Finite Group Databasebeta

← C2×#19133085 #25063690

Subgroups — C2×#19133085 #25063690

Order 11008.

1606 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583412C211yesmaximal, characteristic
2C2×C22⋊C8×D43C211yesmaximal, characteristic, complemented
3C2×#14582746C211yesmaximal, characteristic, complemented
4#19133085C218yesmaximal, direct product factor
5C2×#14582636C211yesmaximal, characteristic, complemented
6C2×#14582634C211yesmaximal, characteristic, complemented
7C2×#14582632C211yesmaximal, characteristic, complemented
8C2×C43×#328C211yesmaximal, characteristic, complemented
9C22×#10621902C411yescharacteristic, complemented
10C23×C4×D43C2211yescharacteristic
11C22×C8×D43—21no—
12#14583412—22no—
13#14583412—22no—
14#14583412C414yescomplemented
15#14583412C2214yes—
16C2×#13063310—21no—
17C2×#13063301C411yescharacteristic, complemented
18C2×#13063300C411yescharacteristic, complemented
19C2×#13063299C2211yescharacteristic
20C2×#13063295—21no—
21C2×#13063287—21no—
22C2×(C22⋊D43)⋊C4—21no—
23C2×#13063283C411yescharacteristic, complemented
24C22×(C2×D43)⋊C4—21no—
25C22×C4×Dic43—21no—
26C2×C22⋊(C43⋊C8)C2211yescharacteristic
27C2×(C2×D43)⋊C8—21no—
28C22⋊C8×D43—22no—
29C22⋊C8×D43C2214yescomplemented
30#14582746—22no—
31#14582746C2214yescomplemented
32C2×C43⋊#95C2211yescharacteristic
33#14582636C2214yescomplemented
34#14582634C2214yescomplemented
35#14582632C2214yescomplemented
36C2×C22⋊Q8×C43C2211yescharacteristic
37C2×C22⋊C8×C43C2211yescharacteristic
38C2×#95×C43C2211yescharacteristic
39C43×#328C2214yescomplemented
40C24×D43D411yescharacteristic
41C2×#10621902—22no—
42C2×#10621902—44no—
43C2×#10621902C2×C414yescomplemented
44C22×D172—21no—
45C22×D172—21no—
46C22×D172C2×C411yescharacteristic
47C22×C22⋊D43—21no—
48C23×Dic43—21no—
49C23×Dic43D411yescharacteristic
50C22×C4×D43—21no—
51C22×C4×D43—44no—
52C22×C4×D43C2×C411yescharacteristic
53C22×C4×D43C2×C411yescharacteristic
54C22×C4×D43C2×C412yes—
55C22×C4×D43D411yescharacteristic
56C22×C4×D43D412yes—
57C22×C4×D43D412yes—
58C22×C4×D43D411yescharacteristic
59C22×C4×D43C2312yes—
60C22×C43⋊C8—21no—
61C2×C8×D43—24no—
62C2×C8×D43—44no—
63#13063310—24no—
64#13063310—24no—
65#13063301—22no—
66#13063301C2×C414yescomplemented
67#13063300—22no—
68#13063300C2×C414yescomplemented
69#13063299—21no—
70#13063299—21no—
71#13063299C2×C412yes—
72#13063299C2312yes—
73#13063295—24no—
74#13063295—24no—
75#13063287—24no—
76#13063287—24no—
77(C22⋊D43)⋊C4—24no—
78(C22⋊D43)⋊C4—24no—
79#13063283—22no—
80#13063283C2×C414yescomplemented
81C2×C4⋊Dic43C2×C411yescharacteristic
82C2×Dic43⋊C4—21no—
83C2×(C2×D43)⋊C4—28no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—24no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43—24no—
91C2×C4×Dic43—44no—
92C22⋊(C43⋊C8)—21no—
93C22⋊(C43⋊C8)C2312yes—
94(C2×D43)⋊C8—24no—
95C43⋊#95—21no—
96C43⋊#95C2312yes—
97C22×Q8×C43C2×C411yescharacteristic
98C23×C4×C43—21no—
99C23×C4×C43C2311yescharacteristic
100C22×C8×C43—21no—
101C22⋊Q8×C43—21no—
102C22⋊Q8×C43—21no—
103C22⋊Q8×C43C2×C412yes—
104C22⋊Q8×C43C2312yes—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43C2×C411yescharacteristic
107C2×C22⋊C4×C43—21no—
108C22⋊C8×C43—21no—
109C22⋊C8×C43C2312yes—
110#95×C43—21no—
111#95×C43C2312yes—
112C24×C43C2×D411yescharacteristic
113C23×D43—22no—
114C23×D43—22no—
115C23×D43—24no—
116C23×D43—21no—
117C23×D43—42no—
118C23×D43C22⋊C411yescharacteristic
119C23×D43C22⋊C412yes—
120C23×D43C22⋊C411yescharacteristic
121C23×D43C2×D412yes—
122C2×Q8×C43—21no—
123C2×Q8×C43—42no—
124C2×Q8×C43C22×C412yes—
125C22×C4×C43—24no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—22no—
129C22×C4×C43—42no—
130C22×C4×C43—42no—
131C22×C4×C43—42no—
132C22×C4×C43C22×C411yescharacteristic
133C22×C4×C43C22×C411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2411yescharacteristic
138C2×C22⋊D43—22no—
139C2×C22⋊D43—22no—
140C2×C22⋊D43—42no—
141C2×C22⋊D43—42no—
142C22×Dic43—24no—
143C22×Dic43—24no—
144C22×Dic43—21no—
145C22×Dic43—22no—
146C22×Dic43—42no—
147C22×Dic43—42no—
148C22×Dic43C22⋊C411yescharacteristic
149C22×Dic43C22⋊C412yes—
150C22×Dic43C22⋊C411yescharacteristic
151C22×Dic43C2×D412yes—
152#10621902—48no—
153#10621902—48no—
154C2×D172—21no—
155C2×D172—24no—
156C2×D172—24no—
157C2×D172—44no—
158C2×D172—44no—
159C2×D172—42no—
160C2×D172C22×C412yes—
161C2×C4×D43—24no—
162C2×C4×D43—24no—
163C2×C4×D43—24no—
164C2×C4×D43—42no—
165C2×C4×D43—42no—
166C2×C4×D43—44no—
167C2×C4×D43—44no—
168C2×C4×D43—44no—
169C2×C4×D43—44no—
170C2×C4×D43—44no—
171C2×C4×D43C22⋊C412yes—
172C2×C4×D43C22⋊C412yes—
173C2×C4×D43C22⋊C412yes—
174C2×C4×D43C22⋊C412yes—
175C2×C4×D43C22×C412yes—
176C2×C4×D43C22×C412yes—
177C2×C4×D43C2×D412yes—
178C2×C4×D43C2×D412yes—
179C2×C8×C43—22no—
180C2×C8×C43—42no—
181C4⋊C4×C43—22no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—22no—
184C4⋊C4×C43C22×C412yes—
185C22⋊C4×C43—22no—
186C22⋊C4×C43—22no—
187(C2×D43)⋊C4—216no—
188(C2×D43)⋊C4—22no—
189(C2×D43)⋊C4—22no—
190(C2×D43)⋊C4—24no—
191(C2×D43)⋊C4—24no—
192(C2×D43)⋊C4—24no—
193C4⋊Dic43—21no—
194C4⋊Dic43C22×C412yes—
195Dic43⋊C4—24no—
196C4×Dic43—24no—
197C4×Dic43—48no—
198C2×C43⋊C8—22no—
199C2×C43⋊C8—42no—
200C8×D43—48no—
201C23×C43—22no—
202C23×C43—22no—
203C23×C43C2×C22⋊C411yescharacteristic
204C23×C43C2×C22⋊C411yescharacteristic
205C23×C43#13512yes—
206C23×C43#13512yes—
207C23×C43C22×D411yescharacteristic
208C22×D43—22no—
209C22×D43—22no—
210C22×D43—22no—
211C22×D43—22no—
212C22×D43—22no—
213C22×D43—24no—
214C22×D43—22no—
215C22×D43—22no—
216C22×D43—24no—
217C22×D43—24no—
218C22×D43—22no—
219C22×D43—42no—
220C22×D43—42no—
221C22×D43—48no—
222C22×D43—48no—
223C22×D43—42no—
224C22×D43—42no—
225C22×D43—42no—
226C22×D43#10414yes—
227C22×D43C2×C22⋊C412yes—
228C22×D43C2×C22⋊C412yes—
229Q8×C43—42no—
230Q8×C43—42no—
231C2×C4×C43—22no—
232C2×C4×C43—22no—
233C2×C4×C43—24no—
234C2×C4×C43—22no—
235C2×C4×C43—22no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—42no—
241C2×C4×C43—48no—
242C2×C4×C43—42no—
243C2×C4×C43—42no—
244C2×C4×C43—42no—
245C2×C4×C43C2×C22⋊C411yescharacteristic
246C2×C4×C43C2×C22⋊C411yescharacteristic
247C2×C4×C43C23×C411yescharacteristic
248C2×C4×C43C22×D411yescharacteristic
249C22⋊D43—42no—
250C22⋊D43—42no—
251C22⋊D43—44no—
252C2×Dic43—22no—
253C2×Dic43—24no—
254C2×Dic43—24no—
255C2×Dic43—24no—
256C2×Dic43—22no—
257C2×Dic43—42no—
258C2×Dic43—48no—
259C2×Dic43—42no—
260C2×Dic43—42no—
261C2×Dic43#9914yes—
262C2×Dic43C2×C22⋊C412yes—
263C2×Dic43C2×C22⋊C412yes—
264D172—42no—
265D172—42no—
266D172—48no—
267D172—48no—
268C4×D43—24no—
269C4×D43—24no—
270C4×D43—24no—
271C4×D43—24no—
272C4×D43—42no—
273C4×D43—42no—
274C4×D43—42no—
275C4×D43—42no—
276C4×D43—48no—
277C8×C43—42no—
278C43⋊C8—42no—
279C2×#1501—431nomaximal, Sylow
280C22×C43—21no—
281C22×C43—21no—
282C22×C43—21no—
283C22×C43—21no—
284C22×C43—24no—
285C22×C43—24no—
286C22×C43C2×#9912yes—
287C22×C43#41612yes—
288C22×C43#41612yes—
289C22×C43C2×#10412yes—
290C22×C43C22×C22⋊C411yescharacteristic
291C22×C43C2×#13511yescharacteristic
292C22×C43C2×#13511yescharacteristic
293C2×D43—22no—
294C2×D43—22no—
295C2×D43—28no—
296C2×D43—22no—
297C2×D43—22no—
298C2×D43—22no—
299C2×D43—44no—
300C2×D43—44no—
301C2×D43—48no—
302C2×D43—44no—
303C2×D43—42no—
304C2×D43—42no—
305C2×D43—42no—
306C2×D43—84no—
307C2×D43C2×#10414yes—
308C4×C43—21no—
309C4×C43—21no—
310C4×C43—21no—
311C4×C43—21no—
312C4×C43—44no—
313C4×C43—42no—
314C4×C43—42no—
315Dic43—22no—
316Dic43—44no—
317Dic43—42no—
318Dic43C2×#9914yes—
319C2×#525—431no—
320C22×C22⋊C8—431no—
321C2×C4×C22⋊C4—431no—
322#1501—438no—
323C2×#328—431no—
324C2×#328D4311yescharacteristic, complemented
325C2×#327—431no—
326C2×#327—431no—
327C2×C43—21no—
328C2×C43—21no—
329C2×C43—22no—
330C2×C43#150114yescomplemented
331C2×C43C22×#9911yescharacteristic
332C2×C43C2×#41611yescharacteristic
333C2×C43C22×#10411yescharacteristic
334D43—24no—
335D43—42no—
336D43—82no—
337C22×#41—431no—
338C24×C4—431no—
339C23×C8—861no—
340#525—434no—
341#525—434no—
342#525—862no—
343#525—862no—
344C2×#123—861no—
345C2×C22⋊Q8—431no—
346C2×C22⋊Q8C2×D4311yescharacteristic
347C2×#121—431no—
348C2×#121—431no—
349C2×#120—861no—
350C2×C4×D4—861no—
351C2×C4×D4—861no—
352C2×#117—431no—
353C22×C22⋊C4—861no—
354C22×C42—861no—
355C2×C22⋊C8—431no—
356C2×C22⋊C8—434no—
357C2×C22⋊C8—862no—
358C2×C22⋊C8—861no—
359C2×C22⋊C8C2×D4311yescharacteristic
360C4×C22⋊C4—434no—
361C4×C22⋊C4—862no—
362C2×#95—431no—
363C2×#95C2×D4311yescharacteristic
364#328—434no—
365#328C2×D4314yescomplemented
366#327—434no—
367#327—434no—
368C43C2×#150111yescharacteristic, complemented, Sylow
369C25—431no—
370C2×#41—434no—
371C2×#41—862no—
372C2×#41—1724no—
373C22×Q8C4×D4311yescharacteristic
374C22×D4—431no—
375C22×D4—861no—
376C22×D4—861no—
377C22×D4—861no—
378C23×C4—21no—
379C23×C4—431no—
380C23×C4—431no—
381C23×C4—431no—
382C23×C4—431no—
383C23×C4—432no—
384C23×C4—431no—
385C23×C4—432no—
386C23×C4—432no—
387C23×C4—432no—
388C23×C4—861no—
389C23×C4—861no—
390C23×C4—1724no—
391C23×C4C22×D4311yescharacteristic
392C22×C8—21no—
393C22×C8—864no—
394C22×C8—861no—
395C22×C8—1724no—
396#123—864no—
397#123—864no—
398C22⋊Q8—21no—
399C22⋊Q8—21no—
400C22⋊Q8—434no—
401C22⋊Q8—862no—
402C22⋊Q8C4×D4312yes—
403C22⋊Q8C22×D4312yes—
404#121—432no—
405#121—432no—
406#121—434no—
407#121—862no—
408#121—861no—
409#121—861no—
410#120—864no—
411#120—864no—
412C4×D4—864no—
413C4×D4—864no—
414C4×D4—864no—
415C4×D4—864no—
416#117—434no—
417#117—862no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4C4×D4311yescharacteristic
422C2×C22⋊C4—21no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—864no—
425C2×C22⋊C4—861no—
426C2×C22⋊C4—861no—
427C2×C22⋊C4—868no—
428C2×C22⋊C4—861no—
429C2×C42—861no—
430C2×C42—864no—
431C2×C42—1724no—
432C22⋊C8—21no—
433C22⋊C8—432no—
434C22⋊C8—864no—
435C22⋊C8—861no—
436C22⋊C8C22×D4312yes—
437#95—21no—
438#95—432no—
439#95—861no—
440#95C22×D4312yes—
441C24—431no—
442C24—431no—
443C24—432no—
444C24—432no—
445C24—864no—
446C24—862no—
447C24—862no—
448C24—861no—
449C24—1722no—
450C24D4×D4311yescharacteristic
451#41—1728no—
452#41—1728no—
453C2×Q8—21no—
454C2×Q8—42no—
455C2×Q8C2×C4×D4312yes—
456C2×D4—432no—
457C2×D4—864no—
458C2×D4—864no—
459C2×D4—862no—
460C2×D4—862no—
461C2×D4—861no—
462C2×D4—1722no—
463C2×D4—1724no—
464C2×D4—1724no—
465C2×D4—1722no—
466C2×D4—1722no—
467C22×C4—24no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—431no—
475C22×C4—432no—
476C22×C4—431no—
477C22×C4—432no—
478C22×C4—432no—
479C22×C4—432no—
480C22×C4—432no—
481C22×C4—432no—
482C22×C4—432no—
483C22×C4—432no—
484C22×C4—432no—
485C22×C4—432no—
486C22×C4—864no—
487C22×C4—864no—
488C22×C4—864no—
489C22×C4—864no—
490C22×C4—864no—
491C22×C4—861no—
492C22×C4—862no—
493C22×C4—1722no—
494C22×C4—1722no—
495C22×C4—1724no—
496C22×C4—1724no—
497C22×C4—1724no—
498C22×C4—1724no—
499C22×C4—1724no—
500C22×C4—1722no—
501C22×C4—1722no—
502C22×C4C2×C4×D4311yescharacteristic
503C22×C4C2×C4×D4311yescharacteristic
504C22×C4D4×D4311yescharacteristic
505C22×C4D4×D4311yescharacteristic
506C22×C4D4×D4311yescharacteristic
507C22×C4C23×D4311yescharacteristic
508C2×C8—22no—
509C2×C8—42no—
510C2×C8—862no—
511C2×C8—1728no—
512C2×C8—1722no—
513C4⋊C4—22no—
514C4⋊C4—21no—
515C4⋊C4—22no—
516C4⋊C4—432no—
517C4⋊C4—864no—
518C4⋊C4—861no—
519C4⋊C4C2×C4×D4312yes—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—864no—
523C22⋊C4—864no—
524C22⋊C4—864no—
525C22⋊C4—8616no—
526C22⋊C4—862no—
527C22⋊C4—862no—
528C42—864no—
529C42—1728no—
530C23—22no—
531C23—22no—
532C23—432no—
533C23—434no—
534C23—432no—
535C23—864no—
536C23—864no—
537C23—862no—
538C23—862no—
539C23—862no—
540C23—864no—
541C23—862no—
542C23—862no—
543C23—862no—
544C23—862no—
545C23—862no—
546C23—1722no—
547C23—1722no—
548C23—1728no—
549C23—1728no—
550C23—1722no—
551C23—1722no—
552C23—1722no—
553C23C22⋊C4×D4311yescharacteristic
554C23C22⋊C4×D4311yescharacteristic
555C23#1306334612yes—
556C23#1306334812yes—
557C23C2×D4×D4311yescharacteristic
558Q8—42no—
559Q8—42no—
560D4—1722no—
561D4—1722no—
562D4—1728no—
563D4—1728no—
564D4—1724no—
565D4—1722no—
566D4—1722no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—42no—
577C2×C4—48no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—432no—
582C2×C4—434no—
583C2×C4—432no—
584C2×C4—864no—
585C2×C4—864no—
586C2×C4—864no—
587C2×C4—864no—
588C2×C4—864no—
589C2×C4—864no—
590C2×C4—862no—
591C2×C4—864no—
592C2×C4—862no—
593C2×C4—1722no—
594C2×C4—1722no—
595C2×C4—1722no—
596C2×C4—1722no—
597C2×C4—1728no—
598C2×C4—1722no—
599C2×C4—1728no—
600C2×C4—1722no—
601C2×C4—1722no—
602C2×C4C22⋊C4×D4311yescharacteristic
603C2×C4C22⋊C4×D4311yescharacteristic
604C2×C4C22×C4×D4311yescharacteristic
605C2×C4C2×D4×D4311yescharacteristic
606C8—42no—
607C8—1722no—
608C22—21no—
609C22—21no—
610C22—24no—
611C22—24no—
612C22—21no—
613C22—21no—
614C22—434no—
615C22—862no—
616C22—868no—
617C22—862no—
618C22—862no—
619C22—862no—
620C22—862no—
621C22—3444no—
622C22—1724no—
623C22—1724no—
624C22—1728no—
625C22—1722no—
626C22—1722no—
627C22—1722no—
628C22—1724no—
629C22#99×D4312yes—
630C22#1458289412yes—
631C22#1458289412yes—
632C22#104×D4312yes—
633C22C2×C22⋊C4×D4311yescharacteristic
634C22C2×#1306334611yescharacteristic
635C22C2×#1306334811yescharacteristic
636C4—21no—
637C4—21no—
638C4—21no—
639C4—21no—
640C4—44no—
641C4—42no—
642C4—42no—
643C4—434no—
644C4—862no—
645C4—1724no—
646C4—1722no—
647C2—21no—
648C2—21no—
649C2—22no—
650C2—864no—
651C2—3442no—
652C2—1722no—
653C2#1913308514yesdirect product factor
654C2C2×#99×D4311yescharacteristic
655C2C2×#1458289411yescharacteristic
656C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#328C2
socleC23×C43C2×C22⋊C4
prime radicalC2×#14583412C2
cosocleC22×C4×C43C24
hypercenterC2×#328D43
hypocenterC43C2×#1501
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊C8×D43C2semidirect
3. C2×#14582746C2semidirect
4. #19133085C2direct (N × H)
5. C2×#14582636C2semidirect
6. C2×#14582634C2semidirect
7. C2×#14582632C2semidirect
8. C2×C43×#328C2semidirect
9. C22×#10621902C4semidirect
14. #14583412C4semidirect
17. C2×#13063301C4semidirect
18. C2×#13063300C4semidirect
23. C2×#13063283C4semidirect
29. C22⋊C8×D43C22semidirect
31. #14582746C22semidirect
33. #14582636C22semidirect
34. #14582634C22semidirect
35. #14582632C22semidirect
39. C43×#328C22semidirect
43. C2×#10621902C2×C4semidirect
66. #13063301C2×C4semidirect
68. #13063300C2×C4semidirect
80. #13063283C2×C4semidirect
324. C2×#328D43semidirect
330. C2×C43#1501semidirect
365. #328C2×D43semidirect
368. C43C2×#1501semidirect
653. C2#19133085direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834122
C2×C22⋊C8×D432
C2×#145827462
#191330852
C2×#145826362
C2×#145826342
C2×#145826322
C2×C43×#3282
C2×#150143