Finite Group Databasebeta

← #14656248

Subgroups — #14656248

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#13078084C212yesmaximal, complemented
2#13069551C211yesmaximal, characteristic, complemented
3#13067067C212yesmaximal, complemented
4#13066491C211yesmaximal, characteristic, complemented
5C11×#3245C211yesmaximal, characteristic
6C11×#532C2212yes—
7C2×#67004—22no—
8C2×C4×Dic22C2211yescharacteristic
9C11×#474—22no—
10C11×#466—22no—
11C11×#459—22no—
12C2×C11×C4⋊C8C2211yescharacteristic
13#10622845—22no—
14#10622703—22no—
15#10622688—22no—
16#10622667—24no—
17#10622537C2212yes—
18C2×C4×C11⋊C8C2211yescharacteristic
19#10622188—22no—
20D4⋊(C11⋊C8)—24no—
21C2×C11×#41—22no—
22C22×Dic22D411yescharacteristic
23C2×C11×D8—22no—
24C22×C8×C11D412yes—
25C11×C4⋊Q8D412yes—
26C11×#127D412yes—
27C11×#124—22no—
28C11×#121—22no—
29C11×#121—22no—
30C4×D4×C11—22no—
31C4×D4×C11—22no—
32C2×C42×C11C2311yescharacteristic
33#67004—44no—
34#67004—44no—
35C2×#4326—24no—
36C2×#4324—24no—
37C2×C4⋊Dic11D411yescharacteristic
38C2×Dic11⋊C4—21no—
39C2×C4×Dic11—21no—
40C2×#4318—22no—
41C22×C11⋊C8—21no—
42C4×Dic22—22no—
43C4×Dic22—22no—
44C11×#107—22no—
45C11×C4⋊C8—22no—
46C11×#102—24no—
47#66899—24no—
48#66896—24no—
49C4⋊(C11⋊C8)—22no—
50C4⋊(C11⋊C8)D414yes—
51C4×C11⋊C8—22no—
52#10255—111nomaximal, Sylow
53C11×#41—42no—
54C11×#41—42no—
55C11×#41—42no—
56C11×#41—42no—
57C2×Q8×C11—22no—
58C2×D4×C11—22no—
59C2×D4×C11—22no—
60C2×D4×C11—22no—
61C2×D4×C11—42no—
62C22×C4×C11—42no—
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11#4111yescharacteristic
66C22×Dic11—21no—
67C22×Dic11—21no—
68C2×Dic22—22no—
69C2×Dic22—21no—
70C2×Dic22—22no—
71C2×Dic22D812yescomplemented
72C11×D8—82no—
73C2×C8×C11—22no—
74C2×C8×C11—42no—
75C11×C4⋊C4—22no—
76C11×C4⋊C4—22no—
77C11×C22⋊C4—42no—
78C11×C22⋊C4—42no—
79C42×C11C2×D412yes—
80C42×C11C2×D412yes—
81#4326—48no—
82#4324—48no—
83C4⋊Dic11—22no—
84Dic11⋊C4—42no—
85C4×Dic11—41no—
86C4×Dic11—41no—
87#4318—42no—
88#4318—42no—
89C2×C11⋊C8—22no—
90C2×C11⋊C8—24no—
91C2×C11⋊C8—41no—
92C2×C11⋊C8—41no—
93#3245D1111yescharacteristic
94#3037—112no—
95#1984—111no—
96#1492—112no—
97#1292—111no—
98C23×C11—42no—
99C23×C11#12111yescharacteristic
100Q8×C11—42no—
101Q8×C11—42no—
102D4×C11—44no—
103D4×C11—42no—
104D4×C11—42no—
105D4×C11—42no—
106D4×C11—42no—
107D4×C11—82no—
108D4×C11—82no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—41no—
112C2×C4×C11—42no—
113C2×C4×C11—82no—
114C2×C4×C11—82no—
115C2×C4×C11#12012yes—
116C2×C4×C11#12011yescharacteristic
117C2×C4×C11#12112yes—
118C2×C4×C11#12711yescharacteristic
119C2×C4×C11C2×D811yescharacteristic
120C2×C4×C11#13511yescharacteristic
121C2×C4×C11AGL(1,ℤ/8)12yes—
122C2×Dic11—22no—
123C2×Dic11—41no—
124C2×Dic11—41no—
125C2×Dic11—42no—
126C2×Dic11—41no—
127Dic22—24no—
128Dic22—42no—
129C8×C11—42no—
130C11⋊C8—42no—
131C11⋊C8—44no—
132C2×#137—222no—
133#532C2×D1112yes—
134C2×C4×Q8—111no—
135#474—22no—
136#466—22no—
137#464—224no—
138#462—222no—
139#460—222no—
140#459—22no—
141#423—112no—
142C2×C4⋊C8C2×D1111yescharacteristic
143#417—222no—
144C2×C4×C8—111no—
145#336—222no—
146D4⋊C8—224no—
147C22×C11—21no—
148C22×C11—21no—
149C22×C11—82no—
150C22×C11—82no—
151C22×C11—82no—
152C22×C11#39211yescharacteristic
153C22×C11#46611yescharacteristic
154C22×C11#46911yescharacteristic
155C4×C11—21no—
156C4×C11—22no—
157C4×C11—82no—
158C4×C11#44712yes—
159C4×C11#44912yes—
160C4×C11#45511yescharacteristic
161C4×C11#45611yescharacteristic
162Dic11—42no—
163Dic11—81no—
164C2×#41—22no—
165C22×Q8—111no—
166#137—444no—
167#137—444no—
168C2×Q16—224no—
169C2×SD16—224no—
170C2×D8—22no—
171C2×M16—222no—
172C22×C8—221no—
173C22×C8C22⋊D1112yes—
174C4⋊Q8C22⋊D1112yes—
175#127C22⋊D1112yes—
176#124—22no—
177#121—22no—
178#121—22no—
179C4×Q8—222no—
180C4×Q8—222no—
181C4×D4—22no—
182C4×D4—22no—
183C2×C4⋊C4—111no—
184C2×C4⋊C4—221no—
185C2×C42—221no—
186C2×C42C22×D1111yescharacteristic
187#107—22no—
188C4⋊C8—22no—
189C4⋊C8—114no—
190C4⋊C8—222no—
191#103—224no—
192#102—24no—
193#102—224no—
194C4×C8—222no—
195C2×C11—21no—
196C2×C11—21no—
197C2×C11—162no—
198C2×C11#199911yescharacteristic
199C2×C11#200711yescharacteristic
200C2×C11#201711yescharacteristic
201#41—42no—
202#41—42no—
203#41—42no—
204#41—42no—
205C2×Q8—22no—
206C2×Q8—112no—
207C2×Q8—221no—
208C2×Q8—222no—
209C2×Q8—222no—
210C2×D4—22no—
211C2×D4—22no—
212C2×D4—22no—
213C2×D4—42no—
214C22×C4—42no—
215C22×C4—221no—
216C22×C4—221no—
217C22×C4D4×D1111yescharacteristic
218C22×C4#434111yescharacteristic
219C22×C4C2×C22⋊D1111yescharacteristic
220Q16—448no—
221SD16—448no—
222D8—82no—
223M16—442no—
224M16—442no—
225C2×C8—22no—
226C2×C8—42no—
227C2×C8—222no—
228C2×C8—224no—
229C2×C8—441no—
230C2×C8—441no—
231C4⋊C4—22no—
232C4⋊C4—22no—
233C4⋊C4—222no—
234C4⋊C4—442no—
235C22⋊C4—42no—
236C22⋊C4—42no—
237C42—441no—
238C42—441no—
239C42D4×D1112yes—
240C42C2×C22⋊D1112yes—
241C11#1025511yescharacteristic, complemented, Sylow
242C23—42no—
243C23#6699111yescharacteristic
244Q8—42no—
245Q8—42no—
246Q8—224no—
247Q8—442no—
248D4—44no—
249D4—42no—
250D4—42no—
251D4—42no—
252D4—42no—
253D4—82no—
254D4—82no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4—82no—
260C2×C4—82no—
261C2×C4—222no—
262C2×C4—441no—
263C2×C4—441no—
264C2×C4—442no—
265C2×C4—441no—
266C2×C4D8×D1111yescharacteristic
267C2×C4#6696412yes—
268C2×C4#6696511yescharacteristic
269C2×C4#6699012yes—
270C2×C4#6699212yes—
271C2×C4#6699311yescharacteristic
272C2×C4#6700611yescharacteristic
273C8—42no—
274C8—442no—
275C8—444no—
276C22—21no—
277C22—21no—
278C22—82no—
279C22—82no—
280C22—82no—
281C22#1062277011yescharacteristic
282C22#1062277211yescharacteristic
283C22#1062283611yescharacteristic
284C4—21no—
285C4—22no—
286C4—82no—
287C4—442no—
288C4—881no—
289C4#1062276912yes—
290C4#1062277112yes—
291C4#1062285511yescharacteristic
292C4#1062285911yescharacteristic
293C2—21no—
294C2—21no—
295C2—162no—
296C2#1306961111yescharacteristic
297C2#1306966311yescharacteristic
298C2#1306971911yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#3245C2
socleC22×C11#392
hypercenter#3245D11
hypocenterC11#10255
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3245

Complements

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

NH ≅ G/Ntype
1. #13078084C2semidirect
2. #13069551C2semidirect
3. #13067067C2semidirect
4. #13066491C2semidirect
71. C2×Dic22D8semidirect
241. C11#10255semidirect

Maximal subgroups

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

subgroupindex
#130780842
#130695512
#130670672
#130664912
C11×#32452
#1025511