Finite Group Databasebeta

← #25245437

Subgroups — #25245437

Order 11008.

1468 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#10621900C211yesmaximal, characteristic
2C2×#14583110C211yesmaximal, characteristic, complemented
3C2×#14583104C211yesmaximal, characteristic, complemented
4C2×#14583062C212yesmaximal
5#19142948C211yesmaximal, characteristic, complemented
6#19134937C212yesmaximal, complemented
7#19134927C212yesmaximal, complemented
8#19134906C212yesmaximal, complemented
9#19134597C211yesmaximal, characteristic, complemented
10#19134572C211yesmaximal, characteristic, complemented
11C43×#1802C211yesmaximal, characteristic, complemented
12C22×#10621900C2211yescharacteristic
13C22×Dic172C2212yes—
14C22×#10621883C2212yes—
15C2×#13063325C2211yescharacteristic
16C2×#13063305C2212yes—
17C4×#10621900—24no—
18C4×#10621900—24no—
19C2×C4×Dic86C2211yescharacteristic
20C2×#13063290C2211yescharacteristic
21C2×D4×Dic43C2211yescharacteristic
22C2×C4×C22⋊D43—21no—
23C2×(C22⋊D43)⋊C4—21no—
24C2×#13063283C2211yescharacteristic
25C2×#13063281—21no—
26C22×C4×Dic43—21no—
27C2×C42×D43C2211yescharacteristic
28#14583110—24no—
29#14583104—24no—
30#14583062—28no—
31C2×C4⋊(C43⋊C8)C2211yescharacteristic
32C2×#13063250C2212yes—
33C2×#13063248C2212yes—
34C2×#13063248C2212yes—
35C2×(C2×D43)⋊C8C2212yes—
36#14582804C2212yes—
37#14582798—21no—
38#14582798—21no—
39#14582756—21no—
40#14582756—21no—
41#14582661C2212yes—
42#14582653C2212yes—
43C2×C4×D4×C43C2211yescharacteristic
44C2×C4⋊C8×C43C2211yescharacteristic
45C2×#102×C43C2212yes—
46C43×#384C2211yescharacteristic
47C43×#340C2212yes—
48C2×#10621900—22no—
49C2×#10621900—22no—
50C2×#10621900—22no—
51C2×#10621900—22no—
52C2×#10621900—22no—
53C2×#10621900D414yes—
54C22×Dic86C2312yes—
55C22×Dic86C2311yescharacteristic
56C22×C22⋊D43—21no—
57C23×Dic43—21no—
58C23×Dic43—21no—
59C22×C4×D43D411yescharacteristic
60C22×C4×D43D411yescharacteristic
61C22×C4×D43C2311yescharacteristic
62C2×Dic172—24no—
63C2×Dic172—24no—
64C2×Dic172—24no—
65C2×#10621883—24no—
66C2×#10621883—24no—
67C2×#10621883—24no—
68C22×C43⋊C8C2312yes—
69#13063325—22no—
70#13063325—22no—
71#13063305—24no—
72#13063305—24no—
73C4×Dic86—22no—
74C4×Dic86D414yes—
75#13063290—22no—
76#13063290—22no—
77D4×Dic43—22no—
78D4×Dic43—22no—
79C4×C22⋊D43—28no—
80(C22⋊D43)⋊C4—28no—
81#13063283—22no—
82#13063283—22no—
83#13063281—28no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43—22no—
87C2×C4⋊Dic43C2311yescharacteristic
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×C22⋊Dic43—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—22no—
93C2×C4×Dic43—28no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43—21no—
97C2×C4×Dic43D411yescharacteristic
98C2×C4×Dic43D411yescharacteristic
99C2×C4×Dic43C2311yescharacteristic
100C42×D43—22no—
101C42×D43—22no—
102C4⋊(C43⋊C8)—22no—
103#13063250—24no—
104#13063248—24no—
105#13063248—24no—
106(C2×D43)⋊C8—24no—
107C43⋊#95—22no—
108C43⋊#95—22no—
109C22×D4×C43C2311yescharacteristic
110C23×C4×C43—21no—
111C22×C8×C43C2312yes—
112C4×D4×C43—22no—
113C4×D4×C43D414yes—
114C2×C4⋊C4×C43—21no—
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43C2312yes—
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C22⋊C4×C43—21no—
119C2×C42×C43C2311yescharacteristic
120C4⋊C8×C43—22no—
121#102×C43—24no—
122C24×C43—21no—
123C23×D43C2×D411yescharacteristic
124C2×D4×C43—21no—
125C2×D4×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43C2×D412yes—
128C2×D4×C43C2×D412yes—
129C2×D4×C43#4112yes—
130C22×C4×C43—24no—
131C22×C4×C43—21no—
132C22×C4×C43—22no—
133C22×C4×C43—42no—
134C22×C4×C43—42no—
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2411yescharacteristic
138C2×C22⋊D43—24no—
139C2×C22⋊D43—24no—
140C2×C22⋊D43—24no—
141C22×Dic43—24no—
142C22×Dic43—24no—
143C22×Dic43—24no—
144C22×Dic43—24no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—22no—
148C22×Dic43—42no—
149C22×Dic43—42no—
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153#10621900—28no—
154#10621900—28no—
155#10621900—28no—
156#10621900—28no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—22no—
162C2×C4×D43—22no—
163C2×C4×D43—22no—
164C2×C4×D43—22no—
165C2×C4×D43—22no—
166C2×C4×D43—41no—
167C2×C4×D43C2×D412yes—
168C2×C4×D43#4112yes—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86—22no—
173C2×Dic86—22no—
174C2×Dic86—22no—
175C2×Dic86—22no—
176C2×Dic86—22no—
177C2×Dic86—22no—
178C2×Dic86C2×D412yes—
179C2×Dic86C2×D412yes—
180C2×Dic86#4112yes—
181C2×C8×C43—22no—
182C2×C8×C43—22no—
183C2×C8×C43—22no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—22no—
186C4⋊C4×C43—22no—
187C4⋊C4×C43—42no—
188C4⋊C4×C43—42no—
189C4⋊C4×C43C2×D412yes—
190C22⋊C4×C43—24no—
191C42×C43C2×D412yes—
192C42×C43C2×D412yes—
193C22⋊Dic43—24no—
194#10621883—48no—
195(C2×D43)⋊C4—24no—
196(C2×D43)⋊C4—44no—
197C4⋊Dic43—21no—
198C4⋊Dic43—42no—
199C4⋊Dic43—42no—
200C4⋊Dic43—44no—
201C4⋊Dic43C2×D412yes—
202Dic43⋊C4—24no—
203Dic43⋊C4—24no—
204C4×Dic43—24no—
205C4×Dic43—24no—
206C4×Dic43—22no—
207C4×Dic43—22no—
208C4×Dic43—24no—
209C4×Dic43—21no—
210C4×Dic43—21no—
211C2×C43⋊C8—22no—
212C2×C43⋊C8—22no—
213C2×C43⋊C8—22no—
214Dic172—48no—
215C23×C43—22no—
216C23×C43—22no—
217C23×C43—22no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43C22×D411yescharacteristic
223C22×D43—21no—
224C22×D43—21no—
225C22×D43—21no—
226C22×D43—21no—
227C22×D43—21no—
228C22×D43—21no—
229C22×D43#12112yes—
230D4×C43—22no—
231D4×C43—22no—
232D4×C43—22no—
233D4×C43#12114yes—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—22no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—48no—
240C2×C4×C43—42no—
241C2×C4×C43—42no—
242C2×C4×C43—42no—
243C2×C4×C43#12012yes—
244C2×C4×C43#12012yes—
245C2×C4×C43#13512yes—
246C2×C4×C43#13712yes—
247C2×C4×C43C22×D411yescharacteristic
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C43C22×D411yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C22⋊D43—216no—
254C2×Dic43—216no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—22no—
258C2×Dic43—22no—
259C2×Dic43—22no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—22no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—48no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—42no—
270C2×Dic43—42no—
271C2×Dic43—42no—
272C2×Dic43#12112yes—
273C2×Dic43#13712yes—
274C4×D43—22no—
275C4×D43—22no—
276C4×D43—22no—
277C4×D43—22no—
278C4×D43—44no—
279C4×D43—44no—
280Dic86—22no—
281Dic86—22no—
282Dic86—22no—
283Dic86—42no—
284Dic86—42no—
285Dic86—42no—
286Dic86—42no—
287Dic86#12114yes—
288C8×C43—42no—
289C43⋊C8—42no—
290#32907—431nomaximal, Sylow
291C22×C43—24no—
292C22×C43—42no—
293C22×C43—42no—
294C22×C43—42no—
295C22×C43—42no—
296C22×C43—42no—
297C22×C43—42no—
298C22×C43C2×#12011yescharacteristic
299C22×C43C2×#12111yescharacteristic
300C22×C43#52511yescharacteristic
301C22×C43C2×#13511yescharacteristic
302C22×C43C2×#13711yescharacteristic
303C22×C43C2×#13711yescharacteristic
304C22×C43#57511yescharacteristic
305C2×D43—22no—
306C2×D43—22no—
307C2×D43—22no—
308C2×D43—41no—
309C2×D43—41no—
310C2×D43—41no—
311C2×D43—41no—
312C4×C43—22no—
313C4×C43—42no—
314C4×C43—82no—
315C4×C43#45214yescomplemented
316C4×C43C2×#12111yescharacteristic
317C4×C43C2×#12111yescharacteristic
318C4×C43#52511yescharacteristic
319C4×C43#52511yescharacteristic
320Dic43—24no—
321Dic43—22no—
322Dic43—22no—
323Dic43—41no—
324Dic43—42no—
325Dic43—82no—
326C2×C4×#41—431no—
327C2×#462—431no—
328C2×#461—431no—
329C2×#452—432no—
330#2857—431no—
331#1878—432no—
332#1877—432no—
333#1873—432no—
334#1803—431no—
335#1802D4311yescharacteristic, complemented
336#1797—431no—
337C2×C43—44no—
338C2×C43#284711yescharacteristic
339C2×C43C2×#45211yescharacteristic
340C2×C43#300711yescharacteristic
341C2×C43#303511yescharacteristic
342C2×C43#303911yescharacteristic
343C2×C43#310711yescharacteristic
344C2×C43#311611yescharacteristic
345D43—42no—
346C22×#41—431no—
347C22×Q16—432no—
348C22×SD16—432no—
349C2×C4⋊Q8—431no—
350C2×C22⋊Q8—432no—
351C4×#41—864no—
352C4×#41—864no—
353C2×C4×Q8—431no—
354C2×C4×Q8—431no—
355C2×C4×D4—431no—
356C2×C4×D4—861no—
357C2×C4×D4—861no—
358C2×C4×D4C2×D4311yescharacteristic
359C2×#117—431no—
360C2×#117—861no—
361C22×C42—431no—
362C22×C42—861no—
363#462—864no—
364#461—864no—
365#452—868no—
366C2×C4⋊C8—431no—
367C2×C4⋊C8C2×D4311yescharacteristic
368C2×#103—432no—
369C2×#103—432no—
370C2×#103—432no—
371C2×#102C2×D4312yes—
372C2×C22⋊C8—432no—
373#391—432no—
374#389—861no—
375#389—861no—
376#384C2×D4311yescharacteristic
377#380—861no—
378#380—861no—
379#340—432no—
380#340C2×D4312yes—
381#336—432no—
382C43#3290711yescharacteristic, complemented, Sylow
383C2×#41—434no—
384C2×#41—862no—
385C2×#41—862no—
386C2×#41—862no—
387C2×#41—862no—
388C2×#41—862no—
389C22×Q8—431no—
390C22×Q8—432no—
391C22×D4—861no—
392C22×D4C22×D4311yescharacteristic
393C23×C4—21no—
394C23×C4—431no—
395C23×C4—431no—
396C23×C4—431no—
397C23×C4—861no—
398C23×C4—861no—
399C2×Q16—864no—
400C2×Q16—864no—
401C2×Q16—864no—
402C2×SD16—864no—
403C2×SD16—864no—
404C2×SD16—864no—
405C22×C8—432no—
406C22×C8C22×D4312yes—
407C4⋊Q8—862no—
408C4⋊Q8—862no—
409C22⋊Q8—864no—
410C22⋊Q8—864no—
411C4×Q8—434no—
412C4×Q8—862no—
413C4×Q8—862no—
414C4×Q8—862no—
415C4×D4—22no—
416C4×D4—868no—
417C4×D4—862no—
418C4×D4—868no—
419C4×D4—862no—
420C4×D4D17214yes—
421#117—868no—
422#117—862no—
423#117—862no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—431no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—862no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4C22×D4312yes—
433C2×C4⋊C4C22×D4311yescharacteristic
434C2×C22⋊C4—21no—
435C2×C22⋊C4—861no—
436C2×C22⋊C4—861no—
437C2×C22⋊C4—862no—
438C2×C42—431no—
439C2×C42—431no—
440C2×C42—431no—
441C2×C42—861no—
442C2×C42—861no—
443C2×C42—868no—
444C2×C42—861no—
445C2×C42—862no—
446C2×C42—862no—
447C2×C42C22×D4311yescharacteristic
448C4⋊C8—22no—
449C4⋊C8—862no—
450#103—864no—
451#103—864no—
452#103—864no—
453#102—24no—
454C22⋊C8—864no—
455#95—862no—
456#95—862no—
457C24—21no—
458C24—431no—
459#41—868no—
460#41—868no—
461#41—868no—
462#41—868no—
463C2×Q8—432no—
464C2×Q8—432no—
465C2×Q8—432no—
466C2×Q8—861no—
467C2×Q8—861no—
468C2×Q8—861no—
469C2×Q8—862no—
470C2×Q8—862no—
471C2×Q8—862no—
472C2×Q8—862no—
473C2×Q8—862no—
474C2×Q8—862no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—864no—
479C2×D4—864no—
480C2×D4—864no—
481C2×D4C2×D17212yes—
482C2×D4D4×D4312yes—
483C2×D4#1062190212yes—
484C22×C4—21no—
485C22×C4—24no—
486C22×C4—22no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—431no—
490C22×C4—431no—
491C22×C4—432no—
492C22×C4—432no—
493C22×C4—431no—
494C22×C4—862no—
495C22×C4—864no—
496C22×C4—864no—
497C22×C4—864no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4—864no—
504C22×C4—861no—
505C22×C4—862no—
506C22×C4—862no—
507C22×C4—862no—
508C22×C4—862no—
509C22×C4—862no—
510C22×C4—1721no—
511C22×C4—1722no—
512C22×C4—1722no—
513C22×C4D4×D4311yescharacteristic
514C22×C4D4×D4311yescharacteristic
515C22×C4C23×D4311yescharacteristic
516Q16—1728no—
517SD16—1728no—
518C2×C8—22no—
519C2×C8—22no—
520C2×C8—22no—
521C2×C8—862no—
522C2×C8—862no—
523C2×C8—862no—
524C4⋊C4—21no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—42no—
528C4⋊C4—42no—
529C4⋊C4—432no—
530C4⋊C4—864no—
531C4⋊C4—864no—
532C4⋊C4—861no—
533C4⋊C4—1724no—
534C4⋊C4—1722no—
535C4⋊C4—1722no—
536C4⋊C4C2×D17212yes—
537C22⋊C4—24no—
538C22⋊C4—864no—
539C22⋊C4—864no—
540C22⋊C4—1724no—
541C42—864no—
542C42—864no—
543C42—862no—
544C42—862no—
545C42—864no—
546C42—861no—
547C42—861no—
548C42C2×D17212yes—
549C42D4×D4312yes—
550C23—22no—
551C23—22no—
552C23—22no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—432no—
558C23—861no—
559C23—861no—
560C23—861no—
561C23—861no—
562C23—861no—
563C23—861no—
564C23C2×D4×D4311yescharacteristic
565Q8—434no—
566Q8—862no—
567Q8—862no—
568Q8—862no—
569Q8—1722no—
570Q8—1722no—
571Q8—1722no—
572Q8—1722no—
573D4—22no—
574D4—22no—
575D4—22no—
576D4—8616no—
577D4#1306330014yes—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—48no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—432no—
588C2×C4—432no—
589C2×C4—8616no—
590C2×C4—861no—
591C2×C4—861no—
592C2×C4—862no—
593C2×C4—862no—
594C2×C4—861no—
595C2×C4—862no—
596C2×C4—861no—
597C2×C4—862no—
598C2×C4—862no—
599C2×C4—862no—
600C2×C4—862no—
601C2×C4—862no—
602C2×C4—861no—
603C2×C4—861no—
604C2×C4—861no—
605C2×C4—1724no—
606C2×C4—1728no—
607C2×C4—1722no—
608C2×C4—1722no—
609C2×C4—1722no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1724no—
613C2×C4#1306329512yes—
614C2×C4#1306329512yes—
615C2×C4#1306334412yes—
616C2×C4#1306335412yes—
617C2×C4C2×D4×D4311yescharacteristic
618C2×C4C2×D4×D4311yescharacteristic
619C2×C4C22×D17211yescharacteristic
620C2×C4#41×D4311yescharacteristic
621C2×C4#41×D4311yescharacteristic
622C2×C4C2×#1062190211yescharacteristic
623C8—42no—
624C8—1722no—
625C22—24no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—862no—
633C22—862no—
634C22—862no—
635C22—1721no—
636C22—1721no—
637C22—1721no—
638C22—1721no—
639C22C2×#1306329511yescharacteristic
640C22#121×D4311yescharacteristic
641C22#1458341211yescharacteristic
642C22C2×#1306334411yescharacteristic
643C22#137×D4311yescharacteristic
644C22C2×#1306335411yescharacteristic
645C22#1458369511yescharacteristic
646C4—22no—
647C4—42no—
648C4—82no—
649C4—862no—
650C4—862no—
651C4—864no—
652C4—3442no—
653C4—1721no—
654C4—1722no—
655C4#1458306214yescomplemented
656C4#121×D4311yescharacteristic
657C4C2×#1306330011yescharacteristic
658C4#1458341111yescharacteristic
659C4#1458341211yescharacteristic
660C2—44no—
661C2—1722no—
662C2#1914287811yescharacteristic
663C2C2×#1458306211yescharacteristic
664C2#1914385611yescharacteristic
665C2#1914404311yescharacteristic
666C2#1914407711yescharacteristic
667C2#1914466811yescharacteristic
668C2#1914475911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1802C2
socleC23×C43C22×D4
prime radicalC22×#10621900C22
hypercenter#1802D43
hypocenterC43#32907
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
2. C2×#14583110C2semidirect
3. C2×#14583104C2semidirect
5. #19142948C2semidirect
6. #19134937C2semidirect
7. #19134927C2semidirect
8. #19134906C2semidirect
9. #19134597C2semidirect
10. #19134572C2semidirect
11. C43×#1802C2semidirect
315. C4×C43#452semidirect
335. #1802D43semidirect
382. C43#32907semidirect
655. C4#14583062semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#106219002
C2×#145831102
C2×#145831042
C2×#145830622
#191429482
#191349372
#191349272
#191349062
#191345972
#191345722
C43×#18022
#3290743