Finite Group Databasebeta

← #14666855

Subgroups — #14666855

Order 2816.

330 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 57 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#13076889C211yesmaximal, characteristic
2#13069963C211yesmaximal, characteristic
3#13067658C211yesmaximal, characteristic
4#13066644C211yesmaximal, characteristic
5#13066643C211yesmaximal, characteristic
6#13066559C211yesmaximal, characteristic
7C11×#1617C211yesmaximal, characteristic
8C11×#544C2211yescharacteristic
9C11×#484—21no—
10C11×#400C2211yescharacteristic
11#10622657—21no—
12#10622608—21no—
13#10622599C2211yescharacteristic
14#10622592—21no—
15#10622590C2211yescharacteristic
16#10622272—21no—
17#10622271—21no—
18#10622269—21no—
19#10622269—21no—
20#10622263—21no—
21C11×#328—21no—
22C11×#324C2211yescharacteristic
23#10622176—21no—
24#10622170—21no—
25#10622168C2211yescharacteristic
26#10622166C2211yescharacteristic
27C22×Dic22—21no—
28C11×C4⋊Q8—41no—
29C11×#125—41no—
30C11×C22⋊Q8—21no—
31C11×C22⋊Q8—21no—
32C11×#117—21no—
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C4⋊C4C2311yescharacteristic
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11D411yescharacteristic
37C2×C4⋊Dic11D411yescharacteristic
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×C4×Dic11D411yescharacteristic
42C2×#4318—21no—
43C11×#107—41no—
44C11×#103—41no—
45C11×C22⋊C8—21no—
46C11×#95—21no—
47C11×#95—21no—
48C11×#95D411yescharacteristic
49#66899—41no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95D411yescharacteristic
58C22⋊(C11⋊C8)—21no—
59#66872—41no—
60#66871—41no—
61#66871—41no—
62#12261—111nomaximal, Sylow
63C2×Q8×C11—21no—
64C2×Q8×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×Dic11—21no—
71C22×Dic11—21no—
72C22×Dic11—21no—
73C22×Dic11—21no—
74C2×Dic22—81no—
75C2×Dic22—81no—
76C2×Dic22—81no—
77C2×C8×C11—41no—
78C11×C4⋊C4—21no—
79C11×C4⋊C4—21no—
80C11×C4⋊C4—21no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C22⋊C4—41no—
87C42×C11—41no—
88C4⋊Dic11—41no—
89C4⋊Dic11—41no—
90C4⋊Dic11—81no—
91Dic11⋊C4—81no—
92Dic11⋊C4—81no—
93Dic11⋊C4—81no—
94C4×Dic11—21no—
95C4×Dic11Q1612yes—
96#4318—22no—
97#4318—41no—
98C2×C11⋊C8—41no—
99C2×C11⋊C8—41no—
100#2844—111no—
101#2061—111no—
102#1617—111no—
103#1617D1111yescharacteristic
104#1353—111no—
105#1353—111no—
106#1324—111no—
107C23×C11#12011yescharacteristic
108Q8×C11—81no—
109Q8×C11—81no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11C2×Q1611yescharacteristic
125C2×C4×C11#13711yescharacteristic
126C2×Dic11—22no—
127C2×Dic11—41no—
128C2×Dic11—41no—
129C2×Dic11—41no—
130C2×Dic11—41no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138Dic22—84no—
139C8×C11—81no—
140C11⋊C8—42no—
141C11⋊C8—81no—
142#544C2×D1111yescharacteristic
143#484—21no—
144#484—221no—
145#428—221no—
146#400—111no—
147#400—221no—
148#400—221no—
149#400C2×D1111yescharacteristic
150#395—221no—
151#395—221no—
152#395—221no—
153#382—111no—
154#382—221no—
155#343—111no—
156#339—221no—
157#328—21no—
158#328—221no—
159#324—111no—
160#324C2×D1111yescharacteristic
161C22×C11—21no—
162C22×C11—21no—
163C22×C11#45111yescharacteristic
164C22×C11#45611yescharacteristic
165C22×C11B(4,𝔽2)11yescharacteristic
166C4×C11—21no—
167C4×C11—21no—
168C4×C11—41no—
169C4×C11—41no—
170C4×C11—81no—
171C4×C11—81no—
172C4×C11—81no—
173C4×C11—81no—
174Dic11—42no—
175Dic11—81no—
176Dic11—81no—
177Dic11—81no—
178C22×Q8—221no—
179C2×M16—221no—
180C4⋊Q8—41no—
181#125—41no—
182C22⋊Q8—21no—
183C22⋊Q8—21no—
184#117—21no—
185C2×C4⋊C4—111no—
186C2×C4⋊C4—111no—
187C2×C4⋊C4—221no—
188C2×C4⋊C4—221no—
189C2×C4⋊C4—221no—
190C2×C4⋊C4—221no—
191C2×C4⋊C4C22⋊D1111yescharacteristic
192C2×C4⋊C4C22×D1111yescharacteristic
193C2×C42—111no—
194#107—41no—
195#107—441no—
196#107—441no—
197#106—441no—
198#103—41no—
199#103—441no—
200C22⋊C8—21no—
201C22⋊C8—221no—
202#95—21no—
203#95—21no—
204#95—111no—
205#95—221no—
206#95—221no—
207#95—221no—
208#95—221no—
209#95—221no—
210#95—221no—
211#95—221no—
212#95C22⋊D1111yescharacteristic
213C2×C11—21no—
214C2×C11—21no—
215C2×C11#160511yescharacteristic
216C2×C11#220111yescharacteristic
217C2×C11#220211yescharacteristic
218C2×Q8—21no—
219C2×Q8—21no—
220C2×Q8—881no—
221C2×Q8—881no—
222C2×Q8—881no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—221no—
226C22×C4—221no—
227C22×C4—221no—
228C22×C4—221no—
229C22×C4D4×D1111yescharacteristic
230C22×C4D4×D1111yescharacteristic
231C22×C4C2×C22⋊D1111yescharacteristic
232M16—222no—
233M16—441no—
234C2×C8—41no—
235C2×C8—441no—
236C2×C8—441no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—441no—
246C4⋊C4—441no—
247C4⋊C4—881no—
248C4⋊C4—881no—
249C4⋊C4—881no—
250C4⋊C4—881no—
251C22⋊C4—41no—
252C42—41no—
253C42—112no—
254C42—221no—
255C11#1226111yescharacteristic, complemented, Sylow
256C23#6699011yescharacteristic
257Q8—81no—
258Q8—81no—
259Q8—884no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—222no—
275C2×C4—441no—
276C2×C4—441no—
277C2×C4—441no—
278C2×C4—441no—
279C2×C4—441no—
280C2×C4—441no—
281C2×C4—441no—
282C2×C4—441no—
283C2×C4—441no—
284C2×C4—441no—
285C2×C4—441no—
286C2×C4Q16×D1111yescharacteristic
287C2×C4#6697111yescharacteristic
288C8—81no—
289C8—442no—
290C8—881no—
291C22—21no—
292C22—21no—
293C22#1062264511yescharacteristic
294C22#1062279911yescharacteristic
295C22#1062281811yescharacteristic
296C4—21no—
297C4—21no—
298C4—41no—
299C4—41no—
300C4—81no—
301C4—81no—
302C4—81no—
303C4—81no—
304C4—442no—
305C4—881no—
306C4—881no—
307C4—881no—
308C2—21no—
309C2—21no—
310C2#1306758811yescharacteristic
311C2#1307062711yescharacteristic
312C2#1307063211yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1617C2
socleC22×C11B(4,𝔽2)
prime radicalC23×C11#120
hypercenter#1617D11
hypocenterC11#12261
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1617

Complements

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

NH ≅ G/Ntype
255. C11#12261semidirect

Maximal subgroups

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

subgroupindex
#130768892
#130699632
#130676582
#130666442
#130666432
#130665592
C11×#16172
#1226111