Finite Group Databasebeta

← #14657290

Subgroups — #14657290

Order 2816.

630 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 125 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#13073532C211yesmaximal, characteristic
2#13068772C211yesmaximal, characteristic, complemented
3#13068617C212yesmaximal, complemented
4C2×#10622121C212yesmaximal, complemented
5C11×#1296C211yesmaximal, characteristic, complemented
6C2×#66948—22no—
7C2×C4×D44C2212yes—
8C2×C11×C4⋊C8C2212yes—
9C11×#384C2211yescharacteristic
10C2×#66885—22no—
11#10622604—22no—
12#10622600—22no—
13C2×#66872—22no—
14#10622548C2211yescharacteristic
15C2×C4×C11⋊C8C2211yescharacteristic
16#10622189—22no—
17#10622121—24no—
18C22×D44—22no—
19C22×D44D412yes—
20C22×C4×D11—22no—
21C22×C8×C11—22no—
22C2×C11×C4⋊C4—22no—
23C2×C11×C4⋊C4D412yes—
24C2×C42×C11C2311yescharacteristic
25C2×(C2×D11)⋊C4—24no—
26C2×(C2×D11)⋊C4—22no—
27C2×C4⋊Dic11—22no—
28C2×C4⋊Dic11—21no—
29C2×C4⋊Dic11D412yes—
30C22×C11⋊C8—21no—
31#66948—44no—
32#66948—44no—
33C4×D44—22no—
34C4×D44—22no—
35C4×D44—22no—
36C4×D44—22no—
37C11×C4⋊C8—22no—
38C11×C4⋊C8—22no—
39C11⋊#95—22no—
40#66885—44no—
41#66872—44no—
42C4×C11⋊C8—21no—
43C4×C11⋊C8D412yescomplemented
44#10432—111nomaximal, Sylow
45C23×D11—22no—
46C22×C4×C11—22no—
47C22×C4×C11C2×D411yescharacteristic
48C22×C4×C11C2×D412yes—
49C22×Dic11—22no—
50C22×Dic11—41no—
51C2×D44—22no—
52C2×D44—22no—
53C2×D44—22no—
54C2×D44—22no—
55C2×D44—22no—
56C2×D44—48no—
57C2×D44—82no—
58C2×D44SD1614yes—
59C2×C4×D11—42no—
60C2×C4×D11—42no—
61C2×C4×D11—42no—
62C2×C4×D11—42no—
63C2×C4×D11—42no—
64C2×C4×D11—42no—
65C2×C8×C11—42no—
66C2×C8×C11—42no—
67C2×C8×C11—42no—
68C11×C4⋊C4—42no—
69C11×C4⋊C4—42no—
70C11×C4⋊C4—42no—
71C42×C11C2×D411yescharacteristic
72C42×C11#4111yescharacteristic
73C42×C11#4112yes—
74(C2×D11)⋊C4—48no—
75(C2×D11)⋊C4—42no—
76(C2×D11)⋊C4—42no—
77C4⋊Dic11—22no—
78C4⋊Dic11—22no—
79C4⋊Dic11—42no—
80C4⋊Dic11—42no—
81C4⋊Dic11—42no—
82C2×C11⋊C8—22no—
83C2×C11⋊C8—22no—
84C2×C11⋊C8—22no—
85#2537—111no—
86#1844—111no—
87#1802—112no—
88C2×D4⋊C8—112no—
89#1296D1111yescharacteristic, complemented
90C23×C11#12011yescharacteristic
91C22×D11—24no—
92C22×D11—42no—
93C22×D11—42no—
94C22×D11—42no—
95C22×D11—42no—
96C22×D11—42no—
97C22×D11—42no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—44no—
101C2×C4×C11—42no—
102C2×C4×C11#12112yes—
103C2×C4×C11#12111yescharacteristic
104C2×C4×C11#12312yes—
105C2×C4×C11#12411yescharacteristic
106C2×C4×C11C2×SD1612yes—
107C2×C4×C11#13512yes—
108C2×C4×C11AGL(1,ℤ/8)12yes—
109C2×C4×C11AGL(1,ℤ/8)12yes—
110C2×Dic11—42no—
111C2×Dic11—42no—
112C2×Dic11—42no—
113C2×Dic11—82no—
114C2×Dic11—81no—
115D44—24no—
116D44—24no—
117D44—42no—
118D44—42no—
119D44—88no—
120C4×D11—82no—
121C4×D11—82no—
122C4×D11—82no—
123C4×D11—82no—
124C8×C11—82no—
125C11⋊C8—24no—
126C2×#121—222no—
127C2×C4×D4—112no—
128C2×#106—222no—
129C2×C4⋊C8C2×D1112yes—
130C2×#102—222no—
131C2×C4×C8—111no—
132#394—222no—
133#384—111no—
134#384C2×D1111yescharacteristic
135#380—222no—
136#340—222no—
137D4⋊C8—224no—
138C22×C11#39411yescharacteristic
139C22×C11#44912yes—
140C22×C11#45012yes—
141C22×C11#45311yescharacteristic
142C22×C11#45611yescharacteristic
143C2×D11—44no—
144C2×D11—44no—
145C2×D11—44no—
146C2×D11—82no—
147C2×D11—82no—
148C2×D11—82no—
149C2×D11—82no—
150C4×C11—21no—
151C4×C11—21no—
152C4×C11—82no—
153C4×C11#46512yes—
154C4×C11#46912yes—
155C4×C11#48112yes—
156C4×C11#48212yes—
157Dic11—82no—
158Dic11—161no—
159C22×D4—112no—
160C22×D4—222no—
161C23×C4—222no—
162C22×C8—22no—
163C22×C8—221no—
164#121—444no—
165#121—444no—
166C4×D4—222no—
167C4×D4—222no—
168C4×D4—222no—
169C4×D4—222no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—112no—
172C2×C4⋊C4—221no—
173C2×C4⋊C4—222no—
174C2×C4⋊C4D4412yes—
175C2×C22⋊C4—224no—
176C2×C22⋊C4—222no—
177C2×C42C22×D1111yescharacteristic
178#106—444no—
179C4⋊C8—22no—
180C4⋊C8—22no—
181#102—444no—
182C4×C8—112no—
183C4×C8—221no—
184#95—222no—
185C2×C11#162411yescharacteristic
186C2×C11#162911yescharacteristic
187C2×C11#165412yes—
188C2×C11#203412yes—
189C2×C11#203911yescharacteristic
190D11—84no—
191C24—222no—
192C2×D4—114no—
193C2×D4—222no—
194C2×D4—222no—
195C2×D4—222no—
196C2×D4—222no—
197C2×D4—222no—
198C2×D4—448no—
199C2×D4—882no—
200C22×C4—22no—
201C22×C4—222no—
202C22×C4—442no—
203C22×C4—442no—
204C22×C4—442no—
205C22×C4—442no—
206C22×C4—442no—
207C22×C4—442no—
208C22×C4—441no—
209C22×C4C2×D4411yescharacteristic
210C22×C4D4×D1112yes—
211C2×C8—42no—
212C2×C8—42no—
213C2×C8—42no—
214C2×C8—222no—
215C2×C8—222no—
216C2×C8—222no—
217C4⋊C4—42no—
218C4⋊C4—42no—
219C4⋊C4—42no—
220C4⋊C4—222no—
221C4⋊C4—222no—
222C4⋊C4—442no—
223C4⋊C4—442no—
224C4⋊C4—442no—
225C22⋊C4—448no—
226C22⋊C4—442no—
227C22⋊C4—442no—
228C42#433912yes—
229C42D4×D1111yescharacteristic
230C42#434311yescharacteristic
231C11#1043211yescharacteristic, complemented, Sylow
232C23—224no—
233C23—442no—
234C23—442no—
235C23—442no—
236C23—442no—
237C23—442no—
238C23—442no—
239C23#6693511yescharacteristic
240D4—224no—
241D4—224no—
242D4—442no—
243D4—442no—
244D4—888no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—42no—
248C2×C4—44no—
249C2×C4—442no—
250C2×C4—442no—
251C2×C4—442no—
252C2×C4—882no—
253C2×C4—882no—
254C2×C4—882no—
255C2×C4—882no—
256C2×C4—881no—
257C2×C4—882no—
258C2×C4#6692811yescharacteristic
259C2×C4#6693712yes—
260C2×C4#6694712yes—
261C2×C4#6694811yescharacteristic
262C2×C4#6696412yes—
263C2×C4SD16×D1112yes—
264C2×C4#6696712yes—
265C2×C4#6697212yes—
266C8—82no—
267C8—224no—
268C22—444no—
269C22—444no—
270C22—444no—
271C22—882no—
272C22—882no—
273C22—882no—
274C22—882no—
275C22#1062228511yescharacteristic
276C22#1062236011yescharacteristic
277C22#1062236511yescharacteristic
278C22#1062238912yes—
279C22#1062242412yes—
280C4—21no—
281C4—21no—
282C4—82no—
283C4—882no—
284C4—1761no—
285C4#1062239512yes—
286C4#1062242012yes—
287C4#1062247612yes—
288C4#1062249812yes—
289C2—884no—
290C2#1306770011yescharacteristic
291C2#1306773311yescharacteristic
292C2#1306790112yes—
293C2#1306980812yes—
294C2#1306984111yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1296C2
socleC23×C11#120
prime radical#13073532C2
hypercenter#1296D11
hypocenterC11#10432
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
2. #13068772C2semidirect
3. #13068617C2semidirect
4. C2×#10622121C2semidirect
5. C11×#1296C2semidirect
43. C4×C11⋊C8D4semidirect
89. #1296D11semidirect
231. C11#10432semidirect

Maximal subgroups

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

subgroupindex
#130735322
#130687722
#130686172
C2×#106221212
C11×#12962
#1043211