Finite Group Databasebeta

← C2×#9095 #196170

Subgroups — C2×#9095 #196170

Order 512.

1528 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C8×#41C211yesmaximal, characteristic, complemented
2C2×C4×AGL(1,ℤ/8)C211yesmaximal, characteristic
3C2×#1477C211yesmaximal, characteristic, complemented
4C22×D4⋊C8C211yesmaximal, characteristic, complemented
5C2×#1460C211yesmaximal, characteristic, complemented
6#9095C218yesmaximal, direct product factor
7C2×#1283C211yesmaximal, characteristic, complemented
8C2×#1278C211yesmaximal, characteristic, complemented
9C22×AGL(1,ℤ/8)C411yescharacteristic
10C2×C4×#41C2211yescharacteristic
11C22×C4×D4C2211yescharacteristic
12C8×#41—22no—
13C8×#41—22no—
14C8×#41—22no—
15C8×#41C2214yescomplemented
16C2×C8×Q8—21no—
17C4×AGL(1,ℤ/8)—22no—
18C4×AGL(1,ℤ/8)—22no—
19C4×AGL(1,ℤ/8)C414yes—
20C4×AGL(1,ℤ/8)C2214yes—
21C2×#442—21no—
22C2×#440—21no—
23C2×C4×SD16—21no—
24C2×C4×D8—21no—
25C2×C8×D4—22no—
26C2×C8×D4—21no—
27C2×#431—21no—
28C2×#431C2211yescharacteristic
29C2×#431C2211yescharacteristic
30C2×#428C411yescharacteristic
31C22×C4⋊C8C2211yescharacteristic
32C2×#417C411yescharacteristic
33C2×#418C411yescharacteristic
34C2×C4×M16C2211yescharacteristic
35C22×C4×C8—21no—
36C22×C4×C8C2211yescharacteristic
37#1477—22no—
38#1477C2214yescomplemented
39C2×Q8⋊C8—21no—
40C2×D4⋊C8—21no—
41C2×D4⋊C8—21no—
42C2×D4⋊C8—22no—
43C2×D4⋊C8—21no—
44C2×D4⋊C8C2214yescomplemented
45#1460—22no—
46#1460C2214yescomplemented
47C2×#323—22no—
48#1283C2214yescomplemented
49#1278C2214yescomplemented
50C22×#41C2×C411yescharacteristic
51C23×D4C2×C411yescharacteristic
52C24×C4—21no—
53C2×AGL(1,ℤ/8)—22no—
54C2×AGL(1,ℤ/8)—24no—
55C2×AGL(1,ℤ/8)C818yescomplemented
56C2×AGL(1,ℤ/8)C2×C414yes—
57C22×SD16—21no—
58C22×D8—21no—
59C22×M16C2×C411yescharacteristic
60C22×M16C2×C411yescharacteristic
61C23×C8—22no—
62C23×C8—21no—
63C23×C8—21no—
64C4×#41—21no—
65C4×#41—21no—
66C4×#41—21no—
67C4×#41—21no—
68C4×#41C2×C412yes—
69C4×#41D412yes—
70C4×#41D412yes—
71C4×#41C2312yes—
72C2×C4×Q8D411yescharacteristic
73C2×C4×Q8D411yescharacteristic
74C2×C4×D4—21no—
75C2×C4×D4—21no—
76C2×C4×D4—21no—
77C2×C4×D4—21no—
78C2×C4×D4—21no—
79C2×C4×D4—21no—
80C2×C4×D4—21no—
81C2×C4×D4—21no—
82C2×C4×D4—21no—
83C2×C4×D4—21no—
84C2×C4×D4—21no—
85C2×C4×D4—21no—
86C2×C4×D4C2×C412yes—
87C2×C4×D4D411yescharacteristic
88C2×C4×D4D411yescharacteristic
89C2×C4×D4C2312yes—
90C2×#117—21no—
91C2×#117C2×C411yescharacteristic
92C22×C4⋊C4C2×C411yescharacteristic
93C22×C22⋊C4—21no—
94C22×C42—21no—
95C22×C42C2311yescharacteristic
96C8×Q8—24no—
97C8×Q8—24no—
98#442—24no—
99#442—24no—
100#440—24no—
101#440—24no—
102C4×SD16—24no—
103C4×SD16—24no—
104C4×D8—24no—
105C4×D8—24no—
106C8×D4—28no—
107C8×D4—24no—
108C8×D4—24no—
109C8×D4—28no—
110#431—24no—
111#431—21no—
112#431—21no—
113#431—21no—
114#431—24no—
115#431—21no—
116#431—21no—
117#431D412yes—
118#431C2312yes—
119#431C2312yes—
120#428—22no—
121#428C2×C414yes—
122C2×#107—21no—
123C2×#106—21no—
124C2×C4⋊C8—22no—
125C2×C4⋊C8—21no—
126C2×C4⋊C8—21no—
127C2×C4⋊C8—21no—
128C2×C4⋊C8—21no—
129C2×C4⋊C8—21no—
130C2×C4⋊C8—21no—
131C2×C4⋊C8—21no—
132C2×C4⋊C8C2312yes—
133#418—22no—
134#418C2×C414yes—
135#417—22no—
136#417C2×C414yes—
137C2×#103—21no—
138C2×#102—21no—
139C2×#102—21no—
140C2×#102—21no—
141C2×C22⋊C8—22no—
142C2×C22⋊C8—21no—
143C2×C22⋊C8D412yes—
144C4×M16—21no—
145C4×M16—21no—
146C4×M16C2×C412yes—
147C4×M16C2312yes—
148C2×#97—21no—
149C2×C4×C8—22no—
150C2×C4×C8—24no—
151C2×C4×C8—21no—
152C2×C4×C8—21no—
153C2×C4×C8—21no—
154C2×C4×C8—21no—
155C2×C4×C8—21no—
156C2×C4×C8—24no—
157C2×C4×C8—21no—
158C2×C4×C8D411yescharacteristic
159C2×C4×C8D411yescharacteristic
160C2×C4×C8D412yes—
161C2×C4×C8C2312yes—
162Q8⋊C8—24no—
163D4⋊C8—24no—
164D4⋊C8—24no—
165D4⋊C8—24no—
166#323—28no—
167C25—21no—
168C2×#41—21no—
169C2×#41—21no—
170C2×#41—22no—
171C2×#41—22no—
172C2×#41C22⋊C412yes—
173C2×#41C2×C814yes—
174C2×#41M1614yes—
175C2×#41C22×C412yes—
176C22×Q8C22⋊C411yescharacteristic
177C22×D4—21no—
178C22×D4—21no—
179C22×D4—21no—
180C22×D4—21no—
181C22×D4—21no—
182C22×D4—21no—
183C22×D4—22no—
184C22×D4—22no—
185C22×D4—22no—
186C22×D4C22⋊C411yescharacteristic
187C22×D4C2×C814yescomplemented
188C22×D4C22×C412yes—
189C23×C4—21no—
190C23×C4—21no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—22no—
194C23×C4—22no—
195C23×C4—41no—
196C23×C4—41no—
197C23×C4—41no—
198C23×C4—41no—
199C23×C4—82no—
200C23×C4—82no—
201C23×C4C22×C411yescharacteristic
202C23×C4C2×D411yescharacteristic
203C23×C4#4111yescharacteristic
204AGL(1,ℤ/8)—216no—
205AGL(1,ℤ/8)—28no—
206AGL(1,ℤ/8)C2×C8116yescomplemented
207C2×SD16—28no—
208C2×SD16—24no—
209C2×D8—28no—
210C2×D8—24no—
211C2×M16—21no—
212C2×M16—22no—
213C2×M16—21no—
214C2×M16—22no—
215C2×M16—22no—
216C2×M16C2×C814yescomplemented
217C2×M16C22×C412yes—
218C2×M16C22×C412yes—
219C22×C8—21no—
220C22×C8—21no—
221C22×C8—28no—
222C22×C8—21no—
223C22×C8—22no—
224C22×C8—21no—
225C22×C8—22no—
226C22×C8—22no—
227C22×C8—22no—
228C22×C8—44no—
229C22×C8—48no—
230C22×C8—41no—
231C22×C8—41no—
232C22×C8—41no—
233C22×C8—82no—
234C4×Q8—21no—
235C4×Q8—21no—
236C4×Q8—21no—
237C4×Q8—21no—
238C4×Q8C22⋊C412yes—
239C4×Q8C22⋊C412yes—
240C4×Q8C2×D412yes—
241C4×Q8C2×D412yes—
242C4×D4—22no—
243C4×D4—22no—
244C4×D4—22no—
245C4×D4—22no—
246C4×D4—22no—
247C4×D4—22no—
248C4×D4—22no—
249C4×D4—22no—
250C4×D4—22no—
251C4×D4—22no—
252C4×D4—22no—
253C4×D4—22no—
254C4×D4—21no—
255C4×D4—21no—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4—22no—
259C4×D4—22no—
260C4×D4—22no—
261C4×D4—22no—
262C4×D4—41no—
263C4×D4—41no—
264C4×D4—41no—
265C4×D4—41no—
266C4×D4—41no—
267C4×D4—41no—
268C4×D4—41no—
269C4×D4—41no—
270C4×D4C22⋊C412yes—
271C4×D4C22⋊C412yes—
272C4×D4C2×D412yes—
273C4×D4C2×D412yes—
274#117—21no—
275#117—21no—
276#117—22no—
277#117—22no—
278#117—22no—
279#117—22no—
280#117C22⋊C412yes—
281#117C22×C412yes—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4C22⋊C411yescharacteristic
290C2×C4⋊C4C22⋊C411yescharacteristic
291C2×C4⋊C4C22×C412yes—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—22no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4—41no—
298C2×C22⋊C4—41no—
299C2×C22⋊C4—41no—
300C2×C22⋊C4—41no—
301C2×C42—21no—
302C2×C42—21no—
303C2×C42—21no—
304C2×C42—22no—
305C2×C42—22no—
306C2×C42—22no—
307C2×C42—22no—
308C2×C42C22×C411yescharacteristic
309C2×C42C2×D411yescharacteristic
310C2×C42C2×D411yescharacteristic
311C2×C42C2×D411yescharacteristic
312C2×C42C2×D411yescharacteristic
313C2×C42C2×D411yescharacteristic
314C2×C42C2×D411yescharacteristic
315C2×C42C2×D411yescharacteristic
316C2×C42#4111yescharacteristic
317C2×C42#4111yescharacteristic
318C2×C42#4111yescharacteristic
319C2×C42C2411yescharacteristic
320#107—24no—
321#106—24no—
322C4⋊C8—28no—
323C4⋊C8—22no—
324C4⋊C8—22no—
325C4⋊C8—22no—
326C4⋊C8—22no—
327C4⋊C8—22no—
328C4⋊C8—41no—
329C4⋊C8—41no—
330C4⋊C8—41no—
331#103—24no—
332#102—24no—
333#102—24no—
334#102—24no—
335C22⋊C8—28no—
336C22⋊C8—22no—
337C22⋊C8—22no—
338C22⋊C8—41no—
339C22⋊C8C2×D414yes—
340#97—22no—
341#97—22no—
342C4×C8—28no—
343C4×C8—22no—
344C4×C8—21no—
345C4×C8—22no—
346C4×C8—21no—
347C4×C8—22no—
348C4×C8—22no—
349C4×C8—22no—
350C4×C8—22no—
351C4×C8—22no—
352C4×C8—41no—
353C4×C8C2×D412yes—
354C4×C8C2×D412yes—
355C24—21no—
356C24—22no—
357C24—24no—
358C24—41no—
359C24—41no—
360C24—42no—
361C24—82no—
362C24—82no—
363C24C4×D411yescharacteristic
364#41—22no—
365#41—22no—
366#41—24no—
367#41—24no—
368#41—24no—
369#41—24no—
370#41—24no—
371#41C22⋊C818yes—
372#41C22×C814yes—
373#41C2×M1614yes—
374C2×Q8—21no—
375C2×Q8—22no—
376C2×Q8C22⋊C814yes—
377C2×Q8C2×C22⋊C412yes—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—24no—
381C2×D4—24no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—21no—
388C2×D4—24no—
389C2×D4—24no—
390C2×D4—22no—
391C2×D4—24no—
392C2×D4—24no—
393C2×D4—24no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4—42no—
397C2×D4—42no—
398C2×D4—42no—
399C2×D4—42no—
400C2×D4—42no—
401C2×D4C22⋊C814yes—
402C2×D4C2×C22⋊C412yes—
403C2×D4C22×C814yescomplemented
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—42no—
419C22×C4—44no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—84no—
429C22×C4—84no—
430C22×C4—82no—
431C22×C4—82no—
432C22×C4—84no—
433C22×C4—82no—
434C22×C4—82no—
435C22×C4—82no—
436C22×C4—82no—
437C22×C4—82no—
438C22×C4C2×C22⋊C411yescharacteristic
439C22×C4C2×C22⋊C411yescharacteristic
440C22×C4C4×D411yescharacteristic
441C22×C4C4×D411yescharacteristic
442C22×C4C4×D411yescharacteristic
443C22×C4C4×D411yescharacteristic
444C22×C4C4×D411yescharacteristic
445C22×C4#12011yescharacteristic
446C22×C4#12011yescharacteristic
447C22×C4#12111yescharacteristic
448C22×C4#12111yescharacteristic
449C22×C4#12111yescharacteristic
450C22×C4#12111yescharacteristic
451C22×C4#12311yescharacteristic
452C22×C4#12311yescharacteristic
453C22×C4C22×C812yes—
454C22×C4C2×M1612yes—
455C22×C4#13112yes—
456C22×C4#13112yes—
457C22×C4C23×C411yescharacteristic
458C22×C4C22×D411yescharacteristic
459C22×C4C2×#4111yescharacteristic
460SD16—216no—
461D8—216no—
462M16—22no—
463M16—24no—
464M16—22no—
465M16—22no—
466M16—42no—
467M16C22×C814yescomplemented
468C2×C8—24no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—24no—
472C2×C8—22no—
473C2×C8—24no—
474C2×C8—22no—
475C2×C8—44no—
476C2×C8—44no—
477C2×C8—416no—
478C2×C8—44no—
479C2×C8—42no—
480C2×C8—42no—
481C2×C8—42no—
482C2×C8—42no—
483C2×C8—82no—
484C2×C8—82no—
485C2×C8—82no—
486C2×C8—82no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C4⋊C4C2×C22⋊C412yes—
498C4⋊C4C2×C22⋊C412yes—
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—42no—
506C22⋊C4—42no—
507C22⋊C4—42no—
508C22⋊C4—42no—
509C42—22no—
510C42—22no—
511C42—22no—
512C42—22no—
513C42—22no—
514C42—22no—
515C42C2×C22⋊C411yescharacteristic
516C42C2×C22⋊C411yescharacteristic
517C42C4×D411yescharacteristic
518C42C4×D411yescharacteristic
519C42#12011yescharacteristic
520C42#12011yescharacteristic
521C42#12111yescharacteristic
522C42#12111yescharacteristic
523C42#12111yescharacteristic
524C42#12111yescharacteristic
525C42#12311yescharacteristic
526C42#12311yescharacteristic
527C42C22×D411yescharacteristic
528C42C22×D411yescharacteristic
529C42C22×D411yescharacteristic
530C42C2×#4111yescharacteristic
531C23—22no—
532C23—22no—
533C23—24no—
534C23—22no—
535C23—24no—
536C23—42no—
537C23—42no—
538C23—44no—
539C23—44no—
540C23—42no—
541C23—42no—
542C23—82no—
543C23—82no—
544C23—88no—
545C23—82no—
546C23—82no—
547C23—88no—
548C23—82no—
549C23—82no—
550C23#38611yescharacteristic
551C23#38611yescharacteristic
552C23C8×D412yes—
553C23#43512yes—
554C23C2×C4×D411yescharacteristic
555Q8—22no—
556Q8—24no—
557Q8C2×C22⋊C814yes—
558D4—28no—
559D4—24no—
560D4—24no—
561D4—24no—
562D4—22no—
563D4—24no—
564D4—24no—
565D4—42no—
566D4—44no—
567D4—44no—
568D4—42no—
569D4C2×C22⋊C814yes—
570C2×C4—24no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—28no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—44no—
591C2×C4—44no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—44no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—84no—
599C2×C4—84no—
600C2×C4—82no—
601C2×C4—82no—
602C2×C4—84no—
603C2×C4—82no—
604C2×C4—82no—
605C2×C4—82no—
606C2×C4#38611yescharacteristic
607C2×C4#38611yescharacteristic
608C2×C4#38611yescharacteristic
609C2×C4#38611yescharacteristic
610C2×C4#38611yescharacteristic
611C2×C4#38611yescharacteristic
612C2×C4C2×C22⋊C812yes—
613C2×C4C2×C22⋊C812yes—
614C2×C4#40812yes—
615C2×C4#40812yes—
616C2×C4C8×D412yes—
617C2×C4C8×D412yes—
618C2×C4C8×D412yes—
619C2×C4#43512yes—
620C2×C4#43512yes—
621C2×C4#43512yes—
622C2×C4#47112yes—
623C2×C4#47212yes—
624C2×C4C22×C22⋊C411yescharacteristic
625C2×C4C2×C4×D411yescharacteristic
626C2×C4C2×#12011yescharacteristic
627C2×C4C2×#12111yescharacteristic
628C2×C4C2×#12111yescharacteristic
629C2×C4C2×#12311yescharacteristic
630C2×C4C23×C811yescharacteristic
631C2×C4C22×M1611yescharacteristic
632C2×C4C2×#13111yescharacteristic
633C2×C4C2×#13111yescharacteristic
634C8—24no—
635C8—24no—
636C8—44no—
637C8—42no—
638C8—42no—
639C8—82no—
640C8—82no—
641C22—21no—
642C22—21no—
643C22—21no—
644C22—21no—
645C22—24no—
646C22—24no—
647C22—24no—
648C22—42no—
649C22—42no—
650C22—48no—
651C22—44no—
652C22—84no—
653C22—88no—
654C22—84no—
655C22—82no—
656C22—82no—
657C22—88no—
658C22#186912yes—
659C22#186912yes—
660C22#190612yes—
661C22#190712yes—
662C22C2×#38611yescharacteristic
663C22C2×C8×D411yescharacteristic
664C22C2×#43511yescharacteristic
665C4—21no—
666C4—21no—
667C4—21no—
668C4—21no—
669C4—21no—
670C4—21no—
671C4—24no—
672C4—42no—
673C4—42no—
674C4—82no—
675C4#186912yes—
676C4#186912yes—
677C4#190712yes—
678C4C22×C22⋊C811yescharacteristic
679C4C2×#40811yescharacteristic
680C4C2×C8×D411yescharacteristic
681C4C2×#43511yescharacteristic
682C4C2×#47111yescharacteristic
683C4C2×#47211yescharacteristic
684C2—22no—
685C2—21no—
686C2—21no—
687C2—44no—
688C2—84no—
689C2#909514yesdirect product factor
690C2C2×#186911yescharacteristic
691C2C2×#190611yescharacteristic
692C2C2×#190711yescharacteristic
subgroupG/H
centerC22×C4#121
commutatorC2×C4C23×C8
Frattini, cosocleC2×C42C24
socleC23#386
prime radicalC22×AGL(1,ℤ/8)C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×C8×#41C2semidirect
3. C2×#1477C2semidirect
4. C22×D4⋊C8C2semidirect
5. C2×#1460C2semidirect
6. #9095C2direct (N × H)
7. C2×#1283C2semidirect
8. C2×#1278C2semidirect
15. C8×#41C22semidirect
38. #1477C22semidirect
44. C2×D4⋊C8C22semidirect
46. #1460C22semidirect
48. #1283C22semidirect
49. #1278C22semidirect
55. C2×AGL(1,ℤ/8)C8semidirect
187. C22×D4C2×C8semidirect
206. AGL(1,ℤ/8)C2×C8semidirect
216. C2×M16C2×C8semidirect
403. C2×D4C22×C8semidirect
467. M16C22×C8semidirect
689. C2#9095direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C8×#412
C2×C4×AGL(1,ℤ/8)2
C2×#14772
C22×D4⋊C82
C2×#14602
#90952
C2×#12832
C2×#12782