Finite Group Databasebeta

← #25132983

Subgroups — #25132983

Order 11008.

1070 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583626C211yesmaximal, characteristic, complemented
2C2×#14583177C211yesmaximal, characteristic
3C2×#14582990C211yesmaximal, characteristic
4#19139515C211yesmaximal, characteristic
5#19135936C211yesmaximal, characteristic, complemented
6#19135930C211yesmaximal, characteristic, complemented
7#19135739C211yesmaximal, characteristic
8#19135554C211yesmaximal, characteristic, complemented
9#19135529C211yesmaximal, characteristic, complemented
10#19134953C211yesmaximal, characteristic
11#19134947C211yesmaximal, characteristic
12#19134852C211yesmaximal, characteristic, complemented
13#19134850C211yesmaximal, characteristic, complemented
14#19134599C211yesmaximal, characteristic, complemented
15C43×#2025C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17#14583626—24no—
18#14583626—24no—
19C2×#13063324—21no—
20C2×#13063324C2211yescharacteristic
21C2×#13063316C2211yescharacteristic
22C2×#13063315—21no—
23C2×#13063315—21no—
24C2×#13063302—21no—
25C2×C4×Dic86C2211yescharacteristic
26C2×C4×Dic86C2211yescharacteristic
27C2×#13063290—21no—
28C2×#13063290C2211yescharacteristic
29C2×#13063290C2211yescharacteristic
30C2×D4×Dic43C2211yescharacteristic
31#14583177—24no—
32#14582990—24no—
33C2×#13063259C2211yescharacteristic
34C2×#13063258C2211yescharacteristic
35C2×#13063256C2211yescharacteristic
36C2×Dic43⋊C8C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063250C2211yescharacteristic
39C2×#13063248C2211yescharacteristic
40C2×#13063246C2211yescharacteristic
41C2×C8×Dic43C2211yescharacteristic
42#14582822—21no—
43#14582822—21no—
44#14582802C2211yescharacteristic
45#14582798C2211yescharacteristic
46#14582797C2211yescharacteristic
47#14582768C2211yescharacteristic
48#14582757—21no—
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582654C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C2×#125×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C43×#390C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86D411yescharacteristic
65C22×Dic86C2311yescharacteristic
66C23×Dic43—21no—
67C2×#10621883—22no—
68C2×#10621883—22no—
69C2×#10621883Q814yescomplemented
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72#13063324—28no—
73#13063324—22no—
74#13063324D414yes—
75#13063316—22no—
76#13063316—22no—
77#13063315—28no—
78#13063315—28no—
79#13063302—44no—
80C4×Dic86—22no—
81C4×Dic86—22no—
82C4×Dic86—22no—
83C4×Dic86—22no—
84#13063290—28no—
85#13063290—22no—
86#13063290—22no—
87#13063290—22no—
88#13063290D414yes—
89D4×Dic43—22no—
90D4×Dic43—22no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43D411yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4—21no—
105C2×Dic43⋊C4D411yescharacteristic
106C2×Dic43⋊C4D411yescharacteristic
107C2×C22⋊Dic43—21no—
108C2×C22⋊Dic43—21no—
109C2×C22⋊Dic43—21no—
110C2×C4×Dic43—21no—
111C2×C4×Dic43—21no—
112C2×C4×Dic43—21no—
113C2×C4×Dic43C2311yescharacteristic
114C2×C4×Dic43C2311yescharacteristic
115#13063259—22no—
116#13063258—22no—
117#13063256—22no—
118Dic43⋊C8—22no—
119#13063250—22no—
120#13063250—22no—
121#13063248—22no—
122#13063246—22no—
123C8×Dic43—22no—
124C43⋊#95—21no—
125C43⋊#95—21no—
126C22×D4×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129#125×C43—22no—
130#125×C43—22no—
131C2×C4⋊C4×C43—21no—
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—
138C2×C42×C43C2311yescharacteristic
139#102×C43—22no—
140#102×C43—22no—
141C24×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43C2×Q812yes—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2411yescharacteristic
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—42no—
159C22×Dic43—42no—
160C22×Dic43—42no—
161C22×Dic43C2×D411yescharacteristic
162C22×Dic43C2×D411yescharacteristic
163C22×Dic43C2×D411yescharacteristic
164C22×Dic43C2×D411yescharacteristic
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—24no—
169C2×Dic86—22no—
170C2×Dic86—22no—
171C2×Dic86—22no—
172C2×Dic86—42no—
173C2×Dic86—42no—
174C2×Dic86C2×D412yes—
175C2×Dic86C2×Q812yes—
176C2×Dic86#4112yes—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C4⋊C4×C43—24no—
184C4⋊C4×C43—24no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43C2×D412yes—
190C4⋊C4×C43C2×D412yes—
191C22⋊C4×C43—42no—
192C22⋊C4×C43—81no—
193C42×C43—21no—
194C42×C43—21no—
195C22⋊Dic43—42no—
196C22⋊Dic43—42no—
197C22⋊Dic43—81no—
198#10621883—28no—
199C4⋊Dic43—24no—
200C4⋊Dic43—21no—
201C4⋊Dic43—22no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—42no—
207C4⋊Dic43C2×D412yes—
208Dic43⋊C4—24no—
209Dic43⋊C4—24no—
210Dic43⋊C4—24no—
211Dic43⋊C4—24no—
212Dic43⋊C4—24no—
213Dic43⋊C4—22no—
214Dic43⋊C4—22no—
215Dic43⋊C4—42no—
216Dic43⋊C4—42no—
217Dic43⋊C4—81no—
218C4×Dic43—24no—
219C4×Dic43—24no—
220C4×Dic43—21no—
221C4×Dic43—21no—
222C4×Dic43—24no—
223C4×Dic43C2×D412yes—
224C4×Dic43C2×D412yes—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8C2×Q812yes—
231C23×C43—22no—
232C23×C43—41no—
233C23×C43—41no—
234C23×C43—41no—
235C23×C43—41no—
236C23×C43—41no—
237C23×C43—41no—
238C23×C43C22×D411yescharacteristic
239D4×C43—22no—
240D4×C43—22no—
241D4×C43—41no—
242D4×C43—41no—
243C2×C4×C43—21no—
244C2×C4×C43—22no—
245C2×C4×C43—22no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—41no—
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×C43C22×D411yescharacteristic
259C2×C4×C43C22×D411yescharacteristic
260C2×C4×C43C22×Q811yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C432−1+411yescharacteristic
263C2×C4×C432−1+411yescharacteristic
264C2×Dic43—22no—
265C2×Dic43—22no—
266C2×Dic43—22no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—22no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—84no—
285C2×Dic43#12012yes—
286C2×Dic43#12012yes—
287C2×Dic43#13512yes—
288C2×Dic43AGL(1,ℤ/8)12yes—
289Dic86—22no—
290Dic86—22no—
291Dic86—22no—
292Dic86—44no—
293Dic86—48no—
294Dic86C22⋊Q814yescomplemented
295C8×C43—41no—
296C8×C43—41no—
297C43⋊C8—22no—
298C43⋊C8—41no—
299#24328—431nomaximal, Sylow
300C22×C43—42no—
301C22×C43—42no—
302C22×C43—42no—
303C22×C43—81no—
304C22×C43—81no—
305C22×C43—81no—
306C22×C43—81no—
307C22×C43C2×#12011yescharacteristic
308C22×C43#54811yescharacteristic
309C22×C43D4×Q811yescharacteristic
310C22×C43C2×#13511yescharacteristic
311C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
312C22×C43#57711yescharacteristic
313C22×C43#57811yescharacteristic
314C4×C43—41no—
315C4×C43—42no—
316C4×C43—41no—
317C4×C43—42no—
318C4×C43—81no—
319C4×C43C2×C22⋊Q811yescharacteristic
320C4×C43#53611yescharacteristic
321C4×C43#54811yescharacteristic
322C4×C43D4×Q811yescharacteristic
323Dic43—24no—
324Dic43—22no—
325Dic43—41no—
326Dic43—42no—
327Dic43—41no—
328Dic43—81no—
329Dic43—81no—
330Dic43#44914yes—
331C2×#557—431no—
332C2×#474—431no—
333C2×C4×SD16—431no—
334#2538—431no—
335#2059—431no—
336#2059—431no—
337#2025—431no—
338#2025D4311yescharacteristic
339#1990—431no—
340#1984—431no—
341#1880—431no—
342#1880—431no—
343#1863—431no—
344#1863—431no—
345#1803—431no—
346C2×C43—82no—
347C2×C43#240911yescharacteristic
348C2×C43C2×#44911yescharacteristic
349C2×C43#301311yescharacteristic
350C2×C43#336411yescharacteristic
351C2×C43#336811yescharacteristic
352C2×C43#338111yescharacteristic
353C2×C43#338611yescharacteristic
354C22×SD16—431no—
355#557—864no—
356#557—864no—
357C2×C4⋊Q8—431no—
358C2×C4⋊Q8—861no—
359C2×#125—431no—
360C2×#125—861no—
361C2×#125—861no—
362C2×#125C2×D4311yescharacteristic
363C2×C22⋊Q8—861no—
364C2×C4×Q8—431no—
365C2×C4×Q8—431no—
366C2×C4×Q8—431no—
367C2×C4×Q8—431no—
368C2×C4×Q8—861no—
369C2×C4×D4—431no—
370#474—864no—
371C4×SD16—864no—
372C2×#107—431no—
373C2×#107—431no—
374C2×#106—431no—
375C2×C4⋊C8—431no—
376C2×#103—431no—
377C2×#103—431no—
378C2×#103—431no—
379C2×#102—431no—
380C2×#102C2×D4311yescharacteristic
381C2×#102C2×D4311yescharacteristic
382C2×C4×C8—431no—
383#396—861no—
384#396—861no—
385#390—431no—
386#390C2×D4311yescharacteristic
387#389—431no—
388#389—431no—
389#384—431no—
390#380—861no—
391#340—431no—
392#340—431no—
393#340—431no—
394#340—431no—
395#340C2×D4311yescharacteristic
396#340C2×D4311yescharacteristic
397#336—431no—
398#336—431no—
399#336—431no—
400#336C2×D4311yescharacteristic
401C43#2432811yescharacteristic, complemented, Sylow
402C22×Q8—431no—
403C22×Q8—431no—
404C22×Q8—861no—
405C22×D4C22×D4311yescharacteristic
406C23×C4—861no—
407C2×SD16—434no—
408C2×SD16—862no—
409C2×SD16—862no—
410C22×C8—431no—
411C22×C8—431no—
412C22×C8C22×D4311yescharacteristic
413C22×C8C22×D4311yescharacteristic
414C4⋊Q8—434no—
415C4⋊Q8—862no—
416C4⋊Q8—868no—
417#125—22no—
418#125—22no—
419#125—862no—
420#125—868no—
421#125—868no—
422#125—862no—
423C22⋊Q8—1724no—
424C4×Q8—434no—
425C4×Q8—862no—
426C4×Q8—862no—
427C4×Q8—862no—
428C4×Q8—862no—
429C4×Q8—862no—
430C4×Q8—862no—
431C4×Q8—868no—
432C4×Q8—862no—
433C4×D4—862no—
434C4×D4—862no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—431no—
438C2×C4⋊C4—431no—
439C2×C4⋊C4—431no—
440C2×C4⋊C4—431no—
441C2×C4⋊C4—431no—
442C2×C4⋊C4—431no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4—861no—
445C2×C4⋊C4—861no—
446C2×C4⋊C4—861no—
447C2×C4⋊C4—861no—
448C2×C4⋊C4—861no—
449C2×C4⋊C4—861no—
450C2×C4⋊C4—861no—
451C2×C4⋊C4—861no—
452C2×C4⋊C4—861no—
453C2×C4⋊C4C22×D4311yescharacteristic
454C2×C4⋊C4C22×D4311yescharacteristic
455C2×C4⋊C4C22×D4311yescharacteristic
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—861no—
459C2×C22⋊C4—861no—
460C2×C22⋊C4—861no—
461C2×C42—431no—
462C2×C42—431no—
463C2×C42—861no—
464C2×C42—861no—
465C2×C42—861no—
466C2×C42C22×D4311yescharacteristic
467#107—862no—
468#107—862no—
469#106—862no—
470C4⋊C8—862no—
471#103—862no—
472#103—862no—
473#103—862no—
474#102—22no—
475#102—22no—
476#102—862no—
477C4×C8—862no—
478#95—861no—
479#95—861no—
480C24—21no—
481C2×Q8—432no—
482C2×Q8—432no—
483C2×Q8—432no—
484C2×Q8—864no—
485C2×Q8—862no—
486C2×Q8—862no—
487C2×Q8—862no—
488C2×Q8—861no—
489C2×Q8—861no—
490C2×Q8—861no—
491C2×Q8—1722no—
492C2×Q8—1722no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4Q8×D4312yes—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—431no—
503C22×C4—431no—
504C22×C4—431no—
505C22×C4—431no—
506C22×C4—861no—
507C22×C4—861no—
508C22×C4—861no—
509C22×C4—861no—
510C22×C4—1722no—
511C22×C4—1722no—
512C22×C4—1722no—
513C22×C4D4×D4311yescharacteristic
514C22×C4D4×D4311yescharacteristic
515C22×C4C23×D4311yescharacteristic
516SD16—868no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—432no—
524C2×C8—861no—
525C2×C8—861no—
526C2×C8—861no—
527C2×C8—861no—
528C2×C8—861no—
529C4⋊C4—24no—
530C4⋊C4—24no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—432no—
536C4⋊C4—862no—
537C4⋊C4—862no—
538C4⋊C4—862no—
539C4⋊C4—864no—
540C4⋊C4—864no—
541C4⋊C4—864no—
542C4⋊C4—864no—
543C4⋊C4—864no—
544C4⋊C4—864no—
545C4⋊C4—861no—
546C4⋊C4—861no—
547C4⋊C4—861no—
548C4⋊C4—861no—
549C4⋊C4—861no—
550C4⋊C4—3441no—
551C4⋊C4—1722no—
552C4⋊C4—1722no—
553C4⋊C4—1722no—
554C4⋊C4D4×D4312yes—
555C4⋊C4D4×D4312yes—
556C22⋊C4—42no—
557C22⋊C4—81no—
558C22⋊C4—3441no—
559C22⋊C4—1722no—
560C22⋊C4—1722no—
561C42—21no—
562C42—21no—
563C42—432no—
564C42—432no—
565C42—864no—
566C42—864no—
567C42—864no—
568C42—861no—
569C42—861no—
570C23—22no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23C2×D4×D4311yescharacteristic
578Q8—434no—
579Q8—862no—
580Q8—862no—
581Q8—862no—
582Q8—1724no—
583Q8—1728no—
584D4—22no—
585D4—22no—
586D4—41no—
587D4—41no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
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—862no—
608C2×C4—862no—
609C2×C4—862no—
610C2×C4—861no—
611C2×C4—861no—
612C2×C4—861no—
613C2×C4—862no—
614C2×C4—861no—
615C2×C4—861no—
616C2×C4—861no—
617C2×C4—861no—
618C2×C4—861no—
619C2×C4—3444no—
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×C4C2×D4×D4311yescharacteristic
629C2×C4C2×D4×D4311yescharacteristic
630C2×C4C2×Q8×D4311yescharacteristic
631C2×C4#41×D4311yescharacteristic
632C2×C4#1306337211yescharacteristic
633C2×C4#1306337211yescharacteristic
634C8—41no—
635C8—41no—
636C8—862no—
637C8—1721no—
638C22—42no—
639C22—42no—
640C22—42no—
641C22—81no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22#120×D4311yescharacteristic
646C22#1458355711yescharacteristic
647C22#1458356211yescharacteristic
648C22#135×D4311yescharacteristic
649C22AGL(1,ℤ/8)×D4311yescharacteristic
650C22#1458370911yescharacteristic
651C22#1458371311yescharacteristic
652C4—41no—
653C4—42no—
654C4—41no—
655C4—42no—
656C4—81no—
657C4—434no—
658C4—864no—
659C4—862no—
660C4—3441no—
661C4—3441no—
662C4—1721no—
663C4—1722no—
664C4—1721no—
665C4C22⋊Q8×D4311yescharacteristic
666C4#1458346911yescharacteristic
667C4#1458355711yescharacteristic
668C4#1458356211yescharacteristic
669C2—82no—
670C2#1913795311yescharacteristic
671C2#449×D4311yescharacteristic
672C2#1914390811yescharacteristic
673C2#1914727711yescharacteristic
674C2#1914732111yescharacteristic
675C2#1914746511yescharacteristic
676C2#1914751111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2025C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#2025D43
hypocenterC43#24328
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2025

Complements

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

NH ≅ G/Ntype
1. C2×#14583626C2semidirect
5. #19135936C2semidirect
6. #19135930C2semidirect
8. #19135554C2semidirect
9. #19135529C2semidirect
12. #19134852C2semidirect
13. #19134850C2semidirect
14. #19134599C2semidirect
69. C2×#10621883Q8semidirect
294. Dic86C22⋊Q8semidirect
401. C43#24328semidirect

Maximal subgroups

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

subgroupindex
C2×#145836262
C2×#145831772
C2×#145829902
#191395152
#191359362
#191359302
#191357392
#191355542
#191355292
#191349532
#191349472
#191348522
#191348502
#191345992
C43×#20252
#2432843