Finite Group Databasebeta

← #25103288

Subgroups — #25103288

Order 11008.

954 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
1C2×#14583156C211yesmaximal, characteristic
2C2×#14582991C211yesmaximal, characteristic, complemented
3C2×#14582853C211yesmaximal, characteristic
4#19137280C211yesmaximal, characteristic
5#19137275C211yesmaximal, characteristic
6#19135465C211yesmaximal, characteristic, complemented
7#19135335C211yesmaximal, characteristic, complemented
8#19135271C211yesmaximal, characteristic, complemented
9#19135017C211yesmaximal, characteristic
10#19135015C211yesmaximal, characteristic
11#19134627C211yesmaximal, characteristic
12#19134483C211yesmaximal, characteristic, complemented
13#19134427C211yesmaximal, characteristic, complemented
14#19134424C211yesmaximal, characteristic, complemented
15C43×#1933C211yesmaximal, characteristic, complemented
16C22×#10621885C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19C2×#13063305C2211yescharacteristic
20C2×#13063301C2211yescharacteristic
21C2×Q8×Dic43C2211yescharacteristic
22C2×#13063290C2211yescharacteristic
23C2×#13063282C2211yescharacteristic
24#14583156C418yescomplemented
25#14582991—24no—
26C2×#13063258C2211yescharacteristic
27C2×#13063256C2211yescharacteristic
28C2×#13063256C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063248C2211yescharacteristic
33#14582853—24no—
34C2×#13063236C2211yescharacteristic
35C2×#13063235C2211yescharacteristic
36C2×C8×Dic43C2211yescharacteristic
37#14582805C2211yescharacteristic
38#14582797C2211yescharacteristic
39#14582796—21no—
40#14582795—21no—
41#14582791—21no—
42#14582789—21no—
43#14582788—21no—
44#14582788—21no—
45#14582782—21no—
46#14582781—21no—
47#14582756C2211yescharacteristic
48#14582756C2211yescharacteristic
49C4⋊C4×Dic43C2211yescharacteristic
50C4⋊C4×Dic43C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×C4×C8×C43C2211yescharacteristic
58C43×#391C2211yescharacteristic
59C43×#389C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C22×Dic86C2311yescharacteristic
63C22×C4×D43C2311yescharacteristic
64C2×#10621885—22no—
65C2×#10621885—22no—
66C2×#10621885C2×C414yes—
67C2×#10621872—22no—
68C2×#10621872—22no—
69C2×#10621872C2×C414yes—
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72C2×C8×D43—22no—
73C2×C8×D43—22no—
74C2×C8×D43—22no—
75#13063305—22no—
76#13063305C2×C414yes—
77#13063301—22no—
78#13063301C2×C414yes—
79Q8×Dic43—22no—
80Q8×Dic43—22no—
81#13063290—22no—
82#13063290—22no—
83#13063282—22no—
84#13063282—22no—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4D411yescharacteristic
94C2×Dic43⋊C4D411yescharacteristic
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4D411yescharacteristic
100C2×(C2×D43)⋊C4D411yescharacteristic
101C2×C4×Dic43—21no—
102C2×C4×Dic43—21no—
103C2×C4×Dic43—21no—
104C2×C4×Dic43—21no—
105C2×C4×Dic43C2311yescharacteristic
106#13063258—22no—
107#13063256—22no—
108#13063256C2×C414yes—
109#13063250—22no—
110#13063250C2×C414yes—
111#13063249—22no—
112#13063248—22no—
113#13063236—22no—
114#13063235—22no—
115C8×Dic43D414yes—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C22×Q8×C43C2311yescharacteristic
124C22×C8×C43C2311yescharacteristic
125C22×C8×C43C2311yescharacteristic
126C2×C4⋊C4×C43—21no—
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C42×C43C2311yescharacteristic
131#103×C43—22no—
132#103×C43C2×C414yes—
133C4×C8×C43—22no—
134#95×C43—21no—
135#95×C43—21no—
136#95×C43—21no—
137C23×D43C2×D411yescharacteristic
138C2×Q8×C43—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43C22×C412yes—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2411yescharacteristic
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43C2×D411yescharacteristic
156C22×Dic43C2×D411yescharacteristic
157C22×Dic43C2×D411yescharacteristic
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×C4×D43C22×C412yes—
163C2×C4×D43#4112yes—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86C22×C412yes—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43C22×C412yes—
175C2×C8×C43C2×D412yes—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—81no—
182C4⋊C4×C43C22×C412yes—
183C42×C43—21no—
184C42×C43—21no—
185#10621885—28no—
186(C2×D43)⋊C4—22no—
187(C2×D43)⋊C4—22no—
188(C2×D43)⋊C4—24no—
189(C2×D43)⋊C4—24no—
190(C2×D43)⋊C4—81no—
191(C2×D43)⋊C4—81no—
192C4⋊Dic43—21no—
193C4⋊Dic43—24no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—42no—
199C4⋊Dic43C22×C412yes—
200Dic43⋊C4—24no—
201Dic43⋊C4—22no—
202Dic43⋊C4—22no—
203Dic43⋊C4—42no—
204Dic43⋊C4—81no—
205C4×Dic43—42no—
206C4×Dic43—42no—
207C4×Dic43—81no—
208C4×Dic43—81no—
209C4×Dic43C2×D412yes—
210C4×Dic43#4112yes—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8C22×C412yes—
214C2×C43⋊C8C2×D412yes—
215C2×C43⋊C8#4112yes—
216C2×C43⋊C8#4112yes—
217#10621872—28no—
218C8×D43—28no—
219C23×C43C22×D411yescharacteristic
220C22×D43—21no—
221C22×D43—21no—
222C22×D43—21no—
223C22×D43—21no—
224C22×D43—21no—
225C22×D43—21no—
226C22×D43C4×D412yes—
227Q8×C43—22no—
228Q8×C43—22no—
229Q8×C43—41no—
230Q8×C43—41no—
231C2×C4×C43—22no—
232C2×C4×C43—22no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
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—41no—
248C2×C4×C43—41no—
249C2×C4×C43C23×C411yescharacteristic
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
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—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43C4×D412yes—
274C2×Dic43#12112yes—
275C2×Dic43#12112yes—
276C4×D43—22no—
277C4×D43—22no—
278C4×D43—22no—
279C4×D43—22no—
280Dic86—22no—
281Dic86—22no—
282Dic86—41no—
283Dic86—41no—
284C8×C43—22no—
285C8×C43—22no—
286C43⋊C8—22no—
287C43⋊C8C4×D414yes—
288#21537—431nomaximal, Sylow
289C22×C43C2×C4×D411yescharacteristic
290C22×C43C2×#12111yescharacteristic
291C22×C43#53211yescharacteristic
292C22×C43#57711yescharacteristic
293C22×C43#57711yescharacteristic
294C22×C43#57811yescharacteristic
295C22×C43#57811yescharacteristic
296C2×D43—22no—
297C2×D43—22no—
298C2×D43—22no—
299C2×D43—41no—
300C2×D43—41no—
301C2×D43—41no—
302C2×D43—41no—
303C4×C43—42no—
304C4×C43—41no—
305C4×C43—41no—
306C4×C43—42no—
307C4×C43—81no—
308C4×C43—81no—
309C4×C43C2×C4×D411yescharacteristic
310C4×C43C4×#4111yescharacteristic
311C4×C43#52511yescharacteristic
312C4×C43#52911yescharacteristic
313Dic43—22no—
314Dic43—22no—
315Dic43—22no—
316Dic43—42no—
317Dic43—42no—
318Dic43—81no—
319Dic43—81no—
320C2×#470—431no—
321C2×C4×Q16—431no—
322C2×#405—431no—
323#2323—431no—
324#2323—431no—
325#1971—431no—
326#1944—431no—
327#1933—431no—
328#1933D4311yescharacteristic, complemented
329#1892—431no—
330#1892—431no—
331#1809—431no—
332C4×#106—431no—
333#1763—431no—
334#1763—431no—
335C2×C43C4×#12111yescharacteristic
336C2×C43#294711yescharacteristic
337C2×C43#294711yescharacteristic
338C2×C43#305911yescharacteristic
339C2×C43#306011yescharacteristic
340C2×C43#317811yescharacteristic
341C2×C43#317811yescharacteristic
342D43—42no—
343C22×Q16—431no—
344C22×M16—431no—
345C23×C8—431no—
346C2×C22⋊Q8—431no—
347C2×C22⋊Q8—431no—
348C2×C4×Q8—431no—
349C2×C4×Q8—431no—
350C2×#117—431no—
351#470—438no—
352C4×Q16—864no—
353C2×#107—431no—
354C2×#106—431no—
355C2×#106—431no—
356C2×#103—431no—
357C2×#103—431no—
358C2×#103—431no—
359C2×#103—431no—
360C2×#103C2×D4311yescharacteristic
361C2×#103C2×D4311yescharacteristic
362#405—864no—
363C2×#97—431no—
364C2×#97—431no—
365C2×C4×C8—431no—
366C2×C4×C8C2×D4311yescharacteristic
367#391—431no—
368#391C2×D4311yescharacteristic
369#389—431no—
370#389—861no—
371#389—861no—
372#389C2×D4311yescharacteristic
373#388—861no—
374#388—861no—
375#388—861no—
376#388—861no—
377#387—861no—
378#387—861no—
379#380—431no—
380#380—431no—
381C4×C4⋊C4—431no—
382C4×C4⋊C4—431no—
383#340—431no—
384#340—431no—
385#340—431no—
386#340—431no—
387#340C2×D4311yescharacteristic
388#340C2×D4311yescharacteristic
389C43#2153711yescharacteristic, complemented, Sylow
390C22×Q8—431no—
391C22×Q8C22×D4311yescharacteristic
392C23×C4—431no—
393C2×Q16—434no—
394C2×Q16—862no—
395C2×Q16—862no—
396C2×M16—434no—
397C2×M16—862no—
398C2×M16—862no—
399C22×C8—431no—
400C22×C8—431no—
401C22×C8—862no—
402C22×C8—862no—
403C22×C8—862no—
404C22×C8C22×D4311yescharacteristic
405C22×C8C22×D4311yescharacteristic
406C22⋊Q8—434no—
407C22⋊Q8—434no—
408C22⋊Q8—862no—
409C22⋊Q8—862no—
410C4×Q8—862no—
411C4×Q8—862no—
412C4×Q8—862no—
413C4×Q8—862no—
414#117—862no—
415#117—862no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4C22×D4311yescharacteristic
428C2×C4⋊C4C22×D4311yescharacteristic
429C2×C4⋊C4C22×D4311yescharacteristic
430C2×C22⋊C4—431no—
431C2×C22⋊C4—431no—
432C2×C22⋊C4—861no—
433C2×C22⋊C4—861no—
434C2×C22⋊C4—861no—
435C2×C22⋊C4—861no—
436C2×C42—431no—
437C2×C42—861no—
438C2×C42—861no—
439C2×C42—861no—
440C2×C42—861no—
441C2×C42C22×D4311yescharacteristic
442#107—862no—
443#106—434no—
444#106—862no—
445#103—22no—
446#103—434no—
447#103—862no—
448#103—862no—
449#103—862no—
450#103C4×D4314yes—
451#97—862no—
452#97—862no—
453C4×C8—22no—
454C4×C8—434no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95—861no—
459#95—861no—
460#95—861no—
461#95—861no—
462#95—861no—
463#95—861no—
464#95—861no—
465C24—431no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—432no—
472C2×Q8—861no—
473C2×Q8—861no—
474C2×Q8—861no—
475C2×Q8—861no—
476C2×Q8—861no—
477C2×Q8C2×C4×D4312yes—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—431no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—432no—
486C22×C4—432no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4—861no—
493C22×C4—861no—
494C22×C4—861no—
495C22×C4D4×D4311yescharacteristic
496C22×C4D4×D4311yescharacteristic
497C22×C4C23×D4311yescharacteristic
498Q16—868no—
499M16—868no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—432no—
505C2×C8—432no—
506C2×C8—432no—
507C2×C8—432no—
508C2×C8—868no—
509C2×C8—861no—
510C2×C8—861no—
511C2×C8C2×C4×D4312yes—
512C2×C8D4×D4312yes—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—81no—
519C4⋊C4—432no—
520C4⋊C4—862no—
521C4⋊C4—862no—
522C4⋊C4—864no—
523C4⋊C4—864no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—3441no—
530C4⋊C4—1722no—
531C4⋊C4—1722no—
532C4⋊C4C2×C4×D4312yes—
533C22⋊C4—862no—
534C22⋊C4—862no—
535C22⋊C4—864no—
536C22⋊C4—864no—
537C22⋊C4—3441no—
538C22⋊C4—3441no—
539C42—21no—
540C42—21no—
541C42—432no—
542C42—432no—
543C42—3441no—
544C42—3441no—
545C42—1722no—
546C42—1722no—
547C23—432no—
548C23—861no—
549C23—861no—
550C23—861no—
551C23—861no—
552C23—861no—
553C23—861no—
554C23C2×D4×D4311yescharacteristic
555Q8—22no—
556Q8—22no—
557Q8—41no—
558Q8—41no—
559Q8—862no—
560Q8—862no—
561Q8—1721no—
562Q8—1721no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—432no—
582C2×C4—432no—
583C2×C4—432no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—862no—
591C2×C4—862no—
592C2×C4—862no—
593C2×C4—862no—
594C2×C4—862no—
595C2×C4—862no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4C22×C4×D4311yescharacteristic
607C2×C4C2×D4×D4311yescharacteristic
608C2×C4#41×D4311yescharacteristic
609C2×C4#41×D4311yescharacteristic
610C2×C4#41×D4311yescharacteristic
611C2×C4#41×D4311yescharacteristic
612C8—22no—
613C8—22no—
614C8—434no—
615C8—862no—
616C22—862no—
617C22—862no—
618C22—862no—
619C22—1721no—
620C22—1721no—
621C22—1721no—
622C22—1721no—
623C22C4×D4×D4311yescharacteristic
624C22#121×D4311yescharacteristic
625C22#1458344811yescharacteristic
626C22#1458370511yescharacteristic
627C22#1458370611yescharacteristic
628C22#1458371211yescharacteristic
629C22#1458371311yescharacteristic
630C4—42no—
631C4—41no—
632C4—41no—
633C4—42no—
634C4—81no—
635C4—81no—
636C4—862no—
637C4—862no—
638C4—862no—
639C4—3441no—
640C4—3441no—
641C4—1722no—
642C4—1722no—
643C4C4×D4×D4311yescharacteristic
644C4#1458336711yescharacteristic
645C4#1458340711yescharacteristic
646C4#1458343211yescharacteristic
647C2—1722no—
648C2#1913710711yescharacteristic
649C2#1914343111yescharacteristic
650C2#1914343311yescharacteristic
651C2#1914424511yescharacteristic
652C2#1914425211yescharacteristic
653C2#1914526211yescharacteristic
654C2#1914527011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1933C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenter#1933D43
hypocenterC43#21537
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1933

Complements

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

NH ≅ G/Ntype
2. C2×#14582991C2semidirect
6. #19135465C2semidirect
7. #19135335C2semidirect
8. #19135271C2semidirect
12. #19134483C2semidirect
13. #19134427C2semidirect
14. #19134424C2semidirect
15. C43×#1933C2semidirect
24. #14583156C4semidirect
328. #1933D43semidirect
389. C43#21537semidirect

Maximal subgroups

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

subgroupindex
C2×#145831562
C2×#145829912
C2×#145828532
#191372802
#191372752
#191354652
#191353352
#191352712
#191350172
#191350152
#191346272
#191344832
#191344272
#191344242
C43×#19332
#2153743