Finite Group Databasebeta

← #14658224

Subgroups — #14658224

Order 2816.

406 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 129 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#13069379C212yesmaximal
2#13068775C211yesmaximal, characteristic
3#13066499C211yesmaximal, characteristic
4#13066457C212yesmaximal
5C11×#2571C211yesmaximal, characteristic
6C11×#400—22no—
7C11×#389—22no—
8C11×#384C2211yescharacteristic
9C11×#382—22no—
10C4×C11×C4⋊C4C2212yes—
11C2×#66872—22no—
12C2×#66871—22no—
13#10622548C2211yescharacteristic
14C2×C4⋊(C11⋊C8)C2212yes—
15C2×C4×C11⋊C8C2211yescharacteristic
16#10622167—22no—
17C2×C11×C4⋊C4—22no—
18C2×C11×C4⋊C4—22no—
19C2×C11×C4⋊C4D412yes—
20C2×C11×C4⋊C4D412yes—
21C2×C11×C4⋊C4D412yes—
22C2×C42×C11—22no—
23C2×C42×C11C2311yescharacteristic
24C2×C4⋊Dic11—21no—
25C2×C4⋊Dic11—22no—
26C22×C11⋊C8—21no—
27C22×C11⋊C8—22no—
28C11×#95—22no—
29C11×#95—24no—
30C11×#95—22no—
31#66872—44no—
32#66871—44no—
33C4⋊(C11⋊C8)—22no—
34C4⋊(C11⋊C8)Q814yes—
35C4×C11⋊C8—21no—
36C4×C11⋊C8Q812yes—
37#10576—111nomaximal, Sylow
38C22×C4×C11—22no—
39C22×C4×C11—22no—
40C22×C4×C11—22no—
41C22×C4×C11C2×D411yescharacteristic
42C22×C4×C11C2×D412yes—
43C22×Dic11—41no—
44C11×C4⋊C4—22no—
45C11×C4⋊C4—22no—
46C11×C4⋊C4—22no—
47C11×C4⋊C4—22no—
48C11×C4⋊C4—42no—
49C11×C4⋊C4—42no—
50C11×C4⋊C4—42no—
51C11×C4⋊C4—82no—
52C42×C11—42no—
53C42×C11—42no—
54C42×C11C2×Q811yescharacteristic
55C42×C11C2×Q812yes—
56C42×C11#4111yescharacteristic
57C4⋊Dic11—42no—
58C4⋊Dic11—42no—
59C4⋊Dic11—42no—
60C2×C11⋊C8—22no—
61C2×C11⋊C8—22no—
62C2×C11⋊C8—22no—
63C2×C11⋊C8—24no—
64C2×C11⋊C8—42no—
65C2×C11⋊C8—42no—
66#2571D1111yescharacteristic
67#1948—112no—
68#1845—111no—
69#1296—111no—
70#1279—112no—
71C23×C11#12011yescharacteristic
72C2×C4×C11—21no—
73C2×C4×C11—21no—
74C2×C4×C11—42no—
75C2×C4×C11—44no—
76C2×C4×C11—42no—
77C2×C4×C11—42no—
78C2×C4×C11—42no—
79C2×C4×C11—42no—
80C2×C4×C11—42no—
81C2×C4×C11—42no—
82C2×C4×C11C22⋊Q811yescharacteristic
83C2×C4×C11C22⋊Q812yes—
84C2×C4×C11C4⋊Q811yescharacteristic
85C2×C4×C11C4⋊Q812yes—
86C2×C4×C11#13512yes—
87C2×C4×C11#13512yes—
88C2×C4×C11AGL(1,ℤ/8)12yes—
89C2×C4×C11#13712yes—
90C2×Dic11—82no—
91C2×Dic11—81no—
92C11⋊C8—24no—
93C11⋊C8—44no—
94C2×#107—222no—
95C2×#106—222no—
96C2×C4⋊C8—112no—
97C2×C4×C8—111no—
98#400—22no—
99#389—22no—
100#384—111no—
101#384C2×D1111yescharacteristic
102#382—22no—
103C4×C4⋊C4C2×D1112yes—
104#340—222no—
105C22×C11#39511yescharacteristic
106C22×C11#44912yes—
107C22×C11#45212yes—
108C22×C11#45311yescharacteristic
109C22×C11#45611yescharacteristic
110C4×C11—21no—
111C4×C11—21no—
112C4×C11—82no—
113C4×C11—82no—
114C4×C11—82no—
115C4×C11#47812yes—
116C4×C11#47912yes—
117C4×C11#49912yes—
118C4×C11#50112yes—
119Dic11—161no—
120C22×C8—221no—
121C22×C8—222no—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4—222no—
125C2×C4⋊C4—221no—
126C2×C4⋊C4C22⋊D1112yes—
127C2×C4⋊C4C22⋊D1112yes—
128C2×C4⋊C4C22⋊D1112yes—
129C2×C42—22no—
130C2×C42C22×D1111yescharacteristic
131#107—444no—
132#106—444no—
133C4⋊C8—114no—
134C4⋊C8—222no—
135C4×C8—112no—
136C4×C8—221no—
137#95—22no—
138#95—24no—
139#95—22no—
140C2×C11#162011yescharacteristic
141C2×C11#163411yescharacteristic
142C2×C11#165012yes—
143C2×C11#205912yes—
144C2×C11#206011yescharacteristic
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—441no—
149C22×C4C2×C22⋊D1111yescharacteristic
150C22×C4C2×C22⋊D1112yes—
151C2×C8—222no—
152C2×C8—222no—
153C2×C8—222no—
154C2×C8—224no—
155C2×C8—442no—
156C2×C8—442no—
157C4⋊C4—22no—
158C4⋊C4—22no—
159C4⋊C4—22no—
160C4⋊C4—22no—
161C4⋊C4—42no—
162C4⋊C4—42no—
163C4⋊C4—42no—
164C4⋊C4—82no—
165C4⋊C4—442no—
166C4⋊C4—442no—
167C4⋊C4—442no—
168C42—42no—
169C42—42no—
170C42Q8×D1111yescharacteristic
171C42Q8×D1112yes—
172C42#434311yescharacteristic
173C11#1057611yescharacteristic, complemented, Sylow
174C23#6700611yescharacteristic
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—42no—
178C2×C4—44no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—882no—
186C2×C4—881no—
187C2×C4#6699711yescharacteristic
188C2×C4#6699712yes—
189C2×C4#6699911yescharacteristic
190C2×C4#6699912yes—
191C2×C4#6700212yes—
192C2×C4#6700312yes—
193C2×C4#6700312yes—
194C2×C4#6700412yes—
195C8—224no—
196C8—444no—
197C22#1062284211yescharacteristic
198C22#1062285112yes—
199C22#1062285212yes—
200C22#1062285411yescharacteristic
201C22#1062285911yescharacteristic
202C4—21no—
203C4—21no—
204C4—82no—
205C4—82no—
206C4—82no—
207C4—1761no—
208C4#1062267612yes—
209C4#1062267712yes—
210C4#1062267812yes—
211C4#1062267912yes—
212C2#1306767511yescharacteristic
213C2#1306776111yescharacteristic
214C2#1306787212yes—
215C2#1306995112yes—
216C2#1306995811yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2571C2
socle, prime radicalC23×C11#120
hypercenter#2571D11
hypocenterC11#10576
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2571

Complements

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

NH ≅ G/Ntype
173. C11#10576semidirect

Maximal subgroups

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

subgroupindex
#130693792
#130687752
#130664992
#130664572
C11×#25712
#1057611