Finite Group Databasebeta

← C2×#13067700 #14729656

Subgroups — C2×#13067700 #14729656

Order 2816.

1190 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1190 conjugacy classes of subgroups — too many to draw. Only its 203 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×#10623265C211yesmaximal, characteristic, complemented
2C2×#10622698C211yesmaximal, characteristic, complemented
3C2×#10622456C212yesmaximal, complemented
4#13067700C218yesmaximal, direct product factor
5C2×#10622121C212yesmaximal, complemented
6C2×C11×#333C211yesmaximal, characteristic, complemented
7C2×C11×C4⋊Q8C2211yescharacteristic
8C2×#67000—22no—
9C22×#4325—22no—
10C22×D88—22no—
11#10623265—22no—
12#10623265—24no—
13#10623265C2214yescomplemented
14C2×#66948—22no—
15C2×#66945—22no—
16C2×#66927C2211yescharacteristic
17C2×C4×D44C2212yes—
18C2×C11×C4⋊C8C2212yes—
19C2×#66885—22no—
20#10622698—22no—
21#10622698C2214yescomplemented
22C2×C4×C11⋊C8C2211yescharacteristic
23#10622456—24no—
24#10622456C2218yescomplemented
25C11×#333C2214yescomplemented
26#10622121C2218yescomplemented
27C22×Q8×C11D412yes—
28C22×D44—22no—
29C22×D44—22no—
30C22×D44—21no—
31C22×D44D412yes—
32C22×C4×D11—22no—
33C22×C8×C11—22no—
34C11×C4⋊Q8—22no—
35C11×C4⋊Q8D412yes—
36C11×C4⋊Q8C2312yes—
37C2×C11×C4⋊C4—22no—
38C2×C42×C11C2311yescharacteristic
39#67000—28no—
40#67000—28no—
41C2×#4325—28no—
42C2×#4325—48no—
43C2×(C2×D11)⋊C4—24no—
44C2×(C2×D11)⋊C4—22no—
45C2×C4⋊Dic11D412yes—
46C2×C4×Dic11—22no—
47C22×C11⋊C8—21no—
48C2×D88—28no—
49C2×D88—48no—
50#66948—28no—
51#66948—28no—
52#66945—28no—
53#66945—28no—
54#66927—21no—
55#66927—22no—
56#66927C2312yes—
57C4×D44—22no—
58C4×D44—22no—
59C4×D44D414yes—
60C4×D44C2314yes—
61C11×C4⋊C8—22no—
62C11×C4⋊C8C2314yes—
63#66885—28no—
64C4×C11⋊C8—21no—
65C4×C11⋊C8C2312yes—
66C2×#1624—111nomaximal, Sylow
67C23×D11—22no—
68C23×D11—41no—
69C2×Q8×C11—22no—
70C2×Q8×C11—44no—
71C2×Q8×C11C2×D414yes—
72C22×C4×C11—22no—
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D412yes—
75C22×Dic11—22no—
76C2×D44—28no—
77C2×D44—22no—
78C2×D44—24no—
79C2×D44—24no—
80C2×D44—24no—
81C2×D44—22no—
82C2×D44—44no—
83C2×D44—41no—
84C2×D44—42no—
85C2×D44—44no—
86C2×D44—44no—
87C2×D44—84no—
88C2×D44C2×D414yes—
89C2×C4×D11—24no—
90C2×C4×D11—24no—
91C2×C4×D11—44no—
92C2×C4×D11—44no—
93C2×C8×C11—24no—
94C2×C8×C11—44no—
95C11×C4⋊C4—24no—
96C11×C4⋊C4—24no—
97C42×C11C2×D411yescharacteristic
98C42×C11C2×D412yes—
99C42×C11C2411yescharacteristic
100#4325—416no—
101(C2×D11)⋊C4—216no—
102(C2×D11)⋊C4—24no—
103(C2×D11)⋊C4—24no—
104C4⋊Dic11—22no—
105C4⋊Dic11C2×D414yes—
106C4×Dic11—28no—
107C2×C11⋊C8—24no—
108C2×C11⋊C8—22no—
109D88—416no—
110C2×#555—111no—
111C2×#492—111no—
112C2×#459—112no—
113#1624—118no—
114C2×#333D1111yescharacteristic, complemented
115C2×D4⋊C8—112no—
116C23×C11#12011yescharacteristic
117C22×D11—24no—
118C22×D11—44no—
119C22×D11—44no—
120C22×D11—44no—
121C22×D11—42no—
122C22×D11—84no—
123C22×D11—82no—
124Q8×C11—44no—
125Q8×C11—82no—
126C2×C4×C11—22no—
127C2×C4×C11—24no—
128C2×C4×C11—44no—
129C2×C4×C11#12011yescharacteristic
130C2×C4×C11#12012yes—
131C2×C4×C11#13514yes—
132C2×C4×C11AGL(1,ℤ/8)14yes—
133C2×C4×C11C22×D411yescharacteristic
134C2×C4×C11C22×D412yes—
135C2×Dic11—24no—
136C2×Dic11—44no—
137D44—24no—
138D44—24no—
139D44—44no—
140D44—44no—
141D44—44no—
142D44—44no—
143D44—82no—
144D44—88no—
145D44—84no—
146C4×D11—44no—
147C4×D11—44no—
148C4×D11—48no—
149C8×C11—44no—
150C11⋊C8—24no—
151C22×SD16—222no—
152C22×D8—222no—
153#555—114no—
154#555—224no—
155#555—222no—
156C2×C4⋊Q8C2×D1111yescharacteristic
157C2×#127—111no—
158C2×#124—222no—
159C2×#121—222no—
160C2×C4×D4—112no—
161C2×#117—222no—
162#492—114no—
163#492—222no—
164#459—118no—
165#459—224no—
166C2×C4⋊C8C2×D1112yes—
167C2×#102—222no—
168C2×C4×C8—111no—
169#333C2×D1114yescomplemented
170D4⋊C8—118no—
171C22×C11#44914yes—
172C22×C11#45312yes—
173C22×C11C2×#12011yescharacteristic
174C2×D11—44no—
175C2×D11—44no—
176C2×D11—44no—
177C2×D11—88no—
178C2×D11—84no—
179C2×D11—82no—
180C2×D11—164no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—44no—
184C4×C11#44914yes—
185C4×C11C2×#13512yes—
186C4×C11C2×AGL(1,ℤ/8)12yes—
187Dic11—44no—
188C22×Q8D4412yes—
189C22×D4—112no—
190C22×D4—222no—
191C22×D4—221no—
192C22×D4—222no—
193C23×C4—222no—
194C2×SD16—228no—
195C2×SD16—448no—
196C2×D8—228no—
197C2×D8—448no—
198C22×C8—22no—
199C22×C8—221no—
200C4⋊Q8—22no—
201C4⋊Q8D4412yes—
202C4⋊Q8C22×D1112yes—
203#127—112no—
204#127—221no—
205#127—222no—
206#124—228no—
207#124—228no—
208#121—228no—
209#121—228no—
210C4×D4—114no—
211C4×D4—114no—
212C4×D4—222no—
213C4×D4—222no—
214#117—228no—
215#117—228no—
216C2×C4⋊C4—22no—
217C2×C4⋊C4—112no—
218C2×C22⋊C4—224no—
219C2×C22⋊C4—222no—
220C2×C42—222no—
221C2×C42C22×D1111yescharacteristic
222C4⋊C8—22no—
223C4⋊C8C22×D1114yes—
224#102—228no—
225C4×C8—112no—
226C4×C8—221no—
227C2×C11#162414yescomplemented
228C2×C11C2×#44912yes—
229C2×C11C2×#45311yescharacteristic
230D11—84no—
231D11—162no—
232C24—222no—
233C24—441no—
234C2×Q8—22no—
235C2×Q8—44no—
236C2×Q8C2×D4414yes—
237C2×D4—114no—
238C2×D4—228no—
239C2×D4—222no—
240C2×D4—224no—
241C2×D4—224no—
242C2×D4—222no—
243C2×D4—224no—
244C2×D4—444no—
245C2×D4—441no—
246C2×D4—442no—
247C2×D4—444no—
248C2×D4—444no—
249C2×D4—884no—
250C22×C4—22no—
251C22×C4—222no—
252C22×C4—224no—
253C22×C4—224no—
254C22×C4—444no—
255C22×C4—444no—
256C22×C4C2×D4411yescharacteristic
257C22×C4D4×D1112yes—
258SD16—4416no—
259D8—4416no—
260C2×C8—24no—
261C2×C8—44no—
262C2×C8—224no—
263C2×C8—222no—
264C4⋊C4—24no—
265C4⋊C4—24no—
266C4⋊C4—114no—
267C4⋊C4—222no—
268C22⋊C4—2216no—
269C22⋊C4—224no—
270C22⋊C4—224no—
271C42—228no—
272C42C2×D4411yescharacteristic
273C42D4×D1112yes—
274C42C23×D1111yescharacteristic
275C11C2×#162411yescharacteristic, complemented, Sylow
276C23—224no—
277C23—444no—
278C23—444no—
279C23—444no—
280C23—442no—
281C23—882no—
282C23—884no—
283C23#6693511yescharacteristic
284Q8—44no—
285Q8—82no—
286D4—224no—
287D4—224no—
288D4—444no—
289D4—444no—
290D4—444no—
291D4—444no—
292D4—882no—
293D4—888no—
294D4—884no—
295C2×C4—22no—
296C2×C4—24no—
297C2×C4—44no—
298C2×C4—224no—
299C2×C4—444no—
300C2×C4—444no—
301C2×C4—444no—
302C2×C4—448no—
303C2×C4#6693511yescharacteristic
304C2×C4#6693512yes—
305C2×C4#6696714yes—
306C2×C4#6697214yes—
307C2×C4C22×D4411yescharacteristic
308C2×C4C2×D4×D1112yes—
309C8—44no—
310C8—224no—
311C22—444no—
312C22—444no—
313C22—444no—
314C22—888no—
315C22—884no—
316C22—882no—
317C22—1764no—
318C22#1062236012yes—
319C22#1062242414yes—
320C22C2×#6693511yescharacteristic
321C4—21no—
322C4—21no—
323C4—44no—
324C4—444no—
325C4#1062242414yes—
326C4C2×#6696712yes—
327C4C2×#6697212yes—
328C2—884no—
329C2—1762no—
330C2#1306770014yesdirect product factor
331C2C2×#1062242412yes—
332C2C2×#1062236011yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#333C2
socleC23×C11#120
hypercenterC2×#333D11
hypocenterC11C2×#1624
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
1. C2×#10623265C2semidirect
2. C2×#10622698C2semidirect
3. C2×#10622456C2semidirect
4. #13067700C2direct (N × H)
5. C2×#10622121C2semidirect
6. C2×C11×#333C2semidirect
13. #10623265C22semidirect
21. #10622698C22semidirect
24. #10622456C22semidirect
25. C11×#333C22semidirect
26. #10622121C22semidirect
114. C2×#333D11semidirect
169. #333C2×D11semidirect
227. C2×C11#1624semidirect
275. C11C2×#1624semidirect
330. C2#13067700direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232652
C2×#106226982
C2×#106224562
#130677002
C2×#106221212
C2×C11×#3332
C2×#162411