Finite Group Databasebeta

← C11×#10259 #14587452

Subgroups — C11×#10259 #14587452

Order 2816.

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

normal subgroups only

This group has 474 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
1C11×#3249C211yesmaximal, characteristic
2C11×#3078C212yesmaximal
3C11×#1984C211yesmaximal, characteristic
4C11×#1493C212yesmaximal
5C11×#1292C211yesmaximal, characteristic
6C11×#533C2212yes—
7C2×C4×Q8×C11C2211yescharacteristic
8C11×#479—24no—
9C11×#477—22no—
10C11×#477—22no—
11C11×#475—22no—
12C11×#467—22no—
13C11×#462—22no—
14C11×#428—22no—
15C11×#423C2212yes—
16C2×C11×C4⋊C8C2211yescharacteristic
17C11×#419—22no—
18C2×C4×C8×C11C2211yescharacteristic
19C11×#336—22no—
20C11×Q8⋊C8—24no—
21C22×Q8×C11D411yescharacteristic
22C2×C11×Q16—22no—
23C2×C11×M16—22no—
24C22×C8×C11—21no—
25C22×C8×C11D412yes—
26C11×C4⋊Q8D412yes—
27C11×C4⋊Q8D412yes—
28C11×#125—22no—
29C11×C22⋊Q8—22no—
30C11×C22⋊Q8—22no—
31C4×Q8×C11—22no—
32C4×Q8×C11—22no—
33C4×Q8×C11—22no—
34C4×Q8×C11—22no—
35C11×#117—22no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4D411yescharacteristic
38C2×C42×C11—21no—
39C2×C42×C11C2311yescharacteristic
40C11×#107—24no—
41C11×#107—22no—
42C11×#106—24no—
43C11×C4⋊C8—22no—
44C11×C4⋊C8—22no—
45C11×C4⋊C8D414yes—
46C11×#103—24no—
47C11×#103—24no—
48C11×#103—24no—
49C4×C8×C11—22no—
50#10259C1111yesmaximal, characteristic, direct product factor, Sylow
51C2×Q8×C11—21no—
52C2×Q8×C11—22no—
53C2×Q8×C11—22no—
54C2×Q8×C11—22no—
55C2×Q8×C11—22no—
56C2×Q8×C11Q1612yescomplemented
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11C2×D411yescharacteristic
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11#4111yescharacteristic
62C11×Q16—82no—
63C11×M16—42no—
64C11×M16—42no—
65C2×C8×C11—22no—
66C2×C8×C11—22no—
67C2×C8×C11—24no—
68C2×C8×C11—42no—
69C2×C8×C11—41no—
70C2×C8×C11—41no—
71C11×C4⋊C4—22no—
72C11×C4⋊C4—22no—
73C11×C4⋊C4—22no—
74C11×C4⋊C4—22no—
75C11×C4⋊C4—22no—
76C11×C4⋊C4—42no—
77C11×C4⋊C4—42no—
78C11×C4⋊C4—42no—
79C11×C22⋊C4—42no—
80C42×C11—41no—
81C42×C11—42no—
82C42×C11—41no—
83C42×C11C2×D412yes—
84C42×C11C2×D412yes—
85#3249C2×C1111yescharacteristic
86#3078C2×C1112yes—
87#1984C2×C1111yescharacteristic
88#1493C2×C1112yes—
89#1292C2×C1111yescharacteristic
90C23×C11#12111yescharacteristic
91Q8×C11—24no—
92Q8×C11—44no—
93Q8×C11—42no—
94Q8×C11—42no—
95Q8×C11—42no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—22no—
99C2×C4×C11—41no—
100C2×C4×C11—41no—
101C2×C4×C11—41no—
102C2×C4×C11—42no—
103C2×C4×C11—41no—
104C2×C4×C11—42no—
105C2×C4×C11—42no—
106C2×C4×C11#12012yes—
107C2×C4×C11#12011yescharacteristic
108C2×C4×C11#12112yes—
109C2×C4×C11#12711yescharacteristic
110C2×C4×C11C2×Q1611yescharacteristic
111C2×C4×C11#13511yescharacteristic
112C2×C4×C11#13712yes—
113C8×C11—42no—
114C8×C11—44no—
115C8×C11—42no—
116#533C22×C1112yes—
117C2×C4×Q8C22×C1111yescharacteristic
118#479—24no—
119#477—22no—
120#477—22no—
121#475—22no—
122#467—22no—
123#462—22no—
124#428—22no—
125#423C22×C1112yes—
126C2×C4⋊C8C22×C1111yescharacteristic
127#419—22no—
128C2×C4×C8C22×C1111yescharacteristic
129#336—22no—
130Q8⋊C8—24no—
131C22×C11—21no—
132C22×C11—21no—
133C22×C11#39211yescharacteristic
134C22×C11#46711yescharacteristic
135C22×C11#47011yescharacteristic
136C4×C11—21no—
137C4×C11—22no—
138C4×C11—42no—
139C4×C11—82no—
140C4×C11—81no—
141C4×C11—82no—
142C4×C11#45112yes—
143C4×C11#45212yes—
144C4×C11#45511yescharacteristic
145C4×C11#45611yescharacteristic
146C22×Q8D4×C1111yescharacteristic
147C2×Q16—22no—
148C2×M16—22no—
149C22×C8—21no—
150C22×C8D4×C1112yes—
151C4⋊Q8D4×C1112yes—
152C4⋊Q8D4×C1112yes—
153#125—22no—
154C22⋊Q8—22no—
155C22⋊Q8—22no—
156C4×Q8—22no—
157C4×Q8—22no—
158C4×Q8—22no—
159C4×Q8—22no—
160#117—22no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4D4×C1111yescharacteristic
163C2×C42—21no—
164C2×C42C23×C1111yescharacteristic
165#107—24no—
166#107—22no—
167#106—24no—
168C4⋊C8—22no—
169C4⋊C8—22no—
170C4⋊C8D4×C1114yes—
171#103—24no—
172#103—24no—
173#103—24no—
174C4×C8—22no—
175C2×C11—21no—
176C2×C11—21no—
177C2×C11#200111yescharacteristic
178C2×C11#200711yescharacteristic
179C2×C11#201711yescharacteristic
180C2×Q8—21no—
181C2×Q8—22no—
182C2×Q8—22no—
183C2×Q8—22no—
184C2×Q8—22no—
185C2×Q8C11×Q1612yescomplemented
186C22×C4—21no—
187C22×C4—21no—
188C22×C4C2×D4×C1111yescharacteristic
189C22×C4C2×D4×C1111yescharacteristic
190C22×C4C11×#4111yescharacteristic
191Q16—82no—
192M16—42no—
193M16—42no—
194C2×C8—22no—
195C2×C8—22no—
196C2×C8—24no—
197C2×C8—41no—
198C2×C8—41no—
199C2×C8—42no—
200C4⋊C4—22no—
201C4⋊C4—22no—
202C4⋊C4—22no—
203C4⋊C4—22no—
204C4⋊C4—22no—
205C4⋊C4—42no—
206C4⋊C4—42no—
207C4⋊C4—42no—
208C22⋊C4—42no—
209C42—41no—
210C42—42no—
211C42—41no—
212C42C2×D4×C1112yes—
213C42C2×D4×C1112yes—
214C11#1025911yescharacteristic, direct product factor, Sylow
215C23C11×#12111yescharacteristic
216Q8—24no—
217Q8—44no—
218Q8—42no—
219Q8—42no—
220Q8—42no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—41no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4C11×#12012yes—
232C2×C4C11×#12011yescharacteristic
233C2×C4C11×#12112yes—
234C2×C4C11×#12711yescharacteristic
235C2×C4C2×C11×Q1611yescharacteristic
236C2×C4C11×#13511yescharacteristic
237C2×C4C11×#13712yes—
238C8—42no—
239C8—44no—
240C8—42no—
241C22—21no—
242C22—21no—
243C22C11×#39211yescharacteristic
244C22C11×#46711yescharacteristic
245C22C11×#47011yescharacteristic
246C4—21no—
247C4—22no—
248C4—42no—
249C4—82no—
250C4—81no—
251C4—82no—
252C4C11×#45112yes—
253C4C11×#45212yes—
254C4C11×#45511yescharacteristic
255C4C11×#45611yescharacteristic
256C2—21no—
257C2—21no—
258C2C11×#200111yescharacteristic
259C2C11×#200711yescharacteristic
260C2C11×#201711yescharacteristic
subgroupG/H
center, socleC22×C11#392
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
50. #10259C11direct (N × H)
56. C2×Q8×C11Q16semidirect
185. C2×Q8C11×Q16semidirect
214. C11#10259direct (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×#30782
C11×#19842
C11×#14932
C11×#12922
#1025911