Finite Group Databasebeta

← C2×#9476 #201445

Subgroups — C2×#9476 #201445

Order 512.

2494 conjugacy classes of subgroups.

The subgroup lattice has 557 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2406C211yesmaximal, characteristic
2C2×#2274C211yesmaximal, characteristic, complemented
3C2×#1789C212yesmaximal
4C2×#1463C211yesmaximal, characteristic, complemented
5#9476C218yesmaximal, direct product factor
6C2×#1284C212yesmaximal, complemented
7C23×#41C2211yescharacteristic
8C22×#123—21no—
9C22×#117—21no—
10C23×C4⋊C4C2211yescharacteristic
11C22×#104—24no—
12C2×#407C2212yes—
13#2406—22no—
14#2406—22no—
15#2406C414yescomplemented
16#2406C2214yes—
17C2×#395C412yescomplemented
18C2×#394C412yescomplemented
19C2×#386—21no—
20C2×#385—22no—
21C2×#381C2211yescharacteristic
22#2274—24no—
23#2274—22no—
24#2274C2214yescomplemented
25C2×C4×C4⋊C4—24no—
26C2×C4×C22⋊C4—21no—
27C2×C4×C22⋊C4C2212yes—
28#1789—24no—
29#1789C2218yes—
30#1463—22no—
31#1463C2214yescomplemented
32C2×#324—22no—
33#1284C2218yescomplemented
34C22×#41—21no—
35C22×#41—21no—
36C22×#41—22no—
37C22×#41—22no—
38C22×#41—22no—
39C22×#41—22no—
40C22×#41—48no—
41C22×#41C2×C412yes—
42C22×#41C2312yes—
43C23×Q8C2×C411yescharacteristic
44C23×D4—21no—
45C23×D4C2×C411yescharacteristic
46C24×C4—21no—
47C24×C4D411yescharacteristic
48C24×C4D411yescharacteristic
49C24×C4C2311yescharacteristic
50C22×M16—22no—
51C2×#123—24no—
52C2×#123—24no—
53C2×#123—48no—
54C2×#117—216no—
55C2×#117—24no—
56C2×#117—24no—
57C22×C4⋊C4—22no—
58C22×C4⋊C4—22no—
59C22×C4⋊C4—22no—
60C22×C4⋊C4—22no—
61C22×C4⋊C4—22no—
62C22×C4⋊C4—22no—
63C22×C4⋊C4C2×C412yes—
64C22×C4⋊C4C2×C412yes—
65C22×C4⋊C4D412yes—
66C22×C4⋊C4D412yes—
67C22×C4⋊C4D412yes—
68C22×C4⋊C4C2312yes—
69C22×C22⋊C4—22no—
70C22×C22⋊C4—21no—
71C22×C22⋊C4—22no—
72C22×C22⋊C4—22no—
73C22×C42—22no—
74C22×C42—22no—
75C22×C42D414yes—
76C2×#104—216no—
77C2×#104—416no—
78#407—22no—
79#407—22no—
80#407—22no—
81#407C2314yes—
82C2×C22⋊C8—22no—
83C2×C22⋊C8—22no—
84#395—24no—
85#395C2×C418yescomplemented
86#394—24no—
87#394C2×C418yescomplemented
88#386—24no—
89#386—24no—
90#385—28no—
91#385—28no—
92#381—21no—
93#381—21no—
94#381C2×C412yes—
95#381C2312yes—
96C4×C4⋊C4—216no—
97C4×C4⋊C4—216no—
98C4×C22⋊C4—24no—
99C4×C22⋊C4—24no—
100C4×C22⋊C4—22no—
101C4×C22⋊C4—22no—
102C4×C22⋊C4D414yes—
103C4×C22⋊C4C2314yes—
104C2×#95—22no—
105C2×#95—22no—
106C2×#95—22no—
107C2×#95—21no—
108C2×#95C2×C412yes—
109#324—28no—
110C25—21no—
111C25C2×D411yescharacteristic
112C2×#41—216no—
113C2×#41—24no—
114C2×#41—24no—
115C2×#41—24no—
116C2×#41—24no—
117C2×#41—48no—
118C2×#41—48no—
119C2×#41—48no—
120C2×#41—48no—
121C2×#41—48no—
122C2×#41—48no—
123C2×#41—48no—
124C2×#41—416no—
125C2×#41—416no—
126C2×#41—42no—
127C2×#41—42no—
128C2×#41—42no—
129C2×#41—42no—
130C22×Q8—21no—
131C22×Q8—22no—
132C22×Q8—22no—
133C22×Q8—44no—
134C22×Q8C22×C412yes—
135C22×D4—28no—
136C22×D4—22no—
137C22×D4—22no—
138C22×D4—21no—
139C22×D4—22no—
140C22×D4—22no—
141C22×D4—44no—
142C22×D4—44no—
143C22×D4—41no—
144C22×D4—41no—
145C22×D4—41no—
146C22×D4—41no—
147C22×D4C22×C412yes—
148C23×C4—21no—
149C23×C4—21no—
150C23×C4—21no—
151C23×C4—21no—
152C23×C4—28no—
153C23×C4—21no—
154C23×C4—24no—
155C23×C4—21no—
156C23×C4—21no—
157C23×C4—21no—
158C23×C4—21no—
159C23×C4—22no—
160C23×C4—22no—
161C23×C4—22no—
162C23×C4—44no—
163C23×C4—44no—
164C23×C4—44no—
165C23×C4—42no—
166C23×C4—42no—
167C23×C4—44no—
168C23×C4C22⋊C412yes—
169C23×C4C22⋊C412yes—
170C23×C4C22⋊C412yes—
171C23×C4C22⋊C412yes—
172C23×C4C22×C411yescharacteristic
173C23×C4C22×C411yescharacteristic
174C23×C4C2×D412yes—
175C23×C4C2×D412yes—
176C23×C4C2×D412yes—
177C23×C4C2×D411yescharacteristic
178C23×C4C2×D411yescharacteristic
179C23×C4C2×D411yescharacteristic
180C23×C4C2×D412yes—
181C23×C4#4112yes—
182C23×C4#4112yes—
183C23×C4C2411yescharacteristic
184C2×M16—24no—
185C2×M16—42no—
186C2×M16—48no—
187C22×C8—42no—
188#123—416no—
189#123—416no—
190#117—232no—
191#117—232no—
192C2×C4⋊C4—216no—
193C2×C4⋊C4—28no—
194C2×C4⋊C4—24no—
195C2×C4⋊C4—24no—
196C2×C4⋊C4—24no—
197C2×C4⋊C4—24no—
198C2×C4⋊C4—24no—
199C2×C4⋊C4—24no—
200C2×C4⋊C4—24no—
201C2×C4⋊C4—24no—
202C2×C4⋊C4—24no—
203C2×C4⋊C4—24no—
204C2×C4⋊C4—24no—
205C2×C4⋊C4—24no—
206C2×C4⋊C4—28no—
207C2×C4⋊C4—48no—
208C2×C4⋊C4C22⋊C414yes—
209C2×C4⋊C4C22⋊C414yes—
210C2×C4⋊C4C22×C414yes—
211C2×C4⋊C4C2×D414yes—
212C2×C22⋊C4—216no—
213C2×C22⋊C4—24no—
214C2×C22⋊C4—24no—
215C2×C22⋊C4—22no—
216C2×C22⋊C4—22no—
217C2×C22⋊C4—28no—
218C2×C22⋊C4—28no—
219C2×C22⋊C4—48no—
220C2×C22⋊C4—44no—
221C2×C22⋊C4—48no—
222C2×C42—28no—
223C2×C42—216no—
224C2×C42—28no—
225C2×C42—24no—
226C2×C42—48no—
227C2×C42—84no—
228C2×C42C2×D418yes—
229#104—432no—
230C22⋊C8—24no—
231C22⋊C8—24no—
232C22⋊C8—42no—
233C22⋊C8—42no—
234#95—28no—
235#95—22no—
236#95—28no—
237#95—22no—
238#95—24no—
239#95—24no—
240#95—22no—
241#95C22×C414yes—
242C24—24no—
243C24—24no—
244C24—24no—
245C24—22no—
246C24—42no—
247C24—42no—
248C24—44no—
249C24—41no—
250C24—41no—
251C24—44no—
252C24C2×C22⋊C411yescharacteristic
253C24C2×C22⋊C411yescharacteristic
254C24#12011yescharacteristic
255C24#12011yescharacteristic
256C24#12311yescharacteristic
257C24#12311yescharacteristic
258C24C22×D411yescharacteristic
259#41—216no—
260#41—216no—
261#41—416no—
262#41—48no—
263#41—48no—
264#41—416no—
265#41—48no—
266#41—48no—
267#41—48no—
268#41—48no—
269#41—416no—
270#41—416no—
271C2×Q8—28no—
272C2×Q8—24no—
273C2×Q8—44no—
274C2×Q8—44no—
275C2×Q8—44no—
276C2×Q8—48no—
277C2×Q8—42no—
278C2×D4—28no—
279C2×D4—28no—
280C2×D4—28no—
281C2×D4—24no—
282C2×D4—44no—
283C2×D4—44no—
284C2×D4—48no—
285C2×D4—44no—
286C2×D4—44no—
287C2×D4—48no—
288C2×D4—44no—
289C2×D4—48no—
290C2×D4—48no—
291C2×D4—42no—
292C2×D4—42no—
293C2×D4—42no—
294C2×D4—42no—
295C2×D4—48no—
296C2×D4—42no—
297C22×C4—24no—
298C22×C4—24no—
299C22×C4—28no—
300C22×C4—28no—
301C22×C4—28no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—24no—
309C22×C4—28no—
310C22×C4—28no—
311C22×C4—28no—
312C22×C4—216no—
313C22×C4—24no—
314C22×C4—22no—
315C22×C4—28no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—24no—
323C22×C4—42no—
324C22×C4—42no—
325C22×C4—42no—
326C22×C4—42no—
327C22×C4—44no—
328C22×C4—42no—
329C22×C4—44no—
330C22×C4—44no—
331C22×C4—42no—
332C22×C4—44no—
333C22×C4—44no—
334C22×C4—416no—
335C22×C4—48no—
336C22×C4—42no—
337C22×C4—44no—
338C22×C4—44no—
339C22×C4—416no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—48no—
343C22×C4—44no—
344C22×C4—44no—
345C22×C4—44no—
346C22×C4—44no—
347C22×C4—44no—
348C22×C4—44no—
349C22×C4—44no—
350C22×C4—44no—
351C22×C4—44no—
352C22×C4—82no—
353C22×C4—82no—
354C22×C4—82no—
355C22×C4#10418yescomplemented
356C22×C4C2×C22⋊C414yes—
357C22×C4C2×C22⋊C414yes—
358C22×C4C2×C22⋊C411yescharacteristic
359C22×C4C2×C22⋊C411yescharacteristic
360C22×C4C4×D412yes—
361C22×C4C4×D412yes—
362C22×C4C4×D412yes—
363C22×C4C4×D412yes—
364C22×C4#12012yes—
365C22×C4#12112yes—
366C22×C4#12112yes—
367C22×C4#12112yes—
368C22×C4#12112yes—
369C22×C4#12312yes—
370C22×C4C23×C411yescharacteristic
371C22×C4C22×D412yes—
372C22×C4C22×D411yescharacteristic
373C22×C4C2×#4112yes—
374M16—48no—
375M16—84no—
376C2×C8—44no—
377C2×C8—84no—
378C4⋊C4—232no—
379C4⋊C4—28no—
380C4⋊C4—28no—
381C4⋊C4—28no—
382C4⋊C4—28no—
383C4⋊C4—416no—
384C22⋊C4—216no—
385C22⋊C4—216no—
386C22⋊C4—416no—
387C22⋊C4—44no—
388C22⋊C4—44no—
389C22⋊C4—416no—
390C42—232no—
391C42—48no—
392C42—84no—
393C42—88no—
394C23—22no—
395C23—22no—
396C23—22no—
397C23—22no—
398C23—22no—
399C23—22no—
400C23—22no—
401C23—22no—
402C23—22no—
403C23—22no—
404C23—22no—
405C23—22no—
406C23—22no—
407C23—22no—
408C23—22no—
409C23—24no—
410C23—41no—
411C23—41no—
412C23—41no—
413C23—41no—
414C23—416no—
415C23—42no—
416C23—44no—
417C23—416no—
418C23—44no—
419C23—44no—
420C23—44no—
421C23—42no—
422C23—88no—
423C23—82no—
424C23—82no—
425C23—82no—
426C23—82no—
427C23#38611yescharacteristic
428C23#38611yescharacteristic
429C23#38611yescharacteristic
430C23#38611yescharacteristic
431C23C2×#10414yes—
432C23B(4,𝔽2)14yes—
433C23C22×C22⋊C411yescharacteristic
434C23C2×#12011yescharacteristic
435C23C2×#12311yescharacteristic
436Q8—28no—
437Q8—44no—
438Q8—48no—
439D4—28no—
440D4—44no—
441D4—48no—
442D4—48no—
443D4—48no—
444D4—48no—
445D4—48no—
446C2×C4—24no—
447C2×C4—24no—
448C2×C4—28no—
449C2×C4—28no—
450C2×C4—28no—
451C2×C4—24no—
452C2×C4—24no—
453C2×C4—24no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—28no—
457C2×C4—28no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—216no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—41no—
465C2×C4—42no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—416no—
475C2×C4—416no—
476C2×C4—432no—
477C2×C4—48no—
478C2×C4—42no—
479C2×C4—44no—
480C2×C4—44no—
481C2×C4—44no—
482C2×C4—44no—
483C2×C4—48no—
484C2×C4—44no—
485C2×C4—42no—
486C2×C4—44no—
487C2×C4—44no—
488C2×C4—44no—
489C2×C4—44no—
490C2×C4—82no—
491C2×C4—82no—
492C2×C4—82no—
493C2×C4—88no—
494C2×C4#38612yes—
495C2×C4#38612yes—
496C2×C4C2×#10418yescomplemented
497C2×C4C2×C4×D412yes—
498C2×C4C2×#12112yes—
499C8—84no—
500C22—28no—
501C22—28no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—44no—
517C22—44no—
518C22—44no—
519C22—44no—
520C22—48no—
521C22—44no—
522C22—44no—
523C22—84no—
524C22—88no—
525C22—88no—
526C22—82no—
527C22—82no—
528C22#188912yes—
529C22#188912yes—
530C22#189612yes—
531C22#189612yes—
532C22#191212yes—
533C22C2×#38611yescharacteristic
534C22C22×#10412yes—
535C22C2×B(4,𝔽2)12yes—
536C4—22no—
537C4—22no—
538C4—22no—
539C4—22no—
540C4—28no—
541C4—416no—
542C4—44no—
543C4—44no—
544C4—84no—
545C2—22no—
546C2—22no—
547C2—22no—
548C2—22no—
549C2—41no—
550C2—41no—
551C2—84no—
552C2#947614yesdirect product factor
553C2C2×#188911yescharacteristic
554C2C2×#189611yescharacteristic
555C2C2×#191211yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×#41C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C24×C4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2274C2semidirect
4. C2×#1463C2semidirect
5. #9476C2direct (N × H)
6. C2×#1284C2semidirect
15. #2406C4semidirect
17. C2×#395C4semidirect
18. C2×#394C4semidirect
24. #2274C22semidirect
31. #1463C22semidirect
33. #1284C22semidirect
85. #395C2×C4semidirect
87. #394C2×C4semidirect
355. C22×C4#104semidirect
496. C2×C4C2×#104semidirect
552. C2#9476direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#24062
C2×#22742
C2×#17892
C2×#14632
#94762
C2×#12842