Finite Group Databasebeta

← C2×#11850 #482170

Subgroups — C2×#11850 #482170

Order 512.

1058 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2484C211yesmaximal, characteristic
2C2×#1821C211yesmaximal, characteristic
3C22×#324C211yesmaximal, characteristic
4#11850C218yesmaximal, direct product factor
5C2×#1353C212yesmaximal, complemented
6C2×#1346C212yesmaximal, complemented
7C22×#117C411yescharacteristic
8C23×C4⋊C4C2211yescharacteristic
9C2×#407—21no—
10C22×C22⋊C8—21no—
11#2484—22no—
12#2484—22no—
13#2484C414yes—
14#2484C2214yes—
15C2×#400C411yescharacteristic
16C2×#400C2211yescharacteristic
17C2×#398C411yescharacteristic
18C2×#398C2211yescharacteristic
19C2×#387—21no—
20C2×#387—21no—
21C2×#385—21no—
22C2×#381—21no—
23C2×#381C411yescharacteristic
24#1821—22no—
25#1821C2214yes—
26C2×#343—21no—
27C2×#343C2212yes—
28C2×#324—22no—
29C2×#324—21no—
30C2×#324C2214yes—
31C2×#324C2212yes—
32#1353C2218yescomplemented
33#1346C2218yescomplemented
34C24×C4C2×C411yescharacteristic
35C24×C4D411yescharacteristic
36C24×C4D411yescharacteristic
37C22×M16—22no—
38C23×C8—41no—
39C2×#117—22no—
40C2×#117—42no—
41C2×#117—41no—
42C2×#117—41no—
43C2×#117C2×C414yes—
44C22×C4⋊C4—21no—
45C22×C4⋊C4—21no—
46C22×C4⋊C4—41no—
47C22×C4⋊C4—41no—
48C22×C4⋊C4—42no—
49C22×C4⋊C4C2×C411yescharacteristic
50C22×C4⋊C4C2×C411yescharacteristic
51C22×C4⋊C4C2×C411yescharacteristic
52C22×C4⋊C4C2×C412yes—
53C22×C4⋊C4D412yes—
54C22×C4⋊C4D412yes—
55C22×C4⋊C4D411yescharacteristic
56C22×C4⋊C4D411yescharacteristic
57C22×C4⋊C4C2312yes—
58C22×C4⋊C4C2311yescharacteristic
59C22×C22⋊C4—21no—
60C22×C22⋊C4—21no—
61C22×C42—21no—
62#407—24no—
63#407—42no—
64C2×C22⋊C8—22no—
65C2×C22⋊C8—24no—
66C2×C22⋊C8—42no—
67C2×C22⋊C8—41no—
68C2×C22⋊C8—41no—
69C2×C22⋊C8—41no—
70#400—22no—
71#400—21no—
72#400—21no—
73#400C2×C414yes—
74#400C2×C412yes—
75#400C2312yes—
76#398—22no—
77#398—21no—
78#398—21no—
79#398C2×C414yes—
80#398C2×C412yes—
81#398C2312yes—
82#387—24no—
83#387—24no—
84#387—24no—
85#387—24no—
86#385—24no—
87#385—24no—
88#381—22no—
89#381—24no—
90#381—24no—
91#381C2×C414yes—
92C2×#95—21no—
93C2×#95—21no—
94C2×#95—21no—
95C2×#95—21no—
96C2×#95—21no—
97C2×#95—21no—
98C2×#95—21no—
99C2×#95C2×C411yescharacteristic
100C2×#95C2×C411yescharacteristic
101#343—22no—
102#343—24no—
103#343C2314yes—
104#324—24no—
105#324—22no—
106#324C2314yes—
107C25C22⋊C411yescharacteristic
108C23×C4—22no—
109C23×C4—21no—
110C23×C4—21no—
111C23×C4—21no—
112C23×C4—21no—
113C23×C4—21no—
114C23×C4—22no—
115C23×C4—22no—
116C23×C4—21no—
117C23×C4—24no—
118C23×C4—21no—
119C23×C4—21no—
120C23×C4—21no—
121C23×C4—21no—
122C23×C4—42no—
123C23×C4—44no—
124C23×C4—44no—
125C23×C4C22⋊C411yescharacteristic
126C23×C4C22⋊C412yes—
127C23×C4C22⋊C411yescharacteristic
128C23×C4C22⋊C412yes—
129C23×C4C22⋊C412yes—
130C23×C4C22⋊C411yescharacteristic
131C23×C4C22×C411yescharacteristic
132C23×C4C22×C412yes—
133C23×C4C2×D412yes—
134C23×C4C2×D411yescharacteristic
135C23×C4C2×D411yescharacteristic
136C23×C4C2×D412yes—
137C2×M16—24no—
138C2×M16—42no—
139C2×M16—44no—
140C2×M16—44no—
141C22×C8—44no—
142C22×C8—42no—
143C22×C8—42no—
144C22×C8—84no—
145#117—44no—
146#117—44no—
147#117—44no—
148#117—44no—
149C2×C4⋊C4—24no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—41no—
155C2×C4⋊C4—42no—
156C2×C4⋊C4—42no—
157C2×C4⋊C4—41no—
158C2×C4⋊C4—41no—
159C2×C4⋊C4—41no—
160C2×C4⋊C4—42no—
161C2×C4⋊C4—42no—
162C2×C4⋊C4—41no—
163C2×C4⋊C4—42no—
164C2×C4⋊C4—42no—
165C2×C4⋊C4—41no—
166C2×C4⋊C4—41no—
167C2×C4⋊C4—41no—
168C2×C4⋊C4—42no—
169C2×C4⋊C4—42no—
170C2×C4⋊C4—41no—
171C2×C4⋊C4—41no—
172C2×C4⋊C4—41no—
173C2×C4⋊C4—41no—
174C2×C4⋊C4—44no—
175C2×C4⋊C4—44no—
176C2×C4⋊C4C22⋊C412yes—
177C2×C4⋊C4C22⋊C412yes—
178C2×C4⋊C4C22⋊C412yes—
179C2×C4⋊C4C22×C412yes—
180C2×C4⋊C4C22×C412yes—
181C2×C4⋊C4C22×C412yes—
182C2×C4⋊C4C22×C411yescharacteristic
183C2×C4⋊C4C2×D412yes—
184C2×C4⋊C4C2×D411yescharacteristic
185C2×C4⋊C4C2×D412yes—
186C2×C4⋊C4C2×D411yescharacteristic
187C2×C4⋊C4C2411yescharacteristic
188C2×C22⋊C4—24no—
189C2×C22⋊C4—24no—
190C2×C22⋊C4—44no—
191C2×C22⋊C4—42no—
192C2×C22⋊C4—41no—
193C2×C22⋊C4—41no—
194C2×C42—24no—
195C2×C42—42no—
196C2×C42—42no—
197C22⋊C8—24no—
198C22⋊C8—44no—
199C22⋊C8—42no—
200C22⋊C8—44no—
201C22⋊C8—44no—
202#95—24no—
203#95—22no—
204#95—24no—
205#95—22no—
206#95—24no—
207#95—24no—
208#95—22no—
209#95—21no—
210#95—21no—
211#95—22no—
212#95—22no—
213#95—22no—
214#95C22×C412yes—
215#95C22×C412yes—
216C24—24no—
217C24—22no—
218C24—22no—
219C24—42no—
220C24#9911yescharacteristic
221C24#9912yes—
222C24#9911yescharacteristic
223C24C2×C22⋊C412yes—
224C24C2×C22⋊C411yescharacteristic
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—21no—
250C22×C4—22no—
251C22×C4—21no—
252C22×C4—24no—
253C22×C4—24no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—44no—
261C22×C4—44no—
262C22×C4—48no—
263C22×C4—48no—
264C22×C4—44no—
265C22×C4—44no—
266C22×C4—44no—
267C22×C4—42no—
268C22×C4—44no—
269C22×C4—42no—
270C22×C4—44no—
271C22×C4—42no—
272C22×C4—44no—
273C22×C4—42no—
274C22×C4—44no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—44no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—84no—
289C22×C4—82no—
290C22×C4C2×C22⋊C412yes—
291C22×C4C2×C22⋊C411yescharacteristic
292C22×C4C2×C22⋊C411yescharacteristic
293C22×C4C2×C22⋊C412yes—
294C22×C4C2×C22⋊C412yes—
295C22×C4C2×C22⋊C411yescharacteristic
296C22×C4#13514yes—
297C22×C4C23×C411yescharacteristic
298C22×C4C22×D411yescharacteristic
299C22×C4C22×D411yescharacteristic
300M16—44no—
301M16—44no—
302M16—84no—
303C2×C8—44no—
304C2×C8—44no—
305C2×C8—84no—
306C2×C8—88no—
307C2×C8—84no—
308C4⋊C4—42no—
309C4⋊C4—42no—
310C4⋊C4—42no—
311C4⋊C4—41no—
312C4⋊C4—42no—
313C4⋊C4—42no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—42no—
317C4⋊C4—41no—
318C4⋊C4—42no—
319C4⋊C4—42no—
320C4⋊C4—48no—
321C4⋊C4—42no—
322C4⋊C4—42no—
323C4⋊C4—44no—
324C4⋊C4—44no—
325C22⋊C4—48no—
326C22⋊C4—44no—
327C22⋊C4—44no—
328C42—48no—
329C23—22no—
330C23—22no—
331C23—22no—
332C23—22no—
333C23—24no—
334C23—24no—
335C23—22no—
336C23—22no—
337C23—22no—
338C23—22no—
339C23—24no—
340C23—22no—
341C23—42no—
342C23—42no—
343C23—48no—
344C23—48no—
345C23#35214yes—
346C23C2×#9912yes—
347C23C2×#9912yes—
348C23C2×#9911yescharacteristic
349C23C2×#9911yescharacteristic
350C23#41612yes—
351C23#42112yes—
352C23C22×C22⋊C411yescharacteristic
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—24no—
358C2×C4—24no—
359C2×C4—22no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—22no—
364C2×C4—21no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—44no—
369C2×C4—44no—
370C2×C4—44no—
371C2×C4—44no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—44no—
375C2×C4—44no—
376C2×C4—44no—
377C2×C4—42no—
378C2×C4—44no—
379C2×C4—44no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—44no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—44no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—81no—
404C2×C4—82no—
405C2×C4—81no—
406C2×C4—82no—
407C2×C4—84no—
408C2×C4—84no—
409C2×C4—82no—
410C2×C4—82no—
411C2×C4—82no—
412C2×C4—82no—
413C2×C4#41612yes—
414C2×C4C2×#13512yes—
415C8—84no—
416C8—84no—
417C22—21no—
418C22—21no—
419C22—24no—
420C22—24no—
421C22—28no—
422C22—21no—
423C22—21no—
424C22—22no—
425C22—22no—
426C22—22no—
427C22—22no—
428C22—22no—
429C22—44no—
430C22—44no—
431C22—48no—
432C22—44no—
433C22#151612yes—
434C22#151612yes—
435C22C2×#35214yes—
436C22C2×#35212yes—
437C22#213312yes—
438C22C22×#9911yescharacteristic
439C22C2×#41611yescharacteristic
440C22C2×#42111yescharacteristic
441C4—22no—
442C4—22no—
443C4—41no—
444C4—42no—
445C4—41no—
446C4—41no—
447C4—42no—
448C4—41no—
449C4—42no—
450C4—82no—
451C4—82no—
452C4—82no—
453C4—82no—
454C2—21no—
455C2—21no—
456C2—24no—
457C2—22no—
458C2—42no—
459C2#1185014yesdirect product factor
460C2C2×#151611yescharacteristic
461C2C22×#35211yescharacteristic
462C2C2×#213311yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C4⋊C4C24
prime radicalC25C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C25 ◁ C23×C4⋊C4 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #11850C2direct (N × H)
5. C2×#1353C2semidirect
6. C2×#1346C2semidirect
32. #1353C22semidirect
33. #1346C22semidirect
459. C2#11850direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#24842
C2×#18212
C22×#3242
#118502
C2×#13532
C2×#13462