Finite Group Databasebeta

← #25160159

Subgroups — #25160159

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#19137631C211yesmaximal, characteristic
2#19136162C211yesmaximal, characteristic, complemented
3#19136097C211yesmaximal, characteristic, complemented
4#19135966C211yesmaximal, characteristic, complemented
5#19135728C211yesmaximal, characteristic, complemented
6#19135548C211yesmaximal, characteristic, complemented
7#19135184C211yesmaximal, characteristic, complemented
8#19135021C211yesmaximal, characteristic
9#19134917C211yesmaximal, characteristic
10#19134841C211yesmaximal, characteristic, complemented
11#19134792C211yesmaximal, characteristic, complemented
12#19134775C211yesmaximal, characteristic, complemented
13#19134602C211yesmaximal, characteristic, complemented
14#19134311C211yesmaximal, characteristic, complemented
15C43×#2439C211yesmaximal, characteristic, complemented
16C23×C43⋊C8C2211yescharacteristic
17C2×#13063299C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19C2×#13063284C2211yescharacteristic
20C2×#13063258C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×C4⋊(C43⋊C8)C2211yescharacteristic
23C2×C4⋊(C43⋊C8)C2211yescharacteristic
24C2×#13063245C2211yescharacteristic
25C2×#13063245C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×C22⋊(C43⋊C8)C2211yescharacteristic
29#14582801C2211yescharacteristic
30#14582799—21no—
31#14582797C2211yescharacteristic
32#14582788—21no—
33#14582775—21no—
34C4×C4⋊Dic43C2211yescharacteristic
35#14582746—21no—
36#14582661C2211yescharacteristic
37#14582661C2211yescharacteristic
38#14582661C2211yescharacteristic
39#14582661C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C2×C4⋊Q8×C43C2211yescharacteristic
49C2×#117×C43C2211yescharacteristic
50C43×#396—21no—
51C43×#393—21no—
52C43×#391—21no—
53C43×#389C2211yescharacteristic
54C43×#389C2211yescharacteristic
55C43×#387—21no—
56C43×#382C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C4×C22⋊C4×C43C2211yescharacteristic
59C22×D172C2311yescharacteristic
60C22×C22⋊D43—21no—
61C22×C4×D43—21no—
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#13063299—22no—
70#13063299Q814yescomplemented
71C4×D172—22no—
72C4×D172—41no—
73#13063284—22no—
74#13063284—41no—
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×Dic43⋊C4—21no—
79C2×C22⋊Dic43—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86#13063258—22no—
87#13063256—41no—
88C4⋊(C43⋊C8)—41no—
89C4⋊(C43⋊C8)—41no—
90#13063245—22no—
91#13063245—41no—
92#13063245—41no—
93#13063245—41no—
94C22⋊(C43⋊C8)—22no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C22×Q8×C43—21no—
98C23×C4×C43C2311yescharacteristic
99C4⋊Q8×C43—22no—
100C4⋊Q8×C43—41no—
101#117×C43—22no—
102#117×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×C4⋊C4×C43C2311yescharacteristic
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×C43—21no—
120#95×C43—21no—
121#95×C43—21no—
122#95×C43D411yescharacteristic
123#95×C43D411yescharacteristic
124C24×C43C2×D411yescharacteristic
125C23×D43—21no—
126C2×Q8×C43—42no—
127C2×Q8×C43—42no—
128C2×Q8×C43—81no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
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×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×Q812yes—
143C22×C4×C43#4112yes—
144C22×C4×C43C2411yescharacteristic
145C2×C22⋊D43—24no—
146C2×C22⋊D43—81no—
147C2×C22⋊D43—81no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172C2×Q812yes—
157C2×C4×D43—42no—
158C2×C4×D43—42no—
159C2×C4×D43—81no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—42no—
168C4⋊C4×C43—42no—
169C4⋊C4×C43—81no—
170C4⋊C4×C43#4112yes—
171C22⋊C4×C43—22no—
172C22⋊C4×C43—41no—
173C22⋊C4×C43—42no—
174C22⋊C4×C43—81no—
175C42×C43—21no—
176C42×C43—21no—
177C42×C43—21no—
178C42×C43—21no—
179C42×C43—42no—
180C22⋊Dic43—42no—
181(C2×D43)⋊C4—24no—
182(C2×D43)⋊C4—42no—
183(C2×D43)⋊C4—42no—
184(C2×D43)⋊C4—81no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43C2×Q812yes—
190C4⋊Dic43#4112yes—
191Dic43⋊C4—81no—
192C4×Dic43—42no—
193C4×Dic43—81no—
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—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—44no—
207C23×C43—21no—
208C23×C43—21no—
209C23×C43—21no—
210C23×C43—21no—
211C23×C43—21no—
212C23×C43—21no—
213C23×C43C22⋊Q812yes—
214C23×C43C22×D411yescharacteristic
215C22×D43—22no—
216C22×D43—41no—
217C22×D43—41no—
218C22×D43—41no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—41no—
222Q8×C43—84no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—22no—
228C2×C4×C43—22no—
229C2×C4×C43—22no—
230C2×C4×C43—22no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—22no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
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—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43C22⋊Q812yes—
253C2×C4×C43#13512yes—
254C2×C4×C43C22×Q811yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43H(5,𝔽2)11yescharacteristic
259C2×C4×C43H(5,𝔽2)11yescharacteristic
260C22⋊D43—84no—
261C2×Dic43—22no—
262C2×Dic43—22no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270D172—22no—
271D172—22no—
272D172—41no—
273D172—41no—
274C4×D43—84no—
275C43⋊C8—41no—
276C43⋊C8—41no—
277C43⋊C8—41no—
278C43⋊C8—41no—
279#26409—431nomaximal, Sylow
280C22×C43—22no—
281C22×C43—22no—
282C22×C43—22no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43—41no—
286C22×C43—41no—
287C22×C43C2×C22⋊Q811yescharacteristic
288C22×C43#54611yescharacteristic
289C22×C43#54611yescharacteristic
290C22×C43C2×#13511yescharacteristic
291C22×C43#57511yescharacteristic
292C22×C43#57611yescharacteristic
293C22×C43#57711yescharacteristic
294C2×D43—42no—
295C2×D43—42no—
296C2×D43—42no—
297C2×D43—81no—
298C2×D43—81no—
299C2×D43—81no—
300C2×D43—81no—
301C4×C43—22no—
302C4×C43—22no—
303C4×C43—42no—
304C4×C43—41no—
305C4×C43—41no—
306C4×C43—41no—
307C4×C43—81no—
308C4×C43—81no—
309C4×C43—81no—
310C4×C43#52911yescharacteristic
311C4×C43#53811yescharacteristic
312C4×C43#55411yescharacteristic
313C4×C43#55411yescharacteristic
314Dic43—42no—
315Dic43—42no—
316Dic43—81no—
317#2439D4311yescharacteristic, complemented
318#2363—431no—
319#2101—431no—
320#2088—431no—
321#2065—431no—
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—42no—
333C2×C43#245011yescharacteristic
334C2×C43#307611yescharacteristic
335C2×C43#308111yescharacteristic
336C2×C43#329711yescharacteristic
337C2×C43#330411yescharacteristic
338C2×C43#331911yescharacteristic
339C2×C43#332111yescharacteristic
340D43—82no—
341C23×C8—431no—
342C2×C4⋊Q8C2×D4311yescharacteristic
343C2×#121—431no—
344C2×C4×D4—431no—
345C2×#117—431no—
346C2×#117C2×D4311yescharacteristic
347C2×#107—431no—
348C2×#106—431no—
349C2×C4⋊C8—431no—
350C2×C4⋊C8—431no—
351C2×#102—431no—
352C2×#102—431no—
353C2×#102—431no—
354C2×#102—431no—
355C2×C22⋊C8—431no—
356#396—21no—
357#393—21no—
358#391—21no—
359#390—431no—
360#390—861no—
361#389—431no—
362#389C2×D4311yescharacteristic
363#389C2×D4311yescharacteristic
364#388—861no—
365#387—21no—
366#386—861no—
367#382C2×D4311yescharacteristic
368#380C2×D4311yescharacteristic
369C4×C4⋊C4—431no—
370C4×C22⋊C4—861no—
371C4×C22⋊C4C2×D4311yescharacteristic
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#340—431no—
382#336—431no—
383#336—431no—
384C43#2640911yescharacteristic, complemented, Sylow
385C22×Q8—21no—
386C22×D4—431no—
387C22×D4—861no—
388C23×C4—861no—
389C23×C4C22×D4311yescharacteristic
390C22×C8—431no—
391C22×C8—431no—
392C22×C8—431no—
393C22×C8—431no—
394C22×C8—862no—
395C22×C8—1721no—
396C22×C8—1721no—
397C4⋊Q8—22no—
398C4⋊Q8—41no—
399#121—434no—
400#121—862no—
401C4×D4—862no—
402C4×D4—1721no—
403#117—22no—
404#117—41no—
405#117—862no—
406#117—1721no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4C22×D4311yescharacteristic
415C2×C4⋊C4C22×D4311yescharacteristic
416C2×C4⋊C4C22×D4311yescharacteristic
417C2×C4⋊C4C22×D4311yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—861no—
421C2×C22⋊C4—861no—
422C2×C22⋊C4—861no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4C22⋊D4311yescharacteristic
426C2×C22⋊C4C22⋊D4311yescharacteristic
427C2×C42—21no—
428C2×C42—861no—
429C2×C42—861no—
430C2×C42C22×D4311yescharacteristic
431C2×C42C22×D4311yescharacteristic
432#107—862no—
433#106—1721no—
434C4⋊C8—1721no—
435C4⋊C8—1721no—
436#102—862no—
437#102—1721no—
438#102—1721no—
439#102—1721no—
440C22⋊C8—862no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—861no—
447#95—861no—
448#95C22⋊D4311yescharacteristic
449#95C22⋊D4311yescharacteristic
450C24—861no—
451C24C2×C22⋊D4311yescharacteristic
452C2×Q8—42no—
453C2×Q8—42no—
454C2×Q8—81no—
455C2×D4—432no—
456C2×D4—864no—
457C2×D4—861no—
458C2×D4—861no—
459C2×D4—861no—
460C2×D4—861no—
461C2×D4—861no—
462C2×D4—3441no—
463C2×D4—3441no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—3441no—
476C22×C4—1722no—
477C22×C4—1722no—
478C22×C4Q8×D4312yes—
479C22×C4#1062190212yes—
480C22×C4C2×C22⋊D4311yescharacteristic
481C22×C4C2×C22⋊D4311yescharacteristic
482C22×C4C2×C22⋊D4311yescharacteristic
483C22×C4C2×C22⋊D4311yescharacteristic
484C22×C4C2×C22⋊D4311yescharacteristic
485C22×C4C23×D4311yescharacteristic
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8—861no—
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—21no—
506C4⋊C4—42no—
507C4⋊C4—42no—
508C4⋊C4—81no—
509C4⋊C4—432no—
510C4⋊C4—432no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—3441no—
516C4⋊C4#1062190012yes—
517C22⋊C4—22no—
518C22⋊C4—41no—
519C22⋊C4—42no—
520C22⋊C4—81no—
521C22⋊C4—864no—
522C22⋊C4—3441no—
523C22⋊C4—1722no—
524C22⋊C4—1722no—
525C22⋊C4—1722no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—42no—
531C42—3441no—
532C42—1722no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—862no—
540C23—1721no—
541C23—1721no—
542C23—1721no—
543C23—1721no—
544C23—1721no—
545C23—1721no—
546C23#1306330112yes—
547C23C22×C22⋊D4311yescharacteristic
548Q8—84no—
549D4—862no—
550D4—862no—
551D4—3444no—
552D4—1721no—
553D4—1721no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—22no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—862no—
584C2×C4—862no—
585C2×C4—3444no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4#1306330112yes—
594C2×C4#1306334512yes—
595C2×C4C2×Q8×D4311yescharacteristic
596C2×C4#41×D4311yescharacteristic
597C2×C4C2×#1062190011yescharacteristic
598C2×C4C2×#1062190211yescharacteristic
599C2×C4#1306337011yescharacteristic
600C2×C4#1306337111yescharacteristic
601C8—1721no—
602C8—1721no—
603C8—1721no—
604C8—1721no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—3441no—
613C22—3441no—
614C22—3441no—
615C22—3441no—
616C22—1722no—
617C22—1722no—
618C22—1722no—
619C22C2×#1306330111yescharacteristic
620C22#1458353711yescharacteristic
621C22#1458354311yescharacteristic
622C22C2×#1306334511yescharacteristic
623C22#1458369711yescharacteristic
624C22#1458370211yescharacteristic
625C22#1458370711yescharacteristic
626C4—22no—
627C4—22no—
628C4—41no—
629C4—41no—
630C4—42no—
631C4—41no—
632C4—81no—
633C4—81no—
634C4—81no—
635C4—3441no—
636C4—1722no—
637C4—1722no—
638C4#1458343511yescharacteristic
639C4#1458348911yescharacteristic
640C4#1458360311yescharacteristic
641C4#1458360711yescharacteristic
642C2—42no—
643C2—3442no—
644C2#1913841511yescharacteristic
645C2#1914437711yescharacteristic
646C2#1914442011yescharacteristic
647C2#1914644511yescharacteristic
648C2#1914652811yescharacteristic
649C2#1914674511yescharacteristic
650C2#1914678111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2439C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
hypercenter#2439D43
hypocenterC43#26409
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2439

Complements

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

NH ≅ G/Ntype
2. #19136162C2semidirect
3. #19136097C2semidirect
4. #19135966C2semidirect
5. #19135728C2semidirect
6. #19135548C2semidirect
7. #19135184C2semidirect
10. #19134841C2semidirect
11. #19134792C2semidirect
12. #19134775C2semidirect
13. #19134602C2semidirect
14. #19134311C2semidirect
15. C43×#2439C2semidirect
70. #13063299Q8semidirect
317. #2439D43semidirect
384. C43#26409semidirect

Maximal subgroups

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

subgroupindex
#191376312
#191361622
#191360972
#191359662
#191357282
#191355482
#191351842
#191350212
#191349172
#191348412
#191347922
#191347752
#191346022
#191343112
C43×#24392
#2640943