Finite Group Databasebeta

← C2×#13074383 #14920985

Subgroups — C2×#13074383 #14920985

Order 2816.

3046 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
1C22×#66999C212yesmaximal
2C22×#66925C211yesmaximal, characteristic
3#13074383C2116yesmaximal, direct product factor
4C2×#10622593C214yesmaximal, complemented
5C2×#10622606C214yesmaximal
6C2×#10622843C212yesmaximal, complemented
7C2×#10622549C211yesmaximal, characteristic, complemented
8C22×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
9C23×Q8×C11C2212yes—
10C23×C4×D11C2211yescharacteristic
11C2×C11×C4⋊Q8—28no—
12C2×C11×C4⋊Q8C2218yescomplemented
13C22×C11×C4⋊C4C2214yes—
14C22×C42×C11C2211yescharacteristic
15C2×#66999—216no—
16C2×#66999C22116yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2214yes—
19C22×C4⋊Dic11C2212yes—
20C22×Dic11⋊C4C2212yes—
21C22×Dic11⋊C4C2214yes—
22C22×C4×Dic11C2211yescharacteristic
23C2×#66925—28no—
24C2×#66925C2218yes—
25#10622843C22116yescomplemented
26C2×C11⋊#95C2214yes—
27C2×C11⋊#95C2218yes—
28#10622606C22132yes—
29#10622593C22132yescomplemented
30#10622549C2218yescomplemented
31C24×D11C2311yescharacteristic
32C22×Q8×C11—28no—
33C22×Q8×C11—28no—
34C22×Q8×C11—28no—
35C22×Q8×C11C2318yes—
36C23×C4×C11C2314yes—
37C23×C4×C11C2312yes—
38C23×C4×C11C2311yescharacteristic
39C23×Dic11C2312yes—
40C23×Dic11C2314yes—
41C23×Dic11C2311yescharacteristic
42C22×C4×D11—24no—
43C22×C4×D11—24no—
44C22×C4×D11D418yes—
45C22×C4×D11C2314yes—
46C11×C4⋊Q8—232no—
47C2×C11×C4⋊C4—216no—
48C2×C11×C4⋊C4C23116yes—
49C2×C42×C11D418yes—
50C2×C42×C11C2314yes—
51#66999—264no—
52C2×(C2×D11)⋊C4—216no—
53C2×(C2×D11)⋊C4—28no—
54C2×(C2×D11)⋊C4C2318yes—
55C2×(C2×D11)⋊C4C23116yes—
56C2×C4⋊Dic11—28no—
57C2×C4⋊Dic11C2318yes—
58C2×Dic11⋊C4—28no—
59C2×Dic11⋊C4—216no—
60C2×Dic11⋊C4C2318yes—
61C2×Dic11⋊C4C23116yes—
62C2×C4×Dic11—24no—
63C2×C4×Dic11C2314yes—
64#66925—232no—
65C11⋊#95C23116yes—
66C11⋊#95C23132yes—
67C2×#2621—111nomaximal, Sylow
68C24×C11C2411yescharacteristic
69C23×D11—22no—
70C23×D11—22no—
71C23×D11—28no—
72C23×D11C2×D414yes—
73C23×D11C2412yes—
74C2×Q8×C11—216no—
75C2×Q8×C11—216no—
76C2×Q8×C11—216no—
77C2×Q8×C11—432no—
78C22×C4×C11—28no—
79C22×C4×C11—28no—
80C22×C4×C11—28no—
81C22×C4×C11—28no—
82C22×C4×C11C2×D418yes—
83C22×C4×C11C2×D414yes—
84C22×C4×C11C2×D414yes—
85C22×C4×C11#4114yes—
86C22×C4×C11C2418yes—
87C22×C4×C11C2414yes—
88C22×C4×C11C2412yes—
89C22×Dic11—22no—
90C22×Dic11—24no—
91C22×Dic11—28no—
92C22×Dic11—22no—
93C22×Dic11—28no—
94C22×Dic11—216no—
95C22×Dic11C2×D414yes—
96C22×Dic11C2414yes—
97C22×Dic11C2418yes—
98C22×Dic11C2412yes—
99C2×C4×D11—232no—
100C2×C4×D11—28no—
101C2×C4×D11—28no—
102C2×C4×D11C2×D4116yes—
103C11×C4⋊C4—232no—
104C42×C11C2×D4116yes—
105(C2×D11)⋊C4—232no—
106(C2×D11)⋊C4—216no—
107C4⋊Dic11—216no—
108Dic11⋊C4—232no—
109Dic11⋊C4—216no—
110C4×Dic11—28no—
111C22×C4⋊Q8D1111yescharacteristic, complemented
112C22×C22⋊Q8—112no—
113C22×#117—111no—
114#2621—1116no—
115C2×#398—114no—
116C2×#397—114no—
117C2×#391—112no—
118C2×#382—111no—
119C23×C11C22×D412yes—
120C23×C11C22×D412yes—
121C23×C11C2×#4112yes—
122C23×C112−1+418yes—
123C23×C11C2511yescharacteristic
124C22×D11—28no—
125C22×D11—216no—
126C22×D11—22no—
127C22×D11—22no—
128C22×D11—28no—
129C22×D11—48no—
130C22×D11—48no—
131C22×D11C22×D414yes—
132Q8×C11—432no—
133C2×C4×C11—216no—
134C2×C4×C11—28no—
135C2×C4×C11—28no—
136C2×C4×C11—28no—
137C2×C4×C11—28no—
138C2×C4×C11—416no—
139C2×C4×C11#121116yes—
140C2×C4×C11C22×D414yes—
141C2×C4×C11C22×D418yes—
142C2×C4×C11C22×D414yes—
143C2×C4×C11C2×#4114yes—
144C2×Dic11—28no—
145C2×Dic11—22no—
146C2×Dic11—22no—
147C2×Dic11—24no—
148C2×Dic11—28no—
149C2×Dic11—28no—
150C2×Dic11—216no—
151C2×Dic11—416no—
152C2×Dic11—48no—
153C2×Dic11C22×D414yes—
154C4×D11—232no—
155C23×Q8C2×D1112yes—
156C24×C4—111no—
157C2×C4⋊Q8—28no—
158C2×C4⋊Q8C2×D1118yescomplemented
159C2×C22⋊Q8—1116no—
160C2×C22⋊Q8—2216no—
161C2×#117—118no—
162C2×#117—228no—
163C22×C4⋊C4—112no—
164C22×C4⋊C4—114no—
165C22×C4⋊C4—112no—
166C22×C4⋊C4C2×D1114yes—
167C22×C22⋊C4—112no—
168C22×C22⋊C4—114no—
169C22×C42—111no—
170C22×C42C2×D1111yescharacteristic
171#398—1132no—
172#397—1132no—
173#391—1116no—
174#382—118no—
175C2×#95—114no—
176C2×#95—118no—
177C22×C11C2×#12114yes—
178C22×C11#53618yes—
179C22×C11#53618yes—
180C22×C11#54118yes—
181C22×C11C23×D411yescharacteristic
182C22×C11C23×D411yescharacteristic
183C22×C11C22×#4111yescharacteristic
184C22×C11C2×2−1+414yes—
185C2×D11—24no—
186C2×D11—28no—
187C2×D11—416no—
188C2×D11—44no—
189C2×D11—44no—
190C4×C11—28no—
191C4×C11—48no—
192C4×C11C2×#12118yes—
193Dic11—24no—
194Dic11—44no—
195Dic11—48no—
196C25—111no—
197C22×Q8—28no—
198C22×Q8—28no—
199C22×Q8—28no—
200C22×Q8C22×D1118yes—
201C23×C4—111no—
202C23×C4—118no—
203C23×C4—114no—
204C23×C4—114no—
205C23×C4—112no—
206C23×C4—224no—
207C23×C4—224no—
208C23×C4C22×D1114yes—
209C23×C4C22×D1112yes—
210C23×C4C22×D1111yescharacteristic
211C4⋊Q8—232no—
212C22⋊Q8—2264no—
213#117—2232no—
214C2×C4⋊C4—216no—
215C2×C4⋊C4—118no—
216C2×C4⋊C4—118no—
217C2×C4⋊C4—1116no—
218C2×C4⋊C4—2216no—
219C2×C4⋊C4—228no—
220C2×C4⋊C4—228no—
221C2×C4⋊C4C22×D11116yes—
222C2×C22⋊C4—118no—
223C2×C22⋊C4—1116no—
224C2×C22⋊C4—2216no—
225C2×C22⋊C4—228no—
226C2×C42—114no—
227C2×C42—224no—
228C2×C42C22⋊D1118yes—
229C2×C42C22×D1114yes—
230#95—1116no—
231#95—1132no—
232C2×C11#262118yescomplemented
233C2×C11C22×#12111yescharacteristic
234C2×C11C2×#53612yes—
235C2×C11C2×#53612yes—
236C2×C11C2×#54112yes—
237D11—44no—
238C24—114no—
239C24—112no—
240C24—222no—
241C24—228no—
242C24—222no—
243C24C23×D1111yescharacteristic
244C2×Q8—216no—
245C2×Q8—216no—
246C2×Q8—216no—
247C2×Q8—432no—
248C22×C4—28no—
249C22×C4—28no—
250C22×C4—28no—
251C22×C4—28no—
252C22×C4—114no—
253C22×C4—112no—
254C22×C4—1116no—
255C22×C4—114no—
256C22×C4—118no—
257C22×C4—222no—
258C22×C4—222no—
259C22×C4—2232no—
260C22×C4—228no—
261C22×C4—228no—
262C22×C4—228no—
263C22×C4—2216no—
264C22×C4—228no—
265C22×C4—224no—
266C22×C4D4×D1114yes—
267C22×C4#434114yes—
268C22×C4C2×C22⋊D1118yes—
269C22×C4C2×C22⋊D1114yes—
270C22×C4C23×D1118yes—
271C22×C4C23×D1114yes—
272C22×C4C23×D1112yes—
273C4⋊C4—232no—
274C4⋊C4—2232no—
275C4⋊C4—2216no—
276C4⋊C4—2216no—
277C22⋊C4—2232no—
278C22⋊C4—2216no—
279C42—228no—
280C42C2×C22⋊D11116yes—
281C11C2×#262111yescharacteristic, complemented, Sylow
282C23—114no—
283C23—2216no—
284C23—228no—
285C23—222no—
286C23—228no—
287C23—222no—
288C23—448no—
289C23—448no—
290C23C2×D4×D1112yes—
291C23C2×#434112yes—
292C23#6704018yes—
293C23C22×C22⋊D1112yes—
294C23C24×D1111yescharacteristic
295Q8—432no—
296C2×C4—216no—
297C2×C4—28no—
298C2×C4—28no—
299C2×C4—28no—
300C2×C4—28no—
301C2×C4—416no—
302C2×C4—114no—
303C2×C4—228no—
304C2×C4—222no—
305C2×C4—222no—
306C2×C4—2232no—
307C2×C4—228no—
308C2×C4—228no—
309C2×C4—2216no—
310C2×C4—224no—
311C2×C4—4416no—
312C2×C4—448no—
313C2×C4#66991116yes—
314C2×C4C2×D4×D1114yes—
315C2×C4C2×#434114yes—
316C2×C4C22×C22⋊D1118yes—
317C2×C4C22×C22⋊D1114yes—
318C22—228no—
319C22—224no—
320C22—444no—
321C22—444no—
322C22—4416no—
323C22#1062325518yes—
324C22#1062326218yes—
325C22C2×#6699114yes—
326C22#1062334718yes—
327C22C22×D4×D1111yescharacteristic
328C22C22×#434111yescharacteristic
329C22C2×#6704014yes—
330C22C23×C22⋊D1111yescharacteristic
331C4—28no—
332C4—48no—
333C4—224no—
334C4—444no—
335C4—448no—
336C4C2×#6699118yes—
337C2—444no—
338C2#1307438318yesdirect product factor
339C2C22×#6699111yescharacteristic
340C2C2×#1062334712yes—
341C2C2×#1062325512yes—
342C2C2×#1062326212yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×C4⋊Q8C2
socleC24×C11C24
prime radicalC24×D11C23
hypercenterC22×C4⋊Q8D11
hypocenterC11C2×#2621
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #13074383C2direct (N × H)
4. C2×#10622593C2semidirect
6. C2×#10622843C2semidirect
7. C2×#10622549C2semidirect
8. C22×C11×C4⋊Q8C2semidirect
12. C2×C11×C4⋊Q8C22semidirect
25. #10622843C22semidirect
29. #10622593C22semidirect
30. #10622549C22semidirect
111. C22×C4⋊Q8D11semidirect
158. C2×C4⋊Q8C2×D11semidirect
232. C2×C11#2621semidirect
281. C11C2×#2621semidirect
338. C2#13074383direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669992
C22×#669252
#130743832
C2×#106225932
C2×#106226062
C2×#106228432
C2×#106225492
C22×C11×C4⋊Q82
C2×#262111