Finite Group Databasebeta

← C11×#12305 #14589498

Subgroups — C11×#12305 #14589498

Order 2816.

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

normal subgroups only

This group has 262 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×#3261C211yesmaximal, characteristic
2C11×#2239C212yesmaximal
3C11×#2103C211yesmaximal, characteristic
4C11×#1342C212yesmaximal
5C11×#1328C211yesmaximal, characteristic
6C11×#541—21no—
7C11×#479—22no—
8C11×#470C2212yes—
9C11×#467—21no—
10C11×#462—22no—
11C11×#430C2211yescharacteristic
12C11×#424C2211yescharacteristic
13C11×#365—22no—
14C11×#362—22no—
15C11×#349C2212yes—
16C11×#344—21no—
17C11×#341—21no—
18C11×#338C2211yescharacteristic
19C2×C11×Q16—21no—
20C2×C11×Q16D412yes—
21C2×C11×M16—21no—
22C2×C11×M16—21no—
23C2×C11×M16C2311yescharacteristic
24C22×C8×C11D411yescharacteristic
25C11×C4⋊Q8—21no—
26C11×#126—42no—
27C11×#125—21no—
28C11×#125—42no—
29C11×C22⋊Q8—22no—
30C4×Q8×C11—22no—
31C11×#117D411yescharacteristic
32C11×M32—22no—
33C11×#108—22no—
34C11×#107—21no—
35C11×#106D412yes—
36C11×C4⋊C8—22no—
37C11×#103—22no—
38C11×#103—22no—
39#12305C1111yesmaximal, characteristic, direct product factor, Sylow
40C2×Q8×C11—22no—
41C22×C4×C11C2×D411yescharacteristic
42C11×Q16—42no—
43C11×Q16—81no—
44C11×M16—41no—
45C11×M16—41no—
46C11×M16—41no—
47C11×M16—41no—
48C11×M16—41no—
49C2×C8×C11—21no—
50C2×C8×C11—41no—
51C2×C8×C11—41no—
52C2×C8×C11—41no—
53C2×C8×C11C2×D412yes—
54C11×C4⋊C4—21no—
55C11×C4⋊C4—22no—
56C11×C4⋊C4—42no—
57C11×C4⋊C4—42no—
58C11×C4⋊C4—42no—
59C11×C4⋊C4—42no—
60C11×C22⋊C4—42no—
61C11×C22⋊C4SD1612yes—
62C42×C11—21no—
63C42×C11—42no—
64C11×C16—42no—
65#3261C2×C1111yescharacteristic
66#2239C2×C1112yes—
67#2103C2×C1111yescharacteristic
68#1342C2×C1112yes—
69#1328C2×C1111yescharacteristic
70C23×C11C2×SD1611yescharacteristic
71Q8×C11—42no—
72Q8×C11—42no—
73C2×C4×C11—21no—
74C2×C4×C11—21no—
75C2×C4×C11—22no—
76C2×C4×C11—42no—
77C2×C4×C11—42no—
78C2×C4×C11#12011yescharacteristic
79C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
80C8×C11—22no—
81C8×C11—41no—
82C8×C11—81no—
83C8×C11—81no—
84#541—21no—
85#479—22no—
86#470C22×C1112yes—
87#467—21no—
88#462—22no—
89#430C22×C1111yescharacteristic
90#424C22×C1111yescharacteristic
91#365—22no—
92#362—22no—
93#349C22×C1112yes—
94#344—21no—
95#341—21no—
96#338C22×C1111yescharacteristic
97C22×C11—21no—
98C22×C11—41no—
99C22×C11#45011yescharacteristic
100C4×C11—21no—
101C4×C11—42no—
102C4×C11—82no—
103C4×C11—82no—
104C4×C11#45411yescharacteristic
105C4×C11#45811yescharacteristic
106C2×Q16—21no—
107C2×Q16D4×C1112yes—
108C2×M16—21no—
109C2×M16—21no—
110C2×M16C23×C1111yescharacteristic
111C22×C8D4×C1111yescharacteristic
112C4⋊Q8—21no—
113#126—42no—
114#125—21no—
115#125—42no—
116C22⋊Q8—22no—
117C4×Q8—22no—
118#117D4×C1111yescharacteristic
119M32—22no—
120#108—22no—
121#107—21no—
122#106D4×C1112yes—
123C4⋊C8—22no—
124#103—22no—
125#103—22no—
126C2×C11—21no—
127C2×C11—41no—
128C2×C11#161611yescharacteristic
129C2×Q8—22no—
130C22×C4C2×D4×C1111yescharacteristic
131Q16—42no—
132Q16—81no—
133M16—41no—
134M16—41no—
135M16—41no—
136M16—41no—
137M16—41no—
138C2×C8—21no—
139C2×C8—41no—
140C2×C8—41no—
141C2×C8—41no—
142C2×C8C2×D4×C1112yes—
143C4⋊C4—21no—
144C4⋊C4—22no—
145C4⋊C4—42no—
146C4⋊C4—42no—
147C4⋊C4—42no—
148C4⋊C4—42no—
149C22⋊C4—42no—
150C22⋊C4C11×SD1612yes—
151C42—21no—
152C42—42no—
153C16—42no—
154C11#1230511yescharacteristic, direct product factor, Sylow
155C23C2×C11×SD1611yescharacteristic
156Q8—42no—
157Q8—42no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4C11×#12011yescharacteristic
164C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
165C8—22no—
166C8—41no—
167C8—81no—
168C8—81no—
169C22—21no—
170C22—41no—
171C22C11×#45011yescharacteristic
172C4—21no—
173C4—42no—
174C4—82no—
175C4—82no—
176C4C11×#45411yescharacteristic
177C4C11×#45811yescharacteristic
178C2—21no—
179C2—41no—
180C2C11×#161611yescharacteristic
subgroupG/H
center, socleC2×C11#1616
commutator, Frattini, cosocleC2×M16C23×C11
prime radicalC23×C11C2×SD16
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
39. #12305C11direct (N × H)
154. C11#12305direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32612
C11×#22392
C11×#21032
C11×#13422
C11×#13282
#1230511