Finite Group Databasebeta

← #14647341

Subgroups — #14647341

Order 2816.

498 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 123 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#13071526C211yesmaximal, characteristic
2#13066937C211yesmaximal, characteristic
3#13066517C212yesmaximal, complemented
4#13066476C212yesmaximal, complemented
5C11×#1800C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C2×D4×Dic11—21no—
8C11×#423C2212yes—
9C2×C11×#100—21no—
10#10622825C412yes—
11C2×C11⋊#95C412yes—
12#10622598—21no—
13#10622563—22no—
14#10622549C2211yescharacteristic
15C4×C4⋊Dic11C2211yescharacteristic
16#10622538C2212yes—
17C11×#343—21no—
18#10622163—22no—
19C22×D4×C11D411yescharacteristic
20C23×C4×C11C2×C412yes—
21C23×Dic11—22no—
22C2×C11×M16—22no—
23C4×D4×C11—22no—
24C4×D4×C11—22no—
25C2×C11×C4⋊C4D411yescharacteristic
26C2×C11×C22⋊C4D412yes—
27C2×C42×C11C2311yescharacteristic
28C2×C22⋊Dic11—22no—
29D4×Dic11—44no—
30C2×C4⋊Dic11—21no—
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11—22no—
33C2×C4×Dic11—21no—
34C11×C4⋊C8—22no—
35C11×C4⋊C8—22no—
36C11×#100—42no—
37C11⋊#95—22no—
38C11⋊#95—21no—
39C11⋊#95C2×C411yescharacteristic
40C11⋊#95C2×C411yescharacteristic
41C11⋊#95C2×C412yes—
42C22⋊(C11⋊C8)—22no—
43C4⋊(C11⋊C8)—22no—
44C4×C11⋊C8—22no—
45#8765—111nomaximal, Sylow
46C24×C11C22⋊C412yes—
47C2×D4×C11—22no—
48C2×D4×C11—22no—
49C2×D4×C11SD1612yes—
50C2×D4×C11Q1612yes—
51C22×C4×C11—22no—
52C22×C4×C11—22no—
53C22×C4×C11—82no—
54C22×C4×C11C22⋊C412yes—
55C22×C4×C11C22×C411yescharacteristic
56C22×C4×C11C2×D411yescharacteristic
57C22×C4×C11C2×D411yescharacteristic
58C22×Dic11—21no—
59C22×Dic11—22no—
60C22×Dic11—21no—
61C22×Dic11—44no—
62C22×Dic11—44no—
63C22×Dic11—82no—
64C11×M16—42no—
65C11×M16—42no—
66C2×C8×C11—42no—
67C11×C4⋊C4—22no—
68C11×C22⋊C4—24no—
69C42×C11#4112yes—
70C42×C11#4112yes—
71C22⋊Dic11—44no—
72C4⋊Dic11—42no—
73C4⋊Dic11—42no—
74C4⋊Dic11—82no—
75C4×Dic11—42no—
76C2×C11⋊C8—42no—
77#2349—111no—
78#1800D1111yescharacteristic
79#1460—111no—
80#1303—112no—
81#1286—112no—
82C23×C11—22no—
83C23×C11—22no—
84C23×C11—42no—
85C23×C11—42no—
86C23×C11#10314yes—
87C23×C11C2×C22⋊C411yescharacteristic
88D4×C11—24no—
89D4×C11—24no—
90C2×C4×C11—22no—
91C2×C4×C11—41no—
92C2×C4×C11—41no—
93C2×C4×C11—42no—
94C2×C4×C11—82no—
95C2×C4×C11—82no—
96C2×C4×C11#11711yescharacteristic
97C2×C4×C11#11711yescharacteristic
98C2×C4×C11#12312yes—
99C2×C4×C11#12312yes—
100C2×C4×C11C2×SD1611yescharacteristic
101C2×C4×C11C2×Q1611yescharacteristic
102C2×C4×C11AGL(1,ℤ/8)12yes—
103C2×Dic11—22no—
104C2×Dic11—41no—
105C2×Dic11—41no—
106C2×Dic11—41no—
107C2×Dic11—41no—
108C2×Dic11—42no—
109C2×Dic11—42no—
110C2×Dic11—41no—
111C2×Dic11—42no—
112C2×Dic11—88no—
113C8×C11—82no—
114C11⋊C8—82no—
115C2×C4×D4—221no—
116C2×C4×D4C2×D1111yescharacteristic
117#431—112no—
118#423C2×D1112yes—
119C2×#100—21no—
120#389—221no—
121#385—222no—
122#382—111no—
123#380—112no—
124C4×C4⋊C4—111no—
125C2×#95—112no—
126#343—21no—
127#323—222no—
128C22×C11—21no—
129C22×C11—21no—
130C22×C11—24no—
131C22×C11—44no—
132C22×C11—44no—
133C22×C11—42no—
134C22×C11—42no—
135C22×C11#38111yescharacteristic
136C22×C11C2×#10311yescharacteristic
137C22×C11#41811yescharacteristic
138C4×C11—22no—
139C4×C11—21no—
140C4×C11—21no—
141C4×C11—42no—
142C4×C11#48112yes—
143C4×C11#48412yes—
144Dic11—42no—
145Dic11—81no—
146Dic11—82no—
147C22×D4C22⋊D1111yescharacteristic
148C23×C4—222no—
149C23×C4C4×D1112yes—
150C2×M16—22no—
151C4×D4—22no—
152C4×D4—22no—
153C4×D4—444no—
154C2×C4⋊C4—221no—
155C2×C4⋊C4—221no—
156C2×C4⋊C4—222no—
157C2×C4⋊C4C22⋊D1111yescharacteristic
158C2×C22⋊C4—222no—
159C2×C22⋊C4D4412yes—
160C2×C42—221no—
161C2×C42C22×D1111yescharacteristic
162C4⋊C8—22no—
163C4⋊C8—22no—
164C4⋊C8—222no—
165#100—42no—
166C22⋊C8—222no—
167C4×C8—222no—
168#95—111no—
169#95—112no—
170#95—111no—
171#95—222no—
172#95—221no—
173C2×C11—21no—
174C2×C11—21no—
175C2×C11—44no—
176C2×C11#182411yescharacteristic
177C2×C11#182711yescharacteristic
178C2×C11#182911yescharacteristic
179C24(C2×D11)⋊C412yes—
180C2×D4—22no—
181C2×D4—22no—
182C2×D4#432412yes—
183C2×D4#432612yes—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4—82no—
187C22×C4—221no—
188C22×C4—222no—
189C22×C4—221no—
190C22×C4—444no—
191C22×C4—444no—
192C22×C4—882no—
193C22×C4(C2×D11)⋊C412yes—
194C22×C4C2×C4×D1111yescharacteristic
195C22×C4C2×D4411yescharacteristic
196C22×C4C2×C22⋊D1111yescharacteristic
197M16—42no—
198M16—42no—
199C2×C8—42no—
200C2×C8—442no—
201C4⋊C4—22no—
202C4⋊C4—442no—
203C4⋊C4—442no—
204C4⋊C4—882no—
205C22⋊C4—24no—
206C22⋊C4—444no—
207C42—442no—
208C42#434112yes—
209C42#434112yes—
210C11#876511yescharacteristic, complemented, Sylow
211C23—22no—
212C23—22no—
213C23—42no—
214C23—42no—
215C23#6687414yes—
216C23C2×(C2×D11)⋊C411yescharacteristic
217D4—24no—
218D4—24no—
219C2×C4—22no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—42no—
223C2×C4—82no—
224C2×C4—82no—
225C2×C4—222no—
226C2×C4—441no—
227C2×C4—441no—
228C2×C4—441no—
229C2×C4—441no—
230C2×C4—442no—
231C2×C4—442no—
232C2×C4—441no—
233C2×C4—442no—
234C2×C4—888no—
235C2×C4#6693011yescharacteristic
236C2×C4#6693011yescharacteristic
237C2×C4#6693912yes—
238C2×C4C2×#432411yescharacteristic
239C2×C4#6698812yes—
240C2×C4C2×#432611yescharacteristic
241C2×C4#6700212yes—
242C8—82no—
243C8—882no—
244C22—21no—
245C22—21no—
246C22—24no—
247C22—44no—
248C22—44no—
249C22—42no—
250C22—42no—
251C22#1062255611yescharacteristic
252C22C2×#6687411yescharacteristic
253C22#1062261411yescharacteristic
254C4—22no—
255C4—21no—
256C4—21no—
257C4—42no—
258C4—442no—
259C4—882no—
260C4—881no—
261C4#1062264712yes—
262C4#1062265712yes—
263C2—21no—
264C2—21no—
265C2—44no—
266C2#1306870411yescharacteristic
267C2#1306872111yescharacteristic
268C2#1306872511yescharacteristic
subgroupG/H
centerC22#10622556
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1800C2
socleC22×C11#381
prime radicalC22×D4×C11D4
cosocleC2×C42×C11C23
hypercenter#1800D11
hypocenterC11#8765
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1800

Complements

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

NH ≅ G/Ntype
3. #13066517C2semidirect
4. #13066476C2semidirect
210. C11#8765semidirect

Maximal subgroups

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

subgroupindex
#130715262
#130669372
#130665172
#130664762
C11×#18002
#876511