Finite Group Databasebeta

← #25133052

Subgroups — #25133052

Order 11008.

1042 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583626C211yesmaximal, characteristic, complemented
2C2×C4×#10621883C211yesmaximal, characteristic
3#19139949C211yesmaximal, characteristic
4#19135931C211yesmaximal, characteristic, complemented
5#19135926C211yesmaximal, characteristic, complemented
6#19135739C211yesmaximal, characteristic
7#19135729C211yesmaximal, characteristic
8#19135561C211yesmaximal, characteristic, complemented
9#19135530C211yesmaximal, characteristic, complemented
10#19134947C211yesmaximal, characteristic
11#19134947C211yesmaximal, characteristic
12#19134860C211yesmaximal, characteristic, complemented
13#19134846C211yesmaximal, characteristic, complemented
14#19134611C211yesmaximal, characteristic, complemented
15C2×C43×#478C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17#14583626—24no—
18#14583626—24no—
19C2×#13063324—21no—
20C2×#13063324C2211yescharacteristic
21C2×#13063316C2211yescharacteristic
22C2×#13063315—21no—
23C2×#13063315—21no—
24C2×C4×Dic86C2211yescharacteristic
25C2×C4×Dic86C2211yescharacteristic
26C2×#13063290—21no—
27C2×#13063290C2211yescharacteristic
28C2×#13063290C2211yescharacteristic
29C4×#10621883—24no—
30C2×#13063256C2211yescharacteristic
31C2×#13063250C2211yescharacteristic
32C2×#13063250C2211yescharacteristic
33C2×#13063248C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×C4×C43⋊C8C2211yescharacteristic
36#14582835—21no—
37#14582811—21no—
38#14582802C2211yescharacteristic
39#14582802C2211yescharacteristic
40#14582795C2211yescharacteristic
41#14582795C2211yescharacteristic
42#14582772—21no—
43#14582772—21no—
44#14582765C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54#14582653C2211yescharacteristic
55C2×#125×C43C2211yescharacteristic
56C2×C4×D4×C43C2211yescharacteristic
57C43×#478—24no—
58C2×#107×C43C2211yescharacteristic
59C2×#106×C43C2211yescharacteristic
60C2×C4⋊C8×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C2×#102×C43C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86D411yescharacteristic
65C22×Dic86C2311yescharacteristic
66C2×#10621883—22no—
67C2×#10621883—22no—
68C2×#10621883Q814yescomplemented
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71#13063324—28no—
72#13063324—22no—
73#13063324—22no—
74#13063316—22no—
75#13063316—22no—
76#13063315—28no—
77#13063315—28no—
78C4×Dic86—22no—
79C4×Dic86—22no—
80C4×Dic86—22no—
81C4×Dic86D414yes—
82#13063290—28no—
83#13063290—22no—
84#13063290—22no—
85#13063290—22no—
86#13063290—22no—
87C2×C4⋊Dic43—21no—
88C2×C4⋊Dic43D411yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
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×Dic43⋊C4—21no—
99C2×Dic43⋊C4D411yescharacteristic
100C2×Dic43⋊C4D411yescharacteristic
101C2×C22⋊Dic43—21no—
102C2×C22⋊Dic43—21no—
103C2×C22⋊Dic43—21no—
104C2×C22⋊Dic43—21no—
105C2×C4×Dic43—21no—
106C2×C4×Dic43—21no—
107C2×C4×Dic43—21no—
108C2×C4×Dic43C2311yescharacteristic
109C2×C4×Dic43C2311yescharacteristic
110#13063256—22no—
111#13063250—22no—
112#13063250—22no—
113#13063248—22no—
114#13063246—22no—
115C4×C43⋊C8—22no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C22×D4×C43C2311yescharacteristic
121C23×C4×C43—21no—
122C22×C8×C43C2311yescharacteristic
123C22×C8×C43C2311yescharacteristic
124#125×C43—22no—
125#125×C43D414yes—
126C4×D4×C43—22no—
127C4×D4×C43—22no—
128C2×C4⋊C4×C43—21no—
129C2×C4⋊C4×C43—21no—
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C22⋊C4×C43—21no—
134C2×C42×C43C2311yescharacteristic
135#107×C43—22no—
136#106×C43—22no—
137C4⋊C8×C43—22no—
138#102×C43—22no—
139#102×C43—22no—
140C24×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43C2×Q812yes—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—42no—
151C22×C4×C43—81no—
152C22×C4×C43—81no—
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2411yescharacteristic
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43C2×D411yescharacteristic
161C22×Dic43C2×D411yescharacteristic
162C22×Dic43C2×D411yescharacteristic
163C22×Dic43C2×D411yescharacteristic
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—24no—
168C2×Dic86—22no—
169C2×Dic86—22no—
170C2×Dic86—41no—
171C2×Dic86—42no—
172C2×Dic86—42no—
173C2×Dic86C2×D412yes—
174C2×Dic86C2×Q812yes—
175C2×Dic86#4112yes—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C4⋊C4×C43—24no—
183C4⋊C4×C43—24no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43C2×D412yes—
189C4⋊C4×C43C2×D412yes—
190C22⋊C4×C43—42no—
191C42×C43C2×D412yes—
192C42×C43C2×D412yes—
193C22⋊Dic43—42no—
194C22⋊Dic43—42no—
195C22⋊Dic43—81no—
196C22⋊Dic43—81no—
197#10621883—28no—
198C4⋊Dic43—24no—
199C4⋊Dic43—22no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43C2×D412yes—
206Dic43⋊C4—24no—
207Dic43⋊C4—24no—
208Dic43⋊C4—24no—
209Dic43⋊C4—24no—
210Dic43⋊C4—24no—
211Dic43⋊C4—22no—
212Dic43⋊C4—22no—
213Dic43⋊C4—81no—
214Dic43⋊C4—81no—
215C4×Dic43—24no—
216C4×Dic43—24no—
217C4×Dic43—24no—
218C4×Dic43—21no—
219C4×Dic43—21no—
220C4×Dic43—21no—
221C4×Dic43—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8C2×Q812yes—
228C23×C43—22no—
229C23×C43—41no—
230C23×C43—41no—
231C23×C43—41no—
232C23×C43—41no—
233C23×C43—41no—
234C23×C43—41no—
235C23×C43C22×D411yescharacteristic
236D4×C43—22no—
237D4×C43—22no—
238D4×C43—41no—
239D4×C43—41no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
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—84no—
254C2×C4×C43#12012yes—
255C2×C4×C43#12012yes—
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43C22×D411yescharacteristic
258C2×C4×C43C22×Q811yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C432−1+411yescharacteristic
261C2×C4×C432−1+411yescharacteristic
262C2×Dic43—22no—
263C2×Dic43—21no—
264C2×Dic43—22no—
265C2×Dic43—22no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—22no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—21no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43#13512yes—
286Dic86—22no—
287Dic86—22no—
288Dic86—22no—
289Dic86—44no—
290Dic86—48no—
291Dic86C22⋊Q814yes—
292C8×C43—41no—
293C8×C43—41no—
294C43⋊C8—22no—
295C43⋊C8—41no—
296#24334—431nomaximal, Sylow
297C22×C43—42no—
298C22×C43—42no—
299C22×C43—42no—
300C22×C43—81no—
301C22×C43—81no—
302C22×C43—81no—
303C22×C43—81no—
304C22×C43C2×#12011yescharacteristic
305C22×C43#54811yescharacteristic
306C22×C43D4×Q811yescharacteristic
307C22×C43C2×#13511yescharacteristic
308C22×C43#57511yescharacteristic
309C22×C43#57711yescharacteristic
310C22×C43#57711yescharacteristic
311C4×C43—22no—
312C4×C43—22no—
313C4×C43—42no—
314C4×C43—42no—
315C4×C43—81no—
316C4×C43C2×C22⋊Q811yescharacteristic
317C4×C43#53611yescharacteristic
318C4×C43#54811yescharacteristic
319C4×C43D4×Q811yescharacteristic
320Dic43—24no—
321Dic43—22no—
322Dic43—41no—
323Dic43—42no—
324Dic43—41no—
325Dic43—41no—
326Dic43—81no—
327Dic43—81no—
328C2×#557—431no—
329C2×#478D4311yescharacteristic
330C2×C4×SD16—431no—
331#2580—431no—
332#2059—431no—
333#2058—431no—
334#2025—431no—
335#2023—431no—
336#1991—431no—
337#1984—431no—
338#1880—431no—
339#1880—431no—
340#1865—431no—
341#1863—431no—
342#1805—431no—
343C2×C43—82no—
344C2×C43#240911yescharacteristic
345C2×C43#300211yescharacteristic
346C2×C43#301011yescharacteristic
347C2×C43#336511yescharacteristic
348C2×C43#337111yescharacteristic
349C2×C43#338111yescharacteristic
350C2×C43#338811yescharacteristic
351C22×SD16—431no—
352#557—864no—
353#557—864no—
354C2×C4⋊Q8—431no—
355C2×C4⋊Q8—861no—
356C2×#125—431no—
357C2×#125—861no—
358C2×#125—861no—
359C2×#125C2×D4311yescharacteristic
360C2×C4×Q8—431no—
361C2×C4×Q8—431no—
362C2×C4×Q8—431no—
363C2×C4×Q8—431no—
364C2×C4×Q8—861no—
365C2×C4×D4C2×D4311yescharacteristic
366#478—24no—
367C4×SD16—864no—
368C2×#107C2×D4311yescharacteristic
369C2×#106—431no—
370C2×#106C2×D4311yescharacteristic
371C2×C4⋊C8C2×D4311yescharacteristic
372C2×#103—431no—
373C2×#103—431no—
374C2×#103—431no—
375C2×#102—431no—
376C2×#102C2×D4311yescharacteristic
377C2×#102C2×D4311yescharacteristic
378C2×C4×C8—431no—
379#399—861no—
380#393—861no—
381#390—431no—
382#390—431no—
383#389—431no—
384#389—431no—
385#385—861no—
386#385—861no—
387#382—431no—
388#340—431no—
389#340—431no—
390#340—431no—
391#340—431no—
392#340—431no—
393#340—431no—
394#336—431no—
395#336—431no—
396#336—431no—
397#336—431no—
398C43#2433411yescharacteristic, complemented, Sylow
399C22×Q8—431no—
400C22×Q8—431no—
401C22×Q8—861no—
402C22×D4C22×D4311yescharacteristic
403C23×C4—21no—
404C2×SD16—434no—
405C2×SD16—862no—
406C2×SD16—862no—
407C22×C8—431no—
408C22×C8—431no—
409C22×C8C22×D4311yescharacteristic
410C22×C8C22×D4311yescharacteristic
411C4⋊Q8—862no—
412C4⋊Q8—868no—
413C4⋊Q8—862no—
414#125—22no—
415#125—862no—
416#125—868no—
417#125—868no—
418#125—862no—
419#125C22⋊D4314yes—
420C4×Q8—434no—
421C4×Q8—862no—
422C4×Q8—862no—
423C4×Q8—868no—
424C4×Q8—862no—
425C4×Q8—862no—
426C4×Q8—862no—
427C4×Q8—862no—
428C4×Q8—862no—
429C4×D4—22no—
430C4×D4—22no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—431no—
434C2×C4⋊C4—431no—
435C2×C4⋊C4—431no—
436C2×C4⋊C4—431no—
437C2×C4⋊C4—431no—
438C2×C4⋊C4—431no—
439C2×C4⋊C4—861no—
440C2×C4⋊C4—861no—
441C2×C4⋊C4—861no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4—861no—
445C2×C4⋊C4—861no—
446C2×C4⋊C4—861no—
447C2×C4⋊C4C22×D4311yescharacteristic
448C2×C4⋊C4C22×D4311yescharacteristic
449C2×C4⋊C4C22×D4311yescharacteristic
450C2×C22⋊C4—21no—
451C2×C22⋊C4—861no—
452C2×C22⋊C4—861no—
453C2×C22⋊C4—861no—
454C2×C22⋊C4—861no—
455C2×C42—431no—
456C2×C42—431no—
457C2×C42—861no—
458C2×C42—861no—
459C2×C42—861no—
460C2×C42C22×D4311yescharacteristic
461#107—22no—
462#106—22no—
463#106—862no—
464C4⋊C8—22no—
465#103—862no—
466#103—862no—
467#103—862no—
468#102—22no—
469#102—22no—
470#102—862no—
471C4×C8—862no—
472#95—861no—
473#95—861no—
474#95—861no—
475#95—861no—
476C24—21no—
477C2×Q8—432no—
478C2×Q8—432no—
479C2×Q8—432no—
480C2×Q8—862no—
481C2×Q8—864no—
482C2×Q8—862no—
483C2×Q8—861no—
484C2×Q8—861no—
485C2×Q8—861no—
486C2×Q8—1721no—
487C2×Q8—1722no—
488C2×Q8—1722no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4Q8×D4312yes—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—42no—
499C22×C4—81no—
500C22×C4—81no—
501C22×C4—431no—
502C22×C4—431no—
503C22×C4—431no—
504C22×C4—431no—
505C22×C4—861no—
506C22×C4—861no—
507C22×C4—861no—
508C22×C4—861no—
509C22×C4D4×D4311yescharacteristic
510C22×C4D4×D4311yescharacteristic
511C22×C4C23×D4311yescharacteristic
512SD16—868no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—432no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—861no—
523C2×C8—861no—
524C2×C8—861no—
525C4⋊C4—24no—
526C4⋊C4—24no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—432no—
532C4⋊C4—864no—
533C4⋊C4—864no—
534C4⋊C4—864no—
535C4⋊C4—864no—
536C4⋊C4—864no—
537C4⋊C4—862no—
538C4⋊C4—862no—
539C4⋊C4—862no—
540C4⋊C4—864no—
541C4⋊C4—861no—
542C4⋊C4—861no—
543C4⋊C4—861no—
544C4⋊C4—861no—
545C4⋊C4—861no—
546C4⋊C4—3441no—
547C4⋊C4—3441no—
548C4⋊C4C2×C22⋊D4312yes—
549C4⋊C4C2×C22⋊D4312yes—
550C22⋊C4—42no—
551C22⋊C4—3441no—
552C22⋊C4—3441no—
553C22⋊C4—1722no—
554C22⋊C4—1722no—
555C42—864no—
556C42—864no—
557C42—864no—
558C42—861no—
559C42—861no—
560C42—861no—
561C42—861no—
562C42D4×D4312yes—
563C42C2×C22⋊D4312yes—
564C23—22no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23C2×D4×D4311yescharacteristic
572Q8—434no—
573Q8—862no—
574Q8—862no—
575Q8—862no—
576Q8—1724no—
577Q8—1728no—
578D4—22no—
579D4—22no—
580D4—41no—
581D4—41no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—84no—
596C2×C4—432no—
597C2×C4—862no—
598C2×C4—862no—
599C2×C4—862no—
600C2×C4—861no—
601C2×C4—861no—
602C2×C4—861no—
603C2×C4—862no—
604C2×C4—861no—
605C2×C4—861no—
606C2×C4—861no—
607C2×C4—861no—
608C2×C4—861no—
609C2×C4—861no—
610C2×C4—861no—
611C2×C4—861no—
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×C4#1306329312yes—
621C2×C4#1306329312yes—
622C2×C4C2×D4×D4311yescharacteristic
623C2×C4C22×C22⋊D4311yescharacteristic
624C2×C4C2×Q8×D4311yescharacteristic
625C2×C4#41×D4311yescharacteristic
626C2×C4#1306337211yescharacteristic
627C2×C4#1306337311yescharacteristic
628C8—41no—
629C8—41no—
630C8—862no—
631C8—1721no—
632C22—42no—
633C22—42no—
634C22—42no—
635C22—81no—
636C22—81no—
637C22—81no—
638C22—81no—
639C22C2×#1306329311yescharacteristic
640C22#1458355911yescharacteristic
641C22#1458356211yescharacteristic
642C22#135×D4311yescharacteristic
643C22#1458369611yescharacteristic
644C22#1458370911yescharacteristic
645C22#1458370911yescharacteristic
646C4—22no—
647C4—22no—
648C4—42no—
649C4—42no—
650C4—81no—
651C4—862no—
652C4—864no—
653C4—3441no—
654C4—3441no—
655C4—1721no—
656C4—1722no—
657C4—1721no—
658C4—1721no—
659C4C22⋊Q8×D4311yescharacteristic
660C4#1458347211yescharacteristic
661C4#1458355611yescharacteristic
662C4Q8×C22⋊D4311yescharacteristic
663C2—82no—
664C2#1913795611yescharacteristic
665C2#1914380911yescharacteristic
666C2#1914388011yescharacteristic
667C2#1914729411yescharacteristic
668C2#1914736111yescharacteristic
669C2#1914746511yescharacteristic
670C2#1914754411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#478C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenterC2×#478D43
hypocenterC43#24334
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#14583626C2semidirect
4. #19135931C2semidirect
5. #19135926C2semidirect
8. #19135561C2semidirect
9. #19135530C2semidirect
12. #19134860C2semidirect
13. #19134846C2semidirect
14. #19134611C2semidirect
68. C2×#10621883Q8semidirect
398. C43#24334semidirect

Maximal subgroups

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

subgroupindex
C2×#145836262
C2×C4×#106218832
#191399492
#191359312
#191359262
#191357392
#191357292
#191355612
#191355302
#191349472
#191348602
#191348462
#191346112
C2×C43×#4782
#2433443