Finite Group Databasebeta

← C2×#9328 #199430

Subgroups — C2×#9328 #199430

Order 512.

1182 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3113C211yesmaximal, characteristic
2C2×#2320C211yesmaximal, characteristic
3C2×#1986C211yesmaximal, characteristic
4C2×#1506C211yesmaximal, characteristic
5C2×#1491C211yesmaximal, characteristic
6#9328C218yesmaximal, direct product factor
7C2×#1300C211yesmaximal, characteristic
8C2×#1285C211yesmaximal, characteristic
9C2×#533C2211yescharacteristic
10C22×C4×Q8C2211yescharacteristic
11#3113—22no—
12#3113—22no—
13#3113C414yescomplemented
14#3113C2214yes—
15C2×#483—21no—
16C2×#475C412yescomplemented
17C2×#462C412yescomplemented
18C2×#451—21no—
19C2×#441—22no—
20C2×#432C2211yescharacteristic
21C2×#432C2211yescharacteristic
22C2×C4×M16C2211yescharacteristic
23#2320—22no—
24#2320—22no—
25#2320—22no—
26#2320C2214yes—
27C2×#391—21no—
28C2×#389—21no—
29C2×#387—22no—
30C2×#383—21no—
31C2×#382—21no—
32C2×C4×C4⋊C4C2211yescharacteristic
33C2×#376C2211yescharacteristic
34#1986—22no—
35#1986C2214yes—
36C2×#339—22no—
37#1506—22no—
38#1506C2214yes—
39C2×#328—21no—
40C2×#328—21no—
41#1491—22no—
42#1491C2214yes—
43C2×Q8⋊C8—22no—
44#1300C2214yes—
45#1285C2214yes—
46C23×Q8D411yescharacteristic
47C22×Q16—22no—
48C22×M16—21no—
49#533—21no—
50#533—21no—
51#533—21no—
52#533—21no—
53#533—21no—
54#533—21no—
55#533C2×C412yes—
56#533C2312yes—
57C2×C4⋊Q8C2×C411yescharacteristic
58C2×C4⋊Q8C2×C411yescharacteristic
59C2×#125—21no—
60C2×C22⋊Q8—21no—
61C2×C22⋊Q8—21no—
62C2×C4×Q8—21no—
63C2×C4×Q8—21no—
64C2×C4×Q8—21no—
65C2×C4×Q8—21no—
66C2×C4×Q8—21no—
67C2×C4×Q8—21no—
68C2×C4×Q8—21no—
69C2×C4×Q8—21no—
70C2×C4×Q8C2×C412yes—
71C2×C4×Q8C2×C412yes—
72C2×C4×Q8D412yes—
73C2×C4×Q8D412yes—
74C2×C4×Q8D412yes—
75C2×C4×Q8C2312yes—
76C2×#117—21no—
77C22×C4⋊C4—21no—
78C22×C4⋊C4—21no—
79C22×C4⋊C4—22no—
80C22×C4⋊C4D411yescharacteristic
81C22×C42—21no—
82C22×C42—21no—
83C22×C42D412yes—
84C22×C42C2311yescharacteristic
85#483—24no—
86#483—24no—
87#475—24no—
88#475C2×C418yescomplemented
89#462—24no—
90#462C2×C418yescomplemented
91#451—24no—
92#451—24no—
93#441—28no—
94#441—28no—
95#432—21no—
96#432—21no—
97#432—21no—
98#432—21no—
99#432—21no—
100#432C2×C412yes—
101#432C2312yes—
102#432C2312yes—
103C2×#106—22no—
104C2×C4⋊C8—21no—
105C2×C4⋊C8C2×C412yes—
106C2×#103—22no—
107C2×#103—22no—
108C2×C22⋊C8—21no—
109C2×C22⋊C8—21no—
110C4×M16—21no—
111C4×M16—21no—
112C4×M16—21no—
113C4×M16C2312yes—
114C2×#97—21no—
115C2×#97—21no—
116C2×#97—21no—
117C2×C4×C8—21no—
118#391—24no—
119#391—24no—
120#389—24no—
121#389—24no—
122#387—28no—
123#387—28no—
124#383—24no—
125#383—24no—
126#382—24no—
127#382—24no—
128C4×C4⋊C4—21no—
129C4×C4⋊C4—21no—
130C4×C4⋊C4D412yes—
131C4×C4⋊C4C2312yes—
132#376—21no—
133#376—21no—
134#376D412yes—
135#376C2312yes—
136C2×#95—22no—
137C2×#95—22no—
138C2×#95—22no—
139C2×#95—21no—
140C2×#95—21no—
141C2×#95D411yescharacteristic
142C2×#95D411yescharacteristic
143#339—28no—
144#328—24no—
145#328—24no—
146Q8⋊C8—28no—
147C22×Q8—21no—
148C22×Q8—21no—
149C22×Q8—21no—
150C22×Q8—21no—
151C22×Q8—21no—
152C22×Q8—44no—
153C22×Q8C22⋊C412yes—
154C22×Q8C22⋊C412yes—
155C22×Q8C2×D412yes—
156C23×C4—21no—
157C23×C4—21no—
158C23×C4—22no—
159C23×C4—21no—
160C23×C4—21no—
161C23×C4C2×D411yescharacteristic
162C23×C4C2×D411yescharacteristic
163C23×C4C2×D411yescharacteristic
164C2×Q16—28no—
165C2×Q16—48no—
166C2×M16—24no—
167C2×M16—22no—
168C2×M16—42no—
169C2×M16—41no—
170C22×C8—22no—
171C22×C8—41no—
172C22×C8—41no—
173C4⋊Q8—21no—
174C4⋊Q8—21no—
175C4⋊Q8—21no—
176C4⋊Q8—21no—
177C4⋊Q8—21no—
178C4⋊Q8—21no—
179C4⋊Q8C22×C412yes—
180C4⋊Q8C22×C412yes—
181#125—22no—
182#125—22no—
183#125—41no—
184#125—41no—
185C22⋊Q8—22no—
186C22⋊Q8—22no—
187C22⋊Q8—22no—
188C22⋊Q8—22no—
189C22⋊Q8—41no—
190C22⋊Q8—41no—
191C22⋊Q8—41no—
192C22⋊Q8—41no—
193C4×Q8—22no—
194C4×Q8—22no—
195C4×Q8—22no—
196C4×Q8—22no—
197C4×Q8—22no—
198C4×Q8—22no—
199C4×Q8—22no—
200C4×Q8—22no—
201C4×Q8—22no—
202C4×Q8—22no—
203C4×Q8—22no—
204C4×Q8—22no—
205C4×Q8—22no—
206C4×Q8—22no—
207C4×Q8—22no—
208C4×Q8—22no—
209C4×Q8—41no—
210C4×Q8—41no—
211C4×Q8—41no—
212C4×Q8—41no—
213C4×Q8C22⋊C414yes—
214C4×Q8C22⋊C414yes—
215C4×Q8C22×C414yes—
216C4×Q8C2×D414yes—
217#117—22no—
218#117—22no—
219#117—41no—
220#117—41no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4—22no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—28no—
237C2×C4⋊C4—44no—
238C2×C4⋊C4—41no—
239C2×C4⋊C4—41no—
240C2×C4⋊C4—84no—
241C2×C4⋊C4C22⋊C412yes—
242C2×C4⋊C4C22⋊C412yes—
243C2×C4⋊C4C2×D412yes—
244C2×C22⋊C4—41no—
245C2×C42—22no—
246C2×C42—22no—
247C2×C42—22no—
248C2×C42—22no—
249C2×C42—22no—
250C2×C42—22no—
251C2×C42—22no—
252C2×C42—22no—
253C2×C42—22no—
254C2×C42—44no—
255C2×C42—41no—
256C2×C42—44no—
257C2×C42C22×C411yescharacteristic
258C2×C42C22×C411yescharacteristic
259C2×C42C2×D414yes—
260C2×C42C2×D411yescharacteristic
261C2×C42C2×D411yescharacteristic
262C2×C42C2×D411yescharacteristic
263C2×C42C2×D411yescharacteristic
264C2×C42C2×D411yescharacteristic
265C2×C42#4111yescharacteristic
266C2×C42#4111yescharacteristic
267C2×C42#4111yescharacteristic
268C2×C42#4111yescharacteristic
269C2×C42C2411yescharacteristic
270#106—28no—
271C4⋊C8—22no—
272C4⋊C8—22no—
273C4⋊C8—41no—
274C4⋊C8C22×C414yes—
275#103—28no—
276#103—28no—
277C22⋊C8—22no—
278C22⋊C8—22no—
279C22⋊C8—22no—
280C22⋊C8—41no—
281#97—22no—
282#97—22no—
283#97—22no—
284#97—22no—
285#97—41no—
286#97—41no—
287C4×C8—22no—
288C4×C8—41no—
289#95—28no—
290#95—28no—
291#95—28no—
292#95—22no—
293#95—22no—
294#95—21no—
295#95—21no—
296#95—22no—
297#95—22no—
298#95C2×D412yes—
299#95C2×D412yes—
300C24#12011yescharacteristic
301C2×Q8—22no—
302C2×Q8—22no—
303C2×Q8—22no—
304C2×Q8—22no—
305C2×Q8—22no—
306C2×Q8—24no—
307C2×Q8—24no—
308C2×Q8—44no—
309C2×Q8—44no—
310C2×Q8—44no—
311C2×Q8—44no—
312C2×Q8—44no—
313C2×Q8—41no—
314C2×Q8—41no—
315C2×Q8—44no—
316C2×Q8—82no—
317C2×Q8C2×C22⋊C414yes—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—24no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—24no—
329C22×C4—22no—
330C22×C4—42no—
331C22×C4—44no—
332C22×C4—42no—
333C22×C4—42no—
334C22×C4—42no—
335C22×C4—42no—
336C22×C4—44no—
337C22×C4—44no—
338C22×C4—42no—
339C22×C4—42no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—44no—
343C22×C4—42no—
344C22×C4—42no—
345C22×C4C2×C22⋊C411yescharacteristic
346C22×C4C2×C22⋊C411yescharacteristic
347C22×C4C4×D411yescharacteristic
348C22×C4C4×D411yescharacteristic
349C22×C4C4×D411yescharacteristic
350C22×C4C4×D411yescharacteristic
351C22×C4#12011yescharacteristic
352C22×C4#12011yescharacteristic
353C22×C4#12011yescharacteristic
354C22×C4#12111yescharacteristic
355C22×C4#12111yescharacteristic
356C22×C4#12111yescharacteristic
357C22×C4#12111yescharacteristic
358C22×C4#12311yescharacteristic
359C22×C4#12311yescharacteristic
360C22×C4C22×D411yescharacteristic
361C22×C4C22×D411yescharacteristic
362C22×C4C22×D411yescharacteristic
363Q16—416no—
364M16—24no—
365M16—44no—
366M16—42no—
367C2×C8—24no—
368C2×C8—44no—
369C2×C8—42no—
370C2×C8—44no—
371C2×C8—42no—
372C2×C8—82no—
373C4⋊C4—24no—
374C4⋊C4—24no—
375C4⋊C4—22no—
376C4⋊C4—24no—
377C4⋊C4—24no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—22no—
384C4⋊C4—44no—
385C4⋊C4—44no—
386C4⋊C4—42no—
387C4⋊C4—42no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4—41no—
392C4⋊C4—42no—
393C4⋊C4—42no—
394C4⋊C4—88no—
395C4⋊C4C2×C22⋊C414yes—
396C22⋊C4—42no—
397C22⋊C4—42no—
398C42—24no—
399C42—24no—
400C42—24no—
401C42—24no—
402C42—44no—
403C42—44no—
404C42—44no—
405C42—42no—
406C42—42no—
407C42—82no—
408C42C2×C22⋊C411yescharacteristic
409C42C2×C22⋊C411yescharacteristic
410C42C4×D411yescharacteristic
411C42C4×D411yescharacteristic
412C42C4×D411yescharacteristic
413C42C4×D411yescharacteristic
414C42#12111yescharacteristic
415C42#12111yescharacteristic
416C42#12111yescharacteristic
417C42#12111yescharacteristic
418C42#12311yescharacteristic
419C42#12311yescharacteristic
420C42C23×C411yescharacteristic
421C42C22×D411yescharacteristic
422C42C2×#4111yescharacteristic
423C42C2×#4111yescharacteristic
424C23—22no—
425C23—22no—
426C23#38611yescharacteristic
427C23#38611yescharacteristic
428C23#45512yes—
429C23#45612yes—
430C23C2×#12011yescharacteristic
431Q8—24no—
432Q8—24no—
433Q8—44no—
434Q8—44no—
435Q8—44no—
436Q8—44no—
437Q8—82no—
438Q8—82no—
439Q8—82no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—44no—
462C2×C4—44no—
463C2×C4—44no—
464C2×C4—44no—
465C2×C4—44no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—44no—
471C2×C4—42no—
472C2×C4—44no—
473C2×C4—42no—
474C2×C4—44no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—84no—
480C2×C4—88no—
481C2×C4—84no—
482C2×C4—82no—
483C2×C4—82no—
484C2×C4#38611yescharacteristic
485C2×C4#38611yescharacteristic
486C2×C4#38611yescharacteristic
487C2×C4#38611yescharacteristic
488C2×C4#38611yescharacteristic
489C2×C4#38611yescharacteristic
490C2×C4#42114yes—
491C2×C4C22×C22⋊C411yescharacteristic
492C2×C4C2×C4×D411yescharacteristic
493C2×C4C2×C4×D411yescharacteristic
494C2×C4C2×#12111yescharacteristic
495C2×C4C2×#12111yescharacteristic
496C2×C4C2×#12311yescharacteristic
497C8—44no—
498C8—44no—
499C8—82no—
500C22—21no—
501C22—21no—
502C22—24no—
503C22—24no—
504C22—21no—
505C22—21no—
506C22#188212yes—
507C22#188212yes—
508C22#189712yes—
509C22#190512yes—
510C22C2×#38611yescharacteristic
511C22C2×#45511yescharacteristic
512C22C2×#45611yescharacteristic
513C4—21no—
514C4—21no—
515C4—21no—
516C4—21no—
517C4—21no—
518C4—21no—
519C4—21no—
520C4—21no—
521C4—21no—
522C4—21no—
523C4—44no—
524C4—44no—
525C4—82no—
526C4—84no—
527C4—82no—
528C4—82no—
529C4—82no—
530C4#189712yes—
531C4C2×#42112yes—
532C2—21no—
533C2—21no—
534C2—22no—
535C2#932814yesdirect product factor
536C2C2×#188211yescharacteristic
537C2C2×#189711yescharacteristic
538C2C2×#190511yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC42C23×C4
Frattini, cosocleC2×C42C24
prime radicalC24#120
LCSG ▷ C42 ▷ 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
6. #9328C2direct (N × H)
13. #3113C4semidirect
16. C2×#475C4semidirect
17. C2×#462C4semidirect
88. #475C2×C4semidirect
90. #462C2×C4semidirect
535. C2#9328direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#31132
C2×#23202
C2×#19862
C2×#15062
C2×#14912
#93282
C2×#13002
C2×#12852