Finite Group Databasebeta

← #14655713

Subgroups — #14655713

Order 2816.

476 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 105 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#13079769C211yesmaximal, characteristic
2C2×#10622293C211yesmaximal, characteristic
3#13078997C211yesmaximal, characteristic
4#13069605C211yesmaximal, characteristic
5#13067287C211yesmaximal, characteristic
6#13067072C211yesmaximal, characteristic
7C11×#1278C211yesmaximal, characteristic
8#10623001C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C4×C11×M16C2211yescharacteristic
13C2×C4×C8×C11C2211yescharacteristic
14#10622733—22no—
15C2×#66881—22no—
16#10622537C2211yescharacteristic
17#10622463—22no—
18#10622335—22no—
19#10622316—22no—
20#10622295—21no—
21#10622294—21no—
22#10622294—21no—
23#10622294—21no—
24#10622293—22no—
25#10622293—22no—
26#10622192—22no—
27#10622124—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#66882—24no—
63#66881—28no—
64#66880—24no—
65#66880—24no—
66#66880—24no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)—21no—
69#10173—111nomaximal, Sylow
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11#4111yescharacteristic
73C22×Dic11—22no—
74C22×Dic11—41no—
75C2×Dic22—21no—
76C2×Dic22—22no—
77C2×Dic22—21no—
78C2×Dic22—41no—
79C2×Dic22—41no—
80C2×Dic22—41no—
81C2×Dic22—42no—
82C2×Dic22—42no—
83C2×Dic22—82no—
84C11×M16—22no—
85C11×M16—22no—
86C2×C8×C11—24no—
87C2×C8×C11—22no—
88C2×C8×C11—22no—
89C2×C8×C11—22no—
90C42×C11C2×D411yescharacteristic
91C42×C11C2×D411yescharacteristic
92C42×C11C2×D411yescharacteristic
93C42×C11C2×D411yescharacteristic
94C22⋊Dic11—41no—
95C4⋊Dic11—21no—
96C4⋊Dic11—21no—
97C4⋊Dic11—22no—
98C4⋊Dic11—22no—
99C4⋊Dic11—22no—
100C4⋊Dic11—21no—
101C4⋊Dic11—21no—
102C4⋊Dic11—22no—
103C4⋊Dic11—41no—
104C4⋊Dic11—41no—
105C4⋊Dic11—41no—
106C4⋊Dic11—41no—
107Dic11⋊C4—41no—
108Dic11⋊C4—41no—
109C4×Dic11—41no—
110#4318—42no—
111C2×C11⋊C8—41no—
112#3230—111no—
113C2×#498—111no—
114#3139—111no—
115#1997—111no—
116#1546—111no—
117#1493—111no—
118#1278D1111yescharacteristic
119C23×C11#12111yescharacteristic
120C2×C4×C11—22no—
121C2×C4×C11—22no—
122C2×C4×C11#12011yescharacteristic
123C2×C4×C11#12011yescharacteristic
124C2×C4×C11#12011yescharacteristic
125C2×C4×C11#12111yescharacteristic
126C2×C4×C11#12111yescharacteristic
127C2×C4×C11#12711yescharacteristic
128C2×C4×C11#13512yes—
129C2×C4×C11#13712yes—
130C2×Dic11—41no—
131C2×Dic11—41no—
132C2×Dic11—42no—
133C2×Dic11—42no—
134C2×Dic11—82no—
135C2×Dic11—82no—
136Dic22—44no—
137Dic22—42no—
138Dic22—42no—
139Dic22—82no—
140Dic22—82no—
141Dic22—81no—
142Dic22—81no—
143C8×C11—24no—
144C8×C11—42no—
145C8×C11—42no—
146C11⋊C8—81no—
147#533—111no—
148C2×C4⋊Q8—111no—
149C2×C4⋊Q8—111no—
150#500—221no—
151#498—222no—
152#498—222no—
153#491—222no—
154#487—221no—
155#487—221no—
156#487—221no—
157#484—222no—
158#477—222no—
159#431C2×D1111yescharacteristic
160C2×#106—222no—
161#423—111no—
162#419—222no—
163C4×M16C2×D1111yescharacteristic
164C2×C4×C8C2×D1111yescharacteristic
165#343—222no—
166#332—222no—
167Q8⋊C8—222no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11#39211yescharacteristic
171C22×C11#46412yes—
172C4×C11—21no—
173C4×C11—21no—
174C4×C11#45212yes—
175C4×C11#45612yes—
176C4×C11#47112yes—
177C4×C11#49511yescharacteristic
178C4×C11#49711yescharacteristic
179Dic11—81no—
180Dic11—82no—
181Dic11—81no—
182Dic11—82no—
183C22×Q8—221no—
184C22×Q8—221no—
185C2×M16—221no—
186C2×M16D4412yes—
187C22×C8—21no—
188C4⋊Q8—112no—
189C4⋊Q8—111no—
190C4⋊Q8—111no—
191C4⋊Q8—221no—
192C4⋊Q8—221no—
193C4⋊Q8—221no—
194C4⋊Q8—221no—
195C4⋊Q8—221no—
196C4⋊Q8—221no—
197C4⋊Q8—221no—
198#125—221no—
199C22⋊Q8—221no—
200C22⋊Q8—221no—
201C4×Q8—221no—
202C4×Q8—221no—
203#117—221no—
204C2×C4⋊C4—112no—
205C2×C4⋊C4—221no—
206C2×C4⋊C4—221no—
207C2×C4⋊C4—221no—
208C2×C42C22×D1111yescharacteristic
209#107—224no—
210#106—228no—
211C4⋊C8—221no—
212C4⋊C8—221no—
213C4⋊C8D4412yes—
214#103—224no—
215#103—224no—
216#103—224no—
217C22⋊C8—21no—
218#97—21no—
219C4×C8—21no—
220C4×C8—21no—
221C4×C8—21no—
222C4×C8D4412yes—
223C2×C11—22no—
224C2×C11#200511yescharacteristic
225C2×C11#201511yescharacteristic
226C2×C11#201911yescharacteristic
227C2×Q8—221no—
228C2×Q8—222no—
229C2×Q8—221no—
230C2×Q8—441no—
231C2×Q8—441no—
232C2×Q8—441no—
233C2×Q8—442no—
234C2×Q8—442no—
235C2×Q8—882no—
236C22×C4—222no—
237C22×C4—441no—
238C22×C4C2×D4411yescharacteristic
239C22×C4D4×D1111yescharacteristic
240C22×C4#434311yescharacteristic
241M16—22no—
242M16—22no—
243M16—442no—
244C2×C8—24no—
245C2×C8—22no—
246C2×C8—22no—
247C2×C8—22no—
248C2×C8—441no—
249C4⋊C4—221no—
250C4⋊C4—221no—
251C4⋊C4—222no—
252C4⋊C4—222no—
253C4⋊C4—222no—
254C4⋊C4—221no—
255C4⋊C4—222no—
256C4⋊C4—221no—
257C4⋊C4—441no—
258C4⋊C4—441no—
259C4⋊C4—441no—
260C4⋊C4—441no—
261C4⋊C4—441no—
262C4⋊C4—441no—
263C22⋊C4—441no—
264C42—441no—
265C42C2×D4411yescharacteristic
266C42C2×D4411yescharacteristic
267C42D4×D1111yescharacteristic
268C42D4×D1111yescharacteristic
269C11#1017311yescharacteristic, complemented, Sylow
270C23#6694811yescharacteristic
271Q8—442no—
272Q8—444no—
273Q8—442no—
274Q8—882no—
275Q8—882no—
276Q8—881no—
277Q8—881no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—441no—
281C2×C4—441no—
282C2×C4—442no—
283C2×C4—442no—
284C2×C4—882no—
285C2×C4—882no—
286C2×C4#6692711yescharacteristic
287C2×C4#6693511yescharacteristic
288C2×C4#6693511yescharacteristic
289C2×C4#6693511yescharacteristic
290C2×C4#6694811yescharacteristic
291C2×C4#6694811yescharacteristic
292C2×C4#6695712yes—
293C2×C4#6696212yes—
294C8—24no—
295C8—42no—
296C8—42no—
297C8—881no—
298C22—21no—
299C22—21no—
300C22#1062228411yescharacteristic
301C22#1062245812yes—
302C4—21no—
303C4—21no—
304C4—881no—
305C4—882no—
306C4—882no—
307C4—881no—
308C4#1062230911yescharacteristic
309C4#1062232811yescharacteristic
310C4#1062234612yes—
311C4#1062243912yes—
312C4#1062251112yes—
313C2—22no—
314C2#1306965511yescharacteristic
315C2#1306971311yescharacteristic
316C2#1306973311yescharacteristic
subgroupG/H
centerC22#10622284
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1278C2
socleC22×C11#392
prime radicalC23×C11#121
hypercenter#1278D11
hypocenterC11#10173
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
269. C11#10173semidirect

Maximal subgroups

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

subgroupindex
#130797692
C2×#106222932
#130789972
#130696052
#130672872
#130670722
C11×#12782
#1017311