Finite Group Databasebeta

← #25116039

Subgroups — #25116039

Order 11008.

866 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583000C211yesmaximal, characteristic
2#19137543C211yesmaximal, characteristic
3#19137513C211yesmaximal, characteristic, complemented
4#19135289C211yesmaximal, characteristic
5#19135281C211yesmaximal, characteristic
6#19135186C211yesmaximal, characteristic, complemented
7#19135167C211yesmaximal, characteristic, complemented
8#19134952C211yesmaximal, characteristic
9#19134727C211yesmaximal, characteristic, complemented
10#19134603C211yesmaximal, characteristic
11#19134598C211yesmaximal, characteristic, complemented
12#19134466C211yesmaximal, characteristic, complemented
13#19134427C211yesmaximal, characteristic, complemented
14C4×#13063249C211yesmaximal, characteristic, complemented
15C43×#1880C211yesmaximal, characteristic
16C2×Q8×Dic43C2211yescharacteristic
17C2×Q8×Dic43C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19C2×#13063281—21no—
20#14583000C418yescomplemented
21C2×#13063259C2211yescharacteristic
22C2×Dic43⋊C8C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063235C2211yescharacteristic
28C2×#13063235C2211yescharacteristic
29C2×C4×C43⋊C8C2211yescharacteristic
30#14582802C2211yescharacteristic
31#14582797—21no—
32#14582797C2211yescharacteristic
33#14582795—21no—
34#14582795C2211yescharacteristic
35#14582793—21no—
36#14582787—21no—
37#14582768C2211yescharacteristic
38#14582764—21no—
39#14582764C2211yescharacteristic
40#14582757—21no—
41C4⋊C4×Dic43C2211yescharacteristic
42C4×Dic43⋊C4—21no—
43C4×Dic43⋊C4C2211yescharacteristic
44C4×C4⋊Dic43C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582653C2211yescharacteristic
53C22×SD16×C43C2211yescharacteristic
54C2×C4×Q8×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C43×#390C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C23×Dic43—21no—
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63Q8×Dic43—22no—
64Q8×Dic43—22no—
65Q8×Dic43—41no—
66Q8×Dic43C2×C414yes—
67D4×Dic43—22no—
68D4×Dic43C2×C414yes—
69#13063281—44no—
70C2×C4⋊Dic43—21no—
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—
80C2×Dic43⋊C4D411yescharacteristic
81C2×Dic43⋊C4D411yescharacteristic
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43C2311yescharacteristic
90C2×C4×Dic43C2311yescharacteristic
91#13063259C2×C414yes—
92Dic43⋊C8—22no—
93#13063249—22no—
94#13063249C2×C414yes—
95#13063246—41no—
96#13063246C2×C414yes—
97#13063235—41no—
98#13063235C2×C414yes—
99C4×C43⋊C8—41no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95D411yescharacteristic
107C43⋊#95D411yescharacteristic
108C22×Q8×C43C2311yescharacteristic
109C22×D4×C43C2311yescharacteristic
110C2×SD16×C43—22no—
111C2×SD16×C43—22no—
112C2×SD16×C43C2×C414yes—
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C4×Q8×C43—22no—
116C4×Q8×C43—41no—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122C2×C42×C43—21no—
123C2×C42×C43C2311yescharacteristic
124#103×C43—22no—
125#102×C43—41no—
126C24×C43—21no—
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43C22×C412yes—
131C2×Q8×C43#4112yes—
132C2×Q8×C43#4112yes—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43C22×C412yes—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2411yescharacteristic
145C22×Dic43—24no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—42no—
151C22×Dic43—42no—
152C22×Dic43C2×D411yescharacteristic
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156SD16×C43—28no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43C22×C412yes—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—42no—
168C22⋊C4×C43—42no—
169C22⋊C4×C43—81no—
170C42×C43—21no—
171C42×C43—21no—
172C42×C43—42no—
173C22⋊Dic43—24no—
174C22⋊Dic43—42no—
175C22⋊Dic43—81no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—24no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—42no—
184C4⋊Dic43C22×C412yes—
185C4⋊Dic43C22×C412yes—
186Dic43⋊C4—22no—
187Dic43⋊C4—41no—
188Dic43⋊C4—42no—
189Dic43⋊C4—42no—
190Dic43⋊C4—42no—
191Dic43⋊C4—81no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—24no—
195C4×Dic43—42no—
196C4×Dic43—42no—
197C4×Dic43—42no—
198C4×Dic43C22×C412yes—
199C4×Dic43#4112yes—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8C22×C412yes—
206C23×C43—22no—
207C23×C43—41no—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43C22×D411yescharacteristic
214Q8×C43—22no—
215Q8×C43—22no—
216Q8×C43—22no—
217Q8×C43#11714yescomplemented
218D4×C43—22no—
219D4×C43—22no—
220D4×C43—41no—
221D4×C43—41no—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—21no—
225C2×C4×C43—22no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
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×C43AGL(1,ℤ/8)12yes—
237C2×C4×C43C23×C411yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×C4×C43H(5,𝔽2)11yescharacteristic
242C2×C4×C432−1+411yescharacteristic
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—22no—
248C2×Dic43—22no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—48no—
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×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43C4×D412yes—
267C2×Dic43C4×D412yes—
268C8×C43—22no—
269C8×C43—41no—
270C43⋊C8—22no—
271C43⋊C8—41no—
272#22781—431nomaximal, Sylow
273C22×C43—42no—
274C22×C43—42no—
275C22×C43—42no—
276C22×C43—81no—
277C22×C43—81no—
278C22×C43—81no—
279C22×C43—81no—
280C22×C43C2×C4×D411yescharacteristic
281C22×C43#54611yescharacteristic
282C22×C43#54811yescharacteristic
283C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
284C22×C43#57511yescharacteristic
285C22×C43#57711yescharacteristic
286C22×C43#57811yescharacteristic
287C4×C43—24no—
288C4×C43—22no—
289C4×C43—41no—
290C4×C43—81no—
291C4×C43—81no—
292C4×C43C2×#11711yescharacteristic
293C4×C43#52011yescharacteristic
294C4×C43#55211yescharacteristic
295C4×C43#55311yescharacteristic
296Dic43—22no—
297Dic43—22no—
298Dic43—42no—
299Dic43—42no—
300Dic43—41no—
301Dic43—41no—
302Dic43—81no—
303Dic43—81no—
304C2×#440—431no—
305#2354—431no—
306#2351—431no—
307#1936—431no—
308#1934—431no—
309#1921—431no—
310#1918—431no—
311#1880—431no—
312#1880D4311yescharacteristic
313#1836—431no—
314#1804—431no—
315#1803—431no—
316#1771—431no—
317#1763—431no—
318C4×#103—431no—
319C2×C43—82no—
320C2×C43#235211yescharacteristic
321C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
322C2×C43#294711yescharacteristic
323C2×C43#330811yescharacteristic
324C2×C43#332111yescharacteristic
325C2×C43#336811yescharacteristic
326C2×C43#337711yescharacteristic
327C22×SD16C2×D4311yescharacteristic
328C2×C4×Q8—431no—
329C2×C4×Q8—431no—
330C2×C4×Q8C2×D4311yescharacteristic
331C2×C4×D4—431no—
332C2×#117—861no—
333#440—438no—
334C2×#107—431no—
335C2×C4⋊C8—431no—
336C2×#103—431no—
337C2×#103—431no—
338C2×#103C2×D4311yescharacteristic
339C2×#102—431no—
340C2×#102—431no—
341C2×#102C2×D4311yescharacteristic
342C2×#97—431no—
343C2×#97—431no—
344C2×C4×C8—431no—
345#390—431no—
346#390C2×D4311yescharacteristic
347#389—431no—
348#389—431no—
349#389—861no—
350#389—861no—
351#388—861no—
352#388—861no—
353#384—431no—
354#382—431no—
355#382—861no—
356#380—861no—
357C4×C4⋊C4—431no—
358C4×C4⋊C4—431no—
359C4×C4⋊C4—431no—
360C4×C4⋊C4—861no—
361#340—431no—
362#340—431no—
363#340—431no—
364#340—431no—
365#340—431no—
366#340—431no—
367#340—431no—
368#340C2×D4311yescharacteristic
369#336—431no—
370#336C2×D4311yescharacteristic
371C43#2278111yescharacteristic, complemented, Sylow
372C22×Q8C22×D4311yescharacteristic
373C22×D4C22×D4311yescharacteristic
374C23×C4—861no—
375C2×SD16—22no—
376C2×SD16—22no—
377C2×SD16C4×D4314yes—
378C22×C8—431no—
379C22×C8—431no—
380C22×C8C22×D4311yescharacteristic
381C22×C8C22×D4311yescharacteristic
382C4×Q8—22no—
383C4×Q8—41no—
384C4×Q8—434no—
385C4×Q8—862no—
386C4×Q8—862no—
387C4×Q8—1721no—
388C4×D4—434no—
389C4×D4—862no—
390#117—1724no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—431no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4C22×D4311yescharacteristic
405C2×C4⋊C4C22×D4311yescharacteristic
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—861no—
409C2×C22⋊C4—861no—
410C2×C22⋊C4—861no—
411C2×C42—21no—
412C2×C42—431no—
413C2×C42—431no—
414C2×C42—861no—
415C2×C42—861no—
416C2×C42—861no—
417C2×C42—861no—
418C2×C42C22×D4311yescharacteristic
419#107—434no—
420C4⋊C8—862no—
421#103—22no—
422#103—434no—
423#103—862no—
424#102—41no—
425#102—434no—
426#102—1721no—
427#97—434no—
428#97—1721no—
429C4×C8—1721no—
430#95—431no—
431#95—431no—
432#95—861no—
433#95—861no—
434#95—861no—
435#95—861no—
436#95—861no—
437#95—861no—
438C24—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8C2×C4×D4312yes—
443C2×Q8#1062190012yes—
444C2×Q8#1062190012yes—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4C2×C4×D4312yes—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—431no—
455C22×C4—431no—
456C22×C4—431no—
457C22×C4—431no—
458C22×C4—864no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—1722no—
464C22×C4—1722no—
465C22×C4D4×D4311yescharacteristic
466C22×C4D4×D4311yescharacteristic
467C22×C4C23×D4311yescharacteristic
468SD16—28no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—432no—
475C2×C8—861no—
476C2×C8—861no—
477C2×C8—861no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8C2×C4×D4312yes—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—42no—
486C4⋊C4—432no—
487C4⋊C4—432no—
488C4⋊C4—864no—
489C4⋊C4—862no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—3441no—
497C4⋊C4—1721no—
498C4⋊C4—1722no—
499C4⋊C4—1722no—
500C4⋊C4—1722no—
501C4⋊C4—1722no—
502C22⋊C4—42no—
503C22⋊C4—81no—
504C22⋊C4—864no—
505C22⋊C4—3441no—
506C22⋊C4—1722no—
507C42—21no—
508C42—21no—
509C42—42no—
510C42—432no—
511C42—432no—
512C42—864no—
513C42—861no—
514C42—861no—
515C42—1722no—
516C42—1722no—
517C42—1722no—
518C23—22no—
519C23—41no—
520C23—41no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23C2×D4×D4311yescharacteristic
526Q8—22no—
527Q8—22no—
528Q8—22no—
529Q8#1306328114yescomplemented
530D4—22no—
531D4—22no—
532D4—41no—
533D4—41no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—432no—
549C2×C4—432no—
550C2×C4—861no—
551C2×C4—861no—
552C2×C4—861no—
553C2×C4—861no—
554C2×C4—862no—
555C2×C4—862no—
556C2×C4—861no—
557C2×C4—861no—
558C2×C4—861no—
559C2×C4—861no—
560C2×C4—861no—
561C2×C4—861no—
562C2×C4—1728no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4#1306335212yes—
574C2×C4C22×C4×D4311yescharacteristic
575C2×C4#41×D4311yescharacteristic
576C2×C4C2×#1062190011yescharacteristic
577C2×C4C2×#1062190011yescharacteristic
578C2×C4#1306337011yescharacteristic
579C2×C4#1306337211yescharacteristic
580C8—22no—
581C8—41no—
582C8—862no—
583C8—1721no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22C4×D4×D4311yescharacteristic
592C22#1458353611yescharacteristic
593C22#1458355511yescharacteristic
594C22C2×#1306335211yescharacteristic
595C22#1458369611yescharacteristic
596C22#1458370911yescharacteristic
597C22#1458371511yescharacteristic
598C4—22no—
599C4—24no—
600C4—41no—
601C4—81no—
602C4—81no—
603C4—862no—
604C4—862no—
605C4—3441no—
606C4—3441no—
607C4—1721no—
608C4—1721no—
609C4—1722no—
610C4—1722no—
611C4C2×#1306328111yescharacteristic
612C4#1458337811yescharacteristic
613C4#1458358611yescharacteristic
614C4#1458359211yescharacteristic
615C2—82no—
616C2#1913752211yescharacteristic
617C2C4×#1306335211yescharacteristic
618C2#1914343511yescharacteristic
619C2#1914659011yescharacteristic
620C2#1914678511yescharacteristic
621C2#1914732811yescharacteristic
622C2#1914744111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1880C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
cosocleC22×C4×C43C24
hypercenter#1880D43
hypocenterC43#22781
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1880

Complements

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

NH ≅ G/Ntype
3. #19137513C2semidirect
6. #19135186C2semidirect
7. #19135167C2semidirect
9. #19134727C2semidirect
11. #19134598C2semidirect
12. #19134466C2semidirect
13. #19134427C2semidirect
14. C4×#13063249C2semidirect
20. #14583000C4semidirect
217. Q8×C43#117semidirect
371. C43#22781semidirect
529. Q8#13063281semidirect

Maximal subgroups

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

subgroupindex
C2×#145830002
#191375432
#191375132
#191352892
#191352812
#191351862
#191351672
#191349522
#191347272
#191346032
#191345982
#191344662
#191344272
C4×#130632492
C43×#18802
#2278143