Finite Group Databasebeta

← #14665708

Subgroups — #14665708

Order 2816.

224 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 77 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×#66891C211yesmaximal, characteristic
2C8×Dic44C211yesmaximal, characteristic, complemented
3#13066687C211yesmaximal, characteristic, complemented
4#13066579C211yesmaximal, characteristic, complemented
5#13066577C211yesmaximal, characteristic
6#13066534C211yesmaximal, characteristic, complemented
7C11×#1589C211yesmaximal, characteristic
8C4×C11×D8C2211yescharacteristic
9C11×#436—21no—
10C2×#66891C411yescharacteristic
11C4×Dic44C2211yescharacteristic
12C8×Dic22—21no—
13C11×#335C2211yescharacteristic
14C11×D4⋊C8—21no—
15C82×C11C2211yescharacteristic
16#10622200C411yescharacteristic
17#10622130C411yescharacteristic
18#10622128C411yescharacteristic
19C4×C11⋊C16C2211yescharacteristic
20C4×C11⋊C16C2211yescharacteristic
21#10622096C2211yescharacteristic
22#10622094—21no—
23C2×C11×D8C2×C411yescharacteristic
24C2×C11×M16—41no—
25C4×D4×C11—21no—
26C2×Dic44C2×C411yescharacteristic
27C4×Dic22—21no—
28C11×#107C2×C411yescharacteristic
29C11×C4⋊C8—21no—
30C11×#102—21no—
31C11×C22⋊C8—41no—
32C4×C8×C11D411yescharacteristic
33C4×C8×C11D411yescharacteristic
34C4×C8×C11C2311yescharacteristic
35#66891—22no—
36#66882C2×C411yescharacteristic
37#66880—21no—
38Dic11⋊C8—41no—
39C8×Dic11—41no—
40C2×C11⋊C16—21no—
41C2×C11⋊C16C2×C411yescharacteristic
42C2×C11⋊C16C2×C411yescharacteristic
43C4⋊(C11⋊C8)—21no—
44#12075—111nomaximal, Sylow
45C2×D4×C11—21no—
46C22×C4×C11—41no—
47C2×Dic22—21no—
48C11×D8—21no—
49C11×D8—21no—
50C11×M16—82no—
51C2×C8×C11—21no—
52C2×C8×C11—41no—
53C2×C8×C11D811yescharacteristic
54C2×C8×C11D811yescharacteristic
55C2×C8×C11C22×C411yescharacteristic
56C2×C8×C11#4111yescharacteristic
57C11×C4⋊C4—21no—
58C11×C22⋊C4—41no—
59C42×C11C2×D411yescharacteristic
60C4⋊Dic11—21no—
61Dic11⋊C4—41no—
62C4×Dic11—41no—
63C2×C11⋊C8—41no—
64Dic44—21no—
65Dic44M1612yescomplemented
66C11⋊C16—21no—
67C11⋊C16—21no—
68C11⋊C16—41no—
69C4×SD32—111no—
70#1589D1111yescharacteristic
71C8×Q16—111no—
72#1371—111no—
73#1332—111no—
74#1331—111no—
75#1312—111no—
76C23×C11—41no—
77D4×C11—41no—
78D4×C11—41no—
79C2×C4×C11—41no—
80C2×C4×C11—81no—
81C2×C4×C11—81no—
82C2×C4×C11C4×D411yescharacteristic
83C2×C4×C11C2×D811yescharacteristic
84C2×C4×C11#13511yescharacteristic
85C2×Dic11—41no—
86C2×Dic11—41no—
87Dic22—22no—
88Dic22—41no—
89C8×C11—22no—
90C8×C11—21no—
91C8×C11—21no—
92C8×C11—21no—
93C8×C11—81no—
94C8×C11C2×M1611yescharacteristic
95C8×C11#13111yescharacteristic
96C11⋊C8—81no—
97C2×SD32—111no—
98C8×Q8—221no—
99C4×Q16—111no—
100C4×D8C2×D1111yescharacteristic
101#436—21no—
102#367—111no—
103#358—111no—
104#357—111no—
105C4×C16—111no—
106C4×C16—111no—
107#335—111no—
108#335C2×D1111yescharacteristic
109Q8⋊C8—221no—
110D4⋊C8—21no—
111C82C2×D1111yescharacteristic
112C22×C11—81no—
113C22×C11—81no—
114C22×C11—81no—
115C22×C11C4×D811yescharacteristic
116C4×C11—21no—
117C4×C11—81no—
118C4×C11#43511yescharacteristic
119C4×C11#44411yescharacteristic
120C4×C11#50911yescharacteristic
121C4×C11#51011yescharacteristic
122Dic11—42no—
123Dic11—81no—
124C2×Q16—111no—
125C2×D8C4×D1111yescharacteristic
126C2×M16—41no—
127C4×Q8—221no—
128C4×D4—21no—
129SD32—222no—
130C2×C16—111no—
131C2×C16—111no—
132C2×C16—221no—
133#107—111no—
134#107C4×D1111yescharacteristic
135C4⋊C8—21no—
136C4⋊C8—221no—
137C4⋊C8—441no—
138#103—221no—
139#102—21no—
140C22⋊C8—41no—
141C4×C8—441no—
142C4×C8C22⋊D1111yescharacteristic
143C4×C8C22⋊D1111yescharacteristic
144C4×C8C22×D1111yescharacteristic
145C2×C11—161no—
146C2×C11#158111yescharacteristic
147C2×C11#217511yescharacteristic
148C2×C11#217811yescharacteristic
149C2×Q8—221no—
150C2×D4—21no—
151C22×C4—41no—
152Q16—112no—
153Q16—221no—
154D8—21no—
155D8—21no—
156M16—82no—
157C2×C8—21no—
158C2×C8—41no—
159C2×C8—441no—
160C2×C8#432311yescharacteristic
161C2×C8#432311yescharacteristic
162C2×C8C2×C4×D1111yescharacteristic
163C2×C8#433911yescharacteristic
164C4⋊C4—21no—
165C4⋊C4—221no—
166C4⋊C4—441no—
167C22⋊C4—41no—
168C42—441no—
169C42C2×C22⋊D1111yescharacteristic
170C16—221no—
171C16—221no—
172C16—441no—
173C11#1207511yescharacteristic, complemented, Sylow
174C23—41no—
175Q8—222no—
176Q8—441no—
177D4—41no—
178D4—41no—
179C2×C4—41no—
180C2×C4—81no—
181C2×C4—81no—
182C2×C4—441no—
183C2×C4—441no—
184C2×C4C4×C22⋊D1111yescharacteristic
185C2×C4C2×#432311yescharacteristic
186C2×C4#6700311yescharacteristic
187C8—22no—
188C8—21no—
189C8—21no—
190C8—21no—
191C8—81no—
192C8—881no—
193C8M16×D1111yescharacteristic
194C8#6696011yescharacteristic
195C22—81no—
196C22—81no—
197C22—81no—
198C22C4×#432311yescharacteristic
199C4—21no—
200C4—81no—
201C4—442no—
202C4—881no—
203C4#1062274011yescharacteristic
204C4#1062275811yescharacteristic
205C4#1062276011yescharacteristic
206C4#1062280811yescharacteristic
207C2—161no—
208C2#1306744311yescharacteristic
209C2#1307048011yescharacteristic
210C2#1307049511yescharacteristic
subgroupG/H
centerC2×C4C2×#4323
commutatorC2×C8×C11C22×C4
FrattiniC4×C8C22×D11
FittingC11×#1589C2
socleC22×C11C4×D8
prime radicalC2×C11×D8C2×C4
cosocleC4×C8×C11C23
hypercenter#1589D11
hypocenterC11#12075
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C82 ◁ #1589

Complements

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

NH ≅ G/Ntype
2. C8×Dic44C2semidirect
3. #13066687C2semidirect
4. #13066579C2semidirect
6. #13066534C2semidirect
65. Dic44M16semidirect
173. C11#12075semidirect

Maximal subgroups

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

subgroupindex
C4×#668912
C8×Dic442
#130666872
#130665792
#130665772
#130665342
C11×#15892
#1207511