Finite Group Databasebeta

← C2×#19479 #6354547

Subgroups — C2×#19479 #6354547

Order 512.

1768 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3228C211yesmaximal, characteristic
2C2×#3104C211yesmaximal, characteristic, complemented
3C2×#3037C211yesmaximal, characteristic
4C2×#2984C211yesmaximal, characteristic, complemented
5#19479C2116yesmaximal, direct product factor
6C2×#1702C211yesmaximal, characteristic, complemented
7C2×#1698C211yesmaximal, characteristic, complemented
8C2×#1694C211yesmaximal, characteristic, complemented
9C2×#1692C211yesmaximal, characteristic, complemented
10C2×#1682C211yesmaximal, characteristic, complemented
11C2×#1678C211yesmaximal, characteristic, complemented
12C2×#1674C211yesmaximal, characteristic, complemented
13C2×#1672C211yesmaximal, characteristic, complemented
14C2×#1574C211yesmaximal, characteristic, complemented
15C2×#1559C211yesmaximal, characteristic, complemented
16C2×#1553C211yesmaximal, characteristic
17C22×#137—21no—
18C2×#533C2211yescharacteristic
19C2×#532C2211yescharacteristic
20C22×C4×Q8C2211yescharacteristic
21#3228—24no—
22#3228C2218yes—
23C2×#500C2211yescharacteristic
24C2×#498C2211yescharacteristic
25C2×#486C2211yescharacteristic
26C2×#486C2211yescharacteristic
27#3104—24no—
28#3104C2218yescomplemented
29C2×#484—21no—
30C2×#482—21no—
31C2×#482—21no—
32C2×#477C2211yescharacteristic
33C2×#477C2211yescharacteristic
34C2×#478—21no—
35C2×#478—21no—
36#3037—24no—
37#3037C2218yes—
38C2×#464—21no—
39C2×#464—21no—
40C2×#462C2211yescharacteristic
41C2×#462C2211yescharacteristic
42C2×#462C2211yescharacteristic
43C2×#462C2211yescharacteristic
44C2×#460C2211yescharacteristic
45C2×#460C2211yescharacteristic
46C2×#451—21no—
47#2984—24no—
48#2984C2218yescomplemented
49C2×#446—21no—
50C2×#446—21no—
51C2×#446C2211yescharacteristic
52C2×#446C2211yescharacteristic
53C2×C8×Q8C2211yescharacteristic
54C2×C8×Q8C2211yescharacteristic
55C2×C4×Q16—21no—
56C2×C4×Q16—21no—
57C2×#432—21no—
58C2×#432C2211yescharacteristic
59C2×#431—21no—
60C2×#431C2211yescharacteristic
61C2×#431C2211yescharacteristic
62C2×#423C2211yescharacteristic
63C2×#417—21no—
64#1702C2218yescomplemented
65#1698C2218yescomplemented
66#1694C2218yescomplemented
67#1692C2218yescomplemented
68#1682C2218yescomplemented
69#1678C2218yescomplemented
70#1674C2218yescomplemented
71#1672C2218yescomplemented
72#1574C2218yescomplemented
73C2×#335C2211yescharacteristic
74C2×#335C2211yescharacteristic
75C2×#334C2211yescharacteristic
76C2×#334C2211yescharacteristic
77#1559C2218yescomplemented
78#1553C2218yes—
79C2×#333C2211yescharacteristic
80C2×#333C2211yescharacteristic
81C2×#332C2211yescharacteristic
82C2×#332C2211yescharacteristic
83C2×#332C2211yescharacteristic
84C2×#332C2211yescharacteristic
85C2×#331C2211yescharacteristic
86C2×#331C2211yescharacteristic
87C22×#41—21no—
88C23×Q8D411yescharacteristic
89C2×#137—28no—
90C2×#137—48no—
91C22×Q16—21no—
92C22×Q16—21no—
93C22×Q16—21no—
94C22×Q16—21no—
95C22×SD16—21no—
96C22×SD16—21no—
97C22×M16—21no—
98#533—22no—
99#533—22no—
100#533—22no—
101#533C2314yes—
102#532—22no—
103#532—22no—
104#532—22no—
105#532C2314yes—
106C2×C4⋊Q8C2311yescharacteristic
107C2×C4⋊Q8C2311yescharacteristic
108C2×C4⋊Q8C2311yescharacteristic
109C2×#127C2311yescharacteristic
110C2×#125—21no—
111C2×#124—21no—
112C2×C22⋊Q8—21no—
113C2×C22⋊Q8—21no—
114C2×#121—21no—
115C2×#121—21no—
116C2×C4×Q8—21no—
117C2×C4×Q8—22no—
118C2×C4×Q8—21no—
119C2×C4×Q8—22no—
120C2×C4×Q8—21no—
121C2×C4×Q8—21no—
122C2×C4×Q8D414yes—
123C2×C4×Q8D411yescharacteristic
124C2×C4×Q8D411yescharacteristic
125C2×C4×Q8C2311yescharacteristic
126C2×C4×Q8C2311yescharacteristic
127C2×C4×Q8C2314yes—
128C2×C4×D4—21no—
129C2×C4×D4—21no—
130C2×#117—21no—
131C22×C4⋊C4—21no—
132C22×C4⋊C4D411yescharacteristic
133C22×C42—21no—
134C22×C42C2311yescharacteristic
135#500—22no—
136#500C2314yes—
137#498—22no—
138#498C2314yes—
139#486—22no—
140#486—22no—
141#486C2314yes—
142#486C2314yes—
143#484—28no—
144#482—28no—
145#482—28no—
146#478—28no—
147#478—28no—
148#477—22no—
149#477—22no—
150#477C2314yes—
151#477C2314yes—
152#464—28no—
153#464—28no—
154#462—22no—
155#462—22no—
156#462—22no—
157#462—22no—
158#462C2314yes—
159#462C2314yes—
160#462C2314yes—
161#462C2314yes—
162#460—22no—
163#460—22no—
164#460C2314yes—
165#460C2314yes—
166#451—28no—
167#446—28no—
168#446—28no—
169#446—22no—
170#446—22no—
171#446C2314yes—
172#446C2314yes—
173C8×Q8—22no—
174C8×Q8—22no—
175C8×Q8C2314yes—
176C8×Q8C2314yes—
177C4×Q16—28no—
178C4×Q16—28no—
179#432—22no—
180#432—28no—
181#432C2314yes—
182#431—22no—
183#431—28no—
184#431D414yes—
185#431C2314yes—
186#431C2314yes—
187C2×#107—21no—
188C2×#107—21no—
189C2×#107—21no—
190C2×#107—21no—
191C2×#106—21no—
192C2×#106—21no—
193#423—22no—
194#423C2314yes—
195C2×C4⋊C8—21no—
196C2×C4⋊C8—21no—
197C2×C4⋊C8—21no—
198C2×C4⋊C8—21no—
199C2×C4⋊C8—21no—
200C2×C4⋊C8D411yescharacteristic
201C2×C4⋊C8D411yescharacteristic
202C2×C4⋊C8C2311yescharacteristic
203C2×C4⋊C8C2311yescharacteristic
204C2×C4⋊C8C2311yescharacteristic
205C2×C4⋊C8C2311yescharacteristic
206C2×C4⋊C8C2311yescharacteristic
207C2×C4⋊C8C2311yescharacteristic
208#417—28no—
209C2×#103—21no—
210C2×#103—21no—
211C2×#103—21no—
212C2×#103—21no—
213C2×#103—21no—
214C2×#103—21no—
215C2×#102—21no—
216C2×#102—21no—
217C2×#102—21no—
218C2×#102—21no—
219C2×#102—21no—
220C2×#102—21no—
221C2×C22⋊C8—21no—
222C2×C22⋊C8—21no—
223C2×C22⋊C8D411yescharacteristic
224C2×C22⋊C8D411yescharacteristic
225C2×#97—21no—
226C2×#97—21no—
227C2×#97—21no—
228C2×C4×C8—21no—
229C2×C4×C8—21no—
230C2×C4×C8—21no—
231C2×C4×C8C2311yescharacteristic
232C2×C4×C8C2311yescharacteristic
233#335C2314yes—
234#335C2314yes—
235#334C2314yes—
236#334C2314yes—
237#333C2314yes—
238#333C2314yes—
239#332C2314yes—
240#332C2314yes—
241#332C2314yes—
242#332C2314yes—
243#331C2314yes—
244#331C2314yes—
245C2×#41—24no—
246C2×#41—44no—
247C2×#41—44no—
248C2×#41—42no—
249C22×Q8—21no—
250C22×Q8—22no—
251C22×Q8—24no—
252C22×Q8—21no—
253C22×Q8—21no—
254C22×Q8—21no—
255C22×Q8—42no—
256C22×Q8C2×D411yescharacteristic
257C22×Q8C2×D414yes—
258C22×Q8C2×D411yescharacteristic
259C22×D4—21no—
260C22×D4—21no—
261C22×D4—21no—
262C22×D4—41no—
263C23×C4—21no—
264C23×C4—21no—
265C23×C4—41no—
266C23×C4C2×D411yescharacteristic
267C23×C4C2×D411yescharacteristic
268C23×C4#4111yescharacteristic
269#137—432no—
270C2×Q16—24no—
271C2×Q16—24no—
272C2×Q16—24no—
273C2×Q16—24no—
274C2×Q16—44no—
275C2×Q16—44no—
276C2×Q16—44no—
277C2×Q16—44no—
278C2×SD16—24no—
279C2×SD16—24no—
280C2×SD16—44no—
281C2×SD16—44no—
282C2×M16—24no—
283C2×M16—44no—
284C22×C8—21no—
285C22×C8—21no—
286C22×C8—21no—
287C22×C8—21no—
288C22×C8—21no—
289C22×C8—21no—
290C22×C8C2×D411yescharacteristic
291C22×C8C2×D411yescharacteristic
292C22×C8C2×D411yescharacteristic
293C22×C8C2×D411yescharacteristic
294C4⋊Q8—21no—
295C4⋊Q8—21no—
296C4⋊Q8—21no—
297C4⋊Q8—21no—
298C4⋊Q8—21no—
299C4⋊Q8—21no—
300C4⋊Q8—21no—
301C4⋊Q8—21no—
302C4⋊Q8—21no—
303C4⋊Q8C2412yes—
304C4⋊Q8C2412yes—
305C4⋊Q8C2412yes—
306#127—21no—
307#127—21no—
308#127—21no—
309#127C2412yes—
310#125—24no—
311#125—42no—
312#124—24no—
313#124—42no—
314C22⋊Q8—24no—
315C22⋊Q8—24no—
316C22⋊Q8—42no—
317C22⋊Q8—42no—
318#121—24no—
319#121—24no—
320#121—42no—
321#121—42no—
322C4×Q8—24no—
323C4×Q8—24no—
324C4×Q8—22no—
325C4×Q8—22no—
326C4×Q8—21no—
327C4×Q8—24no—
328C4×Q8—21no—
329C4×Q8—24no—
330C4×Q8—21no—
331C4×Q8—21no—
332C4×Q8—24no—
333C4×Q8—24no—
334C4×Q8—42no—
335C4×Q8—42no—
336C4×Q8C2×D414yes—
337C4×Q8C2×D414yes—
338C4×Q8C2×D412yes—
339C4×Q8C2×D412yes—
340C4×Q8C2412yes—
341C4×Q8C2412yes—
342C4×D4—24no—
343C4×D4—24no—
344C4×D4—42no—
345C4×D4—42no—
346#117—24no—
347#117—42no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—41no—
363C2×C4⋊C4—41no—
364C2×C4⋊C4C2×D411yescharacteristic
365C2×C4⋊C4C2×D411yescharacteristic
366C2×C4⋊C4C2×D414yes—
367C2×C22⋊C4—41no—
368C2×C22⋊C4—41no—
369C2×C22⋊C4—41no—
370C2×C42—21no—
371C2×C42—24no—
372C2×C42—21no—
373C2×C42—21no—
374C2×C42—21no—
375C2×C42—24no—
376C2×C42—41no—
377C2×C42C2×D411yescharacteristic
378C2×C42C2×D411yescharacteristic
379C2×C42C2×D412yes—
380C2×C42C2×D412yes—
381C2×C42#4111yescharacteristic
382C2×C42#4112yes—
383C2×C42C2411yescharacteristic
384C2×C42C2412yes—
385#107—24no—
386#107—24no—
387#107—24no—
388#107—24no—
389#106—24no—
390#106—24no—
391C4⋊C8—24no—
392C4⋊C8—24no—
393C4⋊C8—24no—
394C4⋊C8—24no—
395C4⋊C8—24no—
396C4⋊C8—21no—
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8—21no—
400C4⋊C8—21no—
401C4⋊C8—21no—
402C4⋊C8C2×D414yes—
403C4⋊C8C2×D414yes—
404C4⋊C8C2412yes—
405C4⋊C8C2412yes—
406C4⋊C8C2412yes—
407C4⋊C8C2412yes—
408C4⋊C8C2412yes—
409C4⋊C8C2412yes—
410#103—24no—
411#103—24no—
412#103—24no—
413#103—24no—
414#103—24no—
415#103—24no—
416#102—24no—
417#102—24no—
418#102—24no—
419#102—24no—
420#102—24no—
421#102—24no—
422C22⋊C8—24no—
423C22⋊C8—24no—
424C22⋊C8C2×D414yes—
425C22⋊C8C2×D414yes—
426#97—24no—
427#97—24no—
428#97—24no—
429C4×C8—24no—
430C4×C8—24no—
431C4×C8—24no—
432C4×C8C2×D412yes—
433C4×C8C2×D412yes—
434C4×C8C2412yes—
435C4×C8C2412yes—
436C24—41no—
437C24#12111yescharacteristic
438#41—48no—
439#41—48no—
440#41—88no—
441C2×Q8—21no—
442C2×Q8—24no—
443C2×Q8—21no—
444C2×Q8—22no—
445C2×Q8—28no—
446C2×Q8—22no—
447C2×Q8—22no—
448C2×Q8—22no—
449C2×Q8—22no—
450C2×Q8—22no—
451C2×Q8—44no—
452C2×Q8—44no—
453C2×Q8—48no—
454C2×Q8—41no—
455C2×Q8—41no—
456C2×Q8—41no—
457C2×Q8—42no—
458C2×Q8—42no—
459C2×Q8—42no—
460C2×Q8—42no—
461C2×Q8—82no—
462C2×Q8AGL(1,ℤ/8)14yes—
463C2×Q8C22×D412yes—
464C2×Q8C22×D412yes—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—44no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4—42no—
473C2×D4—42no—
474C2×D4—42no—
475C2×D4—42no—
476C2×D4—82no—
477C2×D4—84no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—42no—
489C22×C4—44no—
490C22×C4—44no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—44no—
495C22×C4—84no—
496C22×C4#12112yes—
497C22×C4#12112yes—
498C22×C4#12111yescharacteristic
499C22×C4#12111yescharacteristic
500C22×C4#12111yescharacteristic
501C22×C4#12112yes—
502C22×C4C22×D412yes—
503C22×C4C22×D412yes—
504C22×C4C22×D411yescharacteristic
505C22×C4C22×D411yescharacteristic
506C22×C4C2×#4111yescharacteristic
507C22×C4C2×#4112yes—
508Q16—48no—
509Q16—48no—
510Q16—48no—
511Q16—48no—
512SD16—48no—
513SD16—48no—
514M16—48no—
515C2×C8—22no—
516C2×C8—22no—
517C2×C8—22no—
518C2×C8—22no—
519C2×C8—22no—
520C2×C8—22no—
521C2×C8—22no—
522C2×C8—22no—
523C2×C8—22no—
524C2×C8—22no—
525C2×C8—42no—
526C2×C8—42no—
527C2×C8—42no—
528C2×C8—42no—
529C2×C8—42no—
530C2×C8—42no—
531C2×C8C22×D412yes—
532C2×C8C22×D412yes—
533C2×C8C22×D412yes—
534C2×C8C22×D412yes—
535C4⋊C4—24no—
536C4⋊C4—22no—
537C4⋊C4—24no—
538C4⋊C4—22no—
539C4⋊C4—24no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—22no—
543C4⋊C4—22no—
544C4⋊C4—22no—
545C4⋊C4—22no—
546C4⋊C4—22no—
547C4⋊C4—22no—
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—41no—
551C4⋊C4—41no—
552C4⋊C4—41no—
553C4⋊C4—41no—
554C4⋊C4—41no—
555C4⋊C4—41no—
556C4⋊C4—44no—
557C4⋊C4—44no—
558C4⋊C4C22×D412yes—
559C4⋊C4C22×D412yes—
560C22⋊C4—44no—
561C22⋊C4—44no—
562C22⋊C4—44no—
563C42—24no—
564C42—22no—
565C42—24no—
566C42—22no—
567C42—22no—
568C42—22no—
569C42—44no—
570C42#12112yes—
571C42#12112yes—
572C42#12112yes—
573C42C22×D412yes—
574C42C22×D411yescharacteristic
575C42C22×D412yes—
576C42C22×D411yescharacteristic
577C42C2×#4112yes—
578C42C2×#4111yescharacteristic
579C42C2511yescharacteristic
580C23—22no—
581C23—22no—
582C23—22no—
583C23—42no—
584C23—82no—
585C23—82no—
586C23—82no—
587C23C2×#12112yes—
588C23C2×#12111yescharacteristic
589Q8—24no—
590Q8—22no—
591Q8—22no—
592Q8—22no—
593Q8—48no—
594Q8—42no—
595Q8—42no—
596Q8—42no—
597Q8—42no—
598Q8—42no—
599Q8—82no—
600Q8—82no—
601Q8—82no—
602Q8—82no—
603Q8C2×AGL(1,ℤ/8)14yes—
604D4—42no—
605D4—42no—
606D4—42no—
607D4—42no—
608D4—82no—
609D4—82no—
610D4—88no—
611D4—82no—
612D4—82no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—24no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—24no—
620C2×C4—24no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—48no—
631C2×C4—48no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—88no—
639C2×C4—82no—
640C2×C4—82no—
641C2×C4—82no—
642C2×C4C2×#12112yes—
643C2×C4C2×#12112yes—
644C2×C4C2×#12111yescharacteristic
645C2×C4C2×#12112yes—
646C2×C4C2×#12111yescharacteristic
647C2×C4C2×#12111yescharacteristic
648C2×C4C2×AGL(1,ℤ/8)12yes—
649C2×C4#57512yes—
650C2×C4#57812yes—
651C2×C4#57812yes—
652C2×C4C23×D411yescharacteristic
653C2×C4C23×D411yescharacteristic
654C2×C4C22×#4111yescharacteristic
655C8—22no—
656C8—22no—
657C8—22no—
658C8—22no—
659C8—42no—
660C8—42no—
661C8—42no—
662C8—42no—
663C8—42no—
664C8—42no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—44no—
669C22—82no—
670C22—82no—
671C22—82no—
672C22—164no—
673C22#304412yes—
674C22#305512yes—
675C22#306712yes—
676C22C22×#12111yescharacteristic
677C4—22no—
678C4—22no—
679C4—24no—
680C4—22no—
681C4—21no—
682C4—21no—
683C4—42no—
684C4—42no—
685C4—42no—
686C4—82no—
687C4—82no—
688C4—82no—
689C4#304412yes—
690C4#305512yes—
691C4C22×AGL(1,ℤ/8)11yescharacteristic
692C4C2×#57511yescharacteristic
693C4C2×#57811yescharacteristic
694C4C2×#57811yescharacteristic
695C2—42no—
696C2—162no—
697C2#1947914yesdirect product factor
698C2C2×#304411yescharacteristic
699C2C2×#305511yescharacteristic
700C2C2×#306711yescharacteristic
subgroupG/H
center, socleC23C2×#121
commutator, Frattini, cosocleC42C25
prime radicalC2×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3104C2semidirect
4. C2×#2984C2semidirect
5. #19479C2direct (N × H)
6. C2×#1702C2semidirect
7. C2×#1698C2semidirect
8. C2×#1694C2semidirect
9. C2×#1692C2semidirect
10. C2×#1682C2semidirect
11. C2×#1678C2semidirect
12. C2×#1674C2semidirect
13. C2×#1672C2semidirect
14. C2×#1574C2semidirect
15. C2×#1559C2semidirect
28. #3104C22semidirect
48. #2984C22semidirect
64. #1702C22semidirect
65. #1698C22semidirect
66. #1694C22semidirect
67. #1692C22semidirect
68. #1682C22semidirect
69. #1678C22semidirect
70. #1674C22semidirect
71. #1672C22semidirect
72. #1574C22semidirect
77. #1559C22semidirect
697. C2#19479direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#32282
C2×#31042
C2×#30372
C2×#29842
#194792
C2×#17022
C2×#16982
C2×#16942
C2×#16922
C2×#16822
C2×#16782
C2×#16742
C2×#16722
C2×#15742
C2×#15592
C2×#15532