Finite Group Databasebeta

← #14658654

Subgroups — #14658654

Order 2816.

258 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 69 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#13067392C211yesmaximal, characteristic, complemented
2#13067311C211yesmaximal, characteristic
3#13067085C211yesmaximal, characteristic
4#13066527C211yesmaximal, characteristic, complemented
5#13066485C211yesmaximal, characteristic, complemented
6#13066479C211yesmaximal, characteristic, complemented
7C11×#1557C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C11×#432C2211yescharacteristic
10C11×#423C2211yescharacteristic
11#10622539C2211yescharacteristic
12#10622539C2211yescharacteristic
13#10622538C2211yescharacteristic
14C2×C4⋊(C11⋊C8)C2211yescharacteristic
15C11×#332—21no—
16C11×#331—21no—
17#10622184—21no—
18#10622182—21no—
19D4⋊(C11⋊C8)—22no—
20#10622117—22no—
21C2×C11×#41—21no—
22C2×C11×M16—21no—
23C11×C4⋊Q8D411yescharacteristic
24C11×#127D411yescharacteristic
25C11×#124—21no—
26C11×#121—21no—
27C11×#121—21no—
28C4×D4×C11—21no—
29C4×D4×C11—21no—
30C2×C42×C11C2311yescharacteristic
31C22×C11⋊C8—21no—
32C11×C4⋊C8—21no—
33C11×C4⋊C8—21no—
34C11×C4⋊C8—21no—
35C11×C22⋊C8—21no—
36C11×#97—21no—
37C22⋊(C11⋊C8)—21no—
38C22⋊(C11⋊C8)—21no—
39C22⋊(C11⋊C8)—21no—
40C4⋊(C11⋊C8)—21no—
41C4⋊(C11⋊C8)—21no—
42C4⋊(C11⋊C8)—21no—
43C4⋊(C11⋊C8)—21no—
44C4⋊(C11⋊C8)—21no—
45#66867—21no—
46#66867—21no—
47C4×C11⋊C8D412yes—
48#10645—111nomaximal, Sylow
49C11×#41—82no—
50C2×Q8×C11—21no—
51C2×D4×C11—21no—
52C2×D4×C11—21no—
53C2×D4×C11—21no—
54C2×D4×C11—41no—
55C22×C4×C11—41no—
56C22×C4×C11#4111yescharacteristic
57C22×C4×C11#4111yescharacteristic
58C22×C4×C11#4111yescharacteristic
59C11×M16—81no—
60C2×C8×C11—41no—
61C2×C8×C11—41no—
62C11×C4⋊C4—21no—
63C11×C4⋊C4—21no—
64C11×C22⋊C4—41no—
65C11×C22⋊C4—41no—
66C42×C11C2×D411yescharacteristic
67C42×C11C2×D411yescharacteristic
68C42×C11#4111yescharacteristic
69C42×C11#4111yescharacteristic
70C2×C11⋊C8—22no—
71C2×C11⋊C8—41no—
72C2×C11⋊C8—41no—
73C2×C11⋊C8—41no—
74C2×C11⋊C8—81no—
75#1571—111no—
76#1557D1111yescharacteristic
77#1551—111no—
78#1496—111no—
79#1307—111no—
80#1290—111no—
81#1287—111no—
82C23×C11—41no—
83C23×C11#12611yescharacteristic
84Q8×C11—81no—
85D4×C11—41no—
86D4×C11—41no—
87D4×C11—81no—
88D4×C11—81no—
89D4×C11—82no—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11—41no—
93C2×C4×C11—41no—
94C2×C4×C11—41no—
95C2×C4×C11—82no—
96C2×C4×C11#12111yescharacteristic
97C2×C4×C11#12311yescharacteristic
98C2×C4×C11#12311yescharacteristic
99C2×C4×C11#12311yescharacteristic
100C2×C4×C11#12411yescharacteristic
101C2×C4×C11#12611yescharacteristic
102C8×C11—81no—
103C8×C11—81no—
104C11⋊C8—42no—
105C11⋊C8—81no—
106C11⋊C8—81no—
107C11⋊C8—81no—
108#532C2×D1111yescharacteristic
109#432—111no—
110#432—111no—
111#432C2×D1111yescharacteristic
112#431—111no—
113#423C2×D1111yescharacteristic
114C2×C4⋊C8—111no—
115#335—222no—
116#333—221no—
117#332—21no—
118#331—21no—
119#331—221no—
120D4⋊C8—222no—
121C22×C11—21no—
122C22×C11—21no—
123C22×C11—21no—
124C22×C11—81no—
125C22×C11—81no—
126C22×C11—81no—
127C22×C11#39711yescharacteristic
128C4×C11—21no—
129C4×C11—21no—
130C4×C11—21no—
131C4×C11—21no—
132C4×C11—21no—
133C4×C11—81no—
134C4×C11#47211yescharacteristic
135C4×C11#47311yescharacteristic
136C2×#41—21no—
137C2×M16—21no—
138C22×C8—221no—
139C4⋊Q8C22⋊D1111yescharacteristic
140#127C22⋊D1111yescharacteristic
141#124—21no—
142#121—21no—
143#121—21no—
144C4×D4—21no—
145C4×D4—21no—
146C2×C42C22×D1111yescharacteristic
147C4⋊C8—21no—
148C4⋊C8—21no—
149C4⋊C8—21no—
150C4⋊C8—221no—
151C4⋊C8—221no—
152C4⋊C8—221no—
153C4⋊C8—221no—
154C4⋊C8—221no—
155C22⋊C8—21no—
156C22⋊C8—221no—
157C22⋊C8—221no—
158C22⋊C8—221no—
159#97—21no—
160#97—221no—
161#97—221no—
162C4×C8—112no—
163C2×C11—41no—
164C2×C11—161no—
165C2×C11#207811yescharacteristic
166C2×C11#208011yescharacteristic
167C2×C11#208111yescharacteristic
168#41—82no—
169C2×Q8—21no—
170C2×D4—21no—
171C2×D4—21no—
172C2×D4—21no—
173C2×D4—41no—
174C22×C4—41no—
175C22×C4#433911yescharacteristic
176C22×C4#434111yescharacteristic
177C22×C4#434111yescharacteristic
178M16—81no—
179C2×C8—41no—
180C2×C8—41no—
181C2×C8—222no—
182C2×C8—441no—
183C2×C8—441no—
184C2×C8—441no—
185C2×C8—881no—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C22⋊C4—41no—
189C22⋊C4—41no—
190C42#433911yescharacteristic
191C42D4×D1111yescharacteristic
192C42#434111yescharacteristic
193C42C2×C22⋊D1111yescharacteristic
194C11#1064511yescharacteristic, complemented, Sylow
195C23—41no—
196C23#6693211yescharacteristic
197Q8—81no—
198D4—41no—
199D4—41no—
200D4—81no—
201D4—81no—
202D4—82no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—82no—
209C2×C4#6693211yescharacteristic
210C2×C4#6693611yescharacteristic
211C2×C4#6693811yescharacteristic
212C2×C4#6698211yescharacteristic
213C2×C4#6698811yescharacteristic
214C2×C4#6699211yescharacteristic
215C8—81no—
216C8—81no—
217C8—442no—
218C8—881no—
219C8—881no—
220C8—881no—
221C22—21no—
222C22—21no—
223C22—21no—
224C22—81no—
225C22—81no—
226C22—81no—
227C22#1062256511yescharacteristic
228C4—21no—
229C4—21no—
230C4—21no—
231C4—21no—
232C4—21no—
233C4—81no—
234C4#1062281211yescharacteristic
235C4#1062281711yescharacteristic
236C2—41no—
237C2—161no—
238C2#1307005911yescharacteristic
239C2#1307006911yescharacteristic
240C2#1307007711yescharacteristic
subgroupG/H
centerC22#10622565
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1557C2
socleC22×C11#397
prime radicalC11×#532C22
hypercenter#1557D11
hypocenterC11#10645
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1557

Complements

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

NH ≅ G/Ntype
1. #13067392C2semidirect
4. #13066527C2semidirect
5. #13066485C2semidirect
6. #13066479C2semidirect
194. C11#10645semidirect

Maximal subgroups

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

subgroupindex
#130673922
#130673112
#130670852
#130665272
#130664852
#130664792
C11×#15572
#1064511