Finite Group Databasebeta

← #25196586

Subgroups — #25196586

Order 11008.

784 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#19142905C211yesmaximal, characteristic
2#19136163C211yesmaximal, characteristic, complemented
3#19136143C211yesmaximal, characteristic, complemented
4#19135933C211yesmaximal, characteristic, complemented
5#19135746C211yesmaximal, characteristic, complemented
6#19135180C211yesmaximal, characteristic, complemented
7#19135166C211yesmaximal, characteristic, complemented
8#19135019C211yesmaximal, characteristic
9#19135019C211yesmaximal, characteristic
10#19134863C211yesmaximal, characteristic, complemented
11#19134849C211yesmaximal, characteristic, complemented
12#19134622C211yesmaximal, characteristic
13#19134618C211yesmaximal, characteristic
14C2×#14582654C211yesmaximal, characteristic
15C4×C22⋊Q8×C43C211yesmaximal, characteristic
16C23×C43⋊C8C2211yescharacteristic
17C23×C43⋊C8C2211yescharacteristic
18C2×#13063317C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×#13063258C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27#14582797C2211yescharacteristic
28#14582797C2211yescharacteristic
29#14582783—21no—
30#14582783—21no—
31#14582772—21no—
32#14582772—21no—
33#14582765C2211yescharacteristic
34#14582759C2211yescharacteristic
35#14582759C2211yescharacteristic
36#14582661C2211yescharacteristic
37#14582661C2211yescharacteristic
38#14582661C2211yescharacteristic
39#14582661C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582654C2211yescharacteristic
45#14582654C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C2×C22⋊Q8×C43C2211yescharacteristic
49C2×C4×Q8×C43C2211yescharacteristic
50C22×C42×C43C2211yescharacteristic
51C43×#391C2211yescharacteristic
52C43×#389C2211yescharacteristic
53C43×#387—21no—
54C43×#385—21no—
55C43×#380C2211yescharacteristic
56C4×C4⋊C4×C43—21no—
57C4×C4⋊C4×C43C2211yescharacteristic
58C4×C22⋊C4×C43—21no—
59C22×C43⋊C8—22no—
60C22×C43⋊C8—22no—
61C22×C43⋊C8—22no—
62C22×C43⋊C8—22no—
63C22×C43⋊C8—41no—
64C22×C43⋊C8—41no—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69#13063317—41no—
70#13063317—41no—
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81#13063258—22no—
82#13063258—41no—
83#13063256—22no—
84#13063256—41no—
85#13063249—22no—
86#13063249—22no—
87#13063249—41no—
88#13063249—41no—
89C43⋊#95—21no—
90C43⋊#95—21no—
91C43⋊#95—21no—
92C43⋊#95—21no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C22×Q8×C43C2311yescharacteristic
96C23×C4×C43D411yescharacteristic
97C23×C4×C43D411yescharacteristic
98C23×C4×C43C2311yescharacteristic
99C22⋊Q8×C43—22no—
100C22⋊Q8×C43Q814yes—
101C4×Q8×C43—41no—
102C4×Q8×C43—41no—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43C2311yescharacteristic
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C22⋊C4×C43—21no—
110C2×C22⋊C4×C43—21no—
111C2×C42×C43—21no—
112C2×C42×C43—21no—
113C2×C42×C43—41no—
114C2×C42×C43—41no—
115C2×C42×C43D411yescharacteristic
116C2×C42×C43D411yescharacteristic
117C2×C42×C43C2311yescharacteristic
118C2×C42×C43C2311yescharacteristic
119#95×C43—21no—
120#95×C43—21no—
121#95×C43—21no—
122#95×C43—21no—
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—22no—
136C22×C4×C43—22no—
137C22×C4×C43—22no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—41no—
143C22×C4×C43—41no—
144C22×C4×C43—41no—
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×Q812yes—
151C22×C4×C43#4112yes—
152C22×C4×C43C2411yescharacteristic
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C4⋊C4×C43—24no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—42no—
164C4⋊C4×C43—42no—
165C4⋊C4×C43C2×Q812yes—
166C22⋊C4×C43—24no—
167C22⋊C4×C43—42no—
168C42×C43—21no—
169C42×C43—21no—
170C42×C43—21no—
171C42×C43—21no—
172C42×C43—41no—
173C42×C43—41no—
174C42×C43—42no—
175C42×C43—42no—
176C22⋊Dic43—42no—
177C22⋊Dic43—42no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186Dic43⋊C4—42no—
187Dic43⋊C4—42no—
188Dic43⋊C4—42no—
189Dic43⋊C4—42no—
190C2×C43⋊C8—21no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—44no—
201C2×C43⋊C8—44no—
202C2×C43⋊C8#4112yes—
203C2×C43⋊C8#4112yes—
204C23×C43—21no—
205C23×C43—21no—
206C23×C43—21no—
207C23×C43—21no—
208C23×C43C22⋊Q812yes—
209C23×C43#13512yes—
210C23×C43#13712yes—
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—21no—
219C2×C4×C43—21no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—22no—
225C2×C4×C43—22no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—44no—
236C2×C4×C43—44no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43C22⋊Q812yes—
248C2×C4×C43#13512yes—
249C2×C4×C43C22×Q811yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43H(5,𝔽2)11yescharacteristic
254C2×C4×C43H(5,𝔽2)11yescharacteristic
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—41no—
267C43⋊C8—22no—
268C43⋊C8—22no—
269C43⋊C8—41no—
270C43⋊C8—41no—
271#29158—431nomaximal, Sylow
272C22×C43—22no—
273C22×C43—22no—
274C22×C43—22no—
275C22×C43—22no—
276C22×C43—22no—
277C22×C43—22no—
278C22×C43#47914yes—
279C22×C43C2×C22⋊Q811yescharacteristic
280C22×C43#53211yescharacteristic
281C22×C43#53411yescharacteristic
282C22×C43C2×#13511yescharacteristic
283C22×C43C2×#13511yescharacteristic
284C22×C43C2×#13711yescharacteristic
285C22×C43#57511yescharacteristic
286C4×C43—22no—
287C4×C43—22no—
288C4×C43—42no—
289C4×C43—42no—
290C4×C43—41no—
291C4×C43—41no—
292C4×C43—41no—
293C4×C43—81no—
294C4×C43—81no—
295C4×C43#55111yescharacteristic
296C4×C43#55111yescharacteristic
297C4×C43#55411yescharacteristic
298C4×C43#55411yescharacteristic
299Dic43—81no—
300Dic43—81no—
301Dic43—81no—
302Dic43—81no—
303#2851—431no—
304C4×C22⋊Q8D4311yescharacteristic
305#2101—431no—
306#2097—431no—
307#2059—431no—
308#2026—431no—
309#1920—431no—
310#1918—431no—
311#1892—431no—
312#1892—431no—
313#1865—431no—
314#1863—431no—
315#1808—431no—
316#1807—431no—
317C2×#336—431no—
318C2×C43—24no—
319C2×C43#256411yescharacteristic
320C2×C43C2×#47911yescharacteristic
321C2×C43#307611yescharacteristic
322C2×C43#316811yescharacteristic
323C2×C43#318111yescharacteristic
324C2×C43#319011yescharacteristic
325C2×C43#319111yescharacteristic
326C23×C8—431no—
327C23×C8—431no—
328C2×#125—431no—
329C2×C22⋊Q8C2×D4311yescharacteristic
330C2×C4×Q8C2×D4311yescharacteristic
331C22×C42C2×D4311yescharacteristic
332C2×#107—431no—
333C2×#107—431no—
334C2×#106—431no—
335C2×#106—431no—
336C2×#103—431no—
337C2×#103—431no—
338C2×#103—431no—
339C2×#103—431no—
340#391C2×D4311yescharacteristic
341#389—431no—
342#389—431no—
343#389C2×D4311yescharacteristic
344#387—21no—
345#387—861no—
346#387—861no—
347#385—21no—
348#385—861no—
349#385—861no—
350#382—431no—
351#380—431no—
352#380—431no—
353#380C2×D4311yescharacteristic
354C4×C4⋊C4—21no—
355C4×C4⋊C4C2×D4311yescharacteristic
356C4×C22⋊C4—21no—
357#340—431no—
358#340—431no—
359#340—431no—
360#340—431no—
361#340—431no—
362#340—431no—
363#340—431no—
364#340—431no—
365#336—431no—
366#336—431no—
367#336—431no—
368#336—431no—
369C43#2915811yescharacteristic, complemented, Sylow
370C22×Q8C22×D4311yescharacteristic
371C23×C4C22⋊D4311yescharacteristic
372C23×C4C22⋊D4311yescharacteristic
373C23×C4C22×D4311yescharacteristic
374C22×C8—431no—
375C22×C8—431no—
376C22×C8—431no—
377C22×C8—431no—
378C22×C8—862no—
379C22×C8—862no—
380C22×C8—862no—
381C22×C8—862no—
382C22×C8—1721no—
383C22×C8—1721no—
384#125—1721no—
385#125—1721no—
386C22⋊Q8—22no—
387C22⋊Q8Dic8614yes—
388C4×Q8—41no—
389C4×Q8—41no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—431no—
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—21no—
409C2×C42—21no—
410C2×C42—41no—
411C2×C42—41no—
412C2×C42C22⋊D4311yescharacteristic
413C2×C42C22⋊D4311yescharacteristic
414C2×C42C22×D4311yescharacteristic
415C2×C42C22×D4311yescharacteristic
416#107—862no—
417#107—1721no—
418#106—862no—
419#106—1721no—
420#103—862no—
421#103—862no—
422#103—1721no—
423#103—1721no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—861no—
430#95—861no—
431#95—861no—
432#95—861no—
433#95—861no—
434#95—861no—
435C24C2×C22⋊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—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4C2×Dic8612yes—
461C22×C4#1062189812yes—
462C22×C4C2×C22⋊D4311yescharacteristic
463C22×C4C2×C22⋊D4311yescharacteristic
464C22×C4C2×C22⋊D4311yescharacteristic
465C22×C4C2×C22⋊D4311yescharacteristic
466C22×C4C2×C22⋊D4311yescharacteristic
467C22×C4C23×D4311yescharacteristic
468C2×C8—432no—
469C2×C8—432no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—861no—
476C2×C8—861no—
477C2×C8—861no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—1724no—
481C2×C8—1724no—
482C4⋊C4—24no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—42no—
489C4⋊C4—42no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
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—21no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—41no—
512C42—41no—
513C42—42no—
514C42—42no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23#1306330412yes—
520C23#1306334512yes—
521C23#1306335612yes—
522C23C22×C22⋊D4311yescharacteristic
523Q8—22no—
524Q8—22no—
525Q8—41no—
526Q8—41no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—44no—
547C2×C4—44no—
548C2×C4—41no—
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—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#1306330412yes—
571C2×C4#1306334512yes—
572C2×C4C22×Dic8611yescharacteristic
573C2×C4#41×D4311yescharacteristic
574C2×C4#41×D4311yescharacteristic
575C2×C4C2×#1062189811yescharacteristic
576C2×C4#1306337011yescharacteristic
577C2×C4#1306337011yescharacteristic
578C8—862no—
579C8—862no—
580C8—1721no—
581C8—1721no—
582C22—22no—
583C22—22no—
584C22—22no—
585C22—22no—
586C22—22no—
587C22—22no—
588C22#1458320614yes—
589C22C2×#1306330411yescharacteristic
590C22#1458344511yescharacteristic
591C22#1458345811yescharacteristic
592C22C2×#1306334511yescharacteristic
593C22C2×#1306334511yescharacteristic
594C22C2×#1306335611yescharacteristic
595C22#1458369711yescharacteristic
596C4—22no—
597C4—22no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—42no—
602C4—42no—
603C4—81no—
604C4—81no—
605C4—3441no—
606C4—3441no—
607C4—3441no—
608C4—3441no—
609C4#1458357811yescharacteristic
610C4#1458357811yescharacteristic
611C4#1458360811yescharacteristic
612C4#1458360811yescharacteristic
613C2—24no—
614C2#1913977111yescharacteristic
615C2C2×#1458320611yescharacteristic
616C2#1914438311yescharacteristic
617C2#1914515911yescharacteristic
618C2#1914529811yescharacteristic
619C2#1914537611yescharacteristic
620C2#1914538311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC4×C22⋊Q8×C43C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenterC4×C22⋊Q8D43
hypocenterC43#29158
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #19136163C2semidirect
3. #19136143C2semidirect
4. #19135933C2semidirect
5. #19135746C2semidirect
6. #19135180C2semidirect
7. #19135166C2semidirect
10. #19134863C2semidirect
11. #19134849C2semidirect
369. C43#29158semidirect

Maximal subgroups

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

subgroupindex
#191429052
#191361632
#191361432
#191359332
#191357462
#191351802
#191351662
#191350192
#191348632
#191348492
#191346222
#191346182
C2×#145826542
C4×C22⋊Q8×C432
#2915843