Finite Group Databasebeta

← #25127689

Subgroups — #25127689

Order 11008.

1734 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C22⋊D43C211yesmaximal, characteristic
2C2×#14583055C211yesmaximal, characteristic, complemented
3C2×#14583053C212yesmaximal, complemented
4#19137954C211yesmaximal, characteristic
5#19135693C212yesmaximal, complemented
6#19135602C212yesmaximal, complemented
7#19135018C211yesmaximal, characteristic, complemented
8#19134938C212yesmaximal, complemented
9#19134887C211yesmaximal, characteristic
10#19134530C211yesmaximal, characteristic, complemented
11C23×Q16×C43C211yesmaximal, characteristic, complemented
12C22×Q8×D43C2211yescharacteristic
13C22×#10621885C2212yes—
14Q8×C22⋊D43—24no—
15Q8×C22⋊D43—24no—
16C2×#13063323—21no—
17C2×#13063323C2211yescharacteristic
18C2×#13063304—21no—
19C2×#13063304C2211yescharacteristic
20C2×#13063301—21no—
21C2×#13063301C2211yescharacteristic
22C2×#13063301C2212yes—
23C2×Q8×Dic43C2211yescharacteristic
24C2×C4×C22⋊D43—21no—
25C2×C4×C22⋊D43C2211yescharacteristic
26#14583055—24no—
27#14583053—28no—
28C2×#13063250C2212yes—
29C2×#13063249C2212yes—
30C2×#13063249C2212yes—
31C2×#13063249C2212yes—
32C2×C22⋊(C43⋊C8)C2211yescharacteristic
33C2×(C2×D43)⋊C8C2212yes—
34#14582818—21no—
35#14582810—21no—
36#14582806C2212yes—
37#14582778—21no—
38#14582772—21no—
39#14582759C2211yescharacteristic
40#14582662C2212yes—
41#14582653C2212yes—
42C23×Q8×C43C2211yescharacteristic
43C23×Q8×C43C2211yescharacteristic
44C22×Q16×C43—24no—
45C22×Q16×C43—28no—
46C22×Q16×C43C2212yes—
47C22×Q16×C43C2212yes—
48C23×C8×C43C2211yescharacteristic
49C22×Dic86—21no—
50C22×Dic86C2311yescharacteristic
51C2×Q8×D43—22no—
52C2×Q8×D43—22no—
53C2×Q8×D43—24no—
54C2×Q8×D43—42no—
55C22×C22⋊D43D411yescharacteristic
56C22×C4×D43—21no—
57C22×C4×D43C2311yescharacteristic
58C2×#10621885—24no—
59C2×#10621885—24no—
60C2×#10621885—42no—
61C22×C43⋊C8C2312yes—
62#13063323—28no—
63#13063323—22no—
64#13063323—22no—
65#13063304—28no—
66#13063304—22no—
67#13063304D414yes—
68#13063301—28no—
69#13063301—22no—
70#13063301—22no—
71#13063301—24no—
72#13063301—42no—
73Q8×Dic43—22no—
74Q8×Dic43—22no—
75C4×C22⋊D43—28no—
76C4×C22⋊D43—22no—
77C4×C22⋊D43—22no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43C2312yes—
80C2×C4⋊Dic43C2311yescharacteristic
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—22no—
86C2×Dic43⋊C4D411yescharacteristic
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43D411yescharacteristic
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—22no—
92C2×(C2×D43)⋊C4D411yescharacteristic
93C2×C4×Dic43—21no—
94C2×C4×Dic43C2311yescharacteristic
95#13063250—24no—
96#13063249—24no—
97#13063249—24no—
98#13063249—42no—
99C22⋊(C43⋊C8)—22no—
100(C2×D43)⋊C8—24no—
101C43⋊#95—21no—
102C43⋊#95—22no—
103C43⋊#95—22no—
104C22×Q8×C43—22no—
105C22×Q8×C43—21no—
106C22×Q8×C43—21no—
107C22×Q8×C43—24no—
108C22×Q8×C43—24no—
109C22×Q8×C43—22no—
110C22×Q8×C43—22no—
111C22×Q8×C43—42no—
112C22×Q8×C43—42no—
113C22×Q8×C43D414yes—
114C22×Q8×C43C2312yes—
115C22×Q8×C43C2311yescharacteristic
116C22×Q8×C43C2311yescharacteristic
117C23×C4×C43—21no—
118C23×C4×C43—21no—
119C23×C4×C43C2311yescharacteristic
120C2×Q16×C43—232no—
121C2×Q16×C43—24no—
122C2×Q16×C43—24no—
123C2×Q16×C43—24no—
124C2×Q16×C43—24no—
125C2×Q16×C43—24no—
126C2×Q16×C43D418yescomplemented
127C22×C8×C43—22no—
128C22×C8×C43—24no—
129C22×C8×C43C2312yes—
130C24×C43C2×D411yescharacteristic
131C23×D43C2×D411yescharacteristic
132C2×Q8×C43—24no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—22no—
136C2×Q8×C43—22no—
137C2×Q8×C43—28no—
138C2×Q8×C43—28no—
139C2×Q8×C43—22no—
140C2×Q8×C43—22no—
141C2×Q8×C43—22no—
142C2×Q8×C43—22no—
143C2×Q8×C43—22no—
144C2×Q8×C43—22no—
145C2×Q8×C43—44no—
146C2×Q8×C43—44no—
147C2×Q8×C43—44no—
148C2×Q8×C43—48no—
149C2×Q8×C43—48no—
150C2×Q8×C43—44no—
151C2×Q8×C43—42no—
152C2×Q8×C43C2×D412yes—
153C2×Q8×C43C2×D414yes—
154C2×Q8×C43C2×D412yes—
155C2×Q8×C43C2×D414yes—
156C22×C4×C43—22no—
157C22×C4×C43—22no—
158C22×C4×C43—24no—
159C22×C4×C43—21no—
160C22×C4×C43—22no—
161C22×C4×C43—21no—
162C22×C4×C43—44no—
163C22×C4×C43—44no—
164C22×C4×C43—42no—
165C22×C4×C43C2×D412yes—
166C22×C4×C43C2×D412yes—
167C22×C4×C43C2×D411yescharacteristic
168C22×C4×C43C2411yescharacteristic
169C2×C22⋊D43—22no—
170C2×C22⋊D43—22no—
171C2×C22⋊D43Q1614yescomplemented
172C22×Dic43—21no—
173C22×Dic43—21no—
174C22×Dic43—22no—
175C22×Dic43C2×D411yescharacteristic
176C22×Dic43C2×D411yescharacteristic
177C22×Dic43C2×D411yescharacteristic
178Q8×D43—48no—
179Q8×D43—44no—
180Q8×D43—44no—
181C2×C4×D43—24no—
182C2×C4×D43—22no—
183C2×C4×D43—21no—
184C2×C4×D43—21no—
185C2×C4×D43—22no—
186C2×C4×D43—44no—
187C2×Dic86—22no—
188C2×Dic86—22no—
189C2×Dic86—24no—
190C2×Dic86—21no—
191C2×Dic86—44no—
192C2×Dic86C2×D412yes—
193Q16×C43—216no—
194Q16×C43—216no—
195C2×C8×C43—28no—
196C2×C8×C43—22no—
197C2×C8×C43—22no—
198C2×C8×C43C2×D414yes—
199C22⋊Dic43—24no—
200C22⋊Dic43—22no—
201C22⋊Dic43—42no—
202#10621885—48no—
203(C2×D43)⋊C4—24no—
204(C2×D43)⋊C4—22no—
205(C2×D43)⋊C4—44no—
206C4⋊Dic43—24no—
207C4⋊Dic43—21no—
208C4⋊Dic43—22no—
209C4⋊Dic43—22no—
210C4⋊Dic43C2×D412yes—
211Dic43⋊C4—24no—
212Dic43⋊C4—24no—
213Dic43⋊C4—24no—
214Dic43⋊C4—24no—
215Dic43⋊C4—22no—
216Dic43⋊C4—44no—
217C4×Dic43—24no—
218C4×Dic43—21no—
219C4×Dic43—21no—
220C2×C43⋊C8—22no—
221C2×C43⋊C8—22no—
222C2×C43⋊C8—22no—
223C23×C43—22no—
224C23×C43—22no—
225C23×C43#12012yes—
226C23×C43C2×Q1612yes—
227C23×C43#13712yes—
228C23×C43C22×D411yescharacteristic
229C22×D43—21no—
230C22×D43—22no—
231C22×D43—21no—
232C22×D43—22no—
233C22×D43C2×Q1612yescomplemented
234Q8×C43—22no—
235Q8×C43—24no—
236Q8×C43—22no—
237Q8×C43—24no—
238Q8×C43—22no—
239Q8×C43—24no—
240Q8×C43—48no—
241Q8×C43—48no—
242Q8×C43—42no—
243Q8×C43—42no—
244Q8×C43—42no—
245Q8×C43#12014yes—
246C2×C4×C43—22no—
247C2×C4×C43—24no—
248C2×C4×C43—22no—
249C2×C4×C43—22no—
250C2×C4×C43—22no—
251C2×C4×C43—24no—
252C2×C4×C43—22no—
253C2×C4×C43—24no—
254C2×C4×C43—48no—
255C2×C4×C43—48no—
256C2×C4×C43—42no—
257C2×C4×C43—42no—
258C2×C4×C43—42no—
259C2×C4×C43#12012yes—
260C2×C4×C43C22×D411yescharacteristic
261C2×C4×C43C22×D411yescharacteristic
262C2×C4×C43C22×D412yes—
263C2×C4×C43H(5,𝔽2)12yes—
264C22⋊D43—28no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—22no—
269C2×Dic43—21no—
270C2×Dic43—22no—
271C2×Dic43—22no—
272C2×Dic43—22no—
273C2×Dic43—42no—
274C2×Dic43—42no—
275C2×Dic43—42no—
276C2×Dic43—42no—
277C2×Dic43—42no—
278C2×Dic43C2×Q1612yescomplemented
279C4×D43—48no—
280C4×D43—41no—
281C4×D43—41no—
282C4×D43—42no—
283Dic86—24no—
284Dic86—48no—
285Dic86—41no—
286Dic86—41no—
287C8×C43—24no—
288C43⋊C8—42no—
289#23856—431nomaximal, Sylow
290C22×C43—22no—
291C22×C43—22no—
292C22×C43—24no—
293C22×C43—24no—
294C22×C43#45114yescomplemented
295C22×C43C2×#12011yescharacteristic
296C22×C43D4212yes—
297C22×C43C22×Q1611yescharacteristic
298C22×C43C2×#13711yescharacteristic
299C22×C43#57812yes—
300C2×D43—22no—
301C2×D43—24no—
302C2×D43—41no—
303C2×D43—41no—
304C2×D43—42no—
305C4×C43—24no—
306C4×C43—22no—
307C4×C43—42no—
308C4×C43—44no—
309C4×C43C2×#12011yescharacteristic
310C4×C43#53411yescharacteristic
311C4×C43D4212yes—
312Dic43—22no—
313Dic43—42no—
314Dic43—41no—
315Dic43—41no—
316Dic43—42no—
317Dic43—82no—
318C23×Q16D4311yescharacteristic, complemented
319C2×D4×Q8—431no—
320C2×#451—431no—
321C2×#451—432no—
322#2409—431no—
323#2016—432no—
324#2001—432no—
325#1892—431no—
326#1878—432no—
327#1869—431no—
328#1787—431no—
329C2×C43—24no—
330C2×C43#240311yescharacteristic
331C2×C43C2×#45111yescharacteristic
332C2×C43#301111yescharacteristic
333C2×C43#327012yes—
334C2×C43D4×Q1612yes—
335D43—42no—
336C23×Q8—431no—
337C23×Q8C2×D4311yescharacteristic
338C23×Q8C2×D4311yescharacteristic
339C22×Q16—24no—
340C22×Q16—28no—
341C22×Q16—432no—
342C22×Q16C2×D4312yes—
343C22×Q16C2×D4312yes—
344C23×C8C2×D4311yescharacteristic
345D4×Q8—864no—
346D4×Q8—864no—
347C2×C4⋊Q8—431no—
348C2×C4⋊Q8—861no—
349C2×C22⋊Q8—431no—
350C2×C22⋊Q8—431no—
351C2×C22⋊Q8—432no—
352C2×C22⋊Q8—861no—
353C2×C22⋊Q8—861no—
354C2×C4×Q8—431no—
355C2×C4×D4—431no—
356C2×C4×D4—861no—
357#451—864no—
358#451—868no—
359C2×#103—432no—
360C2×#103—432no—
361C2×#103—432no—
362C2×#103—432no—
363C2×C22⋊C8—431no—
364C2×C22⋊C8—432no—
365#395—861no—
366#393—861no—
367#391—432no—
368#386—861no—
369#385—861no—
370#380—431no—
371#340—432no—
372#336—432no—
373C43#2385611yescharacteristic, complemented, Sylow
374C22×Q8—21no—
375C22×Q8—22no—
376C22×Q8—21no—
377C22×Q8—24no—
378C22×Q8—24no—
379C22×Q8—22no—
380C22×Q8—22no—
381C22×Q8—42no—
382C22×Q8—42no—
383C22×Q8—431no—
384C22×Q8—861no—
385C22×Q8—862no—
386C22×Q8—862no—
387C22×Q8—864no—
388C22×Q8—1722no—
389C22×Q8C22⋊D4314yes—
390C22×Q8C22×D4311yescharacteristic
391C22×Q8C22×D4312yes—
392C22×Q8C22×D4311yescharacteristic
393C22×D4—431no—
394C23×C4—21no—
395C23×C4—21no—
396C23×C4—431no—
397C23×C4—861no—
398C23×C4C22×D4311yescharacteristic
399C2×Q16—232no—
400C2×Q16—24no—
401C2×Q16—24no—
402C2×Q16—24no—
403C2×Q16—24no—
404C2×Q16—24no—
405C2×Q16—864no—
406C2×Q16—864no—
407C2×Q16—1722no—
408C2×Q16C22⋊D4318yescomplemented
409C22×C8—22no—
410C22×C8—24no—
411C22×C8—432no—
412C22×C8C22×D4312yes—
413C4⋊Q8—862no—
414C4⋊Q8—868no—
415C4⋊Q8—862no—
416C22⋊Q8—434no—
417C22⋊Q8—862no—
418C22⋊Q8—868no—
419C22⋊Q8—868no—
420C22⋊Q8—862no—
421C22⋊Q8—862no—
422C22⋊Q8—864no—
423C22⋊Q8—1722no—
424C4×Q8—862no—
425C4×Q8—862no—
426C4×D4—868no—
427C4×D4—862no—
428C4×D4—862no—
429C2×C4⋊C4—431no—
430C2×C4⋊C4—431no—
431C2×C4⋊C4—432no—
432C2×C4⋊C4—861no—
433C2×C4⋊C4—861no—
434C2×C4⋊C4—861no—
435C2×C4⋊C4—861no—
436C2×C4⋊C4—861no—
437C2×C4⋊C4—862no—
438C2×C22⋊C4—431no—
439C2×C22⋊C4—431no—
440C2×C22⋊C4—861no—
441C2×C22⋊C4—861no—
442C2×C22⋊C4—862no—
443C2×C22⋊C4—861no—
444C2×C42—431no—
445C2×C42—861no—
446#103—864no—
447#103—864no—
448#103—864no—
449#103—1722no—
450C22⋊C8—862no—
451C22⋊C8—864no—
452#95—862no—
453#95—862no—
454#95—861no—
455C24—431no—
456C24D4×D4311yescharacteristic
457C2×Q8—24no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—22no—
461C2×Q8—22no—
462C2×Q8—28no—
463C2×Q8—28no—
464C2×Q8—22no—
465C2×Q8—22no—
466C2×Q8—22no—
467C2×Q8—22no—
468C2×Q8—22no—
469C2×Q8—22no—
470C2×Q8—44no—
471C2×Q8—44no—
472C2×Q8—44no—
473C2×Q8—48no—
474C2×Q8—48no—
475C2×Q8—44no—
476C2×Q8—42no—
477C2×Q8—432no—
478C2×Q8—864no—
479C2×Q8—861no—
480C2×Q8—862no—
481C2×Q8—862no—
482C2×Q8—1724no—
483C2×Q8—1728no—
484C2×Q8—1724no—
485C2×Q8—1724no—
486C2×Q8C2×C22⋊D4312yes—
487C2×Q8C2×C22⋊D4314yes—
488C2×Q8C2×C22⋊D4314yes—
489C2×Q8C2×C22⋊D4312yes—
490C2×D4—434no—
491C2×D4—862no—
492C2×D4—862no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—44no—
500C22×C4—44no—
501C22×C4—42no—
502C22×C4—431no—
503C22×C4—431no—
504C22×C4—431no—
505C22×C4—864no—
506C22×C4—861no—
507C22×C4—861no—
508C22×C4—861no—
509C22×C4—862no—
510C22×C4—861no—
511C22×C4—862no—
512C22×C4—862no—
513C22×C4—1724no—
514C22×C4D4×D4311yescharacteristic
515C22×C4D4×D4312yes—
516C22×C4C2×C22⋊D4312yes—
517C22×C4C23×D4311yescharacteristic
518Q16—216no—
519Q16—216no—
520Q16—1728no—
521C2×C8—28no—
522C2×C8—22no—
523C2×C8—22no—
524C2×C8—862no—
525C2×C8—862no—
526C2×C8—862no—
527C2×C8C2×C22⋊D4314yes—
528C4⋊C4—432no—
529C4⋊C4—864no—
530C4⋊C4—864no—
531C4⋊C4—864no—
532C4⋊C4—864no—
533C4⋊C4—862no—
534C4⋊C4—864no—
535C4⋊C4—861no—
536C4⋊C4—862no—
537C4⋊C4—862no—
538C4⋊C4—1724no—
539C22⋊C4—864no—
540C22⋊C4—862no—
541C22⋊C4—864no—
542C22⋊C4—862no—
543C22⋊C4—1724no—
544C22⋊C4—1722no—
545C42—864no—
546C42—861no—
547C42—861no—
548C23—22no—
549C23—22no—
550C23—432no—
551C23—861no—
552C23—861no—
553C23—862no—
554C23—862no—
555C23#1306329312yes—
556C23Q16×D4312yes—
557C23#1306335712yes—
558C23C2×D4×D4311yescharacteristic
559Q8—22no—
560Q8—24no—
561Q8—22no—
562Q8—24no—
563Q8—22no—
564Q8—24no—
565Q8—48no—
566Q8—48no—
567Q8—42no—
568Q8—42no—
569Q8—42no—
570Q8—864no—
571Q8—1728no—
572Q8—1721no—
573Q8—1721no—
574Q8#1306329414yes—
575D4—868no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—24no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—24no—
582C2×C4—22no—
583C2×C4—24no—
584C2×C4—48no—
585C2×C4—48no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—432no—
590C2×C4—861no—
591C2×C4—861no—
592C2×C4—862no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—862no—
596C2×C4—862no—
597C2×C4—862no—
598C2×C4—1728no—
599C2×C4—1722no—
600C2×C4—1722no—
601C2×C4—1722no—
602C2×C4—1722no—
603C2×C4—1722no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1722no—
607C2×C4#1306329312yes—
608C2×C4C2×D4×D4311yescharacteristic
609C2×C4C22×C22⋊D4311yescharacteristic
610C2×C4C22×C22⋊D4312yes—
611C2×C4#1306337012yes—
612C8—24no—
613C8—1722no—
614C22—24no—
615C22—22no—
616C22—24no—
617C22—22no—
618C22—864no—
619C22—862no—
620C22—1721no—
621C22—1722no—
622C22—1721no—
623C22#1458305314yescomplemented
624C22C2×#1306329311yescharacteristic
625C22D4×C22⋊D4312yes—
626C22C2×Q16×D4311yescharacteristic
627C22C2×#1306335711yescharacteristic
628C22#1458371212yes—
629C4—22no—
630C4—24no—
631C4—42no—
632C4—44no—
633C4—862no—
634C4—3442no—
635C4—1721no—
636C4—1722no—
637C4—1721no—
638C4—1722no—
639C4C2×#1306329411yescharacteristic
640C4#1458345811yescharacteristic
641C4D4×C22⋊D4312yes—
642C2—24no—
643C2—1722no—
644C2#1913790511yescharacteristic
645C2C2×#1458305311yescharacteristic
646C2#1914388611yescharacteristic
647C2#1914616512yes—
648C2Q16×C22⋊D4312yes—
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC23×Q16×C43C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
hypercenterC23×Q16D43
hypocenterC43#23856
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×Q16

Complements

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

NH ≅ G/Ntype
2. C2×#14583055C2semidirect
3. C2×#14583053C2semidirect
5. #19135693C2semidirect
6. #19135602C2semidirect
7. #19135018C2semidirect
8. #19134938C2semidirect
10. #19134530C2semidirect
11. C23×Q16×C43C2semidirect
126. C2×Q16×C43D4semidirect
171. C2×C22⋊D43Q16semidirect
233. C22×D43C2×Q16semidirect
278. C2×Dic43C2×Q16semidirect
294. C22×C43#451semidirect
318. C23×Q16D43semidirect
373. C43#23856semidirect
408. C2×Q16C22⋊D43semidirect
623. C22#14583053semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C22⋊D432
C2×#145830552
C2×#145830532
#191379542
#191356932
#191356022
#191350182
#191349382
#191348872
#191345302
C23×Q16×C432
#2385643