Finite Group Databasebeta

← C2×#11882 #482059

Subgroups — C2×#11882 #482059

Order 512.

1312 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2548C211yesmaximal, characteristic
2C2×#1801C211yesmaximal, characteristic, complemented
3C2×#1461C211yesmaximal, characteristic, complemented
4#11882C218yesmaximal, direct product factor
5C2×#1345C214yesmaximal, complemented
6C22×#127C411yescharacteristic
7C22×#124—21no—
8C22×C4×Q8C2211yescharacteristic
9C2×#431—21no—
10C2×#423—21no—
11C22×#101—21no—
12#2548—22no—
13#2548—22no—
14#2548C414yes—
15#2548C2214yes—
16C2×#394C412yes—
17C2×#394C2212yes—
18C2×#390—21no—
19C2×#390—21no—
20C2×#390—21no—
21C2×C4×C4⋊C4C411yescharacteristic
22#1801—22no—
23#1801C2214yescomplemented
24C2×#343C2212yes—
25#1461—22no—
26#1461C2214yescomplemented
27C2×#324—21no—
28C2×#324C2212yes—
29#1345C22116yescomplemented
30C23×Q8D411yescharacteristic
31C23×D4—21no—
32C23×D4—21no—
33C23×D4C2×C412yes—
34C22×M16—22no—
35C2×#127—22no—
36C2×#127—42no—
37C2×#127—41no—
38C2×#127—41no—
39C2×#127C2×C414yes—
40C2×#124—24no—
41C2×#124—24no—
42C2×#124—44no—
43C2×#124—44no—
44C2×C4×Q8—41no—
45C2×C4×Q8—41no—
46C2×C4×Q8—42no—
47C2×C4×Q8C2×C412yes—
48C2×C4×Q8D412yes—
49C2×C4×Q8D412yes—
50C2×C4×Q8C2312yes—
51C22×C4⋊C4—21no—
52C22×C4⋊C4C2×C411yescharacteristic
53C22×C4⋊C4D411yescharacteristic
54C22×C4⋊C4C2311yescharacteristic
55C22×C22⋊C4—22no—
56C22×C22⋊C4—22no—
57C22×C22⋊C4—22no—
58C22×C22⋊C4—22no—
59C22×C42—21no—
60C22×C42C2×C411yescharacteristic
61C22×C42D411yescharacteristic
62C22×C42D411yescharacteristic
63#431—24no—
64#431—42no—
65#423—24no—
66#423—42no—
67C2×C4⋊C8—41no—
68C2×C4⋊C8—41no—
69C2×C4⋊C8—41no—
70C2×#101—24no—
71C2×#101—44no—
72C2×C22⋊C8—22no—
73C2×C4×C8—41no—
74#394—24no—
75#394—22no—
76#394—22no—
77#394C2×C418yes—
78#394C2×C414yes—
79#394C2314yes—
80#390—24no—
81#390—24no—
82#390—24no—
83#390—24no—
84#390—24no—
85#390—24no—
86C4×C4⋊C4—22no—
87C4×C4⋊C4C2×C414yes—
88C2×#95C2×C412yes—
89#343—22no—
90#343C2314yes—
91#324—24no—
92#324—22no—
93#324C2314yes—
94C25—22no—
95C22×Q8—41no—
96C22×Q8—41no—
97C22×Q8—42no—
98C22×Q8C22⋊C412yes—
99C22×Q8D814yes—
100C22×Q8SD1614yes—
101C22×Q8C2×D412yes—
102C22×D4—24no—
103C22×D4—24no—
104C22×D4—22no—
105C22×D4—42no—
106C22×D4—42no—
107C22×D4—42no—
108C22×D4—42no—
109C22×D4—44no—
110C22×D4—44no—
111C22×D4—44no—
112C22×D4—42no—
113C22×D4—41no—
114C22×D4—41no—
115C22×D4—44no—
116C22×D4—84no—
117C22×D4C22×C414yes—
118C23×C4—22no—
119C23×C4C22⋊C411yescharacteristic
120C23×C4C22⋊C411yescharacteristic
121C23×C4C22⋊C411yescharacteristic
122C23×C4C22⋊C411yescharacteristic
123C23×C4C22×C411yescharacteristic
124C23×C4C2×D411yescharacteristic
125C23×C4C2×D411yescharacteristic
126C2×M16—24no—
127C2×M16—42no—
128C2×M16—44no—
129C2×M16—44no—
130C22×C8—42no—
131C22×C8—42no—
132#127—44no—
133#127—44no—
134#127—44no—
135#127—44no—
136#124—416no—
137#124—48no—
138#124—48no—
139C4×Q8—42no—
140C4×Q8—42no—
141C4×Q8—42no—
142C4×Q8—42no—
143C4×Q8—42no—
144C4×Q8—42no—
145C4×Q8—42no—
146C4×Q8—42no—
147C2×C4⋊C4—24no—
148C2×C4⋊C4—41no—
149C2×C4⋊C4—41no—
150C2×C4⋊C4—41no—
151C2×C4⋊C4—41no—
152C2×C4⋊C4—41no—
153C2×C4⋊C4—41no—
154C2×C4⋊C4—44no—
155C2×C4⋊C4C22⋊C412yes—
156C2×C4⋊C4C22⋊C412yes—
157C2×C4⋊C4C22×C412yes—
158C2×C4⋊C4C22×C411yescharacteristic
159C2×C4⋊C4C2×D412yes—
160C2×C4⋊C4C2×D411yescharacteristic
161C2×C4⋊C4C2×D411yescharacteristic
162C2×C4⋊C4C2411yescharacteristic
163C2×C22⋊C4—24no—
164C2×C22⋊C4—28no—
165C2×C22⋊C4—24no—
166C2×C22⋊C4—24no—
167C2×C22⋊C4—28no—
168C2×C22⋊C4—24no—
169C2×C22⋊C4—48no—
170C2×C22⋊C4—44no—
171C2×C22⋊C4—44no—
172C2×C22⋊C4—84no—
173C2×C22⋊C4—84no—
174C2×C42—22no—
175C2×C42—21no—
176C2×C42—21no—
177C2×C42—21no—
178C2×C42—21no—
179C2×C42—21no—
180C2×C42—21no—
181C2×C42—22no—
182C2×C42—22no—
183C2×C42—24no—
184C2×C42—44no—
185C2×C42C22⋊C412yes—
186C2×C42C22⋊C412yes—
187C2×C42C22⋊C412yes—
188C2×C42C22×C412yes—
189C2×C42C2×D412yes—
190C2×C42C2×D412yes—
191C4⋊C8—44no—
192C4⋊C8—44no—
193C4⋊C8—44no—
194#101—48no—
195C22⋊C8—24no—
196C22⋊C8—42no—
197C4×C8—44no—
198#95—22no—
199#95C22×C414yes—
200C24—24no—
201C24—44no—
202C24—44no—
203C24—44no—
204C24—44no—
205C24—42no—
206C24—42no—
207C24—44no—
208C24—44no—
209C24C2×C22⋊C411yescharacteristic
210C2×Q8—42no—
211C2×Q8—42no—
212C2×Q8—42no—
213C2×Q8—44no—
214C2×Q8—44no—
215C2×Q8—44no—
216C2×Q8—44no—
217C2×Q8—42no—
218C2×Q8#10218yes—
219C2×Q8C2×D814yes—
220C2×Q8C2×SD1614yes—
221C2×D4—44no—
222C2×D4—48no—
223C2×D4—44no—
224C2×D4—48no—
225C2×D4—48no—
226C2×D4—48no—
227C2×D4—44no—
228C2×D4—44no—
229C2×D4—48no—
230C2×D4—84no—
231C2×D4—88no—
232C2×D4—88no—
233C2×D4—88no—
234C2×D4—84no—
235C2×D4—88no—
236C2×D4—88no—
237C2×D4—84no—
238C2×D4—84no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—24no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—24no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4—42no—
259C22×C4—44no—
260C22×C4—44no—
261C22×C4—44no—
262C22×C4#9912yes—
263C22×C4#9911yescharacteristic
264C22×C4#9911yescharacteristic
265C22×C4#10214yes—
266C22×C4#10214yes—
267C22×C4C2×C22⋊C412yes—
268C22×C4C2×C22⋊C412yes—
269C22×C4C2×C22⋊C411yescharacteristic
270C22×C4C2×C22⋊C412yes—
271C22×C4C2×C22⋊C411yescharacteristic
272C22×C4C2×C22⋊C411yescharacteristic
273C22×C4C2×C22⋊C412yes—
274C22×C4C2×D812yes—
275C22×C4C2×SD1612yes—
276C22×C4C23×C411yescharacteristic
277C22×C4C22×D411yescharacteristic
278C22×C4C22×D411yescharacteristic
279M16—44no—
280M16—44no—
281M16—84no—
282C2×C8—44no—
283C2×C8—44no—
284C2×C8—84no—
285C2×C8—84no—
286C4⋊C4—42no—
287C4⋊C4—42no—
288C4⋊C4—42no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—42no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—48no—
295C22⋊C4—44no—
296C22⋊C4—44no—
297C22⋊C4—416no—
298C22⋊C4—48no—
299C22⋊C4—88no—
300C22⋊C4—84no—
301C22⋊C4—84no—
302C42—22no—
303C42—22no—
304C42—22no—
305C42—22no—
306C42—22no—
307C42—22no—
308C42—22no—
309C42—22no—
310C42—22no—
311C42—22no—
312C42—22no—
313C42—22no—
314C42—48no—
315C23—22no—
316C23—22no—
317C23—44no—
318C23—44no—
319C23—44no—
320C23—44no—
321C23—44no—
322C23—44no—
323C23—44no—
324C23—84no—
325C23—84no—
326C23—88no—
327C23—88no—
328C23—88no—
329C23—88no—
330C23—84no—
331C23—84no—
332C23—84no—
333C23—84no—
334C23C2×#9911yescharacteristic
335C23C2×#9911yescharacteristic
336C23C2×#10212yes—
337C23#42112yes—
338C23C22×C22⋊C411yescharacteristic
339Q8—48no—
340Q8—44no—
341Q8—44no—
342D4—88no—
343D4—816no—
344D4—88no—
345D4—88no—
346D4—88no—
347C2×C4—21no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—21no—
351C2×C4—22no—
352C2×C4—21no—
353C2×C4—22no—
354C2×C4—21no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—24no—
359C2×C4—24no—
360C2×C4—24no—
361C2×C4—24no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—24no—
365C2×C4—24no—
366C2×C4—21no—
367C2×C4—22no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—44no—
381C2×C4—44no—
382C2×C4—44no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—88no—
386C2×C4#35514yes—
387C2×C4C2×#9912yes—
388C2×C4C2×#9912yes—
389C2×C4C2×#10214yes—
390C2×C4C2×#10214yes—
391C2×C4C2×#10212yes—
392C2×C4C22×D811yescharacteristic
393C2×C4C22×SD1611yescharacteristic
394C8—84no—
395C8—84no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—24no—
401C22—24no—
402C22—84no—
403C22—84no—
404C22—84no—
405C22—84no—
406C22—84no—
407C22—84no—
408C22—84no—
409C22—168no—
410C22—168no—
411C22#151912yes—
412C22#151912yes—
413C22#212212yes—
414C22C2×#35512yes—
415C22C22×#9911yescharacteristic
416C22C22×#10211yescharacteristic
417C22C2×#42111yescharacteristic
418C4—22no—
419C4—21no—
420C4—21no—
421C4—24no—
422C4—22no—
423C4—24no—
424C4—41no—
425C4—41no—
426C4—41no—
427C4—41no—
428C4—42no—
429C4—84no—
430C4C2×#35514yes—
431C2—21no—
432C2—21no—
433C2—22no—
434C2—164no—
435C2#1188214yesdirect product factor
436C2C2×#151911yescharacteristic
437C2C2×#212211yescharacteristic
438C2C22×#35511yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C4⋊C4C24
prime radicalC22×#127C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4×Q8 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1801C2semidirect
3. C2×#1461C2semidirect
4. #11882C2direct (N × H)
5. C2×#1345C2semidirect
23. #1801C22semidirect
26. #1461C22semidirect
29. #1345C22semidirect
435. C2#11882direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#25482
C2×#18012
C2×#14612
#118822
C2×#13452