Finite Group Databasebeta

← C2×#9390 #200443

Subgroups — C2×#9390 #200443

Order 512.

1196 conjugacy classes of subgroups.

The subgroup lattice has 481 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2921C211yesmaximal, characteristic
2C2×#2611C211yesmaximal, characteristic
3C2×#1528C212yesmaximal, complemented
4C2×#1464C211yesmaximal, characteristic
5#9390C218yesmaximal, direct product factor
6C2×#1300C212yesmaximal, complemented
7C22×#125C2211yescharacteristic
8C22×#117C2211yescharacteristic
9#2921—24no—
10#2921—22no—
11#2921C2214yes—
12C2×#433—24no—
13C2×#432C2212yes—
14C2×#423—21no—
15C2×#407—21no—
16C2×C4×M16C2212yes—
17#2611—22no—
18#2611—22no—
19#2611C414yes—
20#2611C2214yes—
21C2×#400C411yescharacteristic
22C2×#399C411yescharacteristic
23C2×#398C411yescharacteristic
24C2×#397C411yescharacteristic
25C2×#389—21no—
26C2×#388—21no—
27C2×#387—21no—
28C2×#385—21no—
29C2×#376C2211yescharacteristic
30#1528—24no—
31#1528C2218yescomplemented
32C2×#330—24no—
33#1464—22no—
34#1464C2214yes—
35C2×#324—21no—
36C2×#323—21no—
37#1300C2218yescomplemented
38C24×C4D411yescharacteristic
39C22×M16—22no—
40C2×#125—21no—
41C2×#125—21no—
42C2×#125—22no—
43C2×#125—22no—
44C2×#125—22no—
45C2×#125—22no—
46C2×#125C2×C412yes—
47C2×#125C2312yes—
48C2×#117—22no—
49C2×#117—22no—
50C2×#117—22no—
51C2×#117—22no—
52C2×#117C2×C412yes—
53C2×#117D412yes—
54C2×#117D412yes—
55C2×#117C2312yes—
56C22×C4⋊C4—21no—
57C22×C4⋊C4—21no—
58C22×C4⋊C4—21no—
59C22×C4⋊C4—21no—
60C22×C4⋊C4C2×C411yescharacteristic
61C22×C4⋊C4C2×C411yescharacteristic
62C22×C4⋊C4C2×C411yescharacteristic
63C22×C4⋊C4D411yescharacteristic
64C22×C22⋊C4—21no—
65C22×C22⋊C4—21no—
66C22×C22⋊C4C2×C411yescharacteristic
67C22×C22⋊C4D411yescharacteristic
68C22×C42—21no—
69C22×C42D411yescharacteristic
70C22×C42C2311yescharacteristic
71#433—216no—
72#433—216no—
73#432—22no—
74#432—22no—
75#432—22no—
76#432C2314yes—
77#423—24no—
78#423—24no—
79C2×C4⋊C8—24no—
80C2×C4⋊C8—22no—
81#407—24no—
82#407—24no—
83C2×C22⋊C8—24no—
84C2×C22⋊C8—22no—
85C4×M16—22no—
86C4×M16—22no—
87C4×M16D414yes—
88C4×M16C2314yes—
89C2×#97—22no—
90C2×#97D414yes—
91C2×C4×C8—22no—
92#400—22no—
93#400C2×C414yes—
94#399—22no—
95#399C2×C414yes—
96#398—22no—
97#398C2×C414yes—
98#397—22no—
99#397C2×C414yes—
100#389—24no—
101#389—24no—
102#388—24no—
103#388—24no—
104#387—24no—
105#387—24no—
106#385—24no—
107#385—24no—
108#376—21no—
109#376—21no—
110#376C2×C412yes—
111#376C2312yes—
112C2×#95—21no—
113C2×#95—21no—
114C2×#95—21no—
115C2×#95—21no—
116C2×#95—21no—
117C2×#95C2×C411yescharacteristic
118C2×#95C2×C411yescharacteristic
119#330—216no—
120#324—24no—
121#323—24no—
122C25C22⋊C411yescharacteristic
123C23×C4—21no—
124C23×C4—21no—
125C23×C4—21no—
126C23×C4—21no—
127C23×C4—21no—
128C23×C4—21no—
129C23×C4—21no—
130C23×C4—21no—
131C23×C4—42no—
132C23×C4—42no—
133C23×C4C22⋊C411yescharacteristic
134C23×C4C22⋊C411yescharacteristic
135C23×C4C22⋊C411yescharacteristic
136C23×C4C22⋊C412yes—
137C23×C4C22×C411yescharacteristic
138C23×C4C2×D411yescharacteristic
139C23×C4C2×D412yes—
140C23×C4C2×D411yescharacteristic
141C2×M16—24no—
142C2×M16—24no—
143C2×M16—44no—
144C2×M16—44no—
145C22×C8—24no—
146C22×C8—42no—
147#125—24no—
148#125—24no—
149#125—24no—
150#125—24no—
151#125—42no—
152#125—42no—
153#125—42no—
154#125—42no—
155#117—24no—
156#117—24no—
157#117—24no—
158#117—24no—
159#117—24no—
160#117—24no—
161#117—24no—
162#117—24no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—24no—
174C2×C4⋊C4—24no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—44no—
180C2×C4⋊C4—44no—
181C2×C4⋊C4—41no—
182C2×C4⋊C4—41no—
183C2×C4⋊C4—42no—
184C2×C4⋊C4—42no—
185C2×C4⋊C4—41no—
186C2×C4⋊C4—41no—
187C2×C4⋊C4C22⋊C412yes—
188C2×C4⋊C4C22⋊C412yes—
189C2×C4⋊C4C22×C412yes—
190C2×C4⋊C4C22×C412yes—
191C2×C4⋊C4C22×C412yes—
192C2×C4⋊C4C2×D412yes—
193C2×C22⋊C4—22no—
194C2×C22⋊C4—22no—
195C2×C22⋊C4—22no—
196C2×C22⋊C4—22no—
197C2×C22⋊C4—24no—
198C2×C22⋊C4—24no—
199C2×C22⋊C4—44no—
200C2×C22⋊C4—44no—
201C2×C22⋊C4C22⋊C412yes—
202C2×C22⋊C4C22⋊C412yes—
203C2×C22⋊C4C22×C412yes—
204C2×C22⋊C4C2×D412yes—
205C2×C42—21no—
206C2×C42—21no—
207C2×C42—21no—
208C2×C42—21no—
209C2×C42—22no—
210C2×C42—22no—
211C2×C42—44no—
212C2×C42C22⋊C412yes—
213C2×C42C22×C411yescharacteristic
214C2×C42C2×D412yes—
215C2×C42C2×D412yes—
216C2×C42C2×D412yes—
217C2×C42C2×D411yescharacteristic
218C2×C42C2×D411yescharacteristic
219C2×C42#4112yes—
220C2×C42#4112yes—
221C2×C42C2411yescharacteristic
222C4⋊C8—216no—
223C4⋊C8—24no—
224C4⋊C8—42no—
225C22⋊C8—216no—
226C22⋊C8—24no—
227C22⋊C8—42no—
228#97—24no—
229#97—24no—
230#97—42no—
231#97C2×D418yes—
232C4×C8—24no—
233C4×C8—24no—
234#95—22no—
235#95—24no—
236#95—24no—
237#95—24no—
238#95—24no—
239#95—21no—
240#95—21no—
241#95—22no—
242#95C22×C412yes—
243#95C22×C412yes—
244C24—21no—
245C24—22no—
246C24—21no—
247C24—22no—
248C24—42no—
249C24—42no—
250C24C2×C22⋊C411yescharacteristic
251C24C2×C22⋊C412yes—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—24no—
255C22×C4—22no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4—44no—
278C22×C4—44no—
279C22×C4—44no—
280C22×C4—44no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4C2×C22⋊C412yes—
297C22×C4C2×C22⋊C411yescharacteristic
298C22×C4C2×C22⋊C412yes—
299C22×C4C2×C22⋊C412yes—
300C22×C4C2×C22⋊C411yescharacteristic
301C22×C4C2×C22⋊C411yescharacteristic
302C22×C4C4×D412yes—
303C22×C4C4×D412yes—
304C22×C4#12011yescharacteristic
305C22×C4#12011yescharacteristic
306C22×C4#12112yes—
307C22×C4#12112yes—
308C22×C4#12311yescharacteristic
309C22×C4#12311yescharacteristic
310C22×C4C23×C411yescharacteristic
311C22×C4C22×D411yescharacteristic
312C22×C4C22×D411yescharacteristic
313M16—44no—
314M16—44no—
315M16—48no—
316C2×C8—28no—
317C2×C8—48no—
318C2×C8—44no—
319C2×C8—84no—
320C4⋊C4—24no—
321C4⋊C4—24no—
322C4⋊C4—24no—
323C4⋊C4—24no—
324C4⋊C4—24no—
325C4⋊C4—24no—
326C4⋊C4—48no—
327C4⋊C4—48no—
328C4⋊C4—42no—
329C4⋊C4—44no—
330C4⋊C4—42no—
331C4⋊C4—42no—
332C4⋊C4—42no—
333C4⋊C4—42no—
334C4⋊C4—42no—
335C4⋊C4—44no—
336C22⋊C4—24no—
337C22⋊C4—24no—
338C22⋊C4—24no—
339C22⋊C4—24no—
340C22⋊C4—48no—
341C22⋊C4—48no—
342C42—22no—
343C42—22no—
344C42—22no—
345C42—22no—
346C42—44no—
347C42—44no—
348C42C4×D412yes—
349C42C4×D412yes—
350C42#12012yes—
351C42#12112yes—
352C42#12112yes—
353C42#12312yes—
354C42C22×D412yes—
355C42C2×#4112yes—
356C23—22no—
357C23—22no—
358C23—22no—
359C23—22no—
360C23—22no—
361C23—42no—
362C23—42no—
363C23—48no—
364C23—42no—
365C23—42no—
366C23—42no—
367C23—42no—
368C23—81no—
369C23—81no—
370C23—84no—
371C23#38611yescharacteristic
372C23#38611yescharacteristic
373C23#42112yes—
374C23#42112yes—
375C23C22×C22⋊C411yescharacteristic
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—24no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—24no—
386C2×C4—24no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—41no—
398C2×C4—44no—
399C2×C4—44no—
400C2×C4—44no—
401C2×C4—44no—
402C2×C4—42no—
403C2×C4—48no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—81no—
421C2×C4—81no—
422C2×C4—84no—
423C2×C4—82no—
424C2×C4—82no—
425C2×C4—82no—
426C2×C4—82no—
427C2×C4#38611yescharacteristic
428C2×C4#38611yescharacteristic
429C2×C4#38612yes—
430C2×C4#38612yes—
431C2×C4C2×C4×D412yes—
432C2×C4C2×#12011yescharacteristic
433C2×C4C2×#12112yes—
434C2×C4C2×#12311yescharacteristic
435C8—48no—
436C8—84no—
437C22—21no—
438C22—21no—
439C22—24no—
440C22—24no—
441C22—21no—
442C22—21no—
443C22—44no—
444C22—42no—
445C22—42no—
446C22—42no—
447C22—82no—
448C22—84no—
449C22—84no—
450C22#188412yes—
451C22#189712yes—
452C22#189712yes—
453C22#191512yes—
454C22C2×#38611yescharacteristic
455C22C2×#42111yescharacteristic
456C22C2×#42111yescharacteristic
457C4—22no—
458C4—22no—
459C4—22no—
460C4—22no—
461C4—21no—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—44no—
466C4—42no—
467C4—42no—
468C4—42no—
469C4—82no—
470C4—82no—
471C4—82no—
472C2—21no—
473C2—21no—
474C2—22no—
475C2—82no—
476C2#939014yesdirect product factor
477C2C2×#188411yescharacteristic
478C2C2×#189711yescharacteristic
479C2C2×#191511yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
prime radicalC25C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×#1528C2semidirect
5. #9390C2direct (N × H)
6. C2×#1300C2semidirect
31. #1528C22semidirect
37. #1300C22semidirect
476. C2#9390direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#29212
C2×#26112
C2×#15282
C2×#14642
#93902
C2×#13002