Finite Group Databasebeta

← #13069972

Subgroups — #13069972

Order 1408.

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

normal subgroups only

This group has 228 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
1C2×C11×#100C211yesmaximal, characteristic
2#10622828C211yesmaximal, characteristic
3C2×#66896C211yesmaximal, characteristic
4C2×#66886C211yesmaximal, characteristic, complemented
5#10622734C211yesmaximal, characteristic, complemented
6#10622732C211yesmaximal, characteristic, complemented
7#10622192C211yesmaximal, characteristic, complemented
8C22×D4×C11C2211yescharacteristic
9C2×C11×M16C2211yescharacteristic
10C2×C11×M16C2211yescharacteristic
11#66979C2211yescharacteristic
12C2×C4⋊Dic11C2211yescharacteristic
13C2×#4318C2211yescharacteristic
14C22×C11⋊C8C2211yescharacteristic
15C11×#100—22no—
16#66896—21no—
17#66896—21no—
18#66896—22no—
19#66886—22no—
20#66882—21no—
21#66881—21no—
22Dic11⋊C8—22no—
23C24×C11—21no—
24C2×D4×C11—21no—
25C2×D4×C11—21no—
26C2×D4×C11—21no—
27C2×D4×C11—21no—
28C2×D4×C11—21no—
29C2×D4×C11Q812yes—
30C22×C4×C11C2311yescharacteristic
31C22×Dic11—21no—
32C11×M16—21no—
33C11×M16—21no—
34C11×M16—21no—
35C11×M16D412yes—
36C2×C8×C11—21no—
37C2×C8×C11—21no—
38C22⋊Dic11—21no—
39C4⋊Dic11—21no—
40C4⋊Dic11—21no—
41C4⋊Dic11D411yescharacteristic
42C4⋊Dic11D411yescharacteristic
43C4×Dic11—21no—
44#4318—21no—
45#4318—21no—
46C2×C11⋊C8—21no—
47C2×C11⋊C8—21no—
48C2×C11⋊C8—21no—
49C2×C11⋊C8D412yes—
50#2063—111nomaximal, Sylow
51C23×C11—22no—
52C23×C11—41no—
53C23×C11—41no—
54C23×C11—81no—
55C23×C11—81no—
56C23×C11#4111yescharacteristic
57D4×C11—22no—
58D4×C11—22no—
59D4×C11—41no—
60D4×C11—41no—
61C2×C4×C11C2×D411yescharacteristic
62C2×C4×C11C2×D411yescharacteristic
63C2×C4×C11C2×D411yescharacteristic
64C2×C4×C11C2×Q811yescharacteristic
65C2×C4×C11#4111yescharacteristic
66C2×C4×C11#4111yescharacteristic
67C2×Dic11—21no—
68C2×Dic11—21no—
69C2×Dic11—41no—
70C2×Dic11—81no—
71C8×C11—22no—
72C8×C11—41no—
73C11⋊C8—22no—
74C11⋊C8—41no—
75C2×#108—111no—
76#428—111no—
77#424—111no—
78#418—111no—
79C2×#102—111no—
80C2×#100D1111yescharacteristic
81#343—111no—
82C22×C11—21no—
83C22×C11—21no—
84C22×C11—42no—
85C22×C11—82no—
86C22×C11—82no—
87C22×C11—81no—
88C22×C11—81no—
89C22×C11#12111yescharacteristic
90C22×C11C22⋊Q811yescharacteristic
91C22×C11#12611yescharacteristic
92C4×C11#12111yescharacteristic
93C4×C11#12111yescharacteristic
94C4×C11C22⋊Q811yescharacteristic
95C4×C11C22⋊Q811yescharacteristic
96Dic11—41no—
97Dic11—41no—
98Dic11—81no—
99C22×D4C2×D1111yescharacteristic
100C2×M16—111no—
101C2×M16C2×D1111yescharacteristic
102C2×M16C2×D1111yescharacteristic
103C22×C8—111no—
104#117—111no—
105C2×C4⋊C4—111no—
106#108—222no—
107#107—221no—
108#106—221no—
109C4⋊C8—222no—
110#102—221no—
111#102—221no—
112#102—222no—
113#100—22no—
114C2×C11—21no—
115C2×C11—21no—
116C2×C11—82no—
117C2×C11#39611yescharacteristic
118C2×C11#47111yescharacteristic
119C2×C11#47211yescharacteristic
120C24—21no—
121C2×D4—21no—
122C2×D4—21no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4Dic2212yes—
127C22×C4—221no—
128C22×C4C22×D1111yescharacteristic
129M16—21no—
130M16—21no—
131M16—21no—
132M16—221no—
133M16—221no—
134M16C22⋊D1112yes—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—112no—
138C2×C8—221no—
139C2×C8—221no—
140C2×C8—221no—
141C4⋊C4—111no—
142C4⋊C4—111no—
143C4⋊C4—221no—
144C4⋊C4—221no—
145C22⋊C4—221no—
146C42—221no—
147C11#206311yescharacteristic, complemented, Sylow
148C23—22no—
149C23—41no—
150C23—41no—
151C23—81no—
152C23—81no—
153C23#433911yescharacteristic
154D4—22no—
155D4—22no—
156D4—41no—
157D4—41no—
158C2×C4—221no—
159C2×C4—221no—
160C2×C4—441no—
161C2×C4—881no—
162C2×C4C2×Dic2211yescharacteristic
163C2×C4D4×D1111yescharacteristic
164C2×C4D4×D1111yescharacteristic
165C2×C4#434111yescharacteristic
166C2×C4#434111yescharacteristic
167C2×C4C2×C22⋊D1111yescharacteristic
168C8—22no—
169C8—41no—
170C8—222no—
171C8—441no—
172C22—21no—
173C22—21no—
174C22—42no—
175C22—82no—
176C22—82no—
177C22—81no—
178C22—81no—
179C22#6693211yescharacteristic
180C22#6693711yescharacteristic
181C22#6697711yescharacteristic
182C4—441no—
183C4—441no—
184C4—881no—
185C4#6693111yescharacteristic
186C4#6693111yescharacteristic
187C4#6699111yescharacteristic
188C4#6699211yescharacteristic
189C2—21no—
190C2—21no—
191C2—82no—
192C2#1062236111yescharacteristic
193C2#1062236211yescharacteristic
194C2#1062256111yescharacteristic
subgroupG/H
centerC22#66937
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC2×C11×#100C2
socleC22×C11#121
prime radicalC22×D4×C11C22
hypercenterC2×#100D11
hypocenterC11#2063
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
4. C2×#66886C2semidirect
5. #10622734C2semidirect
6. #10622732C2semidirect
7. #10622192C2semidirect
147. C11#2063semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1002
#106228282
C2×#668962
C2×#668862
#106227342
#106227322
#106221922
#206311