Finite Group Databasebeta

← #14656773

Subgroups — #14656773

Order 2816.

500 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 107 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#13074586C211yesmaximal, characteristic
2#13068702C212yesmaximal
3#13066495C212yesmaximal
4#13066459C211yesmaximal, characteristic
5C11×#1445C211yesmaximal, characteristic
6C22×C11×C4⋊C4C2211yescharacteristic
7C2×C11×#95—22no—
8C2×C11×#95C2211yescharacteristic
9C2×C11×#95C2211yescharacteristic
10#10622825C2212yes—
11#10622823—22no—
12C2×C22⋊(C11⋊C8)C2212yes—
13#10622273—22no—
14#10622270—22no—
15#10622167—22no—
16#10622167—22no—
17C23×C4×C11—21no—
18C23×C4×C11—21no—
19C23×C4×C11D412yes—
20C23×C4×C11C2311yescharacteristic
21C2×C11×C4⋊C4—22no—
22C2×C11×C4⋊C4—22no—
23C2×C11×C4⋊C4—21no—
24C2×C11×C4⋊C4Q812yes—
25C2×C22⋊Dic11—22no—
26C2×C4⋊Dic11D412yes—
27C2×C4⋊Dic11D412yes—
28C2×Dic11⋊C4—22no—
29C2×Dic11⋊C4—22no—
30C22×C11⋊C8—22no—
31C11×#95—22no—
32C11×#95—22no—
33C11×#95—44no—
34C11⋊#95—22no—
35C11⋊#95—22no—
36C11⋊#95—22no—
37C22⋊(C11⋊C8)—22no—
38C22⋊(C11⋊C8)—22no—
39#10346—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×C11—41no—
50C22×C4×C11—42no—
51C22×C4×C11—41no—
52C22×C4×C11—41no—
53C22×C4×C11—41no—
54C22×C4×C11—42no—
55C22×C4×C11—42no—
56C22×C4×C11—42no—
57C22×C4×C11C2×D412yes—
58C22×C4×C11C2×Q811yescharacteristic
59C22×C4×C11#4112yes—
60C22×C4×C11#4111yescharacteristic
61C22×Dic11—22no—
62C22×Dic11—22no—
63C11×C4⋊C4—24no—
64C11×C4⋊C4—42no—
65C22⋊Dic11—42no—
66C22⋊Dic11—42no—
67C4⋊Dic11—42no—
68C4⋊Dic11—42no—
69Dic11⋊C4—82no—
70Dic11⋊C4—82no—
71C2×C11⋊C8—42no—
72C2×C11⋊C8—42no—
73C2×C11⋊C8—42no—
74#2646—111no—
75#1823—112no—
76#1445D1111yescharacteristic
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×C11AGL(1,ℤ/8)12yes—
87C2×C4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11—41no—
90C2×C4×C11—41no—
91C2×C4×C11—42no—
92C2×C4×C11—44no—
93C2×C4×C11—42no—
94C2×C4×C11—44no—
95C2×C4×C11—42no—
96C2×C4×C11—42no—
97C2×C4×C11—42no—
98C2×C4×C11—42no—
99C2×C4×C11—44no—
100C2×C4×C11—82no—
101C2×C4×C11—81no—
102C2×C4×C11—82no—
103C2×C4×C11—81no—
104C2×C4×C11—81no—
105C2×C4×C11—81no—
106C2×C4×C11—82no—
107C2×C4×C11C22⋊Q812yes—
108C2×C4×C11#12412yes—
109C2×Dic11—42no—
110C2×Dic11—42no—
111C2×Dic11—42no—
112C2×Dic11—42no—
113C2×Dic11—42no—
114C2×Dic11—42no—
115C11⋊C8—82no—
116C22×C4⋊C4C2×D1111yescharacteristic
117C2×C22⋊C8—112no—
118#400—222no—
119#398—222no—
120#385—222no—
121#380—112no—
122C2×#95—22no—
123C2×#95C2×D1111yescharacteristic
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#44912yes—
137C22×C11#45511yescharacteristic
138C22×C11#45611yescharacteristic
139C22×C11#45812yes—
140C22×C11#47812yes—
141C22×C11#48811yescharacteristic
142C22×C11#49011yescharacteristic
143C4×C11—22no—
144C4×C11—22no—
145C4×C11—82no—
146C4×C11—82no—
147C4×C11—82no—
148Dic11—82no—
149Dic11—82no—
150C23×C4—21no—
151C23×C4—21no—
152C23×C4C22⋊D1112yes—
153C23×C4C22×D1111yescharacteristic
154C22×C8—222no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—112no—
159C2×C4⋊C4—112no—
160C2×C4⋊C4—222no—
161C2×C4⋊C4—222no—
162C2×C4⋊C4Dic2212yes—
163C2×C22⋊C4—222no—
164C22⋊C8—222no—
165C22⋊C8—222no—
166#95—22no—
167#95—22no—
168#95—44no—
169#95—222no—
170#95—222no—
171#95—222no—
172C2×C11—21no—
173C2×C11—22no—
174C2×C11—21no—
175C2×C11#160912yes—
176C2×C11#161212yes—
177C2×C11#202511yescharacteristic
178C2×C11#202811yescharacteristic
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—42no—
190C22×C4—41no—
191C22×C4—42no—
192C22×C4—42no—
193C22×C4—41no—
194C22×C4—41no—
195C22×C4—41no—
196C22×C4—42no—
197C22×C4—222no—
198C22×C4—222no—
199C22×C4C2×Dic2211yescharacteristic
200C22×C4#433911yescharacteristic
201C22×C4D4×D1112yes—
202C22×C4#434112yes—
203C2×C8—442no—
204C2×C8—442no—
205C2×C8—442no—
206C4⋊C4—24no—
207C4⋊C4—42no—
208C4⋊C4—442no—
209C4⋊C4—442no—
210C4⋊C4—882no—
211C4⋊C4—882no—
212C22⋊C4—442no—
213C22⋊C4—442no—
214C11#1034611yescharacteristic, complemented, Sylow
215C23—22no—
216C23—21no—
217C23—21no—
218C23#6697711yescharacteristic
219C23#6698512yes—
220C23#6698911yescharacteristic
221C23#6699011yescharacteristic
222C23#6700312yes—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—44no—
229C2×C4—42no—
230C2×C4—44no—
231C2×C4—42no—
232C2×C4—44no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—82no—
237C2×C4—81no—
238C2×C4—82no—
239C2×C4—81no—
240C2×C4—81no—
241C2×C4—81no—
242C2×C4—82no—
243C2×C4—442no—
244C2×C4—442no—
245C2×C4—442no—
246C2×C4—442no—
247C2×C4—442no—
248C2×C4—442no—
249C2×C4#6693112yes—
250C2×C4#6693812yes—
251C8—882no—
252C22—22no—
253C22—22no—
254C22—22no—
255C22—22no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22#1062256011yescharacteristic
261C22#1062262212yes—
262C22#1062265012yes—
263C22#1062266612yes—
264C22#1062266911yescharacteristic
265C22#1062267411yescharacteristic
266C22#1062268411yescharacteristic
267C22#1062270811yescharacteristic
268C4—22no—
269C4—22no—
270C4—82no—
271C4—82no—
272C4—82no—
273C4—882no—
274C4—882no—
275C2—21no—
276C2—22no—
277C2—21no—
278C2#1306761112yes—
279C2#1306762812yes—
280C2#1306976211yescharacteristic
281C2#1306977711yescharacteristic
282C2#1306978311yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1445C2
socleC23×C11#120
prime radicalC24×C11C2×D4
hypercenter#1445D11
hypocenterC11#10346
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1445

Complements

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

NH ≅ G/Ntype
214. C11#10346semidirect

Maximal subgroups

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

subgroupindex
#130745862
#130687022
#130664952
#130664592
C11×#14452
#1034611