Finite Group Databasebeta

← C2×#2783 #52224

Subgroups — C2×#2783 #52224

Order 256.

981 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2783C2116yesmaximal, direct product factor
2C2×#400C211yesmaximal, characteristic, complemented
3C2×#398C211yesmaximal, characteristic, complemented
4C2×#397C211yesmaximal, characteristic
5C2×#397C211yesmaximal, characteristic
6C2×#396C211yesmaximal, characteristic
7C2×#396C211yesmaximal, characteristic
8C2×#389C211yesmaximal, characteristic, complemented
9C2×#389C211yesmaximal, characteristic, complemented
10C2×#388C211yesmaximal, characteristic
11C2×#388C211yesmaximal, characteristic
12C2×#388C211yesmaximal, characteristic
13C2×#387C211yesmaximal, characteristic, complemented
14C2×#387C211yesmaximal, characteristic, complemented
15C2×#387C211yesmaximal, characteristic, complemented
16C2×#382C211yesmaximal, characteristic, complemented
17C22×C4⋊C4C2211yescharacteristic
18C22×C4⋊C4C2211yescharacteristic
19C22×C4⋊C4C2211yescharacteristic
20C22×C4⋊C4C2211yescharacteristic
21C22×C4⋊C4C2211yescharacteristic
22C22×C4⋊C4C2211yescharacteristic
23C22×C4⋊C4C2211yescharacteristic
24C22×C4⋊C4C2211yescharacteristic
25C22×C4⋊C4C2211yescharacteristic
26C22×C4⋊C4C2211yescharacteristic
27C22×C4⋊C4C2211yescharacteristic
28C22×C22⋊C4C2211yescharacteristic
29C22×C22⋊C4C2211yescharacteristic
30C22×C22⋊C4C2211yescharacteristic
31C22×C22⋊C4C2211yescharacteristic
32C22×C22⋊C4C2211yescharacteristic
33C22×C22⋊C4C2211yescharacteristic
34C22×C22⋊C4C2211yescharacteristic
35C22×C42C2211yescharacteristic
36C22×C42C2211yescharacteristic
37C22×C42C2211yescharacteristic
38#400C2218yescomplemented
39#398C2218yescomplemented
40#397C2218yes—
41#397C2218yes—
42#396C2218yes—
43#396C2218yes—
44#389C2218yescomplemented
45#389C2218yescomplemented
46#388C2218yes—
47#388C2218yes—
48#388C2218yes—
49#387C2218yescomplemented
50#387C2218yescomplemented
51#387C2218yescomplemented
52#382C2218yescomplemented
53C2×#95C2211yescharacteristic
54C2×#95C2211yescharacteristic
55C2×#95C2211yescharacteristic
56C2×#95C2211yescharacteristic
57C2×#95C2211yescharacteristic
58C2×#95C2211yescharacteristic
59C2×#95C2211yescharacteristic
60C2×#95C2211yescharacteristic
61C2×#95C2211yescharacteristic
62C2×#95C2211yescharacteristic
63C2×#95C2211yescharacteristic
64C2×#95C2211yescharacteristic
65C2×#95C2211yescharacteristic
66C2×#95C2211yescharacteristic
67C25C2311yescharacteristic
68C23×C4C2311yescharacteristic
69C23×C4C2311yescharacteristic
70C23×C4C2311yescharacteristic
71C23×C4C2311yescharacteristic
72C23×C4C2311yescharacteristic
73C23×C4C2311yescharacteristic
74C23×C4C2311yescharacteristic
75C23×C4C2311yescharacteristic
76C23×C4C2311yescharacteristic
77C23×C4C2311yescharacteristic
78C23×C4C2311yescharacteristic
79C23×C4C2311yescharacteristic
80C23×C4C2311yescharacteristic
81C23×C4C2311yescharacteristic
82C2×C4⋊C4—24no—
83C2×C4⋊C4—24no—
84C2×C4⋊C4—24no—
85C2×C4⋊C4—24no—
86C2×C4⋊C4—24no—
87C2×C4⋊C4—42no—
88C2×C4⋊C4—42no—
89C2×C4⋊C4—42no—
90C2×C4⋊C4—42no—
91C2×C4⋊C4—42no—
92C2×C4⋊C4—42no—
93C2×C4⋊C4C2314yes—
94C2×C4⋊C4C2314yes—
95C2×C4⋊C4C2314yes—
96C2×C4⋊C4C2314yes—
97C2×C4⋊C4C2314yes—
98C2×C4⋊C4C2314yes—
99C2×C4⋊C4C2314yes—
100C2×C4⋊C4C2314yes—
101C2×C4⋊C4C2314yes—
102C2×C4⋊C4C2314yes—
103C2×C4⋊C4C2314yes—
104C2×C22⋊C4—24no—
105C2×C22⋊C4—24no—
106C2×C22⋊C4—24no—
107C2×C22⋊C4—42no—
108C2×C22⋊C4—42no—
109C2×C22⋊C4—42no—
110C2×C22⋊C4—42no—
111C2×C22⋊C4C2314yes—
112C2×C22⋊C4C2314yes—
113C2×C22⋊C4C2314yes—
114C2×C22⋊C4C2314yes—
115C2×C22⋊C4C2314yes—
116C2×C22⋊C4C2314yes—
117C2×C22⋊C4C2314yes—
118C2×C42—24no—
119C2×C42—42no—
120C2×C42—42no—
121C2×C42C2314yes—
122C2×C42C2314yes—
123C2×C42C2314yes—
124#95C2314yes—
125#95C2314yes—
126#95C2314yes—
127#95C2314yes—
128#95C2314yes—
129#95C2314yes—
130#95C2314yes—
131#95C2314yes—
132#95C2314yes—
133#95C2314yes—
134#95C2314yes—
135#95C2314yes—
136#95C2314yes—
137#95C2314yes—
138C24—22no—
139C24—22no—
140C24—22no—
141C24—22no—
142C24—22no—
143C24—22no—
144C24—22no—
145C24C2412yes—
146C24C2411yescharacteristic
147C22×C4—22no—
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—22no—
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—22no—
156C22×C4—22no—
157C22×C4—22no—
158C22×C4—22no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—22no—
163C22×C4—22no—
164C22×C4—22no—
165C22×C4—22no—
166C22×C4—22no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—22no—
175C22×C4—22no—
176C22×C4—22no—
177C22×C4—22no—
178C22×C4—22no—
179C22×C4—22no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4#4114yes—
187C22×C4#4114yes—
188C22×C4#4114yes—
189C22×C4C2412yes—
190C22×C4C2412yes—
191C22×C4C2412yes—
192C22×C4C2412yes—
193C22×C4C2412yes—
194C22×C4C2412yes—
195C22×C4C2412yes—
196C22×C4C2412yes—
197C22×C4C2412yes—
198C22×C4C2412yes—
199C22×C4C2412yes—
200C22×C4C2412yes—
201C22×C4C2412yes—
202C22×C4C2412yes—
203C4⋊C4—28no—
204C4⋊C4—28no—
205C4⋊C4—28no—
206C4⋊C4—28no—
207C4⋊C4—28no—
208C4⋊C4—44no—
209C4⋊C4—44no—
210C4⋊C4—44no—
211C4⋊C4—44no—
212C4⋊C4—44no—
213C4⋊C4—44no—
214C22⋊C4—28no—
215C22⋊C4—28no—
216C22⋊C4—28no—
217C22⋊C4—44no—
218C22⋊C4—44no—
219C22⋊C4—44no—
220C22⋊C4—44no—
221C42—28no—
222C42—44no—
223C42—44no—
224C23—22no—
225C23—22no—
226C23—22no—
227C23—22no—
228C23—22no—
229C23—22no—
230C23—22no—
231C23—44no—
232C23—44no—
233C23—44no—
234C23—44no—
235C23—44no—
236C23—44no—
237C23—44no—
238C23C2×#4112yes—
239C23C2×#4112yes—
240C23C2×#4112yes—
241C23H(5,𝔽2)12yes—
242C23H(5,𝔽2)12yes—
243C232−1+412yes—
244C232−1+412yes—
245C23C2511yescharacteristic
246C2×C4—28no—
247C2×C4—28no—
248C2×C4—28no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—44no—
289C2×C4—44no—
290C2×C4—44no—
291C2×C4—44no—
292C2×C4—44no—
293C2×C4—44no—
294C2×C4—44no—
295C2×C4—44no—
296C2×C4—44no—
297C2×C4—44no—
298C2×C4—44no—
299C2×C4C2×#4114yes—
300C2×C4C2×#4114yes—
301C2×C4C2×#4114yes—
302C22—42no—
303C22—42no—
304C22—42no—
305C22—42no—
306C22—42no—
307C22—42no—
308C22—42no—
309C22—88no—
310C22#53914yes—
311C22#53914yes—
312C22#54114yes—
313C22#55314yes—
314C22#55514yes—
315C22#55614yes—
316C22#56214yes—
317C22C22×#4111yescharacteristic
318C22C22×#4111yescharacteristic
319C22C22×#4111yescharacteristic
320C22C2×H(5,𝔽2)11yescharacteristic
321C22C2×H(5,𝔽2)11yescharacteristic
322C22C2×2−1+411yescharacteristic
323C22C2×2−1+411yescharacteristic
324C4—24no—
325C4—24no—
326C4—24no—
327C4—42no—
328C4—42no—
329C4—42no—
330C4—42no—
331C4—42no—
332C4—42no—
333C4—42no—
334C4—42no—
335C4—42no—
336C4—42no—
337C4—42no—
338C2—82no—
339C2#278318yesdirect product factor
340C2C2×#53911yescharacteristic
341C2C2×#53911yescharacteristic
342C2C2×#54111yescharacteristic
343C2C2×#55311yescharacteristic
344C2C2×#55511yescharacteristic
345C2C2×#55611yescharacteristic
346C2C2×#56211yescharacteristic
subgroupG/H
center, socleC24C24
commutator, Frattini, cosocleC23C25
prime radicalC25C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #2783C2direct (N × H)
2. C2×#400C2semidirect
3. C2×#398C2semidirect
8. C2×#389C2semidirect
9. C2×#389C2semidirect
13. C2×#387C2semidirect
14. C2×#387C2semidirect
15. C2×#387C2semidirect
16. C2×#382C2semidirect
38. #400C22semidirect
39. #398C22semidirect
44. #389C22semidirect
45. #389C22semidirect
49. #387C22semidirect
50. #387C22semidirect
51. #387C22semidirect
52. #382C22semidirect
339. C2#2783direct (N × H)

Maximal subgroups

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

subgroupindex
#27832
C2×#4002
C2×#3982
C2×#3972
C2×#3962
C2×#3892
C2×#3882
C2×#3872
C2×#3822