Finite Group Databasebeta

← #14651176

Subgroups — #14651176

Order 2816.

534 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 115 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#13077657C211yesmaximal, characteristic
2#13073608C211yesmaximal, characteristic
3#13067289C212yesmaximal, complemented
4#13066517C212yesmaximal, complemented
5C11×#1800C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66989—21no—
8C2×#66922C2211yescharacteristic
9C11×#423C2212yes—
10C2×C11×#100—21no—
11#10622825—22no—
12#10622820—22no—
13#10622625—24no—
14#10622587—21no—
15#10622566C414yes—
16C4×C4⋊Dic11C2211yescharacteristic
17#10622538C2212yes—
18C11×#343—21no—
19#10622120—24no—
20C22×D4×C11D411yescharacteristic
21C23×C4×C11D412yes—
22C22×Dic22—21no—
23C2×C11×M16—22no—
24C4×D4×C11—22no—
25C4×D4×C11—22no—
26C2×C11×C4⋊C4D411yescharacteristic
27C2×C11×C22⋊C4C2×C412yes—
28C2×C42×C11C2311yescharacteristic
29C2×C22⋊Dic11—24no—
30#66989—44no—
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11C2×C412yes—
34C2×C4×Dic11—21no—
35C2×#4318—24no—
36#66922—22no—
37#66922—22no—
38C11×C4⋊C8—22no—
39C11×C4⋊C8—22no—
40C11×#100—42no—
41C11⋊#95—24no—
42C11⋊#95C2×C412yes—
43C22⋊(C11⋊C8)—24no—
44C22⋊(C11⋊C8)—22no—
45C4⋊(C11⋊C8)D414yes—
46C4×C11⋊C8—22no—
47#9401—111nomaximal, Sylow
48C24×C11C22⋊C412yes—
49C2×D4×C11—22no—
50C2×D4×C11—21no—
51C2×D4×C11—22no—
52C2×D4×C11—21no—
53C22×C4×C11—22no—
54C22×C4×C11—22no—
55C22×C4×C11—44no—
56C22×C4×C11C22⋊C412yes—
57C22×C4×C11C22×C411yescharacteristic
58C22×C4×C11C2×D411yescharacteristic
59C22×C4×C11C2×D411yescharacteristic
60C22×Dic11—22no—
61C22×Dic11—22no—
62C2×Dic22—42no—
63C2×Dic22—42no—
64C2×Dic22—41no—
65C2×Dic22—41no—
66C11×M16—42no—
67C11×M16—42no—
68C2×C8×C11—42no—
69C11×C4⋊C4—22no—
70C11×C22⋊C4—24no—
71C42×C11C2×D412yes—
72C42×C11#4112yes—
73C22⋊Dic11—48no—
74C4⋊Dic11—24no—
75C4⋊Dic11—42no—
76C4⋊Dic11—41no—
77C4⋊Dic11—41no—
78C4×Dic11—42no—
79#4318—84no—
80C2×C11⋊C8—24no—
81#2975—111no—
82#2547—111no—
83#1800D1111yescharacteristic
84#1546—112no—
85#1303—112no—
86C23×C11—22no—
87C23×C11—22no—
88C23×C11—22no—
89C23×C11—42no—
90C23×C11—42no—
91C23×C11C2×C22⋊C411yescharacteristic
92D4×C11—42no—
93D4×C11—42no—
94C2×C4×C11—22no—
95C2×C4×C11—22no—
96C2×C4×C11—41no—
97C2×C4×C11—44no—
98C2×C4×C11—42no—
99C2×C4×C11—82no—
100C2×C4×C11C4×D412yes—
101C2×C4×C11#12011yescharacteristic
102C2×C4×C11#12112yes—
103C2×C4×C11#12311yescharacteristic
104C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
105C2×C4×C11AGL(1,ℤ/8)12yes—
106C2×C4×C11#13711yescharacteristic
107C2×Dic11—42no—
108C2×Dic11—42no—
109C2×Dic11—42no—
110C2×Dic11—42no—
111C2×Dic11—42no—
112C2×Dic11—42no—
113Dic22—82no—
114Dic22—82no—
115C8×C11—82no—
116C11⋊C8—44no—
117C2×C4⋊Q8—111no—
118C2×#124—221no—
119C2×C4×D4C2×D1111yescharacteristic
120#436—224no—
121#431—112no—
122#423C2×D1112yes—
123C2×#100—21no—
124#407—222no—
125#397—114no—
126#391—221no—
127#380—222no—
128C4×C4⋊C4—111no—
129#343—21no—
130#332—224no—
131C22×C11—21no—
132C22×C11—21no—
133C22×C11—44no—
134C22×C11—42no—
135C22×C11—42no—
136C22×C11—42no—
137C22×C11—82no—
138C22×C11#38611yescharacteristic
139C22×C11#41711yescharacteristic
140C22×C11#41811yescharacteristic
141C4×C11—21no—
142C4×C11—22no—
143C4×C11—42no—
144C4×C11#45512yes—
145C4×C11#46812yes—
146C4×C11#46912yes—
147Dic11—82no—
148Dic11—82no—
149C22×Q8—221no—
150C22×D4C22⋊D1111yescharacteristic
151C23×C4D4412yes—
152C2×M16—22no—
153C2×M16—224no—
154C4⋊Q8—222no—
155C4⋊Q8—222no—
156#124—444no—
157C4×D4—22no—
158C4×D4—22no—
159C2×C4⋊C4—112no—
160C2×C4⋊C4—221no—
161C2×C4⋊C4—221no—
162C2×C4⋊C4C22⋊D1111yescharacteristic
163C2×C22⋊C4—224no—
164C2×C22⋊C4C4×D1112yes—
165C2×C42—221no—
166C2×C42C22×D1111yescharacteristic
167C4⋊C8—22no—
168C4⋊C8—22no—
169C4⋊C8—114no—
170#100—42no—
171C22⋊C8—224no—
172C22⋊C8—222no—
173C4×C8—222no—
174#95—112no—
175#95—224no—
176C2×C11—21no—
177C2×C11—21no—
178C2×C11—82no—
179C2×C11#188511yescharacteristic
180C2×C11#189511yescharacteristic
181C2×C11#191511yescharacteristic
182C24(C2×D11)⋊C412yes—
183C2×Q8—441no—
184C2×Q8—442no—
185C2×Q8—441no—
186C2×Q8—442no—
187C2×D4—21no—
188C2×D4—22no—
189C2×D4—21no—
190C2×D4—22no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—44no—
194C22×C4—222no—
195C22×C4—222no—
196C22×C4(C2×D11)⋊C412yes—
197C22×C4C2×C4×D1111yescharacteristic
198C22×C4C2×D4411yescharacteristic
199C22×C4C2×C22⋊D1111yescharacteristic
200M16—42no—
201M16—42no—
202M16—884no—
203C2×C8—42no—
204C2×C8—224no—
205C4⋊C4—22no—
206C4⋊C4—224no—
207C4⋊C4—442no—
208C4⋊C4—441no—
209C4⋊C4—441no—
210C22⋊C4—24no—
211C22⋊C4—448no—
212C42—442no—
213C42D4×D1112yes—
214C42#434112yes—
215C11#940111yescharacteristic, complemented, Sylow
216C23—22no—
217C23—22no—
218C23—22no—
219C23—42no—
220C23—42no—
221C23C2×(C2×D11)⋊C411yescharacteristic
222Q8—882no—
223Q8—882no—
224D4—42no—
225D4—42no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—41no—
229C2×C4—44no—
230C2×C4—42no—
231C2×C4—82no—
232C2×C4—442no—
233C2×C4—442no—
234C2×C4—442no—
235C2×C4—442no—
236C2×C4—442no—
237C2×C4—442no—
238C2×C4(C22⋊D11)⋊C412yes—
239C2×C4#6693511yescharacteristic
240C2×C4#6693911yescharacteristic
241C2×C4#6698511yescharacteristic
242C2×C4#6699212yes—
243C2×C4#6699511yescharacteristic
244C2×C4#6700212yes—
245C8—82no—
246C8—444no—
247C22—21no—
248C22—21no—
249C22—44no—
250C22—42no—
251C22—42no—
252C22—42no—
253C22—82no—
254C22#1062257111yescharacteristic
255C22#1062257911yescharacteristic
256C22#1062261411yescharacteristic
257C4—22no—
258C4—21no—
259C4—42no—
260C4—882no—
261C4—882no—
262C4#1062235912yes—
263C4#1062265212yes—
264C4#1062266212yes—
265C2—21no—
266C2—21no—
267C2—82no—
268C2#1306900211yescharacteristic
269C2#1306905211yescharacteristic
270C2#1306916611yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1800C2
socleC22×C11#386
prime radicalC22×D4×C11D4
cosocleC2×C42×C11C23
hypercenter#1800D11
hypocenterC11#9401
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. #13067289C2semidirect
4. #13066517C2semidirect
215. C11#9401semidirect

Maximal subgroups

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

subgroupindex
#130776572
#130736082
#130672892
#130665172
C11×#18002
#940111