Finite Group Databasebeta

← #25160158

Subgroups — #25160158

Order 11008.

802 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138288C211yesmaximal, characteristic, complemented
2#19137638C211yesmaximal, characteristic
3#19136167C211yesmaximal, characteristic, complemented
4#19136094C211yesmaximal, characteristic, complemented
5#19135731C211yesmaximal, characteristic, complemented
6#19135546C211yesmaximal, characteristic, complemented
7#19135184C211yesmaximal, characteristic, complemented
8#19135020C211yesmaximal, characteristic
9#19134914C211yesmaximal, characteristic
10#19134840C211yesmaximal, characteristic, complemented
11#19134793C211yesmaximal, characteristic, complemented
12#19134771C211yesmaximal, characteristic, complemented
13#19134603C211yesmaximal, characteristic, complemented
14#19134310C211yesmaximal, characteristic, complemented
15C43×#2065C211yesmaximal, characteristic, complemented
16C22×C8×D43C2211yescharacteristic
17C2×#13063325C2211yescharacteristic
18C2×#13063296C2211yescharacteristic
19C2×D4×Dic43C2211yescharacteristic
20C2×#13063283C2211yescharacteristic
21C2×#13063283C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×Dic43⋊C8C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×(C2×D43)⋊C8C2211yescharacteristic
27#14582821—21no—
28#14582812—21no—
29#14582803—21no—
30#14582799—21no—
31#14582795C2211yescharacteristic
32#14582795C2211yescharacteristic
33#14582793—21no—
34#14582785—21no—
35#14582776—21no—
36#14582764C2211yescharacteristic
37#14582756C2211yescharacteristic
38C4×C4⋊Dic43C2211yescharacteristic
39C22⋊C4×Dic43—21no—
40C4×(C2×D43)⋊C4C2211yescharacteristic
41#14582662C2211yescharacteristic
42#14582662C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#106×C43C2211yescharacteristic
53C2×C4⋊C8×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C43×#390C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×Dic86—21no—
60C22×C22⋊D43—21no—
61C23×Dic43—21no—
62C22×C4×D43C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65C2×C8×D43—22no—
66C2×C8×D43—41no—
67C2×C8×D43—41no—
68#13063325—22no—
69#13063325—41no—
70#13063296—22no—
71#13063296Q814yescomplemented
72D4×Dic43—22no—
73D4×Dic43—41no—
74#13063283—22no—
75#13063283—22no—
76#13063283—41no—
77#13063283—41no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4D411yescharacteristic
91C2×(C2×D43)⋊C4D411yescharacteristic
92C2×C4×Dic43—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43C2311yescharacteristic
96#13063258—22no—
97Dic43⋊C8—41no—
98#13063246—22no—
99#13063246—41no—
100(C2×D43)⋊C8—22no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95D411yescharacteristic
108C43⋊#95D411yescharacteristic
109C22×D4×C43C2311yescharacteristic
110C22×C8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C22⋊C4×C43—21no—
117C2×C22⋊C4×C43—21no—
118C2×C42×C43C2311yescharacteristic
119#106×C43—41no—
120C4⋊C8×C43—41no—
121#102×C43—41no—
122#102×C43—41no—
123#95×C43—21no—
124C24×C43—21no—
125C23×D43C2×D411yescharacteristic
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43C2×Q812yes—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2411yescharacteristic
138C2×C22⋊D43—24no—
139C2×C22⋊D43—81no—
140C2×C22⋊D43—81no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—42no—
146C22×Dic43—42no—
147C22×Dic43—81no—
148C22×Dic43C2×D411yescharacteristic
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C2×C4×D43—21no—
152C2×C4×D43—21no—
153C2×C4×D43—21no—
154C2×C4×D43—21no—
155C2×C4×D43C2×Q812yes—
156C2×C4×D43#4112yes—
157C2×Dic86—42no—
158C2×Dic86—42no—
159C2×Dic86—81no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—42no—
173C22⋊C4×C43—42no—
174C22⋊C4×C43—81no—
175C42×C43—21no—
176C42×C43—21no—
177C22⋊Dic43—24no—
178C22⋊Dic43—42no—
179(C2×D43)⋊C4—22no—
180(C2×D43)⋊C4—41no—
181(C2×D43)⋊C4—42no—
182(C2×D43)⋊C4—42no—
183(C2×D43)⋊C4—81no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—42no—
190C4⋊Dic43C2×Q812yes—
191C4⋊Dic43#4112yes—
192C4⋊Dic43#4112yes—
193Dic43⋊C4—81no—
194Dic43⋊C4—81no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—42no—
198C4×Dic43—42no—
199C4×Dic43—81no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C8×D43—44no—
207C23×C43—22no—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43C22×D411yescharacteristic
215C22×D43—21no—
216C22×D43—21no—
217C22×D43—21no—
218C22×D43—21no—
219C22×D43—21no—
220C22×D43—21no—
221C22×D43C22⋊Q812yes—
222D4×C43—22no—
223D4×C43—22no—
224D4×C43—41no—
225D4×C43—41no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
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×C43—41no—
240C2×C4×C43#13512yes—
241C2×C4×C43C22×Q811yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43H(5,𝔽2)11yescharacteristic
246C2×C4×C43H(5,𝔽2)11yescharacteristic
247C22⋊D43—84no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—22no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—22no—
254C2×Dic43—22no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
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—84no—
269C2×Dic43C22⋊Q812yes—
270C4×D43—22no—
271C4×D43—22no—
272C4×D43—22no—
273C4×D43—22no—
274Dic86—84no—
275C8×C43—41no—
276C8×C43—41no—
277C43⋊C8—41no—
278C43⋊C8—41no—
279#26409—431nomaximal, Sylow
280C22×C43—42no—
281C22×C43—42no—
282C22×C43—42no—
283C22×C43—81no—
284C22×C43—81no—
285C22×C43—81no—
286C22×C43—81no—
287C22×C43C2×C22⋊Q811yescharacteristic
288C22×C43#54611yescharacteristic
289C22×C43#54611yescharacteristic
290C22×C43C2×#13511yescharacteristic
291C22×C43#57511yescharacteristic
292C22×C43#57611yescharacteristic
293C22×C43#57711yescharacteristic
294C2×D43—22no—
295C2×D43—22no—
296C2×D43—22no—
297C2×D43—41no—
298C2×D43—41no—
299C2×D43—41no—
300C2×D43—41no—
301C4×C43—22no—
302C4×C43—41no—
303C4×C43—81no—
304C4×C43—81no—
305C4×C43—81no—
306C4×C43#52911yescharacteristic
307C4×C43#53811yescharacteristic
308C4×C43#55411yescharacteristic
309C4×C43#55411yescharacteristic
310Dic43—22no—
311Dic43—42no—
312Dic43—42no—
313Dic43—41no—
314Dic43—41no—
315Dic43—42no—
316Dic43—81no—
317#2439—431no—
318#2363—431no—
319#2101—431no—
320#2088—431no—
321#2065D4311yescharacteristic, complemented
322#2023—431no—
323#1988—431no—
324#1921—431no—
325#1893—431no—
326#1875—431no—
327#1862—431no—
328#1854—431no—
329#1850—431no—
330#1804—431no—
331#1735—431no—
332C2×C43—82no—
333C2×C43#245011yescharacteristic
334C2×C43#307611yescharacteristic
335C2×C43#308111yescharacteristic
336C2×C43#329711yescharacteristic
337C2×C43#330411yescharacteristic
338C2×C43#331911yescharacteristic
339C2×C43#332111yescharacteristic
340D43—42no—
341C23×C8—431no—
342C2×C4⋊Q8—431no—
343C2×#121—431no—
344C2×C4×D4—431no—
345C2×#117—431no—
346C2×#117—431no—
347C2×#107—431no—
348C2×#106C2×D4311yescharacteristic
349C2×C4⋊C8—431no—
350C2×C4⋊C8C2×D4311yescharacteristic
351C2×#102—431no—
352C2×#102—431no—
353C2×#102C2×D4311yescharacteristic
354C2×#102C2×D4311yescharacteristic
355C2×C22⋊C8—431no—
356#396—861no—
357#393—861no—
358#391—861no—
359#390—861no—
360#390C2×D4311yescharacteristic
361#389—431no—
362#389—431no—
363#389C2×D4311yescharacteristic
364#388—861no—
365#387—861no—
366#386—861no—
367#382—431no—
368#380—431no—
369C4×C4⋊C4—431no—
370C4×C22⋊C4—431no—
371C4×C22⋊C4—861no—
372#340—431no—
373#340—431no—
374#340—431no—
375#340—431no—
376#340—431no—
377#340—431no—
378#340—431no—
379#340—431no—
380#340—431no—
381#340C2×D4311yescharacteristic
382#336—431no—
383#336—431no—
384C43#2640911yescharacteristic, complemented, Sylow
385C22×Q8—861no—
386C22×D4—861no—
387C22×D4C22×D4311yescharacteristic
388C23×C4—431no—
389C23×C4—861no—
390C22×C8—431no—
391C22×C8—431no—
392C22×C8—862no—
393C22×C8—1721no—
394C22×C8—1721no—
395C22×C8C22×D4311yescharacteristic
396C22×C8C22×D4311yescharacteristic
397C4⋊Q8—862no—
398C4⋊Q8—1721no—
399#121—434no—
400#121—862no—
401C4×D4—862no—
402C4×D4—1721no—
403#117—862no—
404#117—862no—
405#117—1721no—
406#117—1721no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—431no—
409C2×C4⋊C4—431no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4C22×D4311yescharacteristic
416C2×C4⋊C4C22×D4311yescharacteristic
417C2×C4⋊C4C22×D4311yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—431no—
421C2×C22⋊C4—431no—
422C2×C22⋊C4—861no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4—861no—
426C2×C22⋊C4—861no—
427C2×C42—431no—
428C2×C42—861no—
429C2×C42—861no—
430C2×C42—861no—
431C2×C42C22×D4311yescharacteristic
432#107—862no—
433#106—41no—
434C4⋊C8—41no—
435C4⋊C8—1721no—
436#102—41no—
437#102—41no—
438#102—862no—
439#102—1721no—
440C22⋊C8—862no—
441#95—21no—
442#95—431no—
443#95—431no—
444#95—861no—
445#95—861no—
446#95—861no—
447#95—861no—
448#95—861no—
449#95—861no—
450C24—21no—
451C24—431no—
452C2×Q8—3441no—
453C2×Q8—1722no—
454C2×Q8—1722no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—864no—
461C2×D4—3441no—
462C2×D4—3441no—
463C2×D4Q8×D4312yes—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—431no—
468C22×C4—432no—
469C22×C4—432no—
470C22×C4—431no—
471C22×C4—431no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4—861no—
478C22×C4—861no—
479C22×C4—861no—
480C22×C4—3441no—
481C22×C4—1722no—
482C22×C4—1722no—
483C22×C4D4×D4311yescharacteristic
484C22×C4D4×D4311yescharacteristic
485C22×C4C23×D4311yescharacteristic
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—861no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8—861no—
496C2×C8—861no—
497C2×C8—861no—
498C2×C8—1724no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—42no—
506C4⋊C4—432no—
507C4⋊C4—432no—
508C4⋊C4—432no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—3441no—
515C4⋊C4—3441no—
516C4⋊C4—1722no—
517C22⋊C4—42no—
518C22⋊C4—81no—
519C22⋊C4—864no—
520C22⋊C4—862no—
521C22⋊C4—3441no—
522C22⋊C4—1721no—
523C22⋊C4—1722no—
524C22⋊C4—1722no—
525C22⋊C4—1722no—
526C42—21no—
527C42—21no—
528C42—861no—
529C42—861no—
530C42—3441no—
531C42—1722no—
532C42—1722no—
533C23—22no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—432no—
541C23—861no—
542C23—861no—
543C23—861no—
544C23—861no—
545C23—861no—
546C23—861no—
547C23C2×D4×D4311yescharacteristic
548Q8—3444no—
549D4—22no—
550D4—22no—
551D4—41no—
552D4—41no—
553D4—3444no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—41no—
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—432no—
569C2×C4—861no—
570C2×C4—861no—
571C2×C4—862no—
572C2×C4—862no—
573C2×C4—862no—
574C2×C4—862no—
575C2×C4—862no—
576C2×C4—861no—
577C2×C4—861no—
578C2×C4—861no—
579C2×C4—861no—
580C2×C4—862no—
581C2×C4—861no—
582C2×C4—861no—
583C2×C4—862no—
584C2×C4—3444no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4#1306334612yes—
595C2×C4C2×Q8×D4311yescharacteristic
596C2×C4#41×D4311yescharacteristic
597C2×C4#41×D4311yescharacteristic
598C2×C4#41×D4311yescharacteristic
599C2×C4#1306337011yescharacteristic
600C2×C4#1306337011yescharacteristic
601C8—41no—
602C8—41no—
603C8—1721no—
604C8—1721no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—862no—
613C22—862no—
614C22—862no—
615C22—1721no—
616C22—1721no—
617C22—1721no—
618C22—1721no—
619C22C22⋊Q8×D4311yescharacteristic
620C22#1458353811yescharacteristic
621C22#1458354611yescharacteristic
622C22C2×#1306334611yescharacteristic
623C22#1458369511yescharacteristic
624C22#1458370111yescharacteristic
625C22#1458370911yescharacteristic
626C4—22no—
627C4—41no—
628C4—81no—
629C4—81no—
630C4—81no—
631C4—862no—
632C4—3441no—
633C4—1721no—
634C4—1722no—
635C4—1721no—
636C4—1722no—
637C4—1722no—
638C4#1458343211yescharacteristic
639C4#1458348111yescharacteristic
640C4#1458360311yescharacteristic
641C4#1458360311yescharacteristic
642C2—82no—
643C2—1722no—
644C2#1913841411yescharacteristic
645C2#1914438411yescharacteristic
646C2#1914442311yescharacteristic
647C2#1914645111yescharacteristic
648C2#1914653711yescharacteristic
649C2#1914675811yescharacteristic
650C2#1914677611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2065C2
socleC23×C43C22×D4
prime radicalC2×#13063296C22
hypercenter#2065D43
hypocenterC43#26409
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2065

Complements

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

NH ≅ G/Ntype
1. #19138288C2semidirect
3. #19136167C2semidirect
4. #19136094C2semidirect
5. #19135731C2semidirect
6. #19135546C2semidirect
7. #19135184C2semidirect
10. #19134840C2semidirect
11. #19134793C2semidirect
12. #19134771C2semidirect
13. #19134603C2semidirect
14. #19134310C2semidirect
15. C43×#2065C2semidirect
71. #13063296Q8semidirect
321. #2065D43semidirect
384. C43#26409semidirect

Maximal subgroups

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

subgroupindex
#191382882
#191376382
#191361672
#191360942
#191357312
#191355462
#191351842
#191350202
#191349142
#191348402
#191347932
#191347712
#191346032
#191343102
C43×#20652
#2640943