Finite Group Databasebeta

← #25156720

Subgroups — #25156720

Order 11008.

894 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×Dic43C211yesmaximal, characteristic, complemented
2#19138389C211yesmaximal, characteristic, complemented
3#19137500C211yesmaximal, characteristic, complemented
4#19136118C211yesmaximal, characteristic, complemented
5#19136093C211yesmaximal, characteristic, complemented
6#19136016C211yesmaximal, characteristic, complemented
7#19135831C211yesmaximal, characteristic, complemented
8#19135275C211yesmaximal, characteristic, complemented
9#19135149C211yesmaximal, characteristic, complemented
10#19134945C211yesmaximal, characteristic
11#19134945C211yesmaximal, characteristic
12#19134931C211yesmaximal, characteristic, complemented
13#19134847C211yesmaximal, characteristic, complemented
14#19134842C211yesmaximal, characteristic, complemented
15C2×C43×#463C211yesmaximal, characteristic
16C2×Q8×Dic43C2211yescharacteristic
17C2×D4×Dic43C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19SD16×Dic43—24no—
20C2×#13063258C2211yescharacteristic
21C2×#13063257C2211yescharacteristic
22C2×#13063249C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×C8×Dic43C2211yescharacteristic
29#14582835—21no—
30#14582824—21no—
31#14582806C2211yescharacteristic
32#14582802C2211yescharacteristic
33#14582802C2211yescharacteristic
34#14582797C2211yescharacteristic
35#14582797C2211yescharacteristic
36#14582795C2211yescharacteristic
37#14582787—21no—
38#14582787—21no—
39#14582772—21no—
40#14582771—21no—
41#14582764C2211yescharacteristic
42#14582757—21no—
43C4×Dic43⋊C4C2211yescharacteristic
44C2×C43⋊#95—21no—
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C22×SD16×C43C2211yescharacteristic
54C22×D8×C43C2211yescharacteristic
55C2×#124×C43C2211yescharacteristic
56C2×C4×D4×C43C2211yescharacteristic
57C43×#463—24no—
58C2×C4⋊C8×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C23×Dic43—21no—
62C23×Dic43—21no—
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65Q8×Dic43—22no—
66Q8×Dic43—41no—
67D4×Dic43—22no—
68D4×Dic43—22no—
69D4×Dic43—22no—
70D4×Dic43—41no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4D411yescharacteristic
80C2×Dic43⋊C4D411yescharacteristic
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43C2311yescharacteristic
89C2×C4×Dic43C2311yescharacteristic
90#13063258—41no—
91#13063257—22no—
92#13063249—22no—
93#13063249—22no—
94#13063246—22no—
95#13063246—22no—
96#13063246—22no—
97#13063246—41no—
98C8×Dic43—22no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95D411yescharacteristic
107C43⋊#95D411yescharacteristic
108C22×Q8×C43C2311yescharacteristic
109C22×D4×C43C2311yescharacteristic
110C22×D4×C43C2311yescharacteristic
111C23×C4×C43—21no—
112C2×SD16×C43—22no—
113C2×SD16×C43—22no—
114C2×SD16×C43D414yes—
115C2×D8×C43—22no—
116C2×D8×C43—22no—
117C2×D8×C43—22no—
118C22×C8×C43C2311yescharacteristic
119C22×C8×C43C2311yescharacteristic
120#124×C43—22no—
121#124×C43—41no—
122C4×D4×C43—22no—
123C4×D4×C43—41no—
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C42×C43C2311yescharacteristic
129C4⋊C8×C43—22no—
130#103×C43—22no—
131#102×C43—22no—
132C24×C43—21no—
133C24×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43C2×D412yes—
140C2×D4×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43C2×D412yes—
150C2×D4×C43#4112yes—
151C2×D4×C43#4112yes—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—42no—
155C22×C4×C43—42no—
156C22×C4×C43—81no—
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2411yescharacteristic
160C22×Dic43—24no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43—42no—
166C22×Dic43—42no—
167C22×Dic43—81no—
168C22×Dic43—81no—
169C22×Dic43—81no—
170C22×Dic43C2×D411yescharacteristic
171C22×Dic43C2×D411yescharacteristic
172C22×Dic43C2×D411yescharacteristic
173C22×Dic43C2×D411yescharacteristic
174SD16×C43—28no—
175D8×C43—44no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43C2×D412yes—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C22⋊C4×C43—42no—
185C22⋊C4×C43—42no—
186C22⋊C4×C43—42no—
187C42×C43—21no—
188C42×C43—21no—
189C22⋊Dic43—24no—
190C22⋊Dic43—42no—
191C22⋊Dic43—42no—
192C22⋊Dic43—42no—
193C22⋊Dic43—81no—
194C22⋊Dic43—81no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—42no—
203C4⋊Dic43#4112yes—
204Dic43⋊C4—22no—
205Dic43⋊C4—41no—
206Dic43⋊C4—81no—
207Dic43⋊C4—81no—
208Dic43⋊C4—81no—
209C4×Dic43—21no—
210C4×Dic43—21no—
211C4×Dic43—21no—
212C4×Dic43—21no—
213C4×Dic43—42no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C23×C43—22no—
221C23×C43—22no—
222C23×C43—22no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43—41no—
229C23×C43—41no—
230C23×C43—41no—
231C23×C43—41no—
232C23×C43—41no—
233C23×C43—41no—
234C23×C43C22×D411yescharacteristic
235Q8×C43—22no—
236Q8×C43—22no—
237Q8×C43—41no—
238Q8×C43—41no—
239D4×C43—22no—
240D4×C43—22no—
241D4×C43—22no—
242D4×C43—41no—
243D4×C43—41no—
244D4×C43—41no—
245D4×C43—41no—
246D4×C43#12314yes—
247C2×C4×C43—22no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—84no—
260C2×C4×C43C22×D411yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C43C2×#4111yescharacteristic
263C2×C4×C43C2×#4111yescharacteristic
264C2×C4×C43H(5,𝔽2)11yescharacteristic
265C2×C4×C432−1+411yescharacteristic
266C2×Dic43—21no—
267C2×Dic43—21no—
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—21no—
277C2×Dic43—21no—
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—41no—
288C2×Dic43—41no—
289C2×Dic43—84no—
290C2×Dic43—84no—
291C2×Dic43#13512yes—
292C8×C43—22no—
293C8×C43—41no—
294C43⋊C8—41no—
295C43⋊C8—41no—
296#26168—431nomaximal, Sylow
297C22×C43—24no—
298C22×C43—42no—
299C22×C43—42no—
300C22×C43—42no—
301C22×C43—42no—
302C22×C43—42no—
303C22×C43—42no—
304C22×C43—81no—
305C22×C43—81no—
306C22×C43—81no—
307C22×C43—81no—
308C22×C43—81no—
309C22×C43—81no—
310C22×C43—81no—
311C22×C43#52511yescharacteristic
312C22×C43D4211yescharacteristic
313C22×C43#54811yescharacteristic
314C22×C43C2×#13511yescharacteristic
315C22×C43#57511yescharacteristic
316C22×C43#57611yescharacteristic
317C22×C43#57711yescharacteristic
318C4×C43—42no—
319C4×C43—41no—
320C4×C43—41no—
321C4×C43—81no—
322C4×C43C2×#12311yescharacteristic
323C4×C43#53911yescharacteristic
324C4×C43#54711yescharacteristic
325C4×C43#55311yescharacteristic
326Dic43—22no—
327Dic43—41no—
328Dic43—41no—
329Dic43—42no—
330Dic43—41no—
331Dic43—81no—
332Dic43—81no—
333Dic43—81no—
334C2×#463D4311yescharacteristic
335C2×C4×SD16—431no—
336#2448—431no—
337#2349—431no—
338#2092—431no—
339#2088—431no—
340#2074—431no—
341#2042—431no—
342#1934—431no—
343#1916—431no—
344#1879—431no—
345#1879—431no—
346#1877—431no—
347#1863—431no—
348#1862—431no—
349C2×C43—44no—
350C2×C43—161no—
351C2×C43#244311yescharacteristic
352C2×C43#310211yescharacteristic
353C2×C43#311811yescharacteristic
354C2×C43#326811yescharacteristic
355C2×C43#328211yescharacteristic
356C2×C43#336111yescharacteristic
357C2×C43#337611yescharacteristic
358C22×SD16C2×D4311yescharacteristic
359C22×D8C2×D4311yescharacteristic
360C2×#124C2×D4311yescharacteristic
361C2×C4×Q8—431no—
362C2×C4×D4—431no—
363C2×C4×D4—431no—
364C2×C4×D4C2×D4311yescharacteristic
365#463—24no—
366C4×SD16—864no—
367C2×#107—431no—
368C2×#106—431no—
369C2×C4⋊C8C2×D4311yescharacteristic
370C2×#103—431no—
371C2×#103—431no—
372C2×#103C2×D4311yescharacteristic
373C2×#102—431no—
374C2×#102—431no—
375C2×#102—431no—
376C2×#102—431no—
377C2×#102C2×D4311yescharacteristic
378C2×C4×C8—431no—
379#399—861no—
380#397—861no—
381#391—431no—
382#390—431no—
383#390—431no—
384#389—431no—
385#389—431no—
386#389—431no—
387#388—861no—
388#388—861no—
389#385—861no—
390#385—861no—
391#382—431no—
392#380—861no—
393C4×C4⋊C4—431no—
394C2×#95—861no—
395#340—431no—
396#340—431no—
397#340—431no—
398#340—431no—
399#336—431no—
400#336—431no—
401#336—431no—
402#336—431no—
403C43#2616811yescharacteristic, complemented, Sylow
404C22×Q8C22×D4311yescharacteristic
405C22×D4C22×D4311yescharacteristic
406C22×D4C22×D4311yescharacteristic
407C23×C4—21no—
408C23×C4—861no—
409C23×C4—861no—
410C2×SD16—22no—
411C2×SD16—22no—
412C2×SD16C22⋊D4314yes—
413C2×D8—22no—
414C2×D8—22no—
415C2×D8—22no—
416C22×C8—431no—
417C22×C8—431no—
418C22×C8C22×D4311yescharacteristic
419C22×C8C22×D4311yescharacteristic
420#124—22no—
421#124—41no—
422C4×Q8—862no—
423C4×Q8—1721no—
424C4×D4—22no—
425C4×D4—41no—
426C4×D4—862no—
427C4×D4—862no—
428C4×D4—862no—
429C4×D4—1721no—
430C2×C4⋊C4—431no—
431C2×C4⋊C4—431no—
432C2×C4⋊C4—431no—
433C2×C4⋊C4—431no—
434C2×C4⋊C4—431no—
435C2×C4⋊C4—431no—
436C2×C4⋊C4—861no—
437C2×C4⋊C4—861no—
438C2×C4⋊C4—861no—
439C2×C4⋊C4—861no—
440C2×C4⋊C4C22×D4311yescharacteristic
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—861no—
445C2×C22⋊C4—861no—
446C2×C22⋊C4—861no—
447C2×C22⋊C4—861no—
448C2×C22⋊C4—861no—
449C2×C22⋊C4—861no—
450C2×C42—431no—
451C2×C42—431no—
452C2×C42—861no—
453C2×C42C22×D4311yescharacteristic
454#107—1721no—
455#106—862no—
456C4⋊C8—22no—
457#103—22no—
458#103—862no—
459#103—862no—
460#102—22no—
461#102—862no—
462#102—862no—
463#102—862no—
464#102—1721no—
465C4×C8—862no—
466#95—431no—
467#95—431no—
468#95—861no—
469#95—861no—
470#95—861no—
471#95—861no—
472#95—861no—
473#95—861no—
474#95—861no—
475C24—21no—
476C24—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8C2×C22⋊D4312yes—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4#1062190012yes—
493C2×D4#1062190012yes—
494C2×D4C2×C22⋊D4312yes—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—81no—
500C22×C4—431no—
501C22×C4—431no—
502C22×C4—431no—
503C22×C4—431no—
504C22×C4—864no—
505C22×C4—861no—
506C22×C4—861no—
507C22×C4—861no—
508C22×C4—861no—
509C22×C4—3441no—
510C22×C4—3441no—
511C22×C4—3441no—
512C22×C4—1722no—
513C22×C4—1722no—
514C22×C4D4×D4311yescharacteristic
515C22×C4D4×D4311yescharacteristic
516C22×C4C23×D4311yescharacteristic
517SD16—28no—
518D8—44no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—861no—
525C2×C8—861no—
526C2×C8—861no—
527C2×C8—861no—
528C2×C8—861no—
529C2×C8—861no—
530C2×C8C2×C22⋊D4312yes—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—432no—
534C4⋊C4—862no—
535C4⋊C4—861no—
536C4⋊C4—861no—
537C4⋊C4—861no—
538C4⋊C4—861no—
539C4⋊C4—861no—
540C4⋊C4—861no—
541C4⋊C4—861no—
542C4⋊C4—3441no—
543C4⋊C4—3441no—
544C4⋊C4—3441no—
545C4⋊C4—1721no—
546C4⋊C4—1722no—
547C22⋊C4—42no—
548C22⋊C4—42no—
549C22⋊C4—42no—
550C22⋊C4—864no—
551C22⋊C4—3441no—
552C22⋊C4—3441no—
553C22⋊C4—1722no—
554C22⋊C4—1722no—
555C22⋊C4—1722no—
556C42—21no—
557C42—21no—
558C42—861no—
559C42—861no—
560C42—861no—
561C42—861no—
562C42—1722no—
563C23—22no—
564C23—22no—
565C23—22no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23C2×D4×D4311yescharacteristic
578Q8—22no—
579Q8—22no—
580Q8—41no—
581Q8—41no—
582D4—22no—
583D4—22no—
584D4—22no—
585D4—41no—
586D4—41no—
587D4—41no—
588D4—41no—
589D4#1306330614yes—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—22no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—84no—
603C2×C4—432no—
604C2×C4—861no—
605C2×C4—861no—
606C2×C4—861no—
607C2×C4—861no—
608C2×C4—862no—
609C2×C4—861no—
610C2×C4—861no—
611C2×C4—861no—
612C2×C4—861no—
613C2×C4—861no—
614C2×C4—861no—
615C2×C4—861no—
616C2×C4—3444no—
617C2×C4—3444no—
618C2×C4—1721no—
619C2×C4—1721no—
620C2×C4—1721no—
621C2×C4—1721no—
622C2×C4—1721no—
623C2×C4—1721no—
624C2×C4—1721no—
625C2×C4—1721no—
626C2×C4—1721no—
627C2×C4—1721no—
628C2×C4—1721no—
629C2×C4C22×C22⋊D4311yescharacteristic
630C2×C4#41×D4311yescharacteristic
631C2×C4C2×#1062190011yescharacteristic
632C2×C4C2×#1062190011yescharacteristic
633C2×C4#1306337011yescharacteristic
634C2×C4#1306337211yescharacteristic
635C8—22no—
636C8—41no—
637C8—1721no—
638C8—1721no—
639C22—24no—
640C22—42no—
641C22—42no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—42no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22#1458340911yescharacteristic
654C22D4×C22⋊D4311yescharacteristic
655C22#1458355511yescharacteristic
656C22#135×D4311yescharacteristic
657C22#1458369511yescharacteristic
658C22#1458370311yescharacteristic
659C22#1458370611yescharacteristic
660C4—42no—
661C4—41no—
662C4—41no—
663C4—81no—
664C4—862no—
665C4—3441no—
666C4—3441no—
667C4—3441no—
668C4—1721no—
669C4—1722no—
670C4—1721no—
671C4—1721no—
672C4C2×#1306330611yescharacteristic
673C4#1458349411yescharacteristic
674C4#1458354811yescharacteristic
675C4#1458359211yescharacteristic
676C2—44no—
677C2—161no—
678C2#1913832611yescharacteristic
679C2#1914461011yescharacteristic
680C2#1914477811yescharacteristic
681C2#1914612911yescharacteristic
682C2#1914629611yescharacteristic
683C2#1914725011yescharacteristic
684C2#1914741911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#463C2
socleC23×C43C22×D4
prime radicalC22×D8×C43C22
hypercenterC2×#463D43
hypocenterC43#26168
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×SD16×Dic43C2semidirect
2. #19138389C2semidirect
3. #19137500C2semidirect
4. #19136118C2semidirect
5. #19136093C2semidirect
6. #19136016C2semidirect
7. #19135831C2semidirect
8. #19135275C2semidirect
9. #19135149C2semidirect
12. #19134931C2semidirect
13. #19134847C2semidirect
14. #19134842C2semidirect
403. C43#26168semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×Dic432
#191383892
#191375002
#191361182
#191360932
#191360162
#191358312
#191352752
#191351492
#191349452
#191349312
#191348472
#191348422
C2×C43×#4632
#2616843