Finite Group Databasebeta

← C2×#13067699 #14729655

Subgroups — C2×#13067699 #14729655

Order 2816.

1190 conjugacy classes of subgroups; only the 219 normal subgroups are shown.

normal subgroups only

This group has 1190 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×#10622698C211yesmaximal, characteristic, complemented
2C2×#10622628C212yesmaximal, complemented
3#13067699C218yesmaximal, direct product factor
4C2×#10622184C211yesmaximal, characteristic, complemented
5C2×D4⋊(C11⋊C8)C212yesmaximal, complemented
6C2×C11×#555C211yesmaximal, characteristic, complemented
7C11×#555—22no—
8C11×#555—24no—
9C11×#555C2214yescomplemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×#124—22no—
12C2×C11×#121—22no—
13C2×C4×D4×C11C2212yes—
14C2×C11×#117—22no—
15C22×#4325—22no—
16C22×#4323—22no—
17C2×#66927C2211yescharacteristic
18#10622698—22no—
19#10622698C2214yescomplemented
20#10622628—24no—
21#10622628C2218yescomplemented
22C2×#66873—22no—
23C2×C4⋊(C11⋊C8)C2212yes—
24C2×C4×C11⋊C8C2211yescharacteristic
25#10622184C2214yescomplemented
26D4⋊(C11⋊C8)C2218yescomplemented
27C22×Q8×C11D412yes—
28C22×D4×C11—22no—
29C22×D4×C11D412yes—
30C23×C4×C11—22no—
31C22×D44—22no—
32C22×D44—21no—
33C11×C4⋊Q8—22no—
34C11×C4⋊Q8D412yes—
35C11×C4⋊Q8C2312yes—
36C11×#124—28no—
37C11×#124—28no—
38C11×#121—28no—
39C11×#121—28no—
40C4×D4×C11—22no—
41C4×D4×C11—22no—
42C4×D4×C11D414yes—
43C4×D4×C11C2314yes—
44C11×#117—28no—
45C11×#117—28no—
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4D412yes—
48C2×C11×C22⋊C4—24no—
49C2×C11×C22⋊C4—22no—
50C2×C42×C11—22no—
51C2×C42×C11C2311yescharacteristic
52C2×#4325—28no—
53C2×#4325—48no—
54C2×#4323—28no—
55C2×#4323—48no—
56C22×C11⋊C8—21no—
57C22×C11⋊C8—22no—
58#66927—22no—
59#66927—21no—
60#66927C2312yes—
61#66873—28no—
62C4⋊(C11⋊C8)—22no—
63C4⋊(C11⋊C8)C2314yes—
64C4×C11⋊C8—21no—
65C4×C11⋊C8C2312yes—
66C2×#1624—111nomaximal, Sylow
67C24×C11—22no—
68C23×D11—41no—
69C2×Q8×C11—22no—
70C2×Q8×C11—44no—
71C2×Q8×C11C2×D414yes—
72C2×D4×C11—28no—
73C2×D4×C11—22no—
74C2×D4×C11—24no—
75C2×D4×C11—24no—
76C2×D4×C11—84no—
77C2×D4×C11C2×D414yes—
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11—24no—
81C22×C4×C11—24no—
82C22×C4×C11—44no—
83C22×C4×C11—44no—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D412yes—
86C2×D44—24no—
87C2×D44—22no—
88C2×D44—44no—
89C2×D44—41no—
90C2×D44—42no—
91C2×D44—44no—
92C2×D44—44no—
93C11×C4⋊C4—24no—
94C11×C4⋊C4—22no—
95C11×C4⋊C4—24no—
96C11×C4⋊C4C2×D414yes—
97C11×C22⋊C4—216no—
98C11×C22⋊C4—24no—
99C11×C22⋊C4—24no—
100C42×C11—28no—
101C42×C11C2×D411yescharacteristic
102C42×C11C2×D412yes—
103C42×C11C2411yescharacteristic
104#4325—416no—
105#4323—416no—
106C2×C11⋊C8—24no—
107C2×C11⋊C8—22no—
108C2×C11⋊C8—24no—
109C2×C11⋊C8—44no—
110C2×#555D1111yescharacteristic, complemented
111C2×#492—111no—
112C2×#459—112no—
113#1624—118no—
114C2×#333—111no—
115C2×D4⋊C8—112no—
116C23×C11—24no—
117C23×C11—44no—
118C23×C11—44no—
119C23×C11—44no—
120C23×C11#12011yescharacteristic
121C22×D11—42no—
122C22×D11—84no—
123C22×D11—82no—
124Q8×C11—44no—
125Q8×C11—82no—
126D4×C11—24no—
127D4×C11—24no—
128D4×C11—44no—
129D4×C11—88no—
130C2×C4×C11—22no—
131C2×C4×C11—24no—
132C2×C4×C11—24no—
133C2×C4×C11—44no—
134C2×C4×C11—44no—
135C2×C4×C11—44no—
136C2×C4×C11—44no—
137C2×C4×C11—48no—
138C2×C4×C11#12011yescharacteristic
139C2×C4×C11#12012yes—
140C2×C4×C11#13514yes—
141C2×C4×C11AGL(1,ℤ/8)14yes—
142C2×C4×C11C22×D411yescharacteristic
143C2×C4×C11C22×D412yes—
144D44—44no—
145D44—44no—
146D44—44no—
147D44—82no—
148D44—84no—
149C11⋊C8—24no—
150C11⋊C8—44no—
151C22×SD16—222no—
152C22×D8—222no—
153#555—22no—
154#555—24no—
155#555C2×D1114yescomplemented
156C2×C4⋊Q8C2×D1111yescharacteristic
157C2×#127—111no—
158C2×#124—22no—
159C2×#121—22no—
160C2×C4×D4C2×D1112yes—
161C2×#117—22no—
162#492—114no—
163#492—222no—
164#459—118no—
165#459—224no—
166C2×C4⋊C8—112no—
167C2×#102—222no—
168C2×C4×C8—111no—
169#333—114no—
170D4⋊C8—118no—
171C22×C11—44no—
172C22×C11—44no—
173C22×C11—44no—
174C22×C11—88no—
175C22×C11#44914yes—
176C22×C11#45312yes—
177C22×C11C2×#12011yescharacteristic
178C2×D11—84no—
179C2×D11—82no—
180C2×D11—164no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—44no—
184C4×C11—44no—
185C4×C11#44914yes—
186C4×C11C2×#13512yes—
187C4×C11C2×AGL(1,ℤ/8)12yes—
188C22×Q8C22⋊D1112yes—
189C22×D4—22no—
190C22×D4—222no—
191C22×D4—221no—
192C22×D4C22⋊D1112yes—
193C23×C4—22no—
194C2×SD16—228no—
195C2×SD16—448no—
196C2×D8—228no—
197C2×D8—448no—
198C22×C8—221no—
199C22×C8—222no—
200C4⋊Q8—22no—
201C4⋊Q8C22⋊D1112yes—
202C4⋊Q8C22×D1112yes—
203#127—112no—
204#127—222no—
205#127—221no—
206#124—28no—
207#124—28no—
208#121—28no—
209#121—28no—
210C4×D4—22no—
211C4×D4—22no—
212C4×D4C22⋊D1114yes—
213C4×D4C22×D1114yes—
214#117—28no—
215#117—28no—
216C2×C4⋊C4—22no—
217C2×C4⋊C4C22⋊D1112yes—
218C2×C22⋊C4—24no—
219C2×C22⋊C4—22no—
220C2×C42—22no—
221C2×C42C22×D1111yescharacteristic
222C4⋊C8—114no—
223C4⋊C8—222no—
224#102—228no—
225C4×C8—112no—
226C4×C8—221no—
227C2×C11—84no—
228C2×C11#162414yescomplemented
229C2×C11C2×#44912yes—
230C2×C11C2×#45311yescharacteristic
231D11—162no—
232C24—22no—
233C24—441no—
234C2×Q8—22no—
235C2×Q8—44no—
236C2×Q8C2×C22⋊D1114yes—
237C2×D4—28no—
238C2×D4—24no—
239C2×D4—24no—
240C2×D4—22no—
241C2×D4—84no—
242C2×D4—224no—
243C2×D4—222no—
244C2×D4—444no—
245C2×D4—444no—
246C2×D4—444no—
247C2×D4—441no—
248C2×D4—442no—
249C2×D4C2×C22⋊D1114yes—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—24no—
253C22×C4—24no—
254C22×C4—44no—
255C22×C4—44no—
256C22×C4C2×C22⋊D1111yescharacteristic
257C22×C4C2×C22⋊D1112yes—
258SD16—4416no—
259D8—4416no—
260C2×C8—224no—
261C2×C8—222no—
262C2×C8—224no—
263C2×C8—444no—
264C4⋊C4—24no—
265C4⋊C4—22no—
266C4⋊C4—24no—
267C4⋊C4C2×C22⋊D1114yes—
268C22⋊C4—216no—
269C22⋊C4—24no—
270C22⋊C4—24no—
271C42—28no—
272C42C2×C22⋊D1111yescharacteristic
273C42C2×C22⋊D1112yes—
274C42C23×D1111yescharacteristic
275C11C2×#162411yescharacteristic, complemented, Sylow
276C23—24no—
277C23—44no—
278C23—44no—
279C23—44no—
280C23—442no—
281C23—884no—
282C23—882no—
283C23#6700611yescharacteristic
284Q8—44no—
285Q8—82no—
286D4—24no—
287D4—24no—
288D4—44no—
289D4—88no—
290D4—444no—
291D4—444no—
292D4—444no—
293D4—882no—
294D4—884no—
295C2×C4—22no—
296C2×C4—24no—
297C2×C4—24no—
298C2×C4—44no—
299C2×C4—44no—
300C2×C4—44no—
301C2×C4—44no—
302C2×C4—48no—
303C2×C4#6700214yes—
304C2×C4#6700314yes—
305C2×C4#6700611yescharacteristic
306C2×C4#6700612yes—
307C2×C4C22×C22⋊D1111yescharacteristic
308C2×C4C22×C22⋊D1112yes—
309C8—224no—
310C8—444no—
311C22—44no—
312C22—44no—
313C22—44no—
314C22—88no—
315C22—884no—
316C22—882no—
317C22—1764no—
318C22#1062285114yes—
319C22#1062285412yes—
320C22C2×#6700611yescharacteristic
321C4—21no—
322C4—21no—
323C4—44no—
324C4—44no—
325C4#1062285114yes—
326C4C2×#6700212yes—
327C4C2×#6700312yes—
328C2—84no—
329C2—1762no—
330C2#1306769914yesdirect product factor
331C2C2×#1062285112yes—
332C2C2×#1062285411yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#555C2
socleC23×C11#120
hypercenterC2×#555D11
hypocenterC11C2×#1624
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
1. C2×#10622698C2semidirect
2. C2×#10622628C2semidirect
3. #13067699C2direct (N × H)
4. C2×#10622184C2semidirect
5. C2×D4⋊(C11⋊C8)C2semidirect
6. C2×C11×#555C2semidirect
9. C11×#555C22semidirect
19. #10622698C22semidirect
21. #10622628C22semidirect
25. #10622184C22semidirect
26. D4⋊(C11⋊C8)C22semidirect
110. C2×#555D11semidirect
155. #555C2×D11semidirect
228. C2×C11#1624semidirect
275. C11C2×#1624semidirect
330. C2#13067699direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226982
C2×#106226282
#130676992
C2×#106221842
C2×D4⋊(C11⋊C8)2
C2×C11×#5552
C2×#162411