Finite Group Databasebeta

← C2×#8855 #192060

Subgroups — C2×#8855 #192060

Order 512.

1550 conjugacy classes of subgroups.

The subgroup lattice has 609 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2313C211yesmaximal, characteristic
2C2×#1853C211yesmaximal, characteristic
3C2×#1852C211yesmaximal, characteristic
4C22×#324C211yesmaximal, characteristic
5C2×#1441C211yesmaximal, characteristic
6#8855C218yesmaximal, direct product factor
7C2×#1294C211yesmaximal, characteristic
8C2×#1294C211yesmaximal, characteristic
9C23×C4⋊C4C2211yescharacteristic
10C23×C4⋊C4C2211yescharacteristic
11C22×#107—21no—
12C22×#106—21no—
13C22×C22⋊C8C2211yescharacteristic
14C22×C22⋊C8C2211yescharacteristic
15#2313—22no—
16#2313—22no—
17#2313—22no—
18#2313C2214yes—
19C2×#387—21no—
20C2×#387—21no—
21C2×#387—21no—
22C2×#387—21no—
23C2×#381—21no—
24C2×#380C2211yescharacteristic
25C2×#380C2211yescharacteristic
26C2×C4×C22⋊C4—21no—
27C22×#95—21no—
28C22×#95—21no—
29C22×#95C2211yescharacteristic
30#1853—22no—
31#1853C2214yes—
32#1852—22no—
33#1852C2214yes—
34C2×#340—21no—
35C2×#340—21no—
36C2×#324C418yescomplemented
37C2×#324C2214yes—
38#1441—22no—
39#1441C2214yes—
40#1294C2214yes—
41#1294C2214yes—
42C24×C4—21no—
43C24×C4—21no—
44C24×C4D411yescharacteristic
45C24×C4D411yescharacteristic
46C24×C4C2311yescharacteristic
47C23×C8—21no—
48C23×C8—21no—
49C22×C4⋊C4—21no—
50C22×C4⋊C4—21no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4—22no—
54C22×C4⋊C4—22no—
55C22×C4⋊C4—21no—
56C22×C4⋊C4—21no—
57C22×C4⋊C4—21no—
58C22×C4⋊C4—21no—
59C22×C4⋊C4—21no—
60C22×C4⋊C4—44no—
61C22×C4⋊C4C2×C414yes—
62C22×C4⋊C4D412yes—
63C22×C4⋊C4D411yescharacteristic
64C22×C4⋊C4D411yescharacteristic
65C22×C4⋊C4D411yescharacteristic
66C22×C4⋊C4D411yescharacteristic
67C22×C4⋊C4Q814yes—
68C22×C4⋊C4C2312yes—
69C22×C4⋊C4C2312yes—
70C22×C22⋊C4—21no—
71C22×C22⋊C4—21no—
72C22×C42—21no—
73C22×C42—21no—
74C2×#107—24no—
75C2×#107—44no—
76C2×#106—24no—
77C2×#106—44no—
78C2×C22⋊C8—21no—
79C2×C22⋊C8—21no—
80C2×C22⋊C8—22no—
81C2×C22⋊C8—22no—
82C2×C22⋊C8C2×C414yes—
83C2×C22⋊C8C2×C414yes—
84C2×C22⋊C8C2312yes—
85C2×C22⋊C8C2312yes—
86#387—24no—
87#387—24no—
88#387—24no—
89#387—24no—
90#387—24no—
91#387—24no—
92#387—24no—
93#387—24no—
94#381—24no—
95#381—24no—
96#380—21no—
97#380—21no—
98#380—21no—
99#380—21no—
100#380D412yes—
101#380D412yes—
102#380C2312yes—
103#380C2312yes—
104C4×C22⋊C4—24no—
105C4×C22⋊C4—24no—
106C2×#95—21no—
107C2×#95—21no—
108C2×#95—21no—
109C2×#95—21no—
110C2×#95—21no—
111C2×#95—21no—
112C2×#95—21no—
113C2×#95—21no—
114C2×#95—22no—
115C2×#95—22no—
116C2×#95—21no—
117C2×#95—24no—
118C2×#95—24no—
119C2×#95—44no—
120C2×#95—44no—
121C2×#95C2312yes—
122#340—24no—
123#340—24no—
124#324C2×C4116yescomplemented
125C25C2×D411yescharacteristic
126C23×C4—21no—
127C23×C4—21no—
128C23×C4—21no—
129C23×C4—22no—
130C23×C4—22no—
131C23×C4—22no—
132C23×C4—22no—
133C23×C4—22no—
134C23×C4—21no—
135C23×C4—22no—
136C23×C4—24no—
137C23×C4—24no—
138C23×C4—21no—
139C23×C4—21no—
140C23×C4—21no—
141C23×C4—21no—
142C23×C4—22no—
143C23×C4—22no—
144C23×C4—42no—
145C23×C4—42no—
146C23×C4—42no—
147C23×C4—42no—
148C23×C4—42no—
149C23×C4—42no—
150C23×C4—42no—
151C23×C4—42no—
152C23×C4—42no—
153C23×C4—42no—
154C23×C4—41no—
155C23×C4—41no—
156C23×C4—42no—
157C23×C4—42no—
158C23×C4—42no—
159C23×C4—42no—
160C23×C4—42no—
161C23×C4C4⋊C414yes—
162C23×C4C4⋊C414yes—
163C23×C4C22×C412yes—
164C23×C4C2×D412yes—
165C23×C4C2×D411yescharacteristic
166C23×C4C2×D411yescharacteristic
167C23×C4C2×D412yes—
168C23×C4C2×D411yescharacteristic
169C23×C4C2×D411yescharacteristic
170C23×C4C2×D411yescharacteristic
171C23×C4C2×Q812yes—
172C23×C4#4112yes—
173C23×C4#4112yes—
174C23×C4C2411yescharacteristic
175C22×C8—24no—
176C22×C8—24no—
177C22×C8—22no—
178C22×C8—22no—
179C22×C8—42no—
180C22×C8—42no—
181C22×C8—42no—
182C22×C8—42no—
183C2×C4⋊C4—24no—
184C2×C4⋊C4—24no—
185C2×C4⋊C4—24no—
186C2×C4⋊C4—24no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—24no—
190C2×C4⋊C4—24no—
191C2×C4⋊C4—24no—
192C2×C4⋊C4—24no—
193C2×C4⋊C4—24no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—24no—
199C2×C4⋊C4—24no—
200C2×C4⋊C4—22no—
201C2×C4⋊C4—22no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—44no—
207C2×C4⋊C4—44no—
208C2×C4⋊C4—44no—
209C2×C4⋊C4—42no—
210C2×C4⋊C4—42no—
211C2×C4⋊C4—44no—
212C2×C4⋊C4—41no—
213C2×C4⋊C4—41no—
214C2×C4⋊C4—42no—
215C2×C4⋊C4—42no—
216C2×C4⋊C4—42no—
217C2×C4⋊C4—42no—
218C2×C4⋊C4C4⋊C418yes—
219C2×C4⋊C4C22×C414yes—
220C2×C4⋊C4C2×D412yes—
221C2×C4⋊C4C2×D412yes—
222C2×C4⋊C4C2×D412yes—
223C2×C4⋊C4C2×D412yes—
224C2×C4⋊C4C2×Q814yes—
225C2×C22⋊C4—22no—
226C2×C22⋊C4—22no—
227C2×C22⋊C4—22no—
228C2×C22⋊C4—22no—
229C2×C22⋊C4—42no—
230C2×C22⋊C4—42no—
231C2×C22⋊C4—42no—
232C2×C22⋊C4—42no—
233C2×C42—24no—
234C2×C42—24no—
235C2×C42—82no—
236C2×C42—82no—
237#107—48no—
238#106—48no—
239C22⋊C8—24no—
240C22⋊C8—24no—
241C22⋊C8—22no—
242C22⋊C8—22no—
243C22⋊C8C22×C414yes—
244C22⋊C8C22×C414yes—
245#95—24no—
246#95—24no—
247#95—24no—
248#95—24no—
249#95—24no—
250#95—24no—
251#95—22no—
252#95—22no—
253#95—22no—
254#95—22no—
255#95—22no—
256#95—22no—
257#95—48no—
258#95—48no—
259#95—42no—
260C24—22no—
261C24—22no—
262C24—22no—
263C24—22no—
264C24C2×C4⋊C412yes—
265C24#12011yescharacteristic
266C24#12011yescharacteristic
267C24#12312yes—
268C24#13512yes—
269C24#13512yes—
270C24AGL(1,ℤ/8)12yes—
271C24#13712yes—
272C24C22×D411yescharacteristic
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—24no—
285C22×C4—24no—
286C22×C4—24no—
287C22×C4—28no—
288C22×C4—28no—
289C22×C4—22no—
290C22×C4—24no—
291C22×C4—24no—
292C22×C4—24no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—41no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—44no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—44no—
306C22×C4—44no—
307C22×C4—44no—
308C22×C4—41no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—44no—
316C22×C4—44no—
317C22×C4—42no—
318C22×C4—48no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—44no—
323C22×C4—48no—
324C22×C4—48no—
325C22×C4—48no—
326C22×C4—42no—
327C22×C4—42no—
328C22×C4—48no—
329C22×C4—48no—
330C22×C4—42no—
331C22×C4—42no—
332C22×C4—42no—
333C22×C4—42no—
334C22×C4—42no—
335C22×C4—42no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4—42no—
339C22×C4—42no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—42no—
344C22×C4—42no—
345C22×C4—42no—
346C22×C4—42no—
347C22×C4—42no—
348C22×C4—44no—
349C22×C4—42no—
350C22×C4—42no—
351C22×C4—84no—
352C22×C4—81no—
353C22×C4—81no—
354C22×C4—84no—
355C22×C4—84no—
356C22×C4—84no—
357C22×C4—84no—
358C22×C4—84no—
359C22×C4—82no—
360C22×C4—82no—
361C22×C4—82no—
362C22×C4—82no—
363C22×C4—84no—
364C22×C4C2×C4⋊C414yes—
365C22×C4C2×C4⋊C414yes—
366C22×C4C2×C4⋊C412yes—
367C22×C4C4×D412yes—
368C22×C4C4×D412yes—
369C22×C4C4×D412yes—
370C22×C4C4×D412yes—
371C22×C4#12011yescharacteristic
372C22×C4#12011yescharacteristic
373C22×C4C22⋊Q812yes—
374C22×C4C22⋊Q812yes—
375C22×C4C22⋊Q812yes—
376C22×C4C22⋊Q812yes—
377C22×C4#12312yes—
378C22×C4C23×C411yescharacteristic
379C22×C4C22×D411yescharacteristic
380C22×C4C22×D411yescharacteristic
381C22×C4C22×Q811yescharacteristic
382C22×C4C2×#4111yescharacteristic
383C22×C4C2×#4111yescharacteristic
384C2×C8—24no—
385C2×C8—24no—
386C2×C8—42no—
387C2×C8—42no—
388C2×C8—48no—
389C2×C8—48no—
390C2×C8—42no—
391C2×C8—42no—
392C4⋊C4—24no—
393C4⋊C4—24no—
394C4⋊C4—24no—
395C4⋊C4—24no—
396C4⋊C4—28no—
397C4⋊C4—28no—
398C4⋊C4—24no—
399C4⋊C4—24no—
400C4⋊C4—42no—
401C4⋊C4—42no—
402C4⋊C4—42no—
403C4⋊C4—42no—
404C4⋊C4—42no—
405C4⋊C4—42no—
406C4⋊C4—44no—
407C4⋊C4—44no—
408C4⋊C4—81no—
409C4⋊C4—81no—
410C4⋊C4—81no—
411C4⋊C4—81no—
412C22⋊C4—42no—
413C22⋊C4—42no—
414C22⋊C4—42no—
415C22⋊C4—42no—
416C22⋊C4—44no—
417C22⋊C4—44no—
418C42—84no—
419C42—84no—
420C23—24no—
421C23—24no—
422C23—24no—
423C23—24no—
424C23—24no—
425C23—24no—
426C23—24no—
427C23—24no—
428C23—24no—
429C23—24no—
430C23—24no—
431C23—24no—
432C23—21no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—21no—
440C23#38512yes—
441C23#38512yes—
442C23#42714yes—
443C23#42814yes—
444C23#44912yes—
445C23#44912yes—
446C23#45212yes—
447C23#45212yes—
448C23#45412yes—
449C23#45612yes—
450C23B(4,𝔽2)12yes—
451C23#45812yes—
452C23#48214yes—
453C23#48514yes—
454C23C22×C4⋊C411yescharacteristic
455C23C2×#12011yescharacteristic
456C23C2×#12311yescharacteristic
457C23C2×#13511yescharacteristic
458C23C2×#13511yescharacteristic
459C23C2×AGL(1,ℤ/8)11yescharacteristic
460C23C2×#13711yescharacteristic
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—48no—
490C2×C4—48no—
491C2×C4—48no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—44no—
497C2×C4—44no—
498C2×C4—44no—
499C2×C4—44no—
500C2×C4—44no—
501C2×C4—44no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—44no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—82no—
516C2×C4—84no—
517C2×C4—816no—
518C2×C4—82no—
519C2×C4—82no—
520C2×C4—82no—
521C2×C4—82no—
522C2×C4—82no—
523C2×C4—88no—
524C2×C4—82no—
525C2×C4—84no—
526C2×C4—88no—
527C2×C4—84no—
528C2×C4—84no—
529C2×C4—84no—
530C2×C4—82no—
531C2×C4—82no—
532C2×C4#38512yes—
533C2×C4#38512yes—
534C2×C4C2×C4×D411yescharacteristic
535C2×C4C2×C4×D411yescharacteristic
536C2×C4C2×C22⋊Q811yescharacteristic
537C2×C4C2×C22⋊Q811yescharacteristic
538C8—44no—
539C8—44no—
540C22—21no—
541C22—21no—
542C22—22no—
543C22—28no—
544C22—28no—
545C22—28no—
546C22—28no—
547C22—21no—
548C22—21no—
549C22—22no—
550C22—21no—
551C22—21no—
552C22—22no—
553C22—21no—
554C22—21no—
555C22—22no—
556C22—21no—
557C22—21no—
558C22—22no—
559C22—21no—
560C22—21no—
561C22—22no—
562C22#159714yes—
563C22#160314yes—
564C22#160914yes—
565C22#161514yes—
566C22#185414yes—
567C22#185414yes—
568C22#185714yes—
569C22#186714yes—
570C22C2×#38511yescharacteristic
571C22C2×#42711yescharacteristic
572C22C2×#42811yescharacteristic
573C22C2×#44911yescharacteristic
574C22C2×#45211yescharacteristic
575C22C2×#45411yescharacteristic
576C22C2×#45611yescharacteristic
577C22C2×B(4,𝔽2)11yescharacteristic
578C22C2×#45811yescharacteristic
579C22C2×#48211yescharacteristic
580C22C2×#48511yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—22no—
586C4—22no—
587C4—44no—
588C4—44no—
589C4—84no—
590C4—82no—
591C4—84no—
592C4—82no—
593C4—82no—
594C4—82no—
595C2—21no—
596C2—21no—
597C2—24no—
598C2—21no—
599C2—21no—
600C2#885518yesdirect product factor
601C2C2×#159711yescharacteristic
602C2C2×#160311yescharacteristic
603C2C2×#160911yescharacteristic
604C2C2×#161511yescharacteristic
605C2C2×#185411yescharacteristic
606C2C2×#185711yescharacteristic
607C2C2×#186711yescharacteristic
subgroupG/H
center, socleC24#120
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C24 ◁ C24×C4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
6. #8855C2direct (N × H)
36. C2×#324C4semidirect
124. #324C2×C4semidirect
600. C2#8855direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#23132
C2×#18532
C2×#18522
C22×#3242
C2×#14412
#88552
C2×#12942