Finite Group Databasebeta

← #14665761

Subgroups — #14665761

Order 2816.

210 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 75 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×#66893C211yesmaximal, characteristic
2#13067513C211yesmaximal, characteristic
3#13067512C211yesmaximal, characteristic
4#13066687C211yesmaximal, characteristic
5#13066581C211yesmaximal, characteristic
6C16×C11⋊C8C211yesmaximal, characteristic
7C11×#1332C211yesmaximal, characteristic
8C4×C11×Q16C2211yescharacteristic
9C2×#66893C411yescharacteristic
10#10622637—21no—
11#10622444—21no—
12C4×Dic44C2211yescharacteristic
13C4×C11×C16C2211yescharacteristic
14C11×#335C2211yescharacteristic
15#10622202C411yescharacteristic
16Q8⋊(C11⋊C8)—21no—
17#10622130C411yescharacteristic
18#10622127C411yescharacteristic
19#10622122—21no—
20C4×C11⋊C16C2211yescharacteristic
21#10622096C2211yescharacteristic
22C8×C11⋊C8C2211yescharacteristic
23C2×C11×Q16C2×C411yescharacteristic
24C4×Q8×C11—21no—
25C2×Dic44C2×C411yescharacteristic
26C4×Dic22—21no—
27C2×C11×C16—21no—
28C11×#107C2×C411yescharacteristic
29C11×C4⋊C8—21no—
30C11×#103—21no—
31C4×C8×C11C2311yescharacteristic
32#66893—22no—
33#66882C2×C411yescharacteristic
34#66880—21no—
35#66879—41no—
36Dic11⋊C8—41no—
37C2×C11⋊C16C2×C411yescharacteristic
38C2×C11⋊C16C2×C411yescharacteristic
39C4⋊(C11⋊C8)—21no—
40C4⋊(C11⋊C8)—41no—
41#66867—41no—
42C4×C11⋊C8D411yescharacteristic
43C4×C11⋊C8D411yescharacteristic
44#12083—111nomaximal, Sylow
45C2×Q8×C11—21no—
46C2×Dic22—21no—
47C11×Q16—21no—
48C11×Q16—21no—
49C2×C8×C11—41no—
50C2×C8×C11C22×C411yescharacteristic
51C2×C8×C11#4111yescharacteristic
52C11×C4⋊C4—21no—
53C11×C4⋊C4—41no—
54C42×C11—41no—
55C42×C11C2×D411yescharacteristic
56C4⋊Dic11—21no—
57Dic11⋊C4—41no—
58C4×Dic11—41no—
59C2×C11⋊C8—21no—
60C2×C11⋊C8—41no—
61C2×C11⋊C8D811yescharacteristic
62C2×C11⋊C8D811yescharacteristic
63Dic44—21no—
64Dic44—21no—
65C11×C16—22no—
66C11⋊C16—21no—
67C11⋊C16M1612yes—
68C4×Q32—111no—
69#1591—111no—
70#1591—111no—
71#1371—111no—
72#1332—111no—
73#1332D1111yescharacteristic
74C8×C16—111no—
75Q8×C11—41no—
76Q8×C11—41no—
77C2×C4×C11—41no—
78C2×C4×C11—41no—
79C2×C4×C11C4×D411yescharacteristic
80C2×C4×C11C2×D811yescharacteristic
81C2×C4×C11#13511yescharacteristic
82C2×Dic11—41no—
83C2×Dic11—41no—
84Dic22—41no—
85Dic22—41no—
86C8×C11—21no—
87C8×C11—81no—
88C8×C11C2×M1611yescharacteristic
89C8×C11#13111yescharacteristic
90C11⋊C8—22no—
91C11⋊C8—21no—
92C11⋊C8—81no—
93C11⋊C8Q3212yescomplemented
94C2×Q32—111no—
95#446—221no—
96#446—221no—
97C4×Q16—111no—
98C4×Q16C2×D1111yescharacteristic
99#366—111no—
100#358—111no—
101#358—111no—
102C4×C16—111no—
103C4×C16C2×D1111yescharacteristic
104#335—111no—
105#335C2×D1111yescharacteristic
106Q8⋊C8—221no—
107Q8⋊C8—221no—
108C82—111no—
109C22×C11C4×D811yescharacteristic
110C4×C11—21no—
111C4×C11—81no—
112C4×C11—81no—
113C4×C11#43611yescharacteristic
114C4×C11#44311yescharacteristic
115C4×C11C2×Q3211yescharacteristic
116C4×C11#50811yescharacteristic
117Dic11—81no—
118Dic11—81no—
119C2×Q16—111no—
120C2×Q16C4×D1111yescharacteristic
121C4×Q8—21no—
122C4×Q8—221no—
123Q32—222no—
124C2×C16—21no—
125C2×C16—111no—
126C2×C16—111no—
127#107—111no—
128#107C4×D1111yescharacteristic
129C4⋊C8—21no—
130C4⋊C8—221no—
131C4⋊C8—441no—
132C4⋊C8—441no—
133#103—21no—
134#103—221no—
135#97—441no—
136#97—441no—
137C4×C8—111no—
138C4×C8—111no—
139C4×C8C22×D1111yescharacteristic
140C2×C11#158911yescharacteristic
141C2×C11C4×Q3211yescharacteristic
142C2×C11#217811yescharacteristic
143C2×Q8—21no—
144C2×Q8—221no—
145Q16—21no—
146Q16—21no—
147Q16—221no—
148Q16—221no—
149C2×C8—41no—
150C2×C8—111no—
151C2×C8—111no—
152C2×C8—221no—
153C2×C8—441no—
154C2×C8C2×C4×D1111yescharacteristic
155C2×C8#434111yescharacteristic
156C4⋊C4—21no—
157C4⋊C4—41no—
158C4⋊C4—221no—
159C4⋊C4—441no—
160C42—41no—
161C42—441no—
162C42D4×D1111yescharacteristic
163C16—22no—
164C16—112no—
165C16—221no—
166C11#1208311yescharacteristic, complemented, Sylow
167Q8—41no—
168Q8—41no—
169Q8—441no—
170Q8—441no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—441no—
174C2×C4—441no—
175C2×C4(C22⋊D11)⋊C411yescharacteristic
176C2×C4D8×D1111yescharacteristic
177C2×C4#6696911yescharacteristic
178C8—21no—
179C8—81no—
180C8—112no—
181C8—222no—
182C8—221no—
183C8—881no—
184C8#6695411yescharacteristic
185C8M16×D1111yescharacteristic
186C22#1062236911yescharacteristic
187C4—21no—
188C4—81no—
189C4—81no—
190C4—881no—
191C4—881no—
192C4#1062234211yescharacteristic
193C4#1062243711yescharacteristic
194C4#1062252911yescharacteristic
195C4D11×Q3211yescharacteristic
196C2#1306749811yescharacteristic
197C2#1307047211yescharacteristic
198C2#1307049411yescharacteristic
subgroupG/H
centerC2×C4D8×D11
commutatorC2×C8×C11C22×C4
FrattiniC4×C8C22×D11
FittingC11×#1332C2
socle, prime radicalC22×C11C4×D8
cosocleC4×C8×C11C23
hypercenter#1332D11
hypocenterC11#12083
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ #1332

Complements

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

NH ≅ G/Ntype
93. C11⋊C8Q32semidirect
166. C11#12083semidirect

Maximal subgroups

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

subgroupindex
C4×#668932
#130675132
#130675122
#130666872
#130665812
C16×C11⋊C82
C11×#13322
#1208311