Finite Group Databasebeta

← C2×#9154 #196809

Subgroups — C2×#9154 #196809

Order 512.

2906 conjugacy classes of subgroups.

The subgroup lattice has 489 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2848C211yesmaximal, characteristic
2C22×#381C211yesmaximal, characteristic
3C2×#1779C211yesmaximal, characteristic
4C22×#328C212yesmaximal, complemented
5#9154C218yesmaximal, direct product factor
6C2×#1294C212yesmaximal, complemented
7C25×C4C2211yescharacteristic
8C22×C22⋊Q8C412yescomplemented
9C22×C22⋊Q8C2211yescharacteristic
10C23×C22⋊C4—21no—
11C22×C22⋊C8—22no—
12C22×C22⋊C8C2212yes—
13#2848—22no—
14#2848—22no—
15#2848C414yescomplemented
16#2848C2214yes—
17C2×#385—22no—
18C2×#385—21no—
19C2×#381—28no—
20C2×#381—22no—
21C2×#381C2214yes—
22C2×#380C412yescomplemented
23C2×#380C2211yescharacteristic
24C2×#379—21no—
25C22×#95—21no—
26C22×#95C2212yes—
27#1779—22no—
28#1779C2214yes—
29C2×#328—28no—
30C2×#328C2218yescomplemented
31#1294C2218yescomplemented
32C26D411yescharacteristic
33C23×Q8C2×C411yescharacteristic
34C24×C4—24no—
35C24×C4—24no—
36C24×C4—22no—
37C24×C4—48no—
38C24×C4C2×C412yes—
39C24×C4C2×C412yes—
40C24×C4D412yes—
41C24×C4D412yes—
42C24×C4D411yescharacteristic
43C24×C4D412yes—
44C24×C4C2312yes—
45C24×C4C2311yescharacteristic
46C23×C8—22no—
47C2×C22⋊Q8—24no—
48C2×C22⋊Q8—21no—
49C2×C22⋊Q8—21no—
50C2×C22⋊Q8—24no—
51C2×C22⋊Q8—24no—
52C2×C22⋊Q8—48no—
53C2×C22⋊Q8C2×C412yes—
54C2×C22⋊Q8C2×C418yescomplemented
55C2×C22⋊Q8C2312yes—
56C22×C4⋊C4—22no—
57C22×C4⋊C4—21no—
58C22×C4⋊C4C2×C411yescharacteristic
59C22×C4⋊C4C2×C412yes—
60C22×C22⋊C4—28no—
61C22×C22⋊C4—22no—
62C22×C22⋊C4—22no—
63C22×C22⋊C4—24no—
64C22×C22⋊C4—21no—
65C22×C22⋊C4—21no—
66C22×C22⋊C4—48no—
67C2×C22⋊C8—24no—
68C2×C22⋊C8—24no—
69C2×C22⋊C8—28no—
70C2×C22⋊C8—22no—
71C2×C22⋊C8—48no—
72C2×C22⋊C8C2314yes—
73#385—28no—
74#385—24no—
75#385—24no—
76#385—28no—
77#381—216no—
78#381—216no—
79#380—24no—
80#380—21no—
81#380—21no—
82#380C2×C412yes—
83#380C2×C418yescomplemented
84#380C2312yes—
85#379—24no—
86#379—24no—
87C2×#95—28no—
88C2×#95—22no—
89C2×#95—24no—
90C2×#95—22no—
91C2×#95—24no—
92C2×#95—21no—
93C2×#95D418yes—
94C2×#95C2314yes—
95#328—216no—
96C25—28no—
97C25—22no—
98C25—22no—
99C25—24no—
100C25—24no—
101C25—44no—
102C25C22⋊C412yes—
103C25C22⋊C412yes—
104C25C2×D412yes—
105C25C2×D411yescharacteristic
106C22×Q8—21no—
107C22×Q8—24no—
108C22×Q8—44no—
109C22×Q8C22×C412yes—
110C23×C4—28no—
111C23×C4—28no—
112C23×C4—22no—
113C23×C4—22no—
114C23×C4—28no—
115C23×C4—28no—
116C23×C4—24no—
117C23×C4—28no—
118C23×C4—28no—
119C23×C4—24no—
120C23×C4—24no—
121C23×C4—24no—
122C23×C4—21no—
123C23×C4—21no—
124C23×C4—22no—
125C23×C4—28no—
126C23×C4—24no—
127C23×C4—44no—
128C23×C4—48no—
129C23×C4—44no—
130C23×C4—48no—
131C23×C4—44no—
132C23×C4—48no—
133C23×C4—44no—
134C23×C4—48no—
135C23×C4—432no—
136C23×C4—432no—
137C23×C4—48no—
138C23×C4—48no—
139C23×C4—44no—
140C23×C4—44no—
141C23×C4C22⋊C412yes—
142C23×C4C22⋊C414yes—
143C23×C4C22⋊C414yes—
144C23×C4C22⋊C412yes—
145C23×C4C22×C414yes—
146C23×C4C22×C411yescharacteristic
147C23×C4C22×C411yescharacteristic
148C23×C4C2×D414yes—
149C23×C4C2×D411yescharacteristic
150C23×C4C2×D412yes—
151C23×C4C2×D411yescharacteristic
152C23×C4C2×D411yescharacteristic
153C23×C4C2×D414yes—
154C23×C4#4114yes—
155C23×C4C2411yescharacteristic
156C22×C8—24no—
157C22×C8—48no—
158C22×C8—44no—
159C22⋊Q8—28no—
160C22⋊Q8—24no—
161C22⋊Q8—24no—
162C22⋊Q8—416no—
163C22⋊Q8—42no—
164C22⋊Q8—44no—
165C22⋊Q8—42no—
166C22⋊Q8—416no—
167C2×C4⋊C4—24no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—28no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—44no—
174C2×C4⋊C4—48no—
175C2×C4⋊C4—44no—
176C2×C4⋊C4C22×C412yes—
177C2×C4⋊C4C22×C414yes—
178C2×C22⋊C4—216no—
179C2×C22⋊C4—22no—
180C2×C22⋊C4—28no—
181C2×C22⋊C4—22no—
182C2×C22⋊C4—28no—
183C2×C22⋊C4—22no—
184C2×C22⋊C4—22no—
185C2×C22⋊C4—48no—
186C2×C22⋊C4—432no—
187C2×C22⋊C4—416no—
188C2×C22⋊C4—48no—
189C2×C22⋊C4—42no—
190C2×C22⋊C4—42no—
191C2×C22⋊C4—44no—
192C22⋊C8—24no—
193C22⋊C8—24no—
194C22⋊C8—416no—
195C22⋊C8—44no—
196#95—216no—
197#95—22no—
198#95—28no—
199#95—28no—
200#95—24no—
201#95—22no—
202#95C2×D418yes—
203C24—24no—
204C24—24no—
205C24—216no—
206C24—216no—
207C24—22no—
208C24—22no—
209C24—24no—
210C24—24no—
211C24—28no—
212C24—28no—
213C24—24no—
214C24—24no—
215C24—24no—
216C24—24no—
217C24—24no—
218C24—24no—
219C24—24no—
220C24—24no—
221C24—24no—
222C24—44no—
223C24—44no—
224C24—432no—
225C24—432no—
226C24—48no—
227C24—48no—
228C24—48no—
229C24—48no—
230C24#9918yes—
231C24C2×C22⋊C414yes—
232C24C2×C22⋊C411yescharacteristic
233C24C2×C22⋊C411yescharacteristic
234C24#12012yes—
235C24#12312yes—
236C24#13514yes—
237C24#13714yes—
238C24C22×D411yescharacteristic
239C2×Q8—24no—
240C2×Q8—44no—
241C2×Q8—44no—
242C2×Q8—42no—
243C2×Q8—88no—
244C22×C4—24no—
245C22×C4—24no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—24no—
249C22×C4—24no—
250C22×C4—28no—
251C22×C4—24no—
252C22×C4—28no—
253C22×C4—28no—
254C22×C4—28no—
255C22×C4—24no—
256C22×C4—28no—
257C22×C4—28no—
258C22×C4—28no—
259C22×C4—28no—
260C22×C4—24no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—28no—
264C22×C4—44no—
265C22×C4—44no—
266C22×C4—44no—
267C22×C4—42no—
268C22×C4—44no—
269C22×C4—42no—
270C22×C4—42no—
271C22×C4—44no—
272C22×C4—48no—
273C22×C4—44no—
274C22×C4—48no—
275C22×C4—42no—
276C22×C4—432no—
277C22×C4—432no—
278C22×C4—432no—
279C22×C4—416no—
280C22×C4—432no—
281C22×C4—416no—
282C22×C4—416no—
283C22×C4—416no—
284C22×C4—48no—
285C22×C4—48no—
286C22×C4—48no—
287C22×C4—416no—
288C22×C4—48no—
289C22×C4—416no—
290C22×C4—44no—
291C22×C4—44no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—44no—
295C22×C4—44no—
296C22×C4—44no—
297C22×C4—44no—
298C22×C4—44no—
299C22×C4—416no—
300C22×C4—816no—
301C22×C4—816no—
302C22×C4C2×C22⋊C414yes—
303C22×C4C2×C22⋊C411yescharacteristic
304C22×C4C2×C22⋊C411yescharacteristic
305C22×C4C4×D414yes—
306C22×C4C4×D414yes—
307C22×C4#12012yes—
308C22×C4#12114yes—
309C22×C4#12114yes—
310C22×C4#12312yes—
311C22×C4C23×C411yescharacteristic
312C22×C4C22×D411yescharacteristic
313C22×C4C22×D412yes—
314C22×C4C2×#4112yes—
315C2×C8—48no—
316C2×C8—44no—
317C2×C8—88no—
318C4⋊C4—24no—
319C4⋊C4—44no—
320C4⋊C4—44no—
321C4⋊C4—416no—
322C4⋊C4—44no—
323C4⋊C4—42no—
324C4⋊C4—44no—
325C22⋊C4—416no—
326C22⋊C4—432no—
327C22⋊C4—42no—
328C22⋊C4—42no—
329C22⋊C4—44no—
330C22⋊C4—44no—
331C22⋊C4—416no—
332C22⋊C4—44no—
333C23—22no—
334C23—22no—
335C23—22no—
336C23—22no—
337C23—24no—
338C23—24no—
339C23—24no—
340C23—24no—
341C23—216no—
342C23—216no—
343C23—28no—
344C23—28no—
345C23—216no—
346C23—24no—
347C23—24no—
348C23—24no—
349C23—24no—
350C23—24no—
351C23—216no—
352C23—216no—
353C23—216no—
354C23—24no—
355C23—416no—
356C23—416no—
357C23—416no—
358C23—416no—
359C23—464no—
360C23—464no—
361C23—44no—
362C23—44no—
363C23—48no—
364C23—44no—
365C23—48no—
366C23—48no—
367C23—48no—
368C23—44no—
369C23—48no—
370C23—48no—
371C23#38612yes—
372C23#38612yes—
373C23C2×#9918yes—
374C23C2×#9914yes—
375C23#41612yes—
376C23#41612yes—
377C23#41912yes—
378C23#41912yes—
379C23#42114yes—
380C23#45218yes—
381C23#48518yes—
382C23C22×C22⋊C411yescharacteristic
383C23C2×#12011yescharacteristic
384C23C2×#12311yescharacteristic
385C23C2×#13512yes—
386C23C2×#13712yes—
387Q8—84no—
388Q8—84no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—28no—
394C2×C4—28no—
395C2×C4—24no—
396C2×C4—24no—
397C2×C4—24no—
398C2×C4—44no—
399C2×C4—42no—
400C2×C4—44no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—416no—
405C2×C4—416no—
406C2×C4—416no—
407C2×C4—416no—
408C2×C4—44no—
409C2×C4—44no—
410C2×C4—48no—
411C2×C4—48no—
412C2×C4—48no—
413C2×C4—48no—
414C2×C4—44no—
415C2×C4—44no—
416C2×C4—44no—
417C2×C4—44no—
418C2×C4—44no—
419C2×C4—48no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—88no—
423C2×C4—88no—
424C2×C4—832no—
425C2×C4—84no—
426C2×C4—84no—
427C2×C4—88no—
428C2×C4#38612yes—
429C2×C4#38612yes—
430C2×C4C2×C4×D412yes—
431C2×C4C2×#12112yes—
432C8—84no—
433C22—24no—
434C22—24no—
435C22—24no—
436C22—24no—
437C22—216no—
438C22—216no—
439C22—21no—
440C22—21no—
441C22—22no—
442C22—21no—
443C22—21no—
444C22—22no—
445C22—28no—
446C22—28no—
447C22—28no—
448C22—416no—
449C22—416no—
450C22—432no—
451C22—44no—
452C22—44no—
453C22—44no—
454C22—432no—
455C22—44no—
456C22#151118yes—
457C22#151618yes—
458C22#187314yes—
459C22#187314yes—
460C22#189714yes—
461C22#189814yes—
462C22C2×#38611yescharacteristic
463C22C22×#9912yes—
464C22C2×#41611yescharacteristic
465C22C2×#41911yescharacteristic
466C22C2×#42112yes—
467C22C2×#45212yes—
468C22C2×#48512yes—
469C4—22no—
470C4—22no—
471C4—22no—
472C4—22no—
473C4—44no—
474C4—88no—
475C4—84no—
476C4—82no—
477C4—82no—
478C2—22no—
479C2—22no—
480C2—24no—
481C2—48no—
482C2#915418yesdirect product factor
483C2C2×#151112yes—
484C2C2×#151612yes—
485C2C2×#187311yescharacteristic
486C2C2×#189711yescharacteristic
487C2C2×#189811yescharacteristic
subgroupG/H
center, socleC24C2×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC26D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C24 ◁ C25×C4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C22×#328C2semidirect
5. #9154C2direct (N × H)
6. C2×#1294C2semidirect
8. C22×C22⋊Q8C4semidirect
15. #2848C4semidirect
22. C2×#380C4semidirect
30. C2×#328C22semidirect
31. #1294C22semidirect
54. C2×C22⋊Q8C2×C4semidirect
83. #380C2×C4semidirect
482. C2#9154direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#28482
C22×#3812
C2×#17792
C22×#3282
#91542
C2×#12942