Finite Group Databasebeta

← C2×#9448 #201132

Subgroups — C2×#9448 #201132

Order 512.

1336 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2983C211yesmaximal, characteristic, complemented
2C2×#2545C211yesmaximal, characteristic
3C2×#1533C212yesmaximal
4C2×#1467C211yesmaximal, characteristic, complemented
5#9448C218yesmaximal, direct product factor
6C2×#1285C212yesmaximal, complemented
7C22×C4⋊Q8C411yescharacteristic
8C22×#124C411yescharacteristic
9C22×#124C2211yescharacteristic
10C22×C4×Q8C2211yescharacteristic
11#2983—24no—
12#2983—22no—
13#2983C2214yescomplemented
14C2×#446—24no—
15C2×#432—21no—
16C2×#432C2212yes—
17C2×#432C2212yes—
18C2×#431—21no—
19#2545—22no—
20#2545—22no—
21#2545C414yes—
22#2545C2214yes—
23C2×#396—21no—
24C2×#396—21no—
25C2×#391C411yescharacteristic
26C2×#390C411yescharacteristic
27C2×#388—21no—
28C2×#388—21no—
29C2×C4×C4⋊C4C2211yescharacteristic
30#1533—24no—
31#1533C2218yes—
32C2×#329—24no—
33#1467—22no—
34#1467C2214yescomplemented
35C2×#324—21no—
36C2×#324—21no—
37#1285C2218yescomplemented
38C23×Q8C2×C411yescharacteristic
39C23×Q8C2×C411yescharacteristic
40C23×D4C2×C411yescharacteristic
41C2×C4⋊Q8—22no—
42C2×C4⋊Q8—44no—
43C2×C4⋊Q8C2×C414yes—
44C2×#124—22no—
45C2×#124—21no—
46C2×#124—21no—
47C2×#124—22no—
48C2×#124—22no—
49C2×#124—22no—
50C2×#124—22no—
51C2×#124—44no—
52C2×#124C2×C412yes—
53C2×#124C2×C414yes—
54C2×#124C2312yes—
55C2×C4×Q8—22no—
56C2×C4×Q8—22no—
57C2×C4×Q8—22no—
58C2×C4×Q8—22no—
59C2×C4×Q8C2×C412yes—
60C2×C4×Q8D412yes—
61C2×C4×Q8D412yes—
62C2×C4×Q8C2312yes—
63C22×C4⋊C4—21no—
64C22×C4⋊C4—21no—
65C22×C4⋊C4—21no—
66C22×C4⋊C4C2×C411yescharacteristic
67C22×C4⋊C4D411yescharacteristic
68C22×C4⋊C4D411yescharacteristic
69C22×C22⋊C4—21no—
70C22×C22⋊C4—21no—
71C22×C22⋊C4—21no—
72C22×C22⋊C4—21no—
73C22×C22⋊C4—21no—
74C22×C22⋊C4—21no—
75C22×C42C2×C411yescharacteristic
76C22×C42C2×C411yescharacteristic
77C22×C42D411yescharacteristic
78C22×C42D411yescharacteristic
79C22×C42C2311yescharacteristic
80#446—216no—
81#446—216no—
82#432—24no—
83#432—24no—
84#432—22no—
85#432—22no—
86#432—22no—
87#432—22no—
88#432—22no—
89#432D414yes—
90#432C2314yes—
91#432C2314yes—
92#431—24no—
93#431—24no—
94C2×C4⋊C8—22no—
95C2×C4⋊C8—22no—
96C2×C4⋊C8—22no—
97C2×C4⋊C8—22no—
98C2×C22⋊C8—22no—
99C2×C22⋊C8—22no—
100C2×#97—22no—
101C2×#97—22no—
102C2×#97D414yes—
103C2×C4×C8—22no—
104#396—24no—
105#396—24no—
106#396—24no—
107#396—24no—
108#391—22no—
109#391C2×C414yes—
110#390—22no—
111#390C2×C414yes—
112#388—24no—
113#388—24no—
114#388—24no—
115#388—24no—
116C4×C4⋊C4—21no—
117C4×C4⋊C4—21no—
118C4×C4⋊C4C2×C412yes—
119C4×C4⋊C4C2312yes—
120C2×#95—21no—
121C2×#95—21no—
122C2×#95—21no—
123#329—216no—
124#324—24no—
125#324—24no—
126C25—21no—
127C22×Q8—24no—
128C22×Q8—21no—
129C22×Q8—22no—
130C22×Q8—22no—
131C22×Q8—22no—
132C22×Q8—22no—
133C22×Q8—42no—
134C22×Q8—42no—
135C22×Q8—42no—
136C22×Q8C22⋊C412yes—
137C22×Q8C22×C412yes—
138C22×Q8C22×C412yes—
139C22×D4—21no—
140C22×D4—22no—
141C22×D4—22no—
142C22×D4—42no—
143C22×D4—42no—
144C22×D4C22×C412yes—
145C23×C4—21no—
146C23×C4—21no—
147C23×C4—21no—
148C23×C4C22⋊C411yescharacteristic
149C23×C4C22⋊C411yescharacteristic
150C23×C4C22⋊C411yescharacteristic
151C23×C4C22⋊C411yescharacteristic
152C23×C4C22×C411yescharacteristic
153C23×C4C2×D411yescharacteristic
154C23×C4C2×D411yescharacteristic
155C22×C8—24no—
156C22×C8—42no—
157C4⋊Q8—48no—
158C4⋊Q8—48no—
159#124—24no—
160#124—24no—
161#124—24no—
162#124—24no—
163#124—48no—
164#124—48no—
165#124—42no—
166#124—42no—
167#124—42no—
168#124—42no—
169C4×Q8—24no—
170C4×Q8—24no—
171C4×Q8—24no—
172C4×Q8—24no—
173C4×Q8—24no—
174C4×Q8—24no—
175C4×Q8—24no—
176C4×Q8—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—24no—
184C2×C4⋊C4—24no—
185C2×C4⋊C4—22no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—44no—
188C2×C4⋊C4—44no—
189C2×C4⋊C4—44no—
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×C22⋊C4—22no—
197C2×C22⋊C4—24no—
198C2×C22⋊C4—24no—
199C2×C22⋊C4—22no—
200C2×C22⋊C4—24no—
201C2×C22⋊C4—24no—
202C2×C22⋊C4—22no—
203C2×C22⋊C4—22no—
204C2×C22⋊C4—44no—
205C2×C22⋊C4—44no—
206C2×C22⋊C4—44no—
207C2×C22⋊C4—44no—
208C2×C22⋊C4—41no—
209C2×C22⋊C4—41no—
210C2×C22⋊C4—42no—
211C2×C22⋊C4—42no—
212C2×C22⋊C4—41no—
213C2×C22⋊C4—41no—
214C2×C42—21no—
215C2×C42—21no—
216C2×C42—21no—
217C2×C42—21no—
218C2×C42—21no—
219C2×C42—21no—
220C2×C42—21no—
221C2×C42—21no—
222C2×C42—21no—
223C2×C42—21no—
224C2×C42—42no—
225C2×C42—42no—
226C2×C42C22⋊C412yes—
227C2×C42C22⋊C412yes—
228C2×C42C22×C412yes—
229C2×C42C22×C412yes—
230C2×C42C22×C411yescharacteristic
231C2×C42C2×D412yes—
232C2×C42C2×D412yes—
233C2×C42C2×D412yes—
234C2×C42C2×D412yes—
235C2×C42C2×D411yescharacteristic
236C2×C42C2×D411yescharacteristic
237C2×C42#4112yes—
238C2×C42#4112yes—
239C2×C42C2411yescharacteristic
240C4⋊C8—28no—
241C4⋊C8—28no—
242C4⋊C8—24no—
243C4⋊C8—24no—
244C4⋊C8—24no—
245C4⋊C8—42no—
246C22⋊C8—24no—
247C22⋊C8—24no—
248C22⋊C8—24no—
249C22⋊C8—42no—
250#97—28no—
251#97—24no—
252#97—24no—
253#97—42no—
254#97C2×D418yes—
255C4×C8—28no—
256#95—22no—
257#95—24no—
258#95—24no—
259#95—22no—
260C24—22no—
261C24—42no—
262C24—42no—
263C24—42no—
264C24—42no—
265C24—41no—
266C24—41no—
267C24—42no—
268C24—42no—
269C24C2×C22⋊C411yescharacteristic
270C2×Q8—24no—
271C2×Q8—24no—
272C2×Q8—24no—
273C2×Q8—24no—
274C2×Q8—24no—
275C2×Q8—42no—
276C2×Q8—42no—
277C2×Q8—48no—
278C2×Q8—48no—
279C2×Q8—42no—
280C2×Q8—42no—
281C2×Q8—42no—
282C2×Q8—42no—
283C2×Q8—42no—
284C2×Q8—84no—
285C2×Q8—84no—
286C2×D4—24no—
287C2×D4—42no—
288C2×D4—42no—
289C2×D4—42no—
290C2×D4—42no—
291C2×D4—42no—
292C2×D4—84no—
293C2×D4—84no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—24no—
300C22×C4—22no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4—42no—
324C22×C4#10014yes—
325C22×C4C2×C22⋊C412yes—
326C22×C4C2×C22⋊C411yescharacteristic
327C22×C4C2×C22⋊C412yes—
328C22×C4C2×C22⋊C412yes—
329C22×C4C2×C22⋊C412yes—
330C22×C4C2×C22⋊C411yescharacteristic
331C22×C4C2×C22⋊C411yescharacteristic
332C22×C4C4×D412yes—
333C22×C4C4×D412yes—
334C22×C4#12011yescharacteristic
335C22×C4#12011yescharacteristic
336C22×C4#12112yes—
337C22×C4#12112yes—
338C22×C4#12311yescharacteristic
339C22×C4#12311yescharacteristic
340C22×C4C23×C411yescharacteristic
341C22×C4C22×D411yescharacteristic
342C22×C4C22×D411yescharacteristic
343C2×C8—28no—
344C2×C8—48no—
345C2×C8—44no—
346C2×C8—84no—
347C4⋊C4—24no—
348C4⋊C4—24no—
349C4⋊C4—24no—
350C4⋊C4—24no—
351C4⋊C4—24no—
352C4⋊C4—24no—
353C4⋊C4—44no—
354C4⋊C4—44no—
355C4⋊C4—48no—
356C4⋊C4—48no—
357C22⋊C4—48no—
358C22⋊C4—48no—
359C22⋊C4—48no—
360C22⋊C4—42no—
361C22⋊C4—44no—
362C22⋊C4—42no—
363C22⋊C4—42no—
364C22⋊C4—42no—
365C22⋊C4—44no—
366C22⋊C4—48no—
367C42—22no—
368C42—22no—
369C42—22no—
370C42—22no—
371C42—22no—
372C42—22no—
373C42—22no—
374C42—22no—
375C42—42no—
376C42—42no—
377C42—42no—
378C42—42no—
379C42C4×D412yes—
380C42C4×D412yes—
381C42#12012yes—
382C42#12112yes—
383C42#12112yes—
384C42#12312yes—
385C42C22×D412yes—
386C42C2×#4112yes—
387C23—22no—
388C23—22no—
389C23—42no—
390C23—42no—
391C23—42no—
392C23—42no—
393C23—42no—
394C23—42no—
395C23—42no—
396C23—82no—
397C23—82no—
398C23—84no—
399C23—84no—
400C23—84no—
401C23—84no—
402C23—82no—
403C23—82no—
404C23—82no—
405C23—82no—
406C23#38611yescharacteristic
407C23#38611yescharacteristic
408C23C2×#10012yes—
409C23#41312yes—
410C23C22×C22⋊C411yescharacteristic
411Q8—48no—
412Q8—48no—
413Q8—84no—
414Q8—84no—
415D4—84no—
416D4—84no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—22no—
421C2×C4—21no—
422C2×C4—24no—
423C2×C4—24no—
424C2×C4—24no—
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—24no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—42no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—42no—
444C2×C4—48no—
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—42no—
458C2×C4—81no—
459C2×C4—81no—
460C2×C4—84no—
461C2×C4—82no—
462C2×C4—82no—
463C2×C4#38611yescharacteristic
464C2×C4#38611yescharacteristic
465C2×C4#38612yes—
466C2×C4#38612yes—
467C2×C4C2×#10014yes—
468C2×C4C2×C4×D412yes—
469C2×C4C2×#12011yescharacteristic
470C2×C4C2×#12112yes—
471C2×C4C2×#12311yescharacteristic
472C8—48no—
473C8—84no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—24no—
479C22—24no—
480C22—82no—
481C22—82no—
482C22—82no—
483C22—82no—
484C22—82no—
485C22—82no—
486C22—82no—
487C22—164no—
488C22—164no—
489C22#188412yes—
490C22#190012yes—
491C22#190012yes—
492C22#191212yes—
493C22C2×#38611yescharacteristic
494C22C22×#10011yescharacteristic
495C22C2×#41311yescharacteristic
496C4—21no—
497C4—21no—
498C4—21no—
499C4—21no—
500C4—22no—
501C4—22no—
502C4—22no—
503C4—22no—
504C4—24no—
505C4—44no—
506C4—42no—
507C4—42no—
508C4—42no—
509C4—82no—
510C4—82no—
511C2—21no—
512C2—21no—
513C2—22no—
514C2—162no—
515C2#944814yesdirect product factor
516C2C2×#188411yescharacteristic
517C2C2×#190011yescharacteristic
518C2C2×#191211yescharacteristic
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
1. C2×#2983C2semidirect
4. C2×#1467C2semidirect
5. #9448C2direct (N × H)
6. C2×#1285C2semidirect
13. #2983C22semidirect
34. #1467C22semidirect
37. #1285C22semidirect
515. C2#9448direct (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×#25452
C2×#15332
C2×#14672
#94482
C2×#12852