Finite Group Databasebeta

← #25063786

Subgroups — #25063786

Order 11008.

1194 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147892C211yesmaximal, characteristic
2#19143223C211yesmaximal, characteristic, complemented
3C4×C4⋊C4×D43C211yesmaximal, characteristic, complemented
4#19133119C214yesmaximal, complemented
5#19133098C214yesmaximal, complemented
6#19133094C211yesmaximal, characteristic, complemented
7#19133091C211yesmaximal, characteristic, complemented
8#19133089C211yesmaximal, characteristic, complemented
9C43×#1503C211yesmaximal, characteristic, complemented
10#14583454C411yescharacteristic, complemented
11#14583454C411yescharacteristic, complemented
12#14583450C411yescharacteristic, complemented
13#14583450C411yescharacteristic, complemented
14#14583449C2211yescharacteristic
15#14583436—21no—
16#14583436C412yescomplemented
17#14583435—21no—
18#14583435C2212yes—
19#14583434—21no—
20#14583434—21no—
21#14583412—21no—
22#14583412C2212yes—
23#14583411—21no—
24C4×#10621902—21no—
25C4×#10621902C412yescomplemented
26#14583367—21no—
27C2×C4⋊C4×D43—21no—
28C2×C42×D43—21no—
29C2×C42×D43C2211yescharacteristic
30#14582955—21no—
31#14582953C2212yes—
32#14582952C2211yescharacteristic
33#14582950—21no—
34#14582921—21no—
35#14582861C2212yes—
36C4×#10621872—21no—
37C4⋊C4×Dic43—21no—
38C4×Dic43⋊C4—21no—
39C4×C4⋊Dic43C2211yescharacteristic
40#14582750C2212yes—
41#95×D43C2212yes—
42#14582636C2214yes—
43#14582634C2214yes—
44#14582632C2214yes—
45C43×#533C2211yescharacteristic
46C43×#431C2211yescharacteristic
47C4×C4⋊C4×C43C2211yescharacteristic
48C43×#328C2214yes—
49C2×#10621902—21no—
50C2×#10621902C2×C412yes—
51C2×#10621898—21no—
52C22×C4×D43—22no—
53C22×C4×D43D411yescharacteristic
54C22×C4×D43D411yescharacteristic
55C22×C4×D43C2311yescharacteristic
56C2×#10621872—22no—
57#13063325C2×C411yescharacteristic, complemented
58#13063322C2×C411yescharacteristic, complemented
59#13063320—22no—
60#13063320—22no—
61#13063316—21no—
62#13063316C2×C412yescomplemented
63#13063314—21no—
64#13063314C2×C412yescomplemented
65#13063313—21no—
66#13063310—22no—
67#13063310—22no—
68#13063309—22no—
69#13063305—21no—
70#13063305—21no—
71#13063301—21no—
72#13063301C2×C412yes—
73#13063300—21no—
74#13063300—21no—
75#13063300—21no—
76#13063300C2×C412yes—
77#13063299—21no—
78#13063299C2312yes—
79#13063295—22no—
80Q8×Dic43—21no—
81Q8×Dic43C2×C412yescomplemented
82#13063290—21no—
83#13063290—21no—
84C4×D172—22no—
85C4×D172—22no—
86C4×D172—21no—
87C4×D172C2×C412yescomplemented
88#13063287—22no—
89#13063287—22no—
90#13063287—21no—
91#13063287—21no—
92#13063287—21no—
93#13063287C2×C412yescomplemented
94(C22⋊D43)⋊C4—22no—
95(C22⋊D43)⋊C4—22no—
96#13063283—21no—
97#13063283—22no—
98#13063283—22no—
99#13063283C2×C412yes—
100#13063282—22no—
101C2×C4⋊Dic43—21no—
102C2×Dic43⋊C4—22no—
103C4⋊C4×D43—28no—
104C2×C4×Dic43—21no—
105C2×C4×Dic43—22no—
106C2×C4×Dic43D411yescharacteristic
107C2×C4×Dic43D411yescharacteristic
108C2×C4×Dic43C2311yescharacteristic
109C42×D43—22no—
110C42×D43—44no—
111C42×D43C2×C411yescharacteristic
112C42×D43C2×C411yescharacteristic
113C42×D43C2×C411yescharacteristic
114C42×D43C2×C411yescharacteristic
115C42×D43D411yescharacteristic
116C42×D43D411yescharacteristic
117C42×D43D411yescharacteristic
118C42×D43D411yescharacteristic
119C4⋊(C43⋊C8)—21no—
120Dic43⋊C8—22no—
121C22⋊(C43⋊C8)C2312yes—
122(C2×D43)⋊C8—22no—
123#13063235—22no—
124C4×C43⋊C8—21no—
125C43⋊#95—22no—
126C43⋊#95C2312yes—
127C4⋊Q8×C43C2×C411yescharacteristic, complemented
128C4⋊Q8×C43C2×C411yescharacteristic, complemented
129#125×C43—21no—
130C22⋊Q8×C43—21no—
131C22⋊Q8×C43C2312yes—
132C4×Q8×C43—21no—
133C4×Q8×C43C2×C412yescomplemented
134#117×C43—21no—
135C2×C4⋊C4×C43—21no—
136C2×C42×C43—21no—
137C2×C42×C43C2311yescharacteristic
138C4⋊C8×C43—21no—
139C22⋊C8×C43C2312yes—
140C4×C8×C43—21no—
141#95×C43C2312yes—
142C23×D43C2×D411yescharacteristic
143C2×Q8×C43—21no—
144C2×Q8×C43C22×C412yes—
145C22×C4×C43—22no—
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2411yescharacteristic
149C2×C22⋊D43—22no—
150C22×Dic43—22no—
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C22×Dic43C2×D411yescharacteristic
154#10621902—44no—
155#10621902—44no—
156#10621898—42no—
157#10621898—42no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—22no—
161C2×D172—22no—
162C2×D172C22×C412yes—
163C2×C4×D43—22no—
164C2×C4×D43—22no—
165C2×C4×D43—24no—
166C2×C4×D43—28no—
167C2×C4×D43—22no—
168C2×C4×D43—22no—
169C2×C4×D43—22no—
170C2×C4×D43—42no—
171C2×C4×D43—44no—
172C2×C4×D43—44no—
173C2×C4×D43C22⋊C411yescharacteristic
174C2×C4×D43C22⋊C411yescharacteristic
175C2×C4×D43C22⋊C411yescharacteristic
176C2×C4×D43C22⋊C411yescharacteristic
177C2×C4×D43C22⋊C411yescharacteristic
178C2×C4×D43C22⋊C411yescharacteristic
179C2×C4×D43C22⋊C411yescharacteristic
180C2×C4×D43C22⋊C411yescharacteristic
181C2×C4×D43C22×C411yescharacteristic
182C2×C4×D43C22×C411yescharacteristic
183C2×C4×D43C2×D411yescharacteristic
184C2×C4×D43C2×D411yescharacteristic
185C2×Dic86—21no—
186C2×C8×C43—22no—
187C4⋊C4×C43—24no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—22no—
192C4⋊C4×C43—22no—
193C4⋊C4×C43C22×C412yes—
194C22⋊C4×C43—22no—
195C42×C43—22no—
196C42×C43—42no—
197C42×C43C22×C411yescharacteristic
198C42×C43C22×C411yescharacteristic
199C42×C43C2×D411yescharacteristic
200C42×C43C2×D411yescharacteristic
201(C2×D43)⋊C4—22no—
202(C2×D43)⋊C4—22no—
203(C2×D43)⋊C4—22no—
204(C2×D43)⋊C4—22no—
205(C2×D43)⋊C4—22no—
206(C2×D43)⋊C4—22no—
207(C2×D43)⋊C4—22no—
208(C2×D43)⋊C4—22no—
209C4⋊Dic43—24no—
210C4⋊Dic43—21no—
211C4⋊Dic43—22no—
212C4⋊Dic43—22no—
213C4⋊Dic43C22×C412yes—
214Dic43⋊C4—28no—
215Dic43⋊C4—22no—
216Dic43⋊C4—22no—
217C4×Dic43—22no—
218C4×Dic43—22no—
219C4×Dic43—44no—
220C4×Dic43—42no—
221C4×Dic43C22⋊C411yescharacteristic
222C4×Dic43C22⋊C411yescharacteristic
223C4×Dic43C22⋊C411yescharacteristic
224C4×Dic43C22⋊C411yescharacteristic
225C4×Dic43C22⋊C411yescharacteristic
226C4×Dic43C22⋊C411yescharacteristic
227C4×Dic43C22⋊C411yescharacteristic
228C4×Dic43C22⋊C411yescharacteristic
229C4×Dic43C22×C411yescharacteristic
230C4×Dic43C22×C411yescharacteristic
231C4×Dic43C2×D411yescharacteristic
232C4×Dic43C2×D411yescharacteristic
233C2×C43⋊C8—22no—
234#10621872—44no—
235C23×C43C22×D411yescharacteristic
236C22×D43—21no—
237C22×D43—21no—
238C22×D43—22no—
239C22×D43—22no—
240C22×D43—22no—
241C22×D43C2×C22⋊C411yescharacteristic
242C22×D43C2×C22⋊C411yescharacteristic
243Q8×C43—42no—
244Q8×C43—42no—
245C2×C4×C43—22no—
246C2×C4×C43—24no—
247C2×C4×C43—22no—
248C2×C4×C43—22no—
249C2×C4×C43—41no—
250C2×C4×C43—42no—
251C2×C4×C43—42no—
252C2×C4×C43C2×C22⋊C411yescharacteristic
253C2×C4×C43C2×C22⋊C411yescharacteristic
254C2×C4×C43C2×C22⋊C411yescharacteristic
255C2×C4×C43C2×C22⋊C411yescharacteristic
256C2×C4×C43AGL(1,ℤ/8)12yes—
257C2×C4×C43#13712yes—
258C2×C4×C43C23×C411yescharacteristic
259C2×C4×C43C22×D411yescharacteristic
260C22⋊D43—42no—
261C22⋊D43—42no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—22no—
265C2×Dic43—24no—
266C2×Dic43—22no—
267C2×Dic43—41no—
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
276D172—42no—
277D172—44no—
278D172—44no—
279D172—42no—
280D172—42no—
281C4×D43—22no—
282C4×D43—22no—
283C4×D43—22no—
284C4×D43—22no—
285C4×D43—22no—
286C4×D43—22no—
287C4×D43—22no—
288C4×D43—22no—
289C4×D43—22no—
290C4×D43—41no—
291C4×D43—41no—
292C4×D43—44no—
293C4×D43—416no—
294C4×D43—44no—
295C4×D43—44no—
296C4×D43#10414yes—
297Dic86—42no—
298C8×C43—42no—
299C43⋊C8—42no—
300#17546—431nomaximal, Sylow
301C22×C43—21no—
302C22×C43—21no—
303C22×C43C22×C22⋊C411yescharacteristic
304C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
305C22×C43C2×#13711yescharacteristic
306C2×D43—24no—
307C2×D43—24no—
308C2×D43—21no—
309C2×D43—21no—
310C2×D43—21no—
311C2×D43—21no—
312C2×D43—42no—
313C2×D43—42no—
314C2×D43—42no—
315C2×D43#41012yes—
316C2×D43C2×#10412yes—
317C4×C43—21no—
318C4×C43—21no—
319C4×C43—21no—
320C4×C43—44no—
321C4×C43—42no—
322C4×C43—42no—
323C4×C43#41712yes—
324C4×C43#41712yes—
325C4×C43C2×#10412yes—
326Dic43—21no—
327Dic43—21no—
328Dic43—21no—
329Dic43—21no—
330Dic43—21no—
331Dic43—44no—
332Dic43—42no—
333Dic43C2×#10412yes—
334#3444—431no—
335#2920—431no—
336C2×C4×C4⋊C4—431no—
337#1509—434no—
338#1504—434no—
339#1503—431no—
340#1503D4311yescharacteristic, complemented
341#1502—431no—
342#1502—431no—
343C2×C43—21no—
344C2×C43—21no—
345C2×C43C2×#41011yescharacteristic
346C2×C43C2×#41711yescharacteristic
347C2×C43C22×#10411yescharacteristic
348D43—22no—
349D43—22no—
350D43—82no—
351#533—431no—
352#533—431no—
353#533C2×D4311yescharacteristic
354#532—431no—
355#532—431no—
356#532—431no—
357#529—432no—
358#529—432no—
359#529—861no—
360#529—861no—
361#529—861no—
362#529—861no—
363#525—432no—
364#525—861no—
365#525—861no—
366C4×#41—432no—
367C4×#41—861no—
368C4×#41—861no—
369C22×C4⋊C4—861no—
370C22×C42—431no—
371C22×C42—861no—
372#432—432no—
373#432—861no—
374#431—431no—
375#431—861no—
376#431C2×D4311yescharacteristic
377#423—861no—
378#407—432no—
379C4×M16—861no—
380C4×C4⋊C4—431no—
381C4×C4⋊C4—432no—
382C4×C4⋊C4—861no—
383C4×C4⋊C4—861no—
384C4×C4⋊C4C2×D4311yescharacteristic
385C2×#95—432no—
386#328—434no—
387#328C2×D4314yes—
388#327—434no—
389#327—434no—
390C43#1754611yescharacteristic, complemented, Sylow
391C2×#41—432no—
392C2×#41—861no—
393C2×#41—861no—
394C23×C4—431no—
395C23×C4—431no—
396C23×C4—431no—
397C23×C4—862no—
398C2×M16—862no—
399C4⋊Q8—431no—
400C4⋊Q8C4×D4311yescharacteristic, complemented
401C4⋊Q8C4×D4311yescharacteristic, complemented
402#127—431no—
403#126—862no—
404#126—862no—
405#125—21no—
406#125—432no—
407#125—861no—
408#124—432no—
409#124—861no—
410#124—861no—
411#123—862no—
412#123—862no—
413#123—862no—
414C22⋊Q8—21no—
415C22⋊Q8—432no—
416C22⋊Q8—861no—
417C22⋊Q8—861no—
418C22⋊Q8—861no—
419C22⋊Q8C22×D4312yes—
420#121—432no—
421#121—432no—
422#121—861no—
423#121—861no—
424#121—861no—
425#121—861no—
426#120—862no—
427C4×Q8—21no—
428C4×Q8—432no—
429C4×Q8—861no—
430C4×Q8—861no—
431C4×Q8—861no—
432C4×Q8C4×D4312yescomplemented
433C4×D4—432no—
434C4×D4—432no—
435C4×D4—862no—
436C4×D4—862no—
437C4×D4—861no—
438C4×D4—861no—
439C4×D4—861no—
440C4×D4—862no—
441C4×D4—862no—
442C4×D4—862no—
443C4×D4—862no—
444C4×D4—861no—
445#117—21no—
446#117—432no—
447#117—862no—
448#117—862no—
449#117—862no—
450#117—861no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—868no—
453C2×C4⋊C4—862no—
454C2×C4⋊C4—861no—
455C2×C42—21no—
456C2×C42—431no—
457C2×C42—431no—
458C2×C42—431no—
459C2×C42—431no—
460C2×C42—431no—
461C2×C42—431no—
462C2×C42—431no—
463C2×C42—431no—
464C2×C42—431no—
465C2×C42—431no—
466C2×C42—431no—
467C2×C42—862no—
468C2×C42—862no—
469C2×C42—861no—
470C2×C42—1724no—
471C2×C42C22×D4311yescharacteristic
472C4⋊C8—21no—
473C4⋊C8—862no—
474C4⋊C8—861no—
475C22⋊C8—432no—
476C22⋊C8—862no—
477C22⋊C8C22×D4312yes—
478#97—862no—
479C4×C8—21no—
480C4×C8—861no—
481#95—432no—
482#95—862no—
483#95C22×D4312yes—
484C24—431no—
485#41—1724no—
486#41—1724no—
487#41—1722no—
488#41—1722no—
489C2×Q8—21no—
490C2×Q8—861no—
491C2×Q8C2×C4×D4312yes—
492C2×D4—432no—
493C2×D4—862no—
494C2×D4—862no—
495C2×D4—862no—
496C2×D4—861no—
497C2×D4—861no—
498C22×C4—22no—
499C22×C4—431no—
500C22×C4—431no—
501C22×C4—431no—
502C22×C4—431no—
503C22×C4—431no—
504C22×C4—431no—
505C22×C4—431no—
506C22×C4—431no—
507C22×C4—431no—
508C22×C4—431no—
509C22×C4—431no—
510C22×C4—431no—
511C22×C4—431no—
512C22×C4—431no—
513C22×C4—431no—
514C22×C4—864no—
515C22×C4—862no—
516C22×C4—862no—
517C22×C4—868no—
518C22×C4—862no—
519C22×C4—862no—
520C22×C4—862no—
521C22×C4—862no—
522C22×C4—1722no—
523C22×C4—1724no—
524C22×C4—1724no—
525C22×C4D4×D4311yescharacteristic
526C22×C4D4×D4311yescharacteristic
527C22×C4C23×D4311yescharacteristic
528M16—1724no—
529C2×C8—22no—
530C2×C8—862no—
531C4⋊C4—24no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—432no—
538C4⋊C4—862no—
539C4⋊C4—862no—
540C4⋊C4—862no—
541C4⋊C4—862no—
542C4⋊C4—868no—
543C4⋊C4—864no—
544C4⋊C4—861no—
545C4⋊C4C2×C4×D4312yes—
546C22⋊C4—22no—
547C22⋊C4—862no—
548C22⋊C4—862no—
549C22⋊C4—862no—
550C22⋊C4—862no—
551C22⋊C4—862no—
552C22⋊C4—862no—
553C22⋊C4—862no—
554C22⋊C4—862no—
555C42—22no—
556C42—42no—
557C42—431no—
558C42—431no—
559C42—431no—
560C42—431no—
561C42—431no—
562C42—431no—
563C42—431no—
564C42—431no—
565C42—431no—
566C42—431no—
567C42—431no—
568C42—431no—
569C42—862no—
570C42—862no—
571C42—1724no—
572C42—1722no—
573C42C2×C4×D4311yescharacteristic
574C42C2×C4×D4311yescharacteristic
575C42D4×D4311yescharacteristic
576C42D4×D4311yescharacteristic
577C23—431no—
578C23—431no—
579C23—862no—
580C23—862no—
581C23—861no—
582C23—861no—
583C23—862no—
584C23C2×D4×D4311yescharacteristic
585Q8—42no—
586Q8—42no—
587Q8—1722no—
588D4—1722no—
589D4—1724no—
590D4—1724no—
591D4—1722no—
592D4—1722no—
593D4—1722no—
594D4—1722no—
595C2×C4—22no—
596C2×C4—24no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—41no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—431no—
603C2×C4—434no—
604C2×C4—431no—
605C2×C4—431no—
606C2×C4—431no—
607C2×C4—431no—
608C2×C4—431no—
609C2×C4—862no—
610C2×C4—862no—
611C2×C4—862no—
612C2×C4—862no—
613C2×C4—862no—
614C2×C4—861no—
615C2×C4—861no—
616C2×C4—862no—
617C2×C4—862no—
618C2×C4—862no—
619C2×C4—862no—
620C2×C4—862no—
621C2×C4—864no—
622C2×C4—862no—
623C2×C4—1721no—
624C2×C4—1721no—
625C2×C4—1724no—
626C2×C4—1724no—
627C2×C4—17216no—
628C2×C4—1721no—
629C2×C4—1722no—
630C2×C4—1722no—
631C2×C4—1724no—
632C2×C4C22⋊C4×D4311yescharacteristic
633C2×C4C22⋊C4×D4311yescharacteristic
634C2×C4C22⋊C4×D4311yescharacteristic
635C2×C4C22⋊C4×D4311yescharacteristic
636C2×C4#1306335212yes—
637C2×C4#1306335712yes—
638C2×C4C22×C4×D4311yescharacteristic
639C2×C4C2×D4×D4311yescharacteristic
640C8—42no—
641C8—1722no—
642C22—21no—
643C22—21no—
644C22—432no—
645C22—432no—
646C22—864no—
647C22—864no—
648C22—861no—
649C22—861no—
650C22—861no—
651C22—861no—
652C22—1722no—
653C22—1722no—
654C22—1722no—
655C22C2×C22⋊C4×D4311yescharacteristic
656C22C2×#1306335211yescharacteristic
657C22C2×#1306335711yescharacteristic
658C4—21no—
659C4—21no—
660C4—21no—
661C4—44no—
662C4—42no—
663C4—42no—
664C4—432no—
665C4—861no—
666C4—861no—
667C4—861no—
668C4—861no—
669C4—861no—
670C4—1724no—
671C4—1722no—
672C4#1458289912yes—
673C4#1458289912yes—
674C4#104×D4312yes—
675C2—21no—
676C2—21no—
677C2—862no—
678C2—862no—
679C2—3442no—
680C2#410×D4311yescharacteristic
681C2C2×#1458289911yescharacteristic
682C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1503C2
socleC22×C43C22×C22⋊C4
prime radical#19147892C2
cosocleC22×C4×C43C24
hypercenter#1503D43
hypocenterC43#17546
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1503

Complements

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

NH ≅ G/Ntype
2. #19143223C2semidirect
3. C4×C4⋊C4×D43C2semidirect
4. #19133119C2semidirect
5. #19133098C2semidirect
6. #19133094C2semidirect
7. #19133091C2semidirect
8. #19133089C2semidirect
9. C43×#1503C2semidirect
10. #14583454C4semidirect
11. #14583454C4semidirect
12. #14583450C4semidirect
13. #14583450C4semidirect
16. #14583436C4semidirect
25. C4×#10621902C4semidirect
57. #13063325C2×C4semidirect
58. #13063322C2×C4semidirect
62. #13063316C2×C4semidirect
64. #13063314C2×C4semidirect
81. Q8×Dic43C2×C4semidirect
87. C4×D172C2×C4semidirect
93. #13063287C2×C4semidirect
127. C4⋊Q8×C43C2×C4semidirect
128. C4⋊Q8×C43C2×C4semidirect
133. C4×Q8×C43C2×C4semidirect
340. #1503D43semidirect
390. C43#17546semidirect
400. C4⋊Q8C4×D43semidirect
401. C4⋊Q8C4×D43semidirect
432. C4×Q8C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191478922
#191432232
C4×C4⋊C4×D432
#191331192
#191330982
#191330942
#191330912
#191330892
C43×#15032
#1754643