Finite Group Databasebeta

← #25166451

Subgroups — #25166451

Order 11008.

882 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583257C211yesmaximal, characteristic, complemented
2C2×#14583011C211yesmaximal, characteristic
3#19138448C211yesmaximal, characteristic, complemented
4#19138380C211yesmaximal, characteristic, complemented
5#19135975C211yesmaximal, characteristic, complemented
6#19135927C211yesmaximal, characteristic, complemented
7#19135670C211yesmaximal, characteristic
8#19135448C211yesmaximal, characteristic, complemented
9#19135294C211yesmaximal, characteristic, complemented
10#19135283C211yesmaximal, characteristic, complemented
11#19135281C211yesmaximal, characteristic, complemented
12#19134927C211yesmaximal, characteristic, complemented
13#19134854C211yesmaximal, characteristic, complemented
14#19134465C211yesmaximal, characteristic, complemented
15C43×#2054C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C2×#13063324C2211yescharacteristic
18C2×#13063312C2211yescharacteristic
19C2×#13063302—21no—
20C2×D4×Dic43C2211yescharacteristic
21C2×D4×Dic43C2211yescharacteristic
22#14583257—24no—
23#14583011—24no—
24C2×#13063257C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063235C2211yescharacteristic
33C2×#13063235C2211yescharacteristic
34C2×C4×C43⋊C8C2211yescharacteristic
35#14582824—21no—
36#14582824—21no—
37#14582822—21no—
38#14582811—21no—
39#14582805C2211yescharacteristic
40#14582804C2211yescharacteristic
41#14582802C2211yescharacteristic
42#14582798C2211yescharacteristic
43#14582797C2211yescharacteristic
44#14582795C2211yescharacteristic
45#14582774—21no—
46#14582771—21no—
47#14582760—21no—
48C4×C4⋊Dic43C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C22×D8×C43C2211yescharacteristic
55C2×C4⋊C8×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C43×#390C2211yescharacteristic
59C43×#390C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86—21no—
62C22×Dic86C2311yescharacteristic
63C23×Dic43—21no—
64C23×Dic43—21no—
65C2×#10621883—22no—
66C2×#10621883—22no—
67C2×#10621883—41no—
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70#13063324—22no—
71#13063324—41no—
72#13063312—22no—
73#13063312—41no—
74#13063302—44no—
75D4×Dic43—22no—
76D4×Dic43—22no—
77D4×Dic43—41no—
78D4×Dic43—41no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43D411yescharacteristic
81C2×C4⋊Dic43D411yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—21no—
93C2×C22⋊Dic43—21no—
94C2×C4×Dic43C2311yescharacteristic
95C2×C4×Dic43C2311yescharacteristic
96#13063257—22no—
97#13063256—41no—
98#13063250—22no—
99#13063250—22no—
100#13063248—22no—
101#13063246—22no—
102#13063246—22no—
103#13063246D414yes—
104#13063235—22no—
105#13063235—22no—
106C4×C43⋊C8—22no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95D411yescharacteristic
115C43⋊#95D411yescharacteristic
116C22×D4×C43C2311yescharacteristic
117C22×D4×C43C2311yescharacteristic
118C2×D8×C43—22no—
119C2×D8×C43—22no—
120C2×D8×C43—22no—
121C22×C8×C43C2311yescharacteristic
122C22×C8×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C42×C43C2311yescharacteristic
130C4⋊C8×C43—22no—
131#102×C43—22no—
132#102×C43—22no—
133C24×C43—21no—
134C24×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43C2×D412yes—
146C2×D4×C43#4112yes—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2411yescharacteristic
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—42no—
157C22×Dic43—42no—
158C22×Dic43—42no—
159C22×Dic43—42no—
160C22×Dic43—81no—
161C22×Dic43—81no—
162C22×Dic43C2×D411yescharacteristic
163C22×Dic43C2×D411yescharacteristic
164C22×Dic43C2×D411yescharacteristic
165C22×Dic43C2×D411yescharacteristic
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86—42no—
173C2×Dic86—42no—
174C2×Dic86—81no—
175D8×C43—28no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43#4112yes—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C22⋊C4×C43—42no—
187C22⋊C4×C43—42no—
188C22⋊C4×C43—81no—
189C22⋊C4×C43—81no—
190C42×C43—21no—
191C42×C43—21no—
192C22⋊Dic43—42no—
193C22⋊Dic43—42no—
194C22⋊Dic43—42no—
195C22⋊Dic43—42no—
196C22⋊Dic43—42no—
197C22⋊Dic43—42no—
198#10621883—44no—
199C4⋊Dic43—22no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—41no—
206C4⋊Dic43—81no—
207C4⋊Dic43C2×D412yes—
208Dic43⋊C4—42no—
209Dic43⋊C4—42no—
210Dic43⋊C4—42no—
211C4×Dic43—21no—
212C4×Dic43—21no—
213C4×Dic43—21no—
214C4×Dic43—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8C2×D412yes—
220C2×C43⋊C8#4112yes—
221C23×C43—22no—
222C23×C43—22no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43—41no—
229C23×C43—41no—
230C23×C43—41no—
231C23×C43—41no—
232C23×C43—41no—
233C23×C43—41no—
234C23×C43—41no—
235C23×C43C22×D411yescharacteristic
236D4×C43—22no—
237D4×C43—22no—
238D4×C43—22no—
239D4×C43—22no—
240D4×C43—41no—
241D4×C43—41no—
242D4×C43—41no—
243D4×C43—41no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
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×C43AGL(1,ℤ/8)12yes—
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C43H(5,𝔽2)11yescharacteristic
261C2×C4×C432−1+411yescharacteristic
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—22no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—41no—
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—84no—
287C2×Dic43—84no—
288Dic86—41no—
289Dic86—41no—
290Dic86—41no—
291Dic86—41no—
292Dic86—84no—
293C8×C43—22no—
294C8×C43—41no—
295C43⋊C8—22no—
296C43⋊C8—22no—
297#26842—431nomaximal, Sylow
298C22×C43—42no—
299C22×C43—42no—
300C22×C43—42no—
301C22×C43—42no—
302C22×C43—42no—
303C22×C43—42no—
304C22×C43—81no—
305C22×C43—81no—
306C22×C43—81no—
307C22×C43—81no—
308C22×C43—81no—
309C22×C43—81no—
310C22×C43—81no—
311C22×C43—81no—
312C22×C43#53211yescharacteristic
313C22×C43D4211yescharacteristic
314C22×C43#54811yescharacteristic
315C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
316C22×C43#57511yescharacteristic
317C22×C43#57711yescharacteristic
318C22×C43#57711yescharacteristic
319C4×C43—22no—
320C4×C43—41no—
321C4×C43—81no—
322C4×C43—81no—
323C4×C43#52511yescharacteristic
324C4×C43#54211yescharacteristic
325C4×C43#54711yescharacteristic
326C4×C43#55111yescharacteristic
327Dic43—41no—
328Dic43—42no—
329Dic43—41no—
330Dic43—41no—
331Dic43—41no—
332Dic43—81no—
333Dic43—81no—
334Dic43—81no—
335C2×#489—431no—
336C2×#442—431no—
337#2452—431no—
338#2447—431no—
339#2066—431no—
340#2058—431no—
341#2054D4311yescharacteristic
342#2012—431no—
343#1968—431no—
344#1936—431no—
345#1935—431no—
346#1934—431no—
347#1877—431no—
348#1864—431no—
349#1770—431no—
350C2×C43—82no—
351C2×C43—82no—
352C2×C43#246111yescharacteristic
353C2×C43#317311yescharacteristic
354C2×C43#318011yescharacteristic
355C2×C43#327211yescharacteristic
356C2×C43#327511yescharacteristic
357C2×C43#337311yescharacteristic
358C2×C43#337611yescharacteristic
359C22×SD16—431no—
360C22×D8C2×D4311yescharacteristic
361C2×C4⋊Q8—431no—
362C2×#124—431no—
363C2×C22⋊Q8—861no—
364C2×C4×D4—431no—
365C2×C4×D4—431no—
366#489—864no—
367#442—864no—
368C2×#106—431no—
369C2×#106—431no—
370C2×C4⋊C8C2×D4311yescharacteristic
371C2×#103—431no—
372C2×#103—431no—
373C2×#103—431no—
374C2×#102—431no—
375C2×#102—431no—
376C2×#102—431no—
377C2×#102C2×D4311yescharacteristic
378C2×#102C2×D4311yescharacteristic
379C2×#97—431no—
380C2×#97—431no—
381C2×C4×C8—431no—
382#397—861no—
383#397—861no—
384#396—861no—
385#393—861no—
386#391—431no—
387#391—431no—
388#390—431no—
389#390C2×D4311yescharacteristic
390#390C2×D4311yescharacteristic
391#389—431no—
392#389—431no—
393#389—431no—
394#385—861no—
395#385—861no—
396#381—861no—
397C4×C4⋊C4—431no—
398#340—431no—
399#340—431no—
400#340—431no—
401#340C2×D4311yescharacteristic
402#336—431no—
403#336—431no—
404C43#2684211yescharacteristic, complemented, Sylow
405C22×Q8—431no—
406C22×Q8—861no—
407C22×D4C22×D4311yescharacteristic
408C22×D4C22×D4311yescharacteristic
409C23×C4—861no—
410C23×C4—861no—
411C2×SD16—862no—
412C2×SD16—862no—
413C2×SD16—1721no—
414C2×D8—22no—
415C2×D8—22no—
416C2×D8—22no—
417C22×C8—431no—
418C22×C8—431no—
419C22×C8C22×D4311yescharacteristic
420C22×C8C22×D4311yescharacteristic
421C4⋊Q8—862no—
422C4⋊Q8—1721no—
423#124—862no—
424#124—1721no—
425C22⋊Q8—1724no—
426C4×D4—862no—
427C4×D4—862no—
428C4×D4—1721no—
429C4×D4—1721no—
430C2×C4⋊C4—431no—
431C2×C4⋊C4—431no—
432C2×C4⋊C4—431no—
433C2×C4⋊C4—431no—
434C2×C4⋊C4—431no—
435C2×C4⋊C4—861no—
436C2×C4⋊C4—861no—
437C2×C4⋊C4—861no—
438C2×C4⋊C4—861no—
439C2×C4⋊C4C22×D4311yescharacteristic
440C2×C4⋊C4C22×D4311yescharacteristic
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—861no—
446C2×C22⋊C4—861no—
447C2×C22⋊C4—861no—
448C2×C22⋊C4—861no—
449C2×C22⋊C4—861no—
450C2×C22⋊C4—861no—
451C2×C42—431no—
452C2×C42—431no—
453C2×C42C22×D4311yescharacteristic
454#106—862no—
455#106—1721no—
456C4⋊C8—22no—
457#103—862no—
458#103—862no—
459#103—862no—
460#102—22no—
461#102—22no—
462#102—434no—
463#102—862no—
464#102—862no—
465#97—862no—
466#97—862no—
467C4×C8—862no—
468#95—431no—
469#95—431no—
470#95—861no—
471#95—861no—
472#95—861no—
473#95—861no—
474#95—861no—
475#95—861no—
476#95—861no—
477C24—21no—
478C24—21no—
479C2×Q8—861no—
480C2×Q8—861no—
481C2×Q8—861no—
482C2×Q8—861no—
483C2×Q8—861no—
484C2×Q8—861no—
485C2×Q8—3441no—
486C2×Q8—1722no—
487C2×Q8—1722no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4D4×D4312yes—
499C2×D4#1062190012yes—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—431no—
503C22×C4—431no—
504C22×C4—431no—
505C22×C4—431no—
506C22×C4—861no—
507C22×C4—861no—
508C22×C4—861no—
509C22×C4—861no—
510C22×C4—3441no—
511C22×C4—3441no—
512C22×C4—1722no—
513C22×C4—1722no—
514C22×C4—1722no—
515C22×C4—1722no—
516C22×C4D4×D4311yescharacteristic
517C22×C4D4×D4311yescharacteristic
518C22×C4C23×D4311yescharacteristic
519SD16—1724no—
520D8—28no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—432no—
527C2×C8—432no—
528C2×C8—861no—
529C2×C8—861no—
530C2×C8—861no—
531C2×C8—861no—
532C2×C8#1062190012yes—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—432no—
538C4⋊C4—862no—
539C4⋊C4—861no—
540C4⋊C4—861no—
541C4⋊C4—861no—
542C4⋊C4—861no—
543C4⋊C4—861no—
544C4⋊C4—3441no—
545C4⋊C4—1721no—
546C4⋊C4—1722no—
547C4⋊C4—1722no—
548C4⋊C4—1722no—
549C22⋊C4—42no—
550C22⋊C4—42no—
551C22⋊C4—81no—
552C22⋊C4—81no—
553C22⋊C4—1722no—
554C22⋊C4—1722no—
555C22⋊C4—1722no—
556C22⋊C4—1722no—
557C22⋊C4—1722no—
558C22⋊C4—1722no—
559C42—21no—
560C42—21no—
561C42—861no—
562C42—861no—
563C42—861no—
564C42—861no—
565C23—22no—
566C23—22no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23C2×D4×D4311yescharacteristic
580Q8—3444no—
581Q8—1721no—
582Q8—1721no—
583Q8—1721no—
584Q8—1721no—
585D4—22no—
586D4—22no—
587D4—22no—
588D4—22no—
589D4—41no—
590D4—41no—
591D4—41no—
592D4—41no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—861no—
605C2×C4—861no—
606C2×C4—861no—
607C2×C4—861no—
608C2×C4—861no—
609C2×C4—861no—
610C2×C4—861no—
611C2×C4—861no—
612C2×C4—861no—
613C2×C4—861no—
614C2×C4—861no—
615C2×C4—861no—
616C2×C4—862no—
617C2×C4—3444no—
618C2×C4—3444no—
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—1721no—
629C2×C4—1721no—
630C2×C4#1306334912yes—
631C2×C4C2×D4×D4311yescharacteristic
632C2×C4#41×D4311yescharacteristic
633C2×C4C2×#1062190011yescharacteristic
634C2×C4C2×#1062190011yescharacteristic
635C2×C4#1306337111yescharacteristic
636C2×C4#1306337211yescharacteristic
637C8—22no—
638C8—41no—
639C8—862no—
640C8—862no—
641C22—42no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—42no—
646C22—42no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22—81no—
654C22—81no—
655C22#1458344411yescharacteristic
656C22#1458353311yescharacteristic
657C22#1458355511yescharacteristic
658C22C2×#1306334911yescharacteristic
659C22#1458369611yescharacteristic
660C22#1458370911yescharacteristic
661C22#1458370911yescharacteristic
662C4—22no—
663C4—41no—
664C4—81no—
665C4—81no—
666C4—3441no—
667C4—3441no—
668C4—3441no—
669C4—1721no—
670C4—1721no—
671C4—1722no—
672C4—1721no—
673C4—1721no—
674C4#1458340511yescharacteristic
675C4#1458351811yescharacteristic
676C4#1458354711yescharacteristic
677C4#1458357211yescharacteristic
678C2—82no—
679C2—82no—
680C2#1913855511yescharacteristic
681C2#1914520711yescharacteristic
682C2#1914528811yescharacteristic
683C2#1914619011yescharacteristic
684C2#1914623211yescharacteristic
685C2#1914739111yescharacteristic
686C2#1914742611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2054C2
socleC23×C43C22×D4
prime radicalC22×D8×C43C22
hypercenter#2054D43
hypocenterC43#26842
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2054

Complements

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

NH ≅ G/Ntype
1. C2×#14583257C2semidirect
3. #19138448C2semidirect
4. #19138380C2semidirect
5. #19135975C2semidirect
6. #19135927C2semidirect
8. #19135448C2semidirect
9. #19135294C2semidirect
10. #19135283C2semidirect
11. #19135281C2semidirect
12. #19134927C2semidirect
13. #19134854C2semidirect
14. #19134465C2semidirect
404. C43#26842semidirect

Maximal subgroups

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

subgroupindex
C2×#145832572
C2×#145830112
#191384482
#191383802
#191359752
#191359272
#191356702
#191354482
#191352942
#191352832
#191352812
#191349272
#191348542
#191344652
C43×#20542
#2684243