Finite Group Databasebeta

← #14646810

Subgroups — #14646810

Order 2816.

336 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 109 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#13077551C211yesmaximal, characteristic
2#13067374C211yesmaximal, characteristic
3#13067371C211yesmaximal, characteristic
4#13067354C211yesmaximal, characteristic
5C11⋊#1309C211yesmaximal, characteristic
6C11⋊#1309C211yesmaximal, characteristic
7C11×#1561C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C11×#423C2211yescharacteristic
10C11×#423C2211yescharacteristic
11#10622637—21no—
12#10622637—21no—
13Q8×C11⋊C8—21no—
14Q8×C11⋊C8—21no—
15#10622612C412yes—
16#10622610C412yes—
17#10622537C2211yescharacteristic
18#10622537C2211yescharacteristic
19#10622537C2211yescharacteristic
20C2×C4×C11⋊C8C2211yescharacteristic
21C11×#332—21no—
22C11×#332—21no—
23#10622185—21no—
24#10622185—21no—
25#10622118—21no—
26#10622118—21no—
27#10622117—21no—
28#10622117—21no—
29C2×C11×M16—21no—
30C2×C11×M16—21no—
31C11×C4⋊Q8D411yescharacteristic
32C11×C4⋊Q8D411yescharacteristic
33C11×#125Q812yes—
34C11×C22⋊Q8—21no—
35C11×C22⋊Q8—21no—
36C4×Q8×C11—21no—
37C4×Q8×C11—21no—
38C11×#117C2×C412yes—
39C2×C42×C11C2311yescharacteristic
40C2×#4318—21no—
41C2×#4318—21no—
42C2×#4318C2×C412yes—
43C22×C11⋊C8C2×C411yescharacteristic
44C22×C11⋊C8C2×C411yescharacteristic
45C11×C4⋊C8—21no—
46C11×C4⋊C8—21no—
47C11×C4⋊C8—21no—
48C11×C4⋊C8—21no—
49C4⋊(C11⋊C8)—21no—
50C4⋊(C11⋊C8)—21no—
51C4⋊(C11⋊C8)—22no—
52C4⋊(C11⋊C8)—22no—
53C4⋊(C11⋊C8)—21no—
54C4⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)—21no—
57#66867—22no—
58C4×C11⋊C8—22no—
59C4×C11⋊C8D411yescharacteristic
60C4×C11⋊C8D411yescharacteristic
61C4×C11⋊C8D411yescharacteristic
62C4×C11⋊C8D411yescharacteristic
63#8641—111nomaximal, Sylow
64C2×Q8×C11—21no—
65C2×Q8×C11—21no—
66C22×C4×C11C22×C411yescharacteristic
67C22×C4×C11#4111yescharacteristic
68C22×C4×C11#4111yescharacteristic
69C11×M16—81no—
70C11×M16—81no—
71C2×C8×C11—41no—
72C2×C8×C11—41no—
73C11×C4⋊C4—21no—
74C11×C4⋊C4—21no—
75C11×C4⋊C4—22no—
76C11×C4⋊C4—22no—
77C11×C4⋊C4C4⋊C412yes—
78C11×C4⋊C4C4⋊C412yes—
79C11×C22⋊C4—22no—
80C42×C11—22no—
81C42×C11C2×D411yescharacteristic
82C42×C11C2×D411yescharacteristic
83C42×C11C2×D411yescharacteristic
84C42×C11C2×Q811yescharacteristic
85#4318—42no—
86#4318—81no—
87#4318—81no—
88C2×C11⋊C8—22no—
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#1561D1111yescharacteristic
102#1309—111no—
103#1309—111no—
104C23×C11#11711yescharacteristic
105Q8×C11—41no—
106Q8×C11—41no—
107Q8×C11—41no—
108Q8×C11—41no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—22no—
116C2×C4×C11—22no—
117C2×C4×C11C2×C22⋊C411yescharacteristic
118C2×C4×C11C2×C4⋊C411yescharacteristic
119C2×C4×C11#12111yescharacteristic
120C2×C4×C11#12111yescharacteristic
121C2×C4×C11C22⋊Q811yescharacteristic
122C2×C4×C11C22⋊Q811yescharacteristic
123C8×C11—81no—
124C8×C11—81no—
125C11⋊C8—21no—
126C11⋊C8—21no—
127C11⋊C8—21no—
128C11⋊C8—42no—
129C11⋊C8—81no—
130C11⋊C8—81no—
131C11⋊C8#10112yes—
132#533C2×D1111yescharacteristic
133#446—221no—
134#446—221no—
135C8×Q8—221no—
136C8×Q8—221no—
137#424—112no—
138#423—111no—
139#423—111no—
140#423—111no—
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—21no—
150#332—21no—
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×C11—42no—
161C4×C11—42no—
162C4×C11C2×#10111yescharacteristic
163C4×C11#41311yescharacteristic
164C4×C11#47111yescharacteristic
165C4×C11#47111yescharacteristic
166C4×C11#47211yescharacteristic
167C4×C11#47311yescharacteristic
168C2×M16—21no—
169C2×M16—21no—
170C2×M16—112no—
171C2×M16—221no—
172C2×M16—221no—
173C22×C8—111no—
174C22×C8—111no—
175C4⋊Q8C22⋊D1111yescharacteristic
176C4⋊Q8C22⋊D1111yescharacteristic
177#125Dic2212yes—
178C22⋊Q8—21no—
179C22⋊Q8—21no—
180C4×Q8—21no—
181C4×Q8—21no—
182#117C4×D1112yes—
183C2×C42C22×D1111yescharacteristic
184C4⋊C8—21no—
185C4⋊C8—21no—
186C4⋊C8—21no—
187C4⋊C8—21no—
188C4⋊C8—222no—
189C4⋊C8—222no—
190C4⋊C8—221no—
191C4⋊C8—221no—
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—21no—
207C2×Q8—21no—
208C22×C4C2×C4×D1111yescharacteristic
209C22×C4#434111yescharacteristic
210C22×C4#434111yescharacteristic
211M16—81no—
212M16—81no—
213M16—442no—
214M16—881no—
215M16—881no—
216C2×C8—41no—
217C2×C8—41no—
218C2×C8—111no—
219C2×C8—111no—
220C2×C8—111no—
221C2×C8—111no—
222C2×C8—222no—
223C2×C8—222no—
224C2×C8—441no—
225C2×C8—441no—
226C2×C8—441no—
227C4⋊C4—22no—
228C4⋊C4—22no—
229C4⋊C4—21no—
230C4⋊C4—21no—
231C4⋊C4Dic11⋊C412yes—
232C4⋊C4Dic11⋊C412yes—
233C22⋊C4—22no—
234C42—22no—
235C42C2×Dic2211yescharacteristic
236C42D4×D1111yescharacteristic
237C42D4×D1111yescharacteristic
238C42C2×C22⋊D1111yescharacteristic
239C11#864111yescharacteristic, complemented, Sylow
240C23#6693011yescharacteristic
241Q8—41no—
242Q8—41no—
243Q8—41no—
244Q8—41no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4#6693111yescharacteristic
254C2×C4#6693111yescharacteristic
255C2×C4C22⋊C4×D1111yescharacteristic
256C2×C4C2×Dic11⋊C411yescharacteristic
257C2×C4#6699211yescharacteristic
258C2×C4#6699211yescharacteristic
259C8—81no—
260C8—81no—
261C8—112no—
262C8—221no—
263C8—221no—
264C8—221no—
265C8—442no—
266C8—881no—
267C8—881no—
268C22—21no—
269C22—21no—
270C22—21no—
271C22#1062255511yescharacteristic
272C4—21no—
273C4—21no—
274C4—21no—
275C4—42no—
276C4—42no—
277C4D11×#10111yescharacteristic
278C4#1062236411yescharacteristic
279C4#1062281211yescharacteristic
280C4#1062281311yescharacteristic
281C4#1062281611yescharacteristic
282C4#1062281711yescharacteristic
283C2—41no—
284C2#1306861011yescharacteristic
285C2#1306867311yescharacteristic
286C2#1306867811yescharacteristic
subgroupG/H
centerC22#10622555
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1561C2
socleC22×C11#380
prime radicalC23×C11#117
cosocleC2×C42×C11C23
hypercenter#1561D11
hypocenterC11#8641
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1561

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
#130775512
#130673742
#130673712
#130673542
C11⋊#13092
C11×#15612
#864111