Finite Group Databasebeta

← #25099685

Subgroups — #25099685

Order 11008.

938 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×#14583011C211yesmaximal, characteristic
2#19137232C211yesmaximal, characteristic, complemented
3#19136956C211yesmaximal, characteristic, complemented
4#19135225C211yesmaximal, characteristic, complemented
5#19135212C211yesmaximal, characteristic, complemented
6#19135179C211yesmaximal, characteristic, complemented
7#19135174C211yesmaximal, characteristic, complemented
8#19134945C211yesmaximal, characteristic
9#19134856C211yesmaximal, characteristic, complemented
10#19134840C211yesmaximal, characteristic, complemented
11#19134491C211yesmaximal, characteristic, complemented
12#102×Dic43C211yesmaximal, characteristic, complemented
13#102×Dic43C211yesmaximal, characteristic, complemented
14#19134345C211yesmaximal, characteristic, complemented
15C43×#1879C211yesmaximal, characteristic
16C2×D4×Dic43C2211yescharacteristic
17C2×D4×Dic43C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19#14583011C418yescomplemented
20C2×#13063258C2211yescharacteristic
21C2×#13063257C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063235C2211yescharacteristic
28C2×C8×Dic43C2211yescharacteristic
29#14582802C2211yescharacteristic
30#14582797C2211yescharacteristic
31#14582795C2211yescharacteristic
32#14582793—21no—
33#14582787—21no—
34#14582760—21no—
35#14582757—21no—
36C4⋊C4×Dic43C2211yescharacteristic
37C4⋊C4×Dic43C2211yescharacteristic
38C4⋊C4×Dic43C2211yescharacteristic
39C4×C4⋊Dic43C2211yescharacteristic
40C22⋊C4×Dic43—21no—
41C22⋊C4×Dic43—21no—
42C4×C22⋊Dic43—21no—
43#14582745C2211yescharacteristic
44C2×C43⋊#95—21no—
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C22×D8×C43C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C43×#390C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C23×Dic43—21no—
61C23×Dic43—21no—
62C23×Dic43—21no—
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65D4×Dic43—22no—
66D4×Dic43—22no—
67D4×Dic43—22no—
68D4×Dic43—22no—
69D4×Dic43C2×C414yes—
70D4×Dic43C2×C414yescomplemented
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43C2311yescharacteristic
87C2×C4×Dic43C2311yescharacteristic
88#13063258—22no—
89#13063257C2×C414yescomplemented
90#13063256—22no—
91#13063246—22no—
92#13063246—22no—
93#13063246C2×C414yes—
94#13063246C2×C414yescomplemented
95#13063235C2×C414yescomplemented
96C8×Dic43—22no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95D411yescharacteristic
104C43⋊#95D411yescharacteristic
105C43⋊#95D411yescharacteristic
106C43⋊#95D411yescharacteristic
107C22×D4×C43C2311yescharacteristic
108C22×D4×C43C2311yescharacteristic
109C23×C4×C43—21no—
110C2×D8×C43—22no—
111C2×D8×C43—22no—
112C2×D8×C43C2×C414yes—
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C4×D4×C43—22no—
116C4×D4×C43—22no—
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C22⋊C4×C43—21no—
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122C2×C42×C43C2311yescharacteristic
123#102×C43—22no—
124#102×C43—22no—
125C24×C43—21no—
126C24×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43C22×C412yes—
136C2×D4×C43C22×C412yes—
137C2×D4×C43#4112yes—
138C2×D4×C43#4112yes—
139C22×C4×C43—24no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—81no—
143C22×C4×C43—81no—
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2411yescharacteristic
147C22×Dic43—24no—
148C22×Dic43—24no—
149C22×Dic43—24no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—81no—
155C22×Dic43—81no—
156C22×Dic43—81no—
157C22×Dic43—81no—
158C22×Dic43—81no—
159C22×Dic43—81no—
160C22×Dic43C2×D411yescharacteristic
161C22×Dic43C2×D411yescharacteristic
162C22×Dic43C2×D411yescharacteristic
163C22×Dic43C2×D411yescharacteristic
164D8×C43—28no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43C22×C412yes—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43#4112yes—
175C22⋊C4×C43—24no—
176C22⋊C4×C43—81no—
177C22⋊C4×C43—81no—
178C42×C43—21no—
179C42×C43—21no—
180C22⋊Dic43—24no—
181C22⋊Dic43—24no—
182C22⋊Dic43—24no—
183C22⋊Dic43—81no—
184C22⋊Dic43—81no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43C22×C412yes—
191C4⋊Dic43C22×C412yes—
192C4⋊Dic43#4112yes—
193Dic43⋊C4—81no—
194Dic43⋊C4—81no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—81no—
198C4×Dic43—81no—
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—22no—
211C23×C43—22no—
212C23×C43—22no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43C22×D411yescharacteristic
224D4×C43—22no—
225D4×C43—22no—
226D4×C43—22no—
227D4×C43—22no—
228D4×C43—22no—
229D4×C43—41no—
230D4×C43—41no—
231D4×C43#11714yes—
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—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—84no—
245C2×C4×C43C23×C411yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—22no—
256C2×Dic43—22no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—22no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—84no—
274C2×Dic43—84no—
275C2×Dic43—84no—
276C2×Dic43C4×D412yes—
277C2×Dic43C4×D412yes—
278C8×C43—22no—
279C8×C43—41no—
280C43⋊C8—22no—
281C43⋊C8—41no—
282#21126—431nomaximal, Sylow
283C22×C43—24no—
284C22×C43—42no—
285C22×C43—42no—
286C22×C43—42no—
287C22×C43—42no—
288C22×C43—42no—
289C22×C43—42no—
290C22×C43—42no—
291C22×C43—42no—
292C22×C43—42no—
293C22×C43—81no—
294C22×C43—81no—
295C22×C43—81no—
296C22×C43—81no—
297C22×C43C2×C4×D411yescharacteristic
298C22×C43#52511yescharacteristic
299C22×C43#52511yescharacteristic
300C22×C43#57611yescharacteristic
301C22×C43#57611yescharacteristic
302C22×C43#57711yescharacteristic
303C22×C43#57711yescharacteristic
304C4×C43—41no—
305C4×C43—42no—
306C4×C43—41no—
307C4×C43—81no—
308C4×C43C2×#11711yescharacteristic
309C4×C43C4×#4111yescharacteristic
310C4×C43#52911yescharacteristic
311C4×C43#52911yescharacteristic
312Dic43—22no—
313Dic43—22no—
314Dic43—41no—
315Dic43—42no—
316Dic43—41no—
317Dic43—42no—
318Dic43—42no—
319Dic43—81no—
320C2×#442—431no—
321#2319—431no—
322#2275—431no—
323#1926—431no—
324#1925—431no—
325#1920—431no—
326#1919—431no—
327#1879—431no—
328#1879D4311yescharacteristic
329#1864—431no—
330#1862—431no—
331#1776—431no—
332C4×#102—431no—
333C4×#102—431no—
334#1746—431no—
335C2×C43—44no—
336C2×C43—82no—
337C2×C43#229011yescharacteristic
338C2×C43#294611yescharacteristic
339C2×C43#294611yescharacteristic
340C2×C43#311811yescharacteristic
341C2×C43#311911yescharacteristic
342C2×C43#312211yescharacteristic
343C2×C43#312511yescharacteristic
344C22×D8C2×D4311yescharacteristic
345C2×C4×D4—431no—
346C2×C4×D4—431no—
347C2×C4×D4—431no—
348C2×C4×D4C2×D4311yescharacteristic
349#442—438no—
350C2×#107—431no—
351C2×#106—431no—
352C2×#106—431no—
353C2×#102—431no—
354C2×#102—431no—
355C2×#102—431no—
356C2×#102—431no—
357C2×#102C2×D4311yescharacteristic
358C2×#102C2×D4311yescharacteristic
359C2×#97—431no—
360C2×C4×C8—431no—
361#390—431no—
362#390C2×D4311yescharacteristic
363#389—431no—
364#389—431no—
365#388—861no—
366#388—861no—
367#381—861no—
368#380—861no—
369C4×C4⋊C4—431no—
370C4×C4⋊C4—431no—
371C4×C4⋊C4—431no—
372C4×C4⋊C4—431no—
373C4×C22⋊C4—861no—
374C4×C22⋊C4—861no—
375C4×C22⋊C4—861no—
376#376—431no—
377C2×#95—861no—
378#340—431no—
379#340—431no—
380#340—431no—
381#340—431no—
382#340—431no—
383#340C2×D4311yescharacteristic
384#336—431no—
385#336—431no—
386#336—431no—
387#336C2×D4311yescharacteristic
388C43#2112611yescharacteristic, complemented, Sylow
389C22×D4C22×D4311yescharacteristic
390C22×D4C22×D4311yescharacteristic
391C23×C4—21no—
392C23×C4—861no—
393C23×C4—861no—
394C23×C4—861no—
395C2×D8—22no—
396C2×D8—22no—
397C2×D8C4×D4314yes—
398C22×C8—431no—
399C22×C8—431no—
400C22×C8C22×D4311yescharacteristic
401C22×C8C22×D4311yescharacteristic
402C4×D4—22no—
403C4×D4—22no—
404C4×D4—434no—
405C4×D4—434no—
406C4×D4—862no—
407C4×D4—862no—
408C4×D4—862no—
409C4×D4—862no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4C22×D4311yescharacteristic
417C2×C4⋊C4C22×D4311yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—861no—
422C2×C22⋊C4—861no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4—861no—
426C2×C42—431no—
427C2×C42—431no—
428C2×C42—861no—
429C2×C42—861no—
430C2×C42—861no—
431C2×C42—861no—
432C2×C42C22×D4311yescharacteristic
433#107—862no—
434#106—434no—
435#106—862no—
436#102—22no—
437#102—22no—
438#102—434no—
439#102—434no—
440#102—862no—
441#102—862no—
442#97—434no—
443C4×C8—862no—
444#95—431no—
445#95—431no—
446#95—431no—
447#95—431no—
448#95—861no—
449#95—861no—
450#95—861no—
451#95—861no—
452#95—861no—
453#95—861no—
454C24—21no—
455C24—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4C2×C4×D4312yes—
465C2×D4C2×C4×D4312yes—
466C2×D4#1062190012yes—
467C2×D4#1062190012yes—
468C22×C4—21no—
469C22×C4—24no—
470C22×C4—21no—
471C22×C4—81no—
472C22×C4—81no—
473C22×C4—431no—
474C22×C4—431no—
475C22×C4—431no—
476C22×C4—431no—
477C22×C4—864no—
478C22×C4—864no—
479C22×C4—864no—
480C22×C4—861no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—3441no—
485C22×C4—3441no—
486C22×C4—3441no—
487C22×C4—3441no—
488C22×C4—3441no—
489C22×C4—3441no—
490C22×C4D4×D4311yescharacteristic
491C22×C4D4×D4311yescharacteristic
492C22×C4C23×D4311yescharacteristic
493D8—28no—
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—432no—
510C4⋊C4—432no—
511C4⋊C4—432no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—3441no—
518C4⋊C4—3441no—
519C4⋊C4#1062190012yes—
520C22⋊C4—24no—
521C22⋊C4—81no—
522C22⋊C4—81no—
523C22⋊C4—864no—
524C22⋊C4—864no—
525C22⋊C4—864no—
526C22⋊C4—3441no—
527C22⋊C4—3441no—
528C42—21no—
529C42—21no—
530C42—432no—
531C42—432no—
532C42—861no—
533C42—861no—
534C42—3441no—
535C42—3441no—
536C42—3441no—
537C42—3441no—
538C23—22no—
539C23—22no—
540C23—22no—
541C23—22no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23C2×D4×D4311yescharacteristic
553D4—22no—
554D4—22no—
555D4—22no—
556D4—22no—
557D4—22no—
558D4—41no—
559D4—41no—
560D4#1306328114yes—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—22no—
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—84no—
574C2×C4—432no—
575C2×C4—432no—
576C2×C4—861no—
577C2×C4—861no—
578C2×C4—861no—
579C2×C4—861no—
580C2×C4—862no—
581C2×C4—862no—
582C2×C4—861no—
583C2×C4—861no—
584C2×C4—862no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—3444no—
590C2×C4—3444no—
591C2×C4—3444no—
592C2×C4—1721no—
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×C4C2×#1062190011yescharacteristic
605C2×C4C2×#1062190011yescharacteristic
606C2×C4C2×#1062190011yescharacteristic
607C8—22no—
608C8—41no—
609C8—862no—
610C8—1721no—
611C22—24no—
612C22—42no—
613C22—42no—
614C22—42no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—81no—
622C22—81no—
623C22—81no—
624C22—81no—
625C22C4×D4×D4311yescharacteristic
626C22#1458340511yescharacteristic
627C22#1458340911yescharacteristic
628C22#1458370011yescharacteristic
629C22#1458370311yescharacteristic
630C22#1458370611yescharacteristic
631C22#1458370911yescharacteristic
632C4—41no—
633C4—42no—
634C4—41no—
635C4—81no—
636C4—862no—
637C4—862no—
638C4—3441no—
639C4—1722no—
640C4—1721no—
641C4—1722no—
642C4—1721no—
643C4—1722no—
644C4C2×#1306328111yescharacteristic
645C4C4×#1062190011yescharacteristic
646C4#1458342611yescharacteristic
647C4#1458343011yescharacteristic
648C2—44no—
649C2—82no—
650C2#1913703511yescharacteristic
651C2#1914342011yescharacteristic
652C2#1914342411yescharacteristic
653C2#1914477211yescharacteristic
654C2#1914479511yescharacteristic
655C2#1914483611yescharacteristic
656C2#1914486911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1879C2
socleC23×C43C22×D4
prime radicalC22×D8×C43C22
cosocleC22×C4×C43C24
hypercenter#1879D43
hypocenterC43#21126
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
2. #19137232C2semidirect
3. #19136956C2semidirect
4. #19135225C2semidirect
5. #19135212C2semidirect
6. #19135179C2semidirect
7. #19135174C2semidirect
9. #19134856C2semidirect
10. #19134840C2semidirect
11. #19134491C2semidirect
12. #102×Dic43C2semidirect
13. #102×Dic43C2semidirect
14. #19134345C2semidirect
19. #14583011C4semidirect
70. D4×Dic43C2×C4semidirect
89. #13063257C2×C4semidirect
94. #13063246C2×C4semidirect
95. #13063235C2×C4semidirect
388. C43#21126semidirect

Maximal subgroups

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

subgroupindex
C2×#145830112
#191372322
#191369562
#191352252
#191352122
#191351792
#191351742
#191349452
#191348562
#191348402
#191344912
#102×Dic432
#191343452
C43×#18792
#2112643