Finite Group Databasebeta

← #14655671

Subgroups — #14655671

Order 2816.

492 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 113 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#13079762C211yesmaximal, characteristic
2#13079162C211yesmaximal, characteristic
3C2×#10622293C211yesmaximal, characteristic
4#13069460C211yesmaximal, characteristic
5#13067296C211yesmaximal, characteristic
6#13067072C211yesmaximal, characteristic
7C11×#1278C211yesmaximal, characteristic
8#10623001C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C4×C11×M16C2211yescharacteristic
13C2×C4×C8×C11C2211yescharacteristic
14C2×#66888—22no—
15#10622734—22no—
16C2×#66881—22no—
17#10622537C2211yescharacteristic
18#10622464—22no—
19#10622334—22no—
20#10622315—22no—
21#10622295—21no—
22#10622294—21no—
23#10622293—22no—
24#10622293—21no—
25#10622293—21no—
26#10622293—22no—
27#10622119—22no—
28#10622094—22no—
29C22×Dic22—21no—
30C22×Dic22—21no—
31C2×C11×M16D412yes—
32C22×C8×C11—21no—
33C2×C42×C11C2311yescharacteristic
34#66979—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11D412yes—
39#66977—21no—
40#66977—21no—
41C2×#4318—21no—
42#66923—21no—
43#66922—21no—
44#66922—21no—
45#66922—21no—
46#66922—21no—
47#66922—21no—
48#66922—21no—
49#66922—21no—
50#66922D412yes—
51#66922D411yescharacteristic
52#66922D411yescharacteristic
53C4×Dic22—21no—
54C4×Dic22—21no—
55C11×C4⋊C8D412yes—
56C11×C22⋊C8—21no—
57C11×#97—21no—
58C4×C8×C11—21no—
59C4×C8×C11—21no—
60C4×C8×C11—21no—
61C4×C8×C11D412yes—
62#66888—44no—
63#66882—24no—
64#66881—24no—
65#66881—24no—
66#66881—28no—
67#66880—24no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)—21no—
70#10167—111nomaximal, Sylow
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11#4111yescharacteristic
74C22×Dic11—22no—
75C22×Dic11—41no—
76C2×Dic22—21no—
77C2×Dic22—21no—
78C2×Dic22—22no—
79C2×Dic22—41no—
80C2×Dic22—41no—
81C2×Dic22—41no—
82C2×Dic22—42no—
83C2×Dic22—42no—
84C2×Dic22—82no—
85C11×M16—22no—
86C11×M16SD1614yes—
87C2×C8×C11—24no—
88C2×C8×C11—22no—
89C2×C8×C11—22no—
90C2×C8×C11—22no—
91C42×C11C2×D411yescharacteristic
92C42×C11C2×D411yescharacteristic
93C42×C11C2×D411yescharacteristic
94C42×C11C2×D411yescharacteristic
95C22⋊Dic11—41no—
96C4⋊Dic11—22no—
97C4⋊Dic11—21no—
98C4⋊Dic11—22no—
99C4⋊Dic11—22no—
100C4⋊Dic11—21no—
101C4⋊Dic11—22no—
102C4⋊Dic11—21no—
103C4⋊Dic11—21no—
104C4⋊Dic11—41no—
105C4⋊Dic11—41no—
106C4⋊Dic11—41no—
107C4⋊Dic11—41no—
108Dic11⋊C4—41no—
109Dic11⋊C4—41no—
110C4×Dic11—41no—
111#4318—42no—
112C2×C11⋊C8—41no—
113#3229—111no—
114#3165—111no—
115C2×#498—111no—
116#1966—111no—
117#1548—111no—
118#1493—111no—
119#1278D1111yescharacteristic
120C23×C11#12111yescharacteristic
121C2×C4×C11—22no—
122C2×C4×C11—22no—
123C2×C4×C11#12011yescharacteristic
124C2×C4×C11#12011yescharacteristic
125C2×C4×C11#12011yescharacteristic
126C2×C4×C11#12111yescharacteristic
127C2×C4×C11#12111yescharacteristic
128C2×C4×C11#12711yescharacteristic
129C2×C4×C11C2×SD1612yes—
130C2×C4×C11#13712yes—
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—42no—
134C2×Dic11—42no—
135C2×Dic11—44no—
136C2×Dic11—82no—
137Dic22—42no—
138Dic22—42no—
139Dic22—82no—
140Dic22—82no—
141Dic22—81no—
142Dic22—81no—
143Dic22—82no—
144C8×C11—24no—
145C8×C11—24no—
146C8×C11—42no—
147C11⋊C8—81no—
148#533—111no—
149C2×C4⋊Q8—111no—
150C2×C4⋊Q8—111no—
151#501—222no—
152#500—221no—
153#498—222no—
154#498—221no—
155#498—221no—
156#498—222no—
157#487—221no—
158#483—222no—
159#475—222no—
160#431C2×D1111yescharacteristic
161#428—222no—
162C2×#106—222no—
163#423—111no—
164C2×#101—222no—
165C4×M16C2×D1111yescharacteristic
166C2×C4×C8C2×D1111yescharacteristic
167#333—222no—
168Q8⋊C8—222no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11#39211yescharacteristic
172C22×C11#46112yes—
173C4×C11—21no—
174C4×C11—21no—
175C4×C11#44812yes—
176C4×C11#45612yes—
177C4×C11#47112yes—
178C4×C11#49211yescharacteristic
179C4×C11#49711yescharacteristic
180Dic11—81no—
181Dic11—82no—
182Dic11—81no—
183Dic11—82no—
184C22×Q8—221no—
185C22×Q8—221no—
186C2×M16—221no—
187C2×M16D4412yes—
188C22×C8—21no—
189C4⋊Q8—112no—
190C4⋊Q8—111no—
191C4⋊Q8—111no—
192C4⋊Q8—221no—
193C4⋊Q8—221no—
194C4⋊Q8—221no—
195C4⋊Q8—221no—
196C4⋊Q8—221no—
197C4⋊Q8—221no—
198C4⋊Q8—221no—
199#125—221no—
200C22⋊Q8—221no—
201C22⋊Q8—221no—
202C4×Q8—221no—
203C4×Q8—221no—
204#117—221no—
205C2×C4⋊C4—112no—
206C2×C4⋊C4—221no—
207C2×C4⋊C4—221no—
208C2×C4⋊C4—221no—
209C2×C42C22×D1111yescharacteristic
210#107—224no—
211#106—228no—
212#106—224no—
213#106—224no—
214C4⋊C8—221no—
215C4⋊C8—221no—
216C4⋊C8D4412yes—
217#103—224no—
218#101—444no—
219C22⋊C8—21no—
220#97—21no—
221C4×C8—21no—
222C4×C8—21no—
223C4×C8—21no—
224C4×C8D4412yes—
225C2×C11—22no—
226C2×C11#200511yescharacteristic
227C2×C11#201311yescharacteristic
228C2×C11#201911yescharacteristic
229C2×Q8—221no—
230C2×Q8—221no—
231C2×Q8—222no—
232C2×Q8—441no—
233C2×Q8—441no—
234C2×Q8—441no—
235C2×Q8—442no—
236C2×Q8—442no—
237C2×Q8—882no—
238C22×C4—222no—
239C22×C4—441no—
240C22×C4C2×D4411yescharacteristic
241C22×C4D4×D1111yescharacteristic
242C22×C4#434311yescharacteristic
243M16—22no—
244M16—442no—
245M16#431414yes—
246C2×C8—24no—
247C2×C8—22no—
248C2×C8—22no—
249C2×C8—22no—
250C2×C8—441no—
251C4⋊C4—222no—
252C4⋊C4—222no—
253C4⋊C4—222no—
254C4⋊C4—221no—
255C4⋊C4—221no—
256C4⋊C4—222no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4—441no—
260C4⋊C4—441no—
261C4⋊C4—441no—
262C4⋊C4—441no—
263C4⋊C4—441no—
264C4⋊C4—441no—
265C22⋊C4—441no—
266C42—441no—
267C42C2×D4411yescharacteristic
268C42C2×D4411yescharacteristic
269C42D4×D1111yescharacteristic
270C42D4×D1111yescharacteristic
271C11#1016711yescharacteristic, complemented, Sylow
272C23#6694811yescharacteristic
273Q8—442no—
274Q8—442no—
275Q8—882no—
276Q8—882no—
277Q8—881no—
278Q8—881no—
279Q8—882no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—441no—
283C2×C4—441no—
284C2×C4—442no—
285C2×C4—442no—
286C2×C4—444no—
287C2×C4—882no—
288C2×C4#6692711yescharacteristic
289C2×C4#6693511yescharacteristic
290C2×C4#6693511yescharacteristic
291C2×C4#6693511yescharacteristic
292C2×C4#6694811yescharacteristic
293C2×C4#6694811yescharacteristic
294C2×C4C2×#431412yes—
295C2×C4#6696212yes—
296C8—24no—
297C8—24no—
298C8—42no—
299C8—881no—
300C22—21no—
301C22—21no—
302C22#1062228411yescharacteristic
303C22#1062245412yes—
304C4—21no—
305C4—21no—
306C4—881no—
307C4—882no—
308C4—882no—
309C4—881no—
310C4#1062230611yescharacteristic
311C4#1062232811yescharacteristic
312C4#1062235112yes—
313C4#1062243912yes—
314C4#1062251112yes—
315C2—22no—
316C2#1306965511yescharacteristic
317C2#1306970111yescharacteristic
318C2#1306973311yescharacteristic
subgroupG/H
centerC22#10622284
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1278C2
socleC22×C11#392
prime radicalC23×C11#121
hypercenter#1278D11
hypocenterC11#10167
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1278

Complements

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

NH ≅ G/Ntype
271. C11#10167semidirect

Maximal subgroups

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

subgroupindex
#130797622
#130791622
C2×#106222932
#130694602
#130672962
#130670722
C11×#12782
#1016711