Finite Group Databasebeta

← #25133249

Subgroups — #25133249

Order 11008.

1072 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583608C211yesmaximal, characteristic
2C2×#14583206C211yesmaximal, characteristic, complemented
3#19139965C211yesmaximal, characteristic, complemented
4#19135931C211yesmaximal, characteristic, complemented
5#19135921C211yesmaximal, characteristic, complemented
6#19135744C211yesmaximal, characteristic, complemented
7#19135734C211yesmaximal, characteristic, complemented
8#19135564C211yesmaximal, characteristic, complemented
9#19135535C211yesmaximal, characteristic, complemented
10#19134931C211yesmaximal, characteristic
11#19134931C211yesmaximal, characteristic
12#19134854C211yesmaximal, characteristic
13#19134840C211yesmaximal, characteristic
14#19134595C211yesmaximal, characteristic
15C2×C43×#440C211yesmaximal, characteristic
16#14583608—24no—
17#14583608—24no—
18C2×#13063324C2211yescharacteristic
19C2×#13063317C2211yescharacteristic
20C2×#13063316C2211yescharacteristic
21C2×#13063304—21no—
22C2×#13063302—21no—
23C2×#13063302—21no—
24C2×C4×Dic86C2211yescharacteristic
25C2×D4×Dic43C2211yescharacteristic
26C2×D4×Dic43C2211yescharacteristic
27C22×Dic43⋊C4—21no—
28#14583206—24no—
29C2×#13063258C2211yescharacteristic
30C2×#13063256C2211yescharacteristic
31C2×C4⋊(C43⋊C8)C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×#13063249C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36#14582832—21no—
37#14582832—21no—
38#14582806C2211yescharacteristic
39#14582806C2211yescharacteristic
40#14582805—21no—
41#14582797—21no—
42#14582795C2211yescharacteristic
43#14582795C2211yescharacteristic
44#14582769C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54#14582653C2211yescharacteristic
55C22×SD16×C43C2211yescharacteristic
56C2×C4×Q8×C43C2211yescharacteristic
57C2×C4×D4×C43C2211yescharacteristic
58C43×#440—24no—
59C2×#107×C43C2211yescharacteristic
60C2×#103×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C2×#97×C43C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86D411yescharacteristic
65C23×Dic43—21no—
66C23×Dic43—21no—
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69#13063324—22no—
70#13063324—22no—
71#13063317—22no—
72#13063317D414yes—
73#13063316—22no—
74#13063316—22no—
75#13063304—28no—
76#13063302—28no—
77#13063302—28no—
78C4×Dic86—22no—
79C4×Dic86—22no—
80D4×Dic43—22no—
81D4×Dic43—22no—
82D4×Dic43—22no—
83D4×Dic43—22no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43D411yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×Dic43⋊C4—28no—
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×C4×Dic43C2311yescharacteristic
104C2×C4×Dic43C2311yescharacteristic
105#13063258—22no—
106#13063256—22no—
107C4⋊(C43⋊C8)—22no—
108#13063249—22no—
109#13063249—22no—
110#13063246—22no—
111#13063246—22no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C22×Q8×C43C2311yescharacteristic
119C22×D4×C43C2311yescharacteristic
120C23×C4×C43—21no—
121C2×SD16×C43—22no—
122C2×SD16×C43—22no—
123C2×SD16×C43Q814yescomplemented
124C22×C8×C43C2311yescharacteristic
125C22×C8×C43C2311yescharacteristic
126C4×Q8×C43—22no—
127C4×Q8×C43—22no—
128C4×D4×C43—22no—
129C4×D4×C43D414yes—
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C22⋊C4×C43—21no—
134C2×C42×C43—21no—
135C2×C42×C43C2311yescharacteristic
136#107×C43—22no—
137#103×C43—22no—
138#102×C43—22no—
139#97×C43—22no—
140C24×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×Q812yes—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43C2×D412yes—
151C2×D4×C43C2×Q812yes—
152C2×D4×C43#4112yes—
153C22×C4×C43—24no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—81no—
158C22×C4×C43—81no—
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2411yescharacteristic
162C22×Dic43—24no—
163C22×Dic43—24no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—42no—
169C22×Dic43—42no—
170C22×Dic43—81no—
171C22×Dic43—81no—
172C22×Dic43C2×D411yescharacteristic
173C22×Dic43C2×D411yescharacteristic
174C22×Dic43C2×D411yescharacteristic
175C22×Dic43C2×D411yescharacteristic
176C2×Dic86—22no—
177C2×Dic86—22no—
178C2×Dic86—24no—
179C2×Dic86—41no—
180C2×Dic86—81no—
181C2×Dic86—81no—
182SD16×C43—28no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43C2×Q812yes—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—42no—
193C4⋊C4×C43C2×D412yes—
194C22⋊C4×C43—24no—
195C42×C43—42no—
196C42×C43C2×D412yes—
197C42×C43C2×D412yes—
198C22⋊Dic43—24no—
199C22⋊Dic43—24no—
200C4⋊Dic43—24no—
201C4⋊Dic43—22no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—42no—
209C4⋊Dic43—81no—
210C4⋊Dic43C2×D412yes—
211C4⋊Dic43C2×D412yes—
212Dic43⋊C4—24no—
213Dic43⋊C4—24no—
214Dic43⋊C4—22no—
215Dic43⋊C4—24no—
216Dic43⋊C4—24no—
217Dic43⋊C4—22no—
218Dic43⋊C4—81no—
219Dic43⋊C4—81no—
220C4×Dic43—21no—
221C4×Dic43—21no—
222C4×Dic43—21no—
223C4×Dic43—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C23×C43—22no—
231C23×C43—22no—
232C23×C43—22no—
233C23×C43—41no—
234C23×C43—41no—
235C23×C43—41no—
236C23×C43—41no—
237C23×C43C22×D411yescharacteristic
238Q8×C43—22no—
239Q8×C43—22no—
240Q8×C43—41no—
241Q8×C43—41no—
242D4×C43—22no—
243D4×C43—22no—
244D4×C43—22no—
245D4×C43C22⋊Q814yes—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—22no—
251C2×C4×C43—22no—
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×C43—41no—
259C2×C4×C43—84no—
260C2×C4×C43#12012yes—
261C2×C4×C43#12012yes—
262C2×C4×C43C22×D411yescharacteristic
263C2×C4×C43C22×D411yescharacteristic
264C2×C4×C43C22×Q811yescharacteristic
265C2×C4×C43C2×#4111yescharacteristic
266C2×C4×C432−1+411yescharacteristic
267C2×C4×C432−1+411yescharacteristic
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—22no—
274C2×Dic43—22no—
275C2×Dic43—21no—
276C2×Dic43—21no—
277C2×Dic43—21no—
278C2×Dic43—21no—
279C2×Dic43—21no—
280C2×Dic43—21no—
281C2×Dic43—48no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289C2×Dic43—41no—
290C2×Dic43—41no—
291C2×Dic43—41no—
292C2×Dic43—84no—
293C2×Dic43#13712yes—
294Dic86—44no—
295Dic86—84no—
296C8×C43—22no—
297C8×C43—41no—
298C43⋊C8—41no—
299C43⋊C8—41no—
300#24349—431nomaximal, Sylow
301C22×C43—24no—
302C22×C43—42no—
303C22×C43—42no—
304C22×C43—42no—
305C22×C43—42no—
306C22×C43—42no—
307C22×C43—42no—
308C22×C43C2×#12011yescharacteristic
309C22×C43#54811yescharacteristic
310C22×C43D4×Q811yescharacteristic
311C22×C43C2×#13711yescharacteristic
312C22×C43#57511yescharacteristic
313C22×C43#57611yescharacteristic
314C22×C43#57711yescharacteristic
315C4×C43—22no—
316C4×C43—22no—
317C4×C43—42no—
318C4×C43—42no—
319C4×C43—81no—
320C4×C43C2×C22⋊Q811yescharacteristic
321C4×C43#53611yescharacteristic
322C4×C43#54811yescharacteristic
323C4×C43D4×Q811yescharacteristic
324Dic43—22no—
325Dic43—41no—
326Dic43—42no—
327Dic43—41no—
328Dic43—42no—
329Dic43—41no—
330Dic43—81no—
331Dic43—81no—
332C2×#554—431no—
333C2×#479—431no—
334C2×#440D4311yescharacteristic
335#2582—431no—
336#2059—431no—
337#2057—431no—
338#2026—431no—
339#2024—431no—
340#1992—431no—
341#1985—431no—
342#1877—431no—
343#1877—431no—
344#1864—431no—
345#1862—431no—
346#1802—431no—
347C2×C43—44no—
348C2×C43#240911yescharacteristic
349C2×C43#300711yescharacteristic
350C2×C43#301211yescharacteristic
351C2×C43#337011yescharacteristic
352C2×C43#337211yescharacteristic
353C2×C43#338511yescharacteristic
354C2×C43#338811yescharacteristic
355C22×SD16C2×D4311yescharacteristic
356#554—864no—
357#554—864no—
358C2×C4⋊Q8—431no—
359C2×#125—431no—
360C2×#125—431no—
361C2×C22⋊Q8—861no—
362C2×C22⋊Q8—861no—
363C2×C22⋊Q8—861no—
364C2×C4×Q8—431no—
365C2×C4×Q8C2×D4311yescharacteristic
366C2×C4×D4—431no—
367C2×C4×D4—431no—
368C2×C4×D4C2×D4311yescharacteristic
369C22×C4⋊C4—861no—
370#479—864no—
371#440—24no—
372C2×#107—431no—
373C2×#107C2×D4311yescharacteristic
374C2×#106—431no—
375C2×C4⋊C8—431no—
376C2×#103—431no—
377C2×#103—431no—
378C2×#103C2×D4311yescharacteristic
379C2×#102—431no—
380C2×#102—431no—
381C2×#102C2×D4311yescharacteristic
382C2×#97C2×D4311yescharacteristic
383#398—861no—
384#398—861no—
385#391—431no—
386#391—431no—
387#391—861no—
388#389—431no—
389#389—431no—
390#389—861no—
391#384—431no—
392#340—431no—
393#340—431no—
394#340—431no—
395#340—431no—
396#340—431no—
397#340—431no—
398#336—431no—
399#336—431no—
400#336—431no—
401#336—431no—
402C43#2434911yescharacteristic, complemented, Sylow
403C22×Q8—431no—
404C22×Q8—861no—
405C22×Q8C22×D4311yescharacteristic
406C22×D4C22×D4311yescharacteristic
407C23×C4—21no—
408C23×C4—861no—
409C23×C4—861no—
410C2×SD16—22no—
411C2×SD16—22no—
412C2×SD16Dic8614yescomplemented
413C22×C8—431no—
414C22×C8—431no—
415C22×C8C22×D4311yescharacteristic
416C22×C8C22×D4311yescharacteristic
417C4⋊Q8—862no—
418C4⋊Q8—862no—
419#125—434no—
420#125—862no—
421#125—862no—
422#125—862no—
423C22⋊Q8—868no—
424C22⋊Q8—868no—
425C22⋊Q8—868no—
426C4×Q8—22no—
427C4×Q8—22no—
428C4×Q8—862no—
429C4×Q8—862no—
430C4×D4—22no—
431C4×D4—862no—
432C4×D4—862no—
433C4×D4—862no—
434C4×D4—862no—
435C4×D4C22⋊D4314yes—
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—431no—
444C2×C4⋊C4—861no—
445C2×C4⋊C4—861no—
446C2×C4⋊C4—861no—
447C2×C4⋊C4—868no—
448C2×C4⋊C4—861no—
449C2×C4⋊C4—861no—
450C2×C4⋊C4—861no—
451C2×C4⋊C4—861no—
452C2×C4⋊C4—861no—
453C2×C4⋊C4—861no—
454C2×C4⋊C4C22×D4311yescharacteristic
455C2×C4⋊C4C22×D4311yescharacteristic
456C2×C22⋊C4—21no—
457C2×C22⋊C4—861no—
458C2×C22⋊C4—861no—
459C2×C42—21no—
460C2×C42—431no—
461C2×C42—431no—
462C2×C42C22×D4311yescharacteristic
463#107—22no—
464#107—862no—
465#106—862no—
466C4⋊C8—862no—
467#103—22no—
468#103—862no—
469#103—862no—
470#102—22no—
471#102—862no—
472#102—862no—
473#97—22no—
474#95—861no—
475#95—861no—
476#95—861no—
477#95—861no—
478#95—861no—
479#95—861no—
480C24—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—862no—
487C2×Q8—864no—
488C2×Q8—862no—
489C2×Q8—3441no—
490C2×Q8—3441no—
491C2×Q8—1721no—
492C2×Q8C2×Dic8612yes—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4C2×Dic8612yes—
497C2×D4#1062189812yes—
498C2×D4C2×C22⋊D4312yes—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—24no—
502C22×C4—21no—
503C22×C4—81no—
504C22×C4—81no—
505C22×C4—431no—
506C22×C4—431no—
507C22×C4—431no—
508C22×C4—431no—
509C22×C4—864no—
510C22×C4—864no—
511C22×C4—861no—
512C22×C4—861no—
513C22×C4—861no—
514C22×C4—861no—
515C22×C4—3441no—
516C22×C4—3441no—
517C22×C4—1722no—
518C22×C4—1722no—
519C22×C4D4×D4311yescharacteristic
520C22×C4D4×D4311yescharacteristic
521C22×C4C23×D4311yescharacteristic
522SD16—28no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—861no—
529C2×C8—861no—
530C2×C8—861no—
531C2×C8—861no—
532C2×C8—861no—
533C2×C8—861no—
534C2×C8C2×Dic8612yes—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—42no—
539C4⋊C4—432no—
540C4⋊C4—432no—
541C4⋊C4—864no—
542C4⋊C4—864no—
543C4⋊C4—864no—
544C4⋊C4—862no—
545C4⋊C4—862no—
546C4⋊C4—862no—
547C4⋊C4—864no—
548C4⋊C4—864no—
549C4⋊C4—861no—
550C4⋊C4—861no—
551C4⋊C4—861no—
552C4⋊C4—861no—
553C4⋊C4—861no—
554C4⋊C4—861no—
555C4⋊C4—3441no—
556C4⋊C4—3441no—
557C4⋊C4—3441no—
558C4⋊C4—1722no—
559C4⋊C4C2×C22⋊D4312yes—
560C22⋊C4—24no—
561C22⋊C4—864no—
562C22⋊C4—864no—
563C42—42no—
564C42—861no—
565C42—861no—
566C42—861no—
567C42—861no—
568C42D4×D4312yes—
569C42C2×C22⋊D4312yes—
570C23—22no—
571C23—22no—
572C23—22no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23C2×D4×D4311yescharacteristic
578Q8—22no—
579Q8—22no—
580Q8—41no—
581Q8—41no—
582Q8—3444no—
583Q8—1724no—
584D4—22no—
585D4—22no—
586D4—22no—
587D4#1306330414yes—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—84no—
602C2×C4—432no—
603C2×C4—861no—
604C2×C4—861no—
605C2×C4—861no—
606C2×C4—861no—
607C2×C4—861no—
608C2×C4—862no—
609C2×C4—862no—
610C2×C4—861no—
611C2×C4—861no—
612C2×C4—861no—
613C2×C4—861no—
614C2×C4—861no—
615C2×C4—861no—
616C2×C4—3444no—
617C2×C4—1728no—
618C2×C4—1721no—
619C2×C4—1721no—
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×C4#1306329312yes—
629C2×C4#1306329312yes—
630C2×C4C2×D4×D4311yescharacteristic
631C2×C4C22×C22⋊D4311yescharacteristic
632C2×C4C22×Dic8611yescharacteristic
633C2×C4C2×#1062189811yescharacteristic
634C2×C4#1306337211yescharacteristic
635C2×C4#1306337211yescharacteristic
636C8—22no—
637C8—41no—
638C8—1721no—
639C8—1721no—
640C22—24no—
641C22—42no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—42no—
646C22—42no—
647C22C2×#1306329311yescharacteristic
648C22#1458355811yescharacteristic
649C22D4×Dic8611yescharacteristic
650C22#137×D4311yescharacteristic
651C22#1458369811yescharacteristic
652C22#1458370311yescharacteristic
653C22#1458370911yescharacteristic
654C4—22no—
655C4—22no—
656C4—42no—
657C4—42no—
658C4—81no—
659C4—862no—
660C4—3441no—
661C4—3441no—
662C4—1721no—
663C4—1722no—
664C4—1721no—
665C4—1721no—
666C4—1722no—
667C4C2×#1306330411yescharacteristic
668C4#1458347011yescharacteristic
669C4#1458355811yescharacteristic
670C4D4×Dic8611yescharacteristic
671C2—44no—
672C2#1913796011yescharacteristic
673C2#1914385111yescharacteristic
674C2#1914389811yescharacteristic
675C2#1914734911yescharacteristic
676C2#1914737711yescharacteristic
677C2#1914750611yescharacteristic
678C2#1914754111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#440C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenterC2×#440D43
hypocenterC43#24349
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. C2×#14583206C2semidirect
3. #19139965C2semidirect
4. #19135931C2semidirect
5. #19135921C2semidirect
6. #19135744C2semidirect
7. #19135734C2semidirect
8. #19135564C2semidirect
9. #19135535C2semidirect
123. C2×SD16×C43Q8semidirect
402. C43#24349semidirect
412. C2×SD16Dic86semidirect

Maximal subgroups

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

subgroupindex
C2×#145836082
C2×#145832062
#191399652
#191359312
#191359212
#191357442
#191357342
#191355642
#191355352
#191349312
#191348542
#191348402
#191345952
C2×C43×#4402
#2434943