Finite Group Databasebeta

← C2×#9415 #200692

Subgroups — C2×#9415 #200692

Order 512.

1124 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3182C211yesmaximal, characteristic
2C2×#2980C211yesmaximal, characteristic
3C2×#1537C211yesmaximal, characteristic, complemented
4C2×#1515C211yesmaximal, characteristic, complemented
5C2×#1514C211yesmaximal, characteristic
6#9415C218yesmaximal, direct product factor
7C2×#1291C211yesmaximal, characteristic, complemented
8C2×#1288C211yesmaximal, characteristic, complemented
9C2×#533C2211yescharacteristic
10C2×#532C2211yescharacteristic
11#3182—22no—
12#3182—22no—
13#3182C414yescomplemented
14#3182C2214yes—
15C2×#500C411yescharacteristic, complemented
16C2×#492C411yescharacteristic, complemented
17C2×#487C411yescharacteristic, complemented
18C2×#486C411yescharacteristic, complemented
19C2×#468—22no—
20#2980—22no—
21#2980—22no—
22#2980—22no—
23#2980C2214yes—
24C2×#440—22no—
25C2×#435—22no—
26C2×#435—22no—
27C2×#432C2211yescharacteristic
28C2×#432C2211yescharacteristic
29C2×#432C2211yescharacteristic
30C2×#408—22no—
31C2×C4×M16C2211yescharacteristic
32C2×#383C2211yescharacteristic
33#1537—22no—
34#1537C2214yescomplemented
35C2×#330—22no—
36#1515—22no—
37#1515C2214yescomplemented
38#1514—22no—
39#1514C2214yes—
40C2×#328—22no—
41C2×#327—22no—
42#1291C2214yescomplemented
43#1288C2214yescomplemented
44C22×#41—21no—
45C22×SD16—22no—
46C22×M16—21no—
47C22×M16—22no—
48C23×C8—22no—
49#533—21no—
50#533—21no—
51#533—21no—
52#533—21no—
53#533—21no—
54#533—21no—
55#533C2×C412yes—
56#533C2312yes—
57#532—21no—
58#532—21no—
59#532—21no—
60#532—21no—
61#532C2×C412yes—
62#532D412yes—
63#532D412yes—
64#532C2312yes—
65C2×C4⋊Q8C2×C411yescharacteristic
66C2×C4⋊Q8C2×C411yescharacteristic
67C2×C4⋊Q8C2×C411yescharacteristic
68C2×#127C2×C411yescharacteristic
69C2×#125—21no—
70C2×#124—21no—
71C2×C22⋊Q8—21no—
72C2×C22⋊Q8—21no—
73C2×#121—21no—
74C2×#121D412yes—
75C2×C4×Q8—21no—
76C2×C4×Q8—21no—
77C2×C4×D4—21no—
78C2×C4×D4D412yes—
79C2×#117—21no—
80C22×C42C2311yescharacteristic
81#500—22no—
82#500C2×C414yescomplemented
83#492—22no—
84#492C2×C414yescomplemented
85#487—22no—
86#487C2×C414yescomplemented
87#486—22no—
88#486C2×C414yescomplemented
89#468—28no—
90#468—28no—
91#440—28no—
92#440—28no—
93#435—28no—
94#435—28no—
95#435—28no—
96#435—28no—
97#432—21no—
98#432—21no—
99#432—21no—
100#432—21no—
101#432—21no—
102#432—21no—
103#432—21no—
104#432D412yes—
105#432D412yes—
106#432C2312yes—
107#432C2312yes—
108#432C2312yes—
109C2×#107—22no—
110C2×C4⋊C8—21no—
111C2×C4⋊C8—21no—
112C2×C4⋊C8—21no—
113C2×#103—22no—
114C2×#102—22no—
115#408—28no—
116#408—28no—
117C2×C22⋊C8—24no—
118C2×C22⋊C8—21no—
119C2×C22⋊C8—21no—
120C2×C22⋊C8D412yes—
121C4×M16—21no—
122C4×M16—21no—
123C4×M16C2×C412yes—
124C4×M16C2312yes—
125C2×#97—21no—
126C2×#97—21no—
127C2×#97—21no—
128C2×#97D412yes—
129C2×C4×C8C2×C411yescharacteristic
130C2×C4×C8C2×C411yescharacteristic
131#383—21no—
132#383—21no—
133#383—21no—
134#383C2312yes—
135C2×#95—21no—
136C2×#95—21no—
137C2×#95—21no—
138#330—28no—
139#328—28no—
140#327—28no—
141C2×#41—22no—
142C2×#41—22no—
143C2×#41—22no—
144C2×#41—22no—
145C2×#41—82no—
146C2×#41—82no—
147C22×Q8—21no—
148C22×Q8—21no—
149C22×Q8—21no—
150C22×D4—22no—
151C22×D4—21no—
152C22×D4—21no—
153C22×D4C22⋊C412yes—
154C23×C4—22no—
155C23×C4—41no—
156C23×C4C2×D411yescharacteristic
157C23×C4C2×D411yescharacteristic
158C23×C4#4111yescharacteristic
159C2×SD16—28no—
160C2×SD16—48no—
161C2×M16—22no—
162C2×M16—22no—
163C2×M16—28no—
164C2×M16—44no—
165C2×M16—84no—
166C22×C8—21no—
167C22×C8—21no—
168C22×C8—22no—
169C22×C8—22no—
170C22×C8—28no—
171C22×C8—41no—
172C22×C8—84no—
173C4⋊Q8—21no—
174C4⋊Q8—21no—
175C4⋊Q8—21no—
176C4⋊Q8—21no—
177C4⋊Q8—21no—
178C4⋊Q8—21no—
179C4⋊Q8—21no—
180C4⋊Q8—21no—
181C4⋊Q8C22⋊C412yes—
182C4⋊Q8C22×C412yes—
183C4⋊Q8C22×C412yes—
184C4⋊Q8C22×C412yes—
185#127—21no—
186#127—21no—
187#127C22⋊C412yes—
188#127C22×C412yes—
189#125—22no—
190#125—22no—
191#125—41no—
192#125—41no—
193#124—22no—
194#124—22no—
195#124—22no—
196#124—22no—
197C22⋊Q8—22no—
198C22⋊Q8—22no—
199C22⋊Q8—22no—
200C22⋊Q8—22no—
201C22⋊Q8—41no—
202C22⋊Q8—41no—
203C22⋊Q8—41no—
204C22⋊Q8—41no—
205#121—22no—
206#121—22no—
207#121—22no—
208#121—22no—
209#121—22no—
210#121—22no—
211#121C22⋊C414yes—
212#121C2×D414yes—
213C4×Q8—22no—
214C4×Q8—22no—
215C4×Q8—22no—
216C4×Q8—22no—
217C4×Q8—41no—
218C4×Q8—41no—
219C4×Q8—41no—
220C4×Q8—41no—
221C4×D4—22no—
222C4×D4—22no—
223C4×D4—22no—
224C4×D4—22no—
225C4×D4—22no—
226C4×D4—22no—
227C4×D4C22⋊C414yes—
228C4×D4C2×D414yes—
229#117—22no—
230#117—22no—
231#117—41no—
232#117—41no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—41no—
239C2×C4⋊C4—41no—
240C2×C4⋊C4C22⋊C412yes—
241C2×C22⋊C4—22no—
242C2×C22⋊C4—22no—
243C2×C22⋊C4—41no—
244C2×C42—41no—
245C2×C42C22×C411yescharacteristic
246C2×C42C22×C411yescharacteristic
247C2×C42C2×D411yescharacteristic
248C2×C42C2×D411yescharacteristic
249C2×C42C2×D411yescharacteristic
250C2×C42C2×D411yescharacteristic
251C2×C42C2×D411yescharacteristic
252C2×C42C2×D411yescharacteristic
253C2×C42#4111yescharacteristic
254C2×C42#4111yescharacteristic
255C2×C42#4111yescharacteristic
256C2×C42C2411yescharacteristic
257#107—28no—
258C4⋊C8—22no—
259C4⋊C8—22no—
260C4⋊C8—22no—
261C4⋊C8—22no—
262C4⋊C8—22no—
263C4⋊C8—41no—
264#103—28no—
265#102—28no—
266C22⋊C8—216no—
267C22⋊C8—22no—
268C22⋊C8—22no—
269C22⋊C8—22no—
270C22⋊C8—22no—
271C22⋊C8—41no—
272C22⋊C8C2×D414yes—
273#97—22no—
274#97—22no—
275#97—22no—
276#97—22no—
277#97—22no—
278#97—22no—
279#97—41no—
280#97C2×D414yes—
281C4×C8—21no—
282C4×C8—21no—
283C4×C8C22×C412yes—
284C4×C8C22×C412yes—
285#95—22no—
286#95—22no—
287#95—22no—
288#95—41no—
289#95—41no—
290#95—41no—
291C24—22no—
292C24#12111yescharacteristic
293#41—84no—
294#41—82no—
295#41—82no—
296#41—84no—
297#41—82no—
298#41—82no—
299C2×Q8—22no—
300C2×Q8—22no—
301C2×Q8—22no—
302C2×Q8—22no—
303C2×Q8—44no—
304C2×Q8—41no—
305C2×Q8—41no—
306C2×Q8—82no—
307C2×Q8—82no—
308C2×D4—24no—
309C2×D4—24no—
310C2×D4—22no—
311C2×D4—22no—
312C2×D4—22no—
313C2×D4—22no—
314C2×D4—22no—
315C2×D4—44no—
316C2×D4—82no—
317C2×D4—82no—
318C2×D4—84no—
319C2×D4C2×C22⋊C414yes—
320C22×C4—22no—
321C22×C4—24no—
322C22×C4—24no—
323C22×C4—42no—
324C22×C4—42no—
325C22×C4—42no—
326C22×C4—44no—
327C22×C4—44no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—42no—
331C22×C4—82no—
332C22×C4—82no—
333C22×C4—82no—
334C22×C4C2×C22⋊C411yescharacteristic
335C22×C4C2×C22⋊C411yescharacteristic
336C22×C4C4×D411yescharacteristic
337C22×C4C4×D411yescharacteristic
338C22×C4C4×D411yescharacteristic
339C22×C4C4×D411yescharacteristic
340C22×C4#12011yescharacteristic
341C22×C4#12011yescharacteristic
342C22×C4#12111yescharacteristic
343C22×C4#12111yescharacteristic
344C22×C4#12111yescharacteristic
345C22×C4#12111yescharacteristic
346C22×C4#12111yescharacteristic
347C22×C4#12311yescharacteristic
348C22×C4#12311yescharacteristic
349C22×C4C22×D411yescharacteristic
350C22×C4C22×D411yescharacteristic
351C22×C4C2×#4111yescharacteristic
352SD16—416no—
353M16—44no—
354M16—44no—
355M16—88no—
356C2×C8—24no—
357C2×C8—22no—
358C2×C8—22no—
359C2×C8—24no—
360C2×C8—24no—
361C2×C8—44no—
362C2×C8—44no—
363C2×C8—42no—
364C2×C8—42no—
365C2×C8—88no—
366C2×C8—82no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—42no—
375C4⋊C4—42no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—42no—
381C4⋊C4—42no—
382C4⋊C4C2×C22⋊C414yes—
383C22⋊C4—24no—
384C22⋊C4—24no—
385C22⋊C4—24no—
386C22⋊C4—24no—
387C22⋊C4—42no—
388C22⋊C4—42no—
389C42—42no—
390C42—42no—
391C42C2×C22⋊C411yescharacteristic
392C42C2×C22⋊C411yescharacteristic
393C42C4×D411yescharacteristic
394C42C4×D411yescharacteristic
395C42C4×D411yescharacteristic
396C42C4×D411yescharacteristic
397C42#12011yescharacteristic
398C42#12011yescharacteristic
399C42#12111yescharacteristic
400C42#12111yescharacteristic
401C42#12311yescharacteristic
402C42#12311yescharacteristic
403C42C23×C411yescharacteristic
404C42C22×D411yescharacteristic
405C42C22×D411yescharacteristic
406C42C2×#4111yescharacteristic
407C23—22no—
408C23—22no—
409C23—22no—
410C23—24no—
411C23—44no—
412C23—44no—
413C23—44no—
414C23#38611yescharacteristic
415C23#38611yescharacteristic
416C23C2×#12111yescharacteristic
417Q8—44no—
418Q8—82no—
419Q8—82no—
420Q8—82no—
421Q8—82no—
422Q8—82no—
423D4—44no—
424D4—82no—
425D4—82no—
426D4—82no—
427D4—82no—
428D4—82no—
429D4—84no—
430D4—84no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—24no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—44no—
451C2×C4—44no—
452C2×C4—48no—
453C2×C4—44no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—82no—
457C2×C4—82no—
458C2×C4—82no—
459C2×C4—82no—
460C2×C4—82no—
461C2×C4—164no—
462C2×C4#38611yescharacteristic
463C2×C4#38611yescharacteristic
464C2×C4#38611yescharacteristic
465C2×C4#38611yescharacteristic
466C2×C4#38611yescharacteristic
467C2×C4#38611yescharacteristic
468C2×C4C22×C22⋊C411yescharacteristic
469C2×C4C2×C4×D411yescharacteristic
470C2×C4C2×C4×D411yescharacteristic
471C2×C4C2×#12011yescharacteristic
472C2×C4C2×#12111yescharacteristic
473C2×C4C2×#12311yescharacteristic
474C8—24no—
475C8—44no—
476C8—44no—
477C8—42no—
478C8—82no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—21no—
485C22—44no—
486C22—44no—
487C22—44no—
488C22—44no—
489C22—88no—
490C22#188412yes—
491C22#190212yes—
492C22#190412yes—
493C22C2×#38611yescharacteristic
494C4—21no—
495C4—21no—
496C4—21no—
497C4—21no—
498C4—21no—
499C4—21no—
500C4—21no—
501C4—21no—
502C4—21no—
503C4—21no—
504C4—21no—
505C4—21no—
506C4—44no—
507C4—82no—
508C4—82no—
509C4—162no—
510C2—41no—
511C2—41no—
512C2—84no—
513C2#941514yesdirect product factor
514C2C2×#188411yescharacteristic
515C2C2×#190211yescharacteristic
516C2C2×#190411yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC42C23×C4
Frattini, cosocleC2×C42C24
prime radicalC2×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×#1537C2semidirect
4. C2×#1515C2semidirect
6. #9415C2direct (N × H)
7. C2×#1291C2semidirect
8. C2×#1288C2semidirect
13. #3182C4semidirect
15. C2×#500C4semidirect
16. C2×#492C4semidirect
17. C2×#487C4semidirect
18. C2×#486C4semidirect
34. #1537C22semidirect
37. #1515C22semidirect
42. #1291C22semidirect
43. #1288C22semidirect
82. #500C2×C4semidirect
84. #492C2×C4semidirect
86. #487C2×C4semidirect
88. #486C2×C4semidirect
513. C2#9415direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#31822
C2×#29802
C2×#15372
C2×#15152
C2×#15142
#94152
C2×#12912
C2×#12882