Finite Group Databasebeta

← #14673166

Subgroups — #14673166

Order 2816.

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

normal subgroups only

This group has 436 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×#10622312C211yesmaximal, characteristic
2C2×#10622155C212yesmaximal
3#13070337C212yesmaximal
4#13069364C211yesmaximal, characteristic
5C11×#1376C211yesmaximal, characteristic
6C22×Dic44—21no—
7C22×Dic44C2212yes—
8C2×#66922—21no—
9C2×C11×M32C2212yes—
10C2×C4×C8×C11C2211yescharacteristic
11C2×#66883C2211yescharacteristic
12#10622719C2211yescharacteristic
13#10622715—21no—
14#10622312—24no—
15#10622161—21no—
16#10622155—24no—
17#10622141—24no—
18C22×Dic22—22no—
19C22×C8×C11D411yescharacteristic
20C22×C8×C11C2311yescharacteristic
21C2×C42×C11D411yescharacteristic
22#66979—21no—
23C2×C4⋊Dic11—42no—
24C2×#4318—21no—
25C2×Dic44—22no—
26C2×Dic44—22no—
27C2×Dic44—22no—
28C2×Dic44—22no—
29C2×Dic44—24no—
30C2×Dic44—22no—
31C2×Dic44—42no—
32C2×Dic44—42no—
33C2×Dic44D414yes—
34#66922—24no—
35#66922—42no—
36C11×M32—22no—
37C11×M32—22no—
38C2×C11×C16—22no—
39C4×C8×C11—22no—
40#66883—22no—
41#66882D412yes—
42#66881—21no—
43Dic11⋊C8—42no—
44#13415—111nomaximal, Sylow
45C22×C4×C11—21no—
46C22×C4×C11C2×D411yescharacteristic
47C22×Dic11—42no—
48C2×Dic22—24no—
49C2×Dic22—42no—
50C2×Dic22—42no—
51C2×Dic22—42no—
52C2×Dic22—42no—
53C2×Dic22—42no—
54C2×C8×C11—21no—
55C2×C8×C11—21no—
56C2×C8×C11D812yes—
57C2×C8×C11C2×D412yes—
58C2×C8×C11C2×D411yescharacteristic
59C2×C8×C11#4111yescharacteristic
60C2×C8×C11#4112yes—
61C42×C11—21no—
62C42×C11SD1612yes—
63C22⋊Dic11—41no—
64C4⋊Dic11—22no—
65C4⋊Dic11—48no—
66C4×Dic11—41no—
67#4318—41no—
68#4318—41no—
69C2×C11⋊C8—41no—
70Dic44—24no—
71Dic44—24no—
72Dic44—48no—
73Dic44—42no—
74Dic44—42no—
75C11×C16—42no—
76C2×#494—111no—
77C2×#362—112no—
78#2141—112no—
79#1945—111no—
80#1376D1111yescharacteristic
81C23×C11AGL(1,ℤ/8)11yescharacteristic
82C2×C4×C11—24no—
83C2×C4×C11—22no—
84C2×C4×C11#12011yescharacteristic
85C2×C4×C11#12111yescharacteristic
86C2×C4×C11#12411yescharacteristic
87C2×C4×C11C2×D811yescharacteristic
88C2×C4×C11C2×SD1611yescharacteristic
89C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
90C2×Dic11—44no—
91C2×Dic11—42no—
92C2×Dic11—82no—
93C2×Dic11—82no—
94Dic22—44no—
95Dic22—44no—
96Dic22—82no—
97Dic22—82no—
98C8×C11—22no—
99C8×C11#12112yes—
100C8×C11#12312yes—
101C11⋊C8—81no—
102C22×Q16—112no—
103C22×Q16—221no—
104C2×C4⋊Q8—221no—
105C2×M32C2×D1112yes—
106#494—224no—
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#39411yescharacteristic
120C4×C11#44711yescharacteristic
121C4×C11#46011yescharacteristic
122C4×C11#48611yescharacteristic
123Dic11—82no—
124Dic11—84no—
125C22×Q8—222no—
126C2×Q16—114no—
127C2×Q16—224no—
128C2×Q16—222no—
129C2×Q16—222no—
130C2×Q16—222no—
131C2×Q16—222no—
132C2×Q16—222no—
133C2×Q16—442no—
134C2×Q16—442no—
135C2×M16—221no—
136C22×C8D4411yescharacteristic
137C22×C8C22×D1111yescharacteristic
138C4⋊Q8—224no—
139C4⋊Q8—442no—
140#117—221no—
141C2×C4⋊C4—442no—
142C2×C42D4411yescharacteristic
143M32—22no—
144M32—22no—
145C2×C16—22no—
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—224no—
156C2×Q8—442no—
157C2×Q8—442no—
158C2×Q8—442no—
159C2×Q8—442no—
160C2×Q8—442no—
161C22×C4—21no—
162C22×C4—442no—
163C22×C4C2×D4411yescharacteristic
164Q16—224no—
165Q16—224no—
166Q16—448no—
167Q16—442no—
168Q16—442no—
169M16—441no—
170M16—441no—
171C2×C8—21no—
172C2×C8—21no—
173C2×C8—441no—
174C2×C8D8812yes—
175C2×C8#433912yes—
176C2×C8D4×D1111yescharacteristic
177C2×C8D4×D1112yes—
178C2×C8#434311yescharacteristic
179C4⋊C4—222no—
180C4⋊C4—448no—
181C22⋊C4—441no—
182C42—21no—
183C42—441no—
184C42#431412yes—
185C16—42no—
186C11#1341511yescharacteristic, complemented, Sylow
187C23#6696111yescharacteristic
188Q8—444no—
189Q8—444no—
190Q8—882no—
191Q8—882no—
192C2×C4—24no—
193C2×C4—22no—
194C2×C4—444no—
195C2×C4—442no—
196C2×C4—882no—
197C2×C4—882no—
198C2×C4#6692811yescharacteristic
199C2×C4#6693511yescharacteristic
200C2×C4#6694811yescharacteristic
201C2×C4C2×#431411yescharacteristic
202C2×C4C2×D8811yescharacteristic
203C2×C4#6696111yescharacteristic
204C8—22no—
205C8—881no—
206C8#6693712yes—
207C8#6694712yes—
208C22—22no—
209C22#1062232611yescharacteristic
210C22#1062234411yescharacteristic
211C22#1062245611yescharacteristic
212C4—24no—
213C4—884no—
214C4—882no—
215C4#1062228511yescharacteristic
216C4#1062230711yescharacteristic
217C4#1062234511yescharacteristic
218C4#1062246111yescharacteristic
219C2—21no—
220C2—21no—
221C2#1306985111yescharacteristic
222C2#1307069812yes—
subgroupG/H
centerC22#10622456
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1376C2
socleC22×C11#459
prime radicalC23×C11AGL(1,ℤ/8)
hypercenter#1376D11
hypocenterC11#13415
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ #1376

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×#106223122
C2×#106221552
#130703372
#130693642
C11×#13762
#1341511