Finite Group Databasebeta

← C2×#61887 #10578560

Subgroups — C2×#61887 #10578560

Order 512.

6346 conjugacy classes of subgroups.

The subgroup lattice has 669 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3523C211yesmaximal, characteristic, complemented
2C2×#3480C211yesmaximal, characteristic, complemented
3#61887C2132yesmaximal, direct product factor
4C2×#3395C211yesmaximal, characteristic, complemented
5C2×#3394C213yesmaximal, complemented
6C2×#3393C213yesmaximal, complemented
7C2×#3392C211yesmaximal, characteristic, complemented
8C2×#3365C213yesmaximal, complemented
9C2×#3364C213yesmaximal, complemented
10C2×#3359C211yesmaximal, characteristic, complemented
11C2×#3358C211yesmaximal, characteristic, complemented
12C2×#3212C213yesmaximal, complemented
13C2×#3210C213yesmaximal, complemented
14C2×#3107C213yesmaximal, complemented
15C2×#3102C213yesmaximal, complemented
16C2×#2982C211yesmaximal, characteristic, complemented
17#3523—28no—
18#3523C22116yescomplemented
19#3480—28no—
20#3480C22116yescomplemented
21C2×#559C2213yes—
22C2×#557C2211yescharacteristic
23C2×#557C2211yescharacteristic
24C2×#557C2213yes—
25C2×#556C2213yes—
26C2×#556C2213yes—
27C2×#553—23no—
28C2×#552—23no—
29C2×#550C2211yescharacteristic
30C2×D4×Q8—21no—
31C2×D4×Q8C2211yescharacteristic
32C2×#548—21no—
33C2×#541—23no—
34C2×#533C2213yes—
35C2×#532C2213yes—
36C2×#529—23no—
37C2×#529C2213yes—
38C2×#519—21no—
39C2×C4×#41—21no—
40C2×C4×#41C2213yes—
41C22×C4×Q8C2211yescharacteristic
42#3395C22116yescomplemented
43#3394C22148yescomplemented
44#3393C22148yescomplemented
45#3392C22116yescomplemented
46#3365C22148yescomplemented
47#3364C22148yescomplemented
48#3359C22116yescomplemented
49#3358C22116yescomplemented
50#3212C22148yescomplemented
51#3210C22148yescomplemented
52C2×#495C2216yes—
53C2×#494C2213yes—
54C2×#492C2213yes—
55C2×#488C2216yes—
56C2×#487C2213yes—
57C2×#486C2213yes—
58#3107C22148yescomplemented
59#3102C22148yescomplemented
60C2×#485C2213yes—
61C2×#482C2211yescharacteristic
62C2×#479C2213yes—
63C2×#475C2213yes—
64C2×#478C2213yes—
65C2×#474C2213yes—
66C2×#464C2216yes—
67C2×#464C2216yes—
68C2×#464C2213yes—
69C2×#462C2213yes—
70C2×#462C2213yes—
71C2×#460C2213yes—
72C2×#463C2213yes—
73C2×#461C2213yes—
74C2×#461C2213yes—
75C2×#459C2213yes—
76C2×#452C2213yes—
77C2×#452C2216yes—
78C2×#449C2213yes—
79#2982C22116yescomplemented
80C2×C8×Q8C2211yescharacteristic
81C2×C8×Q8C2211yescharacteristic
82C2×C8×Q8C2213yes—
83C2×C8×Q8C2213yes—
84C2×C4×Q16C2213yes—
85C2×C4×Q16C2216yes—
86C2×C4×SD16C2213yes—
87C2×C4×SD16C2213yes—
88C2×C4×SD16C2216yes—
89C2×C4×D8C2213yes—
90C2×#431C2213yes—
91C2×#431C2213yes—
92C22×#41—21no—
93C22×#41C2313yes—
94C23×Q8—21no—
95C23×Q8D411yescharacteristic
96C22×Q16C2313yes—
97C22×Q16C2316yes—
98C22×SD16C2313yes—
99C22×SD16C2316yes—
100C22×SD16C2313yes—
101C22×D8C2313yes—
102#559—212no—
103#559C23124yes—
104#557—24no—
105#557—24no—
106#557—212no—
107#557C2318yes—
108#557C2318yes—
109#557C23124yes—
110#556—212no—
111#556—212no—
112#556C23124yes—
113#556C23124yes—
114#553—248no—
115#552—248no—
116#550—24no—
117#550C2318yes—
118D4×Q8—216no—
119D4×Q8—24no—
120D4×Q8C2318yes—
121#548—216no—
122#541—248no—
123#533—212no—
124#533C23124yes—
125#532—212no—
126#532C23124yes—
127C2×C4⋊Q8—23no—
128C2×C4⋊Q8C2313yes—
129C2×C4⋊Q8C2313yes—
130C2×C4⋊Q8C2313yes—
131C2×#127C2313yes—
132#529—248no—
133#529—212no—
134#529C23124yes—
135C2×#126—26no—
136C2×#126—26no—
137C2×#126—23no—
138C2×#125—23no—
139C2×#125—26no—
140C2×#125—23no—
141C2×#125—23no—
142C2×#125C2313yes—
143C2×#124—23no—
144C2×#124C2316yes—
145C2×#124C2313yes—
146C2×#123—23no—
147C2×#123—26no—
148C2×C22⋊Q8—23no—
149C2×C22⋊Q8—23no—
150C2×C22⋊Q8—23no—
151C2×C22⋊Q8—23no—
152C2×C22⋊Q8C2313yes—
153C2×#121—23no—
154C2×#121—23no—
155C2×#121—23no—
156C2×#121C2311yescharacteristic
157#519—216no—
158C4×#41—216no—
159C4×#41—212no—
160C4×#41C23124yes—
161C2×C4×Q8—21no—
162C2×C4×Q8—21no—
163C2×C4×Q8—23no—
164C2×C4×Q8—23no—
165C2×C4×Q8D411yescharacteristic
166C2×C4×Q8D413yes—
167C2×C4×Q8D418yes—
168C2×C4×Q8C2313yes—
169C2×C4×Q8C2313yes—
170C2×C4×Q8C2313yes—
171C2×C4×Q8C2316yes—
172C2×C4×Q8C2311yescharacteristic
173C2×C4×Q8C2313yes—
174C2×C4×Q8C2318yes—
175C2×C4×D4—23no—
176C2×C4×D4—23no—
177C2×C4×D4—23no—
178C2×C4×D4—23no—
179C2×C4×D4—23no—
180C2×C4×D4—23no—
181C2×C4×D4C2313yes—
182C2×C4×D4C2313yes—
183C2×C4×D4C2313yes—
184C2×#117—23no—
185C2×#117—23no—
186C2×#117—23no—
187C2×#117—23no—
188C2×#117—23no—
189C2×#117C2311yescharacteristic
190C22×C4⋊C4D413yes—
191C22×C42—23no—
192C22×C42C2313yes—
193#495C23148yes—
194#494C23124yes—
195#492C23124yes—
196#488C23148yes—
197#487C23124yes—
198#486C23124yes—
199#485C23124yes—
200#482C2318yes—
201#479C23124yes—
202#478C23124yes—
203#475C23124yes—
204#474C23124yes—
205#464C23124yes—
206#464C23148yes—
207#464C23148yes—
208#463C23124yes—
209#462C23124yes—
210#462C23124yes—
211#461C23124yes—
212#461C23124yes—
213#460C23124yes—
214#459C23124yes—
215#452C23124yes—
216#452C23148yes—
217#449C23124yes—
218C8×Q8C2318yes—
219C8×Q8C2318yes—
220C8×Q8C23124yes—
221C8×Q8C23124yes—
222C4×Q16C23124yes—
223C4×Q16C23148yes—
224C4×SD16C23124yes—
225C4×SD16C23124yes—
226C4×SD16C23148yes—
227C4×D8C23124yes—
228#431C23124yes—
229#431C23124yes—
230C2×#107C2311yescharacteristic
231C2×#107C2313yes—
232C2×#106C2313yes—
233C2×#106C2311yescharacteristic
234C2×C4⋊C8C2313yes—
235C2×C4⋊C8C2313yes—
236C2×C4⋊C8C2313yes—
237C2×C4⋊C8C2313yes—
238C2×#103C2316yes—
239C2×#103C2313yes—
240C2×#103C2313yes—
241C2×#103C2313yes—
242C2×#103C2313yes—
243C2×#102C2313yes—
244C2×#102C2313yes—
245C2×#102C2311yescharacteristic
246C2×#102C2311yescharacteristic
247C2×#102C2316yes—
248C2×C22⋊C8C2311yescharacteristic
249C2×C22⋊C8C2313yes—
250C2×C4×C8C2313yes—
251C2×C4×C8C2313yes—
252C2×C4×C8C2316yes—
253C2×#41—28no—
254C2×#41—26no—
255C2×#41—46no—
256C2×#41—46no—
257C2×#41—48no—
258C2×#41C24112yes—
259C22×Q8—28no—
260C22×Q8—28no—
261C22×Q8—23no—
262C22×Q8—48no—
263C22×Q8C2×D413yes—
264C22×Q8C2×D418yes—
265C22×Q8C2×D411yescharacteristic
266C22×Q8C2413yes—
267C22×Q8C2413yes—
268C22×D4—21no—
269C22×D4—23no—
270C22×D4—23no—
271C22×D4—23no—
272C22×D4C2411yescharacteristic
273C22×D4C2413yes—
274C23×C4—23no—
275C23×C4—23no—
276C23×C4—23no—
277C23×C4—23no—
278C23×C4C2×D413yes—
279C23×C4C2×D413yes—
280C23×C4C2411yescharacteristic
281C2×Q16—412no—
282C2×Q16—46no—
283C2×Q16C24124yes—
284C2×Q16C24112yes—
285C2×SD16—46no—
286C2×SD16—46no—
287C2×SD16—412no—
288C2×SD16C24112yes—
289C2×SD16C24124yes—
290C2×SD16C24112yes—
291C2×D8—46no—
292C2×D8C24112yes—
293C22×C8C2413yes—
294C22×C8C2411yescharacteristic
295C22×C8C2413yes—
296C22×C8C2411yescharacteristic
297C4⋊Q8—224no—
298C4⋊Q8—26no—
299C4⋊Q8—26no—
300C4⋊Q8—26no—
301C4⋊Q8C24112yes—
302C4⋊Q8C24112yes—
303C4⋊Q8C24112yes—
304#127—26no—
305#127C24112yes—
306#126—248no—
307#126—248no—
308#126—224no—
309#125—224no—
310#125—248no—
311#125—224no—
312#125—224no—
313#125—26no—
314#125C24112yes—
315#124—224no—
316#124—26no—
317#124—212no—
318#124C24112yes—
319#124C24124yes—
320#123—224no—
321#123—248no—
322C22⋊Q8—224no—
323C22⋊Q8—224no—
324C22⋊Q8—224no—
325C22⋊Q8—26no—
326C22⋊Q8—224no—
327C22⋊Q8C24112yes—
328#121—224no—
329#121—224no—
330#121—22no—
331#121—224no—
332#121C2414yes—
333C4×Q8—28no—
334C4×Q8—28no—
335C4×Q8—224no—
336C4×Q8—224no—
337C4×Q8—26no—
338C4×Q8—26no—
339C4×Q8—26no—
340C4×Q8—212no—
341C4×Q8C2×D418yes—
342C4×Q8C2×D4124yes—
343C4×Q8C2×D414yes—
344C4×Q8C2×D4112yes—
345C4×Q8C24112yes—
346C4×Q8C24112yes—
347C4×Q8C24112yes—
348C4×Q8C24124yes—
349C4×Q8C2414yes—
350C4×Q8C24112yes—
351C4×D4—224no—
352C4×D4—224no—
353C4×D4—224no—
354C4×D4—224no—
355C4×D4—224no—
356C4×D4—224no—
357C4×D4—26no—
358C4×D4—26no—
359C4×D4—26no—
360C4×D4C24112yes—
361C4×D4C24112yes—
362C4×D4C24112yes—
363#117—224no—
364#117—22no—
365#117—224no—
366#117—224no—
367#117—224no—
368#117—224no—
369#117C2414yes—
370C2×C4⋊C4—23no—
371C2×C4⋊C4—23no—
372C2×C4⋊C4—23no—
373C2×C4⋊C4—23no—
374C2×C4⋊C4—23no—
375C2×C4⋊C4—23no—
376C2×C4⋊C4—23no—
377C2×C4⋊C4—23no—
378C2×C4⋊C4—23no—
379C2×C4⋊C4—23no—
380C2×C4⋊C4—26no—
381C2×C4⋊C4—23no—
382C2×C4⋊C4C2×D413yes—
383C2×C4⋊C4C2×D413yes—
384C2×C4⋊C4C2×D416yes—
385C2×C4⋊C4C2×D4124yes—
386C2×C4⋊C4C2411yescharacteristic
387C2×C4⋊C4C2411yescharacteristic
388C2×C4⋊C4C2413yes—
389C2×C4⋊C4C2411yescharacteristic
390C2×C22⋊C4—23no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—23no—
394C2×C22⋊C4—26no—
395C2×C22⋊C4—23no—
396C2×C22⋊C4—23no—
397C2×C22⋊C4—26no—
398C2×C22⋊C4—23no—
399C2×C22⋊C4—23no—
400C2×C42—21no—
401C2×C42—23no—
402C2×C42—26no—
403C2×C42—23no—
404C2×C42—23no—
405C2×C42—224no—
406C2×C42C2×D413yes—
407C2×C42C2×D413yes—
408C2×C42C2×D4112yes—
409C2×C42C2413yes—
410C2×C42C2413yes—
411C2×C42C24112yes—
412#107C24112yes—
413#107C2414yes—
414#106C24112yes—
415#106C2414yes—
416C4⋊C8C24112yes—
417C4⋊C8C24112yes—
418C4⋊C8C24112yes—
419C4⋊C8C24112yes—
420#103C24112yes—
421#103C24112yes—
422#103C24112yes—
423#103C24112yes—
424#103C24124yes—
425#102C2414yes—
426#102C24112yes—
427#102C2414yes—
428#102C24112yes—
429#102C24124yes—
430C22⋊C8C24112yes—
431C22⋊C8C2414yes—
432C4×C8C24112yes—
433C4×C8C24112yes—
434C4×C8C24124yes—
435C24—21no—
436C24—23no—
437C24C22×D411yescharacteristic
438#41—412no—
439#41—412no—
440#41—424no—
441#41—432no—
442C2×Q8—232no—
443C2×Q8—212no—
444C2×Q8—23no—
445C2×Q8—212no—
446C2×Q8—23no—
447C2×Q8—26no—
448C2×Q8—26no—
449C2×Q8—26no—
450C2×Q8—26no—
451C2×Q8—432no—
452C2×Q8—412no—
453C2×Q8#13518yes—
454C2×Q8C22×D4112yes—
455C2×Q8C22×D414yes—
456C2×Q8C2516yes—
457C2×Q8C2516yes—
458C2×D4—24no—
459C2×D4—212no—
460C2×D4—21no—
461C2×D4—212no—
462C2×D4—23no—
463C2×D4—212no—
464C2×D4—22no—
465C2×D4—26no—
466C2×D4—22no—
467C2×D4—26no—
468C2×D4—44no—
469C2×D4—412no—
470C2×D4—412no—
471C2×D4—86no—
472C2×D4C2516yes—
473C2×D4C2512yes—
474C22×C4—212no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—23no—
480C22×C4—21no—
481C22×C4—23no—
482C22×C4—23no—
483C22×C4—212no—
484C22×C4—212no—
485C22×C4—212no—
486C22×C4—212no—
487C22×C4—46no—
488C22×C4—412no—
489C22×C4—412no—
490C22×C4—412no—
491C22×C4—86no—
492C22×C4C22×D412yes—
493C22×C4C22×D4112yes—
494C22×C4C22×D413yes—
495C22×C4C22×D411yescharacteristic
496C22×C4C22×D413yes—
497C22×C4C22×D413yes—
498C22×C4C22×D4112yes—
499C22×C4C22×D413yes—
500C22×C4C2512yes—
501C22×C4C2511yescharacteristic
502Q16—424no—
503Q16—412no—
504SD16—412no—
505SD16—412no—
506SD16—424no—
507D8—412no—
508C2×C8—26no—
509C2×C8—22no—
510C2×C8—26no—
511C2×C8—22no—
512C2×C8C2512yes—
513C2×C8C2516yes—
514C2×C8C2512yes—
515C2×C8C2516yes—
516C4⋊C4—212no—
517C4⋊C4—212no—
518C4⋊C4—212no—
519C4⋊C4—212no—
520C4⋊C4—212no—
521C4⋊C4—212no—
522C4⋊C4—212no—
523C4⋊C4—212no—
524C4⋊C4—212no—
525C4⋊C4—212no—
526C4⋊C4—224no—
527C4⋊C4—212no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—23no—
531C4⋊C4—21no—
532C4⋊C4C22×D4112yes—
533C4⋊C4C22×D4112yes—
534C4⋊C4C22×D4124yes—
535C4⋊C4C2516yes—
536C4⋊C4C2512yes—
537C4⋊C4C2512yes—
538C4⋊C4C2512yes—
539C22⋊C4—212no—
540C22⋊C4—24no—
541C22⋊C4—24no—
542C22⋊C4—212no—
543C22⋊C4—224no—
544C22⋊C4—212no—
545C22⋊C4—212no—
546C22⋊C4—224no—
547C22⋊C4—212no—
548C22⋊C4—212no—
549C42—24no—
550C42—212no—
551C42—212no—
552C42—224no—
553C42—212no—
554C42C22×D4112yes—
555C42C22×D4112yes—
556C42C22×D416yes—
557C42C22×D416yes—
558C42C2516yes—
559C42C2516yes—
560C23—22no—
561C23—22no—
562C23—22no—
563C23—22no—
564C23—26no—
565C23—46no—
566C23—42no—
567C23—46no—
568C23—42no—
569C23—42no—
570C23—46no—
571C23C23×D412yes—
572C23C23×D411yescharacteristic
573Q8—224no—
574Q8—26no—
575Q8—26no—
576Q8—26no—
577Q8—26no—
578Q8—46no—
579Q8—46no—
580Q8—424no—
581Q8C2×#135116yes—
582D4—22no—
583D4—26no—
584D4—22no—
585D4—26no—
586D4—48no—
587D4—424no—
588D4—42no—
589D4—46no—
590D4—424no—
591D4—812no—
592C2×C4—26no—
593C2×C4—26no—
594C2×C4—22no—
595C2×C4—26no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—24no—
599C2×C4—224no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—26no—
603C2×C4—22no—
604C2×C4—26no—
605C2×C4—26no—
606C2×C4—412no—
607C2×C4—424no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—46no—
611C2×C4—46no—
612C2×C4—42no—
613C2×C4—46no—
614C2×C4—424no—
615C2×C4—424no—
616C2×C4—812no—
617C2×C4C2×#135112yes—
618C2×C4C23×D416yes—
619C2×C4C23×D412yes—
620C2×C4C23×D416yes—
621C2×C4C23×D416yes—
622C2×C4C23×D411yescharacteristic
623C2×C4C23×D416yes—
624C2×C4#58512yes—
625C2×C4#58512yes—
626C2×C4C2611yescharacteristic
627C8—26no—
628C8—22no—
629C8—26no—
630C8—22no—
631C22—22no—
632C22—22no—
633C22—22no—
634C22—44no—
635C22—46no—
636C22—42no—
637C22—42no—
638C22—46no—
639C22—46no—
640C22—42no—
641C22—812no—
642C22—84no—
643C22#348712yes—
644C22C22×#13512yes—
645C22#358612yes—
646C22C24×D411yescharacteristic
647C4—22no—
648C4—26no—
649C4—26no—
650C4—26no—
651C4—46no—
652C4—46no—
653C4—42no—
654C4—46no—
655C4—42no—
656C4—42no—
657C4#348712yes—
658C4C22×#135112yes—
659C4C2×#58511yescharacteristic
660C4C2×#58511yescharacteristic
661C2—42no—
662C2—86no—
663C2—82no—
664C2#6188714yesdirect product factor
665C2C2×#348711yescharacteristic
666C2C23×#13511yescharacteristic
667C2C2×#358611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×Q8 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3523C2semidirect
2. C2×#3480C2semidirect
3. #61887C2direct (N × H)
4. C2×#3395C2semidirect
5. C2×#3394C2semidirect
6. C2×#3393C2semidirect
7. C2×#3392C2semidirect
8. C2×#3365C2semidirect
9. C2×#3364C2semidirect
10. C2×#3359C2semidirect
11. C2×#3358C2semidirect
12. C2×#3212C2semidirect
13. C2×#3210C2semidirect
14. C2×#3107C2semidirect
15. C2×#3102C2semidirect
16. C2×#2982C2semidirect
18. #3523C22semidirect
20. #3480C22semidirect
42. #3395C22semidirect
43. #3394C22semidirect
44. #3393C22semidirect
45. #3392C22semidirect
46. #3365C22semidirect
47. #3364C22semidirect
48. #3359C22semidirect
49. #3358C22semidirect
50. #3212C22semidirect
51. #3210C22semidirect
58. #3107C22semidirect
59. #3102C22semidirect
79. #2982C22semidirect
664. C2#61887direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#35232
C2×#34802
#618872
C2×#33952
C2×#33942
C2×#33932
C2×#33922
C2×#33652
C2×#33642
C2×#33592
C2×#33582
C2×#32122
C2×#32102
C2×#31072
C2×#31022
C2×#29822