Finite Group Databasebeta

← #24987994

Subgroups — #24987994

Order 11008.

1058 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13063371C211yesmaximal, characteristic
2#19135388C211yesmaximal, characteristic, complemented
3#19132980C211yesmaximal, characteristic, complemented
4#19132977C211yesmaximal, characteristic, complemented
5#19132975C211yesmaximal, characteristic, complemented
6#19132915C211yesmaximal, characteristic, complemented
7C43×#1477C211yesmaximal, characteristic, complemented
8C2×#13063371C411yescharacteristic
9#14583382C411yescharacteristic
10#14583381—21no—
11#14583379—21no—
12#14583379C411yescharacteristic
13#14583373—21no—
14#14583373C411yescharacteristic
15#14583371—22no—
16#14583371—21no—
17C4×#10621902—21no—
18C4×#10621898—21no—
19C4×#10621898C2211yescharacteristic
20C2×C4×D172—21no—
21C2×C4×D172C2211yescharacteristic
22C4×D4×D43—22no—
23C4×D4×D43—21no—
24#14582952C2211yescharacteristic, complemented
25C2×(C2×D43)⋊C8—22no—
26C2×C4×C43⋊C8C2211yescharacteristic, complemented
27Q8⋊(C43⋊C8)—21no—
28#14582629—21no—
29#14582629—21no—
30D4⋊(C43⋊C8)—21no—
31#14582626—21no—
32#14582626—21no—
33#14582622—22no—
34C4×#41×C43C2211yescharacteristic
35C43×#431C2211yescharacteristic, complemented
36C2×C4⋊C8×C43C2211yescharacteristic, complemented
37C43×Q8⋊C8—21no—
38C43×D4⋊C8—21no—
39#13063371—22no—
40#13063371—22no—
41#13063371—22no—
42#13063371C814yescomplemented
43C2×#10621902—21no—
44C2×#10621898—21no—
45C2×#10621898C2×C411yescharacteristic
46C22×D172—21no—
47C22×D172C2×C411yescharacteristic
48C2×D4×D43—22no—
49C2×D4×D43—21no—
50C22×C4×D43—22no—
51C22×C4×D43D412yes—
52C22×C43⋊C8—21no—
53Q8×Dic43—21no—
54C4×Dic86—21no—
55C4×Dic86D411yescharacteristic
56C4×Dic86D411yescharacteristic
57C4×D172—22no—
58C4×D172—22no—
59C4×D172—21no—
60C4×D172—21no—
61C4×D172—21no—
62C4×D172—21no—
63C4×D172—21no—
64C4×D172—21no—
65C4×D172—21no—
66C4×D172D411yescharacteristic
67C4×D172D411yescharacteristic
68D4×Dic43—21no—
69D4×Dic43—22no—
70#13063287—22no—
71#13063287—22no—
72#13063287—21no—
73#13063287—21no—
74C4×C22⋊D43—22no—
75C4×C22⋊D43—22no—
76C4×C22⋊D43—21no—
77C4×C22⋊D43—21no—
78(C22⋊D43)⋊C4—22no—
79(C22⋊D43)⋊C4—22no—
80(C22⋊D43)⋊C4—22no—
81#13063284—21no—
82#13063284C2×C411yescharacteristic
83#13063283—22no—
84#13063283—21no—
85#13063282—22no—
86#13063282—21no—
87C2×C4⋊Dic43—21no—
88C2×C4⋊Dic43C2×C411yescharacteristic
89C4⋊C4×D43—22no—
90C4⋊C4×D43—21no—
91C2×(C2×D43)⋊C4—22no—
92C2×(C2×D43)⋊C4D412yes—
93C22⋊C4×D43—22no—
94C22⋊C4×D43—22no—
95C22⋊C4×D43—22no—
96C42×D43—22no—
97C42×D43—21no—
98C4⋊(C43⋊C8)—21no—
99C22⋊(C43⋊C8)—21no—
100(C2×D43)⋊C8—44no—
101C4×C43⋊C8—21no—
102C4×C43⋊C8—21no—
103C4×C43⋊C8—21no—
104C2×#41×C43C2×C411yescharacteristic
105C22×C8×C43—21no—
106C4×Q8×C43D411yescharacteristic
107C4×Q8×C43D411yescharacteristic
108C4×D4×C43—21no—
109C4×D4×C43—21no—
110C4×D4×C43D411yescharacteristic
111C4×D4×C43D411yescharacteristic
112#117×C43—21no—
113#117×C43C2×C411yescharacteristic
114C2×C42×C43—21no—
115C2×C42×C43C2311yescharacteristic
116C4⋊C8×C43—21no—
117C4⋊C8×C43—21no—
118C4⋊C8×C43—21no—
119C22⋊C8×C43—21no—
120C4×C8×C43—21no—
121C23×D43—22no—
122C23×D43C22⋊C412yes—
123#41×C43—21no—
124#41×C43—21no—
125#41×C43C2×C812yes—
126#41×C43M1612yes—
127C2×Q8×C43C22⋊C411yescharacteristic
128C2×D4×C43—21no—
129C2×D4×C43C22⋊C411yescharacteristic
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43C22×C411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C2×C22⋊D43—22no—
137C2×C22⋊D43—21no—
138C22×Dic43—22no—
139C22×Dic43C22⋊C412yes—
140#10621902—24no—
141#10621902—24no—
142D4×D43—24no—
143D4×D43—28no—
144D4×D43—24no—
145D4×D43—28no—
146#10621898—24no—
147#10621898—21no—
148#10621898—21no—
149#10621898—24no—
150#10621898C2×C812yes—
151#10621898M1612yes—
152C2×D172—22no—
153C2×D172—24no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—24no—
159C2×D172C22⋊C411yescharacteristic
160C2×D172C2×C812yes—
161C2×D172M1612yes—
162C2×C4×D43—22no—
163C2×C4×D43—21no—
164C2×C4×D43—22no—
165C2×C4×D43—21no—
166C2×C4×D43—22no—
167C2×C4×D43—22no—
168C2×C4×D43—22no—
169C2×C4×D43—21no—
170C2×C4×D43—22no—
171C2×C4×D43—42no—
172C2×C4×D43—42no—
173C2×C4×D43—82no—
174C2×C4×D43—82no—
175C2×Dic86C22⋊C411yescharacteristic
176C2×C8×C43—42no—
177C2×C8×C43—41no—
178C2×C8×C43—41no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43C22⋊C411yescharacteristic
182C4⋊C4×C43C22⋊C411yescharacteristic
183C22⋊C4×C43—21no—
184C22⋊C4×C43—21no—
185C22⋊C4×C43—21no—
186C42×C43—21no—
187C42×C43—21no—
188C42×C43—21no—
189C42×C43C2×D411yescharacteristic
190C42×C43C2×D411yescharacteristic
191C42×C43C2×D411yescharacteristic
192C42×C43C2×D411yescharacteristic
193C22⋊Dic43—22no—
194C22⋊Dic43—21no—
195(C2×D43)⋊C4—22no—
196(C2×D43)⋊C4—22no—
197(C2×D43)⋊C4—22no—
198(C2×D43)⋊C4—21no—
199(C2×D43)⋊C4—22no—
200(C2×D43)⋊C4—21no—
201(C2×D43)⋊C4—22no—
202C4⋊Dic43—22no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43C22⋊C411yescharacteristic
206C4⋊Dic43C22⋊C411yescharacteristic
207Dic43⋊C4—22no—
208Dic43⋊C4—21no—
209Dic43⋊C4—21no—
210C4×Dic43—22no—
211C4×Dic43—22no—
212C4×Dic43—21no—
213C4×Dic43—21no—
214C4×Dic43—21no—
215C2×C43⋊C8—22no—
216C2×C43⋊C8—41no—
217C2×C43⋊C8—41no—
218C2×C43⋊C8—41no—
219C23×C43—21no—
220C23×C43C2×C22⋊C411yescharacteristic
221C22×D43—22no—
222C22×D43—21no—
223C22×D43—28no—
224C22×D43—22no—
225C22×D43—42no—
226C22×D43—42no—
227C22×D43—82no—
228C22×D43—82no—
229C22×D43C22⋊C814yes—
230Q8×C43—21no—
231Q8×C43C22⋊C812yescomplemented
232D4×C43—22no—
233D4×C43—22no—
234D4×C43—21no—
235D4×C43C22⋊C812yescomplemented
236C2×C4×C43—21no—
237C2×C4×C43—22no—
238C2×C4×C43—22no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—81no—
247C2×C4×C43C2×C22⋊C411yescharacteristic
248C2×C4×C43C2×C22⋊C411yescharacteristic
249C2×C4×C43#12011yescharacteristic
250C2×C4×C43#12011yescharacteristic
251C2×C4×C43#12011yescharacteristic
252C2×C4×C43#12011yescharacteristic
253C2×C4×C43C22×C811yescharacteristic
254C2×C4×C43C2×M1611yescharacteristic
255C2×C4×C43C2×M1611yescharacteristic
256C2×C4×C43C2×M1611yescharacteristic
257C22⋊D43—28no—
258C22⋊D43—22no—
259C22⋊D43—22no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—22no—
263C2×Dic43—21no—
264C2×Dic43—42no—
265C2×Dic43—82no—
266D172—28no—
267D172—22no—
268D172—22no—
269D172—21no—
270D172—22no—
271D172—22no—
272D172C22⋊C812yescomplemented
273C4×D43—28no—
274C4×D43—22no—
275C4×D43—22no—
276C4×D43—42no—
277C4×D43—41no—
278C4×D43—42no—
279C4×D43—41no—
280C4×D43—81no—
281C4×D43—82no—
282C4×D43—82no—
283C4×D43—82no—
284C4×D43—82no—
285Dic86—21no—
286Dic86C22⋊C812yescomplemented
287C8×C43—81no—
288C8×C43—81no—
289C43⋊C8—42no—
290C43⋊C8—81no—
291#8318—431nomaximal, Sylow
292C22×C43—21no—
293C22×C43—21no—
294C22×C43—22no—
295C22×C43—41no—
296C22×C43—41no—
297C22×C43#37911yescharacteristic
298C22×C43C2×C22⋊C811yescharacteristic
299C22×C43#40711yescharacteristic
300C2×D43—22no—
301C2×D43—24no—
302C2×D43—42no—
303C2×D43—41no—
304C2×D43—42no—
305C2×D43—41no—
306C2×D43—44no—
307C2×D43—82no—
308C2×D43—88no—
309C4×C43—21no—
310C4×C43—21no—
311C4×C43—21no—
312C4×C43—22no—
313C4×C43—41no—
314C4×C43—41no—
315C4×C43C2×C22⋊C811yescharacteristic
316C4×C43C2×C22⋊C811yescharacteristic
317C4×C43#40711yescharacteristic
318C4×C43#40711yescharacteristic
319C4×C43#45311yescharacteristic
320C4×C43#45511yescharacteristic
321Dic43—22no—
322Dic43—42no—
323Dic43—41no—
324Dic43—41no—
325C4×H(5,𝔽2)—431no—
326#1954—431no—
327#1477—431no—
328#1477D4311yescharacteristic, complemented
329#1476—431no—
330#1476—431no—
331#1460—431no—
332C2×C43—21no—
333C2×C43—21no—
334C2×C43—42no—
335C2×C43#177911yescharacteristic
336C2×C43#179211yescharacteristic
337C2×C43#179411yescharacteristic
338D43—44no—
339D43—42no—
340C2×H(5,𝔽2)—431no—
341#520—431no—
342#520—431no—
343#520—861no—
344#520—861no—
345#518—431no—
346#518—862no—
347#518—861no—
348#518—861no—
349C4×#41—431no—
350C4×#41—861no—
351C4×#41—861no—
352C4×#41C2×D4311yescharacteristic
353C2×C4×D4—431no—
354C2×C4×D4—861no—
355C2×C4×D4—862no—
356C2×C4×D4—861no—
357#431—431no—
358#431C2×D4311yescharacteristic, complemented
359C2×C4⋊C8C2×D4311yescharacteristic, complemented
360C2×C22⋊C8—862no—
361C2×C4×C8—431no—
362Q8⋊C8—21no—
363Q8⋊C8—861no—
364Q8⋊C8—861no—
365Q8⋊C8—861no—
366D4⋊C8—21no—
367D4⋊C8—861no—
368D4⋊C8—861no—
369D4⋊C8—861no—
370#323—862no—
371C43#831811yescharacteristic, complemented, Sylow
372H(5,𝔽2)—434no—
373H(5,𝔽2)—862no—
374H(5,𝔽2)—862no—
375H(5,𝔽2)—862no—
376C2×#41—431no—
377C2×#41—861no—
378C2×#41—861no—
379C2×#41C4×D4311yescharacteristic
380C22×D4—431no—
381C22×D4—861no—
382C22×D4—862no—
383C22×D4—861no—
384C23×C4—432no—
385C23×C4—862no—
386C22×C8—21no—
387C22×C8—861no—
388C4×Q8—431no—
389C4×Q8—431no—
390C4×Q8—861no—
391C4×Q8—861no—
392C4×Q8D17211yescharacteristic
393C4×Q8C22⋊D4311yescharacteristic
394C4×D4—21no—
395C4×D4—21no—
396C4×D4—431no—
397C4×D4—431no—
398C4×D4—861no—
399C4×D4—861no—
400C4×D4—861no—
401C4×D4—862no—
402C4×D4—862no—
403C4×D4—862no—
404C4×D4—862no—
405C4×D4—862no—
406C4×D4—862no—
407C4×D4—862no—
408C4×D4—862no—
409C4×D4—862no—
410C4×D4—862no—
411C4×D4—861no—
412C4×D4—861no—
413C4×D4—861no—
414C4×D4—861no—
415C4×D4—861no—
416C4×D4—861no—
417C4×D4—861no—
418C4×D4—861no—
419C4×D4—861no—
420C4×D4D17211yescharacteristic
421C4×D4C22⋊D4311yescharacteristic
422#117—21no—
423#117—431no—
424#117—862no—
425#117—862no—
426#117—861no—
427#117—861no—
428#117—861no—
429#117C4×D4311yescharacteristic
430C2×C4⋊C4—431no—
431C2×C4⋊C4—862no—
432C2×C4⋊C4—861no—
433C2×C4⋊C4—861no—
434C2×C22⋊C4—432no—
435C2×C22⋊C4—862no—
436C2×C22⋊C4—862no—
437C2×C22⋊C4—862no—
438C2×C22⋊C4—862no—
439C2×C42—21no—
440C2×C42—862no—
441C2×C42—861no—
442C2×C42C22×D4311yescharacteristic
443C4⋊C8—21no—
444C4⋊C8—21no—
445C4⋊C8—21no—
446C4⋊C8—861no—
447C22⋊C8—21no—
448C22⋊C8—861no—
449C22⋊C8—1724no—
450C4×C8—21no—
451C4×C8—861no—
452C4×C8—861no—
453C4×C8—861no—
454C24—432no—
455C24—862no—
456#41—21no—
457#41—21no—
458#41—432no—
459#41—432no—
460#41—864no—
461#41—864no—
462#41—864no—
463#41—864no—
464#41—861no—
465#41—861no—
466#41C8×D4312yes—
467#41#1062187212yes—
468C2×Q8—431no—
469C2×Q8(C2×D43)⋊C411yescharacteristic
470C2×D4—21no—
471C2×D4—431no—
472C2×D4—432no—
473C2×D4—432no—
474C2×D4—864no—
475C2×D4—862no—
476C2×D4—864no—
477C2×D4—868no—
478C2×D4—868no—
479C2×D4—864no—
480C2×D4—862no—
481C2×D4—861no—
482C2×D4—864no—
483C2×D4—861no—
484C2×D4—861no—
485C2×D4—861no—
486C2×D4—861no—
487C2×D4(C2×D43)⋊C411yescharacteristic
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—432no—
492C22×C4—862no—
493C22×C4—862no—
494C22×C4—862no—
495C22×C4—862no—
496C22×C4—861no—
497C22×C4—862no—
498C22×C4—861no—
499C22×C4—862no—
500C22×C4—861no—
501C22×C4—862no—
502C22×C4—3442no—
503C22×C4—3442no—
504C22×C4—1722no—
505C22×C4—1722no—
506C22×C4C2×C4×D4311yescharacteristic
507C22×C4D4×D4311yescharacteristic
508C22×C4D4×D4311yescharacteristic
509C2×C8—42no—
510C2×C8—41no—
511C2×C8—41no—
512C2×C8—862no—
513C2×C8—1721no—
514C2×C8—1721no—
515C2×C8—1721no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—431no—
519C4⋊C4—431no—
520C4⋊C4—862no—
521C4⋊C4—862no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4(C2×D43)⋊C411yescharacteristic
527C4⋊C4(C2×D43)⋊C411yescharacteristic
528C22⋊C4—21no—
529C22⋊C4—21no—
530C22⋊C4—21no—
531C22⋊C4—862no—
532C22⋊C4—862no—
533C22⋊C4—862no—
534C22⋊C4—862no—
535C22⋊C4—861no—
536C22⋊C4—862no—
537C22⋊C4—862no—
538C22⋊C4—861no—
539C22⋊C4—861no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—862no—
544C42—862no—
545C42—861no—
546C42—861no—
547C42—861no—
548C42C2×D17211yescharacteristic
549C42D4×D4311yescharacteristic
550C42D4×D4311yescharacteristic
551C42C2×C22⋊D4311yescharacteristic
552C23—21no—
553C23—434no—
554C23—868no—
555C23—862no—
556C23—861no—
557C23—862no—
558C23—3442no—
559C23—3442no—
560C23—1722no—
561C23—1722no—
562C23C22⋊C4×D4311yescharacteristic
563Q8—21no—
564Q8—432no—
565Q8—861no—
566Q8(C2×D43)⋊C812yescomplemented
567D4—22no—
568D4—22no—
569D4—21no—
570D4—432no—
571D4—868no—
572D4—868no—
573D4—862no—
574D4—862no—
575D4—862no—
576D4—862no—
577D4—861no—
578D4—862no—
579D4—862no—
580D4(C2×D43)⋊C812yescomplemented
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—81no—
592C2×C4—868no—
593C2×C4—861no—
594C2×C4—862no—
595C2×C4—862no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—862no—
599C2×C4—3442no—
600C2×C4—3441no—
601C2×C4—3442no—
602C2×C4—3442no—
603C2×C4—3442no—
604C2×C4—3442no—
605C2×C4—1721no—
606C2×C4—1722no—
607C2×C4—1721no—
608C2×C4—1722no—
609C2×C4—1722no—
610C2×C4C22⋊C4×D4311yescharacteristic
611C2×C4C2×(C2×D43)⋊C411yescharacteristic
612C2×C4#1306329311yescharacteristic
613C2×C4#1306329311yescharacteristic
614C2×C4#1306329511yescharacteristic
615C2×C4#1306329511yescharacteristic
616C2×C4C2×C8×D4311yescharacteristic
617C2×C4M16×D4311yescharacteristic
618C2×C4M16×D4311yescharacteristic
619C2×C4C2×#1062187211yescharacteristic
620C8—81no—
621C8—81no—
622C8—3441no—
623C8—1722no—
624C22—21no—
625C22—21no—
626C22—22no—
627C22—41no—
628C22—41no—
629C22—862no—
630C22—864no—
631C22—3442no—
632C22—3448no—
633C22—1724no—
634C22—1721no—
635C22—1722no—
636C22—1721no—
637C22—1722no—
638C22#1458275411yescharacteristic
639C22C22⋊C8×D4311yescharacteristic
640C22#1458286111yescharacteristic
641C4—22no—
642C4—21no—
643C4—21no—
644C4—21no—
645C4—41no—
646C4—41no—
647C4—862no—
648C4—1721no—
649C4—1722no—
650C4—1721no—
651C4C22⋊C8×D4311yescharacteristic
652C4C2×(C2×D43)⋊C811yescharacteristic
653C4#1458286111yescharacteristic
654C4#1458286211yescharacteristic
655C4#1458306511yescharacteristic
656C4#1458307511yescharacteristic
657C2—21no—
658C2—21no—
659C2—42no—
660C2—1722no—
661C2—1724no—
662C2#1913450411yescharacteristic
663C2#1913454711yescharacteristic
664C2#1913455711yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC2×C4×C43C22×C8
FrattiniC2×C42C22×D43
FittingC43×#1477C2
socleC22×C43#379
prime radicalC2×#13063371C4
cosocleC2×C42×C43C23
hypercenter#1477D43
hypocenterC43#8318
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1477

Complements

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

NH ≅ G/Ntype
2. #19135388C2semidirect
3. #19132980C2semidirect
4. #19132977C2semidirect
5. #19132975C2semidirect
6. #19132915C2semidirect
7. C43×#1477C2semidirect
24. #14582952C22semidirect
26. C2×C4×C43⋊C8C22semidirect
35. C43×#431C22semidirect
36. C2×C4⋊C8×C43C22semidirect
42. #13063371C8semidirect
231. Q8×C43C22⋊C8semidirect
235. D4×C43C22⋊C8semidirect
272. D172C22⋊C8semidirect
286. Dic86C22⋊C8semidirect
328. #1477D43semidirect
358. #431C2×D43semidirect
359. C2×C4⋊C8C2×D43semidirect
371. C43#8318semidirect
566. Q8(C2×D43)⋊C8semidirect
580. D4(C2×D43)⋊C8semidirect

Maximal subgroups

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

subgroupindex
C4×#130633712
#191353882
#191329802
#191329772
#191329752
#191329152
C43×#14772
#831843