Finite Group Databasebeta

← #14658207

Subgroups — #14658207

Order 2816.

494 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 145 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#13069374C212yesmaximal
2#13068775C211yesmaximal, characteristic
3#13066499C211yesmaximal, characteristic
4#13066457C212yesmaximal
5C11×#2551C211yesmaximal, characteristic
6C2×C11×C4⋊Q8—22no—
7C11×#395—22no—
8C11×#389—22no—
9C11×#384C2211yescharacteristic
10C4×C11×C4⋊C4C2212yes—
11C2×#66871—22no—
12C2×#66871—22no—
13#10622548C2211yescharacteristic
14C2×C4⋊(C11⋊C8)C2212yes—
15C2×C4×C11⋊C8C2211yescharacteristic
16#10622167—22no—
17C22×Q8×C11—22no—
18C11×C4⋊Q8—44no—
19C11×C4⋊Q8—44no—
20C2×C11×C4⋊C4—24no—
21C2×C11×C4⋊C4—22no—
22C2×C11×C4⋊C4D412yes—
23C2×C11×C4⋊C4D412yes—
24C2×C11×C4⋊C4D412yes—
25C2×C42×C11—22no—
26C2×C42×C11C2311yescharacteristic
27C2×C4⋊Dic11—21no—
28C2×C4⋊Dic11—22no—
29C22×C11⋊C8—21no—
30C22×C11⋊C8—22no—
31C11×#95—22no—
32C11×#95—22no—
33#66871—44no—
34#66871—44no—
35C4⋊(C11⋊C8)—22no—
36C4⋊(C11⋊C8)Q814yescomplemented
37C4×C11⋊C8—21no—
38C4×C11⋊C8Q812yescomplemented
39#10573—111nomaximal, Sylow
40C2×Q8×C11—48no—
41C2×Q8×C11—82no—
42C22×C4×C11—22no—
43C22×C4×C11—22no—
44C22×C4×C11—22no—
45C22×C4×C11C2×D411yescharacteristic
46C22×C4×C11C2×D412yes—
47C22×Dic11—41no—
48C11×C4⋊C4—22no—
49C11×C4⋊C4—22no—
50C11×C4⋊C4—48no—
51C11×C4⋊C4—42no—
52C11×C4⋊C4—42no—
53C11×C4⋊C4—42no—
54C11×C4⋊C4D814yes—
55C11×C4⋊C4Q1614yes—
56C42×C11—42no—
57C42×C11—42no—
58C42×C11C2×Q811yescharacteristic
59C42×C11C2×Q812yes—
60C42×C11#4111yescharacteristic
61C4⋊Dic11—42no—
62C4⋊Dic11—42no—
63C4⋊Dic11—42no—
64C2×C11⋊C8—22no—
65C2×C11⋊C8—22no—
66C2×C11⋊C8—22no—
67C2×C11⋊C8—24no—
68C2×C11⋊C8—42no—
69C2×C11⋊C8—42no—
70#2551D1111yescharacteristic
71#1947—112no—
72#1845—111no—
73#1296—111no—
74#1279—112no—
75C23×C11#12011yescharacteristic
76Q8×C11—88no—
77C2×C4×C11—21no—
78C2×C4×C11—21no—
79C2×C4×C11—24no—
80C2×C4×C11—24no—
81C2×C4×C11—42no—
82C2×C4×C11—42no—
83C2×C4×C11—42no—
84C2×C4×C11—42no—
85C2×C4×C11—44no—
86C2×C4×C11—42no—
87C2×C4×C11C22⋊Q811yescharacteristic
88C2×C4×C11C22⋊Q812yes—
89C2×C4×C11C4⋊Q811yescharacteristic
90C2×C4×C11C4⋊Q812yes—
91C2×C4×C11C2×D812yes—
92C2×C4×C11C2×Q1612yes—
93C2×C4×C11AGL(1,ℤ/8)12yes—
94C2×C4×C11#13712yes—
95C2×Dic11—82no—
96C2×Dic11—81no—
97C11⋊C8—24no—
98C11⋊C8—44no—
99C2×C4⋊Q8—22no—
100C2×#107—222no—
101C2×#107—222no—
102C2×C4⋊C8—112no—
103C2×C4×C8—111no—
104#395—22no—
105#389—22no—
106#384—111no—
107#384C2×D1111yescharacteristic
108C4×C4⋊C4C2×D1112yes—
109#340—222no—
110C22×C11#39511yescharacteristic
111C22×C11#44712yes—
112C22×C11#45112yes—
113C22×C11#45311yescharacteristic
114C22×C11#45611yescharacteristic
115C4×C11—21no—
116C4×C11—21no—
117C4×C11—44no—
118C4×C11—44no—
119C4×C11—82no—
120C4×C11#47412yes—
121C4×C11#47712yes—
122C4×C11#50012yes—
123C4×C11#50112yes—
124Dic11—161no—
125C22×Q8—22no—
126C22×C8—221no—
127C22×C8—222no—
128C4⋊Q8—44no—
129C4⋊Q8—44no—
130C2×C4⋊C4—24no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—222no—
133C2×C4⋊C4—221no—
134C2×C4⋊C4C22⋊D1112yes—
135C2×C4⋊C4C22⋊D1112yes—
136C2×C4⋊C4C22⋊D1112yes—
137C2×C42—22no—
138C2×C42C22×D1111yescharacteristic
139#107—444no—
140#107—444no—
141C4⋊C8—114no—
142C4⋊C8—222no—
143C4×C8—112no—
144C4×C8—221no—
145#95—22no—
146#95—22no—
147C2×C11#161911yescharacteristic
148C2×C11#163311yescharacteristic
149C2×C11#164912yes—
150C2×C11#205712yes—
151C2×C11#206011yescharacteristic
152C2×Q8—48no—
153C2×Q8—82no—
154C22×C4—22no—
155C22×C4—22no—
156C22×C4—22no—
157C22×C4—441no—
158C22×C4C2×C22⋊D1111yescharacteristic
159C22×C4C2×C22⋊D1112yes—
160C2×C8—222no—
161C2×C8—222no—
162C2×C8—222no—
163C2×C8—224no—
164C2×C8—442no—
165C2×C8—442no—
166C4⋊C4—22no—
167C4⋊C4—22no—
168C4⋊C4—42no—
169C4⋊C4—48no—
170C4⋊C4—42no—
171C4⋊C4—42no—
172C4⋊C4—442no—
173C4⋊C4—442no—
174C4⋊C4—442no—
175C4⋊C4#432314yes—
176C4⋊C4#432614yes—
177C42—42no—
178C42—42no—
179C42Q8×D1111yescharacteristic
180C42Q8×D1112yes—
181C42#434311yescharacteristic
182C11#1057311yescharacteristic, complemented, Sylow
183C23#6700611yescharacteristic
184Q8—88no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—24no—
188C2×C4—24no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—44no—
194C2×C4—42no—
195C2×C4—882no—
196C2×C4—881no—
197C2×C4C2×#432312yes—
198C2×C4#6698512yes—
199C2×C4#6699512yes—
200C2×C4C2×#432612yes—
201C2×C4#6699711yescharacteristic
202C2×C4#6699712yes—
203C2×C4#6699911yescharacteristic
204C2×C4#6699912yes—
205C8—224no—
206C8—444no—
207C22#1062283012yes—
208C22#1062284112yes—
209C22#1062284211yescharacteristic
210C22#1062285411yescharacteristic
211C22#1062285911yescharacteristic
212C4—21no—
213C4—21no—
214C4—44no—
215C4—44no—
216C4—82no—
217C4—1761no—
218C4#1062269112yes—
219C4#1062269312yes—
220C4#1062270012yes—
221C4#1062270412yes—
222C2#1306767011yescharacteristic
223C2#1306775611yescharacteristic
224C2#1306786512yes—
225C2#1306994112yes—
226C2#1306995811yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2551C2
socle, prime radicalC23×C11#120
hypercenter#2551D11
hypocenterC11#10573
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2551

Complements

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

NH ≅ G/Ntype
36. C4⋊(C11⋊C8)Q8semidirect
38. C4×C11⋊C8Q8semidirect
182. C11#10573semidirect

Maximal subgroups

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

subgroupindex
#130693742
#130687752
#130664992
#130664572
C11×#25512
#1057311