Finite Group Databasebeta

← C11×#10297 #14587490

Subgroups — C11×#10297 #14587490

Order 2816.

528 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 130 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×#3209C212yesmaximal
2C11×#2862C211yesmaximal, characteristic
3C11×#1994C211yesmaximal, characteristic
4C11×#1548C212yesmaximal
5C11×#1276C211yesmaximal, characteristic
6C11×#533C2211yescharacteristic
7C2×C11×C4⋊Q8C2212yes—
8C11×#494—22no—
9C11×#487—22no—
10C11×#462—24no—
11C11×#451—24no—
12C11×#431C2212yes—
13C11×#423C2211yescharacteristic
14C11×#391—24no—
15C11×#382—22no—
16C43×C11C2211yescharacteristic
17C11×#339—22no—
18C11×#333—24no—
19C22×Q8×C11D414yes—
20C2×C11×Q16—28no—
21C2×C11×M16—21no—
22C11×C4⋊Q8—22no—
23C11×C4⋊Q8—22no—
24C11×C4⋊Q8—22no—
25C11×C4⋊Q8—22no—
26C11×C4⋊Q8D412yes—
27C11×#125—21no—
28C11×C22⋊Q8—22no—
29C4×Q8×C11—22no—
30C11×#117—21no—
31C2×C11×C4⋊C4—22no—
32C2×C11×C4⋊C4—22no—
33C2×C42×C11—22no—
34C2×C42×C11D412yes—
35C2×C42×C11C2311yescharacteristic
36C11×C4⋊C8—22no—
37C11×C4⋊C8D414yes—
38C11×#103—28no—
39C11×C22⋊C8—22no—
40C4×C8×C11—22no—
41C11×#95—28no—
42#10297C1111yesmaximal, characteristic, direct product factor, Sylow
43C2×Q8×C11—24no—
44C2×Q8×C11—22no—
45C2×Q8×C11—24no—
46C2×Q8×C11—48no—
47C22×C4×C11—22no—
48C22×C4×C11—24no—
49C22×C4×C11C2×D412yes—
50C22×C4×C11C2×D411yescharacteristic
51C11×Q16—88no—
52C11×M16—42no—
53C2×C8×C11—24no—
54C2×C8×C11—41no—
55C11×C4⋊C4—22no—
56C11×C4⋊C4—22no—
57C11×C4⋊C4—42no—
58C11×C4⋊C4—42no—
59C11×C4⋊C4—42no—
60C11×C4⋊C4—42no—
61C11×C4⋊C4—42no—
62C11×C22⋊C4—41no—
63C42×C11—22no—
64C42×C11—44no—
65C42×C11—41no—
66C42×C11Q1614yescomplemented
67C42×C11C2×D411yescharacteristic
68C42×C11C2×D412yes—
69C42×C11#4111yescharacteristic
70#3209C2×C1112yes—
71#2862C2×C1111yescharacteristic
72#1994C2×C1111yescharacteristic
73#1548C2×C1112yes—
74#1276C2×C1111yescharacteristic
75C23×C11#12011yescharacteristic
76Q8×C11—44no—
77Q8×C11—48no—
78Q8×C11—84no—
79C2×C4×C11—24no—
80C2×C4×C11—24no—
81C2×C4×C11—44no—
82C2×C4×C11—48no—
83C2×C4×C11—42no—
84C2×C4×C11—44no—
85C2×C4×C11#12012yes—
86C2×C4×C11#12112yes—
87C2×C4×C11#12111yescharacteristic
88C2×C4×C11#12711yescharacteristic
89C2×C4×C11C2×Q1612yes—
90C2×C4×C11#13712yes—
91C8×C11—44no—
92C8×C11—81no—
93#533C22×C1111yescharacteristic
94C2×C4⋊Q8C22×C1112yes—
95#494—22no—
96#487—22no—
97#462—24no—
98#451—24no—
99#431C22×C1112yes—
100#423C22×C1111yescharacteristic
101#391—24no—
102#382—22no—
103C43C22×C1111yescharacteristic
104#339—22no—
105#333—24no—
106C22×C11—22no—
107C22×C11#39211yescharacteristic
108C22×C11#45112yes—
109C4×C11—22no—
110C4×C11—44no—
111C4×C11—84no—
112C4×C11—82no—
113C4×C11#45514yes—
114C4×C11#46212yes—
115C4×C11#49411yescharacteristic
116C4×C11#49711yescharacteristic
117C22×Q8D4×C1114yes—
118C2×Q16—28no—
119C2×M16—21no—
120C4⋊Q8—22no—
121C4⋊Q8—22no—
122C4⋊Q8—22no—
123C4⋊Q8—22no—
124C4⋊Q8D4×C1112yes—
125#125—21no—
126C22⋊Q8—22no—
127C4×Q8—22no—
128#117—21no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—22no—
131C2×C42—22no—
132C2×C42D4×C1112yes—
133C2×C42C23×C1111yescharacteristic
134C4⋊C8—22no—
135C4⋊C8D4×C1114yes—
136#103—28no—
137C22⋊C8—22no—
138C4×C8—22no—
139#95—28no—
140C2×C11—22no—
141C2×C11#200412yes—
142C2×C11#201611yescharacteristic
143C2×Q8—24no—
144C2×Q8—22no—
145C2×Q8—24no—
146C2×Q8—48no—
147C22×C4—22no—
148C22×C4—24no—
149C22×C4C2×D4×C1112yes—
150C22×C4C2×D4×C1111yescharacteristic
151Q16—88no—
152M16—42no—
153C2×C8—24no—
154C2×C8—41no—
155C4⋊C4—22no—
156C4⋊C4—22no—
157C4⋊C4—42no—
158C4⋊C4—42no—
159C4⋊C4—42no—
160C4⋊C4—42no—
161C4⋊C4—42no—
162C22⋊C4—41no—
163C42—22no—
164C42—44no—
165C42—41no—
166C42C11×Q1614yescomplemented
167C42C2×D4×C1111yescharacteristic
168C42C2×D4×C1112yes—
169C42C11×#4111yescharacteristic
170C11#1029711yescharacteristic, direct product factor, Sylow
171C23C11×#12011yescharacteristic
172Q8—44no—
173Q8—48no—
174Q8—84no—
175C2×C4—24no—
176C2×C4—24no—
177C2×C4—44no—
178C2×C4—48no—
179C2×C4—42no—
180C2×C4—44no—
181C2×C4C11×#12012yes—
182C2×C4C11×#12112yes—
183C2×C4C11×#12111yescharacteristic
184C2×C4C11×#12711yescharacteristic
185C2×C4C2×C11×Q1612yes—
186C2×C4C11×#13712yes—
187C8—44no—
188C8—81no—
189C22—22no—
190C22C11×#39211yescharacteristic
191C22C11×#45112yes—
192C4—22no—
193C4—44no—
194C4—84no—
195C4—82no—
196C4C11×#45514yes—
197C4C11×#46212yes—
198C4C11×#49411yescharacteristic
199C4C11×#49711yescharacteristic
200C2—22no—
201C2C11×#200412yes—
202C2C11×#201611yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC23×C11#120
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
42. #10297C11direct (N × H)
66. C42×C11Q16semidirect
166. C42C11×Q16semidirect
170. C11#10297direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32092
C11×#28622
C11×#19942
C11×#15482
C11×#12762
#1029711