Finite Group Databasebeta

← C2×#13071728 #14913452

Subgroups — C2×#13071728 #14913452

Order 2816.

3158 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071728C2116yesmaximal, direct product factor
2C2×#10622843C212yesmaximal, complemented
3C2×#10622564C214yesmaximal, complemented
4C2×#10622833C212yesmaximal
5C2×C22⋊C4×Dic11C214yesmaximal, complemented
6C2×#10622545C212yesmaximal, complemented
7C22×C11×#124C211yesmaximal, characteristic
8C23×Q8×C11C2211yescharacteristic
9C23×D4×C11C2211yescharacteristic
10C24×Dic11C2212yes—
11C2×C11×#124C4116yescomplemented
12C2×C11×#124C2218yes—
13C22×C11×C22⋊C4C2214yes—
14C22×C42×C11C2211yescharacteristic
15C22×C22⋊Dic11C2214yes—
16C22×C22⋊Dic11C2212yes—
17C22×C4⋊Dic11C2212yes—
18C22×C4×Dic11C2214yes—
19C22×C4×Dic11C2212yes—
20#10622843C22116yescomplemented
21#10622833C22116yes—
22C2×C11⋊#95C2212yes—
23C2×C11⋊#95C2214yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2214yes—
26#10622564C22132yescomplemented
27C22⋊C4×Dic11C22132yescomplemented
28#10622545C22116yescomplemented
29C25×C11C2312yes—
30C22×Q8×C11—42no—
31C22×Q8×C11—42no—
32C22×Q8×C11C2×C418yescomplemented
33C22×Q8×C11C2314yes—
34C22×D4×C11—42no—
35C22×D4×C11—42no—
36C22×D4×C11C2×C418yes—
37C22×D4×C11C2314yes—
38C23×C4×C11C2312yes—
39C23×C4×C11C2312yes—
40C23×C4×C11C2311yescharacteristic
41C23×Dic11—216no—
42C23×Dic11—44no—
43C23×Dic11C2314yes—
44C23×Dic11C2318yes—
45C23×Dic11C2314yes—
46C11×#124C2×C4164yescomplemented
47C2×C11×C22⋊C4C2×C4132yescomplemented
48C2×C11×C22⋊C4C23116yes—
49C2×C42×C11C2×C418yescomplemented
50C2×C42×C11C2314yes—
51C2×C22⋊Dic11—216no—
52C2×C22⋊Dic11—44no—
53C2×C22⋊Dic11C23116yes—
54C2×C22⋊Dic11C2318yes—
55C2×C4⋊Dic11—44no—
56C2×C4⋊Dic11C2318yes—
57C2×C4×Dic11—216no—
58C2×C4×Dic11—44no—
59C2×C4×Dic11C23116yes—
60C2×C4×Dic11C2318yes—
61C11⋊#95C2318yes—
62C11⋊#95C2318yes—
63C11⋊#95C23116yes—
64C11⋊#95C23116yes—
65C2×#2372—111nomaximal, Sylow
66C24×C11—28no—
67C24×C11—28no—
68C24×C11—24no—
69C24×C11—24no—
70C24×C11C22×C418yes—
71C24×C11C2414yes—
72C24×C11C2411yescharacteristic
73C2×Q8×C11—416no—
74C2×Q8×C11—44no—
75C2×Q8×C11—44no—
76C2×Q8×C11C22×C4116yescomplemented
77C2×D4×C11—416no—
78C2×D4×C11—44no—
79C2×D4×C11—44no—
80C2×D4×C11C22×C4116yes—
81C22×C4×C11—28no—
82C22×C4×C11—24no—
83C22×C4×C11—24no—
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11C22×C418yes—
87C22×C4×C11C22×C414yes—
88C22×C4×C11C22×C418yes—
89C22×C4×C11C2412yes—
90C22×C4×C11C2414yes—
91C22×C4×C11C2414yes—
92C22×Dic11—232no—
93C22×Dic11—28no—
94C22×Dic11—28no—
95C22×Dic11—28no—
96C22×Dic11—28no—
97C22×Dic11—28no—
98C22×Dic11—48no—
99C22×Dic11—432no—
100C22×Dic11#41116yes—
101C22×Dic11C2418yes—
102C22×Dic11C2418yes—
103C11×C22⋊C4C22×C4164yescomplemented
104C42×C11C22×C4116yescomplemented
105C22⋊Dic11—232no—
106C22⋊Dic11—48no—
107C4⋊Dic11—48no—
108C4×Dic11—232no—
109C4×Dic11—48no—
110C22×#124D1111yescharacteristic
111#2372—1116no—
112C2×#391—112no—
113C2×#388—114no—
114C2×#386—112no—
115C2×C4×C22⋊C4—114no—
116C2×#376—112no—
117C23×C11—232no—
118C23×C11—216no—
119C23×C11—28no—
120C23×C11—28no—
121C23×C11—24no—
122C23×C11—24no—
123C23×C11—48no—
124C23×C11—48no—
125C23×C11—416no—
126C23×C11C23×C418yes—
127C23×C11C23×C412yes—
128C23×C11C2×#4118yes—
129C23×C11H(5,𝔽2)12yes—
130C23×C11H(5,𝔽2)12yes—
131C23×C11C2511yescharacteristic
132Q8×C11—416no—
133D4×C11—416no—
134C2×C4×C11—216no—
135C2×C4×C11—28no—
136C2×C4×C11—216no—
137C2×C4×C11—28no—
138C2×C4×C11—24no—
139C2×C4×C11—24no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11C23×C418yes—
143C2×C4×C11C23×C414yes—
144C2×C4×C11C23×C418yes—
145C2×Dic11—232no—
146C2×Dic11—28no—
147C2×Dic11—28no—
148C2×Dic11—28no—
149C2×Dic11—28no—
150C2×Dic11—28no—
151C2×Dic11—432no—
152C2×Dic11—416no—
153C2×Dic11C2×#41116yes—
154C23×Q8C2×D1111yescharacteristic
155C23×D4C2×D1111yescharacteristic
156C24×C4—112no—
157C2×#124Dic11116yescomplemented
158C2×#124C2×D1118yes—
159C22×C4⋊C4—112no—
160C22×C22⋊C4—114no—
161C22×C22⋊C4—112no—
162C22×C22⋊C4C2×D1114yes—
163C22×C42—114no—
164C22×C42—112no—
165C22×C42C2×D1111yescharacteristic
166#391—1116no—
167#388—1132no—
168#386—1116no—
169C4×C22⋊C4—1132no—
170#376—1116no—
171C2×#95—112no—
172C2×#95—114no—
173C2×#95—112no—
174C2×#95—114no—
175C22×C11—216no—
176C22×C11—28no—
177C22×C11—432no—
178C22×C11—44no—
179C22×C11—44no—
180C22×C11—48no—
181C22×C11C4×#4118yes—
182C22×C11#51814yes—
183C22×C11#55118yes—
184C22×C11#55518yes—
185C22×C11C24×C411yescharacteristic
186C22×C11C22×#4114yes—
187C22×C11C2×H(5,𝔽2)11yescharacteristic
188C22×C11C2×H(5,𝔽2)11yescharacteristic
189C4×C11—28no—
190C4×C11—24no—
191C4×C11—28no—
192Dic11—216no—
193Dic11—48no—
194C25C22×D1112yes—
195C22×Q8—42no—
196C22×Q8—42no—
197C22×Q8C2×Dic1118yescomplemented
198C22×Q8C22×D1114yes—
199C22×D4—42no—
200C22×D4—42no—
201C22×D4C2×Dic1118yes—
202C22×D4C22×D1114yes—
203C23×C4—114no—
204C23×C4—114no—
205C23×C4—118no—
206C23×C4—2216no—
207C23×C4—444no—
208C23×C4C22×D1112yes—
209C23×C4C22×D1112yes—
210C23×C4C22×D1111yescharacteristic
211#124C2×Dic11164yescomplemented
212C2×C4⋊C4—118no—
213C2×C4⋊C4—444no—
214C2×C22⋊C4—1116no—
215C2×C22⋊C4—118no—
216C2×C22⋊C4—2216no—
217C2×C22⋊C4—444no—
218C2×C22⋊C4C2×Dic11132yescomplemented
219C2×C22⋊C4C22×D11116yes—
220C2×C42—1116no—
221C2×C42—118no—
222C2×C42—2216no—
223C2×C42—444no—
224C2×C42C2×Dic1118yescomplemented
225C2×C42C22×D1114yes—
226#95—118no—
227#95—1116no—
228#95—118no—
229#95—1116no—
230C2×C11—48no—
231C2×C11#237218yescomplemented
232C2×C11C2×C4×#4112yes—
233C2×C11C2×#51811yescharacteristic
234C2×C11C2×#55112yes—
235C2×C11C2×#55512yes—
236C24—24no—
237C24—24no—
238C24—28no—
239C24—28no—
240C24C22×Dic1118yes—
241C24C23×D1114yes—
242C24C23×D1111yescharacteristic
243C2×Q8—44no—
244C2×Q8—44no—
245C2×Q8—416no—
246C2×Q8C22×Dic11116yescomplemented
247C2×D4—44no—
248C2×D4—44no—
249C2×D4—416no—
250C2×D4C22×Dic11116yes—
251C22×C4—24no—
252C22×C4—24no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—28no—
256C22×C4—1116no—
257C22×C4—118no—
258C22×C4—118no—
259C22×C4—2232no—
260C22×C4—228no—
261C22×C4—228no—
262C22×C4—228no—
263C22×C4—228no—
264C22×C4—228no—
265C22×C4—448no—
266C22×C4—4432no—
267C22×C4C22×Dic1118yes—
268C22×C4C22×Dic1114yes—
269C22×C4C22×Dic1118yes—
270C22×C4C23×D1112yes—
271C22×C4C23×D1114yes—
272C22×C4C23×D1114yes—
273C4⋊C4—448no—
274C22⋊C4—2232no—
275C22⋊C4—448no—
276C22⋊C4C22×Dic11164yescomplemented
277C42—2232no—
278C42—448no—
279C42C22×Dic11116yescomplemented
280C11C2×#237211yescharacteristic, complemented, Sylow
281C23—216no—
282C23—232no—
283C23—24no—
284C23—24no—
285C23—28no—
286C23—28no—
287C23—416no—
288C23—48no—
289C23—48no—
290C23#6703712yes—
291C23#6703712yes—
292C23#41×D1118yes—
293C23C23×Dic1118yes—
294C23C23×Dic1112yes—
295C23C24×D1111yescharacteristic
296Q8—416no—
297D4—416no—
298C2×C4—28no—
299C2×C4—216no—
300C2×C4—216no—
301C2×C4—24no—
302C2×C4—24no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—28no—
306C2×C4—1116no—
307C2×C4—228no—
308C2×C4—228no—
309C2×C4—2232no—
310C2×C4—228no—
311C2×C4—228no—
312C2×C4—228no—
313C2×C4—4432no—
314C2×C4—4416no—
315C2×C4C23×Dic1118yes—
316C2×C4C23×Dic1114yes—
317C2×C4C23×Dic1118yes—
318C22—216no—
319C22—28no—
320C22—44no—
321C22—44no—
322C22—48no—
323C22—432no—
324C22#1062320118yes—
325C22#1062321018yes—
326C22#1062332914yes—
327C22#41×Dic1118yes—
328C22C2×#6703711yescharacteristic
329C22C2×#6703711yescharacteristic
330C22C2×#41×D1114yes—
331C22C24×Dic1111yescharacteristic
332C4—28no—
333C4—24no—
334C4—28no—
335C4—2216no—
336C4—448no—
337C2—48no—
338C2#1307172818yesdirect product factor
339C2C2×#41×Dic1112yes—
340C2C2×#1062332911yescharacteristic
341C2C2×#1062321012yes—
342C2C2×#1062320112yes—
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC22×C11×#124C2
socleC24×C11C24
prime radicalC23×D4×C11C22
cosocleC23×C11C25
hypercenterC22×#124D11
hypocenterC11C2×#2372
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#124

Complements

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

NH ≅ G/Ntype
1. #13071728C2direct (N × H)
2. C2×#10622843C2semidirect
3. C2×#10622564C2semidirect
5. C2×C22⋊C4×Dic11C2semidirect
6. C2×#10622545C2semidirect
11. C2×C11×#124C4semidirect
20. #10622843C22semidirect
26. #10622564C22semidirect
27. C22⋊C4×Dic11C22semidirect
28. #10622545C22semidirect
32. C22×Q8×C11C2×C4semidirect
46. C11×#124C2×C4semidirect
47. C2×C11×C22⋊C4C2×C4semidirect
49. C2×C42×C11C2×C4semidirect
76. C2×Q8×C11C22×C4semidirect
103. C11×C22⋊C4C22×C4semidirect
104. C42×C11C22×C4semidirect
157. C2×#124Dic11semidirect
197. C22×Q8C2×Dic11semidirect
211. #124C2×Dic11semidirect
218. C2×C22⋊C4C2×Dic11semidirect
224. C2×C42C2×Dic11semidirect
231. C2×C11#2372semidirect
246. C2×Q8C22×Dic11semidirect
276. C22⋊C4C22×Dic11semidirect
279. C42C22×Dic11semidirect
280. C11C2×#2372semidirect
338. C2#13071728direct (N × H)

Maximal subgroups

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

subgroupindex
#130717282
C2×#106228432
C2×#106225642
C2×#106228332
C2×C22⋊C4×Dic112
C2×#106225452
C22×C11×#1242
C2×#237211