Finite Group Databasebeta

← C2×#13068712 #14753555

Subgroups — C2×#13068712 #14753555

Order 2816.

1574 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66979C211yesmaximal, characteristic
2C2×#10622825C211yesmaximal, characteristic
3#13068712C218yesmaximal, direct product factor
4C2×#10622189C212yesmaximal, complemented
5C2×#10622189C212yesmaximal, complemented
6C22×C11×C22⋊C8C211yesmaximal, characteristic
7C24×C4×C11C2211yescharacteristic
8C23×C8×C11C2212yes—
9C22×C22⋊Dic11—21no—
10C22×C22⋊Dic11—21no—
11C2×#66979—22no—
12C2×#66979—24no—
13C2×#66979C418yescomplemented
14C2×#66979C2214yes—
15C22×C4⋊Dic11C2212yes—
16C22×C4⋊Dic11C2211yescharacteristic
17C22×C4⋊Dic11C2211yescharacteristic
18C22×C4×Dic11—21no—
19C2×C11×C22⋊C8—24no—
20C2×C11×C22⋊C8C2214yes—
21#10622825—22no—
22#10622825C2214yes—
23C2×C11⋊#95—21no—
24#10622189C2218yescomplemented
25#10622189C2218yescomplemented
26C25×C11D411yescharacteristic
27C23×C4×C11—28no—
28C23×C4×C11C2×C414yes—
29C23×C4×C11D411yescharacteristic
30C23×C4×C11D412yes—
31C23×C4×C11D414yes—
32C23×C4×C11C2312yes—
33C23×C4×C11C2311yescharacteristic
34C23×Dic11—21no—
35C23×Dic11—21no—
36C23×Dic11—22no—
37C22×C8×C11—24no—
38C22×C8×C11—28no—
39C22×C8×C11C2314yes—
40C2×C22⋊Dic11—28no—
41C2×C22⋊Dic11—24no—
42C2×C22⋊Dic11—24no—
43C2×C22⋊Dic11—44no—
44#66979—216no—
45#66979—28no—
46#66979C2×C4116yescomplemented
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11—22no—
50C2×C4⋊Dic11—22no—
51C2×C4⋊Dic11—28no—
52C2×C4⋊Dic11—22no—
53C2×C4⋊Dic11C2×C414yes—
54C2×C4⋊Dic11C2×C414yes—
55C2×C4⋊Dic11C2314yes—
56C2×C4⋊Dic11C2312yes—
57C2×C4⋊Dic11C2312yes—
58C2×C4×Dic11—28no—
59C2×C4×Dic11—24no—
60C11×C22⋊C8—28no—
61C11⋊#95—24no—
62C2×#1825—111nomaximal, Sylow
63C24×C11—24no—
64C24×C11—24no—
65C24×C11—22no—
66C24×C11—22no—
67C24×C11C22⋊C414yes—
68C24×C11C2×D412yes—
69C24×C11C2×D411yescharacteristic
70C22×C4×C11—24no—
71C22×C4×C11—216no—
72C22×C4×C11—28no—
73C22×C4×C11—216no—
74C22×C4×C11—28no—
75C22×C4×C11C22⋊C414yes—
76C22×C4×C11C22⋊C418yes—
77C22×C4×C11C22×C414yes—
78C22×C4×C11C22×C412yes—
79C22×C4×C11C2×D412yes—
80C22×C4×C11C2×D414yes—
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D412yes—
83C22×C4×C11#4118yes—
84C22×C4×C11C2411yescharacteristic
85C22×Dic11—24no—
86C22×Dic11—24no—
87C22×Dic11—22no—
88C22×Dic11—22no—
89C22×Dic11—24no—
90C22×Dic11—44no—
91C22×Dic11—44no—
92C22×Dic11—44no—
93C22×Dic11—42no—
94C22×Dic11—44no—
95C22×Dic11—42no—
96C2×C8×C11—24no—
97C2×C8×C11—28no—
98C2×C8×C11—48no—
99C22⋊Dic11—216no—
100C22⋊Dic11—48no—
101C4⋊Dic11—24no—
102C4⋊Dic11—24no—
103C4⋊Dic11—22no—
104C4⋊Dic11—22no—
105C4⋊Dic11—28no—
106C4⋊Dic11—44no—
107C4⋊Dic11C22×C414yes—
108C4⋊Dic11C22×C414yes—
109C4×Dic11—216no—
110C22×#117—111no—
111C22×C22⋊C8D1111yescharacteristic
112C2×#380—111no—
113#1825—118no—
114C2×#340—112no—
115C2×#340—112no—
116C23×C11—24no—
117C23×C11—24no—
118C23×C11—22no—
119C23×C11—22no—
120C23×C11—28no—
121C23×C11—28no—
122C23×C11—28no—
123C23×C11—48no—
124C23×C11—48no—
125C23×C11C2×C22⋊C414yes—
126C23×C11C2×C22⋊C412yes—
127C23×C11#12314yes—
128C23×C11#13514yes—
129C23×C11AGL(1,ℤ/8)12yes—
130C23×C11#13712yes—
131C23×C11C22×D411yescharacteristic
132C2×C4×C11—24no—
133C2×C4×C11—28no—
134C2×C4×C11—28no—
135C2×C4×C11—28no—
136C2×C4×C11—216no—
137C2×C4×C11C2×C22⋊C414yes—
138C2×C4×C11C2×C22⋊C412yes—
139C2×C4×C11#11718yes—
140C2×C4×C11#12314yes—
141C2×C4×C11#12318yes—
142C2×C4×C11C23×C411yescharacteristic
143C2×C4×C11C22×D411yescharacteristic
144C2×C4×C11C2×#4114yes—
145C2×Dic11—24no—
146C2×Dic11—24no—
147C2×Dic11—44no—
148C2×Dic11—42no—
149C2×Dic11—42no—
150C2×Dic11—48no—
151C2×Dic11—48no—
152C2×Dic11—44no—
153C2×Dic11—44no—
154C2×Dic11—44no—
155C2×Dic11—88no—
156C8×C11—44no—
157C24×C4C2×D1111yescharacteristic
158C23×C8C2×D1112yes—
159C2×#117—114no—
160C2×#117—118no—
161C2×#117—222no—
162C2×#117—224no—
163C22×C4⋊C4—111no—
164C22×C4⋊C4—111no—
165C22×C4⋊C4—112no—
166C22×C22⋊C4—221no—
167C22×C22⋊C4—221no—
168C22×C42—221no—
169C2×C22⋊C8—24no—
170C2×C22⋊C8C2×D1114yes—
171#380—114no—
172#380—222no—
173C2×#95—221no—
174#340—118no—
175#340—118no—
176C22×C11—24no—
177C22×C11—24no—
178C22×C11—24no—
179C22×C11—44no—
180C22×C11—44no—
181C22×C11—416no—
182C22×C11#38114yes—
183C22×C11#41614yes—
184C22×C11#41714yes—
185C22×C11#48218yes—
186C22×C11#48518yes—
187C22×C11C22×C22⋊C411yescharacteristic
188C22×C11C2×#12312yes—
189C22×C11C2×#13512yes—
190C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
191C22×C11C2×#13711yescharacteristic
192C4×C11—24no—
193C4×C11#38114yes—
194C4×C11C2×#11712yes—
195C4×C11C2×#12312yes—
196Dic11—44no—
197Dic11—44no—
198Dic11—84no—
199C25D4411yescharacteristic
200C23×C4—28no—
201C23×C4—221no—
202C23×C4—221no—
203C23×C4—222no—
204C23×C4C4×D1114yes—
205C23×C4D4412yes—
206C23×C4D4411yescharacteristic
207C23×C4C22⋊D1114yes—
208C23×C4C22×D1112yes—
209C23×C4C22×D1111yescharacteristic
210C22×C8—28no—
211C22×C8—24no—
212C22×C8C22×D1114yes—
213#117—1116no—
214#117—2216no—
215#117—228no—
216C2×C4⋊C4—114no—
217C2×C4⋊C4—114no—
218C2×C4⋊C4—112no—
219C2×C4⋊C4—112no—
220C2×C4⋊C4—114no—
221C2×C4⋊C4—221no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4—222no—
224C2×C4⋊C4—222no—
225C2×C4⋊C4—228no—
226C2×C4⋊C4—222no—
227C2×C22⋊C4—228no—
228C2×C22⋊C4—224no—
229C2×C22⋊C4—224no—
230C2×C22⋊C4—444no—
231C2×C42—228no—
232C2×C42—224no—
233C22⋊C8—28no—
234#95—224no—
235C2×C11—44no—
236C2×C11#182518yescomplemented
237C2×C11C2×#38111yescharacteristic
238C2×C11C2×#41611yescharacteristic
239C2×C11C2×#41711yescharacteristic
240C2×C11C2×#48212yes—
241C2×C11C2×#48512yes—
242C24—24no—
243C24—24no—
244C24—22no—
245C24—22no—
246C24(C2×D11)⋊C414yes—
247C24C2×D4412yes—
248C24C2×D4411yescharacteristic
249C22×C4—24no—
250C22×C4—216no—
251C22×C4—28no—
252C22×C4—216no—
253C22×C4—28no—
254C22×C4—224no—
255C22×C4—224no—
256C22×C4—222no—
257C22×C4—222no—
258C22×C4—224no—
259C22×C4—444no—
260C22×C4—442no—
261C22×C4—442no—
262C22×C4—444no—
263C22×C4—444no—
264C22×C4—444no—
265C22×C4(C2×D11)⋊C414yes—
266C22×C4(C2×D11)⋊C418yes—
267C22×C4C2×C4×D1114yes—
268C22×C4C2×C4×D1112yes—
269C22×C4C2×D4412yes—
270C22×C4C2×D4411yescharacteristic
271C22×C4#434118yes—
272C22×C4C2×C22⋊D1114yes—
273C22×C4C2×C22⋊D1112yes—
274C22×C4C23×D1111yescharacteristic
275C2×C8—28no—
276C2×C8—24no—
277C2×C8—48no—
278C4⋊C4—114no—
279C4⋊C4—114no—
280C4⋊C4—224no—
281C4⋊C4—224no—
282C4⋊C4—222no—
283C4⋊C4—222no—
284C4⋊C4—228no—
285C4⋊C4—444no—
286C22⋊C4—2216no—
287C22⋊C4—448no—
288C42—2216no—
289C11C2×#182511yescharacteristic, complemented, Sylow
290C23—28no—
291C23—28no—
292C23—24no—
293C23—22no—
294C23—22no—
295C23—24no—
296C23—28no—
297C23—48no—
298C23—48no—
299C23#6693914yes—
300C23#6695714yes—
301C23#6696112yes—
302C23#6696212yes—
303C23C2×(C2×D11)⋊C414yes—
304C23C2×(C2×D11)⋊C412yes—
305C23C22×D4411yescharacteristic
306C2×C4—24no—
307C2×C4—28no—
308C2×C4—28no—
309C2×C4—216no—
310C2×C4—28no—
311C2×C4—224no—
312C2×C4—224no—
313C2×C4—448no—
314C2×C4—448no—
315C2×C4—444no—
316C2×C4—442no—
317C2×C4—442no—
318C2×C4—444no—
319C2×C4—444no—
320C2×C4—444no—
321C2×C4—888no—
322C2×C4#6693018yes—
323C2×C4#6693914yes—
324C2×C4C2×(C2×D11)⋊C414yes—
325C2×C4C2×(C2×D11)⋊C412yes—
326C2×C4#6698818yes—
327C2×C4C22×C4×D1111yescharacteristic
328C2×C4C2×#434114yes—
329C2×C4C22×C22⋊D1111yescharacteristic
330C8—44no—
331C22—24no—
332C22—24no—
333C22—24no—
334C22—416no—
335C22—44no—
336C22—44no—
337C22#1062233618yes—
338C22#1062235018yes—
339C22#1062255614yes—
340C22#1062272614yes—
341C22#1062274614yes—
342C22C2×#6693912yes—
343C22C2×#6695712yes—
344C22C2×#6696111yescharacteristic
345C22C2×#6696211yescharacteristic
346C22C22×(C2×D11)⋊C411yescharacteristic
347C4—24no—
348C4—444no—
349C4—444no—
350C4—884no—
351C4#1062255614yes—
352C4C2×#6693012yes—
353C4C2×#6698812yes—
354C2—44no—
355C2#1306871218yesdirect product factor
356C2C2×#1062255611yescharacteristic
357C2C2×#1062272611yescharacteristic
358C2C2×#1062274611yescharacteristic
359C2C2×#1062235012yes—
360C2C2×#1062233612yes—
subgroupG/H
centerC24C2×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×C22⋊C8C2
socleC24×C11C2×D4
prime radicalC25×C11D4
cosocleC22×C4×C11C24
hypercenterC22×C22⋊C8D11
hypocenterC11C2×#1825
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×C22⋊C8

Complements

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

NH ≅ G/Ntype
3. #13068712C2direct (N × H)
4. C2×#10622189C2semidirect
5. C2×#10622189C2semidirect
13. C2×#66979C4semidirect
24. #10622189C22semidirect
25. #10622189C22semidirect
46. #66979C2×C4semidirect
236. C2×C11#1825semidirect
289. C11C2×#1825semidirect
355. C2#13068712direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669792
C2×#106228252
#130687122
C2×#106221892
C22×C11×C22⋊C82
C2×#182511