Finite Group Databasebeta

← C2×#9854 #206366

Subgroups — C2×#9854 #206366

Order 512.

1192 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×#3167C211yesmaximal, characteristic
2C2×#1994C211yesmaximal, characteristic, complemented
3C2×#1962C211yesmaximal, characteristic
4C2×#1744C211yesmaximal, characteristic, complemented
5C2×#1567C211yesmaximal, characteristic, complemented
6C2×#1493C211yesmaximal, characteristic, complemented
7C2×#1492C211yesmaximal, characteristic
8#9854C218yesmaximal, direct product factor
9C2×#533C2211yescharacteristic
10C2×#532C2211yescharacteristic
11#3167—22no—
12#3167—22no—
13#3167C414yescomplemented
14#3167C2214yes—
15C2×#498C411yescharacteristic, complemented
16C2×#492C411yescharacteristic, complemented
17C2×#487C411yescharacteristic, complemented
18C2×#486C411yescharacteristic, complemented
19C2×#465—22no—
20C2×C4×SD16—22no—
21C2×#423C2211yescharacteristic
22C2×#423C2211yescharacteristic
23C22×#104—22no—
24C22×C4×C8C2211yescharacteristic
25C22×C4×C8C2211yescharacteristic
26C2×C43C2211yescharacteristic
27#1994—22no—
28#1994C2214yescomplemented
29#1962—22no—
30#1962C2214yes—
31#1744—22no—
32#1744C2214yescomplemented
33C2×#339—22no—
34C2×#336—22no—
35#1567—22no—
36#1567C2214yescomplemented
37C2×#335—22no—
38#1493—22no—
39#1493C2214yescomplemented
40#1492—22no—
41#1492C2214yes—
42C2×Q8⋊C8—22no—
43C2×D4⋊C8—22no—
44C22×#41—21no—
45C22×SD16—22no—
46C22×M16—21no—
47C22×M16—21no—
48C23×C8—21no—
49C23×C8D412yes—
50#533—21no—
51#533—21no—
52#533—21no—
53#533—21no—
54#533—21no—
55#533—21no—
56#533C2×C412yes—
57#533C2312yes—
58#532—21no—
59#532—21no—
60#532—21no—
61#532—21no—
62#532—21no—
63#532—21no—
64#532C2×C412yes—
65#532C2312yes—
66C2×C4⋊Q8C2×C411yescharacteristic
67C2×C4⋊Q8C2×C411yescharacteristic
68C2×C4⋊Q8C2×C411yescharacteristic
69C2×#127C2×C411yescharacteristic
70C2×#125—21no—
71C2×#124—21no—
72C2×C22⋊Q8—21no—
73C2×C22⋊Q8—21no—
74C2×#121—21no—
75C2×#121—21no—
76C2×C4×Q8—21no—
77C2×C4×Q8—21no—
78C2×C4×D4—21no—
79C2×C4×D4—21no—
80C2×#117—21no—
81C22×C42—21no—
82C22×C42—21no—
83C22×C42D412yes—
84C22×C42C2311yescharacteristic
85#498—22no—
86#498C2×C414yescomplemented
87#492—22no—
88#492C2×C414yescomplemented
89#487—22no—
90#487C2×C414yescomplemented
91#486—22no—
92#486C2×C414yescomplemented
93#465—28no—
94#465—28no—
95C4×SD16—28no—
96C4×SD16—28no—
97C2×#106—22no—
98#423—21no—
99#423—21no—
100#423—21no—
101#423—21no—
102#423—21no—
103#423—21no—
104#423C2312yes—
105#423C2312yes—
106C2×C4⋊C8—21no—
107C2×C4⋊C8—21no—
108C2×C4⋊C8—21no—
109C2×C4⋊C8—21no—
110C2×#104—28no—
111C2×#104—48no—
112C2×#103—22no—
113C2×#102—22no—
114C2×C4×C8—21no—
115C2×C4×C8—21no—
116C2×C4×C8—21no—
117C2×C4×C8C2×C411yescharacteristic
118C2×C4×C8C2×C411yescharacteristic
119C2×C4×C8C2×C412yes—
120C2×C4×C8D412yes—
121C2×C4×C8D412yes—
122C2×C4×C8D412yes—
123C2×C4×C8D412yes—
124C2×C4×C8D412yes—
125C2×C4×C8C2312yes—
126C2×C4×C8C2312yes—
127C43—21no—
128C43—21no—
129C43D412yes—
130C43C2312yes—
131#339—28no—
132#336—28no—
133#335—28no—
134Q8⋊C8—28no—
135D4⋊C8—28no—
136C2×#41—22no—
137C2×#41—22no—
138C2×#41—41no—
139C2×#41—41no—
140C2×#41—44no—
141C2×#41—44no—
142C22×Q8—21no—
143C22×Q8—21no—
144C22×Q8—21no—
145C22×D4—21no—
146C22×D4—21no—
147C22×D4—21no—
148C22×D4—41no—
149C23×C4—22no—
150C23×C4—41no—
151C23×C4C2×D411yescharacteristic
152C23×C4C2×D411yescharacteristic
153C23×C4#4111yescharacteristic
154C2×SD16—28no—
155C2×SD16—48no—
156C2×M16—22no—
157C2×M16—22no—
158C2×M16—41no—
159C2×M16—41no—
160C2×M16—44no—
161C2×M16—44no—
162C22×C8—22no—
163C22×C8—22no—
164C22×C8—22no—
165C22×C8—44no—
166C22×C8—44no—
167C22×C8—41no—
168C22×C8—41no—
169C22×C8C22⋊C412yes—
170C22×C8C22⋊C412yes—
171C22×C8C22⋊C414yes—
172C22×C8C2×D414yes—
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⋊Q8—21no—
182C4⋊Q8C22×C412yes—
183C4⋊Q8C22×C412yes—
184C4⋊Q8C22×C412yes—
185#127—21no—
186#127—21no—
187#127—21no—
188#127C22×C412yes—
189#125—22no—
190#125—22no—
191#125—41no—
192#125—41no—
193#124—22no—
194#124—22no—
195#124—41no—
196#124—41no—
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—41no—
210#121—41no—
211#121—41no—
212#121—41no—
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—41no—
226C4×D4—41no—
227C4×D4—41no—
228C4×D4—41no—
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—21no—
239C2×C4⋊C4—41no—
240C2×C4⋊C4—41no—
241C2×C22⋊C4—41no—
242C2×C22⋊C4—41no—
243C2×C22⋊C4—41no—
244C2×C42—28no—
245C2×C42—22no—
246C2×C42—22no—
247C2×C42—24no—
248C2×C42—24no—
249C2×C42—22no—
250C2×C42—22no—
251C2×C42—22no—
252C2×C42—44no—
253C2×C42—41no—
254C2×C42C22×C411yescharacteristic
255C2×C42C22×C411yescharacteristic
256C2×C42C2×D414yes—
257C2×C42C2×D411yescharacteristic
258C2×C42C2×D411yescharacteristic
259C2×C42C2×D411yescharacteristic
260C2×C42C2×D411yescharacteristic
261C2×C42C2×D411yescharacteristic
262C2×C42C2×D411yescharacteristic
263C2×C42#4111yescharacteristic
264C2×C42#4111yescharacteristic
265C2×C42#4111yescharacteristic
266C2×C42C2411yescharacteristic
267#106—28no—
268C4⋊C8—22no—
269C4⋊C8—22no—
270C4⋊C8—22no—
271C4⋊C8—22no—
272C4⋊C8—41no—
273C4⋊C8—41no—
274C4⋊C8—41no—
275C4⋊C8—41no—
276#104—416no—
277#103—28no—
278#102—28no—
279C4×C8—22no—
280C4×C8—22no—
281C4×C8—22no—
282C4×C8C22⋊C414yes—
283C4×C8C22⋊C412yes—
284C4×C8C22⋊C412yes—
285C4×C8C22×C412yes—
286C4×C8C22×C412yes—
287C4×C8C2×D414yes—
288C4×C8C2×D414yes—
289C24—41no—
290C24#12111yescharacteristic
291#41—44no—
292#41—44no—
293#41—48no—
294#41—84no—
295#41—82no—
296#41—82no—
297C2×Q8—22no—
298C2×Q8—22no—
299C2×Q8—22no—
300C2×Q8—41no—
301C2×Q8—41no—
302C2×Q8—41no—
303C2×Q8—44no—
304C2×Q8—44no—
305C2×Q8—44no—
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—22no—
309C2×D4—42no—
310C2×D4—42no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—44no—
315C2×D4—44no—
316C2×D4—44no—
317C2×D4—84no—
318C22×C4—24no—
319C22×C4—24no—
320C22×C4—28no—
321C22×C4—24no—
322C22×C4—44no—
323C22×C4—44no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—42no—
328C22×C4—42no—
329C22×C4—82no—
330C22×C4—82no—
331C22×C4C2×C22⋊C411yescharacteristic
332C22×C4C2×C22⋊C411yescharacteristic
333C22×C4C4×D411yescharacteristic
334C22×C4C4×D411yescharacteristic
335C22×C4C4×D411yescharacteristic
336C22×C4C4×D411yescharacteristic
337C22×C4#12111yescharacteristic
338C22×C4#12111yescharacteristic
339C22×C4#12111yescharacteristic
340C22×C4#12111yescharacteristic
341C22×C4#12111yescharacteristic
342C22×C4#12411yescharacteristic
343C22×C4#12411yescharacteristic
344C22×C4#12711yescharacteristic
345C22×C4#12711yescharacteristic
346C22×C4AGL(1,ℤ/8)14yes—
347C22×C4#13714yes—
348C22×C4C22×D411yescharacteristic
349C22×C4C22×D411yescharacteristic
350C22×C4C2×#4111yescharacteristic
351SD16—416no—
352M16—44no—
353M16—44no—
354M16—82no—
355M16—82no—
356C2×C8—24no—
357C2×C8—24no—
358C2×C8—24no—
359C2×C8—44no—
360C2×C8—44no—
361C2×C8—44no—
362C2×C8—44no—
363C2×C8—44no—
364C2×C8—42no—
365C2×C8—42no—
366C2×C8—82no—
367C2×C8—82no—
368C2×C8C2×C22⋊C414yes—
369C2×C8C2×C22⋊C414yes—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—42no—
377C4⋊C4—42no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—42no—
385C4⋊C4—42no—
386C22⋊C4—42no—
387C22⋊C4—42no—
388C22⋊C4—42no—
389C22⋊C4—42no—
390C22⋊C4—42no—
391C22⋊C4—42no—
392C42—28no—
393C42—28no—
394C42—24no—
395C42—24no—
396C42—44no—
397C42—44no—
398C42—42no—
399C42—42no—
400C42—44no—
401C42C2×C22⋊C411yescharacteristic
402C42C2×C22⋊C411yescharacteristic
403C42C4×D411yescharacteristic
404C42C4×D411yescharacteristic
405C42C4×D411yescharacteristic
406C42C4×D411yescharacteristic
407C42#12111yescharacteristic
408C42#12111yescharacteristic
409C42#12411yescharacteristic
410C42#12411yescharacteristic
411C42#12711yescharacteristic
412C42#12711yescharacteristic
413C42C23×C411yescharacteristic
414C42C22×D411yescharacteristic
415C42C22×D411yescharacteristic
416C42C2×#4111yescharacteristic
417C23—22no—
418C23—22no—
419C23—42no—
420C23—82no—
421C23—82no—
422C23—82no—
423C23#39011yescharacteristic
424C23#39011yescharacteristic
425C23#46814yes—
426C23C2×#12111yescharacteristic
427Q8—44no—
428Q8—44no—
429Q8—44no—
430Q8—82no—
431Q8—82no—
432Q8—82no—
433D4—44no—
434D4—44no—
435D4—44no—
436D4—84no—
437D4—84no—
438D4—82no—
439D4—82no—
440D4—82no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—28no—
452C2×C4—44no—
453C2×C4—416no—
454C2×C4—44no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—82no—
459C2×C4—82no—
460C2×C4—82no—
461C2×C4—82no—
462C2×C4—82no—
463C2×C4—84no—
464C2×C4#39011yescharacteristic
465C2×C4#39011yescharacteristic
466C2×C4#39011yescharacteristic
467C2×C4#39011yescharacteristic
468C2×C4#39011yescharacteristic
469C2×C4#39011yescharacteristic
470C2×C4#42114yes—
471C2×C4#44014yes—
472C2×C4#44014yes—
473C2×C4#44314yes—
474C2×C4#46814yes—
475C2×C4#49612yes—
476C2×C4#49612yes—
477C2×C4#49712yes—
478C2×C4#49712yes—
479C2×C4C22×C22⋊C411yescharacteristic
480C2×C4C2×C4×D411yescharacteristic
481C2×C4C2×C4×D411yescharacteristic
482C2×C4C2×#12111yescharacteristic
483C2×C4C2×#12411yescharacteristic
484C2×C4C2×#12711yescharacteristic
485C2×C4C2×AGL(1,ℤ/8)12yes—
486C2×C4C2×#13712yes—
487C8—24no—
488C8—24no—
489C8—44no—
490C8—82no—
491C8—82no—
492C22—28no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—82no—
498C22—82no—
499C22—82no—
500C22—164no—
501C22#196312yes—
502C22#197312yes—
503C22#197312yes—
504C22#197412yes—
505C22C2×#39011yescharacteristic
506C22C2×#46812yes—
507C4—21no—
508C4—21no—
509C4—21no—
510C4—21no—
511C4—48no—
512C4—82no—
513C4—82no—
514C4—82no—
515C4#196312yes—
516C4#197312yes—
517C4#197312yes—
518C4#197412yes—
519C4C2×#42112yes—
520C4C2×#44012yes—
521C4C2×#44312yes—
522C4C2×#49611yescharacteristic
523C4C2×#49711yescharacteristic
524C2—22no—
525C2—22no—
526C2—162no—
527C2#985414yesdirect product factor
528C2C2×#196311yescharacteristic
529C2C2×#197311yescharacteristic
530C2C2×#197411yescharacteristic
subgroupG/H
centerC22×C4#127
commutatorC42C23×C4
Frattini, cosocleC2×C42C24
socleC23#390
prime radicalC2×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1994C2semidirect
4. C2×#1744C2semidirect
5. C2×#1567C2semidirect
6. C2×#1493C2semidirect
8. #9854C2direct (N × H)
13. #3167C4semidirect
15. C2×#498C4semidirect
16. C2×#492C4semidirect
17. C2×#487C4semidirect
18. C2×#486C4semidirect
28. #1994C22semidirect
32. #1744C22semidirect
36. #1567C22semidirect
39. #1493C22semidirect
86. #498C2×C4semidirect
88. #492C2×C4semidirect
90. #487C2×C4semidirect
92. #486C2×C4semidirect
527. C2#9854direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#31672
C2×#19942
C2×#19622
C2×#17442
C2×#15672
C2×#14932
C2×#14922
#98542