Finite Group Databasebeta

← #14640593

Subgroups — #14640593

Order 2816.

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

normal subgroups only

This group has 368 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#13066459C212yesmaximal
2C11×#1445C211yesmaximal, characteristic
3C22×C11×C4⋊C4C411yescharacteristic
4C2×C11×#95—22no—
5C2×C11×#95C411yescharacteristic
6C2×C11×#95C2211yescharacteristic
7C2×C22⋊(C11⋊C8)—22no—
8C23×C4×C11—21no—
9C23×C4×C11—21no—
10C23×C4×C11C2×C411yescharacteristic
11C23×C4×C11D412yes—
12C2×C11×C4⋊C4—21no—
13C2×C11×C4⋊C4—41no—
14C2×C11×C4⋊C4—41no—
15C2×C11×C4⋊C4C812yescomplemented
16C22×C11⋊C8—42no—
17C11×#95—41no—
18C11×#95—41no—
19C11×#95—44no—
20C22⋊(C11⋊C8)—24no—
21C22⋊(C11⋊C8)—42no—
22#7132—111nomaximal, Sylow
23C24×C11C22⋊C411yescharacteristic
24C22×C4×C11—22no—
25C22×C4×C11—21no—
26C22×C4×C11—21no—
27C22×C4×C11—22no—
28C22×C4×C11—22no—
29C22×C4×C11—22no—
30C22×C4×C11—42no—
31C22×C4×C11—42no—
32C22×C4×C11—42no—
33C22×C4×C11—42no—
34C22×C4×C11—42no—
35C22×C4×C11—41no—
36C22×C4×C11—42no—
37C22×C4×C11—41no—
38C22×C4×C11—41no—
39C22×C4×C11—41no—
40C22×C4×C11—42no—
41C22×C4×C11C2×C811yescharacteristic
42C22×C4×C11M1611yescharacteristic
43C22×C4×C11SD1612yes—
44C22×C4×C11Q1612yes—
45C11×C4⋊C4—42no—
46C11×C4⋊C4—42no—
47C2×C11⋊C8—44no—
48C2×C11⋊C8—82no—
49C2×C11⋊C8—82no—
50#1445D1111yescharacteristic
51#1280—112no—
52C23×C11—22no—
53C23×C11—21no—
54C23×C11—21no—
55C23×C11C22⋊C811yescharacteristic
56C23×C11#9911yescharacteristic
57C23×C11#10011yescharacteristic
58C23×C11#10312yes—
59C23×C11#10412yes—
60C2×C4×C11—21no—
61C2×C4×C11—21no—
62C2×C4×C11—22no—
63C2×C4×C11—22no—
64C2×C4×C11—42no—
65C2×C4×C11—42no—
66C2×C4×C11—42no—
67C2×C4×C11—42no—
68C2×C4×C11—41no—
69C2×C4×C11—41no—
70C2×C4×C11—42no—
71C2×C4×C11—42no—
72C2×C4×C11—42no—
73C2×C4×C11—44no—
74C2×C4×C11—44no—
75C2×C4×C11—42no—
76C2×C4×C11—82no—
77C2×C4×C11—81no—
78C2×C4×C11—82no—
79C2×C4×C11—82no—
80C2×C4×C11—81no—
81C2×C4×C11—81no—
82C2×C4×C11—81no—
83C11⋊C8—84no—
84C22×C4⋊C4Dic1111yescharacteristic
85C2×C22⋊C8—222no—
86C2×#95—22no—
87C2×#95Dic1111yescharacteristic
88C2×#95C2×D1111yescharacteristic
89C22×C11—21no—
90C22×C11—21no—
91C22×C11—21no—
92C22×C11—21no—
93C22×C11—22no—
94C22×C11—22no—
95C22×C11—22no—
96C22×C11—22no—
97C22×C11#32311yescharacteristic
98C22×C11Q8⋊C812yes—
99C22×C11#32812yes—
100C22×C11#32911yescharacteristic
101C22×C11#33311yescharacteristic
102C22×C11#35212yes—
103C22×C11#35311yescharacteristic
104C22×C11#35511yescharacteristic
105C4×C11—41no—
106C4×C11—41no—
107C4×C11—42no—
108C4×C11—42no—
109C4×C11—82no—
110C4×C11—82no—
111C23×C4—21no—
112C23×C4—21no—
113C23×C4C2×Dic1111yescharacteristic
114C23×C4C22⋊D1112yes—
115C22×C8—442no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4—41no—
118C2×C4⋊C4—41no—
119C2×C4⋊C4C11⋊C812yescomplemented
120C22⋊C8—224no—
121C22⋊C8—442no—
122#95—41no—
123#95—41no—
124#95—44no—
125C2×C11—21no—
126C2×C11—22no—
127C2×C11—21no—
128C2×C11#127211yescharacteristic
129C2×C11#131711yescharacteristic
130C2×C11#131811yescharacteristic
131C2×C11#135212yes—
132C2×C11#135312yes—
133C24C22⋊Dic1111yescharacteristic
134C22×C4—21no—
135C22×C4—21no—
136C22×C4—22no—
137C22×C4—22no—
138C22×C4—22no—
139C22×C4—22no—
140C22×C4—42no—
141C22×C4—42no—
142C22×C4—42no—
143C22×C4—42no—
144C22×C4—42no—
145C22×C4—41no—
146C22×C4—42no—
147C22×C4—41no—
148C22×C4—41no—
149C22×C4—41no—
150C22×C4—42no—
151C22×C4C2×C11⋊C811yescharacteristic
152C22×C4#431811yescharacteristic
153C22×C4#432512yes—
154C22×C4#432612yes—
155C2×C8—444no—
156C2×C8—882no—
157C2×C8—882no—
158C4⋊C4—42no—
159C4⋊C4—42no—
160C11#713211yescharacteristic, complemented, Sylow
161C23—22no—
162C23—21no—
163C23—21no—
164C23C22⋊(C11⋊C8)11yescharacteristic
165C23#6689711yescharacteristic
166C23#6689811yescharacteristic
167C23#6689912yes—
168C23#6690112yes—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—44no—
183C2×C4—44no—
184C2×C4—42no—
185C2×C4—82no—
186C2×C4—81no—
187C2×C4—82no—
188C2×C4—82no—
189C2×C4—81no—
190C2×C4—81no—
191C2×C4—81no—
192C8—884no—
193C22—21no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—22no—
198C22—22no—
199C22—22no—
200C22—22no—
201C22#1062216311yescharacteristic
202C22Q8⋊(C11⋊C8)12yes—
203C22#1062217612yes—
204C22#1062217712yes—
205C22#1062217811yescharacteristic
206C22#1062218011yescharacteristic
207C22#1062218311yescharacteristic
208C22#1062218411yescharacteristic
209C4—41no—
210C4—41no—
211C4—42no—
212C4—42no—
213C4—82no—
214C4—82no—
215C2—21no—
216C2—22no—
217C2—21no—
218C2#1306644211yescharacteristic
219C2#1306654611yescharacteristic
220C2#1306654811yescharacteristic
221C2#1306664012yes—
222C2#1306664312yes—
subgroupG/H
centerC23#66898
commutatorC22×C4×C11C2×C8
FrattiniC2×#95C2×D11
FittingC11×#1445C2
socleC23×C11#99
prime radicalC24×C11C22⋊C4
cosocleC2×C11×#95C22
hypercenter#1445D11
hypocenterC11#7132
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24 ◁ C2×#95 ◁ #1445

Complements

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

NH ≅ G/Ntype
15. C2×C11×C4⋊C4C8semidirect
119. C2×C4⋊C4C11⋊C8semidirect
160. C11#7132semidirect

Maximal subgroups

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

subgroupindex
#130664592
C11×#14452
#713211