Finite Group Databasebeta

← C11×#10516 #14587709

Subgroups — C11×#10516 #14587709

Order 2816.

364 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 94 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×#3249C211yesmaximal, characteristic
2C11×#1843C211yesmaximal, characteristic
3C11×#1552C212yesmaximal
4C11×#1506C212yesmaximal
5C11×#1290C211yesmaximal, characteristic
6C11×#533C2212yes—
7C11×#477—22no—
8C11×#467—22no—
9C11×#462—22no—
10C11×#432C2212yes—
11C2×C11×C4⋊C8—22no—
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14C11×#376C2211yescharacteristic
15C11×#332—22no—
16C11×#332—22no—
17C11×#328—24no—
18C2×C11×Q16—22no—
19C22×C8×C11—21no—
20C22×C8×C11D412yes—
21C11×C4⋊Q8D412yes—
22C11×C4⋊Q8D412yes—
23C11×#125—22no—
24C11×C22⋊Q8—22no—
25C11×C22⋊Q8—22no—
26C4×Q8×C11—22no—
27C4×Q8×C11—22no—
28C11×#117—22no—
29C2×C42×C11—21no—
30C2×C42×C11C2311yescharacteristic
31C11×#107—22no—
32C11×C4⋊C8—22no—
33C11×C4⋊C8—22no—
34C11×C4⋊C8—22no—
35C11×C4⋊C8—44no—
36C11×#103—24no—
37C11×C22⋊C8—22no—
38C11×#97—22no—
39C11×#95—21no—
40C11×#95D412yes—
41#10516C1111yesmaximal, characteristic, direct product factor, Sylow
42C2×Q8×C11—22no—
43C2×Q8×C11—22no—
44C22×C4×C11—22no—
45C22×C4×C11C2×D411yescharacteristic
46C22×C4×C11C2×D411yescharacteristic
47C22×C4×C11#4111yescharacteristic
48C11×Q16—82no—
49C2×C8×C11—22no—
50C2×C8×C11—42no—
51C2×C8×C11—42no—
52C2×C8×C11—41no—
53C2×C8×C11—42no—
54C11×C4⋊C4—22no—
55C11×C4⋊C4—22no—
56C11×C4⋊C4—22no—
57C11×C4⋊C4—22no—
58C11×C4⋊C4—42no—
59C11×C4⋊C4—42no—
60C11×C22⋊C4—42no—
61C42×C11—22no—
62C42×C11—22no—
63C42×C11—42no—
64C42×C11C2×D412yes—
65C42×C11#4112yes—
66#3249C2×C1111yescharacteristic
67#1843C2×C1111yescharacteristic
68#1552C2×C1112yes—
69#1506C2×C1112yes—
70#1290C2×C1111yescharacteristic
71C23×C11#12111yescharacteristic
72Q8×C11—42no—
73Q8×C11—42no—
74Q8×C11—82no—
75C2×C4×C11—22no—
76C2×C4×C11—21no—
77C2×C4×C11—21no—
78C2×C4×C11—24no—
79C2×C4×C11—41no—
80C2×C4×C11—42no—
81C2×C4×C11—42no—
82C2×C4×C11—42no—
83C2×C4×C11—42no—
84C2×C4×C11#12011yescharacteristic
85C2×C4×C11#12112yes—
86C2×C4×C11#12312yes—
87C2×C4×C11#12411yescharacteristic
88C8×C11—42no—
89C8×C11—82no—
90C8×C11—81no—
91#533C22×C1112yes—
92#477—22no—
93#467—22no—
94#462—22no—
95#432C22×C1112yes—
96C2×C4⋊C8—22no—
97C2×C4⋊C8C22×C1111yescharacteristic
98C2×C4⋊C8C22×C1111yescharacteristic
99#376C22×C1111yescharacteristic
100#332—22no—
101#332—22no—
102#328—24no—
103C22×C11—21no—
104C22×C11—21no—
105C22×C11#39411yescharacteristic
106C22×C11#47312yes—
107C4×C11—22no—
108C4×C11—21no—
109C4×C11—22no—
110C4×C11—44no—
111C4×C11—82no—
112C4×C11—82no—
113C4×C11#45311yescharacteristic
114C4×C11#45611yescharacteristic
115C2×Q16—22no—
116C22×C8—21no—
117C22×C8D4×C1112yes—
118C4⋊Q8D4×C1112yes—
119C4⋊Q8D4×C1112yes—
120#125—22no—
121C22⋊Q8—22no—
122C22⋊Q8—22no—
123C4×Q8—22no—
124C4×Q8—22no—
125#117—22no—
126C2×C42—21no—
127C2×C42C23×C1111yescharacteristic
128#107—22no—
129C4⋊C8—22no—
130C4⋊C8—22no—
131C4⋊C8—22no—
132C4⋊C8—44no—
133#103—24no—
134C22⋊C8—22no—
135#97—22no—
136#95—21no—
137#95D4×C1112yes—
138C2×C11—22no—
139C2×C11#203911yescharacteristic
140C2×C11#204711yescharacteristic
141C2×C11#205311yescharacteristic
142C2×Q8—22no—
143C2×Q8—22no—
144C22×C4—22no—
145C22×C4C2×D4×C1111yescharacteristic
146C22×C4C2×D4×C1111yescharacteristic
147C22×C4C11×#4111yescharacteristic
148Q16—82no—
149C2×C8—22no—
150C2×C8—42no—
151C2×C8—42no—
152C2×C8—41no—
153C2×C8—42no—
154C4⋊C4—22no—
155C4⋊C4—22no—
156C4⋊C4—22no—
157C4⋊C4—22no—
158C4⋊C4—42no—
159C4⋊C4—42no—
160C22⋊C4—42no—
161C42—22no—
162C42—22no—
163C42—42no—
164C42C2×D4×C1112yes—
165C42C11×#4112yes—
166C11#1051611yescharacteristic, direct product factor, Sylow
167C23C11×#12111yescharacteristic
168Q8—42no—
169Q8—42no—
170Q8—82no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—24no—
175C2×C4—41no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4C11×#12011yescharacteristic
181C2×C4C11×#12112yes—
182C2×C4C11×#12312yes—
183C2×C4C11×#12411yescharacteristic
184C8—42no—
185C8—82no—
186C8—81no—
187C22—21no—
188C22—21no—
189C22C11×#39411yescharacteristic
190C22C11×#47312yes—
191C4—21no—
192C4—22no—
193C4—22no—
194C4—44no—
195C4—82no—
196C4—82no—
197C4C11×#45311yescharacteristic
198C4C11×#45611yescharacteristic
199C2—22no—
200C2C11×#203911yescharacteristic
201C2C11×#204711yescharacteristic
202C2C11×#205311yescharacteristic
subgroupG/H
center, socleC22×C11#394
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC23×C11#121
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
41. #10516C11direct (N × H)
166. C11#10516direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32492
C11×#18432
C11×#15522
C11×#15062
C11×#12902
#1051611