Finite Group Databasebeta

← #14667103

Subgroups — #14667103

Order 2816.

324 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 59 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
1#13070833C212yesmaximal, complemented
2#13070132C211yesmaximal, characteristic
3#13066610C212yesmaximal, complemented
4#13066552C211yesmaximal, characteristic
5C11×#3195C211yesmaximal, characteristic
6C2×C11×C22⋊Q8—21no—
7C11×#483—22no—
8C11×#470—21no—
9C11×#470C2212yes—
10C11×#451—22no—
11C11×#407C2211yescharacteristic
12#10622820—21no—
13#10622738C2211yescharacteristic
14#10622737—21no—
15#10622203—22no—
16C11⋊#338C2211yescharacteristic
17#10622191C2212yes—
18#10622125—22no—
19C22×Q8×C11—21no—
20C23×C4×C11D411yescharacteristic
21C2×C11×Q16—21no—
22C2×C11×Q16D412yes—
23C2×C11×M16D411yescharacteristic
24C2×C11×M16C2311yescharacteristic
25C11×C22⋊Q8—22no—
26C11×C22⋊Q8—22no—
27C11×C22⋊Q8—41no—
28C11×C22⋊Q8—41no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—41no—
31C2×C11×C22⋊C4—41no—
32C2×#4318—21no—
33C2×#4318—21no—
34C11×#106—21no—
35C11×#106D412yes—
36C11×#103—22no—
37C11×#103—22no—
38C11×C22⋊C8—22no—
39C22⋊(C11⋊C8)—42no—
40#66886—42no—
41#66883—22no—
42#66876—22no—
43#12299—111nomaximal, Sylow
44C24×C11SD1611yescharacteristic
45C2×Q8×C11—22no—
46C2×Q8×C11—41no—
47C2×Q8×C11—81no—
48C2×Q8×C11—81no—
49C22×C4×C11—21no—
50C22×C4×C11—21no—
51C22×C4×C11—41no—
52C22×C4×C11—41no—
53C22×C4×C11—41no—
54C22×C4×C11—41no—
55C22×C4×C11SD1611yescharacteristic
56C22×C4×C11C2×D411yescharacteristic
57C11×Q16—42no—
58C11×Q16—81no—
59C11×M16—41no—
60C11×M16—41no—
61C2×C8×C11—21no—
62C2×C8×C11C2×D412yes—
63C11×C4⋊C4—22no—
64C11×C4⋊C4—41no—
65C11×C4⋊C4—42no—
66C11×C4⋊C4—42no—
67C11×C22⋊C4—42no—
68C11×C22⋊C4—42no—
69#4318—41no—
70#4318—41no—
71#4318—41no—
72#4318—41no—
73C2×C11⋊C8—22no—
74C2×C11⋊C8—41no—
75C11⋊C16—42no—
76#3195D1111yescharacteristic
77#2239—112no—
78#2091—111no—
79#1342—112no—
80#1320—111no—
81C23×C11—21no—
82C23×C11—41no—
83C23×C11—42no—
84C23×C11C2×SD1611yescharacteristic
85Q8×C11—42no—
86Q8×C11—42no—
87Q8×C11—82no—
88C2×C4×C11—21no—
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11—41no—
92C2×C4×C11—41no—
93C2×C4×C11—41no—
94C2×C4×C11—42no—
95C2×C4×C11—42no—
96C2×C4×C11—81no—
97C2×C4×C11—82no—
98C2×C4×C11—82no—
99C2×C4×C11#12011yescharacteristic
100C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
101C8×C11—22no—
102C8×C11—41no—
103C11⋊C8—42no—
104C11⋊C8—81no—
105C2×C22⋊Q8—21no—
106#483—22no—
107#470—21no—
108#470C2×D1112yes—
109#451—22no—
110#430—111no—
111#430—221no—
112#407—221no—
113#407C2×D1111yescharacteristic
114#365—222no—
115#362—222no—
116#349—112no—
117#338—111no—
118C22×C11—22no—
119C22×C11—21no—
120C22×C11—41no—
121C22×C11—41no—
122C22×C11—42no—
123C22×C11—41no—
124C22×C11—81no—
125C22×C11#45011yescharacteristic
126C4×C11—21no—
127C4×C11—41no—
128C4×C11—82no—
129C4×C11—82no—
130C4×C11#45311yescharacteristic
131C4×C11#45811yescharacteristic
132C22×Q8—21no—
133C23×C4C22⋊D1111yescharacteristic
134C2×Q16—21no—
135C2×Q16C22⋊D1112yes—
136C2×M16—221no—
137C2×M16—221no—
138C2×M16C22⋊D1111yescharacteristic
139C2×M16C22×D1111yescharacteristic
140C22⋊Q8—22no—
141C22⋊Q8—22no—
142C22⋊Q8—41no—
143C22⋊Q8—41no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—41no—
146C2×C22⋊C4—41no—
147M32—222no—
148#108—222no—
149#108—442no—
150#106—21no—
151#106C22⋊D1112yes—
152#103—22no—
153#103—22no—
154C22⋊C8—22no—
155C22⋊C8—442no—
156C2×C11—21no—
157C2×C11—42no—
158C2×C11—41no—
159C2×C11#161311yescharacteristic
160C24#432411yescharacteristic
161C2×Q8—22no—
162C2×Q8—41no—
163C2×Q8—81no—
164C2×Q8—81no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—41no—
168C22×C4—41no—
169C22×C4—41no—
170C22×C4—41no—
171C22×C4#432411yescharacteristic
172C22×C4C2×C22⋊D1111yescharacteristic
173Q16—42no—
174Q16—81no—
175M16—41no—
176M16—41no—
177M16—441no—
178M16—441no—
179M16—441no—
180M16—441no—
181C2×C8—21no—
182C2×C8—222no—
183C2×C8—441no—
184C2×C8C2×C22⋊D1112yes—
185C4⋊C4—22no—
186C4⋊C4—41no—
187C4⋊C4—42no—
188C4⋊C4—42no—
189C22⋊C4—42no—
190C22⋊C4—42no—
191C16—442no—
192C11#1229911yescharacteristic, complemented, Sylow
193C23—21no—
194C23—41no—
195C23—42no—
196C23C2×#432411yescharacteristic
197Q8—42no—
198Q8—42no—
199Q8—82no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—81no—
209C2×C4—82no—
210C2×C4—82no—
211C2×C4#6698511yescharacteristic
212C2×C4#6700611yescharacteristic
213C8—22no—
214C8—41no—
215C8—442no—
216C8—881no—
217C22—22no—
218C22—21no—
219C22—41no—
220C22—41no—
221C22—42no—
222C22—41no—
223C22—81no—
224C22#1062283111yescharacteristic
225C4—21no—
226C4—41no—
227C4—82no—
228C4—82no—
229C4#1062285411yescharacteristic
230C4#1062285611yescharacteristic
231C2—21no—
232C2—42no—
233C2—41no—
234C2#1306763611yescharacteristic
subgroupG/H
centerC2#13067636
commutator, cosocleC2×C11×M16C23
FrattiniC2×M16C22×D11
FittingC11×#3195C2
socleC2×C11#1613
prime radicalC24×C11SD16
hypercenter#3195D11
hypocenterC11#12299
LCSG ▷ C2×C11×M16 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #3195

Complements

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

NH ≅ G/Ntype
1. #13070833C2semidirect
3. #13066610C2semidirect
192. C11#12299semidirect

Maximal subgroups

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

subgroupindex
#130708332
#130701322
#130666102
#130665522
C11×#31952
#1229911