Finite Group Databasebeta

← #14658574

Subgroups — #14658574

Order 2816.

294 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 89 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#13069590C211yesmaximal, characteristic
2#13068790C211yesmaximal, characteristic
3#13067301C211yesmaximal, characteristic
4#13066476C211yesmaximal, characteristic
5#13066475C211yesmaximal, characteristic
6#13066460C211yesmaximal, characteristic
7C11×#1548C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C2×#66886—21no—
12C2×#66886—21no—
13#10622549C2211yescharacteristic
14#10622538C2211yescharacteristic
15#10622537C2211yescharacteristic
16C2×#66867C2211yescharacteristic
17C11×#333—22no—
18#10622185—22no—
19#10622167—21no—
20#10622167—21no—
21C22×Q8×C11—21no—
22C2×C11×M16—21no—
23C11×C4⋊Q8—21no—
24C11×C4⋊Q8—21no—
25C11×C4⋊Q8—21no—
26C11×C4⋊Q8D412yes—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—21no—
29C2×C42×C11C2311yescharacteristic
30C2×C4⋊Dic11—21no—
31C2×#4318—21no—
32C22×C11⋊C8D411yescharacteristic
33C22×C11⋊C8D411yescharacteristic
34C11×C4⋊C8—21no—
35C11×C4⋊C8—21no—
36C11×C4⋊C8—21no—
37C11×C22⋊C8—21no—
38C4×C8×C11—21no—
39C11⋊#95—21no—
40C11⋊#95—21no—
41C22⋊(C11⋊C8)—21no—
42#66886—42no—
43#66886—42no—
44C4⋊(C11⋊C8)—21no—
45C4⋊(C11⋊C8)—21no—
46C4⋊(C11⋊C8)—21no—
47#66867—21no—
48#66867—21no—
49C4×C11⋊C8—21no—
50#10633—111nomaximal, Sylow
51C2×Q8×C11—22no—
52C2×Q8×C11—41no—
53C2×Q8×C11—82no—
54C22×C4×C11—41no—
55C22×C4×C11C2×D411yescharacteristic
56C22×C4×C11#4111yescharacteristic
57C22×C4×C11#4111yescharacteristic
58C22×Dic11—41no—
59C11×M16—41no—
60C11×M16—41no—
61C2×C8×C11—41no—
62C2×C8×C11—41no—
63C11×C4⋊C4—22no—
64C11×C4⋊C4—22no—
65C11×C4⋊C4—41no—
66C11×C4⋊C4—41no—
67C42×C11C2×D411yescharacteristic
68C42×C11#4111yescharacteristic
69C42×C11#4111yescharacteristic
70C42×C11#4111yescharacteristic
71C4⋊Dic11—41no—
72C4⋊Dic11—41no—
73#4318—41no—
74#4318—41no—
75C2×C11⋊C8—21no—
76C2×C11⋊C8—21no—
77C2×C11⋊C8—21no—
78C2×C11⋊C8—21no—
79C2×C11⋊C8—41no—
80C2×C11⋊C8—41no—
81C2×C11⋊C8SD1612yes—
82C2×C11⋊C8Q1612yes—
83#1993—111no—
84#1849—111no—
85#1549—111no—
86#1548D1111yescharacteristic
87#1286—111no—
88#1286—111no—
89#1281—111no—
90C23×C11#12411yescharacteristic
91Q8×C11—82no—
92Q8×C11—82no—
93C2×C4×C11—41no—
94C2×C4×C11—41no—
95C2×C4×C11—42no—
96C2×C4×C11—82no—
97C2×C4×C11#12111yescharacteristic
98C2×C4×C11#12311yescharacteristic
99C2×C4×C11#12311yescharacteristic
100C2×C4×C11#12311yescharacteristic
101C2×C4×C11#12611yescharacteristic
102C2×C4×C11#12611yescharacteristic
103C2×C4×C11C2×SD1611yescharacteristic
104C2×C4×C11C2×Q1611yescharacteristic
105C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
106C2×C4×C11#13711yescharacteristic
107C2×Dic11—81no—
108C2×Dic11—81no—
109C2×Dic11—81no—
110C8×C11—81no—
111C8×C11—81no—
112C11⋊C8—22no—
113C11⋊C8—22no—
114C11⋊C8—81no—
115C11⋊C8—81no—
116C2×C4⋊Q8C2×D1111yescharacteristic
117#431—111no—
118#431C2×D1111yescharacteristic
119C2×#108—221no—
120C2×#108—221no—
121#423—111no—
122#423C2×D1111yescharacteristic
123C2×#97—111no—
124#382—111no—
125#340—221no—
126#340—221no—
127#333—22no—
128#332—222no—
129C22×C11—21no—
130C22×C11—21no—
131C22×C11#39711yescharacteristic
132C22×C11#48711yescharacteristic
133C22×C11#48911yescharacteristic
134C4×C11—21no—
135C4×C11—21no—
136C4×C11—21no—
137C4×C11—21no—
138C4×C11—82no—
139C4×C11#46011yescharacteristic
140C4×C11#46211yescharacteristic
141C4×C11#48311yescharacteristic
142C4×C11#48411yescharacteristic
143Dic11—161no—
144C22×Q8—21no—
145C2×M16—21no—
146C2×M16—221no—
147C22×C8—111no—
148C22×C8—111no—
149C4⋊Q8—21no—
150C4⋊Q8—21no—
151C4⋊Q8—21no—
152C4⋊Q8C22⋊D1112yes—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—221no—
156C2×C42C22×D1111yescharacteristic
157#108—442no—
158#108—442no—
159C4⋊C8—21no—
160C4⋊C8—21no—
161C4⋊C8—21no—
162C4⋊C8—221no—
163C4⋊C8—221no—
164C4⋊C8—221no—
165C22⋊C8—21no—
166C22⋊C8—221no—
167#97—221no—
168#97—221no—
169C4×C8—21no—
170C4×C8—221no—
171#95—221no—
172#95—221no—
173C2×C11—21no—
174C2×C11—21no—
175C2×C11#207211yescharacteristic
176C2×C11#208111yescharacteristic
177C2×C11#208211yescharacteristic
178C2×Q8—22no—
179C2×Q8—41no—
180C2×Q8—82no—
181C22×C4—41no—
182C22×C4—441no—
183C22×C4#433911yescharacteristic
184C22×C4D4×D1111yescharacteristic
185C22×C4#434111yescharacteristic
186M16—41no—
187M16—41no—
188M16—441no—
189M16—441no—
190C2×C8—41no—
191C2×C8—41no—
192C2×C8—112no—
193C2×C8—112no—
194C2×C8—221no—
195C2×C8—221no—
196C2×C8—221no—
197C2×C8—221no—
198C2×C8—441no—
199C2×C8—441no—
200C4⋊C4—22no—
201C4⋊C4—22no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—441no—
205C4⋊C4—441no—
206C42#433911yescharacteristic
207C42#434111yescharacteristic
208C42#434111yescharacteristic
209C42C2×C22⋊D1111yescharacteristic
210C11#1063311yescharacteristic, complemented, Sylow
211C23#6693811yescharacteristic
212Q8—82no—
213Q8—82no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—42no—
217C2×C4—82no—
218C2×C4—881no—
219C2×C4—881no—
220C2×C4—881no—
221C2×C4#6693211yescharacteristic
222C2×C4#6693211yescharacteristic
223C2×C4#6693611yescharacteristic
224C2×C4SD16×D1111yescharacteristic
225C2×C4#6696711yescharacteristic
226C2×C4Q16×D1111yescharacteristic
227C2×C4#6697111yescharacteristic
228C2×C4#6698211yescharacteristic
229C2×C4#6698811yescharacteristic
230C2×C4#6699211yescharacteristic
231C8—81no—
232C8—81no—
233C8—222no—
234C8—222no—
235C8—881no—
236C8—881no—
237C22—21no—
238C22—21no—
239C22#1062240511yescharacteristic
240C22#1062240811yescharacteristic
241C22#1062256511yescharacteristic
242C4—21no—
243C4—21no—
244C4—21no—
245C4—21no—
246C4—82no—
247C4—1761no—
248C4#1062241811yescharacteristic
249C4#1062242211yescharacteristic
250C4#1062277611yescharacteristic
251C4#1062279511yescharacteristic
252C2—21no—
253C2—21no—
254C2#1307002711yescharacteristic
255C2#1307007611yescharacteristic
256C2#1307008411yescharacteristic
subgroupG/H
centerC22#10622565
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1548C2
socleC22×C11#397
prime radicalC23×C11#124
hypercenter#1548D11
hypocenterC11#10633
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
210. C11#10633semidirect

Maximal subgroups

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

subgroupindex
#130695902
#130687902
#130673012
#130664762
#130664752
#130664602
C11×#15482
#1063311