Finite Group Databasebeta

← C2×#9450 #201133

Subgroups — C2×#9450 #201133

Order 512.

1130 conjugacy classes of subgroups.

The subgroup lattice has 459 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2983C211yesmaximal, characteristic
2C2×#2565C211yesmaximal, characteristic
3C2×#1534C212yesmaximal
4C2×#1467C211yesmaximal, characteristic
5#9450C218yesmaximal, direct product factor
6C2×#1285C212yesmaximal
7C22×#125C2211yescharacteristic
8C22×C4×Q8C2211yescharacteristic
9#2983—24no—
10#2983—22no—
11#2983C2214yes—
12C2×#446—24no—
13C2×#432—21no—
14C2×#432C2212yes—
15C2×#432C2212yes—
16C2×#431—21no—
17#2565—22no—
18#2565—22no—
19#2565C414yes—
20#2565C2214yes—
21C2×#398—21no—
22C2×#398—21no—
23C2×#391C411yescharacteristic
24C2×#391C411yescharacteristic
25C2×#387—21no—
26C2×#387—21no—
27C2×#384C411yescharacteristic
28C2×#382C411yescharacteristic
29C2×C4×C4⋊C4C2211yescharacteristic
30#1534—24no—
31#1534C2218yes—
32C2×#330—24no—
33#1467—22no—
34#1467C2214yes—
35C2×#324—21no—
36C2×#324—21no—
37#1285C2218yes—
38C23×Q8C2×C411yescharacteristic
39C2×#125—21no—
40C2×#125—21no—
41C2×#125—22no—
42C2×#125—22no—
43C2×#125—22no—
44C2×#125—22no—
45C2×#125C2×C412yes—
46C2×#125C2312yes—
47C2×C4×Q8—22no—
48C2×C4×Q8—22no—
49C2×C4×Q8—22no—
50C2×C4×Q8—22no—
51C2×C4×Q8C2×C412yes—
52C2×C4×Q8D412yes—
53C2×C4×Q8D412yes—
54C2×C4×Q8C2312yes—
55C22×C4⋊C4—21no—
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×C4⋊C4D411yescharacteristic
65C22×C42C2×C411yescharacteristic
66C22×C42C2×C411yescharacteristic
67C22×C42D411yescharacteristic
68C22×C42D411yescharacteristic
69C22×C42C2311yescharacteristic
70#446—216no—
71#446—216no—
72#432—24no—
73#432—24no—
74#432—22no—
75#432—22no—
76#432—22no—
77#432—22no—
78#432—22no—
79#432D414yes—
80#432C2314yes—
81#432C2314yes—
82#431—24no—
83#431—24no—
84C2×C4⋊C8—22no—
85C2×C4⋊C8—22no—
86C2×C4⋊C8—22no—
87C2×C4⋊C8—22no—
88C2×C22⋊C8—22no—
89C2×C22⋊C8—22no—
90C2×#97—22no—
91C2×#97—22no—
92C2×#97D414yes—
93C2×C4×C8—22no—
94#398—24no—
95#398—24no—
96#398—24no—
97#398—24no—
98#391—22no—
99#391—22no—
100#391C2×C414yes—
101#391C2×C414yes—
102#387—24no—
103#387—24no—
104#387—24no—
105#387—24no—
106#384—22no—
107#384C2×C414yes—
108#382—22no—
109#382C2×C414yes—
110C4×C4⋊C4—21no—
111C4×C4⋊C4—21no—
112C4×C4⋊C4C2×C412yes—
113C4×C4⋊C4C2312yes—
114C2×#95—21no—
115C2×#95—21no—
116C2×#95—21no—
117C2×#95—21no—
118C2×#95—21no—
119C2×#95—21no—
120C2×#95—21no—
121#330—216no—
122#324—24no—
123#324—24no—
124C22×Q8—24no—
125C22×Q8—22no—
126C22×Q8—22no—
127C22×Q8—42no—
128C22×Q8C22⋊C412yes—
129C22×Q8C22×C412yes—
130C23×C4—21no—
131C23×C4—21no—
132C23×C4—21no—
133C23×C4—21no—
134C23×C4C22⋊C411yescharacteristic
135C23×C4C22⋊C411yescharacteristic
136C23×C4C22⋊C411yescharacteristic
137C23×C4C22⋊C411yescharacteristic
138C23×C4C22×C411yescharacteristic
139C23×C4C2×D411yescharacteristic
140C23×C4C2×D411yescharacteristic
141C22×C8—24no—
142C22×C8—42no—
143#125—24no—
144#125—24no—
145#125—24no—
146#125—24no—
147#125—42no—
148#125—42no—
149#125—42no—
150#125—42no—
151C4×Q8—24no—
152C4×Q8—24no—
153C4×Q8—24no—
154C4×Q8—24no—
155C4×Q8—24no—
156C4×Q8—24no—
157C4×Q8—24no—
158C4×Q8—24no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—22no—
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—24no—
173C2×C4⋊C4—24no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—44no—
180C2×C4⋊C4—44no—
181C2×C4⋊C4—44no—
182C2×C4⋊C4—41no—
183C2×C4⋊C4—41no—
184C2×C4⋊C4—42no—
185C2×C4⋊C4—42no—
186C2×C4⋊C4—41no—
187C2×C4⋊C4—41no—
188C2×C4⋊C4C22⋊C412yes—
189C2×C4⋊C4C22⋊C412yes—
190C2×C4⋊C4C22⋊C412yes—
191C2×C4⋊C4C22×C412yes—
192C2×C4⋊C4C22×C412yes—
193C2×C4⋊C4C22×C412yes—
194C2×C4⋊C4C2×D412yes—
195C2×C4⋊C4C2×D412yes—
196C2×C42—21no—
197C2×C42—21no—
198C2×C42—21no—
199C2×C42—21no—
200C2×C42—21no—
201C2×C42—21no—
202C2×C42—21no—
203C2×C42—21no—
204C2×C42—21no—
205C2×C42—21no—
206C2×C42—42no—
207C2×C42—42no—
208C2×C42C22⋊C412yes—
209C2×C42C22⋊C412yes—
210C2×C42C22×C412yes—
211C2×C42C22×C412yes—
212C2×C42C22×C411yescharacteristic
213C2×C42C2×D412yes—
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—28no—
223C4⋊C8—28no—
224C4⋊C8—24no—
225C4⋊C8—24no—
226C4⋊C8—24no—
227C4⋊C8—42no—
228C22⋊C8—24no—
229C22⋊C8—24no—
230C22⋊C8—24no—
231C22⋊C8—42no—
232#97—28no—
233#97—24no—
234#97—24no—
235#97—42no—
236#97C2×D418yes—
237C4×C8—28no—
238#95—22no—
239#95—24no—
240#95—24no—
241#95—24no—
242#95—24no—
243#95—24no—
244#95—24no—
245#95—22no—
246C24C2×C22⋊C411yescharacteristic
247C2×Q8—24no—
248C2×Q8—24no—
249C2×Q8—24no—
250C2×Q8—24no—
251C2×Q8—42no—
252C2×Q8—42no—
253C2×Q8—48no—
254C2×Q8—48no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—24no—
261C22×C4—22no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—44no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—42no—
289C22×C4#10114yes—
290C22×C4C2×C22⋊C412yes—
291C22×C4C2×C22⋊C411yescharacteristic
292C22×C4C2×C22⋊C412yes—
293C22×C4C2×C22⋊C412yes—
294C22×C4C2×C22⋊C412yes—
295C22×C4C2×C22⋊C411yescharacteristic
296C22×C4C2×C22⋊C411yescharacteristic
297C22×C4C4×D412yes—
298C22×C4C4×D412yes—
299C22×C4#12011yescharacteristic
300C22×C4#12011yescharacteristic
301C22×C4#12112yes—
302C22×C4#12112yes—
303C22×C4#12311yescharacteristic
304C22×C4#12311yescharacteristic
305C22×C4C23×C411yescharacteristic
306C22×C4C22×D411yescharacteristic
307C22×C4C22×D411yescharacteristic
308C2×C8—28no—
309C2×C8—48no—
310C2×C8—44no—
311C2×C8—84no—
312C4⋊C4—24no—
313C4⋊C4—24no—
314C4⋊C4—24no—
315C4⋊C4—24no—
316C4⋊C4—24no—
317C4⋊C4—24no—
318C4⋊C4—24no—
319C4⋊C4—24no—
320C4⋊C4—44no—
321C4⋊C4—44no—
322C4⋊C4—48no—
323C4⋊C4—48no—
324C4⋊C4—42no—
325C4⋊C4—44no—
326C4⋊C4—42no—
327C4⋊C4—42no—
328C4⋊C4—42no—
329C4⋊C4—42no—
330C4⋊C4—42no—
331C4⋊C4—44no—
332C42—22no—
333C42—22no—
334C42—22no—
335C42—22no—
336C42—22no—
337C42—22no—
338C42—22no—
339C42—22no—
340C42—42no—
341C42—42no—
342C42—42no—
343C42—42no—
344C42C4×D412yes—
345C42C4×D412yes—
346C42#12012yes—
347C42#12112yes—
348C42#12112yes—
349C42#12312yes—
350C42C22×D412yes—
351C42C2×#4112yes—
352C23—22no—
353C23—22no—
354C23#38611yescharacteristic
355C23#38611yescharacteristic
356C23C2×#10112yes—
357C23#41312yes—
358C23C22×C22⋊C411yescharacteristic
359Q8—48no—
360Q8—48no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—22no—
366C2×C4—24no—
367C2×C4—24no—
368C2×C4—24no—
369C2×C4—24no—
370C2×C4—24no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—24no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—48no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—44no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—84no—
407C2×C4—82no—
408C2×C4—82no—
409C2×C4—82no—
410C2×C4—82no—
411C2×C4#38611yescharacteristic
412C2×C4#38611yescharacteristic
413C2×C4#38612yes—
414C2×C4#38612yes—
415C2×C4C2×#10114yes—
416C2×C4C2×C4×D412yes—
417C2×C4C2×#12011yescharacteristic
418C2×C4C2×#12112yes—
419C2×C4C2×#12311yescharacteristic
420C8—48no—
421C8—84no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—24no—
427C22—24no—
428C22#188412yes—
429C22#190112yes—
430C22#190112yes—
431C22#191212yes—
432C22C2×#38611yescharacteristic
433C22C22×#10111yescharacteristic
434C22C2×#41311yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—22no—
440C4—22no—
441C4—22no—
442C4—22no—
443C4—24no—
444C4—44no—
445C4—42no—
446C4—42no—
447C4—42no—
448C4—82no—
449C4—82no—
450C4—82no—
451C2—21no—
452C2—21no—
453C2—22no—
454C2#945014yesdirect product factor
455C2C2×#188411yescharacteristic
456C2C2×#190111yescharacteristic
457C2C2×#191211yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
prime radicalC24C2×C22⋊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
5. #9450C2direct (N × H)
454. C2#9450direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#29832
C2×#25652
C2×#15342
C2×#14672
#94502
C2×#12852