Finite Group Databasebeta

← C11×#13199 #14590392

Subgroups — C11×#13199 #14590392

Order 2816.

406 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 138 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×#2955C211yesmaximal, characteristic
2C11×#2151C211yesmaximal, characteristic, complemented
3C2×C11×#350C212yesmaximal, complemented
4C11×#2115C212yesmaximal, complemented
5C11×#2110C211yesmaximal, characteristic, complemented
6C11×#575C411yescharacteristic
7C2×C11×#131C2212yes—
8C2×C11×M32C2211yescharacteristic
9C2×C11×M32C2212yes—
10C22×C11×C16C2211yescharacteristic
11C11×#444—22no—
12C11×#443—22no—
13C11×#430C411yescharacteristic
14C11×#421C412yes—
15C11×#405C2211yescharacteristic
16C11×C4⋊C16—22no—
17C11×#350—24no—
18C11×#349—24no—
19C11×#347—22no—
20C2×C11×#41C2×C412yes—
21C11×#137—22no—
22C11×AGL(1,ℤ/8)—22no—
23C11×#135—22no—
24C11×#131—22no—
25C11×#131—22no—
26C11×#131—22no—
27C11×#131—22no—
28C2×C11×M16—22no—
29C2×C11×M16C2×C412yes—
30C2×C11×M16C2×C411yescharacteristic
31C22×C8×C11—22no—
32C22×C8×C11C2311yescharacteristic
33C11×#117C2×C411yescharacteristic
34C11×M32—22no—
35C11×M32—22no—
36C11×M32D414yes—
37C2×C11×C16—22no—
38C2×C11×C16—22no—
39C2×C11×C16—21no—
40C2×C11×C16—21no—
41C11×#108—22no—
42C11×#104—24no—
43C11×#97D412yes—
44C4×C8×C11D412yes—
45#13199C1111yesmaximal, characteristic, direct product factor, Sylow
46C11×#41—22no—
47C11×#41—22no—
48C11×#41—22no—
49C11×#41—22no—
50C2×Q8×C11M1612yes—
51C2×D4×C11—22no—
52C2×D4×C11M1612yes—
53C22×C4×C11—22no—
54C22×C4×C11C22×C411yescharacteristic
55C11×Q16—22no—
56C11×SD16—24no—
57C11×D8—22no—
58C11×M16—22no—
59C11×M16—22no—
60C11×M16—22no—
61C11×M16—42no—
62C11×M16—42no—
63C2×C8×C11—22no—
64C2×C8×C11—42no—
65C2×C8×C11—42no—
66C2×C8×C11C22⋊C412yes—
67C2×C8×C11C2×D411yescharacteristic
68C2×C8×C11C2×D411yescharacteristic
69C2×C8×C11C2×D412yes—
70C2×C8×C11#4112yes—
71C11×C4⋊C4—21no—
72C11×C22⋊C4—21no—
73C42×C11C22⋊C412yes—
74C11×C16—24no—
75C11×C16—41no—
76C11×C16—41no—
77#2955C2×C1111yescharacteristic
78#2151C2×C1111yescharacteristic, complemented
79C2×#350C2×C1112yescomplemented
80#2115C2×C1112yescomplemented
81#2110C2×C1111yescharacteristic, complemented
82C23×C11—22no—
83C23×C11#13111yescharacteristic
84Q8×C11—22no—
85Q8×C11—22no—
86D4×C11—22no—
87D4×C11—22no—
88D4×C11—42no—
89D4×C11—42no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11—42no—
93C2×C4×C11—42no—
94C2×C4×C11C2×C22⋊C411yescharacteristic
95C2×C4×C11C4×D412yes—
96C2×C4×C11C2×M1612yes—
97C2×C4×C11#13111yescharacteristic
98C8×C11—22no—
99C8×C11—42no—
100C8×C11#12112yes—
101C8×C11#12411yescharacteristic
102C8×C11#12711yescharacteristic
103#575C4×C1111yescharacteristic
104C2×#131C22×C1112yes—
105C2×M32C22×C1111yescharacteristic
106C2×M32C22×C1112yes—
107C22×C16C22×C1111yescharacteristic
108#444—22no—
109#443—22no—
110#430C4×C1111yescharacteristic
111#421C4×C1112yes—
112#405C22×C1111yescharacteristic
113C4⋊C16—22no—
114#350—24no—
115#349—24no—
116#347—22no—
117C22×C11—41no—
118C22×C11—42no—
119C22×C11—82no—
120C22×C11#40811yescharacteristic
121C22×C11#43512yes—
122C4×C11—42no—
123C4×C11—42no—
124C4×C11#39011yescharacteristic
125C4×C11#40711yescharacteristic
126C4×C11#43512yes—
127C2×#41C2×C4×C1112yes—
128#137—22no—
129AGL(1,ℤ/8)—22no—
130#135—22no—
131#131—22no—
132#131—22no—
133#131—22no—
134#131—22no—
135C2×M16—22no—
136C2×M16C2×C4×C1112yes—
137C2×M16C2×C4×C1111yescharacteristic
138C22×C8—22no—
139C22×C8C23×C1111yescharacteristic
140#117C2×C4×C1111yescharacteristic
141M32—22no—
142M32—22no—
143M32D4×C1114yes—
144C2×C16—22no—
145C2×C16—22no—
146C2×C16—21no—
147C2×C16—21no—
148#108—22no—
149#104—24no—
150#97D4×C1112yes—
151C4×C8D4×C1112yes—
152C2×C11—21no—
153C2×C11—22no—
154C2×C11—82no—
155C2×C11#195511yescharacteristic
156#41—22no—
157#41—22no—
158#41—22no—
159#41—22no—
160C2×Q8C11×M1612yes—
161C2×D4—22no—
162C2×D4C11×M1612yes—
163C22×C4—22no—
164C22×C4C22×C4×C1111yescharacteristic
165Q16—22no—
166SD16—24no—
167D8—22no—
168M16—22no—
169M16—22no—
170M16—22no—
171M16—42no—
172M16—42no—
173C2×C8—22no—
174C2×C8—42no—
175C2×C8—42no—
176C2×C8C11×C22⋊C412yes—
177C2×C8C2×D4×C1111yescharacteristic
178C2×C8C2×D4×C1112yes—
179C2×C8C2×D4×C1111yescharacteristic
180C2×C8C11×#4112yes—
181C4⋊C4—21no—
182C22⋊C4—21no—
183C42C11×C22⋊C412yes—
184C16—24no—
185C16—41no—
186C16—41no—
187C11#1319911yescharacteristic, direct product factor, Sylow
188C23—22no—
189C23C11×#13111yescharacteristic
190Q8—22no—
191Q8—22no—
192D4—22no—
193D4—22no—
194D4—42no—
195D4—42no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4C2×C11×C22⋊C411yescharacteristic
201C2×C4C4×D4×C1112yes—
202C2×C4C2×C11×M1612yes—
203C2×C4C11×#13111yescharacteristic
204C8—22no—
205C8—42no—
206C8C11×#12112yes—
207C8C11×#12411yescharacteristic
208C8C11×#12711yescharacteristic
209C22—41no—
210C22—42no—
211C22—82no—
212C22C11×#40811yescharacteristic
213C22C11×#43512yes—
214C4—42no—
215C4—42no—
216C4C11×#39011yescharacteristic
217C4C11×#40711yescharacteristic
218C4C11×#43512yes—
219C2—21no—
220C2—22no—
221C2—82no—
222C2C11×#195511yescharacteristic
subgroupG/H
centerC8×C11#124
commutatorC22×C4C22×C4×C11
Frattini, cosocleC22×C8C23×C11
socleC2×C11#1955
prime radicalC11×#575C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C8×C11 ◁ C22×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2151C2semidirect
3. C2×C11×#350C2semidirect
4. C11×#2115C2semidirect
5. C11×#2110C2semidirect
45. #13199C11direct (N × H)
78. #2151C2×C11semidirect
79. C2×#350C2×C11semidirect
80. #2115C2×C11semidirect
81. #2110C2×C11semidirect
187. C11#13199direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#29552
C11×#21512
C2×C11×#3502
C11×#21152
C11×#21102
#1319911