Finite Group Databasebeta

← #25063173

Subgroups — #25063173

Order 11008.

984 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148011C211yesmaximal, characteristic
2#19143704C211yesmaximal, characteristic, complemented
3#19143556C211yesmaximal, characteristic, complemented
4#19133010C212yesmaximal, complemented
5#19133007C212yesmaximal, complemented
6#19133002C212yesmaximal, complemented
7#19132992C212yesmaximal, complemented
8#19132987C211yesmaximal, characteristic, complemented
9#19132977C211yesmaximal, characteristic, complemented
10C2×#14582626C211yesmaximal, characteristic, complemented
11C43×#1477C211yesmaximal, characteristic, complemented
12#14583527C411yescharacteristic
13#14583521C412yes—
14#14583520—21no—
15#14583504—21no—
16#14583500C412yes—
17#14583482—22no—
18#14583477C411yescharacteristic
19#14583468C411yescharacteristic
20#14583463C411yescharacteristic
21#14583449—21no—
22#14583446C2212yes—
23#14583436C2212yes—
24#14583433—21no—
25#14583408—22no—
26C4×#10621898C2211yescharacteristic
27C2×C4×D172C2211yescharacteristic
28#14583026—21no—
29#14583023—21no—
30#14582976—21no—
31#14582967—22no—
32#14582964—21no—
33C8×C22⋊D43—22no—
34#14582952C2211yescharacteristic
35#14582951C2212yescomplemented
36#14582950C2212yescomplemented
37C4⋊C8×D43C2212yescomplemented
38C4×#10621872C2212yescomplemented
39C2×C4×C43⋊C8C2211yescharacteristic
40Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
41Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
42#14582628C2212yes—
43#14582628C2212yes—
44D4⋊(C43⋊C8)C2211yescharacteristic, complemented
45D4⋊(C43⋊C8)C2211yescharacteristic, complemented
46#14582626C2212yes—
47#14582626C2212yes—
48C4×#41×C43C2211yescharacteristic
49C43×#431C2211yescharacteristic
50C2×C4⋊C8×C43C2211yescharacteristic
51C43×Q8⋊C8C2212yescomplemented
52C43×D4⋊C8C2212yescomplemented
53C2×#10621898—22no—
54C2×#10621898C2×C411yescharacteristic
55C22×D172C2×C411yescharacteristic
56C22×C4×D43—21no—
57C2×#10621872—22no—
58C22×C43⋊C8—21no—
59C2×C8×D43—22no—
60#13063325—21no—
61#13063324C2×C412yes—
62#13063322—21no—
63#13063321C2×C412yes—
64#13063320—22no—
65#13063319—22no—
66#13063317—21no—
67#13063316C2×C412yes—
68#13063314C2×C412yes—
69#13063313—21no—
70#13063313—22no—
71#13063311—22no—
72#13063310—22no—
73#13063310—22no—
74#13063308—22no—
75#13063307—22no—
76#13063304—21no—
77#13063303—22no—
78#13063302—22no—
79#13063301C2×C412yes—
80#13063300C2×C412yes—
81#13063300C2×C412yes—
82#13063299—21no—
83#13063299—22no—
84#13063299—21no—
85#13063299—21no—
86#13063298—22no—
87#13063298—22no—
88#13063297—22no—
89#13063296C2×C412yes—
90#13063295—22no—
91#13063293—22no—
92C4×Dic86D411yescharacteristic
93C4×Dic86D411yescharacteristic
94C4×D172—22no—
95C4×D172—21no—
96C4×D172—21no—
97C4×D172C2×C412yes—
98C4×D172D411yescharacteristic
99C4×D172D411yescharacteristic
100C4×D172C2312yes—
101C4×C22⋊D43—22no—
102C4×C22⋊D43D412yes—
103C4×C22⋊D43D412yes—
104#13063284C2×C411yescharacteristic
105#13063282—22no—
106#13063282C2×C412yes—
107C2×C4⋊Dic43C2×C411yescharacteristic
108C2×(C2×D43)⋊C4—21no—
109C42×D43C2312yes—
110C4⋊(C43⋊C8)C2311yescharacteristic
111C4⋊(C43⋊C8)C2311yescharacteristic
112Dic43⋊C8—22no—
113Dic43⋊C8—22no—
114C22⋊(C43⋊C8)—21no—
115(C2×D43)⋊C8—22no—
116(C2×D43)⋊C8—22no—
117#13063235—22no—
118C4×C43⋊C8—21no—
119C4×C43⋊C8—21no—
120C4×C43⋊C8C2311yescharacteristic
121C4×C43⋊C8C2311yescharacteristic
122C8×Dic43—22no—
123C2×#41×C43C2×C411yescharacteristic
124C22×C8×C43—21no—
125C4×Q8×C43C2×C411yescharacteristic
126C4×Q8×C43C2311yescharacteristic
127C4×D4×C43—21no—
128C4×D4×C43—21no—
129C4×D4×C43C2×C411yescharacteristic
130C4×D4×C43C2311yescharacteristic
131#117×C43—21no—
132#117×C43C2×C411yescharacteristic
133C2×C42×C43—21no—
134C2×C42×C43C2311yescharacteristic
135C4⋊C8×C43—21no—
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2312yes—
138C22⋊C8×C43—21no—
139C4×C8×C43C2312yes—
140C23×D43—21no—
141#41×C43—22no—
142#41×C43—22no—
143C2×Q8×C43C22×C411yescharacteristic
144C2×D4×C43—21no—
145C2×D4×C43C22×C411yescharacteristic
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43C22×C411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C2×C22⋊D43—22no—
153C2×C22⋊D43—22no—
154C2×C22⋊D43—22no—
155C2×C22⋊D43C22⋊C412yes—
156C22×Dic43—21no—
157#10621898—22no—
158#10621898—22no—
159#10621898—82no—
160#10621898—82no—
161C2×D172—21no—
162C2×D172—22no—
163C2×D172—22no—
164C2×D172—22no—
165C2×D172—22no—
166C2×D172C22⋊C411yescharacteristic
167C2×D172C22×C412yes—
168C2×C4×D43—22no—
169C2×C4×D43—22no—
170C2×C4×D43—81no—
171C2×C4×D43—81no—
172C2×C4×D43C22×C412yes—
173C2×C4×D43C2×D412yes—
174C2×C4×D43C2×D412yes—
175C2×Dic86—22no—
176C2×Dic86C22⋊C411yescharacteristic
177C2×C8×C43—22no—
178C2×C8×C43—22no—
179C2×C8×C43—81no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43C22×C411yescharacteristic
183C4⋊C4×C43C22×C411yescharacteristic
184C22⋊C4×C43—21no—
185C22⋊C4×C43—21no—
186C22⋊C4×C43—21no—
187C42×C43—21no—
188C42×C43—21no—
189C42×C43—21no—
190C42×C43C22×C411yescharacteristic
191C42×C43C2×D411yescharacteristic
192C42×C43C2×D411yescharacteristic
193C42×C43C2411yescharacteristic
194C22⋊Dic43—22no—
195C22⋊Dic43C22⋊C412yes—
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—
203(C2×D43)⋊C4C22⋊C412yes—
204(C2×D43)⋊C4C22⋊C412yes—
205C4⋊Dic43—21no—
206C4⋊Dic43—22no—
207C4⋊Dic43C22⋊C411yescharacteristic
208C4⋊Dic43C22⋊C411yescharacteristic
209C4⋊Dic43C22×C412yes—
210Dic43⋊C4—22no—
211Dic43⋊C4—22no—
212Dic43⋊C4—22no—
213Dic43⋊C4C22⋊C412yes—
214Dic43⋊C4C22⋊C412yes—
215C4×Dic43C22×C412yes—
216C4×Dic43C2×D412yes—
217C4×Dic43C2×D412yes—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—42no—
223#10621872—44no—
224C8×D43—82no—
225C23×C43—21no—
226C23×C43C2×C22⋊C411yescharacteristic
227C22×D43—22no—
228C22×D43—42no—
229C22×D43—81no—
230C22×D43—81no—
231C22×D43C2×C22⋊C412yes—
232Q8×C43—21no—
233Q8×C43—21no—
234D4×C43—21no—
235D4×C43—21no—
236D4×C43—42no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—42no—
246C2×C4×C43—81no—
247C2×C4×C43C2×C22⋊C411yescharacteristic
248C2×C4×C43C2×C22⋊C411yescharacteristic
249C2×C4×C43C2×C22⋊C411yescharacteristic
250C2×C4×C43#13112yes—
251C2×C4×C43#13112yes—
252C2×C4×C43C23×C411yescharacteristic
253C2×C4×C43C22×D411yescharacteristic
254C2×C4×C43C22×D411yescharacteristic
255C22⋊D43—24no—
256C22⋊D43—82no—
257C22⋊D43—82no—
258C22⋊D43—82no—
259C2×Dic43—22no—
260C2×Dic43—81no—
261C2×Dic43C2×C22⋊C412yes—
262C2×Dic43C2×C22⋊C412yes—
263C2×Dic43C2×C22⋊C412yes—
264D172—22no—
265D172—22no—
266D172—22no—
267D172—42no—
268D172—82no—
269D172—82no—
270C4×D43—22no—
271C4×D43—22no—
272C4×D43—22no—
273C4×D43—22no—
274C4×D43—42no—
275C4×D43—42no—
276C4×D43—42no—
277C4×D43—82no—
278Dic86—22no—
279Dic86—82no—
280C8×C43—42no—
281C8×C43—42no—
282C43⋊C8—22no—
283C43⋊C8—41no—
284C43⋊C8—41no—
285C43⋊C8—41no—
286#17468—431nomaximal, Sylow
287C22×C43—21no—
288C22×C43—21no—
289C22×C43—41no—
290C22×C43—41no—
291C22×C43—41no—
292C22×C43#40812yes—
293C22×C43C22×C22⋊C411yescharacteristic
294C2×D43—22no—
295C2×D43—22no—
296C2×D43—22no—
297C2×D43—42no—
298C2×D43—42no—
299C2×D43—42no—
300C2×D43—84no—
301C4×C43—21no—
302C4×C43—21no—
303C4×C43—21no—
304C4×C43—41no—
305C4×C43—41no—
306C4×C43—41no—
307C4×C43#40812yes—
308C4×C43C2×#13111yescharacteristic
309C4×C43C2×#13111yescharacteristic
310C4×C43#57611yescharacteristic
311C4×C43#57711yescharacteristic
312Dic43—22no—
313Dic43—22no—
314Dic43—22no—
315Dic43—42no—
316#3460—431no—
317#2988—431no—
318#2965—431no—
319#1484—432no—
320#1483—432no—
321#1482—432no—
322#1480—432no—
323#1478—431no—
324#1477D4311yescharacteristic, complemented
325#1476—431no—
326C2×D4⋊C8—431no—
327C2×C43—22no—
328C2×C43—81no—
329C2×C43C2×#40811yescharacteristic
330C2×C43#289711yescharacteristic
331C2×C43#290111yescharacteristic
332D43—42no—
333D43—82no—
334#544—431no—
335#542—432no—
336#542—861no—
337#540—432no—
338#540—861no—
339#538—862no—
340#537—431no—
341#535—431no—
342#535—431no—
343#532—432no—
344#532—861no—
345#529—432no—
346#529—861no—
347#525—862no—
348C4×#41—431no—
349C4×#41C2×D4311yescharacteristic
350C2×C4×D4—431no—
351#446—861no—
352C8×Q8—861no—
353#436—861no—
354#435—862no—
355C8×D4—861no—
356C8×D4—862no—
357#431—432no—
358#431—431no—
359#431—432no—
360#431C2×D4311yescharacteristic
361C2×C4⋊C8—432no—
362C2×C4⋊C8C2×D4311yescharacteristic
363C4×M16—432no—
364C2×C4×C8—431no—
365Q8⋊C8—431no—
366Q8⋊C8—431no—
367Q8⋊C8C2×D4312yescomplemented
368D4⋊C8—431no—
369D4⋊C8—431no—
370D4⋊C8—432no—
371D4⋊C8—432no—
372D4⋊C8—432no—
373D4⋊C8—432no—
374D4⋊C8C2×D4312yescomplemented
375C43#1746811yescharacteristic, complemented, Sylow
376C2×#41—431no—
377C2×#41—862no—
378C2×#41C4×D4311yescharacteristic
379C22×D4—431no—
380C23×C4—861no—
381C2×M16—862no—
382C22×C8—21no—
383C22×C8—862no—
384C22×C8—861no—
385C4⋊Q8—432no—
386C4⋊Q8—861no—
387#127—432no—
388#127—861no—
389#126—862no—
390#126—862no—
391#125—432no—
392#125—861no—
393#124—432no—
394#124—862no—
395#124—861no—
396#124—862no—
397#123—862no—
398#123—862no—
399#123—862no—
400#123—862no—
401C22⋊Q8—432no—
402C22⋊Q8—862no—
403C22⋊Q8—862no—
404C22⋊Q8—861no—
405#121—432no—
406#121—432no—
407#121—432no—
408#121—862no—
409#121—862no—
410#121—862no—
411#121—861no—
412#121—861no—
413#121—861no—
414#121—862no—
415#120—862no—
416#120—862no—
417C4×Q8—431no—
418C4×Q8—431no—
419C4×Q8C4×D4311yescharacteristic
420C4×Q8C22×D4311yescharacteristic
421C4×D4—21no—
422C4×D4—21no—
423C4×D4—432no—
424C4×D4—432no—
425C4×D4—432no—
426C4×D4—431no—
427C4×D4—431no—
428C4×D4—432no—
429C4×D4—862no—
430C4×D4—862no—
431C4×D4—861no—
432C4×D4—861no—
433C4×D4C4×D4311yescharacteristic
434C4×D4C22×D4311yescharacteristic
435#117—21no—
436#117—431no—
437#117—432no—
438#117—862no—
439#117C4×D4311yescharacteristic
440C2×C4⋊C4—431no—
441C2×C22⋊C4—861no—
442C2×C42—21no—
443C2×C42—432no—
444C2×C42C22×D4311yescharacteristic
445C4⋊C8—21no—
446C4⋊C8—21no—
447C4⋊C8—431no—
448C4⋊C8—431no—
449C4⋊C8—862no—
450C4⋊C8—862no—
451C4⋊C8C22×D4312yes—
452C22⋊C8—21no—
453C22⋊C8—862no—
454C22⋊C8—862no—
455C22⋊C8—861no—
456#97—862no—
457C4×C8—431no—
458C4×C8—431no—
459C4×C8—862no—
460C4×C8—861no—
461C4×C8—861no—
462C4×C8C22×D4312yes—
463C24—861no—
464#41—22no—
465#41—22no—
466#41—862no—
467#41—862no—
468#41—3442no—
469#41—3442no—
470C2×Q8—431no—
471C2×Q8—862no—
472C2×Q8C2×C4×D4311yescharacteristic
473C2×D4—21no—
474C2×D4—432no—
475C2×D4—431no—
476C2×D4—432no—
477C2×D4—862no—
478C2×D4—862no—
479C2×D4—862no—
480C2×D4—862no—
481C2×D4—862no—
482C2×D4—861no—
483C2×D4—862no—
484C2×D4—862no—
485C2×D4C2×C4×D4311yescharacteristic
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—432no—
490C22×C4—432no—
491C22×C4—432no—
492C22×C4—861no—
493C22×C4—862no—
494C22×C4—862no—
495C22×C4—3441no—
496C22×C4—3441no—
497C22×C4C2×C4×D4311yescharacteristic
498C22×C4D4×D4311yescharacteristic
499C22×C4D4×D4311yescharacteristic
500M16—1724no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—81no—
504C2×C8—861no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8—3442no—
509C2×C8—1722no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—431no—
513C4⋊C4—431no—
514C4⋊C4—432no—
515C4⋊C4—432no—
516C4⋊C4—432no—
517C4⋊C4—862no—
518C4⋊C4—862no—
519C4⋊C4—862no—
520C4⋊C4—862no—
521C4⋊C4—861no—
522C4⋊C4C2×C4×D4311yescharacteristic
523C4⋊C4C2×C4×D4311yescharacteristic
524C22⋊C4—21no—
525C22⋊C4—21no—
526C22⋊C4—21no—
527C22⋊C4—432no—
528C22⋊C4—432no—
529C22⋊C4—432no—
530C22⋊C4—862no—
531C22⋊C4—862no—
532C22⋊C4—862no—
533C22⋊C4—862no—
534C22⋊C4—862no—
535C22⋊C4—862no—
536C22⋊C4—862no—
537C22⋊C4—862no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—432no—
542C42—432no—
543C42—432no—
544C42C2×C4×D4311yescharacteristic
545C42D4×D4311yescharacteristic
546C42D4×D4311yescharacteristic
547C42C23×D4311yescharacteristic
548C23—21no—
549C23—432no—
550C23—862no—
551C23—3441no—
552C23—3441no—
553C23—1722no—
554C23C22⋊C4×D4311yescharacteristic
555Q8—21no—
556Q8—21no—
557Q8—862no—
558Q8—3442no—
559D4—21no—
560D4—21no—
561D4—42no—
562D4—864no—
563D4—862no—
564D4—862no—
565D4—862no—
566D4—3442no—
567D4—3442no—
568D4—3442no—
569D4—3442no—
570D4—3442no—
571D4—1722no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—41no—
578C2×C4—42no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—81no—
582C2×C4—432no—
583C2×C4—432no—
584C2×C4—432no—
585C2×C4—862no—
586C2×C4—862no—
587C2×C4—862no—
588C2×C4—862no—
589C2×C4—862no—
590C2×C4—3442no—
591C2×C4—3441no—
592C2×C4—1722no—
593C2×C4—1722no—
594C2×C4—1722no—
595C2×C4C22⋊C4×D4311yescharacteristic
596C2×C4C22⋊C4×D4311yescharacteristic
597C2×C4C22⋊C4×D4311yescharacteristic
598C2×C4#1306333112yes—
599C2×C4#1306333312yes—
600C2×C4C22×C4×D4311yescharacteristic
601C2×C4C2×D4×D4311yescharacteristic
602C2×C4C2×D4×D4311yescharacteristic
603C8—42no—
604C8—42no—
605C8—862no—
606C8—1721no—
607C8—1721no—
608C8—1721no—
609C22—21no—
610C22—21no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—862no—
615C22—862no—
616C22—862no—
617C22—3444no—
618C22—1722no—
619C22—1722no—
620C22—1722no—
621C22#1458286412yes—
622C22C2×C22⋊C4×D4311yescharacteristic
623C4—21no—
624C4—21no—
625C4—21no—
626C4—41no—
627C4—41no—
628C4—41no—
629C4—862no—
630C4—862no—
631C4—862no—
632C4—1722no—
633C4#1458286412yes—
634C4C2×#1306333111yescharacteristic
635C4C2×#1306333311yescharacteristic
636C4#1458370311yescharacteristic
637C4#1458370811yescharacteristic
638C2—22no—
639C2—81no—
640C2—3442no—
641C2—1722no—
642C2C2×#1458286411yescharacteristic
643C2#1914311911yescharacteristic
644C2#1914314111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1477C2
socleC22×C43C22×C22⋊C4
prime radical#19148011C2
cosocleC42×C43C24
hypercenter#1477D43
hypocenterC43#17468
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1477

Complements

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

NH ≅ G/Ntype
2. #19143704C2semidirect
3. #19143556C2semidirect
4. #19133010C2semidirect
5. #19133007C2semidirect
6. #19133002C2semidirect
7. #19132992C2semidirect
8. #19132987C2semidirect
9. #19132977C2semidirect
10. C2×#14582626C2semidirect
11. C43×#1477C2semidirect
35. #14582951C22semidirect
36. #14582950C22semidirect
37. C4⋊C8×D43C22semidirect
38. C4×#10621872C22semidirect
40. Q8⋊(C43⋊C8)C22semidirect
41. Q8⋊(C43⋊C8)C22semidirect
44. D4⋊(C43⋊C8)C22semidirect
45. D4⋊(C43⋊C8)C22semidirect
51. C43×Q8⋊C8C22semidirect
52. C43×D4⋊C8C22semidirect
324. #1477D43semidirect
367. Q8⋊C8C2×D43semidirect
374. D4⋊C8C2×D43semidirect
375. C43#17468semidirect

Maximal subgroups

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

subgroupindex
#191480112
#191437042
#191435562
#191330102
#191330072
#191330022
#191329922
#191329872
#191329772
C2×#145826262
C43×#14772
#1746843