Finite Group Databasebeta

← #25129235

Subgroups — #25129235

Order 11008.

1500 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×C22⋊Q8×D43C211yesmaximal, characteristic
2C2×#14583229C211yesmaximal, characteristic, complemented
3C2×#14582756C211yesmaximal, characteristic
4#19135793C212yesmaximal, complemented
5#19135789C212yesmaximal, complemented
6#19134903C211yesmaximal, characteristic, complemented
7#19134900C211yesmaximal, characteristic, complemented
8#19134786C212yesmaximal, complemented
9#19134528C212yesmaximal, complemented
10#19134504C211yesmaximal, characteristic
11C2×C43×#483C211yesmaximal, characteristic, complemented
12C22×Q8×D43C2211yescharacteristic
13C23×C4×D43C2211yescharacteristic
14C2×#13063305C2211yescharacteristic
15C2×#13063304C2211yescharacteristic
16C2×#13063303—21no—
17C2×#13063302—21no—
18C2×#13063301C2211yescharacteristic
19C22⋊Q8×D43—24no—
20C22⋊Q8×D43—24no—
21C22×C4⋊Dic43C2211yescharacteristic
22C2×C4⋊C4×D43—21no—
23C2×C4⋊C4×D43C2211yescharacteristic
24C22×(C2×D43)⋊C4—21no—
25C2×C22⋊C4×D43—21no—
26#14583229—24no—
27C2×#13063256C2212yescomplemented
28C2×#13063250C2212yescomplemented
29C2×#13063249C2212yescomplemented
30C2×#13063248C2212yescomplemented
31C2×C22⋊(C43⋊C8)C2211yescharacteristic
32C2×(C2×D43)⋊C8C2212yes—
33C2×(C2×D43)⋊C8C2212yes—
34#14582756—21no—
35#14582756—21no—
36#14582756C2212yes—
37#14582756C2212yes—
38C2×C43⋊#95—21no—
39#14582662C2212yescomplemented
40#14582661C2212yescomplemented
41C2×C22⋊Q8×C43C2211yescharacteristic
42C22×C4⋊C4×C43C2211yescharacteristic
43C43×#483—24no—
44C2×#106×C43C2212yescomplemented
45C2×#103×C43C2212yescomplemented
46C2×C22⋊C8×C43C2211yescharacteristic
47C24×D43D411yescharacteristic
48C22×Dic86—21no—
49C22×Dic86C2311yescharacteristic
50C2×Q8×D43—22no—
51C2×Q8×D43—22no—
52C2×Q8×D43—24no—
53C2×Q8×D43—42no—
54C23×Dic43—21no—
55C23×Dic43D411yescharacteristic
56C22×C4×D43—21no—
57C22×C4×D43—21no—
58C22×C4×D43—22no—
59C22×C4×D43—22no—
60C22×C4×D43—24no—
61C22×C4×D43—42no—
62C22×C4×D43D411yescharacteristic
63C22×C4×D43D411yescharacteristic
64C22×C4×D43C2311yescharacteristic
65C22×C4×D43C2311yescharacteristic
66C22×C43⋊C8C2312yes—
67#13063305—22no—
68#13063305—22no—
69#13063304—22no—
70#13063304D414yes—
71#13063303—28no—
72#13063302—28no—
73#13063301—22no—
74#13063301—22no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43—42no—
78C2×C4⋊Dic43C2312yes—
79C2×C4⋊Dic43C2311yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C4⋊C4×D43—28no—
84C4⋊C4×D43—22no—
85C4⋊C4×D43—22no—
86C2×C22⋊Dic43—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—22no—
90C2×(C2×D43)⋊C4—22no—
91C2×(C2×D43)⋊C4—44no—
92C22⋊C4×D43—28no—
93#13063256—24no—
94#13063250—42no—
95#13063249—42no—
96#13063248—24no—
97C22⋊(C43⋊C8)—22no—
98(C2×D43)⋊C8—24no—
99(C2×D43)⋊C8—42no—
100C43⋊#95—22no—
101C43⋊#95—22no—
102C22×Q8×C43C2311yescharacteristic
103C23×C4×C43—21no—
104C23×C4×C43C2311yescharacteristic
105C22×C8×C43C2312yes—
106C22⋊Q8×C43—22no—
107C22⋊Q8×C43D414yes—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43—22no—
110C2×C4⋊C4×C43—22no—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43C2312yes—
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C22⋊C4×C43—21no—
115#106×C43—24no—
116#103×C43—24no—
117C22⋊C8×C43—22no—
118C24×C43C2×D411yescharacteristic
119C23×D43—22no—
120C23×D43—22no—
121C23×D43—22no—
122C23×D43—22no—
123C23×D43—41no—
124C23×D43—41no—
125C23×D43SD1614yes—
126C23×D43C2×D411yescharacteristic
127C23×D43C2×D411yescharacteristic
128C2×Q8×C43—21no—
129C2×Q8×C43—22no—
130C2×Q8×C43—22no—
131C2×Q8×C43C2×D412yes—
132C22×C4×C43—22no—
133C22×C4×C43—22no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—22no—
137C22×C4×C43—42no—
138C22×C4×C43—42no—
139C22×C4×C43—42no—
140C22×C4×C43C2×D412yes—
141C22×C4×C43C2×D412yes—
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2411yescharacteristic
144C22×Dic43—22no—
145C22×Dic43—22no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—22no—
149C22×Dic43—41no—
150C22×Dic43—42no—
151C22×Dic43—42no—
152C22×Dic43—42no—
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155Q8×D43—48no—
156Q8×D43—48no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—22no—
160C2×C4×D43—24no—
161C2×C4×D43—24no—
162C2×C4×D43—22no—
163C2×C4×D43—22no—
164C2×C4×D43—21no—
165C2×C4×D43—21no—
166C2×C4×D43—22no—
167C2×C4×D43—22no—
168C2×C4×D43—22no—
169C2×C4×D43—22no—
170C2×C4×D43—41no—
171C2×C4×D43—41no—
172C2×C4×D43—42no—
173C2×C4×D43—42no—
174C2×C4×D43—48no—
175C2×C4×D43—48no—
176C2×C4×D43—42no—
177C2×C4×D43—42no—
178C2×C4×D43#4114yes—
179C2×Dic86—22no—
180C2×Dic86—22no—
181C2×Dic86—24no—
182C2×Dic86—21no—
183C2×Dic86—42no—
184C2×Dic86—42no—
185C2×Dic86C2×D412yes—
186C2×C8×C43—22no—
187C2×C8×C43—22no—
188C2×C8×C43—22no—
189C4⋊C4×C43—24no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—22no—
192C4⋊C4×C43—22no—
193C4⋊C4×C43—42no—
194C4⋊C4×C43C2×D412yes—
195C22⋊C4×C43—24no—
196C22⋊Dic43—24no—
197(C2×D43)⋊C4—24no—
198(C2×D43)⋊C4—24no—
199(C2×D43)⋊C4—44no—
200(C2×D43)⋊C4—44no—
201C4⋊Dic43—24no—
202C4⋊Dic43—21no—
203C4⋊Dic43—22no—
204C4⋊Dic43—22no—
205C4⋊Dic43—42no—
206C4⋊Dic43C2×D412yes—
207Dic43⋊C4—24no—
208Dic43⋊C4—24no—
209Dic43⋊C4—24no—
210C2×C43⋊C8—22no—
211C2×C43⋊C8—22no—
212C2×C43⋊C8—22no—
213C23×C43—21no—
214C23×C43—21no—
215C23×C43—21no—
216C23×C43—21no—
217C23×C43#12012yes—
218C23×C43C2×SD1612yes—
219C23×C43#13712yes—
220C23×C43C22×D411yescharacteristic
221C22×D43—21no—
222C22×D43—21no—
223C22×D43—21no—
224C22×D43—21no—
225C22×D43—21no—
226C22×D43—21no—
227C22×D43—21no—
228C22×D43—21no—
229C22×D43—21no—
230C22×D43—21no—
231C22×D43—28no—
232C22×D43—28no—
233C22×D43—44no—
234C22×D43—44no—
235C22×D43—44no—
236C22×D43—44no—
237C22×D43—44no—
238C22×D43#12312yes—
239C22×D43C2×SD1612yes—
240C22×D43C2×SD1612yes—
241C22×D43#13712yes—
242Q8×C43—24no—
243Q8×C43—42no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—24no—
247C2×C4×C43—24no—
248C2×C4×C43—22no—
249C2×C4×C43—22no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—42no—
255C2×C4×C43—42no—
256C2×C4×C43—42no—
257C2×C4×C43—84no—
258C2×C4×C43#12012yes—
259C2×C4×C43C22×D411yescharacteristic
260C2×C4×C43C22×D411yescharacteristic
261C2×C4×C43C2×#4112yes—
262C2×C4×C43H(5,𝔽2)12yes—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—22no—
266C2×Dic43—21no—
267C2×Dic43—22no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—44no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—42no—
276C2×Dic43—42no—
277C2×Dic43—42no—
278C2×Dic43—84no—
279C2×Dic43#12312yes—
280C4×D43—24no—
281C4×D43—24no—
282C4×D43—44no—
283C4×D43—44no—
284C4×D43—48no—
285C4×D43—48no—
286C4×D43—42no—
287C4×D43—42no—
288Dic86—24no—
289Dic86—48no—
290Dic86—42no—
291C8×C43—42no—
292C43⋊C8—42no—
293#24003—431nomaximal, Sylow
294C22×C43—22no—
295C22×C43—22no—
296C22×C43—22no—
297C22×C43—22no—
298C22×C43—22no—
299C22×C43—22no—
300C22×C43#44814yes—
301C22×C43C2×#12011yescharacteristic
302C22×C43C2×#12311yescharacteristic
303C22×C43#53411yescharacteristic
304C22×C43C22×SD1611yescharacteristic
305C22×C43C2×#13711yescharacteristic
306C22×C43C2×#13711yescharacteristic
307C22×C43#57511yescharacteristic
308C2×D43—22no—
309C2×D43—22no—
310C2×D43—22no—
311C2×D43—22no—
312C2×D43—22no—
313C2×D43—22no—
314C2×D43—22no—
315C2×D43—22no—
316C2×D43—22no—
317C2×D43—416no—
318C2×D43—41no—
319C2×D43—41no—
320C2×D43—41no—
321C2×D43—41no—
322C2×D43#48314yescomplemented
323C4×C43—22no—
324C4×C43—42no—
325C4×C43—42no—
326C4×C43—82no—
327C4×C43#54612yes—
328C4×C43#54612yes—
329Dic43—22no—
330Dic43—42no—
331Dic43—41no—
332Dic43—42no—
333Dic43—82no—
334C22×C22⋊Q8—431no—
335C2×#483—431no—
336C2×#483D4311yescharacteristic, complemented
337C2×#380—431no—
338#2035—432no—
339#2035—432no—
340#1872—431no—
341#1872—431no—
342#1853—432no—
343#1787—432no—
344#1779—431no—
345C2×C43—24no—
346C2×C43#240511yescharacteristic
347C2×C43C2×#44811yescharacteristic
348C2×C43#300711yescharacteristic
349C2×C43C2×#48311yescharacteristic
350C2×C43#309511yescharacteristic
351C2×C43#318711yescharacteristic
352C2×C43#319511yescharacteristic
353D43—24no—
354D43—42no—
355C23×Q8—431no—
356C24×C4—431no—
357C2×C22⋊Q8—431no—
358C2×C22⋊Q8—431no—
359C2×C22⋊Q8—431no—
360C2×C22⋊Q8—861no—
361C2×C22⋊Q8—861no—
362C2×C22⋊Q8—864no—
363C2×C22⋊Q8—864no—
364C2×C22⋊Q8C2×D4311yescharacteristic
365C22×C4⋊C4—431no—
366C22×C4⋊C4—431no—
367C22×C4⋊C4—861no—
368C22×C4⋊C4C2×D4311yescharacteristic
369C22×C22⋊C4—861no—
370C22×C22⋊C4—861no—
371#483—24no—
372#483—864no—
373C2×#106—432no—
374C2×#106C2×D4312yescomplemented
375C2×#103—432no—
376C2×#103—432no—
377C2×#103—432no—
378C2×#103C2×D4312yescomplemented
379C2×C22⋊C8—431no—
380C2×C22⋊C8—432no—
381C2×C22⋊C8—432no—
382C2×C22⋊C8C2×D4311yescharacteristic
383#380—432no—
384#380—432no—
385#380—861no—
386#380—861no—
387C2×#95—861no—
388#340—432no—
389#340—432no—
390C43#2400311yescharacteristic, complemented, Sylow
391C25—431no—
392C22×Q8—431no—
393C22×Q8—861no—
394C22×Q8—864no—
395C22×Q8—862no—
396C22×Q8—862no—
397C22×Q8—1722no—
398C22×Q8C22×D4311yescharacteristic
399C23×C4—21no—
400C23×C4—431no—
401C23×C4—431no—
402C23×C4—431no—
403C23×C4—431no—
404C23×C4—431no—
405C23×C4—864no—
406C23×C4—861no—
407C23×C4—861no—
408C23×C4—862no—
409C23×C4—862no—
410C23×C4—861no—
411C23×C4—1722no—
412C23×C4C22×D4311yescharacteristic
413C22×C8—432no—
414C22×C8C22×D4312yes—
415C22⋊Q8—22no—
416C22⋊Q8—434no—
417C22⋊Q8—868no—
418C22⋊Q8—862no—
419C22⋊Q8—868no—
420C22⋊Q8—862no—
421C22⋊Q8—862no—
422C22⋊Q8—862no—
423C22⋊Q8—862no—
424C22⋊Q8C22⋊D4314yes—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—431no—
430C2×C4⋊C4—432no—
431C2×C4⋊C4—862no—
432C2×C4⋊C4—868no—
433C2×C4⋊C4—861no—
434C2×C4⋊C4—861no—
435C2×C4⋊C4—861no—
436C2×C4⋊C4—861no—
437C2×C4⋊C4—862no—
438C2×C4⋊C4—861no—
439C2×C4⋊C4—1722no—
440C2×C4⋊C4C22×D4312yes—
441C2×C4⋊C4C22×D4311yescharacteristic
442C2×C22⋊C4—21no—
443C2×C22⋊C4—868no—
444C2×C22⋊C4—861no—
445C2×C22⋊C4—861no—
446C2×C22⋊C4—861no—
447C2×C22⋊C4—862no—
448C2×C22⋊C4—862no—
449C2×C22⋊C4—1724no—
450#106—24no—
451#106—864no—
452#103—24no—
453#103—864no—
454#103—1722no—
455#103—1722no—
456C22⋊C8—22no—
457C22⋊C8—864no—
458C22⋊C8—862no—
459C22⋊C8—1722no—
460#95—862no—
461#95—862no—
462C24—431no—
463C24—431no—
464C24—434no—
465C24—862no—
466C24—862no—
467C24—862no—
468C24—862no—
469C24—1721no—
470C24—1721no—
471C24D4×D4311yescharacteristic
472C2×Q8—21no—
473C2×Q8—22no—
474C2×Q8—22no—
475C2×Q8—432no—
476C2×Q8—864no—
477C2×Q8—861no—
478C2×Q8—862no—
479C2×Q8—862no—
480C2×Q8—1722no—
481C2×Q8—1722no—
482C2×Q8—1728no—
483C2×Q8—1728no—
484C2×Q8C2×C22⋊D4312yes—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—431no—
494C22×C4—434no—
495C22×C4—431no—
496C22×C4—862no—
497C22×C4—862no—
498C22×C4—864no—
499C22×C4—864no—
500C22×C4—862no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4—862no—
504C22×C4—862no—
505C22×C4—861no—
506C22×C4—861no—
507C22×C4—862no—
508C22×C4—862no—
509C22×C4—861no—
510C22×C4—861no—
511C22×C4—862no—
512C22×C4—862no—
513C22×C4—862no—
514C22×C4—1721no—
515C22×C4—1721no—
516C22×C4—1728no—
517C22×C4—1728no—
518C22×C4—1722no—
519C22×C4—1722no—
520C22×C4—1722no—
521C22×C4—1722no—
522C22×C4—1721no—
523C22×C4—1722no—
524C22×C4—1722no—
525C22×C4—1722no—
526C22×C4D4×D4311yescharacteristic
527C22×C4D4×D4312yes—
528C22×C4C2×C22⋊D4312yes—
529C22×C4C23×D4311yescharacteristic
530C2×C8—22no—
531C2×C8—22no—
532C2×C8—22no—
533C2×C8—862no—
534C2×C8—862no—
535C2×C8—862no—
536C4⋊C4—24no—
537C4⋊C4—21no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—42no—
541C4⋊C4—432no—
542C4⋊C4—864no—
543C4⋊C4—864no—
544C4⋊C4—864no—
545C4⋊C4—864no—
546C4⋊C4—861no—
547C4⋊C4—862no—
548C4⋊C4—862no—
549C4⋊C4—1722no—
550C4⋊C4C2×C22⋊D4312yes—
551C22⋊C4—24no—
552C22⋊C4—864no—
553C22⋊C4—864no—
554C22⋊C4—864no—
555C22⋊C4—1724no—
556C22⋊C4—1724no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—432no—
562C23—432no—
563C23—432no—
564C23—432no—
565C23—868no—
566C23—861no—
567C23—861no—
568C23—861no—
569C23—861no—
570C23—861no—
571C23—861no—
572C23—861no—
573C23—861no—
574C23—861no—
575C23—861no—
576C23—868no—
577C23—1724no—
578C23—1724no—
579C23—1724no—
580C23—1724no—
581C23—1724no—
582C23#1306329312yes—
583C23SD16×D4312yes—
584C23#1306335412yes—
585C23C2×D4×D4311yescharacteristic
586Q8—24no—
587Q8—42no—
588Q8—864no—
589Q8—1728no—
590Q8—1722no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—84no—
605C2×C4—432no—
606C2×C4—861no—
607C2×C4—861no—
608C2×C4—864no—
609C2×C4—864no—
610C2×C4—862no—
611C2×C4—862no—
612C2×C4—861no—
613C2×C4—861no—
614C2×C4—861no—
615C2×C4—3444no—
616C2×C4—1724no—
617C2×C4—1724no—
618C2×C4—1728no—
619C2×C4—1728no—
620C2×C4—1724no—
621C2×C4—1722no—
622C2×C4—1722no—
623C2×C4—1722no—
624C2×C4—1721no—
625C2×C4—1721no—
626C2×C4—1721no—
627C2×C4—1721no—
628C2×C4—1722no—
629C2×C4—1722no—
630C2×C4#1306329312yes—
631C2×C4C2×D4×D4311yescharacteristic
632C2×C4C22×C22⋊D4311yescharacteristic
633C2×C4#41×D4312yes—
634C2×C4#1306337112yes—
635C8—42no—
636C8—1722no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—434no—
644C22—862no—
645C22—862no—
646C22—862no—
647C22—862no—
648C22—862no—
649C22—862no—
650C22—862no—
651C22—862no—
652C22—862no—
653C22—17216no—
654C22—1721no—
655C22—1721no—
656C22—1721no—
657C22—1721no—
658C22#1458303614yes—
659C22C2×#1306329311yescharacteristic
660C22#123×D4311yescharacteristic
661C22#1458346011yescharacteristic
662C22C2×SD16×D4311yescharacteristic
663C22#137×D4311yescharacteristic
664C22C2×#1306335411yescharacteristic
665C22#1458369811yescharacteristic
666C4—22no—
667C4—42no—
668C4—42no—
669C4—82no—
670C4—862no—
671C4—3442no—
672C4—1721no—
673C4—1722no—
674C4—1722no—
675C4#1458353712yes—
676C4#1458354112yes—
677C2—24no—
678C2—864no—
679C2—1722no—
680C2#1913791911yescharacteristic
681C2C2×#1458303611yescharacteristic
682C2#1914385111yescharacteristic
683C2#483×D4311yescharacteristic
684C2#1914453811yescharacteristic
685C2#1914535111yescharacteristic
686C2#1914541811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#483C2
socleC23×C43C22×D4
prime radicalC24×D43D4
hypercenterC2×#483D43
hypocenterC43#24003
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
2. C2×#14583229C2semidirect
4. #19135793C2semidirect
5. #19135789C2semidirect
6. #19134903C2semidirect
7. #19134900C2semidirect
8. #19134786C2semidirect
9. #19134528C2semidirect
11. C2×C43×#483C2semidirect
27. C2×#13063256C22semidirect
28. C2×#13063250C22semidirect
29. C2×#13063249C22semidirect
30. C2×#13063248C22semidirect
39. #14582662C22semidirect
40. #14582661C22semidirect
44. C2×#106×C43C22semidirect
45. C2×#103×C43C22semidirect
322. C2×D43#483semidirect
336. C2×#483D43semidirect
374. C2×#106C2×D43semidirect
378. C2×#103C2×D43semidirect
390. C43#24003semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D432
C2×#145832292
C2×#145827562
#191357932
#191357892
#191349032
#191349002
#191347862
#191345282
#191345042
C2×C43×#4832
#2400343