Finite Group Databasebeta

← C2×#9417 #200693

Subgroups — C2×#9417 #200693

Order 512.

1194 conjugacy classes of subgroups.

The subgroup lattice has 541 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3184C211yesmaximal, characteristic
2C2×#2980C211yesmaximal, characteristic, complemented
3C2×#1536C211yesmaximal, characteristic, complemented
4C2×#1514C211yesmaximal, characteristic, complemented
5C2×#1514C211yesmaximal, characteristic, complemented
6#9417C218yesmaximal, direct product factor
7C2×#1291C211yesmaximal, characteristic, complemented
8C2×#1288C211yesmaximal, characteristic, complemented
9C2×#532C2211yescharacteristic
10C2×#532C2211yescharacteristic
11#3184—22no—
12#3184—22no—
13#3184C414yescomplemented
14#3184C2214yes—
15C2×#498C411yescharacteristic, complemented
16C2×#493C411yescharacteristic, complemented
17C2×#486C411yescharacteristic, complemented
18C2×#486C411yescharacteristic, complemented
19C2×#469—22no—
20#2980—22no—
21#2980—22no—
22#2980—22no—
23#2980C2214yescomplemented
24C2×#442—22no—
25C2×#435—22no—
26C2×#435—22no—
27C2×#432C2211yescharacteristic
28C2×#432C2211yescharacteristic
29C2×#432C2211yescharacteristic
30C2×#408—22no—
31C2×C4×M16C2211yescharacteristic
32C2×#383C2211yescharacteristic
33#1536—22no—
34#1536C2214yescomplemented
35C2×#329—22no—
36#1514—22no—
37#1514—22no—
38#1514C2214yescomplemented
39#1514C2214yescomplemented
40C2×#327—22no—
41C2×#327—22no—
42#1291C2214yescomplemented
43#1288C2214yescomplemented
44C22×#41—21no—
45C22×#41—21no—
46C22×D8—22no—
47C22×M16—21no—
48C22×M16—22no—
49C23×C8—22no—
50#532—21no—
51#532—21no—
52#532—21no—
53#532—21no—
54#532—21no—
55#532—21no—
56#532—21no—
57#532—21no—
58#532—21no—
59#532—21no—
60#532C2×C412yes—
61#532C2×C412yes—
62#532D412yes—
63#532D412yes—
64#532C2312yes—
65#532C2312yes—
66C2×C4⋊Q8C2×C411yescharacteristic
67C2×C4⋊Q8C2×C411yescharacteristic
68C2×#127C2×C411yescharacteristic
69C2×#127C2×C411yescharacteristic
70C2×#124—21no—
71C2×#124—21no—
72C2×#121—21no—
73C2×#121—21no—
74C2×#121—21no—
75C2×#121D412yes—
76C2×C4×D4—21no—
77C2×C4×D4—21no—
78C2×C4×D4—21no—
79C2×C4×D4D412yes—
80C22×C42C2311yescharacteristic
81#498—22no—
82#498C2×C414yescomplemented
83#493—22no—
84#493C2×C414yescomplemented
85#486—22no—
86#486—22no—
87#486C2×C414yescomplemented
88#486C2×C414yescomplemented
89#469—28no—
90#469—28no—
91#442—28no—
92#442—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×#106—22no—
110C2×C4⋊C8—21no—
111C2×C4⋊C8—21no—
112C2×C4⋊C8—21no—
113C2×#102—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#329—28no—
139#327—28no—
140#327—28no—
141C2×#41—22no—
142C2×#41—22no—
143C2×#41—22no—
144C2×#41—22no—
145C2×#41—22no—
146C2×#41—22no—
147C2×#41—41no—
148C2×#41—41no—
149C2×#41—82no—
150C2×#41—82no—
151C2×#41—84no—
152C22×Q8—21no—
153C22×Q8—21no—
154C22×D4—22no—
155C22×D4—21no—
156C22×D4—21no—
157C22×D4—21no—
158C22×D4—21no—
159C22×D4—21no—
160C22×D4—41no—
161C22×D4C22⋊C412yes—
162C23×C4—22no—
163C23×C4—41no—
164C23×C4—41no—
165C23×C4C2×D411yescharacteristic
166C23×C4C2×D411yescharacteristic
167C23×C4#4111yescharacteristic
168C2×D8—28no—
169C2×D8—48no—
170C2×M16—22no—
171C2×M16—22no—
172C2×M16—28no—
173C2×M16—44no—
174C2×M16—84no—
175C22×C8—21no—
176C22×C8—21no—
177C22×C8—22no—
178C22×C8—22no—
179C22×C8—28no—
180C22×C8—41no—
181C22×C8—84no—
182C4⋊Q8—21no—
183C4⋊Q8—21no—
184C4⋊Q8—21no—
185C4⋊Q8—21no—
186C4⋊Q8—21no—
187C4⋊Q8C22⋊C412yes—
188C4⋊Q8C22×C412yes—
189C4⋊Q8C22×C412yes—
190#127—21no—
191#127—21no—
192#127—21no—
193#127—21no—
194#127—21no—
195#127C22⋊C412yes—
196#127C22×C412yes—
197#127C22×C412yes—
198#124—22no—
199#124—22no—
200#124—22no—
201#124—22no—
202#124—22no—
203#124—22no—
204#124—41no—
205#124—41no—
206#121—22no—
207#121—22no—
208#121—22no—
209#121—22no—
210#121—22no—
211#121—22no—
212#121—22no—
213#121—22no—
214#121—22no—
215#121—22no—
216#121—41no—
217#121—41no—
218#121—41no—
219#121—41no—
220#121C22⋊C414yes—
221#121C2×D414yes—
222C4×D4—22no—
223C4×D4—22no—
224C4×D4—22no—
225C4×D4—22no—
226C4×D4—22no—
227C4×D4—22no—
228C4×D4—22no—
229C4×D4—22no—
230C4×D4—22no—
231C4×D4—22no—
232C4×D4—41no—
233C4×D4—41no—
234C4×D4—41no—
235C4×D4—41no—
236C4×D4C22⋊C414yes—
237C4×D4C2×D414yes—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4C22⋊C412yes—
242C2×C22⋊C4—22no—
243C2×C22⋊C4—22no—
244C2×C22⋊C4—41no—
245C2×C22⋊C4—41no—
246C2×C42C22×C411yescharacteristic
247C2×C42C22×C411yescharacteristic
248C2×C42C2×D411yescharacteristic
249C2×C42C2×D411yescharacteristic
250C2×C42C2×D411yescharacteristic
251C2×C42C2×D411yescharacteristic
252C2×C42C2×D411yescharacteristic
253C2×C42C2×D411yescharacteristic
254C2×C42#4111yescharacteristic
255C2×C42#4111yescharacteristic
256C2×C42#4111yescharacteristic
257C2×C42C2411yescharacteristic
258#106—28no—
259C4⋊C8—22no—
260C4⋊C8—22no—
261C4⋊C8—22no—
262C4⋊C8—22no—
263C4⋊C8—22no—
264C4⋊C8—41no—
265#102—28no—
266#102—28no—
267C22⋊C8—216no—
268C22⋊C8—22no—
269C22⋊C8—22no—
270C22⋊C8—22no—
271C22⋊C8—22no—
272C22⋊C8—41no—
273C22⋊C8C2×D414yes—
274#97—22no—
275#97—22no—
276#97—22no—
277#97—22no—
278#97—22no—
279#97—22no—
280#97—41no—
281#97C2×D414yes—
282C4×C8—21no—
283C4×C8—21no—
284C4×C8C22×C412yes—
285C4×C8C22×C412yes—
286#95—22no—
287#95—22no—
288#95—22no—
289#95—41no—
290#95—41no—
291#95—41no—
292C24—22no—
293C24—41no—
294C24#12111yescharacteristic
295#41—84no—
296#41—82no—
297#41—82no—
298#41—84no—
299#41—82no—
300#41—82no—
301#41—84no—
302#41—84no—
303#41—84no—
304#41—84no—
305C2×Q8—22no—
306C2×Q8—22no—
307C2×Q8—22no—
308C2×Q8—41no—
309C2×Q8—82no—
310C2×Q8—82no—
311C2×D4—24no—
312C2×D4—24no—
313C2×D4—22no—
314C2×D4—22no—
315C2×D4—22no—
316C2×D4—22no—
317C2×D4—22no—
318C2×D4—22no—
319C2×D4—22no—
320C2×D4—22no—
321C2×D4—44no—
322C2×D4—44no—
323C2×D4—42no—
324C2×D4—42no—
325C2×D4—41no—
326C2×D4—41no—
327C2×D4—41no—
328C2×D4—82no—
329C2×D4—82no—
330C2×D4—82no—
331C2×D4—82no—
332C2×D4—84no—
333C2×D4—84no—
334C2×D4C2×C22⋊C414yes—
335C22×C4—22no—
336C22×C4—24no—
337C22×C4—24no—
338C22×C4—42no—
339C22×C4—42no—
340C22×C4—42no—
341C22×C4—44no—
342C22×C4—44no—
343C22×C4—41no—
344C22×C4—42no—
345C22×C4—42no—
346C22×C4—42no—
347C22×C4—84no—
348C22×C4—82no—
349C22×C4—82no—
350C22×C4—82no—
351C22×C4C2×C22⋊C411yescharacteristic
352C22×C4C2×C22⋊C411yescharacteristic
353C22×C4C4×D411yescharacteristic
354C22×C4C4×D411yescharacteristic
355C22×C4C4×D411yescharacteristic
356C22×C4C4×D411yescharacteristic
357C22×C4#12011yescharacteristic
358C22×C4#12011yescharacteristic
359C22×C4#12111yescharacteristic
360C22×C4#12111yescharacteristic
361C22×C4#12111yescharacteristic
362C22×C4#12111yescharacteristic
363C22×C4#12111yescharacteristic
364C22×C4#12311yescharacteristic
365C22×C4#12311yescharacteristic
366C22×C4C22×D411yescharacteristic
367C22×C4C22×D411yescharacteristic
368C22×C4C2×#4111yescharacteristic
369D8—416no—
370M16—44no—
371M16—44no—
372M16—88no—
373C2×C8—24no—
374C2×C8—22no—
375C2×C8—22no—
376C2×C8—24no—
377C2×C8—24no—
378C2×C8—44no—
379C2×C8—44no—
380C2×C8—42no—
381C2×C8—42no—
382C2×C8—88no—
383C2×C8—82no—
384C4⋊C4—22no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4C2×C22⋊C414yes—
392C22⋊C4—24no—
393C22⋊C4—24no—
394C22⋊C4—24no—
395C22⋊C4—24no—
396C22⋊C4—42no—
397C22⋊C4—42no—
398C22⋊C4—42no—
399C22⋊C4—42no—
400C42C2×C22⋊C411yescharacteristic
401C42C2×C22⋊C411yescharacteristic
402C42C4×D411yescharacteristic
403C42C4×D411yescharacteristic
404C42C4×D411yescharacteristic
405C42C4×D411yescharacteristic
406C42#12011yescharacteristic
407C42#12011yescharacteristic
408C42#12111yescharacteristic
409C42#12111yescharacteristic
410C42#12311yescharacteristic
411C42#12311yescharacteristic
412C42C23×C411yescharacteristic
413C42C22×D411yescharacteristic
414C42C22×D411yescharacteristic
415C42C2×#4111yescharacteristic
416C23—22no—
417C23—22no—
418C23—22no—
419C23—24no—
420C23—44no—
421C23—44no—
422C23—44no—
423C23—42no—
424C23—82no—
425C23—82no—
426C23—82no—
427C23#38611yescharacteristic
428C23#38611yescharacteristic
429C23C2×#12111yescharacteristic
430Q8—82no—
431Q8—82no—
432Q8—82no—
433Q8—82no—
434D4—44no—
435D4—44no—
436D4—82no—
437D4—82no—
438D4—82no—
439D4—82no—
440D4—82no—
441D4—82no—
442D4—82no—
443D4—82no—
444D4—82no—
445D4—82no—
446D4—84no—
447D4—84no—
448D4—84no—
449D4—84no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—24no—
457C2×C4—41no—
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—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—44no—
470C2×C4—44no—
471C2×C4—48no—
472C2×C4—44no—
473C2×C4—42no—
474C2×C4—84no—
475C2×C4—84no—
476C2×C4—82no—
477C2×C4—82no—
478C2×C4—82no—
479C2×C4—82no—
480C2×C4—164no—
481C2×C4#38611yescharacteristic
482C2×C4#38611yescharacteristic
483C2×C4#38611yescharacteristic
484C2×C4#38611yescharacteristic
485C2×C4#38611yescharacteristic
486C2×C4#38611yescharacteristic
487C2×C4C22×C22⋊C411yescharacteristic
488C2×C4C2×C4×D411yescharacteristic
489C2×C4C2×C4×D411yescharacteristic
490C2×C4C2×#12011yescharacteristic
491C2×C4C2×#12111yescharacteristic
492C2×C4C2×#12311yescharacteristic
493C8—24no—
494C8—44no—
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—82no—
510C22—82no—
511C22—82no—
512C22—164no—
513C22#188412yes—
514C22#190312yes—
515C22#190412yes—
516C22C2×#38611yescharacteristic
517C4—21no—
518C4—21no—
519C4—21no—
520C4—21no—
521C4—21no—
522C4—21no—
523C4—21no—
524C4—21no—
525C4—21no—
526C4—21no—
527C4—21no—
528C4—21no—
529C4—44no—
530C4—82no—
531C4—162no—
532C2—41no—
533C2—41no—
534C2—84no—
535C2—162no—
536C2#941714yesdirect product factor
537C2C2×#188411yescharacteristic
538C2C2×#190311yescharacteristic
539C2C2×#190411yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC42C23×C4
Frattini, cosocleC2×C42C24
prime radicalC2×#3184C2
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
2. C2×#2980C2semidirect
3. C2×#1536C2semidirect
4. C2×#1514C2semidirect
5. C2×#1514C2semidirect
6. #9417C2direct (N × H)
7. C2×#1291C2semidirect
8. C2×#1288C2semidirect
13. #3184C4semidirect
15. C2×#498C4semidirect
16. C2×#493C4semidirect
17. C2×#486C4semidirect
18. C2×#486C4semidirect
23. #2980C22semidirect
34. #1536C22semidirect
38. #1514C22semidirect
39. #1514C22semidirect
42. #1291C22semidirect
43. #1288C22semidirect
82. #498C2×C4semidirect
84. #493C2×C4semidirect
87. #486C2×C4semidirect
88. #486C2×C4semidirect
536. C2#9417direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#31842
C2×#29802
C2×#15362
C2×#15142
#94172
C2×#12912
C2×#12882