Finite Group Databasebeta

← #25196672

Subgroups — #25196672

Order 11008.

760 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
1#19142903C211yesmaximal, characteristic
2C22⋊Q8×Dic43C211yesmaximal, characteristic
3#19136168C211yesmaximal, characteristic, complemented
4#19136141C211yesmaximal, characteristic, complemented
5#19135932C211yesmaximal, characteristic, complemented
6#19135744C211yesmaximal, characteristic, complemented
7#19135186C211yesmaximal, characteristic, complemented
8#19135176C211yesmaximal, characteristic, complemented
9#19135029C211yesmaximal, characteristic
10#19134865C211yesmaximal, characteristic, complemented
11#19134847C211yesmaximal, characteristic, complemented
12#19134628C211yesmaximal, characteristic
13#19134626C211yesmaximal, characteristic
14#19134288C211yesmaximal, characteristic
15C43×#1894C211yesmaximal, characteristic
16C22×#10621877C2211yescharacteristic
17C2×#13063316C2211yescharacteristic
18C2×Q8×Dic43C2211yescharacteristic
19C22×C4×Dic43C2211yescharacteristic
20C2×#13063259C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063257C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26#14582806C2211yescharacteristic
27#14582798C2211yescharacteristic
28#14582798C2211yescharacteristic
29#14582795C2211yescharacteristic
30#14582786—21no—
31#14582785—21no—
32#14582782—21no—
33#14582774—21no—
34#14582774—21no—
35#14582771—21no—
36#14582764C2211yescharacteristic
37#14582759C2211yescharacteristic
38#14582759C2211yescharacteristic
39C4⋊C4×Dic43—21no—
40C4⋊C4×Dic43C2211yescharacteristic
41C22⋊C4×Dic43—21no—
42#14582662C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582653C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C22×M16×C43C2211yescharacteristic
53C2×C22⋊Q8×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C43×#380C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C23×Dic43D411yescharacteristic
60C23×Dic43D411yescharacteristic
61C2×#10621877—22no—
62C2×#10621877—22no—
63C2×#10621877—41no—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66#13063316—41no—
67#13063316—41no—
68Q8×Dic43—41no—
69Q8×Dic43—41no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—41no—
85C2×C4×Dic43—41no—
86C2×C4×Dic43D411yescharacteristic
87C2×C4×Dic43D411yescharacteristic
88C2×C4×Dic43C2311yescharacteristic
89C2×C4×Dic43C2311yescharacteristic
90#13063259—22no—
91#13063258—41no—
92#13063257—41no—
93#13063256—22no—
94#13063249—22no—
95#13063249—41no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C22×Q8×C43C2311yescharacteristic
107C23×C4×C43C2311yescharacteristic
108C2×M16×C43—22no—
109C2×M16×C43—22no—
110C2×M16×C43—41no—
111C22×C8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C22⋊Q8×C43—22no—
114C22⋊Q8×C43Q814yes—
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C22⋊C4×C43—21no—
120C2×C22⋊C4×C43—21no—
121#103×C43—22no—
122#103×C43—41no—
123#95×C43—21no—
124C24×C43C2×D411yescharacteristic
125C2×Q8×C43—21no—
126C2×Q8×C43—21no—
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43C2×Q812yes—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×Q812yes—
141C22×C4×C43#4112yes—
142C22×C4×C43C2411yescharacteristic
143C22×Dic43—22no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—41no—
149C22×Dic43—41no—
150C22×Dic43—41no—
151C22×Dic43—41no—
152C22×Dic43—41no—
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156C22×Dic43C2×D411yescharacteristic
157M16×C43—44no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43#4112yes—
164C4⋊C4×C43—24no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43C2×Q812yes—
171C22⋊C4×C43—24no—
172C22⋊C4×C43—42no—
173C22⋊Dic43—42no—
174C22⋊Dic43—42no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—42no—
184C4⋊Dic43—42no—
185C4⋊Dic43—42no—
186C4⋊Dic43—42no—
187Dic43⋊C4—42no—
188Dic43⋊C4—42no—
189C4×Dic43—21no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—41no—
194C4×Dic43—41no—
195C4×Dic43—42no—
196C4×Dic43—42no—
197#10621877—44no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8#4112yes—
204C23×C43—21no—
205C23×C43—21no—
206C23×C43—21no—
207C23×C43—21no—
208C23×C43—21no—
209C23×C43—21no—
210C23×C43C22⋊Q812yes—
211C23×C43C22×D411yescharacteristic
212Q8×C43—22no—
213Q8×C43—22no—
214Q8×C43—41no—
215Q8×C43—41no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43C22⋊Q812yes—
235C2×C4×C43C22×Q811yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C2×C4×C43H(5,𝔽2)11yescharacteristic
240C2×C4×C43H(5,𝔽2)11yescharacteristic
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—44no—
253C2×Dic43—44no—
254C2×Dic43—41no—
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×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43#13712yes—
267C8×C43—22no—
268C8×C43—41no—
269C43⋊C8—22no—
270C43⋊C8—41no—
271#29164—431nomaximal, Sylow
272C22×C43—22no—
273C22×C43—22no—
274C22×C43—22no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43C2×C22⋊Q811yescharacteristic
280C22×C43#53211yescharacteristic
281C22×C43#53411yescharacteristic
282C22×C43C2×#13711yescharacteristic
283C22×C43#57511yescharacteristic
284C22×C43#57511yescharacteristic
285C22×C43#57511yescharacteristic
286C4×C43—22no—
287C4×C43—42no—
288C4×C43—42no—
289C4×C43—81no—
290C4×C43—81no—
291C4×C43#55111yescharacteristic
292C4×C43#55111yescharacteristic
293C4×C43#55411yescharacteristic
294C4×C43#55411yescharacteristic
295Dic43—22no—
296Dic43—41no—
297Dic43—41no—
298Dic43—41no—
299Dic43—81no—
300Dic43—81no—
301Dic43—81no—
302Dic43—81no—
303#2851—431no—
304C4×C22⋊Q8—431no—
305#2101—431no—
306#2097—431no—
307#2059—431no—
308#2026—431no—
309#1921—431no—
310#1919—431no—
311#1894—431no—
312#1894D4311yescharacteristic
313#1865—431no—
314#1863—431no—
315#1809—431no—
316#1809—431no—
317#1728—431no—
318C2×C43—42no—
319C2×C43#256411yescharacteristic
320C2×C43#307811yescharacteristic
321C2×C43#308011yescharacteristic
322C2×C43#317211yescharacteristic
323C2×C43#318311yescharacteristic
324C2×C43#319611yescharacteristic
325C2×C43#319711yescharacteristic
326C22×M16—431no—
327C22×M16C2×D4311yescharacteristic
328C2×#125—431no—
329C2×C22⋊Q8C2×D4311yescharacteristic
330C2×C4×Q8—431no—
331C22×C42—431no—
332C2×#107—431no—
333C2×#107—431no—
334C2×#106—431no—
335C2×#106—431no—
336C2×#103—431no—
337C2×#103—431no—
338C2×#103C2×D4311yescharacteristic
339C2×#103C2×D4311yescharacteristic
340#391—431no—
341#389—431no—
342#389—431no—
343#389—431no—
344#387—861no—
345#387—861no—
346#387—861no—
347#385—861no—
348#385—861no—
349#385—861no—
350#382—431no—
351#380—431no—
352#380—431no—
353#380C2×D4311yescharacteristic
354C4×C4⋊C4—431no—
355C4×C4⋊C4—861no—
356C4×C22⋊C4—861no—
357#340—431no—
358#340—431no—
359#340—431no—
360#340—431no—
361#340—431no—
362#340—431no—
363#340C2×D4311yescharacteristic
364#340C2×D4311yescharacteristic
365#336—431no—
366#336—431no—
367#336—431no—
368#336—431no—
369C43#2916411yescharacteristic, complemented, Sylow
370C22×Q8C22×D4311yescharacteristic
371C23×C4—431no—
372C23×C4—431no—
373C23×C4C22×D4311yescharacteristic
374C2×M16—22no—
375C2×M16—22no—
376C2×M16—41no—
377C2×M16—862no—
378C2×M16—862no—
379C2×M16—1721no—
380C22×C8—431no—
381C22×C8—431no—
382C22×C8C22×D4311yescharacteristic
383C22×C8C22×D4311yescharacteristic
384#125—1721no—
385#125—1721no—
386C22⋊Q8—22no—
387C22⋊Q8Dic8614yes—
388C4×Q8—1721no—
389C4×Q8—1721no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—431no—
392C2×C4⋊C4—431no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4C22×D4311yescharacteristic
402C2×C4⋊C4C22×D4311yescharacteristic
403C2×C4⋊C4C22×D4311yescharacteristic
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C42—431no—
409C2×C42—431no—
410C2×C42—431no—
411C2×C42—431no—
412C2×C42—861no—
413C2×C42—861no—
414C2×C42—1721no—
415C2×C42—1721no—
416#107—862no—
417#107—1721no—
418#106—862no—
419#106—1721no—
420#103—22no—
421#103—41no—
422#103—862no—
423#103—1721no—
424#95—21no—
425#95—861no—
426#95—861no—
427#95—861no—
428#95—861no—
429#95—861no—
430#95—861no—
431#95—861no—
432#95—861no—
433#95—861no—
434#95—861no—
435C24D4×D4311yescharacteristic
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8C2×Dic8612yes—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—431no—
451C22×C4—431no—
452C22×C4—431no—
453C22×C4—431no—
454C22×C4—862no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—1721no—
460C22×C4—1721no—
461C22×C4—1721no—
462C22×C4—1721no—
463C22×C4—1721no—
464C22×C4C2×Dic8612yes—
465C22×C4D4×D4311yescharacteristic
466C22×C4#1062190012yes—
467C22×C4C23×D4311yescharacteristic
468M16—44no—
469M16—1724no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—432no—
476C2×C8—861no—
477C2×C8—861no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8#1062190012yes—
482C4⋊C4—24no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—1722no—
497C4⋊C4—1722no—
498C4⋊C4—1722no—
499C4⋊C4—1722no—
500C4⋊C4—1722no—
501C4⋊C4—1722no—
502C4⋊C4C2×Dic8612yes—
503C22⋊C4—24no—
504C22⋊C4—42no—
505C22⋊C4—1722no—
506C22⋊C4—1722no—
507C42—861no—
508C42—861no—
509C42—861no—
510C42—861no—
511C42—1721no—
512C42—1721no—
513C42—1722no—
514C42—1722no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23#1306330212yes—
522C23C2×D4×D4311yescharacteristic
523Q8—22no—
524Q8—22no—
525Q8—41no—
526Q8—41no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—432no—
546C2×C4—861no—
547C2×C4—861no—
548C2×C4—861no—
549C2×C4—861no—
550C2×C4—861no—
551C2×C4—861no—
552C2×C4—861no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—861no—
556C2×C4—861no—
557C2×C4—1724no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1724no—
571C2×C4#1306330212yes—
572C2×C4C22×Dic8611yescharacteristic
573C2×C4#41×D4311yescharacteristic
574C2×C4C2×#1062190011yescharacteristic
575C2×C4C2×#1062190011yescharacteristic
576C2×C4#1306337011yescharacteristic
577C2×C4#1306337111yescharacteristic
578C8—22no—
579C8—41no—
580C8—862no—
581C8—1721no—
582C22—22no—
583C22—22no—
584C22—22no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22C2×#1306330211yescharacteristic
590C22#1458344411yescharacteristic
591C22#1458345711yescharacteristic
592C22#137×D4311yescharacteristic
593C22#1458369511yescharacteristic
594C22#1458369811yescharacteristic
595C22#1458369811yescharacteristic
596C4—22no—
597C4—42no—
598C4—42no—
599C4—81no—
600C4—81no—
601C4—862no—
602C4—3441no—
603C4—3441no—
604C4—3441no—
605C4—3441no—
606C4—1721no—
607C4—1721no—
608C4—1721no—
609C4#1458357211yescharacteristic
610C4#1458358011yescharacteristic
611C4#1458360611yescharacteristic
612C4#1458360811yescharacteristic
613C2—42no—
614C2#1913977911yescharacteristic
615C2#1914439711yescharacteristic
616C2#1914441511yescharacteristic
617C2#1914519411yescharacteristic
618C2#1914532511yescharacteristic
619C2#1914542611yescharacteristic
620C2#1914543311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1894C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#1894D43
hypocenterC43#29164
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1894

Complements

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

NH ≅ G/Ntype
3. #19136168C2semidirect
4. #19136141C2semidirect
5. #19135932C2semidirect
6. #19135744C2semidirect
7. #19135186C2semidirect
8. #19135176C2semidirect
10. #19134865C2semidirect
11. #19134847C2semidirect
369. C43#29164semidirect

Maximal subgroups

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

subgroupindex
#191429032
C22⋊Q8×Dic432
#191361682
#191361412
#191359322
#191357442
#191351862
#191351762
#191350292
#191348652
#191348472
#191346282
#191346262
#191342882
C43×#18942
#2916443