Finite Group Databasebeta

← #14667925

Subgroups — #14667925

Order 2816.

218 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 71 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#13070769C211yesmaximal, characteristic
2#13070667C211yesmaximal, characteristic
3#13068213C211yesmaximal, characteristic
4C8×Dic44C211yesmaximal, characteristic
5#13066673C211yesmaximal, characteristic
6#13066666C211yesmaximal, characteristic
7C11×#1367C211yesmaximal, characteristic
8C2×Dic88—21no—
9#10622312C2211yescharacteristic
10C4×Dic44C2211yescharacteristic
11#10622295C2211yescharacteristic
12#10622294—21no—
13#10622293—21no—
14C8×Dic22—21no—
15C11×C4⋊C16C2211yescharacteristic
16C11×C4⋊C16C2211yescharacteristic
17C82×C11C2211yescharacteristic
18#10622142—21no—
19#10622141—21no—
20#10622141—21no—
21#10622096C2211yescharacteristic
22#10622094—21no—
23C2×Dic44—21no—
24C2×Dic44—21no—
25C2×Dic44D411yescharacteristic
26#66922—21no—
27#66922—21no—
28C4×Dic22—21no—
29C2×C11×C16—21no—
30C2×C11×C16—21no—
31C4×C8×C11D411yescharacteristic
32C4×C8×C11D411yescharacteristic
33C4×C8×C11C2311yescharacteristic
34#66882—21no—
35#66882—21no—
36#66882D411yescharacteristic
37#66881—41no—
38#66881—41no—
39#66880—21no—
40#66880—42no—
41Dic11⋊C8—41no—
42C8×Dic11—41no—
43C4⋊(C11⋊C8)—21no—
44Dic88—42no—
45#12421—111nomaximal, Sylow
46C2×Dic22—21no—
47C2×Dic22—41no—
48C2×Dic22—41no—
49C2×C8×C11—21no—
50C2×C8×C11D811yescharacteristic
51C2×C8×C11D811yescharacteristic
52C2×C8×C11C2×D411yescharacteristic
53C2×C8×C11#4111yescharacteristic
54C42×C11C2×D411yescharacteristic
55C4⋊Dic11—21no—
56C4⋊Dic11—41no—
57C4⋊Dic11—41no—
58C4⋊Dic11—41no—
59C4⋊Dic11—41no—
60Dic11⋊C4—41no—
61C4×Dic11—41no—
62C2×C11⋊C8—41no—
63Dic44—21no—
64Dic44—41no—
65Dic44—41no—
66Dic44—81no—
67Dic44SD1612yes—
68C11×C16—41no—
69C11×C16—41no—
70#2227—111no—
71#2209—111no—
72#1707—111no—
73C8×Q16—111no—
74#1367D1111yescharacteristic
75#1365—111no—
76#1362—111no—
77C2×C4×C11#12111yescharacteristic
78C2×C4×C11C2×D811yescharacteristic
79C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
80C2×Dic11—41no—
81C2×Dic11—41no—
82C2×Dic11—81no—
83C2×Dic11—81no—
84Dic22—22no—
85Dic22—41no—
86Dic22—82no—
87Dic22—81no—
88Dic22—81no—
89C8×C11—21no—
90C8×C11—21no—
91C8×C11—41no—
92C8×C11Q3212yescomplemented
93C8×C11C2×SD1611yescharacteristic
94C8×C11#13511yescharacteristic
95C11⋊C8—81no—
96C2×Q32—221no—
97#500—111no—
98#498—221no—
99#494—111no—
100#487—221no—
101C8×Q8—221no—
102C4×Q16—111no—
103#366—221no—
104C4⋊C16C2×D1111yescharacteristic
105C4⋊C16C2×D1111yescharacteristic
106#358—221no—
107#358—221no—
108#335—111no—
109Q8⋊C8—221no—
110C82C2×D1111yescharacteristic
111C22×C11#45911yescharacteristic
112C4×C11—21no—
113C4×C11#46511yescharacteristic
114C4×C11#47111yescharacteristic
115C4×C11C2×Q3211yescharacteristic
116C4×C11#51011yescharacteristic
117Dic11—42no—
118Dic11—81no—
119Dic11—161no—
120Dic11—161no—
121C2×Q16—111no—
122C2×Q16—221no—
123C2×Q16—221no—
124C4⋊Q8—221no—
125C4⋊Q8—221no—
126C4×Q8—221no—
127Q32—442no—
128C2×C16—21no—
129C2×C16—21no—
130#107—111no—
131#107—221no—
132#107—221no—
133#106—441no—
134#106—441no—
135C4⋊C8—221no—
136C4⋊C8—441no—
137#103—221no—
138#103—442no—
139C4×C8—441no—
140C4×C8D4411yescharacteristic
141C4×C8D4411yescharacteristic
142C4×C8C22×D1111yescharacteristic
143C2×C11#166511yescharacteristic
144C2×C11#220911yescharacteristic
145C2×C11#221211yescharacteristic
146C2×Q8—221no—
147C2×Q8—441no—
148C2×Q8—441no—
149Q16—112no—
150Q16—221no—
151Q16—441no—
152Q16—441no—
153Q16—881no—
154C2×C8—21no—
155C2×C8—441no—
156C2×C8D8811yescharacteristic
157C2×C8D8811yescharacteristic
158C2×C8D4×D1111yescharacteristic
159C2×C8#434311yescharacteristic
160C4⋊C4—221no—
161C4⋊C4—441no—
162C4⋊C4—441no—
163C4⋊C4—441no—
164C4⋊C4—441no—
165C4⋊C4—441no—
166C42—441no—
167C42C2×D4411yescharacteristic
168C16—41no—
169C16—41no—
170C11#1242111yescharacteristic, complemented, Sylow
171Q8—222no—
172Q8—441no—
173Q8—882no—
174Q8—881no—
175Q8—881no—
176C2×C4—441no—
177C2×C4—441no—
178C2×C4—881no—
179C2×C4—881no—
180C2×C4#6694811yescharacteristic
181C2×C4C2×D8811yescharacteristic
182C2×C4#6696111yescharacteristic
183C8—21no—
184C8—21no—
185C8—41no—
186C8—881no—
187C8Dic8812yescomplemented
188C8SD16×D1111yescharacteristic
189C8#6696911yescharacteristic
190C22#1062245611yescharacteristic
191C4—21no—
192C4—442no—
193C4—881no—
194C4—1761no—
195C4—1761no—
196C4#1062247711yescharacteristic
197C4#1062251111yescharacteristic
198C4C2×Dic8811yescharacteristic
199C4#1062252211yescharacteristic
200C2#1306795811yescharacteristic
201C2#1307066711yescharacteristic
202C2#1307068611yescharacteristic
subgroupG/H
centerC22#10622456
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1367C2
socle, prime radicalC22×C11#459
hypercenter#1367D11
hypocenterC11#12421
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C82 ◁ #1367

Complements

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

NH ≅ G/Ntype
92. C8×C11Q32semidirect
170. C11#12421semidirect
187. C8Dic88semidirect

Maximal subgroups

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

subgroupindex
#130707692
#130706672
#130682132
C8×Dic442
#130666732
#130666662
C11×#13672
#1242111