Finite Group Databasebeta

← #25103251

Subgroups — #25103251

Order 11008.

1002 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583156C211yesmaximal, characteristic
2C2×#14582991C211yesmaximal, characteristic, complemented
3C2×#14582851C211yesmaximal, characteristic
4#19137133C211yesmaximal, characteristic
5#19137125C211yesmaximal, characteristic
6#19135465C211yesmaximal, characteristic, complemented
7#19135335C211yesmaximal, characteristic, complemented
8#19135285C211yesmaximal, characteristic, complemented
9#19135027C211yesmaximal, characteristic
10#19135025C211yesmaximal, characteristic
11#19134627C211yesmaximal, characteristic
12#19134483C211yesmaximal, characteristic, complemented
13#103×Dic43C211yesmaximal, characteristic, complemented
14#19134414C211yesmaximal, characteristic, complemented
15C43×#1935C211yesmaximal, characteristic, complemented
16C22×#10621885C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C2×#13063305C2211yescharacteristic
20C2×#13063301C2211yescharacteristic
21C2×Q8×Dic43C2211yescharacteristic
22C2×#13063290C2211yescharacteristic
23C2×C42×D43C2211yescharacteristic
24#14583156C418yescomplemented
25#14582991—24no—
26C2×#13063258C2211yescharacteristic
27C2×#13063256C2211yescharacteristic
28C2×#13063256C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063248C2211yescharacteristic
33#14582851—24no—
34C2×#13063236C2211yescharacteristic
35C2×C8×Dic43C2211yescharacteristic
36C2×C8×Dic43C2211yescharacteristic
37#14582805C2211yescharacteristic
38#14582797C2211yescharacteristic
39#14582786—21no—
40#14582782—21no—
41#14582773—21no—
42#14582770—21no—
43#14582756C2211yescharacteristic
44#14582756C2211yescharacteristic
45C4⋊C4×Dic43—21no—
46C4⋊C4×Dic43C2211yescharacteristic
47C4⋊C4×Dic43C2211yescharacteristic
48#14582750—21no—
49#14582746—21no—
50#14582746—21no—
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×#97×C43C2211yescharacteristic
58C43×#391C2211yescharacteristic
59C43×#389C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C22×Dic86C2311yescharacteristic
63C22×C4×D43D411yescharacteristic
64C22×C4×D43D411yescharacteristic
65C22×C4×D43C2311yescharacteristic
66C2×#10621885—22no—
67C2×#10621885—22no—
68C2×#10621885C2×C414yescomplemented
69C2×#10621872—22no—
70C2×#10621872—22no—
71C2×#10621872—22no—
72C2×#10621872—22no—
73C2×#10621872—22no—
74C2×#10621872C2×C414yes—
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77#13063305—22no—
78#13063305C2×C414yes—
79#13063301—22no—
80#13063301C2×C414yes—
81Q8×Dic43—22no—
82Q8×Dic43—22no—
83#13063290—22no—
84#13063290—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×(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×Dic43—21no—
101C2×C4×Dic43D411yescharacteristic
102C2×C4×Dic43D411yescharacteristic
103C2×C4×Dic43C2311yescharacteristic
104C42×D43—22no—
105C42×D43—22no—
106#13063258—22no—
107#13063256—22no—
108#13063256C2×C414yescomplemented
109#13063250—22no—
110#13063250C2×C414yescomplemented
111#13063249—22no—
112#13063248—22no—
113#13063236—22no—
114C8×Dic43—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×C414yescomplemented
133#97×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×D43—22no—
163C2×C4×D43—22no—
164C2×C4×D43—22no—
165C2×C4×D43—22no—
166C2×C4×D43—41no—
167C2×C4×D43—41no—
168C2×C4×D43C22×C412yes—
169C2×C4×D43#4112yes—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86—21no—
173C2×Dic86—21no—
174C2×Dic86—21no—
175C2×Dic86C22×C412yes—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43C22×C412yes—
181C2×C8×C43C2×D412yes—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—42no—
188C4⋊C4×C43C22×C412yes—
189C42×C43—21no—
190C42×C43—21no—
191#10621885—28no—
192(C2×D43)⋊C4—24no—
193(C2×D43)⋊C4—24no—
194(C2×D43)⋊C4—42no—
195(C2×D43)⋊C4—42no—
196C4⋊Dic43—21no—
197C4⋊Dic43—24no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—42no—
203C4⋊Dic43C22×C412yes—
204Dic43⋊C4—24no—
205Dic43⋊C4—42no—
206Dic43⋊C4—42no—
207C4×Dic43—22no—
208C4×Dic43—22no—
209C4×Dic43—42no—
210C4×Dic43—42no—
211C4×Dic43—42no—
212C4×Dic43—42no—
213C4×Dic43C2×D412yes—
214C4×Dic43#4112yes—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8C22×C412yes—
218C2×C43⋊C8C2×D412yes—
219C2×C43⋊C8#4112yes—
220C2×C43⋊C8#4112yes—
221#10621872—28no—
222#10621872—28no—
223C23×C43C22×D411yescharacteristic
224C22×D43—21no—
225C22×D43—21no—
226C22×D43—21no—
227C22×D43—21no—
228C22×D43—21no—
229C22×D43—21no—
230C22×D43C4×D412yes—
231Q8×C43—22no—
232Q8×C43—22no—
233Q8×C43—41no—
234Q8×C43—41no—
235C2×C4×C43—22no—
236C2×C4×C43—22no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
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×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43C23×C411yescharacteristic
254C2×C4×C43C22×D411yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—22no—
264C2×Dic43—22no—
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×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43C4×D412yes—
276C2×Dic43#12112yes—
277C2×Dic43#12112yes—
278C2×Dic43#13712yes—
279C2×Dic43#13712yes—
280C4×D43—22no—
281C4×D43—22no—
282C4×D43—22no—
283C4×D43—22no—
284C4×D43—44no—
285C4×D43—44no—
286Dic86—22no—
287Dic86—22no—
288Dic86—41no—
289Dic86—41no—
290C8×C43—22no—
291C8×C43—22no—
292C43⋊C8—22no—
293C43⋊C8C4×D414yes—
294C4×#470—431nomaximal, Sylow
295C22×C43C2×C4×D411yescharacteristic
296C22×C43C2×#12111yescharacteristic
297C22×C43#53211yescharacteristic
298C22×C43C2×#13711yescharacteristic
299C22×C43C2×#13711yescharacteristic
300C22×C43#57511yescharacteristic
301C22×C43#57511yescharacteristic
302C2×D43—22no—
303C2×D43—22no—
304C2×D43—22no—
305C2×D43—41no—
306C2×D43—41no—
307C2×D43—41no—
308C2×D43—41no—
309C4×C43—42no—
310C4×C43—41no—
311C4×C43—41no—
312C4×C43—42no—
313C4×C43—81no—
314C4×C43—81no—
315C4×C43C2×C4×D411yescharacteristic
316C4×C43C4×#4111yescharacteristic
317C4×C43#52511yescharacteristic
318C4×C43#52911yescharacteristic
319Dic43—22no—
320Dic43—22no—
321Dic43—42no—
322Dic43—42no—
323Dic43—81no—
324Dic43—81no—
325Dic43#47014yescomplemented
326C2×#470—431no—
327C2×C4×Q16—431no—
328C2×C4×M16—431no—
329C4×C22⋊Q8—431no—
330C4×C22⋊Q8—431no—
331#1971—431no—
332#1944—431no—
333#1935—431no—
334#1935D4311yescharacteristic, complemented
335#1894—431no—
336#1894—431no—
337#1809—431no—
338C4×#106—431no—
339C4×#103—431no—
340C4×#103—431no—
341C2×C43C4×#12111yescharacteristic
342C2×C43C4×#13711yescharacteristic
343C2×C43C4×#13711yescharacteristic
344C2×C43C2×#47011yescharacteristic
345C2×C43#305411yescharacteristic
346C2×C43#317211yescharacteristic
347C2×C43#317211yescharacteristic
348D43—42no—
349C22×Q16—431no—
350C22×M16—431no—
351C22×M16—431no—
352C2×C22⋊Q8—431no—
353C2×C22⋊Q8—431no—
354C2×C4×Q8—431no—
355C2×C4×Q8—431no—
356C22×C42—431no—
357#470—438no—
358C4×Q16—864no—
359C2×#107—431no—
360C2×#106—431no—
361C2×#106—431no—
362C2×#103—431no—
363C2×#103—431no—
364C2×#103—431no—
365C2×#103—431no—
366C2×#103C2×D4311yescharacteristic
367C2×#103C2×D4311yescharacteristic
368C4×M16—864no—
369C2×#97—431no—
370C2×#97C2×D4311yescharacteristic
371C2×C4×C8—431no—
372C2×C4×C8—431no—
373#391—431no—
374#391C2×D4311yescharacteristic
375#389—431no—
376#389C2×D4311yescharacteristic
377#387—861no—
378#387—861no—
379#385—861no—
380#385—861no—
381#380—431no—
382#380—431no—
383C4×C4⋊C4—431no—
384C4×C4⋊C4—431no—
385C4×C4⋊C4—861no—
386C4×C4⋊C4—861no—
387C4×C22⋊C4—861no—
388C4×C22⋊C4—861no—
389#340—431no—
390#340—431no—
391#340—431no—
392#340—431no—
393#340C2×D4311yescharacteristic
394#340C2×D4311yescharacteristic
395C43C4×#47011yescharacteristic, complemented, Sylow
396C22×Q8—431no—
397C22×Q8C22×D4311yescharacteristic
398C23×C4—431no—
399C23×C4—431no—
400C23×C4—431no—
401C2×Q16—434no—
402C2×Q16—862no—
403C2×Q16—862no—
404C2×M16—434no—
405C2×M16—862no—
406C2×M16—862no—
407C2×M16—862no—
408C2×M16—862no—
409C2×M16—862no—
410C22×C8—431no—
411C22×C8—431no—
412C22×C8C22×D4311yescharacteristic
413C22×C8C22×D4311yescharacteristic
414C22⋊Q8—434no—
415C22⋊Q8—434no—
416C22⋊Q8—862no—
417C22⋊Q8—862no—
418C4×Q8—862no—
419C4×Q8—862no—
420C4×Q8—862no—
421C4×Q8—862no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—431no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—431no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4C22×D4311yescharacteristic
432C2×C4⋊C4C22×D4311yescharacteristic
433C2×C4⋊C4C22×D4311yescharacteristic
434C2×C22⋊C4—861no—
435C2×C22⋊C4—861no—
436C2×C22⋊C4—861no—
437C2×C22⋊C4—861no—
438C2×C42—431no—
439C2×C42—431no—
440C2×C42—431no—
441C2×C42—862no—
442C2×C42—862no—
443C2×C42—861no—
444C2×C42—861no—
445C2×C42—861no—
446C2×C42—861no—
447C2×C42C22×D4311yescharacteristic
448#107—862no—
449#106—434no—
450#106—862no—
451#103—22no—
452#103—434no—
453#103—862no—
454#103—862no—
455#103—862no—
456#103C4×D4314yescomplemented
457#97—22no—
458#97—862no—
459C4×C8—434no—
460C4×C8—862no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—861no—
465#95—861no—
466#95—861no—
467#95—861no—
468#95—861no—
469#95—861no—
470#95—861no—
471C24—431no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—432no—
478C2×Q8—861no—
479C2×Q8—861no—
480C2×Q8—861no—
481C2×Q8—861no—
482C2×Q8—861no—
483C2×Q8C2×C4×D4312yes—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—431no—
489C22×C4—431no—
490C22×C4—431no—
491C22×C4—432no—
492C22×C4—432no—
493C22×C4—862no—
494C22×C4—862no—
495C22×C4—862no—
496C22×C4—862no—
497C22×C4—861no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4—861no—
504C22×C4—861no—
505C22×C4—1721no—
506C22×C4—1721no—
507C22×C4D4×D4311yescharacteristic
508C22×C4D4×D4311yescharacteristic
509C22×C4C23×D4311yescharacteristic
510Q16—868no—
511M16—868no—
512M16—868no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—432no—
518C2×C8—432no—
519C2×C8—432no—
520C2×C8—432no—
521C2×C8—861no—
522C2×C8—861no—
523C2×C8C2×C4×D4312yes—
524C2×C8D4×D4312yes—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—42no—
531C4⋊C4—432no—
532C4⋊C4—864no—
533C4⋊C4—864no—
534C4⋊C4—861no—
535C4⋊C4—861no—
536C4⋊C4—861no—
537C4⋊C4—861no—
538C4⋊C4—861no—
539C4⋊C4—1722no—
540C4⋊C4—1722no—
541C4⋊C4—1722no—
542C4⋊C4C2×C4×D4312yes—
543C22⋊C4—864no—
544C22⋊C4—864no—
545C22⋊C4—1722no—
546C22⋊C4—1722no—
547C42—21no—
548C42—21no—
549C42—432no—
550C42—432no—
551C42—862no—
552C42—862no—
553C42—1722no—
554C42—1722no—
555C42—1722no—
556C42—1722no—
557C23—432no—
558C23—861no—
559C23—861no—
560C23—861no—
561C23—861no—
562C23—861no—
563C23—861no—
564C23C2×D4×D4311yescharacteristic
565Q8—22no—
566Q8—22no—
567Q8—41no—
568Q8—41no—
569Q8—862no—
570Q8—862no—
571Q8—1721no—
572Q8—1721no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—432no—
592C2×C4—432no—
593C2×C4—432no—
594C2×C4—432no—
595C2×C4—432no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—862no—
601C2×C4—862no—
602C2×C4—862no—
603C2×C4—862no—
604C2×C4—862no—
605C2×C4—862no—
606C2×C4—1724no—
607C2×C4—1724no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4C22×C4×D4311yescharacteristic
619C2×C4C2×D4×D4311yescharacteristic
620C2×C4#41×D4311yescharacteristic
621C2×C4#41×D4311yescharacteristic
622C2×C4#41×D4311yescharacteristic
623C2×C4#41×D4311yescharacteristic
624C8—22no—
625C8—22no—
626C8—434no—
627C8—862no—
628C22—862no—
629C22—862no—
630C22—862no—
631C22—1721no—
632C22—1721no—
633C22—1721no—
634C22—1721no—
635C22C4×D4×D4311yescharacteristic
636C22#121×D4311yescharacteristic
637C22#1458344811yescharacteristic
638C22#137×D4311yescharacteristic
639C22#137×D4311yescharacteristic
640C22#1458369511yescharacteristic
641C22#1458369811yescharacteristic
642C4—41no—
643C4—41no—
644C4—42no—
645C4—42no—
646C4—81no—
647C4—81no—
648C4—434no—
649C4—862no—
650C4—862no—
651C4—3441no—
652C4—3441no—
653C4—1722no—
654C4—1722no—
655C4C4×D4×D4311yescharacteristic
656C4#1458336711yescharacteristic
657C4#1458340711yescharacteristic
658C4#1458343211yescharacteristic
659C2—1722no—
660C2#1913710711yescharacteristic
661C2#1914341111yescharacteristic
662C2#1914341711yescharacteristic
663C2#470×D4311yescharacteristic
664C2#1914419911yescharacteristic
665C2#1914520011yescharacteristic
666C2#1914520411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1935C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenter#1935D43
hypocenterC43C4×#470
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1935

Complements

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

NH ≅ G/Ntype
2. C2×#14582991C2semidirect
6. #19135465C2semidirect
7. #19135335C2semidirect
8. #19135285C2semidirect
12. #19134483C2semidirect
13. #103×Dic43C2semidirect
14. #19134414C2semidirect
15. C43×#1935C2semidirect
24. #14583156C4semidirect
68. C2×#10621885C2×C4semidirect
108. #13063256C2×C4semidirect
110. #13063250C2×C4semidirect
132. #103×C43C2×C4semidirect
325. Dic43#470semidirect
334. #1935D43semidirect
395. C43C4×#470semidirect
456. #103C4×D43semidirect

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×#145828512
#191371332
#191371252
#191354652
#191353352
#191352852
#191350272
#191350252
#191346272
#191344832
#103×Dic432
#191344142
C43×#19352
C4×#47043