Finite Group Databasebeta

← C11×#12308 #14589501

Subgroups — C11×#12308 #14589501

Order 2816.

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

normal subgroups only

This group has 274 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×#3255C211yesmaximal, characteristic
2C11×#2239C212yesmaximal
3C11×#2102C211yesmaximal, characteristic
4C11×#1340C212yesmaximal
5C11×#1327C211yesmaximal, characteristic
6C11×#533—21no—
7C11×#475—22no—
8C11×#470—21no—
9C11×#470C2212yes—
10C11×#462—22no—
11C11×#430C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C11×#365—22no—
14C11×#362—22no—
15C11×#349C2212yes—
16C11×#344—21no—
17C11×#339—21no—
18C11×H(3,ℤ/4)C2211yescharacteristic
19C2×C11×Q16—21no—
20C2×C11×Q16D412yes—
21C2×C11×M16—21no—
22C2×C11×M16D411yescharacteristic
23C2×C11×M16C2311yescharacteristic
24C11×C4⋊Q8—21no—
25C11×C4⋊Q8—21no—
26C11×#125—41no—
27C11×C22⋊Q8—22no—
28C11×C22⋊Q8—41no—
29C4×Q8×C11—22no—
30C4×Q8×C11—41no—
31C11×#117—21no—
32C11×#117—41no—
33C2×C42×C11D411yescharacteristic
34C11×M32—22no—
35C11×#108—22no—
36C11×#106—21no—
37C11×#106D412yes—
38C11×C4⋊C8—22no—
39C11×#103—22no—
40C11×#103—22no—
41#12308C1111yesmaximal, characteristic, direct product factor, Sylow
42C2×Q8×C11—22no—
43C2×Q8×C11—41no—
44C22×C4×C11—21no—
45C22×C4×C11C2×D411yescharacteristic
46C11×Q16—42no—
47C11×Q16—81no—
48C11×M16—41no—
49C11×M16—41no—
50C11×M16—41no—
51C11×M16—41no—
52C2×C8×C11—21no—
53C2×C8×C11—41no—
54C2×C8×C11C2×D412yes—
55C11×C4⋊C4—22no—
56C11×C4⋊C4—41no—
57C11×C4⋊C4—41no—
58C11×C4⋊C4—42no—
59C11×C4⋊C4—41no—
60C11×C4⋊C4—41no—
61C11×C4⋊C4—42no—
62C11×C22⋊C4—42no—
63C11×C22⋊C4—41no—
64C42×C11—21no—
65C42×C11—42no—
66C42×C11—41no—
67C42×C11SD1611yescharacteristic
68C42×C11SD1611yescharacteristic
69C11×C16—42no—
70#3255C2×C1111yescharacteristic
71#2239C2×C1112yes—
72#2102C2×C1111yescharacteristic
73#1340C2×C1112yes—
74#1327C2×C1111yescharacteristic
75C23×C11AGL(1,ℤ/8)11yescharacteristic
76Q8×C11—42no—
77Q8×C11—42no—
78Q8×C11—82no—
79C2×C4×C11—21no—
80C2×C4×C11—21no—
81C2×C4×C11—21no—
82C2×C4×C11—21no—
83C2×C4×C11—42no—
84C2×C4×C11—42no—
85C2×C4×C11—42no—
86C2×C4×C11—81no—
87C2×C4×C11#12011yescharacteristic
88C2×C4×C11C2×SD1611yescharacteristic
89C8×C11—22no—
90C8×C11—41no—
91C8×C11—81no—
92#533—21no—
93#475—22no—
94#470—21no—
95#470C22×C1112yes—
96#462—22no—
97#430C22×C1111yescharacteristic
98#423C22×C1111yescharacteristic
99#365—22no—
100#362—22no—
101#349C22×C1112yes—
102#344—21no—
103#339—21no—
104H(3,ℤ/4)C22×C1111yescharacteristic
105C22×C11—21no—
106C22×C11—41no—
107C22×C11#45011yescharacteristic
108C4×C11—22no—
109C4×C11—21no—
110C4×C11—41no—
111C4×C11—82no—
112C4×C11—82no—
113C4×C11—161no—
114C4×C11#45411yescharacteristic
115C4×C11#45811yescharacteristic
116C2×Q16—21no—
117C2×Q16D4×C1112yes—
118C2×M16—21no—
119C2×M16D4×C1111yescharacteristic
120C2×M16C23×C1111yescharacteristic
121C4⋊Q8—21no—
122C4⋊Q8—21no—
123#125—41no—
124C22⋊Q8—22no—
125C22⋊Q8—41no—
126C4×Q8—22no—
127C4×Q8—41no—
128#117—21no—
129#117—41no—
130C2×C42D4×C1111yescharacteristic
131M32—22no—
132#108—22no—
133#106—21no—
134#106D4×C1112yes—
135C4⋊C8—22no—
136#103—22no—
137#103—22no—
138C2×C11—21no—
139C2×C11—41no—
140C2×C11#161611yescharacteristic
141C2×Q8—22no—
142C2×Q8—41no—
143C22×C4—21no—
144C22×C4C2×D4×C1111yescharacteristic
145Q16—42no—
146Q16—81no—
147M16—41no—
148M16—41no—
149M16—41no—
150M16—41no—
151C2×C8—21no—
152C2×C8—41no—
153C2×C8C2×D4×C1112yes—
154C4⋊C4—22no—
155C4⋊C4—41no—
156C4⋊C4—41no—
157C4⋊C4—42no—
158C4⋊C4—41no—
159C4⋊C4—41no—
160C4⋊C4—42no—
161C22⋊C4—42no—
162C22⋊C4—41no—
163C42—21no—
164C42—42no—
165C42—41no—
166C42C11×SD1611yescharacteristic
167C42C11×SD1611yescharacteristic
168C16—42no—
169C11#1230811yescharacteristic, direct product factor, Sylow
170C23C11×AGL(1,ℤ/8)11yescharacteristic
171Q8—42no—
172Q8—42no—
173Q8—82no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—81no—
182C2×C4C11×#12011yescharacteristic
183C2×C4C2×C11×SD1611yescharacteristic
184C8—22no—
185C8—41no—
186C8—81no—
187C22—21no—
188C22—41no—
189C22C11×#45011yescharacteristic
190C4—22no—
191C4—21no—
192C4—41no—
193C4—82no—
194C4—82no—
195C4—161no—
196C4C11×#45411yescharacteristic
197C4C11×#45811yescharacteristic
198C2—21no—
199C2—41no—
200C2C11×#161611yescharacteristic
subgroupG/H
center, socleC2×C11#1616
commutator, Frattini, cosocleC2×M16C23×C11
prime radicalC23×C11AGL(1,ℤ/8)
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
41. #12308C11direct (N × H)
169. C11#12308direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32552
C11×#22392
C11×#21022
C11×#13402
C11×#13272
#1230811