Finite Group Databasebeta

← #25064667

Subgroups — #25064667

Order 11008.

962 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#125×D43C211yesmaximal, characteristic
2#19143226C211yesmaximal, characteristic
3#19143225C211yesmaximal, characteristic
4#19133220C214yesmaximal, complemented
5#19133198C211yesmaximal, characteristic, complemented
6#19133197C211yesmaximal, characteristic, complemented
7#19133196C211yesmaximal, characteristic, complemented
8#19133195C214yesmaximal, complemented
9C43×#1528C211yesmaximal, characteristic, complemented
10C2×#13063317C2211yescharacteristic
11C2×#13063316C411yescharacteristic
12C2×#13063316C411yescharacteristic
13C2×#13063315—21no—
14C2×#13063315—21no—
15#125×D43—21no—
16#125×D43—21no—
17#125×D43—21no—
18#125×D43—21no—
19#125×D43C412yes—
20#125×D43C412yes—
21#125×D43C2212yes—
22#125×D43C2212yes—
23C2×C4⋊C4×D43—21no—
24C2×C4⋊C4×D43—21no—
25C2×C4⋊C4×D43C411yescharacteristic
26C2×C4⋊C4×D43C411yescharacteristic
27C2×C42×D43C2211yescharacteristic
28#14582956C2211yescharacteristic
29#14582954C2212yes—
30#14582954C2212yes—
31#14582954C2212yes—
32#14582951—21no—
33#14582950—21no—
34#14582950—21no—
35#14582949—21no—
36#14582922—21no—
37#14582921—21no—
38#14582862—21no—
39#14582861—21no—
40C4×#10621877C2211yescharacteristic
41#14582851C2212yes—
42#14582641C2214yescomplemented
43#14582640C2214yescomplemented
44#14582640C2214yescomplemented
45C2×#125×C43C2211yescharacteristic
46C43×#432C2211yescharacteristic
47C4×M16×C43C2211yescharacteristic
48C43×#330C2214yescomplemented
49C22×C4×D43—21no—
50C22×C4×D43—21no—
51C22×C4×D43C2×C411yescharacteristic
52C22×C4×D43D411yescharacteristic
53C22×C4×D43D411yescharacteristic
54C2×#10621877—21no—
55C2×#10621872—22no—
56#13063317—21no—
57#13063317—21no—
58#13063317C2×C412yes—
59#13063317C2312yes—
60#13063316—21no—
61#13063316—21no—
62#13063316—21no—
63#13063316—21no—
64#13063316C2×C412yes—
65#13063316C2×C412yes—
66#13063316C2×C412yes—
67#13063316C2×C412yes—
68#13063315—22no—
69#13063315—22no—
70#13063315—22no—
71#13063315—22no—
72#13063315—22no—
73#13063315—22no—
74#13063315—22no—
75#13063315—22no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43C2×C411yescharacteristic
79C2×C4⋊Dic43C2×C411yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C4⋊C4×D43—22no—
87C4⋊C4×D43—22no—
88C4⋊C4×D43—22no—
89C4⋊C4×D43—22no—
90C4⋊C4×D43—21no—
91C4⋊C4×D43—21no—
92C4⋊C4×D43—21no—
93C4⋊C4×D43—21no—
94C4⋊C4×D43—22no—
95C4⋊C4×D43—22no—
96C4⋊C4×D43—22no—
97C4⋊C4×D43—22no—
98C4⋊C4×D43C2×C412yes—
99C4⋊C4×D43C2×C412yes—
100C4⋊C4×D43C2×C412yes—
101C4⋊C4×D43C2×C412yes—
102C2×C4×Dic43C2×C411yescharacteristic
103C2×C4×Dic43D411yescharacteristic
104C2×C4×Dic43D411yescharacteristic
105C42×D43C2×C411yescharacteristic
106C42×D43C2×C411yescharacteristic
107C42×D43D411yescharacteristic
108C42×D43D411yescharacteristic
109C42×D43D411yescharacteristic
110C42×D43D411yescharacteristic
111C42×D43C2311yescharacteristic
112C42×D43C2311yescharacteristic
113C4⋊(C43⋊C8)—21no—
114Dic43⋊C8—22no—
115Dic43⋊C8—22no—
116Dic43⋊C8—22no—
117C22⋊(C43⋊C8)—21no—
118(C2×D43)⋊C8—22no—
119(C2×D43)⋊C8—22no—
120(C2×D43)⋊C8—22no—
121#13063236C2312yes—
122#13063236C2312yes—
123C4×C43⋊C8—21no—
124C8×Dic43—22no—
125C2×M16×C43—21no—
126#125×C43—21no—
127#125×C43—21no—
128#125×C43C2×C412yes—
129#125×C43C2312yes—
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43C2×C411yescharacteristic
133C2×C4⋊C4×C43C2×C411yescharacteristic
134C2×C42×C43C2311yescharacteristic
135C4⋊C8×C43—21no—
136C22⋊C8×C43—21no—
137#97×C43C2312yes—
138#97×C43C2312yes—
139C4×C8×C43—21no—
140C23×D43C22⋊C411yescharacteristic
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43C22×C411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43C22⋊C411yescharacteristic
149C22×Dic43C22⋊C411yescharacteristic
150C22×Dic43C22⋊C411yescharacteristic
151C2×C4×D43—24no—
152C2×C4×D43—22no—
153C2×C4×D43—22no—
154C2×C4×D43—22no—
155C2×C4×D43—22no—
156C2×C4×D43—42no—
157C2×C4×D43—42no—
158C2×C4×D43—44no—
159C2×C4×D43—44no—
160C2×C4×D43C22⋊C411yescharacteristic
161C2×C4×D43C22⋊C411yescharacteristic
162C2×C4×D43C22⋊C411yescharacteristic
163C2×C4×D43C22⋊C411yescharacteristic
164C2×C4×D43C22⋊C411yescharacteristic
165C2×C4×D43C22⋊C411yescharacteristic
166C2×C4×D43C22×C411yescharacteristic
167C2×C4×D43C22×C411yescharacteristic
168C2×C4×D43C2×D411yescharacteristic
169C2×C4×D43C2×D411yescharacteristic
170C2×C4×D43C2×D411yescharacteristic
171C2×C4×D43C2×D411yescharacteristic
172M16×C43—42no—
173C2×C8×C43—22no—
174C2×C8×C43—22no—
175C4⋊C4×C43—22no—
176C4⋊C4×C43—22no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—22no—
180C4⋊C4×C43—22no—
181C4⋊C4×C43C22×C412yes—
182C4⋊C4×C43C22×C412yes—
183C42×C43C22×C411yescharacteristic
184C42×C43C2×D411yescharacteristic
185C42×C43C2×D411yescharacteristic
186C42×C43C2411yescharacteristic
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—22no—
190C4⋊Dic43—22no—
191C4⋊Dic43—22no—
192C4⋊Dic43—22no—
193C4⋊Dic43C22×C412yes—
194C4⋊Dic43C22×C412yes—
195Dic43⋊C4—22no—
196Dic43⋊C4—22no—
197Dic43⋊C4—22no—
198Dic43⋊C4—22no—
199Dic43⋊C4—22no—
200Dic43⋊C4—22no—
201Dic43⋊C4—22no—
202Dic43⋊C4—22no—
203Dic43⋊C4—22no—
204Dic43⋊C4—22no—
205Dic43⋊C4—22no—
206Dic43⋊C4—22no—
207C4×Dic43C22⋊C411yescharacteristic
208C4×Dic43C22⋊C411yescharacteristic
209C4×Dic43C22⋊C411yescharacteristic
210C4×Dic43C22⋊C411yescharacteristic
211C4×Dic43C22⋊C411yescharacteristic
212C4×Dic43C22⋊C411yescharacteristic
213C4×Dic43C22×C411yescharacteristic
214C4×Dic43C22×C411yescharacteristic
215C4×Dic43C2×D411yescharacteristic
216C4×Dic43C2×D411yescharacteristic
217C4×Dic43C2×D411yescharacteristic
218C4×Dic43C2×D411yescharacteristic
219#10621877—42no—
220C2×C43⋊C8—22no—
221C2×C43⋊C8—22no—
222#10621872—44no—
223C23×C43C2×C22⋊C411yescharacteristic
224C22×D43—22no—
225C22×D43—22no—
226C22×D43—22no—
227C22×D43C2×C22⋊C411yescharacteristic
228C22×D43C2×C22⋊C411yescharacteristic
229C2×C4×C43—22no—
230C2×C4×C43—22no—
231C2×C4×C43—22no—
232C2×C4×C43—22no—
233C2×C4×C43—41no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43C2×C22⋊C411yescharacteristic
237C2×C4×C43C2×C22⋊C411yescharacteristic
238C2×C4×C43C2×C22⋊C411yescharacteristic
239C2×C4×C43C23×C411yescharacteristic
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C22×D411yescharacteristic
242C2×Dic43—22no—
243C2×Dic43—22no—
244C2×Dic43—22no—
245C2×Dic43—22no—
246C2×Dic43—41no—
247C2×Dic43—42no—
248C2×Dic43—42no—
249C2×Dic43C2×C22⋊C411yescharacteristic
250C2×Dic43C2×C22⋊C411yescharacteristic
251C2×Dic43C2×C22⋊C411yescharacteristic
252C2×Dic43C2×C22⋊C411yescharacteristic
253C2×Dic43C2×C22⋊C411yescharacteristic
254C2×Dic43C2×C22⋊C411yescharacteristic
255C4×D43—22no—
256C4×D43—22no—
257C4×D43—22no—
258C4×D43—22no—
259C4×D43—22no—
260C4×D43—41no—
261C4×D43—41no—
262C4×D43—41no—
263C4×D43—41no—
264C4×D43—41no—
265C4×D43—41no—
266C4×D43—44no—
267C4×D43—44no—
268C4×D43—44no—
269C4×D43—44no—
270C4×D43#10114yes—
271C8×C43—42no—
272C8×C43—42no—
273C43⋊C8—42no—
274C43⋊C8—42no—
275#17667—431nomaximal, Sylow
276C22×C43—21no—
277C22×C43—21no—
278C22×C43#42112yes—
279C22×C43C22×C22⋊C411yescharacteristic
280C2×D43—28no—
281C2×D43—21no—
282C2×D43—21no—
283C2×D43—21no—
284C2×D43—21no—
285C2×D43C2×#10112yes—
286C2×D43#42112yes—
287C4×C43—21no—
288C4×C43—21no—
289C4×C43—21no—
290C4×C43—21no—
291C4×C43—21no—
292C4×C43—42no—
293C4×C43—42no—
294C4×C43C2×#10112yes—
295Dic43—21no—
296Dic43—21no—
297Dic43—21no—
298Dic43—21no—
299Dic43—21no—
300Dic43—42no—
301Dic43—42no—
302Dic43C2×#10112yes—
303C22×#125—431no—
304#2920—431no—
305#2920—431no—
306#1534—434no—
307#1528—431no—
308#1528—431no—
309#1528—434no—
310#1528—431no—
311#1528D4311yescharacteristic, complemented
312C2×C43—22no—
313C2×C43C22×#10111yescharacteristic
314C2×C43C2×#42111yescharacteristic
315C2×C43C2×#42111yescharacteristic
316D43—22no—
317D43—22no—
318C2×#125—432no—
319C2×#125—432no—
320C2×#125—432no—
321C2×#125—432no—
322C2×#125—431no—
323C2×#125—431no—
324C2×#125—431no—
325C2×#125—861no—
326C2×#125—861no—
327C2×#125—861no—
328C2×#125—861no—
329C2×#125—861no—
330C2×#125—861no—
331C2×#125C2×D4311yescharacteristic
332C22×C4⋊C4—431no—
333C22×C4⋊C4—431no—
334C22×C4⋊C4—861no—
335C22×C4⋊C4—861no—
336C22×C42—431no—
337#432—431no—
338#432—432no—
339#432—432no—
340#432—432no—
341#432C2×D4311yescharacteristic
342#431—861no—
343#431—861no—
344#431—861no—
345#431—861no—
346#423—861no—
347#423—861no—
348#407—861no—
349#407—861no—
350C4×M16—431no—
351C4×M16—432no—
352C4×M16C2×D4311yescharacteristic
353#330—434no—
354#330—434no—
355#330—434no—
356#330C2×D4314yescomplemented
357C43#1766711yescharacteristic, complemented, Sylow
358C23×C4—431no—
359C23×C4—431no—
360C23×C4—431no—
361C23×C4—861no—
362C23×C4—861no—
363C2×M16—21no—
364C2×M16—862no—
365C2×M16—861no—
366#125—21no—
367#125—21no—
368#125—432no—
369#125—432no—
370#125—432no—
371#125—432no—
372#125—432no—
373#125—432no—
374#125—862no—
375#125—862no—
376#125—862no—
377#125—862no—
378#125—862no—
379#125—862no—
380#125—862no—
381#125—862no—
382#125—861no—
383#125—861no—
384#125—861no—
385#125—861no—
386#125—861no—
387#125—861no—
388#125C4×D4312yes—
389#125C22×D4312yes—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—431no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—432no—
395C2×C4⋊C4—432no—
396C2×C4⋊C4—432no—
397C2×C4⋊C4—432no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—862no—
403C2×C4⋊C4—862no—
404C2×C4⋊C4—862no—
405C2×C4⋊C4—862no—
406C2×C4⋊C4—862no—
407C2×C4⋊C4—862no—
408C2×C4⋊C4—862no—
409C2×C4⋊C4—862no—
410C2×C4⋊C4—861no—
411C2×C4⋊C4—861no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4C4×D4311yescharacteristic
419C2×C4⋊C4C4×D4311yescharacteristic
420C2×C42—431no—
421C2×C42—431no—
422C2×C42—431no—
423C2×C42—431no—
424C2×C42—431no—
425C2×C42—431no—
426C2×C42—431no—
427C2×C42—431no—
428C2×C42—431no—
429C2×C42—431no—
430C2×C42—431no—
431C2×C42C22×D4311yescharacteristic
432C4⋊C8—21no—
433C4⋊C8—862no—
434C4⋊C8—862no—
435C4⋊C8—862no—
436C4⋊C8—861no—
437C22⋊C8—21no—
438C22⋊C8—862no—
439C22⋊C8—862no—
440C22⋊C8—862no—
441C22⋊C8—861no—
442#97—432no—
443#97—432no—
444#97C22×D4312yes—
445#97C22×D4312yes—
446C4×C8—21no—
447C4×C8—862no—
448C4×C8—861no—
449C24—431no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—431no—
453C22×C4—431no—
454C22×C4—431no—
455C22×C4—431no—
456C22×C4—431no—
457C22×C4—431no—
458C22×C4—431no—
459C22×C4—431no—
460C22×C4—431no—
461C22×C4—431no—
462C22×C4—431no—
463C22×C4—431no—
464C22×C4—431no—
465C22×C4—431no—
466C22×C4—431no—
467C22×C4—864no—
468C22×C4—862no—
469C22×C4—862no—
470C22×C4—862no—
471C22×C4—862no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—1722no—
475C22×C4—1722no—
476C22×C4—1724no—
477C22×C4—1724no—
478C22×C4C2×C4×D4311yescharacteristic
479C22×C4D4×D4311yescharacteristic
480C22×C4D4×D4311yescharacteristic
481M16—42no—
482M16—1724no—
483M16—1722no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—862no—
487C2×C8—862no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—432no—
495C4⋊C4—432no—
496C4⋊C4—862no—
497C4⋊C4—862no—
498C4⋊C4—862no—
499C4⋊C4—862no—
500C4⋊C4—862no—
501C4⋊C4—862no—
502C4⋊C4—862no—
503C4⋊C4—862no—
504C4⋊C4—862no—
505C4⋊C4—862no—
506C4⋊C4—862no—
507C4⋊C4—862no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—862no—
511C4⋊C4—862no—
512C4⋊C4—862no—
513C4⋊C4—862no—
514C4⋊C4C2×C4×D4312yes—
515C4⋊C4C2×C4×D4312yes—
516C42—431no—
517C42—431no—
518C42—431no—
519C42—431no—
520C42—431no—
521C42—431no—
522C42—431no—
523C42—431no—
524C42—431no—
525C42—431no—
526C42—431no—
527C42—431no—
528C42C2×C4×D4311yescharacteristic
529C42D4×D4311yescharacteristic
530C42D4×D4311yescharacteristic
531C42C23×D4311yescharacteristic
532C23—431no—
533C23—431no—
534C23—862no—
535C23—862no—
536C23—862no—
537C23C22⋊C4×D4311yescharacteristic
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—41no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—431no—
546C2×C4—434no—
547C2×C4—431no—
548C2×C4—431no—
549C2×C4—431no—
550C2×C4—431no—
551C2×C4—431no—
552C2×C4—862no—
553C2×C4—862no—
554C2×C4—862no—
555C2×C4—862no—
556C2×C4—862no—
557C2×C4—862no—
558C2×C4—862no—
559C2×C4—862no—
560C2×C4—862no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1724no—
568C2×C4—1724no—
569C2×C4—1724no—
570C2×C4—1724no—
571C2×C4—1721no—
572C2×C4—1722no—
573C2×C4—1722no—
574C2×C4C22⋊C4×D4311yescharacteristic
575C2×C4C22⋊C4×D4311yescharacteristic
576C2×C4C22⋊C4×D4311yescharacteristic
577C2×C4C22×C4×D4311yescharacteristic
578C2×C4C2×D4×D4311yescharacteristic
579C2×C4C2×D4×D4311yescharacteristic
580C8—42no—
581C8—42no—
582C8—1722no—
583C8—1722no—
584C22—21no—
585C22—21no—
586C22—432no—
587C22—432no—
588C22—868no—
589C22—861no—
590C22—861no—
591C22—861no—
592C22—861no—
593C22#1458291412yes—
594C22C2×C22⋊C4×D4311yescharacteristic
595C4—21no—
596C4—21no—
597C4—21no—
598C4—21no—
599C4—21no—
600C4—42no—
601C4—42no—
602C4—432no—
603C4—861no—
604C4—861no—
605C4—861no—
606C4—861no—
607C4—861no—
608C4—1722no—
609C4—1722no—
610C4#101×D4312yes—
611C2—22no—
612C2—862no—
613C2—862no—
614C2C2×#101×D4311yescharacteristic
615C2#421×D4311yescharacteristic
616C2C2×#1458291411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1528C2
socleC22×C43C22×C22⋊C4
prime radicalC23×D43C22⋊C4
cosocleC42×C43C24
hypercenter#1528D43
hypocenterC43#17667
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1528

Complements

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

NH ≅ G/Ntype
4. #19133220C2semidirect
5. #19133198C2semidirect
6. #19133197C2semidirect
7. #19133196C2semidirect
8. #19133195C2semidirect
9. C43×#1528C2semidirect
42. #14582641C22semidirect
43. #14582640C22semidirect
44. #14582640C22semidirect
48. C43×#330C22semidirect
311. #1528D43semidirect
356. #330C2×D43semidirect
357. C43#17667semidirect

Maximal subgroups

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

subgroupindex
C2×#125×D432
#191432262
#191432252
#191332202
#191331982
#191331972
#191331962
#191331952
C43×#15282
#1766743