Finite Group Databasebeta

← #25106590

Subgroups — #25106590

Order 11008.

1014 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×#14583509C211yesmaximal, characteristic
2C2×#14582927C211yesmaximal, characteristic
3#19137202C211yesmaximal, characteristic
4#19135551C211yesmaximal, characteristic, complemented
5#19135549C211yesmaximal, characteristic, complemented
6#19135516C211yesmaximal, characteristic, complemented
7#19135516C211yesmaximal, characteristic, complemented
8#19135028C211yesmaximal, characteristic
9#19135019C211yesmaximal, characteristic
10#19135016C211yesmaximal, characteristic
11#19134609C211yesmaximal, characteristic, complemented
12#19134608C211yesmaximal, characteristic, complemented
13#19134599C211yesmaximal, characteristic, complemented
14#19134598C211yesmaximal, characteristic, complemented
15C43×#1894C211yesmaximal, characteristic
16C23×C43⋊C8C2211yescharacteristic
17#14583509—24no—
18#14583509C418yescomplemented
19C2×#13063323C2211yescharacteristic
20C2×#13063318—21no—
21C2×#13063318—21no—
22C2×#13063316—21no—
23C2×#13063316C2211yescharacteristic
24C2×#13063315—21no—
25C2×#13063304C2211yescharacteristic
26C2×Q8×Dic43C2211yescharacteristic
27C2×#13063290C2211yescharacteristic
28C2×#13063284C2211yescharacteristic
29#14582927—24no—
30C2×Dic43⋊C8C2211yescharacteristic
31C2×Dic43⋊C8C2211yescharacteristic
32C2×Dic43⋊C8C2211yescharacteristic
33C2×Dic43⋊C8C2211yescharacteristic
34C2×#13063250C2211yescharacteristic
35C2×#13063250C2211yescharacteristic
36C2×#13063249C2211yescharacteristic
37C2×#13063249C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39C2×#13063248C2211yescharacteristic
40#14582793—21no—
41#14582787—21no—
42#14582784—21no—
43#14582782—21no—
44#14582768C2211yescharacteristic
45#14582764C2211yescharacteristic
46#14582759C2211yescharacteristic
47C4⋊C4×Dic43C2211yescharacteristic
48C4⋊C4×Dic43C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C22×M16×C43C2211yescharacteristic
56C2×C22⋊Q8×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C43×#380C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C22×Dic86C2311yescharacteristic
63C22×C43⋊C8—22no—
64C22×C43⋊C8—41no—
65C22×C43⋊C8—41no—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68#13063323—22no—
69#13063323C2×C414yes—
70#13063318—28no—
71#13063318—28no—
72#13063316—28no—
73#13063316—22no—
74#13063316C2×C414yes—
75#13063315—28no—
76#13063304—22no—
77#13063304C2×C414yes—
78Q8×Dic43—22no—
79Q8×Dic43C2×C414yes—
80#13063290—22no—
81#13063290C2×C414yes—
82#13063284C2×C414yes—
83#13063284D414yes—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43D411yescharacteristic
87C2×C4⋊Dic43D411yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×C22⋊Dic43—21no—
99C2×C22⋊Dic43—21no—
100C2×C22⋊Dic43D411yescharacteristic
101C2×C22⋊Dic43D411yescharacteristic
102C2×C4×Dic43—21no—
103C2×C4×Dic43—21no—
104C2×C4×Dic43—21no—
105C2×C4×Dic43—21no—
106C2×C4×Dic43C2311yescharacteristic
107C2×C4×Dic43C2311yescharacteristic
108Dic43⋊C8—22no—
109Dic43⋊C8—22no—
110Dic43⋊C8—22no—
111Dic43⋊C8—22no—
112#13063250—41no—
113#13063250—41no—
114#13063249—41no—
115#13063249—41no—
116#13063248—41no—
117#13063248—41no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C22×Q8×C43C2311yescharacteristic
124C23×C4×C43C2311yescharacteristic
125C2×M16×C43—22no—
126C2×M16×C43—41no—
127C2×M16×C43—41no—
128C22×C8×C43C2311yescharacteristic
129C22×C8×C43C2311yescharacteristic
130C22⋊Q8×C43—22no—
131C22⋊Q8×C43C2×C414yes—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C22⋊C4×C43—21no—
137C2×C22⋊C4×C43—21no—
138#103×C43—41no—
139#103×C43—41no—
140#95×C43—21no—
141C24×C43C2×D411yescharacteristic
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43C22×C412yes—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43C22×C412yes—
157C22×C4×C43C2×D412yes—
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2411yescharacteristic
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43C2×D411yescharacteristic
165C22×Dic43C2×D411yescharacteristic
166C22×Dic43C2×D411yescharacteristic
167C22×Dic43C2×D411yescharacteristic
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86—21no—
173C2×Dic86C22×C412yes—
174M16×C43—44no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C4⋊C4×C43—24no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43C22×C412yes—
188C22⋊C4×C43—24no—
189C22⋊C4×C43—81no—
190C22⋊Dic43—24no—
191C22⋊Dic43—81no—
192C22⋊Dic43C22⋊C414yes—
193C22⋊Dic43C22⋊C414yes—
194C4⋊Dic43—21no—
195C4⋊Dic43—24no—
196C4⋊Dic43—24no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43C22⋊C414yes—
202C4⋊Dic43C22⋊C414yes—
203C4⋊Dic43C22×C412yes—
204Dic43⋊C4—24no—
205Dic43⋊C4—24no—
206Dic43⋊C4—24no—
207Dic43⋊C4—24no—
208Dic43⋊C4—24no—
209Dic43⋊C4—81no—
210Dic43⋊C4—81no—
211C4×Dic43—24no—
212C4×Dic43—24no—
213C4×Dic43—81no—
214C4×Dic43—81no—
215C4×Dic43C22×C412yes—
216C4×Dic43C22×C412yes—
217C4×Dic43C2×D412yes—
218C4×Dic43C2×D412yes—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—44no—
226C23×C43—21no—
227C23×C43—21no—
228C23×C43—21no—
229C23×C43—21no—
230C23×C43—21no—
231C23×C43—21no—
232C23×C43C2×C22⋊C412yes—
233C23×C43C22×D411yescharacteristic
234Q8×C43—22no—
235Q8×C43—22no—
236Q8×C43—41no—
237Q8×C43—41no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
243C2×C4×C43—22no—
244C2×C4×C43—22no—
245C2×C4×C43—22no—
246C2×C4×C43—41no—
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—41no—
255C2×C4×C43—41no—
256C2×C4×C43C2×C22⋊C412yes—
257C2×C4×C43C23×C411yescharacteristic
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43H(5,𝔽2)11yescharacteristic
260C2×C4×C43H(5,𝔽2)11yescharacteristic
261C2×C4×C432−1+411yescharacteristic
262C2×C4×C432−1+411yescharacteristic
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—22no—
272C2×Dic43—22no—
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—41no—
283C2×Dic43C2×C22⋊C412yes—
284C2×Dic43C2×C22⋊C412yes—
285C2×Dic43C2×C22⋊C412yes—
286C2×Dic43C2×C22⋊C412yes—
287Dic86—22no—
288Dic86—22no—
289Dic86—41no—
290Dic86—41no—
291C8×C43—41no—
292C8×C43—41no—
293C43⋊C8—41no—
294C43⋊C8—41no—
295#21898—431nomaximal, Sylow
296C22×C43—22no—
297C22×C43—22no—
298C22×C43—22no—
299C22×C43—41no—
300C22×C43—41no—
301C22×C43—41no—
302C22×C43—41no—
303C22×C43C22×C22⋊C411yescharacteristic
304C22×C43#53711yescharacteristic
305C22×C43#53711yescharacteristic
306C22×C43#57711yescharacteristic
307C22×C43#57711yescharacteristic
308C22×C43#57811yescharacteristic
309C22×C43#57811yescharacteristic
310C4×C43—22no—
311C4×C43—42no—
312C4×C43—42no—
313C4×C43—81no—
314C4×C43—81no—
315C4×C43#52011yescharacteristic
316C4×C43#52011yescharacteristic
317C4×C43#53511yescharacteristic
318C4×C43#53611yescharacteristic
319Dic43—22no—
320Dic43—22no—
321Dic43—22no—
322Dic43—22no—
323Dic43—42no—
324Dic43—42no—
325Dic43—81no—
326Dic43—81no—
327C2×#541—431no—
328C2×#424—431no—
329#2314—431no—
330#1989—431no—
331#1989—431no—
332#1981—431no—
333#1981—431no—
334#1894—431no—
335#1894D4311yescharacteristic
336#1892—431no—
337#1892—431no—
338#1805—431no—
339#1805—431no—
340#1803—431no—
341#1803—431no—
342C2×C43—42no—
343C2×C43#231111yescharacteristic
344C2×C43#289811yescharacteristic
345C2×C43#289811yescharacteristic
346C2×C43#325811yescharacteristic
347C2×C43#325811yescharacteristic
348C2×C43#326011yescharacteristic
349C2×C43#326111yescharacteristic
350C22×M16C2×D4311yescharacteristic
351C23×C8—431no—
352#541—438no—
353#541—864no—
354C2×C4⋊Q8—431no—
355C2×#126—861no—
356C2×#126—861no—
357C2×#125—431no—
358C2×#125—861no—
359C2×#125—861no—
360C2×C22⋊Q8—431no—
361C2×C22⋊Q8C2×D4311yescharacteristic
362C2×C4×Q8—431no—
363C2×C4×Q8—431no—
364C2×#117—431no—
365#424—864no—
366C2×C4⋊C8—431no—
367C2×C4⋊C8—431no—
368C2×C4⋊C8—431no—
369C2×C4⋊C8—431no—
370C2×#103—431no—
371C2×#103—431no—
372C2×#103—431no—
373C2×#103—431no—
374C2×#103—431no—
375C2×#103—431no—
376C2×#103C2×D4311yescharacteristic
377C2×#103C2×D4311yescharacteristic
378#388—861no—
379#388—861no—
380#387—861no—
381#387—861no—
382#384—431no—
383#382—431no—
384#380—431no—
385#380C2×D4311yescharacteristic
386C4×C4⋊C4—431no—
387C4×C4⋊C4—431no—
388#340—431no—
389#340—431no—
390#340—431no—
391#340—431no—
392#340—431no—
393#340—431no—
394#340C2×D4311yescharacteristic
395#340C2×D4311yescharacteristic
396C43#2189811yescharacteristic, complemented, Sylow
397C22×Q8—431no—
398C22×Q8C22×D4311yescharacteristic
399C23×C4C22×D4311yescharacteristic
400C2×M16—22no—
401C2×M16—41no—
402C2×M16—41no—
403C22×C8—431no—
404C22×C8—431no—
405C22×C8—862no—
406C22×C8—1721no—
407C22×C8—1721no—
408C22×C8C22×D4311yescharacteristic
409C22×C8C22×D4311yescharacteristic
410C4⋊Q8—434no—
411C4⋊Q8—862no—
412#126—868no—
413#126—868no—
414#125—434no—
415#125—862no—
416#125—868no—
417#125—868no—
418C22⋊Q8—22no—
419C22⋊Q8—434no—
420C22⋊Q8—862no—
421C22⋊Q8C4×D4314yes—
422C4×Q8—434no—
423C4×Q8—434no—
424C4×Q8—862no—
425C4×Q8—862no—
426#117—434no—
427#117—434no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—431no—
430C2×C4⋊C4—431no—
431C2×C4⋊C4—431no—
432C2×C4⋊C4—431no—
433C2×C4⋊C4—431no—
434C2×C4⋊C4—861no—
435C2×C4⋊C4—861no—
436C2×C4⋊C4—861no—
437C2×C4⋊C4—861no—
438C2×C4⋊C4—861no—
439C2×C4⋊C4—861no—
440C2×C4⋊C4—861no—
441C2×C4⋊C4—861no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4C22×D4311yescharacteristic
444C2×C4⋊C4C22×D4311yescharacteristic
445C2×C4⋊C4C22×D4311yescharacteristic
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—431no—
449C2×C22⋊C4—431no—
450C2×C22⋊C4—861no—
451C2×C22⋊C4—861no—
452C2×C42—431no—
453C2×C42—431no—
454C2×C42—861no—
455C2×C42—861no—
456C2×C42—861no—
457C2×C42—861no—
458C4⋊C8—862no—
459C4⋊C8—862no—
460C4⋊C8—862no—
461C4⋊C8—862no—
462#103—41no—
463#103—41no—
464#103—1721no—
465#103—1721no—
466#103—1721no—
467#103—1721no—
468#103—1721no—
469#103—1721no—
470#95—21no—
471#95—861no—
472#95—861no—
473#95—861no—
474#95—861no—
475#95—861no—
476C24D4×D4311yescharacteristic
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—432no—
483C2×Q8—861no—
484C2×Q8—861no—
485C2×Q8—861no—
486C2×Q8—861no—
487C2×Q8—861no—
488C2×Q8C2×C4×D4312yes—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—431no—
498C22×C4—431no—
499C22×C4—431no—
500C22×C4—431no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4—861no—
504C22×C4—861no—
505C22×C4C2×C4×D4312yes—
506C22×C4D4×D4311yescharacteristic
507C22×C4D4×D4312yes—
508C22×C4C23×D4311yescharacteristic
509M16—44no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—1724no—
523C4⋊C4—24no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—434no—
530C4⋊C4—434no—
531C4⋊C4—432no—
532C4⋊C4—864no—
533C4⋊C4—864no—
534C4⋊C4—864no—
535C4⋊C4—864no—
536C4⋊C4—864no—
537C4⋊C4—864no—
538C4⋊C4—864no—
539C4⋊C4—861no—
540C4⋊C4—861no—
541C4⋊C4—861no—
542C4⋊C4—861no—
543C4⋊C4—861no—
544C4⋊C4—3441no—
545C4⋊C4—3441no—
546C4⋊C4C2×C4×D4312yes—
547C22⋊C4—24no—
548C22⋊C4—81no—
549C22⋊C4—434no—
550C22⋊C4—434no—
551C22⋊C4—864no—
552C22⋊C4—3441no—
553C42—432no—
554C42—432no—
555C42—432no—
556C42—432no—
557C42—864no—
558C42—864no—
559C42—3441no—
560C42—3441no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23C22⋊C4×D4312yes—
568C23C2×D4×D4311yescharacteristic
569Q8—22no—
570Q8—22no—
571Q8—41no—
572Q8—41no—
573Q8—862no—
574Q8—862no—
575Q8—1721no—
576Q8—1721no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—432no—
596C2×C4—432no—
597C2×C4—432no—
598C2×C4—432no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—861no—
602C2×C4—861no—
603C2×C4—861no—
604C2×C4—861no—
605C2×C4—861no—
606C2×C4—861no—
607C2×C4—862no—
608C2×C4—862no—
609C2×C4—1721no—
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×C4C22⋊C4×D4312yes—
620C2×C4C22×C4×D4311yescharacteristic
621C2×C4C2×D4×D4311yescharacteristic
622C2×C4#1306337011yescharacteristic
623C2×C4#1306337011yescharacteristic
624C2×C4#1306337211yescharacteristic
625C2×C4#1306337211yescharacteristic
626C8—41no—
627C8—41no—
628C8—1721no—
629C8—1721no—
630C22—22no—
631C22—22no—
632C22—22no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22C2×C22⋊C4×D4311yescharacteristic
638C22#1458347611yescharacteristic
639C22#1458347611yescharacteristic
640C22#1458370811yescharacteristic
641C22#1458370911yescharacteristic
642C22#1458371511yescharacteristic
643C22#1458371511yescharacteristic
644C4—22no—
645C4—42no—
646C4—42no—
647C4—81no—
648C4—81no—
649C4—862no—
650C4—862no—
651C4—862no—
652C4—862no—
653C4—3441no—
654C4—3441no—
655C4—1722no—
656C4—1722no—
657C4#1458337811yescharacteristic
658C4#1458337811yescharacteristic
659C4#1458346411yescharacteristic
660C4#1458347111yescharacteristic
661C2—42no—
662C2#1913718211yescharacteristic
663C2#1914312611yescharacteristic
664C2#1914312711yescharacteristic
665C2#1914601611yescharacteristic
666C2#1914602211yescharacteristic
667C2#1914603711yescharacteristic
668C2#1914604611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1894C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
cosocleC22×C4×C43C24
hypercenter#1894D43
hypocenterC43#21898
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1894

Complements

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

NH ≅ G/Ntype
4. #19135551C2semidirect
5. #19135549C2semidirect
6. #19135516C2semidirect
7. #19135516C2semidirect
11. #19134609C2semidirect
12. #19134608C2semidirect
13. #19134599C2semidirect
14. #19134598C2semidirect
18. #14583509C4semidirect
396. C43#21898semidirect

Maximal subgroups

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

subgroupindex
C2×#145835092
C2×#145829272
#191372022
#191355512
#191355492
#191355162
#191350282
#191350192
#191350162
#191346092
#191346082
#191345992
#191345982
C43×#18942
#2189843