Finite Group Databasebeta

← #13069656

Subgroups — #13069656

Order 1408.

406 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 75 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×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2#10623364C211yesmaximal, characteristic, complemented
3C2×#66985C211yesmaximal, characteristic, complemented
4C2×#66901C211yesmaximal, characteristic, complemented
5#10622834C211yesmaximal, characteristic, complemented
6C2×#66889C211yesmaximal, characteristic, complemented
7#10622192C211yesmaximal, characteristic, complemented
8C2×C11×#41C2211yescharacteristic
9C22×D4×C11C2211yescharacteristic
10C2×#4339C2211yescharacteristic
11C11×AGL(1,ℤ/8)—22no—
12C11×AGL(1,ℤ/8)—22no—
13C2×C11×SD16—21no—
14C2×C11×D8—21no—
15C2×C11×M16C2211yescharacteristic
16C2×C22⋊Dic11—22no—
17#66999—21no—
18#66992—22no—
19#66991—21no—
20C2×#4324—21no—
21#66985—22no—
22#66985—22no—
23C2×#4323—21no—
24#66983—21no—
25C2×C4⋊Dic11C2211yescharacteristic
26#66977—21no—
27C2×C4×Dic11C2211yescharacteristic
28C2×#4318C2211yescharacteristic
29#66901—22no—
30#66889—22no—
31C24×C11—21no—
32C11×#41—21no—
33C11×#41—21no—
34C11×#41—21no—
35C11×#41—21no—
36C2×Q8×C11D411yescharacteristic
37C2×D4×C11—21no—
38C2×D4×C11—21no—
39C2×D4×C11—21no—
40C2×D4×C11—21no—
41C2×D4×C11—21no—
42C2×D4×C11—21no—
43C2×D4×C11D411yescharacteristic
44C2×D4×C11D412yescomplemented
45C22×C4×C11—21no—
46C22×C4×C11C2311yescharacteristic
47C2×C22⋊D11—22no—
48C2×C22⋊D11—21no—
49C22×Dic11—21no—
50C22×Dic11D412yes—
51#4339—21no—
52#4339—21no—
53#4339—21no—
54#4339—21no—
55C2×D44D411yescharacteristic
56C2×C4×D11—21no—
57C2×Dic22D411yescharacteristic
58C11×SD16—24no—
59C11×D8—24no—
60C11×M16—21no—
61C11×M16D412yescomplemented
62C2×C8×C11—21no—
63C22⋊Dic11—22no—
64C22⋊Dic11—44no—
65#4324—24no—
66#4323—24no—
67(C2×D11)⋊C4—22no—
68C4⋊Dic11—21no—
69C4⋊Dic11—21no—
70Dic11⋊C4—22no—
71C4×Dic11—21no—
72C4×Dic11—21no—
73#4318—21no—
74#4318D412yescomplemented
75C2×C11⋊C8—21no—
76#2006—111nomaximal, Sylow
77C23×C11—21no—
78C23×C11—22no—
79C23×C11—42no—
80C23×C11—42no—
81C23×C11—41no—
82C23×C11—41no—
83C23×C11C2×D411yescharacteristic
84C22×D11—21no—
85Q8×C11—21no—
86Q8×C11—21no—
87D4×C11—22no—
88D4×C11—21no—
89D4×C11—22no—
90D4×C11—21no—
91D4×C11—41no—
92D4×C11—41no—
93D4×C11—41no—
94D4×C11—41no—
95C2×C4×C11—21no—
96C2×C4×C11—41no—
97C2×C4×C11—41no—
98C2×C4×C11C2×D411yescharacteristic
99C2×C4×C11C2×D411yescharacteristic
100C2×C4×C11C2×D411yescharacteristic
101C2×C4×C11C2×D411yescharacteristic
102C2×C4×C11C2×D411yescharacteristic
103C2×C4×C11#4111yescharacteristic
104C22⋊D11—41no—
105C22⋊D11—41no—
106C22⋊D11—82no—
107C2×Dic11—22no—
108C2×Dic11—21no—
109C2×Dic11—22no—
110C2×Dic11—41no—
111C2×Dic11—41no—
112C2×Dic11—42no—
113D44—21no—
114D44—21no—
115C4×D11—41no—
116C4×D11—41no—
117Dic22—21no—
118Dic22—21no—
119C8×C11—22no—
120C11⋊C8—22no—
121C2×AGL(1,ℤ/8)—111no—
122C2×AGL(1,ℤ/8)D1111yescharacteristic, complemented
123#537—111no—
124C2×#104—111no—
125C2×#104—111no—
126#390—111no—
127#343—111no—
128C22×C11—21no—
129C22×C11—21no—
130C22×C11—44no—
131C22×C11—41no—
132C22×C11—42no—
133C22×C11—41no—
134C22×C11—41no—
135C22×C11—82no—
136C22×C11—81no—
137C22×C11—81no—
138C22×C11#12011yescharacteristic
139C22×C11#12111yescharacteristic
140C22×C11#12711yescharacteristic
141C2×D11—41no—
142C2×D11—41no—
143C2×D11—41no—
144C4×C11—41no—
145C4×C11#12011yescharacteristic
146C4×C11#12011yescharacteristic
147C4×C11#12111yescharacteristic
148C4×C11#12111yescharacteristic
149Dic11—42no—
150Dic11—41no—
151Dic11—42no—
152C2×#41—111no—
153C2×#41C2×D1111yescharacteristic
154C22×D4C2×D1111yescharacteristic
155AGL(1,ℤ/8)—22no—
156AGL(1,ℤ/8)—22no—
157AGL(1,ℤ/8)—222no—
158AGL(1,ℤ/8)—222no—
159C2×SD16—21no—
160C2×SD16—221no—
161C2×D8—21no—
162C2×D8—221no—
163C2×M16—111no—
164C2×M16C2×D1111yescharacteristic
165C22⋊Q8—221no—
166C22⋊Q8—221no—
167#121—221no—
168#121—222no—
169#121—221no—
170C2×C4⋊C4—111no—
171C2×C22⋊C4—222no—
172C2×C42—111no—
173#104—222no—
174#104—222no—
175C2×C11—21no—
176C2×C11—21no—
177C2×C11—81no—
178C2×C11—82no—
179C2×C11#39211yescharacteristic
180C2×C11#45311yescharacteristic
181C2×C11#45411yescharacteristic
182D11—81no—
183C24—21no—
184#41—21no—
185#41—21no—
186#41—21no—
187#41—21no—
188#41—221no—
189#41—221no—
190#41—221no—
191#41—221no—
192C2×Q8—111no—
193C2×Q8C22⋊D1111yescharacteristic
194C2×D4—21no—
195C2×D4—21no—
196C2×D4—21no—
197C2×D4—21no—
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—111no—
201C2×D4—221no—
202C2×D4—222no—
203C2×D4C22⋊D1111yescharacteristic
204C2×D4C22⋊D1112yescomplemented
205C22×C4—21no—
206C22×C4—112no—
207C22×C4—221no—
208C22×C4—221no—
209C22×C4C22×D1111yescharacteristic
210SD16—24no—
211SD16—224no—
212D8—24no—
213D8—224no—
214M16—21no—
215M16—112no—
216M16—221no—
217M16C22⋊D1112yescomplemented
218C2×C8—21no—
219C2×C8—221no—
220C4⋊C4—222no—
221C4⋊C4—221no—
222C4⋊C4—221no—
223C22⋊C4—222no—
224C22⋊C4—222no—
225C22⋊C4—444no—
226C42—221no—
227C42—221no—
228C11#200611yescharacteristic, complemented, Sylow
229C23—21no—
230C23—22no—
231C23—42no—
232C23—42no—
233C23—41no—
234C23—41no—
235C23—221no—
236C23D4×D1111yescharacteristic
237Q8—21no—
238Q8—21no—
239Q8—221no—
240Q8—221no—
241D4—22no—
242D4—21no—
243D4—21no—
244D4—22no—
245D4—41no—
246D4—41no—
247D4—41no—
248D4—41no—
249D4—221no—
250D4—221no—
251D4—441no—
252D4—441no—
253D4—882no—
254C2×C4—21no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—222no—
258C2×C4—222no—
259C2×C4—221no—
260C2×C4—441no—
261C2×C4—441no—
262C2×C4—441no—
263C2×C4—441no—
264C2×C4—442no—
265C2×C4D4×D1111yescharacteristic
266C2×C4D4×D1111yescharacteristic
267C2×C4#434111yescharacteristic
268C2×C4C2×C22⋊D1111yescharacteristic
269C2×C4C2×C22⋊D1111yescharacteristic
270C2×C4C2×C22⋊D1111yescharacteristic
271C8—22no—
272C8—222no—
273C22—21no—
274C22—21no—
275C22—44no—
276C22—41no—
277C22—41no—
278C22—41no—
279C22—42no—
280C22—82no—
281C22—81no—
282C22—81no—
283C22—441no—
284C22—441no—
285C22—441no—
286C22#6699011yescharacteristic
287C22#6699211yescharacteristic
288C22#6699311yescharacteristic
289C4—41no—
290C4—442no—
291C4—442no—
292C4—441no—
293C4#6699011yescharacteristic
294C4#6699111yescharacteristic
295C4#6699211yescharacteristic
296C4#6700611yescharacteristic
297C2—21no—
298C2—21no—
299C2—82no—
300C2—81no—
301C2—881no—
302C2#1062281111yescharacteristic
303C2#1062281411yescharacteristic
304C2#1062283611yescharacteristic
subgroupG/H
centerC22#66990
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC2×C11×AGL(1,ℤ/8)C2
socleC22×C11#120
hypercenterC2×AGL(1,ℤ/8)D11
hypocenterC11#2006
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×C11×AGL(1,ℤ/8)C2semidirect
2. #10623364C2semidirect
3. C2×#66985C2semidirect
4. C2×#66901C2semidirect
5. #10622834C2semidirect
6. C2×#66889C2semidirect
7. #10622192C2semidirect
44. C2×D4×C11D4semidirect
61. C11×M16D4semidirect
74. #4318D4semidirect
122. C2×AGL(1,ℤ/8)D11semidirect
204. C2×D4C22⋊D11semidirect
217. M16C22⋊D11semidirect
228. C11#2006semidirect

Maximal subgroups

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

subgroupindex
C2×C11×AGL(1,ℤ/8)2
#106233642
C2×#669852
C2×#669012
#106228342
C2×#668892
#106221922
#200611