Finite Group Databasebeta

← C2×#13076886 #14960368

Subgroups — C2×#13076886 #14960368

Order 2816.

1806 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076886C2116yesmaximal, direct product factor
2C2×#10622271C212yesmaximal
3C2×#10622270C212yesmaximal
4C2×#10622274C212yesmaximal
5C2×#10622596C212yesmaximal
6C2×#10622269C212yesmaximal
7C2×#10622592C211yesmaximal, characteristic
8C2×#10622589C211yesmaximal, characteristic
9C2×#10622264C212yesmaximal
10C2×C11×#400C211yesmaximal, characteristic
11C23×Dic22C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C4⋊Dic11C2211yescharacteristic
15C22×C4⋊Dic11C2212yes—
16C22×C4⋊Dic11C2212yes—
17C22×Dic11⋊C4C2212yes—
18C22×Dic11⋊C4C2212yes—
19C22×Dic11⋊C4C2212yes—
20C22×Dic11⋊C4C2212yes—
21C22×C4×Dic11C2211yescharacteristic
22C11×#400C2218yes—
23C2×C11×#95C2212yes—
24C2×C11×#95C2212yes—
25C2×C11×#95C2211yescharacteristic
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33#10622596C22116yes—
34#10622592C2218yes—
35#10622589C2218yes—
36#10622274C22116yes—
37#10622271C22116yes—
38#10622270C22116yes—
39#10622269C22116yes—
40#10622264C22116yes—
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2312yes—
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C23×Dic11C2312yes—
47C23×Dic11C2312yes—
48C23×Dic11C2312yes—
49C23×Dic11C2312yes—
50C22×Dic22—44no—
51C22×Dic22—42no—
52C22×Dic22C2314yes—
53C2×C11×C4⋊C4—42no—
54C2×C11×C4⋊C4—42no—
55C2×C11×C4⋊C4C2314yes—
56C2×C11×C4⋊C4C2314yes—
57C2×C4⋊Dic11—44no—
58C2×C4⋊Dic11—42no—
59C2×C4⋊Dic11—44no—
60C2×C4⋊Dic11C2318yes—
61C2×C4⋊Dic11C2318yes—
62C2×C4⋊Dic11C2314yes—
63C2×Dic11⋊C4—44no—
64C2×Dic11⋊C4—44no—
65C2×Dic11⋊C4—44no—
66C2×Dic11⋊C4—44no—
67C2×Dic11⋊C4C2318yes—
68C2×Dic11⋊C4C2318yes—
69C2×Dic11⋊C4C2318yes—
70C2×Dic11⋊C4C2318yes—
71C2×C4×Dic11Q818yescomplemented
72C2×C4×Dic11C2314yes—
73C11×#95C2318yes—
74C11×#95C2318yes—
75C11×#95C2314yes—
76C11⋊#95C2318yes—
77C11⋊#95C2318yes—
78C11⋊#95C2318yes—
79C11⋊#95C2318yes—
80C11⋊#95C2318yes—
81C11⋊#95C2314yes—
82C11⋊#95C2318yes—
83C2×#2843—111nomaximal, Sylow
84C24×C11C2411yescharacteristic
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—24no—
88C22×C4×C11—24no—
89C22×C4×C11—24no—
90C22×C4×C11—24no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—24no—
94C22×C4×C11—24no—
95C22×C4×C11—28no—
96C22×C4×C11C2×Q814yes—
97C22×C4×C11C2414yes—
98C22×C4×C11C2414yes—
99C22×C4×C11C2412yes—
100C22×C4×C11C2412yes—
101C22×C4×C11C2412yes—
102C22×Dic11—24no—
103C22×Dic11—24no—
104C22×Dic11—24no—
105C22×Dic11—24no—
106C22×Dic11—24no—
107C22×Dic11—24no—
108C22×Dic11—24no—
109C22×Dic11—24no—
110C22×Dic11—24no—
111C22×Dic11—24no—
112C22×Dic11—24no—
113C22×Dic11C2×Q818yes—
114C22×Dic11C2414yes—
115C22×Dic11C2414yes—
116C22×Dic11C2414yes—
117C22×Dic11C2414yes—
118C2×Dic22—48no—
119C2×Dic22—44no—
120C2×Dic22—416no—
121C11×C4⋊C4—44no—
122C11×C4⋊C4—44no—
123C4⋊Dic11—44no—
124C4⋊Dic11—48no—
125C4⋊Dic11—48no—
126Dic11⋊C4—48no—
127Dic11⋊C4—48no—
128Dic11⋊C4—48no—
129Dic11⋊C4—48no—
130C4×Dic11C2×Q8116yescomplemented
131#2843—1116no—
132C2×#400—112no—
133C2×#400D1111yescharacteristic
134C2×#398—112no—
135C2×#398—112no—
136C2×#398—112no—
137C2×#395—112no—
138C2×#395—111no—
139C2×#384—111no—
140C2×#383—112no—
141C23×C11C22×Q812yes—
142C23×C11H(5,𝔽2)12yes—
143C23×C11H(5,𝔽2)14yes—
144C23×C112−1+412yes—
145C23×C112−1+414yes—
146C23×C11C2511yescharacteristic
147C2×C4×C11—28no—
148C2×C4×C11—22no—
149C2×C4×C11—22no—
150C2×C4×C11—24no—
151C2×C4×C11—24no—
152C2×C4×C11—24no—
153C2×C4×C11—24no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—28no—
157C2×C4×C11—24no—
158C2×C4×C11—24no—
159C2×C4×C11—44no—
160C2×C4×C11—44no—
161C2×C4×C11—48no—
162C2×C4×C11—48no—
163C2×C4×C11C22×Q814yes—
164C2×Dic11—216no—
165C2×Dic11—24no—
166C2×Dic11—24no—
167C2×Dic11—24no—
168C2×Dic11—24no—
169C2×Dic11—24no—
170C2×Dic11—24no—
171C2×Dic11—24no—
172C2×Dic11—24no—
173C2×Dic11—24no—
174C2×Dic11—24no—
175C2×Dic11—24no—
176C2×Dic11—48no—
177C2×Dic11—48no—
178C2×Dic11—48no—
179C2×Dic11C22×Q818yes—
180Dic22—416no—
181C23×Q8—111no—
182C22×C4⋊C4—112no—
183C22×C4⋊C4—112no—
184C22×C4⋊C4—112no—
185C22×C4⋊C4—112no—
186C22×C4⋊C4—112no—
187C22×C4⋊C4—112no—
188C22×C4⋊C4—111no—
189C22×C4⋊C4C2×D1111yescharacteristic
190C22×C4⋊C4C2×D1111yescharacteristic
191C22×C42—111no—
192#400—1116no—
193#400C2×D1118yes—
194#398—1116no—
195#398—1116no—
196#398—1116no—
197#395—118no—
198#395—1116no—
199#384—118no—
200#383—1116no—
201C2×#95—112no—
202C2×#95—112no—
203C2×#95—112no—
204C2×#95—111no—
205C2×#95—112no—
206C2×#95—112no—
207C2×#95—112no—
208C2×#95C2×D1112yes—
209C2×#95C2×D1111yescharacteristic
210C2×#95C2×D1112yes—
211C22×C11#54414yes—
212C22×C11#54418yes—
213C22×C11#56014yes—
214C22×C11#56318yes—
215C22×C11#56314yes—
216C22×C11C23×Q811yescharacteristic
217C22×C11C2×H(5,𝔽2)11yescharacteristic
218C22×C11C2×H(5,𝔽2)12yes—
219C22×C11C2×2−1+412yes—
220C22×C11C2×2−1+411yescharacteristic
221C4×C11—24no—
222C4×C11—42no—
223C4×C11—42no—
224C4×C11—44no—
225C4×C11—44no—
226Dic11—28no—
227Dic11—44no—
228Dic11—44no—
229Dic11—44no—
230C22×Q8—114no—
231C22×Q8—442no—
232C22×Q8—444no—
233C23×C4—112no—
234C23×C4—112no—
235C23×C4—112no—
236C23×C4—112no—
237C23×C4C22×D1111yescharacteristic
238C23×C4C22×D1111yescharacteristic
239C23×C4C22×D1112yes—
240C23×C4C22×D1112yes—
241C23×C4C22×D1111yescharacteristic
242C2×C4⋊C4—42no—
243C2×C4⋊C4—42no—
244C2×C4⋊C4—118no—
245C2×C4⋊C4—118no—
246C2×C4⋊C4—114no—
247C2×C4⋊C4—118no—
248C2×C4⋊C4—118no—
249C2×C4⋊C4—118no—
250C2×C4⋊C4—118no—
251C2×C4⋊C4—444no—
252C2×C4⋊C4—444no—
253C2×C4⋊C4—444no—
254C2×C4⋊C4—444no—
255C2×C4⋊C4—442no—
256C2×C4⋊C4—444no—
257C2×C4⋊C4—444no—
258C2×C4⋊C4C22×D1114yes—
259C2×C4⋊C4C22×D1114yes—
260C2×C42—118no—
261C2×C42—114no—
262#95—118no—
263#95—118no—
264#95—118no—
265#95—118no—
266#95—118no—
267#95—114no—
268#95—118no—
269#95C22×D1118yes—
270#95C22×D1118yes—
271#95C22×D1114yes—
272C2×C11#284318yescomplemented
273C2×C11C2×#54411yescharacteristic
274C2×C11C2×#54412yes—
275C2×C11C2×#56011yescharacteristic
276C2×C11C2×#56311yescharacteristic
277C2×C11C2×#56312yes—
278C24C23×D1111yescharacteristic
279C2×Q8—444no—
280C2×Q8—448no—
281C2×Q8—4416no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—24no—
286C22×C4—22no—
287C22×C4—24no—
288C22×C4—24no—
289C22×C4—24no—
290C22×C4—24no—
291C22×C4—24no—
292C22×C4—28no—
293C22×C4—118no—
294C22×C4—114no—
295C22×C4—114no—
296C22×C4—114no—
297C22×C4—114no—
298C22×C4—224no—
299C22×C4—224no—
300C22×C4—224no—
301C22×C4—224no—
302C22×C4—224no—
303C22×C4—224no—
304C22×C4—224no—
305C22×C4—224no—
306C22×C4—224no—
307C22×C4—224no—
308C22×C4—224no—
309C22×C4Q8×D1114yes—
310C22×C4C23×D1114yes—
311C22×C4C23×D1114yes—
312C22×C4C23×D1112yes—
313C22×C4C23×D1112yes—
314C22×C4C23×D1112yes—
315C4⋊C4—44no—
316C4⋊C4—44no—
317C4⋊C4—448no—
318C4⋊C4—448no—
319C4⋊C4—448no—
320C4⋊C4—448no—
321C4⋊C4—444no—
322C4⋊C4—448no—
323C4⋊C4—448no—
324C42—1116no—
325C11C2×#284311yescharacteristic, complemented, Sylow
326C23#6703712yes—
327C23C2×Q8×D1112yes—
328C23#6704214yes—
329C23#6704312yes—
330C23#6704314yes—
331C23C24×D1111yescharacteristic
332Q8—4416no—
333C2×C4—28no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—24no—
338C2×C4—22no—
339C2×C4—24no—
340C2×C4—24no—
341C2×C4—24no—
342C2×C4—28no—
343C2×C4—24no—
344C2×C4—24no—
345C2×C4—48no—
346C2×C4—44no—
347C2×C4—44no—
348C2×C4—48no—
349C2×C4—118no—
350C2×C4—224no—
351C2×C4—224no—
352C2×C4—2216no—
353C2×C4—224no—
354C2×C4—224no—
355C2×C4—224no—
356C2×C4—224no—
357C2×C4—224no—
358C2×C4—224no—
359C2×C4—224no—
360C2×C4—224no—
361C2×C4—224no—
362C2×C4—448no—
363C2×C4—448no—
364C2×C4—448no—
365C2×C4C2×Q8×D1114yes—
366C22#1062315414yes—
367C22#1062319714yes—
368C22#1062320314yes—
369C22#1062322018yes—
370C22#1062324318yes—
371C22C2×#6703711yescharacteristic
372C22C22×Q8×D1111yescharacteristic
373C22C2×#6704212yes—
374C22C2×#6704312yes—
375C22C2×#6704311yescharacteristic
376C4—24no—
377C4—42no—
378C4—42no—
379C4—44no—
380C4—44no—
381C4—228no—
382C4—444no—
383C4—444no—
384C4—444no—
385C2#1307688618yesdirect product factor
386C2C2×#1062315411yescharacteristic
387C2C2×#1062322012yes—
388C2C2×#1062319711yescharacteristic
389C2C2×#1062320311yescharacteristic
390C2C2×#1062324312yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#400C2
socle, prime radicalC24×C11C24
hypercenterC2×#400D11
hypocenterC11C2×#2843
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
1. #13076886C2direct (N × H)
71. C2×C4×Dic11Q8semidirect
130. C4×Dic11C2×Q8semidirect
272. C2×C11#2843semidirect
325. C11C2×#2843semidirect
385. C2#13076886direct (N × H)

Maximal subgroups

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

subgroupindex
#130768862
C2×#106222712
C2×#106222702
C2×#106222742
C2×#106225962
C2×#106222692
C2×#106225922
C2×#106225892
C2×#106222642
C2×C11×#4002
C2×#284311