Finite Group Databasebeta

← #14643083

Subgroups — #14643083

Order 2816.

350 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 87 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#13070179C212yesmaximal
2#13070154C211yesmaximal, characteristic
3#13066442C211yesmaximal, characteristic
4#13066439C212yesmaximal
5C11×#2809C211yesmaximal, characteristic
6C11×#400—21no—
7C11×#398—22no—
8C11×#391—21no—
9C11×#391C2211yescharacteristic
10C11×#389C2212yes—
11C11×#387—22no—
12C2×#66899—21no—
13C2×#66871—21no—
14#10622548C2211yescharacteristic
15#10622167—22no—
16#10622167—22no—
17#10622162C2211yescharacteristic
18#10622162C2212yes—
19C22×Q8×C11D411yescharacteristic
20C2×C11×C4⋊C4—22no—
21C2×C11×C4⋊C4—21no—
22C2×C11×C4⋊C4—21no—
23C2×C11×C4⋊C4D412yes—
24C2×C11×C4⋊C4D411yescharacteristic
25C2×C11×C4⋊C4D412yes—
26C2×C42×C11—21no—
27C2×C42×C11C2311yescharacteristic
28C2×C4⋊Dic11—21no—
29C2×C4⋊Dic11—22no—
30C22×C11⋊C8—21no—
31C22×C11⋊C8—22no—
32C11×#95—21no—
33C11×#95—22no—
34C11×#95—22no—
35C11×#95—22no—
36C11×#95—22no—
37#66899—42no—
38#66871—42no—
39#7831—111nomaximal, Sylow
40C2×Q8×C11—21no—
41C2×Q8×C11—41no—
42C2×Q8×C11—41no—
43C2×Q8×C11Q1612yes—
44C22×C4×C11—21no—
45C22×C4×C11—21no—
46C22×C4×C11—22no—
47C22×C4×C11—22no—
48C22×C4×C11C2×D411yescharacteristic
49C22×C4×C11C2×D412yes—
50C22×Dic11—41no—
51C11×C4⋊C4—22no—
52C11×C4⋊C4—22no—
53C11×C4⋊C4—41no—
54C11×C4⋊C4—42no—
55C11×C4⋊C4—42no—
56C11×C4⋊C4—42no—
57C11×C4⋊C4—81no—
58C11×C4⋊C4—81no—
59C42×C11—41no—
60C42×C11—81no—
61C4⋊Dic11—41no—
62C4⋊Dic11—41no—
63C4⋊Dic11—44no—
64C2×C11⋊C8—22no—
65C2×C11⋊C8—41no—
66C2×C11⋊C8—42no—
67C2×C11⋊C8—42no—
68C2×C11⋊C8—42no—
69C2×C11⋊C8—41no—
70#2809D1111yescharacteristic
71#2100—112no—
72#2095—111no—
73#1272—111no—
74#1271—112no—
75C23×C11#12011yescharacteristic
76Q8×C11—42no—
77Q8×C11—81no—
78C2×C4×C11—21no—
79C2×C4×C11—22no—
80C2×C4×C11—22no—
81C2×C4×C11—21no—
82C2×C4×C11—22no—
83C2×C4×C11—41no—
84C2×C4×C11—41no—
85C2×C4×C11—42no—
86C2×C4×C11—42no—
87C2×C4×C11—42no—
88C2×C4×C11—41no—
89C2×C4×C11—42no—
90C2×C4×C11—42no—
91C2×C4×C11—42no—
92C2×C4×C11—42no—
93C2×C4×C11C2×Q1611yescharacteristic
94C2×C4×C11#13512yes—
95C2×C4×C11#13711yescharacteristic
96C2×C4×C11#13712yes—
97C2×Dic11—81no—
98C2×Dic11—82no—
99C11⋊C8—42no—
100C11⋊C8—82no—
101C2×#107—221no—
102C2×#103—221no—
103#400—21no—
104#398—22no—
105#391—21no—
106#391C2×D1111yescharacteristic
107#389C2×D1112yes—
108#387—22no—
109#384—111no—
110#340—222no—
111#340—222no—
112#336—111no—
113#336—112no—
114C22×C11#45111yescharacteristic
115C22×C11#45212yes—
116C22×C11#45311yescharacteristic
117C22×C11#45412yes—
118C22×C11#45811yescharacteristic
119C4×C11—21no—
120C4×C11—21no—
121C4×C11—22no—
122C4×C11—22no—
123C4×C11—42no—
124C4×C11—82no—
125C4×C11—82no—
126C4×C11—81no—
127Dic11—161no—
128C22×Q8C22⋊D1111yescharacteristic
129C22×C8—221no—
130C22×C8—222no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—21no—
133C2×C4⋊C4—21no—
134C2×C4⋊C4—222no—
135C2×C4⋊C4—221no—
136C2×C4⋊C4C22⋊D1112yes—
137C2×C4⋊C4C22⋊D1112yes—
138C2×C4⋊C4C22⋊D1111yescharacteristic
139C2×C42—21no—
140C2×C42C22×D1111yescharacteristic
141#107—442no—
142#103—442no—
143#95—21no—
144#95—22no—
145#95—22no—
146#95—22no—
147#95—22no—
148C2×C11#161411yescharacteristic
149C2×C11#161512yes—
150C2×C11#163411yescharacteristic
151C2×C11#163612yes—
152C2×C11#165711yescharacteristic
153C2×Q8—21no—
154C2×Q8—41no—
155C2×Q8—41no—
156C2×Q8#432612yes—
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—441no—
162C22×C4C2×C22⋊D1111yescharacteristic
163C22×C4C2×C22⋊D1112yes—
164C2×C8—222no—
165C2×C8—441no—
166C2×C8—441no—
167C2×C8—442no—
168C2×C8—442no—
169C2×C8—442no—
170C4⋊C4—22no—
171C4⋊C4—22no—
172C4⋊C4—41no—
173C4⋊C4—42no—
174C4⋊C4—42no—
175C4⋊C4—42no—
176C4⋊C4—81no—
177C4⋊C4—81no—
178C4⋊C4—441no—
179C4⋊C4—441no—
180C4⋊C4—444no—
181C42—41no—
182C42—81no—
183C11#783111yescharacteristic, complemented, Sylow
184C23#6700611yescharacteristic
185Q8—42no—
186Q8—81no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—41no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—881no—
203C2×C4—882no—
204C2×C4#6699511yescharacteristic
205C2×C4C2×#432611yescharacteristic
206C2×C4#6700312yes—
207C2×C4#6700412yes—
208C8—442no—
209C8—882no—
210C22#1062284111yescharacteristic
211C22#1062285212yes—
212C22#1062285411yescharacteristic
213C22#1062285611yescharacteristic
214C22#1062285812yes—
215C4—21no—
216C4—21no—
217C4—22no—
218C4—22no—
219C4—42no—
220C4—82no—
221C4—81no—
222C4—82no—
223C4—1761no—
224C2#1306764111yescharacteristic
225C2#1306764712yes—
226C2#1306776111yescharacteristic
227C2#1306777412yes—
228C2#1306791411yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2809C2
socle, prime radicalC23×C11#120
hypercenter#2809D11
hypocenterC11#7831
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2809

Complements

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

NH ≅ G/Ntype
183. C11#7831semidirect

Maximal subgroups

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

subgroupindex
#130701792
#130701542
#130664422
#130664392
C11×#28092
#783111