Finite Group Databasebeta

← #14666827

Subgroups — #14666827

Order 2816.

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

normal subgroups only

This group has 442 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#13073645C211yesmaximal, characteristic
2#13067590C212yesmaximal
3#13066645C212yesmaximal
4#13066562C211yesmaximal, characteristic
5C11×#2060C211yesmaximal, characteristic
6C11×#544C2211yescharacteristic
7C2×#66941—22no—
8C11×#428—21no—
9C11×#384C2211yescharacteristic
10#10622663—22no—
11#10622592—21no—
12#10622592C2212yes—
13#10622586—22no—
14C4×C4⋊Dic11—21no—
15C11×#343C2211yescharacteristic
16C11×#339—21no—
17#10622176—22no—
18#10622166C2212yes—
19C22×Dic22—21no—
20C22×Dic22D412yes—
21C2×C11×M16—21no—
22C11×C4⋊Q8—41no—
23C11×#125—41no—
24C11×C22⋊Q8—22no—
25C11×#117—21no—
26C2×C11×C4⋊C4—22no—
27C2×C11×C4⋊C4D411yescharacteristic
28C2×C11×C4⋊C4C2311yescharacteristic
29C2×C42×C11D411yescharacteristic
30C2×#4326—42no—
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11—21no—
33C2×Dic11⋊C4—22no—
34C2×Dic11⋊C4—22no—
35C2×C4×Dic11—22no—
36#66941—48no—
37C11×#107—41no—
38C11×#106—41no—
39C11⋊#95—21no—
40C11⋊#95—22no—
41C11⋊#95D412yes—
42C22⋊(C11⋊C8)—22no—
43#66874—42no—
44#12256—111nomaximal, Sylow
45C2×Q8×C11—22no—
46C22×C4×C11—21no—
47C22×C4×C11—21no—
48C22×C4×C11C2×D411yescharacteristic
49C22×C4×C11C2×D412yes—
50C22×Dic11—22no—
51C22×Dic11—22no—
52C2×Dic22—42no—
53C2×Dic22—44no—
54C2×Dic22—44no—
55C2×Dic22—81no—
56C11×M16—22no—
57C11×M16—41no—
58C2×C8×C11—41no—
59C11×C4⋊C4—22no—
60C11×C4⋊C4—21no—
61C11×C4⋊C4—21no—
62C11×C4⋊C4—41no—
63C11×C4⋊C4—44no—
64C11×C4⋊C4—42no—
65C11×C4⋊C4—41no—
66C11×C22⋊C4—41no—
67C42×C11—21no—
68C42×C11—41no—
69C42×C11Q1612yescomplemented
70#4326—84no—
71C4⋊Dic11—24no—
72C4⋊Dic11—24no—
73Dic11⋊C4—44no—
74Dic11⋊C4—44no—
75C4×Dic11—44no—
76C2×C11⋊C8—42no—
77#2551—111no—
78#2060D1111yescharacteristic
79#1605—112no—
80#1354—112no—
81#1325—111no—
82C23×C11#12011yescharacteristic
83Q8×C11—82no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11—21no—
88C2×C4×C11—21no—
89C2×C4×C11—22no—
90C2×C4×C11—42no—
91C2×C4×C11—42no—
92C2×C4×C11—41no—
93C2×C4×C11—41no—
94C2×C4×C11—41no—
95C2×C4×C11C2×Q1611yescharacteristic
96C2×C4×C11#13711yescharacteristic
97C2×Dic11—24no—
98C2×Dic11—24no—
99C2×Dic11—42no—
100C2×Dic11—42no—
101C2×Dic11—42no—
102C2×Dic11—42no—
103Dic22—44no—
104Dic22—82no—
105Dic22—84no—
106C8×C11—42no—
107C11⋊C8—82no—
108#544C2×D1111yescharacteristic
109C2×C4⋊Q8—222no—
110#451—222no—
111#428—21no—
112#395—112no—
113#395—221no—
114#389—222no—
115#384C2×D1111yescharacteristic
116C4×C4⋊C4—221no—
117#343C2×D1111yescharacteristic
118#339—21no—
119#328—222no—
120#324—112no—
121C22×C11—21no—
122C22×C11—21no—
123C22×C11#45111yescharacteristic
124C22×C11#45611yescharacteristic
125C22×C11B(4,𝔽2)11yescharacteristic
126C4×C11—24no—
127C4×C11—21no—
128C4×C11—21no—
129C4×C11—42no—
130C4×C11—81no—
131C4×C11—81no—
132C4×C11—81no—
133Dic11—44no—
134Dic11—44no—
135C22×Q8—112no—
136C22×Q8—221no—
137C2×Q16—442no—
138C2×M16—21no—
139C4⋊Q8—41no—
140C4⋊Q8—448no—
141#125—41no—
142C22⋊Q8—22no—
143#117—21no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—221no—
146C2×C4⋊C4—221no—
147C2×C4⋊C4—222no—
148C2×C4⋊C4—222no—
149C2×C4⋊C4C22⋊D1111yescharacteristic
150C2×C4⋊C4C22×D1111yescharacteristic
151C2×C42—222no—
152C2×C42C22⋊D1111yescharacteristic
153#107—41no—
154#106—41no—
155#103—442no—
156C22⋊C8—222no—
157#95—112no—
158#95—221no—
159#95—222no—
160C2×C11—21no—
161C2×C11—21no—
162C2×C11#160511yescharacteristic
163C2×C11#219611yescharacteristic
164C2×C11#220511yescharacteristic
165C2×Q8—22no—
166C2×Q8—442no—
167C2×Q8—444no—
168C2×Q8—444no—
169C2×Q8—881no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—222no—
173C22×C4—222no—
174C22×C4D4×D1112yes—
175C22×C4C2×C22⋊D1111yescharacteristic
176Q16—884no—
177M16—22no—
178M16—41no—
179C2×C8—41no—
180C2×C8—442no—
181C4⋊C4—22no—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—41no—
185C4⋊C4—41no—
186C4⋊C4—44no—
187C4⋊C4—42no—
188C4⋊C4—224no—
189C4⋊C4—224no—
190C4⋊C4—444no—
191C4⋊C4—444no—
192C22⋊C4—41no—
193C42—21no—
194C42—41no—
195C42—444no—
196C42#432612yescomplemented
197C11#1225611yescharacteristic, complemented, Sylow
198C23#6699011yescharacteristic
199Q8—82no—
200Q8—444no—
201Q8—882no—
202Q8—884no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—224no—
215C2×C4—224no—
216C2×C4—442no—
217C2×C4—442no—
218C2×C4—442no—
219C2×C4—442no—
220C2×C4C2×#432611yescharacteristic
221C2×C4#6700411yescharacteristic
222C8—42no—
223C8—882no—
224C22—21no—
225C22—21no—
226C22#1062264511yescharacteristic
227C22#1062266311yescharacteristic
228C22#1062270811yescharacteristic
229C4—24no—
230C4—21no—
231C4—21no—
232C4—42no—
233C4—81no—
234C4—81no—
235C4—81no—
236C4—444no—
237C4—444no—
238C2—21no—
239C2—21no—
240C2#1306758911yescharacteristic
241C2#1307059911yescharacteristic
242C2#1307064511yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2060C2
socleC22×C11B(4,𝔽2)
prime radicalC23×C11#120
hypercenter#2060D11
hypocenterC11#12256
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2060

Complements

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

NH ≅ G/Ntype
69. C42×C11Q16semidirect
196. C42#4326semidirect
197. C11#12256semidirect

Maximal subgroups

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

subgroupindex
#130736452
#130675902
#130666452
#130665622
C11×#20602
#1225611