Finite Group Databasebeta

← C2×#9446 #201079

Subgroups — C2×#9446 #201079

Order 512.

1402 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2921C211yesmaximal, characteristic, complemented
2C2×#2500C211yesmaximal, characteristic
3C2×#1820C211yesmaximal, characteristic, complemented
4C2×#1510C212yesmaximal
5#9446C218yesmaximal, direct product factor
6C2×#1284C212yesmaximal, complemented
7C22×#121C2211yescharacteristic
8C22×#117C2211yescharacteristic
9#2921—24no—
10#2921—22no—
11#2921C2214yescomplemented
12C2×#433—24no—
13C2×#423—21no—
14C2×#407C2212yes—
15C2×C4×M16—21no—
16#2500—22no—
17#2500—22no—
18#2500C414yescomplemented
19#2500C2214yes—
20C2×#394—21no—
21C2×#394—21no—
22C2×#390C411yescharacteristic, complemented
23C2×#390C411yescharacteristic, complemented
24C2×#388—21no—
25C2×#388—21no—
26C2×#384C411yescharacteristic, complemented
27C2×#382C411yescharacteristic, complemented
28C2×#381C2212yes—
29C2×C4×C22⋊C4C2211yescharacteristic
30#1820—22no—
31#1820C2214yescomplemented
32C2×#342—21no—
33C2×#342—21no—
34#1510—24no—
35#1510C2218yes—
36C2×#327—24no—
37#1284C2218yescomplemented
38C23×D4—21no—
39C23×D4C2×C411yescharacteristic
40C24×C4C2311yescharacteristic
41C22×M16—22no—
42C2×#121—21no—
43C2×#121—21no—
44C2×#121—22no—
45C2×#121—22no—
46C2×#121—22no—
47C2×#121—22no—
48C2×#121C2×C412yes—
49C2×#121C2312yes—
50C2×#117—22no—
51C2×#117—22no—
52C2×#117—22no—
53C2×#117—22no—
54C2×#117C2×C412yes—
55C2×#117D412yes—
56C2×#117D412yes—
57C2×#117C2312yes—
58C22×C4⋊C4—21no—
59C22×C4⋊C4—21no—
60C22×C4⋊C4C2×C411yescharacteristic
61C22×C4⋊C4C2×C411yescharacteristic
62C22×C4⋊C4C2×C411yescharacteristic
63C22×C22⋊C4—21no—
64C22×C22⋊C4—21no—
65C22×C22⋊C4—21no—
66C22×C22⋊C4—21no—
67C22×C22⋊C4—21no—
68C22×C22⋊C4—21no—
69C22×C22⋊C4—22no—
70C22×C22⋊C4D411yescharacteristic
71C22×C22⋊C4D411yescharacteristic
72C22×C42C2×C411yescharacteristic
73C22×C42C2×C411yescharacteristic
74C22×C42D411yescharacteristic
75C22×C42D411yescharacteristic
76#433—216no—
77#433—216no—
78#423—24no—
79#423—24no—
80C2×C4⋊C8—24no—
81#407—22no—
82#407—22no—
83#407D414yes—
84#407C2314yes—
85C2×C22⋊C8—22no—
86C2×C22⋊C8D414yes—
87C4×M16—24no—
88C4×M16—24no—
89C2×#97—22no—
90C2×C4×C8—22no—
91#394—24no—
92#394—24no—
93#394—24no—
94#394—24no—
95#390—22no—
96#390—22no—
97#390C2×C414yescomplemented
98#390C2×C414yescomplemented
99#388—24no—
100#388—24no—
101#388—24no—
102#388—24no—
103#384—22no—
104#384C2×C414yescomplemented
105#382—22no—
106#382C2×C414yescomplemented
107#381—22no—
108#381—22no—
109#381—22no—
110#381C2314yes—
111C4×C22⋊C4—21no—
112C4×C22⋊C4—21no—
113C4×C22⋊C4C2×C412yes—
114C4×C22⋊C4C2312yes—
115C2×#95—21no—
116C2×#95—21no—
117C2×#95—21no—
118C2×#95—22no—
119C2×#95—22no—
120#342—24no—
121#342—24no—
122#327—216no—
123C25—21no—
124C25C2×D411yescharacteristic
125C22×D4—22no—
126C22×D4—22no—
127C22×D4—21no—
128C22×D4—22no—
129C22×D4—22no—
130C22×D4—42no—
131C22×D4—42no—
132C22×D4—42no—
133C22×D4—42no—
134C22×D4—82no—
135C22×D4—82no—
136C22×D4C22×C412yes—
137C23×C4—21no—
138C23×C4—21no—
139C23×C4—21no—
140C23×C4—42no—
141C23×C4—42no—
142C23×C4—42no—
143C23×C4C22⋊C411yescharacteristic
144C23×C4C22⋊C411yescharacteristic
145C23×C4C22⋊C411yescharacteristic
146C23×C4C22⋊C411yescharacteristic
147C23×C4C22×C411yescharacteristic
148C23×C4C22×C411yescharacteristic
149C23×C4C2×D411yescharacteristic
150C23×C4C2×D411yescharacteristic
151C23×C4C2×D411yescharacteristic
152C23×C4C2×D412yes—
153C23×C4C2×D412yes—
154C23×C4#4112yes—
155C23×C4#4112yes—
156C23×C4C2411yescharacteristic
157C2×M16—24no—
158C2×M16—24no—
159C2×M16—44no—
160C2×M16—44no—
161C22×C8—24no—
162#121—24no—
163#121—24no—
164#121—24no—
165#121—24no—
166#121—42no—
167#121—42no—
168#121—42no—
169#121—42no—
170#117—24no—
171#117—24no—
172#117—24no—
173#117—24no—
174#117—24no—
175#117—24no—
176#117—24no—
177#117—24no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—24no—
186C2×C4⋊C4—24no—
187C2×C4⋊C4—82no—
188C2×C4⋊C4—82no—
189C2×C4⋊C4C22⋊C412yes—
190C2×C4⋊C4C22⋊C412yes—
191C2×C4⋊C4C22×C412yes—
192C2×C4⋊C4C22×C412yes—
193C2×C4⋊C4C22×C412yes—
194C2×C22⋊C4—22no—
195C2×C22⋊C4—22no—
196C2×C22⋊C4—22no—
197C2×C22⋊C4—22no—
198C2×C22⋊C4—22no—
199C2×C22⋊C4—22no—
200C2×C22⋊C4—22no—
201C2×C22⋊C4—24no—
202C2×C22⋊C4—24no—
203C2×C22⋊C4—22no—
204C2×C22⋊C4—24no—
205C2×C22⋊C4—24no—
206C2×C22⋊C4—24no—
207C2×C22⋊C4—44no—
208C2×C22⋊C4—44no—
209C2×C22⋊C4—44no—
210C2×C22⋊C4—41no—
211C2×C22⋊C4—41no—
212C2×C22⋊C4—41no—
213C2×C22⋊C4—41no—
214C2×C22⋊C4—44no—
215C2×C22⋊C4—44no—
216C2×C22⋊C4—42no—
217C2×C22⋊C4—82no—
218C2×C22⋊C4—82no—
219C2×C22⋊C4C22⋊C412yes—
220C2×C22⋊C4C22⋊C412yes—
221C2×C22⋊C4C2×D412yes—
222C2×C22⋊C4C2×D412yes—
223C2×C42—21no—
224C2×C42—21no—
225C2×C42—21no—
226C2×C42—21no—
227C2×C42—21no—
228C2×C42—21no—
229C2×C42—21no—
230C2×C42—21no—
231C2×C42—21no—
232C2×C42—21no—
233C2×C42—42no—
234C2×C42—42no—
235C2×C42C22⋊C412yes—
236C2×C42C22⋊C412yes—
237C2×C42C22×C412yes—
238C2×C42C22×C412yes—
239C2×C42C2×D412yes—
240C2×C42C2×D412yes—
241C4⋊C8—216no—
242C22⋊C8—24no—
243C22⋊C8—24no—
244C22⋊C8—24no—
245C22⋊C8C2×D418yes—
246#97—28no—
247C4×C8—28no—
248#95—22no—
249#95—24no—
250#95—24no—
251#95—22no—
252#95—24no—
253#95—24no—
254#95—42no—
255#95—42no—
256C24—22no—
257C24—22no—
258C24—22no—
259C24—42no—
260C24—42no—
261C24—42no—
262C24—42no—
263C24—42no—
264C24—42no—
265C24—41no—
266C24—41no—
267C24—42no—
268C24—42no—
269C24C2×C22⋊C411yescharacteristic
270C24C2×C22⋊C411yescharacteristic
271C24#12112yes—
272C24#12112yes—
273C24C22×D411yescharacteristic
274C2×D4—24no—
275C2×D4—42no—
276C2×D4—42no—
277C2×D4—42no—
278C2×D4—42no—
279C2×D4—44no—
280C2×D4—44no—
281C2×D4—42no—
282C2×D4—84no—
283C2×D4—84no—
284C2×D4—82no—
285C2×D4—82no—
286C2×D4—82no—
287C2×D4—82no—
288C2×D4—88no—
289C2×D4—88no—
290C22×C4—22no—
291C22×C4—22no—
292C22×C4—22no—
293C22×C4—22no—
294C22×C4—24no—
295C22×C4—22no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—44no—
313C22×C4—44no—
314C22×C4—44no—
315C22×C4—44no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4—42no—
324C22×C4—42no—
325C22×C4—42no—
326C22×C4—42no—
327C22×C4—42no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—42no—
331C22×C4—44no—
332C22×C4—84no—
333C22×C4—84no—
334C22×C4—84no—
335C22×C4C2×C22⋊C411yescharacteristic
336C22×C4C2×C22⋊C411yescharacteristic
337C22×C4C2×C22⋊C412yes—
338C22×C4C2×C22⋊C412yes—
339C22×C4C2×C22⋊C412yes—
340C22×C4C2×C22⋊C412yes—
341C22×C4C4×D412yes—
342C22×C4C4×D412yes—
343C22×C4C4×D412yes—
344C22×C4C4×D412yes—
345C22×C4#12011yescharacteristic
346C22×C4#12011yescharacteristic
347C22×C4#12012yes—
348C22×C4#12112yes—
349C22×C4#12112yes—
350C22×C4#12311yescharacteristic
351C22×C4#12311yescharacteristic
352C22×C4#12312yes—
353C22×C4C23×C411yescharacteristic
354C22×C4C22×D411yescharacteristic
355C22×C4C22×D412yes—
356C22×C4C2×#4112yes—
357M16—44no—
358M16—44no—
359M16—48no—
360C2×C8—28no—
361C2×C8—48no—
362C4⋊C4—24no—
363C4⋊C4—24no—
364C4⋊C4—24no—
365C4⋊C4—24no—
366C4⋊C4—24no—
367C4⋊C4—42no—
368C4⋊C4—84no—
369C4⋊C4—84no—
370C22⋊C4—24no—
371C22⋊C4—24no—
372C22⋊C4—24no—
373C22⋊C4—24no—
374C22⋊C4—48no—
375C22⋊C4—48no—
376C22⋊C4—44no—
377C22⋊C4—44no—
378C22⋊C4—42no—
379C22⋊C4—42no—
380C22⋊C4—42no—
381C22⋊C4—42no—
382C22⋊C4—44no—
383C22⋊C4—44no—
384C22⋊C4—84no—
385C22⋊C4—84no—
386C22⋊C4—84no—
387C42—22no—
388C42—22no—
389C42—22no—
390C42—22no—
391C42—22no—
392C42—22no—
393C42—22no—
394C42—22no—
395C42—42no—
396C42—42no—
397C42—42no—
398C42—42no—
399C23—22no—
400C23—22no—
401C23—24no—
402C23—24no—
403C23—24no—
404C23—21no—
405C23—21no—
406C23—21no—
407C23—21no—
408C23—24no—
409C23—41no—
410C23—41no—
411C23—41no—
412C23—42no—
413C23—41no—
414C23—42no—
415C23—42no—
416C23—42no—
417C23—42no—
418C23—42no—
419C23—42no—
420C23—42no—
421C23—42no—
422C23—84no—
423C23—84no—
424C23—82no—
425C23—82no—
426C23—84no—
427C23—84no—
428C23—84no—
429C23—84no—
430C23—82no—
431C23—82no—
432C23—82no—
433C23—82no—
434C23#38612yes—
435C23#38611yescharacteristic
436C23#38611yescharacteristic
437C23#41012yes—
438C23#41012yes—
439C23C22×C22⋊C411yescharacteristic
440C23C2×#12112yes—
441D4—84no—
442D4—84no—
443D4—88no—
444D4—88no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—24no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—48no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—81no—
490C2×C4—81no—
491C2×C4—81no—
492C2×C4—81no—
493C2×C4—84no—
494C2×C4—82no—
495C2×C4—82no—
496C2×C4—84no—
497C2×C4—84no—
498C2×C4—84no—
499C2×C4—168no—
500C2×C4#38611yescharacteristic
501C2×C4#38611yescharacteristic
502C2×C4#38612yes—
503C2×C4C2×C4×D412yes—
504C2×C4C2×#12011yescharacteristic
505C2×C4C2×#12311yescharacteristic
506C8—48no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—24no—
512C22—24no—
513C22—22no—
514C22—22no—
515C22—22no—
516C22—22no—
517C22—22no—
518C22—22no—
519C22—48no—
520C22—81no—
521C22—81no—
522C22—81no—
523C22—81no—
524C22—84no—
525C22—82no—
526C22—82no—
527C22—82no—
528C22—82no—
529C22—82no—
530C22—82no—
531C22—82no—
532C22—164no—
533C22—164no—
534C22#188412yes—
535C22#189912yes—
536C22#189912yes—
537C22#191012yes—
538C22C2×#38611yescharacteristic
539C22C2×#41011yescharacteristic
540C22C2×#41011yescharacteristic
541C4—21no—
542C4—22no—
543C4—21no—
544C4—21no—
545C4—21no—
546C4—22no—
547C4—44no—
548C4—42no—
549C4—42no—
550C4—42no—
551C4—42no—
552C4—82no—
553C4—82no—
554C4—164no—
555C2—21no—
556C2—21no—
557C2—22no—
558C2—42no—
559C2—42no—
560C2—162no—
561C2#944614yesdirect product factor
562C2C2×#188411yescharacteristic
563C2C2×#189911yescharacteristic
564C2C2×#191011yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC22×#121C22
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
1. C2×#2921C2semidirect
3. C2×#1820C2semidirect
5. #9446C2direct (N × H)
6. C2×#1284C2semidirect
11. #2921C22semidirect
18. #2500C4semidirect
22. C2×#390C4semidirect
23. C2×#390C4semidirect
26. C2×#384C4semidirect
27. C2×#382C4semidirect
31. #1820C22semidirect
37. #1284C22semidirect
97. #390C2×C4semidirect
98. #390C2×C4semidirect
104. #384C2×C4semidirect
106. #382C2×C4semidirect
561. C2#9446direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#29212
C2×#25002
C2×#18202
C2×#15102
#94462
C2×#12842