Finite Group Databasebeta

← C11×#12364 #14589557

Subgroups — C11×#12364 #14589557

Order 2816.

358 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 78 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×#3291C211yesmaximal, characteristic
2C11×#2230C212yesmaximal, complemented
3C11×#1705C211yesmaximal, characteristic, complemented
4C11×#1359C211yesmaximal, characteristic, complemented
5C11×#1335C212yesmaximal, complemented
6C11×#577—22no—
7C11×#498—21no—
8C11×#498C2211yescharacteristic, complemented
9C11×#492—21no—
10C11×#492C2211yescharacteristic
11C11×#471—22no—
12C11×#456—21no—
13C11×#453—21no—
14C11×#443C2212yes—
15C11×#365—22no—
16C11×#364C2212yescomplemented
17C11×#360—22no—
18C82×C11C2211yescharacteristic, complemented
19C11×2−1+4—21no—
20C11×H(5,𝔽2)—21no—
21C11×#137—22no—
22C11×#137—42no—
23C11×AGL(1,ℤ/8)—22no—
24C11×AGL(1,ℤ/8)—42no—
25C11×#135—42no—
26C11×#135D412yes—
27C2×C11×SD16—22no—
28C2×C11×SD16—42no—
29C2×C11×SD16—42no—
30C11×#131—22no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8D411yescharacteristic
33C11×#127D411yescharacteristic
34C11×M32—22no—
35C11×#108D412yes—
36C11×#106—22no—
37C11×#106—42no—
38C11×#104—22no—
39C11×#101—21no—
40C11×#100—21no—
41C4×C8×C11—21no—
42C4×C8×C11C2311yescharacteristic
43#12364C1111yesmaximal, characteristic, direct product factor, Sylow
44C11×#41—22no—
45C11×#41—42no—
46C11×#41—42no—
47C11×#41—81no—
48C2×Q8×C11—21no—
49C2×Q8×C11—41no—
50C2×Q8×C11—42no—
51C2×D4×C11—21no—
52C2×D4×C11—41no—
53C2×D4×C11—42no—
54C2×D4×C11—81no—
55C11×Q16—42no—
56C11×Q16SD1612yescomplemented
57C11×SD16—22no—
58C11×SD16—42no—
59C11×SD16—42no—
60C11×SD16—42no—
61C11×SD16—42no—
62C11×SD16—84no—
63C11×D8—42no—
64C11×D8SD1612yescomplemented
65C11×M16—22no—
66C11×M16—42no—
67C2×C8×C11—22no—
68C2×C8×C11—42no—
69C2×C8×C11C2×D412yes—
70C11×C4⋊C4—41no—
71C11×C4⋊C4—41no—
72C11×C4⋊C4—41no—
73C42×C11C2×D411yescharacteristic
74C11×C16—42no—
75#3291C2×C1111yescharacteristic
76#2230C2×C1112yescomplemented
77#1705C2×C1111yescharacteristic, complemented
78#1359C2×C1111yescharacteristic, complemented
79#1335C2×C1112yescomplemented
80C23×C11—41no—
81C23×C11—81no—
82Q8×C11—22no—
83Q8×C11—42no—
84Q8×C11—82no—
85Q8×C11—81no—
86D4×C11—22no—
87D4×C11—42no—
88D4×C11—42no—
89D4×C11—82no—
90D4×C11—82no—
91D4×C11—81no—
92C2×C4×C11—21no—
93C2×C4×C11—42no—
94C2×C4×C11—41no—
95C2×C4×C11—81no—
96C2×C4×C11—82no—
97C2×C4×C11—81no—
98C2×C4×C11#12011yescharacteristic
99C8×C11—24no—
100C8×C11—42no—
101C8×C11C2×SD1612yes—
102C8×C11AGL(1,ℤ/8)12yes—
103#577—22no—
104#498—21no—
105#498C22×C1111yescharacteristic, complemented
106#492—21no—
107#492C22×C1111yescharacteristic
108#471—22no—
109#456—21no—
110#453—21no—
111#443C22×C1112yes—
112#365—22no—
113#364C22×C1112yescomplemented
114#360—22no—
115C82C22×C1111yescharacteristic, complemented
116C22×C11—42no—
117C22×C11—81no—
118C22×C11—161no—
119C22×C11—321no—
120C22×C11#45311yescharacteristic
121C4×C11—22no—
122C4×C11—42no—
123C4×C11—81no—
124C4×C11—161no—
125C4×C11#45012yes—
1262−1+4—21no—
127H(5,𝔽2)—21no—
128#137—22no—
129#137—42no—
130AGL(1,ℤ/8)—22no—
131AGL(1,ℤ/8)—42no—
132#135—42no—
133#135D4×C1112yes—
134C2×SD16—22no—
135C2×SD16—42no—
136C2×SD16—42no—
137#131—22no—
138C4⋊Q8—21no—
139C4⋊Q8D4×C1111yescharacteristic
140#127D4×C1111yescharacteristic
141M32—22no—
142#108D4×C1112yes—
143#106—22no—
144#106—42no—
145#104—22no—
146#101—21no—
147#100—21no—
148C4×C8—21no—
149C4×C8C23×C1111yescharacteristic
150C2×C11—21no—
151C2×C11—82no—
152C2×C11—161no—
153C2×C11#162911yescharacteristic
154#41—22no—
155#41—42no—
156#41—42no—
157#41—81no—
158C2×Q8—21no—
159C2×Q8—41no—
160C2×Q8—42no—
161C2×D4—21no—
162C2×D4—41no—
163C2×D4—42no—
164C2×D4—81no—
165Q16—42no—
166Q16C11×SD1612yescomplemented
167SD16—22no—
168SD16—42no—
169SD16—42no—
170SD16—42no—
171SD16—42no—
172SD16—84no—
173D8—42no—
174D8C11×SD1612yescomplemented
175M16—22no—
176M16—42no—
177C2×C8—22no—
178C2×C8—42no—
179C2×C8C2×D4×C1112yes—
180C4⋊C4—41no—
181C4⋊C4—41no—
182C4⋊C4—41no—
183C42C2×D4×C1111yescharacteristic
184C16—42no—
185C11#1236411yescharacteristic, direct product factor, Sylow
186C23—41no—
187C23—81no—
188Q8—22no—
189Q8—42no—
190Q8—82no—
191Q8—81no—
192D4—22no—
193D4—42no—
194D4—42no—
195D4—82no—
196D4—82no—
197D4—81no—
198C2×C4—21no—
199C2×C4—42no—
200C2×C4—41no—
201C2×C4—81no—
202C2×C4—82no—
203C2×C4—81no—
204C2×C4C11×#12011yescharacteristic
205C8—24no—
206C8—42no—
207C8C2×C11×SD1612yes—
208C8C11×AGL(1,ℤ/8)12yes—
209C22—42no—
210C22—81no—
211C22—161no—
212C22—321no—
213C22C11×#45311yescharacteristic
214C4—22no—
215C4—42no—
216C4—81no—
217C4—161no—
218C4C11×#45012yes—
219C2—21no—
220C2—82no—
221C2—161no—
222C2C11×#162911yescharacteristic
subgroupG/H
center, socleC2×C11#1629
commutator, Frattini, cosocleC4×C8C23×C11
prime radicalC11×#3291C2
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C2×C4×C11 ◁ C4×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2230C2semidirect
3. C11×#1705C2semidirect
4. C11×#1359C2semidirect
5. C11×#1335C2semidirect
8. C11×#498C22semidirect
16. C11×#364C22semidirect
18. C82×C11C22semidirect
43. #12364C11direct (N × H)
56. C11×Q16SD16semidirect
64. C11×D8SD16semidirect
76. #2230C2×C11semidirect
77. #1705C2×C11semidirect
78. #1359C2×C11semidirect
79. #1335C2×C11semidirect
105. #498C22×C11semidirect
113. #364C22×C11semidirect
115. C82C22×C11semidirect
166. Q16C11×SD16semidirect
174. D8C11×SD16semidirect
185. C11#12364direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32912
C11×#22302
C11×#17052
C11×#13592
C11×#13352
#1236411