Finite Group Databasebeta

← C11×#12298 #14589491

Subgroups — C11×#12298 #14589491

Order 2816.

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

normal subgroups only

This group has 376 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×#3192C211yesmaximal, characteristic
2C11×#2238C212yesmaximal, complemented
3C11×#2091C211yesmaximal, characteristic, complemented
4C11×#1341C212yesmaximal, complemented
5C11×#1320C211yesmaximal, characteristic, complemented
6C2×C11×#121—21no—
7C11×#481—22no—
8C11×#469—21no—
9C11×#469C2212yes—
10C11×#447—22no—
11C11×#430—21no—
12C11×#430C2211yescharacteristic, complemented
13C11×#407—21no—
14C11×#407C2211yescharacteristic
15C11×#365—22no—
16C11×#361—22no—
17C11×#349C2212yescomplemented
18C11×#338C2211yescharacteristic, complemented
19C22×D4×C11—21no—
20C22×D4×C11—41no—
21C23×C4×C11D411yescharacteristic
22C2×C11×D8—21no—
23C2×C11×D8D412yes—
24C2×C11×M16—21no—
25C2×C11×M16—21no—
26C2×C11×M16D411yescharacteristic
27C2×C11×M16C2311yescharacteristic
28C11×#121—22no—
29C11×#121—22no—
30C11×#121—41no—
31C11×#121—41no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C22⋊C4—41no—
34C11×M32—22no—
35C11×#108—22no—
36C11×#108—42no—
37C11×#106—21no—
38C11×#106D412yes—
39C11×#102—22no—
40C11×#102—22no—
41C11×C22⋊C8—22no—
42C11×C22⋊C8—42no—
43#12298C1111yesmaximal, characteristic, direct product factor, Sylow
44C24×C11—41no—
45C24×C11SD1611yescharacteristic
46C2×D4×C11—22no—
47C2×D4×C11—41no—
48C2×D4×C11—42no—
49C2×D4×C11—42no—
50C2×D4×C11—81no—
51C2×D4×C11—81no—
52C2×D4×C11—84no—
53C22×C4×C11—21no—
54C22×C4×C11—21no—
55C22×C4×C11—41no—
56C22×C4×C11—41no—
57C22×C4×C11—41no—
58C22×C4×C11SD1611yescharacteristic
59C22×C4×C11C2×D411yescharacteristic
60C11×D8—42no—
61C11×D8—81no—
62C11×M16—41no—
63C11×M16—41no—
64C11×M16—41no—
65C11×M16—41no—
66C11×M16—41no—
67C11×M16—41no—
68C2×C8×C11—22no—
69C2×C8×C11—21no—
70C2×C8×C11—41no—
71C2×C8×C11C2×D412yes—
72C11×C4⋊C4—22no—
73C11×C4⋊C4—41no—
74C11×C22⋊C4—42no—
75C11×C22⋊C4—42no—
76C11×C16—42no—
77#3192C2×C1111yescharacteristic
78#2238C2×C1112yescomplemented
79#2091C2×C1111yescharacteristic, complemented
80#1341C2×C1112yescomplemented
81#1320C2×C1111yescharacteristic, complemented
82C23×C11—21no—
83C23×C11—41no—
84C23×C11—42no—
85C23×C11—42no—
86C23×C11—82no—
87C23×C11—82no—
88C23×C11—82no—
89C23×C11C2×SD1611yescharacteristic
90D4×C11—42no—
91D4×C11—42no—
92D4×C11—82no—
93D4×C11—84no—
94D4×C11—84no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—41no—
99C2×C4×C11—41no—
100C2×C4×C11—41no—
101C2×C4×C11—42no—
102C2×C4×C11—81no—
103C2×C4×C11—82no—
104C2×C4×C11#12011yescharacteristic
105C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
106C8×C11—22no—
107C8×C11—42no—
108C8×C11—41no—
109C8×C11—81no—
110C2×#121—21no—
111#481—22no—
112#469—21no—
113#469C22×C1112yes—
114#447—22no—
115#430—21no—
116#430C22×C1111yescharacteristic, complemented
117#407—21no—
118#407C22×C1111yescharacteristic
119#365—22no—
120#361—22no—
121#349C22×C1112yescomplemented
122#338C22×C1111yescharacteristic, complemented
123C22×C11—22no—
124C22×C11—21no—
125C22×C11—41no—
126C22×C11—41no—
127C22×C11—42no—
128C22×C11—41no—
129C22×C11—82no—
130C22×C11—82no—
131C22×C11—81no—
132C22×C11—82no—
133C22×C11—164no—
134C22×C11#45011yescharacteristic
135C4×C11—21no—
136C4×C11—41no—
137C4×C11—82no—
138C4×C11#45311yescharacteristic
139C4×C11#45811yescharacteristic
140C22×D4—21no—
141C22×D4—41no—
142C23×C4D4×C1111yescharacteristic
143C2×D8—21no—
144C2×D8D4×C1112yes—
145C2×M16—21no—
146C2×M16—21no—
147C2×M16D4×C1111yescharacteristic
148C2×M16C23×C1111yescharacteristic
149#121—22no—
150#121—22no—
151#121—41no—
152#121—41no—
153C2×C4⋊C4—21no—
154C2×C22⋊C4—41no—
155M32—22no—
156#108—22no—
157#108—42no—
158#106—21no—
159#106D4×C1112yes—
160#102—22no—
161#102—22no—
162C22⋊C8—22no—
163C22⋊C8—42no—
164C2×C11—21no—
165C2×C11—41no—
166C2×C11—42no—
167C2×C11—162no—
168C2×C11#161311yescharacteristic
169C24—41no—
170C24C11×SD1611yescharacteristic
171C2×D4—22no—
172C2×D4—41no—
173C2×D4—42no—
174C2×D4—42no—
175C2×D4—81no—
176C2×D4—81no—
177C2×D4—84no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—41no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4C11×SD1611yescharacteristic
184C22×C4C2×D4×C1111yescharacteristic
185D8—42no—
186D8—81no—
187M16—41no—
188M16—41no—
189M16—41no—
190M16—41no—
191M16—41no—
192M16—41no—
193C2×C8—22no—
194C2×C8—21no—
195C2×C8—41no—
196C2×C8C2×D4×C1112yes—
197C4⋊C4—22no—
198C4⋊C4—41no—
199C22⋊C4—42no—
200C22⋊C4—42no—
201C16—42no—
202C11#1229811yescharacteristic, direct product factor, Sylow
203C23—21no—
204C23—41no—
205C23—42no—
206C23—42no—
207C23—82no—
208C23—82no—
209C23—82no—
210C23C2×C11×SD1611yescharacteristic
211D4—42no—
212D4—42no—
213D4—82no—
214D4—84no—
215D4—84no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—42no—
223C2×C4—81no—
224C2×C4—82no—
225C2×C4C11×#12011yescharacteristic
226C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
227C8—22no—
228C8—42no—
229C8—41no—
230C8—81no—
231C22—22no—
232C22—21no—
233C22—41no—
234C22—41no—
235C22—42no—
236C22—41no—
237C22—82no—
238C22—82no—
239C22—81no—
240C22—82no—
241C22—164no—
242C22C11×#45011yescharacteristic
243C4—21no—
244C4—41no—
245C4—82no—
246C4C11×#45311yescharacteristic
247C4C11×#45811yescharacteristic
248C2—21no—
249C2—42no—
250C2—41no—
251C2—162no—
252C2C11×#161311yescharacteristic
subgroupG/H
center, socleC2×C11#1613
commutator, Frattini, cosocleC2×M16C23×C11
prime radicalC11×#3192C2
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
2. C11×#2238C2semidirect
3. C11×#2091C2semidirect
4. C11×#1341C2semidirect
5. C11×#1320C2semidirect
12. C11×#430C22semidirect
17. C11×#349C22semidirect
18. C11×#338C22semidirect
43. #12298C11direct (N × H)
78. #2238C2×C11semidirect
79. #2091C2×C11semidirect
80. #1341C2×C11semidirect
81. #1320C2×C11semidirect
116. #430C22×C11semidirect
121. #349C22×C11semidirect
122. #338C22×C11semidirect
202. C11#12298direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31922
C11×#22382
C11×#20912
C11×#13412
C11×#13202
#1229811