Finite Group Databasebeta

← #25064164

Subgroups — #25064164

Order 11008.

982 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148644C211yesmaximal, characteristic
2#19137238C211yesmaximal, characteristic, complemented
3#19133168C212yesmaximal, complemented
4#19133152C212yesmaximal, complemented
5#19133139C212yesmaximal, complemented
6#19133129C212yesmaximal, complemented
7#19133121C211yesmaximal, characteristic, complemented
8#19133108C211yesmaximal, characteristic, complemented
9#19133095C211yesmaximal, characteristic, complemented
10#19133082C211yesmaximal, characteristic, complemented
11C43×#2974C211yesmaximal, characteristic, complemented
12#14583619C411yescharacteristic, complemented
13#14583604—21no—
14#14583589C412yescomplemented
15#14583575—22no—
16D4×Dic86C411yescharacteristic, complemented
17#14583558C412yescomplemented
18#14583554C411yescharacteristic, complemented
19#14583553C411yescharacteristic, complemented
20#14583543—21no—
21#14583514—21no—
22#14583491—22no—
23#14583456C2211yescharacteristic
24#14583433C2211yescharacteristic
25#14583410C2212yes—
26C2×#13063304C2212yes—
27#14583378—21no—
28#14582802—21no—
29#14582798—21no—
30#14582792—22no—
31#14582762C2212yes—
32#14582759C2212yes—
33C4×C4⋊Dic43C2211yescharacteristic
34#14582745C2211yescharacteristic
35#14582637C2211yescharacteristic
36#14582637C2211yescharacteristic
37#14582637C2212yes—
38#14582637C2212yes—
39#14582637C2212yes—
40#14582637C2212yes—
41#14582637C2212yes—
42#14582634C2211yescharacteristic
43#14582634C2211yescharacteristic
44#14582634C2212yes—
45C2×C4×D4×C43C2211yescharacteristic
46C43×#436—21no—
47C43×#435—22no—
48C8×D4×C43—21no—
49C43×#432C2211yescharacteristic
50C43×#431C2211yescharacteristic
51C43×#407C2212yes—
52C2×C22⋊C8×C43C2212yes—
53C2×#10621898C2×C412yes—
54C2×#10621900—21no—
55C22×Dic86C2×C412yes—
56#13063325C2×C411yescharacteristic
57#13063325C2×C411yescharacteristic
58#13063324—21no—
59#13063319—21no—
60#13063318—22no—
61#13063318—22no—
62#13063317—21no—
63#13063317C2×C411yescharacteristic
64#13063315—22no—
65#13063313C2×C411yescharacteristic
66#13063312—21no—
67#13063311—22no—
68#13063309—22no—
69#13063308—21no—
70#13063308—22no—
71#13063307—22no—
72#13063306—22no—
73#13063305—21no—
74#13063304—22no—
75#13063304—21no—
76#13063304—22no—
77#13063304C2×C412yes—
78#13063304C2×C412yes—
79#13063304C2×C412yes—
80#13063304C2311yescharacteristic
81#13063304C2312yes—
82#13063303—22no—
83#13063302—22no—
84#13063299C2×C412yes—
85#13063299C2311yescharacteristic
86#13063297—22no—
87#13063296—21no—
88#13063294—22no—
89C4×Dic86—21no—
90C4×Dic86C2×C412yes—
91C4×Dic86C2×C411yescharacteristic
92#13063290—21no—
93C4×D172C2×C411yescharacteristic
94D4×Dic43—21no—
95C4×C22⋊D43—22no—
96C4×C22⋊D43—21no—
97C4×C22⋊D43—22no—
98(C22⋊D43)⋊C4—22no—
99#13063284—21no—
100#13063284C2×C412yes—
101#13063282—21no—
102#13063281—22no—
103C2×C4⋊Dic43—21no—
104C2×C4⋊Dic43—22no—
105C2×C4⋊Dic43C2×C412yes—
106C2×Dic43⋊C4—22no—
107C4⋊C4×D43—21no—
108C2×C22⋊Dic43—22no—
109C2×C22⋊Dic43—22no—
110C2×C22⋊Dic43—22no—
111C2×C4×Dic43—21no—
112C2×C4×Dic43—21no—
113C43⋊#95—21no—
114C43⋊#95—22no—
115C43⋊#95C2311yescharacteristic
116C43⋊#95C2311yescharacteristic
117C43⋊#95C2312yes—
118C22×D4×C43D411yescharacteristic
119C23×C4×C43C2312yes—
120C2×M16×C43—22no—
121C22×C8×C43—22no—
122C4×D4×C43C2×C411yescharacteristic
123C4×D4×C43C2×C411yescharacteristic
124C4×D4×C43C2×C412yes—
125C4×D4×C43D411yescharacteristic
126C4×D4×C43D411yescharacteristic
127C4×D4×C43D412yes—
128C2×C4⋊C4×C43D411yescharacteristic
129C2×C22⋊C4×C43D412yes—
130C2×C42×C43C2311yescharacteristic
131C4⋊C8×C43—21no—
132C4⋊C8×C43—21no—
133C22⋊C8×C43—22no—
134C22⋊C8×C43—22no—
135C22⋊C8×C43C2311yescharacteristic
136C22⋊C8×C43C2312yes—
137C22⋊C8×C43C2311yescharacteristic
138#97×C43—21no—
139C4×C8×C43—21no—
140C24×C43C2×D412yes—
141C2×D4×C43—42no—
142C2×D4×C43C22⋊C411yescharacteristic
143C2×D4×C43C22⋊C411yescharacteristic
144C2×D4×C43C22⋊C412yes—
145C22×C4×C43—82no—
146C22×C4×C43C22×C412yes—
147C22×C4×C43C22×C412yes—
148C22×C4×C43C2×D412yes—
149C22×C4×C43C2×D412yes—
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D412yes—
153C22×C4×C43C2411yescharacteristic
154C2×C22⋊D43—22no—
155C2×C22⋊D43—22no—
156C2×C22⋊D43—21no—
157C22×Dic43—22no—
158C22×Dic43—22no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—22no—
162#10621900—44no—
163#10621898—82no—
164C2×D172C22×C411yescharacteristic
165C2×C4×D43—21no—
166C2×C4×D43—22no—
167C2×Dic86—21no—
168C2×Dic86—22no—
169C2×Dic86—82no—
170C2×Dic86C22×C411yescharacteristic
171C2×Dic86C22×C412yes—
172M16×C43—82no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—22no—
176C2×C8×C43—82no—
177C4⋊C4×C43C22⋊C411yescharacteristic
178C4⋊C4×C43C22⋊C412yes—
179C4⋊C4×C43C22⋊C411yescharacteristic
180C22⋊C4×C43C22⋊C412yes—
181C22⋊C4×C43C22⋊C412yes—
182C22⋊C4×C43C22⋊C412yes—
183C22⋊C4×C43C22⋊C412yes—
184C42×C43C22×C411yescharacteristic
185C42×C43C22×C411yescharacteristic
186C42×C43C2×D411yescharacteristic
187C42×C43C2×D411yescharacteristic
188C22⋊Dic43—22no—
189C22⋊Dic43—22no—
190C22⋊Dic43—22no—
191C22⋊Dic43—22no—
192C22⋊Dic43—21no—
193C22⋊Dic43—22no—
194C22⋊Dic43—82no—
195C22⋊Dic43—82no—
196(C2×D43)⋊C4—21no—
197(C2×D43)⋊C4—21no—
198(C2×D43)⋊C4—22no—
199(C2×D43)⋊C4—21no—
200(C2×D43)⋊C4—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—22no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—42no—
206C4⋊Dic43—82no—
207C4⋊Dic43C22×C411yescharacteristic
208C4⋊Dic43C22×C412yes—
209C4⋊Dic43C22×C411yescharacteristic
210Dic43⋊C4—22no—
211Dic43⋊C4—22no—
212Dic43⋊C4—21no—
213Dic43⋊C4—22no—
214Dic43⋊C4—21no—
215Dic43⋊C4—22no—
216Dic43⋊C4—21no—
217Dic43⋊C4—21no—
218Dic43⋊C4—22no—
219C4×Dic43—22no—
220C4×Dic43—22no—
221C4×Dic43—21no—
222C4×Dic43—42no—
223C4×Dic43—81no—
224C23×C43—22no—
225C23×C43—22no—
226C23×C43—42no—
227C23×C43—42no—
228C23×C43C2×C22⋊C412yes—
229C23×C43C2×C22⋊C412yes—
230C23×C43C22×D411yescharacteristic
231C22×D43—21no—
232D4×C43—22no—
233D4×C43—22no—
234D4×C43—42no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—22no—
238C2×C4×C43—42no—
239C2×C4×C43—42no—
240C2×C4×C43—42no—
241C2×C4×C43—42no—
242C2×C4×C43—42no—
243C2×C4×C43—41no—
244C2×C4×C43C2×C22⋊C411yescharacteristic
245C2×C4×C43C2×C22⋊C412yes—
246C2×C4×C43C2×C22⋊C411yescharacteristic
247C2×C4×C43C2×C22⋊C411yescharacteristic
248C2×C4×C43C2×C22⋊C412yes—
249C2×C4×C43C2×C22⋊C411yescharacteristic
250C2×C4×C43C23×C411yescharacteristic
251C2×C4×C43C22×D411yescharacteristic
252C22⋊D43—44no—
253C22⋊D43—41no—
254C22⋊D43—41no—
255C22⋊D43—82no—
256C2×Dic43—21no—
257C2×Dic43—22no—
258C2×Dic43—22no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—44no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—42no—
265C2×Dic43—41no—
266C2×Dic43—42no—
267C2×Dic43—41no—
268C2×Dic43—42no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—82no—
272D172—41no—
273C4×D43—42no—
274C4×D43—82no—
275Dic86—42no—
276Dic86—41no—
277Dic86—42no—
278Dic86—82no—
279C8×C43—41no—
280C8×C43—42no—
281C8×C43—41no—
282#17600—431nomaximal, Sylow
283C22×C43—21no—
284C22×C43—21no—
285C22×C43—22no—
286C22×C43—22no—
287C22×C43—22no—
288C22×C43—22no—
289C22×C43—22no—
290C22×C43—22no—
291C22×C43—82no—
292C22×C43—82no—
293C22×C43C22×C22⋊C411yescharacteristic
294C22×C43#57711yescharacteristic
295C22×C43#57811yescharacteristic
296C2×D43—41no—
297C2×D43—41no—
298C2×D43—41no—
299C4×C43—21no—
300C4×C43—21no—
301C4×C43—22no—
302C4×C43—22no—
303C4×C43—21no—
304C4×C43—21no—
305C4×C43—21no—
306C4×C43#42112yes—
307Dic43—41no—
308Dic43—42no—
309Dic43—41no—
310Dic43—42no—
311Dic43—41no—
312Dic43—81no—
313Dic43—82no—
314Dic43—81no—
315#3520—431no—
316#2974D4311yescharacteristic, complemented
317#2319—431no—
318#1520—432no—
319#1516—432no—
320#1513—432no—
321#1511—432no—
322#1509—431no—
323#1506—431no—
324#1503—431no—
325#1500—431no—
326C2×C43—21no—
327C2×C43—21no—
328C2×C43—42no—
329C2×C43—42no—
330C2×C43#288311yescharacteristic
331C2×C43#289811yescharacteristic
332C2×C43C2×#42111yescharacteristic
333D43—81no—
334#556—431no—
335#554—861no—
336#552—432no—
337#551—862no—
338D4×Q8—431no—
339#548—432no—
340#547—431no—
341#547—431no—
342#546—861no—
343#542—861no—
344#539—862no—
345#533—431no—
346#529—431no—
347#525—432no—
348C2×C22⋊Q8—432no—
349#520—861no—
350C2×C4×D4C2×D4311yescharacteristic
351#436—21no—
352#435—22no—
353C8×D4—21no—
354#432C2×D4311yescharacteristic
355#431C2×D4311yescharacteristic
356#407C2×D4312yes—
357C2×C22⋊C8C2×D4312yes—
358#390—861no—
359#389—861no—
360#388—862no—
361#381—432no—
362#380—432no—
363C4×C4⋊C4—431no—
364#376—431no—
365#328—431no—
366#328—431no—
367#328—432no—
368#328—432no—
369#328—432no—
370#328—432no—
371#328—432no—
372#327—431no—
373#327—431no—
374#327—432no—
375C43#1760011yescharacteristic, complemented, Sylow
376C2×#41—432no—
377C2×#41—861no—
378C22×Q8—432no—
379C22×D4D17211yescharacteristic
380C23×C4C22×D4312yes—
381C2×M16—22no—
382C22×C8—22no—
383C4⋊Q8—431no—
384C4⋊Q8—431no—
385C4⋊Q8—861no—
386#126—862no—
387#126—862no—
388#126—861no—
389#125—431no—
390#125—862no—
391#125—861no—
392#124—431no—
393#124—861no—
394#124—862no—
395#123—862no—
396#123—861no—
397#123—862no—
398#123—862no—
399#123—862no—
400C22⋊Q8—432no—
401C22⋊Q8—432no—
402C22⋊Q8—432no—
403C22⋊Q8—431no—
404C22⋊Q8—432no—
405C22⋊Q8—862no—
406C22⋊Q8—861no—
407C22⋊Q8—862no—
408C22⋊Q8—862no—
409C22⋊Q8—861no—
410C22⋊Q8—862no—
411#121—432no—
412#121—431no—
413#121—862no—
414#121—861no—
415#120—862no—
416C4×Q8—431no—
417C4×Q8—432no—
418C4×Q8—861no—
419C4×Q8—861no—
420C4×D4—431no—
421C4×D4—861no—
422C4×D4—862no—
423C4×D4—861no—
424C4×D4—862no—
425C4×D4—862no—
426C4×D4C4×D4311yescharacteristic
427C4×D4C4×D4311yescharacteristic
428C4×D4C4×D4312yes—
429C4×D4C22⋊D4311yescharacteristic
430C4×D4C22⋊D4312yes—
431C4×D4C22⋊D4311yescharacteristic
432#117—432no—
433#117—861no—
434#117—862no—
435#117—861no—
436C2×C4⋊C4—432no—
437C2×C4⋊C4—862no—
438C2×C4⋊C4—861no—
439C2×C4⋊C4—862no—
440C2×C4⋊C4—861no—
441C2×C4⋊C4D17211yescharacteristic
442C2×C22⋊C4—862no—
443C2×C22⋊C4—862no—
444C2×C22⋊C4—862no—
445C2×C22⋊C4D17212yes—
446C2×C42—861no—
447C2×C42—861no—
448C2×C42C22×D4311yescharacteristic
449C4⋊C8—21no—
450C4⋊C8—21no—
451C22⋊C8—22no—
452C22⋊C8—22no—
453C22⋊C8C22×D4311yescharacteristic
454C22⋊C8C22×D4312yes—
455C22⋊C8C22×D4311yescharacteristic
456#97—21no—
457C4×C8—21no—
458#95—431no—
459#95—431no—
460#95—432no—
461#95—861no—
462#95—862no—
463C24C2×D17212yes—
464#41—3442no—
465#41—1724no—
466C2×Q8—431no—
467C2×Q8—432no—
468C2×Q8—862no—
469C2×Q8—861no—
470C2×Q8—3442no—
471C2×D4—42no—
472C2×D4—431no—
473C2×D4—862no—
474C2×D4—862no—
475C2×D4—861no—
476C2×D4(C2×D43)⋊C411yescharacteristic
477C2×D4(C2×D43)⋊C411yescharacteristic
478C2×D4(C2×D43)⋊C412yes—
479C22×C4—82no—
480C22×C4—862no—
481C22×C4—862no—
482C22×C4—862no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—862no—
487C22×C4C2×C4×D4312yes—
488C22×C4C2×C4×D4312yes—
489C22×C4C2×D17211yescharacteristic
490C22×C4C2×D17211yescharacteristic
491C22×C4C2×D17212yes—
492C22×C4C2×C22⋊D4312yes—
493C22×C4C2×C22⋊D4312yes—
494C22×C4C23×D4311yescharacteristic
495M16—82no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—22no—
499C2×C8—82no—
500C4⋊C4—431no—
501C4⋊C4—432no—
502C4⋊C4—431no—
503C4⋊C4—862no—
504C4⋊C4—862no—
505C4⋊C4—861no—
506C4⋊C4—862no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—862no—
511C4⋊C4—861no—
512C4⋊C4—862no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—862no—
516C4⋊C4—3442no—
517C4⋊C4—1722no—
518C4⋊C4(C2×D43)⋊C411yescharacteristic
519C4⋊C4(C2×D43)⋊C412yes—
520C4⋊C4(C2×D43)⋊C411yescharacteristic
521C22⋊C4—862no—
522C22⋊C4—862no—
523C22⋊C4—862no—
524C22⋊C4—862no—
525C22⋊C4—861no—
526C22⋊C4—862no—
527C22⋊C4—861no—
528C22⋊C4—861no—
529C22⋊C4—862no—
530C22⋊C4—861no—
531C22⋊C4—861no—
532C22⋊C4—3442no—
533C22⋊C4—3442no—
534C22⋊C4(C2×D43)⋊C412yes—
535C22⋊C4(C2×D43)⋊C412yes—
536C22⋊C4(C2×D43)⋊C412yes—
537C22⋊C4(C2×D43)⋊C412yes—
538C42—862no—
539C42—862no—
540C42—861no—
541C42—3441no—
542C42—1722no—
543C42C2×C4×D4311yescharacteristic
544C42C2×C4×D4311yescharacteristic
545C42C2×C22⋊D4311yescharacteristic
546C42C2×C22⋊D4311yescharacteristic
547C23—22no—
548C23—22no—
549C23—42no—
550C23—42no—
551C23—861no—
552C23C2×(C2×D43)⋊C412yes—
553C23C2×(C2×D43)⋊C412yes—
554C23C22×D17211yescharacteristic
555Q8—3442no—
556Q8—1721no—
557Q8—1722no—
558Q8—1722no—
559D4—22no—
560D4—22no—
561D4—42no—
562D4—3442no—
563D4—1721no—
564D4—1724no—
565D4—1721no—
566D4—1721no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—22no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—861no—
577C2×C4—862no—
578C2×C4—861no—
579C2×C4—862no—
580C2×C4—861no—
581C2×C4—3442no—
582C2×C4—3442no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1722no—
587C2×C4—1721no—
588C2×C4—1722no—
589C2×C4—1722no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1724no—
593C2×C4—1722no—
594C2×C4C2×(C2×D43)⋊C411yescharacteristic
595C2×C4C2×(C2×D43)⋊C412yes—
596C2×C4C2×(C2×D43)⋊C411yescharacteristic
597C2×C4C2×(C2×D43)⋊C411yescharacteristic
598C2×C4C2×(C2×D43)⋊C412yes—
599C2×C4C2×(C2×D43)⋊C411yescharacteristic
600C2×C4C22×C4×D4311yescharacteristic
601C2×C4C22×C22⋊D4311yescharacteristic
602C8—41no—
603C8—42no—
604C8—41no—
605C22—21no—
606C22—21no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—82no—
614C22—82no—
615C22—1721no—
616C22—1721no—
617C22—1721no—
618C22C22×(C2×D43)⋊C411yescharacteristic
619C22#1458371111yescharacteristic
620C22#1458371611yescharacteristic
621C4—21no—
622C4—21no—
623C4—22no—
624C4—22no—
625C4—21no—
626C4—21no—
627C4—21no—
628C4—3441no—
629C4—3442no—
630C4—3441no—
631C4—1722no—
632C4—1721no—
633C4—1721no—
634C4—1721no—
635C4—1722no—
636C4#1458291512yes—
637C2—21no—
638C2—21no—
639C2—42no—
640C2—42no—
641C2—3441no—
642C2#1914305511yescharacteristic
643C2#1914312911yescharacteristic
644C2C2×#1458291511yescharacteristic
subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2974C2
socleC22×C43C22×C22⋊C4
prime radical#19148644C2
cosocleC22×C4×C43C24
hypercenter#2974D43
hypocenterC43#17600
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2974

Complements

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

NH ≅ G/Ntype
2. #19137238C2semidirect
3. #19133168C2semidirect
4. #19133152C2semidirect
5. #19133139C2semidirect
6. #19133129C2semidirect
7. #19133121C2semidirect
8. #19133108C2semidirect
9. #19133095C2semidirect
10. #19133082C2semidirect
11. C43×#2974C2semidirect
12. #14583619C4semidirect
14. #14583589C4semidirect
16. D4×Dic86C4semidirect
17. #14583558C4semidirect
18. #14583554C4semidirect
19. #14583553C4semidirect
316. #2974D43semidirect
375. C43#17600semidirect

Maximal subgroups

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

subgroupindex
#191486442
#191372382
#191331682
#191331522
#191331392
#191331292
#191331212
#191331082
#191330952
#191330822
C43×#29742
#1760043