Finite Group Databasebeta

← #14670667

Subgroups — #14670667

Order 2816.

508 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 147 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#13077310C211yesmaximal, characteristic
2C2×#10622146C212yesmaximal, complemented
3#13070227C211yesmaximal, characteristic, complemented
4#13066704C212yesmaximal, complemented
5C23×C11×C16C211yesmaximal, characteristic, complemented
6C23×C8×C11C2211yescharacteristic
7#10623322C411yescharacteristic
8C2×#66954C2211yescharacteristic
9C22×C11×C16—22no—
10C22×C11×C16—24no—
11C22×C11×C16C2212yes—
12#10622820C411yescharacteristic
13#10622724—22no—
14#10622723C411yescharacteristic
15C8×C22⋊D11—22no—
16#10622715C411yescharacteristic
17#10622714C2211yescharacteristic
18C2×#66876C2212yes—
19C22⋊(C11⋊C16)—22no—
20#10622146—24no—
21C23×C4×C11C2×C411yescharacteristic
22C2×#4339C2×C411yescharacteristic
23C22×C8×C11—22no—
24C22×C8×C11—22no—
25C22×C8×C11C2×C411yescharacteristic
26C22×C8×C11D412yes—
27C22×C8×C11D412yes—
28C22×C8×C11C2311yescharacteristic
29#67006—21no—
30#66983C812yes—
31#66982—21no—
32C4×C22⋊D11—22no—
33#66979C2×C411yescharacteristic
34#66977C812yes—
35C2×#4318C2×C411yescharacteristic
36C2×#4318C2×C411yescharacteristic
37#66954—22no—
38#66954—22no—
39C2×#4313—21no—
40C2×C8×D11—21no—
41C2×C11×C16—28no—
42C2×C11×C16—22no—
43C2×C11×C16—22no—
44C2×C11×C16D414yescomplemented
45C22⋊(C11⋊C8)—22no—
46(C2×D11)⋊C8—22no—
47#66879—21no—
48Dic11⋊C8—22no—
49C8×Dic11—21no—
50#66876—22no—
51#66876—22no—
52C2×C11⋊C16—22no—
53#12983—111nomaximal, Sylow
54C24×C11M1611yescharacteristic
55C22×C4×C11—22no—
56C22×C4×C11—22no—
57C22×C4×C11C22⋊C412yes—
58C22×C4×C11C2×C812yes—
59C22×C4×C11M1611yescharacteristic
60C22×C4×C11C22×C411yescharacteristic
61C2×C22⋊D11—22no—
62C2×C22⋊D11—21no—
63#4339—22no—
64#4339—22no—
65C2×D44C2×C811yescharacteristic
66C2×C4×D11—21no—
67C2×Dic22C2×C811yescharacteristic
68C2×C8×C11—22no—
69C2×C8×C11—24no—
70C2×C8×C11—22no—
71C2×C8×C11—22no—
72C2×C8×C11C22⋊C412yes—
73C2×C8×C11C2×D411yescharacteristic
74C2×C8×C11C2×D411yescharacteristic
75C2×C8×C11C2×D412yes—
76C2×C8×C11#4112yes—
77C22⋊Dic11—22no—
78C22⋊Dic11—21no—
79(C2×D11)⋊C4—22no—
80C4⋊Dic11C2×C812yes—
81Dic11⋊C4—22no—
82C4×Dic11—21no—
83#4318—22no—
84#4318—22no—
85C2×C11⋊C8—21no—
86C2×C11⋊C8—21no—
87#4313—41no—
88#4313—41no—
89C8×D11—42no—
90C11×C16—24no—
91C11⋊C16—42no—
92C23×C16D1111yescharacteristic, complemented
93#2929—111no—
94C2×#350—112no—
95#2112—111no—
96#1379—112no—
97C23×C11—24no—
98C23×C11—22no—
99C23×C11C22⋊C812yes—
100C23×C11C2×M1611yescharacteristic
101C22×D11—21no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11—22no—
105C2×C4×C11—24no—
106C2×C4×C11C22⋊C812yes—
107C2×C4×C11C2×C22⋊C411yescharacteristic
108C2×C4×C11C4×D412yes—
109C2×C4×C11C22×C811yescharacteristic
110C2×C4×C11#13112yes—
111C22⋊D11—44no—
112C22⋊D11—42no—
113C2×Dic11—22no—
114C2×Dic11—21no—
115D44—22no—
116C4×D11—41no—
117C4×D11—41no—
118Dic22—22no—
119C8×C11—22no—
120C8×C11#12011yescharacteristic
121C8×C11#12112yes—
122C8×C11#12311yescharacteristic
123C11⋊C8—41no—
124C11⋊C8—41no—
125C2×#131—111no—
126C23×C8C2×D1111yescharacteristic
127#525—111no—
128C2×M32—112no—
129C22×C16—22no—
130C22×C16—24no—
131C22×C16C2×D1112yes—
132#435—222no—
133C8×D4—222no—
134#424—111no—
135#408—111no—
136#407—111no—
137#405—111no—
138#350—224no—
139C22⋊C16—222no—
140C22×C11—28no—
141C22×C11—22no—
142C22×C11—22no—
143C22×C11—22no—
144C22×C11#35014yescomplemented
145C22×C11C2×C22⋊C811yescharacteristic
146C22×C11#43512yes—
147C2×D11—42no—
148C2×D11—41no—
149C4×C11—22no—
150C4×C11#38611yescharacteristic
151C4×C11#40811yescharacteristic
152C4×C11C8×D412yes—
153Dic11—42no—
154Dic11—41no—
155C2×#41—111no—
156C23×C4C4×D1111yescharacteristic
157#131—222no—
158#131—222no—
159C2×M16—111no—
160C2×M16—111no—
161C2×M16—221no—
162C22×C8—22no—
163C22×C8—22no—
164C22×C8—221no—
165C22×C8C4×D1111yescharacteristic
166C22×C8D4412yes—
167C22×C8C22⋊D1112yes—
168C22×C8C22×D1111yescharacteristic
169#123—221no—
170C22⋊Q8—112no—
171#121—112no—
172#120—221no—
173C4×D4—222no—
174#117—111no—
175M32—222no—
176M32—222no—
177C2×C16—28no—
178C2×C16—22no—
179C2×C16—22no—
180C2×C16—222no—
181C2×C16C22⋊D1114yescomplemented
182C4⋊C8—222no—
183C22⋊C8—222no—
184C22⋊C8—222no—
185#97—221no—
186C4×C8—221no—
187C2×C11—24no—
188C2×C11—22no—
189C2×C11#186911yescharacteristic
190C2×C11C2×#35012yes—
191D11—81no—
192C24#431311yescharacteristic
193#41—222no—
194#41—222no—
195C2×Q8—111no—
196C2×D4—111no—
197C2×D4—222no—
198C2×D4—221no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—221no—
202C22×C4C8×D1112yes—
203C22×C4#431311yescharacteristic
204C22×C4(C2×D11)⋊C412yes—
205C22×C4C2×C4×D1111yescharacteristic
206M16—222no—
207M16—222no—
208M16—441no—
209M16—441no—
210C2×C8—22no—
211C2×C8—22no—
212C2×C8—24no—
213C2×C8—22no—
214C2×C8—221no—
215C2×C8—221no—
216C2×C8—442no—
217C2×C8(C2×D11)⋊C412yes—
218C2×C8C2×D4411yescharacteristic
219C2×C8#433912yes—
220C2×C8C2×C22⋊D1111yescharacteristic
221C2×C8C2×C22⋊D1112yes—
222C4⋊C4—112no—
223C4⋊C4—222no—
224C22⋊C4—222no—
225C22⋊C4—221no—
226C22⋊C4—222no—
227C42—221no—
228C16—24no—
229C16—442no—
230C11#1298311yescharacteristic, complemented, Sylow
231C23—22no—
232C23—24no—
233C23—221no—
234C23(C2×D11)⋊C812yes—
235C23C2×#431311yescharacteristic
236Q8—222no—
237D4—222no—
238D4—442no—
239D4—444no—
240C2×C4—22no—
241C2×C4—24no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—222no—
245C2×C4—221no—
246C2×C4—441no—
247C2×C4—441no—
248C2×C4(C2×D11)⋊C812yes—
249C2×C4C2×C8×D1111yescharacteristic
250C2×C4#6695412yes—
251C2×C4C2×(C2×D11)⋊C411yescharacteristic
252C2×C4C4×C22⋊D1112yes—
253C8—22no—
254C8—441no—
255C8—441no—
256C8#6698211yescharacteristic
257C8#6698312yes—
258C8#6700611yescharacteristic
259C22—28no—
260C22—22no—
261C22—22no—
262C22—22no—
263C22—441no—
264C22—442no—
265C22#1062214614yescomplemented
266C22C2×(C2×D11)⋊C811yescharacteristic
267C22#1062272412yes—
268C4—22no—
269C4—441no—
270C4—442no—
271C4C8×C22⋊D1112yes—
272C4#1062272311yescharacteristic
273C4#1062282611yescharacteristic
274C2—22no—
275C2—24no—
276C2—881no—
277C2#1306890811yescharacteristic
278C2C2×#1062214612yes—
subgroupG/H
centerC2×C8C2×D44
commutatorC2×C4×C11C22×C8
FrattiniC22×C8C22×D11
FittingC23×C11×C16C2
socleC22×C11C2×C22⋊C8
prime radical#10623322C4
cosocleC22×C8×C11C23
hypercenterC23×C16D11
hypocenterC11#12983
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C8 ◁ C23×C8 ◁ C23×C16

Complements

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

NH ≅ G/Ntype
2. C2×#10622146C2semidirect
3. #13070227C2semidirect
4. #13066704C2semidirect
5. C23×C11×C16C2semidirect
44. C2×C11×C16D4semidirect
92. C23×C16D11semidirect
144. C22×C11#350semidirect
181. C2×C16C22⋊D11semidirect
230. C11#12983semidirect
265. C22#10622146semidirect

Maximal subgroups

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

subgroupindex
#130773102
C2×#106221462
#130702272
#130667042
C23×C11×C162
#1298311