Finite Group Databasebeta

← #25169278

Subgroups — #25169278

Order 11008.

792 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139028C211yesmaximal, characteristic, complemented
2#19135998C211yesmaximal, characteristic, complemented
3#19135969C211yesmaximal, characteristic, complemented
4#19135781C211yesmaximal, characteristic
5#19135781C211yesmaximal, characteristic
6#19135358C211yesmaximal, characteristic, complemented
7#19135320C211yesmaximal, characteristic, complemented
8#19135203C211yesmaximal, characteristic, complemented
9#19135180C211yesmaximal, characteristic, complemented
10#19135170C211yesmaximal, characteristic, complemented
11#19134856C211yesmaximal, characteristic, complemented
12#19134788C211yesmaximal, characteristic, complemented
13#19134681C211yesmaximal, characteristic, complemented
14C4×#13063246C211yesmaximal, characteristic, complemented
15C43×#2361C211yesmaximal, characteristic
16C2×#13063256C2211yescharacteristic
17C2×#13063256C2211yescharacteristic
18C2×#13063256C2211yescharacteristic
19C2×#13063256C2211yescharacteristic
20C2×C4⋊(C43⋊C8)C2211yescharacteristic
21C2×#13063246C2211yescharacteristic
22C2×#13063246C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×C22⋊(C43⋊C8)C2211yescharacteristic
26C2×C22⋊(C43⋊C8)C2211yescharacteristic
27C2×C4×C43⋊C8C2211yescharacteristic
28#14582841—21no—
29#14582822—21no—
30#14582797C2211yescharacteristic
31#14582797C2211yescharacteristic
32#14582792—21no—
33#14582786—21no—
34#14582769C2211yescharacteristic
35#14582759C2211yescharacteristic
36#14582759C2211yescharacteristic
37C4×C4⋊Dic43C2211yescharacteristic
38#14582661C2211yescharacteristic
39#14582661C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C2×#121×C43C2211yescharacteristic
49C2×C4×D4×C43—21no—
50C2×C4×D4×C43C2211yescharacteristic
51C22×C4⋊C4×C43C2211yescharacteristic
52C43×#390C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C43×#388—21no—
55C43×#386—21no—
56C43×#385—21no—
57C4×C4⋊C4×C43C2211yescharacteristic
58C4×C22⋊C4×C43C2211yescharacteristic
59C22×C43⋊C8C2311yescharacteristic
60C22×C43⋊C8C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63C2×C4⋊Dic43—21no—
64C2×C4⋊Dic43—21no—
65C2×C4⋊Dic43C2311yescharacteristic
66C2×C4⋊Dic43C2311yescharacteristic
67C2×C4⋊Dic43C2311yescharacteristic
68C2×C4⋊Dic43C2311yescharacteristic
69C2×Dic43⋊C4—21no—
70C2×Dic43⋊C4—21no—
71C2×C22⋊Dic43—21no—
72C2×C22⋊Dic43—21no—
73C2×C4×Dic43—21no—
74#13063256—22no—
75#13063256—22no—
76#13063256—22no—
77#13063256—41no—
78C4⋊(C43⋊C8)—22no—
79#13063246—22no—
80#13063246—22no—
81#13063246—22no—
82#13063246—41no—
83C22⋊(C43⋊C8)—22no—
84C22⋊(C43⋊C8)—41no—
85C4×C43⋊C8—41no—
86C43⋊#95—21no—
87C43⋊#95—21no—
88C43⋊#95—21no—
89C43⋊#95—21no—
90C43⋊#95—21no—
91C22×D4×C43—21no—
92C22×D4×C43C2311yescharacteristic
93C23×C4×C43—21no—
94C23×C4×C43—21no—
95C23×C4×C43C2311yescharacteristic
96#121×C43—22no—
97#121×C43—22no—
98C4×D4×C43—22no—
99C4×D4×C43—41no—
100C4×D4×C43—44no—
101C2×C4⋊C4×C43—22no—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43—41no—
105C2×C4⋊C4×C43C2311yescharacteristic
106C2×C4⋊C4×C43C2311yescharacteristic
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C22⋊C4×C43—21no—
109C2×C22⋊C4×C43—21no—
110C2×C22⋊C4×C43—21no—
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43D411yescharacteristic
113C2×C22⋊C4×C43D411yescharacteristic
114C2×C42×C43—21no—
115C2×C42×C43C2311yescharacteristic
116C2×C42×C43C2311yescharacteristic
117#95×C43—21no—
118#95×C43—21no—
119#95×C43D411yescharacteristic
120#95×C43D411yescharacteristic
121C24×C43—21no—
122C24×C43C2×D411yescharacteristic
123C2×D4×C43—24no—
124C2×D4×C43—21no—
125C2×D4×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—42no—
130C2×D4×C43—42no—
131C2×D4×C43#4112yes—
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×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—42no—
142C22×C4×C43—42no—
143C22×C4×C43—42no—
144C22×C4×C43—42no—
145C22×C4×C43—81no—
146C22×C4×C43—81no—
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2411yescharacteristic
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—42no—
162C4⋊C4×C43—42no—
163C4⋊C4×C43#4112yes—
164C4⋊C4×C43#4112yes—
165C22⋊C4×C43—24no—
166C22⋊C4×C43—41no—
167C22⋊C4×C43—42no—
168C22⋊C4×C43—42no—
169C22⋊C4×C43—81no—
170C22⋊C4×C43SD1614yes—
171C42×C43—21no—
172C42×C43—21no—
173C42×C43—21no—
174C42×C43—21no—
175C42×C43—42no—
176C22⋊Dic43—81no—
177C22⋊Dic43—81no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—81no—
187C4⋊Dic43—81no—
188Dic43⋊C4—42no—
189Dic43⋊C4—81no—
190C4×Dic43—81no—
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—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8#4112yes—
203C23×C43—21no—
204C23×C43—21no—
205C23×C43—21no—
206C23×C43—21no—
207C23×C43—21no—
208C23×C43—21no—
209C23×C43—22no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43C2×SD1612yes—
217C23×C43C22×D411yescharacteristic
218D4×C43—22no—
219D4×C43—22no—
220D4×C43—48no—
221D4×C43—41no—
222D4×C43—41no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—22no—
229C2×C4×C43—21no—
230C2×C4×C43—22no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
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×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—84no—
250C2×C4×C43—84no—
251C2×C4×C43C2×SD1612yes—
252C2×C4×C43C2×SD1612yes—
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43H(5,𝔽2)11yescharacteristic
258C2×C4×C432−1+411yescharacteristic
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C43⋊C8—22no—
272C43⋊C8—41no—
273C43⋊C8—41no—
274C43⋊C8—41no—
275#27032—431nomaximal, Sylow
276C22×C43—22no—
277C22×C43—22no—
278C22×C43—22no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—42no—
284C22×C43—42no—
285C22×C43—42no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43—81no—
289C22×C43—81no—
290C22×C43#52511yescharacteristic
291C22×C43#54611yescharacteristic
292C22×C43#54711yescharacteristic
293C22×C43C22×SD1611yescharacteristic
294C22×C43#57511yescharacteristic
295C22×C43#57611yescharacteristic
296C22×C43#57711yescharacteristic
297C4×C43—22no—
298C4×C43—22no—
299C4×C43—41no—
300C4×C43—42no—
301C4×C43—41no—
302C4×C43—42no—
303C4×C43—41no—
304C4×C43—81no—
305C4×C43#52911yescharacteristic
306C4×C43#53911yescharacteristic
307C4×C43#55311yescharacteristic
308C4×C43#55611yescharacteristic
309Dic43—81no—
310Dic43—81no—
311Dic43—81no—
312Dic43—81no—
313#2497—431no—
314#2361D4311yescharacteristic
315#2071—431no—
316#2065—431no—
317#2034—431no—
318#2034—431no—
319#1948—431no—
320#1941—431no—
321#1923—431no—
322#1920—431no—
323#1919—431no—
324#1864—431no—
325#1853—431no—
326#1823—431no—
327C4×#102—431no—
328C2×C43—42no—
329C2×C43—82no—
330C2×C43#246611yescharacteristic
331C2×C43#310111yescharacteristic
332C2×C43#311911yescharacteristic
333C2×C43#329511yescharacteristic
334C2×C43#332111yescharacteristic
335C2×C43#333511yescharacteristic
336C2×C43#335511yescharacteristic
337C2×#121C2×D4311yescharacteristic
338C2×C4×D4—21no—
339C2×C4×D4C2×D4311yescharacteristic
340C22×C4⋊C4C2×D4311yescharacteristic
341C2×#106—431no—
342C2×#106—431no—
343C2×#106—431no—
344C2×#106—431no—
345C2×C4⋊C8—431no—
346C2×#102—431no—
347C2×#102—431no—
348C2×#102—431no—
349C2×#102—431no—
350C2×C22⋊C8—431no—
351C2×C22⋊C8—431no—
352C2×C4×C8—431no—
353#400—861no—
354#396—861no—
355#390C2×D4311yescharacteristic
356#389—431no—
357#389—431no—
358#389C2×D4311yescharacteristic
359#388—21no—
360#388—861no—
361#387—861no—
362#386—21no—
363#385—21no—
364#384—431no—
365#380—431no—
366#380—431no—
367C4×C4⋊C4—431no—
368C4×C4⋊C4C2×D4311yescharacteristic
369C4×C22⋊C4C2×D4311yescharacteristic
370#340—431no—
371#340—431no—
372#340—431no—
373#340—431no—
374#340—431no—
375#340—431no—
376#340—431no—
377#340—431no—
378#336—431no—
379#336—431no—
380C43#2703211yescharacteristic, complemented, Sylow
381C22×D4—21no—
382C22×D4C22×D4311yescharacteristic
383C23×C4—21no—
384C23×C4—21no—
385C23×C4C22×D4311yescharacteristic
386C22×C8—431no—
387C22×C8—431no—
388C22×C8—431no—
389C22×C8—431no—
390#121—22no—
391#121—22no—
392C4×D4—22no—
393C4×D4—41no—
394C4×D4—44no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—41no—
399C2×C4⋊C4—431no—
400C2×C4⋊C4—431no—
401C2×C4⋊C4—431no—
402C2×C4⋊C4—431no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4—861no—
406C2×C4⋊C4—861no—
407C2×C4⋊C4C22×D4311yescharacteristic
408C2×C4⋊C4C22×D4311yescharacteristic
409C2×C4⋊C4C22×D4311yescharacteristic
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—861no—
415C2×C22⋊C4—861no—
416C2×C22⋊C4C22⋊D4311yescharacteristic
417C2×C22⋊C4C22⋊D4311yescharacteristic
418C2×C42—21no—
419C2×C42—861no—
420C2×C42C22×D4311yescharacteristic
421C2×C42C22×D4311yescharacteristic
422#106—862no—
423#106—862no—
424#106—862no—
425#106—1721no—
426C4⋊C8—862no—
427#102—862no—
428#102—862no—
429#102—862no—
430#102—1721no—
431C22⋊C8—862no—
432C22⋊C8—1721no—
433C4×C8—1721no—
434#95—21no—
435#95—21no—
436#95—861no—
437#95—861no—
438#95—861no—
439#95—861no—
440#95—861no—
441#95C22⋊D4311yescharacteristic
442#95C22⋊D4311yescharacteristic
443C24—21no—
444C24C2×C22⋊D4311yescharacteristic
445C2×D4—24no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—42no—
452C2×D4—42no—
453C2×D4#1062189812yes—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—81no—
468C22×C4—81no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4C2×C22⋊D4311yescharacteristic
474C22×C4C2×C22⋊D4311yescharacteristic
475C22×C4C2×C22⋊D4311yescharacteristic
476C22×C4C2×C22⋊D4311yescharacteristic
477C22×C4C2×C22⋊D4311yescharacteristic
478C22×C4C23×D4311yescharacteristic
479C2×C8—432no—
480C2×C8—861no—
481C2×C8—861no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8—861no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—861no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—42no—
496C4⋊C4—42no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—3441no—
506C4⋊C4—3441no—
507C4⋊C4—3441no—
508C4⋊C4—1722no—
509C4⋊C4#1062189812yes—
510C4⋊C4#1062190012yes—
511C22⋊C4—24no—
512C22⋊C4—41no—
513C22⋊C4—42no—
514C22⋊C4—42no—
515C22⋊C4—81no—
516C22⋊C4—3441no—
517C22⋊C4—3441no—
518C22⋊C4#1062188314yes—
519C42—21no—
520C42—21no—
521C42—21no—
522C42—21no—
523C42—42no—
524C42—3441no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—22no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23C2×#1062188312yes—
539C23C22×C22⋊D4311yescharacteristic
540D4—22no—
541D4—22no—
542D4—48no—
543D4—41no—
544D4—41no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—84no—
572C2×C4—84no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4—1721no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4C2×#1062188312yes—
586C2×C4C2×#1062188312yes—
587C2×C4#41×D4311yescharacteristic
588C2×C4C2×#1062190011yescharacteristic
589C2×C4C2×#1062189811yescharacteristic
590C2×C4C2×#1062189811yescharacteristic
591C2×C4#1306337011yescharacteristic
592C2×C4#1306337211yescharacteristic
593C8—862no—
594C8—1721no—
595C8—1721no—
596C8—1721no—
597C22—22no—
598C22—22no—
599C22—22no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—81no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22#1458341011yescharacteristic
612C22#1458354311yescharacteristic
613C22#1458354811yescharacteristic
614C22C22×#1062188311yescharacteristic
615C22#1458369711yescharacteristic
616C22#1458370211yescharacteristic
617C22#1458370711yescharacteristic
618C4—22no—
619C4—22no—
620C4—41no—
621C4—41no—
622C4—42no—
623C4—42no—
624C4—41no—
625C4—81no—
626C4—3441no—
627C4—3441no—
628C4—3441no—
629C4—3441no—
630C4#1458342911yescharacteristic
631C4#1458349111yescharacteristic
632C4#1458359911yescharacteristic
633C4#1458361911yescharacteristic
634C2—42no—
635C2—82no—
636C2#1913862511yescharacteristic
637C2#1914460311yescharacteristic
638C2#1914479411yescharacteristic
639C2#1914641911yescharacteristic
640C2#1914678111yescharacteristic
641C2#1914695211yescharacteristic
642C2#1914719511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2361C2
socleC23×C43C22×D4
prime radicalC2×#121×C43C22
hypercenter#2361D43
hypocenterC43#27032
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2361

Complements

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

NH ≅ G/Ntype
1. #19139028C2semidirect
2. #19135998C2semidirect
3. #19135969C2semidirect
6. #19135358C2semidirect
7. #19135320C2semidirect
8. #19135203C2semidirect
9. #19135180C2semidirect
10. #19135170C2semidirect
11. #19134856C2semidirect
12. #19134788C2semidirect
13. #19134681C2semidirect
14. C4×#13063246C2semidirect
380. C43#27032semidirect

Maximal subgroups

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

subgroupindex
#191390282
#191359982
#191359692
#191357812
#191353582
#191353202
#191352032
#191351802
#191351702
#191348562
#191347882
#191346812
C4×#130632462
C43×#23612
#2703243