Finite Group Databasebeta

← C2×#9478 #201448

Subgroups — C2×#9478 #201448

Order 512.

1706 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2484C211yesmaximal, characteristic
2C2×#2274C211yesmaximal, characteristic
3C2×#1826C212yesmaximal
4C2×#1463C211yesmaximal, characteristic
5#9478C218yesmaximal, direct product factor
6C2×#1284C212yesmaximal
7C22×#117—21no—
8C22×#117C2211yescharacteristic
9C23×C4⋊C4C2211yescharacteristic
10C2×#407C2212yes—
11#2484—22no—
12#2484—22no—
13#2484C414yescomplemented
14#2484C2214yes—
15C2×#400C412yescomplemented
16C2×#398C412yescomplemented
17C2×#387—22no—
18C2×#385—21no—
19C2×#381—21no—
20C2×#381C2211yescharacteristic
21#2274—24no—
22#2274—22no—
23#2274C2214yes—
24C2×C4×C4⋊C4—24no—
25C2×C4×C22⋊C4—21no—
26C2×C4×C22⋊C4C2212yes—
27#1826—24no—
28#1826C2218yes—
29C2×#339—24no—
30#1463—22no—
31#1463C2214yes—
32C2×#324—22no—
33#1284C2218yes—
34C24×C4D411yescharacteristic
35C24×C4D411yescharacteristic
36C24×C4C2311yescharacteristic
37C22×M16—22no—
38C2×#117—216no—
39C2×#117—24no—
40C2×#117—24no—
41C2×#117—21no—
42C2×#117—21no—
43C2×#117—22no—
44C2×#117—22no—
45C2×#117—22no—
46C2×#117—22no—
47C2×#117C2×C412yes—
48C2×#117C2312yes—
49C22×C4⋊C4—22no—
50C22×C4⋊C4—22no—
51C22×C4⋊C4—22no—
52C22×C4⋊C4—22no—
53C22×C4⋊C4—22no—
54C22×C4⋊C4—22no—
55C22×C4⋊C4C2×C411yescharacteristic
56C22×C4⋊C4C2×C411yescharacteristic
57C22×C4⋊C4C2×C412yes—
58C22×C4⋊C4C2×C412yes—
59C22×C4⋊C4D412yes—
60C22×C4⋊C4D412yes—
61C22×C4⋊C4D412yes—
62C22×C4⋊C4C2312yes—
63C22×C22⋊C4—22no—
64C22×C22⋊C4—21no—
65C22×C22⋊C4—21no—
66C22×C42—22no—
67C22×C42—21no—
68C22×C42—22no—
69C22×C42D414yes—
70#407—22no—
71#407—22no—
72#407—22no—
73#407C2314yes—
74C2×C22⋊C8—22no—
75C2×C22⋊C8—22no—
76#400—24no—
77#400C2×C418yescomplemented
78#398—24no—
79#398C2×C418yescomplemented
80#387—28no—
81#387—28no—
82#385—24no—
83#385—24no—
84#381—24no—
85#381—21no—
86#381—21no—
87#381—24no—
88#381C2×C412yes—
89#381C2312yes—
90C4×C4⋊C4—216no—
91C4×C4⋊C4—216no—
92C4×C22⋊C4—24no—
93C4×C22⋊C4—24no—
94C4×C22⋊C4—22no—
95C4×C22⋊C4—22no—
96C4×C22⋊C4D414yes—
97C4×C22⋊C4C2314yes—
98C2×#95—22no—
99C2×#95—22no—
100C2×#95—22no—
101C2×#95—22no—
102C2×#95—22no—
103C2×#95—21no—
104C2×#95C2×C412yes—
105#339—216no—
106#324—28no—
107C25C2×D411yescharacteristic
108C23×C4—21no—
109C23×C4—21no—
110C23×C4—21no—
111C23×C4—21no—
112C23×C4—28no—
113C23×C4—24no—
114C23×C4—21no—
115C23×C4—21no—
116C23×C4—21no—
117C23×C4—21no—
118C23×C4—21no—
119C23×C4—22no—
120C23×C4—21no—
121C23×C4—44no—
122C23×C4—44no—
123C23×C4C22⋊C412yes—
124C23×C4C22⋊C412yes—
125C23×C4C22⋊C412yes—
126C23×C4C22⋊C412yes—
127C23×C4C22×C411yescharacteristic
128C23×C4C22×C411yescharacteristic
129C23×C4C2×D412yes—
130C23×C4C2×D412yes—
131C23×C4C2×D412yes—
132C23×C4C2×D411yescharacteristic
133C23×C4C2×D411yescharacteristic
134C23×C4C2×D411yescharacteristic
135C23×C4C2×D412yes—
136C23×C4#4112yes—
137C23×C4#4112yes—
138C23×C4C2411yescharacteristic
139C2×M16—24no—
140C2×M16—42no—
141C2×M16—48no—
142C22×C8—42no—
143#117—232no—
144#117—232no—
145#117—24no—
146#117—24no—
147#117—24no—
148#117—24no—
149#117—42no—
150#117—42no—
151#117—42no—
152#117—42no—
153C2×C4⋊C4—216no—
154C2×C4⋊C4—28no—
155C2×C4⋊C4—24no—
156C2×C4⋊C4—24no—
157C2×C4⋊C4—24no—
158C2×C4⋊C4—24no—
159C2×C4⋊C4—24no—
160C2×C4⋊C4—24no—
161C2×C4⋊C4—24no—
162C2×C4⋊C4—24no—
163C2×C4⋊C4—24no—
164C2×C4⋊C4—24no—
165C2×C4⋊C4—24no—
166C2×C4⋊C4—24no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—28no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—48no—
175C2×C4⋊C4C22⋊C414yes—
176C2×C4⋊C4C22⋊C414yes—
177C2×C4⋊C4C22×C412yes—
178C2×C4⋊C4C22×C412yes—
179C2×C4⋊C4C22×C414yes—
180C2×C4⋊C4C2×D414yes—
181C2×C22⋊C4—216no—
182C2×C22⋊C4—24no—
183C2×C22⋊C4—24no—
184C2×C22⋊C4—22no—
185C2×C22⋊C4—22no—
186C2×C22⋊C4—22no—
187C2×C22⋊C4—22no—
188C2×C22⋊C4—44no—
189C2×C22⋊C4—41no—
190C2×C22⋊C4—41no—
191C2×C22⋊C4—41no—
192C2×C22⋊C4—41no—
193C2×C42—28no—
194C2×C42—216no—
195C2×C42—22no—
196C2×C42—22no—
197C2×C42—28no—
198C2×C42—24no—
199C2×C42—42no—
200C2×C42—42no—
201C2×C42—48no—
202C2×C42—84no—
203C2×C42C2×D418yes—
204C22⋊C8—24no—
205C22⋊C8—24no—
206C22⋊C8—42no—
207C22⋊C8—42no—
208#95—28no—
209#95—28no—
210#95—28no—
211#95—22no—
212#95—28no—
213#95—22no—
214#95—24no—
215#95—24no—
216#95—22no—
217#95C22×C414yes—
218C24—24no—
219C24—24no—
220C24—42no—
221C24C2×C22⋊C411yescharacteristic
222C24C2×C22⋊C411yescharacteristic
223C24#12011yescharacteristic
224C24#12011yescharacteristic
225C24#12311yescharacteristic
226C24#12311yescharacteristic
227C24C22×D411yescharacteristic
228C22×C4—24no—
229C22×C4—24no—
230C22×C4—28no—
231C22×C4—28no—
232C22×C4—28no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—24no—
240C22×C4—28no—
241C22×C4—28no—
242C22×C4—28no—
243C22×C4—216no—
244C22×C4—28no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—24no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—42no—
255C22×C4—42no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4—44no—
259C22×C4—42no—
260C22×C4—44no—
261C22×C4—44no—
262C22×C4—42no—
263C22×C4—48no—
264C22×C4—48no—
265C22×C4—44no—
266C22×C4—44no—
267C22×C4—44no—
268C22×C4—44no—
269C22×C4—44no—
270C22×C4—44no—
271C22×C4—44no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—44no—
277C22×C4—44no—
278C22×C4—82no—
279C22×C4—82no—
280C22×C4—82no—
281C22×C4#10418yes—
282C22×C4C2×C22⋊C414yes—
283C22×C4C2×C22⋊C414yes—
284C22×C4C2×C22⋊C411yescharacteristic
285C22×C4C2×C22⋊C411yescharacteristic
286C22×C4C4×D412yes—
287C22×C4C4×D412yes—
288C22×C4C4×D412yes—
289C22×C4C4×D412yes—
290C22×C4#12012yes—
291C22×C4#12112yes—
292C22×C4#12112yes—
293C22×C4#12112yes—
294C22×C4#12112yes—
295C22×C4#12312yes—
296C22×C4C23×C411yescharacteristic
297C22×C4C22×D412yes—
298C22×C4C22×D411yescharacteristic
299C22×C4C2×#4112yes—
300M16—48no—
301M16—84no—
302C2×C8—44no—
303C2×C8—84no—
304C4⋊C4—232no—
305C4⋊C4—28no—
306C4⋊C4—28no—
307C4⋊C4—28no—
308C4⋊C4—28no—
309C4⋊C4—24no—
310C4⋊C4—24no—
311C4⋊C4—42no—
312C4⋊C4—42no—
313C4⋊C4—416no—
314C22⋊C4—216no—
315C22⋊C4—216no—
316C22⋊C4—44no—
317C22⋊C4—44no—
318C22⋊C4—42no—
319C22⋊C4—42no—
320C22⋊C4—42no—
321C22⋊C4—42no—
322C42—232no—
323C42—48no—
324C42—44no—
325C42—44no—
326C42—84no—
327C42—88no—
328C23—22no—
329C23—22no—
330C23—22no—
331C23—22no—
332C23—22no—
333C23—22no—
334C23—22no—
335C23—22no—
336C23—22no—
337C23—22no—
338C23—22no—
339C23—22no—
340C23—22no—
341C23—22no—
342C23—22no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—416no—
348C23#38611yescharacteristic
349C23#38611yescharacteristic
350C23#38611yescharacteristic
351C23#38611yescharacteristic
352C23C2×#10414yes—
353C23#45814yes—
354C23C22×C22⋊C411yescharacteristic
355C23C2×#12011yescharacteristic
356C23C2×#12311yescharacteristic
357C2×C4—24no—
358C2×C4—24no—
359C2×C4—28no—
360C2×C4—28no—
361C2×C4—28no—
362C2×C4—24no—
363C2×C4—24no—
364C2×C4—24no—
365C2×C4—24no—
366C2×C4—24no—
367C2×C4—28no—
368C2×C4—28no—
369C2×C4—24no—
370C2×C4—24no—
371C2×C4—24no—
372C2×C4—216no—
373C2×C4—24no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—42no—
384C2×C4—432no—
385C2×C4—48no—
386C2×C4—44no—
387C2×C4—44no—
388C2×C4—48no—
389C2×C4—44no—
390C2×C4—44no—
391C2×C4—44no—
392C2×C4—44no—
393C2×C4—44no—
394C2×C4—44no—
395C2×C4—44no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—82no—
399C2×C4—82no—
400C2×C4—82no—
401C2×C4—88no—
402C2×C4—82no—
403C2×C4—82no—
404C2×C4—82no—
405C2×C4—82no—
406C2×C4#38612yes—
407C2×C4#38612yes—
408C2×C4C2×#10418yes—
409C2×C4C2×C4×D412yes—
410C2×C4C2×#12112yes—
411C8—84no—
412C22—28no—
413C22—28no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—44no—
429C22—44no—
430C22—44no—
431C22—44no—
432C22—44no—
433C22#189012yes—
434C22#189012yes—
435C22#189612yes—
436C22#189612yes—
437C22#191212yes—
438C22C2×#38611yescharacteristic
439C22C22×#10412yes—
440C22C2×#45812yes—
441C4—22no—
442C4—22no—
443C4—22no—
444C4—22no—
445C4—28no—
446C4—416no—
447C4—44no—
448C4—84no—
449C4—82no—
450C4—82no—
451C2—22no—
452C2—22no—
453C2—22no—
454C2—22no—
455C2—41no—
456C2—41no—
457C2#947814yesdirect product factor
458C2C2×#189011yescharacteristic
459C2C2×#189611yescharacteristic
460C2C2×#191211yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C24×C4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
5. #9478C2direct (N × H)
13. #2484C4semidirect
15. C2×#400C4semidirect
16. C2×#398C4semidirect
77. #400C2×C4semidirect
79. #398C2×C4semidirect
457. C2#9478direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#24842
C2×#22742
C2×#18262
C2×#14632
#94782
C2×#12842