Finite Group Databasebeta

← #25199443

Subgroups — #25199443

Order 11008.

868 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137123C211yesmaximal, characteristic, complemented
2#121×Dic43C211yesmaximal, characteristic
3#19136026C211yesmaximal, characteristic, complemented
4#19135799C211yesmaximal, characteristic, complemented
5#19135598C211yesmaximal, characteristic
6#19135228C211yesmaximal, characteristic, complemented
7#19135217C211yesmaximal, characteristic, complemented
8#19135182C211yesmaximal, characteristic, complemented
9#19135165C211yesmaximal, characteristic, complemented
10#19134947C211yesmaximal, characteristic, complemented
11#19134927C211yesmaximal, characteristic, complemented
12#19134850C211yesmaximal, characteristic, complemented
13#19134840C211yesmaximal, characteristic, complemented
14#19134661C211yesmaximal, characteristic, complemented
15C43×#2034C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C2×#13063304C2211yescharacteristic
18C2×#13063290C2211yescharacteristic
19C2×D4×Dic43—21no—
20C2×D4×Dic43C2211yescharacteristic
21C22×C4×Dic43C2211yescharacteristic
22C2×#13063259C2211yescharacteristic
23C2×#13063258C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063248C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×C22⋊(C43⋊C8)C2211yescharacteristic
29#14582804C2211yescharacteristic
30#14582802C2211yescharacteristic
31#14582798C2211yescharacteristic
32#14582795C2211yescharacteristic
33#14582792—21no—
34#14582781—21no—
35#14582779—21no—
36#14582771—21no—
37#14582759C2211yescharacteristic
38C4⋊C4×Dic43C2211yescharacteristic
39C4⋊C4×Dic43C2211yescharacteristic
40#14582750—21no—
41C22⋊C4×Dic43—21no—
42C22⋊C4×Dic43—21no—
43#14582662C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582653C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#121×C43C2211yescharacteristic
53C2×#106×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C23×Dic43—21no—
61C23×Dic43D411yescharacteristic
62C23×Dic43D411yescharacteristic
63C2×#10621883—22no—
64C2×#10621883—22no—
65C2×#10621883—41no—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68#13063304—22no—
69#13063304—22no—
70#13063290—41no—
71#13063290—41no—
72D4×Dic43—41no—
73D4×Dic43—41no—
74D4×Dic43—44no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43—41no—
91C2×C4×Dic43—41no—
92C2×C4×Dic43D411yescharacteristic
93C2×C4×Dic43D411yescharacteristic
94C2×C4×Dic43C2311yescharacteristic
95C2×C4×Dic43C2311yescharacteristic
96#13063259—22no—
97#13063258—41no—
98#13063250—22no—
99#13063250—41no—
100#13063248—22no—
101#13063246—22no—
102C22⋊(C43⋊C8)—41no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C22×D4×C43—21no—
111C22×D4×C43C2311yescharacteristic
112C23×C4×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115#121×C43—22no—
116#121×C43—22no—
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122#106×C43—22no—
123#102×C43—22no—
124#102×C43—41no—
125C22⋊C8×C43—41no—
126#95×C43—21no—
127C24×C43—21no—
128C24×C43C2×D411yescharacteristic
129C2×D4×C43—24no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—42no—
136C2×D4×C43—42no—
137C2×D4×C43#4112yes—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2411yescharacteristic
149C22×Dic43—22no—
150C22×Dic43—22no—
151C22×Dic43—22no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—41no—
157C22×Dic43—41no—
158C22×Dic43—41no—
159C22×Dic43—42no—
160C22×Dic43—42no—
161C22×Dic43—42no—
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#4112yes—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×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#4112yes—
184C22⋊C4×C43—24no—
185C22⋊C4×C43—42no—
186C22⋊Dic43—24no—
187C22⋊Dic43—42no—
188C22⋊Dic43—42no—
189C22⋊Dic43—42no—
190C22⋊Dic43—42no—
191#10621883—44no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—42no—
198C4⋊Dic43#4112yes—
199Dic43⋊C4—24no—
200Dic43⋊C4—42no—
201Dic43⋊C4—42no—
202C4×Dic43—21no—
203C4×Dic43—21no—
204C4×Dic43—21no—
205C4×Dic43—21no—
206C4×Dic43—41no—
207C4×Dic43—41no—
208C4×Dic43—42no—
209C4×Dic43—42no—
210C4×Dic43—42no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C23×C43—21no—
218C23×C43—21no—
219C23×C43—21no—
220C23×C43—21no—
221C23×C43—21no—
222C23×C43—21no—
223C23×C43—22no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43—41no—
229C23×C43—41no—
230C23×C43#13712yes—
231C23×C43C22×D411yescharacteristic
232D4×C43—22no—
233D4×C43—22no—
234D4×C43—48no—
235D4×C43—41no—
236D4×C43—41no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—22no—
240C2×C4×C43—21no—
241C2×C4×C43—41no—
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×C43C2×#4111yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43H(5,𝔽2)11yescharacteristic
258C2×C4×C43H(5,𝔽2)11yescharacteristic
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—22no—
264C2×Dic43—22no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—44no—
272C2×Dic43—44no—
273C2×Dic43—41no—
274C2×Dic43—41no—
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—84no—
284C2×Dic43#13512yes—
285C2×Dic43AGL(1,ℤ/8)12yes—
286Dic86—22no—
287Dic86—22no—
288Dic86—41no—
289Dic86—41no—
290C8×C43—41no—
291C8×C43—41no—
292C43⋊C8—41no—
293C43⋊C8—41no—
294#29414—431nomaximal, Sylow
295C22×C43—22no—
296C22×C43—22no—
297C22×C43—22no—
298C22×C43—41no—
299C22×C43—41no—
300C22×C43—41no—
301C22×C43—41no—
302C22×C43—42no—
303C22×C43—42no—
304C22×C43—42no—
305C22×C43—81no—
306C22×C43—81no—
307C22×C43—81no—
308C22×C43—81no—
309C22×C43#52511yescharacteristic
310C22×C43#52511yescharacteristic
311C22×C43#53411yescharacteristic
312C22×C43C2×#13511yescharacteristic
313C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
314C22×C43C2×#13711yescharacteristic
315C22×C43#57511yescharacteristic
316C4×C43—42no—
317C4×C43—41no—
318C4×C43—81no—
319C4×C43—81no—
320C4×C43#55111yescharacteristic
321C4×C43#55311yescharacteristic
322C4×C43#55311yescharacteristic
323C4×C43#55911yescharacteristic
324Dic43—22no—
325Dic43—22no—
326Dic43—42no—
327Dic43—42no—
328Dic43—41no—
329Dic43—41no—
330Dic43—81no—
331Dic43—81no—
332C4×C22⋊Q8—431no—
333C4×#121—431no—
334#2076—431no—
335#2036—431no—
336#2034D4311yescharacteristic
337#2000—431no—
338#1927—431no—
339#1925—431no—
340#1920—431no—
341#1918—431no—
342#1880—431no—
343#1877—431no—
344#1863—431no—
345#1862—431no—
346#1817—431no—
347C2×C43—42no—
348C2×C43—82no—
349C2×C43#260011yescharacteristic
350C2×C43#310211yescharacteristic
351C2×C43#310611yescharacteristic
352C2×C43#311011yescharacteristic
353C2×C43#311711yescharacteristic
354C2×C43#319011yescharacteristic
355C2×C43#319411yescharacteristic
356C22×SD16—431no—
357C2×C22⋊Q8—431no—
358C2×#121C2×D4311yescharacteristic
359C2×C4×Q8—431no—
360C2×C4×D4—431no—
361C2×C4×D4—861no—
362C22×C42—431no—
363C2×#107—431no—
364C2×#107—431no—
365C2×#106C2×D4311yescharacteristic
366C2×#103—431no—
367C2×#103—431no—
368C2×#103—431no—
369C2×#102—431no—
370C2×#102C2×D4311yescharacteristic
371C2×#102C2×D4311yescharacteristic
372C2×C22⋊C8—431no—
373C2×C22⋊C8C2×D4311yescharacteristic
374#391—431no—
375#390—431no—
376#389—431no—
377#389—431no—
378#388—861no—
379#387—861no—
380#386—861no—
381#385—861no—
382#380—431no—
383#380C2×D4311yescharacteristic
384C4×C4⋊C4—431no—
385C4×C4⋊C4—431no—
386C4×C4⋊C4—861no—
387C4×C22⋊C4—861no—
388C4×C22⋊C4—861no—
389#340—431no—
390#340—431no—
391#340—431no—
392#340—431no—
393#340—431no—
394#340C2×D4311yescharacteristic
395#336—431no—
396#336—431no—
397#336—431no—
398#336—431no—
399C43#2941411yescharacteristic, complemented, Sylow
400C22×Q8—431no—
401C22×D4—21no—
402C22×D4C22×D4311yescharacteristic
403C23×C4—431no—
404C23×C4—431no—
405C23×C4—861no—
406C23×C4C22×D4311yescharacteristic
407C2×SD16—862no—
408C2×SD16—862no—
409C2×SD16—1721no—
410C22×C8—431no—
411C22×C8—431no—
412C22×C8C22×D4311yescharacteristic
413C22×C8C22×D4311yescharacteristic
414C22⋊Q8—862no—
415C22⋊Q8—862no—
416#121—22no—
417#121—22no—
418C4×Q8—1721no—
419C4×Q8—1721no—
420C4×D4—1721no—
421C4×D4—1721no—
422C4×D4—1724no—
423C2×C4⋊C4—431no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—431no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4C22×D4311yescharacteristic
431C2×C4⋊C4C22×D4311yescharacteristic
432C2×C4⋊C4C22×D4311yescharacteristic
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—861no—
436C2×C22⋊C4—861no—
437C2×C22⋊C4—861no—
438C2×C22⋊C4—861no—
439C2×C22⋊C4—861no—
440C2×C42—431no—
441C2×C42—431no—
442C2×C42—431no—
443C2×C42—431no—
444C2×C42—861no—
445C2×C42—861no—
446C2×C42—861no—
447C2×C42—1721no—
448C2×C42—1721no—
449#107—862no—
450#107—1721no—
451#106—22no—
452#103—862no—
453#103—862no—
454#103—1721no—
455#102—22no—
456#102—41no—
457#102—862no—
458C22⋊C8—41no—
459C22⋊C8—1721no—
460#95—21no—
461#95—861no—
462#95—861no—
463#95—861no—
464#95—861no—
465#95—861no—
466#95—861no—
467#95—861no—
468C24—21no—
469C24D4×D4311yescharacteristic
470C2×Q8—432no—
471C2×Q8—861no—
472C2×Q8—861no—
473C2×Q8—861no—
474C2×Q8—861no—
475C2×Q8—861no—
476C2×D4—24no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—42no—
483C2×D4—42no—
484C2×D4#1062190012yes—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—431no—
495C22×C4—431no—
496C22×C4—431no—
497C22×C4—431no—
498C22×C4—862no—
499C22×C4—862no—
500C22×C4—862no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4—861no—
504C22×C4—861no—
505C22×C4—1722no—
506C22×C4—1721no—
507C22×C4—1721no—
508C22×C4—1721no—
509C22×C4—1722no—
510C22×C4—1722no—
511C22×C4D4×D4311yescharacteristic
512C22×C4C23×D4311yescharacteristic
513SD16—1724no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—861no—
523C2×C8—861no—
524C2×C8—861no—
525C2×C8—861no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—432no—
532C4⋊C4—864no—
533C4⋊C4—861no—
534C4⋊C4—861no—
535C4⋊C4—861no—
536C4⋊C4—861no—
537C4⋊C4—861no—
538C4⋊C4—1722no—
539C4⋊C4—1722no—
540C4⋊C4—1722no—
541C4⋊C4#1062190012yes—
542C22⋊C4—24no—
543C22⋊C4—42no—
544C22⋊C4—864no—
545C22⋊C4—1722no—
546C22⋊C4—1722no—
547C22⋊C4—1722no—
548C22⋊C4—1722no—
549C42—861no—
550C42—861no—
551C42—861no—
552C42—861no—
553C42—1721no—
554C42—1721no—
555C42—1722no—
556C42—1722no—
557C42—1722no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—22no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23#1306335412yes—
572C23C2×D4×D4311yescharacteristic
573Q8—862no—
574Q8—862no—
575Q8—1721no—
576Q8—1721no—
577D4—22no—
578D4—22no—
579D4—48no—
580D4—41no—
581D4—41no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—21no—
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—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—432no—
599C2×C4—432no—
600C2×C4—861no—
601C2×C4—861no—
602C2×C4—861no—
603C2×C4—861no—
604C2×C4—862no—
605C2×C4—862no—
606C2×C4—861no—
607C2×C4—861no—
608C2×C4—861no—
609C2×C4—861no—
610C2×C4—861no—
611C2×C4—861no—
612C2×C4—3444no—
613C2×C4—1724no—
614C2×C4—1724no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4—1721no—
620C2×C4—1721no—
621C2×C4—1721no—
622C2×C4—1721no—
623C2×C4—1721no—
624C2×C4—1721no—
625C2×C4#41×D4311yescharacteristic
626C2×C4#41×D4311yescharacteristic
627C2×C4C2×#1062190011yescharacteristic
628C2×C4C2×#1062190011yescharacteristic
629C2×C4#1306337011yescharacteristic
630C2×C4#1306337111yescharacteristic
631C8—41no—
632C8—41no—
633C8—1721no—
634C8—1721no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—81no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22#1458340511yescharacteristic
650C22#1458340711yescharacteristic
651C22#1458345711yescharacteristic
652C22#135×D4311yescharacteristic
653C22AGL(1,ℤ/8)×D4311yescharacteristic
654C22C2×#1306335411yescharacteristic
655C22#1458369511yescharacteristic
656C4—41no—
657C4—42no—
658C4—81no—
659C4—81no—
660C4—862no—
661C4—862no—
662C4—3441no—
663C4—3441no—
664C4—1722no—
665C4—1721no—
666C4—1721no—
667C4—1722no—
668C4#1458357211yescharacteristic
669C4#1458359211yescharacteristic
670C4#1458359611yescharacteristic
671C4#1458363111yescharacteristic
672C2—42no—
673C2—82no—
674C2#1914017811yescharacteristic
675C2#1914460611yescharacteristic
676C2#1914465011yescharacteristic
677C2#1914468911yescharacteristic
678C2#1914476311yescharacteristic
679C2#1914537111yescharacteristic
680C2#1914540411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2034C2
socleC23×C43C22×D4
prime radicalC2×#121×C43C22
hypercenter#2034D43
hypocenterC43#29414
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2034

Complements

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

NH ≅ G/Ntype
1. #19137123C2semidirect
3. #19136026C2semidirect
4. #19135799C2semidirect
6. #19135228C2semidirect
7. #19135217C2semidirect
8. #19135182C2semidirect
9. #19135165C2semidirect
10. #19134947C2semidirect
11. #19134927C2semidirect
12. #19134850C2semidirect
13. #19134840C2semidirect
14. #19134661C2semidirect
399. C43#29414semidirect

Maximal subgroups

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

subgroupindex
#191371232
#121×Dic432
#191360262
#191357992
#191355982
#191352282
#191352172
#191351822
#191351652
#191349472
#191349272
#191348502
#191348402
#191346612
C43×#20342
#2941443