Finite Group Databasebeta

← #24987970

Subgroups — #24987970

Order 11008.

1120 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#10621900C211yesmaximal, characteristic
2#19134572C211yesmaximal, characteristic, complemented
3C4×(C2×D43)⋊C8C211yesmaximal, characteristic, complemented
4C2×#14582631C211yesmaximal, characteristic, complemented
5C2×#14582629C211yesmaximal, characteristic, complemented
6C2×D4⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
7C2×C43×D4⋊C8C211yesmaximal, characteristic, complemented
8C22×#10621900C411yescharacteristic
9C4×#10621900—22no—
10C4×#10621900—22no—
11C4×#10621900—22no—
12C4×#10621900—22no—
13C2×C4×Dic86C2211yescharacteristic
14C2×#13063290C411yescharacteristic
15C2×D4×Dic43C411yescharacteristic
16C2×C4×C22⋊D43—21no—
17C2×(C22⋊D43)⋊C4—21no—
18C2×#13063283C411yescharacteristic
19C2×#13063281—21no—
20C22×C4×Dic43—21no—
21C2×C42×D43C2211yescharacteristic
22C2×C4⋊(C43⋊C8)C2211yescharacteristic
23C2×(C2×D43)⋊C8—21no—
24C2×(C2×D43)⋊C8—21no—
25C2×C4×C43⋊C8C2211yescharacteristic
26#14582653—21no—
27#14582653—21no—
28#14582631—22no—
29#14582629—22no—
30D4⋊(C43⋊C8)—22no—
31C2×C4×D4×C43C2211yescharacteristic
32C2×C4⋊C8×C43C2211yescharacteristic
33C2×C4×C8×C43C2211yescharacteristic
34C43×D4⋊C8—22no—
35C2×#10621900—22no—
36C2×#10621900—22no—
37C2×#10621900—22no—
38C2×#10621900—22no—
39C2×#10621900—22no—
40C2×#10621900C814yescomplemented
41C22×Dic86C2×C411yescharacteristic
42C22×C22⋊D43—21no—
43C23×Dic43—21no—
44C23×Dic43—21no—
45C22×C4×D43C2×C411yescharacteristic
46C22×C4×D43D411yescharacteristic
47C22×C4×D43D411yescharacteristic
48C22×C43⋊C8—21no—
49C22×C43⋊C8—21no—
50C4×Dic86—21no—
51C4×Dic86—21no—
52C4×Dic86D412yes—
53C4×Dic86D412yes—
54#13063290—22no—
55#13063290—22no—
56D4×Dic43—22no—
57D4×Dic43—22no—
58C4×C22⋊D43—24no—
59C4×C22⋊D43—24no—
60(C22⋊D43)⋊C4—24no—
61(C22⋊D43)⋊C4—24no—
62#13063283—22no—
63#13063283—22no—
64#13063281—24no—
65#13063281—24no—
66C2×C4⋊Dic43C2×C411yescharacteristic
67C2×Dic43⋊C4—21no—
68C2×Dic43⋊C4—21no—
69C2×C22⋊Dic43—21no—
70C2×(C2×D43)⋊C4—21no—
71C2×C4×Dic43—24no—
72C2×C4×Dic43—24no—
73C2×C4×Dic43—21no—
74C2×C4×Dic43—21no—
75C2×C4×Dic43—21no—
76C2×C4×Dic43C2×C411yescharacteristic
77C2×C4×Dic43D411yescharacteristic
78C2×C4×Dic43D411yescharacteristic
79C42×D43—21no—
80C42×D43—21no—
81C42×D43—21no—
82C42×D43—21no—
83C4⋊(C43⋊C8)—21no—
84C4⋊(C43⋊C8)—21no—
85(C2×D43)⋊C8—24no—
86(C2×D43)⋊C8—42no—
87C4×C43⋊C8—21no—
88C4×C43⋊C8—21no—
89C22×D4×C43C2×C411yescharacteristic
90C23×C4×C43—21no—
91C22×C8×C43—21no—
92C22×C8×C43—21no—
93C4×D4×C43—21no—
94C4×D4×C43—21no—
95C4×D4×C43D412yes—
96C4×D4×C43D412yes—
97C2×C4⋊C4×C43C2×C411yescharacteristic
98C2×C22⋊C4×C43—21no—
99C2×C42×C43C2311yescharacteristic
100C4⋊C8×C43—21no—
101C4⋊C8×C43—21no—
102C4×C8×C43—21no—
103C4×C8×C43—21no—
104C24×C43—21no—
105C23×D43C22⋊C411yescharacteristic
106C2×D4×C43—21no—
107C2×D4×C43—21no—
108C2×D4×C43—21no—
109C2×D4×C43C22⋊C412yes—
110C2×D4×C43C2×C812yes—
111C2×D4×C43M1612yes—
112C22×C4×C43—22no—
113C22×C4×C43—22no—
114C22×C4×C43—21no—
115C22×C4×C43—41no—
116C22×C4×C43—41no—
117C22×C4×C43—41no—
118C22×C4×C43—41no—
119C22×C4×C43C22×C411yescharacteristic
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2×D411yescharacteristic
122C2×C22⋊D43—24no—
123C2×C22⋊D43—24no—
124C2×C22⋊D43—24no—
125C22×Dic43—24no—
126C22×Dic43—24no—
127C22×Dic43—24no—
128C22×Dic43—24no—
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43—42no—
132C22×Dic43—42no—
133C22×Dic43C22⋊C411yescharacteristic
134C22×Dic43C22⋊C411yescharacteristic
135C22×Dic43C22⋊C411yescharacteristic
136#10621900—28no—
137#10621900—28no—
138#10621900—28no—
139#10621900—28no—
140C2×C4×D43—21no—
141C2×C4×D43—21no—
142C2×C4×D43—21no—
143C2×C4×D43—21no—
144C2×C4×D43—21no—
145C2×C4×D43—21no—
146C2×C4×D43—21no—
147C2×C4×D43—21no—
148C2×C4×D43—21no—
149C2×C4×D43—21no—
150C2×C4×D43—21no—
151C2×C4×D43—21no—
152C2×C4×D43—22no—
153C2×C4×D43—41no—
154C2×C4×D43C2×C812yes—
155C2×C4×D43M1612yes—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86C22⋊C412yes—
160C2×Dic86C2×C812yes—
161C2×Dic86M1612yes—
162C2×C8×C43—22no—
163C2×C8×C43—41no—
164C2×C8×C43—41no—
165C2×C8×C43—41no—
166C2×C8×C43—41no—
167C2×C8×C43—41no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43C22⋊C412yes—
170C22⋊C4×C43—22no—
171C22⋊C4×C43—22no—
172C42×C43C2×D411yescharacteristic
173C42×C43C2×D411yescharacteristic
174C42×C43C2×D411yescharacteristic
175C42×C43C2×D411yescharacteristic
176C22⋊Dic43—24no—
177(C2×D43)⋊C4—24no—
178C4⋊Dic43—21no—
179C4⋊Dic43C22⋊C412yes—
180Dic43⋊C4—24no—
181Dic43⋊C4—22no—
182Dic43⋊C4—22no—
183C4×Dic43—24no—
184C4×Dic43—24no—
185C4×Dic43—21no—
186C4×Dic43—21no—
187C4×Dic43—21no—
188C4×Dic43—21no—
189C4×Dic43—21no—
190C4×Dic43—21no—
191C4×Dic43—22no—
192C4×Dic43—22no—
193C2×C43⋊C8—22no—
194C2×C43⋊C8—41no—
195C2×C43⋊C8—41no—
196C2×C43⋊C8—41no—
197C2×C43⋊C8—41no—
198C2×C43⋊C8—41no—
199C23×C43—22no—
200C23×C43—22no—
201C23×C43—22no—
202C23×C43—41no—
203C23×C43—41no—
204C23×C43—41no—
205C23×C43—41no—
206C23×C43C2×C22⋊C411yescharacteristic
207C22×D43—21no—
208C22×D43—21no—
209C22×D43—21no—
210C22×D43—21no—
211C22×D43—21no—
212C22×D43—21no—
213C22×D43C22⋊C812yes—
214D4×C43—22no—
215D4×C43—22no—
216D4×C43—22no—
217D4×C43C22⋊C814yescomplemented
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—22no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—42no—
224C2×C4×C43—42no—
225C2×C4×C43—42no—
226C2×C4×C43—42no—
227C2×C4×C43C2×C22⋊C411yescharacteristic
228C2×C4×C43C2×C22⋊C411yescharacteristic
229C2×C4×C43#12011yescharacteristic
230C2×C4×C43#12011yescharacteristic
231C2×C4×C43#12011yescharacteristic
232C2×C4×C43#12011yescharacteristic
233C2×C4×C43C22×C811yescharacteristic
234C2×C4×C43C2×M1611yescharacteristic
235C2×C4×C43C2×M1611yescharacteristic
236C2×C4×C43C2×M1611yescharacteristic
237C2×C4×C43#13511yescharacteristic
238C2×C4×C43#13511yescharacteristic
239C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
240C2×C4×C43#13711yescharacteristic
241C22⋊D43—216no—
242C2×Dic43—216no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—22no—
246C2×Dic43—22no—
247C2×Dic43—22no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—22no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—48no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43C22⋊C812yes—
258C2×Dic43#10412yes—
259C4×D43—22no—
260C4×D43—22no—
261C4×D43—22no—
262C4×D43—22no—
263C4×D43—42no—
264C4×D43—42no—
265C4×D43—41no—
266C4×D43—41no—
267C4×D43—41no—
268C4×D43—41no—
269Dic86—22no—
270Dic86—22no—
271Dic86—22no—
272Dic86C22⋊C814yescomplemented
273C8×C43—42no—
274C8×C43—81no—
275C43⋊C8—42no—
276C43⋊C8—81no—
277#8312—431nomaximal, Sylow
278C22×C43—24no—
279C22×C43—42no—
280C22×C43—42no—
281C22×C43—42no—
282C22×C43—42no—
283C22×C43—42no—
284C22×C43—42no—
285C22×C43#37911yescharacteristic
286C22×C43C2×C22⋊C811yescharacteristic
287C22×C43#40711yescharacteristic
288C22×C43#41611yescharacteristic
289C22×C43#41711yescharacteristic
290C22×C43C2×#10411yescharacteristic
291C22×C43#42111yescharacteristic
292C2×D43—22no—
293C2×D43—22no—
294C2×D43—22no—
295C2×D43—41no—
296C2×D43—41no—
297C2×D43—41no—
298C2×D43—41no—
299C4×C43—21no—
300C4×C43—21no—
301C4×C43—42no—
302C4×C43C2×C22⋊C811yescharacteristic
303C4×C43C2×C22⋊C811yescharacteristic
304C4×C43#40711yescharacteristic
305C4×C43#40711yescharacteristic
306C4×C43#44911yescharacteristic
307C4×C43#44911yescharacteristic
308C4×C43#45211yescharacteristic
309C4×C43#45211yescharacteristic
310Dic43—24no—
311Dic43—22no—
312Dic43—22no—
313Dic43—41no—
314Dic43—42no—
315C2×C4×#41—431no—
316#1797—431no—
317C4×C22⋊C8—431no—
318C2×Q8⋊C8—431no—
319C2×Q8⋊C8—431no—
320C2×D4⋊C8—431no—
321C2×D4⋊C8D4311yescharacteristic, complemented
322C2×C43—44no—
323C2×C43#147611yescharacteristic
324C2×C43#147711yescharacteristic
325C2×C43#148811yescharacteristic
326C2×C43#148911yescharacteristic
327C2×C43#177911yescharacteristic
328C2×C43#178811yescharacteristic
329C2×C43#178911yescharacteristic
330D43—42no—
331C22×#41—431no—
332C4×#41—862no—
333C4×#41—862no—
334C4×#41—862no—
335C4×#41—862no—
336C2×C4×Q8—431no—
337C2×C4×Q8—431no—
338C2×C4×D4—431no—
339C2×C4×D4—861no—
340C2×C4×D4—861no—
341C2×C4×D4C2×D4311yescharacteristic
342C2×#117—431no—
343C2×#117—861no—
344C22×C42—431no—
345C22×C42—861no—
346C2×C4⋊C8—431no—
347C2×C4⋊C8C2×D4311yescharacteristic
348C2×C22⋊C8—861no—
349C2×C22⋊C8—861no—
350C2×C4×C8—431no—
351C2×C4×C8C2×D4311yescharacteristic
352#336—861no—
353#336—861no—
354Q8⋊C8—862no—
355Q8⋊C8—862no—
356D4⋊C8—22no—
357D4⋊C8—862no—
358C43#831211yescharacteristic, complemented, Sylow
359C2×#41—434no—
360C2×#41—862no—
361C2×#41—862no—
362C2×#41—862no—
363C2×#41—862no—
364C2×#41—862no—
365C22×Q8—431no—
366C22×D4—861no—
367C22×D4C4×D4311yescharacteristic
368C23×C4—21no—
369C23×C4—431no—
370C23×C4—431no—
371C23×C4—431no—
372C23×C4—861no—
373C23×C4—861no—
374C22×C8—21no—
375C22×C8—21no—
376C22×C8—861no—
377C22×C8—861no—
378C4×Q8—432no—
379C4×Q8—432no—
380C4×Q8—862no—
381C4×Q8—862no—
382C4×Q8—861no—
383C4×Q8—861no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—864no—
387C4×D4—864no—
388C4×D4—862no—
389C4×D4—864no—
390C4×D4—864no—
391C4×D4—862no—
392C4×D4D17212yes—
393C4×D4C22⋊D4312yes—
394#117—864no—
395#117—864no—
396#117—862no—
397#117—862no—
398C2×C4⋊C4—431no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4C4×D4311yescharacteristic
402C2×C22⋊C4—21no—
403C2×C22⋊C4—861no—
404C2×C22⋊C4—861no—
405C2×C42—431no—
406C2×C42—431no—
407C2×C42—431no—
408C2×C42—861no—
409C2×C42—861no—
410C2×C42—864no—
411C2×C42—864no—
412C2×C42—861no—
413C2×C42—861no—
414C2×C42—861no—
415C2×C42—861no—
416C2×C42—861no—
417C2×C42C22×D4311yescharacteristic
418C4⋊C8—21no—
419C4⋊C8—21no—
420C4⋊C8—861no—
421C4⋊C8—861no—
422C22⋊C8—864no—
423C22⋊C8—1722no—
424C4×C8—21no—
425C4×C8—21no—
426C4×C8—861no—
427C4×C8—861no—
428C24—21no—
429C24—431no—
430#41—868no—
431#41—868no—
432#41—868no—
433#41—868no—
434C2×Q8—432no—
435C2×Q8—432no—
436C2×Q8—432no—
437C2×Q8—861no—
438C2×Q8—861no—
439C2×Q8—861no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—864no—
444C2×D4—864no—
445C2×D4—864no—
446C2×D4C8×D4312yes—
447C2×D4#1062187212yes—
448C2×D4(C2×D43)⋊C412yes—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—431no—
457C22×C4—431no—
458C22×C4—432no—
459C22×C4—432no—
460C22×C4—431no—
461C22×C4—862no—
462C22×C4—864no—
463C22×C4—864no—
464C22×C4—864no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—864no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4—861no—
478C22×C4—861no—
479C22×C4—861no—
480C22×C4—1721no—
481C22×C4—1722no—
482C22×C4—1722no—
483C22×C4C2×C4×D4311yescharacteristic
484C22×C4D4×D4311yescharacteristic
485C22×C4D4×D4311yescharacteristic
486C2×C8—22no—
487C2×C8—41no—
488C2×C8—41no—
489C2×C8—41no—
490C2×C8—41no—
491C2×C8—41no—
492C2×C8—862no—
493C2×C8—1721no—
494C2×C8—1721no—
495C2×C8—1721no—
496C2×C8—1721no—
497C2×C8—1721no—
498C4⋊C4—21no—
499C4⋊C4—432no—
500C4⋊C4—864no—
501C4⋊C4—861no—
502C4⋊C4—862no—
503C4⋊C4—862no—
504C4⋊C4(C2×D43)⋊C412yes—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—864no—
508C22⋊C4—864no—
509C42—864no—
510C42—864no—
511C42—861no—
512C42—861no—
513C42—861no—
514C42—861no—
515C42—862no—
516C42—861no—
517C42—861no—
518C42—862no—
519C42C2×D17211yescharacteristic
520C42D4×D4311yescharacteristic
521C42D4×D4311yescharacteristic
522C42C2×C22⋊D4311yescharacteristic
523C23—22no—
524C23—22no—
525C23—22no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—432no—
531C23—861no—
532C23—861no—
533C23—861no—
534C23—861no—
535C23—861no—
536C23—861no—
537C23C22⋊C4×D4311yescharacteristic
538Q8—434no—
539Q8—862no—
540Q8—862no—
541Q8—862no—
542D4—22no—
543D4—22no—
544D4—22no—
545D4—8616no—
546D4(C2×D43)⋊C814yescomplemented
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—432no—
557C2×C4—432no—
558C2×C4—8616no—
559C2×C4—862no—
560C2×C4—861no—
561C2×C4—862no—
562C2×C4—861no—
563C2×C4—861no—
564C2×C4—861no—
565C2×C4—862no—
566C2×C4—862no—
567C2×C4—862no—
568C2×C4—862no—
569C2×C4—862no—
570C2×C4—861no—
571C2×C4—861no—
572C2×C4—862no—
573C2×C4—861no—
574C2×C4—1722no—
575C2×C4—1722no—
576C2×C4—1728no—
577C2×C4—1721no—
578C2×C4—1721no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4C22⋊C4×D4311yescharacteristic
584C2×C4C2×(C2×D43)⋊C411yescharacteristic
585C2×C4#1306329311yescharacteristic
586C2×C4#1306329311yescharacteristic
587C2×C4#1306329511yescharacteristic
588C2×C4#1306329511yescharacteristic
589C2×C4C2×C8×D4311yescharacteristic
590C2×C4M16×D4311yescharacteristic
591C2×C4M16×D4311yescharacteristic
592C2×C4C2×#1062187211yescharacteristic
593C2×C4#1306334411yescharacteristic
594C2×C4#1306334611yescharacteristic
595C2×C4#1306334911yescharacteristic
596C2×C4#1306335411yescharacteristic
597C8—42no—
598C8—81no—
599C8—3441no—
600C8—1722no—
601C22—24no—
602C22—42no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—862no—
609C22—862no—
610C22—862no—
611C22—1721no—
612C22—1721no—
613C22—1721no—
614C22—1721no—
615C22#1458275411yescharacteristic
616C22C22⋊C8×D4311yescharacteristic
617C22#1458286111yescharacteristic
618C22#1458289211yescharacteristic
619C22#1458289711yescharacteristic
620C22#104×D4311yescharacteristic
621C22#1458291411yescharacteristic
622C4—21no—
623C4—21no—
624C4—42no—
625C4—862no—
626C4—864no—
627C4—862no—
628C4—1721no—
629C4—1722no—
630C4C22⋊C8×D4311yescharacteristic
631C4C2×(C2×D43)⋊C811yescharacteristic
632C4#1458286111yescharacteristic
633C4#1458286211yescharacteristic
634C4#1458304111yescharacteristic
635C4#1458304511yescharacteristic
636C4#1458305811yescharacteristic
637C4#1458306211yescharacteristic
638C2—44no—
639C2—1722no—
640C2#1913297411yescharacteristic
641C2#1913297911yescharacteristic
642C2#1913302611yescharacteristic
643C2#1913303111yescharacteristic
644C2#1913450411yescharacteristic
645C2#1913453211yescharacteristic
646C2#1913453711yescharacteristic
subgroupG/H
centerC22×C4D4×D43
commutatorC2×C4×C43C22×C8
FrattiniC2×C42C22×D43
FittingC2×C43×D4⋊C8C2
socleC23×C43C2×C22⋊C4
prime radicalC22×#10621900C4
cosocleC2×C42×C43C23
hypercenterC2×D4⋊C8D43
hypocenterC43#8312
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #19134572C2semidirect
3. C4×(C2×D43)⋊C8C2semidirect
4. C2×#14582631C2semidirect
5. C2×#14582629C2semidirect
6. C2×D4⋊(C43⋊C8)C2semidirect
7. C2×C43×D4⋊C8C2semidirect
40. C2×#10621900C8semidirect
217. D4×C43C22⋊C8semidirect
272. Dic86C22⋊C8semidirect
321. C2×D4⋊C8D43semidirect
358. C43#8312semidirect
546. D4(C2×D43)⋊C8semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#106219002
#191345722
C4×(C2×D43)⋊C82
C2×#145826312
C2×#145826292
C2×D4⋊(C43⋊C8)2
C2×C43×D4⋊C82
#831243