Finite Group Databasebeta

← C2×#9407 #200614

Subgroups — C2×#9407 #200614

Order 512.

2154 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2561C211yesmaximal, characteristic
2C2×#2273C211yesmaximal, characteristic
3C2×#1508C212yesmaximal, complemented
4C2×#1462C211yesmaximal, characteristic
5#9407C218yesmaximal, direct product factor
6C2×#1297C212yesmaximal, complemented
7C22×C22⋊Q8C2211yescharacteristic
8C23×C22⋊C4—21no—
9C23×C22⋊C4C2211yescharacteristic
10C2×#407C2212yes—
11#2561—22no—
12#2561—22no—
13#2561C414yescomplemented
14#2561C2214yes—
15C2×#397C412yescomplemented
16C2×#393C412yescomplemented
17C2×#388—22no—
18C2×#381—21no—
19C2×#379—21no—
20#2273—24no—
21#2273—22no—
22#2273C2214yes—
23C2×C4×C22⋊C4—24no—
24C2×C4×C22⋊C4—21no—
25C2×C4×C22⋊C4C2211yescharacteristic
26C2×C4×C22⋊C4C2212yes—
27#1508—24no—
28#1508C2218yescomplemented
29C2×#328—24no—
30#1462—22no—
31#1462C2214yes—
32C2×#323—22no—
33#1297C2218yescomplemented
34C26D411yescharacteristic
35C23×Q8C2×C411yescharacteristic, complemented
36C24×C4—22no—
37C24×C4D411yescharacteristic
38C24×C4C2311yescharacteristic
39C22×M16—22no—
40C2×C22⋊Q8—21no—
41C2×C22⋊Q8—21no—
42C2×C22⋊Q8—22no—
43C2×C22⋊Q8—22no—
44C2×C22⋊Q8—22no—
45C2×C22⋊Q8—22no—
46C2×C22⋊Q8C2×C412yescomplemented
47C2×C22⋊Q8C2312yes—
48C22×C4⋊C4—21no—
49C22×C4⋊C4C2×C411yescharacteristic, complemented
50C22×C22⋊C4—216no—
51C22×C22⋊C4—22no—
52C22×C22⋊C4—24no—
53C22×C22⋊C4—22no—
54C22×C22⋊C4—24no—
55C22×C22⋊C4—22no—
56C22×C22⋊C4—22no—
57C22×C22⋊C4—22no—
58C22×C22⋊C4—22no—
59C22×C22⋊C4—22no—
60C22×C22⋊C4—21no—
61C22×C22⋊C4—21no—
62C22×C22⋊C4—22no—
63C22×C22⋊C4C2×C412yes—
64C22×C22⋊C4C2×C412yes—
65C22×C22⋊C4D412yes—
66C22×C22⋊C4D412yes—
67C22×C22⋊C4D412yes—
68C22×C22⋊C4C2312yes—
69C22×C42—22no—
70C22×C42—22no—
71C22×C42—21no—
72#407—22no—
73#407—22no—
74#407—22no—
75#407C2314yes—
76C2×C22⋊C8—22no—
77C2×C22⋊C8—22no—
78#397—24no—
79#397C2×C418yescomplemented
80#393—24no—
81#393C2×C418yescomplemented
82#388—28no—
83#388—28no—
84#381—24no—
85#381—24no—
86#379—24no—
87#379—24no—
88C4×C22⋊C4—24no—
89C4×C22⋊C4—216no—
90C4×C22⋊C4—21no—
91C4×C22⋊C4—21no—
92C4×C22⋊C4—24no—
93C4×C22⋊C4—22no—
94C4×C22⋊C4—22no—
95C4×C22⋊C4—216no—
96C4×C22⋊C4C2×C412yescomplemented
97C4×C22⋊C4D414yes—
98C4×C22⋊C4C2312yes—
99C4×C22⋊C4C2314yes—
100C2×#95—22no—
101C2×#95—22no—
102C2×#95—22no—
103C2×#95C2×C412yescomplemented
104C2×#95D414yes—
105#328—216no—
106#323—28no—
107C25—21no—
108C25—28no—
109C25—21no—
110C25—21no—
111C25—21no—
112C25—44no—
113C25—82no—
114C25C22⋊C412yes—
115C25C22⋊C412yes—
116C25C2×D411yescharacteristic
117C25C2×D412yes—
118C22×Q8—21no—
119C22×Q8—22no—
120C22×Q8—22no—
121C22×Q8—82no—
122C22×Q8C22×C412yescomplemented
123C23×C4—24no—
124C23×C4—21no—
125C23×C4—216no—
126C23×C4—28no—
127C23×C4—21no—
128C23×C4—21no—
129C23×C4—21no—
130C23×C4—21no—
131C23×C4—21no—
132C23×C4—22no—
133C23×C4—44no—
134C23×C4—82no—
135C23×C4—84no—
136C23×C4—84no—
137C23×C4C22⋊C412yes—
138C23×C4C22⋊C412yes—
139C23×C4C22×C411yescharacteristic
140C23×C4C22×C411yescharacteristic
141C23×C4C2×D412yes—
142C23×C4C2×D411yescharacteristic
143C23×C4C2×D412yes—
144C23×C4C2×D411yescharacteristic
145C23×C4C2×D411yescharacteristic
146C23×C4C2×D412yes—
147C23×C4#4112yes—
148C23×C4#4112yes—
149C23×C4C2411yescharacteristic
150C2×M16—24no—
151C2×M16—42no—
152C2×M16—84no—
153C22×C8—42no—
154C22⋊Q8—24no—
155C22⋊Q8—24no—
156C22⋊Q8—24no—
157C22⋊Q8—24no—
158C22⋊Q8—42no—
159C22⋊Q8—42no—
160C22⋊Q8—42no—
161C22⋊Q8—42no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—42no—
168C2×C4⋊C4—42no—
169C2×C4⋊C4C22×C412yescomplemented
170C2×C22⋊C4—216no—
171C2×C22⋊C4—216no—
172C2×C22⋊C4—232no—
173C2×C22⋊C4—232no—
174C2×C22⋊C4—28no—
175C2×C22⋊C4—24no—
176C2×C22⋊C4—24no—
177C2×C22⋊C4—24no—
178C2×C22⋊C4—24no—
179C2×C22⋊C4—24no—
180C2×C22⋊C4—24no—
181C2×C22⋊C4—24no—
182C2×C22⋊C4—24no—
183C2×C22⋊C4—24no—
184C2×C22⋊C4—24no—
185C2×C22⋊C4—24no—
186C2×C22⋊C4—24no—
187C2×C22⋊C4—24no—
188C2×C22⋊C4—24no—
189C2×C22⋊C4—22no—
190C2×C22⋊C4—22no—
191C2×C22⋊C4—28no—
192C2×C22⋊C4—22no—
193C2×C22⋊C4—22no—
194C2×C22⋊C4—28no—
195C2×C22⋊C4—44no—
196C2×C22⋊C4—48no—
197C2×C22⋊C4—41no—
198C2×C22⋊C4—41no—
199C2×C22⋊C4—41no—
200C2×C22⋊C4—41no—
201C2×C22⋊C4—84no—
202C2×C22⋊C4C22⋊C414yes—
203C2×C22⋊C4C22⋊C414yes—
204C2×C22⋊C4C22×C414yes—
205C2×C22⋊C4C2×D414yes—
206C2×C42—28no—
207C2×C42—22no—
208C2×C42—24no—
209C2×C42—24no—
210C2×C42—22no—
211C2×C42—84no—
212C2×C42—82no—
213C2×C42—84no—
214C22⋊C8—24no—
215C22⋊C8—24no—
216C22⋊C8—42no—
217C22⋊C8—42no—
218#95—28no—
219#95—28no—
220#95—28no—
221#95—22no—
222#95—24no—
223#95C22×C414yescomplemented
224#95C2×D418yes—
225C24—24no—
226C24—24no—
227C24—28no—
228C24—28no—
229C24—28no—
230C24—22no—
231C24—22no—
232C24—22no—
233C24—24no—
234C24—24no—
235C24—22no—
236C24—22no—
237C24—22no—
238C24—28no—
239C24—28no—
240C24—24no—
241C24—42no—
242C24—44no—
243C24—44no—
244C24—44no—
245C24—44no—
246C24—44no—
247C24—44no—
248C24—82no—
249C24—82no—
250C24—82no—
251C24—82no—
252C24—82no—
253C24—82no—
254C24—832no—
255C24—82no—
256C24—82no—
257C24#10418yes—
258C24C2×C22⋊C411yescharacteristic
259C24C2×C22⋊C411yescharacteristic
260C24C2×C22⋊C414yes—
261C24#12011yescharacteristic
262C24#12011yescharacteristic
263C24#12311yescharacteristic
264C24#12311yescharacteristic
265C24C22×D411yescharacteristic
266C2×Q8—24no—
267C2×Q8—42no—
268C2×Q8—84no—
269C2×Q8—82no—
270C2×Q8—82no—
271C2×Q8—84no—
272C22×C4—216no—
273C22×C4—22no—
274C22×C4—28no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—232no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—24no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—42no—
285C22×C4—44no—
286C22×C4—44no—
287C22×C4—42no—
288C22×C4—48no—
289C22×C4—44no—
290C22×C4—48no—
291C22×C4—44no—
292C22×C4—44no—
293C22×C4—44no—
294C22×C4—44no—
295C22×C4—44no—
296C22×C4—44no—
297C22×C4—41no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—44no—
302C22×C4—44no—
303C22×C4—81no—
304C22×C4—81no—
305C22×C4—82no—
306C22×C4—81no—
307C22×C4—82no—
308C22×C4—81no—
309C22×C4—82no—
310C22×C4—82no—
311C22×C4—82no—
312C22×C4—88no—
313C22×C4—832no—
314C22×C4—88no—
315C22×C4C2×C22⋊C414yes—
316C22×C4C2×C22⋊C411yescharacteristic
317C22×C4C2×C22⋊C411yescharacteristic
318C22×C4C4×D412yes—
319C22×C4C4×D412yes—
320C22×C4C4×D412yes—
321C22×C4C4×D412yes—
322C22×C4#12012yes—
323C22×C4#12112yes—
324C22×C4#12112yes—
325C22×C4#12112yes—
326C22×C4#12112yes—
327C22×C4#12312yes—
328C22×C4C23×C411yescharacteristic
329C22×C4C22×D412yes—
330C22×C4C22×D411yescharacteristic
331C22×C4C2×#4112yes—
332M16—84no—
333M16—84no—
334C2×C8—44no—
335C2×C8—84no—
336C4⋊C4—24no—
337C4⋊C4—44no—
338C4⋊C4—42no—
339C4⋊C4—44no—
340C22⋊C4—232no—
341C22⋊C4—216no—
342C22⋊C4—216no—
343C22⋊C4—28no—
344C22⋊C4—28no—
345C22⋊C4—28no—
346C22⋊C4—28no—
347C22⋊C4—44no—
348C22⋊C4—44no—
349C22⋊C4—42no—
350C22⋊C4—42no—
351C22⋊C4—42no—
352C22⋊C4—42no—
353C22⋊C4—416no—
354C22⋊C4—88no—
355C42—82no—
356C42—84no—
357C42—84no—
358C42—82no—
359C42—88no—
360C23—22no—
361C23—22no—
362C23—22no—
363C23—22no—
364C23—24no—
365C23—24no—
366C23—28no—
367C23—28no—
368C23—28no—
369C23—22no—
370C23—22no—
371C23—22no—
372C23—22no—
373C23—22no—
374C23—22no—
375C23—28no—
376C23—22no—
377C23—22no—
378C23—22no—
379C23—22no—
380C23—22no—
381C23—24no—
382C23—24no—
383C23—28no—
384C23—41no—
385C23—41no—
386C23—41no—
387C23—41no—
388C23—416no—
389C23—44no—
390C23—416no—
391C23—44no—
392C23—416no—
393C23—44no—
394C23—44no—
395C23—416no—
396C23—44no—
397C23—44no—
398C23—44no—
399C23—44no—
400C23—82no—
401C23—88no—
402C23—82no—
403C23—82no—
404C23—82no—
405C23—82no—
406C23—82no—
407C23—816no—
408C23—816no—
409C23—816no—
410C23—816no—
411C23—816no—
412C23#38611yescharacteristic
413C23#38611yescharacteristic
414C23#38611yescharacteristic
415C23#38611yescharacteristic
416C23C2×#10414yes—
417C23C2×#10418yes—
418C23#45514yes—
419C23C22×C22⋊C411yescharacteristic
420C23C2×#12011yescharacteristic
421C23C2×#12311yescharacteristic
422Q8—84no—
423Q8—84no—
424C2×C4—24no—
425C2×C4—24no—
426C2×C4—216no—
427C2×C4—24no—
428C2×C4—41no—
429C2×C4—42no—
430C2×C4—41no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—41no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—41no—
442C2×C4—48no—
443C2×C4—432no—
444C2×C4—44no—
445C2×C4—44no—
446C2×C4—44no—
447C2×C4—48no—
448C2×C4—44no—
449C2×C4—44no—
450C2×C4—44no—
451C2×C4—44no—
452C2×C4—44no—
453C2×C4—44no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—82no—
457C2×C4—82no—
458C2×C4—82no—
459C2×C4—832no—
460C2×C4—88no—
461C2×C4—82no—
462C2×C4—82no—
463C2×C4—82no—
464C2×C4—82no—
465C2×C4#38612yes—
466C2×C4#38612yes—
467C2×C4C2×C4×D412yes—
468C2×C4C2×#12112yes—
469C8—84no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—28no—
475C22—28no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—21no—
485C22—21no—
486C22—28no—
487C22—44no—
488C22—44no—
489C22—44no—
490C22—44no—
491C22—48no—
492C22—48no—
493C22—48no—
494C22—416no—
495C22—44no—
496C22—44no—
497C22—416no—
498C22—44no—
499C22—84no—
500C22—88no—
501C22—88no—
502C22—88no—
503C22#188512yes—
504C22#188512yes—
505C22#189612yes—
506C22#189612yes—
507C22#191312yes—
508C22C2×#38611yescharacteristic
509C22C22×#10412yes—
510C22C2×#45512yes—
511C4—22no—
512C4—22no—
513C4—22no—
514C4—22no—
515C4—416no—
516C4—44no—
517C4—84no—
518C4—82no—
519C4—82no—
520C2—22no—
521C2—22no—
522C2—22no—
523C2—22no—
524C2—41no—
525C2—41no—
526C2—48no—
527C2#940714yesdirect product factor
528C2C2×#188511yescharacteristic
529C2C2×#189611yescharacteristic
530C2C2×#191311yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC26D4
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
3. C2×#1508C2semidirect
5. #9407C2direct (N × H)
6. C2×#1297C2semidirect
13. #2561C4semidirect
15. C2×#397C4semidirect
16. C2×#393C4semidirect
28. #1508C22semidirect
33. #1297C22semidirect
35. C23×Q8C2×C4semidirect
46. C2×C22⋊Q8C2×C4semidirect
49. C22×C4⋊C4C2×C4semidirect
79. #397C2×C4semidirect
81. #393C2×C4semidirect
96. C4×C22⋊C4C2×C4semidirect
103. C2×#95C2×C4semidirect
122. C22×Q8C22×C4semidirect
169. C2×C4⋊C4C22×C4semidirect
223. #95C22×C4semidirect
527. C2#9407direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#25612
C2×#22732
C2×#15082
C2×#14622
#94072
C2×#12972