Finite Group Databasebeta

← C11×#7829 #14585022

Subgroups — C11×#7829 #14585022

Order 2816.

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

normal subgroups only

This group has 394 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×#2734C211yesmaximal, characteristic
2C11×#2100C212yesmaximal
3C11×#2095C211yesmaximal, characteristic
4C11×#1272C211yesmaximal, characteristic
5C11×#1271C212yesmaximal
6C2×C11×C4⋊Q8—21no—
7C2×C11×#107—21no—
8C2×C11×#103—21no—
9C11×#398—21no—
10C11×#395—22no—
11C11×#391C2211yescharacteristic
12C11×#389C2212yes—
13C11×#387—22no—
14C11×#384C2211yescharacteristic
15C11×#340—22no—
16C11×#340—22no—
17C11×#336C2211yescharacteristic
18C11×#336C2212yes—
19C22×Q8×C11—21no—
20C22×Q8×C11D411yescharacteristic
21C22×C8×C11—21no—
22C22×C8×C11—22no—
23C11×C4⋊Q8—42no—
24C11×C4⋊Q8—42no—
25C2×C11×C4⋊C4—22no—
26C2×C11×C4⋊C4—22no—
27C2×C11×C4⋊C4—22no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4D412yes—
31C2×C11×C4⋊C4D412yes—
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C42×C11—21no—
34C2×C42×C11C2311yescharacteristic
35C11×#107—42no—
36C11×#103—42no—
37C11×#95—21no—
38C11×#95—22no—
39C11×#95—22no—
40C11×#95—22no—
41#7829C1111yesmaximal, characteristic, direct product factor, Sylow
42C2×Q8×C11—21no—
43C2×Q8×C11—42no—
44C2×Q8×C11—41no—
45C2×Q8×C11—41no—
46C2×Q8×C11—81no—
47C2×Q8×C11—81no—
48C2×Q8×C11SD1612yes—
49C22×C4×C11—22no—
50C22×C4×C11—21no—
51C22×C4×C11—21no—
52C22×C4×C11—22no—
53C22×C4×C11—41no—
54C22×C4×C11C2×D411yescharacteristic
55C22×C4×C11C2×D412yes—
56C2×C8×C11—22no—
57C2×C8×C11—41no—
58C2×C8×C11—42no—
59C2×C8×C11—42no—
60C2×C8×C11—41no—
61C2×C8×C11—42no—
62C11×C4⋊C4—22no—
63C11×C4⋊C4—44no—
64C11×C4⋊C4—41no—
65C11×C4⋊C4—42no—
66C11×C4⋊C4—41no—
67C11×C4⋊C4—41no—
68C11×C4⋊C4—44no—
69C11×C4⋊C4—42no—
70C11×C4⋊C4—42no—
71C11×C4⋊C4—81no—
72C11×C4⋊C4Q1614yes—
73C42×C11—41no—
74C42×C11—42no—
75#2734C2×C1111yescharacteristic
76#2100C2×C1112yes—
77#2095C2×C1111yescharacteristic
78#1272C2×C1111yescharacteristic
79#1271C2×C1112yes—
80C23×C11#12011yescharacteristic
81Q8×C11—42no—
82Q8×C11—81no—
83Q8×C11—84no—
84C2×C4×C11—21no—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11—21no—
88C2×C4×C11—22no—
89C2×C4×C11—24no—
90C2×C4×C11—42no—
91C2×C4×C11—41no—
92C2×C4×C11—42no—
93C2×C4×C11—41no—
94C2×C4×C11—42no—
95C2×C4×C11—41no—
96C2×C4×C11—42no—
97C2×C4×C11—42no—
98C2×C4×C11—42no—
99C2×C4×C11—81no—
100C2×C4×C11—82no—
101C2×C4×C11C2×SD1611yescharacteristic
102C2×C4×C11C2×Q1612yes—
103C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
104C2×C4×C11#13712yes—
105C8×C11—42no—
106C8×C11—82no—
107C2×C4⋊Q8—21no—
108C2×#107—21no—
109C2×#103—21no—
110#398—21no—
111#395—22no—
112#391C22×C1111yescharacteristic
113#389C22×C1112yes—
114#387—22no—
115#384C22×C1111yescharacteristic
116#340—22no—
117#340—22no—
118#336C22×C1111yescharacteristic
119#336C22×C1112yes—
120C22×C11#45011yescharacteristic
121C22×C11#45112yes—
122C22×C11#45311yescharacteristic
123C22×C11#45412yes—
124C22×C11#45811yescharacteristic
125C4×C11—21no—
126C4×C11—21no—
127C4×C11—22no—
128C4×C11—22no—
129C4×C11—42no—
130C4×C11—44no—
131C4×C11—82no—
132C4×C11—81no—
133C4×C11—161no—
134C22×Q8—21no—
135C22×Q8D4×C1111yescharacteristic
136C22×C8—21no—
137C22×C8—22no—
138C4⋊Q8—42no—
139C4⋊Q8—42no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4D4×C1112yes—
146C2×C4⋊C4D4×C1112yes—
147C2×C4⋊C4D4×C1111yescharacteristic
148C2×C42—21no—
149C2×C42C23×C1111yescharacteristic
150#107—42no—
151#103—42no—
152#95—21no—
153#95—22no—
154#95—22no—
155#95—22no—
156C2×C11#161311yescharacteristic
157C2×C11#161712yes—
158C2×C11#163311yescharacteristic
159C2×C11#163712yes—
160C2×C11#165711yescharacteristic
161C2×Q8—21no—
162C2×Q8—42no—
163C2×Q8—41no—
164C2×Q8—41no—
165C2×Q8—81no—
166C2×Q8—81no—
167C2×Q8C11×SD1612yes—
168C22×C4—22no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—22no—
172C22×C4—41no—
173C22×C4C2×D4×C1111yescharacteristic
174C22×C4C2×D4×C1112yes—
175C2×C8—22no—
176C2×C8—41no—
177C2×C8—41no—
178C2×C8—42no—
179C2×C8—42no—
180C2×C8—42no—
181C4⋊C4—22no—
182C4⋊C4—41no—
183C4⋊C4—42no—
184C4⋊C4—44no—
185C4⋊C4—41no—
186C4⋊C4—41no—
187C4⋊C4—44no—
188C4⋊C4—42no—
189C4⋊C4—42no—
190C4⋊C4—81no—
191C4⋊C4C11×Q1614yes—
192C42—41no—
193C42—42no—
194C11#782911yescharacteristic, direct product factor, Sylow
195C23C11×#12011yescharacteristic
196Q8—42no—
197Q8—81no—
198Q8—84no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—24no—
205C2×C4—42no—
206C2×C4—41no—
207C2×C4—42no—
208C2×C4—41no—
209C2×C4—42no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—81no—
215C2×C4—82no—
216C2×C4C2×C11×SD1611yescharacteristic
217C2×C4C2×C11×Q1612yes—
218C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
219C2×C4C11×#13712yes—
220C8—42no—
221C8—82no—
222C22C11×#45011yescharacteristic
223C22C11×#45112yes—
224C22C11×#45311yescharacteristic
225C22C11×#45412yes—
226C22C11×#45811yescharacteristic
227C4—21no—
228C4—21no—
229C4—22no—
230C4—22no—
231C4—42no—
232C4—44no—
233C4—82no—
234C4—81no—
235C4—161no—
236C2C11×#161311yescharacteristic
237C2C11×#161712yes—
238C2C11×#163311yescharacteristic
239C2C11×#163712yes—
240C2C11×#165711yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C11#120
commutator, Frattini, cosocleC2×C42C23×C11
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
41. #7829C11direct (N × H)
194. C11#7829direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#27342
C11×#21002
C11×#20952
C11×#12722
C11×#12712
#782911