Finite Group Databasebeta

← C2×#11782 #481612

Subgroups — C2×#11782 #481612

Order 512.

1112 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2546C211yesmaximal, characteristic
2C2×C4×#101C211yesmaximal, characteristic
3C2×#1467C211yesmaximal, characteristic
4#11782C218yesmaximal, direct product factor
5C2×#1346C214yesmaximal
6C22×C4⋊Q8—21no—
7C22×C4⋊Q8C411yescharacteristic
8C22×C4×Q8C2211yescharacteristic
9C2×#432—21no—
10C22×#101—21no—
11C2×C4×M16—21no—
12#2546—22no—
13#2546—22no—
14#2546C414yes—
15#2546C2214yes—
16C2×#398C412yes—
17C2×#398C2212yes—
18C2×#391—21no—
19C2×#389—21no—
20C2×#389—21no—
21C2×C4×C4⋊C4C411yescharacteristic
22C4×#101—22no—
23C4×#101C2214yes—
24C2×#343C2212yes—
25#1467—22no—
26#1467C2214yes—
27C2×#324—21no—
28C2×#324C2212yes—
29#1346C22116yes—
30C23×Q8—21no—
31C23×Q8D411yescharacteristic
32C22×M16—22no—
33C2×C4⋊Q8—24no—
34C2×C4⋊Q8—24no—
35C2×C4⋊Q8—22no—
36C2×C4⋊Q8—42no—
37C2×C4⋊Q8—41no—
38C2×C4⋊Q8—41no—
39C2×C4⋊Q8—48no—
40C2×C4⋊Q8C2×C414yes—
41C2×C4×Q8—41no—
42C2×C4×Q8—41no—
43C2×C4×Q8—42no—
44C2×C4×Q8C2×C412yes—
45C2×C4×Q8D412yes—
46C2×C4×Q8D412yes—
47C2×C4×Q8C2312yes—
48C22×C4⋊C4—21no—
49C22×C4⋊C4—22no—
50C22×C4⋊C4—21no—
51C22×C4⋊C4—22no—
52C22×C4⋊C4C2×C412yes—
53C22×C4⋊C4C2×C411yescharacteristic
54C22×C4⋊C4D411yescharacteristic
55C22×C4⋊C4C2311yescharacteristic
56C22×C42—21no—
57C22×C42C2×C411yescharacteristic
58C22×C42D411yescharacteristic
59C22×C42D411yescharacteristic
60#432—24no—
61#432—42no—
62C2×C4⋊C8—41no—
63C2×#101—28no—
64C2×#101—24no—
65C2×C22⋊C8—22no—
66C4×M16—24no—
67C4×M16—42no—
68C2×#97—41no—
69C2×#97—41no—
70C2×C4×C8—41no—
71#398—24no—
72#398—22no—
73#398—22no—
74#398C2×C418yes—
75#398C2×C414yes—
76#398C2314yes—
77#391—24no—
78#391—24no—
79#389—24no—
80#389—24no—
81#389—24no—
82#389—24no—
83C4×C4⋊C4—22no—
84C4×C4⋊C4C2×C414yes—
85C2×#95—22no—
86C2×#95—22no—
87C2×#95C2×C412yes—
88#343—22no—
89#343C2314yes—
90#324—24no—
91#324—22no—
92#324C2314yes—
93C22×Q8—24no—
94C22×Q8—24no—
95C22×Q8—24no—
96C22×Q8—41no—
97C22×Q8—41no—
98C22×Q8—42no—
99C22×Q8—42no—
100C22×Q8—44no—
101C22×Q8—44no—
102C22×Q8C22⋊C412yes—
103C22×Q8C2×D412yes—
104C23×C4—22no—
105C23×C4—22no—
106C23×C4C22⋊C411yescharacteristic
107C23×C4C22⋊C411yescharacteristic
108C23×C4C22⋊C411yescharacteristic
109C23×C4C22⋊C411yescharacteristic
110C23×C4C22×C411yescharacteristic
111C23×C4C2×D411yescharacteristic
112C23×C4C2×D411yescharacteristic
113C2×M16—28no—
114C2×M16—24no—
115C2×M16—42no—
116C2×M16—44no—
117C22×C8—42no—
118C22×C8—42no—
119C4⋊Q8—44no—
120C4⋊Q8—44no—
121C4⋊Q8—44no—
122C4⋊Q8—44no—
123C4⋊Q8—416no—
124C4⋊Q8—416no—
125C4×Q8—42no—
126C4×Q8—42no—
127C4×Q8—42no—
128C4×Q8—42no—
129C4×Q8—42no—
130C4×Q8—42no—
131C4×Q8—42no—
132C4×Q8—42no—
133C2×C4⋊C4—28no—
134C2×C4⋊C4—24no—
135C2×C4⋊C4—28no—
136C2×C4⋊C4—24no—
137C2×C4⋊C4—24no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—24no—
140C2×C4⋊C4—41no—
141C2×C4⋊C4—41no—
142C2×C4⋊C4—41no—
143C2×C4⋊C4—41no—
144C2×C4⋊C4—41no—
145C2×C4⋊C4—41no—
146C2×C4⋊C4—42no—
147C2×C4⋊C4—42no—
148C2×C4⋊C4—48no—
149C2×C4⋊C4—42no—
150C2×C4⋊C4—41no—
151C2×C4⋊C4—41no—
152C2×C4⋊C4—48no—
153C2×C4⋊C4C22⋊C412yes—
154C2×C4⋊C4C22⋊C412yes—
155C2×C4⋊C4C22×C414yes—
156C2×C4⋊C4C22×C412yes—
157C2×C4⋊C4C22×C411yescharacteristic
158C2×C4⋊C4C2×D412yes—
159C2×C4⋊C4C2×D411yescharacteristic
160C2×C4⋊C4C2×D411yescharacteristic
161C2×C4⋊C4C2411yescharacteristic
162C2×C42—22no—
163C2×C42—21no—
164C2×C42—21no—
165C2×C42—21no—
166C2×C42—21no—
167C2×C42—21no—
168C2×C42—22no—
169C2×C42—21no—
170C2×C42—22no—
171C2×C42—24no—
172C2×C42—44no—
173C2×C42C22⋊C412yes—
174C2×C42C22⋊C412yes—
175C2×C42C22⋊C412yes—
176C2×C42C22×C412yes—
177C2×C42C2×D412yes—
178C2×C42C2×D412yes—
179C4⋊C8—44no—
180#101—216no—
181C22⋊C8—24no—
182C22⋊C8—42no—
183#97—44no—
184#97—44no—
185C4×C8—44no—
186#95—24no—
187#95—28no—
188#95—22no—
189#95—24no—
190#95C22×C414yes—
191C24C2×C22⋊C411yescharacteristic
192C2×Q8—24no—
193C2×Q8—24no—
194C2×Q8—24no—
195C2×Q8—24no—
196C2×Q8—42no—
197C2×Q8—42no—
198C2×Q8—48no—
199C2×Q8—48no—
200C2×Q8—48no—
201C2×Q8—48no—
202C2×Q8—48no—
203C2×Q8—88no—
204C2×Q8—88no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—24no—
212C22×C4—28no—
213C22×C4—24no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—24no—
225C22×C4—44no—
226C22×C4—44no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—42no—
232C22×C4—44no—
233C22×C4—44no—
234C22×C4#9912yes—
235C22×C4#9911yescharacteristic
236C22×C4#9911yescharacteristic
237C22×C4#10414yes—
238C22×C4C2×C22⋊C412yes—
239C22×C4C2×C22⋊C412yes—
240C22×C4C2×C22⋊C411yescharacteristic
241C22×C4C2×C22⋊C412yes—
242C22×C4C2×C22⋊C411yescharacteristic
243C22×C4C2×C22⋊C412yes—
244C22×C4C2×C22⋊C411yescharacteristic
245C22×C4AGL(1,ℤ/8)14yes—
246C22×C4C23×C411yescharacteristic
247C22×C4C22×D411yescharacteristic
248C22×C4C22×D411yescharacteristic
249M16—28no—
250M16—48no—
251M16—44no—
252C2×C8—44no—
253C2×C8—48no—
254C2×C8—44no—
255C2×C8—84no—
256C4⋊C4—216no—
257C4⋊C4—42no—
258C4⋊C4—42no—
259C4⋊C4—41no—
260C4⋊C4—42no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—42no—
264C4⋊C4—41no—
265C4⋊C4—44no—
266C4⋊C4—44no—
267C4⋊C4—416no—
268C4⋊C4—48no—
269C4⋊C4—44no—
270C4⋊C4—44no—
271C4⋊C4—48no—
272C42—22no—
273C42—22no—
274C42—22no—
275C42—22no—
276C42—22no—
277C42—22no—
278C42—22no—
279C42—22no—
280C42—22no—
281C42—22no—
282C42—22no—
283C42—22no—
284C42—48no—
285C23—22no—
286C23—22no—
287C23C2×#9911yescharacteristic
288C23C2×#9911yescharacteristic
289C23#41812yes—
290C23C2×#10412yes—
291C23C22×C22⋊C411yescharacteristic
292Q8—48no—
293Q8—48no—
294Q8—816no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—24no—
303C2×C4—24no—
304C2×C4—24no—
305C2×C4—24no—
306C2×C4—24no—
307C2×C4—24no—
308C2×C4—28no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—22no—
313C2×C4—21no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—416no—
318C2×C4—44no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—44no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—44no—
332C2×C4—44no—
333C2×C4—44no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—84no—
337C2×C4—84no—
338C2×C4#35614yes—
339C2×C4C2×#9912yes—
340C2×C4C2×#9912yes—
341C2×C4#41812yes—
342C2×C4C2×#10414yes—
343C2×C4C2×AGL(1,ℤ/8)12yes—
344C8—48no—
345C8—84no—
346C22—24no—
347C22—24no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22#150712yes—
353C22#150712yes—
354C22#212312yes—
355C22C2×#35612yes—
356C22C22×#9911yescharacteristic
357C22C2×#41811yescharacteristic
358C22C22×#10411yescharacteristic
359C4—22no—
360C4—22no—
361C4—22no—
362C4—24no—
363C4—48no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—42no—
369C4—42no—
370C4—84no—
371C4C2×#35614yes—
372C2—21no—
373C2—21no—
374C2—22no—
375C2#1178214yesdirect product factor
376C2C2×#150711yescharacteristic
377C2C2×#212311yescharacteristic
378C2C22×#35611yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C4⋊C4C24
prime radicalC24C2×C22⋊C4
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
4. #11782C2direct (N × H)
375. C2#11782direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#25462
C2×C4×#1012
C2×#14672
#117822
C2×#13462