Finite Group Databasebeta

← C11×#10301 #14587494

Subgroups — C11×#10301 #14587494

Order 2816.

554 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 106 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×#3254C212yesmaximal, complemented
2C11×#3253C211yesmaximal, characteristic
3C11×#1994C211yesmaximal, characteristic, complemented
4C11×#1962C212yesmaximal, complemented
5C11×#1309C211yesmaximal, characteristic, complemented
6C11×#533C2211yescharacteristic
7C11×#532C2212yes—
8C11×#477—22no—
9C11×#476—22no—
10C11×#474—22no—
11C11×#469—22no—
12C11×#468—24no—
13C11×#461—22no—
14C11×#460—22no—
15C11×#459—22no—
16C11×#423C2212yes—
17C11×#423C2211yescharacteristic
18C2×C11×#104—24no—
19C43×C11C2211yescharacteristic
20C11×#339—22no—
21C2×C11×#41—22no—
22C2×C11×SD16—24no—
23C2×C11×D8—22no—
24C2×C11×M16D412yes—
25C2×C11×M16D414yes—
26C11×C4⋊Q8D412yes—
27C11×C4⋊Q8D412yes—
28C11×#127D412yes—
29C11×#125—21no—
30C11×#124—22no—
31C11×C22⋊Q8—22no—
32C11×#121—22no—
33C11×#121—22no—
34C4×Q8×C11—22no—
35C4×D4×C11—22no—
36C4×D4×C11—22no—
37C11×#117—21no—
38C2×C42×C11—21no—
39C2×C42×C11—22no—
40C2×C42×C11C2311yescharacteristic
41C11×#107—24no—
42C11×#106—22no—
43C11×C4⋊C8—22no—
44C11×C4⋊C8—22no—
45C11×C4⋊C8—22no—
46C11×#104—48no—
47C11×#103—24no—
48C11×#102—24no—
49C11×#102—24no—
50#10301C1111yesmaximal, characteristic, direct product factor, Sylow
51C11×#41—44no—
52C11×#41—44no—
53C2×Q8×C11—22no—
54C2×Q8×C11—22no—
55C2×D4×C11—22no—
56C2×D4×C11—22no—
57C2×D4×C11—22no—
58C2×D4×C11—42no—
59C22×C4×C11—41no—
60C22×C4×C11—42no—
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11C2×D412yes—
63C11×SD16—84no—
64C11×D8—82no—
65C11×M16—44no—
66C11×M16—42no—
67C2×C8×C11—22no—
68C2×C8×C11—24no—
69C11×C4⋊C4—22no—
70C11×C4⋊C4—22no—
71C11×C4⋊C4—22no—
72C11×C4⋊C4—22no—
73C11×C4⋊C4—42no—
74C11×C22⋊C4—41no—
75C11×C22⋊C4—42no—
76C11×C22⋊C4—42no—
77C42×C11—24no—
78C42×C11—22no—
79C42×C11—42no—
80C42×C11—41no—
81C42×C11—41no—
82C42×C11C2×D411yescharacteristic
83C42×C11C2×D412yes—
84C42×C11#4111yescharacteristic
85#3254C2×C1112yescomplemented
86#3253C2×C1111yescharacteristic
87#1994C2×C1111yescharacteristic, complemented
88#1962C2×C1112yescomplemented
89#1309C2×C1111yescharacteristic, complemented
90C23×C11—42no—
91C23×C11#12711yescharacteristic
92Q8×C11—44no—
93Q8×C11—42no—
94Q8×C11—42no—
95D4×C11—44no—
96D4×C11—42no—
97D4×C11—42no—
98D4×C11—42no—
99D4×C11—42no—
100D4×C11—84no—
101C2×C4×C11—22no—
102C2×C4×C11—22no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—44no—
106C2×C4×C11—42no—
107C2×C4×C11—42no—
108C2×C4×C11—42no—
109C2×C4×C11—82no—
110C2×C4×C11—82no—
111C2×C4×C11#12012yes—
112C2×C4×C11#12011yescharacteristic
113C2×C4×C11#12111yescharacteristic
114C2×C4×C11#12112yes—
115C8×C11—44no—
116C8×C11—42no—
117#533C22×C1111yescharacteristic
118#532C22×C1112yes—
119#477—22no—
120#476—22no—
121#474—22no—
122#469—22no—
123#468—24no—
124#461—22no—
125#460—22no—
126#459—22no—
127#423C22×C1112yes—
128#423C22×C1111yescharacteristic
129C2×#104—24no—
130C43C22×C1111yescharacteristic
131#339—22no—
132C22×C11—22no—
133C22×C11—21no—
134C22×C11—82no—
135C22×C11—82no—
136C22×C11—82no—
137C22×C11#39211yescharacteristic
138C4×C11—22no—
139C4×C11—21no—
140C4×C11—44no—
141C4×C11—82no—
142C4×C11—82no—
143C4×C11#45312yes—
144C4×C11#45412yes—
145C4×C11#45511yescharacteristic
146C4×C11#45611yescharacteristic
147C2×#41—22no—
148C2×SD16—24no—
149C2×D8—22no—
150C2×M16D4×C1112yes—
151C2×M16D4×C1114yes—
152C4⋊Q8D4×C1112yes—
153C4⋊Q8D4×C1112yes—
154#127D4×C1112yes—
155#125—21no—
156#124—22no—
157C22⋊Q8—22no—
158#121—22no—
159#121—22no—
160C4×Q8—22no—
161C4×D4—22no—
162C4×D4—22no—
163#117—21no—
164C2×C42—21no—
165C2×C42—22no—
166C2×C42C23×C1111yescharacteristic
167#107—24no—
168#106—22no—
169C4⋊C8—22no—
170C4⋊C8—22no—
171C4⋊C8—22no—
172#104—48no—
173#103—24no—
174#102—24no—
175#102—24no—
176C2×C11—41no—
177C2×C11—162no—
178C2×C11#200612yes—
179C2×C11#200711yescharacteristic
180#41—44no—
181#41—44no—
182C2×Q8—22no—
183C2×Q8—22no—
184C2×D4—22no—
185C2×D4—22no—
186C2×D4—22no—
187C2×D4—42no—
188C22×C4—41no—
189C22×C4—42no—
190C22×C4C2×D4×C1111yescharacteristic
191C22×C4C2×D4×C1112yes—
192SD16—84no—
193D8—82no—
194M16—44no—
195M16—42no—
196C2×C8—22no—
197C2×C8—24no—
198C4⋊C4—22no—
199C4⋊C4—22no—
200C4⋊C4—22no—
201C4⋊C4—22no—
202C4⋊C4—42no—
203C22⋊C4—41no—
204C22⋊C4—42no—
205C22⋊C4—42no—
206C42—24no—
207C42—22no—
208C42—42no—
209C42—41no—
210C42—41no—
211C42C2×D4×C1111yescharacteristic
212C42C2×D4×C1112yes—
213C42C11×#4111yescharacteristic
214C11#1030111yescharacteristic, direct product factor, Sylow
215C23—42no—
216C23C11×#12711yescharacteristic
217Q8—44no—
218Q8—42no—
219Q8—42no—
220D4—44no—
221D4—42no—
222D4—42no—
223D4—42no—
224D4—42no—
225D4—84no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—44no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—82no—
235C2×C4—82no—
236C2×C4C11×#12012yes—
237C2×C4C11×#12011yescharacteristic
238C2×C4C11×#12111yescharacteristic
239C2×C4C11×#12112yes—
240C8—44no—
241C8—42no—
242C22—22no—
243C22—21no—
244C22—82no—
245C22—82no—
246C22—82no—
247C22C11×#39211yescharacteristic
248C4—22no—
249C4—21no—
250C4—44no—
251C4—82no—
252C4—82no—
253C4C11×#45312yes—
254C4C11×#45412yes—
255C4C11×#45511yescharacteristic
256C4C11×#45611yescharacteristic
257C2—41no—
258C2—162no—
259C2C11×#200612yes—
260C2C11×#200711yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC11×#3253C2
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
1. C11×#3254C2semidirect
3. C11×#1994C2semidirect
4. C11×#1962C2semidirect
5. C11×#1309C2semidirect
50. #10301C11direct (N × H)
85. #3254C2×C11semidirect
87. #1994C2×C11semidirect
88. #1962C2×C11semidirect
89. #1309C2×C11semidirect
214. C11#10301direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32542
C11×#32532
C11×#19942
C11×#19622
C11×#13092
#1030111