Finite Group Databasebeta

← #14646811

Subgroups — #14646811

Order 2816.

336 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 101 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#13077546C211yesmaximal, characteristic
2#13067374C211yesmaximal, characteristic
3#13067371C211yesmaximal, characteristic
4#13067353C211yesmaximal, characteristic
5#13067353C211yesmaximal, characteristic
6C11⋊#1309C211yesmaximal, characteristic
7C11×#1309C211yesmaximal, characteristic
8#10623001C2211yescharacteristic
9C11×#423C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C11×#423C2211yescharacteristic
12#10622735C412yes—
13#10622732C412yes—
14#10622537C2211yescharacteristic
15#10622537C2211yescharacteristic
16C2×C4×C11⋊C8C2211yescharacteristic
17#10622444—21no—
18#10622444—21no—
19#10622443—21no—
20#10622443—21no—
21#10622124—21no—
22#10622124—21no—
23#10622120—21no—
24#10622120—21no—
25#10622118—21no—
26#10622118—21no—
27#10622117—21no—
28#10622117—21no—
29C2×C11×M16—21no—
30C2×C11×M16—21no—
31C2×C11×M16C2×C412yes—
32C2×C42×C11C2311yescharacteristic
33#66979C2×C412yes—
34#66977—21no—
35#66977—21no—
36C2×#4318—21no—
37C2×#4318—21no—
38C22×C11⋊C8C2×C411yescharacteristic
39C22×C11⋊C8C2×C411yescharacteristic
40#66923Q812yes—
41#66922D411yescharacteristic
42#66922D411yescharacteristic
43C4×Dic22—21no—
44C4×Dic22—21no—
45C11×C4⋊C8—21no—
46C11×C4⋊C8—21no—
47C11×C4⋊C8—21no—
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8—21no—
51#66879—22no—
52Dic11⋊C8—22no—
53Dic11⋊C8—22no—
54C8×Dic11—22no—
55C4⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)—21no—
57C4⋊(C11⋊C8)—21no—
58C4⋊(C11⋊C8)—21no—
59C4×C11⋊C8D411yescharacteristic
60C4×C11⋊C8D411yescharacteristic
61C4×C11⋊C8D411yescharacteristic
62C4×C11⋊C8D411yescharacteristic
63#8641—111nomaximal, Sylow
64C22×C4×C11C22×C411yescharacteristic
65C22×C4×C11#4111yescharacteristic
66C22×C4×C11#4111yescharacteristic
67C2×Dic22—21no—
68C2×Dic22—21no—
69C11×M16—42no—
70C11×M16—81no—
71C11×M16—81no—
72C2×C8×C11—22no—
73C2×C8×C11—41no—
74C2×C8×C11—41no—
75C42×C11C2×D411yescharacteristic
76C42×C11C2×D411yescharacteristic
77C42×C11C2×D411yescharacteristic
78C42×C11C2×Q811yescharacteristic
79C22⋊Dic11—22no—
80C4⋊Dic11—21no—
81C4⋊Dic11—21no—
82C4⋊Dic11C4⋊C412yes—
83C4⋊Dic11C4⋊C412yes—
84Dic11⋊C4—22no—
85Dic11⋊C4—22no—
86C4×Dic11—22no—
87#4318—81no—
88#4318—81no—
89C2×C11⋊C8—22no—
90C2×C11⋊C8—41no—
91C2×C11⋊C8—41no—
92C2×C11⋊C8—41no—
93C2×C11⋊C8C22⋊C411yescharacteristic
94C2×C11⋊C8C22⋊C411yescharacteristic
95C2×C11⋊C8C22⋊C411yescharacteristic
96C2×C11⋊C8C22⋊C411yescharacteristic
97#2960—111no—
98#1567—111no—
99#1566—111no—
100#1561—111no—
101#1561—111no—
102#1309—111no—
103#1309D1111yescharacteristic
104C23×C11#11711yescharacteristic
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11C2×C22⋊C411yescharacteristic
112C2×C4×C11C2×C4⋊C411yescharacteristic
113C2×C4×C11#12111yescharacteristic
114C2×C4×C11#12111yescharacteristic
115C2×C4×C11C22⋊Q811yescharacteristic
116C2×C4×C11C22⋊Q811yescharacteristic
117C2×Dic11—22no—
118C2×Dic11—22no—
119Dic22—41no—
120Dic22—41no—
121Dic22—41no—
122Dic22—41no—
123C8×C11—42no—
124C8×C11—81no—
125C8×C11—81no—
126C11⋊C8—21no—
127C11⋊C8—21no—
128C11⋊C8—21no—
129C11⋊C8—81no—
130C11⋊C8—81no—
131C11⋊C8#10112yes—
132#533—111no—
133#446—221no—
134#446—221no—
135C8×Q8—221no—
136C8×Q8—221no—
137#424—112no—
138#423—111no—
139#423—111no—
140#423C2×D1111yescharacteristic
141#423C2×D1111yescharacteristic
142#423C2×D1111yescharacteristic
143#405—112no—
144C2×C4×C8—111no—
145#335—221no—
146#335—221no—
147#334—221no—
148#334—221no—
149#332—221no—
150#332—221no—
151#332—221no—
152#332—221no—
153C22×C11—21no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11#38011yescharacteristic
157C4×C11—21no—
158C4×C11—21no—
159C4×C11—21no—
160C4×C11C2×#10111yescharacteristic
161C4×C11#41311yescharacteristic
162C4×C11#47111yescharacteristic
163C4×C11#47111yescharacteristic
164C4×C11#47211yescharacteristic
165C4×C11#47311yescharacteristic
166Dic11—42no—
167Dic11—42no—
168C2×M16—21no—
169C2×M16—21no—
170C2×M16—221no—
171C2×M16—221no—
172C2×M16C4×D1112yes—
173C22×C8—111no—
174C22×C8—111no—
175C4⋊Q8—111no—
176C4⋊Q8—111no—
177#125—112no—
178C22⋊Q8—221no—
179C22⋊Q8—221no—
180C4×Q8—221no—
181C4×Q8—221no—
182#117—112no—
183C2×C42C22×D1111yescharacteristic
184C4⋊C8—21no—
185C4⋊C8—21no—
186C4⋊C8—21no—
187C4⋊C8—21no—
188C4⋊C8—21no—
189C4⋊C8—21no—
190C4⋊C8—222no—
191C4⋊C8—222no—
192C4⋊C8—221no—
193C4⋊C8—221no—
194C4⋊C8—221no—
195C4⋊C8—221no—
196#97—222no—
197C4×C8—111no—
198C4×C8—111no—
199C4×C8—111no—
200C4×C8—111no—
201C4×C8—222no—
202C2×C11—41no—
203C2×C11#180111yescharacteristic
204C2×C11#181511yescharacteristic
205C2×C11#181611yescharacteristic
206C2×Q8—221no—
207C2×Q8—221no—
208C22×C4C2×C4×D1111yescharacteristic
209C22×C4#433911yescharacteristic
210C22×C4#433911yescharacteristic
211M16—42no—
212M16—81no—
213M16—81no—
214M16—881no—
215M16—881no—
216C2×C8—22no—
217C2×C8—41no—
218C2×C8—41no—
219C2×C8—111no—
220C2×C8—111no—
221C2×C8—111no—
222C2×C8—111no—
223C2×C8—222no—
224C2×C8—441no—
225C2×C8—441no—
226C2×C8—441no—
227C4⋊C4—112no—
228C4⋊C4—112no—
229C4⋊C4—221no—
230C4⋊C4—221no—
231C4⋊C4—222no—
232C4⋊C4—222no—
233C22⋊C4—222no—
234C42—222no—
235C42D4×D1111yescharacteristic
236C42D4×D1111yescharacteristic
237C42D4×D1111yescharacteristic
238C42Q8×D1111yescharacteristic
239C11#864111yescharacteristic, complemented, Sylow
240C23#6692511yescharacteristic
241Q8—441no—
242Q8—441no—
243Q8—441no—
244Q8—441no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—222no—
252C2×C4—222no—
253C2×C4C22⋊C4×D1111yescharacteristic
254C2×C4#6693711yescharacteristic
255C2×C4#6693711yescharacteristic
256C2×C4C4⋊C4×D1111yescharacteristic
257C2×C4#6694911yescharacteristic
258C2×C4#6694911yescharacteristic
259C8—42no—
260C8—81no—
261C8—81no—
262C8—112no—
263C8—221no—
264C8—221no—
265C8—221no—
266C8—881no—
267C8—881no—
268C22—21no—
269C22—21no—
270C22—21no—
271C22#1062228011yescharacteristic
272C4—21no—
273C4—21no—
274C4—21no—
275C4—442no—
276C4—442no—
277C4#1062235811yescharacteristic
278C4#1062236111yescharacteristic
279C4#1062236211yescharacteristic
280C4D11×#10111yescharacteristic
281C4#1062236711yescharacteristic
282C4#1062236811yescharacteristic
283C2—41no—
284C2#1306861111yescharacteristic
285C2#1306867411yescharacteristic
286C2#1306867911yescharacteristic
subgroupG/H
centerC22#10622280
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1309C2
socleC22×C11#380
prime radicalC23×C11#117
cosocleC2×C42×C11C23
hypercenter#1309D11
hypocenterC11#8641
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1309

Complements

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

NH ≅ G/Ntype
239. C11#8641semidirect

Maximal subgroups

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

subgroupindex
#130775462
#130673742
#130673712
#130673532
C11⋊#13092
C11×#13092
#864111