Finite Group Databasebeta

← C2×#19377 #6354063

Subgroups — C2×#19377 #6354063

Order 512.

1914 conjugacy classes of subgroups.

The subgroup lattice has 733 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3251C211yesmaximal, characteristic
2C2×#3239C211yesmaximal, characteristic, complemented
3C2×#3152C211yesmaximal, characteristic, complemented
4C2×#2969C211yesmaximal, characteristic, complemented
5#19377C2116yesmaximal, direct product factor
6C2×#1690C211yesmaximal, characteristic, complemented
7C2×#1686C211yesmaximal, characteristic, complemented
8C2×#1689C211yesmaximal, characteristic, complemented
9C2×#1685C211yesmaximal, characteristic, complemented
10C2×#1670C211yesmaximal, characteristic, complemented
11C2×#1666C211yesmaximal, characteristic, complemented
12C2×#1669C211yesmaximal, characteristic, complemented
13C2×#1665C211yesmaximal, characteristic, complemented
14C2×#1569C211yesmaximal, characteristic, complemented
15C2×#1553C211yesmaximal, characteristic, complemented
16C2×#1549C211yesmaximal, characteristic, complemented
17C22×#137—21no—
18C22×#137—21no—
19C2×#532C2211yescharacteristic
20C22×C4⋊Q8C2211yescharacteristic
21C2×#529C2211yescharacteristic
22#3251—24no—
23#3251C2218yes—
24#3239—24no—
25#3239C2218yescomplemented
26C2×#501—21no—
27#3152—24no—
28#3152C2218yescomplemented
29C2×#497—21no—
30C2×#497—21no—
31C2×#494C2211yescharacteristic
32C2×#494C2211yescharacteristic
33C2×#492C2211yescharacteristic
34C2×#492C2211yescharacteristic
35C2×#489—21no—
36C2×#484—21no—
37C2×#481—21no—
38C2×#475C2211yescharacteristic
39C2×#475C2211yescharacteristic
40C2×#475C2211yescharacteristic
41C2×#478—21no—
42C2×#474C2211yescharacteristic
43C2×#474C2211yescharacteristic
44C2×#474C2211yescharacteristic
45C2×#469—21no—
46C2×#468—21no—
47C2×#460C2211yescharacteristic
48C2×#463—21no—
49C2×#459C2211yescharacteristic
50#2969—24no—
51#2969C2218yescomplemented
52C2×#446C2211yescharacteristic
53C2×C8×Q8C2211yescharacteristic
54C2×#436—21no—
55C2×#436C2211yescharacteristic
56C2×#435—21no—
57C2×C8×D4C2211yescharacteristic
58C2×#433—21no—
59C2×#432C2211yescharacteristic
60C2×#431C2211yescharacteristic
61C2×#423C2211yescharacteristic
62C2×#405—21no—
63C2×C4×M16C2211yescharacteristic
64#1690C2218yescomplemented
65#1689C2218yescomplemented
66#1686C2218yescomplemented
67#1685C2218yescomplemented
68#1670C2218yescomplemented
69#1669C2218yescomplemented
70#1666C2218yescomplemented
71#1665C2218yescomplemented
72#1569C2218yescomplemented
73C2×#335C2211yescharacteristic
74C2×#335C2211yescharacteristic
75C2×#334C2211yescharacteristic
76C2×#334C2211yescharacteristic
77#1553C2218yescomplemented
78#1549C2218yescomplemented
79C2×#332C2211yescharacteristic
80C2×#332C2211yescharacteristic
81C2×#332C2211yescharacteristic
82C2×#332C2211yescharacteristic
83C2×#332C2211yescharacteristic
84C2×#332C2211yescharacteristic
85C2×#331C2211yescharacteristic
86C2×#331C2211yescharacteristic
87C22×#41—21no—
88C23×Q8—21no—
89C2×#137—28no—
90C2×#137—28no—
91C2×#137—48no—
92C2×#137—48no—
93C22×Q16—21no—
94C22×Q16—21no—
95C22×Q16—21no—
96C22×Q16—21no—
97C22×SD16—21no—
98C22×SD16—21no—
99C22×SD16—21no—
100C22×SD16—21no—
101C22×SD16—21no—
102C22×D8—21no—
103C22×M16—21no—
104C22×M16—21no—
105C22×M16D411yescharacteristic
106C22×M16D411yescharacteristic
107C23×C8—21no—
108#532—22no—
109#532—22no—
110#532—22no—
111#532C2314yes—
112C2×C4⋊Q8—21no—
113C2×C4⋊Q8—22no—
114C2×C4⋊Q8—21no—
115C2×C4⋊Q8—22no—
116C2×C4⋊Q8—21no—
117C2×C4⋊Q8—22no—
118C2×C4⋊Q8C2311yescharacteristic
119C2×C4⋊Q8C2311yescharacteristic
120C2×C4⋊Q8C2311yescharacteristic
121C2×C4⋊Q8C2314yes—
122C2×#127C2311yescharacteristic
123#529—22no—
124#529—22no—
125#529D414yes—
126#529C2314yes—
127C2×#126—21no—
128C2×#125D411yescharacteristic
129C2×#124—21no—
130C2×#124D411yescharacteristic
131C2×#123—21no—
132C2×C22⋊Q8D411yescharacteristic
133C2×#121—21no—
134C2×#121—21no—
135C2×#121D411yescharacteristic
136C2×C4×Q8C2311yescharacteristic
137C2×C4×D4—21no—
138C2×C4×D4—21no—
139C2×C4×D4—21no—
140C2×C4×D4C2311yescharacteristic
141C2×#117—21no—
142C22×C4⋊C4—21no—
143C22×C4⋊C4—21no—
144C22×C42C2311yescharacteristic
145#501—28no—
146#497—28no—
147#497—28no—
148#494—22no—
149#494—22no—
150#494C2314yes—
151#494C2314yes—
152#492—22no—
153#492—22no—
154#492C2314yes—
155#492C2314yes—
156#489—28no—
157#484—28no—
158#481—28no—
159#478—28no—
160#475—22no—
161#475—22no—
162#475—22no—
163#475C2314yes—
164#475C2314yes—
165#475C2314yes—
166#474—22no—
167#474—22no—
168#474—22no—
169#474C2314yes—
170#474C2314yes—
171#474C2314yes—
172#469—28no—
173#468—28no—
174#463—28no—
175#460—22no—
176#460C2314yes—
177#459—22no—
178#459C2314yes—
179#446—22no—
180#446C2314yes—
181C8×Q8—22no—
182C8×Q8C2314yes—
183#436—28no—
184#436—22no—
185#436C2314yes—
186#435—28no—
187C8×D4—22no—
188C8×D4C2314yes—
189#433—28no—
190#432—22no—
191#432C2314yes—
192#431—22no—
193#431C2314yes—
194C2×#107—21no—
195C2×#107—21no—
196C2×#107—21no—
197C2×#106—21no—
198C2×#106—21no—
199C2×#106—21no—
200#423—22no—
201#423C2314yes—
202C2×C4⋊C8—21no—
203C2×C4⋊C8—21no—
204C2×C4⋊C8—21no—
205C2×C4⋊C8C2311yescharacteristic
206C2×C4⋊C8C2311yescharacteristic
207C2×C4⋊C8C2311yescharacteristic
208C2×C4⋊C8C2311yescharacteristic
209C2×C4⋊C8C2311yescharacteristic
210C2×C4⋊C8C2311yescharacteristic
211C2×#103—21no—
212C2×#103—21no—
213C2×#103—21no—
214C2×#102—21no—
215C2×#102—21no—
216C2×#102—21no—
217C2×#102—21no—
218C2×#102—21no—
219C2×C22⋊C8—21no—
220C2×C22⋊C8—21no—
221C2×C22⋊C8—21no—
222C2×C22⋊C8—21no—
223#405—28no—
224C4×M16D414yes—
225C4×M16C2314yes—
226C2×#97—21no—
227C2×#97—21no—
228C2×#97D411yescharacteristic
229C2×#97D411yescharacteristic
230C2×C4×C8—21no—
231C2×C4×C8—21no—
232C2×C4×C8C2311yescharacteristic
233C2×C4×C8C2311yescharacteristic
234#335C2314yes—
235#335C2314yes—
236#334C2314yes—
237#334C2314yes—
238#332C2314yes—
239#332C2314yes—
240#332C2314yes—
241#332C2314yes—
242#332C2314yes—
243#332C2314yes—
244#331C2314yes—
245#331C2314yes—
246C2×#41—24no—
247C2×#41—44no—
248C2×#41—44no—
249C2×#41—42no—
250C22×Q8—21no—
251C22×Q8—21no—
252C22×Q8—21no—
253C22×Q8—24no—
254C22×Q8—44no—
255C22×Q8—44no—
256C22×Q8—42no—
257C22×Q8—41no—
258C22×Q8C2×D411yescharacteristic
259C22×D4—21no—
260C22×D4—21no—
261C22×D4—21no—
262C22×D4—21no—
263C22×D4—41no—
264C22×D4C2×D411yescharacteristic
265C23×C4—21no—
266C23×C4—41no—
267C23×C4—41no—
268C23×C4C2×D411yescharacteristic
269C23×C4C2×D411yescharacteristic
270C23×C4#4111yescharacteristic
271#137—432no—
272#137—432no—
273C2×Q16—24no—
274C2×Q16—24no—
275C2×Q16—24no—
276C2×Q16—24no—
277C2×Q16—44no—
278C2×Q16—44no—
279C2×Q16—44no—
280C2×Q16—44no—
281C2×SD16—24no—
282C2×SD16—24no—
283C2×SD16—24no—
284C2×SD16—24no—
285C2×SD16—24no—
286C2×SD16—44no—
287C2×SD16—44no—
288C2×SD16—44no—
289C2×SD16—44no—
290C2×SD16—82no—
291C2×D8—24no—
292C2×D8—82no—
293C2×M16—24no—
294C2×M16—24no—
295C2×M16—24no—
296C2×M16—24no—
297C2×M16—44no—
298C2×M16—82no—
299C2×M16C2×D414yes—
300C2×M16C2×D414yes—
301C22×C8—21no—
302C22×C8—21no—
303C22×C8—21no—
304C22×C8—21no—
305C22×C8—21no—
306C22×C8—21no—
307C22×C8—24no—
308C22×C8—44no—
309C22×C8C2×D411yescharacteristic
310C22×C8C2×D411yescharacteristic
311C22×C8C2×D411yescharacteristic
312C22×C8C2×D411yescharacteristic
313C4⋊Q8—21no—
314C4⋊Q8—21no—
315C4⋊Q8—24no—
316C4⋊Q8—21no—
317C4⋊Q8—21no—
318C4⋊Q8—21no—
319C4⋊Q8—24no—
320C4⋊Q8—21no—
321C4⋊Q8—24no—
322C4⋊Q8—21no—
323C4⋊Q8—21no—
324C4⋊Q8—21no—
325C4⋊Q8—42no—
326C4⋊Q8—42no—
327C4⋊Q8—42no—
328C4⋊Q8C2412yes—
329C4⋊Q8C2412yes—
330C4⋊Q8C2412yes—
331#127—21no—
332#127—21no—
333#127—21no—
334#127C2412yes—
335#126—24no—
336#126—24no—
337#125—22no—
338#125C2×D414yes—
339#124—22no—
340#124—24no—
341#124—42no—
342#124C2×D414yes—
343#123—24no—
344#123—24no—
345C22⋊Q8—22no—
346C22⋊Q8C2×D414yes—
347#121—22no—
348#121—24no—
349#121—24no—
350#121—42no—
351#121—42no—
352#121C2×D414yes—
353C4×Q8—21no—
354C4×Q8—21no—
355C4×Q8C2×D412yes—
356C4×Q8C2412yes—
357C4×D4—24no—
358C4×D4—24no—
359C4×D4—21no—
360C4×D4—24no—
361C4×D4—21no—
362C4×D4—24no—
363C4×D4—42no—
364C4×D4—42no—
365C4×D4C2×D412yes—
366C4×D4C2412yes—
367#117—24no—
368#117—24no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—42no—
382C2×C4⋊C4—42no—
383C2×C4⋊C4—41no—
384C2×C4⋊C4—41no—
385C2×C4⋊C4C2×D411yescharacteristic
386C2×C4⋊C4C2×D411yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—41no—
393C2×C22⋊C4—41no—
394C2×C42—21no—
395C2×C42C2×D411yescharacteristic
396C2×C42C2×D411yescharacteristic
397C2×C42C2×D412yes—
398C2×C42C2×D412yes—
399C2×C42#4111yescharacteristic
400C2×C42#4112yes—
401C2×C42C2411yescharacteristic
402C2×C42C2412yes—
403#107—24no—
404#107—24no—
405#107—24no—
406#106—24no—
407#106—24no—
408#106—24no—
409C4⋊C8—24no—
410C4⋊C8—24no—
411C4⋊C8—24no—
412C4⋊C8—21no—
413C4⋊C8—21no—
414C4⋊C8—21no—
415C4⋊C8—21no—
416C4⋊C8—21no—
417C4⋊C8—21no—
418C4⋊C8C2412yes—
419C4⋊C8C2412yes—
420C4⋊C8C2412yes—
421C4⋊C8C2412yes—
422C4⋊C8C2412yes—
423C4⋊C8C2412yes—
424#103—24no—
425#103—24no—
426#103—24no—
427#102—24no—
428#102—24no—
429#102—24no—
430#102—24no—
431#102—24no—
432C22⋊C8—24no—
433C22⋊C8—24no—
434C22⋊C8—24no—
435C22⋊C8—24no—
436#97—24no—
437#97—24no—
438#97C2×D414yes—
439#97C2×D414yes—
440C4×C8—24no—
441C4×C8—24no—
442C4×C8C2×D412yes—
443C4×C8C2×D412yes—
444C4×C8C2412yes—
445C4×C8C2412yes—
446C24—21no—
447C24—41no—
448C24#12111yescharacteristic
449#41—48no—
450#41—48no—
451#41—88no—
452C2×Q8—21no—
453C2×Q8—22no—
454C2×Q8—22no—
455C2×Q8—22no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8—48no—
459C2×Q8—48no—
460C2×Q8—41no—
461C2×Q8—44no—
462C2×Q8—41no—
463C2×Q8—41no—
464C2×Q8—42no—
465C2×Q8—42no—
466C2×Q8—42no—
467C2×Q8—42no—
468C2×Q8—42no—
469C2×Q8—42no—
470C2×Q8—84no—
471C2×Q8—88no—
472C2×Q8C22×D412yes—
473C2×D4—24no—
474C2×D4—21no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—44no—
481C2×D4—41no—
482C2×D4—41no—
483C2×D4—41no—
484C2×D4—42no—
485C2×D4—42no—
486C2×D4—42no—
487C2×D4—42no—
488C2×D4—82no—
489C2×D4—82no—
490C2×D4—84no—
491C2×D4C22×D412yes—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—44no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—44no—
509C22×C4—84no—
510C22×C4—84no—
511C22×C4#12112yes—
512C22×C4#12112yes—
513C22×C4#12111yescharacteristic
514C22×C4#12111yescharacteristic
515C22×C4#12111yescharacteristic
516C22×C4#12112yes—
517C22×C4C22×D412yes—
518C22×C4C22×D412yes—
519C22×C4C22×D411yescharacteristic
520C22×C4C22×D411yescharacteristic
521C22×C4C2×#4111yescharacteristic
522C22×C4C2×#4112yes—
523Q16—48no—
524Q16—48no—
525Q16—48no—
526Q16—48no—
527SD16—48no—
528SD16—48no—
529SD16—48no—
530SD16—48no—
531SD16—84no—
532D8—84no—
533M16—28no—
534M16—28no—
535M16—48no—
536M16—84no—
537C2×C8—22no—
538C2×C8—22no—
539C2×C8—22no—
540C2×C8—22no—
541C2×C8—22no—
542C2×C8—22no—
543C2×C8—22no—
544C2×C8—22no—
545C2×C8—42no—
546C2×C8—42no—
547C2×C8—42no—
548C2×C8—42no—
549C2×C8—42no—
550C2×C8—42no—
551C2×C8—48no—
552C2×C8AGL(1,ℤ/8)14yes—
553C2×C8AGL(1,ℤ/8)14yes—
554C2×C8C22×D412yes—
555C2×C8C22×D412yes—
556C2×C8C22×D412yes—
557C2×C8C22×D412yes—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—24no—
561C4⋊C4—22no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—44no—
572C4⋊C4—41no—
573C4⋊C4—41no—
574C4⋊C4—44no—
575C4⋊C4—41no—
576C4⋊C4—41no—
577C4⋊C4—41no—
578C4⋊C4—41no—
579C4⋊C4C22×D412yes—
580C4⋊C4C22×D412yes—
581C22⋊C4—24no—
582C22⋊C4—24no—
583C22⋊C4—24no—
584C22⋊C4—24no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—44no—
588C22⋊C4—44no—
589C42—22no—
590C42—22no—
591C42#12112yes—
592C42#12112yes—
593C42#12112yes—
594C42C22×D412yes—
595C42C22×D411yescharacteristic
596C42C22×D412yes—
597C42C22×D411yescharacteristic
598C42C2×#4112yes—
599C42C2×#4111yescharacteristic
600C42C2511yescharacteristic
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—82no—
610C23—82no—
611C23—82no—
612C23C2×#12112yes—
613C23C2×#12111yescharacteristic
614Q8—22no—
615Q8—22no—
616Q8—42no—
617Q8—42no—
618Q8—42no—
619Q8—42no—
620Q8—42no—
621Q8—42no—
622Q8—42no—
623Q8—88no—
624Q8—82no—
625Q8—82no—
626Q8—82no—
627D4—22no—
628D4—22no—
629D4—42no—
630D4—42no—
631D4—42no—
632D4—42no—
633D4—42no—
634D4—82no—
635D4—82no—
636D4—84no—
637D4—88no—
638D4—82no—
639D4—82no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—44no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—88no—
665C2×C4—88no—
666C2×C4—82no—
667C2×C4—82no—
668C2×C4—82no—
669C2×C4C2×#12112yes—
670C2×C4C2×#12111yescharacteristic
671C2×C4C2×#12112yes—
672C2×C4C2×#12112yes—
673C2×C4C2×#12111yescharacteristic
674C2×C4C2×#12111yescharacteristic
675C2×C4C2×AGL(1,ℤ/8)12yes—
676C2×C4C2×AGL(1,ℤ/8)12yes—
677C2×C4#57712yes—
678C2×C4#57812yes—
679C2×C4C23×D411yescharacteristic
680C2×C4C23×D411yescharacteristic
681C2×C4C22×#4111yescharacteristic
682C8—22no—
683C8—22no—
684C8—42no—
685C8—42no—
686C8—42no—
687C8—42no—
688C8—42no—
689C8—42no—
690C8C2×AGL(1,ℤ/8)14yes—
691C8C2×AGL(1,ℤ/8)14yes—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—44no—
696C22—42no—
697C22—42no—
698C22—42no—
699C22—84no—
700C22—82no—
701C22—82no—
702C22—82no—
703C22—164no—
704C22#303812yes—
705C22#306312yes—
706C22#306912yes—
707C22C22×#12111yescharacteristic
708C4—22no—
709C4—22no—
710C4—21no—
711C4—21no—
712C4—22no—
713C4—42no—
714C4—42no—
715C4—42no—
716C4—82no—
717C4—82no—
718C4—82no—
719C4#303812yes—
720C4#306312yes—
721C4C22×AGL(1,ℤ/8)11yescharacteristic
722C4C22×AGL(1,ℤ/8)11yescharacteristic
723C4C2×#57711yescharacteristic
724C4C2×#57811yescharacteristic
725C2—42no—
726C2—82no—
727C2—162no—
728C2#1937714yesdirect product factor
729C2C2×#303811yescharacteristic
730C2C2×#306311yescharacteristic
731C2C2×#306911yescharacteristic
subgroupG/H
center, socleC23C2×#121
commutator, Frattini, cosocleC42C25
prime radicalC2×#3251C2
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×#3239C2semidirect
3. C2×#3152C2semidirect
4. C2×#2969C2semidirect
5. #19377C2direct (N × H)
6. C2×#1690C2semidirect
7. C2×#1686C2semidirect
8. C2×#1689C2semidirect
9. C2×#1685C2semidirect
10. C2×#1670C2semidirect
11. C2×#1666C2semidirect
12. C2×#1669C2semidirect
13. C2×#1665C2semidirect
14. C2×#1569C2semidirect
15. C2×#1553C2semidirect
16. C2×#1549C2semidirect
25. #3239C22semidirect
28. #3152C22semidirect
51. #2969C22semidirect
64. #1690C22semidirect
65. #1689C22semidirect
66. #1686C22semidirect
67. #1685C22semidirect
68. #1670C22semidirect
69. #1669C22semidirect
70. #1666C22semidirect
71. #1665C22semidirect
72. #1569C22semidirect
77. #1553C22semidirect
78. #1549C22semidirect
728. C2#19377direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#32512
C2×#32392
C2×#31522
C2×#29692
#193772
C2×#16902
C2×#16862
C2×#16892
C2×#16852
C2×#16702
C2×#16662
C2×#16692
C2×#16652
C2×#15692
C2×#15532
C2×#15492