Finite Group Databasebeta

← #25099309

Subgroups — #25099309

Order 11008.

1122 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582906C211yesmaximal, characteristic
2C2×#14582906C211yesmaximal, characteristic
3C2×C4×#10621872C211yesmaximal, characteristic
4#19137076C211yesmaximal, characteristic
5#391×D43C211yesmaximal, characteristic
6#19135287C211yesmaximal, characteristic, complemented
7#19135286C211yesmaximal, characteristic, complemented
8#19135283C211yesmaximal, characteristic, complemented
9#19135282C211yesmaximal, characteristic, complemented
10#19135274C211yesmaximal, characteristic, complemented
11#19135271C211yesmaximal, characteristic, complemented
12#19135270C211yesmaximal, characteristic, complemented
13#19134313C211yesmaximal, characteristic
14#19134313C211yesmaximal, characteristic
15C43×#1933C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C2×#13063283C2211yescharacteristic
20C2×#13063283C2211yescharacteristic
21C2×C4⋊C4×D43C2211yescharacteristic
22C2×C42×D43C2211yescharacteristic
23#14582906—24no—
24#14582906C418yescomplemented
25C2×#13063250C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C4×#10621872—24no—
32C2×#13063235C2211yescharacteristic
33C2×#13063235C2211yescharacteristic
34C2×C4×C43⋊C8C2211yescharacteristic
35#14582806C2211yescharacteristic
36#14582805C2211yescharacteristic
37#14582804C2211yescharacteristic
38#14582803—21no—
39#14582803—21no—
40#14582798C2211yescharacteristic
41#14582797C2211yescharacteristic
42#14582795C2211yescharacteristic
43#14582773—21no—
44#14582770—21no—
45C4⋊C4×Dic43—21no—
46#14582750—21no—
47#95×D43—21no—
48#95×D43—21no—
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×C4×C8×C43C2211yescharacteristic
58C43×#391C2211yescharacteristic
59C43×#389C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C22×Dic86—21no—
63C22×Dic86C2311yescharacteristic
64C2×Q8×D43—22no—
65C2×Q8×D43—22no—
66C2×Q8×D43—22no—
67C2×Q8×D43—22no—
68C2×Q8×D43—22no—
69C2×Q8×D43C2×C414yes—
70C22×C4×D43—21no—
71C22×C4×D43—21no—
72C22×C4×D43D411yescharacteristic
73C22×C4×D43D411yescharacteristic
74C22×C4×D43C2311yescharacteristic
75C2×#10621872—22no—
76C2×#10621872—22no—
77C2×#10621872—22no—
78C2×#10621872—22no—
79C2×#10621872C2×C414yes—
80C2×#10621872D414yes—
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83#13063283—22no—
84#13063283—22no—
85#13063283—22no—
86#13063283C2×C414yes—
87C2×C4⋊Dic43—21no—
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C4⋊C4×D43—22no—
95C4⋊C4×D43—22no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×C4×Dic43—21no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43D411yescharacteristic
101C2×C4×Dic43D411yescharacteristic
102C2×C4×Dic43C2311yescharacteristic
103C42×D43—22no—
104C42×D43—22no—
105#13063250—22no—
106#13063250C2×C414yescomplemented
107#13063249—22no—
108#13063249C2×C414yescomplemented
109#13063248—22no—
110#13063248C2×C414yescomplemented
111#13063235—22no—
112#13063235—22no—
113C4×C43⋊C8—22no—
114C43⋊#95—21no—
115C43⋊#95—21no—
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
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
158Q8×D43—28no—
159Q8×D43—28no—
160Q8×D43—44no—
161Q8×D43—44no—
162C2×C4×D43—22no—
163C2×C4×D43—22no—
164C2×C4×D43—24no—
165C2×C4×D43—22no—
166C2×C4×D43—22no—
167C2×C4×D43—41no—
168C2×C4×D43—41no—
169C2×C4×D43—42no—
170C2×C4×D43—42no—
171C2×C4×D43—42no—
172C2×C4×D43—42no—
173C2×C4×D43—42no—
174C2×C4×D43C22×C412yes—
175C2×C4×D43C2×D412yes—
176C2×C4×D43#4112yes—
177C2×C4×D43#4112yes—
178C2×C4×D43#4112yes—
179C2×C4×D43#4112yes—
180C2×Dic86—21no—
181C2×Dic86—21no—
182C2×Dic86—21no—
183C2×Dic86—21no—
184C2×Dic86—21no—
185C2×Dic86—24no—
186C2×Dic86—42no—
187C2×Dic86—42no—
188C2×Dic86C22×C412yes—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43C22×C412yes—
194C2×C8×C43C2×D412yes—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—42no—
201C4⋊C4×C43C22×C412yes—
202C42×C43—21no—
203C42×C43—21no—
204(C2×D43)⋊C4—24no—
205(C2×D43)⋊C4—42no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—42no—
212C4⋊Dic43C22×C412yes—
213Dic43⋊C4—42no—
214Dic43⋊C4—42no—
215Dic43⋊C4—42no—
216C4×Dic43—21no—
217C4×Dic43—21no—
218C4×Dic43—24no—
219C4×Dic43—22no—
220C4×Dic43—22no—
221C4×Dic43—42no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8C22×C412yes—
227C2×C43⋊C8C2×D412yes—
228#10621872—28no—
229#10621872—28no—
230C23×C43C22×D411yescharacteristic
231C22×D43—21no—
232C22×D43—21no—
233C22×D43—21no—
234C22×D43—21no—
235C22×D43C4×D412yes—
236C22×D43#12112yes—
237C22×D43#12412yes—
238Q8×C43—22no—
239Q8×C43—22no—
240Q8×C43—41no—
241Q8×C43—41no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—22no—
247C2×C4×C43—22no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43#13712yes—
259C2×C4×C43#13712yes—
260C2×C4×C43C23×C411yescharacteristic
261C2×C4×C43C22×D411yescharacteristic
262C2×C4×C43C2×#4111yescharacteristic
263C2×C4×C43C2×#4111yescharacteristic
264C2×C4×C43C2×#4111yescharacteristic
265C2×C4×C43C2×#4111yescharacteristic
266C2×Dic43—22no—
267C2×Dic43—22no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43C4×D412yes—
285C2×Dic43#12112yes—
286C2×Dic43#12412yes—
287C4×D43—44no—
288C4×D43—44no—
289C4×D43—48no—
290C4×D43—84no—
291C4×D43#11714yes—
292C4×D43C4×D414yes—
293C4×D43#12314yes—
294C4×D43#12614yes—
295Dic86—22no—
296Dic86—22no—
297Dic86—41no—
298Dic86—41no—
299Dic86—48no—
300C8×C43—22no—
301C8×C43—22no—
302C43⋊C8—22no—
303C43⋊C8—22no—
304#21094—431nomaximal, Sylow
305C22×C43C2×C4×D411yescharacteristic
306C22×C43C2×#12111yescharacteristic
307C22×C43C2×#12411yescharacteristic
308C22×C43C2×#13711yescharacteristic
309C22×C43C2×#13711yescharacteristic
310C22×C43#57511yescharacteristic
311C22×C43#57511yescharacteristic
312C2×D43—22no—
313C2×D43—22no—
314C2×D43—22no—
315C2×D43—22no—
316C2×D43—22no—
317C2×D43—22no—
318C2×D43#38814yes—
319C4×C43—22no—
320C4×C43—22no—
321C4×C43—42no—
322C4×C43—42no—
323C4×C43—81no—
324C4×C43—81no—
325C4×C43C2×#11711yescharacteristic
326C4×C43C2×C4×D411yescharacteristic
327C4×C43C2×#12311yescharacteristic
328C4×C43C2×#12611yescharacteristic
329Dic43—42no—
330Dic43—41no—
331Dic43—41no—
332Dic43—42no—
333Dic43—81no—
334Dic43—81no—
335Dic43#38814yes—
336C2×#419—431no—
337C2×#419—431no—
338C2×C4×M16—431no—
339#2296—431no—
340C2×#391—431no—
341#1935—431no—
342#1935—431no—
343#1935—431no—
344#1935—431no—
345#1933—431no—
346#1933—431no—
347#1933—431no—
348#1933D4311yescharacteristic, complemented
349#1736—431no—
350#1736—431no—
351C2×C43C2×#38811yescharacteristic
352C2×C43C4×#13711yescharacteristic
353C2×C43C4×#13711yescharacteristic
354C2×C43#305611yescharacteristic
355C2×C43#305611yescharacteristic
356C2×C43#313911yescharacteristic
357C2×C43#314011yescharacteristic
358D43—24no—
359C23×Q8—431no—
360C22×M16—431no—
361C22×M16—431no—
362C2×#117—431no—
363C2×#117—431no—
364C22×C4⋊C4—431no—
365C22×C42—431no—
366#419—438no—
367#419—864no—
368C2×#103—431no—
369C2×#103—431no—
370C2×#103—431no—
371C2×#103—431no—
372C2×#103—431no—
373C2×#103—431no—
374C2×#103C2×D4311yescharacteristic
375C2×#103C2×D4311yescharacteristic
376C4×M16—864no—
377C2×#97—431no—
378C2×#97—431no—
379C2×C4×C8—431no—
380C2×C4×C8C2×D4311yescharacteristic
381#391—431no—
382#391—431no—
383#391—431no—
384#391—861no—
385#391—861no—
386#391C2×D4311yescharacteristic
387#389—431no—
388#389—431no—
389#389—431no—
390#389C2×D4311yescharacteristic
391#385—861no—
392#385—861no—
393C4×C4⋊C4—861no—
394C4×C4⋊C4—861no—
395C2×#95—861no—
396C2×#95—861no—
397#340—431no—
398#340—431no—
399#340—431no—
400#340—431no—
401#340—431no—
402#340—431no—
403#340C2×D4311yescharacteristic
404#340C2×D4311yescharacteristic
405C43#2109411yescharacteristic, complemented, Sylow
406C22×Q8—434no—
407C22×Q8—431no—
408C22×Q8—861no—
409C22×Q8—862no—
410C22×Q8—862no—
411C22×Q8—862no—
412C22×Q8—862no—
413C22×Q8—862no—
414C22×Q8C22×D4311yescharacteristic
415C23×C4—431no—
416C23×C4—431no—
417C23×C4—431no—
418C23×C4—861no—
419C23×C4—861no—
420C2×M16—434no—
421C2×M16—434no—
422C2×M16—862no—
423C2×M16—862no—
424C2×M16—862no—
425C2×M16—862no—
426C22×C8—431no—
427C22×C8—431no—
428C22×C8C22×D4311yescharacteristic
429C22×C8C22×D4311yescharacteristic
430#117—434no—
431#117—862no—
432#117—862no—
433#117—862no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—431no—
436C2×C4⋊C4—431no—
437C2×C4⋊C4—431no—
438C2×C4⋊C4—862no—
439C2×C4⋊C4—862no—
440C2×C4⋊C4—861no—
441C2×C4⋊C4—861no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4C22×D4311yescharacteristic
445C2×C4⋊C4C22×D4311yescharacteristic
446C2×C4⋊C4C22×D4311yescharacteristic
447C2×C22⋊C4—861no—
448C2×C22⋊C4—861no—
449C2×C42—431no—
450C2×C42—431no—
451C2×C42—431no—
452C2×C42—862no—
453C2×C42—862no—
454C2×C42—861no—
455C2×C42—861no—
456C2×C42C22×D4311yescharacteristic
457#103—22no—
458#103—434no—
459#103—434no—
460#103—434no—
461#103—862no—
462#103—862no—
463#103—862no—
464#103C4×D4314yescomplemented
465#97—862no—
466#97—862no—
467C4×C8—22no—
468C4×C8—862no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—861no—
473#95—861no—
474#95—861no—
475#95—861no—
476#95—861no—
477#95—861no—
478#95—861no—
479#95—861no—
480#95—861no—
481C24—431no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—432no—
488C2×Q8—864no—
489C2×Q8—868no—
490C2×Q8—868no—
491C2×Q8—861no—
492C2×Q8—861no—
493C2×Q8—861no—
494C2×Q8—861no—
495C2×Q8—861no—
496C2×Q8—1722no—
497C2×Q8—1722no—
498C2×Q8—1724no—
499C2×Q8—1724no—
500C2×Q8C2×C4×D4312yes—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—431no—
506C22×C4—432no—
507C22×C4—432no—
508C22×C4—432no—
509C22×C4—432no—
510C22×C4—432no—
511C22×C4—432no—
512C22×C4—431no—
513C22×C4—431no—
514C22×C4—862no—
515C22×C4—862no—
516C22×C4—864no—
517C22×C4—861no—
518C22×C4—861no—
519C22×C4—862no—
520C22×C4—862no—
521C22×C4—861no—
522C22×C4—861no—
523C22×C4—1721no—
524C22×C4—1721no—
525C22×C4—1722no—
526C22×C4—1722no—
527C22×C4—1722no—
528C22×C4—1722no—
529C22×C4—1722no—
530C22×C4D4×D4311yescharacteristic
531C22×C4D4×D4311yescharacteristic
532C22×C4C23×D4311yescharacteristic
533M16—868no—
534M16—868no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—432no—
540C2×C8—432no—
541C2×C8—861no—
542C2×C8—861no—
543C2×C8—861no—
544C2×C8—861no—
545C2×C8C2×C4×D4312yes—
546C2×C8D4×D4312yes—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—42no—
553C4⋊C4—432no—
554C4⋊C4—861no—
555C4⋊C4—861no—
556C4⋊C4—861no—
557C4⋊C4—861no—
558C4⋊C4—861no—
559C4⋊C4—1722no—
560C4⋊C4—1722no—
561C4⋊C4—1722no—
562C4⋊C4—1722no—
563C4⋊C4C2×C4×D4312yes—
564C22⋊C4—864no—
565C22⋊C4—1722no—
566C42—21no—
567C42—21no—
568C42—862no—
569C42—862no—
570C42—864no—
571C42—861no—
572C42—861no—
573C42—1722no—
574C23—432no—
575C23—432no—
576C23—432no—
577C23—861no—
578C23—861no—
579C23—861no—
580C23—861no—
581C23C2×D4×D4311yescharacteristic
582Q8—22no—
583Q8—22no—
584Q8—41no—
585Q8—41no—
586Q8—862no—
587Q8—862no—
588Q8—1728no—
589Q8—1721no—
590Q8—1721no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—432no—
608C2×C4—432no—
609C2×C4—432no—
610C2×C4—434no—
611C2×C4—434no—
612C2×C4—434no—
613C2×C4—434no—
614C2×C4—862no—
615C2×C4—862no—
616C2×C4—861no—
617C2×C4—861no—
618C2×C4—861no—
619C2×C4—861no—
620C2×C4—861no—
621C2×C4—861no—
622C2×C4—3444no—
623C2×C4—1724no—
624C2×C4—1724no—
625C2×C4—1728no—
626C2×C4—1721no—
627C2×C4—1721no—
628C2×C4—1721no—
629C2×C4—1721no—
630C2×C4—1721no—
631C2×C4—1721no—
632C2×C4—1721no—
633C2×C4—1721no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4#1306335412yes—
637C2×C4#1306335712yes—
638C2×C4C22×C4×D4311yescharacteristic
639C2×C4C2×D4×D4311yescharacteristic
640C2×C4#41×D4311yescharacteristic
641C2×C4#41×D4311yescharacteristic
642C2×C4#41×D4311yescharacteristic
643C2×C4#41×D4311yescharacteristic
644C8—22no—
645C8—22no—
646C8—862no—
647C8—862no—
648C22—434no—
649C22—862no—
650C22—862no—
651C22—862no—
652C22—862no—
653C22—862no—
654C22—862no—
655C22C4×D4×D4311yescharacteristic
656C22#121×D4311yescharacteristic
657C22#124×D4311yescharacteristic
658C22C2×#1306335411yescharacteristic
659C22C2×#1306335711yescharacteristic
660C22#1458369611yescharacteristic
661C22#1458369611yescharacteristic
662C4—22no—
663C4—22no—
664C4—42no—
665C4—42no—
666C4—81no—
667C4—81no—
668C4—434no—
669C4—3441no—
670C4—3441no—
671C4—1721no—
672C4—1721no—
673C4—1722no—
674C4—1722no—
675C4#117×D4311yescharacteristic
676C4C4×D4×D4311yescharacteristic
677C4#123×D4311yescharacteristic
678C4#126×D4311yescharacteristic
679C2—864no—
680C2#388×D4311yescharacteristic
681C2C4×#1306335411yescharacteristic
682C2C4×#1306335711yescharacteristic
683C2#1914421811yescharacteristic
684C2#1914422211yescharacteristic
685C2#1914497211yescharacteristic
686C2#1914497811yescharacteristic
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#21094
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
6. #19135287C2semidirect
7. #19135286C2semidirect
8. #19135283C2semidirect
9. #19135282C2semidirect
10. #19135274C2semidirect
11. #19135271C2semidirect
12. #19135270C2semidirect
15. C43×#1933C2semidirect
24. #14582906C4semidirect
106. #13063250C2×C4semidirect
108. #13063249C2×C4semidirect
110. #13063248C2×C4semidirect
132. #103×C43C2×C4semidirect
348. #1933D43semidirect
405. C43#21094semidirect
464. #103C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145829062
C2×C4×#106218722
#191370762
#391×D432
#191352872
#191352862
#191352832
#191352822
#191352742
#191352712
#191352702
#191343132
C43×#19332
#2109443