Finite Group Databasebeta

← #14656243

Subgroups — #14656243

Order 2816.

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

normal subgroups only

This group has 634 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#13078076C212yesmaximal, complemented
2#13069409C211yesmaximal, characteristic, complemented
3#13067067C212yesmaximal, complemented
4#13066491C211yesmaximal, characteristic, complemented
5C11×#3245C211yesmaximal, characteristic, complemented
6C11×#532C2212yes—
7C2×#67002—22no—
8C2×C4×D44C2211yescharacteristic
9C11×#474—22no—
10C11×#466—22no—
11C11×#459—22no—
12C2×C11×C4⋊C8C2211yescharacteristic
13#10622845—22no—
14C2×(C2×D11)⋊C8—22no—
15#10622696—22no—
16#10622685—22no—
17#10622670—24no—
18#10622537C2212yes—
19C2×C4×C11⋊C8C2211yescharacteristic
20D4⋊(C11⋊C8)—24no—
21C2×C11×#41—22no—
22C22×D44D411yescharacteristic
23C22×C4×D11—21no—
24C2×C11×D8—22no—
25C22×C8×C11D412yes—
26C11×C4⋊Q8D412yes—
27C11×#127D412yes—
28C11×#124—22no—
29C11×#121—22no—
30C11×#121—22no—
31C4×D4×C11—22no—
32C4×D4×C11—22no—
33C2×C42×C11C2311yescharacteristic
34#67002—44no—
35#67002—44no—
36C2×#4325—24no—
37C2×#4323—24no—
38C2×(C2×D11)⋊C4—21no—
39C2×C4⋊Dic11D411yescharacteristic
40C2×#4318—22no—
41C22×C11⋊C8—21no—
42C4×D44—22no—
43C4×D44—22no—
44C11×#107—22no—
45C11×C4⋊C8—22no—
46C11×#102—24no—
47#66899—24no—
48#66896—24no—
49(C2×D11)⋊C8—44no—
50C4⋊(C11⋊C8)—22no—
51C4⋊(C11⋊C8)D414yes—
52C4×C11⋊C8—22no—
53#10254—111nomaximal, Sylow
54C23×D11—21no—
55C11×#41—42no—
56C11×#41—42no—
57C11×#41—42no—
58C11×#41—42no—
59C2×Q8×C11—22no—
60C2×D4×C11—22no—
61C2×D4×C11—22no—
62C2×D4×C11—22no—
63C2×D4×C11—42no—
64C22×C4×C11—42no—
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11#4111yescharacteristic
68C22×Dic11—21no—
69C2×D44—22no—
70C2×D44—21no—
71C2×D44—22no—
72C2×D44D812yescomplemented
73C2×C4×D11—42no—
74C2×C4×D11—42no—
75C2×C4×D11—41no—
76C2×C4×D11—41no—
77C11×D8—82no—
78C2×C8×C11—22no—
79C2×C8×C11—42no—
80C11×C4⋊C4—22no—
81C11×C4⋊C4—22no—
82C11×C22⋊C4—42no—
83C11×C22⋊C4—42no—
84C42×C11C2×D412yes—
85C42×C11C2×D412yes—
86#4325—48no—
87#4323—48no—
88(C2×D11)⋊C4—42no—
89C4⋊Dic11—22no—
90#4318—42no—
91#4318—42no—
92C2×C11⋊C8—22no—
93C2×C11⋊C8—24no—
94C2×C11⋊C8—41no—
95C2×C11⋊C8—41no—
96#3245D1111yescharacteristic, complemented
97#3036—112no—
98#1954—111no—
99#1492—112no—
100#1292—111no—
101C23×C11—42no—
102C23×C11#12111yescharacteristic
103C22×D11—22no—
104C22×D11—42no—
105C22×D11—42no—
106C22×D11—41no—
107C22×D11—41no—
108Q8×C11—42no—
109Q8×C11—42no—
110D4×C11—44no—
111D4×C11—42no—
112D4×C11—42no—
113D4×C11—42no—
114D4×C11—42no—
115D4×C11—82no—
116D4×C11—82no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—41no—
120C2×C4×C11—42no—
121C2×C4×C11—82no—
122C2×C4×C11—82no—
123C2×C4×C11#12012yes—
124C2×C4×C11#12011yescharacteristic
125C2×C4×C11#12112yes—
126C2×C4×C11#12711yescharacteristic
127C2×C4×C11C2×D811yescharacteristic
128C2×C4×C11#13511yescharacteristic
129C2×C4×C11AGL(1,ℤ/8)12yes—
130C2×Dic11—42no—
131C2×Dic11—41no—
132D44—24no—
133D44—42no—
134C4×D11—82no—
135C4×D11—81no—
136C4×D11—81no—
137C8×C11—42no—
138C11⋊C8—42no—
139C11⋊C8—44no—
140C2×AGL(1,ℤ/8)—222no—
141#532C2×D1112yes—
142C2×C4×D4—111no—
143#474—22no—
144#466—22no—
145#463—224no—
146#461—222no—
147#459—22no—
148#459—222no—
149#423—112no—
150C2×C4⋊C8C2×D1111yescharacteristic
151#417—222no—
152C2×C22⋊C8—222no—
153C2×C4×C8—111no—
154D4⋊C8—224no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11—82no—
158C22×C11—82no—
159C22×C11—82no—
160C22×C11#39211yescharacteristic
161C22×C11#46611yescharacteristic
162C22×C11#46911yescharacteristic
163C2×D11—44no—
164C2×D11—42no—
165C2×D11—82no—
166C2×D11—81no—
167C2×D11—81no—
168C4×C11—21no—
169C4×C11—22no—
170C4×C11—82no—
171C4×C11#44712yes—
172C4×C11#44912yes—
173C4×C11#45311yescharacteristic
174C4×C11#45411yescharacteristic
175Dic11—81no—
176C2×#41—22no—
177C22×D4—111no—
178C23×C4—221no—
179AGL(1,ℤ/8)—444no—
180AGL(1,ℤ/8)—444no—
181C2×SD16—224no—
182C2×D8—22no—
183C2×D8—224no—
184C2×M16—222no—
185C22×C8—221no—
186C22×C8C22⋊D1112yes—
187C4⋊Q8C22⋊D1112yes—
188#127C22⋊D1112yes—
189#124—22no—
190#121—22no—
191#121—22no—
192C4×D4—22no—
193C4×D4—22no—
194C4×D4—222no—
195C4×D4—222no—
196C2×C4⋊C4—111no—
197C2×C22⋊C4—221no—
198C2×C42C22×D1111yescharacteristic
199#107—22no—
200C4⋊C8—22no—
201C4⋊C8—114no—
202C4⋊C8—222no—
203#103—224no—
204#102—24no—
205#102—224no—
206C22⋊C8—444no—
207C4×C8—222no—
208C2×C11—21no—
209C2×C11—21no—
210C2×C11—162no—
211C2×C11#199911yescharacteristic
212C2×C11#200611yescharacteristic
213C2×C11#201711yescharacteristic
214D11—82no—
215C24—221no—
216#41—42no—
217#41—42no—
218#41—42no—
219#41—42no—
220C2×Q8—22no—
221C2×D4—22no—
222C2×D4—22no—
223C2×D4—22no—
224C2×D4—42no—
225C2×D4—112no—
226C2×D4—222no—
227C2×D4—221no—
228C2×D4—222no—
229C22×C4—42no—
230C22×C4—221no—
231C22×C4—442no—
232C22×C4—442no—
233C22×C4—441no—
234C22×C4—441no—
235C22×C4D4×D1111yescharacteristic
236C22×C4#434111yescharacteristic
237C22×C4C2×C22⋊D1111yescharacteristic
238SD16—448no—
239D8—82no—
240D8—448no—
241M16—442no—
242M16—442no—
243C2×C8—22no—
244C2×C8—42no—
245C2×C8—222no—
246C2×C8—224no—
247C2×C8—441no—
248C2×C8—441no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—222no—
252C22⋊C4—42no—
253C22⋊C4—42no—
254C22⋊C4—442no—
255C42D4×D1112yes—
256C42C2×C22⋊D1112yes—
257C11#1025411yescharacteristic, complemented, Sylow
258C23—42no—
259C23—222no—
260C23—442no—
261C23—442no—
262C23—441no—
263C23—441no—
264C23#6699111yescharacteristic
265Q8—42no—
266Q8—42no—
267D4—44no—
268D4—42no—
269D4—42no—
270D4—42no—
271D4—42no—
272D4—82no—
273D4—82no—
274D4—224no—
275D4—442no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—82no—
281C2×C4—82no—
282C2×C4—442no—
283C2×C4—441no—
284C2×C4—882no—
285C2×C4—881no—
286C2×C4—881no—
287C2×C4D8×D1111yescharacteristic
288C2×C4#6696412yes—
289C2×C4#6696511yescharacteristic
290C2×C4#6699012yes—
291C2×C4#6699212yes—
292C2×C4#6699311yescharacteristic
293C2×C4#6700611yescharacteristic
294C8—42no—
295C8—442no—
296C8—444no—
297C22—21no—
298C22—21no—
299C22—82no—
300C22—82no—
301C22—82no—
302C22—444no—
303C22—442no—
304C22—882no—
305C22—881no—
306C22—881no—
307C22#1062277011yescharacteristic
308C22#1062277211yescharacteristic
309C22#1062283611yescharacteristic
310C4—21no—
311C4—22no—
312C4—82no—
313C4—881no—
314C4#1062276912yes—
315C4#1062277112yes—
316C4#1062285411yescharacteristic
317C4#1062285811yescharacteristic
318C2—21no—
319C2—21no—
320C2—162no—
321C2—882no—
322C2#1306961111yescharacteristic
323C2#1306965811yescharacteristic
324C2#1306971911yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3245C2
socleC22×C11#392
hypercenter#3245D11
hypocenterC11#10254
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. #13078076C2semidirect
2. #13069409C2semidirect
3. #13067067C2semidirect
4. #13066491C2semidirect
5. C11×#3245C2semidirect
72. C2×D44D8semidirect
96. #3245D11semidirect
257. C11#10254semidirect

Maximal subgroups

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

subgroupindex
#130780762
#130694092
#130670672
#130664912
C11×#32452
#1025411