Finite Group Databasebeta

← #14673165

Subgroups — #14673165

Order 2816.

436 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 99 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×#10622134C212yesmaximal
3#13070335C212yesmaximal
4#13066698C211yesmaximal, characteristic
5C11×#1945C211yesmaximal, characteristic
6C22×Dic44—21no—
7C22×Dic44C2212yes—
8C2×#66922—21no—
9C2×C11×#108C2211yescharacteristic
10C11×#427C2211yescharacteristic
11C11×#424—21no—
12C2×C4×C8×C11C2211yescharacteristic
13C2×#66876C2212yes—
14#10622312—24no—
15C11×#339—21no—
16#10622134—24no—
17#10622130—24no—
18C22×Dic22—22no—
19C2×C11×M16—21no—
20C22×C8×C11D411yescharacteristic
21C22×C8×C11C2311yescharacteristic
22C11×#117—21no—
23C2×C42×C11D411yescharacteristic
24C2×C4⋊Dic11—42no—
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×#108—22no—
37C11×#107D412yes—
38C11×#106—21no—
39C11×C4⋊C8—42no—
40C4×C8×C11—22no—
41#66876—22no—
42#66876—22no—
43C2×C11⋊C16—22no—
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—
54C11×M16—41no—
55C11×M16—41no—
56C2×C8×C11—21no—
57C2×C8×C11—21no—
58C2×C8×C11—41no—
59C2×C8×C11D812yes—
60C2×C8×C11C2×D412yes—
61C2×C8×C11C2×D411yescharacteristic
62C2×C8×C11#4111yescharacteristic
63C2×C8×C11#4112yes—
64C11×C4⋊C4—22no—
65C11×C22⋊C4—41no—
66C42×C11—21no—
67C42×C11—41no—
68C42×C11SD1612yes—
69C4⋊Dic11—48no—
70Dic44—24no—
71Dic44—24no—
72Dic44—48no—
73Dic44—42no—
74Dic44—42no—
75C11⋊C16—42no—
76C2×#494—111no—
77C2×#362—112no—
78#2141—112no—
79#1945D1111yescharacteristic
80#1376—111no—
81C23×C11AGL(1,ℤ/8)11yescharacteristic
82C2×C4×C11—24no—
83C2×C4×C11—22no—
84C2×C4×C11—42no—
85C2×C4×C11#12011yescharacteristic
86C2×C4×C11#12111yescharacteristic
87C2×C4×C11#12411yescharacteristic
88C2×C4×C11C2×D811yescharacteristic
89C2×C4×C11C2×SD1611yescharacteristic
90C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
91C2×Dic11—44no—
92C2×Dic11—82no—
93C2×Dic11—82no—
94Dic22—44no—
95Dic22—44no—
96Dic22—82no—
97Dic22—82no—
98C8×C11—22no—
99C8×C11—81no—
100C8×C11#12112yes—
101C8×C11#12312yes—
102C22×Q16—112no—
103C22×Q16—221no—
104C2×C4⋊Q8—221no—
105C2×M32—112no—
106#494—224no—
107C2×#108C2×D1111yescharacteristic
108#427C2×D1111yescharacteristic
109#424—21no—
110C2×C4×C8C2×D1111yescharacteristic
111#362—224no—
112#358—224no—
113#339—21no—
114C22×C11—22no—
115C22×C11#45011yescharacteristic
116C22×C11#45911yescharacteristic
117C22×C11#49011yescharacteristic
118C4×C11—24no—
119C4×C11—82no—
120C4×C11#39411yescharacteristic
121C4×C11#44711yescharacteristic
122C4×C11#46011yescharacteristic
123C4×C11#48611yescharacteristic
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—21no—
136C22×C8C22⋊D1111yescharacteristic
137C22×C8C22×D1111yescharacteristic
138C4⋊Q8—224no—
139C4⋊Q8—442no—
140#117—21no—
141C2×C4⋊C4—442no—
142C2×C42C22⋊D1111yescharacteristic
143M32—222no—
144M32—222no—
145C2×C16—222no—
146#108—22no—
147#107D4412yes—
148#106—21no—
149C4⋊C8—42no—
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×C22⋊D1111yescharacteristic
164Q16—224no—
165Q16—224no—
166Q16—448no—
167Q16—442no—
168Q16—442no—
169M16—41no—
170M16—41no—
171C2×C8—21no—
172C2×C8—21no—
173C2×C8—41no—
174C2×C8#432312yes—
175C2×C8C2×D4411yescharacteristic
176C2×C8#433911yescharacteristic
177C2×C8D4×D1112yes—
178C2×C8#434312yes—
179C4⋊C4—22no—
180C4⋊C4—448no—
181C22⋊C4—41no—
182C42—21no—
183C42—41no—
184C42#432512yes—
185C16—442no—
186C11#1341511yescharacteristic, complemented, Sylow
187C23#6700211yescharacteristic
188Q8—444no—
189Q8—444no—
190Q8—882no—
191Q8—882no—
192C2×C4—24no—
193C2×C4—22no—
194C2×C4—42no—
195C2×C4—444no—
196C2×C4—882no—
197C2×C4—882no—
198C2×C4#6698311yescharacteristic
199C2×C4C2×#432311yescharacteristic
200C2×C4#6699011yescharacteristic
201C2×C4C2×#432511yescharacteristic
202C2×C4#6700011yescharacteristic
203C2×C4#6700211yescharacteristic
204C8—22no—
205C8—81no—
206C8#6694712yes—
207C8#6694812yes—
208C22—22no—
209C22#1062262811yescharacteristic
210C22#1062265911yescharacteristic
211C22#1062268011yescharacteristic
212C4—24no—
213C4—82no—
214C4—884no—
215C4#1062260411yescharacteristic
216C4#1062264011yescharacteristic
217C4#1062264911yescharacteristic
218C4#1062270111yescharacteristic
219C2—21no—
220C2—21no—
221C2#1306985011yescharacteristic
222C2#1307069712yes—
subgroupG/H
centerC22#10622628
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1945C2
socleC22×C11#459
prime radicalC23×C11AGL(1,ℤ/8)
hypercenter#1945D11
hypocenterC11#13415
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ #1945

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×#106221342
#130703352
#130666982
C11×#19452
#1341511