Finite Group Databasebeta

← C2×#9528 #202062

Subgroups — C2×#9528 #202062

Order 512.

1058 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3113C211yesmaximal, characteristic
2C2×#2985C211yesmaximal, characteristic
3C2×#1559C211yesmaximal, characteristic
4C2×#1487C211yesmaximal, characteristic
5C2×#1467C211yesmaximal, characteristic
6#9528C218yesmaximal, direct product factor
7C2×#1307C211yesmaximal, characteristic
8C2×#1287C211yesmaximal, characteristic
9C2×#533C2211yescharacteristic
10C22×C4×Q8C2211yescharacteristic
11#3113—22no—
12#3113—22no—
13#3113C414yes—
14#3113C2214yes—
15C2×#483C412yes—
16C2×#475—21no—
17C2×#462—21no—
18C2×#451C412yes—
19#2985—22no—
20#2985—22no—
21#2985—22no—
22#2985C2214yes—
23C2×#446—21no—
24C2×#446—22no—
25C2×C8×Q8—21no—
26C2×#441—22no—
27C2×#433—22no—
28C2×#432C2211yescharacteristic
29C2×#432C2211yescharacteristic
30C2×#432C2211yescharacteristic
31C2×#431C2211yescharacteristic
32C2×#423C2211yescharacteristic
33#1559—22no—
34#1559C2214yes—
35C2×#333—21no—
36C2×#332—21no—
37#1487—22no—
38#1487C2214yes—
39C2×Q8⋊C8—21no—
40C2×Q8⋊C8—21no—
41#1467—22no—
42#1467C2214yes—
43C2×#324—22no—
44#1307C2214yes—
45#1287C2214yes—
46C23×Q8C2×C411yescharacteristic
47C22×Q16—22no—
48C22×M16—21no—
49#533—21no—
50#533—21no—
51#533—21no—
52#533—21no—
53#533C2×C412yes—
54#533D412yes—
55#533D412yes—
56#533C2312yes—
57C2×C4⋊Q8D411yescharacteristic
58C2×C4⋊Q8D411yescharacteristic
59C2×#125—21no—
60C2×C22⋊Q8—21no—
61C2×C22⋊Q8C2×C412yes—
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×Q8—21no—
71C2×C4×Q8—21no—
72C2×C4×Q8—21no—
73C2×C4×Q8C2×C412yes—
74C2×C4×Q8D412yes—
75C2×C4×Q8C2312yes—
76C2×#117—21no—
77C22×C4⋊C4—21no—
78C22×C4⋊C4C2×C411yescharacteristic
79C22×C42—21no—
80C22×C42C2311yescharacteristic
81#483—24no—
82#483C2×C418yes—
83#475—24no—
84#475—24no—
85#462—24no—
86#462—24no—
87#451—24no—
88#451C2×C418yes—
89#446—28no—
90#446—24no—
91#446—28no—
92#446—24no—
93C8×Q8—24no—
94C8×Q8—24no—
95#441—28no—
96#441—28no—
97#433—28no—
98#433—28no—
99#432—21no—
100#432—21no—
101#432—21no—
102#432—21no—
103#432—21no—
104#432—21no—
105#432—21no—
106#432C2×C412yes—
107#432D412yes—
108#432C2312yes—
109#432C2312yes—
110#432C2312yes—
111#431—21no—
112#431—21no—
113#431D412yes—
114#431C2312yes—
115C2×#106—22no—
116#423—21no—
117#423—21no—
118#423—21no—
119#423C2312yes—
120C2×C4⋊C8—22no—
121C2×C4⋊C8—22no—
122C2×C4⋊C8—21no—
123C2×C4⋊C8—21no—
124C2×C4⋊C8—21no—
125C2×C4⋊C8—21no—
126C2×C4⋊C8—21no—
127C2×C4⋊C8—21no—
128C2×#103—22no—
129C2×#103—22no—
130C2×C22⋊C8—21no—
131C2×C22⋊C8—21no—
132C2×C22⋊C8C2×C412yes—
133C2×C22⋊C8D412yes—
134C2×#97—22no—
135C2×#97—21no—
136C2×#97—21no—
137C2×#97—21no—
138C2×C4×C8—22no—
139C2×C4×C8D411yescharacteristic
140C2×C4×C8D411yescharacteristic
141#333—24no—
142#332—24no—
143Q8⋊C8—24no—
144Q8⋊C8—24no—
145#324—28no—
146C22×Q8—21no—
147C22×Q8—21no—
148C22×Q8—21no—
149C22×Q8—21no—
150C22×Q8—21no—
151C22×Q8—21no—
152C22×Q8—44no—
153C22×Q8C22⋊C412yes—
154C22×Q8C22×C412yes—
155C23×C4—21no—
156C23×C4—21no—
157C23×C4C22×C411yescharacteristic
158C23×C4C2×D411yescharacteristic
159C23×C4#4111yescharacteristic
160C2×Q16—28no—
161C2×Q16—48no—
162C2×M16—22no—
163C2×M16—41no—
164C2×M16—82no—
165C22×C8—22no—
166C22×C8—21no—
167C22×C8—22no—
168C22×C8—21no—
169C22×C8—41no—
170C22×C8—41no—
171C4⋊Q8—21no—
172C4⋊Q8—21no—
173C4⋊Q8—21no—
174C4⋊Q8—21no—
175C4⋊Q8C22⋊C412yes—
176C4⋊Q8C22⋊C412yes—
177C4⋊Q8C2×D412yes—
178C4⋊Q8C2×D412yes—
179#125—22no—
180#125—22no—
181#125—22no—
182#125—22no—
183C22⋊Q8—22no—
184C22⋊Q8—22no—
185C22⋊Q8—22no—
186C22⋊Q8—22no—
187C22⋊Q8—22no—
188C22⋊Q8—22no—
189C22⋊Q8C22⋊C414yes—
190C22⋊Q8C22×C414yes—
191C4×Q8—22no—
192C4×Q8—22no—
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—41no—
206C4×Q8—41no—
207C4×Q8—41no—
208C4×Q8—41no—
209C4×Q8—41no—
210C4×Q8—41no—
211C4×Q8—41no—
212C4×Q8—41no—
213C4×Q8C22⋊C414yes—
214C4×Q8C2×D414yes—
215#117—22no—
216#117—22no—
217#117—22no—
218#117—22no—
219C2×C4⋊C4—22no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—22no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—41no—
232C2×C4⋊C4—41no—
233C2×C4⋊C4—41no—
234C2×C4⋊C4—41no—
235C2×C4⋊C4C22⋊C412yes—
236C2×C4⋊C4C22×C412yes—
237C2×C22⋊C4—22no—
238C2×C42—22no—
239C2×C42—22no—
240C2×C42—22no—
241C2×C42—41no—
242C2×C42—41no—
243C2×C42—41no—
244C2×C42—41no—
245C2×C42C22×C411yescharacteristic
246C2×C42C2×D411yescharacteristic
247C2×C42C2×D411yescharacteristic
248C2×C42C2×D411yescharacteristic
249C2×C42C2×D411yescharacteristic
250C2×C42C2×D411yescharacteristic
251C2×C42C2×D411yescharacteristic
252C2×C42C2×D411yescharacteristic
253C2×C42#4111yescharacteristic
254C2×C42#4111yescharacteristic
255C2×C42#4111yescharacteristic
256C2×C42C2411yescharacteristic
257#106—28no—
258C4⋊C8—28no—
259C4⋊C8—28no—
260C4⋊C8—22no—
261C4⋊C8—22no—
262C4⋊C8—22no—
263C4⋊C8—22no—
264C4⋊C8—22no—
265C4⋊C8—22no—
266C4⋊C8—22no—
267C4⋊C8—22no—
268C4⋊C8—22no—
269C4⋊C8—41no—
270C4⋊C8—41no—
271C4⋊C8—41no—
272#103—28no—
273#103—28no—
274C22⋊C8—22no—
275C22⋊C8—22no—
276C22⋊C8—22no—
277C22⋊C8—22no—
278C22⋊C8—22no—
279C22⋊C8—41no—
280C22⋊C8C22×C414yes—
281C22⋊C8C2×D414yes—
282#97—28no—
283#97—22no—
284#97—22no—
285#97—22no—
286#97—22no—
287#97—22no—
288#97—41no—
289C4×C8—28no—
290C4×C8—21no—
291C4×C8—21no—
292C4×C8C2×D412yes—
293C4×C8C2×D412yes—
294C24C4×D411yescharacteristic
295C2×Q8—22no—
296C2×Q8—22no—
297C2×Q8—22no—
298C2×Q8—24no—
299C2×Q8—24no—
300C2×Q8—22no—
301C2×Q8—22no—
302C2×Q8—44no—
303C2×Q8—42no—
304C2×Q8—42no—
305C2×Q8—44no—
306C2×Q8—44no—
307C2×Q8—44no—
308C2×Q8—44no—
309C2×Q8—41no—
310C2×Q8—41no—
311C2×Q8—42no—
312C2×Q8—42no—
313C2×Q8C2×C22⋊C414yes—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—24no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4—42no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—82no—
329C22×C4C2×C22⋊C411yescharacteristic
330C22×C4C2×C22⋊C411yescharacteristic
331C22×C4C4×D411yescharacteristic
332C22×C4C4×D411yescharacteristic
333C22×C4C4×D411yescharacteristic
334C22×C4C4×D411yescharacteristic
335C22×C4C4×D411yescharacteristic
336C22×C4#12011yescharacteristic
337C22×C4#12011yescharacteristic
338C22×C4#12111yescharacteristic
339C22×C4#12111yescharacteristic
340C22×C4#12111yescharacteristic
341C22×C4#12111yescharacteristic
342C22×C4#12311yescharacteristic
343C22×C4#12311yescharacteristic
344C22×C4C23×C411yescharacteristic
345C22×C4C22×D411yescharacteristic
346C22×C4C2×#4111yescharacteristic
347Q16—416no—
348M16—82no—
349M16—82no—
350C2×C8—24no—
351C2×C8—22no—
352C2×C8—24no—
353C2×C8—22no—
354C2×C8—42no—
355C2×C8—44no—
356C2×C8—42no—
357C2×C8—44no—
358C2×C8—42no—
359C2×C8—42no—
360C2×C8—82no—
361C2×C8—82no—
362C4⋊C4—24no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—24no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—24no—
371C4⋊C4—24no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—42no—
376C4⋊C4—42no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4—42no—
380C4⋊C4—42no—
381C4⋊C4C2×C22⋊C414yes—
382C22⋊C4—24no—
383C22⋊C4—24no—
384C42—24no—
385C42—24no—
386C42—42no—
387C42—42no—
388C42—42no—
389C42—42no—
390C42C2×C22⋊C411yescharacteristic
391C42C2×C22⋊C411yescharacteristic
392C42C4×D411yescharacteristic
393C42C4×D411yescharacteristic
394C42#12011yescharacteristic
395C42#12011yescharacteristic
396C42#12111yescharacteristic
397C42#12111yescharacteristic
398C42#12111yescharacteristic
399C42#12111yescharacteristic
400C42#12311yescharacteristic
401C42#12311yescharacteristic
402C42C22×D411yescharacteristic
403C42C22×D411yescharacteristic
404C42C22×D411yescharacteristic
405C42C2×#4111yescharacteristic
406C23—22no—
407C23—22no—
408C23—22no—
409C23#38611yescharacteristic
410C23#38611yescharacteristic
411C23C2×C4×D411yescharacteristic
412Q8—24no—
413Q8—24no—
414Q8—44no—
415Q8—42no—
416Q8—42no—
417Q8—44no—
418Q8—44no—
419Q8—44no—
420Q8—42no—
421Q8—42no—
422Q8—82no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—24no—
435C2×C4—24no—
436C2×C4—24no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—44no—
447C2×C4—44no—
448C2×C4—44no—
449C2×C4—44no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—82no—
453C2×C4—82no—
454C2×C4—82no—
455C2×C4#38611yescharacteristic
456C2×C4#38611yescharacteristic
457C2×C4#38611yescharacteristic
458C2×C4#38611yescharacteristic
459C2×C4#38611yescharacteristic
460C2×C4#38611yescharacteristic
461C2×C4#47112yes—
462C2×C4#47312yes—
463C2×C4C22×C22⋊C411yescharacteristic
464C2×C4C2×C4×D411yescharacteristic
465C2×C4C2×#12011yescharacteristic
466C2×C4C2×#12111yescharacteristic
467C2×C4C2×#12111yescharacteristic
468C2×C4C2×#12311yescharacteristic
469C8—42no—
470C8—44no—
471C8—42no—
472C8—44no—
473C8—82no—
474C8—82no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—44no—
482C22#189112yes—
483C22#190512yes—
484C22#190812yes—
485C22C2×#38611yescharacteristic
486C4—21no—
487C4—21no—
488C4—21no—
489C4—21no—
490C4—21no—
491C4—21no—
492C4—21no—
493C4—21no—
494C4—21no—
495C4—21no—
496C4—44no—
497C4—44no—
498C4—44no—
499C4—82no—
500C4#190812yes—
501C4C2×#47111yescharacteristic
502C4C2×#47311yescharacteristic
503C2—41no—
504C2—41no—
505C2#952814yesdirect product factor
506C2C2×#189111yescharacteristic
507C2C2×#190511yescharacteristic
508C2C2×#190811yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
prime radicalC24C4×D4
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
6. #9528C2direct (N × H)
505. C2#9528direct (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×#29852
C2×#15592
C2×#14872
C2×#14672
#95282
C2×#13072
C2×#12872