Finite Group Databasebeta

← C2×#13074447 #14920841

Subgroups — C2×#13074447 #14920841

Order 2816.

2614 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66925C211yesmaximal, characteristic
2#13074447C2116yesmaximal, direct product factor
3C2×#10622597C214yesmaximal, complemented
4C2×#10622607C214yesmaximal
5C2×#10622586C212yesmaximal, complemented
6C2×#10622548C211yesmaximal, characteristic, complemented
7C2×#10622600C212yesmaximal
8C22×C11×#125C211yesmaximal, characteristic, complemented
9C23×C4×D11C2211yescharacteristic
10C2×C11×#125—28no—
11C2×C11×#125C2218yescomplemented
12C22×C11×C4⋊C4C2212yes—
13C22×C11×C4⋊C4C2214yes—
14C22×C42×C11C2211yescharacteristic
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2214yes—
17C22×C4⋊Dic11C2212yes—
18C22×C4⋊Dic11C2214yes—
19C22×Dic11⋊C4C2212yes—
20C22×Dic11⋊C4C2214yes—
21C22×C4×Dic11C2211yescharacteristic
22C2×#66925—28no—
23C2×#66925C2218yes—
24C2×C11⋊#95C2214yes—
25C2×C11⋊#95C2214yes—
26#10622607C22132yes—
27#10622600C22116yes—
28#10622597C22132yescomplemented
29#10622586C22116yescomplemented
30#10622548C2218yescomplemented
31C24×D11C2311yescharacteristic
32C23×C4×C11C2314yes—
33C23×C4×C11C2312yes—
34C23×C4×C11C2311yescharacteristic
35C23×Dic11C2312yes—
36C23×Dic11C2314yes—
37C23×Dic11C2311yescharacteristic
38C22×C4×D11—24no—
39C22×C4×D11—24no—
40C22×C4×D11Q818yes—
41C22×C4×D11C2314yes—
42C11×#125—232no—
43C2×C11×C4⋊C4—216no—
44C2×C11×C4⋊C4—28no—
45C2×C11×C4⋊C4C2318yes—
46C2×C11×C4⋊C4C23116yes—
47C2×C42×C11D418yes—
48C2×C42×C11C2314yes—
49C2×(C2×D11)⋊C4—28no—
50C2×(C2×D11)⋊C4—48no—
51C2×(C2×D11)⋊C4C2318yes—
52C2×(C2×D11)⋊C4C23116yes—
53C2×C4⋊Dic11—28no—
54C2×C4⋊Dic11—48no—
55C2×C4⋊Dic11C2318yes—
56C2×C4⋊Dic11C23116yes—
57C2×Dic11⋊C4—28no—
58C2×Dic11⋊C4—48no—
59C2×Dic11⋊C4C2318yes—
60C2×Dic11⋊C4C23116yes—
61C2×C4×Dic11—24no—
62C2×C4×Dic11C2314yes—
63#66925—232no—
64C11⋊#95C23116yes—
65C11⋊#95C23116yes—
66C2×#2629—111nomaximal, Sylow
67C24×C11C2411yescharacteristic
68C23×D11—22no—
69C23×D11—22no—
70C23×D11—24no—
71C23×D11—24no—
72C23×D11C2×Q814yes—
73C23×D11C2412yes—
74C22×C4×C11—24no—
75C22×C4×C11—24no—
76C22×C4×C11—28no—
77C22×C4×C11—28no—
78C22×C4×C11—28no—
79C22×C4×C11C2×D418yes—
80C22×C4×C11C2×D414yes—
81C22×C4×C11C2×Q814yes—
82C22×C4×C11#4114yes—
83C22×C4×C11C2418yes—
84C22×C4×C11C2414yes—
85C22×C4×C11C2412yes—
86C22×Dic11—22no—
87C22×Dic11—24no—
88C22×Dic11—22no—
89C22×Dic11—28no—
90C22×Dic11—24no—
91C22×Dic11—28no—
92C22×Dic11—28no—
93C22×Dic11—24no—
94C22×Dic11C2×Q814yes—
95C22×Dic11C2414yes—
96C22×Dic11C2418yes—
97C22×Dic11C2412yes—
98C2×C4×D11—232no—
99C2×C4×D11—28no—
100C2×C4×D11—28no—
101C2×C4×D11C2×Q8116yes—
102C11×C4⋊C4—232no—
103C11×C4⋊C4—216no—
104C42×C11C2×D4116yes—
105(C2×D11)⋊C4—216no—
106(C2×D11)⋊C4—416no—
107C4⋊Dic11—216no—
108C4⋊Dic11—416no—
109Dic11⋊C4—216no—
110Dic11⋊C4—416no—
111C4×Dic11—28no—
112C22×#125D1111yescharacteristic, complemented
113C22×#117—111no—
114#2629—1116no—
115C2×#398—114no—
116C2×#396—114no—
117C2×#389—112no—
118C2×#384—111no—
119C2×#380—112no—
120C23×C11C22×D412yes—
121C23×C11C22×Q812yes—
122C23×C11C2×#4112yes—
123C23×C11H(5,𝔽2)14yes—
124C23×C112−1+414yes—
125C23×C11C2511yescharacteristic
126C22×D11—28no—
127C22×D11—216no—
128C22×D11—22no—
129C22×D11—22no—
130C22×D11—24no—
131C22×D11—24no—
132C22×D11—48no—
133C22×D11—44no—
134C22×D11—44no—
135C22×D11C22×Q814yes—
136C2×C4×C11—216no—
137C2×C4×C11—24no—
138C2×C4×C11—24no—
139C2×C4×C11—28no—
140C2×C4×C11—28no—
141C2×C4×C11—28no—
142C2×C4×C11—416no—
143C2×C4×C11C22⋊Q8116yes—
144C2×C4×C11C22×D418yes—
145C2×C4×C11C22×D414yes—
146C2×C4×C11C22×Q814yes—
147C2×C4×C11C2×#4114yes—
148C2×Dic11—28no—
149C2×Dic11—22no—
150C2×Dic11—22no—
151C2×Dic11—24no—
152C2×Dic11—28no—
153C2×Dic11—24no—
154C2×Dic11—28no—
155C2×Dic11—28no—
156C2×Dic11—24no—
157C2×Dic11—48no—
158C2×Dic11—416no—
159C2×Dic11C22×Q814yes—
160C4×D11—232no—
161C24×C4—111no—
162C2×#125—28no—
163C2×#125C2×D1118yescomplemented
164C2×#117—118no—
165C2×#117—228no—
166C22×C4⋊C4—112no—
167C22×C4⋊C4—112no—
168C22×C4⋊C4—114no—
169C22×C4⋊C4—114no—
170C22×C4⋊C4C2×D1114yes—
171C22×C4⋊C4C2×D1112yes—
172C22×C22⋊C4—112no—
173C22×C22⋊C4—114no—
174C22×C42—111no—
175C22×C42C2×D1111yescharacteristic
176#398—1132no—
177#396—1132no—
178#389—1116no—
179#384—118no—
180#380—1116no—
181C2×#95—114no—
182C2×#95—114no—
183C22×C11C2×C22⋊Q814yes—
184C22×C11#53718yes—
185C22×C11#54014yes—
186C22×C11#54114yes—
187C22×C11#54418yes—
188C22×C11C23×D411yescharacteristic
189C22×C11C23×Q811yescharacteristic
190C22×C11C22×#4111yescharacteristic
191C22×C11C2×H(5,𝔽2)12yes—
192C22×C11C2×2−1+412yes—
193C2×D11—24no—
194C2×D11—28no—
195C2×D11—416no—
196C2×D11—44no—
197C2×D11—42no—
198C2×D11—42no—
199C4×C11—28no—
200C4×C11—48no—
201C4×C11C2×C22⋊Q818yes—
202Dic11—24no—
203Dic11—44no—
204Dic11—48no—
205C25—111no—
206C23×C4—111no—
207C23×C4—118no—
208C23×C4—114no—
209C23×C4—114no—
210C23×C4—112no—
211C23×C4—224no—
212C23×C4—224no—
213C23×C4C22×D1114yes—
214C23×C4C22×D1112yes—
215C23×C4C22×D1111yescharacteristic
216#125—232no—
217#117—2232no—
218C2×C4⋊C4—216no—
219C2×C4⋊C4—28no—
220C2×C4⋊C4—118no—
221C2×C4⋊C4—118no—
222C2×C4⋊C4—1116no—
223C2×C4⋊C4—1116no—
224C2×C4⋊C4—228no—
225C2×C4⋊C4—228no—
226C2×C4⋊C4—448no—
227C2×C4⋊C4—448no—
228C2×C4⋊C4C22×D1118yes—
229C2×C4⋊C4C22×D11116yes—
230C2×C22⋊C4—118no—
231C2×C22⋊C4—1116no—
232C2×C22⋊C4—228no—
233C2×C22⋊C4—448no—
234C2×C42—114no—
235C2×C42—224no—
236C2×C42C22⋊D1118yes—
237C2×C42C22×D1114yes—
238#95—1116no—
239#95—1116no—
240C2×C11#262918yescomplemented
241C2×C11C22×C22⋊Q811yescharacteristic
242C2×C11C2×#53712yes—
243C2×C11C2×#54011yescharacteristic
244C2×C11C2×#54111yescharacteristic
245C2×C11C2×#54412yes—
246D11—44no—
247C24—114no—
248C24—112no—
249C24—222no—
250C24—224no—
251C24—224no—
252C24—222no—
253C24C23×D1111yescharacteristic
254C22×C4—24no—
255C22×C4—24no—
256C22×C4—28no—
257C22×C4—28no—
258C22×C4—28no—
259C22×C4—114no—
260C22×C4—112no—
261C22×C4—1116no—
262C22×C4—114no—
263C22×C4—118no—
264C22×C4—222no—
265C22×C4—222no—
266C22×C4—2232no—
267C22×C4—228no—
268C22×C4—228no—
269C22×C4—228no—
270C22×C4—228no—
271C22×C4—224no—
272C22×C4—228no—
273C22×C4—224no—
274C22×C4—224no—
275C22×C4Q8×D1114yes—
276C22×C4#434314yes—
277C22×C4C2×C22⋊D1118yes—
278C22×C4C2×C22⋊D1114yes—
279C22×C4C23×D1118yes—
280C22×C4C23×D1114yes—
281C22×C4C23×D1112yes—
282C4⋊C4—232no—
283C4⋊C4—216no—
284C4⋊C4—2216no—
285C4⋊C4—2216no—
286C4⋊C4—4416no—
287C4⋊C4—4416no—
288C22⋊C4—2216no—
289C22⋊C4—4416no—
290C42—228no—
291C42C2×C22⋊D11116yes—
292C11C2×#262911yescharacteristic, complemented, Sylow
293C23—114no—
294C23—228no—
295C23—222no—
296C23—224no—
297C23—224no—
298C23—222no—
299C23—2216no—
300C23—448no—
301C23—444no—
302C23—444no—
303C23C2×Q8×D1112yes—
304C23C2×#434312yes—
305C23#6704214yes—
306C23#6704314yes—
307C23C22×C22⋊D1112yes—
308C23C24×D1111yescharacteristic
309C2×C4—216no—
310C2×C4—24no—
311C2×C4—24no—
312C2×C4—28no—
313C2×C4—28no—
314C2×C4—28no—
315C2×C4—416no—
316C2×C4—114no—
317C2×C4—228no—
318C2×C4—222no—
319C2×C4—222no—
320C2×C4—2232no—
321C2×C4—228no—
322C2×C4—228no—
323C2×C4—224no—
324C2×C4—228no—
325C2×C4—224no—
326C2×C4—224no—
327C2×C4—448no—
328C2×C4—4416no—
329C2×C4#66999116yes—
330C2×C4C2×Q8×D1114yes—
331C2×C4C2×#434314yes—
332C2×C4C22×C22⋊D1118yes—
333C2×C4C22×C22⋊D1114yes—
334C22—228no—
335C22—224no—
336C22—4416no—
337C22—444no—
338C22—442no—
339C22—442no—
340C22#1062322018yes—
341C22#1062322814yes—
342C22#1062322914yes—
343C22C2×#6699914yes—
344C22#1062336418yes—
345C22C22×Q8×D1111yescharacteristic
346C22C22×#434311yescharacteristic
347C22C2×#6704212yes—
348C22C2×#6704312yes—
349C22C23×C22⋊D1111yescharacteristic
350C4—28no—
351C4—48no—
352C4—224no—
353C4—444no—
354C4—448no—
355C4C2×#6699918yes—
356C2—444no—
357C2#1307444718yesdirect product factor
358C2C22×#6699911yescharacteristic
359C2C2×#1062336412yes—
360C2C2×#1062322911yescharacteristic
361C2C2×#1062322811yescharacteristic
362C2C2×#1062322012yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#125C2
socleC24×C11C24
prime radicalC24×D11C23
hypercenterC22×#125D11
hypocenterC11C2×#2629
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
2. #13074447C2direct (N × H)
3. C2×#10622597C2semidirect
5. C2×#10622586C2semidirect
6. C2×#10622548C2semidirect
8. C22×C11×#125C2semidirect
11. C2×C11×#125C22semidirect
28. #10622597C22semidirect
29. #10622586C22semidirect
30. #10622548C22semidirect
112. C22×#125D11semidirect
163. C2×#125C2×D11semidirect
240. C2×C11#2629semidirect
292. C11C2×#2629semidirect
357. C2#13074447direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669252
#130744472
C2×#106225972
C2×#106226072
C2×#106225862
C2×#106225482
C2×#106226002
C22×C11×#1252
C2×#262911