Finite Group Databasebeta

← C2×#13067668 #14729375

Subgroups — C2×#13067668 #14729375

Order 2816.

1838 conjugacy classes of subgroups; only the 219 normal subgroups are shown.

normal subgroups only

This group has 1838 conjugacy classes of subgroups — too many to draw. Only its 219 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623248C211yesmaximal, characteristic, complemented
2C2×#10622685C212yesmaximal, complemented
3#13067668C218yesmaximal, direct product factor
4C2×#10622182C211yesmaximal, characteristic, complemented
5C2×#10622097C212yesmaximal, complemented
6C2×C11×#493C211yesmaximal, characteristic, complemented
7C22×D4×D11—22no—
8C22×C11×D8—22no—
9C2×C11×#127C2211yescharacteristic
10C2×C11×#127C2211yescharacteristic, complemented
11C2×#66991—22no—
12C2×#66990—22no—
13C22×#4323—22no—
14#10623248—22no—
15#10623248—24no—
16#10623248C2214yescomplemented
17C2×C4×D44C2212yes—
18C11×#493—22no—
19C11×#493C2214yescomplemented
20C2×C4×C8×C11C2211yescharacteristic, complemented
21C2×#66896—22no—
22#10622685—24no—
23#10622685C2218yescomplemented
24C2×C4⋊(C11⋊C8)C2212yescomplemented
25#10622182C2214yescomplemented
26#10622097C2218yescomplemented
27C24×D11—22no—
28C22×D4×C11—22no—
29C22×D4×C11—22no—
30C22×D4×C11—21no—
31C22×D4×C11D412yes—
32C22×C22⋊D11—24no—
33C2×D4×D11—28no—
34C2×D4×D11—28no—
35C2×D4×D11—48no—
36C2×D4×D11—48no—
37C22×D44D412yes—
38C22×C4×D11—22no—
39C2×C11×D8—28no—
40C2×C11×D8—48no—
41C22×C8×C11—21no—
42C11×#127—22no—
43C11×#127—21no—
44C11×#127—22no—
45C11×#127D412yes—
46C11×#127C2312yes—
47C11×#127C2312yescomplemented
48C2×C42×C11C2311yescharacteristic
49C2×C22⋊Dic11—22no—
50#66991—28no—
51#66991—28no—
52#66990—28no—
53#66990—28no—
54C2×#4323—28no—
55C2×#4323—48no—
56C2×(C2×D11)⋊C4—22no—
57C2×C4⋊Dic11D412yes—
58C22×C11⋊C8—22no—
59C4×D44—22no—
60C4×D44—22no—
61C4×D44D414yes—
62C4×D44C2314yes—
63C4×C8×C11—21no—
64C4×C8×C11C2312yescomplemented
65#66896—28no—
66C4⋊(C11⋊C8)—22no—
67C4⋊(C11⋊C8)C2314yescomplemented
68C2×#1619—111nomaximal, Sylow
69C24×C11—22no—
70C24×C11—41no—
71C23×D11—22no—
72C23×D11—28no—
73C23×D11—416no—
74C23×D11—84no—
75C2×D4×C11—24no—
76C2×D4×C11—22no—
77C2×D4×C11—24no—
78C2×D4×C11—24no—
79C2×D4×C11—22no—
80C2×D4×C11—44no—
81C2×D4×C11—44no—
82C2×D4×C11—41no—
83C2×D4×C11—42no—
84C2×D4×C11—44no—
85C2×D4×C11—44no—
86C2×D4×C11—44no—
87C2×D4×C11—44no—
88C2×D4×C11C2×D414yes—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D412yes—
91C2×C22⋊D11—216no—
92C2×C22⋊D11—416no—
93C22×Dic11—22no—
94D4×D11—416no—
95D4×D11—432no—
96D4×D11—416no—
97C2×D44—22no—
98C2×D44—24no—
99C2×D44D818yescomplemented
100C2×D44C2×D414yes—
101C2×C4×D11—24no—
102C2×C4×D11—24no—
103C2×C4×D11—44no—
104C2×C4×D11—44no—
105C11×D8—416no—
106C2×C8×C11—24no—
107C2×C8×C11—22no—
108C42×C11C2×D412yes—
109C42×C11C2×D411yescharacteristic
110C42×C11C2411yescharacteristic
111C22⋊Dic11—28no—
112#4323—416no—
113(C2×D11)⋊C4—24no—
114(C2×D11)⋊C4—24no—
115C4⋊Dic11—22no—
116C4⋊Dic11C2×D414yes—
117C2×C11⋊C8—24no—
118C2×C11⋊C8—44no—
119C2×D42—111no—
120C2×#493D1111yescharacteristic, complemented
121C2×#459—112no—
122#1619—118no—
123C2×#331—111no—
124C2×D4⋊C8—112no—
125C23×C11—24no—
126C23×C11—48no—
127C23×C11—44no—
128C23×C11—42no—
129C23×C11—84no—
130C23×C11—82no—
131C23×C11#12011yescharacteristic
132C22×D11—24no—
133C22×D11—28no—
134C22×D11—432no—
135C22×D11—44no—
136C22×D11—44no—
137C22×D11—88no—
138C22×D11—832no—
139D4×C11—44no—
140D4×C11—44no—
141D4×C11—44no—
142D4×C11—44no—
143D4×C11—44no—
144D4×C11—44no—
145D4×C11—48no—
146D4×C11—82no—
147D4×C11—82no—
148D4×C11—84no—
149C2×C4×C11—22no—
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12012yes—
152C2×C4×C11C2×D814yes—
153C2×C4×C11AGL(1,ℤ/8)14yes—
154C2×C4×C11C22×D412yes—
155C2×C4×C11C22×D411yescharacteristic
156C22⋊D11—432no—
157C2×Dic11—24no—
158C2×Dic11—44no—
159D44—24no—
160D44—28no—
161D44C2×D818yescomplemented
162C4×D11—44no—
163C4×D11—44no—
164C4×D11—48no—
165C8×C11—24no—
166C11⋊C8—44no—
167C23×D4—222no—
168C22×D8—22no—
169C22×D8—222no—
170D42—114no—
171D42—224no—
172D42—222no—
173C2×#127C2×D1111yescharacteristic
174C2×#127C2×D1111yescharacteristic, complemented
175C2×#121—222no—
176C2×#120—222no—
177C2×C4×D4—112no—
178#493—22no—
179#493C2×D1114yescomplemented
180#459—118no—
181#459—224no—
182C2×C4⋊C8—112no—
183C2×#102—222no—
184C2×C4×C8C2×D1111yescharacteristic, complemented
185#331—114no—
186D4⋊C8—118no—
187C22×C11—48no—
188C22×C11—44no—
189C22×C11—88no—
190C22×C11—84no—
191C22×C11—82no—
192C22×C11—164no—
193C22×C11#44714yes—
194C22×C11#45312yes—
195C22×C11C2×#12011yescharacteristic
196C2×D11—28no—
197C2×D11—416no—
198C2×D11—44no—
199C2×D11—44no—
200C2×D11—832no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11#44714yes—
204C4×C11C22×D812yes—
205C4×C11C2×AGL(1,ℤ/8)12yes—
206Dic11—44no—
207C25—222no—
208C22×D4—22no—
209C22×D4—22no—
210C22×D4—21no—
211C22×D4—112no—
212C22×D4—228no—
213C22×D4—228no—
214C22×D4—224no—
215C22×D4—448no—
216C22×D4—448no—
217C22×D4C22⋊D1112yes—
218C23×C4—222no—
219C2×D8—28no—
220C2×D8—48no—
221C2×D8—228no—
222C2×D8—448no—
223C22×C8—21no—
224C22×C8—222no—
225#127—22no—
226#127—22no—
227#127—21no—
228#127C22⋊D1112yes—
229#127C22×D1112yes—
230#127C22×D1112yescomplemented
231#121—228no—
232#121—228no—
233#120—228no—
234#120—228no—
235C4×D4—114no—
236C4×D4—114no—
237C4×D4—222no—
238C4×D4—222no—
239C2×C4⋊C4—112no—
240C2×C22⋊C4—222no—
241C2×C22⋊C4—222no—
242C2×C42C22×D1111yescharacteristic
243C4⋊C8—114no—
244C4⋊C8—222no—
245#102—228no—
246C4×C8—21no—
247C4×C8C22×D1112yescomplemented
248C2×C11—84no—
249C2×C11—162no—
250C2×C11#161914yescomplemented
251C2×C11C2×#44712yes—
252C2×C11C2×#45311yescharacteristic
253D11—48no—
254C24—22no—
255C24—41no—
256C24—228no—
257C24—222no—
258C24—4416no—
259C24—884no—
260C2×D4—24no—
261C2×D4—22no—
262C2×D4—24no—
263C2×D4—24no—
264C2×D4—22no—
265C2×D4—44no—
266C2×D4—44no—
267C2×D4—44no—
268C2×D4—44no—
269C2×D4—44no—
270C2×D4—44no—
271C2×D4—41no—
272C2×D4—42no—
273C2×D4—118no—
274C2×D4—114no—
275C2×D4—2216no—
276C2×D4—224no—
277C2×D4—222no—
278C2×D4—4416no—
279C2×D4—4432no—
280C2×D4—4416no—
281C2×D4—4416no—
282C2×D4C2×C22⋊D1114yes—
283C22×C4—222no—
284C22×C4—224no—
285C22×C4—224no—
286C22×C4—444no—
287C22×C4—444no—
288C22×C4D4×D1112yes—
289C22×C4C2×C22⋊D1111yescharacteristic
290D8—416no—
291D8—4416no—
292C2×C8—24no—
293C2×C8—22no—
294C2×C8—224no—
295C2×C8—444no—
296C4⋊C4—114no—
297C4⋊C4—222no—
298C22⋊C4—228no—
299C22⋊C4—224no—
300C22⋊C4—224no—
301C42D4×D1112yes—
302C42C2×C22⋊D1111yescharacteristic
303C42C23×D1111yescharacteristic
304C11C2×#161911yescharacteristic, complemented, Sylow
305C23—24no—
306C23—48no—
307C23—44no—
308C23—42no—
309C23—84no—
310C23—82no—
311C23—228no—
312C23—224no—
313C23—4432no—
314C23—444no—
315C23—444no—
316C23—888no—
317C23—8832no—
318C23#6699011yescharacteristic
319D4—44no—
320D4—44no—
321D4—48no—
322D4—44no—
323D4—44no—
324D4—44no—
325D4—44no—
326D4—82no—
327D4—82no—
328D4—84no—
329D4—118no—
330D4—228no—
331D4—224no—
332D4—4432no—
333C2×C4—22no—
334C2×C4—224no—
335C2×C4—444no—
336C2×C4—448no—
337C2×C4—444no—
338C2×C4—444no—
339C2×C4D8×D1114yes—
340C2×C4#6696414yes—
341C2×C4#6699011yescharacteristic
342C2×C4#6699012yes—
343C2×C4C2×D4×D1112yes—
344C2×C4C22×C22⋊D1111yescharacteristic
345C8—24no—
346C8—444no—
347C22—48no—
348C22—44no—
349C22—88no—
350C22—84no—
351C22—82no—
352C22—164no—
353C22—228no—
354C22—444no—
355C22—4416no—
356C22—444no—
357C22—8832no—
358C22#1062269012yes—
359C22#1062276914yes—
360C22C2×#6699011yescharacteristic
361C4—21no—
362C4—21no—
363C4—444no—
364C4#1062276914yes—
365C4C2×D8×D1112yes—
366C4C2×#6696412yes—
367C2—84no—
368C2—162no—
369C2—448no—
370C2#1306766814yesdirect product factor
371C2C2×#1062276912yes—
372C2C2×#1062269011yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#493C2
socleC23×C11#120
hypercenterC2×#493D11
hypocenterC11C2×#1619
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#493

Complements

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

NH ≅ G/Ntype
1. C2×#10623248C2semidirect
2. C2×#10622685C2semidirect
3. #13067668C2direct (N × H)
4. C2×#10622182C2semidirect
5. C2×#10622097C2semidirect
6. C2×C11×#493C2semidirect
10. C2×C11×#127C22semidirect
16. #10623248C22semidirect
19. C11×#493C22semidirect
20. C2×C4×C8×C11C22semidirect
23. #10622685C22semidirect
24. C2×C4⋊(C11⋊C8)C22semidirect
25. #10622182C22semidirect
26. #10622097C22semidirect
47. C11×#127C23semidirect
64. C4×C8×C11C23semidirect
67. C4⋊(C11⋊C8)C23semidirect
99. C2×D44D8semidirect
120. C2×#493D11semidirect
161. D44C2×D8semidirect
174. C2×#127C2×D11semidirect
179. #493C2×D11semidirect
184. C2×C4×C8C2×D11semidirect
230. #127C22×D11semidirect
247. C4×C8C22×D11semidirect
250. C2×C11#1619semidirect
304. C11C2×#1619semidirect
370. C2#13067668direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232482
C2×#106226852
#130676682
C2×#106221822
C2×#106220972
C2×C11×#4932
C2×#161911