Finite Group Databasebeta

← #14673884

Subgroups — #14673884

Order 2816.

354 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×#10622132C212yesmaximal, complemented
2C2×#10622133C212yesmaximal
3#13069492C211yesmaximal, characteristic
4#13066700C211yesmaximal, characteristic, complemented
5C11×#1849C211yesmaximal, characteristic, complemented
6C22×D88C2211yescharacteristic
7C2×C11×#108—21no—
8C2×C11×#108C2212yes—
9C11×#423—21no—
10C2×C11×#97C2211yescharacteristic
11C2×#66885—21no—
12C2×#66881C2211yescharacteristic
13C2×#66876C2212yes—
14#10622552—21no—
15#10622133—24no—
16#10622132—24no—
17C22×D44—21no—
18C2×C11×M16—22no—
19C22×C8×C11D411yescharacteristic
20C22×C8×C11C2311yescharacteristic
21C2×C42×C11D411yescharacteristic
22C2×(C2×D11)⋊C4—42no—
23C2×C4⋊Dic11—21no—
24C2×D88—22no—
25C2×D88—22no—
26C2×D88—21no—
27C2×D88Q812yes—
28C11×#108—22no—
29C11×#108—22no—
30C11×#108—42no—
31C11×C4⋊C8—42no—
32C11×#97—22no—
33#66885—42no—
34#66881—22no—
35#66876—22no—
36#66876D414yes—
37C2×C11⋊C16—22no—
38#13535—111nomaximal, Sylow
39C23×D11—41no—
40C22×C4×C11SD1612yes—
41C22×C4×C11C2×D411yescharacteristic
42C22×Dic11—41no—
43C2×D44—22no—
44C2×D44—41no—
45C2×D44—41no—
46C2×D44—41no—
47C2×D44—41no—
48C2×D44—41no—
49C11×M16—42no—
50C11×M16—42no—
51C2×C8×C11—21no—
52C2×C8×C11—21no—
53C2×C8×C11—42no—
54C2×C8×C11SD1612yes—
55C2×C8×C11C2×D412yes—
56C2×C8×C11C2×Q811yescharacteristic
57C2×C8×C11#4111yescharacteristic
58C2×C8×C11#4112yes—
59C42×C11—21no—
60C42×C11—21no—
61(C2×D11)⋊C4—84no—
62C4⋊Dic11—41no—
63C4⋊Dic11—41no—
64D88—24no—
65D88—42no—
66C11⋊C16—24no—
67C2×#365—112no—
68C2×#361—112no—
69#1972—111no—
70#1849D1111yescharacteristic, complemented
71#1377—111no—
72C23×C11C2×SD1611yescharacteristic
73C22×D11—42no—
74C22×D11—82no—
75C22×D11—82no—
76C22×D11—81no—
77C22×D11—81no—
78C2×C4×C11—22no—
79C2×C4×C11—42no—
80C2×C4×C11C22⋊Q811yescharacteristic
81C2×C4×C11#12311yescharacteristic
82C2×C4×C11#12711yescharacteristic
83C2×C4×C11C2×SD1611yescharacteristic
84C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
85C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
86C2×Dic11—82no—
87C2×Dic11—81no—
88D44—42no—
89D44—42no—
90D44—81no—
91D44—81no—
92C8×C11—22no—
93C8×C11—82no—
94C8×C11C22⋊Q812yes—
95C8×C11#12312yes—
96C22×D8—111no—
97C2×M32—112no—
98C2×#108—21no—
99C2×#108C2×D1112yes—
100C2×#106—111no—
101#423—21no—
102C2×#102—221no—
103C2×#97C2×D1111yescharacteristic
104#390—221no—
105#365—224no—
106#361—224no—
107C22×C11—22no—
108C22×C11#47611yescharacteristic
109C22×C11#48111yescharacteristic
110C22×C11#49211yescharacteristic
111C2×D11—84no—
112C2×D11—82no—
113C2×D11—161no—
114C2×D11—161no—
115C2×D11—162no—
116C4×C11—42no—
117C4×C11#39911yescharacteristic
118C4×C11#47611yescharacteristic
119C4×C11#48111yescharacteristic
120C4×C11#49611yescharacteristic
121Dic11—161no—
122C22×D4—221no—
123C2×D8—112no—
124C2×D8—222no—
125C2×D8—222no—
126C2×D8—221no—
127C2×M16—22no—
128C22×C8C22⋊D1111yescharacteristic
129C22×C8C22×D1111yescharacteristic
130C2×C4⋊C4—221no—
131C2×C22⋊C4—442no—
132C2×C42C22⋊D1111yescharacteristic
133M32—114no—
134M32—222no—
135C2×C16—222no—
136#108—22no—
137#108—22no—
138#108—42no—
139#106—222no—
140C4⋊C8—42no—
141#102—442no—
142#97—22no—
143C2×C11—21no—
144C2×C11—21no—
145C2×C11#209411yescharacteristic
146C2×C11#223812yes—
147D11—162no—
148C24—441no—
149C2×D4—222no—
150C2×D4—441no—
151C2×D4—441no—
152C2×D4—441no—
153C2×D4—441no—
154C2×D4—441no—
155C22×C4—441no—
156C22×C4#432512yes—
157C22×C4C2×C22⋊D1111yescharacteristic
158D8—224no—
159D8—442no—
160M16—42no—
161M16—42no—
162C2×C8—21no—
163C2×C8—21no—
164C2×C8—42no—
165C2×C8#432512yes—
166C2×C8#433912yes—
167C2×C8D4×D1112yes—
168C2×C8Q8×D1111yescharacteristic
169C2×C8#434311yescharacteristic
170C4⋊C4—441no—
171C4⋊C4—441no—
172C22⋊C4—884no—
173C42—21no—
174C42—21no—
175C16—224no—
176C11#1353511yescharacteristic, complemented, Sylow
177C23—442no—
178C23—882no—
179C23—882no—
180C23—881no—
181C23—881no—
182C23C2×#432511yescharacteristic
183D4—442no—
184D4—442no—
185D4—881no—
186D4—881no—
187C2×C4—22no—
188C2×C4—42no—
189C2×C4—882no—
190C2×C4—881no—
191C2×C4#6698211yescharacteristic
192C2×C4#6698511yescharacteristic
193C2×C4#6698511yescharacteristic
194C2×C4#6699311yescharacteristic
195C2×C4C2×#432511yescharacteristic
196C2×C4#6699911yescharacteristic
197C8—22no—
198C8—82no—
199C8#6694712yes—
200C8#6694912yes—
201C22—22no—
202C22—884no—
203C22—882no—
204C22—1761no—
205C22—1761no—
206C22—1762no—
207C22#1062258111yescharacteristic
208C22#1062269711yescharacteristic
209C22#1062269811yescharacteristic
210C4—42no—
211C4—1761no—
212C4#1062258111yescharacteristic
213C4#1062260511yescharacteristic
214C4#1062268711yescharacteristic
215C4#1062269711yescharacteristic
216C2—21no—
217C2—21no—
218C2—1762no—
219C2#1307015011yescharacteristic
220C2#1307083012yes—
subgroupG/H
centerC22#10622581
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1849C2
socleC22×C11#481
prime radicalC22×D88C22
hypercenter#1849D11
hypocenterC11#13535
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#97 ◁ #1849

Complements

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

NH ≅ G/Ntype
1. C2×#10622132C2semidirect
4. #13066700C2semidirect
5. C11×#1849C2semidirect
70. #1849D11semidirect
176. C11#13535semidirect

Maximal subgroups

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

subgroupindex
C2×#106221322
C2×#106221332
#130694922
#130667002
C11×#18492
#1353511