Finite Group Databasebeta

← #25103816

Subgroups — #25103816

Order 11008.

964 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583233C211yesmaximal, characteristic
2#19137133C211yesmaximal, characteristic
3C4×C4⋊C4×D43C211yesmaximal, characteristic
4#19135226C211yesmaximal, characteristic, complemented
5#19135167C211yesmaximal, characteristic, complemented
6#19135166C211yesmaximal, characteristic, complemented
7#19134899C211yesmaximal, characteristic
8#19134786C211yesmaximal, characteristic
9#19134684C211yesmaximal, characteristic
10#19134495C211yesmaximal, characteristic, complemented
11#19134491C211yesmaximal, characteristic, complemented
12#19134427C211yesmaximal, characteristic, complemented
13#19134427C211yesmaximal, characteristic, complemented
14#19134356C211yesmaximal, characteristic
15C43×#1927C211yesmaximal, characteristic, complemented
16C2×#13063301C2211yescharacteristic
17C2×Q8×Dic43C2211yescharacteristic
18C2×C4⋊C4×D43C2211yescharacteristic
19C2×C4⋊C4×D43C2211yescharacteristic
20C2×C42×D43—21no—
21C2×C42×D43C2211yescharacteristic
22#14583233C418yescomplemented
23C2×#13063259C2211yescharacteristic
24C2×#13063258C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×(C2×D43)⋊C8C2211yescharacteristic
29C2×(C2×D43)⋊C8C2211yescharacteristic
30C2×#13063235C2211yescharacteristic
31C2×#13063235C2211yescharacteristic
32#14582797C2211yescharacteristic
33#14582786—21no—
34#14582773—21no—
35#14582756C2211yescharacteristic
36C4⋊C4×Dic43C2211yescharacteristic
37C4⋊C4×Dic43C2211yescharacteristic
38C4⋊C4×Dic43C2211yescharacteristic
39C4×Dic43⋊C4—21no—
40C4×C4⋊Dic43C2211yescharacteristic
41#14582750—21no—
42#14582750—21no—
43#14582746—21no—
44#95×D43—21no—
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582654C2211yescharacteristic
53C2×#106×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C43×#391C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C22×C4×D43—21no—
61C22×C4×D43—21no—
62C22×C4×D43D411yescharacteristic
63C22×C4×D43D411yescharacteristic
64C22×C4×D43C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063301—22no—
68#13063301C2×C414yes—
69Q8×Dic43—22no—
70Q8×Dic43—22no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C4⋊C4×D43—22no—
81C4⋊C4×D43—22no—
82C4⋊C4×D43—22no—
83C4⋊C4×D43C2×C414yes—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43D411yescharacteristic
92C2×C4×Dic43D411yescharacteristic
93C2×C4×Dic43C2311yescharacteristic
94C42×D43—22no—
95C42×D43—22no—
96C42×D43—44no—
97#13063259C2×C414yescomplemented
98#13063258C2×C414yescomplemented
99#13063256—22no—
100#13063249—22no—
101#13063249C2×C414yescomplemented
102(C2×D43)⋊C8—22no—
103(C2×D43)⋊C8C2×C414yes—
104#13063235—22no—
105#13063235—22no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C22×Q8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C42×C43—21no—
119C2×C42×C43C2311yescharacteristic
120#106×C43—22no—
121#103×C43—22no—
122#103×C43C2×C414yescomplemented
123#95×C43—21no—
124#95×C43—21no—
125#95×C43—21no—
126C23×D43C2×D411yescharacteristic
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43C22×C412yes—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2411yescharacteristic
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C2×C4×D43—22no—
148C2×C4×D43—21no—
149C2×C4×D43—21no—
150C2×C4×D43—21no—
151C2×C4×D43—21no—
152C2×C4×D43—22no—
153C2×C4×D43—24no—
154C2×C4×D43—22no—
155C2×C4×D43—24no—
156C2×C4×D43—22no—
157C2×C4×D43—22no—
158C2×C4×D43—41no—
159C2×C4×D43—42no—
160C2×C4×D43—42no—
161C2×C4×D43—42no—
162C2×C4×D43—42no—
163C2×C4×D43C22×C412yes—
164C2×C4×D43#4112yes—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43C22×C412yes—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43C22×C412yes—
176C4⋊C4×C43#4112yes—
177C42×C43—21no—
178C42×C43—21no—
179C42×C43—42no—
180(C2×D43)⋊C4—24no—
181(C2×D43)⋊C4—42no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—42no—
188C4⋊Dic43C22×C412yes—
189C4⋊Dic43C22×C412yes—
190C4⋊Dic43#4112yes—
191Dic43⋊C4—24no—
192Dic43⋊C4—24no—
193Dic43⋊C4—24no—
194Dic43⋊C4—42no—
195C4×Dic43—22no—
196C4×Dic43—22no—
197C4×Dic43—42no—
198C4×Dic43—42no—
199C4×Dic43—42no—
200C4×Dic43—42no—
201C4×Dic43—42no—
202C4×Dic43#4112yes—
203C4×Dic43#4112yes—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8C22×C412yes—
210C23×C43C22×D411yescharacteristic
211C22×D43—21no—
212C22×D43—21no—
213C22×D43—21no—
214C22×D43—21no—
215C22×D43C4×D412yes—
216C22×D43#13712yes—
217C22×D43#13712yes—
218Q8×C43—22no—
219Q8×C43—22no—
220Q8×C43—41no—
221Q8×C43—41no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—22no—
225C2×C4×C43—22no—
226C2×C4×C43—21no—
227C2×C4×C43—22no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43AGL(1,ℤ/8)12yes—
240C2×C4×C43C23×C411yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—22no—
253C2×Dic43—22no—
254C2×Dic43—22no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43C4×D412yes—
265C2×Dic43#12312yes—
266C2×Dic43#12312yes—
267C4×D43—28no—
268C4×D43—22no—
269C4×D43—22no—
270C4×D43—22no—
271C4×D43—22no—
272C4×D43—44no—
273C4×D43—48no—
274C4×D43—48no—
275C8×C43—22no—
276C8×C43—41no—
277C43⋊C8—22no—
278C43⋊C8—41no—
279#21581—431nomaximal, Sylow
280C22×C43C2×C4×D411yescharacteristic
281C22×C43C2×#12311yescharacteristic
282C22×C43#52511yescharacteristic
283C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
284C22×C43C2×#13711yescharacteristic
285C22×C43C2×#13711yescharacteristic
286C22×C43#57511yescharacteristic
287C2×D43—22no—
288C2×D43—22no—
289C2×D43—22no—
290C2×D43—22no—
291C2×D43—22no—
292C2×D43—22no—
293C2×D43#44114yes—
294C4×C43—22no—
295C4×C43—41no—
296C4×C43—42no—
297C4×C43—42no—
298C4×C43—42no—
299C4×C43—81no—
300C4×C43C4×#4111yescharacteristic
301C4×C43C4×#4111yescharacteristic
302C4×C43#52911yescharacteristic
303C4×C43#52911yescharacteristic
304Dic43—22no—
305Dic43—22no—
306Dic43—22no—
307Dic43—42no—
308Dic43—42no—
309Dic43—42no—
310Dic43—81no—
311C2×#484—431no—
312C4×C22⋊Q8—431no—
313C2×C4×C4⋊C4—431no—
314#1927—431no—
315#1927D4311yescharacteristic, complemented
316#1918—431no—
317#1918—431no—
318#1872—431no—
319#1853—431no—
320#1824—431no—
321#1776—431no—
322#1776—431no—
323#1763—431no—
324#1763—431no—
325#1749—431no—
326C2×C43C4×#12311yescharacteristic
327C2×C43C2×#44111yescharacteristic
328C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
329C2×C43#309211yescharacteristic
330C2×C43#309511yescharacteristic
331C2×C43#311011yescharacteristic
332C2×C43#311711yescharacteristic
333D43—24no—
334C2×C22⋊Q8—431no—
335C2×C4×Q8—431no—
336C22×C4⋊C4—431no—
337C22×C4⋊C4—431no—
338C22×C42—431no—
339C22×C42—861no—
340#484—438no—
341C2×#107—431no—
342C2×#107—431no—
343C2×#106—431no—
344C2×#106C2×D4311yescharacteristic
345C2×#103—431no—
346C2×#103—431no—
347C2×#103C2×D4311yescharacteristic
348C2×#103C2×D4311yescharacteristic
349C2×C22⋊C8—431no—
350C2×C22⋊C8—431no—
351C2×#97—431no—
352C2×#97—431no—
353#391C2×D4311yescharacteristic
354#389—431no—
355#387—861no—
356#385—861no—
357#380—431no—
358C4×C4⋊C4—431no—
359C4×C4⋊C4—431no—
360C4×C4⋊C4—431no—
361C4×C4⋊C4—431no—
362C4×C4⋊C4—861no—
363C4×C4⋊C4—861no—
364C4×C4⋊C4—861no—
365C4×C4⋊C4C2×D4311yescharacteristic
366C4×C22⋊C4—861no—
367C2×#95—861no—
368#340—431no—
369#340—431no—
370#340—431no—
371#340—431no—
372#340—431no—
373#340—431no—
374#340—431no—
375#340C2×D4311yescharacteristic
376#336—431no—
377#336C2×D4311yescharacteristic
378C43#2158111yescharacteristic, complemented, Sylow
379C22×Q8C22×D4311yescharacteristic
380C23×C4—431no—
381C23×C4—431no—
382C23×C4—431no—
383C23×C4—861no—
384C23×C4—861no—
385C22×C8—431no—
386C22×C8—431no—
387C22×C8C22×D4311yescharacteristic
388C22×C8C22×D4311yescharacteristic
389C22⋊Q8—434no—
390C22⋊Q8—862no—
391C4×Q8—862no—
392C4×Q8—862no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—434no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—862no—
399C2×C4⋊C4—862no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4—862no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4—861no—
406C2×C4⋊C4C22×D4311yescharacteristic
407C2×C4⋊C4C22×D4311yescharacteristic
408C2×C4⋊C4C22×D4311yescharacteristic
409C2×C22⋊C4—861no—
410C2×C22⋊C4—861no—
411C2×C42—21no—
412C2×C42—431no—
413C2×C42—431no—
414C2×C42—431no—
415C2×C42—862no—
416C2×C42—862no—
417C2×C42—861no—
418C2×C42—861no—
419C2×C42—861no—
420C2×C42—861no—
421C2×C42—861no—
422C2×C42—1724no—
423C2×C42C22×D4311yescharacteristic
424#107—434no—
425#107—434no—
426#106—22no—
427#106—862no—
428#103—22no—
429#103—434no—
430#103—862no—
431#103C4×D4314yescomplemented
432C22⋊C8—434no—
433C22⋊C8—862no—
434#97—862no—
435#97—862no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—861no—
440#95—861no—
441#95—861no—
442#95—861no—
443#95—861no—
444#95—861no—
445C24—431no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8C2×C4×D4312yes—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—431no—
457C22×C4—431no—
458C22×C4—431no—
459C22×C4—432no—
460C22×C4—432no—
461C22×C4—862no—
462C22×C4—862no—
463C22×C4—862no—
464C22×C4—864no—
465C22×C4—862no—
466C22×C4—864no—
467C22×C4—862no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—1721no—
477C22×C4—1722no—
478C22×C4—1722no—
479C22×C4—1722no—
480C22×C4—1722no—
481C22×C4D4×D4311yescharacteristic
482C22×C4D4×D4311yescharacteristic
483C22×C4C23×D4311yescharacteristic
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—432no—
490C2×C8—861no—
491C2×C8—861no—
492C2×C8—861no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8C2×C4×D4312yes—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—432no—
501C4⋊C4—432no—
502C4⋊C4—432no—
503C4⋊C4—864no—
504C4⋊C4—864no—
505C4⋊C4—864no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—1722no—
512C4⋊C4—1722no—
513C4⋊C4C2×C4×D4312yes—
514C4⋊C4#1062190012yes—
515C22⋊C4—864no—
516C22⋊C4—1722no—
517C42—21no—
518C42—21no—
519C42—42no—
520C42—432no—
521C42—432no—
522C42—862no—
523C42—862no—
524C42—1722no—
525C42—1722no—
526C42—1722no—
527C42—1722no—
528C42—1722no—
529C23—432no—
530C23—432no—
531C23—432no—
532C23—861no—
533C23—861no—
534C23—861no—
535C23—861no—
536C23C2×D4×D4311yescharacteristic
537Q8—22no—
538Q8—22no—
539Q8—41no—
540Q8—41no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—432no—
559C2×C4—432no—
560C2×C4—432no—
561C2×C4—868no—
562C2×C4—861no—
563C2×C4—861no—
564C2×C4—861no—
565C2×C4—861no—
566C2×C4—861no—
567C2×C4—861no—
568C2×C4—862no—
569C2×C4—862no—
570C2×C4—862no—
571C2×C4—862no—
572C2×C4—862no—
573C2×C4—862no—
574C2×C4—862no—
575C2×C4—1724no—
576C2×C4—1728no—
577C2×C4—1728no—
578C2×C4—1721no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4#1306335212yes—
588C2×C4C22×C4×D4311yescharacteristic
589C2×C4#41×D4311yescharacteristic
590C2×C4#41×D4311yescharacteristic
591C2×C4#41×D4311yescharacteristic
592C2×C4#41×D4311yescharacteristic
593C2×C4C2×#1062190011yescharacteristic
594C8—22no—
595C8—41no—
596C8—862no—
597C8—1721no—
598C22—434no—
599C22—862no—
600C22—862no—
601C22—862no—
602C22—862no—
603C22—862no—
604C22—862no—
605C22C4×D4×D4311yescharacteristic
606C22#123×D4311yescharacteristic
607C22#1458340911yescharacteristic
608C22C2×#1306335211yescharacteristic
609C22#137×D4311yescharacteristic
610C22#137×D4311yescharacteristic
611C22#1458369611yescharacteristic
612C4—22no—
613C4—41no—
614C4—42no—
615C4—42no—
616C4—42no—
617C4—81no—
618C4—862no—
619C4—862no—
620C4—862no—
621C4—3441no—
622C4—1722no—
623C4—1722no—
624C4—1722no—
625C4C4×#1062190011yescharacteristic
626C4#1458336711yescharacteristic
627C4#1458342811yescharacteristic
628C4#1458343211yescharacteristic
629C2—864no—
630C2#1913712211yescharacteristic
631C2#441×D4311yescharacteristic
632C2C4×#1306335211yescharacteristic
633C2#1914451911yescharacteristic
634C2#1914454211yescharacteristic
635C2#1914469311yescharacteristic
636C2#1914476511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1927C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenter#1927D43
hypocenterC43#21581
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1927

Complements

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

NH ≅ G/Ntype
4. #19135226C2semidirect
5. #19135167C2semidirect
6. #19135166C2semidirect
10. #19134495C2semidirect
11. #19134491C2semidirect
12. #19134427C2semidirect
13. #19134427C2semidirect
15. C43×#1927C2semidirect
22. #14583233C4semidirect
97. #13063259C2×C4semidirect
98. #13063258C2×C4semidirect
101. #13063249C2×C4semidirect
122. #103×C43C2×C4semidirect
315. #1927D43semidirect
378. C43#21581semidirect
431. #103C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145832332
#191371332
C4×C4⋊C4×D432
#191352262
#191351672
#191351662
#191348992
#191347862
#191346842
#191344952
#191344912
#191344272
#191343562
C43×#19272
#2158143