Finite Group Databasebeta

← #25129906

Subgroups — #25129906

Order 11008.

1072 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583453C211yesmaximal, characteristic
2C2×#14583242C211yesmaximal, characteristic
3C2×#14583238C211yesmaximal, characteristic
4#19137076C211yesmaximal, characteristic
5#19135927C211yesmaximal, characteristic, complemented
6#19135921C211yesmaximal, characteristic, complemented
7#19135840C211yesmaximal, characteristic, complemented
8#19135839C211yesmaximal, characteristic, complemented
9#19134906C211yesmaximal, characteristic
10#19134904C211yesmaximal, characteristic
11#19134866C211yesmaximal, characteristic, complemented
12#19134863C211yesmaximal, characteristic, complemented
13#19134848C211yesmaximal, characteristic, complemented
14#19134662C211yesmaximal, characteristic
15C43×#1863C211yesmaximal, characteristic, complemented
16#14583453—24no—
17#14583453—24no—
18C2×#13063324C2211yescharacteristic
19C2×#13063323C2211yescharacteristic
20C2×#13063315—21no—
21C2×#13063305C2211yescharacteristic
22C2×#13063303—21no—
23C2×#13063301C2211yescharacteristic
24C2×C4×Dic86—21no—
25C2×C4×Dic86C2211yescharacteristic
26C2×#13063283C2211yescharacteristic
27C2×#13063283C2211yescharacteristic
28C2×#13063282—21no—
29C2×C42×D43C2211yescharacteristic
30#14583242—24no—
31#14583238—24no—
32C2×#13063258C2211yescharacteristic
33C2×#13063257C2211yescharacteristic
34C2×#13063256C2211yescharacteristic
35C2×#13063250C2211yescharacteristic
36C2×#13063250C2211yescharacteristic
37C2×#13063249C2211yescharacteristic
38C2×#13063249C2211yescharacteristic
39C2×#13063248C2211yescharacteristic
40C2×#13063248C2211yescharacteristic
41C2×(C2×D43)⋊C8C2211yescharacteristic
42C2×(C2×D43)⋊C8C2211yescharacteristic
43#14582798C2211yescharacteristic
44#14582797C2211yescharacteristic
45#14582795C2211yescharacteristic
46#14582773—21no—
47#14582770—21no—
48C4⋊C4×Dic43—21no—
49#14582750—21no—
50#14582662C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582654C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C2×C4×Q8×C43C2211yescharacteristic
57C2×#107×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C43×#389C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86C2311yescharacteristic
65C22×C4×D43D411yescharacteristic
66C22×C4×D43D411yescharacteristic
67C22×C4×D43C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70#13063324—22no—
71#13063324—22no—
72#13063323—22no—
73#13063323—22no—
74#13063315—28no—
75#13063305—22no—
76#13063305D414yes—
77#13063303—28no—
78#13063301—22no—
79#13063301D414yes—
80C4×Dic86—28no—
81C4×Dic86—22no—
82C4×Dic86—22no—
83#13063283—22no—
84#13063283—22no—
85#13063283—22no—
86#13063283—22no—
87#13063282—28no—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×C4×Dic43—21no—
105C2×C4×Dic43—21no—
106C2×C4×Dic43—21no—
107C2×C4×Dic43D411yescharacteristic
108C2×C4×Dic43D411yescharacteristic
109C2×C4×Dic43C2311yescharacteristic
110C42×D43—22no—
111C42×D43—22no—
112#13063258—22no—
113#13063257—22no—
114#13063256—22no—
115#13063250—22no—
116#13063250—22no—
117#13063249—22no—
118#13063249—22no—
119#13063248—22no—
120#13063248—22no—
121(C2×D43)⋊C8—22no—
122(C2×D43)⋊C8—22no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C43⋊#95—21no—
126C22×Q8×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129C4×Q8×C43—22no—
130C4×Q8×C43—22no—
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C42×C43—21no—
137C2×C42×C43C2311yescharacteristic
138#107×C43—22no—
139#103×C43—22no—
140#103×C43—22no—
141#95×C43—21no—
142C23×D43C2×D411yescharacteristic
143C2×Q8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43C2×D412yes—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2411yescharacteristic
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43C2×D411yescharacteristic
161C22×Dic43C2×D411yescharacteristic
162C22×Dic43C2×D411yescharacteristic
163C2×C4×D43—22no—
164C2×C4×D43—21no—
165C2×C4×D43—21no—
166C2×C4×D43—21no—
167C2×C4×D43—21no—
168C2×C4×D43—22no—
169C2×C4×D43—22no—
170C2×C4×D43—22no—
171C2×C4×D43—22no—
172C2×C4×D43—41no—
173C2×C4×D43C2×D412yes—
174C2×C4×D43C2×D412yes—
175C2×Dic86—21no—
176C2×Dic86—21no—
177C2×Dic86—21no—
178C2×Dic86—21no—
179C2×Dic86—24no—
180C2×Dic86—21no—
181C2×Dic86—42no—
182C2×Dic86—42no—
183C2×Dic86C2×D412yes—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C4⋊C4×C43—24no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—42no—
196C4⋊C4×C43C2×D412yes—
197C4⋊C4×C43#4112yes—
198C42×C43—24no—
199C42×C43—21no—
200C42×C43—21no—
201(C2×D43)⋊C4—24no—
202(C2×D43)⋊C4—24no—
203(C2×D43)⋊C4—24no—
204(C2×D43)⋊C4—42no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—24no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—42no—
211C4⋊Dic43C2×D412yes—
212C4⋊Dic43#4112yes—
213Dic43⋊C4—24no—
214Dic43⋊C4—24no—
215Dic43⋊C4—24no—
216Dic43⋊C4—24no—
217Dic43⋊C4—24no—
218Dic43⋊C4—42no—
219Dic43⋊C4—42no—
220C4×Dic43—24no—
221C4×Dic43—24no—
222C4×Dic43—21no—
223C4×Dic43—21no—
224C4×Dic43—22no—
225C4×Dic43—22no—
226C4×Dic43—42no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C23×C43C22×D411yescharacteristic
234C22×D43—21no—
235C22×D43—21no—
236C22×D43—21no—
237C22×D43—21no—
238C22×D43—21no—
239C22×D43—21no—
240C22×D43#12012yes—
241Q8×C43—22no—
242Q8×C43—22no—
243Q8×C43—41no—
244Q8×C43—41no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—22no—
249C2×C4×C43—22no—
250C2×C4×C43—22no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43#13712yes—
263C2×C4×C43C22×D411yescharacteristic
264C2×C4×C43C22×D411yescharacteristic
265C2×C4×C43C2×#4111yescharacteristic
266C2×C4×C43C2×#4111yescharacteristic
267C2×C4×C432−1+411yescharacteristic
268C2×C4×C432−1+411yescharacteristic
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—22no—
276C2×Dic43—22no—
277C2×Dic43—22no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43#12012yes—
288C2×Dic43#13512yes—
289C2×Dic43#13712yes—
290C4×D43—28no—
291C4×D43—22no—
292C4×D43—22no—
293C4×D43—22no—
294C4×D43—22no—
295C4×D43—44no—
296Dic86—22no—
297Dic86—22no—
298Dic86—48no—
299Dic86—41no—
300Dic86—41no—
301C8×C43—41no—
302C8×C43—41no—
303C43⋊C8—41no—
304C43⋊C8—41no—
305#24065—431nomaximal, Sylow
306C22×C43C2×#12011yescharacteristic
307C22×C43#52511yescharacteristic
308C22×C43#53611yescharacteristic
309C22×C43C2×#13511yescharacteristic
310C22×C43C2×#13711yescharacteristic
311C22×C43C2×#13711yescharacteristic
312C22×C43#57511yescharacteristic
313C2×D43—22no—
314C2×D43—22no—
315C2×D43—22no—
316C2×D43—41no—
317C2×D43—41no—
318C2×D43—41no—
319C2×D43—41no—
320C4×C43—22no—
321C4×C43—42no—
322C4×C43—42no—
323C4×C43—42no—
324C4×C43—41no—
325C4×C43—81no—
326C4×C43#54711yescharacteristic
327C4×C43#54711yescharacteristic
328C4×C43#54711yescharacteristic
329C4×C43#54711yescharacteristic
330Dic43—22no—
331Dic43—22no—
332Dic43—22no—
333Dic43—42no—
334Dic43—42no—
335Dic43—42no—
336Dic43—81no—
337C2×#533—431no—
338C2×#485—431no—
339C2×#485—431no—
340#2296—431no—
341#2058—431no—
342#2057—431no—
343#2043—431no—
344#2043—431no—
345#1873—431no—
346#1873—431no—
347#1865—431no—
348#1865—431no—
349#1863—431no—
350#1863D4311yescharacteristic, complemented
351#1817—431no—
352C2×C43#240611yescharacteristic
353C2×C43#300211yescharacteristic
354C2×C43#300411yescharacteristic
355C2×C43#310711yescharacteristic
356C2×C43#311611yescharacteristic
357C2×C43#323111yescharacteristic
358C2×C43#323711yescharacteristic
359D43—42no—
360#533—864no—
361#533—864no—
362C2×C4⋊Q8—431no—
363C2×C4⋊Q8—431no—
364C2×#125—861no—
365C2×C22⋊Q8—431no—
366C2×C22⋊Q8—431no—
367C2×C22⋊Q8—861no—
368C2×C4×Q8—431no—
369C2×C4×Q8—861no—
370C2×C4×Q8C2×D4311yescharacteristic
371C2×#117—431no—
372C2×#117—431no—
373C2×#117—861no—
374C22×C42—431no—
375#485—864no—
376#485—864no—
377C2×#107—431no—
378C2×#107C2×D4311yescharacteristic
379C2×#106—431no—
380C2×#106—431no—
381C2×#103—431no—
382C2×#103—431no—
383C2×#103—431no—
384C2×#103—431no—
385C2×#103—431no—
386C2×#103—431no—
387C2×#103C2×D4311yescharacteristic
388C2×#103C2×D4311yescharacteristic
389C2×C22⋊C8—431no—
390C2×C22⋊C8—431no—
391#389—431no—
392#389—431no—
393#389—431no—
394#389C2×D4311yescharacteristic
395#385—861no—
396#385—861no—
397C4×C4⋊C4—861no—
398C4×C4⋊C4—861no—
399#340—431no—
400#340—431no—
401#340—431no—
402#340C2×D4311yescharacteristic
403#336—431no—
404#336—431no—
405#336—431no—
406#336C2×D4311yescharacteristic
407C43#2406511yescharacteristic, complemented, Sylow
408C22×Q8—431no—
409C22×Q8—861no—
410C22×Q8C22×D4311yescharacteristic
411C23×C4—431no—
412C23×C4—431no—
413C23×C4—431no—
414C22×C8—431no—
415C22×C8—431no—
416C22×C8C22×D4311yescharacteristic
417C22×C8C22×D4311yescharacteristic
418C4⋊Q8—862no—
419C4⋊Q8—862no—
420C4⋊Q8—862no—
421C4⋊Q8—862no—
422#125—868no—
423C22⋊Q8—434no—
424C22⋊Q8—434no—
425C22⋊Q8—862no—
426C22⋊Q8—868no—
427C22⋊Q8—862no—
428C4×Q8—22no—
429C4×Q8—22no—
430C4×Q8—862no—
431C4×Q8—862no—
432C4×Q8—868no—
433#117—868no—
434#117—862no—
435#117—862no—
436#117—862no—
437#117—862no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—431no—
441C2×C4⋊C4—431no—
442C2×C4⋊C4—431no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4—861no—
445C2×C4⋊C4—861no—
446C2×C4⋊C4—861no—
447C2×C4⋊C4—861no—
448C2×C4⋊C4—861no—
449C2×C4⋊C4—861no—
450C2×C4⋊C4—861no—
451C2×C4⋊C4—861no—
452C2×C4⋊C4C22×D4311yescharacteristic
453C2×C4⋊C4C22×D4311yescharacteristic
454C2×C4⋊C4C22×D4311yescharacteristic
455C2×C22⋊C4—861no—
456C2×C22⋊C4—861no—
457C2×C22⋊C4—861no—
458C2×C22⋊C4—861no—
459C2×C42—21no—
460C2×C42—431no—
461C2×C42—431no—
462C2×C42—431no—
463C2×C42—862no—
464C2×C42—862no—
465C2×C42—861no—
466C2×C42—861no—
467C2×C42—861no—
468C2×C42C22×D4311yescharacteristic
469#107—22no—
470#107—862no—
471#106—862no—
472#106—862no—
473#103—22no—
474#103—22no—
475#103—862no—
476#103—862no—
477#103—862no—
478#103—862no—
479#103—862no—
480#103—862no—
481C22⋊C8—862no—
482C22⋊C8—862no—
483#95—21no—
484#95—861no—
485#95—861no—
486#95—861no—
487C24—431no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—432no—
494C2×Q8—864no—
495C2×Q8—861no—
496C2×Q8—861no—
497C2×Q8—861no—
498C2×Q8—861no—
499C2×Q8—861no—
500C2×Q8—1722no—
501C2×Q8—1722no—
502C2×Q8D4×D4312yes—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—431no—
508C22×C4—431no—
509C22×C4—431no—
510C22×C4—432no—
511C22×C4—432no—
512C22×C4—862no—
513C22×C4—862no—
514C22×C4—862no—
515C22×C4—862no—
516C22×C4—862no—
517C22×C4—861no—
518C22×C4—861no—
519C22×C4—861no—
520C22×C4—861no—
521C22×C4—861no—
522C22×C4—861no—
523C22×C4—861no—
524C22×C4—861no—
525C22×C4—1721no—
526C22×C4D4×D4311yescharacteristic
527C22×C4D4×D4311yescharacteristic
528C22×C4C23×D4311yescharacteristic
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—861no—
536C2×C8—861no—
537C2×C8—861no—
538C2×C8—861no—
539C2×C8—861no—
540C2×C8—861no—
541C4⋊C4—24no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—42no—
547C4⋊C4—432no—
548C4⋊C4—432no—
549C4⋊C4—864no—
550C4⋊C4—864no—
551C4⋊C4—864no—
552C4⋊C4—864no—
553C4⋊C4—864no—
554C4⋊C4—864no—
555C4⋊C4—861no—
556C4⋊C4—861no—
557C4⋊C4—861no—
558C4⋊C4—861no—
559C4⋊C4—1722no—
560C4⋊C4—1722no—
561C4⋊C4—1722no—
562C4⋊C4#1062189812yes—
563C4⋊C4D4×D4312yes—
564C22⋊C4—864no—
565C22⋊C4—864no—
566C22⋊C4—864no—
567C22⋊C4—1722no—
568C42—24no—
569C42—21no—
570C42—21no—
571C42—862no—
572C42—862no—
573C42—864no—
574C42—864no—
575C42—861no—
576C42—861no—
577C42—1722no—
578C23—432no—
579C23—861no—
580C23—861no—
581C23—861no—
582C23—861no—
583C23—861no—
584C23—861no—
585C23C2×D4×D4311yescharacteristic
586Q8—22no—
587Q8—22no—
588Q8—41no—
589Q8—41no—
590Q8—862no—
591Q8—862no—
592Q8—1728no—
593Q8—1721no—
594Q8—1721no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—432no—
613C2×C4—432no—
614C2×C4—432no—
615C2×C4—868no—
616C2×C4—861no—
617C2×C4—861no—
618C2×C4—861no—
619C2×C4—861no—
620C2×C4—861no—
621C2×C4—861no—
622C2×C4—862no—
623C2×C4—862no—
624C2×C4—862no—
625C2×C4—862no—
626C2×C4—862no—
627C2×C4—862no—
628C2×C4—862no—
629C2×C4—1724no—
630C2×C4—1721no—
631C2×C4—1721no—
632C2×C4—1721no—
633C2×C4—1721no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4—1721no—
637C2×C4—1721no—
638C2×C4—1721no—
639C2×C4#1306335712yes—
640C2×C4C2×D4×D4311yescharacteristic
641C2×C4C2×D4×D4311yescharacteristic
642C2×C4#41×D4311yescharacteristic
643C2×C4C2×#1062189811yescharacteristic
644C2×C4#1306337211yescharacteristic
645C2×C4#1306337311yescharacteristic
646C8—41no—
647C8—41no—
648C8—1721no—
649C8—1721no—
650C22—862no—
651C22—862no—
652C22—862no—
653C22—1721no—
654C22—1721no—
655C22—1721no—
656C22—1721no—
657C22#120×D4311yescharacteristic
658C22#1458340811yescharacteristic
659C22#1458347211yescharacteristic
660C22#135×D4311yescharacteristic
661C22#137×D4311yescharacteristic
662C22C2×#1306335711yescharacteristic
663C22#1458369511yescharacteristic
664C4—22no—
665C4—42no—
666C4—41no—
667C4—42no—
668C4—42no—
669C4—81no—
670C4—862no—
671C4—862no—
672C4—862no—
673C4—3441no—
674C4—1722no—
675C4—1722no—
676C4—1722no—
677C4#1458354711yescharacteristic
678C4#1458355011yescharacteristic
679C4#1458355111yescharacteristic
680C4#1458355411yescharacteristic
681C2—1722no—
682C2#1913792811yescharacteristic
683C2#1914381011yescharacteristic
684C2#1914383011yescharacteristic
685C2#1914466411yescharacteristic
686C2#1914475311yescharacteristic
687C2#1914575311yescharacteristic
688C2#1914580711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1863C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#1863D43
hypocenterC43#24065
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1863

Complements

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

NH ≅ G/Ntype
5. #19135927C2semidirect
6. #19135921C2semidirect
7. #19135840C2semidirect
8. #19135839C2semidirect
11. #19134866C2semidirect
12. #19134863C2semidirect
13. #19134848C2semidirect
15. C43×#1863C2semidirect
350. #1863D43semidirect
407. C43#24065semidirect

Maximal subgroups

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

subgroupindex
C2×#145834532
C2×#145832422
C2×#145832382
#191370762
#191359272
#191359212
#191358402
#191358392
#191349062
#191349042
#191348662
#191348632
#191348482
#191346622
C43×#18632
#2406543