Finite Group Databasebeta

← #25146681

Subgroups — #25146681

Order 11008.

840 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583260C211yesmaximal, characteristic
2C2×#14583124C211yesmaximal, characteristic
3#19139801C211yesmaximal, characteristic, complemented
4#19137671C211yesmaximal, characteristic
5#19136002C211yesmaximal, characteristic
6#19135917C211yesmaximal, characteristic, complemented
7#19135914C211yesmaximal, characteristic
8#19135545C211yesmaximal, characteristic, complemented
9#19135317C211yesmaximal, characteristic, complemented
10#19134934C211yesmaximal, characteristic, complemented
11#19134928C211yesmaximal, characteristic
12#19134598C211yesmaximal, characteristic, complemented
13#19134592C211yesmaximal, characteristic
14#19134424C211yesmaximal, characteristic, complemented
15C43×#2072C211yesmaximal, characteristic, complemented
16C22×#10621885C2211yescharacteristic
17C22×#10621873C2211yescharacteristic
18C2×#13063324C2211yescharacteristic
19C2×#13063314C2211yescharacteristic
20C2×Q8×Dic43C2211yescharacteristic
21C2×#13063290C2211yescharacteristic
22C2×C4×D172C2211yescharacteristic
23#14583260—24no—
24#14583124—24no—
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×Dic43⋊C8C2211yescharacteristic
27C2×Dic43⋊C8C2211yescharacteristic
28C2×#13063250C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×#13063247C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×#13063235C2211yescharacteristic
35#14582819—21no—
36#14582819—21no—
37#14582805C2211yescharacteristic
38#14582804C2211yescharacteristic
39#14582800C2211yescharacteristic
40#14582794—21no—
41#14582794—21no—
42#14582791—21no—
43#14582788—21no—
44#14582773—21no—
45#14582768C2211yescharacteristic
46C4⋊C4×Dic43C2211yescharacteristic
47C4×Dic43⋊C4C2211yescharacteristic
48#14582746—21no—
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C43×#391C2211yescharacteristic
57C43×#384C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×Dic86—21no—
62C22×Dic86C2311yescharacteristic
63C22×D172C2311yescharacteristic
64C22×C4×D43—21no—
65C2×#10621885—22no—
66C2×#10621885—22no—
67C2×#10621885—41no—
68C2×#10621873—22no—
69C2×#10621873—22no—
70C2×#10621873—41no—
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73#13063324—22no—
74#13063324—22no—
75#13063314—22no—
76#13063314D414yes—
77Q8×Dic43—22no—
78Q8×Dic43—41no—
79#13063290—22no—
80#13063290—22no—
81C4×D172—22no—
82C4×D172—41no—
83C2×C4⋊Dic43—21no—
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4D411yescharacteristic
91C2×Dic43⋊C4D411yescharacteristic
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43—21no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43C2311yescharacteristic
101C2×C4×Dic43C2311yescharacteristic
102C4⋊(C43⋊C8)—41no—
103Dic43⋊C8—22no—
104Dic43⋊C8—41no—
105#13063250—22no—
106#13063249—22no—
107#13063248—22no—
108#13063247—22no—
109#13063245—22no—
110#13063245—22no—
111#13063235—22no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95D411yescharacteristic
118C43⋊#95D411yescharacteristic
119C22×Q8×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C2×C4⋊C4×C43—21no—
123C2×C4⋊C4×C43—21no—
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C42×C43C2311yescharacteristic
128#103×C43—22no—
129#103×C43—22no—
130#95×C43—21no—
131#95×C43—21no—
132C23×D43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43C2×D412yes—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2411yescharacteristic
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172C2×D412yes—
159C2×C4×D43—42no—
160C2×C4×D43—42no—
161C2×C4×D43—81no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—42no—
168C2×Dic86—81no—
169C2×Dic86—81no—
170C2×Dic86#4112yes—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—81no—
184C4⋊C4×C43—81no—
185C42×C43—21no—
186C42×C43—21no—
187#10621885—44no—
188(C2×D43)⋊C4—24no—
189(C2×D43)⋊C4—24no—
190(C2×D43)⋊C4—42no—
191(C2×D43)⋊C4—42no—
192(C2×D43)⋊C4—81no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—42no—
197C4⋊Dic43#4112yes—
198Dic43⋊C4—22no—
199Dic43⋊C4—22no—
200Dic43⋊C4—42no—
201Dic43⋊C4—42no—
202Dic43⋊C4—81no—
203Dic43⋊C4—81no—
204C4×Dic43—21no—
205C4×Dic43—21no—
206C4×Dic43—42no—
207C4×Dic43—42no—
208C4×Dic43—81no—
209C4×Dic43C2×D412yes—
210C4×Dic43#4112yes—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217#10621873—44no—
218C23×C43C22×D411yescharacteristic
219C22×D43—22no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—41no—
223C22×D43—41no—
224C22×D43—41no—
225C22×D43—41no—
226Q8×C43—22no—
227Q8×C43—22no—
228Q8×C43—41no—
229Q8×C43—41no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—22no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43#13712yes—
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43H(5,𝔽2)11yescharacteristic
253C2×C4×C432−1+411yescharacteristic
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—22no—
262C2×Dic43—22no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43#12112yes—
273C2×Dic43#12112yes—
274C2×Dic43#13712yes—
275D172—22no—
276D172—22no—
277D172—41no—
278D172—41no—
279C4×D43—84no—
280Dic86—22no—
281Dic86—22no—
282Dic86—41no—
283Dic86—41no—
284Dic86—84no—
285C8×C43—41no—
286C8×C43—41no—
287C43⋊C8—41no—
288C43⋊C8—41no—
289#25336—431nomaximal, Sylow
290C22×C43C2×#12111yescharacteristic
291C22×C43#54611yescharacteristic
292C22×C43#54811yescharacteristic
293C22×C43C2×#13711yescharacteristic
294C22×C43C2×#13711yescharacteristic
295C22×C43#57611yescharacteristic
296C22×C43#57711yescharacteristic
297C2×D43—42no—
298C2×D43—42no—
299C2×D43—42no—
300C2×D43—81no—
301C2×D43—81no—
302C2×D43—81no—
303C2×D43—81no—
304C4×C43—22no—
305C4×C43—42no—
306C4×C43—41no—
307C4×C43—81no—
308C4×C43—81no—
309C4×C43—81no—
310C4×C43#52911yescharacteristic
311C4×C43#54211yescharacteristic
312C4×C43#54611yescharacteristic
313C4×C43#54711yescharacteristic
314Dic43—22no—
315Dic43—22no—
316Dic43—22no—
317Dic43—42no—
318Dic43—42no—
319Dic43—41no—
320Dic43—81no—
321C2×#489—431no—
322C2×#464—431no—
323#2567—431no—
324#2367—431no—
325#2072D4311yescharacteristic, complemented
326#2071—431no—
327#2056—431no—
328#2055—431no—
329#1988—431no—
330#1940—431no—
331#1878—431no—
332#1877—431no—
333#1803—431no—
334#1802—431no—
335#1763—431no—
336C2×C43#242711yescharacteristic
337C2×C43#303911yescharacteristic
338C2×C43#304511yescharacteristic
339C2×C43#331411yescharacteristic
340C2×C43#331611yescharacteristic
341C2×C43#336911yescharacteristic
342C2×C43#337511yescharacteristic
343D43—82no—
344C22×Q16—431no—
345C22×SD16—431no—
346C2×C4⋊Q8—431no—
347C2×#124—431no—
348C2×C4×Q8—431no—
349C2×C4×Q8—431no—
350C2×C4×D4—431no—
351#489—864no—
352#464—864no—
353C2×C4⋊C8—431no—
354C2×C4⋊C8—431no—
355C2×C4⋊C8—431no—
356C2×#103—431no—
357C2×#103—431no—
358C2×#103—431no—
359C2×#103C2×D4311yescharacteristic
360C2×#103C2×D4311yescharacteristic
361C2×#102—431no—
362C2×#102—431no—
363C2×#102—431no—
364C2×#97—431no—
365#395—861no—
366#395—861no—
367#391—431no—
368#391—431no—
369#391C2×D4311yescharacteristic
370#390—431no—
371#389—861no—
372#389—861no—
373#388—861no—
374#388—861no—
375#385—861no—
376#384—431no—
377#384C2×D4311yescharacteristic
378C4×C4⋊C4—431no—
379C4×C4⋊C4—431no—
380C4×C22⋊C4—861no—
381#340—431no—
382#340—431no—
383#340—431no—
384#340—431no—
385#340C2×D4311yescharacteristic
386#340C2×D4311yescharacteristic
387#336—431no—
388#336C2×D4311yescharacteristic
389C43#2533611yescharacteristic, complemented, Sylow
390C22×Q8—431no—
391C22×Q8—861no—
392C22×Q8C22×D4311yescharacteristic
393C22×D4—431no—
394C23×C4—861no—
395C2×Q16—862no—
396C2×Q16—862no—
397C2×Q16—1721no—
398C2×SD16—862no—
399C2×SD16—862no—
400C2×SD16—1721no—
401C22×C8—431no—
402C22×C8—431no—
403C22×C8C22×D4311yescharacteristic
404C22×C8C22×D4311yescharacteristic
405C4⋊Q8—862no—
406C4⋊Q8—862no—
407#124—434no—
408#124—862no—
409C4×Q8—862no—
410C4×Q8—862no—
411C4×Q8—862no—
412C4×Q8—1721no—
413C4×D4—862no—
414C4×D4—1721no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4C22×D4311yescharacteristic
427C2×C4⋊C4C22×D4311yescharacteristic
428C2×C4⋊C4C22×D4311yescharacteristic
429C2×C22⋊C4—861no—
430C2×C22⋊C4—861no—
431C2×C22⋊C4—861no—
432C2×C22⋊C4—861no—
433C2×C22⋊C4—861no—
434C2×C42—431no—
435C2×C42—431no—
436C2×C42—861no—
437C2×C42—861no—
438C2×C42—861no—
439C2×C42C22×D4311yescharacteristic
440C4⋊C8—862no—
441C4⋊C8—1721no—
442C4⋊C8—1721no—
443#103—22no—
444#103—22no—
445#103—862no—
446#103—862no—
447#103—862no—
448#102—862no—
449#102—862no—
450#102—862no—
451#97—862no—
452#95—21no—
453#95—21no—
454#95—431no—
455#95—431no—
456#95—861no—
457#95—861no—
458#95—861no—
459#95—861no—
460#95—861no—
461C24—861no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—432no—
468C2×Q8—861no—
469C2×Q8—861no—
470C2×Q8—861no—
471C2×Q8—861no—
472C2×Q8—861no—
473C2×Q8—3441no—
474C2×Q8—3441no—
475C2×Q8—1722no—
476C2×Q8D4×D4312yes—
477C2×D4—432no—
478C2×D4—861no—
479C2×D4—861no—
480C2×D4—861no—
481C2×D4—861no—
482C2×D4—861no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—431no—
488C22×C4—431no—
489C22×C4—431no—
490C22×C4—431no—
491C22×C4—861no—
492C22×C4—861no—
493C22×C4—861no—
494C22×C4—3441no—
495C22×C4—1722no—
496C22×C4—1722no—
497C22×C4D4×D4311yescharacteristic
498C22×C4D4×D4311yescharacteristic
499C22×C4C23×D4311yescharacteristic
500Q16—1724no—
501SD16—1724no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—861no—
509C2×C8—861no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8—861no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—81no—
521C4⋊C4—81no—
522C4⋊C4—432no—
523C4⋊C4—862no—
524C4⋊C4—862no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—3441no—
529C4⋊C4—3441no—
530C4⋊C4—1722no—
531C4⋊C4—1722no—
532C4⋊C4—1722no—
533C22⋊C4—864no—
534C22⋊C4—864no—
535C22⋊C4—3441no—
536C22⋊C4—1722no—
537C22⋊C4—1722no—
538C42—21no—
539C42—21no—
540C42—432no—
541C42—432no—
542C42—861no—
543C42—861no—
544C42—3441no—
545C42—1722no—
546C42—1722no—
547C23—862no—
548C23—1721no—
549C23—1721no—
550C23—1721no—
551C23—1721no—
552C23—1721no—
553C23—1721no—
554C23C2×D4×D4311yescharacteristic
555Q8—22no—
556Q8—22no—
557Q8—41no—
558Q8—41no—
559Q8—862no—
560Q8—862no—
561Q8—3444no—
562Q8—1721no—
563Q8—1721no—
564D4—862no—
565D4—862no—
566D4—1721no—
567D4—1721no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—22no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—432no—
586C2×C4—432no—
587C2×C4—432no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—861no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—862no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—862no—
599C2×C4—3444no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4#1306335712yes—
608C2×C4C2×D4×D4311yescharacteristic
609C2×C4#41×D4311yescharacteristic
610C2×C4#41×D4311yescharacteristic
611C2×C4#41×D4311yescharacteristic
612C2×C4#1306337111yescharacteristic
613C2×C4#1306337211yescharacteristic
614C8—41no—
615C8—41no—
616C8—1721no—
617C8—1721no—
618C22—3441no—
619C22—3441no—
620C22—3441no—
621C22—3441no—
622C22—1722no—
623C22—1722no—
624C22—1722no—
625C22#121×D4311yescharacteristic
626C22#1458354111yescharacteristic
627C22#1458355711yescharacteristic
628C22#137×D4311yescharacteristic
629C22C2×#1306335711yescharacteristic
630C22#1458370311yescharacteristic
631C22#1458370511yescharacteristic
632C4—22no—
633C4—42no—
634C4—41no—
635C4—81no—
636C4—81no—
637C4—81no—
638C4—862no—
639C4—862no—
640C4—862no—
641C4—3441no—
642C4—1722no—
643C4—1721no—
644C4—1722no—
645C4#1458343211yescharacteristic
646C4#1458351511yescharacteristic
647C4#1458354111yescharacteristic
648C4#1458354711yescharacteristic
649C2—3442no—
650C2#1913816711yescharacteristic
651C2#1914407911yescharacteristic
652C2#1914413111yescharacteristic
653C2#1914667411yescharacteristic
654C2#1914670911yescharacteristic
655C2#1914734011yescharacteristic
656C2#1914740611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2072C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#2072D43
hypocenterC43#25336
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2072

Complements

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

NH ≅ G/Ntype
3. #19139801C2semidirect
6. #19135917C2semidirect
8. #19135545C2semidirect
9. #19135317C2semidirect
10. #19134934C2semidirect
12. #19134598C2semidirect
14. #19134424C2semidirect
15. C43×#2072C2semidirect
325. #2072D43semidirect
389. C43#25336semidirect

Maximal subgroups

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

subgroupindex
C2×#145832602
C2×#145831242
#191398012
#191376712
#191360022
#191359172
#191359142
#191355452
#191353172
#191349342
#191349282
#191345982
#191345922
#191344242
C43×#20722
#2533643