Finite Group Databasebeta

← C11×#10363 #14587556

Subgroups — C11×#10363 #14587556

Order 2816.

416 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 114 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×#2862C211yesmaximal, characteristic
2C11×#1994C211yesmaximal, characteristic
3C11×#1518C212yesmaximal
4C11×#1286C212yesmaximal
5C11×#1276C211yesmaximal, characteristic
6C11×#533C2211yescharacteristic
7C2×C11×C4⋊Q8—21no—
8C11×#431C2212yes—
9C11×#423C2211yescharacteristic
10C11×#391—24no—
11C11×#382—21no—
12C11×#382C2212yes—
13C43×C11C2211yescharacteristic
14C11×#339—21no—
15C11×#339—21no—
16C11×#328—24no—
17C22×Q8×C11—22no—
18C2×C11×M16—21no—
19C11×C4⋊Q8—42no—
20C11×C4⋊Q8—42no—
21C11×C4⋊Q8Q812yescomplemented
22C11×#125—21no—
23C11×C22⋊Q8—22no—
24C4×Q8×C11—22no—
25C11×#117—21no—
26C2×C11×C4⋊C4—22no—
27C2×C11×C4⋊C4—22no—
28C2×C42×C11—22no—
29C2×C42×C11D411yescharacteristic
30C2×C42×C11D411yescharacteristic
31C2×C42×C11C2311yescharacteristic
32C11×C4⋊C8—22no—
33C11×C4⋊C8—22no—
34C11×C22⋊C8—22no—
35C4×C8×C11—22no—
36C11×#95—24no—
37C11×#95—22no—
38C11×#95D414yes—
39#10363C1111yesmaximal, characteristic, direct product factor, Sylow
40C2×Q8×C11—22no—
41C2×Q8×C11—44no—
42C2×Q8×C11—48no—
43C22×C4×C11—21no—
44C22×C4×C11—21no—
45C22×C4×C11—24no—
46C22×C4×C11C2×D412yes—
47C22×C4×C11C2×D411yescharacteristic
48C11×M16—41no—
49C11×M16—41no—
50C2×C8×C11—42no—
51C2×C8×C11—41no—
52C11×C4⋊C4—22no—
53C11×C4⋊C4—22no—
54C11×C4⋊C4—44no—
55C11×C4⋊C4—42no—
56C11×C4⋊C4—42no—
57C11×C4⋊C4—42no—
58C11×C22⋊C4—41no—
59C42×C11—21no—
60C42×C11—21no—
61C42×C11—44no—
62C42×C11—41no—
63C42×C11SD1612yes—
64C42×C11Q1612yes—
65C42×C11C2×Q811yescharacteristic
66C42×C11#4111yescharacteristic
67C42×C11#4112yes—
68#2862C2×C1111yescharacteristic
69#1994C2×C1111yescharacteristic
70#1518C2×C1112yes—
71#1286C2×C1112yes—
72#1276C2×C1111yescharacteristic
73C23×C11#12011yescharacteristic
74Q8×C11—82no—
75Q8×C11—88no—
76C2×C4×C11—24no—
77C2×C4×C11—22no—
78C2×C4×C11—22no—
79C2×C4×C11—42no—
80C2×C4×C11—42no—
81C2×C4×C11—48no—
82C2×C4×C11—42no—
83C2×C4×C11—44no—
84C2×C4×C11C22⋊Q812yes—
85C2×C4×C11C22⋊Q811yescharacteristic
86C2×C4×C11#12412yes—
87C2×C4×C11#12411yescharacteristic
88C2×C4×C11C2×SD1611yescharacteristic
89C2×C4×C11C2×Q1611yescharacteristic
90C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
91C2×C4×C11#13711yescharacteristic
92C8×C11—82no—
93C8×C11—81no—
94#533C22×C1111yescharacteristic
95C2×C4⋊Q8—21no—
96#431C22×C1112yes—
97#423C22×C1111yescharacteristic
98#391—24no—
99#382—21no—
100#382C22×C1112yes—
101C43C22×C1111yescharacteristic
102#339—21no—
103#339—21no—
104#328—24no—
105C22×C11—22no—
106C22×C11#39311yescharacteristic
107C22×C11#45011yescharacteristic
108C22×C11#45111yescharacteristic
109C4×C11—24no—
110C4×C11—22no—
111C4×C11—22no—
112C4×C11—42no—
113C4×C11—84no—
114C4×C11—82no—
115C4×C11#47511yescharacteristic
116C4×C11#47711yescharacteristic
117C4×C11#48711yescharacteristic
118C4×C11#48911yescharacteristic
119C22×Q8—22no—
120C2×M16—21no—
121C4⋊Q8—42no—
122C4⋊Q8—42no—
123C4⋊Q8Q8×C1112yescomplemented
124#125—21no—
125C22⋊Q8—22no—
126C4×Q8—22no—
127#117—21no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—22no—
130C2×C42—22no—
131C2×C42D4×C1111yescharacteristic
132C2×C42D4×C1111yescharacteristic
133C2×C42C23×C1111yescharacteristic
134C4⋊C8—22no—
135C4⋊C8—22no—
136C22⋊C8—22no—
137C4×C8—22no—
138#95—24no—
139#95—22no—
140#95D4×C1114yes—
141C2×C11—21no—
142C2×C11—21no—
143C2×C11#202411yescharacteristic
144C2×C11#203112yes—
145C2×Q8—22no—
146C2×Q8—44no—
147C2×Q8—48no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—24no—
151C22×C4C2×D4×C1112yes—
152C22×C4C2×D4×C1111yescharacteristic
153M16—41no—
154M16—41no—
155C2×C8—42no—
156C2×C8—41no—
157C4⋊C4—22no—
158C4⋊C4—22no—
159C4⋊C4—44no—
160C4⋊C4—42no—
161C4⋊C4—42no—
162C4⋊C4—42no—
163C22⋊C4—41no—
164C42—21no—
165C42—21no—
166C42—44no—
167C42—41no—
168C42C11×SD1612yes—
169C42C11×Q1612yes—
170C42C2×Q8×C1111yescharacteristic
171C42C11×#4111yescharacteristic
172C42C11×#4112yes—
173C11#1036311yescharacteristic, direct product factor, Sylow
174C23C11×#12011yescharacteristic
175Q8—82no—
176Q8—88no—
177C2×C4—24no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—48no—
183C2×C4—42no—
184C2×C4—44no—
185C2×C4C11×C22⋊Q812yes—
186C2×C4C11×C22⋊Q811yescharacteristic
187C2×C4C11×#12412yes—
188C2×C4C11×#12411yescharacteristic
189C2×C4C2×C11×SD1611yescharacteristic
190C2×C4C2×C11×Q1611yescharacteristic
191C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
192C2×C4C11×#13711yescharacteristic
193C8—82no—
194C8—81no—
195C22—22no—
196C22C11×#39311yescharacteristic
197C22C11×#45011yescharacteristic
198C22C11×#45111yescharacteristic
199C4—24no—
200C4—22no—
201C4—22no—
202C4—42no—
203C4—84no—
204C4—82no—
205C4C11×#47511yescharacteristic
206C4C11×#47711yescharacteristic
207C4C11×#48711yescharacteristic
208C4C11×#48911yescharacteristic
209C2—21no—
210C2—21no—
211C2C11×#202411yescharacteristic
212C2C11×#203112yes—
subgroupG/H
center, socleC22×C11#393
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
21. C11×C4⋊Q8Q8semidirect
39. #10363C11direct (N × H)
123. C4⋊Q8Q8×C11semidirect
173. C11#10363direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28622
C11×#19942
C11×#15182
C11×#12862
C11×#12762
#1036311