Finite Group Databasebeta

← #14674739

Subgroups — #14674739

Order 2816.

160 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 49 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#13070725C211yesmaximal, characteristic
2#13070409C211yesmaximal, characteristic
3#13066821C211yesmaximal, characteristic, complemented
4#13066810C211yesmaximal, characteristic, complemented
5#13066808C211yesmaximal, characteristic, complemented
6#13066755C211yesmaximal, characteristic
7C11×#1426C211yesmaximal, characteristic, complemented
8C2×Dic88C2211yescharacteristic
9C2×#66862C2211yescharacteristic
10D11×#108—21no—
11#10622500—21no—
12C11×M64C2211yescharacteristic
13C11×#368C2211yescharacteristic
14C11×#367C2211yescharacteristic
15#10622144C2211yescharacteristic
16#10622137C2211yescharacteristic
17#10622131—21no—
18#10622130—21no—
19M16×D11—41no—
20C2×Dic44—21no—
21C2×C8×D11D411yescharacteristic
22#66950—41no—
23C2×C11×C16C2311yescharacteristic
24C11×#108—21no—
25C11×#107—21no—
26#66886—41no—
27#66883—21no—
28C2×C11⋊C16D411yescharacteristic
29#66874—41no—
30Dic88—21no—
31Dic88—21no—
32#66862—21no—
33#66862—21no—
34C11×C32—21no—
35C11⋊C32—21no—
36#13718—111nomaximal, Sylow
37C2×C4×D11D811yescharacteristic
38C2×Dic22—41no—
39C11×M16—41no—
40C2×C8×C11C2×D411yescharacteristic
41C11×C4⋊C4—41no—
42(C2×D11)⋊C4—81no—
43C4⋊Dic11—81no—
44#4318—41no—
45C2×C11⋊C8D811yescharacteristic
46Dic44—41no—
47Dic44—41no—
48#4313—81no—
49C8×D11—21no—
50C8×D11—21no—
51C8×D11—81no—
52C11×C16#4111yescharacteristic
53C11×C16#4111yescharacteristic
54C11⋊C16—21no—
55#2219—111no—
56#2161—111no—
57#1426—111no—
58#1426D1111yescharacteristic, complemented
59#1420—111no—
60#1420—111no—
61#1400—111no—
62C22×D11SD3211yescharacteristic
63C2×C4×C11—81no—
64C2×C4×C11C2×D811yescharacteristic
65C2×Dic11—81no—
66C2×Dic11SD3211yescharacteristic
67C4×D11—21no—
68C4×D11—21no—
69Dic22—81no—
70Dic22—81no—
71C8×C11—81no—
72C8×C11#12311yescharacteristic
73C8×C11#13711yescharacteristic
74C11⋊C8—21no—
75C11⋊C8—81no—
76C2×Q32—111no—
77C2×M32—111no—
78#467—221no—
79C2×#108—221no—
80M64—111no—
81M64C2×D1111yescharacteristic
82#368—111no—
83#368—221no—
84#368C2×D1111yescharacteristic
85#367C2×D1111yescharacteristic
86#358—221no—
87C22×C11C2×SD3211yescharacteristic
88C2×D11—21no—
89C2×D11—41no—
90C4×C11—161no—
91C4×C11#48011yescharacteristic
92C4×C11#50911yescharacteristic
93Dic11—21no—
94Dic11—161no—
95C2×Q16—221no—
96C2×M16—441no—
97C22×C8—111no—
98C22⋊Q8—441no—
99Q32—221no—
100Q32—221no—
101M32—221no—
102M32—221no—
103C2×C16—111no—
104C2×C16C22×D1111yescharacteristic
105#108—21no—
106#108—221no—
107#108—441no—
108#107—21no—
109#103—441no—
110C32—21no—
111C32—221no—
112C2×C11—21no—
113C2×C11#223311yescharacteristic
114D11—41no—
115C2×Q8—441no—
116C22×C4—111no—
117Q16—441no—
118Q16—441no—
119M16—41no—
120M16—441no—
121M16—881no—
122C2×C8—111no—
123C2×C8—221no—
124C2×C8—221no—
125C2×C8—881no—
126C2×C8D4×D1111yescharacteristic
127C4⋊C4—41no—
128C4⋊C4—881no—
129C22⋊C4—881no—
130C16—221no—
131C16#433911yescharacteristic
132C16#434311yescharacteristic
133C11#1371811yescharacteristic, complemented, Sylow
134C23—111no—
135Q8—881no—
136Q8—881no—
137C2×C4—81no—
138C2×C4—111no—
139C2×C4—221no—
140C2×C4—221no—
141C2×C4—881no—
142C2×C4D8×D1111yescharacteristic
143C8—81no—
144C8—221no—
145C8—881no—
146C8#6694711yescharacteristic
147C8#6697111yescharacteristic
148C22—221no—
149C22—441no—
150C22D11×SD3211yescharacteristic
151C4—161no—
152C4—221no—
153C4—1761no—
154C4#1062249511yescharacteristic
155C4#1062252711yescharacteristic
156C2—21no—
157C2—441no—
158C2#1307080311yescharacteristic
subgroupG/H
centerC2#13070803
commutator, cosocleC2×C11×C16C23
FrattiniC2×C16C22×D11
FittingC11×#1426C2
socleC2×C11#2233
prime radicalC22×D11SD32
hypercenter#1426D11
hypocenterC11#13718
LCSG ▷ C2×C11×C16 ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1426

Complements

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

NH ≅ G/Ntype
3. #13066821C2semidirect
4. #13066810C2semidirect
5. #13066808C2semidirect
7. C11×#1426C2semidirect
58. #1426D11semidirect
133. C11#13718semidirect

Maximal subgroups

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

subgroupindex
#130707252
#130704092
#130668212
#130668102
#130668082
#130667552
C11×#14262
#1371811