Finite Group Databasebeta

← #14665716

Subgroups — #14665716

Order 2816.

210 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C4×Dic88C211yesmaximal, characteristic
2#13067512C211yesmaximal, characteristic
3#13067422C211yesmaximal, characteristic
4#13066579C211yesmaximal, characteristic
5#13066579C211yesmaximal, characteristic
6#13066535C211yesmaximal, characteristic
7C11×#1372C211yesmaximal, characteristic
8C2×Dic88C411yescharacteristic
9#10622444—21no—
10#10622443—21no—
11C4×Dic44C2211yescharacteristic
12C4×Dic44C2211yescharacteristic
13C4×C11×C16C2211yescharacteristic
14C11×#335C2211yescharacteristic
15C11×#335C2211yescharacteristic
16#10622142C411yescharacteristic
17#10622141C411yescharacteristic
18#10622141C411yescharacteristic
19#10622122—21no—
20#10622122—21no—
21C4×C11⋊C16C2211yescharacteristic
22C8×C11⋊C8C2211yescharacteristic
23C2×Dic44C2×C411yescharacteristic
24C2×Dic44C2×C411yescharacteristic
25C4×Dic22—21no—
26C4×Dic22—21no—
27C2×C11×C16C2×C411yescharacteristic
28C2×C11×C16C2×C411yescharacteristic
29C11×C4⋊C8—21no—
30C11×C4⋊C8—21no—
31C4×C8×C11C2311yescharacteristic
32#66882C2×C411yescharacteristic
33#66882C2×C411yescharacteristic
34#66880—21no—
35#66880—21no—
36#66879—41no—
37Dic11⋊C8—41no—
38Dic11⋊C8—41no—
39C8×Dic11—41no—
40C2×C11⋊C16—21no—
41C4×C11⋊C8D411yescharacteristic
42C4×C11⋊C8D411yescharacteristic
43Dic88—22no—
44#12076—111nomaximal, Sylow
45C2×Dic22—21no—
46C2×Dic22—21no—
47C2×C8×C11—41no—
48C2×C8×C11—41no—
49C2×C8×C11C22×C411yescharacteristic
50C2×C8×C11#4111yescharacteristic
51C42×C11C2×D411yescharacteristic
52C4⋊Dic11—21no—
53C4⋊Dic11—21no—
54Dic11⋊C4—41no—
55Dic11⋊C4—41no—
56C4×Dic11—41no—
57C4×Dic11—41no—
58C2×C11⋊C8—21no—
59C2×C11⋊C8D811yescharacteristic
60C2×C11⋊C8D811yescharacteristic
61Dic44—21no—
62Dic44—21no—
63Dic44—21no—
64Dic44M1612yes—
65C11×C16—21no—
66C11×C16—21no—
67C11⋊C16—41no—
68C4×Q32—111no—
69#1591—111no—
70C8×Q16—111no—
71#1372D1111yescharacteristic
72#1332—111no—
73#1332—111no—
74#1312—111no—
75C2×C4×C11C4×D411yescharacteristic
76C2×C4×C11C2×D811yescharacteristic
77C2×C4×C11#13511yescharacteristic
78C2×Dic11—41no—
79C2×Dic11—41no—
80C2×Dic11—41no—
81C2×Dic11—41no—
82Dic22—22no—
83Dic22—41no—
84Dic22—41no—
85Dic22—41no—
86C8×C11—21no—
87C8×C11—81no—
88C8×C11—81no—
89C8×C11C2×M1611yescharacteristic
90C8×C11#13111yescharacteristic
91C11⋊C8—22no—
92C11⋊C8—21no—
93C11⋊C8—21no—
94C2×Q32—111no—
95#446—221no—
96C8×Q8—221no—
97C4×Q16—111no—
98C4×Q16—111no—
99#366—111no—
100#358—111no—
101#358—111no—
102C4×C16—111no—
103C4×C16C2×D1111yescharacteristic
104#335C2×D1111yescharacteristic
105#335C2×D1111yescharacteristic
106Q8⋊C8—221no—
107Q8⋊C8—221no—
108C82—111no—
109C22×C11C4×D811yescharacteristic
110C4×C11—21no—
111C4×C11#43511yescharacteristic
112C4×C11#44411yescharacteristic
113C4×C11#51011yescharacteristic
114C4×C11#51011yescharacteristic
115Dic11—42no—
116Dic11—81no—
117Dic11—81no—
118Dic11—81no—
119C2×Q16—111no—
120C2×Q16—111no—
121C4×Q8—221no—
122C4×Q8—221no—
123Q32—222no—
124C2×C16—221no—
125C2×C16C4×D1111yescharacteristic
126C2×C16C4×D1111yescharacteristic
127#107—111no—
128#107—111no—
129C4⋊C8—21no—
130C4⋊C8—21no—
131C4⋊C8—441no—
132C4⋊C8—441no—
133#103—221no—
134#103—221no—
135#97—441no—
136C4×C8—111no—
137C4×C8—111no—
138C4×C8—441no—
139C4×C8C22×D1111yescharacteristic
140C2×C11#158111yescharacteristic
141C2×C11#217611yescharacteristic
142C2×C11#217811yescharacteristic
143C2×Q8—221no—
144C2×Q8—221no—
145Q16—112no—
146Q16—221no—
147Q16—221no—
148Q16—221no—
149C2×C8—41no—
150C2×C8—41no—
151C2×C8—111no—
152C2×C8—111no—
153C2×C8—221no—
154C2×C8C2×C4×D1111yescharacteristic
155C2×C8#434311yescharacteristic
156C4⋊C4—221no—
157C4⋊C4—221no—
158C4⋊C4—441no—
159C4⋊C4—441no—
160C42—441no—
161C42—441no—
162C42D4×D1111yescharacteristic
163C16—21no—
164C16—21no—
165C16—441no—
166C11#1207611yescharacteristic, complemented, Sylow
167Q8—222no—
168Q8—441no—
169Q8—441no—
170Q8—441no—
171C2×C4—441no—
172C2×C4—441no—
173C2×C4—441no—
174C2×C4—441no—
175C2×C4#6694611yescharacteristic
176C2×C4D8×D1111yescharacteristic
177C2×C4#6697211yescharacteristic
178C8—21no—
179C8—81no—
180C8—81no—
181C8—222no—
182C8—221no—
183C8—221no—
184C8#6695411yescharacteristic
185C8M16×D1111yescharacteristic
186C22#1062248511yescharacteristic
187C4—21no—
188C4—442no—
189C4—881no—
190C4—881no—
191C4—881no—
192C4#1062244911yescharacteristic
193C4#1062250711yescharacteristic
194C4#1062252811yescharacteristic
195C4#1062252811yescharacteristic
196C2#1306744411yescharacteristic
197C2#1307048611yescharacteristic
198C2#1307049611yescharacteristic
subgroupG/H
centerC2×C4D8×D11
commutatorC2×C8×C11C22×C4
FrattiniC4×C8C22×D11
FittingC11×#1372C2
socle, prime radicalC22×C11C4×D8
cosocleC4×C8×C11C23
hypercenter#1372D11
hypocenterC11#12076
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ #1372

Complements

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

NH ≅ G/Ntype
166. C11#12076semidirect

Maximal subgroups

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

subgroupindex
C4×Dic882
#130675122
#130674222
#130665792
#130665352
C11×#13722
#1207611