Finite Group Databasebeta

← #25119065

Subgroups — #25119065

Order 11008.

982 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×#14583102C211yesmaximal, characteristic
2C2×#14582990C211yesmaximal, characteristic
3#19137649C211yesmaximal, characteristic, complemented
4#19137500C211yesmaximal, characteristic
5#19135413C211yesmaximal, characteristic, complemented
6#19135360C211yesmaximal, characteristic, complemented
7#19135285C211yesmaximal, characteristic, complemented
8#19135268C211yesmaximal, characteristic, complemented
9#19134931C211yesmaximal, characteristic
10#19134929C211yesmaximal, characteristic
11#19134863C211yesmaximal, characteristic, complemented
12#19134846C211yesmaximal, characteristic, complemented
13#19134471C211yesmaximal, characteristic, complemented
14#19134422C211yesmaximal, characteristic
15C2×C43×#440C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C2×#13063323C2211yescharacteristic
18C2×#13063290C2211yescharacteristic
19C2×D4×Dic43C2211yescharacteristic
20C2×D4×Dic43C2211yescharacteristic
21#14583102C418yescomplemented
22#14582990—24no—
23C2×#13063256C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063235C2211yescharacteristic
32C2×C8×Dic43C2211yescharacteristic
33#14582806C2211yescharacteristic
34#14582805C2211yescharacteristic
35#14582797C2211yescharacteristic
36#14582795C2211yescharacteristic
37#14582794—21no—
38#14582783—21no—
39#14582780—21no—
40#14582772—21no—
41#14582771—21no—
42#14582764C2211yescharacteristic
43#14582757—21no—
44C4⋊C4×Dic43C2211yescharacteristic
45C4×Dic43⋊C4—21no—
46C4×Dic43⋊C4C2211yescharacteristic
47C2×C43⋊#95—21no—
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582654C2211yescharacteristic
53#14582653C2211yescharacteristic
54C22×SD16×C43C2211yescharacteristic
55C2×C4×Q8×C43C2211yescharacteristic
56C2×C4×D4×C43C2211yescharacteristic
57C43×#440—24no—
58C2×#107×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C2×#97×C43C2211yescharacteristic
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
72#13063290—22no—
73#13063290—41no—
74D4×Dic43—22no—
75D4×Dic43—22no—
76D4×Dic43—41no—
77D4×Dic43C2×C414yes—
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4D411yescharacteristic
87C2×Dic43⋊C4D411yescharacteristic
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43C2311yescharacteristic
93C2×C4×Dic43C2311yescharacteristic
94#13063256—22no—
95Dic43⋊C8C2×C414yescomplemented
96#13063250—22no—
97#13063250C2×C414yescomplemented
98#13063249—41no—
99#13063249C2×C414yescomplemented
100#13063248—41no—
101#13063246—22no—
102#13063235—22no—
103C8×Dic43—22no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95D411yescharacteristic
114C43⋊#95D411yescharacteristic
115C22×Q8×C43C2311yescharacteristic
116C22×D4×C43C2311yescharacteristic
117C23×C4×C43—21no—
118C2×SD16×C43—22no—
119C2×SD16×C43—22no—
120C2×SD16×C43C2×C414yes—
121C22×C8×C43C2311yescharacteristic
122C22×C8×C43C2311yescharacteristic
123C4×Q8×C43—22no—
124C4×Q8×C43—41no—
125C4×D4×C43—22no—
126C4×D4×C43—41no—
127C2×C4⋊C4×C43—21no—
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C22⋊C4×C43—21no—
131C2×C42×C43—21no—
132C2×C42×C43C2311yescharacteristic
133#107×C43—22no—
134#103×C43—22no—
135#102×C43D414yes—
136#97×C43—22no—
137C24×C43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43C22×C412yes—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43C22×C412yes—
148C2×D4×C43C2×D412yes—
149C2×D4×C43#4112yes—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—42no—
154C22×C4×C43—42no—
155C22×C4×C43—81no—
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2411yescharacteristic
159C22×Dic43—24no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—42no—
165C22×Dic43—42no—
166C22×Dic43—81no—
167C22×Dic43—81no—
168C22×Dic43—81no—
169C22×Dic43C2×D411yescharacteristic
170C22×Dic43C2×D411yescharacteristic
171C22×Dic43C2×D411yescharacteristic
172C22×Dic43C2×D411yescharacteristic
173C2×Dic86—21no—
174C2×Dic86—21no—
175C2×Dic86—21no—
176C2×Dic86—21no—
177C2×Dic86—21no—
178C2×Dic86C22×C412yes—
179SD16×C43—28no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43C22×C412yes—
185C2×C8×C43C2×D412yes—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—42no—
190C4⋊C4×C43C2×D412yes—
191C22⋊C4×C43—42no—
192C42×C43—21no—
193C42×C43—21no—
194C42×C43—42no—
195C22⋊Dic43—24no—
196C22⋊Dic43—42no—
197#10621883—28no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43C22×C412yes—
204Dic43⋊C4—24no—
205Dic43⋊C4—24no—
206Dic43⋊C4—22no—
207Dic43⋊C4—41no—
208Dic43⋊C4—42no—
209Dic43⋊C4—81no—
210Dic43⋊C4—81no—
211C4×Dic43—21no—
212C4×Dic43—21no—
213C4×Dic43—42no—
214C4×Dic43—42no—
215C4×Dic43C22×C412yes—
216C4×Dic43#4112yes—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8C22×C412yes—
223C23×C43—22no—
224C23×C43—22no—
225C23×C43—22no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43—41no—
229C23×C43—41no—
230C23×C43C22×D411yescharacteristic
231Q8×C43—22no—
232Q8×C43—22no—
233Q8×C43—41no—
234Q8×C43—41no—
235D4×C43—22no—
236D4×C43—22no—
237D4×C43—22no—
238D4×C43C4×D414yes—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—84no—
255C2×C4×C43C23×C411yescharacteristic
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C43H(5,𝔽2)11yescharacteristic
260C2×C4×C432−1+411yescharacteristic
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—22no—
268C2×Dic43—22no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—84no—
283C2×Dic43—84no—
284C2×Dic43C4×D412yes—
285C2×Dic43C4×D412yes—
286C2×Dic43#13712yes—
287Dic86—22no—
288Dic86—22no—
289Dic86—41no—
290Dic86—41no—
291C8×C43—22no—
292C8×C43—22no—
293C43⋊C8—22no—
294C43⋊C8—41no—
295#23012—431nomaximal, Sylow
296C22×C43—24no—
297C22×C43—42no—
298C22×C43—42no—
299C22×C43—42no—
300C22×C43—42no—
301C22×C43—42no—
302C22×C43—42no—
303C22×C43C2×C4×D411yescharacteristic
304C22×C43D4211yescharacteristic
305C22×C43#54811yescharacteristic
306C22×C43C2×#13711yescharacteristic
307C22×C43#57511yescharacteristic
308C22×C43#57711yescharacteristic
309C22×C43#57711yescharacteristic
310C4×C43—42no—
311C4×C43—41no—
312C4×C43—41no—
313C4×C43—42no—
314C4×C43—81no—
315C4×C43C2×C4×D411yescharacteristic
316C4×C43#52011yescharacteristic
317C4×C43#54711yescharacteristic
318C4×C43#55311yescharacteristic
319Dic43—22no—
320Dic43—22no—
321Dic43—22no—
322Dic43—42no—
323Dic43—42no—
324Dic43—41no—
325Dic43—81no—
326Dic43—81no—
327C2×#461—431no—
328C2×#440D4311yescharacteristic
329C2×C4×SD16—431no—
330#2365—431no—
331#2349—431no—
332#1960—431no—
333#1949—431no—
334#1935—431no—
335#1933—431no—
336#1877—431no—
337#1877—431no—
338#1865—431no—
339#1863—431no—
340#1771—431no—
341#1762—431no—
342C2×C43—44no—
343C2×C43#236111yescharacteristic
344C2×C43C4×#13711yescharacteristic
345C2×C43#294911yescharacteristic
346C2×C43#326611yescharacteristic
347C2×C43#326711yescharacteristic
348C2×C43#337211yescharacteristic
349C2×C43#337611yescharacteristic
350C22×SD16—431no—
351C22×SD16C2×D4311yescharacteristic
352C2×C4⋊Q8—431no—
353C2×C4×Q8—431no—
354C2×C4×Q8C2×D4311yescharacteristic
355C2×C4×D4—431no—
356C2×C4×D4—431no—
357C2×C4×D4C2×D4311yescharacteristic
358#461—438no—
359#440—24no—
360C4×SD16—864no—
361C2×#107C2×D4311yescharacteristic
362C2×#106—431no—
363C2×C4⋊C8—431no—
364C2×#103—431no—
365C2×#103—431no—
366C2×#103—431no—
367C2×#103—431no—
368C2×#103—431no—
369C2×#103C2×D4311yescharacteristic
370C2×#102—431no—
371C2×#102C2×D4311yescharacteristic
372C2×#97—431no—
373C2×#97C2×D4311yescharacteristic
374C2×C4×C8—431no—
375#391—431no—
376#391—431no—
377#389—431no—
378#389—431no—
379#389—861no—
380#387—861no—
381#387—861no—
382#385—861no—
383#385—861no—
384#382—431no—
385#380—861no—
386C4×C4⋊C4—431no—
387C4×C4⋊C4—431no—
388C4×C4⋊C4—861no—
389C2×#95—861no—
390#340—431no—
391#340—431no—
392#340—431no—
393#340—431no—
394#336—431no—
395#336—431no—
396C43#2301211yescharacteristic, complemented, Sylow
397C22×Q8—431no—
398C22×Q8C22×D4311yescharacteristic
399C22×D4C22×D4311yescharacteristic
400C23×C4—21no—
401C23×C4—861no—
402C23×C4—861no—
403C2×SD16—22no—
404C2×SD16—22no—
405C2×SD16—434no—
406C2×SD16—862no—
407C2×SD16—862no—
408C2×SD16C4×D4314yes—
409C22×C8—431no—
410C22×C8—431no—
411C22×C8C22×D4311yescharacteristic
412C22×C8C22×D4311yescharacteristic
413C4⋊Q8—434no—
414C4⋊Q8—862no—
415C4×Q8—22no—
416C4×Q8—41no—
417C4×Q8—862no—
418C4×Q8—1721no—
419C4×D4—22no—
420C4×D4—41no—
421C4×D4—434no—
422C4×D4—862no—
423C4×D4—862no—
424C4×D4—1721no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—431no—
427C2×C4⋊C4—431no—
428C2×C4⋊C4—431no—
429C2×C4⋊C4—431no—
430C2×C4⋊C4—431no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4—861no—
433C2×C4⋊C4—861no—
434C2×C4⋊C4—861no—
435C2×C4⋊C4—861no—
436C2×C4⋊C4C22×D4311yescharacteristic
437C2×C4⋊C4C22×D4311yescharacteristic
438C2×C22⋊C4—21no—
439C2×C22⋊C4—861no—
440C2×C22⋊C4—861no—
441C2×C42—21no—
442C2×C42—431no—
443C2×C42—431no—
444C2×C42—861no—
445C2×C42—861no—
446C2×C42C22×D4311yescharacteristic
447#107—22no—
448#106—862no—
449C4⋊C8—434no—
450#103—22no—
451#103—434no—
452#103—434no—
453#103—862no—
454#103—1721no—
455#103—1721no—
456#102—862no—
457#102C22⋊D4314yes—
458#97—22no—
459#97—862no—
460C4×C8—862no—
461#95—431no—
462#95—431no—
463#95—861no—
464#95—861no—
465#95—861no—
466#95—861no—
467#95—861no—
468#95—861no—
469#95—861no—
470#95—861no—
471#95—861no—
472C24—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—432no—
479C2×Q8—861no—
480C2×Q8—861no—
481C2×Q8—861no—
482C2×Q8—861no—
483C2×Q8—861no—
484C2×Q8C2×C4×D4312yes—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4C2×C4×D4312yes—
489C2×D4#1062189812yes—
490C2×D4C2×C22⋊D4312yes—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—81no—
497C22×C4—431no—
498C22×C4—431no—
499C22×C4—431no—
500C22×C4—431no—
501C22×C4—864no—
502C22×C4—861no—
503C22×C4—861no—
504C22×C4—861no—
505C22×C4—861no—
506C22×C4—3441no—
507C22×C4—3441no—
508C22×C4—3441no—
509C22×C4—1722no—
510C22×C4—1722no—
511C22×C4D4×D4311yescharacteristic
512C22×C4D4×D4311yescharacteristic
513C22×C4C23×D4311yescharacteristic
514SD16—28no—
515SD16—868no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—432no—
521C2×C8—861no—
522C2×C8—861no—
523C2×C8—861no—
524C2×C8—861no—
525C2×C8—861no—
526C2×C8C2×C4×D4312yes—
527C2×C8C2×C22⋊D4312yes—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—42no—
532C4⋊C4—432no—
533C4⋊C4—862no—
534C4⋊C4—864no—
535C4⋊C4—864no—
536C4⋊C4—861no—
537C4⋊C4—861no—
538C4⋊C4—861no—
539C4⋊C4—861no—
540C4⋊C4—861no—
541C4⋊C4—3441no—
542C4⋊C4—3441no—
543C4⋊C4—1721no—
544C4⋊C4—1722no—
545C4⋊C4C2×C22⋊D4312yes—
546C22⋊C4—42no—
547C22⋊C4—864no—
548C22⋊C4—1722no—
549C42—21no—
550C42—21no—
551C42—42no—
552C42—432no—
553C42—432no—
554C42—861no—
555C42—861no—
556C42—1722no—
557C42—1722no—
558C23—22no—
559C23—22no—
560C23—22no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23C2×D4×D4311yescharacteristic
566Q8—22no—
567Q8—22no—
568Q8—41no—
569Q8—41no—
570Q8—862no—
571Q8—862no—
572Q8—1721no—
573Q8—1721no—
574D4—22no—
575D4—22no—
576D4—22no—
577D4C4×C22⋊D4314yes—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—84no—
594C2×C4—432no—
595C2×C4—432no—
596C2×C4—432no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—861no—
602C2×C4—861no—
603C2×C4—862no—
604C2×C4—862no—
605C2×C4—861no—
606C2×C4—861no—
607C2×C4—861no—
608C2×C4—3444no—
609C2×C4—3444no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4—1721no—
620C2×C4C22×C4×D4311yescharacteristic
621C2×C4C22×C22⋊D4311yescharacteristic
622C2×C4#41×D4311yescharacteristic
623C2×C4C2×#1062189811yescharacteristic
624C2×C4#1306337011yescharacteristic
625C2×C4#1306337211yescharacteristic
626C8—22no—
627C8—22no—
628C8—862no—
629C8—1721no—
630C22—24no—
631C22—42no—
632C22—42no—
633C22—42no—
634C22—42no—
635C22—42no—
636C22—42no—
637C22C4×D4×D4311yescharacteristic
638C22D4×C22⋊D4311yescharacteristic
639C22#1458355811yescharacteristic
640C22#137×D4311yescharacteristic
641C22#1458369511yescharacteristic
642C22#1458370811yescharacteristic
643C22#1458370911yescharacteristic
644C4—42no—
645C4—41no—
646C4—41no—
647C4—42no—
648C4—81no—
649C4—862no—
650C4—862no—
651C4—862no—
652C4—3441no—
653C4—3441no—
654C4—1722no—
655C4—1722no—
656C4—1721no—
657C4C2×C4×C22⋊D4311yescharacteristic
658C4#1458337811yescharacteristic
659C4#1458354811yescharacteristic
660C4#1458359811yescharacteristic
661C2—44no—
662C2#1913761211yescharacteristic
663C2#1914341711yescharacteristic
664C2#1914345111yescharacteristic
665C2#1914609911yescharacteristic
666C2#1914611411yescharacteristic
667C2#1914737711yescharacteristic
668C2#1914742711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#440C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
cosocleC22×C4×C43C24
hypercenterC2×#440D43
hypocenterC43#23012
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
3. #19137649C2semidirect
5. #19135413C2semidirect
6. #19135360C2semidirect
7. #19135285C2semidirect
8. #19135268C2semidirect
11. #19134863C2semidirect
12. #19134846C2semidirect
13. #19134471C2semidirect
21. #14583102C4semidirect
71. #13063323C2×C4semidirect
95. Dic43⋊C8C2×C4semidirect
97. #13063250C2×C4semidirect
99. #13063249C2×C4semidirect
396. C43#23012semidirect

Maximal subgroups

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

subgroupindex
C2×#145831022
C2×#145829902
#191376492
#191375002
#191354132
#191353602
#191352852
#191352682
#191349312
#191349292
#191348632
#191348462
#191344712
#191344222
C2×C43×#4402
#2301243