Finite Group Databasebeta

← #14651163

Subgroups — #14651163

Order 2816.

574 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 135 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#13073615C211yesmaximal, characteristic
2#13068612C211yesmaximal, characteristic, complemented
3#13067283C212yesmaximal
4#13066518C212yesmaximal, complemented
5C11×#2982C211yesmaximal, characteristic, complemented
6C2×C4×Q8×C11C2211yescharacteristic
7C2×#67000—21no—
8C2×#66927C2211yescharacteristic
9C8×Q8×C11—24no—
10C11×#431—22no—
11C11×#431C2212yes—
12C2×#66900—21no—
13#10622604C414yes—
14#10622601—21no—
15#10622552—22no—
16C4×C4⋊Dic11C2211yescharacteristic
17#10622537C2212yes—
18#10622168—21no—
19#10622123—24no—
20C22×Q8×C11D411yescharacteristic
21C22×D44—21no—
22C22×D44—21no—
23C22×D44C2×C412yes—
24C4×Q8×C11—22no—
25C4×Q8×C11—22no—
26C2×C11×C4⋊C4C2×C412yes—
27C2×C11×C4⋊C4D411yescharacteristic
28C2×C42×C11D412yes—
29C2×C42×C11C2311yescharacteristic
30#67000—42no—
31#67000—42no—
32C2×(C2×D11)⋊C4—24no—
33C2×(C2×D11)⋊C4—24no—
34C2×C4⋊Dic11—21no—
35C2×C4×Dic11—21no—
36C2×#4318—22no—
37#66927—22no—
38#66927—22no—
39C11×C4⋊C8—24no—
40C11×C4⋊C8D414yes—
41C11×C22⋊C8—22no—
42C4×C8×C11—24no—
43C4×C8×C11—22no—
44#66900—42no—
45C11⋊#95C2×C412yes—
46C4⋊(C11⋊C8)—22no—
47C4⋊(C11⋊C8)—22no—
48#9398—111nomaximal, Sylow
49C23×D11—22no—
50C2×Q8×C11—22no—
51C2×Q8×C11—22no—
52C2×Q8×C11D812yes—
53C2×Q8×C11SD1612yes—
54C22×C4×C11C22⋊C412yes—
55C22×C4×C11C22⋊C412yes—
56C22×C4×C11C22×C411yescharacteristic
57C22×C4×C11C2×D411yescharacteristic
58C22×C4×C11C2×D411yescharacteristic
59C22×Dic11—22no—
60C2×D44—24no—
61C2×D44—44no—
62C2×D44—41no—
63C2×D44—42no—
64C2×D44—41no—
65C2×D44—41no—
66C2×D44—41no—
67C2×D44—42no—
68C2×D44—82no—
69C2×C8×C11—24no—
70C11×C4⋊C4—24no—
71C11×C4⋊C4—22no—
72C42×C11—22no—
73C42×C11—22no—
74C42×C11C2×D412yes—
75C42×C11#4112yes—
76(C2×D11)⋊C4—48no—
77(C2×D11)⋊C4—84no—
78C4⋊Dic11—42no—
79C4×Dic11—41no—
80C4×Dic11—41no—
81#4318—42no—
82#4318—42no—
83C2×C11⋊C8—42no—
84#2982D1111yescharacteristic, complemented
85#2548—111no—
86#1801—111no—
87#1545—112no—
88#1303—112no—
89C23×C11C2×C22⋊C411yescharacteristic
90C22×D11—44no—
91C22×D11—44no—
92C22×D11—42no—
93C22×D11—42no—
94C22×D11—42no—
95Q8×C11—24no—
96Q8×C11—24no—
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—41no—
102C2×C4×C11—42no—
103C2×C4×C11#10214yes—
104C2×C4×C11C4×D412yes—
105C2×C4×C11#12011yescharacteristic
106C2×C4×C11#12112yes—
107C2×C4×C11#12311yescharacteristic
108C2×C4×C11C2×D811yescharacteristic
109C2×C4×C11C2×SD1611yescharacteristic
110C2×C4×C11#13512yes—
111C2×Dic11—42no—
112C2×Dic11—42no—
113C2×Dic11—42no—
114D44—84no—
115D44—82no—
116D44—82no—
117D44—82no—
118D44—82no—
119C8×C11—44no—
120C11⋊C8—82no—
121C2×#127—111no—
122C2×#124—221no—
123C2×C4×Q8C2×D1111yescharacteristic
124C8×Q8—24no—
125#431—22no—
126#431C2×D1112yes—
127#423—112no—
128C2×#101—221no—
129#394—114no—
130#390—221no—
131#390—222no—
132C4×C4⋊C4—111no—
133#343—221no—
134#331—224no—
135C22×C11—21no—
136C22×C11—21no—
137C22×C11#38611yescharacteristic
138C22×C11C2×#10211yescharacteristic
139C22×C11#41611yescharacteristic
140C2×D11—84no—
141C2×D11—84no—
142C2×D11—82no—
143C2×D11—82no—
144C2×D11—82no—
145C4×C11—21no—
146C4×C11—24no—
147C4×C11—22no—
148C4×C11—42no—
149C4×C11#45412yes—
150C4×C11#46512yes—
151C4×C11#46612yes—
152Dic11—82no—
153C22×Q8D4411yescharacteristic
154C22×D4—112no—
155C22×D4—221no—
156C22×D4—221no—
157C2×M16—222no—
158#127—222no—
159#127—222no—
160#124—442no—
161#124—442no—
162C4×Q8—22no—
163C4×Q8—22no—
164C2×C4⋊C4—221no—
165C2×C4⋊C4C4×D1112yes—
166C2×C4⋊C4D4411yescharacteristic
167C2×C22⋊C4—224no—
168C2×C22⋊C4—224no—
169C2×C42—221no—
170C2×C42C22⋊D1112yes—
171C2×C42C22×D1111yescharacteristic
172C4⋊C8—24no—
173C4⋊C8—222no—
174C4⋊C8—222no—
175C4⋊C8C22⋊D1114yes—
176#101—442no—
177C22⋊C8—22no—
178C4×C8—24no—
179C4×C8—22no—
180#95—112no—
181C2×C11—21no—
182C2×C11—21no—
183C2×C11#188811yescharacteristic
184C2×C11#189311yescharacteristic
185C2×C11#191411yescharacteristic
186D11—162no—
187C24—222no—
188C2×Q8—22no—
189C2×Q8—22no—
190C2×Q8#431412yes—
191C2×Q8D8812yes—
192C2×D4—224no—
193C2×D4—444no—
194C2×D4—441no—
195C2×D4—441no—
196C2×D4—442no—
197C2×D4—441no—
198C2×D4—442no—
199C2×D4—441no—
200C2×D4—882no—
201C22×C4—222no—
202C22×C4(C2×D11)⋊C412yes—
203C22×C4(C2×D11)⋊C412yes—
204C22×C4C2×C4×D1111yescharacteristic
205C22×C4C2×D4411yescharacteristic
206C22×C4C2×C22⋊D1111yescharacteristic
207M16—442no—
208M16—442no—
209C2×C8—24no—
210C2×C8—442no—
211C4⋊C4—24no—
212C4⋊C4—22no—
213C4⋊C4—442no—
214C22⋊C4—448no—
215C22⋊C4—884no—
216C42—22no—
217C42—22no—
218C42—441no—
219C42—441no—
220C42#433912yes—
221C42C2×C22⋊D1112yes—
222C11#939811yescharacteristic, complemented, Sylow
223C23—444no—
224C23—444no—
225C23—442no—
226C23—442no—
227C23—442no—
228C23C2×(C2×D11)⋊C411yescharacteristic
229Q8—24no—
230Q8—24no—
231D4—884no—
232D4—882no—
233D4—882no—
234D4—882no—
235D4—882no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—442no—
243C2×C4—442no—
244C2×C4—442no—
245C2×C4#6688514yes—
246C2×C4C2×#431411yescharacteristic
247C2×C4C2×D8811yescharacteristic
248C2×C4#6695712yes—
249C2×C4C4×C22⋊D1112yes—
250C2×C4#6698211yescharacteristic
251C2×C4#6698312yes—
252C2×C4#6700611yescharacteristic
253C8—44no—
254C8—882no—
255C22—21no—
256C22—21no—
257C22—884no—
258C22—884no—
259C22—882no—
260C22—882no—
261C22—882no—
262C22C2×#6688511yescharacteristic
263C22#1062272611yescharacteristic
264C22#1062282611yescharacteristic
265C4—22no—
266C4—21no—
267C4—24no—
268C4—42no—
269C4—882no—
270C4#1062272712yes—
271C4#1062272812yes—
272C4#1062285812yes—
273C2—21no—
274C2—21no—
275C2—1762no—
276C2#1306901911yescharacteristic
277C2#1306904411yescharacteristic
278C2#1306916311yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2982C2
socleC22×C11#386
prime radicalC2×#66927C22
cosocleC2×C42×C11C23
hypercenter#2982D11
hypocenterC11#9398
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2982

Complements

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

NH ≅ G/Ntype
2. #13068612C2semidirect
4. #13066518C2semidirect
5. C11×#2982C2semidirect
84. #2982D11semidirect
222. C11#9398semidirect

Maximal subgroups

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

subgroupindex
#130736152
#130686122
#130672832
#130665182
C11×#29822
#939811