Finite Group Databasebeta

← #25106250

Subgroups — #25106250

Order 11008.

1200 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147892C211yesmaximal, characteristic
2#423×D43C211yesmaximal, characteristic, complemented
3C4×#13063282C211yesmaximal, characteristic, complemented
4#19135573C211yesmaximal, characteristic, complemented
5#19135423C211yesmaximal, characteristic, complemented
6#19135422C211yesmaximal, characteristic, complemented
7#19134896C214yesmaximal, complemented
8#19134614C214yesmaximal, complemented
9C43×#1994C211yesmaximal, characteristic, complemented
10C2×M16×D43C2212yes—
11#14583454C411yescharacteristic, complemented
12#14583454C411yescharacteristic, complemented
13#14583450C411yescharacteristic, complemented
14#14583450C411yescharacteristic, complemented
15#14583449C2211yescharacteristic
16#14583436—21no—
17#14583436—21no—
18#14583435—21no—
19#14583435—21no—
20#14583434C412yescomplemented
21#14583434C412yescomplemented
22#14583412—21no—
23#14583412—21no—
24#14583411C2212yes—
25C4×#10621902—21no—
26C4×#10621902—21no—
27#14583367C2212yes—
28C2×#13063282—21no—
29C2×C42×D43C2211yescharacteristic
30#14582923C2211yescharacteristic
31#14582922C2212yes—
32#14582921—21no—
33#14582921—21no—
34C4⋊C8×D43—21no—
35C4⋊C8×D43—21no—
36C2×#13063253C2214yes—
37C2×#13063251C2214yes—
38C4×Dic43⋊C4—21no—
39C4×Dic43⋊C4C2212yes—
40C4×(C2×D43)⋊C4—21no—
41C4×(C2×D43)⋊C4C2212yes—
42#14582745—21no—
43C42×Dic43C2211yescharacteristic
44#14582658C2214yes—
45C43×#533C2211yescharacteristic
46C43×#423C2211yescharacteristic
47C43×C43C2211yescharacteristic
48C43×#339C2214yes—
49C2×#10621902—21no—
50C2×#10621902—21no—
51C2×#10621898C2312yes—
52C22×C4×D43D411yescharacteristic
53C22×C4×D43D411yescharacteristic
54C22×C4×D43C2311yescharacteristic
55C2×#10621877C2312yes—
56C2×#10621872—22no—
57M16×D43—44no—
58C2×C8×D43—22no—
59#13063325C2×C411yescharacteristic
60#13063322C2×C411yescharacteristic
61#13063320—22no—
62#13063320—22no—
63#13063316—21no—
64#13063316—21no—
65#13063314—21no—
66#13063314—21no—
67#13063313C2×C412yes—
68#13063310—22no—
69#13063310—22no—
70#13063309—22no—
71#13063305C2×C412yes—
72#13063305C2×C412yes—
73#13063301—21no—
74#13063301—21no—
75#13063300—21no—
76#13063300—21no—
77#13063300C2×C412yes—
78#13063300C2×C412yes—
79#13063299—21no—
80#13063299—21no—
81#13063295—22no—
82Q8×Dic43—21no—
83Q8×Dic43—21no—
84#13063290C2×C412yes—
85#13063290C2×C412yes—
86C4×D172—22no—
87C4×D172—22no—
88C4×D172—21no—
89C4×D172—21no—
90#13063287—22no—
91#13063287—22no—
92#13063287—21no—
93#13063287—21no—
94#13063287C2×C412yes—
95#13063287C2×C412yes—
96(C22⋊D43)⋊C4—22no—
97(C22⋊D43)⋊C4—22no—
98#13063283—21no—
99#13063283—21no—
100#13063283—22no—
101#13063283—22no—
102#13063282—28no—
103#13063282—22no—
104C2×Dic43⋊C4—22no—
105C2×(C2×D43)⋊C4—22no—
106C2×C4×Dic43—21no—
107C2×C4×Dic43—21no—
108C2×C4×Dic43D411yescharacteristic
109C2×C4×Dic43D411yescharacteristic
110C2×C4×Dic43C2312yes—
111C2×C4×Dic43C2311yescharacteristic
112C42×D43—22no—
113C42×D43C2×C411yescharacteristic
114C42×D43C2×C411yescharacteristic
115C42×D43C2×C411yescharacteristic
116C42×D43C2×C411yescharacteristic
117C42×D43D411yescharacteristic
118C42×D43D411yescharacteristic
119C42×D43D411yescharacteristic
120C42×D43D411yescharacteristic
121C4⋊(C43⋊C8)—21no—
122C4⋊(C43⋊C8)—21no—
123Dic43⋊C8—22no—
124Dic43⋊C8—22no—
125#13063253—44no—
126#13063251—44no—
127C43⋊#95—22no—
128C43⋊#95—22no—
129C2×M16×C43C2312yes—
130C4⋊Q8×C43C2×C411yescharacteristic
131C4⋊Q8×C43C2×C411yescharacteristic
132#125×C43C2×C412yes—
133C22⋊Q8×C43—21no—
134C22⋊Q8×C43—21no—
135C4×Q8×C43—21no—
136C4×Q8×C43—21no—
137#117×C43C2312yes—
138C2×C42×C43—21no—
139C2×C42×C43—21no—
140C2×C42×C43C2312yes—
141C2×C42×C43C2311yescharacteristic
142C4⋊C8×C43—21no—
143C4⋊C8×C43—21no—
144C23×D43C2×D411yescharacteristic
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C22×C4×C43—22no—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2411yescharacteristic
151C2×C22⋊D43—22no—
152C22×Dic43—22no—
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156#10621902—44no—
157#10621902—44no—
158#10621898—24no—
159#10621898—24no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—22no—
163C2×D172—22no—
164C2×D172C22×C412yes—
165C2×C4×D43—22no—
166C2×C4×D43—22no—
167C2×C4×D43—24no—
168C2×C4×D43—22no—
169C2×C4×D43—22no—
170C2×C4×D43—22no—
171C2×C4×D43—42no—
172C2×C4×D43C22⋊C411yescharacteristic
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×D43C2×D411yescharacteristic
183C2×C4×D43C2×D411yescharacteristic
184C2×Dic86C22×C412yes—
185M16×C43—24no—
186C2×C8×C43—22no—
187C4⋊C4×C43—22no—
188C4⋊C4×C43—22no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43C22×C412yes—
192C4⋊C4×C43C22×C412yes—
193C22⋊C4×C43—22no—
194C42×C43—24no—
195C42×C43—22no—
196C42×C43—22no—
197C42×C43—22no—
198C42×C43—42no—
199C42×C43C22×C411yescharacteristic
200C42×C43C22×C411yescharacteristic
201C42×C43C2×D411yescharacteristic
202C42×C43C2×D411yescharacteristic
203(C2×D43)⋊C4—28no—
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—
209(C2×D43)⋊C4—22no—
210(C2×D43)⋊C4—22no—
211(C2×D43)⋊C4—22no—
212C4⋊Dic43—21no—
213C4⋊Dic43—21no—
214C4⋊Dic43—22no—
215C4⋊Dic43—22no—
216Dic43⋊C4—28no—
217Dic43⋊C4—22no—
218Dic43⋊C4—22no—
219C4×Dic43—24no—
220C4×Dic43—22no—
221C4×Dic43—22no—
222C4×Dic43—22no—
223C4×Dic43—22no—
224C4×Dic43—42no—
225C4×Dic43C22⋊C411yescharacteristic
226C4×Dic43C22⋊C411yescharacteristic
227C4×Dic43C22⋊C411yescharacteristic
228C4×Dic43C22⋊C411yescharacteristic
229C4×Dic43C22⋊C411yescharacteristic
230C4×Dic43C22⋊C411yescharacteristic
231C4×Dic43C22⋊C411yescharacteristic
232C4×Dic43C22⋊C411yescharacteristic
233C4×Dic43C22×C411yescharacteristic
234C4×Dic43C22×C411yescharacteristic
235C4×Dic43C2×D411yescharacteristic
236C4×Dic43C2×D411yescharacteristic
237#10621877—24no—
238C2×C43⋊C8—22no—
239#10621872—44no—
240C8×D43—44no—
241C23×C43C22×D411yescharacteristic
242C22×D43—22no—
243C22×D43—22no—
244C22×D43—22no—
245C22×D43—41no—
246C22×D43C2×C22⋊C411yescharacteristic
247C22×D43C2×C22⋊C411yescharacteristic
248Q8×C43—42no—
249Q8×C43—42no—
250C2×C4×C43—22no—
251C2×C4×C43—22no—
252C2×C4×C43—24no—
253C2×C4×C43—22no—
254C2×C4×C43—22no—
255C2×C4×C43—42no—
256C2×C4×C43—42no—
257C2×C4×C43C2×C22⋊C411yescharacteristic
258C2×C4×C43C2×C22⋊C411yescharacteristic
259C2×C4×C43C2×C22⋊C411yescharacteristic
260C2×C4×C43C2×C22⋊C411yescharacteristic
261C2×C4×C43C23×C411yescharacteristic
262C2×C4×C43C22×D411yescharacteristic
263C2×C4×C43H(5,𝔽2)12yes—
264C2×C4×C432−1+412yes—
265C22⋊D43—44no—
266C2×Dic43—22no—
267C2×Dic43—22no—
268C2×Dic43—24no—
269C2×Dic43—22no—
270C2×Dic43—41no—
271C2×Dic43—42no—
272C2×Dic43—42no—
273C2×Dic43C2×C22⋊C411yescharacteristic
274C2×Dic43C2×C22⋊C411yescharacteristic
275C2×Dic43C2×C22⋊C411yescharacteristic
276C2×Dic43C2×C22⋊C411yescharacteristic
277C2×Dic43C2×C22⋊C411yescharacteristic
278C2×Dic43C2×C22⋊C411yescharacteristic
279D172—24no—
280D172—44no—
281D172—44no—
282D172—42no—
283D172—42no—
284C4×D43—22no—
285C4×D43—22no—
286C4×D43—22no—
287C4×D43—21no—
288C4×D43—21no—
289C4×D43—21no—
290C4×D43—21no—
291C4×D43—22no—
292C4×D43—22no—
293C4×D43—22no—
294C4×D43—22no—
295C4×D43—41no—
296C4×D43—41no—
297C4×D43—44no—
298C4×D43—42no—
299C4×D43—42no—
300C4×D43—44no—
301C4×D43#10414yescomplemented
302Dic86—24no—
303C8×C43—42no—
304C43⋊C8—42no—
305#21856—431nomaximal, Sylow
306C22×C43—21no—
307C22×C43—21no—
308C22×C43C22×C22⋊C411yescharacteristic
309C22×C43#53712yes—
310C2×D43—21no—
311C2×D43—21no—
312C2×D43—21no—
313C2×D43—21no—
314C2×D43—21no—
315C2×D43—44no—
316C2×D43—42no—
317C2×D43—42no—
318C2×D43—42no—
319C2×D43C2×#10412yes—
320C4×C43—21no—
321C4×C43—21no—
322C4×C43—44no—
323C4×C43—42no—
324C4×C43—42no—
325C4×C43C2×#10412yes—
326C4×C43#42112yes—
327C4×C43#52012yes—
328C4×C43#53511yescharacteristic
329C4×C43#53611yescharacteristic
330Dic43—21no—
331Dic43—21no—
332Dic43—21no—
333Dic43—21no—
334Dic43—21no—
335Dic43—44no—
336Dic43—42no—
337Dic43C2×#10412yes—
338#3444—431no—
339C2×#423—431no—
340C4×#117—431no—
341#1994—431no—
342#1994D4311yescharacteristic, complemented
343#1962—431no—
344#1962—431no—
345#1871—434no—
346#1806—434no—
347C2×C43—22no—
348C2×C43#231111yescharacteristic
349C2×C43C22×#10411yescharacteristic
350C2×C43C2×#42111yescharacteristic
351D43—22no—
352D43—41no—
353D43—82no—
354C22×M16—432no—
355#533—431no—
356#533—431no—
357#533C2×D4311yescharacteristic
358#532—431no—
359#532—431no—
360#532—431no—
361#529—432no—
362#529—432no—
363#529—861no—
364#529—861no—
365#529—861no—
366#529—861no—
367#525—432no—
368#525—861no—
369#525—861no—
370C4×#41—432no—
371C4×#41—861no—
372C4×#41—861no—
373C2×#117—861no—
374C22×C42—431no—
375#423—432no—
376#423—431no—
377#423—861no—
378#423—861no—
379#423C2×D4311yescharacteristic
380C2×C4⋊C8—861no—
381C2×C4⋊C8—861no—
382C2×#104—434no—
383C2×#104—434no—
384C4×C4⋊C4—432no—
385C4×C4⋊C4—861no—
386C4×C22⋊C4—432no—
387C4×C22⋊C4—861no—
388#376—861no—
389C43—431no—
390C43C2×D4311yescharacteristic
391#339—434no—
392#339C2×D4314yes—
393C43#2185611yescharacteristic, complemented, Sylow
394C2×#41—432no—
395C2×#41—861no—
396C2×#41—861no—
397C23×C4—431no—
398C23×C4—431no—
399C23×C4—431no—
400C2×M16—432no—
401C2×M16—862no—
402C2×M16—1724no—
403C2×M16C22×D4312yes—
404C22×C8—862no—
405C4⋊Q8—431no—
406C4⋊Q8C4×D4311yescharacteristic
407C4⋊Q8C4×D4311yescharacteristic
408#127—431no—
409#126—862no—
410#126—862no—
411#125—861no—
412#125—861no—
413#125C4×D4312yes—
414#124—432no—
415#124—861no—
416#124—861no—
417#123—862no—
418#123—862no—
419#123—862no—
420C22⋊Q8—21no—
421C22⋊Q8—21no—
422C22⋊Q8—432no—
423C22⋊Q8—432no—
424C22⋊Q8—861no—
425C22⋊Q8—861no—
426#121—432no—
427#121—432no—
428#121—861no—
429#121—861no—
430#121—861no—
431#121—861no—
432#120—862no—
433C4×Q8—21no—
434C4×Q8—21no—
435C4×Q8—432no—
436C4×Q8—432no—
437C4×Q8—861no—
438C4×Q8—861no—
439C4×D4—432no—
440C4×D4—432no—
441C4×D4—862no—
442C4×D4—862no—
443C4×D4—861no—
444C4×D4—861no—
445C4×D4—862no—
446C4×D4—862no—
447C4×D4—862no—
448C4×D4—862no—
449C4×D4—861no—
450C4×D4—861no—
451#117—862no—
452#117—868no—
453#117—862no—
454#117—862no—
455#117—861no—
456#117—861no—
457#117C22×D4312yes—
458C2×C4⋊C4—862no—
459C2×C22⋊C4—862no—
460C2×C42—21no—
461C2×C42—21no—
462C2×C42—431no—
463C2×C42—431no—
464C2×C42—431no—
465C2×C42—431no—
466C2×C42—431no—
467C2×C42—431no—
468C2×C42—431no—
469C2×C42—431no—
470C2×C42—431no—
471C2×C42—431no—
472C2×C42—431no—
473C2×C42—432no—
474C2×C42—862no—
475C2×C42—861no—
476C2×C42—861no—
477C2×C42C22×D4312yes—
478C2×C42C22×D4311yescharacteristic
479C4⋊C8—21no—
480C4⋊C8—21no—
481C4⋊C8—862no—
482C4⋊C8—862no—
483C4⋊C8—861no—
484C4⋊C8—861no—
485#104—1724no—
486#104—1724no—
487#95—862no—
488#95—862no—
489C24—431no—
490#41—864no—
491#41—864no—
492#41—1724no—
493#41—1724no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—432no—
497C2×D4—432no—
498C2×D4—862no—
499C2×D4—862no—
500C2×D4—862no—
501C2×D4—861no—
502C2×D4—861no—
503C22×C4—22no—
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—431no—
515C22×C4—431no—
516C22×C4—431no—
517C22×C4—431no—
518C22×C4—431no—
519C22×C4—864no—
520C22×C4—862no—
521C22×C4—862no—
522C22×C4—862no—
523C22×C4—862no—
524C22×C4—862no—
525C22×C4—862no—
526C22×C4—1722no—
527C22×C4D4×D4311yescharacteristic
528C22×C4D4×D4311yescharacteristic
529C22×C4C23×D4311yescharacteristic
530M16—24no—
531M16—864no—
532M16—1724no—
533C2×C8—22no—
534C2×C8—862no—
535C2×C8—1724no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—862no—
541C4⋊C4—862no—
542C4⋊C4—862no—
543C4⋊C4—862no—
544C4⋊C4—868no—
545C4⋊C4—861no—
546C4⋊C4—861no—
547C4⋊C4C2×C4×D4312yes—
548C4⋊C4C2×C4×D4312yes—
549C22⋊C4—22no—
550C22⋊C4—862no—
551C22⋊C4—862no—
552C22⋊C4—862no—
553C22⋊C4—862no—
554C22⋊C4—862no—
555C22⋊C4—862no—
556C22⋊C4—868no—
557C22⋊C4—862no—
558C22⋊C4—862no—
559C42—24no—
560C42—22no—
561C42—22no—
562C42—22no—
563C42—42no—
564C42—431no—
565C42—431no—
566C42—431no—
567C42—431no—
568C42—431no—
569C42—431no—
570C42—431no—
571C42—431no—
572C42—431no—
573C42—431no—
574C42—431no—
575C42—431no—
576C42—862no—
577C42—862no—
578C42—864no—
579C42—862no—
580C42—862no—
581C42—1722no—
582C42C2×C4×D4311yescharacteristic
583C42C2×C4×D4311yescharacteristic
584C42D4×D4311yescharacteristic
585C42D4×D4311yescharacteristic
586C23—431no—
587C23—431no—
588C23—862no—
589C23—862no—
590C23—862no—
591C23—1721no—
592C23C2×D4×D4311yescharacteristic
593Q8—42no—
594Q8—42no—
595Q8—864no—
596D4—864no—
597D4—1724no—
598D4—1724no—
599D4—1724no—
600D4—1722no—
601D4—1722no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—24no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—431no—
610C2×C4—434no—
611C2×C4—431no—
612C2×C4—431no—
613C2×C4—431no—
614C2×C4—431no—
615C2×C4—431no—
616C2×C4—862no—
617C2×C4—862no—
618C2×C4—862no—
619C2×C4—862no—
620C2×C4—862no—
621C2×C4—862no—
622C2×C4—862no—
623C2×C4—862no—
624C2×C4—862no—
625C2×C4—861no—
626C2×C4—861no—
627C2×C4—861no—
628C2×C4—861no—
629C2×C4—864no—
630C2×C4—862no—
631C2×C4—1721no—
632C2×C4—1721no—
633C2×C4—1724no—
634C2×C4—1724no—
635C2×C4—1721no—
636C2×C4—1722no—
637C2×C4—1722no—
638C2×C4—1722no—
639C2×C4—1722no—
640C2×C4C22⋊C4×D4311yescharacteristic
641C2×C4C22⋊C4×D4311yescharacteristic
642C2×C4C22⋊C4×D4311yescharacteristic
643C2×C4C22⋊C4×D4311yescharacteristic
644C2×C4C22×C4×D4311yescharacteristic
645C2×C4C2×D4×D4311yescharacteristic
646C2×C4#1306337112yes—
647C2×C4#1306337312yes—
648C8—42no—
649C8—1722no—
650C22—21no—
651C22—21no—
652C22—432no—
653C22—861no—
654C22—861no—
655C22—861no—
656C22—861no—
657C22—861no—
658C22—1724no—
659C22—1722no—
660C22—1722no—
661C22—1722no—
662C22C2×C22⋊C4×D4311yescharacteristic
663C22#1458347912yes—
664C4—21no—
665C4—21no—
666C4—44no—
667C4—42no—
668C4—42no—
669C4—432no—
670C4—861no—
671C4—861no—
672C4—861no—
673C4—861no—
674C4—861no—
675C4—1724no—
676C4—1722no—
677C4#104×D4312yes—
678C4#1458291412yes—
679C4#1458338112yes—
680C4#1458346711yescharacteristic
681C4#1458347411yescharacteristic
682C2—22no—
683C2—862no—
684C2—3442no—
685C2—1721no—
686C2#1913718611yescharacteristic
687C2C2×#104×D4311yescharacteristic
688C2C2×#1458291411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1994C2
socleC22×C43C22×C22⋊C4
prime radical#19147892C2
cosocleC22×C4×C43C24
hypercenter#1994D43
hypocenterC43#21856
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1994

Complements

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

NH ≅ G/Ntype
2. #423×D43C2semidirect
3. C4×#13063282C2semidirect
4. #19135573C2semidirect
5. #19135423C2semidirect
6. #19135422C2semidirect
7. #19134896C2semidirect
8. #19134614C2semidirect
9. C43×#1994C2semidirect
11. #14583454C4semidirect
12. #14583454C4semidirect
13. #14583450C4semidirect
14. #14583450C4semidirect
20. #14583434C4semidirect
21. #14583434C4semidirect
301. C4×D43#104semidirect
342. #1994D43semidirect
393. C43#21856semidirect

Maximal subgroups

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

subgroupindex
#191478922
#423×D432
C4×#130632822
#191355732
#191354232
#191354222
#191348962
#191346142
C43×#19942
#2185643