Finite Group Databasebeta

← #25153671

Subgroups — #25153671

Order 11008.

966 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583182C211yesmaximal, characteristic, complemented
2C2×#14582895C211yesmaximal, characteristic
3#19138287C211yesmaximal, characteristic, complemented
4#19137436C211yesmaximal, characteristic
5#19136114C211yesmaximal, characteristic, complemented
6#19135967C211yesmaximal, characteristic, complemented
7#19135965C211yesmaximal, characteristic, complemented
8#19135729C211yesmaximal, characteristic, complemented
9#19134861C211yesmaximal, characteristic, complemented
10#19134851C211yesmaximal, characteristic, complemented
11#19134796C211yesmaximal, characteristic, complemented
12#19134772C211yesmaximal, characteristic, complemented
13#19134618C211yesmaximal, characteristic, complemented
14#19134608C211yesmaximal, characteristic, complemented
15C43×#1788C211yesmaximal, characteristic
16C23×C43⋊C8C2211yescharacteristic
17C2×#13063324C2211yescharacteristic
18C2×Q8×Dic43C2211yescharacteristic
19C2×Q8×Dic43C2211yescharacteristic
20C2×#13063284C2211yescharacteristic
21#14583182—24no—
22C2×#13063259C2211yescharacteristic
23C2×#13063257C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×Dic43⋊C8C2211yescharacteristic
27C2×Dic43⋊C8C2211yescharacteristic
28#14582895—24no—
29C2×#13063249C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33#14582822—21no—
34#14582811—21no—
35#14582803—21no—
36#14582802—21no—
37#14582802—21no—
38#14582802C2211yescharacteristic
39#14582802C2211yescharacteristic
40#14582798C2211yescharacteristic
41#14582795C2211yescharacteristic
42#14582782—21no—
43#14582764C2211yescharacteristic
44#14582759—21no—
45#14582759C2211yescharacteristic
46C4×C22⋊Dic43—21no—
47C4×C22⋊Dic43C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C22×#41×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C43×#380C2211yescharacteristic
61C22×Dic86—21no—
62C22×C43⋊C8—22no—
63C22×C43⋊C8—22no—
64C22×C43⋊C8—41no—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063324—22no—
68#13063324—41no—
69Q8×Dic43—22no—
70Q8×Dic43—22no—
71Q8×Dic43—41no—
72Q8×Dic43—41no—
73#13063284—22no—
74#13063284—41no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43D411yescharacteristic
91C2×C22⋊Dic43D411yescharacteristic
92C2×C4×Dic43—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43C2311yescharacteristic
96C2×C4×Dic43C2311yescharacteristic
97#13063259—41no—
98#13063257—22no—
99#13063256—22no—
100#13063256—41no—
101Dic43⋊C8—22no—
102Dic43⋊C8—41no—
103#13063249—22no—
104#13063249D414yes—
105#13063246—22no—
106#13063246—22no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95D411yescharacteristic
113C43⋊#95D411yescharacteristic
114C2×#41×C43—22no—
115C2×#41×C43—22no—
116C2×#41×C43—22no—
117C2×#41×C43—41no—
118C2×#41×C43—41no—
119C2×#41×C43Q814yescomplemented
120C22×Q8×C43C2311yescharacteristic
121C22×D4×C43—21no—
122C22×D4×C43C2311yescharacteristic
123C23×C4×C43—21no—
124C23×C4×C43C2311yescharacteristic
125C22×C8×C43C2311yescharacteristic
126C22×C8×C43C2311yescharacteristic
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C22⋊C4×C43—21no—
130#103×C43—22no—
131#103×C43—22no—
132#102×C43—41no—
133#102×C43—41no—
134C22⋊C8×C43—22no—
135#95×C43—21no—
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×C43C2×D412yes—
146C2×Q8×C43C2×Q812yes—
147C2×Q8×C43#4112yes—
148C2×D4×C43—21no—
149C2×D4×C43—24no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—42no—
155C2×D4×C43—42no—
156C2×D4×C43C2×Q812yes—
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×Dic43C2×D411yescharacteristic
176C22×Dic43C2×D411yescharacteristic
177C22×Dic43C2×D411yescharacteristic
178C22×Dic43C2×D411yescharacteristic
179C2×Dic86—42no—
180C2×Dic86—42no—
181C2×Dic86—81no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C22⋊C4×C43—81no—
193C22⋊Dic43—22no—
194C22⋊Dic43—41no—
195C22⋊Dic43—42no—
196C22⋊Dic43—42no—
197C22⋊Dic43—42no—
198C22⋊Dic43—81no—
199C22⋊Dic43—81no—
200C22⋊Dic43—81no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—42no—
209C4⋊Dic43—42no—
210C4⋊Dic43—42no—
211C4⋊Dic43C2×D412yes—
212Dic43⋊C4—42no—
213Dic43⋊C4—81no—
214C4×Dic43—21no—
215C4×Dic43—21no—
216C4×Dic43—21no—
217C4×Dic43—21no—
218C4×Dic43—42no—
219C4×Dic43—42no—
220C4×Dic43—42no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—44no—
227C2×C43⋊C8C2×D412yes—
228C23×C43—21no—
229C23×C43—21no—
230C23×C43—21no—
231C23×C43—21no—
232C23×C43—21no—
233C23×C43—21no—
234C23×C43—22no—
235C23×C43—41no—
236C23×C43—41no—
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—22no—
246Q8×C43C22⋊Q814yes—
247D4×C43—22no—
248D4×C43—22no—
249D4×C43—48no—
250D4×C43—41no—
251D4×C43—41no—
252C2×C4×C43—22no—
253C2×C4×C43—21no—
254C2×C4×C43—22no—
255C2×C4×C43—22no—
256C2×C4×C43—21no—
257C2×C4×C43—22no—
258C2×C4×C43—22no—
259C2×C4×C43—22no—
260C2×C4×C43—22no—
261C2×C4×C43—48no—
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—22no—
279C2×Dic43—21no—
280C2×Dic43—21no—
281C2×Dic43—21no—
282C2×Dic43—21no—
283C2×Dic43—21no—
284C2×Dic43—21no—
285C2×Dic43—21no—
286C2×Dic43—21no—
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#13512yes—
299Dic86—84no—
300C8×C43—41no—
301C8×C43—41no—
302C43⋊C8—22no—
303C43⋊C8—41no—
304#25951—431nomaximal, Sylow
305C22×C43—22no—
306C22×C43—22no—
307C22×C43—22no—
308C22×C43—41no—
309C22×C43—41no—
310C22×C43—41no—
311C22×C43—41no—
312C22×C43—42no—
313C22×C43—42no—
314C22×C43—42no—
315C22×C43—81no—
316C22×C43—81no—
317C22×C43—81no—
318C22×C43—81no—
319C22×C43C2×C22⋊Q811yescharacteristic
320C22×C43D4211yescharacteristic
321C22×C43#54611yescharacteristic
322C22×C43C2×#13511yescharacteristic
323C22×C43#57511yescharacteristic
324C22×C43#57711yescharacteristic
325C22×C43#57711yescharacteristic
326C4×C43—22no—
327C4×C43—24no—
328C4×C43—81no—
329C4×C43—81no—
330C4×C43C2×C22⋊Q811yescharacteristic
331C4×C43#54311yescharacteristic
332C4×C43#54611yescharacteristic
333C4×C43#55111yescharacteristic
334Dic43—22no—
335Dic43—41no—
336Dic43—42no—
337Dic43—41no—
338Dic43—41no—
339Dic43—81no—
340Dic43—81no—
341Dic43—81no—
342C2×#475—431no—
343C2×#416—431no—
344#2439—431no—
345#2341—431no—
346#2092—431no—
347#2065—431no—
348#2065—431no—
349#2023—431no—
350#1865—431no—
351#1863—431no—
352#1854—431no—
353#1850—431no—
354#1807—431no—
355#1805—431no—
356#1788D4311yescharacteristic
357C2×C43—42no—
358C2×C43—82no—
359C2×C43#243711yescharacteristic
360C2×C43#307611yescharacteristic
361C2×C43#308411yescharacteristic
362C2×C43#327111yescharacteristic
363C2×C43#328211yescharacteristic
364C2×C43#330411yescharacteristic
365C2×C43#332111yescharacteristic
366C22×#41C2×D4311yescharacteristic
367C23×C8—431no—
368C2×C4⋊Q8—431no—
369C2×C4×Q8—431no—
370C2×C4×Q8—431no—
371C2×#117—431no—
372#475—864no—
373C2×#107—431no—
374C2×#106—431no—
375C2×#106—431no—
376C2×#106—431no—
377C2×C4⋊C8—431no—
378C2×C4⋊C8—431no—
379#416—864no—
380C2×#103—431no—
381C2×#103—431no—
382C2×#103C2×D4311yescharacteristic
383C2×#103C2×D4311yescharacteristic
384C2×#102—431no—
385C2×#102—431no—
386C2×#102C2×D4311yescharacteristic
387C2×#102C2×D4311yescharacteristic
388C2×C22⋊C8C2×D4311yescharacteristic
389#396—861no—
390#393—861no—
391#391—861no—
392#390—431no—
393#390—431no—
394#390—861no—
395#390—861no—
396#389—431no—
397#389—431no—
398#387—861no—
399#382—431no—
400#380—431no—
401#380—861no—
402#380C2×D4311yescharacteristic
403C4×C22⋊C4—431no—
404C4×C22⋊C4—861no—
405#340—431no—
406#340—431no—
407#340—431no—
408#340—431no—
409#336—431no—
410#336—431no—
411C43#2595111yescharacteristic, complemented, Sylow
412C2×#41—22no—
413C2×#41—22no—
414C2×#41—22no—
415C2×#41—41no—
416C2×#41—41no—
417C2×#41Dic8614yescomplemented
418C22×Q8—861no—
419C22×Q8C22×D4311yescharacteristic
420C22×D4—21no—
421C22×D4C22×D4311yescharacteristic
422C23×C4—21no—
423C23×C4C22×D4311yescharacteristic
424C22×C8—431no—
425C22×C8—431no—
426C22×C8—862no—
427C22×C8—862no—
428C22×C8—1721no—
429C22×C8C22×D4311yescharacteristic
430C22×C8C22×D4311yescharacteristic
431C4⋊Q8—862no—
432C4⋊Q8—1721no—
433C4×Q8—862no—
434C4×Q8—862no—
435C4×Q8—1721no—
436C4×Q8—1721no—
437#117—862no—
438#117—1721no—
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⋊C4C22×D4311yescharacteristic
449C2×C4⋊C4C22×D4311yescharacteristic
450C2×C22⋊C4—21no—
451C2×C22⋊C4—431no—
452C2×C22⋊C4—431no—
453C2×C22⋊C4—861no—
454C2×C22⋊C4—861no—
455C2×C22⋊C4—861no—
456C2×C22⋊C4—861no—
457C2×C22⋊C4—861no—
458C2×C22⋊C4—861no—
459C2×C42—431no—
460C2×C42—431no—
461C2×C42—861no—
462C2×C42—861no—
463C2×C42—861no—
464#107—1721no—
465#106—862no—
466#106—862no—
467#106—1721no—
468C4⋊C8—862no—
469C4⋊C8—1721no—
470#103—22no—
471#103—22no—
472#103—434no—
473#103—862no—
474#102—41no—
475#102—41no—
476#102—862no—
477#102—862no—
478C22⋊C8—22no—
479#95—21no—
480#95—431no—
481#95—431no—
482#95—861no—
483#95—861no—
484#95—861no—
485#95—861no—
486#95—861no—
487C24—21no—
488C24D4×D4311yescharacteristic
489#41—28no—
490#41—44no—
491#41—44no—
492#41—44no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—3441no—
497C2×Q8—1722no—
498C2×Q8—1722no—
499C2×Q8C2×Dic8612yes—
500C2×Q8D4×D4312yes—
501C2×Q8#1062190012yes—
502C2×D4—24no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4C2×Dic8612yes—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—24no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—431no—
522C22×C4—431no—
523C22×C4—431no—
524C22×C4—431no—
525C22×C4—861no—
526C22×C4—861no—
527C22×C4—861no—
528C22×C4—861no—
529C22×C4C2×Dic8612yes—
530C22×C4D4×D4311yescharacteristic
531C22×C4#1062190012yes—
532C22×C4C23×D4311yescharacteristic
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—432no—
540C2×C8—861no—
541C2×C8—861no—
542C2×C8—861no—
543C2×C8—861no—
544C2×C8—861no—
545C2×C8—1724no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—432no—
551C4⋊C4—861no—
552C4⋊C4—861no—
553C4⋊C4—861no—
554C4⋊C4—861no—
555C4⋊C4—861no—
556C4⋊C4—861no—
557C4⋊C4—861no—
558C4⋊C4—3441no—
559C4⋊C4—1722no—
560C4⋊C4—1722no—
561C4⋊C4—1722no—
562C4⋊C4—1722no—
563C22⋊C4—81no—
564C22⋊C4—862no—
565C22⋊C4—3441no—
566C22⋊C4—3441no—
567C22⋊C4—3441no—
568C22⋊C4—1722no—
569C22⋊C4—1721no—
570C22⋊C4—1722no—
571C22⋊C4—1722no—
572C42—861no—
573C42—861no—
574C42—861no—
575C42—861no—
576C42—1722no—
577C42—1722no—
578C42—1722no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—22no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23#1306330212yes—
593C23C2×D4×D4311yescharacteristic
594Q8—22no—
595Q8—22no—
596Q8—22no—
597Q8—3444no—
598Q8#1306330214yes—
599D4—22no—
600D4—22no—
601D4—48no—
602D4—41no—
603D4—41no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—21no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—48no—
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—862no—
631C2×C4—861no—
632C2×C4—861no—
633C2×C4—1721no—
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#1306330212yes—
645C2×C4C2×D4×D4311yescharacteristic
646C2×C4C22×Dic8611yescharacteristic
647C2×C4C2×#1062190011yescharacteristic
648C2×C4C2×#1062190011yescharacteristic
649C2×C4#1306337011yescharacteristic
650C2×C4#1306337011yescharacteristic
651C8—41no—
652C8—41no—
653C8—862no—
654C8—1721no—
655C22—22no—
656C22—22no—
657C22—22no—
658C22—41no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22—42no—
663C22—42no—
664C22—42no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22C2×#1306330211yescharacteristic
670C22#1458353111yescharacteristic
671C22#1458353611yescharacteristic
672C22#135×D4311yescharacteristic
673C22#1458369611yescharacteristic
674C22#1458370811yescharacteristic
675C22#1458370911yescharacteristic
676C4—22no—
677C4—24no—
678C4—81no—
679C4—81no—
680C4—862no—
681C4—3441no—
682C4—3441no—
683C4—3441no—
684C4—1721no—
685C4—1721no—
686C4—1722no—
687C4—1721no—
688C4C2×#1306330211yescharacteristic
689C4#1458352511yescharacteristic
690C4#1458353611yescharacteristic
691C4#1458358011yescharacteristic
692C2—42no—
693C2—82no—
694C2#1913826111yescharacteristic
695C2#1914437911yescharacteristic
696C2#1914446111yescharacteristic
697C2#1914618411yescharacteristic
698C2#1914630511yescharacteristic
699C2#1914652711yescharacteristic
700C2#1914678511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1788C2
socleC23×C43C22×D4
prime radicalC22×#41×C43C22
hypercenter#1788D43
hypocenterC43#25951
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
1. C2×#14583182C2semidirect
3. #19138287C2semidirect
5. #19136114C2semidirect
6. #19135967C2semidirect
7. #19135965C2semidirect
8. #19135729C2semidirect
9. #19134861C2semidirect
10. #19134851C2semidirect
11. #19134796C2semidirect
12. #19134772C2semidirect
13. #19134618C2semidirect
14. #19134608C2semidirect
119. C2×#41×C43Q8semidirect
411. C43#25951semidirect
417. C2×#41Dic86semidirect

Maximal subgroups

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

subgroupindex
C2×#145831822
C2×#145828952
#191382872
#191374362
#191361142
#191359672
#191359652
#191357292
#191348612
#191348512
#191347962
#191347722
#191346182
#191346082
C43×#17882
#2595143