Finite Group Databasebeta

← #25063945

Subgroups — #25063945

Order 11008.

1036 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147890C211yesmaximal, characteristic
2#431×D43C211yesmaximal, characteristic, complemented
3#19136988C211yesmaximal, characteristic, complemented
4#19133160C211yesmaximal, characteristic, complemented
5#19133158C211yesmaximal, characteristic, complemented
6#19133155C211yesmaximal, characteristic, complemented
7#19133148C214yesmaximal, complemented
8#19133078C214yesmaximal, complemented
9C43×#1517C211yesmaximal, characteristic, complemented
10#14583456C2211yescharacteristic
11#14583454C411yescharacteristic, complemented
12#14583454C411yescharacteristic, complemented
13#14583447C411yescharacteristic, complemented
14#14583447C411yescharacteristic, complemented
15#14583431—21no—
16#14583431C412yescomplemented
17#14583430—21no—
18#14583430C2212yes—
19#14583428—21no—
20#14583428—21no—
21#14583409—21no—
22#14583409C2212yes—
23#14583406—21no—
24#41×Dic43—21no—
25C4×#10621900—21no—
26C4×#10621900C412yescomplemented
27C2×C42×D43C2211yescharacteristic
28#14582952C2211yescharacteristic
29#14582951—21no—
30#14582950—21no—
31#14582949C2212yes—
32C4⋊C8×D43—21no—
33C22⋊C8×D43C2212yes—
34C4×C8×D43—21no—
35#14582766—21no—
36#14582765C2211yescharacteristic
37#14582761C2212yes—
38#14582756—21no—
39C4⋊C4×Dic43—21no—
40#14582746—21no—
41#14582744C2212yes—
42#14582637C2214yes—
43#14582635C2214yes—
44#14582633C2214yes—
45C43×#532C2211yescharacteristic
46C43×#431C2211yescharacteristic
47C43×#382C2211yescharacteristic
48C43×#327C2214yes—
49C2×#10621900—21no—
50C2×#10621900C2×C412yes—
51C22×C4×D43D411yescharacteristic
52C22×C4×D43D411yescharacteristic
53C22×C4×D43C2311yescharacteristic
54C2×C8×D43—22no—
55#13063325C2×C411yescharacteristic
56#13063325C2×C411yescharacteristic
57#13063318—22no—
58#13063318—22no—
59#13063317—21no—
60#13063316—21no—
61#13063316C2×C412yes—
62#13063312—21no—
63#13063312C2×C412yes—
64#13063307—22no—
65#13063307—22no—
66#13063306—22no—
67#13063305—21no—
68#13063305C2×C412yes—
69#13063304—21no—
70#13063304C2312yes—
71#13063301—21no—
72#13063301—21no—
73#13063296—21no—
74#13063296—21no—
75#13063296—21no—
76#13063296C2×C412yes—
77#13063293—22no—
78Q8×Dic43—21no—
79Q8×Dic43—21no—
80C4×Dic86—21no—
81C4×Dic86C2×C412yes—
82#13063290—21no—
83#13063290C2×C412yes—
84D4×Dic43—22no—
85D4×Dic43—22no—
86D4×Dic43—21no—
87D4×Dic43—21no—
88D4×Dic43—21no—
89D4×Dic43C2×C412yes—
90C4×C22⋊D43—22no—
91C4×C22⋊D43—22no—
92(C22⋊D43)⋊C4—22no—
93(C22⋊D43)⋊C4—22no—
94#13063284—21no—
95#13063284—22no—
96#13063283—21no—
97#13063283C2×C412yes—
98#13063281—22no—
99#13063281—22no—
100C2×C4⋊Dic43—21no—
101C2×(C2×D43)⋊C4—22no—
102C2×C4×Dic43—22no—
103C2×C4×Dic43—22no—
104C2×C4×Dic43D411yescharacteristic
105C2×C4×Dic43D411yescharacteristic
106C2×C4×Dic43C2311yescharacteristic
107C42×D43C2×C411yescharacteristic
108C42×D43C2×C411yescharacteristic
109C42×D43C2×C411yescharacteristic
110C42×D43C2×C411yescharacteristic
111C42×D43D411yescharacteristic
112C42×D43D411yescharacteristic
113C42×D43D411yescharacteristic
114C42×D43D411yescharacteristic
115C4⋊(C43⋊C8)—21no—
116Dic43⋊C8—22no—
117C22⋊(C43⋊C8)C2312yes—
118(C2×D43)⋊C8—22no—
119C4×C43⋊C8—21no—
120C8×Dic43—22no—
121C43⋊#95—21no—
122C43⋊#95—22no—
123C43⋊#95—22no—
124C43⋊#95C2312yes—
125C2×#41×C43—21no—
126C4⋊Q8×C43C2×C411yescharacteristic
127#127×C43C2×C411yescharacteristic
128#124×C43—21no—
129#121×C43—21no—
130#121×C43C2312yes—
131C4×D4×C43—21no—
132C4×D4×C43C2×C412yes—
133C2×C4⋊C4×C43—21no—
134C2×C42×C43C2311yescharacteristic
135C4⋊C8×C43—21no—
136C22⋊C8×C43C2312yes—
137C4×C8×C43—21no—
138#95×C43—21no—
139#95×C43C2312yes—
140C23×D43C2×D411yescharacteristic
141#41×C43—42no—
142#41×C43—42no—
143C2×Q8×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—22no—
147C2×D4×C43C22×C412yes—
148C22×C4×C43—22no—
149C22×C4×C43—22no—
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2411yescharacteristic
153C2×C22⋊D43—22no—
154C2×C22⋊D43—22no—
155C22×Dic43—22no—
156C22×Dic43—22no—
157C22×Dic43—22no—
158C22×Dic43C2×D411yescharacteristic
159C22×Dic43C2×D411yescharacteristic
160C22×Dic43C2×D411yescharacteristic
161#10621900—44no—
162#10621900—44no—
163C2×C4×D43—22no—
164C2×C4×D43—22no—
165C2×C4×D43—42no—
166C2×C4×D43—42no—
167C2×C4×D43C22⋊C411yescharacteristic
168C2×C4×D43C22⋊C411yescharacteristic
169C2×C4×D43C22⋊C411yescharacteristic
170C2×C4×D43C22⋊C411yescharacteristic
171C2×C4×D43C22⋊C411yescharacteristic
172C2×C4×D43C22⋊C411yescharacteristic
173C2×C4×D43C22⋊C411yescharacteristic
174C2×C4×D43C22⋊C411yescharacteristic
175C2×C4×D43C22×C411yescharacteristic
176C2×C4×D43C22×C411yescharacteristic
177C2×C4×D43C2×D411yescharacteristic
178C2×C4×D43C2×D411yescharacteristic
179C2×Dic86—21no—
180C2×Dic86C22×C412yes—
181C2×C8×C43—22no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—42no—
184C4⋊C4×C43C22×C412yes—
185C22⋊C4×C43—22no—
186C22⋊C4×C43—22no—
187C42×C43C22×C411yescharacteristic
188C42×C43C22×C411yescharacteristic
189C42×C43C2×D411yescharacteristic
190C42×C43C2×D411yescharacteristic
191C22⋊Dic43—22no—
192C22⋊Dic43—22no—
193C22⋊Dic43—22no—
194C22⋊Dic43—22no—
195C22⋊Dic43—22no—
196(C2×D43)⋊C4—22no—
197(C2×D43)⋊C4—22no—
198(C2×D43)⋊C4—44no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—22no—
203C4⋊Dic43—22no—
204C4⋊Dic43—42no—
205C4⋊Dic43C22×C412yes—
206Dic43⋊C4—22no—
207Dic43⋊C4—22no—
208Dic43⋊C4—22no—
209Dic43⋊C4—22no—
210C4×Dic43—22no—
211C4×Dic43—22no—
212C4×Dic43—22no—
213C4×Dic43—44no—
214C4×Dic43C22⋊C411yescharacteristic
215C4×Dic43C22⋊C411yescharacteristic
216C4×Dic43C22⋊C411yescharacteristic
217C4×Dic43C22⋊C411yescharacteristic
218C4×Dic43C22⋊C411yescharacteristic
219C4×Dic43C22⋊C411yescharacteristic
220C4×Dic43C22⋊C411yescharacteristic
221C4×Dic43C22⋊C411yescharacteristic
222C4×Dic43C22×C411yescharacteristic
223C4×Dic43C22×C411yescharacteristic
224C4×Dic43C2×D411yescharacteristic
225C4×Dic43C2×D411yescharacteristic
226C2×C43⋊C8—22no—
227C8×D43—44no—
228C23×C43—22no—
229C23×C43C22×D411yescharacteristic
230C22×D43—21no—
231C22×D43—21no—
232C22×D43—22no—
233C22×D43—41no—
234C22×D43C2×C22⋊C411yescharacteristic
235C22×D43C2×C22⋊C411yescharacteristic
236Q8×C43—42no—
237D4×C43—42no—
238D4×C43—42no—
239D4×C43—42no—
240D4×C43—42no—
241D4×C43—42no—
242C2×C4×C43—22no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—44no—
246C2×C4×C43—42no—
247C2×C4×C43—42no—
248C2×C4×C43—42no—
249C2×C4×C43C2×C22⋊C411yescharacteristic
250C2×C4×C43C2×C22⋊C411yescharacteristic
251C2×C4×C43C2×C22⋊C411yescharacteristic
252C2×C4×C43C2×C22⋊C411yescharacteristic
253C2×C4×C43#13512yes—
254C2×C4×C43#13512yes—
255C2×C4×C43C23×C411yescharacteristic
256C2×C4×C43C22×D411yescharacteristic
257C22⋊D43—44no—
258C22⋊D43—44no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—22no—
262C2×Dic43—22no—
263C2×Dic43—22no—
264C2×Dic43—41no—
265C2×Dic43—44no—
266C2×Dic43—44no—
267C2×Dic43—42no—
268C2×Dic43—42no—
269C2×Dic43—42no—
270C2×Dic43C2×C22⋊C411yescharacteristic
271C2×Dic43C2×C22⋊C411yescharacteristic
272C2×Dic43C2×C22⋊C411yescharacteristic
273C2×Dic43C2×C22⋊C411yescharacteristic
274C2×Dic43C2×C22⋊C411yescharacteristic
275C2×Dic43C2×C22⋊C411yescharacteristic
276C4×D43—22no—
277C4×D43—22no—
278C4×D43—22no—
279C4×D43—22no—
280C4×D43—22no—
281C4×D43—22no—
282C4×D43—22no—
283C4×D43—22no—
284C4×D43—41no—
285C4×D43—41no—
286C4×D43—41no—
287C4×D43—41no—
288Dic86—42no—
289Dic86—42no—
290C8×C43—42no—
291C43⋊C8—42no—
292#17571—431nomaximal, Sylow
293C22×C43—21no—
294C22×C43—21no—
295C22×C43—42no—
296C22×C43—42no—
297C22×C43—42no—
298C22×C43C22×C22⋊C411yescharacteristic
299C22×C43C2×#13511yescharacteristic
300C22×C43C2×#13511yescharacteristic
301C2×D43—21no—
302C2×D43—21no—
303C2×D43—21no—
304C2×D43—21no—
305C2×D43—21no—
306C2×D43—42no—
307C2×D43—42no—
308C2×D43#41012yes—
309C4×C43—21no—
310C4×C43—21no—
311C4×C43—21no—
312C4×C43—21no—
313C4×C43—42no—
314C4×C43—82no—
315C4×C43#41612yes—
316C4×C43#41612yes—
317Dic43—21no—
318Dic43—21no—
319Dic43—21no—
320Dic43—21no—
321Dic43—21no—
322Dic43—42no—
323Dic43—42no—
324Dic43—82no—
325Dic43#42112yes—
326#3444—431no—
327C2×#431—431no—
328#2283—431no—
329#1518—431no—
330#1518—431no—
331#1517—431no—
332#1517D4311yescharacteristic, complemented
333#1516—434no—
334#1500—434no—
335C2×C43—21no—
336C2×C43—21no—
337C2×C43—82no—
338C2×C43C2×#41011yescharacteristic
339C2×C43C2×#41611yescharacteristic
340C2×C43C2×#42111yescharacteristic
341D43—22no—
342D43—41no—
343#533—431no—
344#533—431no—
345#533—431no—
346#532—431no—
347#532—431no—
348#532C2×D4311yescharacteristic
349#529—432no—
350#529—432no—
351#529—861no—
352#529—861no—
353#529—861no—
354#529—861no—
355#525—432no—
356#525—861no—
357#525—861no—
358C4×#41—432no—
359C4×#41—861no—
360C4×#41—861no—
361C22×C42—431no—
362#431—431no—
363#431—432no—
364#431—861no—
365#431—861no—
366#431C2×D4311yescharacteristic
367C2×C4⋊C8—861no—
368C2×C22⋊C8—432no—
369C2×C4×C8—861no—
370#383—861no—
371#382—431no—
372#382C2×D4311yescharacteristic
373#381—432no—
374#380—861no—
375C4×C4⋊C4—861no—
376C4×C22⋊C4—861no—
377#376—432no—
378#328—434no—
379#328—434no—
380#327—434no—
381#327C2×D4314yes—
382C43#1757111yescharacteristic, complemented, Sylow
383C2×#41—21no—
384C2×#41—432no—
385C2×#41—861no—
386C23×C4—431no—
387C23×C4—431no—
388C23×C4—431no—
389C22×C8—862no—
390C4⋊Q8—431no—
391C4⋊Q8—431no—
392C4⋊Q8C4×D4311yescharacteristic
393#127C4×D4311yescharacteristic
394#126—862no—
395#126—862no—
396#125—432no—
397#125—861no—
398#125—861no—
399#124—21no—
400#124—432no—
401#124—861no—
402#123—862no—
403#123—862no—
404#123—862no—
405C22⋊Q8—432no—
406C22⋊Q8—432no—
407C22⋊Q8—861no—
408C22⋊Q8—861no—
409C22⋊Q8—861no—
410C22⋊Q8—861no—
411#121—21no—
412#121—432no—
413#121—861no—
414#121—861no—
415#121—861no—
416#121C22×D4312yes—
417#120—862no—
418C4×Q8—432no—
419C4×Q8—432no—
420C4×Q8—861no—
421C4×Q8—861no—
422C4×Q8—861no—
423C4×Q8—861no—
424C4×D4—21no—
425C4×D4—432no—
426C4×D4—861no—
427C4×D4—861no—
428C4×D4—861no—
429C4×D4—862no—
430C4×D4—862no—
431C4×D4—862no—
432C4×D4—862no—
433C4×D4—862no—
434C4×D4—862no—
435C4×D4C4×D4312yes—
436#117—432no—
437#117—862no—
438#117—862no—
439#117—862no—
440#117—861no—
441#117—861no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—861no—
444C2×C22⋊C4—862no—
445C2×C42—431no—
446C2×C42—431no—
447C2×C42—431no—
448C2×C42—431no—
449C2×C42—431no—
450C2×C42—431no—
451C2×C42—431no—
452C2×C42—431no—
453C2×C42—431no—
454C2×C42—431no—
455C2×C42—431no—
456C2×C42—862no—
457C2×C42—862no—
458C2×C42C22×D4311yescharacteristic
459C4⋊C8—21no—
460C4⋊C8—862no—
461C4⋊C8—861no—
462C22⋊C8—432no—
463C22⋊C8—862no—
464C22⋊C8C22×D4312yes—
465C4×C8—21no—
466C4×C8—862no—
467C4×C8—861no—
468#95—21no—
469#95—432no—
470#95—862no—
471#95—862no—
472#95—861no—
473#95C22×D4312yes—
474C24—431no—
475#41—42no—
476#41—42no—
477#41—1724no—
478#41—1724no—
479C2×Q8—21no—
480C2×Q8—432no—
481C2×Q8—861no—
482C2×D4—22no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—862no—
486C2×D4—862no—
487C2×D4C2×C4×D4312yes—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—431no—
491C22×C4—431no—
492C22×C4—431no—
493C22×C4—431no—
494C22×C4—431no—
495C22×C4—431no—
496C22×C4—431no—
497C22×C4—431no—
498C22×C4—431no—
499C22×C4—431no—
500C22×C4—431no—
501C22×C4—431no—
502C22×C4—431no—
503C22×C4—431no—
504C22×C4—431no—
505C22×C4—862no—
506C22×C4—862no—
507C22×C4—862no—
508C22×C4—862no—
509C22×C4—862no—
510C22×C4—1722no—
511C22×C4—1722no—
512C22×C4D4×D4311yescharacteristic
513C22×C4D4×D4311yescharacteristic
514C22×C4C23×D4311yescharacteristic
515C2×C8—22no—
516C2×C8—862no—
517C2×C8—1724no—
518C4⋊C4—21no—
519C4⋊C4—42no—
520C4⋊C4—432no—
521C4⋊C4—862no—
522C4⋊C4—862no—
523C4⋊C4—862no—
524C4⋊C4—862no—
525C4⋊C4—862no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—862no—
530C4⋊C4—1722no—
531C4⋊C4C2×C4×D4312yes—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—862no—
535C22⋊C4—862no—
536C22⋊C4—862no—
537C22⋊C4—862no—
538C22⋊C4—862no—
539C22⋊C4—862no—
540C22⋊C4—862no—
541C22⋊C4—1724no—
542C42—431no—
543C42—431no—
544C42—431no—
545C42—431no—
546C42—431no—
547C42—431no—
548C42—431no—
549C42—431no—
550C42—431no—
551C42—431no—
552C42—431no—
553C42—431no—
554C42—862no—
555C42—862no—
556C42—862no—
557C42—1724no—
558C42C2×C4×D4311yescharacteristic
559C42C2×C4×D4311yescharacteristic
560C42D4×D4311yescharacteristic
561C42D4×D4311yescharacteristic
562C23—22no—
563C23—431no—
564C23—431no—
565C23—862no—
566C23—861no—
567C23—861no—
568C23—1721no—
569C23C2×D4×D4311yescharacteristic
570Q8—42no—
571Q8—1722no—
572Q8—1722no—
573D4—42no—
574D4—42no—
575D4—42no—
576D4—42no—
577D4—42no—
578D4—1724no—
579D4—1724no—
580C2×C4—22no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—44no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—431no—
588C2×C4—431no—
589C2×C4—431no—
590C2×C4—431no—
591C2×C4—431no—
592C2×C4—431no—
593C2×C4—862no—
594C2×C4—862no—
595C2×C4—862no—
596C2×C4—862no—
597C2×C4—862no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—862no—
601C2×C4—862no—
602C2×C4—862no—
603C2×C4—862no—
604C2×C4—862no—
605C2×C4—862no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1724no—
611C2×C4—1721no—
612C2×C4—1724no—
613C2×C4—1722no—
614C2×C4—1722no—
615C2×C4—1722no—
616C2×C4C22⋊C4×D4311yescharacteristic
617C2×C4C22⋊C4×D4311yescharacteristic
618C2×C4C22⋊C4×D4311yescharacteristic
619C2×C4C22⋊C4×D4311yescharacteristic
620C2×C4#1306334412yes—
621C2×C4#1306334612yes—
622C2×C4C22×C4×D4311yescharacteristic
623C2×C4C2×D4×D4311yescharacteristic
624C8—42no—
625C8—1722no—
626C22—21no—
627C22—21no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22—432no—
632C22—861no—
633C22—861no—
634C22—861no—
635C22—861no—
636C22—861no—
637C22—1722no—
638C22—1722no—
639C22C2×C22⋊C4×D4311yescharacteristic
640C22C2×#1306334411yescharacteristic
641C22C2×#1306334611yescharacteristic
642C4—21no—
643C4—21no—
644C4—21no—
645C4—21no—
646C4—42no—
647C4—82no—
648C4—432no—
649C4—861no—
650C4—861no—
651C4—861no—
652C4—861no—
653C4—861no—
654C4—3442no—
655C4—1722no—
656C4—1722no—
657C4#1458289212yes—
658C4#1458289212yes—
659C2—21no—
660C2—21no—
661C2—82no—
662C2—862no—
663C2—1721no—
664C2#410×D4311yescharacteristic
665C2C2×#1458289211yescharacteristic
666C2#421×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1517C2
socleC22×C43C22×C22⋊C4
prime radical#19147890C2
cosocleC22×C4×C43C24
hypercenter#1517D43
hypocenterC43#17571
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1517

Complements

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

NH ≅ G/Ntype
2. #431×D43C2semidirect
3. #19136988C2semidirect
4. #19133160C2semidirect
5. #19133158C2semidirect
6. #19133155C2semidirect
7. #19133148C2semidirect
8. #19133078C2semidirect
9. C43×#1517C2semidirect
11. #14583454C4semidirect
12. #14583454C4semidirect
13. #14583447C4semidirect
14. #14583447C4semidirect
16. #14583431C4semidirect
26. C4×#10621900C4semidirect
332. #1517D43semidirect
382. C43#17571semidirect

Maximal subgroups

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

subgroupindex
#191478902
#431×D432
#191369882
#191331602
#191331582
#191331552
#191331482
#191330782
C43×#15172
#1757143