Finite Group Databasebeta

← #14641570

Subgroups — #14641570

Order 2816.

266 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 59 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#13070301C211yesmaximal, characteristic
2#13069449C211yesmaximal, characteristic
3C11×#2132C211yesmaximal, characteristic
4C11×#532C2211yescharacteristic
5C11×#413—21no—
6#10622850—21no—
7C2×#66901—21no—
8C2×#66901—21no—
9#10622545C411yescharacteristic
10#10622537C411yescharacteristic
11C11×#356—21no—
12C11×#355C412yescomplemented
13#10622186—21no—
14#10622180C412yescomplemented
15C2×C11×#41D411yescharacteristic
16C2×C11×#41D411yescharacteristic
17C2×C11×M16—41no—
18C11×C4⋊Q8D411yescharacteristic
19C11×#127Q811yescharacteristic
20C11×#124C2×C411yescharacteristic
21C11×#124C2×C411yescharacteristic
22C11×#121—41no—
23C4×D4×C11—41no—
24C2×C42×C11C2×C411yescharacteristic
25C2×C4×Dic11—21no—
26C2×#4318—21no—
27C2×#4318—41no—
28C11×#101—22no—
29C11×#100—41no—
30#66901—42no—
31#66901—42no—
32#66900—22no—
33#66897—41no—
34C11⋊#95—41no—
35C4⋊(C11⋊C8)—41no—
36#7507—111nomaximal, Sylow
37C11×#41—41no—
38C11×#41—41no—
39C11×#41—41no—
40C11×#41—41no—
41C2×Q8×C11C22⋊C411yescharacteristic
42C2×Q8×C11C22⋊C411yescharacteristic
43C2×D4×C11—21no—
44C2×D4×C11—21no—
45C2×D4×C11—41no—
46C2×D4×C11C4⋊C411yescharacteristic
47C2×D4×C11C4⋊C411yescharacteristic
48C22×C4×C11—21no—
49C22×C4×C11—21no—
50C22×C4×C11—21no—
51C22×C4×C11C22⋊C411yescharacteristic
52C22×Dic11—41no—
53C11×M16—42no—
54C11×M16—81no—
55C2×C8×C11—81no—
56C11×C4⋊C4—41no—
57C11×C22⋊C4—41no—
58C11×C22⋊C4—41no—
59C42×C11—21no—
60C42×C11C4211yescharacteristic
61C42×C11C4⋊C411yescharacteristic
62C4×Dic11—22no—
63C4×Dic11—41no—
64#4318—42no—
65#4318—41no—
66#4318—41no—
67#4318—81no—
68C2×C11⋊C8—41no—
69C2×C11⋊C8—81no—
70#2132—111no—
71#2132D1111yescharacteristic
72#1963—111no—
73C23×C11—21no—
74C23×C11—21no—
75C23×C11#9911yescharacteristic
76Q8×C11—41no—
77Q8×C11—41no—
78D4×C11—41no—
79D4×C11—41no—
80D4×C11—81no—
81D4×C11—81no—
82D4×C11—82no—
83C2×C4×C11—21no—
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11—21no—
87C2×C4×C11—21no—
88C2×C4×C11—21no—
89C2×C4×C11—41no—
90C2×C4×C11—41no—
91C2×C4×C11—41no—
92C2×C4×C11—41no—
93C2×C4×C11—81no—
94C2×C4×C11#9511yescharacteristic
95C2×C4×C11#9911yescharacteristic
96C2×Dic11—42no—
97C2×Dic11—82no—
98C8×C11—82no—
99C11⋊C8—82no—
100C11⋊C8—81no—
101#532C2×D1111yescharacteristic
102#423—111no—
103C2×#104—221no—
104C2×#104—221no—
105#413—21no—
106#413—221no—
107#376—111no—
108#356—21no—
109#356—221no—
110#355—112no—
111#355Dic1112yescomplemented
112C22×C11—21no—
113C22×C11—41no—
114C22×C11—41no—
115C22×C11—41no—
116C22×C11—81no—
117C22×C11—81no—
118C22×C11#34211yescharacteristic
119C4×C11—21no—
120C4×C11—41no—
121C4×C11—41no—
122C4×C11—41no—
123C4×C11—41no—
124C4×C11#35311yescharacteristic
125C4×C11#35411yescharacteristic
126Dic11—82no—
127C2×#41D4411yescharacteristic
128C2×#41C22⋊D1111yescharacteristic
129C2×M16—41no—
130C2×M16—221no—
131C2×M16—441no—
132C4⋊Q8C22⋊D1111yescharacteristic
133#127Dic2211yescharacteristic
134#124C4×D1111yescharacteristic
135#124C2×Dic1111yescharacteristic
136#121—41no—
137C4×D4—41no—
138C2×C42—221no—
139C2×C42C4×D1111yescharacteristic
140C4⋊C8—441no—
141#104—442no—
142#104—442no—
143#101—22no—
144#101—222no—
145#100—41no—
146#100—441no—
147#95—441no—
148C2×C11—21no—
149C2×C11—41no—
150C2×C11—81no—
151C2×C11—81no—
152C2×C11#139311yescharacteristic
153#41—41no—
154#41—41no—
155#41—41no—
156#41—41no—
157C2×Q8(C2×D11)⋊C411yescharacteristic
158C2×Q8C22⋊Dic1111yescharacteristic
159C2×D4—21no—
160C2×D4—21no—
161C2×D4—41no—
162C2×D4Dic11⋊C411yescharacteristic
163C2×D4C4⋊Dic1111yescharacteristic
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—441no—
168C22×C4(C2×D11)⋊C411yescharacteristic
169M16—42no—
170M16—81no—
171M16—442no—
172M16—441no—
173M16—441no—
174M16—881no—
175C2×C8—81no—
176C2×C8—441no—
177C2×C8—881no—
178C4⋊C4—41no—
179C22⋊C4—41no—
180C22⋊C4—41no—
181C42—21no—
182C42—222no—
183C42—441no—
184C42C4×Dic1111yescharacteristic
185C42Dic11⋊C411yescharacteristic
186C11#750711yescharacteristic, complemented, Sylow
187C23—21no—
188C23—21no—
189C23#6687011yescharacteristic
190Q8—41no—
191Q8—41no—
192D4—41no—
193D4—41no—
194D4—81no—
195D4—81no—
196D4—82no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—81no—
208C2×C4—442no—
209C2×C4—882no—
210C2×C4#6687011yescharacteristic
211C2×C4C11⋊#9511yescharacteristic
212C8—82no—
213C8—882no—
214C8—881no—
215C22—21no—
216C22—41no—
217C22—41no—
218C22—41no—
219C22—81no—
220C22—81no—
221C22#1062216511yescharacteristic
222C4—21no—
223C4—41no—
224C4—41no—
225C4—41no—
226C4—41no—
227C4—882no—
228C4#1062211111yescharacteristic
229C4#1062211211yescharacteristic
230C2—21no—
231C2—41no—
232C2—81no—
233C2—81no—
234C2#1306674011yescharacteristic
subgroupG/H
centerC4#10622112
commutatorC42×C11C42
Frattini#532C2×D11
FittingC11×#2132C2
socleC2×C11#1393
prime radical, cosocleC11×#532C22
hypercenter#2132D11
hypocenterC11#7507
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #532 ◁ #2132

Complements

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

NH ≅ G/Ntype
12. C11×#355C4semidirect
14. #10622180C4semidirect
111. #355Dic11semidirect
186. C11#7507semidirect

Maximal subgroups

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

subgroupindex
#130703012
#130694492
C11×#21322
#750711