Finite Group Databasebeta

← C2×#11881 #482055

Subgroups — C2×#11881 #482055

Order 512.

1270 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2486C211yesmaximal, characteristic
2C2×#1800C211yesmaximal, characteristic
3C2×#1459C211yesmaximal, characteristic
4#11881C218yesmaximal, direct product factor
5C2×#1346C214yesmaximal, complemented
6C22×#123—21no—
7C22×C4×D4C2211yescharacteristic
8C23×C4⋊C4C411yescharacteristic
9C2×#423—21no—
10C22×#100—21no—
11C22×C22⋊C8—21no—
12#2486—22no—
13#2486—22no—
14#2486C414yes—
15#2486C2214yes—
16C2×#398C2212yes—
17C2×#397C412yes—
18C2×#389—21no—
19C2×#381—21no—
20C2×#380—21no—
21C2×#380C411yescharacteristic
22#1800—22no—
23#1800C2214yes—
24C2×#343C2212yes—
25#1459—22no—
26#1459C2214yes—
27C2×#324C2212yes—
28C2×#323—21no—
29#1346C22116yescomplemented
30C23×D4D411yescharacteristic
31C24×C4—21no—
32C24×C4C2×C411yescharacteristic
33C24×C4D411yescharacteristic
34C22×M16—22no—
35C23×C8—41no—
36C2×#123—24no—
37C2×#123—24no—
38C2×#123—44no—
39C2×#123—44no—
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—22no—
51C22×C4⋊C4—42no—
52C22×C4⋊C4—41no—
53C22×C4⋊C4—41no—
54C22×C4⋊C4C2×C412yes—
55C22×C4⋊C4C2×C414yes—
56C22×C4⋊C4C2311yescharacteristic
57C22×C22⋊C4—22no—
58C22×C22⋊C4—21no—
59C22×C22⋊C4C2×C411yescharacteristic
60C22×C22⋊C4D411yescharacteristic
61C22×C42D411yescharacteristic
62#423—24no—
63#423—42no—
64C2×C4⋊C8—41no—
65C2×C4⋊C8—41no—
66C2×#100—24no—
67C2×#100—44no—
68C2×C22⋊C8—22no—
69C2×C22⋊C8—24no—
70C2×C22⋊C8—42no—
71C2×C22⋊C8—41no—
72#398—22no—
73#398—22no—
74#398C2×C414yes—
75#398C2314yes—
76#397—24no—
77#397C2×C418yes—
78#389—24no—
79#389—24no—
80#381—24no—
81#381—24no—
82#380—22no—
83#380—24no—
84#380—24no—
85#380C2×C414yes—
86C2×#95—22no—
87C2×#95—22no—
88C2×#95C2×C412yes—
89#343—22no—
90#343C2314yes—
91#324—22no—
92#324C2314yes—
93#323—24no—
94C25C22⋊C411yescharacteristic
95C25C22⋊C411yescharacteristic
96C22×D4—41no—
97C22×D4—41no—
98C22×D4—42no—
99C22×D4C22⋊C412yes—
100C22×D4D814yes—
101C22×D4SD1614yes—
102C22×D4C2×D412yes—
103C23×C4—22no—
104C23×C4—21no—
105C23×C4—21no—
106C23×C4—21no—
107C23×C4—21no—
108C23×C4—22no—
109C23×C4—22no—
110C23×C4—22no—
111C23×C4—24no—
112C23×C4—44no—
113C23×C4—44no—
114C23×C4—42no—
115C23×C4—42no—
116C23×C4—44no—
117C23×C4—44no—
118C23×C4C22⋊C411yescharacteristic
119C23×C4C22⋊C412yes—
120C23×C4C22⋊C412yes—
121C23×C4C22⋊C411yescharacteristic
122C23×C4C22×C411yescharacteristic
123C23×C4C22×C412yes—
124C23×C4C2×D411yescharacteristic
125C23×C4C2×D411yescharacteristic
126C23×C4C2×D412yes—
127C2×M16—24no—
128C2×M16—42no—
129C2×M16—44no—
130C2×M16—44no—
131C22×C8—42no—
132C22×C8—44no—
133C22×C8—42no—
134C22×C8—84no—
135#123—416no—
136#123—48no—
137#123—48no—
138C4×D4—42no—
139C4×D4—42no—
140C4×D4—42no—
141C4×D4—42no—
142C4×D4—42no—
143C4×D4—42no—
144C4×D4—42no—
145C4×D4—42no—
146C2×C4⋊C4—24no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—24no—
149C2×C4⋊C4—24no—
150C2×C4⋊C4—24no—
151C2×C4⋊C4—41no—
152C2×C4⋊C4—41no—
153C2×C4⋊C4—42no—
154C2×C4⋊C4—42no—
155C2×C4⋊C4—44no—
156C2×C4⋊C4—44no—
157C2×C4⋊C4—44no—
158C2×C4⋊C4—42no—
159C2×C4⋊C4—41no—
160C2×C4⋊C4—41no—
161C2×C4⋊C4—44no—
162C2×C4⋊C4—44no—
163C2×C4⋊C4—44no—
164C2×C4⋊C4—44no—
165C2×C4⋊C4C22×C414yes—
166C2×C4⋊C4C22×C411yescharacteristic
167C2×C4⋊C4C2×D411yescharacteristic
168C2×C4⋊C4C2×D411yescharacteristic
169C2×C4⋊C4C2411yescharacteristic
170C2×C22⋊C4—28no—
171C2×C22⋊C4—24no—
172C2×C22⋊C4—41no—
173C2×C22⋊C4—41no—
174C2×C22⋊C4—41no—
175C2×C22⋊C4—41no—
176C2×C22⋊C4—44no—
177C2×C22⋊C4—48no—
178C2×C22⋊C4C22⋊C412yes—
179C2×C22⋊C4C22⋊C412yes—
180C2×C22⋊C4C22×C412yes—
181C2×C22⋊C4C2×D412yes—
182C2×C42—21no—
183C2×C42—21no—
184C2×C42—22no—
185C2×C42C22⋊C412yes—
186C2×C42C2×D412yes—
187C4⋊C8—44no—
188C4⋊C8—44no—
189#100—48no—
190C22⋊C8—24no—
191C22⋊C8—42no—
192C22⋊C8—44no—
193#95—24no—
194#95—28no—
195#95—22no—
196#95—24no—
197#95C22×C414yes—
198C24—21no—
199C24—21no—
200C24—21no—
201C24—22no—
202C24—21no—
203C24—22no—
204C24—42no—
205C24—42no—
206C24—42no—
207C24—42no—
208C24#10214yes—
209C24#10214yes—
210C24C2×C22⋊C411yescharacteristic
211C24C2×C22⋊C412yes—
212C24C2×C22⋊C412yes—
213C2×D4—42no—
214C2×D4—42no—
215C2×D4—42no—
216C2×D4—44no—
217C2×D4—44no—
218C2×D4—44no—
219C2×D4—44no—
220C2×D4—42no—
221C2×D4#10218yes—
222C2×D4C2×D814yes—
223C2×D4C2×SD1614yes—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—22no—
227C22×C4—24no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—24no—
243C22×C4—24no—
244C22×C4—44no—
245C22×C4—48no—
246C22×C4—44no—
247C22×C4—44no—
248C22×C4—44no—
249C22×C4—44no—
250C22×C4—44no—
251C22×C4—44no—
252C22×C4—42no—
253C22×C4—42no—
254C22×C4—42no—
255C22×C4—48no—
256C22×C4—44no—
257C22×C4—44no—
258C22×C4—48no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4—44no—
262C22×C4—44no—
263C22×C4—48no—
264C22×C4—44no—
265C22×C4—84no—
266C22×C4—82no—
267C22×C4—88no—
268C22×C4—88no—
269C22×C4#9912yes—
270C22×C4#9911yescharacteristic
271C22×C4#9911yescharacteristic
272C22×C4C2×C22⋊C412yes—
273C22×C4C2×C22⋊C411yescharacteristic
274C22×C4C2×C22⋊C412yes—
275C22×C4C2×C22⋊C411yescharacteristic
276C22×C4C2×C22⋊C411yescharacteristic
277C22×C4C2×D812yes—
278C22×C4C2×SD1612yes—
279C22×C4C23×C411yescharacteristic
280C22×C4C22×D411yescharacteristic
281C22×C4C22×D411yescharacteristic
282M16—44no—
283M16—44no—
284M16—84no—
285C2×C8—44no—
286C2×C8—44no—
287C2×C8—84no—
288C2×C8—84no—
289C2×C8—88no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—44no—
295C4⋊C4—48no—
296C4⋊C4—44no—
297C4⋊C4—44no—
298C4⋊C4—44no—
299C4⋊C4—44no—
300C4⋊C4—44no—
301C4⋊C4—48no—
302C22⋊C4—42no—
303C22⋊C4—42no—
304C22⋊C4—42no—
305C22⋊C4—42no—
306C22⋊C4—48no—
307C22⋊C4—416no—
308C42—22no—
309C42—22no—
310C42—22no—
311C42—22no—
312C23—22no—
313C23—22no—
314C23—22no—
315C23—22no—
316C23—22no—
317C23—24no—
318C23—24no—
319C23—24no—
320C23—22no—
321C23—24no—
322C23—42no—
323C23—48no—
324C23—42no—
325C23—42no—
326C23—42no—
327C23—48no—
328C23—42no—
329C23—48no—
330C23—42no—
331C23—42no—
332C23—42no—
333C23—42no—
334C23—42no—
335C23—81no—
336C23—81no—
337C23—84no—
338C23C2×#9911yescharacteristic
339C23C2×#9911yescharacteristic
340C23C2×#10212yes—
341C23C2×#10214yes—
342C23C2×#10214yes—
343C23#42112yes—
344C23C22×C22⋊C411yescharacteristic
345D4—48no—
346D4—44no—
347D4—44no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—22no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—24no—
358C2×C4—24no—
359C2×C4—22no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—44no—
365C2×C4—44no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—44no—
371C2×C4—44no—
372C2×C4—44no—
373C2×C4—44no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—44no—
380C2×C4—44no—
381C2×C4—44no—
382C2×C4—44no—
383C2×C4—44no—
384C2×C4—44no—
385C2×C4—82no—
386C2×C4—82no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—88no—
390C2×C4—816no—
391C2×C4—84no—
392C2×C4—84no—
393C2×C4#35214yes—
394C2×C4C2×#9912yes—
395C2×C4C2×#9912yes—
396C2×C4C2×#10212yes—
397C2×C4C22×D811yescharacteristic
398C2×C4C22×SD1611yescharacteristic
399C8—84no—
400C8—84no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—24no—
406C22—24no—
407C22—24no—
408C22—24no—
409C22—44no—
410C22—44no—
411C22—44no—
412C22—48no—
413C22—42no—
414C22—42no—
415C22—42no—
416C22—42no—
417C22—48no—
418C22—48no—
419C22—82no—
420C22—84no—
421C22#151912yes—
422C22#151912yes—
423C22C2×#35212yes—
424C22#213512yes—
425C22C22×#9911yescharacteristic
426C22C22×#10211yescharacteristic
427C22C2×#42111yescharacteristic
428C4—22no—
429C4—21no—
430C4—21no—
431C4—22no—
432C4—41no—
433C4—41no—
434C4—41no—
435C4—41no—
436C4—42no—
437C4—84no—
438C4—84no—
439C4C2×#35214yes—
440C2—21no—
441C2—21no—
442C2—22no—
443C2—44no—
444C2—44no—
445C2#1188114yesdirect product factor
446C2C2×#151911yescharacteristic
447C2C22×#35211yescharacteristic
448C2C2×#213511yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C4⋊C4C24
prime radicalC23×D4D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4×D4 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #11881C2direct (N × H)
5. C2×#1346C2semidirect
29. #1346C22semidirect
445. C2#11881direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#24862
C2×#18002
C2×#14592
#118812
C2×#13462