Finite Group Databasebeta

← #25115751

Subgroups — #25115751

Order 11008.

978 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582979C211yesmaximal, characteristic
2#19137543C211yesmaximal, characteristic, complemented
3#19137496C211yesmaximal, characteristic, complemented
4#19135294C211yesmaximal, characteristic, complemented
5#19135190C211yesmaximal, characteristic, complemented
6#19135184C211yesmaximal, characteristic, complemented
7#19134946C211yesmaximal, characteristic
8#19134940C211yesmaximal, characteristic
9#19134721C211yesmaximal, characteristic, complemented
10#19134594C211yesmaximal, characteristic, complemented
11#19134593C211yesmaximal, 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
21C2×#13063281—21no—
22C2×C4⋊C4×D43—21no—
23#14582979C418yescomplemented
24C2×#13063258C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063235C2211yescharacteristic
31C2×C8×Dic43C2211yescharacteristic
32#14582802C2211yescharacteristic
33#14582798C2211yescharacteristic
34#14582793—21no—
35#14582787—21no—
36#14582773—21no—
37#14582770—21no—
38#14582768C2211yescharacteristic
39#14582768C2211yescharacteristic
40#14582758—21no—
41#14582757—21no—
42C4⋊C4×Dic43C2211yescharacteristic
43C4×Dic43⋊C4C2211yescharacteristic
44C4×C4⋊Dic43C2211yescharacteristic
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—
78#13063281—44no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4D411yescharacteristic
88C2×Dic43⋊C4D411yescharacteristic
89C4⋊C4×D43—44no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×C4×Dic43—21no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43C2311yescharacteristic
99C2×C4×Dic43C2311yescharacteristic
100#13063258C2×C414yescomplemented
101Dic43⋊C8—22no—
102#13063247—22no—
103#13063247C2×C414yes—
104#13063246—41no—
105#13063245—22no—
106#13063235—41no—
107C8×Dic43C2×C414yescomplemented
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95D411yescharacteristic
112C43⋊#95D411yescharacteristic
113C22×D4×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122C2×C42×C43C2311yescharacteristic
123#102×C43—41no—
124#102×C43C2×C414yescomplemented
125#97×C43—41no—
126#95×C43—21no—
127C24×C43—21no—
128C23×D43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43C22×C412yes—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2411yescharacteristic
141C22×Dic43—24no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—42no—
146C22×Dic43—42no—
147C22×Dic43C2×D411yescharacteristic
148C22×Dic43C2×D411yescharacteristic
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172C22×C412yes—
155C2×D172#4112yes—
156C2×D172#4112yes—
157C2×C4×D43—24no—
158C2×C4×D43—42no—
159C2×C4×D43—42no—
160C2×C4×D43—42no—
161C2×C4×D43—42no—
162C2×C4×D43—42no—
163C2×C4×D43—42no—
164C2×C4×D43—81no—
165C2×C4×D43—81no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43C22×C412yes—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—42no—
178C4⋊C4×C43C22×C412yes—
179C22⋊C4×C43—42no—
180C22⋊C4×C43—81no—
181C42×C43—21no—
182C42×C43—21no—
183C22⋊Dic43—24no—
184C22⋊Dic43—42no—
185C22⋊Dic43—81no—
186#10621882—28no—
187(C2×D43)⋊C4—24no—
188(C2×D43)⋊C4—42no—
189(C2×D43)⋊C4—42no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—42no—
196C4⋊Dic43C22×C412yes—
197Dic43⋊C4—22no—
198Dic43⋊C4—22no—
199Dic43⋊C4—42no—
200Dic43⋊C4—42no—
201Dic43⋊C4—81no—
202Dic43⋊C4—81no—
203C4×Dic43—21no—
204C4×Dic43—21no—
205C4×Dic43—42no—
206C4×Dic43—42no—
207C4×Dic43C22×C412yes—
208C4×Dic43#4112yes—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8C22×C412yes—
215C23×C43—22no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43C22×D411yescharacteristic
223C22×D43—22no—
224C22×D43—22no—
225C22×D43—22no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43—41no—
229C22×D43—41no—
230D4×C43—22no—
231D4×C43—22no—
232D4×C43—41no—
233D4×C43—41no—
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×C43C23×C411yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43H(5,𝔽2)11yescharacteristic
254C2×C4×C432−1+411yescharacteristic
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—22no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—48no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43C4×D412yes—
274C2×Dic43C4×D412yes—
275C2×Dic43AGL(1,ℤ/8)12yes—
276C2×Dic43AGL(1,ℤ/8)12yes—
277D172—22no—
278D172—22no—
279D172—22no—
280D172#11714yescomplemented
281C4×D43—48no—
282C4×D43—84no—
283C4×D43—84no—
284C8×C43—22no—
285C8×C43—41no—
286C43⋊C8—22no—
287C43⋊C8—41no—
288#22758—431nomaximal, Sylow
289C22×C43—42no—
290C22×C43—42no—
291C22×C43—42no—
292C22×C43—81no—
293C22×C43—81no—
294C22×C43—81no—
295C22×C43—81no—
296C22×C43C2×C4×D411yescharacteristic
297C22×C43#54611yescharacteristic
298C22×C43#54811yescharacteristic
299C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
300C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
301C22×C43#57611yescharacteristic
302C22×C43#57811yescharacteristic
303C2×D43—24no—
304C2×D43—42no—
305C2×D43—42no—
306C2×D43—42no—
307C2×D43—42no—
308C2×D43—42no—
309C2×D43—42no—
310C4×C43—41no—
311C4×C43—42no—
312C4×C43—41no—
313C4×C43—81no—
314C4×C43—81no—
315C4×C43C2×#11711yescharacteristic
316C4×C43#52011yescharacteristic
317C4×C43#55211yescharacteristic
318C4×C43#55311yescharacteristic
319Dic43—22no—
320Dic43—41no—
321Dic43—42no—
322Dic43—41no—
323Dic43—81no—
324Dic43—81no—
325Dic43#44214yes—
326C2×C4×D8—431no—
327#2354—431no—
328D4×C4⋊C4—431no—
329#1936—431no—
330#1936D4311yescharacteristic, complemented
331#1921—431no—
332#1921—431no—
333#1879—431no—
334#1879—431no—
335#1834—431no—
336#1802—431no—
337#1802—431no—
338#1770—431no—
339#1762—431no—
340#1762—431no—
341C2×C43—82no—
342C2×C43#235211yescharacteristic
343C2×C43C2×#44211yescharacteristic
344C2×C43#295111yescharacteristic
345C2×C43#332511yescharacteristic
346C2×C43#333011yescharacteristic
347C2×C43#336611yescharacteristic
348C2×C43#336711yescharacteristic
349D43—44no—
350C22×D8—431no—
351C2×C4×D4—431no—
352C2×C4×D4—431no—
353C2×C4×D4—431no—
354C2×C4×D4—431no—
355C2×#117—861no—
356C22×C4⋊C4—861no—
357C4×D8—438no—
358C2×#107—431no—
359C2×C4⋊C8—431no—
360C2×#102—431no—
361C2×#102—431no—
362C2×#102—431no—
363C2×#102—431no—
364C2×#102C2×D4311yescharacteristic
365C2×#102C2×D4311yescharacteristic
366C2×#97—431no—
367C2×#97C2×D4311yescharacteristic
368C2×C4×C8—431no—
369#390—431no—
370#390C2×D4311yescharacteristic
371#389—431no—
372#389C2×D4311yescharacteristic
373#388—861no—
374#388—861no—
375#385—861no—
376#385—861no—
377#384—431no—
378#384—431no—
379#380—861no—
380#380—861no—
381C4×C4⋊C4—431no—
382C4×C4⋊C4—431no—
383C4×C4⋊C4—431no—
384#340—431no—
385#340—431no—
386#340—431no—
387#340—431no—
388#340—431no—
389#340—431no—
390#340C2×D4311yescharacteristic
391#340C2×D4311yescharacteristic
392#336—431no—
393#336—431no—
394C43#2275811yescharacteristic, complemented, Sylow
395C22×D4—431no—
396C22×D4C22×D4311yescharacteristic
397C23×C4—861no—
398C23×C4—861no—
399C23×C4—861no—
400C23×C4—861no—
401C2×D8—434no—
402C2×D8—862no—
403C2×D8—862no—
404C22×C8—431no—
405C22×C8—431no—
406C22×C8C22×D4311yescharacteristic
407C22×C8C22×D4311yescharacteristic
408C4×D4—434no—
409C4×D4—434no—
410C4×D4—862no—
411C4×D4—862no—
412C4×D4—862no—
413C4×D4—862no—
414C4×D4—1721no—
415C4×D4—1721no—
416#117—1724no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—1724no—
429C2×C4⋊C4C22×D4311yescharacteristic
430C2×C4⋊C4C22×D4311yescharacteristic
431C2×C4⋊C4C22×D4311yescharacteristic
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—861no—
435C2×C22⋊C4—861no—
436C2×C22⋊C4—861no—
437C2×C22⋊C4—861no—
438C2×C22⋊C4—861no—
439C2×C22⋊C4—861no—
440C2×C42—431no—
441C2×C42—431no—
442C2×C42—861no—
443C2×C42—861no—
444C2×C42C22×D4311yescharacteristic
445#107—434no—
446C4⋊C8—862no—
447#102—41no—
448#102—434no—
449#102—862no—
450#102—862no—
451#102—1721no—
452#102C4×D4314yescomplemented
453#97—41no—
454#97—1721no—
455C4×C8—434no—
456#95—21no—
457#95—431no—
458#95—431no—
459#95—861no—
460#95—861no—
461#95—861no—
462C24—21no—
463C24—861no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—432no—
470C2×D4—432no—
471C2×D4—432no—
472C2×D4—861no—
473C2×D4—861no—
474C2×D4—861no—
475C2×D4C2×C4×D4312yes—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—431no—
482C22×C4—431no—
483C22×C4—864no—
484C22×C4—864no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—3441no—
489C22×C4—3441no—
490C22×C4—1722no—
491C22×C4—1722no—
492C22×C4—1722no—
493C22×C4—1722no—
494C22×C4—1722no—
495C22×C4—1722no—
496C22×C4—1722no—
497C22×C4—1722no—
498C22×C4D4×D4311yescharacteristic
499C22×C4D4×D4311yescharacteristic
500C22×C4C23×D4311yescharacteristic
501D8—868no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—432no—
508C2×C8—861no—
509C2×C8—861no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8C2×C4×D4312yes—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—42no—
520C4⋊C4—432no—
521C4⋊C4—862no—
522C4⋊C4—862no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—3441no—
529C4⋊C4—3441no—
530C4⋊C4—1722no—
531C4⋊C4—1722no—
532C4⋊C4—1722no—
533C4⋊C4C2×C4×D4312yes—
534C22⋊C4—42no—
535C22⋊C4—81no—
536C22⋊C4—864no—
537C22⋊C4—864no—
538C22⋊C4—3441no—
539C22⋊C4—1722no—
540C22⋊C4—1722no—
541C22⋊C4—1722no—
542C42—21no—
543C42—21no—
544C42—432no—
545C42—432no—
546C42—861no—
547C42—861no—
548C42—1722no—
549C42—1722no—
550C23—22no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—862no—
558C23—862no—
559C23—862no—
560C23—1721no—
561C23—1721no—
562C23—1721no—
563C23—1721no—
564C23C2×D4×D4311yescharacteristic
565D4—22no—
566D4—22no—
567D4—41no—
568D4—41no—
569D4—434no—
570D4—862no—
571D4—862no—
572D4—862no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—432no—
589C2×C4—432no—
590C2×C4—432no—
591C2×C4—432no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—862no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—3444no—
602C2×C4—3444no—
603C2×C4—1728no—
604C2×C4—1728no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4C22×C4×D4311yescharacteristic
614C2×C4#41×D4311yescharacteristic
615C2×C4#41×D4311yescharacteristic
616C2×C4#41×D4311yescharacteristic
617C2×C4#1306337011yescharacteristic
618C2×C4#1306337211yescharacteristic
619C8—22no—
620C8—41no—
621C8—862no—
622C8—1721no—
623C22—42no—
624C22—42no—
625C22—42no—
626C22—81no—
627C22—81no—
628C22—81no—
629C22—81no—
630C22—864no—
631C22—1722no—
632C22—1722no—
633C22—1722no—
634C22—1722no—
635C22—1722no—
636C22—1722no—
637C22C4×D4×D4311yescharacteristic
638C22#1458353811yescharacteristic
639C22#1458355711yescharacteristic
640C22AGL(1,ℤ/8)×D4311yescharacteristic
641C22AGL(1,ℤ/8)×D4311yescharacteristic
642C22#1458370311yescharacteristic
643C22#1458371511yescharacteristic
644C4—41no—
645C4—41no—
646C4—42no—
647C4—81no—
648C4—81no—
649C4—434no—
650C4—862no—
651C4—3441no—
652C4—3441no—
653C4—1721no—
654C4—1721no—
655C4—1722no—
656C4#117×D4311yescharacteristic
657C4#1458337811yescharacteristic
658C4#1458358511yescharacteristic
659C4#1458359411yescharacteristic
660C2—82no—
661C2—1724no—
662C2#1913752311yescharacteristic
663C2#442×D4311yescharacteristic
664C2#1914346711yescharacteristic
665C2#1914683211yescharacteristic
666C2#1914689511yescharacteristic
667C2#1914729911yescharacteristic
668C2#1914731011yescharacteristic
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#22758
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. #19137543C2semidirect
3. #19137496C2semidirect
4. #19135294C2semidirect
5. #19135190C2semidirect
6. #19135184C2semidirect
9. #19134721C2semidirect
10. #19134594C2semidirect
11. #19134593C2semidirect
12. #19134463C2semidirect
13. #19134421C2semidirect
14. #19134419C2semidirect
15. C43×#1936C2semidirect
23. #14582979C4semidirect
73. D4×Dic43C2×C4semidirect
100. #13063258C2×C4semidirect
107. C8×Dic43C2×C4semidirect
124. #102×C43C2×C4semidirect
280. D172#117semidirect
330. #1936D43semidirect
394. C43#22758semidirect
452. #102C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145829792
#191375432
#191374962
#191352942
#191351902
#191351842
#191349462
#191349402
#191347212
#191345942
#191345932
#191344632
#191344212
#191344192
C43×#19362
#2275843