Finite Group Databasebeta

← #25105604

Subgroups — #25105604

Order 11008.

1570 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D43C211yesmaximal, characteristic
2C22×(C2×D43)⋊C8C211yesmaximal, characteristic
3#380×D43C211yesmaximal, characteristic
4#19135019C211yesmaximal, characteristic, complemented
5#19135018C211yesmaximal, characteristic, complemented
6#19135016C211yesmaximal, characteristic, complemented
7#19134901C212yesmaximal, complemented
8#19134899C212yesmaximal, complemented
9#19134684C212yesmaximal, complemented
10#19134528C212yesmaximal, complemented
11C43×#1892C211yesmaximal, characteristic, complemented
12C22×Q8×D43C2211yescharacteristic
13C23×C4×D43C2211yescharacteristic
14C23×C43⋊C8C2211yescharacteristic
15C2×#13063305C2211yescharacteristic
16C2×#13063304C2211yescharacteristic
17C2×#13063303—21no—
18C2×#13063302—21no—
19C2×#13063301C2211yescharacteristic
20C22⋊Q8×D43—24no—
21C22⋊Q8×D43C418yescomplemented
22C2×C4⋊C4×D43—21no—
23C2×C4⋊C4×D43C2211yescharacteristic
24C2×C4⋊C4×D43C2212yes—
25C2×C22⋊C4×D43—21no—
26C2×C22⋊C4×D43—21no—
27C2×#13063250C2212yescomplemented
28C2×#13063249C2212yescomplemented
29C2×#13063248C2212yescomplemented
30C2×(C2×D43)⋊C8—24no—
31C2×(C2×D43)⋊C8C2212yes—
32C2×(C2×D43)⋊C8C2212yes—
33#14582759C2211yescharacteristic
34#14582758—21no—
35#14582757—21no—
36#14582756C2212yes—
37#95×D43—21no—
38#14582662C2212yescomplemented
39#14582661C2212yescomplemented
40#14582661C2212yescomplemented
41C23×C8×C43C2211yescharacteristic
42C2×C22⋊Q8×C43C2211yescharacteristic
43C2×#103×C43C2212yescomplemented
44C43×#380C2211yescharacteristic
45C43×#340C2212yescomplemented
46C24×D43D411yescharacteristic
47C22×Dic86—21no—
48C22×Dic86C2311yescharacteristic
49C2×Q8×D43—22no—
50C2×Q8×D43—42no—
51C2×Q8×D43—42no—
52C2×Q8×D43C2×C414yescomplemented
53C23×Dic43D411yescharacteristic
54C22×C4×D43—21no—
55C22×C4×D43—21no—
56C22×C4×D43—22no—
57C22×C4×D43—42no—
58C22×C4×D43—42no—
59C22×C4×D43C2×C414yes—
60C22×C4×D43D411yescharacteristic
61C22×C4×D43D411yescharacteristic
62C22×C4×D43D414yes—
63C22×C4×D43C2311yescharacteristic
64C22×C4×D43C2311yescharacteristic
65C22×C43⋊C8—22no—
66C22×C43⋊C8—42no—
67C22×C43⋊C8C2312yes—
68#13063305—22no—
69#13063305C2×C414yes—
70#13063304—22no—
71#13063304C2×C414yescomplemented
72#13063303—28no—
73#13063302—28no—
74#13063301—22no—
75#13063301C2×C414yes—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43C2312yes—
78C2×C4⋊Dic43C2311yescharacteristic
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—22no—
83C4⋊C4×D43—28no—
84C4⋊C4×D43—22no—
85C4⋊C4×D43—42no—
86C4⋊C4×D43—42no—
87C4⋊C4×D43C2×C414yescomplemented
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—22no—
93C22⋊C4×D43—28no—
94C22⋊C4×D43—44no—
95#13063250—42no—
96#13063249—42no—
97#13063248—42no—
98(C2×D43)⋊C8—24no—
99(C2×D43)⋊C8—24no—
100C43⋊#95—21no—
101C43⋊#95—22no—
102C22×Q8×C43C2311yescharacteristic
103C23×C4×C43C2311yescharacteristic
104C22×C8×C43—22no—
105C22×C8×C43—42no—
106C22×C8×C43C2312yes—
107C22⋊Q8×C43—22no—
108C22⋊Q8×C43C2×C414yescomplemented
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43C2312yes—
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114#103×C43—42no—
115#95×C43—21no—
116C24×C43C2×D411yescharacteristic
117C23×D43—42no—
118C23×D43—42no—
119C23×D43C22⋊C414yes—
120C23×D43SD1614yes—
121C23×D43Q1614yes—
122C23×D43C2×D411yescharacteristic
123C23×D43C2×D411yescharacteristic
124C2×Q8×C43—21no—
125C2×Q8×C43—22no—
126C2×Q8×C43—22no—
127C2×Q8×C43C22×C412yes—
128C22×C4×C43—22no—
129C22×C4×C43—22no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—22no—
133C22×C4×C43C22×C412yes—
134C22×C4×C43C2×D412yes—
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2411yescharacteristic
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—22no—
140C22×Dic43—42no—
141C22×Dic43C22⋊C414yes—
142C22×Dic43C2×D411yescharacteristic
143C22×Dic43C2×D411yescharacteristic
144Q8×D43—48no—
145Q8×D43—44no—
146Q8×D43—44no—
147C2×C4×D43—22no—
148C2×C4×D43—22no—
149C2×C4×D43—22no—
150C2×C4×D43—22no—
151C2×C4×D43—24no—
152C2×C4×D43—24no—
153C2×C4×D43—42no—
154C2×C4×D43—42no—
155C2×C4×D43—44no—
156C2×C4×D43—44no—
157C2×C4×D43—44no—
158C2×C4×D43—44no—
159C2×C4×D43—48no—
160C2×C4×D43—44no—
161C2×C4×D43—44no—
162C2×C4×D43—44no—
163C2×C4×D43C22⋊C414yes—
164C2×C4×D43C22⋊C414yes—
165C2×C4×D43C22×C412yes—
166C2×C4×D43C22×C412yes—
167C2×C4×D43C2×D412yes—
168C2×C4×D43C2×D412yes—
169C2×Dic86—22no—
170C2×Dic86—22no—
171C2×Dic86—21no—
172C2×Dic86—24no—
173C2×Dic86—44no—
174C2×Dic86C22×C412yes—
175C2×C8×C43—22no—
176C2×C8×C43—22no—
177C2×C8×C43—22no—
178C2×C8×C43—44no—
179C4⋊C4×C43—24no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—22no—
182C4⋊C4×C43—22no—
183C4⋊C4×C43C22×C412yes—
184C22⋊C4×C43—24no—
185C22⋊C4×C43—42no—
186C22⋊Dic43—24no—
187C22⋊Dic43—42no—
188(C2×D43)⋊C4—24no—
189(C2×D43)⋊C4—24no—
190(C2×D43)⋊C4—44no—
191C4⋊Dic43—21no—
192C4⋊Dic43—24no—
193C4⋊Dic43—22no—
194C4⋊Dic43—22no—
195C4⋊Dic43C22×C412yes—
196Dic43⋊C4—24no—
197Dic43⋊C4—24no—
198Dic43⋊C4—24no—
199Dic43⋊C4—44no—
200C2×C43⋊C8—22no—
201C2×C43⋊C8—22no—
202C2×C43⋊C8—22no—
203C2×C43⋊C8—44no—
204C23×C43—22no—
205C23×C43—22no—
206C23×C43C2×C22⋊C412yes—
207C23×C43C2×SD1612yes—
208C23×C43C2×Q1612yes—
209C23×C43C22×D411yescharacteristic
210C22×D43—22no—
211C22×D43—22no—
212C22×D43—22no—
213C22×D43—22no—
214C22×D43—44no—
215C22×D43—44no—
216C22×D43—48no—
217C22×D43—48no—
218C22×D43#103116yescomplemented
219C22×D43C2×C22⋊C412yes—
220C22×D43C2×C22⋊C412yes—
221C22×D43C2×SD1612yes—
222C22×D43C2×SD1612yes—
223C22×D43C2×Q1612yes—
224C22×D43C2×Q1612yes—
225Q8×C43—24no—
226Q8×C43—41no—
227Q8×C43—41no—
228C2×C4×C43—22no—
229C2×C4×C43—24no—
230C2×C4×C43—22no—
231C2×C4×C43—22no—
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43—42no—
237C2×C4×C43—42no—
238C2×C4×C43—42no—
239C2×C4×C43C2×C22⋊C412yes—
240C2×C4×C43C23×C411yescharacteristic
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43H(5,𝔽2)12yes—
243C2×C4×C43H(5,𝔽2)12yes—
244C2×Dic43—22no—
245C2×Dic43—22no—
246C2×Dic43—22no—
247C2×Dic43—22no—
248C2×Dic43—44no—
249C2×Dic43—42no—
250C2×Dic43—42no—
251C2×Dic43—42no—
252C2×Dic43—42no—
253C2×Dic43—42no—
254C2×Dic43C2×C22⋊C412yes—
255C2×Dic43C2×C22⋊C412yes—
256C4×D43—24no—
257C4×D43—24no—
258C4×D43—22no—
259C4×D43—22no—
260C4×D43—22no—
261C4×D43—22no—
262C4×D43—44no—
263C4×D43—44no—
264C4×D43—48no—
265C4×D43—48no—
266C4×D43—88no—
267Dic86—24no—
268Dic86—48no—
269Dic86—41no—
270Dic86—41no—
271C8×C43—42no—
272C43⋊C8—42no—
273#21759—431nomaximal, Sylow
274C22×C43—22no—
275C22×C43—22no—
276C22×C43—24no—
277C22×C43—24no—
278C22×C43C2×#10314yes—
279C22×C43C22×C22⋊C411yescharacteristic
280C22×C43#53412yes—
281C22×C43C22×SD1611yescharacteristic
282C22×C43C22×Q1611yescharacteristic
283C22×C43#57512yes—
284C2×D43—22no—
285C2×D43—22no—
286C2×D43—22no—
287C2×D43—22no—
288C2×D43—24no—
289C2×D43—24no—
290C2×D43—24no—
291C2×D43—24no—
292C2×D43—416no—
293C2×D43C2×#10314yes—
294C2×D43C2×#10314yes—
295C4×C43—22no—
296C4×C43—42no—
297C4×C43—42no—
298C4×C43—82no—
299C4×C43#51812yes—
300C4×C43#53411yescharacteristic
301C4×C43#53411yescharacteristic
302Dic43—22no—
303Dic43—22no—
304Dic43—42no—
305Dic43—42no—
306Dic43—82no—
307C22×C22⋊Q8—431no—
308C22×C22⋊C8—431no—
309C2×#380—431no—
310#1892—431no—
311#1892—431no—
312#1892—431no—
313#1892D4311yescharacteristic, complemented
314#1872—432no—
315#1872—432no—
316#1824—432no—
317#1787—432no—
318C2×C43—24no—
319C2×C43#230811yescharacteristic
320C2×C43C22×#10311yescharacteristic
321C2×C43#289611yescharacteristic
322C2×C43#318712yes—
323C2×C43#318912yes—
324D43—24no—
325D43—24no—
326C23×Q8—431no—
327C24×C4—431no—
328C23×C8—431no—
329C23×C8C2×D4311yescharacteristic
330C2×C22⋊Q8—431no—
331C2×C22⋊Q8—431no—
332C2×C22⋊Q8—438no—
333C2×C22⋊Q8—431no—
334C2×C22⋊Q8—861no—
335C2×C22⋊Q8—861no—
336C2×C22⋊Q8—864no—
337C2×C22⋊Q8C2×D4311yescharacteristic
338C22×C4⋊C4—431no—
339C22×C4⋊C4—432no—
340C22×C4⋊C4—861no—
341C22×C22⋊C4—861no—
342C22×C22⋊C4—861no—
343C2×#103—432no—
344C2×#103—432no—
345C2×#103—432no—
346C2×#103C2×D4312yescomplemented
347C2×C22⋊C8—432no—
348C2×C22⋊C8—432no—
349C2×C22⋊C8—864no—
350#380—431no—
351#380—432no—
352#380—861no—
353#380—861no—
354#380C2×D4311yescharacteristic
355C2×#95—861no—
356#340—432no—
357#340—432no—
358#340—432no—
359#340C2×D4312yescomplemented
360C43#2175911yescharacteristic, complemented, Sylow
361C25—431no—
362C22×Q8—434no—
363C22×Q8—431no—
364C22×Q8—861no—
365C22×Q8—862no—
366C22×Q8—1722no—
367C22×Q8—1722no—
368C22×Q8C22×D4311yescharacteristic
369C23×C4—431no—
370C23×C4—431no—
371C23×C4—431no—
372C23×C4—434no—
373C23×C4—431no—
374C23×C4—431no—
375C23×C4—434no—
376C23×C4—861no—
377C23×C4—861no—
378C23×C4—862no—
379C23×C4—1722no—
380C23×C4—1722no—
381C23×C4C22×D4311yescharacteristic
382C22×C8—22no—
383C22×C8—42no—
384C22×C8—432no—
385C22×C8—862no—
386C22×C8—1722no—
387C22×C8C22×D4312yes—
388C22⋊Q8—22no—
389C22⋊Q8—434no—
390C22⋊Q8—434no—
391C22⋊Q8—434no—
392C22⋊Q8—868no—
393C22⋊Q8—868no—
394C22⋊Q8—862no—
395C22⋊Q8—862no—
396C22⋊Q8—862no—
397C22⋊Q8C4×D4314yescomplemented
398C2×C4⋊C4—21no—
399C2×C4⋊C4—431no—
400C2×C4⋊C4—434no—
401C2×C4⋊C4—432no—
402C2×C4⋊C4—862no—
403C2×C4⋊C4—868no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4—861no—
406C2×C4⋊C4—861no—
407C2×C4⋊C4—861no—
408C2×C4⋊C4—862no—
409C2×C4⋊C4—1722no—
410C2×C4⋊C4—1722no—
411C2×C4⋊C4C22×D4312yes—
412C2×C4⋊C4C22×D4311yescharacteristic
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—868no—
416C2×C22⋊C4—861no—
417C2×C22⋊C4—861no—
418C2×C22⋊C4—861no—
419C2×C22⋊C4—862no—
420C2×C22⋊C4—861no—
421C2×C22⋊C4—1724no—
422#103—42no—
423#103—1722no—
424#103—1722no—
425#103—1722no—
426C22⋊C8—864no—
427C22⋊C8—864no—
428#95—21no—
429#95—862no—
430#95—861no—
431C24—431no—
432C24—431no—
433C24—434no—
434C24—434no—
435C24—434no—
436C24—1722no—
437C24—1722no—
438C24D4×D4311yescharacteristic
439C2×Q8—21no—
440C2×Q8—22no—
441C2×Q8—22no—
442C2×Q8—432no—
443C2×Q8—864no—
444C2×Q8—861no—
445C2×Q8—862no—
446C2×Q8—862no—
447C2×Q8—1724no—
448C2×Q8—1728no—
449C2×Q8—1724no—
450C2×Q8—1724no—
451C2×Q8C2×C4×D4312yes—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—431no—
458C22×C4—431no—
459C22×C4—434no—
460C22×C4—432no—
461C22×C4—432no—
462C22×C4—432no—
463C22×C4—432no—
464C22×C4—434no—
465C22×C4—434no—
466C22×C4—864no—
467C22×C4—864no—
468C22×C4—862no—
469C22×C4—862no—
470C22×C4—862no—
471C22×C4—862no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—862no—
475C22×C4—1728no—
476C22×C4—1724no—
477C22×C4—1724no—
478C22×C4—1722no—
479C22×C4—1722no—
480C22×C4—1724no—
481C22×C4—1724no—
482C22×C4—1724no—
483C22×C4—1724no—
484C22×C4—1724no—
485C22×C4—1722no—
486C22×C4C2×C4×D4312yes—
487C22×C4D4×D4311yescharacteristic
488C22×C4D4×D4312yes—
489C22×C4C23×D4311yescharacteristic
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—22no—
493C2×C8—44no—
494C2×C8—862no—
495C2×C8—862no—
496C2×C8—862no—
497C2×C8—1724no—
498C4⋊C4—24no—
499C4⋊C4—21no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—432no—
503C4⋊C4—864no—
504C4⋊C4—864no—
505C4⋊C4—864no—
506C4⋊C4—864no—
507C4⋊C4—861no—
508C4⋊C4—862no—
509C4⋊C4—862no—
510C4⋊C4—1724no—
511C4⋊C4C2×C4×D4312yes—
512C22⋊C4—24no—
513C22⋊C4—42no—
514C22⋊C4—864no—
515C22⋊C4—864no—
516C22⋊C4—864no—
517C22⋊C4—1724no—
518C22⋊C4—1722no—
519C23—22no—
520C23—22no—
521C23—432no—
522C23—432no—
523C23—432no—
524C23—432no—
525C23—432no—
526C23—432no—
527C23—4316no—
528C23—862no—
529C23—862no—
530C23—862no—
531C23—862no—
532C23—1724no—
533C23—1728no—
534C23—1728no—
535C23—1724no—
536C23C22⋊C4×D4312yes—
537C23SD16×D4312yes—
538C23Q16×D4312yes—
539C23C2×D4×D4311yescharacteristic
540Q8—24no—
541Q8—41no—
542Q8—41no—
543Q8—864no—
544Q8—1728no—
545Q8—1721no—
546Q8—1721no—
547C2×C4—22no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—432no—
559C2×C4—432no—
560C2×C4—862no—
561C2×C4—862no—
562C2×C4—864no—
563C2×C4—864no—
564C2×C4—862no—
565C2×C4—862no—
566C2×C4—862no—
567C2×C4—862no—
568C2×C4—862no—
569C2×C4—862no—
570C2×C4—3448no—
571C2×C4—1724no—
572C2×C4—1724no—
573C2×C4—1728no—
574C2×C4—1728no—
575C2×C4—1724no—
576C2×C4—1722no—
577C2×C4—1722no—
578C2×C4—1722no—
579C2×C4—1722no—
580C2×C4—1722no—
581C2×C4C22⋊C4×D4312yes—
582C2×C4C22×C4×D4311yescharacteristic
583C2×C4C2×D4×D4311yescharacteristic
584C2×C4#1306337012yes—
585C2×C4#1306337112yes—
586C8—42no—
587C8—1722no—
588C22—24no—
589C22—22no—
590C22—24no—
591C22—22no—
592C22—434no—
593C22—434no—
594C22—864no—
595C22—864no—
596C22—862no—
597C22—862no—
598C22—864no—
599C22—864no—
600C22—862no—
601C22—862no—
602C22—17216no—
603C22#103×D4314yes—
604C22C2×C22⋊C4×D4311yescharacteristic
605C22#1458345712yes—
606C22C2×SD16×D4311yescharacteristic
607C22C2×Q16×D4311yescharacteristic
608C22#1458369612yes—
609C4—22no—
610C4—42no—
611C4—42no—
612C4—82no—
613C4—862no—
614C4—862no—
615C4—3442no—
616C4—1722no—
617C4—1722no—
618C4#1458337112yes—
619C4#1458345911yescharacteristic
620C4#1458346011yescharacteristic
621C2—24no—
622C2—864no—
623C2—864no—
624C2#1913716911yescharacteristic
625C2C2×#103×D4311yescharacteristic
626C2#1914311011yescharacteristic
627C2#1914534712yes—
628C2#1914536612yes—
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1892C2
socleC23×C43C22×D4
prime radicalC24×D43D4
cosocleC22×C4×C43C24
hypercenter#1892D43
hypocenterC43#21759
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1892

Complements

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

NH ≅ G/Ntype
4. #19135019C2semidirect
5. #19135018C2semidirect
6. #19135016C2semidirect
7. #19134901C2semidirect
8. #19134899C2semidirect
9. #19134684C2semidirect
10. #19134528C2semidirect
11. C43×#1892C2semidirect
21. C22⋊Q8×D43C4semidirect
27. C2×#13063250C22semidirect
28. C2×#13063249C22semidirect
29. C2×#13063248C22semidirect
38. #14582662C22semidirect
39. #14582661C22semidirect
40. #14582661C22semidirect
43. C2×#103×C43C22semidirect
45. C43×#340C22semidirect
52. C2×Q8×D43C2×C4semidirect
71. #13063304C2×C4semidirect
87. C4⋊C4×D43C2×C4semidirect
108. C22⋊Q8×C43C2×C4semidirect
218. C22×D43#103semidirect
313. #1892D43semidirect
346. C2×#103C2×D43semidirect
359. #340C2×D43semidirect
360. C43#21759semidirect
397. C22⋊Q8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D432
C22×(C2×D43)⋊C82
#380×D432
#191350192
#191350182
#191350162
#191349012
#191348992
#191346842
#191345282
C43×#18922
#2175943