Finite Group Databasebeta

← #14667154

Subgroups — #14667154

Order 2816.

274 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 59 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#13070833C212yesmaximal
2#13070191C211yesmaximal, characteristic
3#13066604C212yesmaximal
4#13066567C211yesmaximal, characteristic
5C11×#3255C211yesmaximal, characteristic
6C11×#533—21no—
7C11×#475—22no—
8C11×#470—21no—
9C11×#470C2212yes—
10C11×#462—22no—
11C11×#423C2211yescharacteristic
12#10622738C2211yescharacteristic
13#10622203—22no—
14#10622197—21no—
15#10622195C2211yescharacteristic
16#10622191C2212yes—
17#10622161—21no—
18#10622125—22no—
19C2×C11×Q16—21no—
20C2×C11×Q16D412yes—
21C2×C11×M16D411yescharacteristic
22C2×C11×M16C2311yescharacteristic
23C11×C4⋊Q8—21no—
24C11×C4⋊Q8—21no—
25C11×#125—41no—
26C11×C22⋊Q8—22no—
27C11×C22⋊Q8—41no—
28C4×Q8×C11—22no—
29C4×Q8×C11—41no—
30C11×#117—41no—
31C2×C42×C11D411yescharacteristic
32#66979—21no—
33C2×#4318—21no—
34C11×#106—21no—
35C11×#106D412yes—
36C11×C4⋊C8—22no—
37C11×#103—22no—
38C11×#103—22no—
39#66883—22no—
40#66876—22no—
41#12308—111nomaximal, Sylow
42C2×Q8×C11—22no—
43C2×Q8×C11—41no—
44C22×C4×C11—21no—
45C22×C4×C11C2×D411yescharacteristic
46C11×Q16—42no—
47C11×Q16—81no—
48C11×M16—41no—
49C11×M16—41no—
50C2×C8×C11—21no—
51C2×C8×C11C2×D412yes—
52C11×C4⋊C4—22no—
53C11×C4⋊C4—41no—
54C11×C4⋊C4—41no—
55C11×C4⋊C4—42no—
56C11×C4⋊C4—41no—
57C11×C4⋊C4—42no—
58C11×C22⋊C4—42no—
59C42×C11—21no—
60C42×C11—42no—
61C42×C11SD1611yescharacteristic
62C42×C11SD1611yescharacteristic
63C22⋊Dic11—41no—
64C4⋊Dic11—41no—
65C4×Dic11—41no—
66#4318—41no—
67#4318—41no—
68C2×C11⋊C8—41no—
69C11⋊C16—42no—
70#3255D1111yescharacteristic
71#2239—112no—
72#2102—111no—
73#1340—112no—
74#1327—111no—
75C23×C11AGL(1,ℤ/8)11yescharacteristic
76Q8×C11—42no—
77Q8×C11—42no—
78Q8×C11—82no—
79C2×C4×C11—21no—
80C2×C4×C11—21no—
81C2×C4×C11—21no—
82C2×C4×C11—21no—
83C2×C4×C11—42no—
84C2×C4×C11—42no—
85C2×C4×C11—42no—
86C2×C4×C11#12011yescharacteristic
87C2×C4×C11C2×SD1611yescharacteristic
88C2×Dic11—81no—
89C8×C11—22no—
90C8×C11—41no—
91C11⋊C8—81no—
92#533—21no—
93#475—22no—
94#470—21no—
95#470C2×D1112yes—
96#462—22no—
97#430—111no—
98#423C2×D1111yescharacteristic
99#365—222no—
100#362—222no—
101#349—112no—
102#344—221no—
103#339—221no—
104H(3,ℤ/4)—111no—
105C22×C11—21no—
106C22×C11—41no—
107C22×C11#45011yescharacteristic
108C4×C11—22no—
109C4×C11—21no—
110C4×C11—41no—
111C4×C11—82no—
112C4×C11—82no—
113C4×C11#45411yescharacteristic
114C4×C11#45811yescharacteristic
115Dic11—161no—
116C2×Q16—21no—
117C2×Q16C22⋊D1112yes—
118C2×M16—221no—
119C2×M16C22⋊D1111yescharacteristic
120C2×M16C22×D1111yescharacteristic
121C4⋊Q8—21no—
122C4⋊Q8—21no—
123#125—41no—
124C22⋊Q8—22no—
125C22⋊Q8—41no—
126C4×Q8—22no—
127C4×Q8—41no—
128#117—41no—
129#117—221no—
130C2×C42C22⋊D1111yescharacteristic
131M32—222no—
132#108—222no—
133#106—21no—
134#106C22⋊D1112yes—
135C4⋊C8—22no—
136#103—22no—
137#103—22no—
138C2×C11—21no—
139C2×C11—41no—
140C2×C11#161611yescharacteristic
141C2×Q8—22no—
142C2×Q8—41no—
143C22×C4—21no—
144C22×C4C2×C22⋊D1111yescharacteristic
145Q16—42no—
146Q16—81no—
147M16—41no—
148M16—41no—
149M16—441no—
150M16—441no—
151C2×C8—21no—
152C2×C8—441no—
153C2×C8C2×C22⋊D1112yes—
154C4⋊C4—22no—
155C4⋊C4—41no—
156C4⋊C4—41no—
157C4⋊C4—42no—
158C4⋊C4—41no—
159C4⋊C4—42no—
160C4⋊C4—441no—
161C22⋊C4—42no—
162C22⋊C4—441no—
163C42—21no—
164C42—42no—
165C42—441no—
166C42#432411yescharacteristic
167C42#432411yescharacteristic
168C16—442no—
169C11#1230811yescharacteristic, complemented, Sylow
170C23#6698511yescharacteristic
171Q8—42no—
172Q8—42no—
173Q8—82no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—881no—
182C2×C4C2×#432411yescharacteristic
183C2×C4#6700611yescharacteristic
184C8—22no—
185C8—41no—
186C8—881no—
187C22—21no—
188C22—41no—
189C22#1062283111yescharacteristic
190C4—22no—
191C4—21no—
192C4—41no—
193C4—82no—
194C4—82no—
195C4—1761no—
196C4#1062285611yescharacteristic
197C4#1062285811yescharacteristic
198C2—21no—
199C2—41no—
200C2#1306765311yescharacteristic
subgroupG/H
centerC2#13067653
commutator, cosocleC2×C11×M16C23
FrattiniC2×M16C22×D11
FittingC11×#3255C2
socleC2×C11#1616
prime radicalC23×C11AGL(1,ℤ/8)
hypercenter#3255D11
hypocenterC11#12308
LCSG ▷ C2×C11×M16 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #3255

Complements

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

NH ≅ G/Ntype
169. C11#12308semidirect

Maximal subgroups

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

subgroupindex
#130708332
#130701912
#130666042
#130665672
C11×#32552
#1230811