Finite Group Databasebeta

← #14656126

Subgroups — #14656126

Order 2816.

560 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 131 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×#10622704C212yesmaximal
2#13073989C211yesmaximal, characteristic
3C2×#10622094C212yesmaximal
4#13066499C211yesmaximal, characteristic
5C11×#1956C211yesmaximal, characteristic
6C2×C11×C4⋊Q8C2211yescharacteristic
7C2×C4×Dic22C2212yes—
8C2×C11×#103—22no—
9C2×C4×C8×C11C2211yescharacteristic
10C11×#384C2211yescharacteristic
11#10622704—24no—
12#10622704—24no—
13#10622598—22no—
14#10622596—22no—
15#10622587—22no—
16C2×#66874—22no—
17C2×#66871—22no—
18C2×C4⋊(C11⋊C8)C2212yes—
19#10622094—24no—
20C22×Q8×C11—21no—
21C22×Dic22D412yes—
22C22×C8×C11—21no—
23C11×C4⋊Q8—22no—
24C11×C4⋊Q8—21no—
25C11×C4⋊Q8D412yes—
26C2×C11×C4⋊C4—22no—
27C2×C11×C4⋊C4—22no—
28C2×C11×C4⋊C4D412yes—
29C2×C42×C11C2311yescharacteristic
30C2×C4⋊Dic11—22no—
31C2×C4⋊Dic11D412yes—
32C2×Dic11⋊C4—22no—
33C2×C4×Dic11—22no—
34C22×C11⋊C8—22no—
35C4×Dic22—22no—
36C4×Dic22—22no—
37C4×Dic22—22no—
38C4×Dic22—22no—
39C11×#103—44no—
40C4×C8×C11—22no—
41C11⋊#95—22no—
42C11⋊#95—24no—
43#66874—28no—
44#66871—28no—
45C4⋊(C11⋊C8)—22no—
46C4⋊(C11⋊C8)D414yes—
47#10237—111nomaximal, Sylow
48C2×Q8×C11—22no—
49C2×Q8×C11—42no—
50C2×Q8×C11—42no—
51C2×Q8×C11—41no—
52C22×C4×C11—22no—
53C22×C4×C11—41no—
54C22×C4×C11C2×D411yescharacteristic
55C22×C4×C11C2×D412yes—
56C22×Dic11—22no—
57C22×Dic11—22no—
58C2×Dic22—22no—
59C2×Dic22—22no—
60C2×Dic22—22no—
61C2×Dic22—22no—
62C2×Dic22—22no—
63C2×Dic22Q1614yes—
64C2×C8×C11—22no—
65C2×C8×C11—41no—
66C2×C8×C11—41no—
67C11×C4⋊C4—24no—
68C11×C4⋊C4—42no—
69C11×C4⋊C4—42no—
70C11×C4⋊C4—42no—
71C11×C4⋊C4—42no—
72C42×C11C2×D411yescharacteristic
73C42×C11C2×D412yes—
74C42×C11#4111yescharacteristic
75C4⋊Dic11—22no—
76C4⋊Dic11—22no—
77C4⋊Dic11—82no—
78Dic11⋊C4—42no—
79Dic11⋊C4—42no—
80C4×Dic11—42no—
81C4×Dic11—42no—
82C2×C11⋊C8—24no—
83C2×C11⋊C8—42no—
84C2×C11⋊C8—42no—
85C2×#477—112no—
86#2582—111no—
87#1956D1111yescharacteristic
88C2×Q8⋊C8—112no—
89#1296—111no—
90C23×C11#12011yescharacteristic
91Q8×C11—44no—
92Q8×C11—82no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—42no—
96C2×C4×C11—44no—
97C2×C4×C11—42no—
98C2×C4×C11—81no—
99C2×C4×C11—81no—
100C2×C4×C11#12012yes—
101C2×C4×C11#12112yes—
102C2×C4×C11#12111yescharacteristic
103C2×C4×C11#12711yescharacteristic
104C2×C4×C11C2×Q1612yes—
105C2×C4×C11#13512yes—
106C2×C4×C11#13712yes—
107C2×C4×C11#13712yes—
108C2×Dic11—24no—
109C2×Dic11—42no—
110C2×Dic11—42no—
111C2×Dic11—42no—
112C2×Dic11—42no—
113C2×Dic11—42no—
114Dic22—24no—
115Dic22—24no—
116Dic22—42no—
117Dic22—42no—
118C8×C11—42no—
119C11⋊C8—44no—
120C2×C4⋊Q8C2×D1111yescharacteristic
121C2×C4×Q8—112no—
122#477—224no—
123#477—224no—
124C2×#107—222no—
125C2×C4⋊C8—112no—
126C2×#103—22no—
127C2×#103—222no—
128C2×C4×C8C2×D1111yescharacteristic
129#398—222no—
130#391—222no—
131#389—222no—
132#384C2×D1111yescharacteristic
133Q8⋊C8—224no—
134C22×C11#39211yescharacteristic
135C22×C11#45112yes—
136C22×C11#45212yes—
137C22×C11#45311yescharacteristic
138C22×C11#45411yescharacteristic
139C4×C11—21no—
140C4×C11—21no—
141C4×C11—82no—
142C4×C11—82no—
143C4×C11#45112yes—
144C4×C11#45212yes—
145C4×C11#46712yes—
146C4×C11#47012yes—
147Dic11—44no—
148Dic11—82no—
149C22×Q8—21no—
150C22×Q8—112no—
151C22×C8—21no—
152C22×C8—222no—
153C4⋊Q8—21no—
154C4⋊Q8—22no—
155C4⋊Q8D4412yes—
156C4×Q8—222no—
157C4×Q8—222no—
158C4×Q8—222no—
159C4×Q8—222no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—112no—
163C2×C4⋊C4—222no—
164C2×C4⋊C4—222no—
165C2×C4⋊C4C22⋊D1112yes—
166C2×C42—222no—
167C2×C42C22×D1111yescharacteristic
168#107—228no—
169C4⋊C8—114no—
170C4⋊C8—222no—
171#103—44no—
172#103—228no—
173C4×C8—22no—
174#95—224no—
175#95—222no—
176C2×C11#163011yescharacteristic
177C2×C11#163311yescharacteristic
178C2×C11#163612yes—
179C2×C11#200112yes—
180C2×C11#200611yescharacteristic
181C2×Q8—22no—
182C2×Q8—42no—
183C2×Q8—42no—
184C2×Q8—41no—
185C2×Q8—114no—
186C2×Q8—222no—
187C2×Q8—222no—
188C2×Q8—222no—
189C2×Q8—222no—
190C2×Q8—222no—
191C22×C4—22no—
192C22×C4—41no—
193C22×C4—222no—
194C22×C4—222no—
195C22×C4D4×D1112yes—
196C22×C4C2×C22⋊D1111yescharacteristic
197C2×C8—22no—
198C2×C8—41no—
199C2×C8—41no—
200C2×C8—224no—
201C2×C8—442no—
202C2×C8—442no—
203C4⋊C4—24no—
204C4⋊C4—42no—
205C4⋊C4—42no—
206C4⋊C4—42no—
207C4⋊C4—42no—
208C4⋊C4—222no—
209C4⋊C4—222no—
210C4⋊C4—442no—
211C4⋊C4—442no—
212C4⋊C4—882no—
213C42—442no—
214C42—442no—
215C42C2×D4411yescharacteristic
216C42#433911yescharacteristic
217C42D4×D1112yes—
218C11#1023711yescharacteristic, complemented, Sylow
219C23#6699011yescharacteristic
220Q8—44no—
221Q8—82no—
222Q8—224no—
223Q8—224no—
224Q8—442no—
225Q8—442no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—44no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—81no—
232C2×C4—81no—
233C2×C4—224no—
234C2×C4—442no—
235C2×C4—442no—
236C2×C4—442no—
237C2×C4—442no—
238C2×C4—442no—
239C2×C4#6693512yes—
240C2×C4#6693712yes—
241C2×C4#6696812yes—
242C2×C4#6696912yes—
243C2×C4Q16×D1112yes—
244C2×C4#6697112yes—
245C2×C4#6698311yescharacteristic
246C2×C4#6699311yescharacteristic
247C8—42no—
248C8—444no—
249C22#1062257311yescharacteristic
250C22#1062267511yescharacteristic
251C22#1062269011yescharacteristic
252C22#1062278612yes—
253C22#1062279912yes—
254C4—21no—
255C4—21no—
256C4—82no—
257C4—82no—
258C4—444no—
259C4—882no—
260C4#1062242112yes—
261C4#1062242312yes—
262C4#1062242612yes—
263C4#1062242912yes—
264C2#1306773511yescharacteristic
265C2#1306775411yescharacteristic
266C2#1306777112yes—
267C2#1306962512yes—
268C2#1306965711yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1956C2
socle, prime radicalC23×C11#120
hypercenter#1956D11
hypocenterC11#10237
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1956

Complements

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

NH ≅ G/Ntype
218. C11#10237semidirect

Maximal subgroups

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

subgroupindex
C2×#106227042
#130739892
C2×#106220942
#130664992
C11×#19562
#1023711