Finite Group Databasebeta

← #25102855

Subgroups — #25102855

Order 11008.

1092 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583102C211yesmaximal, characteristic
2C2×#14583000C211yesmaximal, characteristic
3C2×#14582996C211yesmaximal, characteristic
4#19137164C211yesmaximal, characteristic, complemented
5C4×D4×Dic43C211yesmaximal, characteristic
6#19135516C211yesmaximal, characteristic, complemented
7#19135352C211yesmaximal, characteristic, complemented
8#19135237C211yesmaximal, characteristic, complemented
9#19135233C211yesmaximal, characteristic, complemented
10#19134929C211yesmaximal, characteristic
11#19134593C211yesmaximal, characteristic
12#19134447C211yesmaximal, characteristic, complemented
13#19134427C211yesmaximal, characteristic, complemented
14#19134424C211yesmaximal, characteristic, complemented
15C43×#1877C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C2×#13063323C2211yescharacteristic
18C2×Q8×Dic43C2211yescharacteristic
19C2×#13063290C2211yescharacteristic
20C2×D4×Dic43C2211yescharacteristic
21C2×D4×Dic43C2211yescharacteristic
22C22×C4×Dic43—21no—
23#14583102C418yescomplemented
24#14583000—24no—
25#14582996—24no—
26C2×#13063259C2211yescharacteristic
27C2×#13063258C2211yescharacteristic
28C2×Dic43⋊C8C2211yescharacteristic
29C2×Dic43⋊C8C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063250C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×#13063249C2211yescharacteristic
34C2×#13063248C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×#13063235C2211yescharacteristic
37C2×#13063235C2211yescharacteristic
38#14582805C2211yescharacteristic
39#14582796—21no—
40#14582796—21no—
41#14582768C2211yescharacteristic
42C4⋊C4×Dic43C2211yescharacteristic
43C4⋊C4×Dic43C2211yescharacteristic
44C4×C4⋊Dic43C2211yescharacteristic
45#14582750—21no—
46#14582750—21no—
47C22⋊C4×Dic43—21no—
48C22⋊C4×Dic43—21no—
49C4×C22⋊Dic43—21no—
50C42×Dic43C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582654C2211yescharacteristic
55C22×SD16×C43C2211yescharacteristic
56C2×C4×D4×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C43×#391C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C22×Dic86C2311yescharacteristic
63C23×Dic43—21no—
64C23×Dic43—21no—
65C2×#10621883—22no—
66C2×#10621883—22no—
67C2×#10621883C2×C414yes—
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70#13063323—22no—
71#13063323C2×C414yescomplemented
72Q8×Dic43—22no—
73Q8×Dic43—22no—
74#13063290—22no—
75#13063290—22no—
76D4×Dic43—22no—
77D4×Dic43—22no—
78D4×Dic43C2×C414yes—
79D4×Dic43D414yes—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43—44no—
97C2×C4×Dic43D411yescharacteristic
98C2×C4×Dic43D411yescharacteristic
99C2×C4×Dic43D411yescharacteristic
100C2×C4×Dic43D411yescharacteristic
101C2×C4×Dic43C2311yescharacteristic
102C2×C4×Dic43C2311yescharacteristic
103#13063259—22no—
104#13063258—22no—
105Dic43⋊C8—22no—
106Dic43⋊C8C2×C414yescomplemented
107#13063250—22no—
108#13063250C2×C414yescomplemented
109#13063249—22no—
110#13063249C2×C414yescomplemented
111#13063248—22no—
112#13063246—22no—
113#13063235—22no—
114#13063235—22no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C22×Q8×C43C2311yescharacteristic
121C22×D4×C43C2311yescharacteristic
122C23×C4×C43—21no—
123C2×SD16×C43—22no—
124C2×SD16×C43—22no—
125C2×SD16×C43C2×C414yes—
126C22×C8×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128C4×D4×C43—22no—
129C4×D4×C43—22no—
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C22⋊C4×C43—21no—
133C2×C42×C43C2311yescharacteristic
134#103×C43—22no—
135#102×C43—22no—
136#95×C43—21no—
137#95×C43—21no—
138C24×C43—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43C22×C412yes—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43C22×C412yes—
149C2×D4×C43C2×D412yes—
150C2×D4×C43#4112yes—
151C22×C4×C43—24no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—42no—
156C22×C4×C43—42no—
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2411yescharacteristic
160C22×Dic43—24no—
161C22×Dic43—24no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—42no—
167C22×Dic43—42no—
168C22×Dic43—42no—
169C22×Dic43—42no—
170C22×Dic43C2×D411yescharacteristic
171C22×Dic43C2×D411yescharacteristic
172C22×Dic43C2×D411yescharacteristic
173C22×Dic43C2×D411yescharacteristic
174C2×Dic86—21no—
175C2×Dic86—21no—
176C2×Dic86—21no—
177C2×Dic86—21no—
178C2×Dic86—21no—
179C2×Dic86C22×C412yes—
180SD16×C43—28no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43C22×C412yes—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43#4112yes—
191C22⋊C4×C43—24no—
192C42×C43—21no—
193C42×C43—21no—
194C22⋊Dic43—24no—
195C22⋊Dic43—24no—
196#10621883—28no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—42no—
202C4⋊Dic43C22×C412yes—
203C4⋊Dic43C2×D412yes—
204Dic43⋊C4—24no—
205Dic43⋊C4—24no—
206Dic43⋊C4—42no—
207Dic43⋊C4—42no—
208Dic43⋊C4—42no—
209C4×Dic43—22no—
210C4×Dic43—22no—
211C4×Dic43—22no—
212C4×Dic43—41no—
213C4×Dic43—42no—
214C4×Dic43—42no—
215C4×Dic43—42no—
216C4×Dic43—42no—
217C4×Dic43—42no—
218C4×Dic43C22×C412yes—
219C4×Dic43C2×D412yes—
220C4×Dic43#4112yes—
221C4×Dic43#4112yes—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8C22×C412yes—
228C23×C43—22no—
229C23×C43—22no—
230C23×C43—22no—
231C23×C43—41no—
232C23×C43—41no—
233C23×C43—41no—
234C23×C43—41no—
235C23×C43C22×D411yescharacteristic
236Q8×C43—22no—
237Q8×C43—22no—
238Q8×C43—41no—
239Q8×C43—41no—
240D4×C43—22no—
241D4×C43—22no—
242D4×C43—22no—
243D4×C43C4×D414yes—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—22no—
247C2×C4×C43—21no—
248C2×C4×C43—22no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—48no—
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×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—21no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—22no—
273C2×Dic43—22no—
274C2×Dic43—22no—
275C2×Dic43—48no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—48no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43C4×D412yes—
287C2×Dic43C4×D412yes—
288C2×Dic43#12112yes—
289C2×Dic43#12112yes—
290C2×Dic43AGL(1,ℤ/8)12yes—
291C2×Dic43#13712yes—
292Dic86—22no—
293Dic86—22no—
294Dic86—41no—
295Dic86—41no—
296C8×C43—22no—
297C8×C43—41no—
298C43⋊C8—22no—
299C43⋊C8—41no—
300#21504—431nomaximal, Sylow
301C22×C43—24no—
302C22×C43—42no—
303C22×C43—42no—
304C22×C43—42no—
305C22×C43—42no—
306C22×C43—42no—
307C22×C43—42no—
308C22×C43C2×C4×D411yescharacteristic
309C22×C43C2×#12111yescharacteristic
310C22×C43#52511yescharacteristic
311C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
312C22×C43C2×#13711yescharacteristic
313C22×C43C2×#13711yescharacteristic
314C22×C43#57511yescharacteristic
315C4×C43—22no—
316C4×C43—42no—
317C4×C43—41no—
318C4×C43—42no—
319C4×C43—81no—
320C4×C43C2×C4×D411yescharacteristic
321C4×C43C4×#4111yescharacteristic
322C4×C43#52911yescharacteristic
323C4×C43#53211yescharacteristic
324Dic43—22no—
325Dic43—22no—
326Dic43—22no—
327Dic43—42no—
328Dic43—42no—
329Dic43—42no—
330Dic43—81no—
331Dic43#44014yescomplemented
332C2×#461—431no—
333C2×#440—431no—
334C2×#440—431no—
335C4×C4⋊Q8—431no—
336C42×D4—431no—
337#1981—431no—
338#1947—431no—
339#1928—431no—
340#1928—431no—
341#1877—431no—
342#1877D4311yescharacteristic
343#1802—431no—
344#1767—431no—
345#1763—431no—
346#1763—431no—
347C2×C43—44no—
348C2×C43C4×#12111yescharacteristic
349C2×C43C2×#44011yescharacteristic
350C2×C43C4×#13711yescharacteristic
351C2×C43#303611yescharacteristic
352C2×C43#303911yescharacteristic
353C2×C43#311011yescharacteristic
354C2×C43#311611yescharacteristic
355C22×SD16—431no—
356C22×SD16C2×D4311yescharacteristic
357C2×C4⋊Q8—431no—
358C2×C4×Q8—431no—
359C2×C4×Q8—431no—
360C2×C4×D4—431no—
361C2×C4×D4—431no—
362C2×C4×D4C2×D4311yescharacteristic
363C22×C42—861no—
364#461—438no—
365#440—864no—
366#440—864no—
367C2×#107—431no—
368C2×#107—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×#103C2×D4311yescharacteristic
377C2×#102—431no—
378C2×#102C2×D4311yescharacteristic
379C2×#97—431no—
380C2×#97—431no—
381#391—431no—
382#391C2×D4311yescharacteristic
383#389—861no—
384#389—861no—
385#384—431no—
386C4×C4⋊C4—431no—
387C4×C4⋊C4—431no—
388C4×C4⋊C4—431no—
389C4×C4⋊C4—861no—
390C4×C4⋊C4—861no—
391C4×C22⋊C4—861no—
392C4×C22⋊C4—861no—
393C4×C22⋊C4—861no—
394C43—431no—
395#340—431no—
396#340—431no—
397#340—431no—
398#340C2×D4311yescharacteristic
399#336—431no—
400#336C2×D4311yescharacteristic
401C43#2150411yescharacteristic, complemented, Sylow
402C22×Q8—431no—
403C22×Q8C22×D4311yescharacteristic
404C22×D4C22×D4311yescharacteristic
405C23×C4—21no—
406C23×C4—861no—
407C23×C4—861no—
408C2×SD16—22no—
409C2×SD16—22no—
410C2×SD16—434no—
411C2×SD16—862no—
412C2×SD16—862no—
413C2×SD16C4×D4314yes—
414C22×C8—431no—
415C22×C8—431no—
416C22×C8C22×D4311yescharacteristic
417C22×C8C22×D4311yescharacteristic
418C4⋊Q8—434no—
419C4⋊Q8—862no—
420C4×Q8—862no—
421C4×Q8—862no—
422C4×Q8—862no—
423C4×Q8—862no—
424C4×D4—22no—
425C4×D4—22no—
426C4×D4—434no—
427C4×D4—434no—
428C4×D4—862no—
429C4×D4—862no—
430C2×C4⋊C4—431no—
431C2×C4⋊C4—431no—
432C2×C4⋊C4—431no—
433C2×C4⋊C4—861no—
434C2×C4⋊C4—861no—
435C2×C4⋊C4—861no—
436C2×C4⋊C4—861no—
437C2×C4⋊C4—861no—
438C2×C4⋊C4—861no—
439C2×C4⋊C4C22×D4311yescharacteristic
440C2×C4⋊C4C22×D4311yescharacteristic
441C2×C22⋊C4—21no—
442C2×C22⋊C4—861no—
443C2×C22⋊C4—861no—
444C2×C42—431no—
445C2×C42—431no—
446C2×C42—431no—
447C2×C42—431no—
448C2×C42—431no—
449C2×C42—431no—
450C2×C42—861no—
451C2×C42—861no—
452C2×C42—861no—
453C2×C42—861no—
454C2×C42—861no—
455C2×C42—1724no—
456C2×C42C22×D4311yescharacteristic
457#107—862no—
458#107—862no—
459C4⋊C8—434no—
460C4⋊C8—862no—
461#103—22no—
462#103—434no—
463#103—434no—
464#103—862no—
465#103—862no—
466#103—862no—
467#102—22no—
468#102—862no—
469#97—862no—
470#97—862no—
471#95—21no—
472#95—21no—
473#95—861no—
474#95—861no—
475#95—861no—
476#95—861no—
477#95—861no—
478C24—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—432no—
485C2×Q8—861no—
486C2×Q8—861no—
487C2×Q8—861no—
488C2×Q8—861no—
489C2×Q8—861no—
490C2×Q8C2×C4×D4312yes—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4C2×C4×D4312yes—
495C2×D4D4×D4312yes—
496C2×D4#1062190012yes—
497C22×C4—24no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—431no—
504C22×C4—431no—
505C22×C4—431no—
506C22×C4—431no—
507C22×C4—864no—
508C22×C4—864no—
509C22×C4—861no—
510C22×C4—861no—
511C22×C4—861no—
512C22×C4—861no—
513C22×C4—1722no—
514C22×C4—1722no—
515C22×C4—1722no—
516C22×C4—1722no—
517C22×C4D4×D4311yescharacteristic
518C22×C4D4×D4311yescharacteristic
519C22×C4C23×D4311yescharacteristic
520SD16—28no—
521SD16—868no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—432no—
528C2×C8—861no—
529C2×C8—861no—
530C2×C8—861no—
531C2×C8—861no—
532C2×C8—861no—
533C2×C8C2×C4×D4312yes—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—432no—
538C4⋊C4—432no—
539C4⋊C4—864no—
540C4⋊C4—864no—
541C4⋊C4—861no—
542C4⋊C4—861no—
543C4⋊C4—861no—
544C4⋊C4—861no—
545C4⋊C4—1722no—
546C4⋊C4—1722no—
547C4⋊C4—1722no—
548C4⋊C4—1722no—
549C4⋊C4#1062190012yes—
550C22⋊C4—24no—
551C22⋊C4—864no—
552C22⋊C4—864no—
553C42—21no—
554C42—21no—
555C42—432no—
556C42—432no—
557C42—432no—
558C42—432no—
559C42—862no—
560C42—862no—
561C42—862no—
562C42—1721no—
563C42—1722no—
564C42—1722no—
565C42—1722no—
566C42—1722no—
567C42—1722no—
568C23—22no—
569C23—22no—
570C23—22no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23C2×D4×D4311yescharacteristic
576Q8—22no—
577Q8—22no—
578Q8—41no—
579Q8—41no—
580Q8—862no—
581Q8—862no—
582Q8—1721no—
583Q8—1721no—
584D4—22no—
585D4—22no—
586D4—22no—
587D4(C22⋊D43)⋊C414yes—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—21no—
592C2×C4—22no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—48no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—432no—
604C2×C4—432no—
605C2×C4—432no—
606C2×C4—432no—
607C2×C4—432no—
608C2×C4—432no—
609C2×C4—861no—
610C2×C4—861no—
611C2×C4—861no—
612C2×C4—861no—
613C2×C4—861no—
614C2×C4—861no—
615C2×C4—862no—
616C2×C4—862no—
617C2×C4—862no—
618C2×C4—1728no—
619C2×C4—1728no—
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×C4#1306335412yes—
630C2×C4C22×C4×D4311yescharacteristic
631C2×C4C2×D4×D4311yescharacteristic
632C2×C4#41×D4311yescharacteristic
633C2×C4#41×D4311yescharacteristic
634C2×C4C2×#1062190011yescharacteristic
635C2×C4C2×#1062190011yescharacteristic
636C8—22no—
637C8—41no—
638C8—862no—
639C8—1721no—
640C22—24no—
641C22—42no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—42no—
646C22—42no—
647C22C4×D4×D4311yescharacteristic
648C22#121×D4311yescharacteristic
649C22#1458340511yescharacteristic
650C22AGL(1,ℤ/8)×D4311yescharacteristic
651C22#137×D4311yescharacteristic
652C22C2×#1306335411yescharacteristic
653C22#1458369611yescharacteristic
654C4—22no—
655C4—41no—
656C4—42no—
657C4—42no—
658C4—81no—
659C4—434no—
660C4—862no—
661C4—862no—
662C4—862no—
663C4—3441no—
664C4—1722no—
665C4—1722no—
666C4—1722no—
667C4C2×(C22⋊D43)⋊C411yescharacteristic
668C4C4×#1062190011yescharacteristic
669C4#1458342611yescharacteristic
670C4#1458344411yescharacteristic
671C2—44no—
672C2#1913710511yescharacteristic
673C2#440×D4311yescharacteristic
674C2C4×#1306335411yescharacteristic
675C2#1914405711yescharacteristic
676C2#1914407711yescharacteristic
677C2#1914468911yescharacteristic
678C2#1914475011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1877C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
cosocleC22×C4×C43C24
hypercenter#1877D43
hypocenterC43#21504
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1877

Complements

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

NH ≅ G/Ntype
4. #19137164C2semidirect
6. #19135516C2semidirect
7. #19135352C2semidirect
8. #19135237C2semidirect
9. #19135233C2semidirect
12. #19134447C2semidirect
13. #19134427C2semidirect
14. #19134424C2semidirect
23. #14583102C4semidirect
71. #13063323C2×C4semidirect
106. Dic43⋊C8C2×C4semidirect
108. #13063250C2×C4semidirect
110. #13063249C2×C4semidirect
331. Dic43#440semidirect
401. C43#21504semidirect

Maximal subgroups

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

subgroupindex
C2×#145831022
C2×#145830002
C2×#145829962
#191371642
C4×D4×Dic432
#191355162
#191353522
#191352372
#191352332
#191349292
#191345932
#191344472
#191344272
#191344242
C43×#18772
#2150443