Finite Group Databasebeta

← C11×#13457 #14590650

Subgroups — C11×#13457 #14590650

Order 2816.

356 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 122 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
1C2×C11×#498C211yesmaximal, characteristic
2C2×C11×#365C212yesmaximal
3C11×#1945C211yesmaximal, characteristic
4C11×#1386C212yesmaximal
5C11×#1376C211yesmaximal, characteristic
6C2×C11×C4⋊Q8—21no—
7C2×C11×M32C2212yes—
8C11×#498—24no—
9C2×C11×#108C2211yescharacteristic
10C11×#427C2211yescharacteristic
11C2×C11×#106—21no—
12C2×C11×#106C2212yes—
13C11×#424—21no—
14C2×C4×C8×C11C2211yescharacteristic
15C11×#365—24no—
16C11×#339—21no—
17C22×Q8×C11—41no—
18C2×C11×M16—21no—
19C22×C8×C11D411yescharacteristic
20C22×C8×C11C2311yescharacteristic
21C11×C4⋊Q8—24no—
22C11×C4⋊Q8—42no—
23C11×#117—21no—
24C2×C11×C4⋊C4—22no—
25C2×C11×C4⋊C4—41no—
26C2×C42×C11D411yescharacteristic
27C11×M32—22no—
28C11×M32Q814yescomplemented
29C2×C11×C16—22no—
30C11×#108—22no—
31C11×#107Q812yescomplemented
32C11×#106—24no—
33C11×#106—22no—
34C11×#106—21no—
35C11×#106D414yes—
36C11×C4⋊C8—42no—
37C4×C8×C11—22no—
38#13457C1111yesmaximal, characteristic, direct product factor, Sylow
39C2×Q8×C11—44no—
40C2×Q8×C11—84no—
41C22×C4×C11—21no—
42C22×C4×C11—42no—
43C22×C4×C11C2×D411yescharacteristic
44C11×M16—41no—
45C11×M16—41no—
46C2×C8×C11—21no—
47C2×C8×C11—21no—
48C2×C8×C11—41no—
49C2×C8×C11SD1612yes—
50C2×C8×C11C2×D412yes—
51C2×C8×C11C2×Q811yescharacteristic
52C2×C8×C11C2×Q812yes—
53C2×C8×C11#4111yescharacteristic
54C11×C4⋊C4—24no—
55C11×C4⋊C4—22no—
56C11×C4⋊C4—44no—
57C11×C4⋊C4—42no—
58C11×C22⋊C4—41no—
59C42×C11—21no—
60C42×C11—41no—
61C42×C11SD1612yes—
62C11×C16—24no—
63C2×#498C2×C1111yescharacteristic
64C2×#365C2×C1112yes—
65#1945C2×C1111yescharacteristic
66#1386C2×C1112yes—
67#1376C2×C1111yescharacteristic
68C23×C11AGL(1,ℤ/8)11yescharacteristic
69Q8×C11—88no—
70C2×C4×C11—24no—
71C2×C4×C11—22no—
72C2×C4×C11—44no—
73C2×C4×C11—42no—
74C2×C4×C11—84no—
75C2×C4×C11#12011yescharacteristic
76C2×C4×C11C22⋊Q811yescharacteristic
77C2×C4×C11C4⋊Q811yescharacteristic
78C2×C4×C11C2×SD1611yescharacteristic
79C2×C4×C11C2×SD1611yescharacteristic
80C2×C4×C11#13711yescharacteristic
81C8×C11—22no—
82C8×C11—81no—
83C8×C11C22⋊Q812yes—
84C8×C11C4⋊Q812yes—
85C2×C4⋊Q8—21no—
86C2×M32C22×C1112yes—
87#498—24no—
88C2×#108C22×C1111yescharacteristic
89#427C22×C1111yescharacteristic
90C2×#106—21no—
91C2×#106C22×C1112yes—
92#424—21no—
93C2×C4×C8C22×C1111yescharacteristic
94#365—24no—
95#339—21no—
96C22×C11—22no—
97C22×C11#45011yescharacteristic
98C22×C11#47611yescharacteristic
99C22×C11#50111yescharacteristic
100C4×C11—24no—
101C4×C11—84no—
102C4×C11—82no—
103C4×C11#39511yescharacteristic
104C4×C11#44811yescharacteristic
105C4×C11#47511yescharacteristic
106C4×C11#49811yescharacteristic
107C22×Q8—41no—
108C2×M16—21no—
109C22×C8D4×C1111yescharacteristic
110C22×C8C23×C1111yescharacteristic
111C4⋊Q8—24no—
112C4⋊Q8—42no—
113#117—21no—
114C2×C4⋊C4—22no—
115C2×C4⋊C4—41no—
116C2×C42D4×C1111yescharacteristic
117M32—22no—
118M32Q8×C1114yescomplemented
119C2×C16—22no—
120#108—22no—
121#107Q8×C1112yescomplemented
122#106—24no—
123#106—22no—
124#106—21no—
125#106D4×C1114yes—
126C4⋊C8—42no—
127C4×C8—22no—
128C2×C11—21no—
129C2×C11—21no—
130C2×C11#205811yescharacteristic
131C2×C11#223012yes—
132C2×Q8—44no—
133C2×Q8—84no—
134C22×C4—21no—
135C22×C4—42no—
136C22×C4C2×D4×C1111yescharacteristic
137M16—41no—
138M16—41no—
139C2×C8—21no—
140C2×C8—21no—
141C2×C8—41no—
142C2×C8C11×SD1612yes—
143C2×C8C2×D4×C1112yes—
144C2×C8C2×Q8×C1112yes—
145C2×C8C2×Q8×C1111yescharacteristic
146C2×C8C11×#4111yescharacteristic
147C4⋊C4—24no—
148C4⋊C4—22no—
149C4⋊C4—44no—
150C4⋊C4—42no—
151C22⋊C4—41no—
152C42—21no—
153C42—41no—
154C42C11×SD1612yes—
155C16—24no—
156C11#1345711yescharacteristic, direct product factor, Sylow
157C23C11×AGL(1,ℤ/8)11yescharacteristic
158Q8—88no—
159C2×C4—24no—
160C2×C4—22no—
161C2×C4—44no—
162C2×C4—42no—
163C2×C4—84no—
164C2×C4C11×#12011yescharacteristic
165C2×C4C11×C22⋊Q811yescharacteristic
166C2×C4C11×C4⋊Q811yescharacteristic
167C2×C4C2×C11×SD1611yescharacteristic
168C2×C4C2×C11×SD1611yescharacteristic
169C2×C4C11×#13711yescharacteristic
170C8—22no—
171C8—81no—
172C8C11×C22⋊Q812yes—
173C8C11×C4⋊Q812yes—
174C22—22no—
175C22C11×#45011yescharacteristic
176C22C11×#47611yescharacteristic
177C22C11×#50111yescharacteristic
178C4—24no—
179C4—84no—
180C4—82no—
181C4C11×#39511yescharacteristic
182C4C11×#44811yescharacteristic
183C4C11×#47511yescharacteristic
184C4C11×#49811yescharacteristic
185C2—21no—
186C2—21no—
187C2C11×#205811yescharacteristic
188C2C11×#223012yes—
subgroupG/H
center, socleC22×C11#476
commutator, Frattini, cosocleC22×C8C23×C11
prime radicalC23×C11AGL(1,ℤ/8)
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C4×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
28. C11×M32Q8semidirect
31. C11×#107Q8semidirect
38. #13457C11direct (N × H)
118. M32Q8×C11semidirect
121. #107Q8×C11semidirect
156. C11#13457direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4982
C2×C11×#3652
C11×#19452
C11×#13862
C11×#13762
#1345711