Finite Group Databasebeta

← #25132812

Subgroups — #25132812

Order 11008.

1012 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583530C211yesmaximal, characteristic
2C2×#14583204C211yesmaximal, characteristic, complemented
3C2×#14583192C211yesmaximal, characteristic, complemented
4#19137279C211yesmaximal, characteristic
5#19135932C211yesmaximal, characteristic, complemented
6#19135922C211yesmaximal, characteristic, complemented
7#19135744C211yesmaximal, characteristic, complemented
8#19135734C211yesmaximal, characteristic, complemented
9#19135549C211yesmaximal, characteristic, complemented
10#19135545C211yesmaximal, characteristic, complemented
11#19134908C211yesmaximal, characteristic
12#19134796C211yesmaximal, characteristic
13#19134783C211yesmaximal, characteristic
14#19134577C211yesmaximal, characteristic
15C43×#1872C211yesmaximal, characteristic
16#14583530—24no—
17#14583530—24no—
18C2×#13063324—21no—
19C2×#13063324C2211yescharacteristic
20C2×#13063324C2211yescharacteristic
21C2×#13063316—21no—
22C2×#13063316C2211yescharacteristic
23C2×#13063316C2211yescharacteristic
24C2×#13063304—21no—
25C2×#13063304—21no—
26C2×Q8×Dic43C2211yescharacteristic
27C2×#13063284C2211yescharacteristic
28C2×#13063284C2211yescharacteristic
29#14583204—24no—
30#14583192—24no—
31C2×#13063259C2211yescharacteristic
32C2×#13063258C2211yescharacteristic
33C2×#13063258C2211yescharacteristic
34C2×#13063257C2211yescharacteristic
35C2×Dic43⋊C8C2211yescharacteristic
36C2×Dic43⋊C8C2211yescharacteristic
37C2×#13063249C2211yescharacteristic
38C2×#13063249C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40#14582806C2211yescharacteristic
41#14582798—21no—
42#14582798C2211yescharacteristic
43#14582792—21no—
44#14582792—21no—
45#14582785—21no—
46#14582759C2211yescharacteristic
47C4⋊C4×Dic43C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C2×C22⋊Q8×C43C2211yescharacteristic
57C22×C4⋊C4×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86—21no—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063324—28no—
68#13063324—22no—
69#13063324—22no—
70#13063324—22no—
71#13063324D414yes—
72#13063316—28no—
73#13063316—22no—
74#13063316—22no—
75#13063316—22no—
76#13063316D414yes—
77#13063304—28no—
78#13063304—28no—
79Q8×Dic43—22no—
80Q8×Dic43—22no—
81#13063284—22no—
82#13063284—22no—
83#13063284—22no—
84#13063284—22no—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43—21no—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43D411yescharacteristic
90C2×C4⋊Dic43D411yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×C22⋊Dic43—21no—
100C2×C22⋊Dic43—21no—
101C2×C22⋊Dic43D411yescharacteristic
102C2×C22⋊Dic43D411yescharacteristic
103C2×C4×Dic43—21no—
104C2×C4×Dic43—21no—
105C2×C4×Dic43—21no—
106C2×C4×Dic43C2311yescharacteristic
107C2×C4×Dic43C2311yescharacteristic
108#13063259—22no—
109#13063258—22no—
110#13063258—22no—
111#13063257—22no—
112Dic43⋊C8—22no—
113Dic43⋊C8—22no—
114#13063249—22no—
115#13063249—22no—
116C22⋊(C43⋊C8)—22no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C22×Q8×C43C2311yescharacteristic
123C23×C4×C43—21no—
124C23×C4×C43C2311yescharacteristic
125C22×C8×C43C2311yescharacteristic
126C22×C8×C43C2311yescharacteristic
127C22⋊Q8×C43—22no—
128C22⋊Q8×C43Q814yescomplemented
129C2×C4⋊C4×C43—21no—
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43—22no—
132C2×C4⋊C4×C43—22no—
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C22⋊C4×C43—21no—
137#103×C43—22no—
138#103×C43—22no—
139C22⋊C8×C43—22no—
140C24×C43C2×D411yescharacteristic
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×Q812yes—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—24no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—81no—
157C22×C4×C43—81no—
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2×Q812yes—
160C22×C4×C43#4112yes—
161C22×C4×C43C2411yescharacteristic
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43C2×D411yescharacteristic
167C22×Dic43C2×D411yescharacteristic
168C22×Dic43C2×D411yescharacteristic
169C22×Dic43C2×D411yescharacteristic
170C2×Dic86—24no—
171C2×Dic86—24no—
172C2×Dic86—81no—
173C2×Dic86—81no—
174C2×Dic86—81no—
175C2×Dic86—81no—
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×C43C2×D412yes—
188C4⋊C4×C43C2×D412yes—
189C4⋊C4×C43C2×Q812yes—
190C22⋊C4×C43—24no—
191C22⋊Dic43—24no—
192C22⋊Dic43—22no—
193C22⋊Dic43—22no—
194C22⋊Dic43—81no—
195C4⋊Dic43—24no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—24no—
199C4⋊Dic43—22no—
200C4⋊Dic43—22no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—42no—
206C4⋊Dic43—81no—
207C4⋊Dic43C2×D412yes—
208C4⋊Dic43C2×D412yes—
209Dic43⋊C4—24no—
210Dic43⋊C4—24no—
211Dic43⋊C4—24no—
212Dic43⋊C4—24no—
213C4×Dic43—24no—
214C4×Dic43—21no—
215C4×Dic43—21no—
216C4×Dic43—42no—
217C4×Dic43—81no—
218C4×Dic43C2×D412yes—
219C4×Dic43C2×D412yes—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C23×C43—21no—
227C23×C43—21no—
228C23×C43—21no—
229C23×C43—21no—
230C23×C43—21no—
231C23×C43—21no—
232C23×C43C22⋊Q812yes—
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—22no—
247C2×C4×C43—22no—
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×C43—84no—
257C2×C4×C43C22⋊Q812yes—
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—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—22no—
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—41no—
285C2×Dic43—41no—
286C2×Dic43#12012yes—
287C2×Dic43#12012yes—
288Dic86—84no—
289Dic86—84no—
290C8×C43—41no—
291C8×C43—41no—
292C43⋊C8—41no—
293C43⋊C8—41no—
294#24311—431nomaximal, Sylow
295C22×C43—22no—
296C22×C43—22no—
297C22×C43—22no—
298C22×C43—41no—
299C22×C43—41no—
300C22×C43—41no—
301C22×C43—41no—
302C22×C43C2×#12011yescharacteristic
303C22×C43C2×C22⋊Q811yescharacteristic
304C22×C43#53611yescharacteristic
305C22×C43#57611yescharacteristic
306C22×C43#57711yescharacteristic
307C22×C43#57811yescharacteristic
308C22×C43#57811yescharacteristic
309C4×C43—22no—
310C4×C43—42no—
311C4×C43—42no—
312C4×C43—42no—
313C4×C43—42no—
314C4×C43#54811yescharacteristic
315C4×C43#54811yescharacteristic
316C4×C43D4×Q811yescharacteristic
317C4×C43D4×Q811yescharacteristic
318Dic43—22no—
319Dic43—22no—
320Dic43—41no—
321Dic43—42no—
322Dic43—41no—
323Dic43—42no—
324Dic43—81no—
325Dic43—81no—
326C2×#544—431no—
327C2×#479—431no—
328C2×#477—431no—
329#2323—431no—
330#2059—431no—
331#2057—431no—
332#2026—431no—
333#2024—431no—
334#1989—431no—
335#1988—431no—
336#1873—431no—
337#1872D4311yescharacteristic
338#1854—431no—
339#1852—431no—
340#1798—431no—
341C2×C43—42no—
342C2×C43#240911yescharacteristic
343C2×C43#301111yescharacteristic
344C2×C43#301211yescharacteristic
345C2×C43#308211yescharacteristic
346C2×C43#308311yescharacteristic
347C2×C43#324211yescharacteristic
348C2×C43#324311yescharacteristic
349#544—864no—
350#544—864no—
351C2×C4⋊Q8—431no—
352C2×C4⋊Q8—431no—
353C2×C4⋊Q8—861no—
354C2×#125—431no—
355C2×#125—431no—
356C2×#125—861no—
357C2×C22⋊Q8—861no—
358C2×C22⋊Q8—861no—
359C2×C22⋊Q8C2×D4311yescharacteristic
360C2×C4×Q8—431no—
361C2×#117—431no—
362C2×#117—431no—
363C22×C4⋊C4C2×D4311yescharacteristic
364#479—864no—
365#477—864no—
366C2×#107—431no—
367C2×#107—431no—
368C2×#107—431no—
369C2×#106—431no—
370C2×C4⋊C8—431no—
371C2×C4⋊C8—431no—
372C2×#103—431no—
373C2×#103—431no—
374C2×#103C2×D4311yescharacteristic
375C2×#103C2×D4311yescharacteristic
376C2×C22⋊C8—431no—
377C2×C22⋊C8C2×D4311yescharacteristic
378#391—431no—
379#389—431no—
380#389—861no—
381#388—861no—
382#388—861no—
383#387—861no—
384#380—431no—
385C4×C4⋊C4—431no—
386#340—431no—
387#340—431no—
388#340—431no—
389#340—431no—
390#340—431no—
391#340—431no—
392#340C2×D4311yescharacteristic
393#340C2×D4311yescharacteristic
394#336—431no—
395#336—431no—
396C43#2431111yescharacteristic, complemented, Sylow
397C22×Q8—861no—
398C22×Q8—861no—
399C22×Q8C22×D4311yescharacteristic
400C23×C4—21no—
401C23×C4C22×D4311yescharacteristic
402C22×C8—431no—
403C22×C8—431no—
404C22×C8C22×D4311yescharacteristic
405C22×C8C22×D4311yescharacteristic
406C4⋊Q8—434no—
407C4⋊Q8—862no—
408C4⋊Q8—862no—
409C4⋊Q8—868no—
410C4⋊Q8—862no—
411#125—434no—
412#125—862no—
413#125—862no—
414#125—868no—
415#125—862no—
416C22⋊Q8—22no—
417C22⋊Q8—868no—
418C22⋊Q8—868no—
419C22⋊Q8Dic8614yescomplemented
420C4×Q8—862no—
421C4×Q8—862no—
422#117—862no—
423#117—862no—
424#117—862no—
425#117—862no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—431no—
431C2×C4⋊C4—431no—
432C2×C4⋊C4—431no—
433C2×C4⋊C4—431no—
434C2×C4⋊C4—431no—
435C2×C4⋊C4—431no—
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⋊C4—861no—
444C2×C4⋊C4C22×D4311yescharacteristic
445C2×C4⋊C4C22×D4311yescharacteristic
446C2×C4⋊C4C22×D4311yescharacteristic
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—
457#107—862no—
458#107—862no—
459#107—862no—
460#106—862no—
461C4⋊C8—862no—
462C4⋊C8—862no—
463#103—22no—
464#103—22no—
465#103—862no—
466#103—862no—
467C22⋊C8—22no—
468C22⋊C8—862no—
469#95—861no—
470#95—861no—
471#95—861no—
472#95—861no—
473#95—861no—
474C24D4×D4311yescharacteristic
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—864no—
481C2×Q8—864no—
482C2×Q8—3441no—
483C2×Q8—3441no—
484C2×Q8—3441no—
485C2×Q8—3441no—
486C2×Q8C2×Dic8612yes—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—24no—
496C22×C4—81no—
497C22×C4—81no—
498C22×C4—431no—
499C22×C4—431no—
500C22×C4—431no—
501C22×C4—431no—
502C22×C4—861no—
503C22×C4—861no—
504C22×C4—861no—
505C22×C4—861no—
506C22×C4C2×Dic8612yes—
507C22×C4D4×D4311yescharacteristic
508C22×C4#1062190012yes—
509C22×C4C23×D4311yescharacteristic
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—
522C4⋊C4—24no—
523C4⋊C4—24no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—432no—
528C4⋊C4—432no—
529C4⋊C4—862no—
530C4⋊C4—862no—
531C4⋊C4—864no—
532C4⋊C4—864no—
533C4⋊C4—864no—
534C4⋊C4—864no—
535C4⋊C4—864no—
536C4⋊C4—864no—
537C4⋊C4—861no—
538C4⋊C4—861no—
539C4⋊C4—861no—
540C4⋊C4—861no—
541C4⋊C4—861no—
542C4⋊C4—861no—
543C4⋊C4—3441no—
544C4⋊C4—1722no—
545C4⋊C4C2×Dic8612yes—
546C4⋊C4D4×D4312yes—
547C4⋊C4D4×D4312yes—
548C22⋊C4—24no—
549C22⋊C4—862no—
550C22⋊C4—862no—
551C22⋊C4—864no—
552C22⋊C4—3441no—
553C42—432no—
554C42—432no—
555C42—864no—
556C42—861no—
557C42—861no—
558C42—3441no—
559C42—1722no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23#1306330212yes—
567C23C2×D4×D4311yescharacteristic
568Q8—22no—
569Q8—22no—
570Q8—41no—
571Q8—41no—
572Q8—3444no—
573Q8—3444no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
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—41no—
592C2×C4—84no—
593C2×C4—432no—
594C2×C4—432no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—862no—
600C2×C4—862no—
601C2×C4—861no—
602C2×C4—861no—
603C2×C4—861no—
604C2×C4—861no—
605C2×C4—861no—
606C2×C4—861no—
607C2×C4—1721no—
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#1306330212yes—
618C2×C4C2×D4×D4311yescharacteristic
619C2×C4C2×D4×D4311yescharacteristic
620C2×C4C22×Dic8611yescharacteristic
621C2×C4C2×#1062190011yescharacteristic
622C2×C4#1306337211yescharacteristic
623C2×C4#1306337211yescharacteristic
624C8—41no—
625C8—41no—
626C8—1721no—
627C8—1721no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22#120×D4311yescharacteristic
636C22C2×#1306330211yescharacteristic
637C22#1458347111yescharacteristic
638C22#1458370311yescharacteristic
639C22#1458370511yescharacteristic
640C22#1458371211yescharacteristic
641C22#1458371511yescharacteristic
642C4—22no—
643C4—42no—
644C4—42no—
645C4—42no—
646C4—42no—
647C4—862no—
648C4—862no—
649C4—3441no—
650C4—3441no—
651C4—1721no—
652C4—1722no—
653C4—1721no—
654C4—1722no—
655C4#1458355511yescharacteristic
656C4#1458355511yescharacteristic
657C4D4×Dic8611yescharacteristic
658C4D4×Dic8611yescharacteristic
659C2—42no—
660C2#1913795711yescharacteristic
661C2#1914388511yescharacteristic
662C2#1914390011yescharacteristic
663C2#1914443311yescharacteristic
664C2#1914445011yescharacteristic
665C2#1914585911yescharacteristic
666C2#1914588211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1872C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#1872D43
hypocenterC43#24311
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
2. C2×#14583204C2semidirect
3. C2×#14583192C2semidirect
5. #19135932C2semidirect
6. #19135922C2semidirect
7. #19135744C2semidirect
8. #19135734C2semidirect
9. #19135549C2semidirect
10. #19135545C2semidirect
128. C22⋊Q8×C43Q8semidirect
396. C43#24311semidirect
419. C22⋊Q8Dic86semidirect

Maximal subgroups

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

subgroupindex
C2×#145835302
C2×#145832042
C2×#145831922
#191372792
#191359322
#191359222
#191357442
#191357342
#191355492
#191355452
#191349082
#191347962
#191347832
#191345772
C43×#18722
#2431143