Finite Group Databasebeta

← #14673150

Subgroups — #14673150

Order 2816.

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

normal subgroups only

This group has 540 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×#10622201C212yesmaximal, complemented
2#13070332C212yesmaximal, complemented
3#13069364C211yesmaximal, characteristic, complemented
4#13066698C211yesmaximal, characteristic, complemented
5C2×C11×#493C211yesmaximal, characteristic
6C22×C11×D8—21no—
7C22×C11×D8C2212yes—
8C2×C11×#127—21no—
9C11×#493—24no—
10C2×C4×C8×C11C2211yescharacteristic
11C2×#66883C2211yescharacteristic
12#10622719C2211yescharacteristic
13#10622715—21no—
14C2×#66876C2212yes—
15#10622201—24no—
16#10622200—24no—
17#10622161—21no—
18C22×D4×C11—22no—
19C22×D4×C11—42no—
20C2×C11×D8—24no—
21C2×C11×D8—22no—
22C2×C11×D8—22no—
23C2×C11×D8—22no—
24C2×C11×D8—22no—
25C2×C11×D8—22no—
26C2×C11×D8—42no—
27C2×C11×D8—42no—
28C2×C11×D8D414yes—
29C22×C8×C11D411yescharacteristic
30C22×C8×C11C2311yescharacteristic
31C11×#127—24no—
32C11×#127—42no—
33C2×C42×C11D411yescharacteristic
34#66979—21no—
35C2×#4318—21no—
36C4×C8×C11—22no—
37#66883—22no—
38#66882D412yescomplemented
39#66881—21no—
40Dic11⋊C8—42no—
41#66876—22no—
42#66876—22no—
43C2×C11⋊C16—22no—
44#13413—111nomaximal, Sylow
45C24×C11—42no—
46C2×D4×C11—24no—
47C2×D4×C11—48no—
48C2×D4×C11—42no—
49C2×D4×C11—42no—
50C2×D4×C11—42no—
51C2×D4×C11—42no—
52C2×D4×C11—42no—
53C2×D4×C11—88no—
54C22×C4×C11—21no—
55C22×C4×C11C2×D411yescharacteristic
56C11×D8—24no—
57C11×D8—24no—
58C11×D8—48no—
59C11×D8—42no—
60C11×D8—42no—
61C2×C8×C11—21no—
62C2×C8×C11—21no—
63C2×C8×C11D812yes—
64C2×C8×C11C2×D412yes—
65C2×C8×C11C2×D411yescharacteristic
66C2×C8×C11#4111yescharacteristic
67C2×C8×C11#4112yes—
68C42×C11—21no—
69C42×C11SD1612yes—
70C22⋊Dic11—41no—
71C4⋊Dic11—22no—
72C4×Dic11—41no—
73#4318—41no—
74#4318—41no—
75C2×C11⋊C8—41no—
76C11⋊C16—42no—
77C2×#493D1111yescharacteristic
78C2×#361—112no—
79#2140—112no—
80#1945—111no—
81#1376—111no—
82C23×C11—44no—
83C23×C11—88no—
84C23×C11—82no—
85C23×C11—82no—
86C23×C11AGL(1,ℤ/8)11yescharacteristic
87D4×C11—44no—
88D4×C11—44no—
89D4×C11—816no—
90D4×C11—82no—
91D4×C11—82no—
92C2×C4×C11—24no—
93C2×C4×C11—22no—
94C2×C4×C11#12011yescharacteristic
95C2×C4×C11#12111yescharacteristic
96C2×C4×C11#12411yescharacteristic
97C2×C4×C11C2×D811yescharacteristic
98C2×C4×C11C2×SD1611yescharacteristic
99C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
100C2×Dic11—42no—
101C8×C11—22no—
102C8×C11#12112yes—
103C8×C11#12312yes—
104C11⋊C8—81no—
105C22×D8—21no—
106C22×D8C2×D1112yes—
107C2×#127—21no—
108C2×M32—112no—
109#493—24no—
110C2×#108—111no—
111#427—111no—
112#424—221no—
113C2×C4×C8C2×D1111yescharacteristic
114#361—224no—
115#357—224no—
116#339—221no—
117C22×C11—22no—
118C22×C11—88no—
119C22×C11—84no—
120C22×C11—164no—
121C22×C11—164no—
122C22×C11#45011yescharacteristic
123C22×C11#45911yescharacteristic
124C22×C11#49011yescharacteristic
125C4×C11—24no—
126C4×C11#39411yescharacteristic
127C4×C11#44711yescharacteristic
128C4×C11#46011yescharacteristic
129C4×C11#48611yescharacteristic
130Dic11—82no—
131C22×D4—22no—
132C22×D4—42no—
133C2×D8—24no—
134C2×D8—22no—
135C2×D8—22no—
136C2×D8—22no—
137C2×D8—22no—
138C2×D8—22no—
139C2×D8—42no—
140C2×D8—42no—
141C2×D8C22⋊D1114yes—
142C2×M16—221no—
143C22×C8C22⋊D1111yescharacteristic
144C22×C8C22×D1111yescharacteristic
145#127—24no—
146#127—42no—
147#117—221no—
148C2×C42C22⋊D1111yescharacteristic
149M32—222no—
150M32—222no—
151C2×C16—222no—
152#108—222no—
153#107—112no—
154#106—221no—
155C4⋊C8—442no—
156C4×C8—22no—
157C2×C11—21no—
158C2×C11—21no—
159C2×C11—164no—
160C2×C11#204111yescharacteristic
161C2×C11#221312yes—
162C24—42no—
163C2×D4—24no—
164C2×D4—48no—
165C2×D4—42no—
166C2×D4—42no—
167C2×D4—42no—
168C2×D4—42no—
169C2×D4—42no—
170C2×D4—88no—
171C22×C4—21no—
172C22×C4C2×C22⋊D1111yescharacteristic
173D8—24no—
174D8—24no—
175D8—48no—
176D8—42no—
177D8—42no—
178M16—441no—
179M16—441no—
180C2×C8—21no—
181C2×C8—21no—
182C2×C8—441no—
183C2×C8#432312yes—
184C2×C8D4×D1111yescharacteristic
185C2×C8#434111yescharacteristic
186C2×C8#434112yes—
187C2×C8C2×C22⋊D1112yes—
188C4⋊C4—222no—
189C22⋊C4—441no—
190C42—21no—
191C42—441no—
192C42#432412yes—
193C16—442no—
194C11#1341311yescharacteristic, complemented, Sylow
195C23—44no—
196C23—88no—
197C23—82no—
198C23—82no—
199C23#6698511yescharacteristic
200D4—44no—
201D4—44no—
202D4—816no—
203D4—82no—
204D4—82no—
205C2×C4—24no—
206C2×C4—22no—
207C2×C4—442no—
208C2×C4C2×#432311yescharacteristic
209C2×C4#6698511yescharacteristic
210C2×C4C2×#432411yescharacteristic
211C2×C4#6698911yescharacteristic
212C2×C4#6699111yescharacteristic
213C2×C4#6700611yescharacteristic
214C8—22no—
215C8—881no—
216C8#6698812yes—
217C8#6699212yes—
218C22—22no—
219C22—88no—
220C22—84no—
221C22—164no—
222C22—164no—
223C22#1062268411yescharacteristic
224C22#1062268511yescharacteristic
225C22#1062283111yescharacteristic
226C4—24no—
227C4—882no—
228C4#1062268311yescharacteristic
229C4#1062268811yescharacteristic
230C4#1062283011yescharacteristic
231C4#1062283511yescharacteristic
232C2—21no—
233C2—21no—
234C2—164no—
235C2#1306984711yescharacteristic
236C2#1307068912yes—
subgroupG/H
centerC22#10622685
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
Fitting, prime radicalC2×C11×#493C2
socleC22×C11#459
hypercenterC2×#493D11
hypocenterC11#13413
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#493

Complements

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

NH ≅ G/Ntype
1. C2×#10622201C2semidirect
2. #13070332C2semidirect
3. #13069364C2semidirect
4. #13066698C2semidirect
38. #66882D4semidirect
194. C11#13413semidirect

Maximal subgroups

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

subgroupindex
C2×#106222012
#130703322
#130693642
#130666982
C2×C11×#4932
#1341311