Finite Group Databasebeta

← #25105627

Subgroups — #25105627

Order 11008.

1498 conjugacy classes of subgroups.

The subgroup lattice has 622 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#19136977C211yesmaximal, characteristic
4#19135019C211yesmaximal, characteristic, complemented
5#19135018C211yesmaximal, characteristic, complemented
6#19135016C211yesmaximal, characteristic, complemented
7#19134906C212yesmaximal, complemented
8#19134904C212yesmaximal, complemented
9#19134680C212yesmaximal, 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×#13063283C2212yes—
23C2×C4⋊C4×D43—21no—
24C2×C4⋊C4×D43C2211yescharacteristic
25C2×C22⋊C4×D43—21no—
26C2×#13063250C2212yescomplemented
27C2×#13063249C2212yescomplemented
28C2×#13063248C2212yescomplemented
29C2×(C2×D43)⋊C8—24no—
30C2×(C2×D43)⋊C8C2212yes—
31C2×(C2×D43)⋊C8C2212yes—
32#14582761—21no—
33#14582759C2211yescharacteristic
34#14582756C2212yes—
35#14582754—21no—
36C22⋊C4×Dic43—21no—
37#14582746—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×C414yes—
53C23×Dic43D411yescharacteristic
54C22×C4×D43—21no—
55C22×C4×D43—21no—
56C22×C4×D43—42no—
57C22×C4×D43—42no—
58C22×C4×D43C2×C414yes—
59C22×C4×D43D411yescharacteristic
60C22×C4×D43D411yescharacteristic
61C22×C4×D43D414yes—
62C22×C4×D43C2311yescharacteristic
63C22×C4×D43C2311yescharacteristic
64C22×C43⋊C8—22no—
65C22×C43⋊C8—42no—
66C22×C43⋊C8C2312yes—
67#13063305—22no—
68#13063305C2×C414yes—
69#13063304—22no—
70#13063304C2×C414yes—
71#13063303—28no—
72#13063302—28no—
73#13063301—22no—
74#13063301C2×C414yes—
75#13063283—42no—
76#13063283—42no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43C2312yes—
79C2×C4⋊Dic43C2311yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C4⋊C4×D43—28no—
84C4⋊C4×D43—22no—
85C4⋊C4×D43C2×C414yes—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—22no—
91C2×(C2×D43)⋊C4—22no—
92C22⋊C4×D43—28no—
93C2×C4×Dic43—22no—
94#13063250—42no—
95#13063249—42no—
96#13063248—42no—
97(C2×D43)⋊C8—24no—
98(C2×D43)⋊C8—24no—
99C43⋊#95—21no—
100C43⋊#95—22no—
101C22×Q8×C43C2311yescharacteristic
102C23×C4×C43C2311yescharacteristic
103C22×C8×C43—22no—
104C22×C8×C43—42no—
105C22×C8×C43C2312yes—
106C22⋊Q8×C43—22no—
107C22⋊Q8×C43C2×C414yes—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43C2312yes—
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43—21no—
113#103×C43—42no—
114#95×C43—21no—
115C24×C43C2×D411yescharacteristic
116C23×D43—22no—
117C23×D43—22no—
118C23×D43—24no—
119C23×D43—42no—
120C23×D43C22⋊C414yes—
121C23×D43C2×D411yescharacteristic
122C23×D43C2×D411yescharacteristic
123C2×Q8×C43—21no—
124C2×Q8×C43—22no—
125C2×Q8×C43—22no—
126C2×Q8×C43C22×C412yes—
127C22×C4×C43—22no—
128C22×C4×C43—22no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—22no—
132C22×C4×C43C22×C412yes—
133C22×C4×C43C2×D412yes—
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2411yescharacteristic
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—22no—
139C22×Dic43—42no—
140C22×Dic43C22⋊C414yes—
141C22×Dic43C2×D411yescharacteristic
142C22×Dic43C2×D411yescharacteristic
143Q8×D43—48no—
144Q8×D43—44no—
145Q8×D43—44no—
146C2×C4×D43—22no—
147C2×C4×D43—22no—
148C2×C4×D43—22no—
149C2×C4×D43—22no—
150C2×C4×D43—24no—
151C2×C4×D43—24no—
152C2×C4×D43—42no—
153C2×C4×D43—42no—
154C2×C4×D43—44no—
155C2×C4×D43—48no—
156C2×C4×D43—44no—
157C2×C4×D43—44no—
158C2×C4×D43—44no—
159C2×C4×D43C22⋊C414yes—
160C2×C4×D43C22⋊C414yes—
161C2×C4×D43C22×C412yes—
162C2×C4×D43C22×C412yes—
163C2×C4×D43C2×D412yes—
164C2×C4×D43C2×D412yes—
165C2×Dic86—22no—
166C2×Dic86—22no—
167C2×Dic86—21no—
168C2×Dic86—24no—
169C2×Dic86—44no—
170C2×Dic86C22×C412yes—
171C2×C8×C43—22no—
172C2×C8×C43—22no—
173C2×C8×C43—22no—
174C2×C8×C43—44no—
175C4⋊C4×C43—24no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—22no—
178C4⋊C4×C43—22no—
179C4⋊C4×C43C22×C412yes—
180C22⋊C4×C43—24no—
181C22⋊C4×C43—42no—
182C22⋊Dic43—24no—
183C22⋊Dic43—42no—
184(C2×D43)⋊C4—24no—
185(C2×D43)⋊C4—24no—
186(C2×D43)⋊C4—44no—
187(C2×D43)⋊C4—44no—
188C4⋊Dic43—21no—
189C4⋊Dic43—24no—
190C4⋊Dic43—22no—
191C4⋊Dic43—22no—
192C4⋊Dic43C22×C412yes—
193Dic43⋊C4—24no—
194Dic43⋊C4—24no—
195Dic43⋊C4—24no—
196C4×Dic43—44no—
197C2×C43⋊C8—22no—
198C2×C43⋊C8—22no—
199C2×C43⋊C8—22no—
200C2×C43⋊C8—44no—
201C23×C43—22no—
202C23×C43—22no—
203C23×C43C2×C22⋊C412yes—
204C23×C43#13712yes—
205C23×C43#13712yes—
206C23×C43C22×D411yescharacteristic
207C22×D43—22no—
208C22×D43—21no—
209C22×D43—21no—
210C22×D43—22no—
211C22×D43—22no—
212C22×D43—21no—
213C22×D43—21no—
214C22×D43—28no—
215C22×D43—28no—
216C22×D43—44no—
217C22×D43—48no—
218C22×D43—48no—
219C22×D43C2×C22⋊C412yes—
220C22×D43C2×C22⋊C412yes—
221C22×D43#13514yes—
222Q8×C43—24no—
223Q8×C43—41no—
224Q8×C43—41no—
225C2×C4×C43—22no—
226C2×C4×C43—24no—
227C2×C4×C43—22no—
228C2×C4×C43—22no—
229C2×C4×C43—22no—
230C2×C4×C43—22no—
231C2×C4×C43—42no—
232C2×C4×C43—42no—
233C2×C4×C43—42no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43C2×C22⋊C412yes—
237C2×C4×C43C23×C411yescharacteristic
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43H(5,𝔽2)12yes—
240C2×C4×C43H(5,𝔽2)12yes—
241C2×Dic43—22no—
242C2×Dic43—22no—
243C2×Dic43—22no—
244C2×Dic43—22no—
245C2×Dic43—44no—
246C2×Dic43—42no—
247C2×Dic43—42no—
248C2×Dic43—42no—
249C2×Dic43—42no—
250C2×Dic43—42no—
251C2×Dic43C2×C22⋊C412yes—
252C2×Dic43C2×C22⋊C412yes—
253C4×D43—24no—
254C4×D43—24no—
255C4×D43—22no—
256C4×D43—22no—
257C4×D43—22no—
258C4×D43—22no—
259C4×D43—44no—
260C4×D43—44no—
261C4×D43—48no—
262C4×D43—48no—
263Dic86—24no—
264Dic86—48no—
265Dic86—41no—
266Dic86—41no—
267C8×C43—42no—
268C43⋊C8—42no—
269#21762—431nomaximal, Sylow
270C22×C43—22no—
271C22×C43—22no—
272C22×C43—24no—
273C22×C43—24no—
274C22×C43#41914yes—
275C22×C43C22×C22⋊C411yescharacteristic
276C22×C43#53412yes—
277C22×C43C2×#13512yes—
278C22×C43C2×#13711yescharacteristic
279C22×C43C2×#13711yescharacteristic
280C2×D43—22no—
281C2×D43—22no—
282C2×D43—24no—
283C2×D43—24no—
284C2×D43—22no—
285C2×D43—22no—
286C2×D43—22no—
287C2×D43—416no—
288C2×D43—42no—
289C2×D43—42no—
290C2×D43#41614yes—
291C4×C43—22no—
292C4×C43—42no—
293C4×C43—42no—
294C4×C43—82no—
295C4×C43#51812yes—
296C4×C43#53411yescharacteristic
297C4×C43#53411yescharacteristic
298Dic43—22no—
299Dic43—22no—
300Dic43—42no—
301Dic43—42no—
302Dic43—82no—
303C22×C22⋊Q8—431no—
304C22×C22⋊C8—431no—
305#2280—431no—
306#1892—431no—
307#1892—431no—
308#1892—431no—
309#1892D4311yescharacteristic, complemented
310#1873—432no—
311#1873—432no—
312#1823—432no—
313#1787—432no—
314C2×C43—24no—
315C2×C43#230811yescharacteristic
316C2×C43C2×#41611yescharacteristic
317C2×C43C2×#41911yescharacteristic
318C2×C43#319012yes—
319C2×C43#319012yes—
320D43—24no—
321D43—42no—
322C23×Q8—431no—
323C24×C4—431no—
324C23×C8—431no—
325C23×C8C2×D4311yescharacteristic
326C2×C22⋊Q8—431no—
327C2×C22⋊Q8—431no—
328C2×C22⋊Q8—438no—
329C2×C22⋊Q8—431no—
330C2×C22⋊Q8—861no—
331C2×C22⋊Q8—861no—
332C2×C22⋊Q8—864no—
333C2×C22⋊Q8C2×D4311yescharacteristic
334C2×#117—432no—
335C22×C4⋊C4—431no—
336C22×C4⋊C4—861no—
337C22×C22⋊C4—861no—
338C2×#103—432no—
339C2×#103—432no—
340C2×#103—432no—
341C2×#103C2×D4312yescomplemented
342C2×C22⋊C8—432no—
343C2×C22⋊C8—432no—
344C2×C22⋊C8—864no—
345#381—861no—
346#380—431no—
347#380—432no—
348#380C2×D4311yescharacteristic
349#379—861no—
350C4×C22⋊C4—861no—
351C4×C22⋊C4—861no—
352#340—432no—
353#340—432no—
354#340—432no—
355#340C2×D4312yescomplemented
356C43#2176211yescharacteristic, complemented, Sylow
357C25—431no—
358C22×Q8—434no—
359C22×Q8—431no—
360C22×Q8—861no—
361C22×Q8—862no—
362C22×Q8—1722no—
363C22×Q8—1722no—
364C22×Q8C22×D4311yescharacteristic
365C23×C4—431no—
366C23×C4—431no—
367C23×C4—431no—
368C23×C4—434no—
369C23×C4—431no—
370C23×C4—431no—
371C23×C4—434no—
372C23×C4—861no—
373C23×C4—861no—
374C23×C4—1722no—
375C23×C4—1722no—
376C23×C4C22×D4311yescharacteristic
377C22×C8—22no—
378C22×C8—42no—
379C22×C8—432no—
380C22×C8—862no—
381C22×C8—1722no—
382C22×C8C22×D4312yes—
383C22⋊Q8—22no—
384C22⋊Q8—434no—
385C22⋊Q8—434no—
386C22⋊Q8—434no—
387C22⋊Q8—868no—
388C22⋊Q8—868no—
389C22⋊Q8—862no—
390C22⋊Q8—862no—
391C22⋊Q8—862no—
392C22⋊Q8C4×D4314yes—
393#117—1722no—
394#117—1722no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—434no—
398C2×C4⋊C4—432no—
399C2×C4⋊C4—862no—
400C2×C4⋊C4—868no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4C22×D4312yes—
406C2×C4⋊C4C22×D4311yescharacteristic
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—868no—
410C2×C22⋊C4—861no—
411C2×C22⋊C4—861no—
412C2×C22⋊C4—861no—
413C2×C22⋊C4—862no—
414C2×C22⋊C4—862no—
415C2×C22⋊C4—861no—
416C2×C42—862no—
417#103—42no—
418#103—1722no—
419#103—1722no—
420#103—1722no—
421C22⋊C8—864no—
422C22⋊C8—864no—
423#95—21no—
424#95—862no—
425#95—861no—
426C24—431no—
427C24—431no—
428C24—434no—
429C24—864no—
430C24—862no—
431C24—862no—
432C24—1722no—
433C24D4×D4311yescharacteristic
434C2×Q8—21no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—432no—
438C2×Q8—864no—
439C2×Q8—861no—
440C2×Q8—862no—
441C2×Q8—862no—
442C2×Q8—1724no—
443C2×Q8—1728no—
444C2×Q8—1724no—
445C2×Q8—1724no—
446C2×Q8C2×C4×D4312yes—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—431no—
453C22×C4—431no—
454C22×C4—434no—
455C22×C4—432no—
456C22×C4—432no—
457C22×C4—432no—
458C22×C4—432no—
459C22×C4—434no—
460C22×C4—434no—
461C22×C4—864no—
462C22×C4—864no—
463C22×C4—862no—
464C22×C4—862no—
465C22×C4—862no—
466C22×C4—862no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—862no—
470C22×C4—1728no—
471C22×C4—1724no—
472C22×C4—1724no—
473C22×C4—1722no—
474C22×C4—1722no—
475C22×C4—1724no—
476C22×C4—1724no—
477C22×C4—1722no—
478C22×C4C2×C4×D4312yes—
479C22×C4D4×D4311yescharacteristic
480C22×C4D4×D4312yes—
481C22×C4C23×D4311yescharacteristic
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—44no—
486C2×C8—862no—
487C2×C8—862no—
488C2×C8—862no—
489C2×C8—1724no—
490C4⋊C4—24no—
491C4⋊C4—21no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—432no—
495C4⋊C4—864no—
496C4⋊C4—864no—
497C4⋊C4—864no—
498C4⋊C4—864no—
499C4⋊C4—861no—
500C4⋊C4—862no—
501C4⋊C4—862no—
502C4⋊C4C2×C4×D4312yes—
503C22⋊C4—24no—
504C22⋊C4—42no—
505C22⋊C4—864no—
506C22⋊C4—864no—
507C22⋊C4—864no—
508C22⋊C4—1724no—
509C22⋊C4—1724no—
510C22⋊C4—1722no—
511C42—1724no—
512C23—22no—
513C23—22no—
514C23—432no—
515C23—434no—
516C23—432no—
517C23—868no—
518C23—861no—
519C23—861no—
520C23—862no—
521C23—868no—
522C23—862no—
523C23—861no—
524C23—861no—
525C23—862no—
526C23—1724no—
527C23—1728no—
528C23—1728no—
529C23C22⋊C4×D4312yes—
530C23#1306335412yes—
531C23#1306335712yes—
532C23C2×D4×D4311yescharacteristic
533Q8—24no—
534Q8—41no—
535Q8—41no—
536Q8—864no—
537Q8—1728no—
538Q8—1721no—
539Q8—1721no—
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—432no—
552C2×C4—432no—
553C2×C4—862no—
554C2×C4—862no—
555C2×C4—864no—
556C2×C4—864no—
557C2×C4—862no—
558C2×C4—862no—
559C2×C4—862no—
560C2×C4—862no—
561C2×C4—862no—
562C2×C4—862no—
563C2×C4—1724no—
564C2×C4—1724no—
565C2×C4—1728no—
566C2×C4—1728no—
567C2×C4—1724no—
568C2×C4—1722no—
569C2×C4—1722no—
570C2×C4—1722no—
571C2×C4—1722no—
572C2×C4—1722no—
573C2×C4C22⋊C4×D4312yes—
574C2×C4C22×C4×D4311yescharacteristic
575C2×C4C2×D4×D4311yescharacteristic
576C2×C4#1306337012yes—
577C2×C4#1306337112yes—
578C8—42no—
579C8—1722no—
580C22—22no—
581C22—24no—
582C22—24no—
583C22—22no—
584C22—434no—
585C22—862no—
586C22—864no—
587C22—864no—
588C22—862no—
589C22—862no—
590C22—862no—
591C22—862no—
592C22—17216no—
593C22—1722no—
594C22—1722no—
595C22#1458290614yes—
596C22C2×C22⋊C4×D4311yescharacteristic
597C22#1458345712yes—
598C22#135×D4312yes—
599C22C2×#1306335411yescharacteristic
600C22C2×#1306335711yescharacteristic
601C4—22no—
602C4—42no—
603C4—42no—
604C4—82no—
605C4—862no—
606C4—862no—
607C4—3442no—
608C4—1722no—
609C4—1722no—
610C4#1458337112yes—
611C4#1458345911yescharacteristic
612C4#1458346011yescharacteristic
613C2—24no—
614C2—864no—
615C2—1722no—
616C2#1913716911yescharacteristic
617C2#416×D4311yescharacteristic
618C2C2×#1458290611yescharacteristic
619C2#1914537112yes—
620C2#1914537712yes—
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#21762
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. #19134906C2semidirect
8. #19134904C2semidirect
9. #19134680C2semidirect
10. #19134528C2semidirect
11. C43×#1892C2semidirect
21. C22⋊Q8×D43C4semidirect
26. C2×#13063250C22semidirect
27. C2×#13063249C22semidirect
28. C2×#13063248C22semidirect
38. #14582662C22semidirect
39. #14582661C22semidirect
40. #14582661C22semidirect
43. C2×#103×C43C22semidirect
45. C43×#340C22semidirect
309. #1892D43semidirect
341. C2×#103C2×D43semidirect
355. #340C2×D43semidirect
356. C43#21762semidirect

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
#191369772
#191350192
#191350182
#191350162
#191349062
#191349042
#191346802
#191345282
C43×#18922
#2176243