Finite Group Databasebeta

← #25153722

Subgroups — #25153722

Order 11008.

990 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583181C211yesmaximal, characteristic, complemented
2C2×#103×D43C211yesmaximal, characteristic
3#19138293C211yesmaximal, characteristic
4#19137429C211yesmaximal, characteristic
5#19136136C211yesmaximal, characteristic, complemented
6#19135976C211yesmaximal, characteristic, complemented
7#19135972C211yesmaximal, characteristic, complemented
8#19134866C211yesmaximal, characteristic, complemented
9#19134864C211yesmaximal, characteristic, complemented
10#19134789C211yesmaximal, characteristic
11#19134774C211yesmaximal, characteristic
12#19134619C211yesmaximal, characteristic
13#19134599C211yesmaximal, characteristic, complemented
14#19134528C211yesmaximal, characteristic
15C43×#2024C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C2×#13063301—21no—
19C2×C4×Dic86C2211yescharacteristic
20C2×#13063290C2211yescharacteristic
21C2×C4⋊C4×D43C2211yescharacteristic
22#14583181—24no—
23C2×#13063257C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×#13063256C2211yescharacteristic
27C2×C4⋊(C43⋊C8)C2211yescharacteristic
28C2×Dic43⋊C8C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×#13063248C2211yescharacteristic
34C2×#13063248C2211yescharacteristic
35#103×D43—24no—
36C2×(C2×D43)⋊C8C2211yescharacteristic
37#14582832—21no—
38#14582818—21no—
39#14582806C2211yescharacteristic
40#14582803—21no—
41#14582803—21no—
42#14582798C2211yescharacteristic
43#14582797C2211yescharacteristic
44#14582770—21no—
45#14582768C2211yescharacteristic
46#14582758—21no—
47#14582756C2211yescharacteristic
48#14582756C2211yescharacteristic
49C4×(C2×D43)⋊C4C2211yescharacteristic
50#14582746—21no—
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×C4⋊Q8×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C43×#391C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×Dic86—21no—
62C22×Dic86C2311yescharacteristic
63C2×Q8×D43—22no—
64C2×Q8×D43—22no—
65C2×Q8×D43—22no—
66C2×Q8×D43—41no—
67C2×Q8×D43—41no—
68C2×Q8×D43Q814yescomplemented
69C22×C4×D43—21no—
70C22×C4×D43—21no—
71C22×C4×D43C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C2×C8×D43—22no—
75C2×C8×D43—22no—
76C2×C8×D43—41no—
77#13063301—44no—
78C4×Dic86—22no—
79C4×Dic86—41no—
80#13063290—22no—
81#13063290—41no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C4⋊C4×D43—22no—
93C4⋊C4×D43—41no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4D411yescharacteristic
97C2×(C2×D43)⋊C4D411yescharacteristic
98C2×C4×Dic43—21no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43C2311yescharacteristic
101#13063257—41no—
102#13063256—22no—
103#13063256—22no—
104#13063256—41no—
105C4⋊(C43⋊C8)—22no—
106Dic43⋊C8—41no—
107#13063250—22no—
108#13063250—22no—
109#13063249—22no—
110#13063249—41no—
111#13063248—22no—
112#13063248D414yes—
113(C2×D43)⋊C8—22no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95D411yescharacteristic
121C43⋊#95D411yescharacteristic
122C22×Q8×C43—21no—
123C22×Q8×C43C2311yescharacteristic
124C22×C8×C43C2311yescharacteristic
125C22×C8×C43C2311yescharacteristic
126C4⋊Q8×C43—22no—
127C4⋊Q8×C43—41no—
128C2×C4⋊C4×C43—21no—
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C42×C43C2311yescharacteristic
133#103×C43—22no—
134#103×C43—41no—
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×C43—42no—
144C2×Q8×C43—42no—
145C2×Q8×C43—81no—
146C2×Q8×C43C2×Q812yes—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2411yescharacteristic
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43C2×D411yescharacteristic
159C22×Dic43C2×D411yescharacteristic
160C22×Dic43C2×D411yescharacteristic
161Q8×D43—28no—
162Q8×D43—44no—
163Q8×D43—44no—
164Q8×D43—44no—
165C2×C4×D43—21no—
166C2×C4×D43—21no—
167C2×C4×D43—21no—
168C2×C4×D43—21no—
169C2×C4×D43—24no—
170C2×C4×D43—42no—
171C2×C4×D43—42no—
172C2×C4×D43—42no—
173C2×C4×D43—42no—
174C2×C4×D43—81no—
175C2×C4×D43C2×Q812yes—
176C2×C4×D43#4112yes—
177C2×Dic86—21no—
178C2×Dic86—21no—
179C2×Dic86—21no—
180C2×Dic86—24no—
181C2×Dic86—42no—
182C2×Dic86—42no—
183C2×Dic86C2×D412yes—
184C2×Dic86C2×Q812yes—
185C2×Dic86#4112yes—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—42no—
198C4⋊C4×C43C2×D412yes—
199C42×C43—21no—
200C42×C43—21no—
201(C2×D43)⋊C4—22no—
202(C2×D43)⋊C4—42no—
203(C2×D43)⋊C4—42no—
204(C2×D43)⋊C4SD1614yes—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—42no—
212Dic43⋊C4—42no—
213Dic43⋊C4—42no—
214Dic43⋊C4—42no—
215Dic43⋊C4—42no—
216Dic43⋊C4—42no—
217Dic43⋊C4—81no—
218C4×Dic43—21no—
219C4×Dic43—21no—
220C4×Dic43—42no—
221C4×Dic43—42no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8C2×D412yes—
228C8×D43—44no—
229C23×C43C22×D411yescharacteristic
230C22×D43—21no—
231C22×D43—21no—
232C22×D43—21no—
233C22×D43—21no—
234C22×D43C22⋊Q812yes—
235C22×D43C2×SD1612yes—
236C22×D43#13712yes—
237Q8×C43—22no—
238Q8×C43—22no—
239Q8×C43—41no—
240Q8×C43—41no—
241Q8×C43—84no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—22no—
245C2×C4×C43—21no—
246C2×C4×C43—22no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
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—41no—
259C2×C4×C43C2×SD1612yes—
260C2×C4×C43C22×D411yescharacteristic
261C2×C4×C43C22×Q811yescharacteristic
262C2×C4×C43C2×#4111yescharacteristic
263C2×C4×C43C2×#4111yescharacteristic
264C2×C4×C43H(5,𝔽2)11yescharacteristic
265C2×C4×C43H(5,𝔽2)11yescharacteristic
266C2×Dic43—22no—
267C2×Dic43—22no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—22no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—21no—
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×Dic43—41no—
285C2×Dic43C22⋊Q812yes—
286C2×Dic43C2×SD1612yes—
287C4×D43—22no—
288C4×D43—22no—
289C4×D43—22no—
290C4×D43—22no—
291C4×D43—48no—
292C4×D43—84no—
293Dic86—22no—
294Dic86—22no—
295Dic86—22no—
296Dic86—48no—
297Dic86C22⋊Q814yescomplemented
298C8×C43—41no—
299C8×C43—41no—
300C43⋊C8—22no—
301C43⋊C8—41no—
302#25955—431nomaximal, Sylow
303C22×C43C2×C22⋊Q811yescharacteristic
304C22×C43D4211yescharacteristic
305C22×C43#54611yescharacteristic
306C22×C43C22×SD1611yescharacteristic
307C22×C43C2×#13711yescharacteristic
308C22×C43#57711yescharacteristic
309C22×C43#57811yescharacteristic
310C2×D43—22no—
311C2×D43—22no—
312C2×D43—22no—
313C2×D43—22no—
314C2×D43—22no—
315C2×D43—22no—
316C2×D43#47514yescomplemented
317C4×C43—22no—
318C4×C43—42no—
319C4×C43—41no—
320C4×C43—42no—
321C4×C43—81no—
322C4×C43—81no—
323C4×C43C2×C22⋊Q811yescharacteristic
324C4×C43#54311yescharacteristic
325C4×C43#54611yescharacteristic
326C4×C43#55111yescharacteristic
327Dic43—24no—
328Dic43—22no—
329Dic43—22no—
330Dic43—41no—
331Dic43—81no—
332Dic43—81no—
333Dic43—81no—
334C2×#475—431no—
335C22×#103—431no—
336#2440—431no—
337Q8×C22⋊C4—431no—
338#2096—431no—
339#2066—431no—
340#2066—431no—
341#2024D4311yescharacteristic, complemented
342#1865—431no—
343#1865—431no—
344#1853—431no—
345#1850—431no—
346#1807—431no—
347#1803—431no—
348#1787—431no—
349C2×C43#243711yescharacteristic
350C2×C43C2×#47511yescharacteristic
351C2×C43#308211yescharacteristic
352C2×C43#327011yescharacteristic
353C2×C43D4×SD1611yescharacteristic
354C2×C43#329811yescharacteristic
355C2×C43#331611yescharacteristic
356D43—24no—
357C23×Q8—431no—
358C23×C8—431no—
359C2×C4⋊Q8C2×D4311yescharacteristic
360C2×C22⋊Q8—861no—
361C2×C4×Q8—431no—
362C2×C4×Q8—431no—
363C22×C4⋊C4—431no—
364#475—864no—
365C2×#106—431no—
366C2×#106—431no—
367C2×#106—431no—
368C2×#106—431no—
369C2×C4⋊C8—431no—
370C2×C4⋊C8—431no—
371C2×#103—431no—
372C2×#103—431no—
373C2×#103—431no—
374C2×#103—431no—
375C2×#103—431no—
376C2×#103—431no—
377C2×#103—864no—
378C2×#103C2×D4311yescharacteristic
379C2×#103C2×D4311yescharacteristic
380C2×C22⋊C8—431no—
381#398—861no—
382#395—861no—
383#391—431no—
384#391—861no—
385#391—861no—
386#391C2×D4311yescharacteristic
387#389—431no—
388#389—431no—
389#385—861no—
390#384—431no—
391#380—431no—
392#380—431no—
393#380—861no—
394C4×C22⋊C4—431no—
395C4×C22⋊C4—861no—
396#340—431no—
397#340—431no—
398#340C2×D4311yescharacteristic
399#340C2×D4311yescharacteristic
400#336—431no—
401#336C2×D4311yescharacteristic
402C43#2595511yescharacteristic, complemented, Sylow
403C22×Q8—21no—
404C22×Q8—434no—
405C22×Q8—431no—
406C22×Q8—861no—
407C22×Q8—862no—
408C22×Q8—862no—
409C22×Q8—862no—
410C22×Q8—1721no—
411C22×Q8—1721no—
412C22×Q8C22×D4311yescharacteristic
413C23×C4—431no—
414C23×C4—861no—
415C23×C4—861no—
416C22×C8—431no—
417C22×C8—431no—
418C22×C8—862no—
419C22×C8—862no—
420C22×C8—1721no—
421C22×C8C22×D4311yescharacteristic
422C22×C8C22×D4311yescharacteristic
423C4⋊Q8—22no—
424C4⋊Q8—41no—
425C22⋊Q8—1724no—
426C4×Q8—862no—
427C4×Q8—862no—
428C4×Q8—1721no—
429C4×Q8—1721no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—431no—
432C2×C4⋊C4—431no—
433C2×C4⋊C4—431no—
434C2×C4⋊C4—862no—
435C2×C4⋊C4—861no—
436C2×C4⋊C4—861no—
437C2×C4⋊C4—861no—
438C2×C4⋊C4—861no—
439C2×C4⋊C4—861no—
440C2×C4⋊C4—861no—
441C2×C4⋊C4—861no—
442C2×C4⋊C4—1721no—
443C2×C4⋊C4C22×D4311yescharacteristic
444C2×C4⋊C4C22×D4311yescharacteristic
445C2×C4⋊C4C22×D4311yescharacteristic
446C2×C22⋊C4—431no—
447C2×C22⋊C4—431no—
448C2×C22⋊C4—861no—
449C2×C22⋊C4—861no—
450C2×C42—431no—
451C2×C42—861no—
452C2×C42—861no—
453C2×C42C22×D4311yescharacteristic
454#106—862no—
455#106—862no—
456#106—1721no—
457#106—1721no—
458C4⋊C8—862no—
459C4⋊C8—1721no—
460#103—22no—
461#103—41no—
462#103—434no—
463#103—862no—
464#103—862no—
465#103—862no—
466#103—862no—
467#103—1721no—
468C22⋊C8—862no—
469#95—21no—
470#95—21no—
471#95—431no—
472#95—431no—
473#95—861no—
474#95—861no—
475#95—861no—
476#95—861no—
477#95—861no—
478#95—861no—
479C24—431no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—42no—
486C2×Q8—42no—
487C2×Q8—81no—
488C2×Q8—432no—
489C2×Q8—432no—
490C2×Q8—432no—
491C2×Q8—864no—
492C2×Q8—861no—
493C2×Q8—861no—
494C2×Q8—861no—
495C2×Q8—868no—
496C2×Q8—1722no—
497C2×Q8—1722no—
498C2×Q8—1724no—
499C2×Q8—1724no—
500C2×Q8—1724no—
501C2×Q8Q8×D4312yes—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—431no—
507C22×C4—431no—
508C22×C4—432no—
509C22×C4—432no—
510C22×C4—431no—
511C22×C4—864no—
512C22×C4—861no—
513C22×C4—861no—
514C22×C4—861no—
515C22×C4—861no—
516C22×C4—861no—
517C22×C4—861no—
518C22×C4—861no—
519C22×C4—861no—
520C22×C4—3441no—
521C22×C4—1722no—
522C22×C4—1722no—
523C22×C4—1722no—
524C22×C4—1722no—
525C22×C4D4×D4311yescharacteristic
526C22×C4D4×D4311yescharacteristic
527C22×C4C23×D4311yescharacteristic
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—432no—
535C2×C8—861no—
536C2×C8—861no—
537C2×C8—861no—
538C2×C8—861no—
539C2×C8—861no—
540C2×C8—1724no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—42no—
547C4⋊C4—861no—
548C4⋊C4—861no—
549C4⋊C4—861no—
550C4⋊C4—861no—
551C4⋊C4—861no—
552C4⋊C4—861no—
553C4⋊C4—3441no—
554C4⋊C4—1722no—
555C4⋊C4—1722no—
556C4⋊C4—1722no—
557C4⋊C4—1722no—
558C4⋊C4—1722no—
559C4⋊C4—1722no—
560C4⋊C4D4×D4312yes—
561C22⋊C4—434no—
562C22⋊C4—862no—
563C22⋊C4—1722no—
564C22⋊C4—1722no—
565C42—21no—
566C42—21no—
567C42—861no—
568C42—861no—
569C42—1722no—
570C42—1722no—
571C23—432no—
572C23—432no—
573C23—432no—
574C23—861no—
575C23—861no—
576C23—861no—
577C23—861no—
578C23C2×D4×D4311yescharacteristic
579Q8—22no—
580Q8—22no—
581Q8—41no—
582Q8—41no—
583Q8—84no—
584Q8—434no—
585Q8—862no—
586Q8—862no—
587Q8—862no—
588Q8—1728no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—41no—
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—432no—
607C2×C4—432no—
608C2×C4—862no—
609C2×C4—861no—
610C2×C4—862no—
611C2×C4—861no—
612C2×C4—861no—
613C2×C4—862no—
614C2×C4—861no—
615C2×C4—862no—
616C2×C4—862no—
617C2×C4—862no—
618C2×C4—862no—
619C2×C4—861no—
620C2×C4—861no—
621C2×C4—861no—
622C2×C4—3444no—
623C2×C4—1728no—
624C2×C4—1721no—
625C2×C4—1721no—
626C2×C4—1721no—
627C2×C4—1721no—
628C2×C4—1721no—
629C2×C4—1721no—
630C2×C4—1721no—
631C2×C4—1721no—
632C2×C4—1721no—
633C2×C4SD16×D4312yes—
634C2×C4C2×D4×D4311yescharacteristic
635C2×C4C2×Q8×D4311yescharacteristic
636C2×C4#41×D4311yescharacteristic
637C2×C4#41×D4311yescharacteristic
638C2×C4#1306337011yescharacteristic
639C2×C4#1306337111yescharacteristic
640C8—41no—
641C8—41no—
642C8—862no—
643C8—1721no—
644C22—434no—
645C22—862no—
646C22—862no—
647C22—862no—
648C22—862no—
649C22—862no—
650C22—862no—
651C22C22⋊Q8×D4311yescharacteristic
652C22#1458353111yescharacteristic
653C22#1458354211yescharacteristic
654C22C2×SD16×D4311yescharacteristic
655C22#137×D4311yescharacteristic
656C22#1458370911yescharacteristic
657C22#1458371211yescharacteristic
658C4—22no—
659C4—42no—
660C4—41no—
661C4—42no—
662C4—81no—
663C4—81no—
664C4—862no—
665C4—864no—
666C4—862no—
667C4—3441no—
668C4—3441no—
669C4—3441no—
670C4—1721no—
671C4C22⋊Q8×D4311yescharacteristic
672C4#1458352411yescharacteristic
673C4#1458354211yescharacteristic
674C4#1458357911yescharacteristic
675C2—864no—
676C2#1913825511yescharacteristic
677C2#475×D4311yescharacteristic
678C2#1914443211yescharacteristic
679C2#1914616811yescharacteristic
680C2#1914628911yescharacteristic
681C2#1914645911yescharacteristic
682C2#1914670511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2024C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#2024D43
hypocenterC43#25955
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2024

Complements

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

NH ≅ G/Ntype
1. C2×#14583181C2semidirect
5. #19136136C2semidirect
6. #19135976C2semidirect
7. #19135972C2semidirect
8. #19134866C2semidirect
9. #19134864C2semidirect
13. #19134599C2semidirect
15. C43×#2024C2semidirect
68. C2×Q8×D43Q8semidirect
297. Dic86C22⋊Q8semidirect
316. C2×D43#475semidirect
341. #2024D43semidirect
402. C43#25955semidirect

Maximal subgroups

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

subgroupindex
C2×#145831812
C2×#103×D432
#191382932
#191374292
#191361362
#191359762
#191359722
#191348662
#191348642
#191347892
#191347742
#191346192
#191345992
#191345282
C43×#20242
#2595543