Finite Group Databasebeta

← C2×#9279 #198780

Subgroups — C2×#9279 #198780

Order 512.

1126 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3228C211yesmaximal, characteristic
2C2×#2981C211yesmaximal, characteristic
3C2×#1506C211yesmaximal, characteristic, complemented
4C2×#1505C211yesmaximal, characteristic
5C2×#1497C211yesmaximal, characteristic, complemented
6#9279C218yesmaximal, direct product factor
7C2×#1287C211yesmaximal, characteristic, complemented
8C2×#1274C211yesmaximal, characteristic, complemented
9C2×#533C2211yescharacteristic
10C2×#532C2211yescharacteristic
11#3228—22no—
12#3228—22no—
13#3228C414yescomplemented
14#3228C2214yes—
15C2×#500C411yescharacteristic, complemented
16C2×#498C411yescharacteristic, complemented
17C2×#486C411yescharacteristic, complemented
18C2×#486C411yescharacteristic, complemented
19C2×#482—22no—
20C2×#478—22no—
21#2981—22no—
22#2981—22no—
23#2981—22no—
24#2981C2214yes—
25C2×#436—21no—
26C2×#435—22no—
27C2×C8×D4—21no—
28C2×#432C2211yescharacteristic
29C2×#432C2211yescharacteristic
30C2×#431C2211yescharacteristic
31C2×#431C2211yescharacteristic
32C2×#408—22no—
33C2×#376C2211yescharacteristic
34#1506—22no—
35#1506C2214yescomplemented
36#1505—22no—
37#1505C2214yes—
38C2×#328—22no—
39C2×#327—22no—
40#1497—22no—
41#1497C2214yescomplemented
42C2×Q8⋊C8—21no—
43C2×Q8⋊C8—21no—
44#1287C2214yescomplemented
45#1274C2214yescomplemented
46C22×#41—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×C42—21no—
81C22×C42C2311yescharacteristic
82#500—22no—
83#500C2×C414yescomplemented
84#498—22no—
85#498C2×C414yescomplemented
86#486—22no—
87#486—22no—
88#486C2×C414yescomplemented
89#486C2×C414yescomplemented
90#482—28no—
91#482—28no—
92#478—28no—
93#478—28no—
94#436—24no—
95#436—24no—
96#435—28no—
97#435—28no—
98C8×D4—24no—
99C8×D4—24no—
100#432—21no—
101#432—21no—
102#432—21no—
103#432—21no—
104#432—21no—
105#432D412yes—
106#432C2312yes—
107#432C2312yes—
108#431—21no—
109#431—21no—
110#431—21no—
111#431—21no—
112#431C2×C412yes—
113#431D412yes—
114#431C2312yes—
115#431C2312yes—
116C2×#107—22no—
117C2×#106—22no—
118C2×C4⋊C8—21no—
119C2×C4⋊C8—21no—
120C2×C4⋊C8—21no—
121C2×C4⋊C8—21no—
122C2×#102—22no—
123C2×#102—22no—
124#408—28no—
125#408—28no—
126C2×C22⋊C8—22no—
127C2×C22⋊C8—22no—
128C2×C22⋊C8—21no—
129C2×C22⋊C8—21no—
130C2×C22⋊C8—21no—
131C2×C22⋊C8D412yes—
132C2×#97—21no—
133C2×#97—21no—
134C2×C4×C8C2×C411yescharacteristic
135C2×C4×C8C2×C411yescharacteristic
136C2×C4×C8D411yescharacteristic
137C2×C4×C8D411yescharacteristic
138#376—21no—
139#376—21no—
140#376—21no—
141#376C2312yes—
142C2×#95—21no—
143C2×#95—21no—
144#328—28no—
145#327—28no—
146Q8⋊C8—24no—
147Q8⋊C8—24no—
148C2×#41—22no—
149C2×#41—22no—
150C2×#41—22no—
151C2×#41—22no—
152C2×#41—84no—
153C22×Q8—21no—
154C22×Q8—21no—
155C22×Q8—21no—
156C22×D4—22no—
157C22×D4—21no—
158C22×D4—21no—
159C22×D4C22⋊C412yes—
160C23×C4—22no—
161C23×C4—41no—
162C23×C4C2×D411yescharacteristic
163C23×C4C2×D411yescharacteristic
164C23×C4#4111yescharacteristic
165C2×M16—28no—
166C2×M16—84no—
167C22×C8—21no—
168C22×C8—21no—
169C22×C8—21no—
170C22×C8—22no—
171C22×C8—21no—
172C22×C8—28no—
173C22×C8—41no—
174C22×C8—84no—
175C4⋊Q8—21no—
176C4⋊Q8—21no—
177C4⋊Q8—21no—
178C4⋊Q8—21no—
179C4⋊Q8—21no—
180C4⋊Q8—21no—
181C4⋊Q8—21no—
182C4⋊Q8—21no—
183C4⋊Q8C22⋊C412yes—
184C4⋊Q8C22×C412yes—
185C4⋊Q8C22×C412yes—
186C4⋊Q8C22×C412yes—
187#127—21no—
188#127—21no—
189#127C22⋊C412yes—
190#127C22×C412yes—
191#125—22no—
192#125—22no—
193#125—41no—
194#125—41no—
195#124—22no—
196#124—22no—
197#124—22no—
198#124—22no—
199C22⋊Q8—22no—
200C22⋊Q8—22no—
201C22⋊Q8—22no—
202C22⋊Q8—22no—
203C22⋊Q8—41no—
204C22⋊Q8—41no—
205C22⋊Q8—41no—
206C22⋊Q8—41no—
207#121—22no—
208#121—22no—
209#121—22no—
210#121—22no—
211#121—22no—
212#121—22no—
213#121C22⋊C414yes—
214#121C2×D414yes—
215C4×Q8—22no—
216C4×Q8—22no—
217C4×Q8—22no—
218C4×Q8—22no—
219C4×Q8—41no—
220C4×Q8—41no—
221C4×Q8—41no—
222C4×Q8—41no—
223C4×D4—22no—
224C4×D4—22no—
225C4×D4—22no—
226C4×D4—22no—
227C4×D4—22no—
228C4×D4—22no—
229C4×D4C22⋊C414yes—
230C4×D4C2×D414yes—
231#117—22no—
232#117—22no—
233#117—41no—
234#117—41no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—41no—
241C2×C4⋊C4—41no—
242C2×C4⋊C4C22⋊C412yes—
243C2×C22⋊C4—22no—
244C2×C22⋊C4—22no—
245C2×C22⋊C4—41no—
246C2×C42—24no—
247C2×C42—22no—
248C2×C42—42no—
249C2×C42—41no—
250C2×C42—41no—
251C2×C42C22×C411yescharacteristic
252C2×C42C22×C411yescharacteristic
253C2×C42C2×D411yescharacteristic
254C2×C42C2×D411yescharacteristic
255C2×C42C2×D411yescharacteristic
256C2×C42C2×D411yescharacteristic
257C2×C42C2×D411yescharacteristic
258C2×C42C2×D411yescharacteristic
259C2×C42#4111yescharacteristic
260C2×C42#4111yescharacteristic
261C2×C42#4111yescharacteristic
262C2×C42C2411yescharacteristic
263#107—28no—
264#106—28no—
265C4⋊C8—22no—
266C4⋊C8—22no—
267C4⋊C8—22no—
268C4⋊C8—22no—
269C4⋊C8—22no—
270C4⋊C8—22no—
271C4⋊C8—22no—
272C4⋊C8—41no—
273#102—28no—
274#102—28no—
275C22⋊C8—28no—
276C22⋊C8—28no—
277C22⋊C8—22no—
278C22⋊C8—22no—
279C22⋊C8—22no—
280C22⋊C8—22no—
281C22⋊C8—22no—
282C22⋊C8—22no—
283C22⋊C8—41no—
284C22⋊C8C2×D414yes—
285#97—22no—
286#97—22no—
287#97—22no—
288#97—41no—
289C4×C8—21no—
290C4×C8—21no—
291C4×C8—21no—
292C4×C8—21no—
293C4×C8C22×C412yes—
294C4×C8C22×C412yes—
295C4×C8C2×D412yes—
296C4×C8C2×D412yes—
297#95—22no—
298#95—22no—
299#95—41no—
300#95—41no—
301C24—22no—
302C24#12111yescharacteristic
303#41—84no—
304#41—84no—
305#41—84no—
306#41—84no—
307C2×Q8—22no—
308C2×Q8—22no—
309C2×Q8—22no—
310C2×Q8—22no—
311C2×Q8—41no—
312C2×Q8—41no—
313C2×Q8—42no—
314C2×Q8—42no—
315C2×Q8—82no—
316C2×Q8—82no—
317C2×D4—24no—
318C2×D4—24no—
319C2×D4—22no—
320C2×D4—22no—
321C2×D4—22no—
322C2×D4—22no—
323C2×D4—22no—
324C2×D4—44no—
325C2×D4—42no—
326C2×D4—42no—
327C2×D4—82no—
328C2×D4—84no—
329C2×D4C2×C22⋊C414yes—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—24no—
334C22×C4—24no—
335C22×C4—42no—
336C22×C4—42no—
337C22×C4—44no—
338C22×C4—44no—
339C22×C4—44no—
340C22×C4—42no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—82no—
344C22×C4—82no—
345C22×C4C2×C22⋊C411yescharacteristic
346C22×C4C2×C22⋊C411yescharacteristic
347C22×C4C4×D411yescharacteristic
348C22×C4C4×D411yescharacteristic
349C22×C4C4×D411yescharacteristic
350C22×C4C4×D411yescharacteristic
351C22×C4#12011yescharacteristic
352C22×C4#12011yescharacteristic
353C22×C4#12111yescharacteristic
354C22×C4#12111yescharacteristic
355C22×C4#12111yescharacteristic
356C22×C4#12111yescharacteristic
357C22×C4#12111yescharacteristic
358C22×C4#12311yescharacteristic
359C22×C4#12311yescharacteristic
360C22×C4C22×D411yescharacteristic
361C22×C4C22×D411yescharacteristic
362C22×C4C2×#4111yescharacteristic
363M16—88no—
364C2×C8—22no—
365C2×C8—22no—
366C2×C8—22no—
367C2×C8—22no—
368C2×C8—24no—
369C2×C8—42no—
370C2×C8—42no—
371C2×C8—42no—
372C2×C8—44no—
373C2×C8—42no—
374C2×C8—42no—
375C2×C8—88no—
376C2×C8—82no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—22no—
384C4⋊C4—42no—
385C4⋊C4—42no—
386C4⋊C4—41no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—42no—
391C4⋊C4—42no—
392C4⋊C4C2×C22⋊C414yes—
393C22⋊C4—24no—
394C22⋊C4—24no—
395C22⋊C4—24no—
396C22⋊C4—24no—
397C22⋊C4—42no—
398C22⋊C4—42no—
399C42—24no—
400C42—44no—
401C42—42no—
402C42—42no—
403C42—42no—
404C42C2×C22⋊C411yescharacteristic
405C42C2×C22⋊C411yescharacteristic
406C42C4×D411yescharacteristic
407C42C4×D411yescharacteristic
408C42C4×D411yescharacteristic
409C42C4×D411yescharacteristic
410C42#12011yescharacteristic
411C42#12011yescharacteristic
412C42#12111yescharacteristic
413C42#12111yescharacteristic
414C42#12311yescharacteristic
415C42#12311yescharacteristic
416C42C23×C411yescharacteristic
417C42C22×D411yescharacteristic
418C42C22×D411yescharacteristic
419C42C2×#4111yescharacteristic
420C23—22no—
421C23—22no—
422C23—22no—
423C23—24no—
424C23—44no—
425C23—44no—
426C23—44no—
427C23#38611yescharacteristic
428C23#38611yescharacteristic
429C23C2×#12111yescharacteristic
430Q8—42no—
431Q8—42no—
432Q8—82no—
433Q8—82no—
434Q8—82no—
435Q8—82no—
436Q8—82no—
437D4—44no—
438D4—44no—
439D4—42no—
440D4—42no—
441D4—82no—
442D4—82no—
443D4—82no—
444D4—84no—
445D4—84no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—24no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—44no—
467C2×C4—44no—
468C2×C4—48no—
469C2×C4—44no—
470C2×C4—44no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—82no—
474C2×C4—82no—
475C2×C4—88no—
476C2×C4—82no—
477C2×C4—82no—
478C2×C4#38611yescharacteristic
479C2×C4#38611yescharacteristic
480C2×C4#38611yescharacteristic
481C2×C4#38611yescharacteristic
482C2×C4#38611yescharacteristic
483C2×C4#38611yescharacteristic
484C2×C4#44312yes—
485C2×C4#44412yes—
486C2×C4C22×C22⋊C411yescharacteristic
487C2×C4C2×C4×D411yescharacteristic
488C2×C4C2×C4×D411yescharacteristic
489C2×C4C2×#12011yescharacteristic
490C2×C4C2×#12111yescharacteristic
491C2×C4C2×#12311yescharacteristic
492C8—42no—
493C8—42no—
494C8—42no—
495C8—44no—
496C8—42no—
497C8—82no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—44no—
505C22—44no—
506C22—44no—
507C22—44no—
508C22—88no—
509C22#187612yes—
510C22#190412yes—
511C22#190912yes—
512C22C2×#38611yescharacteristic
513C4—21no—
514C4—21no—
515C4—21no—
516C4—21no—
517C4—21no—
518C4—21no—
519C4—21no—
520C4—21no—
521C4—21no—
522C4—21no—
523C4—44no—
524C4—84no—
525C4—82no—
526C4—82no—
527C4#187612yes—
528C4C2×#44311yescharacteristic
529C4C2×#44411yescharacteristic
530C2—41no—
531C2—41no—
532C2—84no—
533C2#927914yesdirect product factor
534C2C2×#187611yescharacteristic
535C2C2×#190411yescharacteristic
536C2C2×#190911yescharacteristic
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×#1506C2semidirect
5. C2×#1497C2semidirect
6. #9279C2direct (N × H)
7. C2×#1287C2semidirect
8. C2×#1274C2semidirect
13. #3228C4semidirect
15. C2×#500C4semidirect
16. C2×#498C4semidirect
17. C2×#486C4semidirect
18. C2×#486C4semidirect
35. #1506C22semidirect
41. #1497C22semidirect
44. #1287C22semidirect
45. #1274C22semidirect
83. #500C2×C4semidirect
85. #498C2×C4semidirect
88. #486C2×C4semidirect
89. #486C2×C4semidirect
533. C2#9279direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#32282
C2×#29812
C2×#15062
C2×#15052
C2×#14972
#92792
C2×#12872
C2×#12742