Finite Group Databasebeta

← C2×#9449 #201131

Subgroups — C2×#9449 #201131

Order 512.

1332 conjugacy classes of subgroups.

The subgroup lattice has 529 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2973C211yesmaximal, characteristic
2C2×#2566C211yesmaximal, characteristic
3C2×#1534C212yesmaximal, complemented
4C2×#1466C211yesmaximal, characteristic
5#9449C218yesmaximal, direct product factor
6C2×#1285C212yesmaximal, complemented
7C22×#125C2211yescharacteristic
8C22×C4×D4C2211yescharacteristic
9#2973—24no—
10#2973—22no—
11#2973C2214yes—
12C2×#435—24no—
13C2×#432C2212yes—
14C2×#432C2212yes—
15C2×#407—21no—
16C22×C22⋊C8—21no—
17#2566—22no—
18#2566—22no—
19#2566C414yes—
20#2566C2214yes—
21C2×#396—21no—
22C2×#396—21no—
23C2×#390C411yescharacteristic
24C2×#390C411yescharacteristic
25C2×#385—21no—
26C2×#385—21no—
27C2×#384C411yescharacteristic
28C2×#382C411yescharacteristic
29C2×C4×C4⋊C4C2211yescharacteristic
30#1534—24no—
31#1534C2218yescomplemented
32C2×#330—24no—
33#1466—22no—
34#1466C2214yes—
35C2×#323—21no—
36C2×#323—21no—
37#1285C2218yescomplemented
38C23×D4C2×C411yescharacteristic
39C24×C4D411yescharacteristic
40C24×C4D411yescharacteristic
41C22×M16—22no—
42C23×C8—22no—
43C2×#125—21no—
44C2×#125—21no—
45C2×#125—22no—
46C2×#125—22no—
47C2×#125—22no—
48C2×#125—22no—
49C2×#125C2×C412yes—
50C2×#125C2312yes—
51C2×C4×D4—22no—
52C2×C4×D4—22no—
53C2×C4×D4—22no—
54C2×C4×D4—22no—
55C2×C4×D4C2×C412yes—
56C2×C4×D4D412yes—
57C2×C4×D4D412yes—
58C2×C4×D4C2312yes—
59C22×C4⋊C4—21no—
60C22×C4⋊C4—21no—
61C22×C4⋊C4—21no—
62C22×C4⋊C4—21no—
63C22×C4⋊C4—21no—
64C22×C4⋊C4C2×C411yescharacteristic
65C22×C4⋊C4C2×C411yescharacteristic
66C22×C4⋊C4C2×C411yescharacteristic
67C22×C22⋊C4—21no—
68C22×C22⋊C4—21no—
69C22×C22⋊C4—21no—
70C22×C22⋊C4—21no—
71C22×C22⋊C4D411yescharacteristic
72C22×C22⋊C4D411yescharacteristic
73C22×C42C2×C411yescharacteristic
74C22×C42C2×C411yescharacteristic
75C22×C42C2311yescharacteristic
76#435—216no—
77#435—216no—
78#432—22no—
79#432—22no—
80#432—22no—
81#432—22no—
82#432—22no—
83#432D414yes—
84#432C2314yes—
85#432C2314yes—
86C2×C4⋊C8—22no—
87C2×C4⋊C8—22no—
88#407—24no—
89#407—24no—
90C2×C22⋊C8—22no—
91C2×C22⋊C8—24no—
92C2×C22⋊C8—22no—
93C2×C22⋊C8—22no—
94C2×C22⋊C8—24no—
95C2×C22⋊C8—22no—
96C2×#97—22no—
97C2×#97D414yes—
98#396—24no—
99#396—24no—
100#396—24no—
101#396—24no—
102#390—22no—
103#390—22no—
104#390C2×C414yes—
105#390C2×C414yes—
106#385—24no—
107#385—24no—
108#385—24no—
109#385—24no—
110#384—22no—
111#384C2×C414yes—
112#382—22no—
113#382C2×C414yes—
114C4×C4⋊C4—21no—
115C4×C4⋊C4—21no—
116C4×C4⋊C4C2×C412yes—
117C4×C4⋊C4C2312yes—
118C2×#95—21no—
119C2×#95—21no—
120C2×#95—21no—
121#330—216no—
122#323—24no—
123#323—24no—
124C25C22⋊C411yescharacteristic
125C25C22⋊C411yescharacteristic
126C22×D4—24no—
127C22×D4—22no—
128C22×D4—22no—
129C22×D4—42no—
130C22×D4C22⋊C412yes—
131C22×D4C22×C412yes—
132C23×C4—21no—
133C23×C4—21no—
134C23×C4—21no—
135C23×C4—21no—
136C23×C4—21no—
137C23×C4—21no—
138C23×C4—21no—
139C23×C4—21no—
140C23×C4—21no—
141C23×C4—21no—
142C23×C4—21no—
143C23×C4—21no—
144C23×C4—82no—
145C23×C4—82no—
146C23×C4C22⋊C411yescharacteristic
147C23×C4C22⋊C411yescharacteristic
148C23×C4C22⋊C412yes—
149C23×C4C22⋊C412yes—
150C23×C4C22×C411yescharacteristic
151C23×C4C2×D412yes—
152C23×C4C2×D412yes—
153C23×C4C2×D411yescharacteristic
154C23×C4C2×D411yescharacteristic
155C2×M16—28no—
156C2×M16—84no—
157C22×C8—24no—
158C22×C8—28no—
159C22×C8—42no—
160C22×C8—84no—
161#125—24no—
162#125—24no—
163#125—24no—
164#125—24no—
165#125—42no—
166#125—42no—
167#125—42no—
168#125—42no—
169C4×D4—24no—
170C4×D4—24no—
171C4×D4—24no—
172C4×D4—24no—
173C4×D4—24no—
174C4×D4—24no—
175C4×D4—24no—
176C4×D4—24no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4—22no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4—22no—
191C2×C4⋊C4—24no—
192C2×C4⋊C4—24no—
193C2×C4⋊C4—44no—
194C2×C4⋊C4—41no—
195C2×C4⋊C4—41no—
196C2×C4⋊C4—42no—
197C2×C4⋊C4—42no—
198C2×C4⋊C4—41no—
199C2×C4⋊C4—41no—
200C2×C4⋊C4—82no—
201C2×C4⋊C4—82no—
202C2×C4⋊C4C22⋊C412yes—
203C2×C4⋊C4C22×C412yes—
204C2×C4⋊C4C22×C412yes—
205C2×C4⋊C4C22×C412yes—
206C2×C22⋊C4—22no—
207C2×C22⋊C4—22no—
208C2×C22⋊C4—22no—
209C2×C22⋊C4—22no—
210C2×C22⋊C4—24no—
211C2×C22⋊C4—24no—
212C2×C22⋊C4—24no—
213C2×C22⋊C4—24no—
214C2×C22⋊C4—44no—
215C2×C22⋊C4—44no—
216C2×C22⋊C4—82no—
217C2×C22⋊C4—82no—
218C2×C22⋊C4C22⋊C412yes—
219C2×C22⋊C4C22⋊C412yes—
220C2×C22⋊C4C2×D412yes—
221C2×C22⋊C4C2×D412yes—
222C2×C42—21no—
223C2×C42—21no—
224C2×C42—42no—
225C2×C42—42no—
226C2×C42C22×C412yes—
227C2×C42C22×C412yes—
228C2×C42C22×C411yescharacteristic
229C2×C42C2×D412yes—
230C2×C42C2×D412yes—
231C2×C42C2×D411yescharacteristic
232C2×C42C2×D411yescharacteristic
233C2×C42#4112yes—
234C2×C42#4112yes—
235C2×C42C2411yescharacteristic
236C4⋊C8—24no—
237C4⋊C8—24no—
238C4⋊C8—24no—
239C4⋊C8—42no—
240C22⋊C8—28no—
241C22⋊C8—28no—
242C22⋊C8—24no—
243C22⋊C8—24no—
244C22⋊C8—24no—
245C22⋊C8—42no—
246#97—24no—
247#97—24no—
248#97—42no—
249#97C2×D418yes—
250#95—22no—
251#95—24no—
252#95—24no—
253#95—22no—
254C24—21no—
255C24—21no—
256C24—22no—
257C24—21no—
258C24—22no—
259C24—21no—
260C24—22no—
261C24—42no—
262C24—42no—
263C24—42no—
264C24—42no—
265C24#10114yes—
266C24C2×C22⋊C411yescharacteristic
267C24C2×C22⋊C412yes—
268C24C2×C22⋊C412yes—
269C2×D4—24no—
270C2×D4—24no—
271C2×D4—24no—
272C2×D4—24no—
273C2×D4—42no—
274C2×D4—42no—
275C2×D4—48no—
276C2×D4—48no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—24no—
280C22×C4—22no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—22no—
291C22×C4—22no—
292C22×C4—22no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—44no—
299C22×C4—44no—
300C22×C4—42no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—42no—
305C22×C4—42no—
306C22×C4—42no—
307C22×C4—42no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—42no—
315C22×C4—82no—
316C22×C4—82no—
317C22×C4—82no—
318C22×C4—82no—
319C22×C4—82no—
320C22×C4—82no—
321C22×C4—82no—
322C22×C4—82no—
323C22×C4—82no—
324C22×C4—82no—
325C22×C4C2×C22⋊C411yescharacteristic
326C22×C4C2×C22⋊C412yes—
327C22×C4C2×C22⋊C412yes—
328C22×C4C2×C22⋊C411yescharacteristic
329C22×C4C2×C22⋊C411yescharacteristic
330C22×C4C4×D412yes—
331C22×C4C4×D412yes—
332C22×C4#12011yescharacteristic
333C22×C4#12011yescharacteristic
334C22×C4#12112yes—
335C22×C4#12112yes—
336C22×C4#12311yescharacteristic
337C22×C4#12311yescharacteristic
338C22×C4C23×C411yescharacteristic
339C22×C4C22×D411yescharacteristic
340C22×C4C22×D411yescharacteristic
341M16—88no—
342C2×C8—28no—
343C2×C8—48no—
344C2×C8—44no—
345C2×C8—88no—
346C2×C8—84no—
347C4⋊C4—24no—
348C4⋊C4—24no—
349C4⋊C4—24no—
350C4⋊C4—24no—
351C4⋊C4—44no—
352C4⋊C4—44no—
353C4⋊C4—42no—
354C4⋊C4—44no—
355C4⋊C4—42no—
356C4⋊C4—42no—
357C4⋊C4—42no—
358C4⋊C4—44no—
359C4⋊C4—42no—
360C4⋊C4—42no—
361C4⋊C4—84no—
362C4⋊C4—84no—
363C22⋊C4—24no—
364C22⋊C4—24no—
365C22⋊C4—24no—
366C22⋊C4—24no—
367C22⋊C4—48no—
368C22⋊C4—48no—
369C22⋊C4—84no—
370C22⋊C4—84no—
371C42—42no—
372C42—42no—
373C42—42no—
374C42—42no—
375C42C4×D412yes—
376C42C4×D412yes—
377C42#12012yes—
378C42#12112yes—
379C42#12112yes—
380C42#12312yes—
381C42C22×D412yes—
382C42C2×#4112yes—
383C23—22no—
384C23—22no—
385C23—24no—
386C23—22no—
387C23—22no—
388C23—24no—
389C23—22no—
390C23—22no—
391C23—22no—
392C23—42no—
393C23—42no—
394C23—42no—
395C23—42no—
396C23—48no—
397C23—48no—
398C23—42no—
399C23—42no—
400C23—42no—
401C23—42no—
402C23—42no—
403C23—42no—
404C23—81no—
405C23—81no—
406C23—81no—
407C23—81no—
408C23—84no—
409C23—84no—
410C23#38611yescharacteristic
411C23#38611yescharacteristic
412C23C2×#10112yes—
413C23C2×#10114yes—
414C23#41312yes—
415C23C22×C22⋊C411yescharacteristic
416D4—48no—
417D4—48no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—24no—
423C2×C4—24no—
424C2×C4—24no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—24no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—44no—
438C2×C4—44no—
439C2×C4—44no—
440C2×C4—44no—
441C2×C4—42no—
442C2×C4—48no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—82no—
458C2×C4—82no—
459C2×C4—82no—
460C2×C4—82no—
461C2×C4—81no—
462C2×C4—81no—
463C2×C4—84no—
464C2×C4—82no—
465C2×C4—82no—
466C2×C4—82no—
467C2×C4—82no—
468C2×C4#38612yes—
469C2×C4#38611yescharacteristic
470C2×C4#38611yescharacteristic
471C2×C4#38612yes—
472C2×C4C2×C4×D412yes—
473C2×C4C2×#12011yescharacteristic
474C2×C4C2×#12112yes—
475C2×C4C2×#12311yescharacteristic
476C8—48no—
477C8—84no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—24no—
483C22—24no—
484C22—24no—
485C22—44no—
486C22—44no—
487C22—42no—
488C22—42no—
489C22—48no—
490C22—42no—
491C22—42no—
492C22—42no—
493C22—82no—
494C22—84no—
495C22—82no—
496C22—84no—
497C22—84no—
498C22#188412yes—
499C22#190112yes—
500C22#190112yes—
501C22#191112yes—
502C22C2×#38611yescharacteristic
503C22C22×#10111yescharacteristic
504C22C2×#41311yescharacteristic
505C4—21no—
506C4—21no—
507C4—21no—
508C4—21no—
509C4—22no—
510C4—22no—
511C4—22no—
512C4—22no—
513C4—44no—
514C4—42no—
515C4—42no—
516C4—82no—
517C4—82no—
518C4—82no—
519C2—21no—
520C2—21no—
521C2—22no—
522C2—44no—
523C2—82no—
524C2#944914yesdirect product factor
525C2C2×#188411yescharacteristic
526C2C2×#190111yescharacteristic
527C2C2×#191111yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
prime radicalC23×D4C2×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×#1534C2semidirect
5. #9449C2direct (N × H)
6. C2×#1285C2semidirect
31. #1534C22semidirect
37. #1285C22semidirect
524. C2#9449direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#29732
C2×#25662
C2×#15342
C2×#14662
#94492
C2×#12852