Finite Group Databasebeta

← C11×#12173 #14589366

Subgroups — C11×#12173 #14589366

Order 2816.

384 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C11×#3253C211yesmaximal, characteristic, complemented
2C11×#2190C212yesmaximal, complemented
3C11×#2050C211yesmaximal, characteristic, complemented
4C11×#1341C212yesmaximal, complemented
5C11×#1327C211yesmaximal, characteristic, complemented
6C11×#575C2211yescharacteristic
7C11×#532—21no—
8C11×#509—22no—
9C11×#476—22no—
10C11×#469—21no—
11C11×#469C2212yes—
12C11×#459—22no—
13C11×#423C2211yescharacteristic
14C2×C11×#104—21no—
15C11×#413—21no—
16C11×#360—22no—
17C11×#349C2212yes—
18C11×#338C2211yescharacteristic
19C2×C11×#41—21no—
20C2×C11×#41—41no—
21C11×#137—41no—
22C11×AGL(1,ℤ/8)—41no—
23C11×#135—22no—
24C2×C11×D8—21no—
25C2×C11×D8D412yes—
26C2×C11×M16—21no—
27C2×C11×M16D411yescharacteristic
28C2×C11×M16C2311yescharacteristic
29C11×C4⋊Q8—21no—
30C11×#127—21no—
31C11×#124—41no—
32C11×#121—22no—
33C11×#121—41no—
34C4×D4×C11—22no—
35C4×D4×C11—41no—
36C2×C42×C11D411yescharacteristic
37C11×SD32—42no—
38C11×D16—42no—
39C11×M32—22no—
40C11×#106—21no—
41C11×#106D412yes—
42C11×C4⋊C8—22no—
43C11×#104—41no—
44C11×#104—41no—
45C11×#102—22no—
46C11×#102—22no—
47C11×#101—41no—
48C11×#100—41no—
49#12173C1111yesmaximal, characteristic, direct product factor, Sylow
50C11×#41—41no—
51C11×#41—41no—
52C11×#41—41no—
53C11×#41—41no—
54C11×#41—84no—
55C2×Q8×C11—21no—
56C2×Q8×C11—41no—
57C2×D4×C11—21no—
58C2×D4×C11—22no—
59C2×D4×C11—41no—
60C2×D4×C11—41no—
61C2×D4×C11—42no—
62C2×D4×C11—41no—
63C22×C4×C11—21no—
64C22×C4×C11—42no—
65C22×C4×C11—41no—
66C22×C4×C11C2×D411yescharacteristic
67C11×Q16—22no—
68C11×SD16—42no—
69C11×D8—22no—
70C11×D8—42no—
71C11×D8—81no—
72C11×M16—41no—
73C11×M16—41no—
74C11×M16—41no—
75C11×M16—41no—
76C2×C8×C11—21no—
77C2×C8×C11—41no—
78C2×C8×C11C2×D412yes—
79C11×C4⋊C4—22no—
80C11×C4⋊C4—41no—
81C11×C22⋊C4—42no—
82C11×C22⋊C4—42no—
83C42×C11—21no—
84C42×C11D811yescharacteristic
85C42×C11D811yescharacteristic
86C11×C16—42no—
87#3253C2×C1111yescharacteristic, complemented
88#2190C2×C1112yescomplemented
89#2050C2×C1111yescharacteristic, complemented
90#1341C2×C1112yescomplemented
91#1327C2×C1111yescharacteristic, complemented
92C23×C11—41no—
93C23×C11—42no—
94C23×C11AGL(1,ℤ/8)11yescharacteristic
95Q8×C11—41no—
96Q8×C11—41no—
97Q8×C11—82no—
98D4×C11—41no—
99D4×C11—42no—
100D4×C11—41no—
101D4×C11—42no—
102D4×C11—82no—
103D4×C11—82no—
104D4×C11—81no—
105D4×C11—84no—
106D4×C11—81no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—42no—
112C2×C4×C11—41no—
113C2×C4×C11—42no—
114C2×C4×C11—81no—
115C2×C4×C11—84no—
116C2×C4×C11—81no—
117C2×C4×C11#12011yescharacteristic
118C2×C4×C11C2×D811yescharacteristic
119C8×C11—22no—
120C8×C11—41no—
121C8×C11—81no—
122#575C22×C1111yescharacteristic
123#532—21no—
124#509—22no—
125#476—22no—
126#469—21no—
127#469C22×C1112yes—
128#459—22no—
129#423C22×C1111yescharacteristic
130C2×#104—21no—
131#413—21no—
132#360—22no—
133#349C22×C1112yes—
134#338C22×C1111yescharacteristic
135C22×C11—21no—
136C22×C11—41no—
137C22×C11—82no—
138C22×C11—82no—
139C22×C11—81no—
140C22×C11—82no—
141C22×C11—161no—
142C22×C11#44711yescharacteristic
143C4×C11—22no—
144C4×C11—21no—
145C4×C11—41no—
146C4×C11—82no—
147C4×C11—81no—
148C4×C11#45411yescharacteristic
149C4×C11B(4,𝔽2)11yescharacteristic
150C2×#41—21no—
151C2×#41—41no—
152#137—41no—
153AGL(1,ℤ/8)—41no—
154#135—22no—
155C2×D8—21no—
156C2×D8D4×C1112yes—
157C2×M16—21no—
158C2×M16D4×C1111yescharacteristic
159C2×M16C23×C1111yescharacteristic
160C4⋊Q8—21no—
161#127—21no—
162#124—41no—
163#121—22no—
164#121—41no—
165C4×D4—22no—
166C4×D4—41no—
167C2×C42D4×C1111yescharacteristic
168SD32—42no—
169D16—42no—
170M32—22no—
171#106—21no—
172#106D4×C1112yes—
173C4⋊C8—22no—
174#104—41no—
175#104—41no—
176#102—22no—
177#102—22no—
178#101—41no—
179#100—41no—
180C2×C11—21no—
181C2×C11—41no—
182C2×C11—162no—
183C2×C11—161no—
184C2×C11#159811yescharacteristic
185#41—41no—
186#41—41no—
187#41—41no—
188#41—41no—
189#41—84no—
190C2×Q8—21no—
191C2×Q8—41no—
192C2×D4—21no—
193C2×D4—22no—
194C2×D4—41no—
195C2×D4—41no—
196C2×D4—42no—
197C2×D4—41no—
198C22×C4—21no—
199C22×C4—42no—
200C22×C4—41no—
201C22×C4C2×D4×C1111yescharacteristic
202Q16—22no—
203SD16—42no—
204D8—22no—
205D8—42no—
206D8—81no—
207M16—41no—
208M16—41no—
209M16—41no—
210M16—41no—
211C2×C8—21no—
212C2×C8—41no—
213C2×C8C2×D4×C1112yes—
214C4⋊C4—22no—
215C4⋊C4—41no—
216C22⋊C4—42no—
217C22⋊C4—42no—
218C42—21no—
219C42C11×D811yescharacteristic
220C42C11×D811yescharacteristic
221C16—42no—
222C11#1217311yescharacteristic, direct product factor, Sylow
223C23—41no—
224C23—42no—
225C23C11×AGL(1,ℤ/8)11yescharacteristic
226Q8—41no—
227Q8—41no—
228Q8—82no—
229D4—41no—
230D4—42no—
231D4—41no—
232D4—42no—
233D4—82no—
234D4—82no—
235D4—81no—
236D4—84no—
237D4—81no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—42no—
243C2×C4—41no—
244C2×C4—42no—
245C2×C4—81no—
246C2×C4—84no—
247C2×C4—81no—
248C2×C4C11×#12011yescharacteristic
249C2×C4C2×C11×D811yescharacteristic
250C8—22no—
251C8—41no—
252C8—81no—
253C22—21no—
254C22—41no—
255C22—82no—
256C22—82no—
257C22—81no—
258C22—82no—
259C22—161no—
260C22C11×#44711yescharacteristic
261C4—22no—
262C4—21no—
263C4—41no—
264C4—82no—
265C4—81no—
266C4C11×#45411yescharacteristic
267C4C11×B(4,𝔽2)11yescharacteristic
268C2—21no—
269C2—41no—
270C2—162no—
271C2—161no—
272C2C11×#159811yescharacteristic
subgroupG/H
center, socleC2×C11#1598
commutator, Frattini, cosocleC2×M16C23×C11
LCSG ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C2×C4×C11 ◁ C2×C11×M16 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3253C2semidirect
2. C11×#2190C2semidirect
3. C11×#2050C2semidirect
4. C11×#1341C2semidirect
5. C11×#1327C2semidirect
49. #12173C11direct (N × H)
87. #3253C2×C11semidirect
88. #2190C2×C11semidirect
89. #2050C2×C11semidirect
90. #1341C2×C11semidirect
91. #1327C2×C11semidirect
222. C11#12173direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32532
C11×#21902
C11×#20502
C11×#13412
C11×#13272
#1217311