Finite Group Databasebeta

← C11×#12292 #14589485

Subgroups — C11×#12292 #14589485

Order 2816.

310 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 82 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×#2236C212yesmaximal
3C11×#2087C211yesmaximal, characteristic
4C11×#1348C212yesmaximal
5C11×#1322C211yesmaximal, characteristic
6C11×#533—21no—
7C11×#477—22no—
8C11×#467—21no—
9C11×#467C2212yes—
10C11×#462—22no—
11C2×C11×#107C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C11×#389—21no—
14C11×#366—22no—
15C11×#358—22no—
16C11×C22⋊C16C2212yes—
17C11×#340—21no—
18C11×#340C2211yescharacteristic
19C2×C11×Q16—21no—
20C2×C11×Q16D412yes—
21C22×C8×C11D411yescharacteristic
22C22×C8×C11C2311yescharacteristic
23C11×C4⋊Q8—21no—
24C11×C4⋊Q8—21no—
25C11×#125—41no—
26C11×C22⋊Q8—22no—
27C11×C22⋊Q8—41no—
28C4×Q8×C11—22no—
29C4×Q8×C11—41no—
30C11×#117—41no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—41no—
34C2×C42×C11D411yescharacteristic
35C2×C11×C16—22no—
36C11×#107—21no—
37C11×#107—22no—
38C11×#107D412yes—
39C11×C4⋊C8—22no—
40C11×#103—22no—
41C11×#103—22no—
42C11×#95—41no—
43#12292C1111yesmaximal, characteristic, direct product factor, Sylow
44C2×Q8×C11—22no—
45C2×Q8×C11—41no—
46C22×C4×C11—41no—
47C22×C4×C11—41no—
48C22×C4×C11D811yescharacteristic
49C22×C4×C11D811yescharacteristic
50C22×C4×C11C2×D411yescharacteristic
51C11×Q16—42no—
52C11×Q16—81no—
53C2×C8×C11—21no—
54C2×C8×C11—41no—
55C2×C8×C11—41no—
56C2×C8×C11C2×D412yes—
57C11×C4⋊C4—22no—
58C11×C4⋊C4—22no—
59C11×C4⋊C4—41no—
60C11×C4⋊C4—41no—
61C11×C4⋊C4—41no—
62C11×C4⋊C4—42no—
63C11×C4⋊C4—41no—
64C11×C4⋊C4—42no—
65C11×C4⋊C4—41no—
66C11×C4⋊C4—41no—
67C11×C4⋊C4—82no—
68C11×C22⋊C4—42no—
69C42×C11—21no—
70C42×C11—21no—
71C42×C11—42no—
72C11×C16—42no—
73#3249C2×C1111yescharacteristic
74#2236C2×C1112yes—
75#2087C2×C1111yescharacteristic
76#1348C2×C1112yes—
77#1322C2×C1111yescharacteristic
78C23×C11C2×D811yescharacteristic
79Q8×C11—42no—
80Q8×C11—42no—
81Q8×C11—82no—
82C2×C4×C11—21no—
83C2×C4×C11—21no—
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11—21no—
87C2×C4×C11—41no—
88C2×C4×C11—42no—
89C2×C4×C11—42no—
90C2×C4×C11—42no—
91C2×C4×C11—81no—
92C2×C4×C11—81no—
93C2×C4×C11—81no—
94C2×C4×C11—81no—
95C2×C4×C11—81no—
96C2×C4×C11Q3212yes—
97C2×C4×C11#12011yescharacteristic
98C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
99C8×C11—22no—
100C8×C11—41no—
101#533—21no—
102#477—22no—
103#467—21no—
104#467C22×C1112yes—
105#462—22no—
106C2×#107C22×C1111yescharacteristic
107C2×C4⋊C8C22×C1111yescharacteristic
108#389—21no—
109#366—22no—
110#358—22no—
111C22⋊C16C22×C1112yes—
112#340—21no—
113#340C22×C1111yescharacteristic
114C22×C11—21no—
115C22×C11—21no—
116C22×C11#44711yescharacteristic
117C22×C11C2×Q3211yescharacteristic
118C22×C11#51011yescharacteristic
119C4×C11—21no—
120C4×C11—22no—
121C4×C11—41no—
122C4×C11—82no—
123C4×C11—82no—
124C4×C11—82no—
125C4×C11—161no—
126C4×C11#45611yescharacteristic
127C4×C11#45811yescharacteristic
128C2×Q16—21no—
129C2×Q16D4×C1112yes—
130C22×C8D4×C1111yescharacteristic
131C22×C8C23×C1111yescharacteristic
132C4⋊Q8—21no—
133C4⋊Q8—21no—
134#125—41no—
135C22⋊Q8—22no—
136C22⋊Q8—41no—
137C4×Q8—22no—
138C4×Q8—41no—
139#117—41no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—41no—
143C2×C42D4×C1111yescharacteristic
144C2×C16—22no—
145#107—21no—
146#107—22no—
147#107D4×C1112yes—
148C4⋊C8—22no—
149#103—22no—
150#103—22no—
151#95—41no—
152C2×C11—21no—
153C2×C11—21no—
154C2×C11#161011yescharacteristic
155C2×C11#218811yescharacteristic
156C2×C11#219011yescharacteristic
157C2×Q8—22no—
158C2×Q8—41no—
159C22×C4—41no—
160C22×C4—41no—
161C22×C4C11×D811yescharacteristic
162C22×C4C11×D811yescharacteristic
163C22×C4C2×D4×C1111yescharacteristic
164Q16—42no—
165Q16—81no—
166C2×C8—21no—
167C2×C8—41no—
168C2×C8—41no—
169C2×C8C2×D4×C1112yes—
170C4⋊C4—22no—
171C4⋊C4—22no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—41no—
175C4⋊C4—42no—
176C4⋊C4—41no—
177C4⋊C4—42no—
178C4⋊C4—41no—
179C4⋊C4—41no—
180C4⋊C4—82no—
181C22⋊C4—42no—
182C42—21no—
183C42—21no—
184C42—42no—
185C16—42no—
186C11#1229211yescharacteristic, direct product factor, Sylow
187C23C2×C11×D811yescharacteristic
188Q8—42no—
189Q8—42no—
190Q8—82no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—41no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—81no—
201C2×C4—81no—
202C2×C4—81no—
203C2×C4—81no—
204C2×C4—81no—
205C2×C4C11×Q3212yes—
206C2×C4C11×#12011yescharacteristic
207C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
208C8—22no—
209C8—41no—
210C22—21no—
211C22—21no—
212C22C11×#44711yescharacteristic
213C22C2×C11×Q3211yescharacteristic
214C22C11×#51011yescharacteristic
215C4—21no—
216C4—22no—
217C4—41no—
218C4—82no—
219C4—82no—
220C4—82no—
221C4—161no—
222C4C11×#45611yescharacteristic
223C4C11×#45811yescharacteristic
224C2—21no—
225C2—21no—
226C2C11×#161011yescharacteristic
227C2C11×#218811yescharacteristic
228C2C11×#219011yescharacteristic
subgroupG/H
center, socleC22×C11#447
commutator, Frattini, cosocleC22×C8C23×C11
prime radicalC23×C11C2×D8
LCSG ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C11×C4⋊C8 ◁ G

Complements

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

NH ≅ G/Ntype
43. #12292C11direct (N × H)
186. C11#12292direct (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×#22362
C11×#20872
C11×#13482
C11×#13222
#1229211