Finite Group Databasebeta

← #14658422

Subgroups — #14658422

Order 2816.

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

normal subgroups only

This group has 306 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
1#13069605C211yesmaximal, characteristic
2#13067390C211yesmaximal, characteristic
3#13067368C211yesmaximal, characteristic
4#13067302C211yesmaximal, characteristic
5C2×#10622124C211yesmaximal, characteristic
6#13066490C211yesmaximal, characteristic
7C11×#1950C211yesmaximal, characteristic
8C2×#66922C2211yescharacteristic
9C2×C11×#108—21no—
10C11×#423C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C4×C11×M16C2211yescharacteristic
13#10622538C2211yescharacteristic
14#10622537C2211yescharacteristic
15C2×C4⋊(C11⋊C8)C2211yescharacteristic
16C11×#341—21no—
17#10622192—21no—
18#10622192—21no—
19#10622124—22no—
20#10622124—21no—
21#10622124—21no—
22#10622117—22no—
23#10622096—21no—
24#10622095—21no—
25C22×Dic22—21no—
26C2×C11×M16—21no—
27C2×C11×M16D411yescharacteristic
28C2×C11×M16D411yescharacteristic
29C22×C8×C11—21no—
30C2×C42×C11C2311yescharacteristic
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11Q812yes—
33C2×#4318—21no—
34C22×C11⋊C8—21no—
35#66922—21no—
36#66922—21no—
37#66922—21no—
38#66922—21no—
39C11×#108—42no—
40C11×C4⋊C8—21no—
41C11×C4⋊C8—21no—
42C11×C4⋊C8—21no—
43C11×C4⋊C8D412yes—
44C11×#97—21no—
45C4×C8×C11—21no—
46C22⋊(C11⋊C8)—21no—
47C4⋊(C11⋊C8)—21no—
48C4⋊(C11⋊C8)—21no—
49C4⋊(C11⋊C8)—21no—
50C4⋊(C11⋊C8)—21no—
51C4⋊(C11⋊C8)D411yescharacteristic
52C4⋊(C11⋊C8)D411yescharacteristic
53C4×C11⋊C8—21no—
54#10606—111nomaximal, Sylow
55C22×C4×C11C2×D411yescharacteristic
56C22×C4×C11C2×Q811yescharacteristic
57C22×C4×C11#4111yescharacteristic
58C22×Dic11—22no—
59C2×Dic22—41no—
60C2×Dic22—41no—
61C2×Dic22—81no—
62C2×Dic22—81no—
63C11×M16—21no—
64C11×M16—21no—
65C11×M16—21no—
66C11×M16—41no—
67C11×M16—41no—
68C11×M16Q1612yes—
69C2×C8×C11—21no—
70C2×C8×C11—21no—
71C2×C8×C11—22no—
72C2×C8×C11—41no—
73C2×C8×C11—41no—
74C2×C8×C11—41no—
75C42×C11C2×D411yescharacteristic
76C42×C11C2×D411yescharacteristic
77C42×C11#4111yescharacteristic
78C42×C11#4111yescharacteristic
79C4⋊Dic11—22no—
80C4⋊Dic11—22no—
81C4⋊Dic11—41no—
82C4⋊Dic11—41no—
83#4318—41no—
84#4318—41no—
85C2×C11⋊C8—21no—
86C2×C11⋊C8—21no—
87C2×C11⋊C8—41no—
88C2×C11⋊C8—41no—
89C2×C11⋊C8—81no—
90#1997—111no—
91#1950D1111yescharacteristic
92#1571—111no—
93#1565—111no—
94#1549—111no—
95C2×#332—111no—
96#1292—111no—
97C23×C11C22⋊Q811yescharacteristic
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—41no—
101C2×C4×C11#12111yescharacteristic
102C2×C4×C11#12111yescharacteristic
103C2×C4×C11#12111yescharacteristic
104C2×C4×C11C22⋊Q811yescharacteristic
105C2×C4×C11C22⋊Q811yescharacteristic
106C2×C4×C11#12611yescharacteristic
107C2×C4×C11C2×Q1611yescharacteristic
108C2×C4×C11#13511yescharacteristic
109C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
110C2×C4×C11#13711yescharacteristic
111C2×Dic11—42no—
112C2×Dic11—82no—
113Dic22—82no—
114Dic22—81no—
115Dic22—81no—
116C8×C11—22no—
117C8×C11—42no—
118C8×C11—41no—
119C8×C11—81no—
120C11⋊C8—41no—
121C11⋊C8—41no—
122C11⋊C8—81no—
123C11⋊C8—81no—
124C2×C4⋊Q8—111no—
125#431—111no—
126C2×#108—21no—
127#423—111no—
128#423C2×D1111yescharacteristic
129C2×C4⋊C8—111no—
130C2×C4⋊C8C2×D1111yescharacteristic
131C4×M16C2×D1111yescharacteristic
132#343—221no—
133#343—221no—
134#341—21no—
135#335—221no—
136#335—222no—
137#334—221no—
138#332—221no—
139#332—221no—
140#332—222no—
141C22×C11—21no—
142C22×C11—21no—
143C22×C11#39611yescharacteristic
144C22×C11#47711yescharacteristic
145C22×C11#47911yescharacteristic
146C4×C11—21no—
147C4×C11—21no—
148C4×C11—21no—
149C4×C11#46211yescharacteristic
150C4×C11#46311yescharacteristic
151C4×C11#46711yescharacteristic
152C4×C11#46811yescharacteristic
153C4×C11#47111yescharacteristic
154C4×C11#47211yescharacteristic
155Dic11—82no—
156C22×Q8—221no—
157C2×M16—21no—
158C2×M16—221no—
159C2×M16C22⋊D1111yescharacteristic
160C2×M16C22⋊D1111yescharacteristic
161C22×C8—21no—
162C22×C8—221no—
163C4⋊Q8—221no—
164C4⋊Q8—221no—
165C4⋊Q8—221no—
166C4⋊Q8—221no—
167C2×C4⋊C4—112no—
168C2×C4⋊C4—221no—
169C2×C42C22×D1111yescharacteristic
170#108—42no—
171C4⋊C8—21no—
172C4⋊C8—21no—
173C4⋊C8—21no—
174C4⋊C8—111no—
175C4⋊C8—111no—
176C4⋊C8—221no—
177C4⋊C8—221no—
178C4⋊C8—221no—
179C4⋊C8—221no—
180C4⋊C8D4412yes—
181C22⋊C8—221no—
182#97—21no—
183C4×C8—21no—
184C4×C8—221no—
185C2×C11—21no—
186C2×C11—21no—
187C2×C11#206311yescharacteristic
188C2×C11#206811yescharacteristic
189C2×C11#207011yescharacteristic
190C2×Q8—441no—
191C2×Q8—441no—
192C2×Q8—881no—
193C2×Q8—881no—
194C22×C4—222no—
195C22×C4Q8×D1111yescharacteristic
196C22×C4#434311yescharacteristic
197C22×C4C2×C22⋊D1111yescharacteristic
198M16—21no—
199M16—21no—
200M16—21no—
201M16—41no—
202M16—41no—
203M16—441no—
204M16—441no—
205M16#432612yes—
206C2×C8—21no—
207C2×C8—22no—
208C2×C8—21no—
209C2×C8—41no—
210C2×C8—41no—
211C2×C8—41no—
212C2×C8—221no—
213C2×C8—221no—
214C2×C8—441no—
215C2×C8—441no—
216C2×C8—881no—
217C4⋊C4—222no—
218C4⋊C4—222no—
219C4⋊C4—441no—
220C4⋊C4—441no—
221C42C2×D4411yescharacteristic
222C42#433911yescharacteristic
223C42D4×D1111yescharacteristic
224C42#434111yescharacteristic
225C11#1060611yescharacteristic, complemented, Sylow
226C23#6699911yescharacteristic
227Q8—882no—
228Q8—881no—
229Q8—881no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—41no—
233C2×C4—442no—
234C2×C4—882no—
235C2×C4#6694811yescharacteristic
236C2×C4#6694911yescharacteristic
237C2×C4#6695011yescharacteristic
238C2×C4#6695111yescharacteristic
239C2×C4#6698311yescharacteristic
240C2×C4#6698511yescharacteristic
241C2×C4#6699211yescharacteristic
242C2×C4C2×#432611yescharacteristic
243C2×C4#6700311yescharacteristic
244C2×C4#6700411yescharacteristic
245C8—22no—
246C8—42no—
247C8—41no—
248C8—81no—
249C8—441no—
250C8—441no—
251C8—881no—
252C8—881no—
253C22—21no—
254C22—21no—
255C22#1062260711yescharacteristic
256C22#1062267611yescharacteristic
257C22#1062270411yescharacteristic
258C4—21no—
259C4—21no—
260C4—21no—
261C4—882no—
262C4#1062251011yescharacteristic
263C4#1062251111yescharacteristic
264C4#1062262911yescharacteristic
265C4#1062264411yescharacteristic
266C4#1062265511yescharacteristic
267C4#1062266411yescharacteristic
268C2—21no—
269C2—21no—
270C2#1306997111yescharacteristic
271C2#1307000811yescharacteristic
272C2#1307001611yescharacteristic
subgroupG/H
centerC22#10622607
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1950C2
socleC22×C11#396
prime radicalC23×C11C22⋊Q8
hypercenter#1950D11
hypocenterC11#10606
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1950

Complements

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

NH ≅ G/Ntype
225. C11#10606semidirect

Maximal subgroups

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

subgroupindex
#130696052
#130673902
#130673682
#130673022
C2×#106221242
#130664902
C11×#19502
#1060611