Finite Group Databasebeta

← #14656775

Subgroups — #14656775

Order 2816.

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

normal subgroups only

This group has 500 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#13068704C212yesmaximal
2#13066885C211yesmaximal, characteristic
3#13066494C212yesmaximal
4#13066459C211yesmaximal, characteristic
5C11×#2646C211yesmaximal, characteristic
6C22×C4⋊Dic11C2211yescharacteristic
7C11×#400—22no—
8C11×#398—22no—
9C11×#385—22no—
10C11×#380C2212yes—
11C2×C11×#95C2211yescharacteristic
12C2×C11⋊#95—22no—
13C2×C11⋊#95C2211yescharacteristic
14C2×C22⋊(C11⋊C8)C2212yes—
15#10622167—22no—
16#10622167—22no—
17C23×C4×C11D412yes—
18C23×C4×C11C2311yescharacteristic
19C23×Dic11—21no—
20C23×Dic11—21no—
21C2×C11×C4⋊C4—22no—
22C2×C11×C4⋊C4—22no—
23C2×C11×C4⋊C4D412yes—
24C2×C11×C4⋊C4D412yes—
25C2×C11×C22⋊C4—22no—
26C2×C4⋊Dic11—22no—
27C2×C4⋊Dic11—22no—
28C2×C4⋊Dic11—21no—
29C2×C4⋊Dic11Q812yes—
30C22×C11⋊C8—22no—
31C11×#95—22no—
32C11×#95—22no—
33C11×#95—22no—
34C11×#95—22no—
35C11⋊#95—22no—
36C11⋊#95—44no—
37C22⋊(C11⋊C8)—22no—
38C22⋊(C11⋊C8)—22no—
39#10347—111nomaximal, Sylow
40C24×C11C2×D411yescharacteristic
41C22×C4×C11—22no—
42C22×C4×C11—22no—
43C22×C4×C11—22no—
44C22×C4×C11—22no—
45C22×C4×C11—22no—
46C22×C4×C11—42no—
47C22×C4×C11—42no—
48C22×C4×C11—42no—
49C22×C4×C11C2×D412yes—
50C22×C4×C11C2×Q811yescharacteristic
51C22×C4×C11#4112yes—
52C22×C4×C11#4111yescharacteristic
53C22×Dic11—22no—
54C22×Dic11—22no—
55C22×Dic11—42no—
56C22×Dic11—41no—
57C22×Dic11—42no—
58C22×Dic11—42no—
59C22×Dic11—41no—
60C22×Dic11—41no—
61C22×Dic11—41no—
62C22×Dic11—42no—
63C11×C4⋊C4—42no—
64C11×C4⋊C4—42no—
65C11×C4⋊C4—82no—
66C11×C4⋊C4—82no—
67C11×C22⋊C4—42no—
68C11×C22⋊C4—42no—
69C4⋊Dic11—24no—
70C4⋊Dic11—42no—
71C2×C11⋊C8—42no—
72C2×C11⋊C8—42no—
73C2×C11⋊C8—42no—
74#2646D1111yescharacteristic
75#1824—112no—
76#1445—111no—
77#1294—112no—
78#1280—111no—
79C23×C11—21no—
80C23×C11—21no—
81C23×C11—22no—
82C23×C11#12011yescharacteristic
83C23×C11C22⋊Q811yescharacteristic
84C23×C11#12411yescharacteristic
85C23×C11#13512yes—
86C23×C11#13712yes—
87C2×C4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11—41no—
90C2×C4×C11—42no—
91C2×C4×C11—41no—
92C2×C4×C11—44no—
93C2×C4×C11—42no—
94C2×C4×C11—42no—
95C2×C4×C11—42no—
96C2×C4×C11—42no—
97C2×C4×C11—42no—
98C2×C4×C11—42no—
99C2×C4×C11—42no—
100C2×C4×C11—42no—
101C2×C4×C11—42no—
102C2×C4×C11—82no—
103C2×C4×C11C22⋊Q812yes—
104C2×C4×C11#12412yes—
105C2×Dic11—44no—
106C2×Dic11—42no—
107C2×Dic11—44no—
108C2×Dic11—42no—
109C2×Dic11—82no—
110C2×Dic11—81no—
111C2×Dic11—82no—
112C2×Dic11—81no—
113C2×Dic11—81no—
114C2×Dic11—81no—
115C11⋊C8—82no—
116C22×C4⋊C4—111no—
117C2×C22⋊C8—112no—
118#400—22no—
119#398—22no—
120#385—22no—
121#380C2×D1112yes—
122C2×#95—111no—
123C2×#95—222no—
124C2×#95C2×D1111yescharacteristic
125#340—222no—
126#340—222no—
127C22×C11—22no—
128C22×C11—22no—
129C22×C11—22no—
130C22×C11—22no—
131C22×C11—21no—
132C22×C11—21no—
133C22×C11—21no—
134C22×C11—21no—
135C22×C11#39311yescharacteristic
136C22×C11#45212yes—
137C22×C11#45311yescharacteristic
138C22×C11#45411yescharacteristic
139C22×C11#45812yes—
140C22×C11#47912yes—
141C22×C11#48811yescharacteristic
142C22×C11#49111yescharacteristic
143C4×C11—22no—
144C4×C11—22no—
145C4×C11—82no—
146C4×C11—82no—
147C4×C11—82no—
148Dic11—82no—
149Dic11—82no—
150C23×C4—221no—
151C23×C4—221no—
152C23×C4C22⋊D1112yes—
153C23×C4C22×D1111yescharacteristic
154C22×C8—222no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—112no—
158C2×C4⋊C4—222no—
159C2×C4⋊C4—222no—
160C2×C4⋊C4—221no—
161C2×C4⋊C4C22⋊D1112yes—
162C2×C4⋊C4C22⋊D1112yes—
163C2×C22⋊C4—22no—
164C22⋊C8—222no—
165C22⋊C8—222no—
166#95—22no—
167#95—22no—
168#95—22no—
169#95—22no—
170#95—222no—
171#95—444no—
172C2×C11—21no—
173C2×C11—22no—
174C2×C11—21no—
175C2×C11#161512yes—
176C2×C11#161812yes—
177C2×C11#202611yescharacteristic
178C2×C11#202711yescharacteristic
179C2×C11#203011yescharacteristic
180C24C2×C22⋊D1111yescharacteristic
181C22×C4—22no—
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4—42no—
187C22×C4—42no—
188C22×C4—42no—
189C22×C4—222no—
190C22×C4—222no—
191C22×C4—442no—
192C22×C4—442no—
193C22×C4—441no—
194C22×C4—442no—
195C22×C4—441no—
196C22×C4—441no—
197C22×C4—442no—
198C22×C4—441no—
199C22×C4Q8×D1111yescharacteristic
200C22×C4#434312yes—
201C22×C4#434311yescharacteristic
202C22×C4C2×C22⋊D1112yes—
203C2×C8—442no—
204C2×C8—442no—
205C2×C8—442no—
206C4⋊C4—42no—
207C4⋊C4—42no—
208C4⋊C4—82no—
209C4⋊C4—82no—
210C4⋊C4—224no—
211C4⋊C4—442no—
212C22⋊C4—42no—
213C22⋊C4—42no—
214C11#1034711yescharacteristic, complemented, Sylow
215C23—21no—
216C23—22no—
217C23—21no—
218C23#6699911yescharacteristic
219C23#6700011yescharacteristic
220C23#6700312yes—
221C23#6700412yes—
222C23#6700611yescharacteristic
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—44no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—82no—
239C2×C4—444no—
240C2×C4—442no—
241C2×C4—444no—
242C2×C4—442no—
243C2×C4—882no—
244C2×C4—881no—
245C2×C4—882no—
246C2×C4—881no—
247C2×C4—881no—
248C2×C4—881no—
249C2×C4#6699912yes—
250C2×C4#6700012yes—
251C8—882no—
252C22—22no—
253C22—22no—
254C22—22no—
255C22—22no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22#1062267612yes—
261C22#1062268111yescharacteristic
262C22#1062268211yescharacteristic
263C22#1062284411yescharacteristic
264C22#1062285212yes—
265C22#1062285411yescharacteristic
266C22#1062285612yes—
267C22#1062285811yescharacteristic
268C4—22no—
269C4—22no—
270C4—82no—
271C4—82no—
272C4—82no—
273C4—882no—
274C4—882no—
275C2—21no—
276C2—22no—
277C2—21no—
278C2#1306764712yes—
279C2#1306766412yes—
280C2#1306976411yescharacteristic
281C2#1306976911yescharacteristic
282C2#1306978211yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#2646C2
socleC23×C11#120
prime radicalC24×C11C2×D4
hypercenter#2646D11
hypocenterC11#10347
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2646

Complements

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

NH ≅ G/Ntype
214. C11#10347semidirect

Maximal subgroups

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

subgroupindex
#130687042
#130668852
#130664942
#130664592
C11×#26462
#1034711