Finite Group Databasebeta

← #25119056

Subgroups — #25119056

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×#14583104C211yesmaximal, characteristic
2C2×#14582996C211yesmaximal, characteristic
3C2×#14582990C211yesmaximal, characteristic
4#19137653C211yesmaximal, characteristic, complemented
5#19137505C211yesmaximal, characteristic
6#19135415C211yesmaximal, characteristic, complemented
7#19135363C211yesmaximal, characteristic, complemented
8#19135286C211yesmaximal, characteristic, complemented
9#19135272C211yesmaximal, characteristic, complemented
10#19134927C211yesmaximal, characteristic
11#19134927C211yesmaximal, characteristic
12#19134864C211yesmaximal, characteristic, complemented
13#19134850C211yesmaximal, characteristic, complemented
14#19134467C211yesmaximal, characteristic, complemented
15C43×#1762C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C2×#13063325C2211yescharacteristic
19C2×#13063290C2211yescharacteristic
20C2×#13063290C2211yescharacteristic
21C2×D4×Dic43C2211yescharacteristic
22C2×D4×Dic43C2211yescharacteristic
23#14583104C418yescomplemented
24#14582996—24no—
25#14582990—24no—
26C2×#13063258C2211yescharacteristic
27C2×#13063256C2211yescharacteristic
28C2×C4⋊(C43⋊C8)C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063250C2211yescharacteristic
32C2×#13063250C2211yescharacteristic
33C2×#13063248C2211yescharacteristic
34C2×#13063248C2211yescharacteristic
35C2×#13063235C2211yescharacteristic
36C2×C8×Dic43C2211yescharacteristic
37#14582804C2211yescharacteristic
38#14582804C2211yescharacteristic
39#14582798C2211yescharacteristic
40#14582798C2211yescharacteristic
41#14582797—21no—
42#14582784—21no—
43#14582784—21no—
44#14582774—21no—
45#14582774—21no—
46#14582765C2211yescharacteristic
47#14582759—21no—
48C4×C4⋊Dic43—21no—
49C4×C4⋊Dic43C2211yescharacteristic
50C2×C43⋊#95—21no—
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582653C2211yescharacteristic
54#14582653C2211yescharacteristic
55C2×C4×D4×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×#97×C43C2211yescharacteristic
59C4×C4⋊C4×C43C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C22×Dic86C2311yescharacteristic
63C22×Dic86C2311yescharacteristic
64C23×Dic43—21no—
65C23×Dic43—21no—
66C2×#10621883—22no—
67C2×#10621883—22no—
68C2×#10621883—22no—
69C2×#10621883—22no—
70C2×#10621883C2×C414yes—
71C2×#10621883C2×C414yes—
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74#13063325—22no—
75#13063325C2×C414yescomplemented
76#13063290—22no—
77#13063290—22no—
78#13063290—41no—
79#13063290—41no—
80D4×Dic43—22no—
81D4×Dic43—22no—
82D4×Dic43—41no—
83D4×Dic43—41no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43—21no—
88C2×C4⋊Dic43D411yescharacteristic
89C2×C4⋊Dic43D411yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—21no—
96C2×C4×Dic43—21no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43C2311yescharacteristic
99C2×C4×Dic43C2311yescharacteristic
100#13063258—22no—
101#13063256—22no—
102C4⋊(C43⋊C8)C2×C414yescomplemented
103#13063250—22no—
104#13063250—22no—
105#13063250—41no—
106#13063250—41no—
107#13063248C2×C414yescomplemented
108#13063248C2×C414yescomplemented
109#13063235—22no—
110C8×Dic43—22no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95D411yescharacteristic
120C43⋊#95D411yescharacteristic
121C22×D4×C43C2311yescharacteristic
122C23×C4×C43—21no—
123C22×C8×C43C2311yescharacteristic
124C22×C8×C43C2311yescharacteristic
125C4×D4×C43—22no—
126C4×D4×C43C2×C414yes—
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C22⋊C4×C43—21no—
131C2×C42×C43—21no—
132C2×C42×C43C2311yescharacteristic
133#102×C43—22no—
134#102×C43D414yes—
135#97×C43—22no—
136#95×C43—21no—
137C24×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43—21no—
141C2×D4×C43C22×C412yes—
142C2×D4×C43C2×D412yes—
143C2×D4×C43#4112yes—
144C22×C4×C43—24no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—81no—
149C22×C4×C43—81no—
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2411yescharacteristic
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—42no—
158C22×Dic43—42no—
159C22×Dic43—42no—
160C22×Dic43—42no—
161C22×Dic43—81no—
162C22×Dic43—81no—
163C22×Dic43C2×D411yescharacteristic
164C22×Dic43C2×D411yescharacteristic
165C22×Dic43C2×D411yescharacteristic
166C22×Dic43C2×D411yescharacteristic
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86—21no—
173C2×Dic86—21no—
174C2×Dic86—21no—
175C2×Dic86—21no—
176C2×Dic86—21no—
177C2×Dic86C22×C412yes—
178C2×Dic86C22×C412yes—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43C2×D412yes—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43C22×C412yes—
190C4⋊C4×C43C2×D412yes—
191C22⋊C4×C43—24no—
192C42×C43—42no—
193C42×C43C22×C412yes—
194C42×C43#4112yes—
195C22⋊Dic43—42no—
196C22⋊Dic43—42no—
197#10621883—28no—
198#10621883—28no—
199C4⋊Dic43—24no—
200C4⋊Dic43—24no—
201C4⋊Dic43—22no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—41no—
207C4⋊Dic43—81no—
208C4⋊Dic43—81no—
209Dic43⋊C4—42no—
210Dic43⋊C4—42no—
211C4×Dic43—21no—
212C4×Dic43—21no—
213C4×Dic43—21no—
214C4×Dic43—21no—
215C4×Dic43—42no—
216C4×Dic43—42no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8C22×C412yes—
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
231D4×C43—22no—
232D4×C43—22no—
233D4×C43—22no—
234D4×C43C4×D414yes—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—84no—
249C2×C4×C43C4×D412yes—
250C2×C4×C43C4×D412yes—
251C2×C4×C43C23×C411yescharacteristic
252C2×C4×C43C22×D411yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C43H(5,𝔽2)11yescharacteristic
256C2×C4×C432−1+411yescharacteristic
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—22no—
260C2×Dic43—22no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—41no—
271C2×Dic43—41no—
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—84no—
281C2×Dic43—84no—
282C2×Dic43#13712yes—
283Dic86—22no—
284Dic86—22no—
285Dic86—22no—
286Dic86—22no—
287Dic86—41no—
288Dic86—41no—
289Dic86—41no—
290Dic86—41no—
291C8×C43—22no—
292C8×C43—41no—
293C43⋊C8—22no—
294C43⋊C8—22no—
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—22no—
311C4×C43—22no—
312C4×C43—42no—
313C4×C43—42no—
314C4×C43—81no—
315C4×C43C2×C4×D411yescharacteristic
316C4×C43#52011yescharacteristic
317C4×C43#54711yescharacteristic
318C4×C43#55311yescharacteristic
319Dic43—22no—
320Dic43—42no—
321Dic43—42no—
322Dic43—41no—
323Dic43—41no—
324Dic43—41no—
325Dic43—81no—
326Dic43—81no—
327C2×#461—431no—
328C2×#440—431no—
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#1762D4311yescharacteristic
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×SD16—431no—
352C2×C4⋊Q8—431no—
353C2×C4×Q8—431no—
354C2×C4×Q8—431no—
355C2×C4×D4—431no—
356C2×C4×D4—431no—
357C2×C4×D4C2×D4311yescharacteristic
358#461—438no—
359#440—864no—
360C4×SD16—864no—
361C2×#107—431no—
362C2×#106—431no—
363C2×C4⋊C8—431no—
364C2×#103—431no—
365C2×#103—431no—
366C2×#103—431no—
367C2×#103—431no—
368C2×#103—431no—
369C2×#103—431no—
370C2×#102C2×D4311yescharacteristic
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—861no—
388C4×C4⋊C4C2×D4311yescharacteristic
389C2×#95—861no—
390#340—431no—
391#340—431no—
392#340C2×D4311yescharacteristic
393#340C2×D4311yescharacteristic
394#336—431no—
395#336—431no—
396C43#2301211yescharacteristic, complemented, Sylow
397C22×Q8—431no—
398C22×Q8—431no—
399C22×D4C22×D4311yescharacteristic
400C23×C4—21no—
401C23×C4—861no—
402C23×C4—861no—
403C2×SD16—434no—
404C2×SD16—434no—
405C2×SD16—862no—
406C2×SD16—862no—
407C2×SD16—862no—
408C2×SD16—862no—
409C22×C8—431no—
410C22×C8—431no—
411C22×C8C22×D4311yescharacteristic
412C22×C8C22×D4311yescharacteristic
413C4⋊Q8—434no—
414C4⋊Q8—862no—
415C4×Q8—862no—
416C4×Q8—862no—
417C4×Q8—1721no—
418C4×Q8—1721no—
419C4×D4—22no—
420C4×D4—862no—
421C4×D4—862no—
422C4×D4—1721no—
423C4×D4—1721no—
424C4×D4C4×D4314yes—
425C2×C4⋊C4—431no—
426C2×C4⋊C4—431no—
427C2×C4⋊C4—431no—
428C2×C4⋊C4—431no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4—861no—
433C2×C4⋊C4—861no—
434C2×C4⋊C4—861no—
435C2×C4⋊C4C22×D4311yescharacteristic
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—862no—
448#106—862no—
449C4⋊C8—434no—
450#103—434no—
451#103—434no—
452#103—862no—
453#103—862no—
454#103—1721no—
455#103—1721no—
456#102—22no—
457#102D17214yes—
458#97—22no—
459#97—862no—
460C4×C8—862no—
461#95—21no—
462#95—431no—
463#95—431no—
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—432no—
474C2×Q8—432no—
475C2×Q8—861no—
476C2×Q8—861no—
477C2×Q8—861no—
478C2×Q8—861no—
479C2×Q8—861no—
480C2×Q8—861no—
481C2×Q8—861no—
482C2×Q8—861no—
483C2×Q8—861no—
484C2×Q8—861no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4C2×C4×D4312yes—
489C2×D4C2×D17212yes—
490C2×D4#1062189812yes—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—24no—
494C22×C4—21no—
495C22×C4—81no—
496C22×C4—81no—
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×C4—3441no—
506C22×C4—3441no—
507C22×C4—1722no—
508C22×C4—1722no—
509C22×C4—1722no—
510C22×C4—1722no—
511C22×C4D4×D4311yescharacteristic
512C22×C4D4×D4311yescharacteristic
513C22×C4C23×D4311yescharacteristic
514SD16—868no—
515SD16—868no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—432no—
522C2×C8—432no—
523C2×C8—861no—
524C2×C8—861no—
525C2×C8—861no—
526C2×C8—861no—
527C2×C8C2×D17212yes—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—862no—
533C4⋊C4—864no—
534C4⋊C4—864no—
535C4⋊C4—861no—
536C4⋊C4—861no—
537C4⋊C4—861no—
538C4⋊C4—861no—
539C4⋊C4—3441no—
540C4⋊C4—3441no—
541C4⋊C4—1721no—
542C4⋊C4—1722no—
543C4⋊C4—1722no—
544C4⋊C4C2×C4×D4312yes—
545C4⋊C4C2×D17212yes—
546C22⋊C4—24no—
547C22⋊C4—1722no—
548C22⋊C4—1722no—
549C42—42no—
550C42—861no—
551C42—861no—
552C42—861no—
553C42—861no—
554C42—1722no—
555C42—1722no—
556C42C2×C4×D4312yes—
557C42#1062190012yes—
558C23—22no—
559C23—22no—
560C23—22no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23C2×D4×D4311yescharacteristic
566Q8—862no—
567Q8—862no—
568Q8—862no—
569Q8—862no—
570Q8—1721no—
571Q8—1721no—
572Q8—1721no—
573Q8—1721no—
574D4—22no—
575D4—22no—
576D4—22no—
577D4C4×D17214yes—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—84no—
592C2×C4—432no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—862no—
596C2×C4—862no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—861no—
602C2×C4—861no—
603C2×C4—861no—
604C2×C4—861no—
605C2×C4—861no—
606C2×C4—3444no—
607C2×C4—3444no—
608C2×C4—1721no—
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(C22⋊D43)⋊C412yes—
619C2×C4(C22⋊D43)⋊C412yes—
620C2×C4C22×C4×D4311yescharacteristic
621C2×C4C22×D17211yescharacteristic
622C2×C4C2×#1062190011yescharacteristic
623C2×C4C2×#1062189811yescharacteristic
624C2×C4#1306337111yescharacteristic
625C2×C4#1306337211yescharacteristic
626C8—22no—
627C8—41no—
628C8—862no—
629C8—862no—
630C22—24no—
631C22—42no—
632C22—42no—
633C22—42no—
634C22—42no—
635C22—42no—
636C22—42no—
637C22C2×(C22⋊D43)⋊C411yescharacteristic
638C22D4×D17211yescharacteristic
639C22#1458355811yescharacteristic
640C22#137×D4311yescharacteristic
641C22#1458369511yescharacteristic
642C22#1458370911yescharacteristic
643C22#1458370911yescharacteristic
644C4—22no—
645C4—22no—
646C4—42no—
647C4—42no—
648C4—81no—
649C4—862no—
650C4—3441no—
651C4—3441no—
652C4—1722no—
653C4—1722no—
654C4—1721no—
655C4—1721no—
656C4—1721no—
657C4C2×C4×D17211yescharacteristic
658C4#1458337911yescharacteristic
659C4#1458355311yescharacteristic
660C4#1458359511yescharacteristic
661C2—44no—
662C2#1913760911yescharacteristic
663C2#1914341911yescharacteristic
664C2#1914345711yescharacteristic
665C2#1914610711yescharacteristic
666C2#1914612211yescharacteristic
667C2#1914737711yescharacteristic
668C2#1914742311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1762C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
cosocleC22×C4×C43C24
hypercenter#1762D43
hypocenterC43#23012
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
4. #19137653C2semidirect
6. #19135415C2semidirect
7. #19135363C2semidirect
8. #19135286C2semidirect
9. #19135272C2semidirect
12. #19134864C2semidirect
13. #19134850C2semidirect
14. #19134467C2semidirect
23. #14583104C4semidirect
75. #13063325C2×C4semidirect
102. C4⋊(C43⋊C8)C2×C4semidirect
107. #13063248C2×C4semidirect
108. #13063248C2×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×#145831042
C2×#145829962
C2×#145829902
#191376532
#191375052
#191354152
#191353632
#191352862
#191352722
#191349272
#191348642
#191348502
#191344672
C43×#17622
#2301243