Finite Group Databasebeta

← #25146946

Subgroups — #25146946

Order 11008.

840 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×#14583184C211yesmaximal, characteristic, complemented
2C2×#14582972C211yesmaximal, characteristic
3#19139764C211yesmaximal, characteristic
4#19139500C211yesmaximal, characteristic
5#19136034C211yesmaximal, characteristic, complemented
6#19136033C211yesmaximal, characteristic, complemented
7#19135796C211yesmaximal, characteristic, complemented
8#19135789C211yesmaximal, characteristic, complemented
9#19135568C211yesmaximal, characteristic, complemented
10#19135363C211yesmaximal, characteristic, complemented
11#19135025C211yesmaximal, characteristic, complemented
12#19135015C211yesmaximal, characteristic, complemented
13#19134627C211yesmaximal, characteristic, complemented
14#19134619C211yesmaximal, characteristic, complemented
15C43×#1763C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C2×#13063325C2211yescharacteristic
19C2×#13063301C2211yescharacteristic
20C2×#13063301C2211yescharacteristic
21C2×C4×D172C2211yescharacteristic
22#14583184—24no—
23#14582972—24no—
24C2×#13063258C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×#13063256C2211yescharacteristic
27C2×#13063256C2211yescharacteristic
28C2×C4⋊(C43⋊C8)C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×(C2×D43)⋊C8C2211yescharacteristic
32C2×(C2×D43)⋊C8C2211yescharacteristic
33#14582829—21no—
34#14582816—21no—
35#14582812—21no—
36#14582812—21no—
37#14582801—21no—
38#14582790—21no—
39#14582790—21no—
40#14582765—21no—
41#14582765C2211yescharacteristic
42#14582756C2211yescharacteristic
43#14582756C2211yescharacteristic
44#14582756C2211yescharacteristic
45#14582756C2211yescharacteristic
46#14582756C2211yescharacteristic
47#14582756C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54C2×C4×Q8×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×#97×C43C2211yescharacteristic
58C4×C4⋊C4×C43C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86—21no—
62C22×D172D411yescharacteristic
63C22×C4×D43C2311yescharacteristic
64C22×C4×D43C2311yescharacteristic
65C2×#10621872—22no—
66C2×#10621872—22no—
67C2×#10621872—41no—
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70C2×C8×D43—22no—
71C2×C8×D43—22no—
72C2×C8×D43—41no—
73#13063325—22no—
74#13063325—22no—
75#13063301—22no—
76#13063301—22no—
77#13063301—41no—
78#13063301—41no—
79C4×D172—22no—
80C4×D172—22no—
81C2×C4⋊Dic43—21no—
82C2×C4⋊Dic43D411yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4D411yescharacteristic
98C2×(C2×D43)⋊C4D411yescharacteristic
99#13063258—41no—
100#13063256—22no—
101#13063256—22no—
102#13063256—41no—
103C4⋊(C43⋊C8)D414yes—
104#13063249—22no—
105#13063249—22no—
106(C2×D43)⋊C8—22no—
107(C2×D43)⋊C8—22no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C22×Q8×C43C2311yescharacteristic
117C22×C8×C43C2311yescharacteristic
118C22×C8×C43C2311yescharacteristic
119C4×Q8×C43—22no—
120C4×Q8×C43—22no—
121C2×C4⋊C4×C43—21no—
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C42×C43—21no—
126C2×C42×C43—21no—
127C2×C42×C43C2311yescharacteristic
128#103×C43—22no—
129#103×C43—22no—
130#97×C43—22no—
131#95×C43—21no—
132C23×D43C2×D411yescharacteristic
133C23×D43C2×D411yescharacteristic
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43#4112yes—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2411yescharacteristic
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C2×D172—22no—
154C2×D172—22no—
155C2×D172—41no—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165C2×C4×D43—21no—
166C2×C4×D43—21no—
167C2×C4×D43—21no—
168C2×Dic86—42no—
169C2×Dic86—81no—
170C2×Dic86—81no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43#4112yes—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—42no—
184C42×C43—42no—
185C42×C43—42no—
186C42×C43C2×D412yes—
187C42×C43#4112yes—
188(C2×D43)⋊C4—22no—
189(C2×D43)⋊C4—22no—
190(C2×D43)⋊C4—42no—
191(C2×D43)⋊C4—42no—
192(C2×D43)⋊C4—42no—
193(C2×D43)⋊C4—42no—
194(C2×D43)⋊C4—81no—
195(C2×D43)⋊C4—81no—
196(C2×D43)⋊C4—81no—
197(C2×D43)⋊C4—81no—
198C4⋊Dic43—22no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—42no—
208Dic43⋊C4—42no—
209Dic43⋊C4—42no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8C2×D412yes—
215C2×C43⋊C8C2×D412yes—
216#10621872—44no—
217C8×D43—44no—
218C23×C43C22×D411yescharacteristic
219C22×D43—21no—
220C22×D43—21no—
221C22×D43—21no—
222C22×D43—21no—
223C22×D43—21no—
224C22×D43—21no—
225C22×D43—21no—
226C22×D43—21no—
227C22×D43—21no—
228C22×D43—21no—
229C22×D43—21no—
230C22×D43—21no—
231C22×D43—21no—
232C22×D43#13712yes—
233Q8×C43—22no—
234Q8×C43—22no—
235Q8×C43—41no—
236Q8×C43—41no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—22no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
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#12112yes—
254C2×C4×C43#12112yes—
255C2×C4×C43C22×D411yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C43H(5,𝔽2)11yescharacteristic
260C2×C4×C432−1+411yescharacteristic
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279D172—44no—
280C4×D43—41no—
281C4×D43—41no—
282C4×D43—41no—
283C4×D43—41no—
284C4×D43—41no—
285C4×D43—41no—
286C4×D43—41no—
287C4×D43—41no—
288Dic86—84no—
289C8×C43—22no—
290C8×C43—41no—
291C43⋊C8—22no—
292C43⋊C8—22no—
293#25356—431nomaximal, Sylow
294C22×C43C2×#12111yescharacteristic
295C22×C43#54611yescharacteristic
296C22×C43#54711yescharacteristic
297C22×C43C2×#13711yescharacteristic
298C22×C43#57511yescharacteristic
299C22×C43#57711yescharacteristic
300C22×C43#57711yescharacteristic
301C2×D43—22no—
302C2×D43—22no—
303C2×D43—22no—
304C2×D43—41no—
305C2×D43—41no—
306C2×D43—41no—
307C2×D43—41no—
308C2×D43—41no—
309C2×D43—41no—
310C2×D43—41no—
311C2×D43—41no—
312C2×D43—41no—
313C2×D43—41no—
314C2×D43—41no—
315C4×C43—22no—
316C4×C43—22no—
317C4×C43—42no—
318C4×C43—81no—
319C4×C43—81no—
320C4×C43—81no—
321C4×C43#52911yescharacteristic
322C4×C43#54211yescharacteristic
323C4×C43#54611yescharacteristic
324C4×C43#54811yescharacteristic
325Dic43—41no—
326Dic43—41no—
327Dic43—81no—
328Dic43—81no—
329Dic43—81no—
330Dic43—81no—
331C2×#475—431no—
332C2×#435—431no—
333#2563—431no—
334#2536—431no—
335#2077—431no—
336#2077—431no—
337#2036—431no—
338#2035—431no—
339#1993—431no—
340#1949—431no—
341#1894—431no—
342#1892—431no—
343#1809—431no—
344#1807—431no—
345#1763D4311yescharacteristic, complemented
346C2×C43#242711yescharacteristic
347C2×C43#305611yescharacteristic
348C2×C43#305711yescharacteristic
349C2×C43#331611yescharacteristic
350C2×C43#332111yescharacteristic
351C2×C43#334411yescharacteristic
352C2×C43#334811yescharacteristic
353D43—42no—
354D43—81no—
355C22×M16—431no—
356C23×C8—431no—
357C2×C4⋊Q8—431no—
358C2×C22⋊Q8—431no—
359C2×C22⋊Q8—431no—
360C2×C4×Q8C2×D4311yescharacteristic
361C2×C4×D4—431no—
362#475—864no—
363#435—864no—
364C2×#107—431no—
365C2×#106—431no—
366C2×#106—431no—
367C2×#106—431no—
368C2×C4⋊C8—431no—
369C2×#103—431no—
370C2×#103—431no—
371C2×#103C2×D4311yescharacteristic
372C2×#103C2×D4311yescharacteristic
373C2×C22⋊C8—431no—
374C2×C22⋊C8—431no—
375C2×#97C2×D4311yescharacteristic
376#398—861no—
377#394—861no—
378#393—861no—
379#393—861no—
380#390—861no—
381#388—861no—
382#388—861no—
383#382—431no—
384#382—861no—
385#380—431no—
386#380—431no—
387#380—431no—
388#380—431no—
389#380—431no—
390#380—431no—
391C4×C4⋊C4C2×D4311yescharacteristic
392#340—431no—
393#340—431no—
394#340—431no—
395#340—431no—
396#340—431no—
397#340—431no—
398#340C2×D4311yescharacteristic
399#340C2×D4311yescharacteristic
400C43#2535611yescharacteristic, complemented, Sylow
401C22×Q8—861no—
402C22×Q8C22×D4311yescharacteristic
403C22×D4—431no—
404C23×C4—431no—
405C23×C4—431no—
406C2×M16—862no—
407C2×M16—862no—
408C2×M16—1721no—
409C22×C8—431no—
410C22×C8—431no—
411C22×C8—862no—
412C22×C8—862no—
413C22×C8—1721no—
414C22×C8C22×D4311yescharacteristic
415C22×C8C22×D4311yescharacteristic
416C4⋊Q8—862no—
417C4⋊Q8—862no—
418C22⋊Q8—862no—
419C22⋊Q8—862no—
420C22⋊Q8—1721no—
421C22⋊Q8—1721no—
422C4×Q8—22no—
423C4×Q8—22no—
424C4×D4—862no—
425C4×D4—862no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—431no—
428C2×C4⋊C4—431no—
429C2×C4⋊C4—431no—
430C2×C4⋊C4—431no—
431C2×C4⋊C4—431no—
432C2×C4⋊C4—861no—
433C2×C4⋊C4—861no—
434C2×C4⋊C4—861no—
435C2×C4⋊C4C22×D4311yescharacteristic
436C2×C4⋊C4C22×D4311yescharacteristic
437C2×C4⋊C4C22×D4311yescharacteristic
438C2×C22⋊C4—431no—
439C2×C22⋊C4—431no—
440C2×C22⋊C4—861no—
441C2×C22⋊C4—861no—
442C2×C22⋊C4—861no—
443C2×C22⋊C4—861no—
444C2×C22⋊C4—861no—
445C2×C22⋊C4—861no—
446C2×C22⋊C4—861no—
447C2×C22⋊C4—861no—
448C2×C42—21no—
449C2×C42—21no—
450C2×C42C22×D4311yescharacteristic
451#107—1721no—
452#106—862no—
453#106—862no—
454#106—1721no—
455C4⋊C8—434no—
456#103—22no—
457#103—22no—
458#103—862no—
459#103—862no—
460C22⋊C8—862no—
461C22⋊C8—862no—
462#97—22no—
463#95—21no—
464#95—861no—
465#95—861no—
466#95—861no—
467#95—861no—
468#95—861no—
469#95—861no—
470#95—861no—
471#95—861no—
472C24—431no—
473C24—431no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—3441no—
480C2×Q8—3441no—
481C2×Q8—1722no—
482C2×Q8#1062189812yes—
483C2×D4—862no—
484C2×D4—862no—
485C2×D4—1721no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—431no—
491C22×C4—431no—
492C22×C4—861no—
493C22×C4—861no—
494C22×C4—861no—
495C22×C4—861no—
496C22×C4—861no—
497C22×C4—861no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4—861no—
504C22×C4—861no—
505C22×C4—861no—
506C22×C4—861no—
507C22×C4—861no—
508C22×C4D4×D4311yescharacteristic
509C22×C4D4×D4311yescharacteristic
510C22×C4C23×D4311yescharacteristic
511M16—1724no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—432no—
518C2×C8—432no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—861no—
523C2×C8—1724no—
524C2×C8#1062189812yes—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—42no—
532C4⋊C4—862no—
533C4⋊C4—861no—
534C4⋊C4—861no—
535C4⋊C4—861no—
536C4⋊C4—861no—
537C4⋊C4—861no—
538C4⋊C4—861no—
539C4⋊C4—861no—
540C4⋊C4—861no—
541C4⋊C4—1722no—
542C4⋊C4—1722no—
543C4⋊C4—1722no—
544C22⋊C4—862no—
545C22⋊C4—862no—
546C22⋊C4—3441no—
547C22⋊C4—3441no—
548C22⋊C4—3441no—
549C22⋊C4—3441no—
550C22⋊C4—1722no—
551C22⋊C4—1722no—
552C22⋊C4—1722no—
553C22⋊C4—1722no—
554C42—42no—
555C42—42no—
556C42#1062189812yes—
557C42D4×D4312yes—
558C23—432no—
559C23—861no—
560C23—861no—
561C23—861no—
562C23—861no—
563C23—861no—
564C23—861no—
565C23—861no—
566C23—861no—
567C23—861no—
568C23—861no—
569C23—861no—
570C23—861no—
571C23—861no—
572C23C2×D4×D4311yescharacteristic
573Q8—22no—
574Q8—22no—
575Q8—41no—
576Q8—41no—
577Q8—3444no—
578D4—1724no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
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—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1721no—
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—1721no—
618C2×C4—1721no—
619C2×C4—1721no—
620C2×C4—1721no—
621C2×C4#1306329812yes—
622C2×C4#1306329812yes—
623C2×C4C2×D4×D4311yescharacteristic
624C2×C4C2×#1062189811yescharacteristic
625C2×C4C2×#1062189811yescharacteristic
626C2×C4C2×#1062189811yescharacteristic
627C2×C4#1306337111yescharacteristic
628C2×C4#1306337211yescharacteristic
629C8—22no—
630C8—41no—
631C8—862no—
632C8—862no—
633C22—862no—
634C22—862no—
635C22—862no—
636C22—1721no—
637C22—1721no—
638C22—1721no—
639C22—1721no—
640C22—1721no—
641C22—1721no—
642C22—1721no—
643C22—1721no—
644C22—1721no—
645C22—1721no—
646C22—1721no—
647C22C2×#1306329811yescharacteristic
648C22#1458354511yescharacteristic
649C22#1458355411yescharacteristic
650C22#137×D4311yescharacteristic
651C22#1458369511yescharacteristic
652C22#1458370811yescharacteristic
653C22#1458370811yescharacteristic
654C4—22no—
655C4—22no—
656C4—42no—
657C4—81no—
658C4—81no—
659C4—81no—
660C4—3441no—
661C4—3441no—
662C4—3441no—
663C4—3441no—
664C4—1721no—
665C4—1721no—
666C4#1458343311yescharacteristic
667C4#1458352011yescharacteristic
668C4#1458354511yescharacteristic
669C4#1458355811yescharacteristic
670C2—3441no—
671C2—1722no—
672C2#1913817211yescharacteristic
673C2#1914422811yescharacteristic
674C2#1914423711yescharacteristic
675C2#1914671111yescharacteristic
676C2#1914678611yescharacteristic
677C2#1914705511yescharacteristic
678C2#1914711511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1763C2
socleC23×C43C22×D4
prime radicalC22×D172D4
hypercenter#1763D43
hypocenterC43#25356
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1763

Complements

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

NH ≅ G/Ntype
1. C2×#14583184C2semidirect
5. #19136034C2semidirect
6. #19136033C2semidirect
7. #19135796C2semidirect
8. #19135789C2semidirect
9. #19135568C2semidirect
10. #19135363C2semidirect
11. #19135025C2semidirect
12. #19135015C2semidirect
13. #19134627C2semidirect
14. #19134619C2semidirect
15. C43×#1763C2semidirect
345. #1763D43semidirect
400. C43#25356semidirect

Maximal subgroups

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

subgroupindex
C2×#145831842
C2×#145829722
#191397642
#191395002
#191360342
#191360332
#191357962
#191357892
#191355682
#191353632
#191350252
#191350152
#191346272
#191346192
C43×#17632
#2535643