Finite Group Databasebeta

← C2×#11577 #480553

Subgroups — C2×#11577 #480553

Order 512.

1148 conjugacy classes of subgroups.

The subgroup lattice has 503 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2579C211yesmaximal, characteristic
2C2×#1465C211yesmaximal, characteristic
3C2×#1460C211yesmaximal, characteristic
4#11577C218yesmaximal, direct product factor
5C2×#1326C212yesmaximal, complemented
6C2×#1326C212yesmaximal, complemented
7C22×C4×D4C2211yescharacteristic
8C23×C4⋊C4C411yescharacteristic
9C2×#431—21no—
10C2×#407—21no—
11#2579—22no—
12#2579—22no—
13#2579C414yes—
14#2579C2214yes—
15C2×#398—21no—
16C2×#396—21no—
17C2×#387—21no—
18C2×#386C411yescharacteristic
19C2×#386C411yescharacteristic
20C2×#385—21no—
21C2×#385C2211yescharacteristic
22C2×#385C2211yescharacteristic
23C2×#380C411yescharacteristic
24#1465—22no—
25#1465C2214yes—
26#1460—22no—
27#1460C2214yes—
28C2×#324—21no—
29C2×#323—21no—
30C2×#323C2212yes—
31C2×#323C2212yes—
32#1326C2218yescomplemented
33#1326C2218yescomplemented
34C23×D4C2×C411yescharacteristic
35C24×C4C2×C411yescharacteristic
36C24×C4C2×C411yescharacteristic
37C24×C4C2×C411yescharacteristic
38C24×C4D411yescharacteristic
39C22×M16—41no—
40C2×C4×D4—41no—
41C2×C4×D4—41no—
42C2×C4×D4—42no—
43C2×C4×D4C2×C412yes—
44C2×C4×D4D412yes—
45C2×C4×D4D412yes—
46C2×C4×D4C2312yes—
47C22×C4⋊C4—22no—
48C22×C4⋊C4—21no—
49C22×C4⋊C4—21no—
50C22×C4⋊C4—21no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4—42no—
54C22×C4⋊C4—41no—
55C22×C4⋊C4—41no—
56C22×C4⋊C4C2×C414yes—
57C22×C4⋊C4D411yescharacteristic
58C22×C22⋊C4—21no—
59C22×C22⋊C4—21no—
60C22×C22⋊C4C2×C411yescharacteristic
61C22×C22⋊C4C2×C411yescharacteristic
62C22×C22⋊C4D411yescharacteristic
63C22×C22⋊C4C2311yescharacteristic
64C22×C42D411yescharacteristic
65#431—24no—
66#431—42no—
67C2×C4⋊C8—41no—
68#407—24no—
69#407—42no—
70C2×C22⋊C8—22no—
71C2×C22⋊C8—22no—
72C2×C22⋊C8—41no—
73C2×C4×C8—41no—
74#398—24no—
75#398—24no—
76#396—24no—
77#396—24no—
78#387—24no—
79#387—24no—
80#386—22no—
81#386—22no—
82#386C2×C414yes—
83#386C2×C414yes—
84#385—24no—
85#385—24no—
86#385—21no—
87#385—21no—
88#385—21no—
89#385—21no—
90#385C2×C412yes—
91#385C2×C412yes—
92#385C2312yes—
93#385C2312yes—
94#380—22no—
95#380C2×C414yes—
96C2×#95—21no—
97C2×#95—21no—
98C2×#95—21no—
99C2×#95—21no—
100C2×#95—21no—
101#324—24no—
102#323—24no—
103#323—22no—
104#323—22no—
105#323C2314yes—
106#323C2314yes—
107C25C22⋊C411yescharacteristic
108C25C22×C411yescharacteristic
109C22×D4—24no—
110C22×D4—24no—
111C22×D4—41no—
112C22×D4—41no—
113C22×D4C22⋊C412yes—
114C22×D4C22×C412yes—
115C23×C4—21no—
116C23×C4—21no—
117C23×C4—22no—
118C23×C4—21no—
119C23×C4—21no—
120C23×C4—21no—
121C23×C4—22no—
122C23×C4—21no—
123C23×C4—21no—
124C23×C4—21no—
125C23×C4—21no—
126C23×C4—21no—
127C23×C4—44no—
128C23×C4—41no—
129C23×C4—41no—
130C23×C4—41no—
131C23×C4—41no—
132C23×C4—82no—
133C23×C4—82no—
134C23×C4—82no—
135C23×C4C22⋊C411yescharacteristic
136C23×C4C22⋊C411yescharacteristic
137C23×C4C22⋊C412yes—
138C23×C4C22⋊C412yes—
139C23×C4C22⋊C411yescharacteristic
140C23×C4C22×C412yes—
141C23×C4C22×C412yes—
142C23×C4C22×C412yes—
143C23×C4C2×D411yescharacteristic
144C23×C4C2×D411yescharacteristic
145C23×C4C2×D412yes—
146C2×M16—44no—
147C2×M16—84no—
148C22×C8—42no—
149C22×C8—42no—
150C4×D4—42no—
151C4×D4—42no—
152C4×D4—42no—
153C4×D4—42no—
154C4×D4—42no—
155C4×D4—42no—
156C4×D4—42no—
157C4×D4—42no—
158C2×C4⋊C4—24no—
159C2×C4⋊C4—24no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—24no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—41no—
166C2×C4⋊C4—41no—
167C2×C4⋊C4—44no—
168C2×C4⋊C4—42no—
169C2×C4⋊C4—42no—
170C2×C4⋊C4—44no—
171C2×C4⋊C4—44no—
172C2×C4⋊C4—42no—
173C2×C4⋊C4—41no—
174C2×C4⋊C4—41no—
175C2×C4⋊C4—44no—
176C2×C4⋊C4—44no—
177C2×C4⋊C4—82no—
178C2×C4⋊C4—82no—
179C2×C4⋊C4C22⋊C412yes—
180C2×C4⋊C4C2×D412yes—
181C2×C22⋊C4—24no—
182C2×C22⋊C4—24no—
183C2×C22⋊C4—24no—
184C2×C22⋊C4—21no—
185C2×C22⋊C4—21no—
186C2×C22⋊C4—24no—
187C2×C22⋊C4—41no—
188C2×C22⋊C4—41no—
189C2×C22⋊C4—41no—
190C2×C22⋊C4—41no—
191C2×C22⋊C4—44no—
192C2×C22⋊C4—82no—
193C2×C22⋊C4C22⋊C412yes—
194C2×C22⋊C4C22×C412yes—
195C2×C22⋊C4C22×C412yes—
196C2×C22⋊C4C22×C411yescharacteristic
197C2×C22⋊C4C2×D412yes—
198C2×C22⋊C4C2×D411yescharacteristic
199C2×C22⋊C4C2×D411yescharacteristic
200C2×C22⋊C4C2411yescharacteristic
201C2×C42—21no—
202C2×C42—21no—
203C2×C42—22no—
204C2×C42C22⋊C412yes—
205C2×C42C2×D412yes—
206C4⋊C8—44no—
207C22⋊C8—24no—
208C22⋊C8—24no—
209C22⋊C8—42no—
210C22⋊C8—42no—
211C22⋊C8—44no—
212C4×C8—44no—
213#95—24no—
214#95—22no—
215#95—22no—
216#95—24no—
217#95—24no—
218#95—22no—
219#95—22no—
220C24—21no—
221C24—21no—
222C24—22no—
223C24—21no—
224C24—22no—
225C24—22no—
226C24—21no—
227C24—42no—
228C24—42no—
229C24—42no—
230C24—42no—
231C24C2×C22⋊C411yescharacteristic
232C24C2×C22⋊C412yes—
233C24C2×C22⋊C411yescharacteristic
234C24#13114yes—
235C24C23×C411yescharacteristic
236C2×D4—24no—
237C2×D4—24no—
238C2×D4—24no—
239C2×D4—24no—
240C2×D4—42no—
241C2×D4—42no—
242C2×D4—48no—
243C2×D4—48no—
244C22×C4—22no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—24no—
248C22×C4—22no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—42no—
267C22×C4—44no—
268C22×C4—44no—
269C22×C4—44no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4—48no—
273C22×C4—44no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—44no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—42no—
293C22×C4—82no—
294C22×C4—82no—
295C22×C4—82no—
296C22×C4—82no—
297C22×C4—82no—
298C22×C4—84no—
299C22×C4—84no—
300C22×C4—82no—
301C22×C4—82no—
302C22×C4—82no—
303C22×C4—82no—
304C22×C4—84no—
305C22×C4—84no—
306C22×C4#9911yescharacteristic
307C22×C4#9911yescharacteristic
308C22×C4#9912yes—
309C22×C4#10114yes—
310C22×C4C2×C22⋊C412yes—
311C22×C4C2×C22⋊C411yescharacteristic
312C22×C4C2×C22⋊C411yescharacteristic
313C22×C4C2×C22⋊C412yes—
314C22×C4C2×C22⋊C412yes—
315C22×C4C22×D411yescharacteristic
316C22×C4C22×D411yescharacteristic
317M16—88no—
318C2×C8—44no—
319C2×C8—44no—
320C2×C8—84no—
321C2×C8—84no—
322C4⋊C4—42no—
323C4⋊C4—42no—
324C4⋊C4—44no—
325C4⋊C4—44no—
326C4⋊C4—48no—
327C4⋊C4—44no—
328C4⋊C4—44no—
329C4⋊C4—84no—
330C4⋊C4—82no—
331C4⋊C4—82no—
332C22⋊C4—24no—
333C22⋊C4—24no—
334C22⋊C4—42no—
335C22⋊C4—41no—
336C22⋊C4—42no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—48no—
341C22⋊C4—42no—
342C22⋊C4—42no—
343C22⋊C4—84no—
344C42—22no—
345C42—22no—
346C42—22no—
347C42—22no—
348C23—22no—
349C23—22no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—24no—
355C23—24no—
356C23—22no—
357C23—22no—
358C23—22no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23—41no—
363C23—48no—
364C23—42no—
365C23—42no—
366C23—48no—
367C23—42no—
368C23—42no—
369C23—48no—
370C23—42no—
371C23—42no—
372C23—42no—
373C23—42no—
374C23—42no—
375C23—42no—
376C23—81no—
377C23—81no—
378C23—84no—
379C23#40812yes—
380C23#40812yes—
381C23C2×#9911yescharacteristic
382C23C2×#9911yescharacteristic
383C23C2×#10112yes—
384C23C22×C22⋊C411yescharacteristic
385C23C2×#13112yes—
386D4—48no—
387D4—48no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—24no—
393C2×C4—24no—
394C2×C4—24no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—22no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—44no—
403C2×C4—44no—
404C2×C4—42no—
405C2×C4—44no—
406C2×C4—42no—
407C2×C4—48no—
408C2×C4—44no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—44no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—41no—
419C2×C4—44no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—82no—
430C2×C4—82no—
431C2×C4—82no—
432C2×C4—82no—
433C2×C4—82no—
434C2×C4—82no—
435C2×C4—81no—
436C2×C4—81no—
437C2×C4—84no—
438C2×C4—84no—
439C2×C4—82no—
440C2×C4—84no—
441C2×C4—82no—
442C2×C4—84no—
443C2×C4C2×#9912yes—
444C2×C4C2×#9912yes—
445C2×C4C2×#10114yes—
446C8—84no—
447C8—84no—
448C22—24no—
449C22—24no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—22no—
455C22—22no—
456C22—42no—
457C22—42no—
458C22—42no—
459C22—42no—
460C22—48no—
461C22—44no—
462C22—48no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—42no—
468C22—42no—
469C22—42no—
470C22—82no—
471C22—84no—
472C22—84no—
473C22#147212yes—
474C22#147212yes—
475C22#212012yes—
476C22#212112yes—
477C22C2×#40811yescharacteristic
478C22C22×#9911yescharacteristic
479C22C22×#10111yescharacteristic
480C4—22no—
481C4—22no—
482C4—24no—
483C4—41no—
484C4—44no—
485C4—41no—
486C4—41no—
487C4—41no—
488C4—42no—
489C4—82no—
490C4—82no—
491C4—82no—
492C2—21no—
493C2—21no—
494C2—22no—
495C2—42no—
496C2—42no—
497C2—82no—
498C2#1157714yesdirect product factor
499C2C2×#147211yescharacteristic
500C2C2×#212011yescharacteristic
501C2C2×#212111yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC24C23×C4
Frattini, cosocleC2×C22⋊C4C24
prime radicalC23×D4C2×C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4×D4 ◁ G
LECSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #11577C2direct (N × H)
5. C2×#1326C2semidirect
6. C2×#1326C2semidirect
32. #1326C22semidirect
33. #1326C22semidirect
498. C2#11577direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#25792
C2×#14652
C2×#14602
#115772
C2×#13262