Finite Group Databasebeta

← #14658231

Subgroups — #14658231

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#13073858C211yesmaximal, characteristic
2#13069375C212yesmaximal
3#13068772C211yesmaximal, characteristic
4#13066455C212yesmaximal
5C11×#1296C211yesmaximal, characteristic
6C2×C11×C4⋊C8C2212yes—
7C11×#384C2211yescharacteristic
8C2×#66882—22no—
9#10622599—22no—
10#10622598—22no—
11#10622590—22no—
12C2×#66872—22no—
13#10622548C2211yescharacteristic
14C4×C4⋊Dic11C2212yes—
15C2×C4×C11⋊C8C2211yescharacteristic
16#10622189—22no—
17C22×C8×C11—22no—
18C2×C11×C4⋊C4—22no—
19C2×C11×C4⋊C4D412yes—
20C2×C42×C11C2311yescharacteristic
21C2×C4⋊Dic11—21no—
22C2×C4⋊Dic11—22no—
23C2×C4⋊Dic11—22no—
24C2×C4⋊Dic11D412yes—
25C2×C4⋊Dic11D412yes—
26C2×C4×Dic11—22no—
27C22×C11⋊C8—21no—
28C11×C4⋊C8—22no—
29C11×C4⋊C8Q814yes—
30C11⋊#95—22no—
31C11⋊#95—24no—
32C11⋊#95—22no—
33#66882—44no—
34#66872—44no—
35C4×C11⋊C8—21no—
36C4×C11⋊C8Q812yes—
37#10577—111nomaximal, Sylow
38C22×C4×C11—22no—
39C22×C4×C11C2×D411yescharacteristic
40C22×C4×C11C2×D412yes—
41C22×Dic11—22no—
42C22×Dic11—22no—
43C22×Dic11—41no—
44C2×C8×C11—24no—
45C2×C8×C11—42no—
46C2×C8×C11—42no—
47C11×C4⋊C4—42no—
48C11×C4⋊C4—42no—
49C11×C4⋊C4—42no—
50C42×C11C2×Q812yes—
51C42×C11C2×Q811yescharacteristic
52C42×C11#4111yescharacteristic
53C4⋊Dic11—22no—
54C4⋊Dic11—22no—
55C4⋊Dic11—22no—
56C4⋊Dic11—22no—
57C4⋊Dic11—42no—
58C4⋊Dic11—42no—
59C4⋊Dic11—42no—
60C4⋊Dic11—82no—
61C4×Dic11—42no—
62C4×Dic11—42no—
63C2×C11⋊C8—22no—
64C2×C11⋊C8—22no—
65C2×C11⋊C8—22no—
66#2571—111no—
67#1947—112no—
68#1844—111no—
69#1296D1111yescharacteristic
70#1279—112no—
71C23×C11#12011yescharacteristic
72C2×C4×C11—21no—
73C2×C4×C11—21no—
74C2×C4×C11—44no—
75C2×C4×C11—42no—
76C2×C4×C11C22⋊Q812yes—
77C2×C4×C11C22⋊Q811yescharacteristic
78C2×C4×C11C4⋊Q811yescharacteristic
79C2×C4×C11C4⋊Q812yes—
80C2×C4×C11#13512yes—
81C2×C4×C11#13512yes—
82C2×C4×C11AGL(1,ℤ/8)12yes—
83C2×C4×C11#13712yes—
84C2×Dic11—42no—
85C2×Dic11—42no—
86C2×Dic11—42no—
87C2×Dic11—42no—
88C2×Dic11—42no—
89C2×Dic11—42no—
90C2×Dic11—82no—
91C2×Dic11—81no—
92C8×C11—44no—
93C11⋊C8—24no—
94C2×#107—222no—
95C2×#106—222no—
96C2×C4⋊C8C2×D1112yes—
97C2×C4×C8—111no—
98#400—222no—
99#389—222no—
100#384—111no—
101#384C2×D1111yescharacteristic
102#382—222no—
103C4×C4⋊C4—112no—
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#47812yes—
114C4×C11#47912yes—
115C4×C11#49912yes—
116C4×C11#50112yes—
117Dic11—82no—
118Dic11—82no—
119Dic11—161no—
120C22×C8—22no—
121C22×C8—221no—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—112no—
124C2×C4⋊C4—112no—
125C2×C4⋊C4—221no—
126C2×C4⋊C4—222no—
127C2×C4⋊C4—222no—
128C2×C4⋊C4D4412yes—
129C2×C42—222no—
130C2×C42C22×D1111yescharacteristic
131#107—444no—
132#106—444no—
133C4⋊C8—22no—
134C4⋊C8Dic2214yes—
135C4×C8—112no—
136C4×C8—221no—
137#95—222no—
138#95—224no—
139#95—222no—
140C2×C11#162411yescharacteristic
141C2×C11#163011yescharacteristic
142C2×C11#165212yes—
143C2×C11#205912yes—
144C2×C11#206011yescharacteristic
145C22×C4—22no—
146C22×C4—222no—
147C22×C4—222no—
148C22×C4—441no—
149C22×C4C2×D4411yescharacteristic
150C22×C4D4×D1112yes—
151C2×C8—24no—
152C2×C8—42no—
153C2×C8—42no—
154C2×C8—222no—
155C2×C8—222no—
156C2×C8—222no—
157C4⋊C4—42no—
158C4⋊C4—42no—
159C4⋊C4—42no—
160C4⋊C4—222no—
161C4⋊C4—222no—
162C4⋊C4—222no—
163C4⋊C4—222no—
164C4⋊C4—442no—
165C4⋊C4—442no—
166C4⋊C4—442no—
167C4⋊C4—882no—
168C42—442no—
169C42—442no—
170C42C2×Dic2212yes—
171C42#434111yescharacteristic
172C42Q8×D1111yescharacteristic
173C11#1057711yescharacteristic, complemented, Sylow
174C23#6693511yescharacteristic
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—42no—
178C2×C4—44no—
179C2×C4—442no—
180C2×C4—442no—
181C2×C4—442no—
182C2×C4—442no—
183C2×C4—442no—
184C2×C4—442no—
185C2×C4—881no—
186C2×C4—882no—
187C2×C4#6692211yescharacteristic
188C2×C4#6693112yes—
189C2×C4#6694112yes—
190C2×C4#6695011yescharacteristic
191C2×C4#6696512yes—
192C2×C4#6696712yes—
193C2×C4#6696812yes—
194C2×C4#6697212yes—
195C8—44no—
196C8—224no—
197C22#1062226911yescharacteristic
198C22#1062236011yescharacteristic
199C22#1062236511yescharacteristic
200C22#1062239612yes—
201C22#1062242412yes—
202C4—21no—
203C4—21no—
204C4—82no—
205C4—882no—
206C4—882no—
207C4—1761no—
208C4#1062237912yes—
209C4#1062240912yes—
210C4#1062246912yes—
211C4#1062249112yes—
212C2#1306770011yescharacteristic
213C2#1306773811yescharacteristic
214C2#1306788712yes—
215C2#1306995712yes—
216C2#1306996211yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1296C2
socle, prime radicalC23×C11#120
hypercenter#1296D11
hypocenterC11#10577
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
173. C11#10577semidirect

Maximal subgroups

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

subgroupindex
#130738582
#130693752
#130687722
#130664552
C11×#12962
#1057711