43D411yescharacteristic
115C42×D43D411yescharacteristic
116C42×D43D411yescharacteristic
117C42×D43D411yescharacteristic
118C4⋊(C43⋊C8)—21no—
119Dic43⋊C8—22no—
120C22⋊(C43⋊C8)C2312yes—
121(C2×D43)⋊C8—22no—
122#13063236—21no—
123#13063235—22no—
124C43⋊#95—21no—
125C43⋊#95C2312yes—
126C4⋊Q8×C43C2×C411yescharacteristic
127C4⋊Q8×C43C2×C411yescharacteristic
128#125×C43—21no—
129C22⋊Q8×C43—21no—
130C22⋊Q8×C43C2312yes—
131C4×Q8×C43—21no—
132C4×Q8×C43C2×C412yes—
133#117×C43—21no—
134C2×C42×C43—21no—
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43—21no—
137C22⋊C8×C43C2312yes—
138#97×C43—21no—
139#95×C43—21no—
140#95×C43C2312yes—
141C23×D43C2×D411yescharacteristic
142C2×Q8×C43—21no—
143C2×Q8×C43C22×C412yes—
144C22×C4×C43—22no—
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2411yescharacteristic
148C2×C22⋊D43—22no—
149C22×Dic43—22no—
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153#10621902—44no—
154#10621902—44no—
155#10621898—44no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—22no—
159C2×D172—22no—
160C2×D172C22×C412yes—
161C2×C4×D43—24no—
162C2×C4×D43—22no—
163C2×C4×D43—22no—
164C2×C4×D43—22no—
165C2×C4×D43—42no—
166C2×C4×D43—42no—
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×D43C22×C411yescharacteristic
176C2×C4×D43C22×C411yescharacteristic
177C2×C4×D43C2×D411yescharacteristic
178C2×C4×D43C2×D411yescharacteristic
179C2×Dic86—21no—
180C2×C8×C43—22no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—22no—
185C4⋊C4×C43—22no—
186C4⋊C4×C43C22×C412yes—
187C22⋊C4×C43—22no—
188C42×C43—24no—
189C42×C43—22no—
190C42×C43C22×C411yescharacteristic
191C42×C43C22×C411yescharacteristic
192C42×C43C2×D411yescharacteristic
193C42×C43C2×D411yescharacteristic
194(C2×D43)⋊C4—28no—
195(C2×D43)⋊C4—22no—
196(C2×D43)⋊C4—22no—
197(C2×D43)⋊C4—22no—
198(C2×D43)⋊C4—22no—
199(C2×D43)⋊C4—22no—
200(C2×D43)⋊C4—22no—
201(C2×D43)⋊C4—22no—
202(C2×D43)⋊C4—22no—
203C4⋊Dic43—21no—
204C4⋊Dic43—22no—
205C4⋊Dic43—22no—
206C4⋊Dic43C22×C412yes—
207Dic43⋊C4—28no—
208Dic43⋊C4—22no—
209Dic43⋊C4—22no—
210C4×Dic43—24no—
211C4×Dic43—22no—
212C4×Dic43—22no—
213C4×Dic43—44no—
214C4×Dic43—44no—
215C4×Dic43C22⋊C411yescharacteristic
216C4×Dic43C22⋊C411yescharacteristic
217C4×Dic43C22⋊C411yescharacteristic
218C4×Dic43C22⋊C411yescharacteristic
219C4×Dic43C22⋊C411yescharacteristic
220C4×Dic43C22⋊C411yescharacteristic
221C4×Dic43C22⋊C411yescharacteristic
222C4×Dic43C22⋊C411yescharacteristic
223C4×Dic43C22×C411yescharacteristic
224C4×Dic43C22×C411yescharacteristic
225C4×Dic43C2×D411yescharacteristic
226C4×Dic43C2×D411yescharacteristic
227C2×C43⋊C8—22no—
228C8×D43—44no—
229C23×C43C22×D411yescharacteristic
230C22×D43—22no—
231C22×D43—22no—
232C22×D43—22no—
233C22×D43—41no—
234C22×D43C2×C22⋊C411yescharacteristic
235C22×D43C2×C22⋊C411yescharacteristic
236Q8×C43—42no—
237Q8×C43—42no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—24no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
243C2×C4×C43—41no—
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—
253C2×Dic43—22no—
254C2×Dic43—22no—
255C2×Dic43—22no—
256C2×Dic43—24no—
257C2×Dic43—22no—
258C2×Dic43—42no—
259C2×Dic43—42no—
260C2×Dic43C2×C22⋊C411yescharacteristic
261C2×Dic43C2×C22⋊C411yescharacteristic
262C2×Dic43C2×C22⋊C411yescharacteristic
263C2×Dic43C2×C22⋊C411yescharacteristic
264C2×Dic43C2×C22⋊C411yescharacteristic
265C2×Dic43C2×C22⋊C411yescharacteristic
266D172—42no—
267D172—42no—
268D172—44no—
269D172—44no—
270D172—42no—
271C4×D43—22no—
272C4×D43—22no—
273C4×D43—22no—
274C4×D43—22no—
275C4×D43—22no—
276C4×D43—41no—
277C4×D43—41no—
278C4×D43—41no—
279C4×D43—41no—
280C4×D43—41no—
281C4×D43—41no—
282C4×D43—44no—
283C4×D43—44no—
284C4×D43—44no—
285C4×D43#10414yes—
286Dic86—42no—
287C8×C43—42no—
288C43⋊C8—42no—
289#17543—431nomaximal, Sylow
290C22×C43—21no—
291C22×C43—21no—
292C22×C43C22×C22⋊C411yescharacteristic
293C22×C43#57512yes—
294C2×D43—21no—
295C2×D43—21no—
296C2×D43—21no—
297C2×D43—21no—
298C2×D43—21no—
299C2×D43—44no—
300C2×D43—42no—
301C2×D43—42no—
302C2×D43—42no—
303C2×D43C2×#10412yes—
304C4×C43—21no—
305C4×C43—21no—
306C4×C43—21no—
307C4×C43—21no—
308C4×C43—21no—
309C4×C43—44no—
310C4×C43—42no—
311C4×C43—42no—
312C4×C43C2×#10412yes—
313Dic43—21no—
314Dic43—21no—
315Dic43—21no—
316Dic43—21no—
317Dic43—44no—
318Dic43—42no—
319Dic43#41012yes—
320Dic43C2×#10412yes—
321#3444—431no—
322C2×#432—431no—
323C4×#117—431no—
324#1509—434no—
325#1506—431no—
326#1506D4311yescharacteristic, complemented
327#1505—431no—
328#1505—431no—
329#1501—434no—
330C2×C43—22no—
331C2×C43C2×#41011yescharacteristic
332C2×C43#289611yescharacteristic
333C2×C43C22×#10411yescharacteristic
334D43—22no—
335D43—41no—
336D43—82no—
337#533—431no—
338#533—431no—
339#533C2×D4311yescharacteristic
340#532—431no—
341#532—431no—
342#532—431no—
343#529—432no—
344#529—432no—
345#529—861no—
346#529—861no—
347#529—861no—
348#529—861no—
349#525—432no—
350#525—861no—
351#525—861no—
352C4×#41—432no—
353C4×#41—861no—
354C4×#41—861no—
355C2×#117—861no—
356C22×C42—431no—
357#432—431no—
358#432—432no—
359#432—861no—
360#432—861no—
361#432C2×D4311yescharacteristic
362C2×C4⋊C8—861no—
363C2×C22⋊C8—432no—
364C2×#97—861no—
365C4×C4⋊C4—432no—
366C4×C4⋊C4—861no—
367C4×C22⋊C4—432no—
368C4×C22⋊C4—861no—
369#376—431no—
370#376C2×D4311yescharacteristic
371C43—861no—
372#328—434no—
373#328C2×D4314yes—
374#327—434no—
375#327—434no—
376C43#1754311yescharacteristic, complemented, Sylow
377C2×#41—432no—
378C2×#41—861no—
379C2×#41—861no—
380C23×C4—431no—
381C23×C4—431no—
382C23×C4—431no—
383C22×C8—862no—
384C4⋊Q8—431no—
385C4⋊Q8C4×D4311yescharacteristic
386C4⋊Q8C4×D4311yescharacteristic
387#127—431no—
388#126—862no—
389#126—862no—
390#125—21no—
391#125—432no—
392#125—861no—
393#124—432no—
394#124—861no—
395#124—861no—
396#123—862no—
397#123—862no—
398#123—862no—
399C22⋊Q8—21no—
400C22⋊Q8—432no—
401C22⋊Q8—861no—
402C22⋊Q8—861no—
403C22⋊Q8—861no—
404C22⋊Q8C22×D4312yes—
405#121—432no—
406#121—432no—
407#121—861no—
408#121—861no—
409#121—861no—
410#121—861no—
411#120—862no—
412C4×Q8—21no—
413C4×Q8—432no—
414C4×Q8—861no—
415C4×Q8—861no—
416C4×Q8—861no—
417C4×Q8C4×D4312yes—
418C4×D4—432no—
419C4×D4—432no—
420C4×D4—862no—
421C4×D4—862no—
422C4×D4—861no—
423C4×D4—861no—
424C4×D4—861no—
425C4×D4—862no—
426C4×D4—862no—
427C4×D4—862no—
428C4×D4—862no—
429C4×D4—861no—
430#117—21no—
431#117—432no—
432#117—862no—
433#117—868no—
434#117—862no—
435#117—862no—
436#117—861no—
437C2×C4⋊C4—862no—
438C2×C22⋊C4—862no—
439C2×C42—21no—
440C2×C42—431no—
441C2×C42—431no—
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—862no—
452C2×C42—861no—
453C2×C42—862no—
454C2×C42—862no—
455C2×C42C22×D4311yescharacteristic
456C4⋊C8—21no—
457C4⋊C8—862no—
458C4⋊C8—861no—
459C22⋊C8—432no—
460C22⋊C8—862no—
461C22⋊C8C22×D4312yes—
462#97—21no—
463#97—862no—
464#97—861no—
465#95—21no—
466#95—432no—
467#95—861no—
468#95C22×D4312yes—
469C24—431no—
470#41—1724no—
471#41—1724no—
472#41—1724no—
473C2×Q8—21no—
474C2×Q8—861no—
475C2×Q8C2×C4×D4312yes—
476C2×D4—432no—
477C2×D4—862no—
478C2×D4—862no—
479C2×D4—862no—
480C2×D4—861no—
481C2×D4—861no—
482C22×C4—22no—
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—431no—
496C22×C4—431no—
497C22×C4—431no—
498C22×C4—864no—
499C22×C4—862no—
500C22×C4—862no—
501C22×C4—862no—
502C22×C4—862no—
503C22×C4—1722no—
504C22×C4—1722no—
505C22×C4D4×D4311yescharacteristic
506C22×C4D4×D4311yescharacteristic
507C22×C4C23×D4311yescharacteristic
508C2×C8—22no—
509C2×C8—862no—
510C2×C8—1724no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—432no—
517C4⋊C4—862no—
518C4⋊C4—862no—
519C4⋊C4—862no—
520C4⋊C4—862no—
521C4⋊C4—868no—
522C4⋊C4—861no—
523C4⋊C4C2×C4×D4312yes—
524C22⋊C4—22no—
525C22⋊C4—862no—
526C22⋊C4—862no—
527C22⋊C4—862no—
528C22⋊C4—862no—
529C22⋊C4—862no—
530C22⋊C4—862no—
531C22⋊C4—868no—
532C22⋊C4—862no—
533C22⋊C4—862no—
534C42—24no—
535C42—22no—
536C42—431no—
537C42—431no—
538C42—431no—
539C42—431no—
540C42—431no—
541C42—431no—
542C42—431no—
543C42—431no—
544C42—431no—
545C42—431no—
546C42—431no—
547C42—431no—
548C42—862no—
549C42—862no—
550C42—864no—
551C42—1724no—
552C42—1724no—
553C42C2×C4×D4311yescharacteristic
554C42C2×C4×D4311yescharacteristic
555C42D4×D4311yescharacteristic
556C42D4×D4311yescharacteristic
557C23—431no—
558C23—431no—
559C23—862no—
560C23—862no—
561C23—862no—
562C23—1721no—
563C23C2×D4×D4311yescharacteristic
564Q8—42no—
565Q8—42no—
566Q8—1722no—
567D4—1722no—
568D4—1722no—
569D4—1724no—
570D4—1724no—
571D4—1724no—
572D4—1722no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—24no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—431no—
582C2×C4—431no—
583C2×C4—434no—
584C2×C4—431no—
585C2×C4—431no—
586C2×C4—431no—
587C2×C4—431no—
588C2×C4—862no—
589C2×C4—862no—
590C2×C4—862no—
591C2×C4—862no—
592C2×C4—862no—
593C2×C4—862no—
594C2×C4—862no—
595C2×C4—862no—
596C2×C4—864no—
597C2×C4—862no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1724no—
605C2×C4—1724no—
606C2×C4—1724no—
607C2×C4—1722no—
608C2×C4—1722no—
609C2×C4C22⋊C4×D4311yescharacteristic
610C2×C4C22⋊C4×D4311yescharacteristic
611C2×C4C22⋊C4×D4311yescharacteristic
612C2×C4C22⋊C4×D4311yescharacteristic
613C2×C4C22×C4×D4311yescharacteristic
614C2×C4C2×D4×D4311yescharacteristic
615C8—42no—
616C8—1722no—
617C22—21no—
618C22—21no—
619C22—432no—
620C22—861no—
621C22—861no—
622C22—861no—
623C22—861no—
624C22—861no—
625C22—1724no—
626C22—1722no—
627C22—1722no—
628C22—1722no—
629C22C2×C22⋊C4×D4311yescharacteristic
630C22#1458369812yes—
631C4—21no—
632C4—21no—
633C4—21no—
634C4—21no—
635C4—21no—
636C4—44no—
637C4—42no—
638C4—42no—
639C4—432no—
640C4—432no—
641C4—861no—
642C4—861no—
643C4—861no—
644C4—861no—
645C4—1724no—
646C4—1722no—
647C4#104×D4312yes—
648C2—22no—
649C2—862no—
650C2—3442no—
651C2—1721no—
652C2#410×D4311yescharacteristic
653C2#1914311311yescharacteristic
654C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1506C2
socleC22×C43C22×C22⋊C4
prime radical#19147892C2
cosocleC22×C4×C43C24
hypercenter#1506D43
hypocenterC43#17543
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1506

Complements

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

NH ≅ G/Ntype
2. #432×D43C2semidirect
3. #19136934C2semidirect
4. #19133119C2semidirect
5. #19133107C2semidirect
6. #19133104C2semidirect
7. #19133102C2semidirect
8. #19133085C2semidirect
9. C43×#1506C2semidirect
10. #14583454C4semidirect
11. #14583454C4semidirect
12. #14583450C4semidirect
13. #14583450C4semidirect
16. #14583436C4semidirect
25. C4×#10621902C4semidirect
326. #1506D43semidirect
376. C43#17543semidirect

Maximal subgroups

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

subgroupindex
#191478922
#432×D432
#191369342
#191331192
#191331072
#191331042
#191331022
#191330852
C43×#15062
#1754343