Finite Group Databasebeta

← #14673162

Subgroups — #14673162

Order 2816.

436 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 101 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×#10622203C212yesmaximal
2#13070336C212yesmaximal
3#13069364C211yesmaximal, characteristic
4#13066698C211yesmaximal, characteristic
5C2×C11×#494C211yesmaximal, characteristic
6C22×C11×Q16—21no—
7C22×C11×Q16C2212yes—
8C2×C11×C4⋊Q8—21no—
9C11×#494—24no—
10C2×C4×C8×C11C2211yescharacteristic
11C2×#66883C2211yescharacteristic
12#10622719C2211yescharacteristic
13#10622715—21no—
14C2×#66876C2212yes—
15#10622203—24no—
16#10622202—24no—
17#10622161—21no—
18C22×Q8×C11—22no—
19C2×C11×Q16—24no—
20C2×C11×Q16—22no—
21C2×C11×Q16—22no—
22C2×C11×Q16—22no—
23C2×C11×Q16—22no—
24C2×C11×Q16—22no—
25C2×C11×Q16—42no—
26C2×C11×Q16—42no—
27C2×C11×Q16D414yes—
28C22×C8×C11D411yescharacteristic
29C22×C8×C11C2311yescharacteristic
30C11×C4⋊Q8—24no—
31C11×C4⋊Q8—42no—
32C2×C11×C4⋊C4—42no—
33C2×C42×C11D411yescharacteristic
34#66979—21no—
35C2×#4318—21no—
36C4×C8×C11—22no—
37#66883—22no—
38#66882D412yes—
39#66881—21no—
40Dic11⋊C8—42no—
41#66876—22no—
42#66876—22no—
43C2×C11⋊C16—22no—
44#13415—111nomaximal, Sylow
45C2×Q8×C11—24no—
46C2×Q8×C11—42no—
47C2×Q8×C11—42no—
48C2×Q8×C11—42no—
49C2×Q8×C11—42no—
50C2×Q8×C11—42no—
51C22×C4×C11—21no—
52C22×C4×C11—42no—
53C22×C4×C11C2×D411yescharacteristic
54C11×Q16—24no—
55C11×Q16—24no—
56C11×Q16—48no—
57C11×Q16—42no—
58C11×Q16—42no—
59C2×C8×C11—21no—
60C2×C8×C11—21no—
61C2×C8×C11D812yes—
62C2×C8×C11C2×D412yes—
63C2×C8×C11C2×D411yescharacteristic
64C2×C8×C11#4111yescharacteristic
65C2×C8×C11#4112yes—
66C11×C4⋊C4—48no—
67C42×C11—21no—
68C42×C11SD1612yes—
69C22⋊Dic11—41no—
70C4⋊Dic11—22no—
71C4×Dic11—41no—
72#4318—41no—
73#4318—41no—
74C2×C11⋊C8—41no—
75C11⋊C16—42no—
76C2×#494D1111yescharacteristic
77C2×#362—112no—
78#2141—112no—
79#1945—111no—
80#1376—111no—
81C23×C11AGL(1,ℤ/8)11yescharacteristic
82Q8×C11—44no—
83Q8×C11—44no—
84Q8×C11—82no—
85Q8×C11—82no—
86C2×C4×C11—24no—
87C2×C4×C11—22no—
88C2×C4×C11—44no—
89C2×C4×C11—82no—
90C2×C4×C11—82no—
91C2×C4×C11#12011yescharacteristic
92C2×C4×C11#12111yescharacteristic
93C2×C4×C11#12411yescharacteristic
94C2×C4×C11C2×D811yescharacteristic
95C2×C4×C11C2×SD1611yescharacteristic
96C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
97C2×Dic11—42no—
98C8×C11—22no—
99C8×C11#12112yes—
100C8×C11#12312yes—
101C11⋊C8—81no—
102C22×Q16—21no—
103C22×Q16C2×D1112yes—
104C2×C4⋊Q8—21no—
105C2×M32—112no—
106#494—24no—
107C2×#108—111no—
108#427—111no—
109#424—221no—
110C2×C4×C8C2×D1111yescharacteristic
111#362—224no—
112#358—224no—
113#339—221no—
114C22×C11—22no—
115C22×C11#45011yescharacteristic
116C22×C11#45911yescharacteristic
117C22×C11#49011yescharacteristic
118C4×C11—24no—
119C4×C11—84no—
120C4×C11#39411yescharacteristic
121C4×C11#44711yescharacteristic
122C4×C11#46011yescharacteristic
123C4×C11#48611yescharacteristic
124Dic11—82no—
125C22×Q8—22no—
126C2×Q16—24no—
127C2×Q16—22no—
128C2×Q16—22no—
129C2×Q16—22no—
130C2×Q16—22no—
131C2×Q16—22no—
132C2×Q16—42no—
133C2×Q16—42no—
134C2×Q16C22⋊D1114yes—
135C2×M16—221no—
136C22×C8C22⋊D1111yescharacteristic
137C22×C8C22×D1111yescharacteristic
138C4⋊Q8—24no—
139C4⋊Q8—42no—
140#117—221no—
141C2×C4⋊C4—42no—
142C2×C42C22⋊D1111yescharacteristic
143M32—222no—
144M32—222no—
145C2×C16—222no—
146#108—222no—
147#107—112no—
148#106—221no—
149C4⋊C8—442no—
150C4×C8—22no—
151C2×C11—21no—
152C2×C11—21no—
153C2×C11#204111yescharacteristic
154C2×C11#221412yes—
155C2×Q8—24no—
156C2×Q8—42no—
157C2×Q8—42no—
158C2×Q8—42no—
159C2×Q8—42no—
160C2×Q8—42no—
161C22×C4—21no—
162C22×C4—42no—
163C22×C4C2×C22⋊D1111yescharacteristic
164Q16—24no—
165Q16—24no—
166Q16—48no—
167Q16—42no—
168Q16—42no—
169M16—441no—
170M16—441no—
171C2×C8—21no—
172C2×C8—21no—
173C2×C8—441no—
174C2×C8#432312yes—
175C2×C8D4×D1111yescharacteristic
176C2×C8#434111yescharacteristic
177C2×C8#434112yes—
178C2×C8C2×C22⋊D1112yes—
179C4⋊C4—48no—
180C4⋊C4—222no—
181C22⋊C4—441no—
182C42—21no—
183C42—441no—
184C42#432412yes—
185C16—442no—
186C11#1341511yescharacteristic, complemented, Sylow
187C23#6698511yescharacteristic
188Q8—44no—
189Q8—44no—
190Q8—82no—
191Q8—82no—
192C2×C4—24no—
193C2×C4—22no—
194C2×C4—44no—
195C2×C4—82no—
196C2×C4—82no—
197C2×C4—442no—
198C2×C4C2×#432311yescharacteristic
199C2×C4#6698511yescharacteristic
200C2×C4C2×#432411yescharacteristic
201C2×C4#6698911yescharacteristic
202C2×C4#6699111yescharacteristic
203C2×C4#6700611yescharacteristic
204C8—22no—
205C8—881no—
206C8#6698812yes—
207C8#6699212yes—
208C22—22no—
209C22#1062268411yescharacteristic
210C22#1062268511yescharacteristic
211C22#1062283111yescharacteristic
212C4—24no—
213C4—84no—
214C4—882no—
215C4#1062268311yescharacteristic
216C4#1062268811yescharacteristic
217C4#1062283011yescharacteristic
218C4#1062283511yescharacteristic
219C2—21no—
220C2—21no—
221C2#1306984711yescharacteristic
222C2#1307069412yes—
subgroupG/H
centerC22#10622685
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC2×C11×#494C2
socleC22×C11#459
prime radicalC23×C11AGL(1,ℤ/8)
hypercenterC2×#494D11
hypocenterC11#13415
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#494

Complements

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

NH ≅ G/Ntype
186. C11#13415semidirect

Maximal subgroups

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

subgroupindex
C2×#106222032
#130703362
#130693642
#130666982
C2×C11×#4942
#1341511