Finite Group Databasebeta

← C2×#9482 #201457

Subgroups — C2×#9482 #201457

Order 512.

1402 conjugacy classes of subgroups.

The subgroup lattice has 451 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2484C211yesmaximal, characteristic
2C2×#2313C211yesmaximal, characteristic
3C2×#1826C212yesmaximal
4C2×#1463C211yesmaximal, characteristic
5#9482C218yesmaximal, direct product factor
6C2×#1284C212yesmaximal
7C22×#117C2211yescharacteristic
8C23×C4⋊C4C2211yescharacteristic
9C2×#407C2212yes—
10#2484—22no—
11#2484—22no—
12#2484C414yescomplemented
13#2484C2214yes—
14C2×#400C412yescomplemented
15C2×#398C412yescomplemented
16#2313—24no—
17#2313—22no—
18#2313C2214yes—
19C2×#387—24no—
20C2×#387—22no—
21C2×#385—21no—
22C2×#381—21no—
23C2×#381—21no—
24C2×#381C2211yescharacteristic
25C2×#380—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—21no—
39C2×#117—21no—
40C2×#117—22no—
41C2×#117—22no—
42C2×#117—22no—
43C2×#117—22no—
44C2×#117C2×C412yes—
45C2×#117C2312yes—
46C22×C4⋊C4—22no—
47C22×C4⋊C4—22no—
48C22×C4⋊C4—22no—
49C22×C4⋊C4—22no—
50C22×C4⋊C4—22no—
51C22×C4⋊C4—22no—
52C22×C4⋊C4C2×C411yescharacteristic
53C22×C4⋊C4C2×C411yescharacteristic
54C22×C4⋊C4C2×C412yes—
55C22×C4⋊C4C2×C412yes—
56C22×C4⋊C4D412yes—
57C22×C4⋊C4D412yes—
58C22×C4⋊C4D412yes—
59C22×C4⋊C4C2312yes—
60C22×C22⋊C4—21no—
61C22×C22⋊C4—22no—
62C22×C22⋊C4—21no—
63C22×C42—21no—
64C22×C42D414yes—
65#407—22no—
66#407—22no—
67#407—22no—
68#407C2314yes—
69C2×C22⋊C8—22no—
70C2×C22⋊C8—22no—
71#400—24no—
72#400C2×C418yescomplemented
73#398—24no—
74#398C2×C418yescomplemented
75#387—216no—
76#387—28no—
77#387—28no—
78#387—216no—
79#385—24no—
80#385—24no—
81#381—24no—
82#381—24no—
83#381—24no—
84#381—21no—
85#381—21no—
86#381—24no—
87#381C2×C412yes—
88#381C2312yes—
89#380—24no—
90#380—24no—
91C4×C22⋊C4—22no—
92C4×C22⋊C4—22no—
93C4×C22⋊C4D414yes—
94C4×C22⋊C4C2314yes—
95C2×#95—22no—
96C2×#95—24no—
97C2×#95—22no—
98C2×#95—22no—
99C2×#95—22no—
100C2×#95—22no—
101C2×#95—21no—
102C2×#95C2×C412yes—
103#339—216no—
104#324—28no—
105C25C2×D411yescharacteristic
106C23×C4—21no—
107C23×C4—21no—
108C23×C4—21no—
109C23×C4—21no—
110C23×C4—21no—
111C23×C4—21no—
112C23×C4—21no—
113C23×C4—21no—
114C23×C4—21no—
115C23×C4—22no—
116C23×C4—21no—
117C23×C4—24no—
118C23×C4—44no—
119C23×C4—44no—
120C23×C4—44no—
121C23×C4C22⋊C412yes—
122C23×C4C22⋊C412yes—
123C23×C4C22⋊C412yes—
124C23×C4C22⋊C412yes—
125C23×C4C22×C411yescharacteristic
126C23×C4C22×C411yescharacteristic
127C23×C4C2×D412yes—
128C23×C4C2×D412yes—
129C23×C4C2×D412yes—
130C23×C4C2×D411yescharacteristic
131C23×C4C2×D411yescharacteristic
132C23×C4C2×D411yescharacteristic
133C23×C4C2×D412yes—
134C23×C4#4112yes—
135C23×C4#4112yes—
136C23×C4C2411yescharacteristic
137C2×M16—24no—
138C2×M16—42no—
139C2×M16—48no—
140C22×C8—42no—
141#117—24no—
142#117—24no—
143#117—24no—
144#117—24no—
145#117—42no—
146#117—42no—
147#117—42no—
148#117—42no—
149C2×C4⋊C4—24no—
150C2×C4⋊C4—24no—
151C2×C4⋊C4—24no—
152C2×C4⋊C4—24no—
153C2×C4⋊C4—24no—
154C2×C4⋊C4—24no—
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—22no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—28no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—28no—
169C2×C4⋊C4—48no—
170C2×C4⋊C4—84no—
171C2×C4⋊C4C22⋊C414yes—
172C2×C4⋊C4C22⋊C414yes—
173C2×C4⋊C4C22×C412yes—
174C2×C4⋊C4C22×C412yes—
175C2×C4⋊C4C22×C414yes—
176C2×C4⋊C4C2×D414yes—
177C2×C22⋊C4—22no—
178C2×C22⋊C4—22no—
179C2×C22⋊C4—24no—
180C2×C22⋊C4—22no—
181C2×C22⋊C4—24no—
182C2×C22⋊C4—22no—
183C2×C22⋊C4—48no—
184C2×C22⋊C4—44no—
185C2×C22⋊C4—41no—
186C2×C22⋊C4—41no—
187C2×C22⋊C4—41no—
188C2×C22⋊C4—41no—
189C2×C42—22no—
190C2×C42—22no—
191C2×C42—24no—
192C2×C42—42no—
193C2×C42—42no—
194C2×C42—48no—
195C2×C42C2×D418yes—
196C22⋊C8—24no—
197C22⋊C8—24no—
198C22⋊C8—42no—
199C22⋊C8—42no—
200#95—28no—
201#95—216no—
202#95—28no—
203#95—28no—
204#95—22no—
205#95—28no—
206#95—22no—
207#95—24no—
208#95—24no—
209#95—22no—
210#95C22×C414yes—
211C24—24no—
212C24—24no—
213C24—42no—
214C24C2×C22⋊C411yescharacteristic
215C24C2×C22⋊C411yescharacteristic
216C24#12011yescharacteristic
217C24#12011yescharacteristic
218C24#12311yescharacteristic
219C24#12311yescharacteristic
220C24C22×D411yescharacteristic
221C22×C4—28no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—24no—
232C22×C4—24no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—24no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—28no—
240C22×C4—44no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—44no—
246C22×C4—42no—
247C22×C4—44no—
248C22×C4—44no—
249C22×C4—44no—
250C22×C4—42no—
251C22×C4—44no—
252C22×C4—44no—
253C22×C4—44no—
254C22×C4—44no—
255C22×C4—44no—
256C22×C4—44no—
257C22×C4—44no—
258C22×C4—44no—
259C22×C4—44no—
260C22×C4—48no—
261C22×C4—44no—
262C22×C4—48no—
263C22×C4—44no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—44no—
269C22×C4—44no—
270C22×C4—48no—
271C22×C4—82no—
272C22×C4—82no—
273C22×C4—82no—
274C22×C4C2×C22⋊C414yes—
275C22×C4C2×C22⋊C414yes—
276C22×C4C2×C22⋊C411yescharacteristic
277C22×C4C2×C22⋊C411yescharacteristic
278C22×C4C4×D412yes—
279C22×C4C4×D412yes—
280C22×C4C4×D412yes—
281C22×C4C4×D412yes—
282C22×C4#12012yes—
283C22×C4#12112yes—
284C22×C4#12112yes—
285C22×C4#12112yes—
286C22×C4#12112yes—
287C22×C4#12312yes—
288C22×C4C23×C411yescharacteristic
289C22×C4C22×D412yes—
290C22×C4C22×D411yescharacteristic
291C22×C4C2×#4112yes—
292M16—48no—
293M16—84no—
294C2×C8—44no—
295C2×C8—84no—
296C4⋊C4—28no—
297C4⋊C4—28no—
298C4⋊C4—28no—
299C4⋊C4—28no—
300C4⋊C4—24no—
301C4⋊C4—24no—
302C4⋊C4—416no—
303C4⋊C4—42no—
304C4⋊C4—42no—
305C4⋊C4—88no—
306C22⋊C4—48no—
307C22⋊C4—44no—
308C22⋊C4—48no—
309C22⋊C4—44no—
310C22⋊C4—42no—
311C22⋊C4—42no—
312C22⋊C4—42no—
313C22⋊C4—42no—
314C42—48no—
315C42—44no—
316C42—44no—
317C42—84no—
318C23—22no—
319C23—22no—
320C23—22no—
321C23—22no—
322C23—22no—
323C23—22no—
324C23—22no—
325C23—22no—
326C23—22no—
327C23—22no—
328C23—22no—
329C23—22no—
330C23—22no—
331C23—22no—
332C23—22no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—416no—
338C23#38611yescharacteristic
339C23#38611yescharacteristic
340C23#38611yescharacteristic
341C23#38611yescharacteristic
342C23#42114yes—
343C23#45814yes—
344C23C22×C22⋊C411yescharacteristic
345C23C2×#12011yescharacteristic
346C23C2×#12311yescharacteristic
347C2×C4—24no—
348C2×C4—24no—
349C2×C4—24no—
350C2×C4—24no—
351C2×C4—24no—
352C2×C4—24no—
353C2×C4—24no—
354C2×C4—24no—
355C2×C4—24no—
356C2×C4—24no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—42no—
367C2×C4—44no—
368C2×C4—44no—
369C2×C4—44no—
370C2×C4—44no—
371C2×C4—44no—
372C2×C4—44no—
373C2×C4—44no—
374C2×C4—44no—
375C2×C4—44no—
376C2×C4—44no—
377C2×C4—44no—
378C2×C4—48no—
379C2×C4—44no—
380C2×C4—48no—
381C2×C4—44no—
382C2×C4—44no—
383C2×C4—44no—
384C2×C4—48no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—82no—
388C2×C4—82no—
389C2×C4—82no—
390C2×C4—816no—
391C2×C4—88no—
392C2×C4—82no—
393C2×C4—82no—
394C2×C4—82no—
395C2×C4—82no—
396C2×C4#38612yes—
397C2×C4#38612yes—
398C2×C4C2×C4×D412yes—
399C2×C4C2×#12112yes—
400C8—84no—
401C22—28no—
402C22—28no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—44no—
418C22—44no—
419C22—44no—
420C22—44no—
421C22—44no—
422C22#189012yes—
423C22#189012yes—
424C22#189712yes—
425C22#189712yes—
426C22#191212yes—
427C22C2×#38611yescharacteristic
428C22C2×#42112yes—
429C22C2×#45812yes—
430C4—22no—
431C4—22no—
432C4—22no—
433C4—22no—
434C4—44no—
435C4—44no—
436C4—88no—
437C4—84no—
438C4—82no—
439C4—82no—
440C2—22no—
441C2—22no—
442C2—22no—
443C2—22no—
444C2—41no—
445C2—41no—
446C2#948214yesdirect product factor
447C2C2×#189011yescharacteristic
448C2C2×#189711yescharacteristic
449C2C2×#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. #9482C2direct (N × H)
12. #2484C4semidirect
14. C2×#400C4semidirect
15. C2×#398C4semidirect
72. #400C2×C4semidirect
74. #398C2×C4semidirect
446. C2#9482direct (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×#23132
C2×#18262
C2×#14632
#94822
C2×#12842