Finite Group Databasebeta

← #25140478

Subgroups — #25140478

Order 11008.

932 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583056C211yesmaximal, characteristic
2C2×#14582991C211yesmaximal, characteristic, complemented
3#19138101C211yesmaximal, characteristic
4Q8×(C2×D43)⋊C4C211yesmaximal, characteristic
5#19136146C211yesmaximal, characteristic, complemented
6#19136022C211yesmaximal, characteristic
7#19135918C211yesmaximal, characteristic, complemented
8#19135794C211yesmaximal, characteristic
9#19135269C211yesmaximal, characteristic, complemented
10#19135200C211yesmaximal, characteristic
11#19134937C211yesmaximal, characteristic, complemented
12#19134936C211yesmaximal, characteristic, complemented
13#19134861C211yesmaximal, characteristic, complemented
14#19134528C211yesmaximal, characteristic
15C43×#1805C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×Dic172C2211yescharacteristic
18C22×#10621885C2211yescharacteristic
19C2×#13063305C2211yescharacteristic
20C2×Q8×Dic43C2211yescharacteristic
21C2×#13063290C2211yescharacteristic
22#14583056—24no—
23#14582991—24no—
24C2×#13063258C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×(C2×D43)⋊C8C2211yescharacteristic
33C2×(C2×D43)⋊C8C2211yescharacteristic
34C2×C8×Dic43C2211yescharacteristic
35#14582841—21no—
36#14582828—21no—
37#14582805—21no—
38#14582805C2211yescharacteristic
39#14582805C2211yescharacteristic
40#14582804—21no—
41#14582804C2211yescharacteristic
42#14582795C2211yescharacteristic
43#14582788—21no—
44#14582786—21no—
45#14582756—21no—
46#14582756C2211yescharacteristic
47#14582756C2211yescharacteristic
48C4×(C2×D43)⋊C4—21no—
49C4×(C2×D43)⋊C4C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582654C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×C4×Q8×C43C2211yescharacteristic
55C2×C4⋊C8×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C43×#382C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86—21no—
62C22×Dic86C2311yescharacteristic
63C22×Dic86C2311yescharacteristic
64C2×Q8×D43—22no—
65C2×Q8×D43—22no—
66C2×Q8×D43—22no—
67C2×Q8×D43—22no—
68C2×Q8×D43—41no—
69C2×Q8×D43—41no—
70C22×C4×D43—21no—
71C22×C4×D43C2311yescharacteristic
72C2×Dic172—22no—
73C2×Dic172—22no—
74C2×Dic172—41no—
75C2×#10621885—22no—
76C2×#10621885—22no—
77C2×#10621885D414yes—
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80#13063305—22no—
81#13063305—41no—
82Q8×Dic43—22no—
83Q8×Dic43—41no—
84#13063290—22no—
85#13063290—41no—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43—21no—
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4D411yescharacteristic
96C2×(C2×D43)⋊C4D411yescharacteristic
97C2×C4×Dic43—21no—
98C2×C4×Dic43—21no—
99C2×C4×Dic43C2311yescharacteristic
100#13063258—22no—
101#13063256—41no—
102#13063250—22no—
103#13063250—22no—
104#13063249—22no—
105#13063248—22no—
106#13063248—41no—
107#13063248—41no—
108(C2×D43)⋊C8—22no—
109(C2×D43)⋊C8—41no—
110C8×Dic43—22no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95D411yescharacteristic
121C43⋊#95D411yescharacteristic
122C22×Q8×C43C2311yescharacteristic
123C22×C8×C43C2311yescharacteristic
124C22×C8×C43C2311yescharacteristic
125C4×Q8×C43—22no—
126C4×Q8×C43—41no—
127C2×C4⋊C4×C43—21no—
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C42×C43—21no—
132C2×C42×C43C2311yescharacteristic
133C4⋊C8×C43—41no—
134#103×C43—22no—
135#103×C43—22no—
136#95×C43—21no—
137#95×C43—21no—
138C23×D43C2×D411yescharacteristic
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43C2×D412yes—
143C2×Q8×C43#4112yes—
144C2×Q8×C43#4112yes—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
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×Dic43C2×D411yescharacteristic
157C22×Dic43C2×D411yescharacteristic
158C22×Dic43C2×D411yescharacteristic
159Q8×D43—44no—
160Q8×D43—44no—
161Q8×D43—44no—
162Q8×D43—44no—
163C2×C4×D43—24no—
164C2×C4×D43—21no—
165C2×C4×D43—21no—
166C2×C4×D43—21no—
167C2×C4×D43—21no—
168C2×C4×D43—21no—
169C2×C4×D43—21no—
170C2×C4×D43—42no—
171C2×C4×D43—42no—
172C2×Dic86—21no—
173C2×Dic86—21no—
174C2×Dic86—21no—
175C2×Dic86—21no—
176C2×Dic86—21no—
177C2×Dic86—21no—
178C2×Dic86—21no—
179C2×Dic86—21no—
180C2×Dic86—24no—
181C2×Dic86—21no—
182C2×Dic86—21no—
183C2×Dic86—42no—
184C2×Dic86—42no—
185C2×Dic86C2×D412yes—
186C2×Dic86#4112yes—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—42no—
200C42×C43—21no—
201C42×C43—21no—
202C42×C43—42no—
203#10621885—28no—
204(C2×D43)⋊C4—22no—
205(C2×D43)⋊C4—22no—
206(C2×D43)⋊C4—42no—
207(C2×D43)⋊C4—42no—
208(C2×D43)⋊C4—42no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—21no—
212C4⋊Dic43—21no—
213C4⋊Dic43—42no—
214C4⋊Dic43—42no—
215Dic43⋊C4—42no—
216Dic43⋊C4—42no—
217C4×Dic43—21no—
218C4×Dic43—21no—
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⋊C8C2×D412yes—
227Dic172—44no—
228C23×C43C22×D411yescharacteristic
229C22×D43—21no—
230C22×D43—21no—
231C22×D43—21no—
232C22×D43—21no—
233C22×D43—21no—
234C22×D43—21no—
235C22×D43#13512yes—
236Q8×C43—22no—
237Q8×C43—22no—
238Q8×C43—22no—
239Q8×C43#12314yes—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
243C2×C4×C43—21no—
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×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C43H(5,𝔽2)11yescharacteristic
263C2×C4×C43H(5,𝔽2)11yescharacteristic
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—22no—
268C2×Dic43—21no—
269C2×Dic43—22no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
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—41no—
284C2×Dic43#13712yes—
285C4×D43—48no—
286C4×D43—41no—
287C4×D43—41no—
288C4×D43—41no—
289C4×D43—41no—
290Dic86—22no—
291Dic86—22no—
292Dic86—22no—
293Dic86—22no—
294Dic86—48no—
295Dic86—41no—
296Dic86—41no—
297Dic86—41no—
298Dic86—41no—
299C8×C43—41no—
300C8×C43—41no—
301C43⋊C8—22no—
302C43⋊C8—41no—
303#24902—431nomaximal, Sylow
304C22×C43#52511yescharacteristic
305C22×C43D4211yescharacteristic
306C22×C43#54611yescharacteristic
307C22×C43C2×#13511yescharacteristic
308C22×C43C2×#13711yescharacteristic
309C22×C43#57811yescharacteristic
310C22×C43#57811yescharacteristic
311C2×D43—22no—
312C2×D43—22no—
313C2×D43—22no—
314C2×D43—41no—
315C2×D43—41no—
316C2×D43—41no—
317C2×D43—41no—
318C4×C43—24no—
319C4×C43—41no—
320C4×C43—41no—
321C4×C43—81no—
322C4×C43—81no—
323C4×C43—81no—
324C4×C43C2×#12311yescharacteristic
325C4×C43#53811yescharacteristic
326C4×C43#54611yescharacteristic
327C4×C43#55111yescharacteristic
328Dic43—22no—
329Dic43—42no—
330Dic43—42no—
331Dic43—41no—
332Dic43—41no—
333Dic43—81no—
334Dic43—81no—
335C2×#451—431no—
336C2×C4×Q16—431no—
337#2421—431no—
338Q8×C22⋊C4—431no—
339#2097—431no—
340#2075—431no—
341#2056—431no—
342#2035—431no—
343#1933—431no—
344#1923—431no—
345#1878—431no—
346#1878—431no—
347#1865—431no—
348#1805D4311yescharacteristic, complemented
349#1787—431no—
350C2×C43#241811yescharacteristic
351C2×C43#310811yescharacteristic
352C2×C43#312711yescharacteristic
353C2×C43#327011yescharacteristic
354C2×C43#328511yescharacteristic
355C2×C43#330011yescharacteristic
356C2×C43#332811yescharacteristic
357D43—42no—
358C23×Q8—431no—
359C22×Q16—431no—
360C22×Q16—431no—
361C2×C22⋊Q8—431no—
362C2×C4×Q8—431no—
363C2×C4×Q8—431no—
364C2×C4×Q8C2×D4311yescharacteristic
365#451—864no—
366C4×Q16—864no—
367C2×#107—431no—
368C2×#106—431no—
369C2×C4⋊C8C2×D4311yescharacteristic
370C2×#103—431no—
371C2×#103—431no—
372C2×#103—431no—
373C2×#103—431no—
374C2×#103—431no—
375C2×#103—431no—
376C2×#103C2×D4311yescharacteristic
377C2×#103C2×D4311yescharacteristic
378C2×C22⋊C8—431no—
379C2×C22⋊C8—431no—
380C2×C4×C8—431no—
381#400—861no—
382#397—861no—
383#391—431no—
384#391—431no—
385#391—431no—
386#391—861no—
387#391—861no—
388#389—431no—
389#388—861no—
390#387—861no—
391#382C2×D4311yescharacteristic
392#380—431no—
393#380—431no—
394#380—861no—
395C4×C22⋊C4—431no—
396C4×C22⋊C4—861no—
397#340—431no—
398#340—431no—
399#340C2×D4311yescharacteristic
400#340C2×D4311yescharacteristic
401#336—431no—
402#336—431no—
403C43#2490211yescharacteristic, complemented, Sylow
404C22×Q8—431no—
405C22×Q8—431no—
406C22×Q8—861no—
407C22×Q8—862no—
408C22×Q8—862no—
409C22×Q8—862no—
410C22×Q8—862no—
411C22×Q8—1721no—
412C22×Q8—1721no—
413C22×Q8C22×D4311yescharacteristic
414C23×C4—431no—
415C23×C4—861no—
416C2×Q16—434no—
417C2×Q16—862no—
418C2×Q16—862no—
419C2×Q16—862no—
420C2×Q16—862no—
421C2×Q16—1721no—
422C22×C8—431no—
423C22×C8—431no—
424C22×C8C22×D4311yescharacteristic
425C22×C8C22×D4311yescharacteristic
426C22⋊Q8—862no—
427C22⋊Q8—1721no—
428C4×Q8—22no—
429C4×Q8—41no—
430C4×Q8—862no—
431C4×Q8—862no—
432C4×Q8—1721no—
433C4×Q8—1721no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—431no—
436C2×C4⋊C4—431no—
437C2×C4⋊C4—861no—
438C2×C4⋊C4—861no—
439C2×C4⋊C4—861no—
440C2×C4⋊C4—861no—
441C2×C4⋊C4C22×D4311yescharacteristic
442C2×C4⋊C4C22×D4311yescharacteristic
443C2×C4⋊C4C22×D4311yescharacteristic
444C2×C22⋊C4—431no—
445C2×C22⋊C4—431no—
446C2×C22⋊C4—861no—
447C2×C22⋊C4—861no—
448C2×C22⋊C4—861no—
449C2×C42—21no—
450C2×C42—431no—
451C2×C42—861no—
452C2×C42—861no—
453C2×C42C22×D4311yescharacteristic
454#107—862no—
455#106—1721no—
456C4⋊C8—41no—
457#103—22no—
458#103—22no—
459#103—862no—
460#103—862no—
461#103—862no—
462#103—862no—
463#103—1721no—
464#103—1721no—
465C22⋊C8—862no—
466C22⋊C8—1721no—
467C4×C8—862no—
468#95—21no—
469#95—21no—
470#95—431no—
471#95—431no—
472#95—861no—
473#95—861no—
474#95—861no—
475#95—861no—
476#95—861no—
477#95—861no—
478#95—861no—
479#95—861no—
480#95—861no—
481C24—431no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—432no—
486C2×Q8—432no—
487C2×Q8—864no—
488C2×Q8—861no—
489C2×Q8—861no—
490C2×Q8—861no—
491C2×Q8—861no—
492C2×Q8—861no—
493C2×Q8—861no—
494C2×Q8—861no—
495C2×Q8—861no—
496C2×Q8—861no—
497C2×Q8—861no—
498C2×Q8—1722no—
499C2×Q8—1722no—
500C2×Q8—1724no—
501C2×Q8—1724no—
502C2×Q8—1724no—
503C2×Q8—1724no—
504C2×Q8#1062189812yes—
505C2×Q8D4×D4312yes—
506C2×Q8#1062190212yes—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—431no—
512C22×C4—431no—
513C22×C4—431no—
514C22×C4—864no—
515C22×C4—861no—
516C22×C4—861no—
517C22×C4—861no—
518C22×C4—861no—
519C22×C4—861no—
520C22×C4—861no—
521C22×C4—861no—
522C22×C4—861no—
523C22×C4—861no—
524C22×C4—861no—
525C22×C4—1722no—
526C22×C4—1722no—
527C22×C4D4×D4311yescharacteristic
528C22×C4D4×D4311yescharacteristic
529C22×C4C23×D4311yescharacteristic
530Q16—868no—
531Q16—1724no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—432no—
539C2×C8—861no—
540C2×C8—861no—
541C2×C8—861no—
542C2×C8—861no—
543C2×C8—861no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—42no—
551C4⋊C4—861no—
552C4⋊C4—861no—
553C4⋊C4—861no—
554C4⋊C4—861no—
555C4⋊C4—1722no—
556C4⋊C4—1722no—
557C4⋊C4—1722no—
558C4⋊C4—1722no—
559C22⋊C4—862no—
560C22⋊C4—862no—
561C22⋊C4—1722no—
562C22⋊C4—1722no—
563C22⋊C4—1722no—
564C42—21no—
565C42—21no—
566C42—42no—
567C42—861no—
568C42—861no—
569C42—1722no—
570C42—1722no—
571C23—432no—
572C23—861no—
573C23—861no—
574C23—861no—
575C23—861no—
576C23—861no—
577C23—861no—
578C23C2×D4×D4311yescharacteristic
579Q8—22no—
580Q8—22no—
581Q8—22no—
582Q8—862no—
583Q8—862no—
584Q8—862no—
585Q8—862no—
586Q8—1728no—
587Q8—1721no—
588Q8—1721no—
589Q8—1721no—
590Q8—1721no—
591Q8#1306331014yes—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—432no—
611C2×C4—861no—
612C2×C4—861no—
613C2×C4—861no—
614C2×C4—862no—
615C2×C4—861no—
616C2×C4—861no—
617C2×C4—861no—
618C2×C4—862no—
619C2×C4—861no—
620C2×C4—861no—
621C2×C4—1728no—
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—1721no—
631C2×C4—1721no—
632C2×C4—1721no—
633C2×C4—1721no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4C2×D4×D4311yescharacteristic
637C2×C4#41×D4311yescharacteristic
638C2×C4C2×#1062189811yescharacteristic
639C2×C4C2×#1062190211yescharacteristic
640C2×C4#1306337011yescharacteristic
641C2×C4#1306337111yescharacteristic
642C8—41no—
643C8—41no—
644C8—862no—
645C8—1721no—
646C22—862no—
647C22—862no—
648C22—862no—
649C22—1721no—
650C22—1721no—
651C22—1721no—
652C22—1721no—
653C22#1458341211yescharacteristic
654C22#1458353311yescharacteristic
655C22#1458353911yescharacteristic
656C22#135×D4311yescharacteristic
657C22#137×D4311yescharacteristic
658C22#1458371311yescharacteristic
659C22#1458371511yescharacteristic
660C4—24no—
661C4—41no—
662C4—41no—
663C4—81no—
664C4—81no—
665C4—81no—
666C4—862no—
667C4—3441no—
668C4—3441no—
669C4—1721no—
670C4—1722no—
671C4—1722no—
672C4—1721no—
673C4C2×#1306331011yescharacteristic
674C4#1458348911yescharacteristic
675C4#1458353811yescharacteristic
676C4#1458357311yescharacteristic
677C2—1722no—
678C2#1913806311yescharacteristic
679C2#1914468011yescharacteristic
680C2#1914489711yescharacteristic
681C2#1914616011yescharacteristic
682C2#1914633111yescharacteristic
683C2#1914648311yescharacteristic
684C2#1914687411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1805C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#1805D43
hypocenterC43#24902
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1805

Complements

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

NH ≅ G/Ntype
2. C2×#14582991C2semidirect
5. #19136146C2semidirect
7. #19135918C2semidirect
9. #19135269C2semidirect
11. #19134937C2semidirect
12. #19134936C2semidirect
13. #19134861C2semidirect
15. C43×#1805C2semidirect
348. #1805D43semidirect
403. C43#24902semidirect

Maximal subgroups

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

subgroupindex
C2×#145830562
C2×#145829912
#191381012
Q8×(C2×D43)⋊C42
#191361462
#191360222
#191359182
#191357942
#191352692
#191352002
#191349372
#191349362
#191348612
#191345282
C43×#18052
#2490243