Finite Group Databasebeta

← #25115817

Subgroups — #25115817

Order 11008.

906 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582979C211yesmaximal, characteristic
2#19137567C211yesmaximal, characteristic, complemented
3#19137504C211yesmaximal, characteristic, complemented
4#19135294C211yesmaximal, characteristic, complemented
5#19135169C211yesmaximal, characteristic, complemented
6#19135163C211yesmaximal, characteristic, complemented
7#19134946C211yesmaximal, characteristic
8#19134940C211yesmaximal, characteristic
9#19134724C211yesmaximal, characteristic, complemented
10#19134604C211yesmaximal, characteristic, complemented
11#19134603C211yesmaximal, characteristic, complemented
12#19134463C211yesmaximal, characteristic, complemented
13#19134421C211yesmaximal, characteristic, complemented
14#19134419C211yesmaximal, characteristic, complemented
15C43×#1936C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C2×C4×D172C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19C2×#13063287C2211yescharacteristic
20C2×#13063287C2211yescharacteristic
21#14582979C418yescomplemented
22C2×#13063258C2211yescharacteristic
23C2×Dic43⋊C8C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063235C2211yescharacteristic
29C2×C8×Dic43C2211yescharacteristic
30#14582802C2211yescharacteristic
31#14582798C2211yescharacteristic
32#14582793—21no—
33#14582787—21no—
34#14582773—21no—
35#14582770—21no—
36#14582764C2211yescharacteristic
37#14582764C2211yescharacteristic
38#14582760—21no—
39#14582756—21no—
40C4⋊C4×Dic43C2211yescharacteristic
41C4×Dic43⋊C4C2211yescharacteristic
42C4×C4⋊Dic43C2211yescharacteristic
43C22⋊C4×Dic43—21no—
44#95×D43—21no—
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582654C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×#102×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#97×C43C2211yescharacteristic
56C43×#390C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C22×D172C2311yescharacteristic
61C23×Dic43—21no—
62C22×C4×D43—21no—
63C22×C4×D43—21no—
64C22×C4×D43—21no—
65C2×#10621882—22no—
66C2×#10621882—22no—
67C2×#10621882C2×C414yes—
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70C4×D172—22no—
71C4×D172—41no—
72D4×Dic43—22no—
73D4×Dic43C2×C414yescomplemented
74#13063287—22no—
75#13063287—22no—
76#13063287—41no—
77#13063287C2×C414yes—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×Dic43⋊C4D411yescharacteristic
83C2×Dic43⋊C4D411yescharacteristic
84C2×C22⋊Dic43—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×C4×Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43C2311yescharacteristic
93C2×C4×Dic43C2311yescharacteristic
94#13063258C2×C414yescomplemented
95Dic43⋊C8—22no—
96#13063247—22no—
97#13063247C2×C414yes—
98#13063246—41no—
99#13063245—22no—
100#13063235—41no—
101C8×Dic43C2×C414yescomplemented
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95D411yescharacteristic
110C43⋊#95D411yescharacteristic
111C22×D4×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C2×C4⋊C4×C43—21no—
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C22⋊C4×C43—21no—
119C2×C22⋊C4×C43—21no—
120C2×C42×C43C2311yescharacteristic
121#102×C43—41no—
122#102×C43C2×C414yescomplemented
123#97×C43—41no—
124#95×C43—21no—
125C24×C43—21no—
126C23×D43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43C22×C412yes—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2411yescharacteristic
139C22×Dic43—24no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—81no—
144C22×Dic43—81no—
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C22×Dic43C2×D411yescharacteristic
148C22×Dic43C2×D411yescharacteristic
149C2×D172—21no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172C22×C412yes—
153C2×D172#4112yes—
154C2×D172#4112yes—
155C2×C4×D43—24no—
156C2×C4×D43—42no—
157C2×C4×D43—42no—
158C2×C4×D43—42no—
159C2×C4×D43—42no—
160C2×C4×D43—81no—
161C2×C4×D43—81no—
162C2×C4×D43—81no—
163C2×C4×D43—81no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43C22×C412yes—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—81no—
176C4⋊C4×C43C22×C412yes—
177C22⋊C4×C43—42no—
178C22⋊C4×C43—81no—
179C42×C43—21no—
180C42×C43—21no—
181C22⋊Dic43—24no—
182C22⋊Dic43—42no—
183C22⋊Dic43—81no—
184#10621882—28no—
185(C2×D43)⋊C4—24no—
186(C2×D43)⋊C4—42no—
187(C2×D43)⋊C4—42no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—81no—
194C4⋊Dic43C22×C412yes—
195Dic43⋊C4—41no—
196Dic43⋊C4—41no—
197C4×Dic43—21no—
198C4×Dic43—21no—
199C4×Dic43—81no—
200C4×Dic43—81no—
201C4×Dic43C22×C412yes—
202C4×Dic43#4112yes—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8C22×C412yes—
209C23×C43—22no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43C22×D411yescharacteristic
217C22×D43—22no—
218C22×D43—22no—
219C22×D43—22no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—41no—
223C22×D43—41no—
224D4×C43—22no—
225D4×C43—22no—
226D4×C43—41no—
227D4×C43—41no—
228C2×C4×C43—22no—
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—41no—
236C2×C4×C43—41no—
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×C43C23×C411yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43H(5,𝔽2)11yescharacteristic
248C2×C4×C432−1+411yescharacteristic
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—22no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
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×Dic43C4×D412yes—
270C2×Dic43C4×D412yes—
271D172—22no—
272D172—22no—
273D172—22no—
274D172#11714yes—
275C4×D43—84no—
276C4×D43—84no—
277C4×D43—84no—
278C8×C43—22no—
279C8×C43—41no—
280C43⋊C8—22no—
281C43⋊C8—41no—
282#22764—431nomaximal, Sylow
283C22×C43—42no—
284C22×C43—42no—
285C22×C43—42no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43—81no—
289C22×C43—81no—
290C22×C43C2×C4×D411yescharacteristic
291C22×C43#54611yescharacteristic
292C22×C43#54811yescharacteristic
293C22×C43#57511yescharacteristic
294C22×C43#57511yescharacteristic
295C22×C43#57611yescharacteristic
296C22×C43#57611yescharacteristic
297C2×D43—24no—
298C2×D43—42no—
299C2×D43—42no—
300C2×D43—42no—
301C2×D43—42no—
302C2×D43—42no—
303C2×D43—42no—
304C4×C43—42no—
305C4×C43—41no—
306C4×C43—41no—
307C4×C43—81no—
308C4×C43—81no—
309C4×C43C2×#11711yescharacteristic
310C4×C43#52011yescharacteristic
311C4×C43#55211yescharacteristic
312C4×C43#55311yescharacteristic
313Dic43—22no—
314Dic43—22no—
315Dic43—42no—
316Dic43—41no—
317Dic43—41no—
318Dic43—81no—
319Dic43—81no—
320C2×C4×D8—431no—
321#2357—431no—
322#2349—431no—
323#1936—431no—
324#1936D4311yescharacteristic, complemented
325#1918—431no—
326#1918—431no—
327#1879—431no—
328#1879—431no—
329#1835—431no—
330#1804—431no—
331#1804—431no—
332#1770—431no—
333#1762—431no—
334#1762—431no—
335C2×C43—82no—
336C2×C43#235211yescharacteristic
337C2×C43#294311yescharacteristic
338C2×C43#294811yescharacteristic
339C2×C43#332211yescharacteristic
340C2×C43#332211yescharacteristic
341C2×C43#337011yescharacteristic
342C2×C43#337011yescharacteristic
343D43—44no—
344C22×D8—431no—
345C2×C4×D4—431no—
346C2×C4×D4—431no—
347C2×C4×D4—431no—
348C2×C4×D4—431no—
349C4×D8—438no—
350C2×#107—431no—
351C2×C4⋊C8—431no—
352C2×#102—431no—
353C2×#102—431no—
354C2×#102—431no—
355C2×#102—431no—
356C2×#102C2×D4311yescharacteristic
357C2×#102C2×D4311yescharacteristic
358C2×#97—431no—
359C2×#97C2×D4311yescharacteristic
360C2×C4×C8—431no—
361#390—431no—
362#390C2×D4311yescharacteristic
363#389—431no—
364#389C2×D4311yescharacteristic
365#388—861no—
366#388—861no—
367#385—861no—
368#385—861no—
369#382—431no—
370#382—431no—
371#381—861no—
372#380—861no—
373C4×C4⋊C4—431no—
374C4×C4⋊C4—431no—
375C4×C4⋊C4—431no—
376C4×C22⋊C4—861no—
377C2×#95—861no—
378#340—431no—
379#340—431no—
380#340—431no—
381#340—431no—
382#340—431no—
383#340—431no—
384#340C2×D4311yescharacteristic
385#340C2×D4311yescharacteristic
386#336—431no—
387#336—431no—
388C43#2276411yescharacteristic, complemented, Sylow
389C22×D4—431no—
390C22×D4C22×D4311yescharacteristic
391C23×C4—861no—
392C23×C4—861no—
393C23×C4—861no—
394C23×C4—861no—
395C2×D8—434no—
396C2×D8—862no—
397C2×D8—862no—
398C22×C8—431no—
399C22×C8—431no—
400C22×C8C22×D4311yescharacteristic
401C22×C8C22×D4311yescharacteristic
402C4×D4—434no—
403C4×D4—434no—
404C4×D4—862no—
405C4×D4—862no—
406C4×D4—862no—
407C4×D4—862no—
408C4×D4—1721no—
409C4×D4—1721no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4C22×D4311yescharacteristic
418C2×C4⋊C4C22×D4311yescharacteristic
419C2×C4⋊C4C22×D4311yescharacteristic
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—861no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4—861no—
426C2×C22⋊C4—861no—
427C2×C22⋊C4—861no—
428C2×C42—431no—
429C2×C42—431no—
430C2×C42—861no—
431C2×C42—861no—
432C2×C42C22×D4311yescharacteristic
433#107—434no—
434C4⋊C8—862no—
435#102—41no—
436#102—434no—
437#102—862no—
438#102—862no—
439#102—1721no—
440#102C4×D4314yescomplemented
441#97—41no—
442#97—1721no—
443C4×C8—434no—
444#95—21no—
445#95—431no—
446#95—431no—
447#95—861no—
448#95—861no—
449#95—861no—
450#95—861no—
451#95—861no—
452#95—861no—
453#95—861no—
454C24—21no—
455C24—861no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—432no—
462C2×D4—432no—
463C2×D4—432no—
464C2×D4—861no—
465C2×D4—861no—
466C2×D4—861no—
467C2×D4C2×C4×D4312yes—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—431no—
472C22×C4—431no—
473C22×C4—431no—
474C22×C4—431no—
475C22×C4—864no—
476C22×C4—864no—
477C22×C4—861no—
478C22×C4—861no—
479C22×C4—861no—
480C22×C4—3441no—
481C22×C4—3441no—
482C22×C4—3441no—
483C22×C4—3441no—
484C22×C4—3441no—
485C22×C4—3441no—
486C22×C4—1722no—
487C22×C4—1722no—
488C22×C4—1722no—
489C22×C4—1722no—
490C22×C4D4×D4311yescharacteristic
491C22×C4D4×D4311yescharacteristic
492C22×C4C23×D4311yescharacteristic
493D8—868no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—432no—
500C2×C8—861no—
501C2×C8—861no—
502C2×C8—861no—
503C2×C8—861no—
504C2×C8—861no—
505C2×C8C2×C4×D4312yes—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—81no—
512C4⋊C4—432no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—3441no—
519C4⋊C4—1721no—
520C4⋊C4—1721no—
521C4⋊C4C2×C4×D4312yes—
522C22⋊C4—42no—
523C22⋊C4—81no—
524C22⋊C4—864no—
525C22⋊C4—864no—
526C22⋊C4—3441no—
527C22⋊C4—1722no—
528C22⋊C4—1722no—
529C22⋊C4—1722no—
530C42—21no—
531C42—21no—
532C42—432no—
533C42—432no—
534C42—861no—
535C42—861no—
536C42—3441no—
537C42—3441no—
538C23—22no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—862no—
546C23—862no—
547C23—862no—
548C23—1721no—
549C23—1721no—
550C23—1721no—
551C23—1721no—
552C23C2×D4×D4311yescharacteristic
553D4—22no—
554D4—22no—
555D4—41no—
556D4—41no—
557D4—434no—
558D4—862no—
559D4—862no—
560D4—862no—
561C2×C4—22no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—432no—
577C2×C4—432no—
578C2×C4—861no—
579C2×C4—861no—
580C2×C4—861no—
581C2×C4—861no—
582C2×C4—862no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—3444no—
590C2×C4—3444no—
591C2×C4—3444no—
592C2×C4—3444no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4C22×C4×D4311yescharacteristic
602C2×C4#41×D4311yescharacteristic
603C2×C4#41×D4311yescharacteristic
604C2×C4#41×D4311yescharacteristic
605C2×C4#1306337011yescharacteristic
606C2×C4#1306337211yescharacteristic
607C8—22no—
608C8—41no—
609C8—862no—
610C8—1721no—
611C22—42no—
612C22—42no—
613C22—42no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—864no—
619C22—1722no—
620C22—1722no—
621C22—1722no—
622C22—1722no—
623C22—1722no—
624C22—1722no—
625C22C4×D4×D4311yescharacteristic
626C22#1458353811yescharacteristic
627C22#1458355711yescharacteristic
628C22#1458369511yescharacteristic
629C22#1458369811yescharacteristic
630C22#1458370311yescharacteristic
631C22#1458370311yescharacteristic
632C4—42no—
633C4—41no—
634C4—41no—
635C4—81no—
636C4—81no—
637C4—862no—
638C4—862no—
639C4—3441no—
640C4—3441no—
641C4—1722no—
642C4—1721no—
643C4—1721no—
644C4#117×D4311yescharacteristic
645C4#1458337811yescharacteristic
646C4#1458358511yescharacteristic
647C4#1458359411yescharacteristic
648C2—82no—
649C2—1724no—
650C2#1913752311yescharacteristic
651C2#1914339011yescharacteristic
652C2#1914344411yescharacteristic
653C2#1914679111yescharacteristic
654C2#1914680211yescharacteristic
655C2#1914734311yescharacteristic
656C2#1914734711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1936C2
socleC23×C43C22×D4
prime radicalC22×#10621882C22
cosocleC22×C4×C43C24
hypercenter#1936D43
hypocenterC43#22764
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1936

Complements

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

NH ≅ G/Ntype
2. #19137567C2semidirect
3. #19137504C2semidirect
4. #19135294C2semidirect
5. #19135169C2semidirect
6. #19135163C2semidirect
9. #19134724C2semidirect
10. #19134604C2semidirect
11. #19134603C2semidirect
12. #19134463C2semidirect
13. #19134421C2semidirect
14. #19134419C2semidirect
15. C43×#1936C2semidirect
21. #14582979C4semidirect
73. D4×Dic43C2×C4semidirect
94. #13063258C2×C4semidirect
101. C8×Dic43C2×C4semidirect
122. #102×C43C2×C4semidirect
324. #1936D43semidirect
388. C43#22764semidirect
440. #102C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145829792
#191375672
#191375042
#191352942
#191351692
#191351632
#191349462
#191349402
#191347242
#191346042
#191346032
#191344632
#191344212
#191344192
C43×#19362
#2276443