Finite Group Databasebeta

← #25153738

Subgroups — #25153738

Order 11008.

986 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583197C211yesmaximal, characteristic, complemented
2#19138302C211yesmaximal, characteristic, complemented
3#19137425C211yesmaximal, characteristic
4#19136131C211yesmaximal, characteristic, complemented
5#19135988C211yesmaximal, characteristic, complemented
6#19135972C211yesmaximal, characteristic, complemented
7#19135744C211yesmaximal, characteristic, complemented
8#19134844C211yesmaximal, characteristic, complemented
9#19134840C211yesmaximal, characteristic, complemented
10#19134794C211yesmaximal, characteristic, complemented
11#19134773C211yesmaximal, characteristic, complemented
12#19134624C211yesmaximal, characteristic, complemented
13#19134593C211yesmaximal, characteristic, complemented
14#19134535C211yesmaximal, characteristic
15C2×C43×#416C211yesmaximal, characteristic
16C2×#13063316C2211yescharacteristic
17C2×D4×Dic43C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19#14583197—24no—
20C2×#13063259C2211yescharacteristic
21C2×#13063259C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×C22⋊(C43⋊C8)C2211yescharacteristic
31#14582835—21no—
32#14582822—21no—
33#14582806C2211yescharacteristic
34#14582806C2211yescharacteristic
35#14582798C2211yescharacteristic
36#14582797—21no—
37#14582795C2211yescharacteristic
38#14582783—21no—
39#14582779—21no—
40#14582779—21no—
41#14582768C2211yescharacteristic
42#14582762—21no—
43#14582759C2211yescharacteristic
44#14582759C2211yescharacteristic
45C4×C22⋊Dic43C2211yescharacteristic
46C2×C43⋊#95—21no—
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C22×#41×C43C2211yescharacteristic
54C23×C8×C43C2211yescharacteristic
55C2×#117×C43C2211yescharacteristic
56C43×#416—24no—
57C2×#103×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C23×Dic43—21no—
62C23×Dic43—21no—
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65#13063316—22no—
66#13063316—41no—
67D4×Dic43—22no—
68D4×Dic43—22no—
69D4×Dic43—41no—
70D4×Dic43—41no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43D411yescharacteristic
86C2×C22⋊Dic43D411yescharacteristic
87C2×C4×Dic43C2311yescharacteristic
88C2×C4×Dic43C2311yescharacteristic
89#13063259—22no—
90#13063259—41no—
91#13063258—41no—
92#13063256—22no—
93Dic43⋊C8—22no—
94Dic43⋊C8—41no—
95#13063249—41no—
96#13063249—41no—
97#13063246—22no—
98#13063246—22no—
99C22⋊(C43⋊C8)—22no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95D411yescharacteristic
109C43⋊#95D411yescharacteristic
110C2×#41×C43—22no—
111C2×#41×C43—22no—
112C2×#41×C43—22no—
113C2×#41×C43—41no—
114C2×#41×C43—41no—
115C2×#41×C43Q814yes—
116C22×Q8×C43C2311yescharacteristic
117C22×D4×C43—21no—
118C22×D4×C43C2311yescharacteristic
119C23×C4×C43—21no—
120C23×C4×C43C2311yescharacteristic
121C22×C8×C43—22no—
122C22×C8×C43—22no—
123C22×C8×C43—41no—
124C22×C8×C43C2311yescharacteristic
125C22×C8×C43C2311yescharacteristic
126#117×C43—22no—
127#117×C43—41no—
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C22⋊C4×C43—21no—
131C2×C42×C43—21no—
132#103×C43—22no—
133#103×C43—22no—
134#102×C43—22no—
135#102×C43D414yes—
136C24×C43—21no—
137C24×C43C2×D411yescharacteristic
138#41×C43—28no—
139#41×C43—44no—
140#41×C43—44no—
141#41×C43—44no—
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43C2×Q812yes—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—24no—
152C2×D4×C43—42no—
153C2×D4×C43—42no—
154C2×D4×C43C2×D412yes—
155C2×D4×C43C2×Q812yes—
156C2×D4×C43#4112yes—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—24no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—42no—
166C22×C4×C43—42no—
167C22×C4×C43C2×D411yescharacteristic
168C22×C4×C43C2×Q812yes—
169C22×C4×C43#4112yes—
170C22×C4×C43C2411yescharacteristic
171C22×Dic43—21no—
172C22×Dic43—21no—
173C22×Dic43—21no—
174C22×Dic43—21no—
175C22×Dic43—42no—
176C22×Dic43—42no—
177C22×Dic43—42no—
178C22×Dic43—42no—
179C22×Dic43—81no—
180C22×Dic43—81no—
181C22×Dic43C2×D411yescharacteristic
182C22×Dic43C2×D411yescharacteristic
183C22×Dic43C2×D411yescharacteristic
184C22×Dic43C2×D411yescharacteristic
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—44no—
191C2×C8×C43C2×D412yes—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43C2×D412yes—
196C22⋊C4×C43—42no—
197C42×C43—42no—
198C22⋊Dic43—22no—
199C22⋊Dic43—41no—
200C22⋊Dic43—42no—
201C22⋊Dic43—42no—
202C22⋊Dic43—81no—
203C22⋊Dic43—81no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—21no—
212C4⋊Dic43—42no—
213C4⋊Dic43—42no—
214Dic43⋊C4—42no—
215Dic43⋊C4—42no—
216Dic43⋊C4—81no—
217Dic43⋊C4—81no—
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⋊C8—21no—
228C23×C43—22no—
229C23×C43—22no—
230C23×C43—21no—
231C23×C43—22no—
232C23×C43—21no—
233C23×C43—21no—
234C23×C43—21no—
235C23×C43—21no—
236C23×C43—21no—
237C23×C43—41no—
238C23×C43—41no—
239C23×C43—41no—
240C23×C43—41no—
241C23×C43C22⋊Q812yes—
242C23×C43C22×D411yescharacteristic
243Q8×C43—22no—
244Q8×C43—22no—
245Q8×C43—41no—
246Q8×C43—41no—
247D4×C43—22no—
248D4×C43—22no—
249D4×C43—22no—
250D4×C43—48no—
251D4×C43C22⋊Q814yes—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—22no—
255C2×C4×C43—22no—
256C2×C4×C43—22no—
257C2×C4×C43—22no—
258C2×C4×C43—22no—
259C2×C4×C43—22no—
260C2×C4×C43—48no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43—41no—
268C2×C4×C43C22⋊Q812yes—
269C2×C4×C43C22×D411yescharacteristic
270C2×C4×C43C22×Q811yescharacteristic
271C2×C4×C43C2×#4111yescharacteristic
272C2×C4×C43C2×#4111yescharacteristic
273C2×C4×C43H(5,𝔽2)11yescharacteristic
274C2×C4×C43H(5,𝔽2)11yescharacteristic
275C2×Dic43—21no—
276C2×Dic43—21no—
277C2×Dic43—21no—
278C2×Dic43—21no—
279C2×Dic43—21no—
280C2×Dic43—21no—
281C2×Dic43—21no—
282C2×Dic43—21no—
283C2×Dic43—21no—
284C2×Dic43—21no—
285C2×Dic43—21no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289C2×Dic43—41no—
290C2×Dic43—41no—
291C2×Dic43—41no—
292C2×Dic43—41no—
293C2×Dic43—41no—
294C2×Dic43—41no—
295C2×Dic43—41no—
296C2×Dic43—41no—
297C2×Dic43—41no—
298C2×Dic43—84no—
299C2×Dic43—84no—
300C2×Dic43#13512yes—
301C8×C43—22no—
302C8×C43—41no—
303C43⋊C8—41no—
304C43⋊C8—41no—
305#25956—431nomaximal, Sylow
306C22×C43—22no—
307C22×C43—22no—
308C22×C43—24no—
309C22×C43—22no—
310C22×C43—42no—
311C22×C43—42no—
312C22×C43—41no—
313C22×C43—42no—
314C22×C43—41no—
315C22×C43—42no—
316C22×C43—41no—
317C22×C43—42no—
318C22×C43—41no—
319C22×C43—42no—
320C22×C43C2×C22⋊Q811yescharacteristic
321C22×C43D4211yescharacteristic
322C22×C43#54611yescharacteristic
323C22×C43C2×#13511yescharacteristic
324C22×C43#57511yescharacteristic
325C22×C43#57611yescharacteristic
326C22×C43#57811yescharacteristic
327C4×C43—22no—
328C4×C43—42no—
329C4×C43—42no—
330C4×C43—81no—
331C4×C43C2×C22⋊Q811yescharacteristic
332C4×C43#54311yescharacteristic
333C4×C43#54611yescharacteristic
334C4×C43#55111yescharacteristic
335Dic43—22no—
336Dic43—41no—
337Dic43—41no—
338Dic43—41no—
339Dic43—81no—
340Dic43—81no—
341Dic43—81no—
342Dic43—81no—
343C2×#478—431no—
344C2×#416D4311yescharacteristic
345#2441—431no—
346#2339—431no—
347#2095—431no—
348#2068—431no—
349#2066—431no—
350#2026—431no—
351#1862—431no—
352#1862—431no—
353#1854—431no—
354#1850—431no—
355#1808—431no—
356#1802—431no—
357#1788—431no—
358C2×C43—42no—
359C2×C43—44no—
360C2×C43#243711yescharacteristic
361C2×C43#307611yescharacteristic
362C2×C43#308311yescharacteristic
363C2×C43#326811yescharacteristic
364C2×C43#328311yescharacteristic
365C2×C43#329711yescharacteristic
366C2×C43#331511yescharacteristic
367C22×#41C2×D4311yescharacteristic
368C23×C8C2×D4311yescharacteristic
369C2×#125—431no—
370C2×C4×D4—431no—
371C2×C4×D4—431no—
372C2×#117C2×D4311yescharacteristic
373#478—864no—
374C2×#107—431no—
375C2×#107—431no—
376C2×#107—431no—
377C2×#106—431no—
378C2×C4⋊C8—431no—
379C2×C4⋊C8—431no—
380#416—24no—
381C2×#103—431no—
382C2×#103—431no—
383C2×#103C2×D4311yescharacteristic
384C2×#103C2×D4311yescharacteristic
385C2×#102—431no—
386C2×#102—431no—
387C2×#102C2×D4311yescharacteristic
388C2×#102C2×D4311yescharacteristic
389C2×C22⋊C8—431no—
390#399—861no—
391#396—861no—
392#391—431no—
393#391—431no—
394#389—431no—
395#389—431no—
396#389—861no—
397#387—861no—
398#386—861no—
399#386—861no—
400#384—431no—
401#381—861no—
402#380—431no—
403#380—431no—
404C4×C22⋊C4—431no—
405C2×#95—861no—
406#340—431no—
407#340—431no—
408#340—431no—
409#340—431no—
410#336—431no—
411#336—431no—
412C43#2595611yescharacteristic, complemented, Sylow
413C2×#41—22no—
414C2×#41—22no—
415C2×#41—22no—
416C2×#41—41no—
417C2×#41—41no—
418C2×#41Dic8614yes—
419C22×Q8C22×D4311yescharacteristic
420C22×D4—21no—
421C22×D4C22×D4311yescharacteristic
422C23×C4—21no—
423C23×C4—861no—
424C23×C4—861no—
425C23×C4C22×D4311yescharacteristic
426C22×C8—22no—
427C22×C8—22no—
428C22×C8—41no—
429C22×C8—431no—
430C22×C8—431no—
431C22×C8C22×D4311yescharacteristic
432C22×C8C22×D4311yescharacteristic
433#125—862no—
434#125—1721no—
435C4×D4—862no—
436C4×D4—862no—
437C4×D4—1721no—
438C4×D4—1721no—
439#117—22no—
440#117—41no—
441C2×C4⋊C4—431no—
442C2×C4⋊C4—431no—
443C2×C4⋊C4—431no—
444C2×C4⋊C4—431no—
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⋊C4C22×D4311yescharacteristic
452C2×C4⋊C4C22×D4311yescharacteristic
453C2×C22⋊C4—21no—
454C2×C22⋊C4—431no—
455C2×C22⋊C4—431no—
456C2×C22⋊C4—861no—
457C2×C22⋊C4—861no—
458C2×C22⋊C4—861no—
459C2×C22⋊C4—861no—
460C2×C42—21no—
461C2×C42—431no—
462C2×C42—431no—
463#107—862no—
464#107—1721no—
465#107—1721no—
466#106—862no—
467C4⋊C8—862no—
468C4⋊C8—1721no—
469#103—22no—
470#103—22no—
471#103—1721no—
472#103—1721no—
473#102—22no—
474#102—862no—
475#102—862no—
476#102C22⋊D4314yes—
477C22⋊C8—862no—
478#95—431no—
479#95—431no—
480#95—861no—
481#95—861no—
482#95—861no—
483#95—861no—
484#95—861no—
485#95—861no—
486#95—861no—
487#95—861no—
488C24—21no—
489C24D4×D4311yescharacteristic
490#41—28no—
491#41—44no—
492#41—44no—
493#41—44no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8C2×Dic8612yes—
500C2×D4—24no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4C2×Dic8612yes—
507C2×D4#1062189812yes—
508C2×D4C2×C22⋊D4312yes—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—24no—
516C22×C4—21no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—431no—
520C22×C4—431no—
521C22×C4—431no—
522C22×C4—431no—
523C22×C4—861no—
524C22×C4—861no—
525C22×C4—861no—
526C22×C4—861no—
527C22×C4—3441no—
528C22×C4—3441no—
529C22×C4—1722no—
530C22×C4—1722no—
531C22×C4—1722no—
532C22×C4—1722no—
533C22×C4C2×Dic8612yes—
534C22×C4D4×D4311yescharacteristic
535C22×C4#1062190012yes—
536C22×C4C23×D4311yescharacteristic
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—44no—
543C2×C8—861no—
544C2×C8—861no—
545C2×C8—861no—
546C2×C8—861no—
547C2×C8—861no—
548C2×C8—861no—
549C2×C8C2×C22⋊D4312yes—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—861no—
554C4⋊C4—861no—
555C4⋊C4—861no—
556C4⋊C4—861no—
557C4⋊C4—861no—
558C4⋊C4—861no—
559C4⋊C4—861no—
560C4⋊C4—861no—
561C4⋊C4—3441no—
562C4⋊C4—3441no—
563C4⋊C4—1722no—
564C4⋊C4—1722no—
565C4⋊C4—1722no—
566C4⋊C4—1722no—
567C4⋊C4C2×C22⋊D4312yes—
568C22⋊C4—42no—
569C22⋊C4—862no—
570C22⋊C4—3441no—
571C22⋊C4—3441no—
572C22⋊C4—1721no—
573C22⋊C4—1722no—
574C22⋊C4—1722no—
575C42—42no—
576C42—861no—
577C42—861no—
578C42—861no—
579C42—861no—
580C23—22no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—22no—
587C23—22no—
588C23—21no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23#1306330212yes—
594C23C2×D4×D4311yescharacteristic
595Q8—22no—
596Q8—22no—
597Q8—41no—
598Q8—41no—
599D4—22no—
600D4—22no—
601D4—22no—
602D4—48no—
603D4#1306330414yes—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—48no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—432no—
621C2×C4—861no—
622C2×C4—861no—
623C2×C4—861no—
624C2×C4—861no—
625C2×C4—861no—
626C2×C4—861no—
627C2×C4—861no—
628C2×C4—861no—
629C2×C4—861no—
630C2×C4—861no—
631C2×C4—861no—
632C2×C4—3444no—
633C2×C4—3444no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4—1721no—
637C2×C4—1721no—
638C2×C4—1721no—
639C2×C4—1721no—
640C2×C4—1721no—
641C2×C4—1721no—
642C2×C4—1721no—
643C2×C4—1721no—
644C2×C4—1721no—
645C2×C4—1721no—
646C2×C4#1306330212yes—
647C2×C4C22×C22⋊D4311yescharacteristic
648C2×C4C22×Dic8611yescharacteristic
649C2×C4C2×#1062190011yescharacteristic
650C2×C4C2×#1062189811yescharacteristic
651C2×C4#1306337011yescharacteristic
652C2×C4#1306337011yescharacteristic
653C8—22no—
654C8—41no—
655C8—1721no—
656C8—1721no—
657C22—22no—
658C22—22no—
659C22—24no—
660C22—22no—
661C22—41no—
662C22—42no—
663C22—42no—
664C22—41no—
665C22—42no—
666C22—41no—
667C22—42no—
668C22—42no—
669C22—41no—
670C22—42no—
671C22C2×#1306330211yescharacteristic
672C22D4×C22⋊D4311yescharacteristic
673C22#1458353911yescharacteristic
674C22#135×D4311yescharacteristic
675C22#1458369611yescharacteristic
676C22#1458370111yescharacteristic
677C22#1458371311yescharacteristic
678C4—22no—
679C4—42no—
680C4—42no—
681C4—81no—
682C4—862no—
683C4—3441no—
684C4—3441no—
685C4—3441no—
686C4—3441no—
687C4—1721no—
688C4—1721no—
689C4—1721no—
690C4C2×#1306330411yescharacteristic
691C4#1458352511yescharacteristic
692C4#1458354311yescharacteristic
693C4#1458357511yescharacteristic
694C2—42no—
695C2—44no—
696C2#1913825611yescharacteristic
697C2#1914437911yescharacteristic
698C2#1914444411yescharacteristic
699C2#1914613511yescharacteristic
700C2#1914631111yescharacteristic
701C2#1914644611yescharacteristic
702C2#1914668711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#416C2
socleC23×C43C22×D4
prime radicalC22×#41×C43C22
hypercenterC2×#416D43
hypocenterC43#25956
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. C2×#14583197C2semidirect
2. #19138302C2semidirect
4. #19136131C2semidirect
5. #19135988C2semidirect
6. #19135972C2semidirect
7. #19135744C2semidirect
8. #19134844C2semidirect
9. #19134840C2semidirect
10. #19134794C2semidirect
11. #19134773C2semidirect
12. #19134624C2semidirect
13. #19134593C2semidirect
412. C43#25956semidirect

Maximal subgroups

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

subgroupindex
C2×#145831972
#191383022
#191374252
#191361312
#191359882
#191359722
#191357442
#191348442
#191348402
#191347942
#191347732
#191346242
#191345932
#191345352
C2×C43×#4162
#2595643