Finite Group Databasebeta

← C2×#9886 #206950

Subgroups — C2×#9886 #206950

Order 512.

1542 conjugacy classes of subgroups.

The subgroup lattice has 485 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2851C211yesmaximal, characteristic
2C2×C4×C22⋊C8C211yesmaximal, characteristic
3C2×#1434C211yesmaximal, characteristic
4#9886C218yesmaximal, direct product factor
5C2×#1294C212yesmaximal
6C2×#1294C212yesmaximal
7C22×#125C411yescharacteristic, complemented
8C23×C42C2211yescharacteristic
9C22×C22⋊C8C2212yes—
10C22×C4×C8—21no—
11#2851—22no—
12#2851—22no—
13#2851C414yescomplemented
14#2851C2214yes—
15C2×#389C411yescharacteristic, complemented
16C2×#389C411yescharacteristic, complemented
17C2×#387—21no—
18C2×#387—21no—
19C2×#385—21no—
20C2×#385—21no—
21C2×#382C411yescharacteristic, complemented
22C2×#380C2211yescharacteristic
23C2×#380C2211yescharacteristic
24C22×#95—21no—
25C22×#95—21no—
26C22×#95C2212yes—
27C4×C22⋊C8—22no—
28C4×C22⋊C8C2214yes—
29C2×#336—21no—
30#1434—22no—
31#1434C2214yes—
32#1294C2218yes—
33#1294C2218yes—
34C24×C4—22no—
35C24×C4D411yescharacteristic
36C24×C4D411yescharacteristic
37C24×C4C2311yescharacteristic
38C23×C8—22no—
39C2×#125—22no—
40C2×#125—44no—
41C2×#125C2×C414yescomplemented
42C22×C4⋊C4—21no—
43C22×C4⋊C4—21no—
44C22×C4⋊C4—21no—
45C22×C4⋊C4—21no—
46C22×C4⋊C4C2×C411yescharacteristic
47C22×C4⋊C4C2×C411yescharacteristic
48C22×C4⋊C4C2×C411yescharacteristic
49C22×C4⋊C4C2×C411yescharacteristic
50C22×C22⋊C4—21no—
51C22×C22⋊C4—21no—
52C22×C42—44no—
53C22×C42C2×C411yescharacteristic
54C22×C42C2×C412yes—
55C22×C42C2×C411yescharacteristic
56C22×C42D411yescharacteristic
57C22×C42D412yes—
58C22×C42D412yes—
59C22×C42D411yescharacteristic
60C22×C42C2312yes—
61C2×C22⋊C8—22no—
62C2×C22⋊C8—24no—
63C2×C22⋊C8Q818yes—
64C2×C22⋊C8C2314yes—
65C2×C4×C8—24no—
66C2×C4×C8—44no—
67#389—22no—
68#389—22no—
69#389C2×C414yescomplemented
70#389C2×C414yescomplemented
71#387—24no—
72#387—24no—
73#387—24no—
74#387—24no—
75#385—24no—
76#385—24no—
77#385—24no—
78#385—24no—
79#382—22no—
80#382C2×C414yescomplemented
81#380—21no—
82#380—21no—
83#380—21no—
84#380—21no—
85#380C2×C412yes—
86#380C2×C412yes—
87#380C2312yes—
88#380C2312yes—
89C2×#95—28no—
90C2×#95—21no—
91C2×#95—21no—
92C2×#95—21no—
93C2×#95—21no—
94C2×#95—24no—
95C2×#95—21no—
96C2×#95—21no—
97C2×#95—28no—
98C2×#95—22no—
99C2×#95—24no—
100C2×#95—44no—
101C2×#95C2314yes—
102#336—24no—
103C25C2×D411yescharacteristic
104C23×C4—24no—
105C23×C4—24no—
106C23×C4—24no—
107C23×C4—24no—
108C23×C4—28no—
109C23×C4—21no—
110C23×C4—21no—
111C23×C4—21no—
112C23×C4—21no—
113C23×C4—24no—
114C23×C4—42no—
115C23×C4—42no—
116C23×C4—42no—
117C23×C4—42no—
118C23×C4—44no—
119C23×C4—44no—
120C23×C4—44no—
121C23×C4—44no—
122C23×C4—44no—
123C23×C4—44no—
124C23×C4C22⋊C411yescharacteristic
125C23×C4C22⋊C411yescharacteristic
126C23×C4C22⋊C412yes—
127C23×C4C22⋊C412yes—
128C23×C4C22⋊C411yescharacteristic
129C23×C4C22⋊C411yescharacteristic
130C23×C4C22×C411yescharacteristic
131C23×C4C22×C411yescharacteristic
132C23×C4C2×D412yes—
133C23×C4C2×D412yes—
134C23×C4C2×D411yescharacteristic
135C23×C4C2×D411yescharacteristic
136C23×C4C2×D411yescharacteristic
137C23×C4C2×Q814yes—
138C23×C4#4114yes—
139C23×C4C2411yescharacteristic
140C22×C8—28no—
141C22×C8—24no—
142C22×C8—44no—
143C22×C8—44no—
144#125—48no—
145#125—48no—
146C2×C4⋊C4—24no—
147C2×C4⋊C4—24no—
148C2×C4⋊C4—24no—
149C2×C4⋊C4—24no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—42no—
155C2×C4⋊C4—42no—
156C2×C4⋊C4—42no—
157C2×C4⋊C4—42no—
158C2×C4⋊C4—44no—
159C2×C4⋊C4—44no—
160C2×C4⋊C4—44no—
161C2×C4⋊C4—44no—
162C2×C4⋊C4C22×C412yes—
163C2×C4⋊C4C22×C412yes—
164C2×C4⋊C4C22×C412yes—
165C2×C4⋊C4C22×C412yes—
166C2×C22⋊C4—22no—
167C2×C22⋊C4—22no—
168C2×C22⋊C4—22no—
169C2×C22⋊C4—22no—
170C2×C22⋊C4—44no—
171C2×C22⋊C4—44no—
172C2×C42—24no—
173C2×C42—24no—
174C2×C42—44no—
175C2×C42—44no—
176C2×C42—44no—
177C2×C42—44no—
178C2×C42—42no—
179C2×C42—42no—
180C2×C42C22⋊C412yes—
181C2×C42C22⋊C412yes—
182C2×C42C22⋊C412yes—
183C2×C42C22⋊C412yes—
184C2×C42C22×C412yes—
185C2×C42C22×C412yes—
186C2×C42C2×D412yes—
187C2×C42C2×D412yes—
188C22⋊C8—28no—
189C22⋊C8—24no—
190C22⋊C8C2×Q818yes—
191C4×C8—48no—
192#95—216no—
193#95—22no—
194#95—22no—
195#95—24no—
196#95—24no—
197#95—24no—
198#95—24no—
199#95—22no—
200#95—22no—
201#95—28no—
202#95—48no—
203#95—44no—
204C24—22no—
205C24—22no—
206C24—22no—
207C24—22no—
208C24C2×C22⋊C411yescharacteristic
209C24C2×C22⋊C411yescharacteristic
210C24#12412yes—
211C24C4⋊Q812yes—
212C24#13514yes—
213C24#13514yes—
214C24C22×D411yescharacteristic
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—24no—
224C22×C4—24no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—24no—
228C22×C4—24no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—24no—
234C22×C4—24no—
235C22×C4—24no—
236C22×C4—24no—
237C22×C4—28no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—42no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—42no—
247C22×C4—41no—
248C22×C4—42no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—42no—
253C22×C4—48no—
254C22×C4—48no—
255C22×C4—41no—
256C22×C4—416no—
257C22×C4—416no—
258C22×C4—44no—
259C22×C4—44no—
260C22×C4—44no—
261C22×C4—416no—
262C22×C4—416no—
263C22×C4—416no—
264C22×C4—44no—
265C22×C4—44no—
266C22×C4—44no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—88no—
280C22×C4—88no—
281C22×C4—88no—
282C22×C4—88no—
283C22×C4#9914yes—
284C22×C4#10414yes—
285C22×C4C2×C22⋊C412yes—
286C22×C4C2×C22⋊C412yes—
287C22×C4C2×C22⋊C411yescharacteristic
288C22×C4C2×C22⋊C411yescharacteristic
289C22×C4C2×C22⋊C412yes—
290C22×C4C2×C22⋊C412yes—
291C22×C4C4×Q814yes—
292C22×C4C4×Q814yes—
293C22×C4C22⋊Q814yes—
294C22×C4C22⋊Q814yes—
295C22×C4#12412yes—
296C22×C4C4⋊Q812yes—
297C22×C4C23×C411yescharacteristic
298C22×C4C22×D411yescharacteristic
299C22×C4C22×Q812yes—
300C22×C4C2×#4112yes—
301C2×C8—28no—
302C2×C8—44no—
303C2×C8—44no—
304C2×C8—416no—
305C4⋊C4—42no—
306C4⋊C4—42no—
307C4⋊C4—42no—
308C4⋊C4—42no—
309C4⋊C4—42no—
310C4⋊C4—42no—
311C4⋊C4—48no—
312C4⋊C4—42no—
313C4⋊C4—42no—
314C4⋊C4—48no—
315C4⋊C4—48no—
316C4⋊C4—48no—
317C22⋊C4—44no—
318C22⋊C4—44no—
319C22⋊C4—44no—
320C22⋊C4—44no—
321C42—24no—
322C42—24no—
323C42—24no—
324C42—24no—
325C42—42no—
326C42—42no—
327C42—42no—
328C42—42no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—21no—
337C23—24no—
338C23—24no—
339C23—24no—
340C23—24no—
341C23—28no—
342C23—28no—
343C23—28no—
344C23—28no—
345C23#39112yes—
346C23#39112yes—
347C23C2×#9912yes—
348C23#41012yes—
349C23#41612yes—
350C23#41612yes—
351C23#41612yes—
352C23#41612yes—
353C23C2×#10412yes—
354C23#42112yes—
355C23#48818yes—
356C23#49918yes—
357C23C22×C22⋊C411yescharacteristic
358C23C2×#12411yescharacteristic
359C23C2×C4⋊Q811yescharacteristic
360C23C2×#13512yes—
361C23C2×#13512yes—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—22no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—28no—
375C2×C4—28no—
376C2×C4—28no—
377C2×C4—28no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—44no—
385C2×C4—44no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—48no—
391C2×C4—48no—
392C2×C4—48no—
393C2×C4—48no—
394C2×C4—44no—
395C2×C4—44no—
396C2×C4—48no—
397C2×C4—48no—
398C2×C4—48no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—84no—
412C2×C4—832no—
413C2×C4—84no—
414C2×C4—84no—
415C2×C4—84no—
416C2×C4—84no—
417C2×C4—84no—
418C2×C4—84no—
419C2×C4—84no—
420C2×C4#39112yes—
421C2×C4#39112yes—
422C2×C4C2×#9914yes—
423C2×C4C2×#10414yes—
424C2×C4C2×C4×Q812yes—
425C2×C4C2×C22⋊Q812yes—
426C8—48no—
427C22—21no—
428C22—21no—
429C22—22no—
430C22—21no—
431C22—21no—
432C22—22no—
433C22—22no—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—216no—
438C22—216no—
439C22—22no—
440C22—22no—
441C22—22no—
442C22—22no—
443C22#150014yes—
444C22#150114yes—
445C22#151614yes—
446C22#152114yes—
447C22#198614yes—
448C22#199114yes—
449C22#199114yes—
450C22#199614yes—
451C22C2×#39111yescharacteristic
452C22C22×#9911yescharacteristic
453C22C2×#41011yescharacteristic
454C22C2×#41611yescharacteristic
455C22C2×#41611yescharacteristic
456C22C22×#10411yescharacteristic
457C22C2×#42111yescharacteristic
458C22C2×#48812yes—
459C22C2×#49912yes—
460C4—22no—
461C4—22no—
462C4—22no—
463C4—22no—
464C4—24no—
465C4—24no—
466C4—42no—
467C4—42no—
468C4—88no—
469C4—82no—
470C4—82no—
471C4—82no—
472C4—82no—
473C2—22no—
474C2—22no—
475C2—24no—
476C2#988618yesdirect product factor
477C2C2×#150011yescharacteristic
478C2C2×#150111yescharacteristic
479C2C2×#152111yescharacteristic
480C2C2×#151611yescharacteristic
481C2C2×#198611yescharacteristic
482C2C2×#199111yescharacteristic
483C2C2×#199611yescharacteristic
subgroupG/H
center, socleC24C2×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C24 ◁ C23×C42 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #9886C2direct (N × H)
7. C22×#125C4semidirect
13. #2851C4semidirect
15. C2×#389C4semidirect
16. C2×#389C4semidirect
21. C2×#382C4semidirect
41. C2×#125C2×C4semidirect
69. #389C2×C4semidirect
70. #389C2×C4semidirect
80. #382C2×C4semidirect
476. C2#9886direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#28512
C2×C4×C22⋊C82
C2×#14342
#98862
C2×#12942