Finite Group Databasebeta

← #14656250

Subgroups — #14656250

Order 2816.

582 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 103 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#13079926C211yesmaximal, characteristic
2#13078088C212yesmaximal, complemented
3#13067068C212yesmaximal, complemented
4#13066491C211yesmaximal, characteristic, complemented
5C11×#1984C211yesmaximal, characteristic, complemented
6C2×C4×Q8×C11C2211yescharacteristic
7C2×#66995—22no—
8#10623008C2212yes—
9C2×C11×C4⋊C8C2211yescharacteristic
10C2×C4×C8×C11C2211yescharacteristic
11#10622728—22no—
12#10622644—22no—
13#10622641—24no—
14#10622640—22no—
15#10622579—22no—
16#10622537C2212yes—
17#10622459—22no—
18#10622456—22no—
19C11×#336—22no—
20#10622097—24no—
21C22×Q8×C11D411yescharacteristic
22C2×#4339—22no—
23C22×C8×C11—21no—
24C22×C8×C11D412yes—
25C4×Q8×C11—22no—
26C4×Q8×C11—22no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C42×C11—21no—
30C2×C42×C11C2311yescharacteristic
31C2×#4326—24no—
32#66995—44no—
33#66995—44no—
34C2×#4325—24no—
35#66983—22no—
36#66983—22no—
37C2×#4318—22no—
38C2×D88—22no—
39#66928—22no—
40#66927D412yes—
41C4×D44—22no—
42C4×D44—22no—
43#66922D412yes—
44C11×C4⋊C8—22no—
45C4×C8×C11—22no—
46#66885—24no—
47#66882—22no—
48#66874—24no—
49#66873—24no—
50C4⋊(C11⋊C8)—22no—
51C4⋊(C11⋊C8)D414yes—
52#10255—111nomaximal, Sylow
53C2×Q8×C11—21no—
54C2×Q8×C11—22no—
55C2×Q8×C11—22no—
56C2×Q8×C11D812yescomplemented
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11C2×D411yescharacteristic
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11#4111yescharacteristic
62C2×C22⋊D11—42no—
63#4339—42no—
64#4339—42no—
65#4339—42no—
66#4339—42no—
67C2×D44—22no—
68C2×D44—22no—
69C2×D44—22no—
70C2×C4×D11—42no—
71C2×Dic22—22no—
72C2×C8×C11—22no—
73C2×C8×C11—22no—
74C2×C8×C11—42no—
75C2×C8×C11—41no—
76C2×C8×C11—41no—
77C11×C4⋊C4—22no—
78C11×C4⋊C4—42no—
79C42×C11—41no—
80C42×C11—41no—
81C42×C11C2×D412yes—
82C42×C11C2×D412yes—
83#4326—48no—
84#4325—48no—
85(C2×D11)⋊C4—42no—
86(C2×D11)⋊C4—42no—
87C4⋊Dic11—22no—
88C4⋊Dic11—22no—
89#4318—42no—
90#4318—42no—
91C2×C11⋊C8—24no—
92D88—82no—
93#3245—111no—
94#3037—112no—
95#1984D1111yescharacteristic, complemented
96#1492—112no—
97#1292—111no—
98C23×C11#12111yescharacteristic
99C22×D11—42no—
100Q8×C11—24no—
101Q8×C11—42no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—22no—
105C2×C4×C11—41no—
106C2×C4×C11—41no—
107C2×C4×C11—41no—
108C2×C4×C11—42no—
109C2×C4×C11—41no—
110C2×C4×C11#12012yes—
111C2×C4×C11#12011yescharacteristic
112C2×C4×C11#12112yes—
113C2×C4×C11#12711yescharacteristic
114C2×C4×C11C2×D811yescharacteristic
115C2×C4×C11#13511yescharacteristic
116C2×C4×C11AGL(1,ℤ/8)12yes—
117C22⋊D11—82no—
118C22⋊D11—82no—
119C2×Dic11—42no—
120D44—44no—
121D44—42no—
122D44—42no—
123D44—42no—
124D44—42no—
125C4×D11—82no—
126C4×D11—82no—
127Dic22—42no—
128Dic22—42no—
129C8×C11—42no—
130C8×C11—42no—
131C11⋊C8—44no—
132C2×#137—222no—
133#532—112no—
134C2×C4×Q8C2×D1111yescharacteristic
135#474—222no—
136#466—222no—
137#464—224no—
138#462—222no—
139#460—222no—
140#459—222no—
141#423—112no—
142C2×C4⋊C8C2×D1111yescharacteristic
143#417—222no—
144C2×C4×C8C2×D1111yescharacteristic
145#336—22no—
146D4⋊C8—224no—
147C22×C11—21no—
148C22×C11—21no—
149C22×C11#39211yescharacteristic
150C22×C11#46611yescharacteristic
151C22×C11#46911yescharacteristic
152C2×D11—82no—
153C2×D11—82no—
154C2×D11—82no—
155C4×C11—21no—
156C4×C11—22no—
157C4×C11—42no—
158C4×C11—81no—
159C4×C11#44712yes—
160C4×C11#44912yes—
161C4×C11#45511yescharacteristic
162C4×C11#45611yescharacteristic
163Dic11—82no—
164C2×#41—222no—
165C22×Q8D4411yescharacteristic
166#137—444no—
167#137—444no—
168C2×Q16—224no—
169C2×SD16—224no—
170C2×D8—222no—
171C2×M16—222no—
172C22×C8—21no—
173C22×C8C22⋊D1112yes—
174C4⋊Q8—112no—
175#127—112no—
176#124—222no—
177#121—222no—
178#121—222no—
179C4×Q8—22no—
180C4×Q8—22no—
181C4×D4—222no—
182C4×D4—222no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4D4411yescharacteristic
185C2×C42—21no—
186C2×C42C22×D1111yescharacteristic
187#107—222no—
188C4⋊C8—22no—
189C4⋊C8—114no—
190C4⋊C8—222no—
191#103—224no—
192#102—224no—
193#102—224no—
194C4×C8—22no—
195C2×C11—21no—
196C2×C11—21no—
197C2×C11#199911yescharacteristic
198C2×C11#200711yescharacteristic
199C2×C11#201711yescharacteristic
200D11—162no—
201#41—442no—
202#41—442no—
203#41—442no—
204#41—442no—
205C2×Q8—21no—
206C2×Q8—22no—
207C2×Q8—22no—
208C2×Q8—222no—
209C2×Q8D8812yescomplemented
210C2×D4—222no—
211C2×D4—222no—
212C2×D4—222no—
213C2×D4—442no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—442no—
217C22×C4C2×D4411yescharacteristic
218C22×C4#433911yescharacteristic
219C22×C4C2×C22⋊D1111yescharacteristic
220Q16—448no—
221SD16—448no—
222D8—882no—
223M16—442no—
224M16—442no—
225C2×C8—22no—
226C2×C8—22no—
227C2×C8—41no—
228C2×C8—41no—
229C2×C8—42no—
230C2×C8—224no—
231C4⋊C4—22no—
232C4⋊C4—42no—
233C4⋊C4—222no—
234C4⋊C4—222no—
235C22⋊C4—442no—
236C22⋊C4—442no—
237C42—41no—
238C42—41no—
239C42D4×D1112yes—
240C42D4×D1112yes—
241C11#1025511yescharacteristic, complemented, Sylow
242C23—442no—
243C23#6698311yescharacteristic
244Q8—24no—
245Q8—42no—
246Q8—442no—
247Q8—442no—
248D4—444no—
249D4—442no—
250D4—442no—
251D4—442no—
252D4—442no—
253D4—882no—
254D4—882no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—42no—
262C2×C4—41no—
263C2×C4—442no—
264C2×C4—882no—
265C2×C4—882no—
266C2×C4#6693512yes—
267C2×C4#6693712yes—
268C2×C4C2×D8811yescharacteristic
269C2×C4#6695711yescharacteristic
270C2×C4#6696112yes—
271C2×C4#6699011yescharacteristic
272C2×C4#6699311yescharacteristic
273C8—42no—
274C8—42no—
275C8—444no—
276C22—21no—
277C22—21no—
278C22—882no—
279C22—882no—
280C22—882no—
281C22#1062257311yescharacteristic
282C22#1062272811yescharacteristic
283C22#1062274811yescharacteristic
284C4—21no—
285C4—22no—
286C4—42no—
287C4—81no—
288C4—882no—
289C4#1062234512yes—
290C4#1062234712yes—
291C4#1062267411yescharacteristic
292C4#1062270811yescharacteristic
293C2—21no—
294C2—21no—
295C2—1762no—
296C2#1306961411yescharacteristic
297C2#1306966211yescharacteristic
298C2#1306972011yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1984C2
socleC22×C11#392
prime radical#13079926C2
hypercenter#1984D11
hypocenterC11#10255
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1984

Complements

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

NH ≅ G/Ntype
2. #13078088C2semidirect
3. #13067068C2semidirect
4. #13066491C2semidirect
5. C11×#1984C2semidirect
56. C2×Q8×C11D8semidirect
95. #1984D11semidirect
209. C2×Q8D88semidirect
241. C11#10255semidirect

Maximal subgroups

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

subgroupindex
#130799262
#130780882
#130670682
#130664912
C11×#19842
#1025511