Finite Group Databasebeta

← #14664973

Subgroups — #14664973

Order 2816.

280 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 61 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#13079018C211yesmaximal, characteristic
2#13070426C212yesmaximal, complemented
3#13066651C211yesmaximal, characteristic, complemented
4#13066648C212yesmaximal, complemented
5C11×#1356C211yesmaximal, characteristic, complemented
6#10623256C411yescharacteristic
7D11×#125C411yescharacteristic
8C11×#491C2211yescharacteristic
9#10622695C411yescharacteristic
10#10622680C411yescharacteristic
11#10622416—22no—
12#10622413—22no—
13#10622326C2211yescharacteristic
14#10622320C2211yescharacteristic
15C11×#347C2212yes—
16#10622152—22no—
17#10622149—22no—
18#10622104C2212yes—
19C2×#4343—21no—
20C11×C4⋊Q8C2×C411yescharacteristic
21C11×#125C2×C411yescharacteristic
22#67000—21no—
23C2×#4313D412yes—
24#66948—41no—
25#66946—41no—
26C4⋊C4×D11—21no—
27C4⋊C4×D11—41no—
28#66943—21no—
29#66942—41no—
30#66927C2×C411yescharacteristic
31C42×D11C2×C411yescharacteristic
32#66923C2×C411yescharacteristic
33C11×M32—22no—
34C11×#103—22no—
35C11×#97C2311yescharacteristic
36#66899—22no—
37#66885—22no—
38C8×Dic11D412yes—
39#66876—22no—
40#66873—22no—
41#66867C2×C411yescharacteristic
42#11917—111nomaximal, Sylow
43C2×Q8×C11—21no—
44#4343—44no—
45C2×D44—21no—
46C2×D44—41no—
47C2×D44—41no—
48C2×C4×D11—21no—
49C2×C4×D11—41no—
50C2×C4×D11—41no—
51C2×C4×D11C22⋊C411yescharacteristic
52C2×C8×C11C2×D412yes—
53C11×C4⋊C4—21no—
54C11×C4⋊C4—41no—
55C11×C4⋊C4—41no—
56C42×C11C22×C411yescharacteristic
57(C2×D11)⋊C4—42no—
58C4⋊Dic11—21no—
59C4⋊Dic11—41no—
60Dic11⋊C4—41no—
61Dic11⋊C4—41no—
62Dic11⋊C4—41no—
63C4×Dic11—21no—
64C4×Dic11C22⋊C411yescharacteristic
65C2×C11⋊C8C22⋊C412yes—
66#4313—42no—
67C11×C16—42no—
68C11⋊C16—42no—
69#3142—111no—
70#2165—112no—
71#1356—111no—
72#1356D1111yescharacteristic, complemented
73#1355—112no—
74C22×D11—41no—
75C22×D11#10011yescharacteristic
76Q8×C11—42no—
77C2×C4×C11—21no—
78C2×C4×C11—41no—
79C2×C4×C11—41no—
80C2×C4×C11C2×C22⋊C411yescharacteristic
81C2×Dic11—21no—
82C2×Dic11—41no—
83C2×Dic11#10011yescharacteristic
84D44—42no—
85D44—82no—
86D44—82no—
87C4×D11—22no—
88C4×D11—82no—
89C4×D11—81no—
90C4×D11—82no—
91C8×C11—22no—
92C11⋊C8—22no—
93#532—111no—
94C2×#125—111no—
95#491—111no—
96#491C2×D1111yescharacteristic
97#490—111no—
98#490—111no—
99#488—222no—
100#417—222no—
101C4×M16—111no—
102#364—222no—
103#349—222no—
104#347—112no—
105#347C2×D1112yes—
106C22×C11C2×#10011yescharacteristic
107C2×D11—21no—
108C2×D11—41no—
109C2×D11—82no—
110C2×D11—81no—
111C4×C11—41no—
112C4×C11—81no—
113C4×C11—81no—
114C4×C11#42112yes—
115Dic11—21no—
116Dic11—41no—
117Dic11—81no—
118C2×#41—221no—
119C2×M16—112no—
120C4⋊Q8C4×D1111yescharacteristic
121#127—111no—
122#125—111no—
123#125—221no—
124#125—441no—
125#125C4×D1111yescharacteristic
126#124—221no—
127#121—441no—
128C4×D4—441no—
129C2×C4⋊C4—221no—
130C2×C4⋊C4—441no—
131C2×C42—111no—
132M32—22no—
133M32—222no—
134#103—22no—
135#103—222no—
136#102—222no—
137#102—222no—
138#97—111no—
139#97C22×D1111yescharacteristic
140C4×C8—112no—
141C2×C11—21no—
142C2×C11#153311yescharacteristic
143D11—41no—
144D11—161no—
145#41—444no—
146C2×Q8—21no—
147C2×D4—221no—
148C2×D4—441no—
149C2×D4—441no—
150C22×C4—111no—
151C22×C4—221no—
152C22×C4—441no—
153C22×C4—441no—
154M16—442no—
155C2×C8—112no—
156C2×C8D4×D1112yes—
157C4⋊C4—21no—
158C4⋊C4—41no—
159C4⋊C4—41no—
160C4⋊C4—221no—
161C4⋊C4—441no—
162C4⋊C4—441no—
163C4⋊C4—441no—
164C4⋊C4—441no—
165C22⋊C4—442no—
166C42—111no—
167C42—221no—
168C42C2×C4×D1111yescharacteristic
169C16—42no—
170C16—442no—
171C11#1191711yescharacteristic, complemented, Sylow
172C23—111no—
173C23—441no—
174Q8—42no—
175D4—442no—
176D4—882no—
177D4—882no—
178C2×C4—21no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—111no—
182C2×C4—222no—
183C2×C4—221no—
184C2×C4—441no—
185C2×C4—881no—
186C2×C4—882no—
187C2×C4—882no—
188C2×C4C22⋊C4×D1111yescharacteristic
189C8—22no—
190C8—222no—
191C22—221no—
192C22—441no—
193C22—882no—
194C22—881no—
195C22D11×#10011yescharacteristic
196C4—41no—
197C4—81no—
198C4—81no—
199C4—221no—
200C4—441no—
201C4—881no—
202C4#1062243412yes—
203C2—21no—
204C2—441no—
205C2—1761no—
206C2#1306723811yescharacteristic
subgroupG/H
centerC2#13067238
commutatorC42×C11C22×C4
Frattini#97C22×D11
FittingC11×#1356C2
socleC2×C11#1533
prime radical#10623256C4
cosocleC11×#97C23
hypercenter#1356D11
hypocenterC11#11917
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #1356

Complements

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

NH ≅ G/Ntype
2. #13070426C2semidirect
3. #13066651C2semidirect
4. #13066648C2semidirect
5. C11×#1356C2semidirect
72. #1356D11semidirect
171. C11#11917semidirect

Maximal subgroups

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

subgroupindex
#130790182
#130704262
#130666512
#130666482
C11×#13562
#1191711