Finite Group Databasebeta

← #25245421

Subgroups — #25245421

Order 11008.

1436 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D43C211yesmaximal, characteristic
2C2×#14583106C211yesmaximal, characteristic, complemented
3C2×#14583053C212yesmaximal
4#19142942C211yesmaximal, characteristic
5#19134938C212yesmaximal, complemented
6#19134933C212yesmaximal, complemented
7#19134899C212yesmaximal
8#19134601C211yesmaximal, characteristic, complemented
9#19134600C211yesmaximal, characteristic, complemented
10#19134572C211yesmaximal, characteristic
11C2×C43×#462C211yesmaximal, characteristic, complemented
12C22×Q8×D43C2211yescharacteristic
13C22×#10621885C2212yes—
14C2×#13063301C2212yes—
15C2×Q8×Dic43C2211yescharacteristic
16C2×C4×Dic86—21no—
17C2×C4×Dic86C2211yescharacteristic
18C2×#13063290—21no—
19C2×#13063290C2211yescharacteristic
20C4×Q8×D43—24no—
21C4×Q8×D43—24no—
22C2×C4⋊C4×D43—21no—
23C2×C4⋊C4×D43C2211yescharacteristic
24C2×C42×D43—21no—
25C2×C42×D43C2211yescharacteristic
26#14583106—24no—
27#14583053—28no—
28C2×C4⋊(C43⋊C8)C2211yescharacteristic
29C2×#13063250C2212yes—
30C2×#13063249C2212yes—
31C2×#13063249C2212yes—
32C2×(C2×D43)⋊C8C2212yes—
33#14582806C2212yes—
34#14582795—21no—
35#14582795—21no—
36#14582769C2211yescharacteristic
37#14582756—21no—
38#14582756—21no—
39#14582662C2212yes—
40#14582661C2212yes—
41#14582653C2212yes—
42C22×Q16×C43C2212yes—
43C2×C4⋊Q8×C43C2211yescharacteristic
44C2×C4×Q8×C43C2211yescharacteristic
45C43×#462—24no—
46C2×C4⋊C8×C43C2211yescharacteristic
47C2×#103×C43C2212yes—
48C22×Dic86—21no—
49C22×Dic86C2311yescharacteristic
50C2×Q8×D43—22no—
51C2×Q8×D43—22no—
52C2×Q8×D43—22no—
53C2×Q8×D43—22no—
54C2×Q8×D43—22no—
55C2×Q8×D43D414yes—
56C22×C4×D43—21no—
57C22×C4×D43—21no—
58C22×C4×D43D411yescharacteristic
59C22×C4×D43D411yescharacteristic
60C22×C4×D43C2311yescharacteristic
61C2×#10621885—24no—
62C2×#10621885—24no—
63C2×#10621885—24no—
64C22×C43⋊C8C2312yes—
65#13063301—24no—
66#13063301—24no—
67Q8×Dic43—22no—
68Q8×Dic43—22no—
69C4×Dic86—28no—
70C4×Dic86—22no—
71C4×Dic86D414yes—
72#13063290—28no—
73#13063290—22no—
74#13063290—22no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43C2312yes—
79C2×C4⋊Dic43C2311yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—22no—
84C4⋊C4×D43—28no—
85C4⋊C4×D43—22no—
86C4⋊C4×D43—22no—
87C2×(C2×D43)⋊C4—22no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43D411yescharacteristic
92C2×C4×Dic43D411yescharacteristic
93C2×C4×Dic43C2311yescharacteristic
94C42×D43—28no—
95C42×D43—22no—
96C42×D43—22no—
97C4⋊(C43⋊C8)—22no—
98#13063250—24no—
99#13063249—24no—
100#13063249—24no—
101(C2×D43)⋊C8—24no—
102C43⋊#95—22no—
103C43⋊#95—22no—
104C22×Q8×C43C2312yes—
105C22×Q8×C43C2311yescharacteristic
106C2×Q16×C43—24no—
107C2×Q16×C43—24no—
108C2×Q16×C43—24no—
109C22×C8×C43C2312yes—
110C4⋊Q8×C43—22no—
111C4⋊Q8×C43—22no—
112C4×Q8×C43—22no—
113C4×Q8×C43D414yes—
114C2×C4⋊C4×C43—21no—
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C42×C43—21no—
119C2×C42×C43C2311yescharacteristic
120C4⋊C8×C43—22no—
121#103×C43—24no—
122C23×D43C2×D411yescharacteristic
123C2×Q8×C43—21no—
124C2×Q8×C43—21no—
125C2×Q8×C43—21no—
126C2×Q8×C43—22no—
127C2×Q8×C43—22no—
128C2×Q8×C43—22no—
129C2×Q8×C43—22no—
130C2×Q8×C43—22no—
131C2×Q8×C43—22no—
132C2×Q8×C43C2×D412yes—
133C2×Q8×C43C2×D412yes—
134C2×Q8×C43#4112yes—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—22no—
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2411yescharacteristic
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—22no—
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147Q8×D43—28no—
148Q8×D43—28no—
149Q8×D43—28no—
150Q8×D43—28no—
151C2×C4×D43—24no—
152C2×C4×D43—24no—
153C2×C4×D43—22no—
154C2×C4×D43—22no—
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—24no—
160C2×C4×D43—22no—
161C2×C4×D43—24no—
162C2×C4×D43—22no—
163C2×C4×D43—41no—
164C2×C4×D43—42no—
165C2×C4×D43—42no—
166C2×C4×D43Q1614yescomplemented
167C2×C4×D43C2×D412yes—
168C2×C4×D43#4112yes—
169C2×Dic86—24no—
170C2×Dic86—24no—
171C2×Dic86—21no—
172C2×Dic86—21no—
173C2×Dic86—21no—
174C2×Dic86—24no—
175C2×Dic86C2×D412yes—
176C2×Dic86C2×D412yes—
177C2×Dic86#4112yes—
178Q16×C43—48no—
179C2×C8×C43—22no—
180C2×C8×C43—22no—
181C2×C8×C43—22no—
182C4⋊C4×C43—24no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—42no—
185C4⋊C4×C43—42no—
186C4⋊C4×C43C2×D412yes—
187C42×C43—24no—
188C42×C43C2×D412yes—
189C42×C43C2×D412yes—
190#10621885—48no—
191(C2×D43)⋊C4—44no—
192C4⋊Dic43—24no—
193C4⋊Dic43—21no—
194C4⋊Dic43—22no—
195C4⋊Dic43—22no—
196C4⋊Dic43—42no—
197C4⋊Dic43—42no—
198C4⋊Dic43C2×D412yes—
199Dic43⋊C4—24no—
200Dic43⋊C4—24no—
201Dic43⋊C4—24no—
202Dic43⋊C4—44no—
203C4×Dic43—24no—
204C4×Dic43—24no—
205C4×Dic43—24no—
206C4×Dic43—22no—
207C4×Dic43—22no—
208C4×Dic43—21no—
209C4×Dic43—21no—
210C2×C43⋊C8—22no—
211C2×C43⋊C8—22no—
212C2×C43⋊C8—22no—
213C23×C43C22×D411yescharacteristic
214C22×D43—21no—
215C22×D43—21no—
216C22×D43—21no—
217C22×D43—21no—
218C22×D43#12112yes—
219C22×D43C2×Q1612yes—
220C22×D43#13712yes—
221Q8×C43—22no—
222Q8×C43—22no—
223Q8×C43—22no—
224Q8×C43—42no—
225Q8×C43—42no—
226Q8×C43—42no—
227Q8×C43—42no—
228Q8×C43#12114yes—
229C2×C4×C43—22no—
230C2×C4×C43—22no—
231C2×C4×C43—22no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—22no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—42no—
238C2×C4×C43—42no—
239C2×C4×C43—42no—
240C2×C4×C43#12012yes—
241C2×C4×C43#12012yes—
242C2×C4×C43C2×Q1612yes—
243C2×C4×C43#13712yes—
244C2×C4×C43C22×D411yescharacteristic
245C2×C4×C43C22×D411yescharacteristic
246C2×C4×C43C22×D411yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—22no—
253C2×Dic43—22no—
254C2×Dic43—21no—
255C2×Dic43—22no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—22no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—42no—
264C2×Dic43—42no—
265C2×Dic43—42no—
266C2×Dic43#12112yes—
267C2×Dic43C2×Q1612yes—
268C4×D43—216no—
269C4×D43—22no—
270C4×D43—22no—
271C4×D43—22no—
272C4×D43—22no—
273C4×D43—28no—
274C4×D43—44no—
275C4×D43—48no—
276Dic86—216no—
277Dic86—22no—
278Dic86—22no—
279Dic86—22no—
280Dic86#12114yes—
281C8×C43—42no—
282C43⋊C8—42no—
283#32906—431nomaximal, Sylow
284C22×C43C2×#12011yescharacteristic
285C22×C43C2×#12111yescharacteristic
286C22×C43#52511yescharacteristic
287C22×C43C22×Q1611yescharacteristic
288C22×C43C2×#13711yescharacteristic
289C22×C43C2×#13711yescharacteristic
290C22×C43#57511yescharacteristic
291C2×D43—22no—
292C2×D43—22no—
293C2×D43—22no—
294C2×D43—22no—
295C2×D43—22no—
296C2×D43—22no—
297C2×D43#46214yescomplemented
298C4×C43—24no—
299C4×C43—22no—
300C4×C43—42no—
301C4×C43—82no—
302C4×C43#45114yescomplemented
303C4×C43C2×#12111yescharacteristic
304C4×C43C2×#12111yescharacteristic
305C4×C43#52511yescharacteristic
306C4×C43#52511yescharacteristic
307Dic43—22no—
308Dic43—24no—
309Dic43—22no—
310Dic43—41no—
311Dic43—42no—
312Dic43—82no—
313C22×C4×Q8—431no—
314C2×#462—431no—
315C2×#462D4311yescharacteristic, complemented
316C2×#451—432no—
317#2857—431no—
318#1878—432no—
319#1878—432no—
320#1872—432no—
321#1803—431no—
322#1803—431no—
323#1797—431no—
324C2×C43#284711yescharacteristic
325C2×C43C2×#45111yescharacteristic
326C2×C43#300711yescharacteristic
327C2×C43C2×#46211yescharacteristic
328C2×C43#303711yescharacteristic
329C2×C43#310411yescharacteristic
330C2×C43#311311yescharacteristic
331D43—24no—
332C23×Q8—431no—
333C22×Q16—432no—
334C22×Q16C2×D4312yes—
335C2×C4⋊Q8C2×D4311yescharacteristic
336C2×C22⋊Q8—432no—
337C2×C4×Q8—431no—
338C2×C4×Q8—431no—
339C2×C4×Q8—431no—
340C2×C4×Q8—861no—
341C2×C4×Q8—861no—
342C2×C4×Q8—864no—
343C2×C4×Q8—864no—
344C2×C4×Q8C2×D4311yescharacteristic
345C22×C4⋊C4—431no—
346C22×C4⋊C4—861no—
347C22×C42—431no—
348C22×C42—861no—
349#462—24no—
350#462—864no—
351#451—868no—
352C2×C4⋊C8—431no—
353C2×C4⋊C8C2×D4311yescharacteristic
354C2×#103—432no—
355C2×#103—432no—
356C2×#103—432no—
357C2×#103C2×D4312yes—
358C2×C22⋊C8—432no—
359#391—432no—
360#389—861no—
361#389—861no—
362#384—431no—
363#380—861no—
364#380—861no—
365#340—432no—
366#340—432no—
367#336—432no—
368C43#3290611yescharacteristic, complemented, Sylow
369C22×Q8—434no—
370C22×Q8—431no—
371C22×Q8—861no—
372C22×Q8—862no—
373C22×Q8—862no—
374C22×Q8—862no—
375C22×Q8—862no—
376C22×Q8—862no—
377C22×Q8C22×D4312yes—
378C22×Q8C22×D4311yescharacteristic
379C23×C4—431no—
380C23×C4—431no—
381C23×C4—431no—
382C23×C4—861no—
383C23×C4—861no—
384C2×Q16—24no—
385C2×Q16—24no—
386C2×Q16—24no—
387C2×Q16—864no—
388C2×Q16—864no—
389C2×Q16—864no—
390C22×C8—432no—
391C22×C8C22×D4312yes—
392C4⋊Q8—22no—
393C4⋊Q8—22no—
394C22⋊Q8—864no—
395C22⋊Q8—864no—
396C4×Q8—22no—
397C4×Q8—434no—
398C4×Q8—868no—
399C4×Q8—862no—
400C4×Q8—868no—
401C4×Q8—862no—
402C4×Q8—862no—
403C4×Q8—862no—
404C4×Q8—862no—
405C4×Q8C22⋊D4314yes—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—431no—
410C2×C4⋊C4—432no—
411C2×C4⋊C4—862no—
412C2×C4⋊C4—868no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—862no—
418C2×C4⋊C4—862no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4C22×D4311yescharacteristic
422C2×C22⋊C4—862no—
423C2×C42—21no—
424C2×C42—431no—
425C2×C42—431no—
426C2×C42—431no—
427C2×C42—868no—
428C2×C42—861no—
429C2×C42—861no—
430C2×C42—861no—
431C2×C42—862no—
432C2×C42—862no—
433C2×C42C22×D4311yescharacteristic
434C4⋊C8—22no—
435C4⋊C8—862no—
436#103—24no—
437#103—864no—
438#103—864no—
439#103—864no—
440C22⋊C8—864no—
441#95—862no—
442#95—862no—
443C24—431no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—22no—
448C2×Q8—22no—
449C2×Q8—22no—
450C2×Q8—22no—
451C2×Q8—22no—
452C2×Q8—22no—
453C2×Q8—432no—
454C2×Q8—432no—
455C2×Q8—432no—
456C2×Q8—864no—
457C2×Q8—864no—
458C2×Q8—864no—
459C2×Q8—868no—
460C2×Q8—868no—
461C2×Q8—868no—
462C2×Q8—868no—
463C2×Q8—861no—
464C2×Q8—861no—
465C2×Q8—861no—
466C2×Q8D4×D4312yes—
467C2×Q8#1062190012yes—
468C2×Q8C2×C22⋊D4312yes—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—431no—
473C22×C4—431no—
474C22×C4—434no—
475C22×C4—432no—
476C22×C4—432no—
477C22×C4—431no—
478C22×C4—864no—
479C22×C4—864no—
480C22×C4—864no—
481C22×C4—862no—
482C22×C4—864no—
483C22×C4—861no—
484C22×C4—862no—
485C22×C4—862no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—862no—
492C22×C4—862no—
493C22×C4—1721no—
494C22×C4—1722no—
495C22×C4—1722no—
496C22×C4D4×D4311yescharacteristic
497C22×C4D4×D4311yescharacteristic
498C22×C4C23×D4311yescharacteristic
499Q16—48no—
500Q16—1728no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—862no—
505C2×C8—862no—
506C2×C8—862no—
507C4⋊C4—24no—
508C4⋊C4—21no—
509C4⋊C4—42no—
510C4⋊C4—42no—
511C4⋊C4—432no—
512C4⋊C4—864no—
513C4⋊C4—864no—
514C4⋊C4—864no—
515C4⋊C4—864no—
516C4⋊C4—861no—
517C4⋊C4—862no—
518C4⋊C4—862no—
519C4⋊C4—1722no—
520C4⋊C4—1724no—
521C4⋊C4—1722no—
522C4⋊C4C2×C22⋊D4312yes—
523C22⋊C4—1724no—
524C42—24no—
525C42—864no—
526C42—864no—
527C42—862no—
528C42—862no—
529C42—864no—
530C42—861no—
531C42—861no—
532C42D4×D4312yes—
533C42C2×C22⋊D4312yes—
534C23—432no—
535C23—432no—
536C23—432no—
537C23—861no—
538C23—861no—
539C23—861no—
540C23—861no—
541C23C2×D4×D4311yescharacteristic
542Q8—22no—
543Q8—22no—
544Q8—22no—
545Q8—42no—
546Q8—42no—
547Q8—42no—
548Q8—42no—
549Q8—434no—
550Q8—8616no—
551Q8—862no—
552Q8—862no—
553Q8—862no—
554Q8#1306329614yes—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—432no—
567C2×C4—432no—
568C2×C4—8616no—
569C2×C4—861no—
570C2×C4—861no—
571C2×C4—862no—
572C2×C4—862no—
573C2×C4—861no—
574C2×C4—862no—
575C2×C4—861no—
576C2×C4—868no—
577C2×C4—862no—
578C2×C4—862no—
579C2×C4—862no—
580C2×C4—862no—
581C2×C4—862no—
582C2×C4—861no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—1724no—
586C2×C4—1728no—
587C2×C4—1722no—
588C2×C4—1722no—
589C2×C4—1722no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4#1306329312yes—
593C2×C4#1306329312yes—
594C2×C4Q16×D4312yes—
595C2×C4#1306335712yes—
596C2×C4C2×D4×D4311yescharacteristic
597C2×C4C2×D4×D4311yescharacteristic
598C2×C4C22×C22⋊D4311yescharacteristic
599C2×C4#41×D4311yescharacteristic
600C2×C4#41×D4311yescharacteristic
601C2×C4C2×#1062190011yescharacteristic
602C8—42no—
603C8—1722no—
604C22—434no—
605C22—862no—
606C22—862no—
607C22—862no—
608C22—862no—
609C22—862no—
610C22—862no—
611C22C2×#1306329311yescharacteristic
612C22#121×D4311yescharacteristic
613C22#1458340911yescharacteristic
614C22C2×Q16×D4311yescharacteristic
615C22#137×D4311yescharacteristic
616C22C2×#1306335711yescharacteristic
617C22#1458369811yescharacteristic
618C4—22no—
619C4—24no—
620C4—42no—
621C4—82no—
622C4—862no—
623C4—862no—
624C4—864no—
625C4—3442no—
626C4—1721no—
627C4—1722no—
628C4#1458305314yescomplemented
629C4#121×D4311yescharacteristic
630C4C2×#1306329611yescharacteristic
631C4#1458340611yescharacteristic
632C4#1458340911yescharacteristic
633C2—864no—
634C2#1914287411yescharacteristic
635C2C2×#1458305311yescharacteristic
636C2#1914385111yescharacteristic
637C2#462×D4311yescharacteristic
638C2#1914406811yescharacteristic
639C2#1914463311yescharacteristic
640C2#1914472411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#462C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenterC2×#462D43
hypocenterC43#32906
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
2. C2×#14583106C2semidirect
5. #19134938C2semidirect
6. #19134933C2semidirect
8. #19134601C2semidirect
9. #19134600C2semidirect
11. C2×C43×#462C2semidirect
166. C2×C4×D43Q16semidirect
297. C2×D43#462semidirect
302. C4×C43#451semidirect
315. C2×#462D43semidirect
368. C43#32906semidirect
628. C4#14583053semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D432
C2×#145831062
C2×#145830532
#191429422
#191349382
#191349332
#191348992
#191346012
#191346002
#191345722
C2×C43×#4622
#3290643